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Predicting Essential Components of Signal Transduction Networks: A Dynamic Model of Guard Cell Abscisic Acid Signaling Song Li1, Sarah M. Assmann1, Re´ka Albert2* 1 Biology Department, Pennsylvania State University, University Park, Pennsylvania, United States of America, 2 Physics Department, Pennsylvania State University, University Park, Pennsylvania, United States of America Plants both lose water and take in carbon dioxide through microscopic stomatal pores, each of which is regulated by a surrounding pair of guard cells. During drought, the plant hormone abscisic acid (ABA) inhibits stomatal opening and promotes stomatal closure, thereby promoting water conservation. Dozens of cellular components have been identified to function in ABA regulation of guard cell volume and thus of stomatal aperture, but a dynamic description is still not available for this complex process. Here we synthesize experimental results into a consistent guard cell signal transduction network for ABA-induced stomatal closure, and develop a dynamic model of this process. Our model captures the regulation of more than 40 identified network components, and accords well with previous experimental results at both the pathway and whole-cell physiological level. By simulating gene disruptions and pharmacological interventions we find that the network is robust against a significant fraction of possible perturbations. Our analysis reveals the novel predictions that the disruption of membrane depolarizability, anion efflux, actin cytoskeleton reorganization, cytosolic pH increase, the phosphatidic acid pathway, or Kþ efflux through slowly activating Kþ channels at the plasma membrane lead to the strongest reduction in ABA responsiveness. Initial experimental analysis assessing ABA-induced stomatal closure in the presence of cytosolic pH clamp imposed by the weak acid butyrate is consistent with model prediction. Simulations of stomatal response as derived from our model provide an efficient tool for the identification of candidate manipulations that have the best chance of conferring increased drought stress tolerance and for the prioritization of future wet bench analyses. Our method can be readily applied to other biological signaling networks to identify key regulatory components in systems where quantitative information is limited. Citation: Li S, Assmann SM, Albert R (2006) Predicting essential components of signal transduction networks: A dynamic model of guard cell abscisic acid signaling. PLoS Biol 4(10): e312. DOI: 10.1371/journal.pbio.0040312 Introduction One central challenge of systems biology is the distillation of systems level information into applications such as drug discovery in biomedicine or genetic modiﬁcation of crops. In terms of applications it is important and practical that we identify the subset of key components and regulatory interactions whose perturbation or tuning leads to signiﬁcant functional changes (e.g., changes in a crop’s ﬁtness under environmental stress or changes in the state of malfunction- ing cells, thereby combating disease). Mathematical modeling can assist in this process by integrating the behavior of multiple components into a comprehensive model that goes beyond human intuition, and also by addressing questions that are not yet accessible to experimental analysis. In recent years, theoretical and computational analysis of biochemical networks has been successfully applied to well- deﬁned metabolic pathways, signal transduction, and gene regulatory networks [1–3]. In parallel, high-throughput experimental methods have enabled the construction of genome-scale maps of transcription factor–DNA and pro- tein–protein interactions [4,5]. The former are quantitative, dynamic descriptions of experimentally well-studied cellular pathways with relatively few components, while the latter are static maps of potential interactions with no information about their timing or kinetics. Here we introduce a novel approach that stands in the middle ground of the above- mentioned methods by incorporating the synthesis and dynamic modeling of complex cellular networks that contain diverse, yet only qualitatively known regulatory interactions. We develop a mathematical model of a highly complex cellular signaling network and explore the extent to which the network topology determines the dynamic behavior of the system. We choose to examine signal transduction in plant guard cells for two reasons. First, guard cells are central components in control of plant water balance, and better Academic Editor: Joanne Chory, The Salk Institute for Biological Studies, United States of America Received April 3, 2006; Accepted July 21, 2006; Published September 12, 2006 DOI: 10.1371/journal.pbio.0040312 Copyright: 2006 Li et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Abbreviations: ABA, abscisic acid; PP2C, protein phosphatase 2C; Atrboh, NADPH oxidase; Ca2þ c , cytosolic Ca2þ increase; CaIM, Ca2þ influx across the plasma membrane; CIS, Ca2þ influx to the cytosol from intracellular stores; CPC, cumulative percentage of closure; GCR1, G protein–coupled receptor 1; GPA1, heterotrimeric G protein a subunit 1; KAP, Kþ efflux through rapidly activating Kþ channels (AP channels) at the plasma membrane; KOUT, Kþ efflux through slowly activating outwardly-rectifying Kþ channels at the plasma membrane; NO, nitric oxide; NOS, nitric oxide synthase; PA, phosphatidic acid; ROS, reactive oxygen species * To whom correspondence should be addressed. E-mail: ralbert@phys.psu.edu PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1732 PLoS BIOLOGY understanding of their regulation is important for the goal of engineering crops with improved drought tolerance. Second, abscisic acid (ABA) signal transduction in guard cells is one of the best characterized signaling systems in plants: more than 20 components, including signal transduction proteins, secondary metabolites, and ion channels, have been shown to participate in ABA-induced stomatal closure. ABA induces guard cell shrinkage and stomatal closure via two major secondary messengers, cytosolic Ca2þ (Ca2þ c) and cytosolic pH (pHc). A number of signaling proteins and secondary messengers have been identiﬁed as regulators of Ca2þ inﬂux from outside the cell or Ca2þ release from internal stores; the downstream components responding to Ca2þ are certain vacuolar and plasma membrane Kþ permeable channels, and anion channels in the plasma membrane [6,7]. Increases in cytosolic pH promote the opening of anion efﬂux channels and enhance the opening of voltage-activated outward Kþ channels in the plasma membrane [8–10]. Stomatal closure is caused by osmotically driven cell volume changes induced by both Kþ and anion efﬂux through plasma membrane– localized channels. Despite the wealth of information that has been collected regarding ABA signal transduction, the majority of the regulatory relationships are known only qualitatively and are studied in relative isolation, without considering their possible feedback or crosstalk with other pathways. Therefore, in order to synthesize this rich knowl- edge, one needs to assemble the information on regulatory mechanisms involved in ABA-induced stomatal closure into a system-level regulatory network that is consistent with experimental observations. Clearly, it is difﬁcult to assemble the network and predict the dynamics of this system from human intuition alone, and thus theoretical tools are needed. We synthesize the experimental information available about the components and processes involved in ABA- induced stomatal closure into a comprehensive network, and study the topology of paths between signal and response. To capture the dynamics of information ﬂow in this network we express synergy between pathways as combinatorial rules for the regulation of each node, and formulate a dynamic model of ABA-induced closure. Both in silico and in initial experimental analysis, we study the resilience of the signaling network to disruptions. We systematically sample functional and dynamic perturbations in network components and uncover a rich dynamic repertoire ranging from ABA hypersensitivity to complete insensitivity. Our model is validated by its agreement with prior experimental results, and yields a variety of novel predictions that provide targets on which further experimental analysis should focus. To our knowledge, this is one of the most complex biological networks ever modeled in a dynamical fashion. Results Extraction and Organization of Data from the Literature We focus on ABA induction of stomatal closure, rather than ABA inhibition of stomatal opening, because these two processes, although related, exhibit distinct mechanisms, and there is substantially more information on the former process than on the latter in the literature. Experimental information about the involvement of a speciﬁc component in ABA- induced stomatal closure can be partitioned into three categories. First, biochemical evidence provides information on enzymatic activity or protein–protein interactions. For example, the putative G protein–coupled receptor 1 (GCR1) can physically interact with the heterotrimeric G protein a component 1 (GPA1) as supported by split-ubiquitin and coimmunoprecipitation experiments [11]. Second, genetic evidence of differential responses to a stimulus in wild-type plants versus mutant plants implicates the product of the mutated gene in the signal transduction process. For example, the ethyl methanesulfonate–generated ost1 mutant is less sensitive to ABA; thus, one can infer that the OST1 protein is a part of the ABA signaling cascade [12]. Third, pharmacological experiments, in which a chemical is used either to mimic the elimination of a particular component, or to exogenously provide a certain component, can lead to similar inferences. For example, a nitric oxide (NO) scavenger inhibits ABA-induced closure, while a NO donor promotes stomatal closure; thus, NO is a part of the ABA network [13]. The last two types of inference do not give direct interactions but correspond to pathways and pathway regulation. The existing theoretical literature on signaling is focused on networks where the ﬁrst category of information is known, along with the kinetics of each interaction. However, the availability of such detailed knowledge is very much the exception rather than the norm in the experimental literature. Here we propose a novel method of representing qualitative and incomplete experimental information and integrating it into a consistent signal transduction network. First, we distill experimental conclusions into qualitative regulatory relationships between cellular components (signal- ing proteins, metabolites, ion channels) and processes. For example, the evidence regarding OST1 and NO is summar- ized as both OST1 and NO promoting ABA-induced stomatal closure. We distinguish between positive and negative regulation by using the verbs ‘‘promote’’ and ‘‘inhibit,’’ represented graphically as ‘‘!’’ and ‘‘—j,’’ respectively, and quantify the severity of the effect by the qualiﬁer ‘‘partial.’’ A partial promoter’s (inhibitor’s) loss has less severe effects than the loss of a promoter (inhibitor), most probably due to other regulatory effects on the target node. Using these relations, we construct a database that contains more than 140 entries and is derived from more than 50 literature citations on ABA regulation of stomatal closure (Table S1). A number of entries in the database correspond to a component-to-component relationship, such as ‘‘A promotes B,’’ which is mostly obtained by pharmacological experiments (e.g., applying A causes B response). However, the majority of the entries belong to the two categories of indirect inference described above, and are of the type ‘‘C promotes the process (A promotes B).’’ This kind of information can be obtained from both genetic and pharmacological experiments (e.g., disrupt- ing C causes less A-induced B response, or applying C and A simultaneously causes a stronger B response than applying A only). There are a few instances of documented independence of two cellular components, which we identify with the qualiﬁer ‘‘no relationship.’’ Most of the information is derived from the model species Arabidopsis thaliana, but data from other species, mostly Vicia faba, are also included where comparable information from Arabidopsis thaliana is lacking. Assembly of the ABA Signal Transduction Network To synthesize all this information into a consistent network, we need to determine how the different pathways PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1733 Model of Guard Cell ABA Signaling suggested by experiments ﬁt together (i.e., we need to ﬁnd the pathways’ branching and crossing points). We develop a set of rules compatible with intuitive inference, aiming to deter- mine the sparsest graph consistent with all experimental observations. We summarize the most important rules in Figure 1; in the following we give examples for their application. If A ! B and C ! process (A ! B), where A ! B is not a biochemical reaction such as an enzyme catalyzed reaction or protein–protein/small molecule interaction, we assume that C is acting on an intermediary node (IN) of the A–B pathway. This IN could be an intermediate protein complex, protein– small molecule complex, or multiple complexes (see Figure 1, panel 1). For example, ABA ! closure, and NO synthase (NOS) ! process (ABA ! closure); therefore, ABA ! IN ! closure, NOS ! IN. If A ! B is a direct process such as a biochemical reaction or a protein–protein interaction, we assume that C ! process (A ! B) corresponds to C ! A ! B. A ! B and C ! process (A ! B) can be transformed to A ! C ! B if A ! C is also documented. This means that the simplest explanation is to identify the putative intermediary node with C. For example, ABA ! NOS, and NOS ! process (ABA ! NO) are experimentally veriﬁed and NOS is an enzyme producing NO, therefore, we infer ABA ! NOS ! NO (see Figure 1, panel 2). A rule similar to rule 1 applies to inhibitory interactions (denoted by —j); however, in the case of A —j B, and C —j process (A —j B), the logically correct representation is: A ! IN —j B, C —j IN (see Figure 1, panel 3). The above rules constitute a heuristic algorithm for ﬁrst expanding the network wherever the experimental relation- ships are known to be indirect, and second, minimizing the uncertainty of the network by ﬁltering synonymous relation- ships. Mathematically, this algorithm is related to the problem of ﬁnding the minimum transitive reduction of a graph (i.e., for ﬁnding the sparsest subgraph with the same reachability relationships as the original) [14]; however, it differs from previously used algorithms by the fact that the edges can have one of two signs (activating and inhibitory), and edges corresponding to direct interactions are main- tained. In the reconstructed network, given in Figure 2, the network input is ABA and the output is the node ‘‘Closure.’’ The small black ﬁlled circles represent putative intermediary nodes mediating indirect regulatory interactions. The edges (lines) of the network represent interactions and processes between two components (nodes); an arrowhead at the end of an edge represents activation, and a short segment at the end of an edge signiﬁes inhibition. Edges that signify interactions derived from species other than Arabidopsis are colored light blue. We indicate two inferred negative feedback loops on S1P and pHc (see below) by dashed light blue lines. Nodes involved in the same metabolic reaction or protein complex are bordered by a gray box; only those arrows that point into or out of the box signify information ﬂow (signal trans- duction). Some of the edges on Figure 2 are not explicitly incorporated in Table S1 because they represent general biochemical or physical knowledge (e.g., reactions inside gray boxes or depolarization caused by anion efﬂux). A brief biological description of this reconstructed net- work (Figure 2) is as follows. ABA induces guard cell shrinkage and stomatal closure via two major secondary messengers, Ca2þ c and pHc. Two mechanisms of Ca2þ c increase have been identiﬁed: Ca2þ inﬂux from outside the cell and Ca2þ release from internal stores. Ca2þ can be released from stores by InsP3 [15] and InsP6 [16], both of which are synthesized in response to ABA, or by cADPR and cGMP [17], whose upstream signaling molecule, NO [13,18], is indirectly activated by ABA. Opening of channels mediating Ca2þ inﬂux is mainly stimulated by reactive oxygen species (ROS) [19], and we reconstruct two ABA-ROS pathways involving OST1 [12] and GPA1 (L. Perfus-Barbeoch and S. M. Assmann, unpublished data), respectively. Based on current experimental evidence these two pathways are distinct, but not independent. The downstream components responding to Ca2þ are certain vacuolar and plasma membrane Kþ permeable channels, and anion channels in the plasma membrane [6,7]. The mechanism of pH control by ABA is less clear, but it is known that pHc increases shortly after ABA treatment [20,21]. Increases in pHc levels promote the opening of anion efﬂux channels and enhance the opening of voltage-activated outward Kþ channels in the plasma membrane [8–10]. Stomatal closure is caused by osmotically driven cell volume changes induced by Kþ and anion efﬂux through plasma membrane-localized channels, and there is a complex interregulation between ion ﬂux and membrane depolarization. In addition to the secondary-messenger–induced pathways, there are two less-well-studied ABA signaling pathways involving the reorganization of the actin cytoskeleton, and the organic anion malate. ABA inactivates the small GTPase protein RAC1, which in turn blocks actin cytoskeleton disruption [22], contributing to an ABA-induced actin cytoskeleton reorganization process that is potentially Ca2þ c dependent [23]. In our model system, Arabidopsis, ABA regulation of malate levels has not been described. However, in V. faba it has been shown that ABA inhibits PEP carboxylase and malate synthesis [24], and that ABA induces malate breakdown [25]. In some conditions sucrose is an osmoticum that contributes to guard cell turgor [26,27] but no mechanisms of ABA regulation of sucrose levels have been described. The recessive mutant of the protein phosphatase 2C (PP2C) Figure 1. Illustration of the Inference Rules Used in Network Reconstruction (1) If A ! B and C ! process (A ! B), where A ! B is not a biochemical reaction such as an enzyme catalyzed reaction or protein-protein/small molecule interaction, we assume that C is acting on an intermediary node (IN) of the A–B pathway. (2) If A ! B, A ! C, and C ! process (A ! B), where A ! B is not a direct interaction, the most parsimonious explanation is that C is a member of the A–B pathway, i.e. A ! C ! B. (3) If A —j B and C —j process (A —j B), where A —j B is not a direct interaction, we assume that C is inhibiting an intermediary node (IN) of the A–B pathway. Note that A! IN —j B is the only logically consistent representation of the A–B pathway. DOI: 10.1371/journal.pbio.0040312.g001 PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1734 Model of Guard Cell ABA Signaling ABI1, abi1-1R, is hypersensitive to ABA [28,29]. ABI1 is negatively regulated by phosphatidic acid (PA) and ROS, and pHc can activate ABI1 [30–32]. ABI1 negatively regulates RAC1 [22]. We hypothesize that ABI1 negatively regulates the NADPH oxidase (Atrboh) because ABI1 negatively regulates ROS production and Atrboh has been shown to be the dominant producer of ROS in guard cells [33]. We also assume that ABI1 inhibits anion efﬂux at the plasma membrane, because the dominant abi1–1 mutant is known to affect the ABA response of anion channels [34] and because anion channels are documented key regulators of ABA-induced stomatal closure [35]. Components functioning downstream from ABI2 and its role in guard cell signaling are not well established, so ABI2 is not included. The newly isolated PP2C recessive mutants, AtP2C-HA [36] and AtPP2CA [37], exhibit minor ABA hypersensitivity. However, their Figure 2. Current Knowledge of Guard Cell ABA Signaling The color of the nodes represents their function: enzymes are shown in red, signal transduction proteins are green, membrane transport–related nodes are blue, and secondary messengers and small molecules are orange. Small black filled circles represent putative intermediary nodes mediating indirect regulatory interactions. Arrowheads represent activation, and short perpendicular bars indicate inhibition. Light blue lines denote interactions derived from species other than Arabidopsis; dashed light-blue lines denote inferred negative feedback loops on pHc and S1P. Nodes involved in the same metabolic pathway or protein complex are bordered by a gray box; only those arrows that point into or out of the box signify information flow (signal transduction). The full names of network components corresponding to each abbreviated node label are: ABA, abscisic acid; ABI1/2, protein phosphatase 2C ABI1/2; ABH1, mRNA cap binding protein; Actin, actin cytoskeleton reorganization; ADPRc, ADP ribose cyclase; AGB1, heterotrimeric G protein b component; AnionEM, anion efflux at the plasma membrane; Arg, arginine; AtPP2C, protein phosphatase 2C; Atrboh, NADPH oxidase; CaIM, Ca2þ influx across the plasma membrane; Ca2þ ATPase, Ca2þ ATPases and Ca2þ/Hþ antiporters responsible for Ca2þ efflux from the cytosol; Ca2þ c , cytosolic Ca2þ increase; cADPR, cyclic ADP-ribose; cGMP, cyclic GMP; CIS, Ca2þ influx to the cytosol from intracellular stores; DAG, diacylglycerol; Depolar, plasma membrane depolarization; ERA1, farnesyl transferase ERA1; GC, guanyl cyclase; GCR1, putative G protein–coupled receptor; GPA1, heterotrimeric G protein a subunit; GTP, guanosine 59-triphosphate; Hþ ATPase, Hþ ATPase at the plasma membrane; InsPK, inositol polyphosphate kinase; InsP3, inositol-1,4,5- trisphosphate; InsP6, inositol hexakisphosphate; KAP, Kþ efflux through rapidly activating Kþ channels (AP channels) at the plasma membrane; KEV, Kþ efflux from the vacuole to the cytosol; KOUT, Kþ efflux through slowly activating outwardly-rectifying Kþ channels at the plasma membrane; NADþ, nicotinamide adenine dinucleotide; NADPH, nicotinamide adenine dinucleotide phosphate; NOS, Nitric oxide synthase; NIA12, Nitrate reductase; NO, Nitric oxide; OST1, protein kinase open stomata 1; PA, phosphatidic acid; PC, phosphatidyl choline; PEPC, phosphoenolpyruvate carboxylase; PIP2, phosphatidylinositol 4,5-bisphosphate; PLC, phospholipase C; PLD, phospholipase D; RAC1, small GTPase RAC1; RCN1, protein phosphatase 2A; ROP2, small GTPase ROP2; ROP10, small GTPase ROP10; ROS, reactive oxygen species; SphK, sphingosine kinase; S1P, sphingosine-1-phosphate. DOI: 10.1371/journal.pbio.0040312.g002 PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1735 Model of Guard Cell ABA Signaling downstream targets remain elusive; thus, we incorporate them as a general inhibitor of closure denoted AtPP2C. Mutation of the gene encoding the mRNA cap-binding protein, ABH1, results in hypersensitivity of ABA-induced Ca2þ c elevation/oscillation and of anion efﬂux in plants grown under some environmental conditions [38,39]. We assume an inhibitory effect of ABH1 on Ca2þ inﬂux across the plasma membrane (CaIM), which can explain both of these effects due to the Ca2þ regulation of anion efﬂux. Since the abh1 mutation affects transcript levels of some genes involved in ABA response, this mutation may also affect ABA sensitivity by altering gene expression rather than by regulation of the rapid signaling events on which our network focuses. Mutations in the gene encoding the farnesyl transferase ERA1 or the gene encoding GCR1 also lead to hypersensitive ABA-induced closure; ERA1 has been shown to negatively regulate CaIM and anion efﬂux [40,41], whereas GCR1 has been shown to be interact with GPA1 [11]. We assume that ERA1 negatively regulates CaIM and GCR1 negatively regulates GPA1. Another assumption in the network is that the protein phosphatase RCN1/PP2A regulates nitrate reductase (NIA12) activity as observed in spinach leaf tissue; this is expected to be a well-conserved mechanism due to the high sequence conservation of NIA-PP2A regulatory domains [42]. Figure 2 contains two putative autoregulatory negative feedback loops acting on S1P and pHc, respectively. The existence of feedback regulation can be inferred from the published timecourse measurements of S1P [43] and pHc [21]—both indicating a fast increase in response to ABA, then a decrease—but the mediators are currently unknown. The assembled network is consistent with our biological knowl- edge with minimal additional assumptions, and it will serve as the starting point for the graph analysis and dynamic modeling described in the following sections. Modeling ABA Signal Transduction Signaling networks can be represented as directed graphs where the orientation of the edges reﬂects the direction of information propagation (signal transduction). In a signal transduction network there exists a clear starting point, the node representing the signal (here, ABA), and one can follow the paths (successions of edges) from that starting point to the node(s) representing the output(s) of the network (here, stomatal closure). The signal–output paths correspond to the propagation of reactions in chemical space, and can be thought of as pseudodynamics [44]. When only static information is available, pseudodynamics takes into account the graph theoretical properties of the signal transduction network. For example, one can measure the number of nodes or distinct network motifs that appear one, two,. . .n edges away from the signal node. Such motifs reﬂect different cellular signaling processing capabilities and provide impor- tant insights into the biological processes under investigation. Graph theoretical measures can also provide information about the importance (centrality) of signal mediators [45] and can predict the changes in path structure when nodes or edges in the network are disrupted. These disruptions, explored experimentally by genetic mutations, voltage- clamping, or pharmacological interventions, can be modeled in silico by removing the perturbed node and all its edges from the graph [46]. The absence of nodes and edges will disrupt the paths in the network, causing a possible increase in the length of the shortest path between signal (ABA) and output (closure), suggesting decreased ABA sensitivity, or in severe cases the loss of all paths connecting input and output (i.e., ABA insensitivity). We ﬁnd that there are several partially or completely independent (nonoverlapping) paths between ABA and closure. The path of pH-induced anion efﬂux is independent of the paths involving changes in Ca2þ c. Based on the current knowledge incorporated in Figure 2, the path mediated by malate breakdown is independent of both Ca2þ and pH signaling. This result could change if evidence of a suggested link between pH and malate regulation [47] is found; note that regulation of malate synthesis in guard cells appears to have cell-speciﬁc aspects [48]. Increase in Ca2þ c can be induced by several independent paths involving ROS, NO, or InsP6. Thanks to the existence of numerous redundant signal (ABA)–output (closure) paths, a complete disconnec- tion of signal from output (loss of all the paths) is possible only if four nodes, corresponding to actin reorganization, pHc increase, malate breakdown, and membrane depolariza- tion, are simultaneously disrupted. This indicates a remark- able topological resilience, and suggests that functionally redundant mechanisms can compensate for single gene disruptions and can maintain at least partial ABA sensitivity. However, path analysis alone cannot capture bidirectional signal propagation and synergy (cooperativity) in living biological systems. For example, two nonoverlapping paths that reach the node closure could be functionally synergistic. Using only path analysis, disruption of either path would not be predicted to lead to a disconnection of the signal (ABA) from the output (closure), but due to the synergy between the two paths, the closure response may be strongly impaired if either of the two paths is disrupted experimentally. Because of such limitations of path analysis, we turn from path analysis to a dynamic description. Dynamic models have as input information (1) the interactions and regulatory relationships between compo- nents (i.e., the interaction network); (2) how the strength of the interactions depends on the state of the interacting components (i.e., the transfer functions); and (3) the initial state of each component in the system. Given these, the model will output the time evolution of the state of the system (e.g., the system’s response to the presence or absence of a given signal). Given the incomplete characterization of the processes involved in ABA-induced stomatal closure (as is typical of the current state of knowledge of cell signaling cascades), we employ a qualitative modeling approach. We assume that the state of the network nodes can have two qualitative values: 0 (inactive/off) and 1 (active/on) [49]. These values can also describe two conformational states of a protein, such as closed and open states of an ion channel, or basal and high activity for enzymes. This assumption is necessary due to the absence of quantitative concentration or activity information for the vast majority of the network components. It is additionally justiﬁed by the fact that in the case of combinatorial regulation or cooperative binding, the input–output relationships are sigmoidal and thus can be distilled into two discrete output states [50]. Since ‘‘stomatal closure’’ does not usually entail the complete closure of the stomatal pore but rather a clear decrease in the stomatal aperture, and since there is a PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1736 Model of Guard Cell ABA Signaling signiﬁcant variability in the response of individual stomata, the threshold separating the off (0) and on (1) state of the node ‘‘Closure’’ needs to invoke a population level descrip- tion. We measured the stomatal aperture size distribution in the absence of ABA or after treatment with 50 lM ABA (see Materials and Methods). Our ﬁrst observation was the population-level heterogeneity of stomatal apertures even in their resting condition (Figure 3A), a fact that may not be widely appreciated when more standard presentations, such as mean 6 standard error, are used (see Figure 3B). The stomatal aperture distribution shifts towards smaller aper- tures after ABA treatment, and also broadens considerably. The latter result is inconsistent with the assumption of each stomate changing its aperture according to a common function that decreases with increasing ABA concentration, and suggests considerable cell-to-cell variation in the degree of response to ABA. Moreover, although there is a clear difference between the most probable ‘‘open’’ (0 ABA) and ‘‘closed’’ (þ ABA) aperture sizes, there also exists an overlap between the aperture size distribution of ‘‘open’’ and ‘‘closed’’ stomata. This result indicates the possibility of differential and cell-autonomous stomatal responses to ABA. In the absence of 6 ABA measurements on the same stomate, we deﬁne the threshold of closure as a statistically signiﬁcant shift of the stomatal aperture distribution towards smaller apertures in response to ABA signal transduction. In our model the dynamics of state changes are governed by logical (Boolean) rules giving the state transition of each node given the state of its regulators (upstream nodes). We determine the Boolean transfer function for each node based on experimental evidence. The state of a node regulated by a single upstream component will follow the state of its regulator with a delay. If two or more pathways can independently lead to a node’s activation, we combine them with a logical ‘‘or’’ function. If two pathways cannot work independently, we model their synergy as a logical ‘‘and’’ function. For nodes regulated by inhibitors we assume that the necessary condition of their activation (state 1) is that the inhibitor is inactive (state 0). As all putative intermediary nodes of Figure 2 are regulated by a single activator, and regulate a single downstream component, they only affect the time delays between known nodes; for this reason we do not explicitly incorporate intermediary nodes as components of the dynamic model. Table 1 lists the regulatory rules of known nodes of Figure 2; we give a detailed justiﬁcation of each rule in Text S1. Frequently in Boolean models time is quantized into regular intervals (timesteps), assuming that the duration of all activation and decay processes is comparable [51]. For generality we do not make this assumption, and in the absence of timing or duration information we follow an asynchronous method that allows for signiﬁcant stochasticity in process durations [52,53]. Choosing as a timestep the longest duration required for a node to respond to a change in the state of its regulator(s) (also called a round of update, as each component’s state will be updated during this time interval), the Boolean updating rules of an asynchronous algorithm can be written as: Sn i ¼ BiðSmj j ; Smk k ; Sml l ; ::Þ; ð1Þ where Si n is the state of component i at timestep n, Bi is the Boolean function associated with the node i and its regulators j,k,l,.. and mj; mk; ml; :: 2 fn 1; ng, signifying that the time- points corresponding to the last change in a input node’s state can be in either the previous or current round of updates. Figure 3. Stomatal Aperture Distributions without ABA Treatment (gray bars) and with 50 lM ABA (white bars) (A) The x axis gives the stomatal aperture size and the y axis indicates the fraction of stomata for which that aperture size was observed. The black columns indicate the overlap between the 0 lM ABA and the 50 lM ABA distributions. (B) Classical bar plot representation of stomatal aperture for treatment with 50 lM ABA (white bar, labeled 1) and without ABA treatment (gray bar, labeled 2) using mean 6 standard error. This representation provides minimal information on population structure. DOI: 10.1371/journal.pbio.0040312.g003 Table 1. Boolean Rules Governing the States of the Known (Named) Nodes in the Signal Transduction Network Node Boolean Regulatory Rule NO NO* ¼ NIA12 and NOS PLC PLC* ¼ ABA and Ca2þ c CaIM CaIM* ¼ (ROS or not ERA1 or not ABH1) and not Depolar GPA1 GPA1* ¼ (S1P or not GCR1) and AGB1 Atrboh Atrboh* ¼ pHc and OST1 and ROP2 and not ABI1 Hþ ATPase Hþ ATPase* ¼ not ROS and not pHc and not Ca2þ c Malate Malate* ¼ PEPC and not ABA and not AnionEM RAC1 RAC1* ¼ not ABA and not ABI1 Actin Actin* ¼ Ca2þ c or not RAC1 ROS ROS* ¼ ABA and PA and pHc ABI1 ABI1* ¼ pHc and not PA and not ROS KAP KAP¼ (not pHc or not Ca2þ c) and Depolar Ca2þ c Ca2þ c¼ (CaIM or CIS) and not Ca2þ ATPase CIS CIS* ¼ (cGMP and cADPR) or (InsP3 and InsP6) AnionEM AnionEM* ¼ ((Ca2þ c or pHc) and not ABI1 ) or (Ca2þ c and pHc) KOUT KOUT* ¼ (pHc or not ROS or not NO) and Depolar Depolar Depolar* ¼ KEV or AnionEM or not Hþ ATPase or not KOUT or Ca2þ c Closure Closure* ¼ (KOUT or KAP ) and AnionEM and Actin and not Malate The nomenclature of the nodes is given in the caption of Figure 2. The nodes that have only one input are not listed to save space; a full description and justification can be found in Text S1. The next state of the node on the left-hand side of the equation (marked by ) is determined by the states of its effector nodes according to the function on the right-hand side of the equation. DOI: 10.1371/journal.pbio.0040312.t001 PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1737 Model of Guard Cell ABA Signaling The relative timing of each process is chosen randomly and is changed after each update round such that we are sampling equally among all possibilities (see Materials and Methods). This approach reﬂects the lack of experimental data on relative reaction speeds. The internal states of signaling proteins and the concentrations of small molecules are not explicitly known for each stomate, and components such as Ca2þ c and cell membrane potential show various states even in a homogenous experimental setup [54,55]. Accordingly, we sample a large number (10,000) of randomly selected initial states for the nodes other than ABA and closure (closure is initially set to 0), and let the system evolve either with ABA always on (1) or ABA always off (0). We quantify the probability of closure (equivalent to the percentage of closed stomata in the population) by the formula PðclosureÞt ¼ X N j¼l St closureðjÞ=N ð2Þ where St closure(j) is the state of the node ‘‘Closure’’ at time t in the jth simulation and N is the total number of simulations, in our case 10,000. We illustrate the main steps of our simulation method in Figure 4. As shown in Figure 5, in eight steps, the system shows complete closure in response to ABA. In contrast, without ABA, although some initial states lead to closure at the beginning, within six steps the probability of closure approaches 0. Initial theoretical analysis of the attractors (stable behaviors) of this nonlinear dynamic system conﬁrms that when given a constant ABA ¼ 1 input, the majority of nodes will approach a steady state value within three to eight steps. This steady-state value does not depend on the initial conditions. For example, OST1, PLC, and InsPK stabilize in the on state, and PEPC settles into the off state within the ﬁrst timestep when ABA is consistently on. The exception is a set of 12 nodes, including Ca2þ c, Ca2þ ATPase, NO, Kþ efﬂux from the vacuole to the cytosol, and Kþ efﬂux through rapidly Figure 4. Schematic Illustration of Our Modeling Methodology and of the Probability of Closure In this four-node network example, node A is the input (as ABA is the input of the ABA signal transduction network), and node D is the output (corresponding to the node ‘‘Closure’’ in the ABA signal transduction network). The nodes’ states are indicated by the shading of their symbols: open symbols represent the off (0) state and filled symbols signify the on (1) state. To indicate the connection between this example and ABA-induced closure, we associate D ¼ off (0) with a picture of an open stomate, and D ¼ on (1) with a picture of a closed stomate. The Boolean transfer functions of this network are A ¼ 1, B* ¼ A, C* ¼ A, D* ¼ B and C (i.e., node A is on commencing immediately after the initial condition, the next states of nodes B and C are determined by A, and D is on only when both B and C are on). (A) The first column represents the networks’ initial states; the input and output are not on, but some of the components in the network are randomly activated (e.g., middle row, node B). The input node A turns on right after initialization, signifying the initiation of the ABA signal. The next three columns in (A) represent the network’s intermediary states during a sequential update of the nodes B, C, and D, where the updated node is given as a gray label above the gray arrow corresponding to the state transition. This sequence of three transitions represents a round of updates from timestep 1 (second column) to timestep 2 (last column). Out of a total of 22 3 3! ¼ 24 possible different normal responses, two sketches of normal responses are shown in the top two rows. The bottom row illustrates a case in which one node (shown as a square) is disrupted (knocked out) and cannot be regulated or regulate downstream nodes (indicated as dashed edges). (B) The probability of closure indicates the fraction of simulations where the output D ¼ 1 is reached in each timestep; thus, in this illustration the probability of closure for the normal response (circles) increases from 0% at time step 1 to 100% at timestep 2. The knockout mutant’s probability of closure (squares) is 0% at both time steps. DOI: 10.1371/journal.pbio.0040312.g004 PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1738 Model of Guard Cell ABA Signaling activating Kþ channels (AP channels) at the plasma membrane (KAP), whose attractors are limit cycles (oscillations) accord- ing to the model. Ca2þ c oscillations have indeed been observed experimentally [56,57]; no time course measure- ments have been reported in the literature for the other components, so it is unknown whether they oscillate or not. We identiﬁed four subsets of behaviors for these nodes— distinguished by different positions on the limit cycle— depending on the initial conditions and relative process durations. Due to the functional redundancy between Kþ efﬂux mechanisms driving stomatal closure (see last entry of Table 1), and the stabilization of the other regulators of the node ‘‘Closure,’’ a closed steady state (Closure ¼ 1) is attained within eight steps for any initial condition. The details of this analysis will be published elsewhere. Identification of Essential Components After testing the wild-type (intact) system, we investigate whether the disruption (loss) of a component changes the system’s response to ABA. We systematically perturb the system by setting the state of a node to 0 (off state), and holding it at 0 for the duration of the simulation. This perturbation mimics the effect of a knockout mutation for a gene or pharmaceutical inhibition of secondary messenger production or of kinase or phosphatase activity. We characterize the effect of the node disruption by calculating the percentage (probability) of closure response to a constant ABA signal at each time step and comparing it with the percentage of closure in the wild-type system. The perturbed system’s responses can be classiﬁed into ﬁve categories with respect to the system’s steady state and the time it takes to reach the steady state. We designate responses identical or very close to the wild-type response as having normal sensitivity; in these cases the probability of closure reaches 100% within eight timesteps. Disruptions that cause the percentage of closed stomata to decrease to zero after the ﬁrst few steps are denoted as conferring ABA insensitivity (in accord with experimental nomenclature). We observe re- sponses where the probability of closure (the percentage of stomata closed at any given timestep) settles at a nonzero value that is less than 100%; we classify these responses as having reduced sensitivity. Finally, in two classes of behavior the probability of closure ultimately reaches 100%, but with a different timing than the normal response. We refer to a response with ABA-induced closure that is slower than wild- type as hyposensitivity, while hypersensitivity corresponds to ABA-induced closure that is faster than wild-type. Therefore, the perturbed system’s responses can be classiﬁed into ﬁve categories in the order of decreasing sensitivity defect: insensitivity to ABA, reduced sensitivity, hyposensitivity, normal sensitivity, and hypersensitivity. We ﬁnd that 25 single node disruptions (65%; compare with Table 2) do not lead to qualitative effects: 100% of the population responds to ABA with timecourses very close to the wild-type response. In contrast, the loss of membrane depolarizability, the disruption of anion efﬂux, and the loss of actin cytoskeleton reorganization present clear vulnerabil- ities: irrespective of initial conditions or of relative timing, all simulated stomata become insensitive to ABA (Figure 5A). Indeed, membrane depolarization is a necessary condition of Kþ efﬂux, which is a necessary condition of closure, as is actin cytoskeleton reorganization and anion efﬂux. The individual disruption of seven other components—PLD, PA, SphK, S1P, GPA1, Kþ efﬂux through slowly activating Kþ channels at the plasma membrane (KOUT), and pHc increase —reduces ABA sensitivity, as the percentage of closed stomata in the population decreases to 20%—80% (see Figure 5B). At least ﬁve components (S1P, SphK, PLD, PA, pHc) of these 7 predicted components have been shown to impair ABA- Figure 5. The Probability of ABA-Induced Closure (i.e., the Percentage of Simulations that Attain Closure) as a Function of Timesteps in the Dynamic Model In all panels, black triangles with dashed lines represent the normal (wild- type) response to ABA stimulus. Open triangles with dashed lines show that in wild-type, the probability of closure decays in the absence of ABA. (A) Perturbations in depolarization (open diamonds) or anion efflux at the plasma membrane (open squares) cause total loss of ABA-induced closure. The effect of disrupting actin reorganization (not shown) is identical to the effect of blocking anion efflux. (B) Perturbations in S1P (dashed squares), PA (dashed circles), or pHc (dashed diamonds) lead to reduced closure probability. The effect of disrupting SphK is nearly identical to the effect of disrupting S1P (dashed squares); perturbations in GPA1 and PLD, KOUT are very close to perturbations in PA (dashed circles); for clarity, these curves are not shown in the plot. (C) abi1 recessive mutants (black squares) show faster than wild-type ABA-induced closure (ABA hypersensitivity). The effect of blocking Ca2þ ATPase(s) (not shown) is very similar to the effect of the abi1 mutation. Blocking Ca2þ c increase (black diamonds) causes slower than wild-type ABA-induced closure (ABA hyposensitivity). The effect of disrupting atrboh or ROS production (not shown) is very similar to the effect of blocking Ca2þ c increase. DOI: 10.1371/journal.pbio.0040312.g005 PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1739 Model of Guard Cell ABA Signaling induced closure when clamped or mutated experimentally [8,31,43,58]. For these disruptions, both theoretical analysis and numerical results indicate that all simulated stomata converge to limit cycles (oscillations) driven by the Ca2þ c oscillations, yet the ratio of open and closed stomata in the population is the same at any timepoint, leading to a constant probability of closure. (The alternative possibility, of a subset of stomata being stably closed and another subset stably open, was not observed for any disruption.) For all other single-node disruptions the probability of closure ultimately reaches 100% (i.e., all simulated stomata reach the closed steady state); however, the rate of con- vergence diverges from the rate of the wild-type response (see Figure 5C). Disruption of Ca2þ c increase or of the production of ROS leads to ABA hyposensitivity (slower than wild-type response). In contrast, the disruption of ABI1 or of the Ca2þ ATPase(s) leads to ABA hypersensitivity (faster than wild type-response) (Figure 5C). The hyposensitive and hyper- sensitive responses are statistically distinguishable (p , 0.05 for all intermediary time steps [i.e., for 0 , t , 8]) from the normal responses. Our model predicts that perturbation of OST1 leads to a slower than normal response that is nevertheless not slow enough to be classiﬁed as hyposensitive. Indeed, ost1 mutants are still responsive to ABA even though not as strongly as wild-type plants [12]. After analyzing all single knockout simulations, we turned to analysis of double and triple knockout simulations. First, to effectively distinguish between normal, hypo- and hyper- sensitive responses (all of which achieve 100% probability of closure, but at different rates), we calculated the cumulative percentage of closure (CPC) by adding the probability of closure over 12 steps; the smaller the CPC value, the more slowly the probability of closure reaches 100%, and vice versa. Plotting the histogram of CPC values reveals a clear separation into three distinct groups of response in the case of single disruptions (Figure 6A). In contrast, the cumulative effects of multiple perturbations lead to a continuous distribution of sensitivities in a broad range around the normal (Figure 6B and 6C). We use the single perturbation results to identify three classes of response that achieve 100% closure, but at varying rates. We deﬁne two CPC thresholds: the midpoint between the most hyposensitive single mutant and normal response, CPChypo ¼ 10.35; and the midpoint between the normal and least hypersensitive single mutant response, CPChyper ¼ 10.7. Disruptions with cumulative closure probability , CPChypo are classiﬁed as hyposensitive, disruptions with cumulative closure probability . CPChyper are hypersensitive; and values between the two thresholds are classiﬁed as normal responses. This hypo/hypersensitive classiﬁcation does not affect the determination of insensitive or reduced sensitivity responses, which are identiﬁed by observing a null or less than 100% probability of closure. For double (triple) knockout simulations, some combina- tions of perturbations exhibit sensitivities that are independ- ent of the sensitivity of each of their components’ perturbation. Normal ABA-induced stomatal closure is Table 2. Single to Triple Node Disruptions in the Dynamic Model Number of Nodes Disrupted Percentage with Normal Sensitivity Percentage Causing Insensitivity Percentage Causing Reduced Sensitivity Percentage Causing Hyposensitivity Percentage Causing Hypersensitivity 1 65% 7.5% 17.5% 5% 5% 2 38% 16% 27% 12% 6% 3 23% 25% 31% 13% 7% In all the perturbations, there are five groups of responses. Normal sensitivity refers to a response close to the wild-type response (shown as black triangles and dashed line in Figure 5). Insensitivity means that the probability of closure is zero after the first three steps (see Figure 5A). Reduced sensitivity means that the probability of closure is less than 100% (see dashed symbols in Figure 5B). Hyposensitivity corresponds to ABA-induced closure that is slower than wild-type (black diamonds in Figure 5C). Hypersensitivity corresponds to ABA-induced closure that is faster than wild-type (black squares in Figure 5C). DOI: 10.1371/journal.pbio.0040312.t002 Figure 6. Classification of Close-to-Normal Responses (A) For all the single mutants that ultimately reach 100% closure, we plot the histogram of the cumulative probability of closure (CPC). We find three distinct types of responses: hypersensitivity (CPC . 10.7, for abi1 and Ca2þ ATPase disruption); hyposensitivity (CPC , 10.35, for Ca2þ c , atrboh, and ROS disruption); and normal responses ( 10.35 , CPC , 10.7). For all the double (B) and triple (C) mutants that eventually reach 100% closure at steady state when ABA ¼ 1, we classify the responses using the CPC thresholds defined by the single mutant responses. The CPC threshold values are indicated by dashed vertical lines in the plot. DOI: 10.1371/journal.pbio.0040312.g006 PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1740 Model of Guard Cell ABA Signaling preserved in 38% (23%) of combinations (see Table 2). In contrast, ABA signaling is completely blocked in 16% (25%) of disruptions. In addition to perturbations involving the three previously found insensitivity-causing single knockouts (loss of membrane depolarizability, the disruption of anion efﬂux, and the loss of actin cytoskeleton reorganization), a large number of novel combinations are found. Interestingly, perturbations of Ca2þ c or Ca2þ release from stores, when combined with disruptions in PLD, PA, GPA1, or pHc, lead to insensitivity (see Figure 7 and Discussion). ABA-induced closure is reduced (but not lost entirely) in 27% (31%) of the cases. Hyposensitive responses are found for 12% (13%) of double (triple) perturbations. All of the double perturbations in this category involve a knockout mutation of Ca2þ c, Atrboh, or ROS. The triple perturbations involve a knockout mutation of Ca2þ c, Atrboh, or ROS, plus two other perturba- tions, or combinations of three disruptions that alone are not predicted to cause quantiﬁable effects (e.g., guanyl cyclase, Ca2þ release from internal stores [CIS], and CaIM; see Figure 7). Around 6% (7%) of double (triple) perturbations, all including a knockout mutation of ABI1 or Ca2þ ATPase, lead to a hypersensitive response. In summary, accumulating perturbations cause a dramatic decrease in the percentage of normal response; the majority of triple knockouts are either insensitive or have reduced sensitivity. The fraction of hyposensitive and hypersensitive knockouts increases only moderately. Experimental Assessment of Model Predictions As a ﬁrst step toward experimental assessment of the model’s predictions, we used a weak acid, Na-butyrate, to clamp cytosolic pH, and then we treated the stomata with 50 lM ABA and observed the stomatal aperture responses. As shown in Figure 8A, the stomatal aperture distributions without butyrate treatments shift towards smaller apertures after ABA treatment, forming a distribution that overlaps with, but is clearly distinguishable from, the 0 ABA distribution. However, when increasing concentrations of butyrate are added in the solution, the ‘‘open’’ (0 ABA) and ‘‘closed’’ (þ ABA) distributions become increasingly over- lapping (Figure 8B–8D). At the highest butyrate concentra- tion (5 mM; Figure 8D), the 0 ABA and þABA populations of stomatal apertures are statistically identical (the null hypoth- esis that the two distributions are the same cannot be Figure 7. Summary of the Dynamic Effects of Calcium Disruptions All curves represent the probability of ABA-induced closure (i.e., the percentage of simulations that attain closure) as a function of time steps. Black triangles with dashed line represent the normal (wild-type) response to ABA stimulus; open triangles with dashed lines show how the probability of closure decays in the absence of ABA. CIS þ PA double mutants (dashed circles) and Ca2þ c þ pHc double mutants (dashed diamonds) show insensitivity to ABA. Ca2þ ATPase þ RCN1 double mutants (black circles) show hyposensitive (delayed) response to ABA. Guanyl cyclase þ CIS þ CaIM triple mutants (black diamonds) also show hyposensitivity; note that none of the guanyl cyclase or CIS or CaIM single knockouts show changed sensitivity (data not shown). Ca2þ ATPase mutants (black squares) show faster than wild-type ABA-induced closure (ABA hypersensitivity). DOI: 10.1371/journal.pbio.0040312.g007 Figure 8. Effect of Cytosolic pH Clamp (Increasing Concentrations of Na- butyrate from 0 to 5 mM) on ABA-Induced Stomatal Closure The histograms show the distribution of stomatal apertures without ABA treatment (gray bars) and with 50 lM ABA (white bars). Throughout, the x-axis gives the stomatal aperture size and the y-axis indicates the fraction of stomata for which that aperture size was observed. The black columns indicate the overlap between the 0 lM ABA and the 50 lM ABA distributions. Note that the data of (A) and those of Figure 3A are identical; these data are reproduced here for ease of comparison with panels (B–D). DOI: 10.1371/journal.pbio.0040312.g008 PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1741 Model of Guard Cell ABA Signaling rejected; two-tailed t test, p . 0.05). These results qualitatively support our prediction of the importance of pHc signaling. For a more quantitative comparison with the theoretically predicted probability of closure corresponding to pH clamping, one can deﬁne a threshold C between open and closed stomatal states, such that stomata with apertures larger than C can be classiﬁed as open and stomata with lower apertures can be classiﬁed as closed. We identify the thresh- old value C ¼ 4.3 lm by simultaneously minimizing the fraction of stomata classiﬁed as closed in the control condition and maximizing this fraction in the ABA treated condition. Using this threshold we ﬁnd that the fraction of closed stomata in the 50 lM ABA þ 5 mM Na-butyrate population is 26%, in agreement with the theoretically predicted probability of closure (Figure 5B). In plant systems, cytosolic pH changes in response to multiple hormones such as ABA [20,59], jasmonates [21], auxin [59], etc. The downstream effectors of pH changes include ion channels [8], protein kinases [60], and protein phosphatases [30]. Previous experiments with guard cells have demonstrated the efﬁcacy of butyrate in imposing a cytosolic pH clamp [8,21]. While these prior experiments focused on a single concentration of butyrate, here we used ﬁve different concentrations (three shown), with 120 stomata sampled for each treatment. As seen in Figure 8, we were able to monitor the effect of butyrate in the þABA treatment in both increasing the mean aperture size and reducing the spread of the aperture sizes. There is a clear indication of saturation between the two highest butyrate concentrations. While detailed measurements of cytosolic pH constitute a full separate study beyond the scope of the present article, the results of Figure 8 support the suggestion from our model that pHc should receive increased attention by experimen- talists as a focal point for transduction of the ABA signal. Discussion Network Synthesis and Path Analysis Logical organization of large-scale data sets is an important challenge in systems biology; our model provides such organization for one guard cell signaling system. As summar- ized in Table S1, we have organized and formalized the large amount of information that has been gathered on ABA induction of stomatal closure from individual experiments. This information has been used to reconstruct the ABA signaling network (Figure 2). Figure 2 uses different types of edges (lines) to depict activation and inhibition, and also uses different edge colors to indicate whether the information was derived from our model species, Arabidopsis, or from another plant species. Different types of nodes (metabolic enzymes, signaling proteins, transporters, and small molecules) are also color coded. An advantage of our method of network construction over other methods such as those used in Science’s Signal Transduction Knowledge Environment (STKE) connection maps [61] is the inclusion of intermediate nodes when direct physical interactions between two compo- nents have not been demonstrated. As is evident from Figure 2, network synthesis organizes complex information sets in a form such that the collective components and their relationships are readily accessible. From such analysis, new relationships are implied and new predictions can be made that would be difﬁcult to derive from less formal analysis. For example, building the network allows one to ‘‘see’’ inferred edges that are not evident from the disparate literature reports. One example is the path from S1P to ABI1 through PLD. Separate literature reports indicate that PLDa null mutants show increased transpira- tion, that PLDa1 physically interacts with GPA1, that S1P promotion of stomatal closure is reduced in gpa1 mutants, that PLD catalyses the production of PA, and that recessive abi1 mutants are hypersensitive to ABA. Network inference allows one to represent all this information as the S1P ! GPA1 ! PLD ! PA—j ABI1—j closure path, and make the prediction that ABA inhibition of ABI1 phosphatase activity will be impaired in sphingosine kinase mutants unable to produce S1P. Another prediction that can be derived from our network analysis is a remarkable redundancy of ABA signaling, as there are eight paths that emanate from ABA in Figure 2 and, based on current knowledge (though see below) these paths are initially independent. The prediction of redundancy is consistent with previous, less formal analyses [62]. The integrated guard cell signal transduction network (which includes the ABA signal transduction network) has been proposed as an example of a robust scale-free network [62]. To classify a network as scale-free, one needs to determine the degree (the number of edges, representing interactions/ regulatory relationships) of each node, and to calculate the distribution of node degrees (denoted degree distribution) [45,46]. Scale-free networks, characterized by a degree distribution described by a power law, retain their connec- tivity in the face of random node disruptions, but break down when the highest-degree nodes (the so-called hubs) are lost [46]. While the guard cell network may ultimately prove to be scale-free, the network is not sufﬁciently large at present to verify the existence of a power-law degree distribution; thus, the analogy with scale-free networks cannot be rigorously satisﬁed. Dynamic Modeling Our model differs from previous models employed in the life sciences in the following fundamental aspects. First, we have reconstructed the signaling network from inferred indirect relationships and pathways as opposed to direct interactions; in graph theoretical terminology, we found the minimal network consistent with a set of reachability relationships. This network predicts the existence of numer- ous additional signal mediators (intermediary nodes), all of which could be targets of regulation. Second, the network obtained is signiﬁcantly more complex than those usually modeled in a dynamic fashion. We bridge the incompleteness of regulatory knowledge and the absence of quantitative dose-response relationships for the vast majority of the interactions in the network by employing qualitative and stochastic dynamic modeling previously applied only in the context of gene regulatory networks [53]. Mathematical models of stomatal behavior in response to environmental change have been studied for decades [63,64]. However, no mathematical model has been formulated that integrates the multitude of recent experimental ﬁndings concerning the molecular signaling network of guard cells. Boolean modeling has been used to describe aspects of plant development such as speciﬁcation of ﬂoral organs [65], and there are a handful of reports describing Boolean models of PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1742 Model of Guard Cell ABA Signaling light and pathogen-, and light by carbon-regulated gene expression [66–68]. Use of a qualitative modeling framework for signaling networks is justiﬁed by the observation that signaling networks maintain their function even when faced with ﬂuctuations in components and reaction rates [69]. Our model uses experimental evidence concerning the effects of gene knockouts and pharmacological interventions for inferring the downstream targets of the corresponding gene products and the sign of the regulatory effect on these targets. However, use of this information does not guarantee that the dynamic model will reproduce the dynamic outcome of the knockout or intervention. Indeed, all model ingre- dients (node states, transfer functions) refer to the node (component) level, and there is no explicit control over pathway-level effects. Moreover, the combinatorial transfer functions we employed are, to varying extents, conjectures, informed by the best available experimental information (see Text S1). Finally, in the absence of detailed knowledge of the timing of each process and of the baseline (resting) activity of each component, we deliberately sample timescales and initial conditions randomly. Thus, an agreement between experimental and theoretical results of node disruptions is not inherent, and would provide a validation of the model. The accuracy of our model is indeed supported by its congruency with experimental observation at multiple levels. At the pathway level, our model captures, for example, the inhibition of ABA-induced ROS production in both ost1 mutants and atrboh mutants [12,19,21] and the block of ABA- induced stomatal closure in a dominant-positive atRAC1 mutant [22]. In our model, as in experiments, ABA-induced NO production is abolished in either nos single or nia12 double mutants [13,18]. Moreover, the model reproduces the outcome that ABA can induce cytosolic Kþ decrease by Kþ efﬂux through the alternative potassium channel KAP, even when ABA-induced NO production leads to the inhibition of the outwardly-rectifying (KOUT) channel [70]. At the level of whole stomatal physiology, our model captures the ﬁndings that anion efﬂux [35,71] and actin cytoskeleton reorganiza- tion [22] are essential to ABA-induced stomatal closure. The importance of other components such as PA, PLD, S1P, GPA1, KOUT, pH c in stomatal closure control [8,20,31,43,58,72], and the ABA hypersensitivity conferred by elimination of signaling through ABI1 [28,29], are also reproduced. Our model is also consistent with the observa- tion that transgenic plants with low PLC expression still display ABA sensitivity [73]. The fact that our model accords well with experimental results suggests that the inferences and assumptions made are correct overall, and enables us to use the model to make predictions about situations that have yet to be put to experimental test. For example, the model predicts that disruption of all Ca2þ ATPases will cause increased ABA sensitivity, a phenomenon difﬁcult to address experimentally due to the large family of calcium ATPases expressed in Arabidopsis guard cells (unpublished data). Most of the multiple perturbation results presented in Figure 5 and Table 2 also represent predictions, as very few of them have been tested experimentally. Results from our model can now be used by experimentalists to prioritize which of the multitude of possible double and triple knockout combina- tions should be studied ﬁrst in wet bench experiments. Most importantly, our model makes novel predictions concerning the relative importance of certain regulatory elements. We predict three essential components whose elimination completely blocks ABA-induced stomatal closure: membrane depolarization, anion efﬂux, and actin cytoskele- ton reorganization. Seven components are predicted to dramatically affect the extent and stability of ABA-induced stomatal closure: pHc control, PLD, PA, SphK, S1P, G protein signaling (GPA1), and Kþ efﬂux. Five additional components, namely increase of cytosolic Ca2þ, Atrboh, ROS, the Ca2þ ATPase(s), and ABI1, are predicted to affect the speed of ABA-induced stomatal closure. Note that a change in stomatal response rate may have signiﬁcant repercussions, as some stimuli to which guard cells respond ﬂuctuate on the order of seconds [74,75]. Thus our model predicts two qualitatively different realizations of a partial response to ABA: ﬂuctuations in individual responses (leading to a reduced steady-state sensitivity at the population level), and delayed response. These predictions provide targets on which further experimental analysis should focus. Six of the 13 key positive regulators, namely increase of cytosolic Ca2þ, depolarization, elevation of pHc, ROS, anion efﬂux, and Kþ efﬂux through outwardly rectifying Kþ channels, can be considered as network hubs [45], as they are in the set of ten highest degree (most interactive) nodes. Other nodes whose disruption leads to reduced ABA sensitivity, namely SphK, S1P, GPA1, PLD, and PA, are part of the ABA ! PA path. While they are not highly connected themselves, their disruption leads to upregulation of the inhibitor ABI1, thus decreasing the efﬁciency of ABA- induced stomatal closure. Similarly, the node representing actin reorganization has a low degree. Thus the intuitive prediction, suggested by studies in yeast gene knockouts [76,77], that there would be a consistent positive correlation between a node’s degree and its dynamic importance, is not supported here, providing another example of how dynamic modeling can reveal insights difﬁcult to achieve by less formal methods. This lack of correlation has also been found in the context of other complex networks [78]. Comparing Figure 3 and Figure 6C, one can notice a similar heterogeneity in the measured stomatal aperture size distributions and the theoretical distribution of the cumu- lative probability of closure in the case of multiple node disruptions. While apparently unconnected, there is a link between the two types of heterogeneity. Due to stochastic effects on gene and protein expression, it is possible that in a real environment not all components of the ABA signal transduction network are fully functional. Therefore, even genetically identical populations of guard cells may be heterogeneous at the regulatory and functional level, and may respond to ABA in slightly different ways. In this case, the heterogeneity in double and triple disruption simulations provides an explanation for the observed heterogeneity in the experimentally normal response: the latter is actually a mixture of responses from genetically highly similar but functionally nonidentical guard cells. Importance of Ca2þ c Oscillations to ABA-Induced Stomatal Closure Through the inclusion of the nodes CaIM, CIS, and the Ca2þ ATPase node representing the Ca2þ ATPases and Ca2þ/ Hþ antiporters [79,80] that drive Ca2þ efﬂux from the cytosolic compartment, our model incorporates the phenom- PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1743 Model of Guard Cell ABA Signaling enon of oscillations in cytosolic Ca2þ concentration, which has been frequently observed in experimental studies [56,81,82]. In experiments where Ca2þ c is manipulated, imposed Ca2þ c oscillations with a long periodicity (e.g., 10 min of Ca2þ elevation with a periodicity of once every 20 min) are effective in triggering and maintaining stomatal closure, yet at 10 min (i.e., after just one Ca2þ c transient elevation and thus before the periodicity of the Ca2þ change can be ‘‘known’’ by the cell), signiﬁcant stomatal closure has already occurred [56]. This result suggests that the Ca2þ c oscillation signature may be more important for the maintenance of closure than for the induction of closure [56,81], and that the induction of closure might only be dependent on the ﬁrst, transient Ca2þ c elevation. According to our model, if Ca2þ c elevation occurs, then stomatal closure is triggered (consistent with numerous experimental studies), but Ca2þ c elevation is not required for ABA-induced stomatal closure. Re-evaluation of the experimental studies on ABA and Ca2þ c reveals support for this prediction. First, although Ca2þ elevation certainly can be observed in guard cell responses to ABA, numerous exper- imental results also show that Ca2þ c elevation is only observed in a fraction of the guard cells assayed [9,83]. Furthermore, absence of Ca2þ c elevation in response to ABA does not prevent the occurrence of downstream events such as ion channel regulation [84,85] and stomatal closure [86,87], a phenomenon also predicted by our in silico analysis. Second, it has been observed that some guard cells exhibit sponta- neous oscillations in Ca2þ c, and in such cells, ABA application actually suppresses further Ca2þ c elevation [88]; thus, ABA and Ca2þ c elevation are clearly decoupled. Our model does predict that disruption of Ca2þ signaling leads to ABA hyposensitivity, or a slower than normal response to ABA. In the real-world environment, even a slight delay or change in responsiveness may have signiﬁcant repercussions, as some stimuli to which guard cells respond ﬂuctuate on the order of seconds; and stomatal responses can have comparable rapidity [74,75]. Moreover, our model predicts that Ca2þ c elevation (although not necessarily oscillation) becomes required for engendering stomatal closure when pHc changes, Kþ efﬂux or the S1P–PA pathway are perturbed (see Figure 7). Thus, Ca2þ c modulation confers an essential redundancy to the network. Support for such a redundant role can be found in a study by Webb et al. [89] where Ca2þ concentration was reduced below normal resting levels by intracellular application of BAPTA (such reduction in baseline Ca2þ c levels has been shown to reduce ABA activation of anion channels [85]) and the epidermal tissue was perfused with CO2-free air, a treatment that has been shown to inhibit outwardly rectifying Kþ channels and slow anion efﬂux channels [90]. The ABA insensitivity of stomatal closure found by Webb et al. under these conditions [89] therefore can be attributed to a combination of multiple perturbations (of Ca2þ c elevation, Kþ efﬂux, and anion efﬂux) and is consistent with the predictions of our model. Our model indicates that double perturbations of the Ca2þ ATPase component and either of RCN1, OST1, NO, NOS, NIA12, or Atrboh are hyposensitive (see Figure 7), consistent with experimental results on disruptions in the latter components [12,13,18,19,21,91]. Since the latter disruptions alone, with unperturbed Ca2þ ATPase, are found to have a close-to-normal response in our model, a Ca2þ ATPase– disrupted and therefore Ca2þ c oscillation–free model seems to be closer to experimental observations on stomatal aperture response recorded for these individual mutant genotypes. This suggests that Ca2þ c elevation (and not Ca2þ c oscillation) is the signal perceived by downstream factors that control the induction of closure. Possibly, certain as-yet- undiscovered interaction motifs, such as a synergistic feed- forward loop [92] or dual positive feedback loops [93], could transform the Ca2þ c oscillation into a stable downstream output. Limitations of the Current Analysis Network topology. Our graph reconstruction is incom- plete, as new signaling molecules will certainly be discovered. Novel nodes may give identity to the intermediary nodes that our model currently incorporates. Discovery of a new interaction among known nodes could simplify the graph by reducing (apparent) redundancy. For example, if it is found that GPA1 ! OST1, the simplest interpretation of the ABA ! ROS pathway becomes ABA ! GPA1 ! OST1 ! ROS, and the graph loses one edge and an alternative pathway. As an effect, the graph’s robustness will be attenuated. Among likely candidates for network reduction are the components currently situated immediately down- stream of ABA because, in the absence of information about guard cell ABA receptors [94], we assumed that ABA independently regulates eight components. It is also possible that a newly found interaction will not change the existing edges, but only add a new edge. A newly added positive regulation edge will further increase the redundancy of signaling and correspondingly its robustness. Newly added inhibitory edges could possibly damage the network’s robust- ness if they affect the main positive regulators of the network, especially anion channels and membrane depolarization. For example, experimental evidence indicates that abi1 abi2 double recessive mutants are more sensitive to ABA-induced stomatal closure than abi1 or abi2 single recessive mutants [29], suggesting that ABI1 and ABI2 act synergistically. Due to limited experimental evidence, we do not explicitly incorpo- rate ABI2, but an independent inhibitory effect of ABI2 would diminish ABA signaling. While it is difﬁcult to estimate the changes in our conclusions due to future knowledge gain, we can gauge the robustness of our results by randomly deleting entries in Table S1 or rewiring edges of Figure 2 (see Texts S2 and S3). We ﬁnd that most of the predicted important nodes are documented in more than one entry, and more than one entry needs to be removed from the database before the topology of the network related to that node changes (Text S2). Random rewiring of up to four edge pairs shows that the dynamics of our current network is moderately resilient to minor topology changes (Text S3 and Figure S1). Dynamic model. In our dynamic model we do not place restrictions on the relative timing of individual interactions but sample all possible updates randomly. This approach reﬂects our lack of knowledge concerning the relative reaction speeds as well as possible environmental noise. The signiﬁcance of our current results is the prediction that whatever the timing is, given the current topology of regulatory relationships in the network, the most essential regulators will not change. Our approach can be iteratively reﬁned when experimental results on the strength and timing PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1744 Model of Guard Cell ABA Signaling of individual interactions become available. For example, we can combine Boolean regulation with continuous synthesis and degradation of small molecules or signal transduction proteins [95,96] as kinetic (rate) data emerge. Our model considers the response of individual guard cell pairs to the local ABA signal; however, there is recent evidence of a synchronized oscillatory behavior of stomatal apertures over spatially extended patches in response to a decrease in humidity [97]. Our model can be extended to incorporate cell-to-cell signaling and spatial aspects by including extrac- ellular regulators when information about them becomes available (see [51]). Node disruptions. A knockout may either deprive the system of an essential signaling element (the gene itself), or it may ‘‘set’’ the entire system into a different state (e.g., by affecting the baseline expression of other, seemingly unre- lated signaling elements). Our analysis and current exper- imental data only address the former. Because of this caveat, in some ways rapid pharmacological inhibition may actually have a more speciﬁc effect on the cell than gene knockouts. Implications Many of the signaling proteins present as nodes in our model are represented by multigene families in Arabidopsis [98], with likely functional redundancy among encoded isoforms. Therefore, the amount of experimental work required to completely disrupt a given node may be considerable. It is also considerable work to make such genetic modiﬁcation in many of the important crop species that are much less amenable than Arabidopsis to genetic manipulation. It is also the case that, at present, there are no reports of successful use of ratiometric pH indicators in the small guard cells of Arabidopsis, suggesting that further technical advances in this area are required. Facts such as these indicate the importance of establishing a prioritization of node disruption in experimental studies seeking to manipulate stomatal responses for either an increase in basic knowledge or an improvement in crop water use efﬁciency. Our model provides information on which such prioritiza- tion can be based. Future work on this model will focus on predicting the changes in ABA-induced closure upon con- stitutive activation of network components or in the face of ﬂuctuating ABA signals. Ultimately, the experimental infor- mation obtained may or may not support the model predictions; the latter instance provides new information that can be used to improve the model. Through such iteration of in silico and wet bench approaches, a more complete understanding of complex signaling cascades can be obtained. Approaches to describe the dynamics of biological net- works include differential equations based on mass-action kinetics for the production and decay of all components [99,100], and stochastic models that address the deviations from population homogeneity by transforming reaction rates into probabilities and concentrations into numbers of molecules [101]. The great complexity of many cellular signal transduction networks makes it a daunting task to recon- struct all the reactions and regulatory interactions in such explicit biochemical and kinetic detail. Our work offers a roadmap for synthesizing incompletely described signal transduction and regulatory networks utilizing network theory and qualitative stochastic dynamic modeling. In addition to being the practical choice, qualitative dynamic descriptions are well suited for networks that need to function robustly despite changes in external and internal parameters. Indeed, several analyses found that the dynamics of network motifs crucial for the stable dynamics and noise- resistance of cellular networks, such as single input modules, feed-forward loops [102,103] and dual positive feedback loops [93], is correctly and completely captured by qualitative modeling [104,105]. For example, at the regulatory module level, several qualitative (Boolean and continuous/discrete hybrid) models [51,53,96] reproduced the Drosophila segment polarity gene network’s resilience when facing variations in kinetic parameters [50], offering the most natural explan- ation of which parameter sets will succeed in forming the correct gene expression pattern [106]. We expect that our methods will ﬁnd extensive applications in systems where modeling is currently not possible by traditional approaches and that they will act as a scaffold on which more quantitative analyses of guard cell signaling in particular and cell signaling in general can later be built. Our analyses have clear implications for the design of future wet bench experiments investigating the signaling network of guard cells and for the translation of experimental results on model species such as Arabidopsis to the improvement of water use efﬁciency and drought tolerance in crop species [107– 109]. Drought stress currently provides one of the greatest limitations to crop productivity worldwide [110,111], and this issue is of even more concern given current trends in global climate change [112,113]. Our methods also have implications in biomedical sciences. The use of systems modeling tools in designing new drugs that overcome the limitation of tradi- tional medicine has been suggested in the recent literature [114]. Many human diseases, such as breast cancer [115] or acute myeloid leukemia [116,117], cause complex alterations to the underlying signal transduction networks. Pathway information relevant to human disease etiologies has been accumulated over decades and such information is stored in several databases such as TRANSPATH [118], BioCarta (http:// www.biocarta.com), and STKE (http://www.stke.org). Our strategy can serve as a tool that guides experiments by integrating qualitative data, building systems models, and identifying potential drug targets. Materials and Methods Plant material and growth conditions. Wild-type Arabidopsis (Col genotype) seeds were germinated on 0.53MS media plates containing 1% sucrose. Seedlings were grown vertically under short-day conditions (8 h light/16 h dark) 120 lmol m2 s1 for 10 d. Vigorous seedlings were selected for transplantation into soil and were grown to 5 wk of age (from germination) under short day conditions (8 h light/16 h dark). Leaves were harvested 30 min after the lights were turned on in the growth chamber. Stomatal aperture measurements. Leaves were incubated in 20 mM KCl, 5 mM Mes-KOH, and 1 mM CaCl2 (pH 6.15) (Tris), at room temperature and kept in the light (250 lmol m2 s1) for 2 h to open stomata. For pHc clamping, different amounts of Na-butyrate stock solution (made up as 1M solution in water [pH 6.1]) were added into the incubation solution, to achieve the concentrations given in Figure 8, 15 min before adding 50 lM ABA. Apertures were recorded after 2.5 h of further incubation in light. Epidermal peels were prepared at the end of each treatment. The maximum width of each stomatal pore was measured under a microscope ﬁtted with an ocular micrometer. Data were collected from 40 stomata for each treatment and each experiment was repeated three times. Model. The network in Figure 2 was drawn with the SmartDraw software (http://www.smartdraw.com/exp/ste/home). The dynamic PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1745 Model of Guard Cell ABA Signaling modeling was implemented by custom Python code (http://www. python.org). To equally sample the space of all possible timescales, the random-order asynchronous updating method developed in [53] was used. Brieﬂy, every node is updated exactly once during each unit time interval, according to a given order. This order is a permutation of the N¼40 nodes in the network, chosen randomly out of a uniform distribution over the set of all N! possible permutations. A new update order is selected at each timestep. As demonstrated in [53], this algorithm is equivalent to a random timing of each node’s state transition. Supporting Information Figure S1. Probability of Closure in Randomized Networks where Pairs of Positive or Negative Edges Are Rewired Found at DOI: 10.1371/journal.pbio.0040312.sg001 (40 KB PDF). Table S1. Synthesis of Experimental Information about Regulatory Interactions between ABA Signal Transduction Pathway Components Found at DOI: 10.1371/journal.pbio.0040312.st001 (407 KB DOC). Text S1. Detailed Justiﬁcation for Each Boolean Transfer Function Found at DOI: 10.1371/journal.pbio.0040312.sd001 (149 KB DOC). Text S2. Veriﬁcation of the Inference Process and the Resulting Network Found at DOI: 10.1371/journal.pbio.0040312.sd002 (45 KB DOC). Text S3. Effect of Random Rewiring on the Network Dynamics Found at DOI: 10.1371/journal.pbio.0040312.sd003 (36 KB DOC). Accession Numbers The Arabidopsis Information Resource (TAIR) (http://www.arabidopsis. org) accession numbers for the genes discussed in this paper are NIA12 (At1g77760/At1g37130), GPA1 (At2g26300), ERA1 (At5g40280), AtrbohD/F (At5g47910/At4g11230), RCN1 (At1g25490), OST1 (At4g33950), ROP2 (At1g20090), RAC1 (At4g35020), ROP10 (At3g48040), AtP2C-HA/AtPP2CA (At1g72770/At3g11410), and GCR1 (At1g48270). Acknowledgments The authors thank Drs. Jayanth Banavar, Vincent Crespi, and Eric Harvill for critically reading a previous version of the manuscript; and Dr. Istva´n Albert for assistance with ﬁgure preparation. Author contributions. SL, SMA, and RA conceived and designed the experiments. SL performed the experiments. SL and RA analyzed the data. SL, SMA, and RA wrote the paper. Funding. RA gratefully acknowledges a Sloan Research Fellowship. Research on guard cell signaling in SMA’s laboratory is supported by NSF-MCB02–09694 and NSF-MCB03–45251. Competing interests. 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PLoS Biology \| www.plosbiology.org October 2006 \| Volume 4 \| Issue 10 \| e312 1748 Model of Guard Cell ABA Signaling	16968132	ROS = ( Atrboh ) PEPC = NOT ( ( ABA ) ) PLD = ( GPA1 ) HTPase = NOT ( ( pH ) OR ( Ca2_c ) OR ( ROS ) ) Ca2_c = ( ( CIS ) AND NOT ( Ca2_ATPase ) ) OR ( ( CaIM ) AND NOT ( Ca2_ATPase ) ) ROP10 = ( ERA1 ) RAC1 = NOT ( ( ABA ) OR ( ABI1 ) ) OST1 = ( ABA ) ROP2 = ( PA ) InsP6 = ( InsPK ) SphK = ( ABA ) Depolar = ( ( KOUT AND ( ( ( NOT AnionEM AND NOT Ca2_c AND NOT HTPase AND NOT KEV ) ) ) ) OR ( Ca2_c ) OR ( KEV ) OR ( HTPase AND ( ( ( NOT AnionEM AND NOT Ca2_c AND NOT KOUT AND NOT KEV ) ) ) ) OR ( AnionEM ) ) OR NOT ( AnionEM OR Ca2_c OR HTPase OR KOUT OR KEV ) RCN1 = ( ABA ) Ca2_ATPase = ( Ca2_c ) NOS = ( Ca2_c ) GPA1 = ( ( AGB1 ) AND NOT ( GCR1 ) ) OR ( S1P AND ( ( ( AGB1 ) ) ) ) Atrboh = ( ( OST1 AND ( ( ( pH AND ROP2 ) ) ) ) AND NOT ( ABI1 ) ) Malate = ( ( ( PEPC ) AND NOT ( AnionEM ) ) AND NOT ( ABA ) ) AnionEM = ( pH AND ( ( ( Ca2_c ) ) OR ( ( NOT ABI1 ) ) ) ) OR ( Ca2_c AND ( ( ( pH ) ) OR ( ( NOT ABI1 ) ) ) ) KAP = ( ( Depolar ) AND NOT ( Ca2_c AND ( ( ( pH ) ) ) ) ) pH = ( ABA ) CIS = ( InsP3 AND ( ( ( InsP6 ) ) ) ) OR ( cGMP AND ( ( ( cADPR ) ) ) ) InsP3 = ( PLC ) PA = ( PLD ) ABI1 = ( ( ( pH ) AND NOT ( PA ) ) AND NOT ( ROS ) ) CaIM = ( ( ( ABH1 AND ( ( ( NOT ERA1 ) ) ) ) AND NOT ( Depolar ) ) OR ( ( ERA1 AND ( ( ( NOT ABH1 ) ) ) ) AND NOT ( Depolar ) ) OR ( ( ROS ) AND NOT ( Depolar ) ) ) OR NOT ( ROS OR ERA1 OR ABH1 OR Depolar ) S1P = ( SphK ) NIA12 = ( RCN1 ) cGMP = ( GC ) PLC = ( ABA AND ( ( ( Ca2_c ) ) ) ) cADPR = ( ADPRc ) ADPRc = ( NO ) Actin = ( ( Ca2_c ) ) OR NOT ( RAC1 OR Ca2_c ) AGB1 = ( GPA1 ) Closure = ( ( KOUT AND ( ( ( AnionEM ) ) AND ( ( Actin ) ) ) ) AND NOT ( Malate ) ) OR ( ( KAP AND ( ( ( AnionEM ) ) AND ( ( Actin ) ) ) ) AND NOT ( Malate ) ) InsPK = ( ABA ) KEV = ( Ca2_c ) KOUT = ( pH AND ( ( ( Depolar ) ) ) ) OR ( ( Depolar ) AND NOT ( ROS AND ( ( ( NO ) ) ) ) ) GC = ( NO ) NO = ( NOS AND ( ( ( NIA12 ) ) ) )
A Logical Model Provides Insights into T Cell Receptor Signaling Julio Saez-Rodriguez1, Luca Simeoni2, Jonathan A. Lindquist2, Rebecca Hemenway1, Ursula Bommhardt2, Boerge Arndt2, Utz-Uwe Haus3, Robert Weismantel3, Ernst D. Gilles1, Steffen Klamt1, Burkhart Schraven2 1 Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany, 2 Institute of Immunology, Otto-von-Guericke University, Magdeburg, Germany, 3 Institute for Mathematical Optimization, Otto-von-Guericke University, Magdeburg, Germany Cellular decisions are determined by complex molecular interaction networks. Large-scale signaling networks are currently being reconstructed, but the kinetic parameters and quantitative data that would allow for dynamic modeling are still scarce. Therefore, computational studies based upon the structure of these networks are of great interest. Here, a methodology relying on a logical formalism is applied to the functional analysis of the complex signaling network governing the activation of T cells via the T cell receptor, the CD4/CD8 co-receptors, and the accessory signaling receptor CD28. Our large-scale Boolean model, which comprises 94 nodes and 123 interactions and is based upon well-established qualitative knowledge from primary T cells, reveals important structural features (e.g., feedback loops and network-wide dependencies) and recapitulates the global behavior of this network for an array of published data on T cell activation in wild-type and knock-out conditions. More importantly, the model predicted unexpected signaling events after antibody-mediated perturbation of CD28 and after genetic knockout of the kinase Fyn that were subsequently experimentally validated. Finally, we show that the logical model reveals key elements and potential failure modes in network functioning and provides candidates for missing links. In summary, our large- scale logical model for T cell activation proved to be a promising in silico tool, and it inspires immunologists to ask new questions. We think that it holds valuable potential in foreseeing the effects of drugs and network modifications. Citation: Saez-Rodriguez J, Simeoni L, Lindquist JA, Hemenway R, Bommhardt U, et al. (2007) A logical model provides insights into T cell receptor signaling. PLoS Comput Biol 3(8): e163. doi:10.1371/journal.pcbi.0030163 Introduction Understanding how cellular networks function in a holistic perspective is the main purpose of systems biology [1]. Dynamic models provide an optimal basis for a detailed study of cellular networks and have been applied successfully to cellular networks of moderate size [2–5]. However, for their construction and analysis they require an enormous amount of mechanistic details and quantitative data which, until now, has been often lacking in large-scale networks. Therefore, there has been considerable effort to develop methods based exclusively on the often well-known network topology [6,7]. One may distinguish between studies on the statistical properties of graphs [8–10] and approaches aiming at predicting functional or dysfunctional states and modes. For the latter, a large corpus of methods has been developed for metabolic networks mainly relying on the constraints- based approach [11,12]. However, for signaling networks, methods facilitating a similar functional analysis—including predictions on the outcome of interventions— have been applied to a much lesser extent [6]. Here we demonstrate that capturing the structure of signaling networks by a recently introduced logical approach [13] allows the analysis of important functional aspects, often leading to predictions that can be veriﬁed in knock-out/ perturbation experiments. Logical networks have until now been used for studying artiﬁcial (random) networks [14] or relatively small gene regulatory networks [15–18]. In contrast, herein we study a large-scale signaling network, structured in input (e.g., receptors), intermediate, and output (e.g., tran- scription factors) layers. Compared with gene regulatory networks, the behavior of signaling networks is mainly governed by their input layer, shifting the interest to input– output relationships. Addressing these issues requires parti- ally different techniques, as compared with gene regulatory networks. We use a special and intuitive representation of logical networks (called logical interaction hypergraph (LIH); see Methods), which is well-suited for this kind of input–output analysis. By applying logical steady state analysis, one may predict how a combination of signals arriving at the input layer leads to a certain response in the intermediate and the output layers. Additionally, this approach facilitates predic- tions of the effect of interventions and, moreover, allows one to search for interventions that repress or provoke a certain logical response [13]. Furthermore, each logical network has a unique underlying interaction graph from which other important network properties such as feedback loops, signaling paths, and network-wide interdependencies can be evaluated. Editor: Rob J. De Boer, Utrecht University, The Netherlands Received February 6, 2007; Accepted July 5, 2007; Published August 24, 2007 A previous version of this article appeared as an Early Online Release on July 5, 2007 (doi:10.1371/journal.pcbi.0030163.eor). Copyright: 2007 Saez-Rodriguez et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Abbreviations: LIH, logical interaction hypergraph; MHC, Major Histocompatibility Complex; MIS, Minimal intervention set; TCR, T cell receptor * To whom correspondence should be addressed. E-mail: inquiries regarding the mathematical methodology should be addressed to Steffen Klamt, klamt@ mpi-magdeburg.mpg.de, and regarding the biological and experimental data to Burkhart Schraven, Burkhart.Schraven@med.ovgu.de PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1580 Importantly, we consider here a logical model to be constructed by collecting and integrating well-known local interactions (e.g., a kinase phosphorylates an adaptor molecule). The logical model is then employed to derive global information (e.g., stimulation of a receptor leads to the activation of a certain transcription factor via several logical connections). Thus, the available data on the global network behavior is not used to construct the model; instead, it is used to verify the model. The model may then be employed to predict global responses that have not yet been studied experimentally. Here, we apply the logical framework to a carefully constructed model of T cell receptor (TCR) signaling. T- lymphocytes play a key role within the immune system: cytotoxic, CD8þ, T cells destroy cells infected by viruses or malignant cells, and CD4þ T helper cells coordinate the functions of other cells of the immune system [19]. The importance of T cells for immune homeostasis is due to their ability to speciﬁcally recognize foreign, potentially danger- ous, agents and, subsequently, to initiate a speciﬁc immune response. T cell reactivity must be exquisitely regulated as either a decrease (which weakens the defense against pathogens with the consequence of immunodeﬁciency) or an increase (which can lead to autoimmune disorders and leukemia) can have severe consequences for the organism. T cells detect foreign antigens by means of the TCR, which recognizes peptides only when presented upon MHC (Major Histocompatibility Complex) molecules. The peptides that are recognized by the TCR are typically derived from foreign (e.g., bacterial, viral) proteins and are generated by proteo- lytic cleavage within so-called antigen presenting cells (APCs). Binding of the TCR to peptide/MHC complexes and the additional binding of a different region of the MHC molecules by the co-receptors (CD4 in the case of T helper cells and CD8 in the case of cytotoxic T cells), together with costimulatory molecules such as CD28, initiates a plethora of signaling cascades within the T cell. These cascades give rise to a complex signaling network, which controls the activation of several transcription factors. These transcription factors, in turn, control the cell’s fate, particularly whether the T cell becomes activated and proliferates or not [20]. Therefore, we chose to focus on a limited number of receptors that are known to be central to the decision making process. The high number of kinases, phosphatases, adaptor molecules, and their interactions give rise to a complex interaction network which cannot be interpreted via pure intuition and requires the aid of mathematical tools. Since no sufﬁcient basis of kinetic data is available for setting up a dynamic model of this network, we opted to use logical modeling as a qualitative and discrete modeling framework. Note that there are kinetic models dealing with a smaller part of the network (e.g., [5,21,22]), as well as models of the gene regulatory network governing T cell activation [23]. We recently introduced our approach for the logical modeling of signaling networks [13], and, to exemplify it, we presented a small logical model for T cell activation (40 nodes). However, this model only served to demonstrate applicability and was too incomplete to address realistic complex input–output patterns. In contrast, the model presented herein has been signiﬁcantly expanded to 94 nodes and reﬁned by a careful reconstruction process (see below). It is thus realistic enough to be veriﬁed with diverse exper- imental data and to test its predictive power. In this report, the large-scale logical model describing T cell activation and the analysis performed therewith will be presented. First we will show that a number of important structural features can be identiﬁed with this model. Then we will show that the model not only reproduces published data on wet lab experiments, but it also predicts non-intuitive and previously unknown responses. Results Setup of a Curated, Comprehensive Logical Model of T Cell Receptor Signaling We have constructed a logical model describing T cell signaling (see Methods and Figure 1), which comprises the main events and elements connecting the TCR, its corecep- tors CD4/CD8, and the costimulatory molecule CD28, to the activation of key transcription factors in T cells such as AP-1, NFAT, and NFjB, all of which determine T cell activation and T cell function. In general, the model includes the following signaling steps emerging from the above receptors: the activation of the Src kinases Lck and Fyn, followed by the activation of the Syk-related protein tyrosine kinase ZAP70, and the subsequent assembly of the LAT signalosome, which in turn triggers activation of PLCc1, calcium cascades, activation of RasGRP, and Grb2/SOS, leading to the activa- tion of MAPKs [20]. Additionally, it includes the activation of the PI3K/PKB pathway that regulates many aspects of cellular activation and differentiation, particularly survival. For the activation of elements that play an important role, but whose regulation is not well-known yet (e.g., Card11, Gadd45), an external input was added. These elements can be considered as points of future extension of the model. As mentioned above, our model, which is documented in a detailed manner in Tables S1 and S2, is based upon local interactions (e.g., kinase ZAP70 phosphorylates the adaptor molecule LAT) that are well-established for primary T cells in PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1581 Author Summary T-lymphocytes are central regulators of the adaptive immune response, and their inappropriate activation can cause autoimmune diseases or cancer. The understanding of the signaling mechanisms underlying T cell activation is a prerequisite to develop new strategies for pharmacological intervention and disease treatments. However, much of the existing literature on T cell signaling is related to T cell development or to activation processes in transformed T cell lines (e.g., Jurkat), whereas information on non-transformed primary T cells is limited. Here, immunologists and theoreticians have compiled data from the existing literature that stem from analysis of primary T cells. They used this information to establish a qualitative Boolean network that describes T cell activation mechanisms after engagement of the TCR, the CD4/CD8 co- receptors, and CD28. The network comprises 94 nodes and can be extended to facilitate interpretation of new data that emerge from experimental analysis of T cell activation. Newly developed tools and methods allow in silico analysis, and manipulation of the network and can uncover hidden/unforeseen signaling pathways. Indeed, by assessing signaling events controlled by CD28 and the protein tyrosine kinase Fyn, we show that computational analysis of even a qualitative network can provide new and non-obvious signaling pathways which can be validated experimentally. A Logical Model of T Cell Receptor Signaling the literature. We did not use the known global information (e.g., stimulation of a receptor leads to the activation of a certain transcription factor) for the model construction. Instead, in simulations, the local interactions give rise to a global behavior which can be compared with available experimental observations (and was thus used to verify the model). Each component in the logical model can be either ON (‘‘1’’) or OFF (‘‘0’’). We consider a compound to be ON only if it is fully activated and able to trigger downstream events properly; otherwise, it is OFF. Furthermore, we consider two timescales [13]: early (s ¼ 1) and late (s ¼ 2), involving processes occurring during or after the ﬁrst minutes of activation, respectively (the time-scale for each interaction is given in Table S2). Some key regulatory processes such as the degradation of signaling proteins mediated by the E3 ubiquitin ligase c-Cbl [24–26] occur after a certain time, and are thus assigned s ¼ 2. Therefore, as will be shown later, analysis of signal propagation during the early events reveals which elements become activated, and the consideration of the late events allows a rough approximation to the dynamic behavior (sustained versus transient) of the network. The model comprises 94 different compounds and 123 interactions that give rise to a complex map of interactions (Figure 1). It is, to the best of our knowledge, the largest Boolean model of a cellular network to date. Interaction-Graph-Based Analyses The ﬁrst step in our analysis was to examine the interaction graph underlying the logical model. The former can be easily derived from the latter when a special representation of Boolean networks is used (see Methods). The interaction graph is less constrained than the Boolean network since it only captures direct (positive or negative) effects of one Figure 1. Logical Model of T Cell Activation (Screenshot of CellNetAnalyzer) Each arrow pointing at a species box is a so-called hyperarc representing one possibility to activate that species (see Methods). All the hyperarcs pointing at a particular species box are OR connected. Yellow species boxes denote output elements, while green ones represent (co)receptors. In the shown ‘‘early-event’’ scenario, the feedback loops were switched off, and only the input for the costimulatory molecule CD28 is active (scenario in column 2 of Table 1). The resulting logical steady state was then computed. Small text boxes display the signal flows along the hyperarcs (blue boxes: fixed values prior to computation; green boxes: hyperarcs activating a species (signal flow is 1); red boxes: hyperarcs which are not active (signal flow is 0)). doi:10.1371/journal.pcbi.0030163.g001 PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1582 A Logical Model of T Cell Receptor Signaling molecule upon another. Thus, unlike the logical model, the interaction graph cannot describe how different causal effects converging at a certain species are combined. For example, in an interaction graph we may say that A and B have a positive inﬂuence on another node C; the logical network is more precise because it expresses that A AND B (or A OR B) are required to activate C. Accordingly, compared with the logical model, an interaction graph requires less a priori knowledge about the network under study which comes at the price that functional predictions are limited. Nevertheless, as demonstrated in this section, a number of important functional features can be revealed from the graph model. First we studied global properties of the graph. As expected, the graph is connected (i.e., neglecting the arc directions, there is always a path from one node to all others). However, the directed graph contains as a core one strongly connected component with 33 nodes (i.e., for each pair (a,b) of nodes taken from this component there is a path from a to b and from b to a). This structural organization is related with the bow-tie structure found in other cellular networks (e.g., [7,27]) and implies that the rest of the network (not contained in the strongly connected component) mainly consists in relatively simple input and output layers (including branch- ing cascades) feeding to and from this component. We continued the interaction-graph-based analysis by computing the feedback loops. Feedback loops are of major importance for the dynamic behavior and functioning of biological networks. Negative feedback loops control homeo- static response and can give rise to oscillations, while positive feedbacks govern multistable behavior (connected to irrever- sible decision-making and differentiation processes) [15,28– 30]. The interaction graph underlying the logical T cell model has 172 feedback loops, 89 thereof being negative. Remark- ably, all feedback loops are only active in the second timescale because each loop contains at least one process of the second timescale. The elements of the MAPK cascade are involved in 92% of the feedback loops. This is due to the fact that there is a connection from ERK to the phosphatase SHP1 from the bottom to the top of the network [5]. Due to this connection, the resulting feedback can return to ERK via many different paths, thereby leading to a high number of loops. Indeed, if the ERK ! SHP1 connection is not considered, the number of loops is reduced dramatically from 172 to 13 (with only 11 being negative), all located in the upper part of the network. c-Cbl is involved in ;85% of them, thus underscoring the importance of c-Cbl in the regulation of signaling processes [25,26]. There are 4,538 paths, each connecting one of the three compounds from the input layer (TCR, CD4/CD8, CD28) with one compound in the output layer (transcription factors and other elements controlling T cell activation). The high number of negative paths (2,058) can be traced back to the presence of two negative connections (via DGK and Gab2). In fact, considering the early signaling events within the network, where DGK and Gab2 are not active yet, the number of paths is reduced to 1,530, with only six of them being negative. These paths are from the TCR and CD28 to negative regulators of the cell cycle (p21, p27, and FKHR), having thus a positive effect on T cell proliferation. These and other global effects can be graphically inspected via the dependency matrix [13,31], depicted in Figure 2. Importantly, when considering the timescale s ¼ 1, there is no ambivalent effect (i.e., via positive and negative paths) between any ordered pair (A,B) of species, i.e., A is either a pure activator of B (only positive paths from A to B), or a pure inhibitor of B (only negative paths from A to B), or has no direct or indirect inﬂuence on B at all. For example, during early activation, the TCR can only have a positive effect upon AP1 (the array element (TCRb, AP1) in Figure 2 is green). Note that this changes for timescale s ¼ 2 where, in several cases, a compound inﬂuences another species in an ambivalent manner. Analysis of the Logical Model An important aspect that can be studied with a logical model is signal processing and signal propagation and the corresponding response (activation/inactivation) of the nodes upon external stimuli and perturbations (see Methods). One starts the analysis of a scenario by deﬁning a pattern of input stimuli, possibly in combination with a set of nodes that are knocked-out or knocked-in. Then, by an iterative evaluation of the Boolean rules in each node, the signal is propagated through the network, switching each node ON or OFF, respectively (see [13] and Methods). For example, since CD28 (an input) is (permanently) ON in the scenario shown in Figure 1, it will (permanently) activate node X, which will in turn (permanently) activate Vav1, and so forth. In the same scenario, since the input CD4 is OFF, Lckp1 and therefore Abl, ZAP70, and other components cannot become activated and therefore are in the OFF state. In the ideal case, each node can be assigned a uniquely determined state that follows from a given input pattern. In terms of Boolean networks, the set of determined node values then represents a logical steady state. In some cases, in particular when negative feedback loops are active, only a fraction of the elements can be assigned a unique steady state value, whereas other (or even all) nodes might oscillate [15]. However, since in the T cell model all negative feedback loops become active only during timescale s ¼ 2 (as described above), a complete logical steady state follows for arbitrary input patterns when considering s ¼ 1. Using this kind of logical steady state analysis, we ﬁrst analyzed the activation pattern of key elements upon differ- ent stimuli (activation of the TCR and/or CD4 and/or CD28; Table 1) for timescale s ¼ 1. The model was able to reproduce data from both the literature and our own experiments, providing a holistic and integrated interpretation for a large body of data. The model also predicted a non-obvious signaling event, namely that the activation of the costimula- tory molecule CD28 alone leads not only to the activation of PI3K—which is to be expected from a large body of literature dealing with CD28 signaling showing that PI3K binds to the motif YxxM of CD28 [32,33]—but also to the selective activation of JNK, but not ERK. The model predicts a pathway from CD28 to JNK which gives a holistic explanation for this result: the pathway does NOT involve the LAT signalosome, activation of PLCc1, and Calcium ﬂux, but clearly depends on the activation of the nucleotide exchange factor Vav1 which activates MEKK1 via the small G-protein Rac1 (Figure 1). Clearly, the activating pathway shown in Figure 1 could be identiﬁed by a visual inspection of the map (note that we have intentionally drawn the network in such a way that this route can be easily seen). However, in large-scale PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1583 A Logical Model of T Cell Receptor Signaling networks the identiﬁcation of long-distance pathways by simply following all possible routes becomes infeasible and is particularly complicated if AND connections are involved. Furthermore, since the CD28-induced JNK activation path- way was not expected, one would probably not have searched speciﬁcally for this pathway, while the algorithm reveals the whole response of the network. The prediction made by the model is particularly surpris- ing in light of published data which either suggest that CD28 stimulation alone does NOT activate JNK [34,35] or induces only a weak activation [36]. Driven by this surprising prediction, we performed the corresponding experiments in vitro. As shown in Figure 3A, stimulation of mouse primary T cells with a non-superagonistic CD28 antibody induced an evident and sustained JNK phosphorylation, thus conﬁrming almost perfectly the predicted binary response. Note, the model also predicted that JNK activation does not depend on the activation of PI3K. Again, this prediction was veriﬁed by applying a pharmacological inhibitor of PI3K (Figure 3D). The discrepancies with the literature could be due either to the different cellular systems (primary T cells versus T cell lines) or to the different stimulation conditions. The nature of the kinase involved in CD28-mediated signaling remains unclear. Indeed, application of the Src- kinase inhibitor PP2 that inactivates both Lck þ Fyn [37], showed that Src-kinases, which were proposed to mediate CD28 signaling [38], are dispensable for the CD28-mediated activation of JNK (Figure 4). To ﬁt the Src-kinase inhibitor data with the model, it would have been possible to simply bypass the Src-kinase and to draw a causal connection from CD28 to Vav. Such a connection would indeed be justiﬁed since it is well established that triggering of CD28 leads to the activation of Vav ([39]; for more details, see Table S2, reactions 35 and 48). However, we preferred to include a to-be-identiﬁed kinase X that gets activated by CD28 (Figure 1), in order to keep within the model the information that there is a component to be identiﬁed. Potential candidates for kinase X would be members of the Tec-family of PTKs. However, it is difﬁcult to study the signaling properties of these kinases in primary non-transformed cells since speciﬁc inhibitors for Tec kinases are not yet available and the corresponding knock-out mice show defects in thymic development. Therefore, as we focused during model generation on well-established data from primary T cells and excluded data obtained from knockout mice showing alterations of thymic development, we did not include it. Figure 2. Dependency Matrix of the Logical T Cell Signaling Model (Figure 1) for the Early Events Scenario (s ¼ 1) The color of a matrix element Mxy has the following meaning [13]: (i) dark green: x is a total activator of y; (ii) dark red: x is a total inhibitor of y; (iii) white: no (direct or indirect) influence from x on y. doi:10.1371/journal.pcbi.0030163.g002 PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1584 A Logical Model of T Cell Receptor Signaling The ability of the model to recapitulate the T cell phenotype of a variety of previously described knock-out mice was also tested (Table 1). Indeed, the model could reproduce the phenotype of several knock-outs and again reported a rather unexpected result: activation of the TCR in Fyn-deﬁcient cells selectively triggers the PI3K/PKB pathway. This prediction was subsequently tested using peripheral primary T cells prepared from spleen of Fyn-deﬁcient mice. As shown in Figure 3B, the wet-lab experiments corroborated the model result again. However, there was an experimental result which the model could not reproduce: TCR-mediated JNK activation is blocked by an inhibitor of PI3K (Figure 3C). In fact, this result is not in accordance with the network because PI3K has no inﬂuence upon JNK (see dependency matrix, Figure 2). To identify potential connections that would explain the experimental data, we applied the concept of Minimal Intervention Sets (MISs; see Methods). A MIS is a irreducible collection of actions (e.g., activation or inactivation of certain compounds), that, if applied, guarantees that a certain goal (a desired behavior) is fulﬁlled [13]. Here, we computed the MISs by which JNK becomes activated under the experimentally obtained constraint (see Figure 3C) that PI3K is OFF (describing the effect of the PI3K inhibitor), ZAP70 is ON, and that the TCR has been activated. These MISs (Table 2) thus provide a list of minimal combinations of elements that should be directly or indirectly affected by PI3K and thus allow us to explain the observed response of JNK upon inhibiting PI3K. Some of them are obvious, e.g., the ﬁrst MIS in Table 2 suggests that JNK activation could be directly interacting with PI3K or elements that are located down- stream of PI3K (e.g., PIP3). There is currently no convincing experimental evidence for an effect of PI3K on JNK, though. Other MISs in Table 2 suggest that a PI3K-mediated activation of Vav (both 1 and 3 isoforms) is involved, which would be an attractive possibility to explain the experimental data. Indeed, Vav possesses a PH domain which can bind to PIP3, and this mechanism could be important for Vav activation [40], thus making it a reasonable extension of the model. Another molecule that could be involved in PI3K-mediated Table 1. Summary of Predicted Activation Pattern upon Different Stimuli and Knock-Out Conditions Input/ Output WT WT WT PI3K PI3K PI3K SLP76 Fyn Fyn Fyn Rlk and Itk Lck and Fyn Lck and Fyn Lck and Fyn Input TCR 1 0 1 1 0 1 1 1 1 1 1 1 0 1 CD4 0 0 0 0 0 0 0 0 1 0 0 0 0 0 CD28 0 1 1 0 1 1 0 0 0 1 0 0 1 1 Output ZAP 1 0 1 1 0 1 1 0 1 0 1 0 0 0 LAT 1 0 1 1 0 1 1 0 1 0 1 0 0 0 PLCga 1 0 1 0 0 0 0 0 1 0 0 0 0 0 ERK 1 0 1 0 0 0 0 0 1 0 0 0 0 0 JNK 1 1 1 1 1 1 1 0 1 1 1 0 1 1 PKB 1 1 1 0 0 0 1 1 1 1 1 0 1 1 AP1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 NFKB 1 0 1 0 0 0 0 0 1 0 0 0 0 0 NFAT 1 0 1 0 0 0 0 0 1 0 0 0 0 0 Reference Figure 3A, 3C Figure 3A, 3D Figures 3A, 4 Figure 3C Figure 3D Figure 4 [49] Figure 3B, [50] Figure 3B, [50] Figure 3B, [50] [51] Figure 4 Figure 4 Figure 4 The headings denote the perturbed (switched-off) element. In the case of PI3K and Lck and Fyn, the perturbation was done via a chemical inhibitor, and for the rest it was through a genetic knock-out. The ‘‘Input’’ rows show the stimuli, and ‘‘Output’’ the predictions of the model for key elements of the network. Here, blue numbers denote results corroborated by published data, while green ones were confirmed by our own data. The red number shows a discrepancy between model and experiment (see discussion in the main text). Finally, the row labeled Reference indicates the Figure where the experimental results are shown or points to the literature reference. doi:10.1371/journal.pcbi.0030163.t001 Figure 3. In Vitro Analysis of Model Predictions (A) Activation of ERK and JNK upon CD28, TCR (CD3), or TCR þ CD28 stimulation in mouse splenic T cells. (B) Activation of PKB upon TCR, TCRþ CD4, and TCR þ CD28 stimulation in Fyn-deficient and heterozygous splenic mouse T cells. (C) Inhibition of PI3K with both Ly294002 and Wortmannin blocks the phosphorylation of PKB, ERK, and JNK, but not ZAP-70 in human T cells. (D) Inhibition of PI3K with both Ly294002 and Wortmannin blocks the phosphorylation of PKB, but not of JNK in human T cells upon CD28 stimulation. As a control, the total amount of ZAP70 (A) or b-actin (B–D) was determined. One representative experiment (of three) is shown. doi:10.1371/journal.pcbi.0030163.g003 PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1585 A Logical Model of T Cell Receptor Signaling activation of JNK is the serine/threonine kinase HPK1 (see Figure 1 and Tables S1 and S2). Interestingly, HPK1 is phosphorylated by Protein Kinase D1 (PKD1) [41], a kinase whose activation depends on PKC (which in turn is depend- ent on DAG, downstream of PI3K) for activation. Since the regulation and functional roles of both PKD1 and PKC (with the exception of the h isoform) are not yet well-established in T cells, we did not include them in the model, but a connection PI3K ! PIP3 ! Itk ! PLCc ! DAG ! PKC ! PKD1 ! HPK1 would be plausible (in which the path from PKC to HPK1 via PKD1 would be new). An alternative could be a Rac-dependent activation of HPK1 [42]; however, this is again a not-well-established connection and thus was not considered. Deﬁnitely, the model requires a direct or indirect connection from PI3K to JNK, and additional experiments are required to assess which of the candidate links predicted by the MISs are relevant in peripheral T cells. This particular example illustrates another useful and important application of our approach: the model not only reveals that a link is missing, but also suggests candidates that can be veriﬁed experimentally. Thus, MIS analysis is capable of guiding the experimentalist and helps to plan the corresponding experi- ments. As an additional application of MISs, we computed combinations of failures (constitutive activation or inactiva- tion of elements caused for example by mutations) which lead to sustained T cell activation without external stimuli. These failure modes would cause uncontrolled proliferation and thus may be connected to diseases such as leukemia or autoimmunity. Interestingly, components occurring in the MISs with few elements (Table 3) are in fact known oncogenes: ZAP70 [43], PI3K [44], Gab2 [45], and PLCc1 [46] (and SLP76 is directly involved in PLCc1 activation). Robustness and Sensitivity Analysis of the Logical Model Strongly related to the idea of MISs is a systematic evaluation of the network response if the model is confronted with failures. By considering a failure as something that happens to the cell by an internal or external event (e.g., a mutation), we may assess the robustness—one of the most important properties of living systems [47]—of the network. In contrast, if we consider the failure as an error that has been introduced during the modeling process (due to incomplete knowledge), then we are assessing the sensitivity of the model with respect to the predictions it makes. Accordingly, to study robustness and sensitivity issues, we (i) removed systematically each single interaction from the network, (ii) recomputed the scenarios given in Table 1, and (iii) compared the new predictions with the 126 original predictions (Table 1), ranking the interactions according to the number of introduced changes produced (Table 4). As an average value, 4.76 errors were introduced per simulated failure, which corresponds to 3.78% of the total numbers of predictions. The most sensitive interactions are mainly located in the upper part of the network and activate components such as the T cell receptor (TCRb), ZAP70, LAT, Fyn, or Abl. It is intuitively clear that the network is very Figure 4. In Vitro Analysis of Src-Kinase Inhibition Inhibition of Src-Kinases (Lck and Fyn) with PP2 blocks TCR-induced but affects only moderately CD28-induced PKB and JNK activation in human T cells; therefore, we concluded that CD28 signaling is not strictly Src-kinase– dependent. The effect was compared with PI3K inhibition via Wortmannin (ccf. Figure 3C and 3D), which blocks the phosphorylation of PKB but not of JNK. b-actin was included as the loading control. One representative experiment (of three) is shown. doi:10.1371/journal.pcbi.0030163.g004 Table 2. Application of the Minimal Intervention Sets To Identify Candidates To Fill the Gap between PI3K and JNK MIS jnk hpk1 rac1r hpk1 sh3bp2 mekk1 mkk4 mekk1 mlk3 hpk1 mekk1 rac1p1 hpk1 mekk1 vav1 hpk1 mkk4 rac1p2 hpk1 mlk3 vav3 hpk1 rac1p1 rac1p2 hpk1 rac1p1 vav3 hpk1 rac1p2 vav1 hpk1 vav1 vav3 hpk1 mlk3 rac1p2 The MISs of maximal size 3 to obtain JNK off under the conditions (i) TCR on, (ii) PI3K off, and (iii) ZAP70 on (as shown in the experiment, see Figure 3D and Table 1) were computed, setting the rest of conditions to the standard values for the early events. Here, each MIS represents one set of molecules that should be influenced by PI3K in order to be consistent with the fact that PI3K inhibition blocks JNK activation. For species abbreviations, see Tables S1 and S2. doi:10.1371/journal.pcbi.0030163.t002 PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1586 A Logical Model of T Cell Receptor Signaling sensitive to failures (again, caused either by internal/external events or modeling errors) in these upper nodes because all pathways branching downstream are governed by them. Accordingly, the validation of our model (with the data from Table 1) is most sensitive to modeling errors in the upper part of the network. We also note that species that can be activated by more than one interaction (e.g., PI3K) are signiﬁcantly less sensitive to single interaction failures since alternative pathways exist. Regarding robustness, it is worth emphasizing that in the worst case about 30% of the original predictions are affected after removal of an interaction, indicating that there is no ‘‘all-or-nothing’’ interaction in the network. We have also performed the same analysis for the removal of a species (instead of an interaction) which basically led to the same results (unpublished data). However, the removal of a node can be seen as a stronger intervention in the network than deleting an interaction, as the former simulates the simultaneous removal of all interactions pointing at that species. Accordingly, deleting nodes implies some stronger deviations from the original predictions. Qualitative Description of the Dynamics So far we have analyzed which elements within the signaling network get activated upon signal triggering (i.e., for the ﬁrst timescale s ¼ 1). This is due to the fact that a large corpus of data for these conditions is available (see Table 1). However, it is important to note that the model is also able to roughly predict the dynamics upon different stimuli and conditions. The modus operandi goes as follows: ﬁrst, one computes the steady state values with no external input (s ¼ 0). Subsequently, the steady state for s ¼ 1 is computed as described above. Finally, one computes the state of the ‘‘slow’’ interactions (those only active at s ¼ 2) as a function of the values at s¼1, and subsequently recomputes the steady states. This provides the response at late events, s ¼ 2. The results obtained can be plotted in a time-dependent manner (Figure 5). Here, one can also investigate the effect of different knock-outs. For example, the absence of PAG has no effect on key downstream elements of the cascade, due to the redundant role of other negative regulatory mechanisms (speciﬁcally, the degradation via c-Cbl and Cbl-b, and Gab-2– mediated inhibition of PLCc1). Only a multiple knock-out of these regulatory molecules leads to sustained activation of key elements. Thus, these results point to a certain degree of redundancy in negative feedbacks for switching off signaling. This sort of qualitative analysis of the dynamics shows the ability of the Boolean approach to reproduce the key dynamic properties (transient versus sustained) of a signaling process. Discussion In this contribution, a logical model describing a large signaling network was established and analyzed. We set up a Table 4. Robustness Analysis: Ranked List of the Most Sensitive Interactions Interaction Caused Errors if Removed !ccblp1 þ tcrlig ! tcrb 39 !ccblp1 þ tcrp þ abl ! ¼ zap70 34 zap70 ! lat 27 tcrb þ lckr ! fyn 26 tcrbþfyn ! tcrp 26 fyn ! abl 26 pi3k þ !ship1 þ !pten ! pip3 21 lat ! plcgb 15 zap70 þ !gab2 þ gads ! slp76 15 lat ! gads 15 pip3 ! pdk1 13 lckp2 þ !cblb ! pi3k 11 lckr þ tcrb ! lckp2 11 !ikkab ! ikb 11 zap70 þ lat ! sh3bp2 10 plcgb þ !ccblp2 þ slp76 þ zap70 þ vav1 þ itk ! plcga 10 pdk1 ! pkb 10 pip3 þ zap70 þ slp76 ! itk 10 zap70 þ sh3bp2 ! vav1 10 !dgk þ plcga ! dag 9 !shp1 þ cd45 þ cd4 þ !csk þ lckr ! lckp1 8 cd28 ! x 8 tcrb þ lckp1 ! tcrp 8 lckp1 ! abl 8 mek ! erk 6 ras ! raf 6 ca ! cam 6 dag ! rasgrp 6 ip3 ! ca 6 lat ! grb2 6 grb2 ! sos 6 plcga ! ip3 6 raf ! mek 6 sos þ !gap þ rasgrp ! ras 6 x ! vav1 5 mkk4 ! jnk 5 mlk3 ! mkk4 5 rac1p1 ! mlk3 5 rac1r þ vav1 ! rac1p1 5 Each single non-input interaction was removed from the network followed by a recomputation of the scenarios given in Table 1. The number of deviations from the 126 predictions made in Table 1 is shown. For abbreviations and comments on the interactions, see Tables S1 and S2. doi:10.1371/journal.pcbi.0030163.t004 Table 3. Minimal Intervention Sets To Produce the Full Activation Pattern in T Cells MIS !gab2 pi3k zap70 !gab2 pip3 zap70 pi3k plcga zap70 pi3k slp76 zap70 pip3 slp76 zap70 pip3 plcga zap70 pdk1 plcga zap70 The MISs of maximal size 3 that induce sustained full activation (namely: ap1, bcat, bclxl, cre, cyc1, nfkb, p70s, sre, and nfat are on, whereas fkhr, p21c, and p27k are off) of T cells without external stimuli. The MISs were computed using CellNetAnalyzer. Note that the exclamation mark ‘‘!’’ denotes ‘‘deactivation’’; species without this symbol have to be activated (constitutively). Interestingly, the compounds involved in these MISs are involved in oncogenesis (ZAP70, PI3K, Gab2, and PLCc1 are oncogenes, and SLP76 is directly involved in PLCc1 activation, see Figure 1 and main text). Note that since PIP3 is a second messenger and not ‘‘mutable’’, for the purpose of this analysis the MISs involving its activation can be considered equivalent to those involving its activator PI3K (i.e., these MISs are equivalent). doi:10.1371/journal.pcbi.0030163.t003 PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1587 A Logical Model of T Cell Receptor Signaling comprehensive Boolean model describing T cell signaling and performed logical steady state analyses unraveling the processing of signals and the global input–output behavior. Moreover, by converting the logical model into an interaction graph, we extracted further important features, such as feedback loops, signaling paths, and network-wide interde- pendencies. The latter can be captured in a dependency matrix (as in Figure 2) which provides thousands of qualitative predictions that can be falsiﬁed in perturbation experiments. The logical model reproduces the global behavior of this complex network for both natural and perturbed conditions (knock-outs, inhibitors, mutations, etc.). Its validity has been proven by reproducing published data and by predicting unexpected results that were then veriﬁed experimentally. Table 1 summarizes the results of 14 different scenarios, in which the logical model predicted 126 states. For 44 of them, experimental data was available (15 from literature and 29 from our own experiments) conﬁrming the predictions, except in the case discussed above. Furthermore, we clearly show that the concept of inter- vention sets allows one (a) to identify missing links in the network, (b) to reveal failure modes that can explain the effects of a physiological dysfunction or disease, and (c) to search for suitable intervention strategies, while keeping track of potential side effects, which is valuable for drug target identiﬁcation. Compared with a kinetic model based on differential equations, a Boolean approach is certainly limited regarding the analysis of quantitative and dynamical aspects, and it certainly cannot answer the same questions. However, to establish such a model requires mainly the topology and only a relatively small amount of quantitative data; hence, a combination of information which is currently available in large-scale networks. Although the model itself is qualitative (i.e., discrete), it enables us not only to study qualitative aspects of signaling networks, but it can also be validated by semi-quantitative measurements such as those in Figures 3 and 4. In summary, with the network involved in T cell activation as a case study, our approach proved to be a Figure 5. Considering Different Time Scales, a Rough Description of the Dynamics Can Be Obtained The activation of key elements upon activation of the TCR, the coreceptor CD4, and the costimulatory molecule CD28 is represented at the resting state, s ¼ 0 (no inputs); early events s ¼ 1 (input(s), no feedback loops); and later-time events, s ¼ 2 (input(s), feedback loops). The black lines correspond to a wild type while the green ones to a PAG KO. Note that the absence of PAG has no effect on key downstream elements of the cascade, due to the redundant role of other negative regulatory mechanisms (degradation via c-Cbl and Cbl-b, Gab-2 mediated inhibition of PLCc1). Multiple knock-out of these regulatory molecules leads to sustained activation of key elements (red lines). doi:10.1371/journal.pcbi.0030163.g005 PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1588 A Logical Model of T Cell Receptor Signaling promising in silico tool for the analysis of a large signaling network, and we think that it holds valuable potential in foreseeing the effects of drugs and network modiﬁcations. Although sometimes the results of a logical model may (afterward) appear to be obvious (as in the case of the CD28- mediated JNK connection), it enables an exhaustive and rigorous analysis of the information processing taking place within a signaling network. Such a systematic analysis becomes infeasible for a human being in large-scale systems. In addition, the LIH can represent the situation of varying cofactor functions; for example, that two substances A AND B are required to activate a third substance C, but activation of C in the presence of A and a fourth substance D requires B not to be present. Certainly, the logical model for T cell activation is far from complete. We are just at the beginning of the reconstruction process and other receptors and their pathways need to be included. However, we feel that already in its current state, the model may prove useful to inspire immunologists to ask new questions which may ﬁrst be answered in silico. Furthermore, the model may also provide a framework for those who may endeavor to quantitatively model TCR signaling. Methods Logical network representation and analysis. We began construc- tion of the signaling network for primary T cells by collecting data from the literature and from our own experiments providing well- established connections (Tables S1 and S2). As a ﬁrst (intermediate) result, we obtain an interaction graph. Interaction graphs are signed directed graphs with the molecules (such as receptor, phosphatase, or transcription factor) as nodes and signed arcs denoting the direct inﬂuence of one species upon another, which can either be activating (þ) or inhibiting (). For example, a positive arc leads from MEK to ERK because the ﬁrst phosphorylates and thereby activates the second (Figure 1). From the incidence matrix of an interaction graph we can identify important features such as feedback loops as well as signaling paths and network-wide interdependencies between pairs of species (e.g., perturbing A may have no effect on B as there is no path connecting A to B). Algorithms related to these analyses are well-known [48] and were recently presented in the context of signaling networks [13]. However, from interaction graphs we cannot conclude which combinations of signals reaching a species along the arcs are required to activate that species. For example, in Figure 1, Jun AND Fos are required to form active AP1. For a reﬁned representation of such relationships, we use a logical (or Boolean) model in which we introduce discrete states for the species (here the simplest (binary) case: 0 ¼ inactive or not present; 1 ¼ active or present) and assign to each species a Boolean function. Here we use a special representation of Boolean functions known as disjunctive normal form (DNF, also called ‘‘sum of product’’ representation) which uses exclusively AND, OR, and NOT oper- ators. A Boolean network with Boolean functions in disjunctive normal form can be intuitively drawn and stored as a hypergraph (LIH) [13], which is well-suited for studying the information ﬂows and input–output relationships in signal transduction networks (Figure 1). In this hypergraph, each hyperarc connects its start nodes with an AND operation (indicated by a blue circle in Figure 1) and each hyperarc represents one possibility for how its end node can be activated or produced (note that hyperacs may also have only one start node, i.e., they are then ‘‘graph-like’’ arcs). Red branches indicate species that enter the hyperarc with their negated value. For example, PLCc-1 (PLCga in Figure 1) AND NOT DGK activates DAG (see Figure 1). Note that each LIH has a unique underlying interaction graph (which can be easily derived from the LIH representation by splitting the AND connections), whereas the opposite is, in general, not true. Within this logical framework we may study the effect of a set of input stimuli (typically ligands) on downstream signaling by comput- ing the logical steady state [13] that results by propagating the signals through the network from the input to the output layer. It seems worthwhile to remark that the updating assumption (synchronous versus asynchronous [14,15])—which must usually be made when dealing with dynamic Boolean networks—is not relevant here as we focus on the logical steady states, which are equivalent in both cases. Sometimes a logical steady state is not unique or does not exist due to the presence of feedbacks loops. However, many feedback loops become active only in a longer timescale justifying setting them OFF in the ﬁrst wave of signal propagation (allowing them to be switched ON for the second timescale). This has been used here for several feedback loops (see main text and Table S2). The effect of knocking- out a species can be tested by re-computing the (new) logical steady state for the respective stimuli. MISs satisfying a given intervention goal can be computed by systematically testing sets of permanently activated or/and deactivated nodes [13,31]. All mathematical analyses and computations have been performed with our software tool CellNetAnalyzer [31], a comprehensive user interface for structural analysis of cellular networks. CellNetAnalyzer and the T cell model can be downloaded for free (for academic use) from http://www.mpi-magdeburg.mpg.de/projects/cna/cna.html. Immunoblotting. Human or mouse T cells were puriﬁed using an AutoMACS magnetic isolation system according to the manufac- turer’s instructions (Miltenyi, http://www.miltenyibiotec.com). Mouse T cells were stimulated with 10 lg/ml of biotinylated CD3e (a subunit of the TCR) antibody (145–2C11, BD Biosciences, http://www. bdbiosciences.com/), 10 lg/ml of biotinylated CD28 antibody (37.51, BD Biosciences), CD3 plus CD28 mAbs, or with CD3 plus 10 lg/ml of biotinylated CD4 (GK1.5, BD Biosciences) followed by crosslinking with 25 lg/ml of streptavidin (Dianova, http://www.dianova.de) at 37 8C for the indicated periods of time. Human T cells were stimulated with CD3e mAb MEM92 (IgM, kindly provided by Dr. V. Horejsi, Prague, Czech Republic) or with CD3 plus CD28 mAbs (248.23.2). Cells were lysed in buffer containing 1% NP-40, 1% laurylmaltoside (N-dodecyl b-D-maltoside), 50 mM Tris pH 7.5, 140 mM NaCl, 10mM EDTA, 10 mM NaF, 1 mM PMSF, 1 mM Na3VO4. Proteins were separated by SDS/PAGE, transferred onto membranes, and blotted with the following antibodies: anti-phosphotyrosine (4G10), anti- ERK1/2 (pT202/pT204), anti-JNK (pT183/pY185), anti-phospho-Akt (S473) (all from Cell Signaling, http://www.cellsignal.com/), anti- ZAP70 (pTyr 319, Cell Signaling), anti-ZAP70 (cloneZ24820, Trans- duction Laboratories, http://www.bdbiosciences.com/), or against b- Actin (Sigma, http://www.sigmaaldrich.com/). Where PI3K and src- kinase inhibitors were used, T cells were treated with 100 nM Wortmannin (Calbiochem, http://www.emdbiosciences.com) or 10 lM PP2 (Calbiochem) for 30 min at 37 8C prior to stimulation. All experiments have been repeated three times and reproduced the shown results. Supporting Information Table S1. List of Compounds in the Logical T Cell Model Model name corresponds to the name in Figure 1 and Table S2. Common abbreviations are those usually used in the literature, while name is the whole name. Type classiﬁes the molecules, if applies, as follows: K ¼ Kinase, T ¼ Transcription Factor, P ¼ Phosphatase, A ¼ Adaptor Protein, R ¼ Receptor, G ¼ GTP-ase. In the case where two pools of a molecule were considered, a ‘‘reservoir’’ was included which was required for both pools. This allows us to perform a simultaneous knock-out of both pools. Found at doi:10.1371/journal.pcbi.0030163.st001 (56 KB PDF). Table S2. Hyperarcs of the Logical T Cell Signaling Model (see Figure 1 and Methods) Exclamation mark (‘‘!’’) denotes a logical NOT, and dots within the equations indicate AND operations. The names of the substances in the explanations are those used in the model and Figure 1; the biological names are displayed in Table S1. In the case where two pools of a molecule were considered (e.g., lckp1 and lckp2), a ‘‘reservoir’’ (lckr) was included which was required for both pools. This allows us to perform a simultaneous knock-out of both pools acting on the reservoir. Found at doi:10.1371/journal.pcbi.0030163.st002 (183 KB PDF). Acknowledgments The authors would like to thank the members of the signaling group at the Institute of Immunology (M. Smida, X. Wang, S. Kliche, R. Pusch, M. PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1589 A Logical Model of T Cell Receptor Signaling Togni, A. Posevitz, V. Posevitz, T. Drewes, U. Ko¨ lsch, S. Engelmann) and I. Merida and J. Huard for essential biological input into the model. Author contributions. JSR set up the model and performed the analysis. LS, JAL, UB, BA, and BS, with the help of the signaling group at the Institute of Immunology, gathered the biological details of the model and analyzed the correctness of the results. LS and BA performed the wet-lab experiments. RH supported the model setup, analysis, and documentation. SK developed the theoretical methods and tools (CellNetAnalyzer) and supported the analysis. UUH and RW contributed to the theoretical methods with useful insights. EDG, BS, and RW coordinated the project. Funding. The authors are thankful for the support of the German Ministry of Research and Education to EDG (Hepatosys), the German Research Society to BS and EDG (FOR521), and the Research Focus Dynamical Systems funded by the Saxony-Anhalt Ministry of Education. Competing interests. The authors have declared that no competing interests exist. References 1. Kitano H (2002) Computational systems biology. Nature 420: 206–210. 2. 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PLoS Computational Biology \| www.ploscompbiol.org August 2007 \| Volume 3 \| Issue 8 \| e163 1590 A Logical Model of T Cell Receptor Signaling	17722974	tcrlig = ( tcrlig ) vav1 = ( zap70 AND ( ( ( sh3bp2 ) ) ) ) OR ( xx ) lat = ( zap70 ) pi3k = ( ( xx ) AND NOT ( cblb ) ) OR ( ( lckp2 ) AND NOT ( cblb ) ) gap = ( unknown_input3 ) rac1r = ( unknown_input ) Dummy = ( ( plcgb AND ( ( ( vav1 AND zap70 AND itk AND slp76 ) ) ) ) AND NOT ( ccblp2 ) ) ca = ( ip3 ) pkb = ( pdk1 ) nfkb = NOT ( ( ikb ) ) lckp1 = ( ( cd45 AND ( ( ( lckr AND cd4 ) AND ( ( ( NOT csk ) ) ) ) ) ) AND NOT ( shp1 ) ) nfat = ( calcin ) bclxl = NOT ( ( bad ) ) gadd45 = ( unknown_input ) bad = NOT ( ( pkb ) ) pag = ( ( fyn ) AND NOT ( tcrb ) ) ccblp2 = ( ccblr AND ( ( ( fyn ) ) ) ) cyc1 = NOT ( ( gsk3 ) ) vav3 = ( sh3bp2 ) sre = ( rac1p2 ) OR ( cdc42 ) ikkg = ( card11a AND ( ( ( pkcth ) ) ) ) calcin = ( ( ( ( cam ) AND NOT ( calpr1 ) ) AND NOT ( akap79 ) ) AND NOT ( cabin1 ) ) cabin1 = NOT ( ( camk4 ) ) grb2 = ( lat ) ship1 = ( unknown_input2 ) plcga = ( ( plcgb AND ( ( ( vav1 AND zap70 AND itk AND slp76 ) ) ) ) AND NOT ( ccblp2 ) ) sh3bp2 = ( zap70 AND ( ( ( lat ) ) ) ) shp2 = ( gab2 ) pten = ( unknown_input2 ) mlk3 = ( hpk1 ) OR ( rac1p1 ) gsk3 = NOT ( ( pkb ) ) cd45 = ( unknown_input ) dag = ( ( plcga ) AND NOT ( dgk ) ) bcl10 = ( unknown_input2 ) gab2 = ( grb2 AND ( ( ( lat AND zap70 ) ) ) ) OR ( gads AND ( ( ( lat AND zap70 ) ) ) ) erk = ( mek ) ap1 = ( fos AND ( ( ( jun ) ) ) ) fos = ( erk ) cblb = NOT ( ( cd28 ) ) gads = ( lat ) pdk1 = ( pip3 ) itk = ( pip3 AND ( ( ( zap70 AND slp76 ) ) ) ) ras = ( ( sos AND ( ( ( rasgrp ) ) ) ) AND NOT ( gap ) ) ikb = NOT ( ( ikkab ) ) ccblp1 = ( ccblr AND ( ( ( zap70 ) ) ) ) p21c = NOT ( ( pkb ) ) tcrp = ( tcrb AND ( ( ( fyn OR lckp1 ) ) ) ) rac1p2 = ( rac1r AND ( ( ( vav3 ) ) ) ) rsk = ( erk ) fyn = ( lckp1 AND ( ( ( cd45 ) ) ) ) OR ( tcrb AND ( ( ( lckr ) ) ) ) hpk1 = ( lat ) cam = ( ca ) cre = ( creb ) akap79 = ( unknown_input2 ) p70s = ( pdk1 ) p38 = ( ( zap70 ) AND NOT ( gadd45 ) ) card11a = ( malt1 AND ( ( ( card11 AND bcl10 ) ) ) ) pip3 = ( ( ( pi3k ) AND NOT ( ship1 ) ) AND NOT ( pten ) ) card11 = ( unknown_input ) ccblr = ( unknown_input ) creb = ( rsk ) zap70 = ( ( tcrp AND ( ( ( abl ) ) ) ) AND NOT ( ccblp1 ) ) jun = ( jnk ) camk2 = ( cam ) jnk = ( mkk4 ) OR ( mekk1 ) sos = ( grb2 ) slp76 = ( ( zap70 AND ( ( ( gads ) ) ) ) AND NOT ( gab2 ) ) mkk4 = ( mekk1 ) OR ( mlk3 ) cdc42 = ( unknown_input2 ) lckp2 = ( lckr AND ( ( ( tcrb ) ) ) ) mekk1 = ( hpk1 ) OR ( cdc42 ) OR ( rac1p2 ) lckr = ( lckr_input ) plcgb = ( lat ) ip3 = ( plcga ) raf = ( ras ) ikkab = ( ikkg AND ( ( ( camk2 ) ) ) ) rlk = ( lckp1 ) fkhr = NOT ( ( pkb ) ) cd28 = ( cd28 ) malt1 = ( unknown_input ) pkcth = ( dag AND ( ( ( pdk1 AND vav1 ) ) ) ) p27k = NOT ( ( pkb ) ) rasgrp = ( dag ) mek = ( raf ) rac1p1 = ( rac1r AND ( ( ( vav1 ) ) ) ) tcrb = ( ( tcrlig ) AND NOT ( ccblp1 ) ) abl = ( fyn ) OR ( lckp1 ) csk = ( pag ) xx = ( cd28 ) shp1 = ( ( lckp1 ) AND NOT ( erk ) ) dgk = ( tcrb ) bcat = NOT ( ( gsk3 ) ) calpr1 = ( unknown_input2 ) camk4 = ( cam )
BioMed Central Page 1 of 26 (page number not for citation purposes) BMC Bioinformatics Open Access Methodology article A methodology for the structural and functional analysis of signaling and regulatory networks Steffen Klamt†1, Julio Saez-Rodriguez†1, Jonathan A Lindquist2, Luca Simeoni2 and Ernst D Gilles1 Address: 1Max-Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, D-39106 Magdeburg, Germany and 2Institute for Immunology, University of Magdeburg, Leipziger Strasse 44, D-39120 Magdeburg, Germany Email: Steffen Klamt - klamt@mpi-magdeburg.mpg.de; Julio Saez-Rodriguez - saezr@mpi-magdeburg.mpg.de; Jonathan A Lindquist - Jon.Lindquist@Medizin.Uni-Magdeburg.de; Luca Simeoni - Luca.Simeoni@Medizin.Uni-Magdeburg.de; Ernst D Gilles - gilles@mpi-magdeburg.mpg.de * Corresponding author †Equal contributors Abstract Background: Structural analysis of cellular interaction networks contributes to a deeper understanding of network-wide interdependencies, causal relationships, and basic functional capabilities. While the structural analysis of metabolic networks is a well-established field, similar methodologies have been scarcely developed and applied to signaling and regulatory networks. Results: We propose formalisms and methods, relying on adapted and partially newly introduced approaches, which facilitate a structural analysis of signaling and regulatory networks with focus on functional aspects. We use two different formalisms to represent and analyze interaction networks: interaction graphs and (logical) interaction hypergraphs. We show that, in interaction graphs, the determination of feedback cycles and of all the signaling paths between any pair of species is equivalent to the computation of elementary modes known from metabolic networks. Knowledge on the set of signaling paths and feedback loops facilitates the computation of intervention strategies and the classification of compounds into activators, inhibitors, ambivalent factors, and non-affecting factors with respect to a certain species. In some cases, qualitative effects induced by perturbations can be unambiguously predicted from the network scheme. Interaction graphs however, are not able to capture AND relationships which do frequently occur in interaction networks. The consequent logical concatenation of all the arcs pointing into a species leads to Boolean networks. For a Boolean representation of cellular interaction networks we propose a formalism based on logical (or signed) interaction hypergraphs, which facilitates in particular a logical steady state analysis (LSSA). LSSA enables studies on the logical processing of signals and the identification of optimal intervention points (targets) in cellular networks. LSSA also reveals network regions whose parametrization and initial states are crucial for the dynamic behavior. We have implemented these methods in our software tool CellNetAnalyzer (successor of FluxAnalyzer) and illustrate their applicability using a logical model of T-Cell receptor signaling providing non-intuitive results regarding feedback loops, essential elements, and (logical) signal processing upon different stimuli. Conclusion: The methods and formalisms we propose herein are another step towards the comprehensive functional analysis of cellular interaction networks. Their potential, shown on a realistic T- cell signaling model, makes them a promising tool. Published: 07 February 2006 BMC Bioinformatics2006, 7:56 doi:10.1186/1471-2105-7-56 Received: 28 July 2005 Accepted: 07 February 2006 This article is available from: http://www.biomedcentral.com/1471-2105/7/56 © 2006Klamt et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 2 of 26 (page number not for citation purposes) Background Evolution has equipped cells with exquisite signaling sys- tems which allow them to sense their environment, receive and process signals in a hierarchically organized manner and to react accordingly [1]. The complexity of the corresponding molecular machineries, in accordance with the complicated tasks they have to perform, is over- whelming. In the last few years, as a key element to the growing popularity of systems biology, mathematical tools have been applied to the analysis of signaling data [2]. Ordinary differential equations relying on kinetic descriptions of the underlying molecular interactions are arguably the most used approach for modeling signaling networks (e.g. [3-6]). A number of theoretical methods have been devised and employed for the reconstruction (reverse engineering) of signaling or, more generally, interaction networks (which may represent signaling but also other types or abstractions of cellular networks such as genetic regulatory networks) based on perturbation experiments [7]. The approaches rely on methods ranging from Bayesian networks (e.g. [8]) to metabolic control analysis [9,10]. Relatively few methods have been proposed so far for ana- lyzing the structure of a given signaling (or any interac- tion) network. This is somewhat surprising since structural analysis of metabolic networks is a well-estab- lished field and proved to be successful to recognize rela- tionships between structure, function, and regulation of metabolic networks [11]. Structural analysis will be partic- ularly useful in large signaling networks, where a simple visual inspection is not possible and at the same time the construction of precise quantitative models is practically infeasible due to the huge amount of required, but gener- ally unknown, kinetic parameters and concentration val- ues. However, the reconstruction of large signaling networks is still in its first stages [2,12]. Structural or qualitative approaches that have been employed for interaction networks include statistical large-scale analyses in protein-protein networks (e.g. [13]). These studies are important for examining statisti- cal properties of the interaction graph and for understand- ing its global organization but they provide relatively few insights into the function of the network. Papin and co- workers [14,15] were the first to adapt methods from the constraint-based approach (frequently used for structural analysis of metabolic networks [11]) to analyze stoichio- metric models of signaling pathways. Recently, graph-the- oretical descriptions of signaling networks have been examined [16-18]. Finally, Boolean networks as discrete approximations of quantitative models have been used for logical analyses of small signaling networks e.g. [19]. However, the majority of studies relying on the Boolean approach deal with genetic interaction networks, many of which have a relatively small size (ca. 10 species; e.g. [20,21]), however, recently more complicated networks have also been investigated [22,23]. In this contribution, we propose formalisms for represent- ing signaling and other interaction networks mathemati- cally and present a collection of methods facilitating structural analysis of the respective network models. Rather than introducing completely new concepts, we will systematize and adapt existing formalisms and methods, often motivated from structural analyses of metabolic net- works, towards a functional analysis of the structure of a signaling network. Issues that can be addressed with the proposed methods include: • check of the plausibility and consistency of the network structure • identification of all or particular signaling pathways, feedback loops and crosstalks • network-wide functional interdependencies between network elements • identification of the different modes of (logical) input/ output behavior • predicting responses (phenotypes) after changes in net- work structure • finding targets and intervention points in the network for repressing or provoking a certain behavior or response • analysis of structural network properties like redun- dancy and robustness Structural analysis is not based on quantitative and dynamic properties and can thus only provide qualitative answers. However, some insights into the dynamic prop- erties can nevertheless often be obtained, because funda- mental properties of the dynamic behavior are often governed by the network structure [24]. While we will focus on signaling networks, the methods can be easily applied to any kind of interaction network, including gene regulatory systems. Apart from a toy model, we will exemplify our methods on a model of signaling pathways in T-cells. Results and discussion Mass and signal flows in cellular interaction networks The reader familiar to the structural analysis of stoichio- metric networks may notice that, in the case of metabolic networks, many of the issues in the task list of the previ- ous section have been handled by the constraint-based approach [11]. For example, the identification of func- BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 3 of 26 (page number not for citation purposes) tional pathways and studying the input (substrates)/out- put (products) behavior of stoichiometric reaction networks is facilitated by elementary-modes analysis [25,26]. Flux Balance Analysis is another related tech- nique often used for phenotype predictions of metabolic mutants [11,27]. Recently, the concept of minimal cut sets has been introduced for identifying targets in metabolic networks [28,29]. Therefore, it seems reasonable to apply these methods to signaling networks. However, some fun- damental differences in the way the network elements interact may complicate a direct transfer: (1) The constraint-based framework assumes steady-state, while in signaling networks a transient behavior can often be observed. (However, as will be discussed below, many useful insights of signaling networks can be obtained from using a static approach.) (2) In stoichiometric networks, any arrow (reaction) lead- ing from educts to products can be seen as an "activating" (producing) connection for the products. Therefore, employing stoichiometric framework it is difficult or only indirectly possible to express an inhibitory action of a spe- cies onto another. (3) Probably the most significant difference is that the edges (i.e. the connections between the species) in meta- bolic networks carry flows of mass whereas edges in sign- aling networks may carry mass and/or information (signal) flow. Of course, at the molecular level, any inter- action between species in the cell can be written as a stoi- chiometric equation. However, whereas mass flow is connected to a real consumption of participating com- pounds, signal flow is usually characterized by a recycling of certain species (e.g. enzymes) so that these species can mediate the signal transfer continuously (until they are degraded). A typical example, namely the activation of a receptor tyrosine kinase (Figure 1(a)) [30], illustrates the simulta- neous occurrence of mass and signal flow. A ligand (Lig) binds to the extracellular domain of a receptor (Rec) yield- ing a receptor-ligand complex which can undergo further changes (e.g. by autophosphorylation or/and dimeriza- tion). We denote the outcome by RecLig. This complex is now able to phosphorylate another molecule (M). Accordingly, M binds to RecLig and becomes phosphor- ylated (M-P) by the expense of ATP. At the end, M-P is released, recycling also the activated receptor-ligand com- plex RecLig. The first step in this scheme can be considered as a mass flow. However, the cycle in which RecLig phosphorylates M, is a mass flow with respect to M and ATP, but a signal- ing flow with respect to RecLig, as the latter is indeed required for driving this cycle but not consumed (because recycled) in the overall stoichiometry. In performing a structural analysis we are interested in extracting signaling paths from the network scheme. Therefore, it may seem reasonable to compute elementary modes, which typically represent pathways in reaction networks with mass flow [25]. A basic property of elemen- tary modes is that the (relative) mass flow represented by an elementary mode keeps the "internal" species in a bal- anced state. Internal species (here: RecLig, RecLig-M, RecLig-M-P) are within the system's boundary, whereas the external species (here: Rec, Lig, M, M-P, ADP, ATP) are considered as pools which are balanced by processes lying outside the system's boundaries. Computing the elemen- tary modes from the respective stoichiometric model of Figure 1(a) gives exactly one mode which reflects the dis- cussed role of RecLig* as a kinase (Figure 1(b)): in its net stoichiometry, this elementary mode converts the external species M and ATP into M-P and ADP, whereas RecLig* is recycled. Since RecLig* is neither consumed nor produced in the overall process, the first step (building the receptor- ligand complex) is not involved in this mode simply because a continuous synthesis of RecLig* would lead to an accumulation of this species, which is inconsistent with the steady-state assumption of elementary modes. Thus, the causal dependency of M-P from the availability of Rec and Lig is not reflected by the mass flow concept of elementary modes. Note that exactly the same conceptual problem would arise when enzymes and enzyme synthe- (a) Example of a typical signaling pathway where mass and signal flow occur simultaneosly (Rec = receptor; Lig = ligand; RecLig* = (active) receptor-ligand-complex; M = molecule; M-P = phosphorylated molecule M) Figure 1 (a) Example of a typical signaling pathway where mass and signal flow occur simultaneosly (Rec = receptor; Lig = ligand; RecLig* = (active) receptor-ligand-complex; M = molecule; M-P = phosphorylated molecule M). (b) The (only) elemen- tary mode in this example which follows when M, M-P, ADP, ATP, Rec and Lig are considered as external (boundary) spe- cies. The involved reactions are indicated by green, thick arrows. In its net stoichiometry, this elementary mode con- verts M and ATP into M-P and ADP, whereas RecLig* is recy- cled in the overall process. Importantly, the mandatory process of building the receptor-ligand-complex RecLig* (hence, the causal dependeny of M-P from the availability of Rec and Lig) is not reflected by this mode. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 4 of 26 (page number not for citation purposes) sis would be considered explicitly in stoichiometric stud- ies of metabolic networks. The example demonstrates that we require a framework with the ability to account for mass and signal flows. Han- dling both mass and signal flows formally equivalent as interactions could be a suitable approach. Interpreting Fig- ure 1(a)) as a diagram of interactions we could redraw it as depicted in Figure 2(a). The dashed arrow indicates that RecLig* catalyzes the phosphorylation of M to M-P. If we assume that ADP, ATP, and M are always present, we get the simple chain shown in Figure 2(b) expressing that Rec and Lig are required to obtain RecLig* (or to activate RecLig), and that RecLig is required to get M-P. If we do not further distinguish between the two types of arrows and thus consider mass and signal flows as formally equivalent, the causal connections between the species would, nevertheless, still be captured correctly. This abstract representation of different types of interactions will thus be used herein. The following two sections will deal first with interaction graphs and later with the more general (logical) interac- tion hypergraphs. The basic difference between these two related approaches can be illustrated by how they deal with a connection such as "Rec + Lig" in Figure 2(b). If we interpret it as "Rec activates RecLig* and Lig activates RecLig" then the concept of interaction graphs is applica- ble (discussed in the following section). However, it would be more accurate to say that "Rec AND Lig are required simultaneously for building RecLig", and it is this more refined approach that leads to the concept of inter- action hypergraphs, which will be discussed in further details later on. Analyzing interaction graphs Definition of interaction graphs Interaction (or causal influence) graphs are frequently used to show direct dependencies between species in sig- naling, genetic, or protein-protein interaction networks. The nodes in these graphs may represent, depending on the network type and the level of abstraction, receptors, ligands, effectors, kinases, genes, transcription factors, metabolites, proteins, and other compounds, while each edge describes a relation between two of these species. In signaling and gene regulatory networks, two further char- acteristics are usually specified for each edge: a direction (which species influences which) and a sign ("+" or "- ", depending on whether the influence is activating (level increasing) or inhibiting (level decreasing)). Formally, we represent a directed interaction or causal influence graph as a signed directed graph G = (V, A), where V is the set of vertices or nodes (species) and A the set of labeled directed edges [31,32]. Directed edges are usually called arcs and an arc from vertex i (tail) to j (head) is denoted by an ordered tuple {i,j,s} with i, j ∈ V and s ∈ {+,- }. Sometimes, for example in protein-protein interaction networks, the directions of the edges remain unspecified. We will not consider such undirected interaction graphs explicitly, however, many of the issues discussed in the following can be transferred to undirected graphs (e.g. by representing an undirected edge by two (forward and backward) arcs). The structure of a signed graph can be stored conveniently by an m x q incidence matrix B in which the columns cor- respond to the q arcs (interactions) and the rows to the m nodes (species), similar as in stoichiometric matrices of metabolic reaction networks [33]. For the k-th arc {i, j, s} a (-1) is stored in the k-th column of B for the tail vertex (i) and (+1) for the head vertex (j) of arc k. Hence, Bi,k = - 1 and Bj,k = 1 and Bl,k = 0 (l≠ i, j). For storing the signs, a q- vector s is introduced whose k-th element is (+1) if arc k is positive and (-1) if k is negative. Self-loops (arcs connecting a species with itself) are not considered here but could be stored in a separate list since they would appear as a zero column in the incidence matrix. Note that, as far as the memory requirement is concerned, the structure of a graph can be stored more efficiently than by an incidence matrix, e.g. by using adjacency lists [34]. However, since we will present methods directly operat- ing on the incidence matrix, we refer herein to this repre- sentation. Signal transduction networks are usually characterized by an input, intermediate, and output layer (cf. [16]). The input domain consists only of species having no predeces- Interpretation of Figure 1 as an interaction network Figure 2 Interpretation of Figure 1 as an interaction network. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 5 of 26 (page number not for citation purposes) sor, which can thus not be activated from other species in the graph. Such sources (typical representatives are recep- tors and ligands) are starting points of signal transduction pathways and can easily be identified from the incidence matrix since their corresponding row contains no positive entry. In contrast, the output layer consists only of nodes having no successor. These sinks, usually corresponding to transcription factors or genes, are identifiable as rows in B which have no negative entry. The set of source and sink nodes define the boundaries of the network under inves- tigation. They play here a similar role as the external metabolites in stoichiometric studies [33]. The intermedi- ate layer functions as the actual signal transduction and processing unit. It consists of the intermediate species, all of which have at least one predecessor and at least one successor, i.e. they are influenced and they influence other elements. Such species contain both -1 and +1 entries in the incidence matrix. In reconstructed signaling networks, the detection of all sink and source species may help to detect gaps in the network, e.g. when a species should be an intermediate but is classified as a sink or source. The presence of sinks and sources are a consequence of setting borders to the system of interest. Sometimes there are no sinks or/and no sources, especially in models of gene regulatory networks (see e.g. the networks studied in [21]), but this does not impose limitations to the approaches presented here. A toy example of a (directed) interaction graph that will serve for illustrations throughout this paper is given in Figure 3. This interaction graph, called TOYNET, consists of two sources (I1, I2), two sinks (O1, O2), 7 intermediate species (A,..., G), two inhibiting (arcs 2 and 7) and 11 acti- vating interactions. Incidence matrix B of TOYNET reads (the sign vector s is given on the top of B): Identification of feedback loops Even though some analysis methods (e.g. Bayesian net- works) rely on acyclic networks where feedbacks are not allowed, one of the most important features of signaling and regulatory networks are their feedback loops [3,5,18,21,35-38]. Positive feedbacks are responsible and even required [39] for multiple steady state behavior in dynamical systems. In biological systems, multistationar- ity plays a central role in differentiation processes and for epigenetic and switch-like behavior. In contrast, negative feedback loops are essential for homeostatic mechanisms (i.e. for adjusting and maintaining levels of system varia- bles) or for generating oscillatory behavior [35]. Most reports demonstrating the role and consequences of feedback loops analyze relatively small networks where the cycles can be easily recognized from the network scheme but rather few works address the question of how feedback cycles can be identified systematically. This is particularly important in large interaction graphs, where a detection by simple visual inspection is impossible, espe- cially when feedback loops overlap. A feedback loop is, in graph theory, a directed cycle or cir- cuit. A circuit is defined as a sequence C = {a1,...,aw} of arcs that starts and ends at the same vertex k and visits (with the exception of k) no vertex twice, i.e. C = {a1,...,aw} = {{k, l1}, {l1,l2},..., {lw-1,k}} such that all nodes k, l1, l2 ... lw-1 are distinct. The parity of the number of negative signs of the arcs in C determines whether the feedback loop is negative (odd number of negative signs) or positive (even). In the example TOYNET two feedback loops can be found: (i) the arc sequence {4,5,6,7} which is negative (since one negative arc (7) is involved), and (ii) the sequence {10,11}, which is positive (because the signs of both arcs in this circuit are positive). Obviously, sinks and sources (and all arcs connected to these nodes) can never be involved in any circuit. B = + − + + + + − + + + + + + − − − − 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 − − − − − − 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 − − −                                   I1 I2 A B C D E F G O1 O2 1( ) Example of a directed interaction graph (TOYNET) Figure 3 Example of a directed interaction graph (TOYNET). Arcs 2 and 7 indicate inhibiting interactions, while all others are acti- vating. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 6 of 26 (page number not for citation purposes) Computing all directed cycles in large graphs is computa- tionally a difficult task. Algorithms that can be found in the literature usually rely on backtracking strategies (e.g. [16,40]). Here, we introduce a different approach where the circuits are identified as elementary modes establish- ing a direct link to metabolic network analysis. Circuits can be formally represented by a q-vector c in which ci = 1 if arc i is involved in the circuit and ci = 0 otherwise. A cir- cuit vector fulfills the equation B c = 0 (2) and hence, lies in the null space of the incidence matrix of the graph [32,41]. Generally, any vector c obeying (2) ful- fills a so-called conservation law and is called a circulation which may be envisioned as a flow cycling around in the network [42]. Eq. (2) is strongly related to the mass bal- ance equation of metabolic networks in steady state. In fact, considering the graph as a reaction network with the arcs being irreversible mono-molecular reactions, the inci- dence matrix would be equivalent to the stoichiometric matrix and any circulation would be equivalent to a sta- tionary flux distribution. Note that not all circulations are circuits: the linear combinations of circuit vectors do also yield circulations but are not (elementary) circuits. Pre- cisely, circuits are special circulations having two addi- tional properties. First, they must be admissible with respect to the directions of the involved arcs, i.e. only non- negative values are allowed for c: ci≥ 0 for all i. (3) Second, circuits are non-decomposable circulations, i.e. the set of arcs building up the circuit c, expressed by P(c) = {i: ci > 0}, is irreducible: There is no non-zero vector d fulfilling eqs. (2) and (3) and P(d)⊂ P(c) (4) Eqs. (2) and (3) and condition (4) close the complete analogy to elementary modes. In fact, cycles or circuits are the elementary modes in the special case of graphs (ele- mentary modes are defined for any matrix in eq. (2), not only for the very special shape of incidence matrices related to graphs). Any feasible stationary flux vector in a metabolic network can be obtained by non-negative lin- ear combinations of elementary modes. Equivalently, any circulation vector can be decomposed into a non-negative linear combination of circuit vectors. Note that, multiply- ing a (circuit) vector c, that fulfills (2)-(4), by a scalar b>0 yields another vector v = bc which represents the same cir- cuit because the same arcs compose it (are unequal to zero). Moreover, all non-zero components in a circuit vec- tor are equal to each other. Therefore we can always nor- malize the vector in such a way that we obtain the binary representative of this circuit where all components are either "1" or "0". In metabolic networks, elementary modes reveal not only internal cycles but also, even with higher relevance, meta- bolic pathways connecting input and output species. Con- tinuing with the analogy to interaction graphs, in the next subsection we will see that elementary modes can be used to identify not only feedback loops but also signaling paths. Signaling (influence) paths between two species When the interaction graph is very large it becomes diffi- cult to see whether a species S1 can influence (activate or inhibit) another species S2 and via which distinct path- ways this can happen. Computing the complete set of directed paths between a given pair (S1, S2) of species is therefore often desirable. A path P = {a1,...,aw} is, similarly to a feedback circuit, a sequence of arcs where none of the nodes is visited more than once, but in the case of a sign- aling path the start node S1 is distinct from the end node S2, i.e. P = {a1,...,aw} = {{S1,l1}, {l1,l2}, ..., {lw-1,S2}} such that all nodes S1, S2, l1, l2 ... lw-1 are distinct. To obtain the signaling pathways from S1 to S2 we pro- ceed as follows (Figure 4(a)): we add an "input arc" for S1 (i.e. a new column in the incidence matrix B containing only zeros except a (+1) for S1) and an "output arc" for S2 (another new column in B containing only zeros except a (-1) for S2. Then, computation of the elementary modes in this network will provide the original feedback loops without participation of the input and the output arc (as shown above) and additionally all paths starting with the input arc at S1 and ending with the output arc at S2, with the latter revealing all possible routes between S1 and S2. Computation of all signaling paths between two species (here: between I1 and O1) Figure 4 Computation of all signaling paths between two species (here: between I1 and O1). (a) via the incorporation of a "simplified" input and output arc; (b) with explicit introduc- tion of an ENV („environment") node. Computing the ele- mentary modes from the respective incidence matrix for (a) and (b) yields basically the same result, namely all paths between I1 and O1, as well as the two feedback circuits in the intermediate layer. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 7 of 26 (page number not for citation purposes) Admittedly, the introduced input and output arcs have no tail or no head, respectively, and would therefore not be edges in the graph-theoretical sense, but this has no con- sequence for the analysis described within this contribu- tion. In fact, this procedure is equivalent to adding in the incidence matrix a "dummy" node representing the envi- ronment (ENV), an "input arc" from ENV to S1 and an "output arc" from S2 to ENV (Figure 4(b)). Computing the elementary modes from the resulting incidence matrix would produce the feedback circuits as well as the circuits running over ENV. The latter represent the paths leading from S1 to S2. In the procedure described above ENV is simply removed from the incidence matrix leading to the same results. In order to obtain only the paths from S1 to S2 (without the feedback loops), one can enforce the input and output arc to be involved by using an extension of the algorithm for computing elementary modes [43]. Furthermore, we may also add several input and output edges simultaneously. For example, if we are interested in all the paths connecting the input layer with the output layer, i.e. all routes leading from a source to a sink node, we add to each source an input edge and to each sink an output edge and compute the elementary modes (and, optionally, discard the feedback circuits where neither a source nor a sink participates). In this way we obtain the same set of signaling paths as if the elementary modes would be computed separately for each possible pair of source and sink nodes. Figure 5 shows the complete set of signaling paths connecting the input with the output layer of TOYNET. Analogously to the feedback loops, we assign to each sig- naling path an "overall sign" indicating whether A acti- vates (+) or inhibts (-) B along this path. Again, the parity of the signs of the arcs in the path determine whether the influence is positive (even number of negative signs) or negative (odd number of signs). To sum up, feedback loops and influence paths in interac- tion graphs can be identified as elementary modes (or, equivalently, as extreme rays of convex cones [44]) from the respective incidence matrix. Similar conclusions have recently been drawn by Xiong et al. [45], albeit the authors computed paths only between sink and source nodes and only within unsigned graphs (i.e. they did not consider inhibitory effects). Feedback circuits were also not consid- ered. Hence, here we extend and generalize those results. The equivalence of signaling paths and loops to elemen- tary modes allows one the advantage to use the highly optimized algorithms for computing elementary modes [43,44,46]. Combinatorial studies on signaling paths The computation of all paths between a pair of species helps us to recognize all the different ways in which a sig- nal can propagate between two nodes. In metabolic path- way analysis, a statistical or combinatorial analysis of the participation and co-occurrences of reactions in elemen- tary modes proved to be useful for obtaining system-wide properties, such as the detection of essential reactions/ enzymes or correlated reaction sets (enzyme subsets) [11,26,47]. In principle, similar features are of interest also for signal- ing paths and feedback loops. However, two important issues arise in interaction graphs that require a special treatment. First, we have two different types of pathways, positives and negatives. Owing to their opposite mean- ings we often need to analyze them separately in statistical assessments. Second, in metabolic networks we are partic- ularly interested in the reactions (edges), because they cor- respond to enzymes that are subject to regulatory processes and can be knocked-out in experiments. In con- trast, in interaction graphs we are usually more interested in the nodes, since they are often knocked-out in experi- ments or medical treatments, either via mutations, siRNA or by specific inhibitors. An edge in signaling networks represents mostly a direct interaction between a pair of species and has therefore no mediator. In some cases, an edge can directly be targeted by e.g. a mutation at the cor- responding binding site of one of the two nodes species All signaling paths linking the input layer (source species) with the output layer (sink species) in TOYNET Figure 5 All signaling paths linking the input layer (source species) with the output layer (sink species) in TOYNET. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 8 of 26 (page number not for citation purposes) involved. Here, we will focus on species participation, albeit similar computations can be made for the edges. As mentioned several times, in signaling networks we are often interested in all the different ways by which a certain transcription factor (or any other species from the output layer) can be activated or inhibited by signals arriving the input layer. For this purpose, we compute all signaling paths leading from source nodes located in the input layer down to a certain sink species s of interest. We denote the set of all these paths by Is, which can be dissected in the two disjoint subsets of activating and inhibiting paths: I = ∫ . Each source species i can then be classified into one of the following four influence classes with respect to s: (1) activator of s (i is involved in at least one path of and in no path of ) (2) inhibitor of s (i is involved in at least one path of and in no path of ) (3) ambivalent factor for s (i is involved in at least one (inhibiting) path of and in at least one (activating) path of ) (4) without any influence on s (i is not involved in any path of Is) In TOYNET, we see from Figure 5 that I2 is a pure activator and I1 an ambivalent factor for O1. With respect to O2, I1 is an inhibitor and I2 again an activator. The qualitative response of s after perturbing the level of a non-affecting species, or of an inhibitor or activator can be predicted unambiguously (namely unchanged or decreasing or increasing, respectively) as long as the network has no negative feedback loop. Negative feedback loops limit such qualitative predictions for activators (or inhibitors): if there is any path from an activator (inhibitor) to s that touches a negative feedback loop (i.e. at least one species on the path is involved in a negative feedback) then the resulting effect in perturbation experiments can not be predicted uniquely (cf. [36]). This case occurs in TOYNET for I2 with respect to O1: I2 is an activator of O1 but the only connecting path (P5 in Figure 5) goes through spe- cies C which participates in the negative feedback circuit. Thus, although at least a transient increase in O1 can be expected after up-regulating I2, we cannot exclude that the negative feedback drives the level of O1 below its initial level at a certain time point after increasing the level of I2. We therefore call an activator (inhibitor) p of s a total acti- vator (total inhibitor) of s if there is no path from p to a spe- cies in a negative feedback circuit that is in turn connected to s. Positive feedbacks do not limit these qualitative up/ down-predictions because they cannot change the mono- tone effect of the respective input signal, e.g. when increasing the level of I2 in TOYNET we can expect an increase in the level of O2 after some time. To summarize, regarding the influence of a species p on another species s we have 6 possible cases: total and non- total activator, total and non-total inhibitor, ambivalent factor and non-influencing species. Note that, by comput- ing the connecting signaling paths, this classification pro- cedure can be applied not only between a source and a sink node but also between any pair of species, e.g. between a source and an intermediate, an intermediate and a sink, and two intermediates. In TOYNET, for exam- ple, F is a total activator of O2 and has no influence on O1, whereas D is an inhibitor but not a total one of O1 because it is connected to (even involved in) a negative feedback circuit. Additionally, as the complement of incoming paths, we can also determine the paths starting in a certain species s showing us which nodes and arcs are reachable from (and influenceable by) s. As a further generalization, sets of incoming and/or outgoing paths can also be defined not only for a single species s but also for a set S of species. This might be useful, for example, when we are interested in all paths ending (starting) in a certain subset of the sink (source) nodes. Investigations of influence and signaling paths as pro- posed above provide, apart from pair-pair relationships (e.g. "a is a (total) activator of b" or "a has no influence on b"), global properties (e.g. a is a (total) activator of all sink species). Some other useful structural features and con- straints can be detected by a statistical or combinatorial analysis of certain path sets (partially, similar ideas have been proposed by [14] for stoichiometric models of sign- aling networks): • Essential species (arcs): When focussing on a specific sig- naling event, e.g. the activation of a certain species by sig- nals from the input layer, we may identify essential species (or arcs) with respect to this event. For example, species E and arc 9 are essential for activating O2 but non- essential for the activating paths leading to O1 in TOYNET. Is + Is − Is + Is − Is − Is + Is − Is + BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 9 of 26 (page number not for citation purposes) • Species (arc) participation: A more quantitative measure can be obtained by giving percentages of all those activat- ing and/or inhibiting pathways, in which the species or arc is involved. One may only relate the relative participa- tion to the paths where the respective species or arc is involved or to the complete set of paths. For example, I2 is involved in 50% of all positive paths coming from the input layer and activating O1, while I2 is involved in 100% of all paths activating O2 (but only 50% of the paths coming from I2 lead to O2). Arc 9 is involved in one activating and one inhibiting path leading to O2. Thus, only 50% of the paths running over this arc are activating, however, it is involved in all (100%) activating paths con- necting sources with O2. Similar considerations can be done regarding feedback loops: in TOYNET, species D and A as well as arcs 6, 7 and 11 are not involved in paths con- necting input with output layers and have thus a special importance in establishing the negative (D, A, arcs 6 and 7) and positive (arc 11) feedback. (Note that a similar measure for the importance of a species or arc is between- ness centrality [48]. This importance measure is well- known in graph theory and checks how many shortest paths between pairs of nodes are running over the respec- tive node or arc.) • Redundancy: The total number of paths activating (inhibiting) a species is a measure for the redundancy in the system. • Path length: The length distribution of signaling paths provides a rough idea on the compactness of the network [18]. • Crosstalk: Using our framework, crosstalk might be defined as a place (node) where paths from different source nodes cross each other for the first time. For exam- ple, E is a crosstalk species in TOYNET (signals of I1 and I2 cross) whereas F and G are not. In some cases, however, crosstalk is a more complex phenomenon where different nodes are involved. For example, at species C a path com- ing from I1 via B and another path from I2 via E meet each other. However, I1 and I2 have also met earlier in E and, additionally, the action of I1 on C via B is already influ- enced by I2 in species B since I2 can act on B via the path visiting E, C, D and A. Distance matrix and dependency matrix Some applications presented in this section require exhaustive enumerations of signaling paths becoming computationally challenging in large networks. However, in some cases we only want to know whether any activat- ing and/or any inhibiting path between two nodes exists or whether there is any positive or any negative feedback circuit in which a certain species is involved. For such "existence questions" we can often apply standard meth- ods from graph theory. A very useful object is the distance matrix D which can be obtained with low computational demand by computing the shortest distances (shortest path lengths) between each pair of species (e.g. Dijkstra's algorithm [32]). D has dimension m × m and the element Dij stores the length of the shortest path for traveling from node i to node j, being Dij = ∞ if no paths exists between i and j. The distance matrix shows immediately • which elements can be influenced by species i (the i-th row of D) • which nodes can influence species i (i-th column of D) • whether feedback circuits exist: if the distance Dii from a node i back to itself is finite, then i is involved in at least one feedback loop. Furthermore, if Dij and the transposed element Dji are finite, Dij, Dji≠∞, then a feedback between species i and j exists. By an extension of the usual shortest path algorithm (not shown), we may also compute separately a matrix Dpos for the shortest positive paths and another Dneg for the shortest negative paths. Table 1 shows the distance matrices Dpos and Dneg from TOYNET. Note that by taking the minimum values from Dpos and Dneg, D can be obtained. Moreover, the two matrices Dpos and Dneg, whose computation is reasonably possible in very large networks, are sufficient to classify all species into (total/non-total) activators, (total/non-total) inhibi- tors, ambivalent factors, and non-influencing nodes with respect to a certain compound y. The reason is that this classification requires only knowledge on the existence of positive and negative paths between species pairs and on the existence of negative feedback loops. For example, a species x is a total activator of y if (i) at least one positive path from x to y exits ( ≠ ∞) and if (ii) no negative path from x to y exists ( = ∞) and if (iii) for any spe- cies z that is influenced by x (Dx, z ≠ ∞) and connected to y (Dz, y ≠ ∞) it holds, that z is not involved in a negative feed- back ( = ∞). For representing species dependencies in a compact man- ner, we introduce the dependency matrix M, which shows all the pair-wise dependencies, e.g. by using 6 different colors (for the 6 possible cases). Thereby, the color of matrix element Mxy indicates whether species x is a total/ non-total activator or a total/non-total inhibitor or an ambivalent factor or a non-influencing node for species y. Dx y pos , Dx y neg , Dz z neg , BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 10 of 26 (page number not for citation purposes) Again, x = y is allowed, indicating feedbacks. Figure 6 shows the dependency matrix for TOYNET. Although the distance and dependency matrices store a wealth of structural information in a very condensed manner, some applications still require a full enumera- tion of all available signaling paths. One case is the sys- tematic determination of minimal cut sets. Minimal cut and intervention sets in interaction graphs Searching for intervention strategies in signaling networks is of high relevance in experimental and, in particular, medical applications. Recently, the concept of minimal cut sets has been introduced, which facilitates the identifica- tion of efficient intervention strategies (cuts) and, at the same time, the recognition of potential failure modes in a given biochemical reaction network [28,29]. Basically, in the most general version, a minimal cut set (MCS) is defined as a minimal (irreducible, non-decomposable) set of cuts (or failures) of edges or/and nodes that represses a certain functionality or behavior in the system [29]. For example, assume we want to prevent the activa- tion of the sink node O1 in TOYNET. By removing nodes {B, E} one can be sure that an activation of O1 by an external stimulus becomes infeasible. The set {B, E} would thus be a cut set for preventing the activation of O1. Moreover, it is minimal since neither the removal of only B nor the removal of only E can guarantee that the "inhibition task" is achieved. Another minimal cut set would be {C}. C is thus essential for activating O1, as would be confirmed by participation analysis of all paths activating O1. A general algorithmic scheme for a system- atic enumeration of MCSs in stoichiometric networks was given in [29]: (i) Define a deletion task (ii) Compute all minimal functional units (elementary modes) and specify the set of target modes that have to be attacked in order to achieve the deletion task (iii) Compute the so-called minimal hitting sets of the tar- get modes We could proceed here in a similar way. First, a deletion task specifying the goal of our intervention is defined. In our example, the deletion task is "Prevent the activation of Dependency matrix of TOYNET Figure 6 Dependency matrix of TOYNET. The color of a matrix ele- ment Mxy has the following meaning: (i) dark green: x is an total activator of y; (ii) light green: x is a (non-total) activator of y; (iii) dark red: x is a total inhibitor of y; (iv) light red: x is a (non-total) inhibitor of y; (v) yellow: x is an ambivalent fac- tor for y; (vi) black: x does not influence y; Table 1: Shortest length of positive/negative paths in TOYNET (∞= no path exists). Values in the diagonal indicate whether the respective element is involved in a positive/negative feedback loop. See also the dependency matrix in Figure 6. I1 I2 A B C D E F G O1 O2 I1 ∞/∞ ∞/∞ 4/4 1/∞ 2/2 3/3 ∞/1 ∞/2 ∞/3 3/3 ∞/4 I2 ∞/∞ ∞/∞ ∞/4 ∞/5 2/∞ 3/∞ 1/∞ 2/∞ 3/∞ 3/∞ 4/∞ A ∞/∞ ∞/∞ ∞/4 1/∞ 2/∞ 3/∞ ∞/∞ ∞/∞ ∞/∞ 3/∞ ∞/∞ B ∞/∞ ∞/∞ ∞/3 ∞/4 1/∞ 2/∞ ∞/∞ ∞/∞ ∞/∞ 2/∞ ∞/∞ C ∞/∞ ∞/∞ ∞/2 ∞/3 ∞/4 1/∞ ∞/∞ ∞/∞ ∞/∞ 1/∞ ∞/∞ D ∞/∞ ∞/∞ ∞/1 ∞/2 ∞/3 ∞/4 ∞/∞ ∞/∞ ∞/∞ ∞/4 ∞/∞ E ∞/∞ ∞/∞ ∞/3 ∞/4 1/∞ 2/∞ ∞/∞ 1/∞ 2/∞ 2/∞ 3/∞ F ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ 2/∞ 1/∞ ∞/∞ 2/∞ G ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ 1/∞ 2/∞ ∞/∞ 1/∞ O1 ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ O2 ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ ∞/∞ BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 11 of 26 (page number not for citation purposes) O1 by any external input". Hence, the signaling paths from the input layer to O1 are computed, which are P1, P2, and P5 (see Figure 5). However, according to our dele- tion task, the target set comprises only the paths P1 and P5, because only these two activate O1. Finally, the mini- mal hitting sets of the target paths have to be computed, which are the MCSs [26,29]. When cutting species, a hit- ting set T is a set of species that "hits" all target paths in a minimal way, i.e. for each target path there is at least one species that is contained in T and in the path. To be a min- imal hitting set, no proper subset of T fulfills the hitting set condition. The minimal hitting sets of the target paths and hence the MCSs of our deletion task would be: {C}, {B, E}, {I2, B}, {I1, E} and {I1, I2}. Deletion tasks may be more complicated: for example, in TOYNET we might be interested to repress the activation of O1 and O2. Accord- ingly, the target paths would increase by one (P4 in Figure 5) resulting in another set of MCSs. This example might suggest that we can use the same pro- cedure as in metabolic networks, namely computing the minimal hitting sets with respect to the target paths. This naive approach works indeed for the case where the target paths do only involve positive arcs (as in our example). It can also be applied for interrupting any set of feedback cir- cuits. For example, removing {A} interrupts the negative feedback circuit and deleting {D, F} interrupts both feed- back circuits in TOYNET. However, in general, negatively signed arcs occurring in interaction graphs require a spe- cial treatment. Even the following simple activating path leading from a source species I to a sink species O contains pitfalls: . If the activation of O is to be repressed, the signal flow along this path must be interrupted. Removal of one species in the chain should be sufficient. However, not all nodes are allowed to be cut. If species B is removed, its negative action on C would be interrupted, enabling in turn C to activate O. The reason is that B, according to the definitions, is an inhibitor of O and is therefore not a proper cut candidate. In fact, we could add (constitutively provide or activate) B to stop an activation of O. Generally, for attacking an activating path, only the species that have an activating effect on the end node of this path are proper cut candidates, whereas spe- cies inhibiting the end node should instead be kept at a high level to prevent an activation along this path. Hence, as a generalization of (minimal) cut sets, we define (min- imal) intervention sets (MISs) in interaction networks as (minimal) sets of elements that are to be removed or to be added in order to achieve a certain intervention task. By allowing only the removal of elements, the set of MISs coincides with the MCSs. The computation of the MISs (or the smaller set of MCSs) for a set of activating target paths that involve negatively signed arcs is a more difficult task than computing only minimal hitting sets. Indeed, each MIS will still represent a hitting set, because at least one species in each target path must be removed or constitutively provided. The dif- ficulty arises by ambivalent factors which have in some target paths an activating and in others an inhibitory effect upon the end node. We could therefore restrict the inter- ventions to those species that are either pure activators with respect to the target paths (these are allowed to be removed) or pure inhibitors (these are allowed to be added). Using only these species, the MISs could again be computed as the minimal hitting sets. However, for computing MISs that may also act on ambiv- alent factors, we present a more general algorithm (here for a given set of activating target paths): (1) In each target path, the involved nodes are labeled by +1 (if the species influences the end node of the respective path positively) or by -1 (if the species has a negative influ- ence on the end node of the respective path). (2) Combinations Ci of one, two, three, ... distinct removed or activated species are constructed systemati- cally. For each combination Ci, it is checked for each target path whether the signal flow from the start node to the end node is interrupted properly. A requirement is that at least one of the positive (+1) species of each path is removed or at least one negative (-1) species is provided (added) by Ci (hitting set property). If, for a certain path, Ci contains several nodes that are visited by this paths then it is only checked whether the node closest to the end node is attacked properly. When all paths have been attacked (hit) properly by a combination Ci, then a new MIS has been found. When constructing further combina- tions of larger cardinality, the algorithm has to ensure that none of the new combinations contains an earlier found MISs completely. Of course, this enumerative algorithm is even more time consuming than computing minimal hitting sets and it will become infeasible to compute all MISs in large net- works. We may then restrict ourselves to MISs of low car- dinality and/or to the subset of MCSs. Besides, the determination of MISs can become even more compli- cated: it might happen that a MIS attacks all activating tar- get paths correctly but simultaneously destroys an inhibiting path (not contained in the set of target paths) which might then become an activating path. The MCS {I1, I2} of our example represents such a problematic I A B C O + − − + →  →  →  →  BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 12 of 26 (page number not for citation purposes) case: it hits the two activating paths to O1 as demanded, but it also attacks the inhibiting path leading from I1 to O1. Thus, the inhibition of E through I1 would be inter- rupted and it could be sufficient to retain E in an active state enabling the activation of O1. Hence, we would not be sure about the activation status of O1 after removing this cut set. To avoid such side-effects, we may extend our algorithm given above by checking also the consequence of each intervention Ci with respect to the non-target paths and exclude combinations that do not fulfill certain criteria. In a completely analogous fashion, we can also determine MCSs or MISs that repress inhibitory paths. For example, removing {I1} is a MCS that attacks the only inhibiting path to O1, alternatively we might use the MISs {#E} or {#C}, where # stands for "constitutively provided". The same issues as discussed above must be taken into account when interrupting a negative path: here, in each target path, only the inhibiting species of the final sink source should be removed whereas the activating nodes can be added. Furthermore, we may also define more compli- cated intervention tasks, e.g. where some activating and some inhibiting paths are selected as target paths. Jacobian matrix and interaction graph Several works have highlighted the strong relationships between interaction graphs and the Jacobian matrix J, the latter obtained from a dynamical model of the network under investigation [10,35,39]. A dynamic model of a sig- naling (or any kind of interaction) network is usually described by a system of ordinary differential equations that model the evolution of the m network components x1 ... xmwith the time: The m × m Jacobian matrix J(x) collects the partial deriva- tives of F with respect to x: The sign of Jik(x) tells whether xk has a (direct) positive or negative influence on xi and sign(J(x)) can thus be seen as the adjacency matrix of the underlying interaction graph. In an adjacency matrix Y, a non-zero entry for Yik indicates an edge from node i to k. Adjacency and incidence matrix are equivalent for describing a graph structure and can be converted into each other: each non-zero element Yik gets a corresponding column in the incidence matrix. The sign structure of the Jacobian matrix is, in biological systems, typically constant and reflects, despite its very qualitative nature, fundamental properties of the dynamic system. For example, multistationarity can only occur if a positive circuit exists in the associated interaction graph [39]. Methods for the detection of multistability in a spe- cial class of dynamical systems – monotone I/O systems – have been developed by Sontag et al. [36]. Monotone I/O systems possess a monotonicity property that can be checked from the interaction graph spanned by the Jaco- bian matrix. In fact, having one source species and one sink species, the required monotonicity property is equiv- alent to our definition of a total activator of the sink node. Thus, the methods developed in the previous section may support such studies, where the structure of the Jacobian matrix is analyzed. Having the absolute values of the Jaco- bian matrix available (which change over time), arcs, paths, and feedback circuits could be assigned an interac- tion strength useful to identify key elements in the net- work. Boolean networks and (logical) interaction hypergraphs Definitions The methods described above consider an interaction as a dependency between two species allowing to employ tools from graph theory. However, in cellular networks, an interaction (edge) often represents a relationship among more than two species (nodes). A typical example is a bimolecular reaction of the form A+B→ C, where three species are involved. The binding of the ligand to the receptor in Figure 2(b) (Rec+Lig→ RecLig) is such a bimolecular interaction. Using an interaction graph, this reaction is modeled with two arcs (Figure 7(a)), namely Rec→ RecLig and Lig→ RecLig, capturing correctly that Rec and Lig have an influence on RecLig. However, this relaxed representation has shortcomings for a functional interpretation of the network. To exemplify this, consider the minimal cut sets repressing the phosphorylation of M in Figure 7(a). As explained in the previous section, we need to attack all positive paths leading to M-P. There are two positive paths, one starting from Rec and the other from Lig and, thus, {Rec, Lig} would be a minimal cut set. But, intuitively, this cut set is not minimal for the real sys- tem because both Rec and Lig are required for activating M, and removing only one of the two species is thus suffi- cient to interrupt the activation of M. (In other words, the existence of a signaling path in an interaction graph does not ensure that a signal can flow along this path.) This example reveals that a proper consideration of AND- connections between species is required. However, AND- relationships are not possible in graphs but in hyper- # # x x x x x = =         =         d x x t f t m m dt t = f 1 F( , ) 1( , ) ( , ) 5 ( ) J x x ik i k df dx ( ) ( ) = ( ) 6 BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 13 of 26 (page number not for citation purposes) graphs, which are generalizations of graphs. Similar to a directed graph, a directed hypergraph H=(V, A) consists of a set V of nodes and a set A of hyperarcs (= directed hyper- edges [49]). A hyperarc aconnects two subsets of nodes: a = {S,E}; S,E⊂ V. S comprises the tail (start) nodes and E the head (end) nodes of the connection. S and E can have arbitrary cardinality, and a graph is a special case of a hypergraph where the cardinality of S and E is 1 for all edges. In our context, without loss of generality, we will usually have only one end node in E and we interpret a hyperarc as an interaction in which the compound contained in E is activated by a combined action of the species contained in S. Figure 7(b) depicts the example with the receptor-lig- and-complex as a hypergraph in which a hyperarc cap- tures now the AND-connection between Rec and Lig yielding RecLig. AND connections facilitate a refined representation of sto- ichiometric conversions within interaction networks, albeit the precise stoichiometric coefficients are not cap- tured here. Apart from stoichiometric interactions, AND connections allow the description of other dependencies, for example, the case where only the presence of an acti- vator AND the absence of an inhibitor leads to the activa- tion of a certain protein. In TOYNET, the four nodes (B, C, E, F) have more than one incoming arc (Figure 3). In these nodes it is undeter- mined how the different stimuli are combined, e.g. whether B AND E are required to activate C or whether one of both is sufficient (B OR E). We could therefore concatenate all incoming edges in a node by logical operations leading to Boolean networks [21,31]. An assumption underlying Boolean networks is to consider only discrete (concentration/activation) levels for each species; in the simplest case a species can only be "off" (= 0 = "inactive" or "absent") and "on" (= 1 = "active" or "present"). Hence, each species is considered as a binary (logical) variable. Next, a Boolean function fi is defined for each node i which determines under which conditions i is on or off, respectively. fi depends only on those nodes in the interaction graph from which an arc points into species i. In general, for constructing a Boolean function, all logical operations like AND, OR, NOT, XOR, NAND can be used. However, here we express each Boolean function by a special representation known as sum of products (SOP; also called (minimal) disjunctive normal form (DNF)) which is possible for any Boolean function [50]. SOP representations require only AND, OR and NOT operators. In a SOP expression, literals, which are Boolean variables or negated Boolean variables, are connected by AND's giving clauses. Several such AND clauses are then in turn connected by OR's. Using the usual symbols '·' for AND, '+' for OR and '!' for NOT, an example of a SOP expression would be: fi = x·y·z + x·!z stating that fi gets value "1" if (x AND y AND z are active) OR (if x is active AND z is NOT) and "0" else. The SOP expression fi = x·!y + !x·y mimics an XOR gate. In our context, writing a Boolean function as a SOP has several advantages. First, many biological mechanisms that lead to the activation of a species correspond directly to SOP representations. Second, by using SOPs, the struc- ture of a Boolean network can be represented and depicted intuitively as a hypergraph: each hyperarc point- ing into a node i is an AND clause of other nodes and rep- resents one way of activating i; hence, all hyperarcs ending in i are OR'ed together. A hyperarc carries a signal flow to its end node and the binary value of the flow depends on the state of all its start nodes. In the following, such a hypergraph induced by a minimal SOP representation of a Boolean network will be called a logical interaction hyper- graph (LIH). In Figure 8 a possible instance of a LIH compatible with the interaction graph of TOYNET in Figure 3 is depicted. In each of the four nodes with more than one incoming arc, the logical concatenation has now been specified. For example, B is now activated if A AND I1 are active simul- taneously (hyperarc "1&4"). In contrast, C is activated if B OR E is present (active), and F is active if E OR G are in an active state. Hence, C and F retain their graph-like struc- ture. (a) the graphical and (b) the more correct hypergraphical representation of the simple interaction network shown in Figure 1 and 2 Figure 7 (a) the graphical and (b) the more correct hypergraphical representation of the simple interaction network shown in Figure 1 and 2. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 14 of 26 (page number not for citation purposes) Inhibiting arcs in the interaction graph are interpreted in the corresponding LIH as NOT-operations. Thus, arc 7 is now interpreted as "A is active if D is not present". Since arc 2 and 3 in Figure 3 have been combined with an AND in Figure 8, we interpret this new hyperarc as "E becomes activated if I2 is present AND I1 NOT". Hence, in contrast to inhibiting arcs in interaction graphs, in general we do not assign a minus sign (a NOT) to the complete hyperarc, but to its negative branches (see hyperarc 2&3 in Figure 8), whereas all other branches get positive signs. Due to the assignment of signs LIHs can formally be seen as signed directed hypergraphs. The pure logical description of a signaling or regulatory network works well when the activation (inhibition) of a species by others follows a sigmoid curve [21]. Problems that might arise while describing a real network within the logical framework and possible solutions are discussed in a later section. LIHs can be formally represented and stored in a similar way as interaction graphs. The underlying hypergraph is stored by an m × n incidence matrix B in which the rows correspond to the species and the columns to the n hyper- arcs. If species i is contained in the set of start (tail) nodes of a hyperarc k then Bik = -1, if i is the endpoint (head) of hyperarc k then Bik = 1, and if i is not involved in k we have Bik = 0. For storing the NOTs operating on certain species in a hyperarc we may use another m × n matrix U that stores in Uik a "1" if species i enters the hyperarc k with its negated value and "0" else. Accordingly, the incidence matrix B for the LIH of TOYNET (Figure 8) reads To be concise, the two non-zeros entries of U are indicated by an asterisk in the incidence matrix. Representing a Boolean network as a LIH we can easily reconstruct the underlying interaction graph from the matrices B and U: we simply split up the hyperarcs having more than one start node (or/and more than one end node in the general case). Thus, a hyperarc with d start and g end nodes is converted into d·g arcs in the interaction graph. The sign of each arc in the graph model can be obtained from U. The reverse, the reconstruction of the LIH from the interaction graph, is not possible in a unique manner underlining the non-deterministic nature of interaction graphs. Time in Boolean networks A logical interaction hypergraph describes only the static structure of a Boolean network. However, it is the dynamic behavior of Boolean networks that has been analyzed intensely in the context of biological (especially genetic) systems [21,31,51]. For studying the evolution of a logical system we need to introduce the (discrete) time variable t and a state vector x(t) that captures the logical values of the m species at time point t. Two fundamental strategies exist to derive the new state vector x(t+1) from the current state x(t). In the synchronous model, the logical value of each node i is updated by evaluating its Boolean function fi with the current state vector: xi (t+1) = fi(x(t)). Synchro- nous models are deterministic but assume for all interac- tions the same time delay which is often too unrealistic for biological systems [21]. In the asynchronous model, we select any (but only one) node i whose current state is unequal to its associated Boolean function: xi (t) ≠ fi(x(t)). Only this node switches in the next iteration. Since there are, in general, degrees of freedom in choosing the switch- ing node, this description is non-deterministic. The advantage is that the complete spectrum of potential tra- jectories is captured, albeit the graph of sequences is usu- ally very dense, complicating its analysis in large systems. The asynchronous description becomes (more) determin- istic if time delays for activation and inhibition events are known [21]. B = − − − − 1 4 2 3 5 6 7 8 9 10 11 12 13 0 0 0 & & 1 1() 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 − − − − − − (*) 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 − − −            1 0 1                        I1 I2 A B C D E F G O1 O2 ( ) 7 Logical interaction hypergraph of TOYNET (compare with interaction graph in Figure 3) Figure 8 Logical interaction hypergraph of TOYNET (compare with interaction graph in Figure 3). BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 15 of 26 (page number not for citation purposes) We are now approaching the main part of this section. Logical steady-state analysis An important characteristic of the dynamic behavior of Boolean networks, which is equivalent for both asynchro- nous and synchronous descriptions, is the set of logical steady states (LSSs). LSSs are state vectors xs obeying = fi(xs) for all nodes i. Hence, in LSS, the state of each node is consistent with the value of its associated Boolean func- tion and, therefore, once a Boolean network has moved into a logical steady state, it will stop to switch and then retain this state. In the following, we will focus on logical steady state anal- ysis (thus circumventing any interpretation problems that might arise by choosing synchronous or asynchronous description), which suffices for a number of applications, especially for predicting potential functional states in sig- naling or regulatory networks. Given a Boolean network we may enumerate all possible LSSs [52]. However, this is computationally difficult in large networks. Besides, we are often interested in particu- lar LSSs that can be reached from a given initial state x0. In some cases, we only know a fraction of all initial node val- ues. For example, a typical scenario in signaling networks would be that initial values from species in the input layer are known (specifying which external signals reach the cell and which not), and we would like to know how the (logical) integration and propagation of these input sig- nals generate a certain logical pattern in the output layer. Of course, we have to "wait" until the signals reach the bottom of the network and, for obtaining a unique answer, there should be a time point from which the states will not change in the future. This is equivalent to deter- mining the LSS in which the network will run from a given starting point. In a possible scenario for TOYNET, the initial values of the source species I1 and I2 might be known to be = 0 and = 1, whereas the initial states of all other nodes are unknown (Figure 9(a)). The states of I1 and I2 will not change anymore because I1 and I2 have no predecessor in the hypergraph model. Assuming that each interaction has a finite time delay, E must become active and B inac- tive. From these fixed values we can conclude that C and F will definitely become active (by E) at a certain time point and not change this state in the future. Proceeding further in the same way, we can resolve the complete LSS resulting from the given initial values of I1 and I2 (Figure 9(b)). The last example illustrated that partial knowledge on ini- tial values, especially from the source nodes, can be suffi- cient to determine the resulting LSS uniquely. However, in general, several LSSs might result from a given set of initial values or a LSS may not exist at all. For example, if we only know = 1 in TOYNET nothing can be concluded regarding a LSS (except that I2 will retain its state). If no complete LSS can be concluded uniquely from initial val- ues, there might nevertheless be a subset of nodes that will reach a state in which they will remain for the future. For example, setting = 1 E will definitely become inacti- vated after some time (again, finite time delay is assumed). Since in this scenario nothing further can be derived for other nodes, we would say that xI1 = 1 and xE = 0 are partial LSSs for the initial value set { = 1}. Note that these two partial steady states would not change when we specified more or even all initial values. We have conceived an algorithm which derives partial LSSs that follow from a given set of initial values (if for each node a partial LSS can be found, then a unique and complete LSS exists for the set of initial values). The itera- tive algorithm uses the following rules in the logical hypergraph model: • initial values of source nodes will not change in the future, hence, are partial LSSs • if species i has a proved partial LSS of 0, all hyperarcs in which i is involved with its non-negated value have a zero flow • if species i has a proved partial LSS of 1, all hyperarcs in which i is involved with its negated value have a zero flow xi s xI1 0 xI2 0 xI2 0 xI1 0 xI1 0 Example of a logical steady state in TOYNET resulting from a particular set of initial states in the input layer Figure 9 Example of a logical steady state in TOYNET resulting from a particular set of initial states in the input layer. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 16 of 26 (page number not for citation purposes) • if all hyperarcs pointing into node i have a zero flow, then i has a partial LSS of 0 • if all start nodes of a hyperarc have a partial LSS of 1 (or of 0 for those start nodes entering the hyperarc with the negated value) then a partial LSS of 1 follows for the end node of this hyperarc • knowing all the positive feedback circuits in the system, we can check whether there is a "self-sustaining" positive circuit where the known initial state values of the involved nodes guarantee a partial LSS for all the nodes in this cycle (see comments below) In each loop, the algorithm tries to identify new partial LSSs (following from the current set of partial LSSs already identified) until no further ones can be found. Setting ini- tial values in the input layer, this can be envisioned as a propagation of signals through the interaction network until signals reach nodes where the available information is not sufficient to derive a unique LSSs. Generally, in logical interaction hypergraphs where the underlying interaction graph has no feedback loop (i.e. is acyclic), specification of the initial values of all the source nodes will always result in a unique and complete LSS since the signals can be propagated step by step from top- down to the output layer. In general, if all initial values are known for the input layer, non-uniqueness or even non- existence of partial LSSs can only be generated by feedback loops. The partial LSSs of nodes involved in positive feed- backs do often depend on the initial values of all the nodes in this loop. For example, defining = 0 we can conclude a partial LSSs of zero for E in TOYNET (Figure 8), but, among others, the values of F, G and O2 remain unknown although the only connection to a source node leads via E. The reason is that F and G build up a positive feedback loop which cannot be resolved without knowl- edge on further initial values. If we know, additionally to = 0, that = 1 then F and G will always keep each other activated so that we can infer a partial LSS of 1 for F, G and O2 (this is the last rule in the list given above). If we have instead = 0, we derive a 0 for the partial LSS of these three nodes. If one of the two nodes F and G has an initial value of 1 and the other 0, nothing can be derived since the positive loop might become fully activated or fully deactivated. However, what can be confirmed in these simple examples is that positive feedback loops induce multistationarity. It is noteworthy that continuous dynamic models of networks with positive feedbacks will depend, apart from kinetic parameters, in a similar fashion on initial state values. In contrast, negative feedback loops are not sensitive against initial values but they can be the source of oscilla- tions, preventing hence the existence of LSSs. In TOYNET we have one negative feedback loop which can potentially generate oscillations, for example, when we set = 1. Then, C cannot be activated via E. Assuming an initial value of 0 for C (the same conclusion would be drawn with 1), D becomes deactivated and thus A actived. Due to the partial LSS of 1 for I1 we get an activation of B and then of C and D which in turn inhibits A leading in the next round to a deactivation of B, C and D and so on. The logical states within this circuit and downstream of it (O1) will thus never reach a steady state. As shown in [21], oscillatory behavior in logical models corresponds to oscillations or a stable equilibrium (lying somehow between the fully activated and fully inactivated level) in the associated continuous model, depending on the cho- sen parameters. Negative feedback loops can thus impede predictions on the basis of logical steady states, but they also point to network structures whose parametrization will have great impact on the dynamic behavior. Note that feedback loops do not always prevent predic- tions on (partial) LSSs as can be seen by the example in Figure 9, it depends on the given initial values. Such a logical steady state or "signal flow" analysis (SFA) as presented herein shares similarities with the established method of metabolic flux analysis [53]. In MFA, uptake and excretion rates of cells are measured in order to recon- struct the intracellular flux distribution within a metabolic network. MFA relies on the quasi-steady state assumption, similarly as SFA relies on LSS. However, whereas MFA tries to reconstruct the reaction rates along the edges and noth- ing can be said on the states of the species, the goal of SFA is to determine the steady states of the nodes (belonging to a given activation scheme) from which then the signal flows along the edges follow. It is noteworthy that the cal- culability of unknown reaction rates in MFA depends only on the set of known rates [54], whereas in SFA the set of given initial states and their respective values determine the unique calculability of (partial) LSSs. Applications of logical steady state analysis The LSS analysis introduced herein offers a number of applications for studying functional aspects in cellular interaction networks: xI2 0 xI2 0 x x F G 0 0 = x x F G 0 0 = xI1 0 BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 17 of 26 (page number not for citation purposes) Input-output behavior Imposing different patterns of signals in the input layer one may check which species become activated or inhib- ited in the intermediate and, in particular, in the output layer. This can also be simulated in combination with dif- ferent initial state values for certain intermediate nodes, albeit this will have an influence on the LSS only in con- nection with positive feedbacks, as shown above. Mutants and interventions The changes in signals flows and in the input-output behavior occurring in a manipulated or malfunctioning network can be studied by removing or adding elements or by fixing the states of certain species in the network. In TOYNET, for example, if we want to study the effect of a mutant missing F (or the effect of adding an inhibitor for F) we may remove species F from the network (or, equiv- alently, fix the state of F to zero) and compute then the partial LSSs again. We will see that, independently of a given pattern in the input layer, G and O1 will be assigned a partial LSS of 0. Removing elements often changes not only the values, but also the determinacy of partial LSSs. Minimal cut sets (MCSs) and minimal intervention sets (MISs) The definiton of MCSs and MISs in logical interaction hypergraphs is similar as in interaction graphs: a MCS is a minimal (irreducible) set of species whose removal will prevent a certain response or functionality as defined by an intervention goal. In the more general MISs we permit, additionally to cuts, also the constitutive activation of cer- tain compounds. Two examples in TOYNET: removing F is a MCS for repressing an activation of G and O2. Assum- ing an initial state of zero for the species in the intermedi- ate layer, adding I1 and removing B would be a proper MIS for repressing the activation of O1 and O2. Note that in the interaction graph of TOYNET, this intervention would not suffice to attack all activating paths leading from the input layer to O1 and O2 (path P4 not attacked, Figure 5). This example underscores again that MCSs and MISs in interaction hypergraphs are usually smaller than those obtained from the underlying interaction graph, simply because more constraints are added by logical combinations. However, the determination of MCSs, and let alone MISs, in logical interaction hypergraphs is com- binatorially complicated as in interaction graphs, in par- ticular when negative signs (NOTs) occur. Here, we can only propose a "brute-force" approach where the LSS analysis serves algorithmically as an oracle: we check sys- tematically for each combination of one, two, three ... knocked out (for MISs also of permanently activated) nodes in the network how this affects the (partial) LSSs, possibly in combination with a given scenario of initial states. From the resulting partial LSSs we can decide whether our intervention goal has been achieved or not. To compute only minimal cut or intervention sets, further combinations with a cut or intervention set already satis- fying our intervention goal have to be avoided. The algo- rithm can be stopped when a user-given maximum cardinality for the MCSs/MISs has been reached. Backward propagation The methods described above compute partial LSSs actu- ally only by forward propagation of signals, but one may also do the opposite, e.g. fixing values in the output layer and tracing back the required states of nodes in the inter- mediate and input layer using similar rules as for forward propagation. Network expansion methods There is an interesting relationship between our LSS anal- ysis and network expansion methods proposed by Eben- höh et al. [55]. Network expansion allows for checking which metabolites can in principle be produced from a provided set of start species within a metabolic (stoichio- metric) reaction network. This is a special case in our log- ical framework. Briefly, metabolic networks are per se hypergraphs and can thus be represented as a LIH by using only AND's (each reaction is an AND clause of its reac- tants; stoichiometric coefficients are not considered) and OR's. Hence, no inhibiting interactions exist. We may then put the supplied set of available species in the input layer, set the initial values of all other species to zero and compute then the LSS. Note that, according to the expla- nations given above, a complete LSS will always be found since all initial values are given and no negative feedback circuit exists. Therefore, the computed LSS indicates which species can be produced from the input set and which not. Extensions for the logical description of interaction networks Several extensions and refinements of the logical frame- work can be introduced which allow a more appropriate description of real signaling and regulatory networks: (1) As already proposed and applied by Thomas et al. [21], the discretization in more than two levels is in prin- ciple possible. This mimics the fact, that in reality multi- ple relevant threshold values for a species may exist. A refined discretization could be relevant, for instance, for a species that activates/inhibits more than one species (with different threshold levels). Another relevant situation occurs if a species can be activated via two paths (con- nected by an OR; see species C in TOYNET): the activation via both paths might be significantly stronger than by only one. However, considering several activation levels for a certain species forces one to often consider multiple levels for elements downstream or/and upstream of this species, increasing hence the complexity of the network, and requiring detailed knowledge which is often not available. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 18 of 26 (page number not for citation purposes) (2) As we have seen, negative feedback can limit the pre- dictability in LSS analysis. However, in cellular networks, negative feedbacks become activated often upon a certain time period after an activation event occurs, for example, when gene expression is involved. This might be consid- ered by classifying species and/or hyperedges by assigning a discrete time constant (or time scale) τ to each element telling us whether this network element appears in an early (τ = 1) or late (τ = 2) state. Using the sub-network with all elements having a time constant of τ = 1 for the first simulation and then using the computed LSSs as ini- tial values for computing the second round (where the complete network is considered) leads often to more real- istic results. As in the case of multiple levels, this extension requires a more detailed knowledge about the network under consideration. An example in TOYNET (Figure 8): we may assume that D is a factor that is transcriptionally regulated by C, thus, arc 6 has a time constant of τ = 2 and all others have τ = 1. Setting the initial values I1 = 1, I2 = 0 and D = 0 and computing the LSSs for τ = 1 activation of C and O1 occurs. We can then fix the state of D (D = 1) and get then a complete deactivation of C and O1. (3) In real signaling and regulatory networks, it is some- times difficult to decide whether arcs from the interaction graph have to be linked by an AND or an OR in the inter- action hypergraph. For example, in TOYNET, species E is inhibited by factor I1 and activated by factor I2. If I1 has a very strong inhibiting effect on E we may formulate the hyperarc as done in Figure 8, suggesting that I1 must not be active for activating E. However, if the interaction strength of both I1 and I2 with respect to E is at the same level (i.e. additive) neither "NOT(I1) OR I2" nor "NOT(I1) AND I2" would reflect the real situation. Indeed, this is a recurring situation in signaling networks, where often a balance between different signals deter- mines the activation of a certain element. At this point it could be helpful to use logical operations that have a par- tially incomplete truth table. In the latter example we could say that E is active if (NOT(I1) AND I2) and E is inactive if (I1 AND NOT(I2)). For the other two possible cases, no decision could be made along this hyperedge. Of course, modeling uncertainty in this way will limit the determinacy but on the other hand a determined result with this model allows a safer interpretation. Analyzing interaction networks using CellNetAnalyzer We have integrated many of the methods and algorithms described herein in our software tool CellNetAnalyzer, which is a MATLAB package and the successor of FluxAna- lyzer [56]. Whereas FluxAnalyzer was originally developed for structural and functional analysis of metabolic net- works, CellNetAnalyzer extends these capabilities conse- quently to the structural analysis of signaling and regulatory networks. Apart from stoichiometric (meta- bolic) reaction networks, CellNetAnalyzer supports now also the composition of logical interaction hypergraphs using AND, OR and NOT connections. Whenever needed, the underlying interaction graph can be deduced from the interaction hypergraph. Alternatively, by using only OR's and NOT's, arbitrary interaction graphs can be con- structed. As in FluxAnalyzer, the network model can be linked with externally created graphics visualizing the net- work. User interfaces (text boxes) enable data input and output directly in these interactive maps (see screenshot in Figure 10). New functions for graph-theoretical and logical analysis have been integrated into the user menu; Screenshot of the CellNetAnalyzer model for T-cell activation Figure 10 Screenshot of the CellNetAnalyzer model for T-cell activation. Each arrow finishing on a species box represents a hyperarc and all the hyperarcs pointing into a species box are OR con- nected. In the shown "early-event" scenario, the feedbacks were switched off whereas all input arcs are active. The resulting logical steady state was then computed. Text boxes display the signal flows along the hyperarcs (green boxes: fixed values prior computation; blue boxes: hyperarcs acti- vating a species (signal flow is 1); red boxes: hyperarcs which are not active (signal flow is 0)). BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 19 of 26 (page number not for citation purposes) the results from computations are directly displayed within the interaction maps or in separate windows. The functions include: • large-scale computation of all (positive and negative) signaling paths connecting inputs with outputs or of all signaling paths between a given pair of nodes; statistical analysis of these paths • large-scale computation of all (positive and negative) feedback loops; statistical analysis of these routes • computation of minimal cut sets for a given set of paths or/and loops • computation of distance (shortest paths) matrices – sep- arately for positive and negative paths • large-scale dependency analysis: identification of (total) activators, (total) inhibitors and ambivalent factors for a given species; display of the dependency matrix • computation of (partial) logical steady states from a given set of initial state values • computation of (logical) minimal cut sets repressing or provoking a user-defined behavior in the logical network To illustrate the ability of our approach to deal with real complex signaling networks, we have set-up and analyzed in CellNetAnalyzer a logical model of T-cell activation (Fig- ure 10), which will be discussed in the next section. CellNetAnalyzer is free for academic purposes (see web-site [57]). Logical model of T-cell activation T-cell activation and the molecular mechanisms behind T-lymphocytes play a key role within the immune system: Cytotoxic, CD8+, T-cells destroy cells infected by viruses or malignant cells, and CD4+ helper T-cells coordinate the functions of other cells of the immune system, such as B- lymphocytes and monocytes [58]. Loss or dysfunction, especially of CD4+ T-cells (as it occurs e.g. in the course of HIV infection or in immuno-deficiencies) has severe con- sequences for the organism and results in susceptibility to viral and fungal infections as well as in the development of malignancies. The importance of T-cells for immune homeostasis is due to their ability to specifically recognize foreign, potentially dangerous, agents and, subsequently, to initiate a specific immune response that is aimed at eliminating them. T-cells detect foreign antigens by means of their T-Cell Receptor (TCR) which recognizes peptides only when presented on MHC (Major Histocompatibility Complex) molecules. The peptides that are recognized by the TCR are typically derived from foreign (e.g. bacterial, viral) proteins and are generated by proteolytic cleavage within so called antigen presenting cells (APCs). Subse- quent to their production the peptides are loaded onto the MHC-molecules and the assembled peptide/MHC-com- plex is then transported to the cell surface of the APC were it can be recognized by T-cells. The whole process of anti- gen uptake, proteolytic cleavage, peptide loading onto MHC, transport of the peptide/MHC complex to the sur- face of the APC and the recognition of the peptide/MHC- complex by the TCR is called antigen presentation and provides the molecular basis for the fine specificity of the adaptive immune response. The binding of peptide/MHC to the TCR, and the addi- tional binding of a different region of the MHC molecules to so called co-receptors (CD4 in the case of helper T-cells and CD8 in the case of cytotoxic T-cells), initiates a pleth- ora of signaling cascades within the T-cell. As a result, sev- eral transcription factors – most importantly, AP1, NFAT and NFκB – are activated. These transcription factors, in turn, control the cell's fate, e.g. whether it becomes acti- vated and proliferates [59] or not. In the following, a logical model describing some of the main steps involved in the activation of CD4+ helper T- cells (also applicable for CD8+ cytotoxic T-cells) will be briefly introduced and analyzed (see Figure 10 and Table 2). Several players, in particular, some whose role and activation is not completely understood, are not included in our model and thus their effects are not considered or lumped with others. Additionally, in several, currently still controversial cases, we have assumed one of the pos- sible hypotheses; however, this does not mean that we propose this to be the correct description of the TCR- induced signaling network; we just want to demonstrate the applicability of our approach on a realistic, complex case. It is out of the scope of this paper to analyze the com- plete, highly-complex signaling machinery of a T-cell. Here, the biochemical steps included in the signaling pathway will be described briefly; for a detailed descrip- tion we refer the reader to reviews such as [59,60] and the references therein: • Upon binding of peptide/MHC to the TCR, the first main step in the TCR-mediated signaling cascade is the activation of the Src-family protein tyrosine kinase p56lck (in the following termed Lck), although the exact mecha- nism is still unclear. We have included one well accepted mechanism [61], which probably plays a major role but may be combined with others (cf. Figure 10): In resting T-cells, the major negative regulator of Lck, the protein tyrosine kinase Csk (C-terminal Src-kinase) is ¾ BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 20 of 26 (page number not for citation purposes) bound via a SH2-domain to the constitutively tyrosine phosphorylated transmembrane adaptor protein PAG (Protein Associated with Glycosphingolipid enriched microdomains) and consequently inhibits membrane- bound Lck by phosphorylating a C-terminal negative reg- ulatory tyrosine residue of the Src kinase. Upon ligand binding, PAG is dephosphorylated by a so far unknown protein tyrosine phosphatase, thereby lead- ing to the detachment of Csk from PAG, and hence releas- ing Lck from the inhibitory effect of Csk. The release of Csk from PAG, together with the activity of the membrane associated tyrosine phosphatase CD45 (which dephos- phorylates Lck on the same inhibitory residue that is phosphorylated by Csk), and the concomitant binding of the MHC molecule to the coreceptor CD4, leads to full activation of Lck (see Figure 10). However, both CD4 and the TCR can also be stimulated individually, e.g. by using monoclonal antibodies specifi- cally directed at either of the molecules or using cell lines expressing mutated forms of CD4 that cannot bind MHC or cannot transmit signals. A regulation of the enzymatic activity of CD45 is not included in the model (basically because it is not yet clear how CD45 is regulated in vivo), but, since CD45 is an important regulatory element for T-cells, it is included as an input signal, allowing the analysis of its effect and the performance of CD45 knock-out experiments. After a few minutes, PAG is rephosphorylated [62], probably by the Src-kinase Fyn, and subsequently Csk is re-recruited to PAG inhibiting Lck again. • Activated Lck can phosphorylate another member of the Src-protein kinases, p59fyn, in the following termed Fyn (Fyn can probably also be activated in a Lck-independent, TCR-dependent manner [63]). Additionally, Lck phos- phorylates the so called ITAMs (Immunoreceptor Tyro- sine-based Activation Motifs) that are present in the cytoplasmic domains of the TCR-complex (the latter if the TCR is close to Lck, i.e., if there is a concurrent activation of the TCR). Subsequently, the Syk-family protein tyrosine kinase ZAP70 (Zeta Associated Phosphoprotein of 70 kDa) binds to the phosphorylated ITAMs and, if Lck is active, becomes activated by Lck-mediated tyrosine phos- phorylation. Thus, during the initial phase of signal trans- duction via the TCR three tyrosine kinases become activated in a sequential manner, first Lck and Fyn and then ZAP70. Together these three kinases propagate the TCR-mediated signal by phosphorylating a number of membrane associated and cytosolic signaling proteins. • Active ZAP70 can phosphorylate LAT (Linker for Activa- tion of T-cells), a second transmembrane adapter protein, at four different tyrosine residues. Subsequently, cytoplas- mic signaling molecules containing SH2-domains, ¾ ¾ ¾ ¾ Table 2: The hyperarcs of the logical T-cell signaling model (see Figure 10). Exclamation mark ('!') denotes a logical NOT and dots within the equations indicate AND operations. → CD45 → CD8 → TCRlig AP1 → Ca → Calcin Calcin → NFAT CRE → CREB → CRE DAG → PKCth ERK → Fos ERK → Rsk Fyn → PAGCsk Fyn → TCRphos Gads → SLP76 Grb2Sos → Ras !IkB → NFkB !IKKbeta → IkB IP3 → Ca JNK → Jun Jun·Fos → AP1 LAT → Gads LAT → Grb2Sos LAT → PLCgbind Lck·CD45 → Fyn Lck → Rlk MEK → ERK NFAT → NFkB → !PAGCsk·CD8·CD45 → Lck PKCth·DAG → RasGRP1 PKCth → IKKbeta PKCth → SEK PLCg(act) → DAG PLCg(act) → IP3 Raf → MEK Ras → Raf RasGRP1 → Ras Rsk → CREB SEK → JNK TCRbind·CD45 → Fyn TCRbind·Lck → TCRphos !TCRbind → PAGCsk TCRlig·!cCbl → TCRbind TCRphos·Lck·!cCbl → ZAP70 ZAP70·SLP76·PLCg(bind)·Itk → PLCg(act) ZAP70·SLP76 → Itk ZAP70 → cCbl ZAP70 → LAT ZAP70·SLP76·Rlk·PLCg(bind) → PLCg(act) BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 21 of 26 (page number not for citation purposes) including the scaffolding proteins Grb2, Gads, and the lipid kinase PLCγ1 (Phospholipase gamma 1), can bind to phosphorylated LAT. Additionally, Grb2 binds to the nucleotide exchange factor Sos (here we lumped Grb2 and Sos in one activation step), and Gads to the adapter pro- tein SLP76. The latter, upon phosphorylation by ZAP70, can bind to the Tec-family tyrosine kinase Itk. Binding to SLP76 and additional phosphorylation by ZAP70 acti- vates Itk. • For the activation of PLCγ1, the following conditions have to be fulfilled: PLCγ1 is bound to LAT, SLP76 bound to Gads, ZAP70 is activated (which hence phosphorylates SLP76, allowing PLCγ1 to bind to SLP76), and Itk is active, and hence is able to phosphorylate and thereby to fully activate PLCγ1. Since all these conditions are needed, a logical AND was included in the model (see Figure 10). Rlk, another Lck-dependent Tec-family tyrosine kinase, can also phosphorylate PLCγ1, hence Rlk has a redundant role to Itk with regard to the activation of PLCγ1 [64]. • Activated PLCγ1 hydrolyses phosphatidyl-inositol-4,5 biphosphate (PIP2), which is considered an ubiquitous membrane associated phospholipid and is therefore not modeled, thereby generating the second messenger mole- cules diacyloglycerol (DAG) and inositol trisphosphate (IP3) [59,61]. • IP3 mediates calcium flux. Calcium (together with cal- modulin) activates the serine phosphatase calcineurin, which dephosphorylates the cytosolic form of the tran- scription factor NFAT (Nuclear Factor of Activated T- cells). The calcineurin-mediated removal of phosphate groups allows NFAT to translocate to the nucleus and to regulate gene expression. • The second messenger DAG activates PKCθ and (together with PKCθ[65]) activates the nucleotide exchange factor RasGRP1. • RasGRP1 and Sos (the latter if it is close to the mem- brane, that is, if it is bound to LAT by means of Grb2), can activate Ras, which in turn activates the Raf/MEK/ERK MAPK Cascade. • PKCθ is involved in the activation of JNK, as well as the essential transcription factor NFκB (via phosphorylation and subsequent degradation of the NFκB inhibitor, Iκ B, by the PKCθ-activated Iκ B-kinase, IKK). • ERK, activated by the Ras/Raf/MEK cascade, activates the transcription factor CRE and (together with JNK) the essential transcription factor AP1. • The E3 ubiquitin ligase cCbl is important for shutting off TCR-mediated signaling processes by ubiquitination of key proteins, which are subsequently targeted for degrada- tion [66]. One important target of cCbl is ZAP70; upon tyrosine phosphorylation of ZAP70, cCbl binds to ZAP70, leading to ZAP70's ubiquitination and degradation as well as to the downregulation of the TCR. From these biological facts we constructed a logical hyper- graph model, containing 40 nodes and 49 hyperarcs, and implemented it in CellNetAnalyzer (Figure 10). The model is summarized in Table 2. Remarks on the logical T-cell activation model Note that a species can represent different states of a mol- ecule: for example, CD45 refers to the availability of CD45 to act on its substrates (Lck and Fyn), PLCg(bind) refers to PLCγ1 bound to LAT, and PLCg(act) to the active (bound to LAT and phosphorylated) form of PLCγ1. It is also important to realize that several steps can be lumped together or expressed in higher detail; for example, the formation of the complex LAT:Grb2:Sos is considered as one step, but intermediate steps could be considered. This would be reasonable, for example, if Grb2 would have other functions apart from binding Sos. Similarly, the two steps of cCbl's effect (ubiquitination and degradation) are lumped in the hyperarcs pointing to its targets ZAP70 and TCR. Also note that some of the logical operators could be modeled in a different manner, as in the case of Sos and RasGRP for the activation of Ras (where we prefer an OR since both can independently activate Ras, although both (AND) may be needed for full Ras activation). Furthermore, our model describes the full activation of the cascade which leads to proliferation; it is known that e.g. stimulation of TCR with antibodies against its CD3 subunits produces a certain activation of the cascade (where probably Fyn overtakes Lck's role [63]) but does not lead to full activation. Therefore, in our model, as an approximation, activated Fyn can phosphorylate the ITAMs of the TCR, but is not able to activate ZAP70. Here a model with more than 2 levels could be envisioned, where activation of Fyn would be enough to produce a weak (level 1) activation of ZAP70 and hence the whole cascade downstream, while full activation via Lck would activate the cascade to a level 2 (full activation). The model has two extracellular input signals (one for the TCR and one for the coreceptor CD4). Additionally, an input arc for CD45 is included because the regulation of CD45 is not modeled, as described above. Therefore, mathematically speaking, the model contains 3 elements in the input layer. On the other hand, the output layer BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 22 of 26 (page number not for citation purposes) contains 4 transcription factors (CRE, AP1, NFAT and NFκB). As explained in the theoretical section, one reasonable way to deal with the effect of negative feedbacks is to con- sider the different time scales of the processes. Hence, since PAG rephosphorylation takes place after a few min- utes [62], and cCbl mediated degradation is an even slower process, we can define several scenarios: -τ = 0, resting-state (no inputs, no feedbacks), -τ = 1, early-events (input(s), no feedbacks), and -τ = 2, mid-time events (input(s), feedbacks). Here, the state of the feedback loops (activation of PAG/Csk by Fyn and recruitment of cCbl to phosphorylated ZAP70) will depend on the state of the respective activators at τ = 1. This can be considered either by fixing manually the state values of cCbl and PAG/Csk for τ = 2 upon inspection at τ = 1 (as was done herein) or by inclusion of a positive self- loop. We use the term mid-time event since one can also envi- sion a long-term scenario (τ = 3), where slow gene expres- sion mechanisms (not considered here) are active. Analysis of the T-cell signaling cascade In the interaction graph underlying the hypergraphical model, there are 1158 paths from the input to the output layer and 9 (7 negative and 2 positive) feedbacks loops, which are listed in Table 3. cCbl is involved in most (88%) of the loops, in accordance to its important role in the regulation of the signaling cascade. Not surprisingly, since the only feedback mechanisms included are the effect of cCbl on ZAP70 and TCR and of Fyn on PagCsk, no loop goes downstream of ZAP70, and a suitable mini- mal cut set attacking all the feedback loops would consist of Fyn and cCbl. We further analyze the interaction graph by computing the dependency matrix (Figure 11). Since downstream of ZAP70 there are only positive connections (except at node IκB), all the elements downstream of ZAP70 are total acti- vators (except of IκB, which is a total inhibitor of NfκB) with respect to the transcription factors in the output layer, that is, they can have only positive effects. Therefore, for these species, a negative intervention via e.g. inhibitors or iRNA would unambiguously lead to a decrease in the activation levels of the transcription factors. For consider- ing the early-events scenario (τ = 1: the feedback loops are not active), we recompute the dependency matrix where the action of Fyn on PAGCsk and of ZAP70 on cCbl is not considered (Figure 12). Then, all inputs (CD45, TCRlig and CD4) are total activators for all species in the output layer. This is not the case when the feedbacks become active (Figure 11): TCRlig and CD45 become then ambiv- alent factors, i.e. have negative connections to the sink species, whereas CD4 is still an activator but no longer a total one, as it is now connected to a negative feedback loop. A further analysis of the interaction graph provides that there is no minimal cut set containing only one (essential) species whose removal would interrupt all the positive paths to all the outputs. In fact, all minimal cut sets satis- fying this intervention task would contain at least two spe- cies, for example MCS1 = {Rlk, ZAP70} and MCS2 = {LAT, PLCg(act)}. The latter examples agree only partially with biological knowledge: removal of MCS1 or MCS2 would indeed prevent the activation of any output, how- ever, from experimental observations one knows that for example LAT alone is essential in TCR signaling [60]. Thus, MCS2 would not be minimal. Interpreting the hypergraphical (logical) model (Figure 10) reveals that, due to several AND connections, the addi- tional removal of PLCg(act) would indeed be redundant because PLCg can anyway not be activated if LAT is removed. This example illustrates the limitations of graph-based methods and we computed therefore the Table 3: All negative and positive feedback loops in the T-cell model as determined by CellNetAnalyzer. Negative influences are indicated by "", positive influences are expressed by "→". 1 (negative) TCRbind → TCRphos → ZAP70 → cCbl TCRbind 2 (negative) TCRbind → Fyn → TCRphos → ZAP70 → cCbl TCRbind 3 (negative) TCRbind PAGCsk Lck → ZAP70 → cCbl TCRbind 4 (negative) TCRbind PAGCsk Lck → TCRphos → ZAP70 → cCbl TCRbind 5 (negative) PAGCsk Lck → Fyn → PAGCsk 6 (negative) TCRbind PAGCsk Lck → Fyn → TCRphos → ZAP70 → cCbl TCRbind 7 (negative) cCbl ZAP70 → cCbl 8 (positive) TCRbind → Fyn → PAGCsk Lck → TCRphos → ZAP70 → cCbl TCRbind 9 (positive) TCRbind → Fyn → PAGCsk Lck → ZAP70 → cCbl TCRbind BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 23 of 26 (page number not for citation purposes) (logical) minimal cut sets from the logical interaction hypergraph revealing that not only LAT, but also ZAP70, Lck, TCR, the ligand for the TCR, TCRphosp, CD4 and CD45 are essential for full T-cell activation. This result is in good agreement with the current knowledge: the T-cell receptor, its ligand, and the ability of the receptor to get phosphorylated are required for T-cell activation; and CD4 (since it binds Lck thus recruiting it to the mem- brane) and CD45 (which dephosphorylates Lck inhibi- tory regulatory site) are required for the activation of the essential kinase Lck. Next we performed a logical steady state analysis for the different time scales given above. These simulations pro- vide a rough approximation to the dynamics of the sign- aling cascade. Figure 10 shows the particular situation in the early-event scenario (τ = 1) as displayed in CellNetAn- alyzer. Figure 13 summarizes the logical steady state values of important components obtained for the three different time scales. The blue line shows the case for TCR+CD4+CD45 stimulation, whereas the dashed red line represents the case when only TCR+CD45 is stimu- lated in the input layer. Similar analysis can be performed using different scenarios, for example, in a cell where a certain element has been knocked-out. Conclusion In this contribution we have presented a collection of methods for the functional analysis of the structure of cel- lular signaling and regulatory networks. As discussed in the theoretical sections, different abstractions and formal- isms can be used to encode and analyze the topology of interaction networks. The simplest representations are interaction graphs, which are restricted to one-to-one rela- tionships but do yet capture important functional and causal dependencies in the system under study. We have shown that arguably the most important features of inter- action graphs, namely feedback circuits and signaling (or influence) pathways, can systematically be identified by the concept and algorithm of elementary modes known from stoichiometric (metabolic) network analysis. Feed- back cycles are mainly responsible for the dynamic behav- ior of the system, whereas signaling paths reveal network- wide dependencies between species. In some cases, analy- sis of feedback cycles and signaling paths may allow one to predict unambiguously the qualitative effect upon per- turbations of certain species (independently of kinetic parameters and mechanisms). Falsification experiments may then be used to identify missing or incorrect interac- tions. Knowledge on all the signaling paths also facilitates a systematic identification of optimal intervention strate- gies. Again, a concept known from metabolic networks, minimal cut sets, can be adapted and employed here. However, inhibitory actions make this kind of analysis more complicated and we therefore generalized the for- Dependency matrix for the T-cell model for the early event scenario (τ = 1: the feedback loops are not active) Figure 12 Dependency matrix for the T-cell model for the early event scenario (τ = 1: the feedback loops are not active). The meaning of the different colors is the same as in Figure 6. Dependency matrix for the T-cell model Figure 11 Dependency matrix for the T-cell model. The meaning of the different colors is the same as in Figure 6. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 24 of 26 (page number not for citation purposes) malism of minimal cut sets leading to minimal interven- tion sets. The applicability of tools from metabolic network analy- sis to interaction graphs relies on the fact that metabolic networks are hypergraphs, which in turn are generaliza- tions of graphs. In our opinion, the importance of hyper- graphs in structural analyses of cellular interaction networks has been underestimated. In fact, whenever AND-connections occur in interactions of species, hyper- graphical approaches become essential. Boolean networks describe interaction networks in a more constrained and deterministic manner than interaction graphs, enabling discrete simulations. Herein we have demonstrated that signed directed hypergraphs are capa- ble to represent the logical structure of any Boolean net- work. The hypergraphical coding of Boolean networks, which relies on the sum-of-product representation of Boolean networks (using only AND, OR and NOT opera- tions), has several advantages: it is rather intuitive, it mostly corresponds to the underlying molecular mecha- nisms, and it is easy to store and to handle. A hypergraph- ical representation of a Boolean network also establishes a direct link to the corresponding (underlying) interaction graph which can easily be derived from the hypergraph. Finally, it facilitates a logical signal flow (or steady state) analysis in Boolean networks which, as demonstrated in this report, is useful for studying and predicting the qual- itative input-output behavior of signaling networks with respect to a given, possibly incomplete, set of initial state values. This can be achieved here without an explicit enu- meration and/or simulation of all possible trajectories. In general, Boolean networks rely on stronger assump- tions and knowledge than interaction graphs and a pure logical description of all interactions is not always possi- ble. We have suggested extensions of the Boolean frame- work, such as incomplete truth tables of logical operations, to handle these problems. As pointed out by many authors (e.g. [67-69]) the logical description and analysis of large signaling networks has a strong relationship to electrical circuit analysis; however, there still seems to be a large potential in employing the- oretical and software tools from electrical engineering and Boolean logic for investigating interaction networks. Sig- nal flow analysis as introduced herein might be another step in this direction. Describing signal and mass flows equivalently as interac- tions, as done herein, offers high flexibility and enables one to integrate several types of cellular networks (such as metabolic, signalling or regulatory ones) into one frame- work. However, the higher level of abstraction comes with the price that some molecular mechanisms are not always precisely represented, as, for instance, the stoichiometric coefficients in mass flows. The potential of the introduced methods were demon- strated on a model of a small part of the signaling machin- ery of T-cells. The size and complexity of the model was chosen so that the methods could be tested on a case study of real size and complexity, while at the same time the results could be (at least in part) intuitively understood and proofed. If enough information is available, similar models could be set up for any other signaling network. Certainly, these tools will be especially useful in larger interaction networks. Our current and future work aims to expand and subsequently analyse the T-cell model, with hopes that further understanding of this complex network can improve current knowledge about important ill- nesses, such as autoimmune diseases and leukemia. This is certainly a challenging task, but the potential described here makes it a worthy endeavour. Availability and requirements For academic purposes,CellNetAnalyzer can be obtained for free via the website http://www.mpi-magdeburg.mpg.de/projects/cna/ cna.html Note that CellNetAnalyzer requires MATLAB® version 6.1 or higher. Simulation results of LSS analysis of key elements of the T- cell model using the two time-scales explained in the text Figure 13 Simulation results of LSS analysis of key elements of the T- cell model using the two time-scales explained in the text. Blue line: upon TCR+CD4+CD45 activation; dashed red line: only TCR+CD45 activation. BMC Bioinformatics 2006, 7:56 http://www.biomedcentral.com/1471-2105/7/56 Page 25 of 26 (page number not for citation purposes) List of abbreviations LIH: logical interaction hypergraph LSS(s): logical steady state(s) MCS(s): minimal cut set(s) MIS(s): minimal intervention set(s) Authors' contributions SK elaborated the framework and the methods for study- ing interaction graphs and logical interaction hypergraphs and implemented algorithms in CellNetAnalyzer. JSR mainly constructed the logical model of T-cell signalling and he also contributed to the methods' development. JL and LS assisted in the construction of the T-cell model. EDG initiated the project on methods for structural anal- ysis of signaling networks. SK and JSR prepared the man- uscript jointly. All authors have read and accepted the manuscript. Acknowledgements The work was supported by grants from the Deutsche Forschungsgemein- schaft (FOR521) and Bundesministerium für Bildung und Forschung. 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Science's STKE 2002, 122:PE11.	16464248	Lck = ( ( CD45 AND ( ( ( CD8 ) ) ) ) AND NOT ( PAGCsk ) ) ZAP70 = ( ( TCRphos AND ( ( ( Lck ) ) ) ) AND NOT ( cCbl ) ) Itk = ( ZAP70 AND ( ( ( SLP76 ) ) ) ) SEK = ( PKCth ) RasGRP1 = ( PKCth AND ( ( ( DAG ) ) ) ) SLP76 = ( Gads ) CREB = ( Rsk ) Rlk = ( Lck ) ERK = ( MEK ) Gads = ( LAT ) IkB = NOT ( ( IKKbeta ) ) Ca = ( IP3 ) Ras = ( RasGRP1 ) OR ( Grb2Sos ) IP3 = ( PLCg_act ) PAGCsk = ( Fyn ) JNK = ( SEK ) Jun = ( JNK ) Fos = ( ERK ) TCRphos = ( Fyn ) TCRbind = ( ( TCRlig ) AND NOT ( cCbl ) ) NFAT = ( Calcin ) Raf = ( Ras ) PKCth = ( DAG ) Grb2Sos = ( LAT ) AP1 = ( Fos AND ( ( ( Jun ) ) ) ) PLCg_act = ( ZAP70 AND ( ( ( SLP76 AND PLCg_bind AND Rlk ) ) ) ) OR ( Itk AND ( ( ( SLP76 AND ZAP70 AND PLCg_bind ) ) ) ) cCbl = ( ZAP70 ) IKKbeta = ( PKCth ) LAT = ( ZAP70 ) Nfkb = NOT ( ( IkB ) ) PLCg_bind = ( LAT ) Fyn = ( TCRbind AND ( ( ( CD45 ) ) ) ) OR ( CD45 AND ( ( ( Lck ) ) ) ) Calcin = ( Ca ) DAG = ( PLCg_act ) MEK = ( Raf ) Rsk = ( ERK ) CRE = ( CREB )
BioMed Central Page 1 of 18 (page number not for citation purposes) Theoretical Biology and Medical Modelling Open Access Research A method for the generation of standardized qualitative dynamical systems of regulatory networks Luis Mendoza* and Ioannis Xenarios Address: Serono Pharmaceutical Research Institute, 14, Chemin des Aulx, 1228 Plan-les-Ouates, Geneva, Switzerland Email: Luis Mendoza* - luis.mendoza@serono.com; Ioannis Xenarios - ioannis.xenarios@serono.com * Corresponding author Abstract Background: Modeling of molecular networks is necessary to understand their dynamical properties. While a wealth of information on molecular connectivity is available, there are still relatively few data regarding the precise stoichiometry and kinetics of the biochemical reactions underlying most molecular networks. This imbalance has limited the development of dynamical models of biological networks to a small number of well-characterized systems. To overcome this problem, we wanted to develop a methodology that would systematically create dynamical models of regulatory networks where the flow of information is known but the biochemical reactions are not. There are already diverse methodologies for modeling regulatory networks, but we aimed to create a method that could be completely standardized, i.e. independent of the network under study, so as to use it systematically. Results: We developed a set of equations that can be used to translate the graph of any regulatory network into a continuous dynamical system. Furthermore, it is also possible to locate its stable steady states. The method is based on the construction of two dynamical systems for a given network, one discrete and one continuous. The stable steady states of the discrete system can be found analytically, so they are used to locate the stable steady states of the continuous system numerically. To provide an example of the applicability of the method, we used it to model the regulatory network controlling T helper cell differentiation. Conclusion: The proposed equations have a form that permit any regulatory network to be translated into a continuous dynamical system, and also find its steady stable states. We showed that by applying the method to the T helper regulatory network it is possible to find its known states of activation, which correspond the molecular profiles observed in the precursor and effector cell types. Background The increasing use of high throughput technologies in dif- ferent areas of biology has generated vast amounts of molecular data. This has, in turn, fueled the drive to incor- porate such data into pathways and networks of interac- tions, so as to provide a context within which molecules operate. As a result, a wealth of connectivity information is available for multiple biological systems, and this has been used to understand some global properties of bio- logical networks, including connectivity distribution [1], recurring motifs [2] and modularity [3]. Such informa- tion, while valuable, provides only a static snapshot of a Published: 16 March 2006 Theoretical Biology and Medical Modelling2006, 3:13 doi:10.1186/1742-4682-3-13 Received: 12 December 2005 Accepted: 16 March 2006 This article is available from: http://www.tbiomed.com/content/3/1/13 © 2006Mendoza and Xenarios; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 2 of 18 (page number not for citation purposes) network. For a better understanding of the functionality of a given network it is important to study its dynamical prop- erties. The consideration of dynamics allows us to answer questions related to the number, nature and stability of the possible patterns of activation, the contribution of individual molecules or interactions to establishing such patterns, and the possibility of simulating the effects of loss- or gain-of-function mutations, for example. Mathematical modeling of metabolic networks requires specification of the biochemical reactions involved. Each reaction has to incorporate the appropriate stoichiometric coefficients to account for the principle of mass conserva- tion. This characteristic simplifies modeling, because it implies that at equilibrium every node of the metabolic network has a total mass flux of zero [4,5]. There are cases, however, where the underlying biochemical reactions are not known for large parts of a pathway, but the direction of the flow of information is known, which is the case for so-called regulatory networks (see for example [6,7]). In these cases, the directionality of signaling is sufficient for developing mathematical models of how the patterns of activation and inhibition determine the state of activation of the network (for a review, see [8]). When cells receive external stimuli such as hormones, mechanical forces, changes in osmolarity, membrane potential etc., there is an internal response in the form of multiple intracellular signals that may be buffered or may eventually be integrated to trigger a global cellular response, such as growth, cell division, differentiation, apoptosis, secretion etc. Modeling the underlying molec- ular networks as dynamical systems can capture this chan- neling of signals into coherent and clearly identifiable Methodology Figure 1 Methodology. Schematic representation of the method for systematically constructing a dynamical model of a regulatory net- work and finding its stable steady states. (t)) (t)...x g(x ) (t x n i 1 1 Convert the network into a discrete dynamical system Find all the stable steady states with the generalized logical analysis ) ...x f(x dt dx n i 1 Convert the network into a continuous dynamical system ... 1 ) ( ;0 ) ( 0 2 0 1 t x t x Use the steady states of the discrete system as initial states to solve numerically the continuous system Let the continuous system run until it converges to a steady state Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 3 of 18 (page number not for citation purposes) stable cellular behaviors, or cellular states. Indeed, quali- tative and semi-quantitative dynamical models provide valuable information about the global properties of regu- latory networks. The stable steady states of a dynamical system can be interpreted as the set of all possible stable patterns of expression that can be attained within the par- ticular biological network that is being modeled. The advantages of focusing the modeling on the stable steady states of the network are two-fold. First, it reduces the quantity of experimental data required to construct a model, e.g. kinetic and rate limiting step constants, because there is no need to describe the transitory response of the network under different conditions, only the final states. Second, it is easier to verify the predictions of the model experimentally, since it requires stable cellu- lar states to be identified; that is, long-term patterns of activation and not short-lived transitory states of activa- tion that may be difficult to determine experimentally. In this paper we propose a method for generating qualita- tive models of regulatory networks in the form of contin- uous dynamical systems. The method also permits the stable steady states of the system to be localized. The pro- cedure is based on the parallel construction of two dynamical systems, one discrete and one continuous, for the same network, as summarized in Figure 1. The charac- teristic that distinguishes our method from others used to model regulatory networks (as summarized in [8]) is that the equations used here, and the method deployed to ana- lyze them, are completely standardized, i.e. they are not network-specific. This feature permits systematic applica- tion and complete automation of the whole process, thus The Th network Figure 2 The Th network. The regulatory network that controls the differentiation process of T helper cells. Positive regulatory interactions are in green and negative interactions in red. IFN-γ IL-4 SOCS1 IL-12R IFN-γR IL-4R JAK1 STAT4 STAT6 GATA3 T-bet IL-12 IL-18 IL-18R IRAK IFN-βR IFN-β IL-10 IL-10R STAT3 STAT1 NFAT TCR Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 4 of 18 (page number not for citation purposes) speeding up the analysis of the dynamical properties of regulatory networks. Moreover, in contrast to methodolo- gies for the automatic analysis of biochemical networks (as in [9]; for example), our method can be applied to net- works for which there is a lack of stoichiometric informa- tion. Indeed, the method requires as sole input the information regarding the nature and directionality of the regulatory interactions. We provide an example of the applicability of our method, using it to create a dynamical model for the regulatory network that controls the differ- entiation of T helper (Th) cells. Results and discussion Equations 1 and 3 (see Methods) provide the means for transforming a static graph representation of a regulatory network into two versions of a dynamical system, a dis- crete and a continuous description, respectively. As an example, we applied these equations to the Th regulatory network, shown in Figure 2. Briefly, the vertebrate immune system contains diverse cell populations, includ- ing antigen presenting cells, natural killer cells, and B and T lymphocytes. T lymphocytes are classified as either T helper cells (Th) or T cytotoxic cells (Tc). T helper cells take part in cell- and antibody-mediated immune responses by secreting various cytokines, and they are fur- ther sub-divided into precursor Th0 cells and effector Th1 and Th2 cells, depending on the array of cytokines that they secrete [10]. The network that controls the differenti- ation from Th0 towards the Th1 or Th2 phenotypes is rather complex, and discrete modeling has been used to understand its dynamical properties [11,12]. In this work we used an updated version of the Th network, the molec- ular basis of which is included in the Methods. Also, we implement for the first time a continuous model of the Th network. By applying Equation 1 to the network in Figure 2, we obtained Equation 2, which constitutes the discrete ver- sion of the dynamical system representing the Th net- work. Similarly, the continuous version of the Th network was obtained by applying Equation 3 to the network in Figure 2. In this case, however, some of the resulting equa- tions are too large to be presented inside the main text, so we included them as the Additional file 1. Moreover, instead of just typing the equations, we decided to present them in a format that might be used directly to run simu- lations. The continuous dynamical system of the Th net- work is included as a plain text file that is able to run on the numerical computation software package GNU Octave http://www.octave.org. The high non-linearity of Equation 3 implies that the con- tinuous version of the dynamical model has to be studied numerically. In contrast, the discrete version can be stud- Table 1: Stable steady states of the dynamical systems. a DISCRETE SYSTEM CONTINUOUS SYSTEM Th0 Th1 Th2 Th0 Th1 Th2 GATA3 0 0 1 0 0 1 IFN-β 0 0 0 0 0 0 IFN-βR 0 0 0 0 0 0 IFN-γ 0 1 0 0 0.71443 0 IFN-γR 0 1 0 0 0.9719 0 IL-10 0 0 1 0 0 1 IL-10R 0 0 1 0 0 1 IL-12 0 0 0 0 0 0 IL-12R 0 0 0 0 0 0 IL-18 0 0 0 0 0 0 IL-18R 0 0 0 0 0 0 IL-4 0 0 1 0 0 1 IL-4R 0 0 1 0 0 1 IRAK 0 0 0 0 0 0 JAK1 0 0 0 0 0.00489 0 NFAT 0 0 0 0 0 0 SOCS1 0 1 0 0 0.89479 0 STAT1 0 0 0 0 0.00051 0 STAT3 0 0 1 0 0 1 STAT4 0 0 0 0 0 0 STAT6 0 0 1 0 0 1 T-bet 0 1 0 0 0.89479 0 TCR 0 0 0 0 0 0 a. Homologous non-zero values between the discrete and the continuous systems are shown in bold Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 5 of 18 (page number not for citation purposes) ied analytically by using generalized logical analysis, allowing all its stable steady states to be located (see Meth- ods). In our example, the discrete system described by Equation 2 has three stable steady states (see Table 1). Importantly, these states correspond to the molecular pro- files observed in Th0, Th1 and Th2 cells. Indeed, the first stable steady state reflects the pattern of Th0 cells, which are precursor cells that do not produce any of the cytokines included in the model (IFN-β, IFN-γ, IL-10, IL- 12, IL-18 and IL-4). The second steady state represents Th1 cells, which show high levels of activation for IFN-γ, IFN-γR, SOCS1 and T-bet, and with low (although not zero) levels of JAK1 and STAT1. Finally, the third steady state corresponds to the activation observed in Th2 cells, with high levels of activation for GATA3, IL-10, IL-10R, IL- 4, IL-4R, STAT3 and STAT6. Equation 3 defines a highly non-linear continuous dynamical system. In contrast with the discrete system, these continuous equations have to be studied numeri- cally. Numerical methods for solving differential equa- tions require the specification of an initial state, since they proceed via iterations. In our method, we propose to use the stable steady states of the discrete system as the initial states to solve the continuous system that results from application of equation 3 to a given network. We used a standard numerical simulation method to solve the con- tinuous version of the Th model (see Methods). Starting alternatively from each of the three stable steady states found in the discrete model, i.e. the Th0, Th1 and Th2 states, the continuous system was solved numerically until it converged. The continuous system converged to values that could be compared directly with the stable steady states of the discrete system (Table 1). Note that the Th0 and Th2 stable steady states fall in exactly the same position for both the discrete and the continuous dynam- ical systems, and in close proximity for the Th1 state. This finding highlights the similarity in qualitative behavior of the two models constructed using equations 1 and 3, despite their different mathematical frameworks. Despite the qualitative similarity between the discrete and continuous systems, there is no guarantee that the contin- uous dynamical system has only three stable steady states; there might be others without a counterpart in the discrete system. To address this possibility, we carried out a statis- tical study by finding the stable steady states reached by the continuous system starting from a large number of ini- Table 2: Regions of the state space reached by the continuous version of the Th model, as revealed by a large number of simulations starting from a random initial state. a Th0 Th1 Th2 Avrg. Std. Dev. Avrg. Std. Dev. Avrg. Std. Dev. GATA3 0.00003 0.00008 0.00000 0.00000 0.99997 0.00007 IFN-β 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 IFN-βR 0.00000 0.00001 0.00000 0.00001 0.00000 0.00001 IFN-γ 0.00005 0.00013 0.71438 0.00059 0.00000 0.00001 IFN-γR 0.00004 0.00011 0.97169 0.00040 0.00001 0.00004 IL-10 0.00003 0.00007 0.00000 0.00001 0.99999 0.00004 IL-10R 0.00005 0.00010 0.00000 0.00001 0.99999 0.00002 IL-12 0.00000 0.00001 0.00000 0.00000 0.00000 0.00001 IL-12R 0.00000 0.00002 0.00000 0.00001 0.00000 0.00001 IL-18 0.00000 0.00001 0.00000 0.00000 0.00000 0.00001 IL-18R 0.00000 0.00002 0.00000 0.00001 0.00000 0.00001 IL-4 0.00002 0.00006 0.00000 0.00001 0.99995 0.00011 IL-4R 0.00002 0.00004 0.00000 0.00001 0.99990 0.00022 IRAK 0.00001 0.00005 0.00000 0.00003 0.00001 0.00004 JAK1 0.00002 0.00008 0.00487 0.00005 0.00001 0.00005 NFAT 0.00001 0.00003 0.00000 0.00002 0.00001 0.00003 SOCS1 0.00009 0.00022 0.89486 0.00037 0.00002 0.00006 STAT1 0.00001 0.00005 0.00051 0.00003 0.00002 0.00005 STAT3 0.00012 0.00023 0.00001 0.00002 1.00000 0.00002 STAT4 0.00001 0.00003 0.00000 0.00003 0.00000 0.00001 STAT6 0.00001 0.00004 0.00000 0.00002 0.99990 0.00023 T-bet 0.00007 0.00018 0.89485 0.00036 0.00000 0.00000 TCR 0.00000 0.00001 0.00000 0.00000 0.00000 0.00001 a. Only three regions of the activation space were found in the continuous Th model after running it from 50,000 different random initial states. The average and standard deviations of all the results are shown. All variables had a random initial state in the closed interval [0,1]. From the 50,000 simulations, 8195 (16.39%) converged to the Th0 state, 25575 (51.15%) to the Th1 state, and 16230 (32.46%) to the Th2 state. Bold numbers as in Table 1. Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 6 of 18 (page number not for citation purposes) Stability of the steady states of the continuous model of the Th network Figure 3 Stability of the steady states of the continuous model of the Th network. a. The Th0 state is stable under small per- turbations. b. A large perturbation on IFN-γ is able to move the system from the Th0 to the Th1 steady state. This latter state is stable to perturbations. c. A large perturbation of IL-4 moves the system from the Th0 state to the Th2 state, which is sta- ble. For clarity, only the responses of key cytokines and transcription factors are plotted. The time is represented in arbitrary units. level of activation level of activation level of activation a c b IFN-γ perturbation IL-4 perturbation IFN-γ perturbation IFN-γ perturbation IL-4 perturbation IL-4 perturbation time time time Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 7 of 18 (page number not for citation purposes) tial states. The continuous system was run 50,000 times, each time with the nodes in a random initial state within the closed interval between 0 and 1. In all cases, the sys- tem converged to one of only three different regions (Table 2), corresponding to the above-mentioned Th0, Th1 and Th2 states. These results still do not eliminate the possibility that other stable steady states exist in the con- tinuous system. Nevertheless, they show that if such addi- tional stable steady states exist, their basin of attractions is relatively small or restricted to a small region of the state space. The three steady states of the continuous system are stable, since they can resist small perturbations, which create transitory responses that eventually disappear. Figure 3a shows a simulation where the system starts in its Th0 state and is then perturbed by sudden changes in the values of IFN-γ and IL-4 consecutively. Note that the system is capa- ble of absorbing the perturbations, returning to the origi- nal Th0 state. If a perturbation is large enough, however, it may move the system from one stable steady state to another. If the system is in the Th0 state and IFN-γ is tran- siently changed to it highest possible value, namely 1, the whole system reacts and moves to its Th1 state (Figure 3b). A large second perturbation by IL-4, now occurring when the system is in its Th1 state, does not push the sys- tem into another stable steady state, showing the stability of the Th1 state. Conversely, if the large perturbation of IL- 4 occurs when the system is in the Th0 state, it moves the system towards the Th2 state (Figure 3c). In this case, a second perturbation, now in IFN-γ, creates a transitory response that is not strong enough to move the system away from the Th2 state, showing the stability of this steady state. These changes from one stable steady state to another reflect the biological capacities of IFN-γ and IL-4 to act as key signals driving differentiation from Th0 towards Th1 and Th2 cells, respectively[10]. Furthermore, note that the Th1 and Th2 steady states are more resistant to large perturbations than the Th0 state, a characteristic that represents the stability of Th1 and Th2 cells under dif- ferent experimental conditions. Alternative Th network Figure 6 Alternative Th network. T helper pathway published in [43], reinterpreted as a signaling network. IL-12 IL-4 STAT1 IL-12R STAT4 T-bet IFN-γ IFN-γR IL-4R STAT6 GATA3 IL-5 IL-13 TCR Alternative Th network Figure 4 Alternative Th network. T helper pathway published in [69], reinterpreted as a signaling network. IL-12 Steroids IFN-γ Inf. Resp. IL-4 IL-5 IL-10 Alternative Th network Figure 5 Alternative Th network. T helper pathway published in [70], reinterpreted as a signaling network. IFN-γ CSIF IL-2 IL-4 Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 8 of 18 (page number not for citation purposes) The whole process resulted in the creation of a model with qualitative characteristics fully comparable to those found in the experimental Th system. Notably, the model used default values for all parameters. Indeed, the continuous dynamical system of the Th network has a total of 58 parameters, all of which were set to the default value of 1, and one parameter (the gain of the sigmoids) with a default value of 10. This set of default values sufficed to capture the correct qualitative behavior of the biological system, namely, the existence of three stable steady states that represent Th0, Th1 and Th2 cells. Readers can run simulations on the model by using the equations pro- vided in the "Th_continuous_model.octave.txt" file. The file was written to allow easy modification of the initial states for the simulations, as well as the values of all parameters. Analysis of previously published regulatory networks related to Th cell differentiation We wanted to compare the results from our method (Fig- ure 1) as applied to our proposed network (Figure 2) with some other similar networks. The objective of this com- parison is to show that our method imposes no restric- tions on the number of steady states in the models. Therefore, if the procedure is applied to wrongly recon- structed networks, the results will not reflect the general characteristics of the biological system. While there have been multiple attempts to reconstruct the signaling path- ways behind the process of Th cell differentiation, they have all been carried out to describe the molecular com- ponents of the process, but not to study the dynamical behavior of the network. As a result, most of the schematic representations of these pathways are not presented as regulatory networks, but as collections of molecules with different degrees of ambiguity to describe their regulatory interactions. To circumvent this problem, we chose four pathways with low numbers of regulatory ambiguities and translated them as signaling networks (Figures 4 through 7). The methodology introduced in this paper was applied to the four reinterpreted networks for Th cell differentiation. Alternative Th network Figure 7 Alternative Th network. T helper pathway published in [71], reinterpreted as a signaling network. Itk NFAT IL-18R c-Maf IL-4R IL-13 STAT6 JNK2 IL-4 IL-5 IL-18 Lck CD4 JNK IRAK NFkB TRAF6 IFN-γ T-bet STAT4 GATA3 TCR Ag/ MHC IL-12R IL-12 ATF2 p38/ MAPK MKK3 Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 9 of 18 (page number not for citation purposes) The stable steady states of the resulting discrete and con- tinuous models are presented in Tables 3 through 6. Notice that none of these four alternative networks could generate the three stable steady states representing Th0, Th1 and Th2 cells. Two networks reached only two stable steady states, while two others reached more than three. Notably, all these four networks included one state repre- senting the Th0 state, and at least one representing the Th2 state. The absence of a Th1 state in two of the net- works might reflect the lack of a full characterization of the IFN-γ signaling pathway at the time of writing the cor- responding papers. It is important to note that the failure of these four alter- native networks to capture the three states representing Th cells is not attributable to the use of very simplistic and/or outdated data. Indeed, the network in Figure 6 comes from a relatively recent review, while that in Figure 7 is rather complex and contains five more nodes than our own proposed network (Figure 2). All this stresses the importance of using a correctly reconstructed network to develop dynamical models, either with our approach or any other. Conclusion There is a great deal of interest in the reconstruction and analysis of regulatory networks. Unfortunately, kinetic information about the elements that constitute a network or pathway is not easily gathered, and hence the analysis of its dynamical properties (via simulation packages such as [13]) is severely restricted to a small set of well-charac- terized systems. Moreover, the translation from a static to a dynamical representation normally requires the use of a network-specific set of equations to represent the expres- sion or concentration of every molecule in the system. We herein propose a method for generating a system of ordinary differential equations to construct a model of a regulatory network. Since the equations can be unambig- uously applied to any signaling or regulatory network, the construction and analysis of the model can be carried out systematically. Moreover, the process of finding the stable steady states is based on the application of an analytical method (generalized logical analysis [14,15] on a discrete version of the model), followed by a numerical method (on the continuous version) starting from specific initial states (the results obtained from the logical analysis). This characteristic allows a fully automated implementation of our methodology for modeling. In order to construct the equations of the continuous dynamical system with the exclusive use of the topological information from the net- work, the equations have to incorporate a set of default values for all the parameters. Therefore, the resulting model is not optimized in any sense. However, the advan- tage of using Equation 3 is that the user can later modify the parameters so as to refine the performance of the Table 4: Stable steady states of the signaling network in Figure 5 Discrete state 1 Discrete state 2 Discrete state 3 Discrete state 4 Discrete state 5 Discrete state 6 Discrete state 7 CSIF 0 0 1 0 0.5 0.5 0 IFN-γ 0 1 0 0.5 0 0 0. 5 IL-2 0 1 0 0.5 0.5 0.5 0 IL-4 0 0 1 0.5 0 0.5 0.5 Continuous state 1 Continuous state 2 Continuous state 3 Continuous state 4 Continuous state 5 Continuous state 6 Continuous state 7 CSIF 0 0.0034416 0.8888881 0.0034999 4.9132E-5 0.8881746 4.3001E-5 IFN-γ 0 0.8888881 0.0034416 0.8881746 4.300E-5 0.0034999 4.9132E-5 IL-2 0 0.8888881 0.0034416 0.8881746 4.3154E-5 0.0035227 4.8979E-5 IL-4 0 0.0034416 0.8888881 0.0035227 4.8979E-5 0.8881746 4.3154E-5 Table 3: Stable steady states of the signaling network in Figure 4 Discrete state 1 Discrete state 2 Continuous state 1 Continuous state 2 IFN-γ 0 0 0 0 IL-10 0 1 0 0.78995 IL-12 0 0 0 0 IL-4 0 1 0 0.89469 IL-5 0 0 0 0.01343 Inf. Resp. 0 0 0 0.00737 Steroids 0 0 0 0.00105 Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 10 of 18 (page number not for citation purposes) model, approximating it to the known behavior of the biological system under study. In this way, the user has a range of possibilities, from a purely qualitative model to one that is highly quantitative. There are studies that compare the dynamical behavior of discrete and continuous dynamical systems. Hence, it is known that while the steady state of a Boolean model will correspond qualitatively to an analogous steady state in a continuous approach, the reverse is not necessarily true. Moreover, periodic solutions in one representation may be absent in the other [16]. This discrepancy between the discrete and continuous models is more evident for steady states where at least one of the nodes has an activation state precisely at, or near, its threshold of activation. Because of this characteristic, discrete and continuous models for a given regulatory network differ in the total number of steady states [17]. For this reason, our method focuses on the study of only one type of steady state; namely, the regular stationary points [18]. These points do not have variables near an activation threshold, and they are always stable steady states. Moreover, it has been shown that this type of stable steady state can be found in discrete models, and then used to locate their analogous states in continuous models of a given genetic regulatory network [19]. It is beyond the scope of this paper to present a detailed mathematical analysis of the dynamical system described by Equation 3. Instead, we present a framework that can help to speed up the analysis of the qualitative behavior of signaling networks. Under this perspective, the useful- ness of our method will ultimately be determined through building and analyzing concrete models. To show the capabilities of our proposed methodology, we applied it to analysis of the regulatory network that controls differ- entiation in T helper cells. This biological system was well suited to evaluating our methodology because the net- work contains several known components, and it has three alternative stable patterns of activation. Moreover, it is of great interest to understand the behavior of this net- work, given the role of T helper cell subsets in immunity and pathology [20]. Our method applied to the Th net- work generated a model with the same qualitative behav- ior as the biological system. Specifically, the model has three stable states of activation, which can be interpreted as the states of activation found in Th0, Th1 and Th2 cells. In addition, the system is capable of being moved from the Th0 state to either the Th1 or Th2 states, given a suffi- ciently large IFN-γ or IL-4 signal, respectively. This charac- teristic reflects the known qualitative properties of IFN-γ and IL-4 as key cytokines that control the fate of T helper cell differentiation. Regarding the numerical values returned by the model, it is not possible yet to evaluate their accuracy, given that (to our knowledge) no quantitative experimental data are available for this biological system. The resulting model, then, should be considered as a qualitative representation of the system. However, representing the nodes in the net- work as normalized continuous variables will eventually permit an easy comparison with quantitative experimen- tal data whenever they become available. Towards this end, the equations in our methodology define a sigmoid function, with values ranging from 0 to 1, regardless of the values of assigned to the parameters in the equations. This characteristic has been used before to represent and model the response of signaling pathways [21,22]. It is important to note, however, that the modification of the parameters allow the model to be fitted against experi- mental data. One benefit of a mathematical model of a particular bio- logical network is the possibility of predicting the behav- Table 5: Stable steady states of the signaling network in Figure 6 Discrete state 1 Discrete state 2 Discrete state 3 Discrete state 4 Continuous state 1 Continuous state 2 Continuous state 3 Continuous state 4 GATA3 0 0 11 1 0 0 0.93037 0.93037 IFN-γ 0 1 0 1 0 0.99914 0 0.90967 IFN-γR 0 1 0 1 0 0.99997 0 0.99617 IL-12 0 0 0 0 0 0 0 0 IL-12R 0 1 0 0 0 0.9096 0 0.00193 IL-13 0 0 1 1 0 0 0.99719 0.99719 IL-4 0 0 1 1 0 0 0.99719 0.99719 IL-4R 0 0 1 1 0 0 0.99991 0.99991 IL-5 0 0 1 1 0 0 0.99719 0.99719 STAT1 0 1 0 1 0 1 0 0.99988 STAT4 0 1 0 0 0 0.99617 0 2.4E-4 STAT6 0 0 1 1 0 0 1 1 T-bet 0 1 0 1 0 0.93037 0 0.93034 TCR 0 0 0 0 0 0 0 0 Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 11 of 18 (page number not for citation purposes) ior of complex experimental setups. Therefore, it is important to be aware of its limitations beforehand, to avoid generating experimental data that cannot be han- dled by the model. The method we present in this paper has been developed to obtain the number and relative position of the stable steady states of a regulatory network. Equations 1 and 3 include a number of parameters that allow the response of the model to be fine-tuned, but the equations were not designed to describe the transitory responses of molecules with great detail. Therefore, failure to predict a stable steady state with high numerical accu- racy should not be interpreted as a failure of the approach presented here. By contrast, failure to describe and/or pre- dict the number and approximate location of stable steady states under a wide range of values for the parame- ters would call the validity of the reconstruction of a par- ticular network into question. Here, however, it is essential to establish the validity of the network used as input. Indeed, we applied our method to four alternative forms of the network that regulates Th cell differentiation. The alternative networks (Figures 4 through 7) were taken from previously published attempts to discover the molecular basis of this differentiation process. Originally, such networks were not developed with the idea of study- ing dynamical properties. It is not surprising, then, that these networks do not reflect the existence of three stable steady states, representing the molecular states of Th0, Th1 and Th2 cells, respectively. In these cases, the failure to find the correct stable steady states is not a problem in the modeling methodology, but a problem in the infer- ence of the regulatory network. In conclusion, we have shown that the creation of a dynamical model of a regulatory network can be consid- erably simplified with the aid of a standardized set of equations, where the feature that distinguishes one mole- cule from another is the number of regulatory inputs. Such standardization permits a continuous dynamical system to be systematically and analytically constructed together with a basic analysis of its global properties, based exclusively on the information provided by the con- nectivity of the network. While the use of a standardized set of functions to model a network may severely restrict the capability to fit specific datasets, we believe that the loss in flexibility is balanced by the possibility of rapidly developing models and gaining knowledge of the dynam- ical behavior of a network, especially in those cases where few kinetic data are available. Thus, we provide a method for incorporating the dynamical perspective in the analy- sis of regulatory networks, using the topological informa- Table 6: Stable steady states of the signaling network in Figure 7 Discrete state 1 Discrete state 2 Continuous state 1 Continuous state 2 Ag/MHC 0 0 0 0 ATF2 0 0 0 0 c-Maf 0 0 0 0 CD4 0 0 0 0 GATA3 0 1 0 0.99999 IFN-γ 0 0 0 0 IL-12 0 0 0 0 IL-12R 0 0 0 0 IL-13 0 1 0 0.8468 IL-18 0 0 0 0 IL-18R 0 0 0 0 IL-4 0 1 0 0.8468 IL-4R 0 1 0 0.99176 IL-5 0 1 0 0.8469 IRAK 0 0 0 0 Itk 0 0 0 0 JNK 0 0 0 0 JNK2 0 0 0 0 Lck 0 0 0 0 MKK3 0 0 0 0 NFAT 0 0 0 0 NFkB 0 0 0 0 p38/MAPK 0 0 0 0 STAT4 0 0 0 0 STAT6 0 1 0 0.99975 T-bet 0 0 0 0 TCR 0 0 0 0 TRAF6 0 0 0 0 Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 12 of 18 (page number not for citation purposes) tion of a network, without the need to collect extensive time-series or kinetic data. Methods Molecular basis of the Th network topology The following paragraphs detail the evidence used to infer the topology of the Th regulatory network, updating the data summarized in [11]. Th1 cells are producers of IFN-γ [10,23], which acts on its target cells by binding to a cell- membrane receptor [24-26] to start a signaling cascade, which involves JAK1 and STAT-1 [27-29]. STAT-1 can be activated by a number of ligands besides IFN-γ, but importantly, it cannot be activated by IL-4 [30], which is a major Th2 signal. In contrast, STAT-1 plays a role in modulating IL-4, being an intermediate in the negative regulation of IFN-γ exerted on IL-4 expression [31]. Differ- ent signals converge in STAT-1, among them that of IFN- β/IFN-βR [32]. The IFN-γ signaling continues downstream to activate SOCS-1 in a STAT-1-dependent pathway [33,34]. SOCS-1, in turn, influences both the IFN-γ and IL-4 pathways. On the one hand, SOCS-1 is a negative reg- ulator of IFN-γ signaling, blocking the interaction of IFN- γR and STAT-1 [35] due to direct inhibition of JAK1 [29,36]. On the other hand, SOCS-1 blocks the IL-4R/ STAT-6 pathway [37]. SOCS-1 is, therefore, a key element for the inhibition from the IFN-γ to the IL-4 pathway. Th1 cells express high levels of SOCS-1 mRNA, while it is barely detectable in Th0 and Th2 cells [38]. Finally, another key molecule is T-bet, which is a transcription fac- tor detected in Th1 but not Th0 or Th2 cells. T-bet expres- sion is upregulated by IFN-γ in a STAT-1-dependent mechanism [39]. Importantly, T-bet is an inhibitor of GATA-3 [40], an activator of IFN-γ [40] and activator of T- bet itself [41,42]. Th2 cells express IL-4, which is the major known determi- nant of the Th2 phenotype itself [43]. IL-4 binds to its receptor, IL-4R, which is preferentially expressed in Th2 cells [23,44]. The IL-4R signaling is transduced by STAT-6, which in turn activates GATA-3 [10]. GATA-3, in turn, is capable of inducing IL-4 [45], thus establishing a feedback loop. The influence from the IL-4 pathway on the IFN-γ pathway seems to be mediated by GATA-3 via STAT-4 [46]. Like T-bet, GATA-3 also presents a self-activation loop [47-49]. IL-12 and IL-18 are two molecules that affect the IFN-γ pathway. IL-12 is a cytokine produced by monocytes and dendritic cells and promotes the development of Th1 cells [50]. The IL-12 receptor is present in its functional form in Th0 and Th1 but not Th2 cells [51]. IL-12R signaling is mediated by STAT-4 [52], which is able to activate IFN-γ Table 7: Circuits of the Th network a 1 IFNγ→IFNγR→JAK1→STAT1¬IL4→IL4R→STAT6¬IL18R→IRAK→ 2 IFNγ→IFNγR→JAK1→STAT1¬IL4→IL4R→STAT6¬IL12R→STAT4→ 3 IFNγ→IFNγR→JAK1→STAT1¬IL4→IL4R→STAT6→GATA3→IL10→IL10R→STAT3¬ 4 IFNγ→IFNγR→JAK1→STAT1¬IL4→IL4R→STAT6→GATA3¬STAT4→ 5 IFNγ→IFNγR→JAK1→STAT1¬IL4→IL4R→STAT6→GATA3¬Tbet→ 6 IFNγ→IFNγR→JAK1→STAT1→SOCS1¬IL4R→STAT6¬IL18R→IRAK→ 7 IFNγ→IFNγR→JAK1→STAT1→SOCS1¬IL4R→STAT6¬IL12R→STAT4→ 8 IFNγ→IFNγR→JAK1→STAT1→SOCS1¬IL4R→STAT6→GATA3→IL10→IL10R→STAT3¬ 9 IFNγ→IFNγR→JAK1→STAT1→SOCS1¬IL4R→STAT6→GATA3¬STAT4→ 10 IFNγ→IFNγR→JAK1→STAT1→SOCS1¬IL4R→STAT6→GATA3¬Tbet→ 11 IFNγ→IFNγR→JAK1→STAT1→Tbet→ 12 IFNγ→IFNγR→JAK1→STAT1→Tbet→SOCS1¬IL4R→STAT6¬IL18R→IRAK→ 13 IFNγ→IFNγR→JAK1→STAT1→Tbet→SOCS1¬IL4R→STAT6¬IL12R→STAT4→ 14 IFNγ→IFNγR→JAK1→STAT1→Tbet→SOCS1¬IL4R→STAT6→GATA3→IL10→IL10R→STAT3¬ 15 IFNγ→IFNγR→JAK1→STAT1→Tbet→SOCS1¬IL4R→STAT6→GATA3¬STAT4→ 16 IFNγ→IFNγR→JAK1→STAT1→Tbet¬GATA3→IL4→IL4R→STAT6¬IL18R→IRAK→ 17 IFNγ→IFNγR→JAK1→STAT1→Tbet¬GATA3→IL4→IL4R→STAT6¬IL12R→STAT4→ 18 IFNγ→IFNγR→JAK1→STAT1→Tbet¬GATA3→IL10→IL10R→STAT3¬ 19 IFNγ→IFNγR→JAK1→STAT1→Tbet¬GATA3¬STAT4→ 20 IL4→IL4R→STAT6→GATA3→ 21 IL4R→STAT6→GATA3¬ Tbet→SOCS1¬ 22 Tbet→ 23 Tbet¬GATA3¬ 24 GATA3→ 25 IL4→IL4R→STAT6→GATA3¬Tbet→SOCS1¬JAK1→STAT1¬ 26 JAK1→STAT1→SOCS1¬ 27 JAK1→STAT1→Tbet→ SOCS1¬ a. If the circuit has zero or an even number of negative interactions, it is considered positive; otherwise the circuit is negative. Circuits 1–24 are positive, and circuits 25–27 are negative. Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 13 of 18 (page number not for citation purposes) [41,46,53]. The IL-12 signaling pathway can be blocked by IL-4 by the STAT-6 dependent down-regulation of one subunit of IL-12R [54]. IL-18 is a cytokine produced by many cell types and promotes IFN-γ production in Th cells [55]. It acts upon binding to its receptor, IL-18R, which acts through IRAK [56]. IL-12 and IL-18 act syner- gistically to increase IFN-γ production, but using different pathways [57,58]. Finally, IL-4 is able to block IL-18 sign- aling in a STAT-6 dependent manner [59]. IL-10 is a cytokine actively produced by Th2 cells, and it inhibits cytokine production by Th1 cells. As with the other cytokines mentioned above, IL-10 acts upon bind- ing to a cell surface receptor, IL-10R, which in turn acti- vates the STAT signaling system [60]. In particular, it has been shown that the functioning of IL-10 signaling is dependent upon the presence of STAT-3 [61]. As for the signals affecting IL-10 expression, it has been shown that IL-4 enhances IL-10 gene expression in Th2 but not Th1 cells [62]. This requirement implies that the intracellular signaling from IL-4 to IL-10 should pass through a Th2 specific molecule, which from the molecules considered here can only be GATA-3. Finally, IL-10 has been shown to be a very powerful inhibitor of IFN-γ production [60,63]. Cytokine gene expression in T cells is induced by the acti- vation of the T cell receptor (TCR) by ligand binding. Dif- ferent signaling pathways are activated by the TCR [64]. Among these is the pathway including the NFAT family of transcription factors, which are implicated in the T cell activation-dependent regulation of numerous cytokines. A constitutively active form of one of the NFAT proteins, specifically NFATc1, increases the expression of IFN-γ [65]. Importantly, the same experimental procedure does not affect the expression of IL-4. All this indicates that the NFAT family members play a central role in the TCR- Activation of a node as a function of one positive input Figure 10 Activation of a node as a function of one positive input. The activation of a node in response to one positive input, plotted for various possible interaction weights. total activation xa Activation of a node as a function of its total input, ω Figure 8 Activation of a node as a function of its total input, ω. Equation 3 ensures that the activation of a node has the form of a sigmoid, bounded in the interval [0,1] regardless of the values of h. total activation ω Total input to a node, ω, as a function of one positive input, xaFigure 9 Total input to a node, ω, as a function of one positive input, xa. The value of ω is a bounded function in the inter- val [0,1] regardless of the interaction weight of the positive input, α. ω xa Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 14 of 18 (page number not for citation purposes) induced expression of cytokines during Th cell differenti- ation, especially in the Th1 pathway. The discrete dynamical system The discrete system represents the network as a series of interconnected elements that have only two possible states of activation, 0 (or inactive) and 1 (or active). Given this property, the network is completely described by the following set of Boolean equations: Equation 1. A node x in the network can have only one of three possi- ble forms depending on whether it has activator and inhibitor input nodes, or only activators, or only inhibi- tors. In the first case, i.e. form § in Eqn.1, the Boolean function can be read as: x will be active in the next time step if at this time any of its activators and none of its inhibitors are acting upon it. Similarly, form §§ can be translated as: x will be active if any of its activators is acting upon it. And finally, form §§§ reads as: x will be active if none of its inhibitors are acting upon it. Note than in all cases inhibitors are strong enough to change the state of a node from 1 to 0, while activators are strong enough to change the state of a node from 0 to 1 if no inhibitor is act- ing on the node of reference. The three alternative forms of representing a node in Equation 1 imply two possible default states of activation, i.e. the state of a node when there are neither activators nor inhibitors acting upon it. If the connectivity of the node includes either only posi- tive inputs, or both positive and negative inputs, then the node has an inactive state by default. Alternatively, if the connectivity of a node has only negative inputs, then the node has an active state by default. The Th network (Figure 2) can be converted into a discrete dynamical system using Equation 1. The resulting system of equations is as follows: Equation 2. GATA3(t + 1) = (GATA3(t) ∨ STAT6(t)) ∧ ¬(T - bet(t)) IFN - βR(t + 1) = IFN - β(t) IFN - γ(t + 1) = (IRAK(t) ∨ NFAT(t) ∨ STAT - 4(t) ∨ T - bet(t)) ∧ ¬(STAT3(t)) Equation 1. x t x t x t x t x t x t i a a n a i i ( ) ( ) ( ) ( ) ( ( ) ( ) + = ∨ ∨ ( ) ∧¬ ∨ 1 1 2 1 2 … … … … ∨ ∨ ∨ ¬ ∨ ∨ x t t x t x t t x t x t m i a n a i m i ( )) ( ) ( ) ( ) ( ) ( ) ( )) § x §§ x 1 a 1 i 2 2 ( §§§        ∨∧ ¬ , , and are the logical operators OR, AND, and NOT is the set of activators of i x x x x i n a i m i ∈{ , } { } { } 0 1 s the set of inhibitors of is used if has activato xi § xi rs and inhibitors is used if has only activators §§ x §§§ i is used if has only inhibitors xi Activation of a node as a function of one negative input Figure 12 Activation of a node as a function of one negative input. The activation of a node in response to one negative input, plotted for various possible interaction weights. total activation xi Total input to a node, ω, as a function of one negative input, xiFigure 11 Total input to a node, ω, as a function of one negative input, xi. The value of ω is a bounded function in the interval [0,1] regardless of the interaction weight of the negative input, β. ω xi Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 15 of 18 (page number not for citation purposes) IFN - γR(t + 1) = IFN - γ(t) IL - 10(t + 1) = GATA3(t) IL - 10R(t + 1) = IL - 10(t) IL - 12R(t + 1) = IL - 12(t) IL - 18R(t + 1) = IL - 18(t) ∧ ¬(STAT6(t)) IL - 4(t + 1) = GATA3(t) ∧ ¬(STAT1(t)) IL - 4R(t + 1) = IL - 4(t) ∧ ¬(SOCS1(t)) IRAK(t + 1) = IL - 18R(t) JAK1(t + 1) = IFN - γR(t) ∧ ¬(SOCS1(t)) NFAT(t + 1) = TCR(t) SOCS1(t + 1) = STAT1(t) ∨ T - bet(t) STAT1(t + 1) = IFN - βR(t) ∨ JAK1(t) STAT3(t + 1) = IL - 10R(t) STAT4(t + 1) = IL - 12R(t) ∧ ¬(GATA3(t)) STAT6(t + 1) = IL - 4R(t) T - bet(t + 1) = (STAT1(t) ∨ T - bet(t)) ∧ ¬(GATA3(t)) Notice that there are only 19 equations out of a total of 23 elements in the Th network. The reason is that four ele- ments, namely IFN-β, IL-12, IL-18 and TCR, do not have inputs. These four elements are thus treated as constants, since there are no interactions that regulate their behavior. Throughout the text, these four elements are considered as having a value of 0. Stable steady states of the discrete system The discrete dynamical system defined by Equation 2 can be solved in different ways to find its attractors, depend- ing on how to update the vector state X(t) to its successor, X(t+1). By far the easiest method for solving the equations is the synchronous approach (as in [66,67]). This method, however, can generate spurious results (see [14]). Hence, we use generalized logical analysis to find all the steady states of the system [15]. Generalized logical analysis allows us to find all the steady states of a discrete dynam- ical system by evaluating the functionality of the feedback loops, also known as circuits, in the system. In this case, the Th network (Figure 2) contains a total of 27 circuits (Table 7), 24 positive and 3 negative. Depending on the set of parameters used, positive feedback loops can gener- ate multistationarity, while negative feedback loops can generate damped or sustained oscillations. Generalized logical analysis is a well-established method and the reader may find in-depth explanations elsewhere [14,15,18]. The continuous dynamical system To describe the network as a continuous dynamical sys- tem, we use the following set of ordinary differential equations: Equation 3. The right-hand side of the differential equation comprises two parts: an activation function and a term for decay. Activation is a sigmoid function of ω, which represents the total input to the node. The equation of the sigmoid was chosen so as to pass through the two points (0,0) and (1,1), regardless of the value of its gain, h; see Figure 8. The bounding of a node x to the closed interval [0,1] implies that its level of activation should be interpreted as a nor- malized, not an absolute, value. This characteristic permits direct comparison between the discrete and the continu- ous dynamical systems, since in both formalisms the min- imum and maximum levels of activation are 0 and 1. Subsequently, the second part of the equation is a decay term, which for simplicity is directly proportional to the level of activation of the node. The total input to a node, represented by ω, is a combina- tion of the multiple activatory and inhibitory interactions acting upon the node of reference. In the general case, dif- ferent nodes have different connectivities; hence it is nec- essary to write a function ω so that it can describe different combinations of activatory and inhibitory inputs. For this Equation 3. dx dt e e e e i h h h h i i = − + − + − − − − 0 5 0 5 0 5 0 5 1 1 . ( . ) . ( . ) ( )( ω ω ) − = +       +         − + ∑ ∑ ∑ ∑ ∑ ∑ γ ω α α α α β β i i i n n n n a n n a m m x x x 1 1 1 1       +                 +       ∑ ∑ ∑ ∑ β β α α α m m i m m i n n n x x 1 1 § x x x x n a n n a m m m m i m m i ∑ ∑ ∑ ∑ ∑ ∑ +         − +       +    1 1 1 1 α β β β β §§                           ≤ ≤ ≤ ≤ > §§§ 0 1 0 1 0 x h x i i n m i n a ω α β γ , , , { } { } is the set of activators of is the set of inhib x x i n i itors of is used if has activators and inhibitors xi § x § i § x §§§ x i i is used if has only activators is used if has only inhibitors Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 16 of 18 (page number not for citation purposes) reason, ω has three possible forms in Equation 3. If a node xi is regulated by both activators and inhibitors, then the first form, §, is used. However, if is regulated exclusively by activators, form §§ is used instead. Finally, the form §§§ is used if xi has only negative regulators. In all cases, the total input is a combination of weighted activators and/or inhibitors, where the weights are represented by the α and β parameters for the activators and inhibitors, respectively. The mathematical form ω was chosen so as to be monotonic and to be bounded in the closed interval [0,1] given that 0≤x≤1, α>0 and β>0. Figure 9 shows the behavior of ω when a node is controlled only by one acti- vator. Notice that regardless of the value of α, the function is monotonically increasing and bounded to [0,1]. The reason for choosing a monotonic bounded function for ω is to preserve the sigmoid form of the total activation act- ing upon a node xi, irrespective of the number and nature of the regulatory inputs acting upon it. Indeed, Figure 10 shows the total activation of a node xi controlled by one positive regulation with different weights. Notice that the total activation retains a bounded sigmoid form inde- pendently of the value of α. This same qualitative behav- ior for total activation on a node xi is observed if it is regulated only by inhibitors. Figure 11 shows ω as a func- tion of one inhibitor, plotted for different strengths of interaction. In this case, the total input to xi is still a bounded sigmoid regardless of the value of the parameter β (see Figure 12). This general qualitative behavior per- sists even with a mixture of activatory and inhibitory inputs acting upon a node. Figure 13 presents the total activation of a node xi as a function of two regulatory inputs, one positive and one negative. Notice again that the equation warrants a bounded sigmoid form for the total input to a node. Once a network is translated to a dynamical system using Equation 3, it is necessary to specify values for all param- eters. For a system with n nodes and m interactions, there are m+2n parameters. However, there are usually insuffi- cient experimental data to assign realistic values for each and every one of the parameters. Nevertheless, it is possi- ble to use a series of default values for all the parameters in Equation 3. The reason is that, as we showed in the pre- vious paragraph, the equations have the same qualitative shape for any value assigned to the parameters. Hence, for the sake of simplicity, it is possible to assign the same val- ues to most of the parameters, as a first approach. For the present study on the Th model, we use a value of 1 for all αs, βs and γs; and we use h = 10, since we currently lack quantitative data to estimate more realistic values. More- over, the use of default values ensures the possibility of creating the dynamical system in a fully automated way. Nonetheless, after the initial construction and analysis of the resulting system, the modeler may modify the values of the parameters so as to fine-tune the dynamical behav- ior of the equations, whenever more experimental quanti- tative data become available. The continuous dynamical system of the Th model, constructed with the use of Equa- tion 3, yields a system of 23 equations, which is included in the file "Th_continuous_model.octave.txt". Stable steady states of the continuous system Nonlinear systems of ordinary differential equations are studied numerically. Hence the continuous dynamical system defined by Equation 3 poses the problem of how to find all its stable steady states without using very time- consuming and computing-intensive methods. This is where the creation of two dynamical systems of the same network, one discrete and one continuous, bears fruit. Since a Boolean (step) function is a limiting case of a very steep sigmoid curve, networks made of binary elements share many qualitative features with systems modeled using continuous functions [68]. Indeed, it has been shown [19] that the qualitative information resulted from generalized logical analysis can be directly used to find the number, nature and approximate location of the steady states of a system of differential equations representing the same network. We therefore decided to use this char- acteristic to speed up the process of finding all the stable steady states in the continuous dynamical system. Specif- ically, the stable steady states of the discrete system are used as initial states to solve the differential equations, running them until the system converges to its own stable steady states. Calculating the convergence of a system of ordinary differential equations from a given initial state is a straightforward procedure using any numerical solver. Activation of a node as a function two inputs, one positive and one negative Figure 13 Activation of a node as a function two inputs, one positive and one negative. The strength of the interac- tions are equal for the activation and the inhibition, α = β = 1. xi xa total activation Theoretical Biology and Medical Modelling 2006, 3:13 http://www.tbiomed.com/content/3/1/13 Page 17 of 18 (page number not for citation purposes) For our simulations we used the lsode function of the GNU Octave package http://www.octave.org, stopping the numerical integration when all the variables of the system changed by less than 10-4 for at least 10 consecutive steps of the procedure. The final values of the variables in the system are considered to be the stable steady states of the continuous model of the network. Implementation The methodology was fully implemented in a java pro- gram, and it has been tested under a linux environment using java version 1.5.0 (JRE 5.0), as well as octave version 2.1.34. The bytecode version of the program is included as Additional file 2. Competing interests The author(s) declare that they have no competing inter- ests. Authors' contributions LM inferred the regulatory network, created the equations, developed the methods and wrote the paper. IX made a substantial contribution to the design and development of the methods, revised the intellectual content, and helped in drafting the manuscript. Additional material Acknowledgements We want to thank Massimo de Francesco, Mark Ibberson, Caroline John- son-Leger, Maria Karmirantzou, Lukasz Salwinski, François Talabot and Francisca Zanoguera for their valuable comments and suggestions. References 1. Jeong H, Tombor B, Albert R, Oltvai ZN, Barabási AL: The large- scale organization of metabolic networks. 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Annu Rev Immunol 2000, 18:451-494.	16542429	IL4 = ( ( GATA3 ) AND NOT ( STAT1 ) ) SOCS1 = ( Tbet ) OR ( STAT1 ) IFNg = ( ( STAT4 ) AND NOT ( STAT3 ) ) OR ( ( IRAK ) AND NOT ( STAT3 ) ) OR ( ( Tbet ) AND NOT ( STAT3 ) ) OR ( ( NFAT ) AND NOT ( STAT3 ) ) STAT3 = ( IL10R ) IRAK = ( IL18R ) IFNgR = ( IFNg ) STAT1 = ( IFNbR ) OR ( JAK1 ) NFAT = ( TCR ) STAT6 = ( IL4R ) IL4R = ( ( IL4 ) AND NOT ( SOCS1 ) ) GATA3 = ( ( STAT6 ) AND NOT ( Tbet ) ) OR ( ( GATA3 ) AND NOT ( Tbet ) ) JAK1 = ( ( IFNgR ) AND NOT ( SOCS1 ) ) IL12R = ( IL12 ) IL18R = ( ( IL18 ) AND NOT ( STAT6 ) ) STAT4 = ( ( IL12R ) AND NOT ( GATA3 ) ) IL10R = ( IL10 ) IFNbR = ( IFNb ) Tbet = ( ( Tbet ) AND NOT ( GATA3 ) ) OR ( ( STAT1 ) AND NOT ( GATA3 ) ) IL10 = ( GATA3 )
Emergent decision-making in biological signal transduction networks Toma´sˇ Helikar, John Konvalina†, Jack Heidel†, and Jim A. Rogers†‡ *Department of Pathology and Microbiology, University of Nebraska Medical Center, 983135 Nebraska Medical Center, Omaha, NE 68198; and †Department of Mathematics, University of Nebraska, 6001 Dodge Street, Omaha, NE 68182 Edited by Eugene V. Koonin, National Institutes of Health, Bethesda, MD, and accepted by the Editorial Board December 14, 2007 (received for review May 30, 2007) The complexity of biochemical intracellular signal transduction net- works has led to speculation that the high degree of interconnectivity that exists in these networks transforms them into an information processing network. To test this hypothesis directly, a large scale model was created with the logical mechanism of each node de- scribed completely to allow simulation and dynamical analysis. Ex- posing the network to tens of thousands of random combinations of inputs and analyzing the combined dynamics of multiple outputs revealed a robust system capable of clustering widely varying input combinations into equivalence classes of biologically relevant cellular responses. This capability was nontrivial in that the network per- formed sharp, nonfuzzy classiﬁcations even in the face of added noise, a hallmark of real-world decision-making. information processing systems biology I ntracellular signal transduction is the process by which chemical signals from outside the cell are passed through the cytoplasm to cellular systems, such as the nucleus or cytoskeleton, where appro- priate responses to those signals are generated. Unlike classical biochemical pathways (such as those involved in various metabolic activities) that are generally well understood and characterized by a degree of understandability and efficiency that can be described as elegant, signal transduction pathways are noted for their non- linear, highly interconnected nature. Stimulation of a given cell surface receptor can induce the activation of a network of tens or even hundreds of cytoplasmic proteins; these networks are not necessarily receptor-specific because different receptors, even those associated with highly differing cellular functions, often activate common sets of proteins (1–3). How differential responses are generated by these networks is not obvious nor is the reason cells evolved such a complicated mechanism for transducing signals. Thus, a full understanding of the mechanism of intracellular signal transduction remains a major challenge in cellular biology. Similarities in the structure of signal transduction networks to parallel distributed processing networks have led to speculation that signal transduction may involve more than simple passing along of signals. One hypothesis is that signal transduction pathways func- tion as an information-processing system that confers nontrivial decision-making ability (4–8). The number and variety of surface receptors indicates that cells, either as single cells or as part of multicellular organisms, likely encounter a large amount of infor- mation from their environments. Thus, surface receptors function as cellular sensory systems that bring in information that must be centralized and integrated and the proper cellular response de- cided. Decision-making in real-world cellular environments (which are often chaotic, noisy, or contradictory) is unlikely to be relatively trivial (e.g., linear feedback) but, rather, a higher-order, nontrivial decision-making function analogous to neural networks. The ability of individual cells to process information and make nontrivial decisions would have an obvious advantage in terms of adaptation but might also characterize a fundamental difference between living and nonliving systems (9, 10). Testing the hypothesis of signal transduction networks as non- trivial decision-making systems requires a systems biology approach because it is likely that the decision-making function is an emergent property of the entire system working in concert (11–13). Numer- ous studies have been performed on the static connectivity maps of signal transduction networks to compare them to other naturally occurring large-scale networks (14). The next major step to extend these results (and a crucial requirement to test explicitly for emergent functions multifamily signal transduction networks) is to study the actual dynamics of a large-scale system (15). To simulate and observe the dynamics of a system, each node’s logic (or ‘‘instruction set’’) for activation must be determined based on the activation states of all of its regulatory inputs; i.e., the complete logic of each node in the system must be taken into account. In this study, we have created a large-scale model of signal transduction consist- ing of three major receptor families; receptor tyrosine kinases (RTKs), G protein-coupled receptors (GPCR), and Integrins. Using logical instruction sets for each node derived from mecha- nistic data in the biochemical literature, we show that this signal transduction network is able to perform nontrivial pattern recog- nition, a high-level activity associated with decision-making in machine learning. Nontrivial pattern recognition involves decision- making based on input information that is not necessarily clean or clear-cut; i.e., decision-making in real-world environments. In ad- dition to the ability to classify clearly even relatively indistinct inputs, we show this pattern recognition function is robust in that it is able to perform even under high noise conditions. Together, these results are strong evidence that intracellular signal transduc- tion networks have emergent functions that are characteristic of a nontrivial decision-making system. Results and Discussion Because of the highly organized nature of the cytoplasm, the size and shape of the kinetic curves representing the in vitro interaction of two signal transduction elements may not represent the true interaction of those elements in the cell. Because of this, continu- ous, differential equation-based models are difficult to parameter- ize realistically. This is an important limitation because the dynam- ics of a continuous model depend highly on the parameter values used. In cases where the function of the system being modeled is known, it is sometimes possible to reverse-engineer the parameters necessary for a continuous model (16–18). In the present study, the emergent functions of the network are only hypothesized, therefore making the reverse-engineering of parameters impossible. To avoid the problem of parameterizing a quantitative model, a discrete Boolean model of signal transduction was created (19, 20). Author contributions: J.K., J.H., and J.A.R. designed research; T.H., J.K., and J.A.R. per- formed research; T.H., J.K., and J.A.R. contributed new reagents/analytic tools; T.H., J.K., and J.A.R. analyzed data; and J.A.R. wrote the paper. The authors declare no conﬂict of interest. This article is a PNAS Direct Submission. E.V.K. is a guest editor invited by the Editorial Board. ‡To whom correspondence should be addressed. E-mail: jrogers@unmc.edu. This article contains supporting information online at www.pnas.org/cgi/content/full/ 0705088105/DC1. © 2008 by The National Academy of Sciences of the USA www.pnas.orgcgidoi10.1073pnas.0705088105 PNAS February 12, 2008 vol. 105 no. 6 1913–1918 CELL BIOLOGY Because Boolean logic is qualitative in nature (21), there is no need to consider the parameters associated with the individual protein interactions (e.g., initial concentration, pH, etc.). The qualitative logic of cytoplasmic protein interactions is generally straightfor- ward to derive from the biochemical literature, where results are usually expressed in qualitative terms (e.g., protein x activates protein y, protein z deactivates y, etc.). Beginning with the classical epidermal growth factor receptor (EGFR) to extracellular signal- regulated kinase (Erk) pathway, all upstream interactions for each member of the pathway were determined by extensive search of the literature, and a logic table (representing an instruction set) was created for each protein node. For each node, the logic table, the literature cited, and an explanation of how the logic was determined can be viewed in an online database, which can be found at http://mathbio.unomaha.edu/Database, and further details on the modeling can be found in Materials and Methods as well as sup- porting information (SI) Text. It should be noted that no automated methods were used in the creation of the database, rather, all papers (nearly 800) were read and all pertinent information added to the database by hand. The extent of the connectivity of the network can be seen in Fig. 1. To test the model’s ability to replicate known qualitative behav- iors of the actual biological network, tests were first conducted to find the optimal input settings to do controlled experiments. This is directly analogous to optimization experiments in actual labora- tory studies (e.g., determining the optimal medium and plating conditions of a cell before performing a growth factor titration). Thus, a sample of 10,000 random inputs was applied to the network and the behavior of individual outputs was correlated with selected inputs as shown in SI Text. Based on these results, optimized conditions were determined and controlled, qualitative input– output experiments were performed by using those conditions with the input of interest varying from 0% to 100%. The results of those controlled experiments can be seen in Fig. 2 and show that many classical, input–output functional relationships in the literature are reproduced by the model. These include the classical relationships of each family of receptors and known interdependencies between those families. These results indicate that Boolean logic can be used to describe each node of a large-scale intracellular signal transduc- tion network qualitatively and the resulting model replicates many of the major known activities of the original system. With a functioning, large-scale Boolean model of intracellular signal transduction in hand, the next step was to test the hypothesis of emergent information-processing functions in the system. This was accomplished by applying a sample of 10,000 random, stress- limited input combinations and categorizing the activity of the individual output nodes by using three different ranges; 0 (0–9% ON), 1 (10–29% ON), and 2 (30–100% ON), as shown in Fig. 1. Based on these categories, the combined response of all four outputs (i.e., the global response) to a given input combination can be expressed as a ternary string of length four, with each bit representing an individual output node. These ranges were chosen because they reduce the global output space to a more manageable size (34 81 states) and because ranges of this size are at the limits of resolution of actual laboratory data commonly used (e.g., blotting). Results presented do not depend on these ranges because experiments were performed with different ranges (from three to six) with very similar results (see SI Text). These runs were performed at 2% noise (a baseline noise level described more fully below). The results of this analysis with 10,000 runs is shown in Table 1. The most striking aspect of the results shown in Table 1 is the relatively small number of global outputs. There are 34 81 possible global outputs of the system, but after 10,000 different inputs, only 38 outputs (50% of the total global output space) are observed, many at low frequency. There are only 15 outputs that Fig. 1. The Boolean model of signal transduction and method of simulation. The actual connection graph of the 130-node Boolean model is shown inside the cell. The inputs are external to the cell and the outputs are nodes that are part of the network and thus inside the cell. The four nonstress output nodes were selected on the basis of their role in regulating other major cellular functions, as indicated. The stress outputs are the two stress-activated protein kinases SAPK and p38. As a demonstration of how simulations are performed, four random inputs are applied to the network, indicated as runs 1–4. These inputs are stress-limited because the stress inputs are limited to values be- tween 0% and 5% ON, whereas the nonstress inputs are random values between 0% and 100% ON. After the application of each of the inputs, the network is iterated until it reaches a cycle, and the percentage ON of each output is calculated. This results in four corresponding individual outputs, shown at the bottom. The global outputs are the combination of all four individual outputs and are represented by conversion to a ternary string (shown on the bottom right) based on the ranges described in the text. Fig. 2. Qualitative, individual input–output relationships in the Boolean model of signal transduction. (A) Positive relationship between EGF and Akt (25). (B) Positive relationship between EGF and Erk (34). (C) EGF dependence on Integrin stimulation by extracellular matrix (ECM) proteins for Erk stimu- lation (27). (D) Low-level stimulation of Erk by high levels of ECM (36). (E) Hormonal stimulators (alphaslig) of G-associated GPCR activation of adenyl- ate cyclase (AC) (37, 38). (F) GPCR activation of Erk. (39) (G) GPCR stimulation of Erk depends on transactivation of the EGFR (40). (H and I) Activation of the stress-associated MAPK’s SAPK and p38 by stress (33, 34). (J and K) Activation of Rac and Cdc42 by ECM (28). (L) Activating mutations of known protoon- cogenes such as Ras result in growth factor-independent activation of Erk (41). Note that the references refer to classical, qualitative input–output relation- ships (not necessarily quantitative dose–response curves), and the dose– response curves presented here are intended to demonstrate how the Bool- ean model qualitatively reproduces the referenced input– output relationships over a range of inputs. 1914 www.pnas.orgcgidoi10.1073pnas.0705088105 Helikar et al. appear 100 times (19% of the total output space), and they account for 9,389 (94%) of the runs. This result is even more dramatic when the global outputs are categorized by using six different ranges; 0–10%, 11–20%, 21–30%, 31–40%, 41–50%, and 50%. With these six ranges, the size of the output space is 64 1,296 states, yet there are only 24 outputs (1.9%) that occur 100 times, accounting for 8,597 (86%) of the inputs run (SI Table 5). The average degree (K) of the current network is 4.4, and the average bias (P) is 69.8%. Although these parameters are predictive of relatively chaotic behavior in autonomous Boolean networks (22), the ordered behavior seen in the relatively small number of global responses may be a reflection of the high proportion of nodes (73.8%) with canalyzing inputs (23). The current network is not autonomous, so interpretation of K, P, and the effects of canalyzing inputs on network behavior may be different from the effects on the random, autonomous networks in which these parameters have been studied (21, 23). However, the fact that the network maps the wide ranging global inputs to a relatively small number of global responses indicates that the current system has a small number of attractors with large basins of attraction, which is consistent with results with autonomous networks with the similar connection parameters (21, 23). The second prominent feature of the results is the biological significance of both the global and individual outputs observed. From the global output prospective, the output states 0000, 1000, and 2000 are prominently represented because those outputs were associated with 3,967 of the 10,000 random inputs. The outputs 1000 and 2000 represent quiescent states in which the outputs are inactive, with the exception of Akt, a protein that must remain active to suppress apoptosis (24). The state 0000 would be associ- ated with apoptosis because Akt activity is very low. Looking at the individual qualitative input–output relationships within these three prominent global outputs, it can be seen that they are characterized by low levels of extracellular matrix (ECM) and increasing levels of EGF. This is consistent with the responsiveness of Akt activity to EGF signaling found in the literature (25, 26) and consistent with the input–output relationship of Akt and EGF presented in Fig. 2. Despite the fact that EGF increases to high levels in the 2000 output, Erk activity does not increase. As expected from the known dependence of EGF on ECM/Integrin stimulation (27), ECM levels associated with these outputs is low, and Erk activity appears in the Table 1. Outputs of the network and their average associated inputs Global output (ternary) Count Average input Average output ECM EGF ExtPump qlig ilig slig 1213lig IL1TNF Stress Akt Erk Cdc42 Rac 1000 2,346 26 26 54 49 48 50 49 2 2 19 3 2 1 2000 1,488 24 67 39 51 49 50 52 1 2 42 4 2 1 1011 952 79 21 55 49 51 50 52 2 2 19 4 19 16 2100 851 31 80 43 51 44 49 50 3 2 49 14 3 1 2110 833 58 78 45 50 53 50 48 2 2 47 15 17 5 2111 626 85 65 28 50 52 50 52 2 2 42 15 21 13 1010 463 50 34 70 46 57 50 44 2 2 21 4 15 5 2010 429 54 70 53 49 54 52 49 1 2 42 5 15 4 2121 361 89 71 55 49 57 47 42 2 2 42 17 37 14 1021 278 87 29 76 48 59 49 45 2 1 19 5 36 20 2011 232 80 46 29 51 55 50 55 1 2 35 6 19 14 1001 149 72 17 40 49 27 55 53 2 2 18 3 5 13 2120 136 69 85 74 48 56 50 38 2 2 52 18 37 6 0000 133 29 12 70 47 9 48 47 2 2 6 2 0 2 1111 112 82 34 48 53 48 54 51 4 2 24 11 21 16 1121 87 89 41 71 51 56 42 41 3 1 23 11 39 19 2021 78 87 61 63 46 63 57 49 1 1 38 6 36 14 1110 71 55 46 64 49 49 48 46 4 2 24 11 17 6 1100 58 35 50 57 51 39 52 46 4 2 25 10 4 2 2020 36 72 79 90 55 58 43 42 0 2 46 5 38 6 0011 30 80 13 90 53 16 52 47 1 2 7 2 18 18 1022 28 98 9 70 52 66 49 46 2 2 16 4 39 31 2200 26 26 97 77 47 26 52 45 4 2 68 37 1 0 2221 25 90 82 47 53 65 27 30 4 1 51 32 46 13 0001 25 79 14 73 54 2 54 45 2 3 6 2 4 14 2001 21 76 52 18 54 36 65 61 1 2 36 6 7 11 2101 20 82 73 22 53 28 40 51 3 2 45 13 6 11 2210 18 62 95 72 64 43 53 37 4 2 62 33 18 4 2220 17 74 95 75 50 53 52 41 4 2 61 33 43 6 1020 14 58 44 91 39 62 45 24 1 2 20 4 34 7 1012 13 98 5 49 46 62 37 51 1 2 18 3 26 30 2211 12 86 84 31 55 36 43 58 4 3 53 31 24 12 0010 10 48 8 90 62 17 47 52 2 2 7 2 12 6 1101 10 78 38 41 42 7 44 58 4 2 22 10 6 12 1120 4 61 56 85 55 50 34 5 4 1 26 14 40 6 0021 3 81 17 97 41 30 68 48 2 0 8 3 34 20 1122 3 96 6 47 53 85 74 21 3 1 21 13 48 31 0022 2 92 3 98 28 15 35 31 2 0 9 2 35 31 qlig, ilig, slig, and 1213lig are abbreviations for generic ligands for the respective G subunit of GPCR. Other abbreviations are as in the text. Standard deviations were calculated but are not shown for clarity because the variance can be observed directly in the scatter plots in Fig. 3 and SI Fig. 5. Helikar et al. PNAS February 12, 2008 vol. 105 no. 6 1915 CELL BIOLOGY global outputs only when input levels of both ECM and EGF are high. Similarly, global outputs with increased Cdc42 and Rac activity correlate strongly with high levels of ECM; both Rac and Cdc42 are classically associated with cytoskeletal regulation in response to ECM (28). As a control, the network was randomly ‘‘rewired’’ 100 times, i.e., the inputs to each node were randomized while preserving the in- and out-degrees as well as the logical table of the individual nodes. The complementary control was also performed 100 times, i.e., the graph of the network was held constant while the logic was randomized. In both controls, the number of outputs diminished to a trivial number of outputs (an average effective number of 1.92 and 1.04, respectively), with no biological significance in the correlation of input and output (see SI Text). This indicates that both the graph and the logic are important for the variety and biological significance of the outputs. The facts that the individual qualitative input–output relation- ships from Fig. 2 are present in Table 1 and that the global outputs are biologically relevant support the validity of characterizing ranges of output activity. However, the real power of this analysis is the ability to observe how the system clusters combinations of inputs and then maps them to the global outputs. To visualize this mapping at a more detailed level, all 9,389 input vectors associated with the 15 most frequent global outputs were subjected to principal component analysis (PCA) (29). In the resulting plot, shown in Fig. 3A, each point (representing an individual input combination) is colored according to the ternary output string with which it was associated. It shows all 9,389 inputs together, and the different colors appear to separate into discrete clusters. To confirm this, the plots in Fig. 3B show several combinations of different colors to indicate the degree of overlap of inputs associated with the most common global outputs. The results show that when the random input vectors are plotted in three-dimensional space based on their values, they form a random scatter as expected. But when each vector in that scatter plot is colored based on the global output with which it is associated, all of the input vectors associated with a particular output are not randomly scattered but, rather, clustered in distinct areas with little overlap with inputs associated with other outputs. Thus, this signal transduction system clusters neighbor- hoods of input combinations into equivalence classes of global outputs; i.e., all input combinations of the same color are consid- ered to be functionally equivalent because they elicit the same global output response. The 100 randomly rewired and random logic control networks were also tested for separation and in rewired networks where there was more than one output to test, the number of outputs that demonstrated clustering of inputs was greatly reduced and separation in the random logic networks was eliminated. The details of PCA, how it was applied to the network, statistical analysis, results with the rewired controls, and further Fig. 3. Scatter plots of all input vectors associated with the ﬁrst 15 global outputs of Table 1. (A) The inputs associated with the 15 most common outputs are plotted in three dimensions by using principle component analysis (PCA, see Ma- terials and Methods). All 9,389 in- puts plotted together, with each in- put colored according to which of the 15 outputs it is associated. It appears that all inputs associated with a given output (indicated by the color) are clustered. (B) To verify that the model uniquely clusters in- puts based on associated outputs, selected colored clusters in A are plotted on separate axes so the sep- aration of each cluster is visible. For example, the 2,346 input values as- sociated with the output 1000 (shown as black points) are clus- tered with little overlap with input values associated with outputs 2000 and 1011, as shown in the ﬁrst plot. Taken together, these results show that the Boolean signal transduc- tion model divides the input space into distinct equivalence classes that are associated with biologically appropriate global outputs. 1916 www.pnas.orgcgidoi10.1073pnas.0705088105 Helikar et al. discussion of the biological relevance of these results can be found in Materials and Methods and SI Text. The results presented show that this signal transduction network model is capable of taking a wide array of random hormonal input combinations and classify them into a relatively small number of biologically appropriate, sharply defined equivalence classes of global responses. This function can, by definition, be called pattern recognition, a concept used in machine learning and neural net- works (30, 31). The ability to recognize input patterns and classify them is a decision-making function that is a form of information processing. It involves dividing a multidimensional space into associated classes, the boundaries of which must be carefully determined to recognize inputs correctly based on their class association (30). The practical effect of this type of processing is that the very large number of combinations of possible hormonal inputs to which a cell may be exposed (many of which are relatively indistinct) are clustered by the signal transduction network accord- ing to the much smaller number of global cellular responses that are possible for a cell to make to each input. Thus, this network is able to make decisions even in the face of less than clear-cut environmental cues that are common in realistic environments. To determine the robustness of signal transduction decision- making, the above experiments were carried out with different noise levels. For example, if in a given run, an input such as EGF is set to 50% ON, no added noise would mean that the node is a exactly 50% throughout the entire run. Adding 2% noise to a 50% value would mean that the input varied chaotically between 48% and 52% with an average of 50%. Five percent noise for that input would result in the input varying chaotically between 45% and 55%, and so on. In the above simulations, noise was added at what was considered to be a normal background level of 2%. The results of testing of other noise levels of up to 20% can be seen in SI Tables 7–9. It is clear that the pattern recognition ability of the network in terms of global responses is nearly unaffected by even high levels of noise. This surprising level of stability was verified by repeating the individual input–output relationships of Fig. 2 with varying levels of noise. Even at high levels of noise, the input–output relations remained intact (data shown SI Fig. 6), confirming the ability of the system to recognize patterns in even very noisy inputs. It has long been noticed that complex, interconnected pathways of biochemical signal transduction networks bear a resemblance to parallel, distributed computer networks. This led to conjecture by some that the overwhelming complexity of these networks might not be an accident of evolution but, rather, a key characteristic of a finely tuned information-processing system that is able to make nontrivial decisions (5, 6, 31, 32). To test this hypothesis directly, we have created a large-scale, literature-based, logically complete model of a multifamily signal transduction network. The model was then exposed to tens of thousands of different combinations of environmental stimuli, and the global responses (i.e., combinations of multiple outputs) were observed. The reason for this approach was to look for emergent properties of the system by moving beyond the exploration of the important and now well established dynamics of specific, individual stimulus–response relationships (e.g., bist- ability) and consider the higher-level relationships between multi- ple stimuli and the corresponding global responses. This is the essence of the systems approach. The results clearly show that the network clustered the vast majority of inputs into a small number of biologically appropriate responses. This nonfuzzy partitioning of a space of random, noisy, chaotic inputs into a small number of equivalence classes is a hallmark of a pattern recognition machine and is strong evidence that signal transduction networks are decision-making systems that process information obtained at the membrane rather than simply passing unmodified signals downstream. Designing systems to perform sophisticated pattern recognition is not a trivial task. Handwriting and face recognition are examples of real-world, sophisticated pattern recognition where noisy inputs must be correctly placed into a nonfuzzy, sharply defined equiva- lence class (e.g., individual handwriting classified as a particular character or an individual face recognized as an acquaintance); a major goal of artificial intelligence research is to develop machines that are capable of such tasks (30, 31). It should not be surprising that cells would require a similar ability to perform sophisticated pattern recognition. An individual cell is faced with any number of stimuli in the form of chemical ligands binding to their cell-surface receptors. These receptors are varied in type and number and form a sensory system that enables a cell to sense and respond to its environment. Given that any physical environment is chaotic, noisy, and, at times, contradictory, it is clear that cells need the ability to make decisions based on these types of inputs and that their survival depends on that ability. Finally, the results presented here use literature-based, Boolean modeling of a large-scale biochemical system. All modeling meth- ods have their downsides, and in the case of Boolean models it is that the logic of each node must be expressed in terms of ON/OFF. This seems counterintuitive to many biologists because it is known that many signal transduction components do not have such simple regulation. In reality, this is not a major obstacle to Boolean modeling because proteins that exhibit more complex regulation can be represented by multiple nodes, each representing a separate activation state of the protein of interest (e.g., Raf in our network). The only real downside to Boolean modeling of biochemical systems is that, for any node with a large number of inputs (N), there are 2N combinations of those inputs that must be accounted for in each logic table. For most input combinations the ON/OFF state of the protein can be derived from the literature in a straightforward way. However, some combinations are not explicitly dealt with in the literature and must be deduced indirectly. For this reason, we do not consider the current network to be perfect. However, this problem is not unsolvable; it only requires laboratory researchers to test qualitatively the input combinations that are unknown. This can be done exactly as the known combinations were determined, thus requiring only an awareness for the need for this information rather than entirely new laboratory methods. Additionally, our develop- ment of tools that are able to input and retrieve continuous data to and from the Boolean model means that the only aspect of the model that is actually ON/OFF is the logic tables for each individual node; once the logic is set, the model is used in the same way as continuous models. Continuous modeling, on the other hand, has the significant problem of parameter estimation. Although there are also ways of dealing with this problem, determination of the large number of parameters of a large-scale network in vivo is a much more complicated technical hurdle. All modeling methods also have upsides, and the parameter-free nature of Boolean modeling is a significant advantage, making it complementary to continuous models used for exploring higher-order functions and emergent properties of biological signal transduction networks. Materials and Methods The Boolean Model of Signal Transduction. To create a Boolean network, a set of nodes must be identiﬁed and a logic table created for each node. The current Boolean model of signal transduction was created by determining the complete logic of the classical EGFR 3 Erk pathway. More detail on how the logic tables were created for each node (as well as how it is possible to use Boolean modeling for proteins that have more complex activation than simple ON/OFF) can be found in SI Text. As guided by the literature, connections to other classical pathways were included in the EGFR 3 Erk pathway until a relatively autono- mous network of 130 nodes was created that included the RTK, GPCR, and Integrin pathways. Given the highly interconnected nature of cytoplasmic pro- tein networks, stopping at even 130 nodes meant that some interactions with proteins outside these three families had to be ignored. However, these were relatively minor compared with the interactions of the three incorporated path- ways; these pathways are so intimately connected that they represent a func- tioningsetofnodesthatwouldbeimpossibletoreducefurtherwithoutignoring important interactions. Although the model is a nonspeciﬁc network in that it Helikar et al. PNAS February 12, 2008 vol. 105 no. 6 1917 CELL BIOLOGY does not represent any one speciﬁc cell type, nodes were not included in the network unless they were generally expressed in a wide range of cell types. However, once a node was included in the network, the best information on the logic was used without regard to the cell type. Inputs to the network are mostly the ligands of surface receptor nodes of which there are seven; epidermal growth factor (EGF), the GPCR stimulators (qlig, ilig, slig, i12/13lig), extracellular matrix (ECM), tumor necrosis fac- tor/interleukin 1 (TNF/IL-1) an idealized hybrid receptor. In addition to those ligands, ‘‘Stress’’ is an input representing environmental stress factors such as UV light or reactive oxygen species (33, 34), and there is a nonregulated calcium pump (external calcium pump). Calcium pumps are regulated mostly by calcium and hormonal factors that are not included in the current network (35). The logic for calcium regulation in the network inherently includes the calcium regulation of the pump, but the other regulators cannot be accounted for. Therefore, the calcium pump is considered to be an input and is set at multiple constant levels of activity. Outputs of the network are nodes in the network whose outputs go out to regulators of major cellular functions. These are (i) Akt, a major regulator of apoptotic systems (24), (ii) the mitogen-activated protein kinase (MAPK) Erk, a major regulator of cell division (34), and (iii) Rac and Cdc42, two important regulatorsofcytoskeletalsystems(28).TheMAPK’sSAPKandp38arealsooutputs of the network, but they respond to stress and TNF/IL-1 (33, 34), as documented in SI Text. The experiments in the present work involve ‘‘stress-limited’’ inputs, meaning that stress and TNF/IL-1 are at low, background levels. Other nodes can be considered to be outputs of the network, and experiments with up to seven different outputs were performed with very similar results. Methods of Simulation. Although the logic of each node and input to the networkisbinary,itispossibletointerpretintermediateactivitybylookingatthe average ON value of each node when the system has reached a cycle, as all Boolean models must do. Similarly, inputs can be set to a speciﬁc average ON by putting the input on an appropriate cycle (for further details on this, see SI Text). The actual simulations are performed by a Boolean simulation program de- veloped by this group called ChemChains. ChemChains is a general Boolean networksimulatorthatisabletoincorporateanynumberofnodesandtheirlogic tables as well as any initial condition or input conditions and iterate the network any desired number of times. The ChemChains program can be freely obtained from J.A.R. Adding Noise to the Inputs. Experiments are performed at different noise levels by introducing a random noise component to the input that forces the input to vary chaotically within a window around the set input level. The window sizes vary from 2% to 20%, representing background noise to highly noisy inputs. In these studies, all noise levels are tested and 2% noise is considered the standard background levels. Noise was added to the inputs by adding or subtracting from each input set point a percentage of the desired range. The percentage varied randomlywithinthespeciﬁedrangebyusingarandomnumbergeneratorwithin the ChemChains program. Principal Component Analysis (PCA). PCA was done on all seven inputs and projected onto three dimensions (accounting for 45% of variance of the system) as shown in SI Fig. 5, where a more detailed explanation of PCA and the statistical analysis of the results can be found. To capture more of the variance, various numbers of inputs were tested and it was found that most of the pattern recognition function could be observed by performing PCA on ECM, EGFR, and the external calcium pump inputs and projecting onto three dimensions. This accounts for 100% of the variance and makes the clustering of inputs the most clearly visible. These results are shown in Fig. 3; however, they are not funda- mentally different from the original seven-input PCA shown in SI Fig. 5. 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Mol Cancer Ther 4:677–685. 1918 www.pnas.orgcgidoi10.1073pnas.0705088105 Helikar et al.	18250321	PTP1b = ( NOT ( ( EGFR AND ( ( ( EGF ) ) ) ) OR ( Stress ) ) ) OR NOT ( EGFR OR EGF OR Stress ) Csk = ( Cbp AND ( ( ( Gbg_i OR PKA OR Gbg_1213 OR Gbg_q ) ) OR ( ( NOT Gbg_i AND NOT PKA AND NOT SHP2 AND NOT Gbg_1213 AND NOT Gbg_q ) ) ) ) OR ( ( Fak AND ( ( ( Src AND Cbp ) ) ) ) AND NOT ( SHP2 ) ) PI3K = ( Gbg_i ) OR ( Gab1 ) OR ( Fak ) OR ( Ras ) OR ( Crk ) OR ( EGFR AND ( ( ( Src ) ) ) ) PIP_4 = ( ( ( PTEN AND ( ( ( NOT PIP_4 ) ) AND ( ( PIP2_34 ) ) ) ) AND NOT ( PI5K AND ( ( ( PIP_4 ) ) ) ) ) AND NOT ( PI3K AND ( ( ( PIP_4 ) ) ) ) ) OR ( ( ( PIP_4 AND ( ( ( NOT PI3K ) ) AND ( ( NOT PI5K ) ) ) ) AND NOT ( PI5K AND ( ( ( PIP_4 ) ) ) ) ) AND NOT ( PI3K AND ( ( ( PIP_4 ) ) ) ) ) OR ( ( ( PI4K AND ( ( ( NOT PIP_4 ) ) ) ) AND NOT ( PI5K AND ( ( ( PIP_4 ) ) ) ) ) AND NOT ( PI3K AND ( ( ( PIP_4 ) ) ) ) ) Talin = ( PIP2_45 AND ( ( ( NOT Talin ) ) ) ) OR ( Talin AND ( ( ( NOT Src ) ) ) ) Gbg_s = ( Gas ) OR ( alpha_sR AND ( ( ( NOT Gbg_s ) ) AND ( ( NOT Gas ) ) ) ) TAO_12 = ( Stress ) Mekk3 = ( ( Trafs ) AND NOT ( Gab1 ) ) OR ( ( IL1_TNFR ) AND NOT ( Gab1 ) ) OR ( ( Rac ) AND NOT ( Gab1 ) ) MKPs = ( p38 AND ( ( ( cAMP ) ) ) ) OR ( SAPK AND ( ( ( cAMP ) ) ) ) OR ( Erk AND ( ( ( cAMP ) ) ) ) Tab_12 = ( ( Trafs ) AND NOT ( p38 ) ) Gas = ( alpha_sR AND ( ( ( NOT Gas ) ) AND ( ( NOT PKA ) ) AND ( ( NOT Gbg_s ) ) ) ) OR ( Gbg_s AND ( ( ( Gas ) ) AND ( ( NOT RGS ) ) ) ) p38 = ( ( ( MKK6 ) AND NOT ( PP2A ) ) AND NOT ( MKPs ) ) OR ( ( ( MKK3 ) AND NOT ( PP2A ) ) AND NOT ( MKPs ) ) OR ( ( ( Sek1 ) AND NOT ( PP2A ) ) AND NOT ( MKPs ) ) Rho = ( Rho AND ( ( ( NOT PKA AND NOT p190RhoGAP AND NOT Graf ) ) ) ) OR ( p115RhoGEF AND ( ( ( NOT Rho AND NOT RhoGDI ) ) ) ) PP2A = ( NOT ( ( EGFR ) ) ) OR NOT ( EGFR ) Gab1 = ( ( Gab1 AND ( ( ( EGFR AND PIP3_345 ) ) ) ) AND NOT ( SHP2 ) ) OR ( ( Grb2 AND ( ( ( EGFR ) AND ( ( ( NOT Gab1 ) ) ) ) ) ) AND NOT ( SHP2 ) ) PIP2_34 = ( PIP2_34 AND ( ( ( NOT PTEN ) ) AND ( ( NOT PI5K ) ) ) ) OR ( PI4K AND ( ( ( NOT PIP2_34 ) ) AND ( ( PI3K ) ) ) ) PIP3_345 = ( ( PI3K AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( PTEN AND ( ( ( PIP3_345 ) ) ) ) ) OR ( ( PI5K AND ( ( ( PIP2_34 ) ) ) ) AND NOT ( PTEN AND ( ( ( PIP3_345 ) ) ) ) ) Vinc = ( Actin AND ( ( ( NOT PIP2_45 ) ) AND ( ( Vinc AND Talin ) ) ) ) OR ( Talin AND ( ( ( Src ) ) ) ) IP3R1 = ( ( ( ( Gbg_i ) AND NOT ( CaM AND ( ( ( Ca ) ) AND ( ( IP3R1 ) ) ) ) ) AND NOT ( IP3R1 AND ( ( ( Gbg_i AND CaM ) ) AND ( ( NOT PP2A AND NOT PKA AND NOT IP3 AND NOT Ca ) ) ) ) ) AND NOT ( Ca AND ( ( ( NOT IP3 ) ) AND ( ( IP3R1 ) ) ) ) ) OR ( ( ( IP3 AND ( ( ( Ca ) ) ) ) AND NOT ( CaM AND ( ( ( Ca ) ) AND ( ( IP3R1 ) ) ) ) ) AND NOT ( Ca AND ( ( ( NOT IP3 ) ) AND ( ( IP3R1 ) ) ) ) ) OR ( ( ( ( PKA ) AND NOT ( CaM AND ( ( ( Ca ) ) AND ( ( IP3R1 ) ) ) ) ) AND NOT ( Ca AND ( ( ( NOT IP3 ) ) AND ( ( IP3R1 ) ) ) ) ) AND NOT ( PP2A AND ( ( ( IP3R1 ) ) ) ) ) PTEN = ( ( Stress ) AND NOT ( Src AND ( ( ( PTEN ) ) ) ) ) OR ( ( Pix_Cool AND ( ( ( Cdc42 ) ) AND ( ( PI3K ) ) AND ( ( Rho ) ) ) ) AND NOT ( Src AND ( ( ( PTEN ) ) ) ) ) ASK1 = ( Trx ) AA = ( PLA2 ) PKC = ( ( AA AND ( ( ( Ca ) ) AND ( ( PKC_primed ) ) ) ) AND NOT ( Trx AND ( ( ( PKC ) ) ) ) ) OR ( ( PKC AND ( ( ( NOT PP2A ) ) AND ( ( NOT Trx ) ) ) ) AND NOT ( Trx AND ( ( ( PKC ) ) ) ) ) OR ( ( DAG AND ( ( ( Ca ) ) AND ( ( PKC_primed ) ) ) ) AND NOT ( Trx AND ( ( ( PKC ) ) ) ) ) Arp_23 = ( WASP ) Gai = ( Gbg_i AND ( ( ( Gai ) ) AND ( ( NOT RGS ) ) ) ) OR ( alpha_iR AND ( ( ( NOT Gbg_i AND NOT Gai ) ) ) ) OR ( PKA AND ( ( ( NOT Gai ) ) AND ( ( NOT Gbg_i ) ) AND ( ( NOT alpha_sR ) ) AND ( ( alpha_sL ) ) ) ) Cas = ( ( Src AND ( ( ( Fak ) ) ) ) AND NOT ( PTPPEST AND ( ( ( Cas ) ) ) ) ) ILK = ( PIP3_345 ) IP3 = ( PLC_B AND ( ( ( PIP2_45 ) ) ) ) OR ( PLC_g AND ( ( ( PIP2_45 ) ) ) ) PLA2 = ( PIP3_345 AND ( ( ( PIP2_45 ) ) AND ( ( CaMK ) ) ) ) OR ( PIP2_45 AND ( ( ( Erk ) ) AND ( ( PIP3_345 ) ) ) ) OR ( CaMK AND ( ( ( Ca ) ) ) ) OR ( Erk AND ( ( ( Ca ) ) ) ) alpha_1213R = ( ( alpha_1213L ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_1213R AND NOT alpha_1213L AND NOT alpha_1213R ) ) OR ( ( Palpha_1213R ) ) ) ) ) OR ( ( Palpha_1213R AND ( ( ( NOT B_Arrestin ) ) ) ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_1213R AND NOT alpha_1213L AND NOT alpha_1213R ) ) OR ( ( Palpha_1213R ) ) ) ) ) OR ( ( alpha_1213R ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_1213R AND NOT alpha_1213L AND NOT alpha_1213R ) ) OR ( ( Palpha_1213R ) ) ) ) ) PI5K = ( PA ) OR ( PI5K AND ( ( ( Talin ) ) ) ) OR ( RhoK ) OR ( Src AND ( ( ( Fak ) ) AND ( ( NOT PI5K ) ) AND ( ( NOT Talin ) ) ) ) OR ( ARF ) Sos = ( ( Grb2 AND ( ( ( PIP3_345 ) ) ) ) AND NOT ( Erk ) ) OR ( Nck AND ( ( ( Crk ) ) AND ( ( PIP3_345 ) ) ) ) PIP2_45 = ( PTEN AND ( ( ( PIP3_345 ) ) ) ) OR ( PI4K AND ( ( ( PI5K ) ) ) ) OR ( PIP2_45 ) Trx = ( Stress ) OR ( Trafs ) GRK = ( ( ( Gbg_i AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( Erk ) ) AND NOT ( RKIP ) ) OR ( ( ( Gbg_q AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( Erk ) ) AND NOT ( RKIP ) ) OR ( ( ( B_Arrestin AND ( ( ( Src ) ) ) ) AND NOT ( Erk ) ) AND NOT ( RKIP ) ) OR ( ( ( Gbg_1213 AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( Erk ) ) AND NOT ( RKIP ) ) OR ( ( ( Gbg_s AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( Erk ) ) AND NOT ( RKIP ) ) p190RhoGAP = ( Src AND ( ( ( NOT p190RhoGAP ) ) OR ( ( Fak ) ) OR ( ( NOT p120RasGAP ) ) ) ) OR ( Fak AND ( ( ( Src ) ) ) ) Myosin = ( ( ILK AND ( ( ( NOT MLCP ) ) OR ( ( NOT Myosin ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) OR ( ( MLCK AND ( ( ( NOT MLCP ) ) AND ( ( CaM ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) OR ( ( PAK AND ( ( ( NOT MLCP ) ) OR ( ( NOT Myosin ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) OR ( ( RhoK AND ( ( ( NOT MLCP ) ) OR ( ( NOT Myosin ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) OR ( ( CaM AND ( ( ( NOT Myosin ) ) AND ( ( MLCK ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) OR ( ( Myosin AND ( ( ( NOT MLCP ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) alpha_qR = ( ( alpha_qL ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_iR AND NOT alpha_qL AND NOT alpha_qR ) ) OR ( ( Palpha_iR ) ) ) ) ) OR ( ( Palpha_iR AND ( ( ( NOT B_Arrestin ) ) ) ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_iR AND NOT alpha_qL AND NOT alpha_qR ) ) OR ( ( Palpha_iR ) ) ) ) ) OR ( ( alpha_qR ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_iR AND NOT alpha_qL AND NOT alpha_qR ) ) OR ( ( Palpha_iR ) ) ) ) ) IL1_TNFR = ( IL1_TNF ) Tiam = ( Src AND ( ( ( Rap1 OR Ras OR PIP2_45 ) ) AND ( ( PIP3_345 OR PIP2_34 ) ) ) ) OR ( PKC AND ( ( ( PIP3_345 OR PIP2_34 ) ) AND ( ( Rap1 OR Ras OR PIP2_45 ) ) ) ) OR ( CaMK AND ( ( ( Rap1 OR Ras OR PIP2_45 ) ) AND ( ( PIP3_345 OR PIP2_34 ) ) ) ) NIK = ( TAK1 ) OR ( Nck ) Cdc42 = ( ( Cdc42 AND ( ( ( Pix_Cool ) ) AND ( ( NOT RhoGDI ) ) ) ) AND NOT ( RhoGDI AND ( ( ( Src ) ) ) ) ) OR ( ( Pix_Cool AND ( ( ( NOT Cdc42 AND NOT Rac ) ) AND ( ( PAK AND Gbg_i ) ) ) ) AND NOT ( RhoGDI AND ( ( ( Src ) ) ) ) ) PAK = ( ( ( Src AND ( ( ( PAK ) AND ( ( ( Cdc42 OR Rac ) ) ) ) ) ) AND NOT ( PKA ) ) AND NOT ( PTP1b ) ) OR ( ( Rac AND ( ( ( Grb2 ) ) OR ( ( Nck ) AND ( ( ( NOT Akt ) ) ) ) ) ) AND NOT ( PKA ) ) OR ( ( Cdc42 AND ( ( ( Nck ) AND ( ( ( NOT Akt ) ) ) ) OR ( ( Grb2 ) ) ) ) AND NOT ( PKA ) ) Rap1 = ( CaMK AND ( ( ( NOT Gai OR NOT Rap1 ) ) AND ( ( Src AND cAMP ) ) ) ) OR ( PKA AND ( ( ( NOT Gai OR NOT Rap1 ) ) AND ( ( Src AND cAMP ) ) ) ) p120RasGAP = ( ( ( PIP3_345 ) AND NOT ( Src ) ) AND NOT ( Fak ) ) OR ( ( ( Ca ) AND NOT ( Src ) ) AND NOT ( Fak ) ) OR ( ( ( PIP2_34 ) AND NOT ( Src ) ) AND NOT ( Fak ) ) OR ( ( ( PIP2_45 ) AND NOT ( Src ) ) AND NOT ( Fak ) ) OR ( ( ( ( EGFR ) AND NOT ( SHP2 ) ) AND NOT ( Src ) ) AND NOT ( Fak ) ) p115RhoGEF = ( Ga_1213 AND ( ( ( PIP3_345 ) ) ) ) Ral = ( CaM ) OR ( RalGDS ) OR ( AND_34 ) Graf = ( Fak AND ( ( ( Src ) ) ) ) GCK = ( Trafs ) alpha_sR = ( ( alpha_sR ) AND NOT ( B_Arrestin AND ( ( ( Palpha_sR ) ) OR ( ( NOT alpha_sR AND NOT Palpha_sR AND NOT alpha_sL ) ) ) ) ) OR ( ( alpha_sL ) AND NOT ( B_Arrestin AND ( ( ( Palpha_sR ) ) OR ( ( NOT alpha_sR AND NOT Palpha_sR AND NOT alpha_sL ) ) ) ) ) OR ( ( Palpha_sR AND ( ( ( NOT B_Arrestin ) ) ) ) AND NOT ( B_Arrestin AND ( ( ( Palpha_sR ) ) OR ( ( NOT alpha_sR AND NOT Palpha_sR AND NOT alpha_sL ) ) ) ) ) PI4K = ( Rho ) OR ( PKC ) OR ( ARF ) OR ( Gai ) OR ( Gaq ) Gbg_q = ( Gaq ) OR ( alpha_qR AND ( ( ( NOT Gaq ) ) AND ( ( NOT Gbg_q ) ) ) ) Ca = ( ( IP3R1 ) AND NOT ( ExtPump ) ) Trafs = ( IL1_TNFR ) Raf_Loc = ( Raf_Loc AND ( ( ( NOT Raf ) ) ) ) OR ( Ras AND ( ( ( Raf_DeP ) ) AND ( ( NOT Raf_Loc ) ) ) ) SHP2 = ( Gab1 ) Actin = ( Arp_23 AND ( ( ( Myosin ) ) ) ) Gaq = ( Gaq AND ( ( ( Gbg_q ) ) AND ( ( NOT RGS AND NOT PLC_B ) ) ) ) OR ( alpha_qR AND ( ( ( NOT Gaq ) AND ( ( ( NOT Gbg_q ) ) ) ) ) ) alpha_iR = ( ( alpha_iL ) AND NOT ( B_Arrestin AND ( ( ( Palpha_iR ) ) OR ( ( NOT alpha_iL AND NOT Palpha_iR AND NOT alpha_iR ) ) ) ) ) OR ( ( Palpha_iR AND ( ( ( NOT B_Arrestin ) ) ) ) AND NOT ( B_Arrestin AND ( ( ( Palpha_iR ) ) OR ( ( NOT alpha_iL AND NOT Palpha_iR AND NOT alpha_iR ) ) ) ) ) OR ( ( alpha_iR ) AND NOT ( B_Arrestin AND ( ( ( Palpha_iR ) ) OR ( ( NOT alpha_iL AND NOT Palpha_iR AND NOT alpha_iR ) ) ) ) ) Mekk4 = ( Cdc42 ) OR ( Rac ) B_Parvin = ( ILK ) MKK6 = ( Mekk4 AND ( ( ( ASK1 ) ) ) ) OR ( MLK3 AND ( ( ( ASK1 ) ) ) ) OR ( PAK AND ( ( ( ASK1 ) ) ) ) OR ( TAK1 AND ( ( ( ASK1 ) ) ) ) OR ( Tpl2 AND ( ( ( ASK1 ) ) ) ) OR ( TAO_12 AND ( ( ( ASK1 ) ) ) ) Palpha_iR = ( alpha_iR AND ( ( ( GRK ) ) ) ) PLD = ( Rho AND ( ( ( Actin ) AND ( ( ( PIP2_45 ) ) OR ( ( PIP3_345 ) ) ) ) AND ( ( NOT ARF ) ) ) ) OR ( PKC AND ( ( ( Actin ) AND ( ( ( PIP3_345 ) ) OR ( ( PIP2_45 ) ) ) ) AND ( ( NOT ARF ) ) ) ) OR ( ARF AND ( ( ( PIP2_45 ) ) OR ( ( PIP3_345 ) ) ) ) OR ( Rac AND ( ( ( NOT ARF ) ) AND ( ( Actin ) AND ( ( ( PIP2_45 ) ) OR ( ( PIP3_345 ) ) ) ) ) ) OR ( Cdc42 AND ( ( ( Actin ) AND ( ( ( PIP2_45 ) ) OR ( ( PIP3_345 ) ) ) ) AND ( ( NOT ARF ) ) ) ) MLCP = ( ( ( ( ( ( PKA AND ( ( ( RhoK ) ) ) ) AND NOT ( ILK ) ) AND NOT ( Raf ) ) AND NOT ( PAK ) ) AND NOT ( PKC ) ) ) OR NOT ( PAK OR PKA OR Raf OR RhoK OR ILK OR PKC ) DGK = ( PKC AND ( ( ( DAG ) ) ) ) OR ( Src AND ( ( ( Ca AND PA ) ) ) ) OR ( EGFR ) cAMP = ( ( AC ) AND NOT ( PDE4 ) ) OR ( ( cAMP ) AND NOT ( PDE4 ) ) RasGRF_GRP = ( CaM AND ( ( ( Cdc42 ) ) ) ) OR ( DAG AND ( ( ( Cdc42 ) ) ) ) TAK1 = ( Tab_12 ) Grb2 = ( Src AND ( ( ( Fak ) ) ) ) OR ( EGFR ) OR ( Shc ) Sek1 = ( Mekk4 AND ( ( ( ASK1 ) ) ) ) OR ( MLK1 AND ( ( ( ASK1 ) ) ) ) OR ( MLK2 AND ( ( ( ASK1 ) ) ) ) OR ( MLK3 AND ( ( ( ASK1 ) ) ) ) OR ( TAK1 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk1 AND ( ( ( ASK1 ) ) ) ) OR ( Tpl2 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk2 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk3 AND ( ( ( ASK1 ) ) ) ) ARF = ( PIP2_45 ) OR ( PIP3_345 ) MLK3 = ( Rac ) OR ( IL1_TNFR ) OR ( Cdc42 ) Cbp = ( ( Src ) AND NOT ( SHP2 ) ) PKA = ( ( PDK1 AND ( ( ( cAMP ) ) ) ) AND NOT ( PP2A AND ( ( ( PKA ) ) ) ) ) OR ( ( PKA AND ( ( ( cAMP ) ) ) ) AND NOT ( PP2A AND ( ( ( PKA ) ) ) ) ) AC = ( Integrins AND ( ( ( ECM ) AND ( ( ( Gas ) ) AND ( ( Gbg_i ) ) ) ) ) ) WASP = ( ( Fak AND ( ( ( Grb2 OR Nck OR PIP2_45 ) ) AND ( ( Cdc42 AND Crk ) ) ) ) AND NOT ( PTPPEST ) ) OR ( ( Src AND ( ( ( Grb2 OR Nck OR PIP2_45 ) ) AND ( ( Cdc42 AND Crk ) ) ) ) AND NOT ( PTPPEST ) ) OR ( ( Cdc42 AND ( ( ( NOT PTPPEST AND NOT Crk ) ) AND ( ( Fak OR Src ) ) AND ( ( Grb2 OR Nck OR PIP2_45 ) ) ) ) AND NOT ( PTPPEST ) ) Rac = ( ( ( ( RasGRF_GRP AND ( ( ( ECM AND Integrins ) ) ) ) AND NOT ( RhoGDI AND ( ( ( NOT PAK ) ) ) ) ) AND NOT ( p190RhoGAP AND ( ( ( Rac ) ) ) ) ) AND NOT ( RalBP1 AND ( ( ( Rac ) ) ) ) ) OR ( ( Pix_Cool AND ( ( ( PAK AND Gbg_i ) AND ( ( ( NOT Cdc42 AND NOT Rac ) ) AND ( ( ECM AND Integrins ) ) ) ) OR ( ( NOT Gbg_i ) AND ( ( ( Cdc42 ) ) AND ( ( NOT Rac ) ) AND ( ( ECM AND Integrins ) ) ) ) OR ( ( NOT PAK ) AND ( ( ( NOT RasGRF_GRP AND NOT DOCK180 AND NOT Tiam ) ) AND ( ( Cdc42 ) ) AND ( ( NOT RhoGDI ) ) AND ( ( ECM AND Integrins ) ) AND ( ( NOT Rac ) ) ) ) ) ) AND NOT ( RhoGDI AND ( ( ( NOT PAK ) ) ) ) ) OR ( ( ( ( Tiam AND ( ( ( ECM AND Integrins ) ) ) ) AND NOT ( RhoGDI AND ( ( ( NOT PAK ) ) ) ) ) AND NOT ( p190RhoGAP AND ( ( ( Rac ) ) ) ) ) AND NOT ( RalBP1 AND ( ( ( Rac ) ) ) ) ) OR ( ( ( ( DOCK180 AND ( ( ( ECM AND Integrins ) ) ) ) AND NOT ( RhoGDI AND ( ( ( NOT PAK ) ) ) ) ) AND NOT ( p190RhoGAP AND ( ( ( Rac ) ) ) ) ) AND NOT ( RalBP1 AND ( ( ( Rac ) ) ) ) ) Gbg_1213 = ( Ga_1213 ) OR ( alpha_1213R AND ( ( ( NOT Ga_1213 ) ) AND ( ( NOT Gbg_1213 ) ) ) ) PDK1 = ( p90RSK ) OR ( Src ) Raf = ( Ras AND ( ( ( Raf ) ) ) ) OR ( Src AND ( ( ( NOT Raf ) ) AND ( ( PAK AND Raf_Loc AND RKIP ) ) ) ) OR ( Raf AND ( ( ( NOT PKA AND NOT Erk AND NOT Akt ) ) ) ) OR ( PAK AND ( ( ( NOT Erk AND NOT Akt AND NOT Ras ) ) AND ( ( Raf ) ) ) ) Akt = ( CaMKK AND ( ( ( NOT Akt ) ) AND ( ( Src AND ILK ) ) AND ( ( PIP3_345 OR PIP2_34 ) ) ) ) OR ( Akt AND ( ( ( NOT PP2A ) ) ) ) OR ( PDK1 AND ( ( ( NOT Akt ) ) AND ( ( PIP3_345 OR PIP2_34 ) ) AND ( ( Src AND ILK ) ) ) ) AND_34 = ( Cas ) RhoK = ( Rho ) PA = ( PLD ) PTPPEST = ( ( ( Integrins AND ( ( ( ECM ) ) ) ) AND NOT ( PKA ) ) AND NOT ( PKC ) ) SAPK = ( ( ( MKK7 ) AND NOT ( MKPs AND ( ( ( SAPK ) ) ) ) ) AND NOT ( PP2A AND ( ( ( SAPK ) ) ) ) ) OR ( ( ( Sek1 ) AND NOT ( MKPs AND ( ( ( SAPK ) ) ) ) ) AND NOT ( PP2A AND ( ( ( SAPK ) ) ) ) ) Palpha_sR = ( alpha_sR AND ( ( ( GRK ) ) ) ) B_Arrestin = ( Palpha_iR ) OR ( Palpha_qR ) OR ( Palpha_1213R ) OR ( Palpha_sR ) Tpl2 = ( Trafs ) Ga_1213 = ( Ga_1213 AND ( ( ( NOT p115RhoGEF ) ) AND ( ( Gbg_1213 ) ) ) ) OR ( alpha_1213R AND ( ( ( NOT Ga_1213 AND NOT Gbg_1213 ) ) ) ) Pix_Cool = ( PIP3_345 AND ( ( ( B_Parvin ) ) ) ) OR ( PIP2_34 AND ( ( ( B_Parvin ) ) ) ) Integrins = ( Talin AND ( ( ( NOT Integrins AND NOT ILK ) ) AND ( ( ECM ) ) ) ) OR ( Src AND ( ( ( NOT PP2A AND NOT ECM AND NOT Talin AND NOT Integrins AND NOT ILK ) ) ) ) OR ( PP2A AND ( ( ( NOT Integrins ) ) AND ( ( ECM AND Talin AND ILK ) ) ) ) OR ( Integrins AND ( ( ( NOT Src AND NOT ILK ) ) ) ) CaM = ( Ca ) Fak = ( ( Integrins AND ( ( ( Talin ) ) ) ) AND NOT ( PTEN AND ( ( ( Fak ) ) ) ) ) OR ( ( Src AND ( ( ( Fak ) ) ) ) AND NOT ( PTEN AND ( ( ( Fak ) ) ) ) ) Shc = ( ( EGFR AND ( ( ( Fak AND Src ) ) ) ) AND NOT ( Shc AND ( ( ( EGFR AND Fak AND Src AND PTEN ) ) ) ) ) Mekk2 = ( PI3K AND ( ( ( EGFR ) ) AND ( ( NOT Mekk2 ) ) ) ) OR ( PLC_g AND ( ( ( NOT Mekk2 ) ) AND ( ( EGFR ) ) ) ) OR ( Src AND ( ( ( EGFR ) ) AND ( ( NOT Mekk2 ) ) ) ) OR ( Grb2 AND ( ( ( EGFR ) ) AND ( ( NOT Mekk2 ) ) ) ) PTPa = ( PKC ) PLC_g = ( Fak AND ( ( ( Src ) ) AND ( ( NOT EGFR AND NOT PIP3_345 AND NOT PA AND NOT AA ) ) ) ) OR ( Src AND ( ( ( PIP3_345 AND Fak ) ) ) ) OR ( ( EGFR AND ( ( ( PIP3_345 ) ) ) ) AND NOT ( PA AND ( ( ( NOT Fak AND NOT Src ) ) AND ( ( AA ) ) ) ) ) Raf_DeP = ( PP2A AND ( ( ( NOT Raf_DeP ) ) AND ( ( Raf_Rest ) ) ) ) OR ( Raf_DeP AND ( ( ( NOT Raf_Loc ) ) ) ) p90RSK = ( Erk AND ( ( ( PDK1 ) ) AND ( ( NOT p90RSK ) ) ) ) PKC_primed = ( PKC AND ( ( ( PDK1 ) ) AND ( ( NOT PKC_primed ) ) ) ) OR ( PKC_primed AND ( ( ( NOT PKC ) ) ) ) OR ( PDK1 AND ( ( ( NOT PKC ) ) ) ) PLC_B = ( ( Gbg_i AND ( ( ( PLC_B ) ) ) ) AND NOT ( PKA AND ( ( ( NOT Gaq ) ) ) ) ) OR ( Gaq ) Raf_Rest = ( ( Raf_Rest AND ( ( ( NOT Raf_DeP ) ) ) ) OR ( Raf_DeP AND ( ( ( NOT Raf AND NOT Raf_Rest ) ) ) ) ) OR NOT ( Raf_Rest OR Raf OR Raf_DeP ) MLCK = ( ( ( CaM AND ( ( ( NOT PAK ) ) AND ( ( NOT PKA ) ) ) ) AND NOT ( PAK ) ) AND NOT ( PKA ) ) OR ( ( ( Erk AND ( ( ( NOT PAK ) ) AND ( ( NOT PKA ) ) ) ) AND NOT ( PAK ) ) AND NOT ( PKA ) ) Crk = ( ( Cas AND ( ( ( Fak OR Src ) ) ) ) AND NOT ( PTPPEST ) ) Palpha_1213R = ( alpha_1213R AND ( ( ( GRK ) ) ) ) Mek = ( ( PAK AND ( ( ( Tpl2 ) ) ) ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) OR ( ( Tpl2 ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) OR ( ( Mekk1 AND ( ( ( Raf ) ) ) ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) OR ( ( Raf AND ( ( ( Tpl2 ) ) ) ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) OR ( ( Mekk2 AND ( ( ( Raf ) ) ) ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) OR ( ( Mekk3 AND ( ( ( Raf ) ) ) ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) PDE4 = ( B_Arrestin AND ( ( ( NOT Erk ) ) ) ) OR ( PKA AND ( ( ( B_Arrestin ) ) ) ) CaMK = ( CaMKK AND ( ( ( CaM ) ) ) ) Mekk1 = ( Rho AND ( ( ( Grb2 ) ) OR ( ( Shc ) ) ) ) OR ( NIK AND ( ( ( Shc ) ) OR ( ( Grb2 ) ) ) ) OR ( Grb2 AND ( ( ( Shc ) ) ) ) OR ( Ras ) OR ( Trafs ) OR ( Rac ) OR ( GCK ) OR ( Cdc42 ) Palpha_qR = ( alpha_qR AND ( ( ( GRK ) ) ) ) DOCK180 = ( Crk AND ( ( ( Cas ) ) AND ( ( PIP3_345 ) ) ) ) MLK1 = ( Cdc42 ) OR ( Rac ) Ras = ( RasGRF_GRP ) OR ( SHP2 ) OR ( Sos ) Gbg_i = ( alpha_iR AND ( ( ( NOT Gbg_i ) ) AND ( ( NOT Gai ) ) ) ) OR ( Gai ) Nck = ( Cas ) OR ( EGFR ) RKIP = ( PKC ) MKK7 = ( Mekk4 AND ( ( ( ASK1 ) ) ) ) OR ( MLK1 AND ( ( ( ASK1 ) ) ) ) OR ( MLK2 AND ( ( ( ASK1 ) ) ) ) OR ( MLK3 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk1 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk2 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk3 AND ( ( ( ASK1 ) ) ) ) Erk = ( Mek ) OR ( ( ( Erk ) AND NOT ( MKPs ) ) AND NOT ( PP2A ) ) MLK2 = ( Cdc42 AND ( ( ( SAPK ) ) ) ) OR ( Rac AND ( ( ( SAPK ) ) ) ) MKK3 = ( Mekk4 AND ( ( ( ASK1 ) ) ) ) OR ( MLK1 AND ( ( ( ASK1 ) ) ) ) OR ( MLK2 AND ( ( ( ASK1 ) ) ) ) OR ( MLK3 AND ( ( ( ASK1 ) ) ) ) OR ( TAK1 AND ( ( ( ASK1 ) ) ) ) OR ( Tpl2 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk2 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk3 AND ( ( ( ASK1 ) ) ) ) OR ( PAK AND ( ( ( ASK1 ) ) ) ) OR ( TAO_12 AND ( ( ( ASK1 ) ) ) ) Src = ( ( Gas AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( PTPa ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( alpha_sR AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( Fak AND ( ( ( PTP1b ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( Cas AND ( ( ( PTP1b ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( Gai AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( EGFR ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) DAG = ( ( PLC_B AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( DGK AND ( ( ( DAG ) ) ) ) ) OR ( ( PLC_g AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( DGK AND ( ( ( DAG ) ) ) ) ) OR ( DAG AND ( ( ( NOT DGK ) ) ) ) RalGDS = ( ( ( alpha_sR AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( Ras AND ( ( ( PDK1 ) ) AND ( ( PIP3_345 ) ) ) ) ) AND NOT ( PKC ) ) OR ( ( ( alpha_qR AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( Ras AND ( ( ( PDK1 ) ) AND ( ( PIP3_345 ) ) ) ) ) AND NOT ( PKC ) ) OR ( ( ( alpha_iR AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( Ras AND ( ( ( PDK1 ) ) AND ( ( PIP3_345 ) ) ) ) ) AND NOT ( PKC ) ) OR ( ( ( alpha_1213R AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( Ras AND ( ( ( PDK1 ) ) AND ( ( PIP3_345 ) ) ) ) ) AND NOT ( PKC ) ) RGS = ( CaM AND ( ( ( PIP3_345 ) ) ) ) RalBP1 = ( Ral ) CaMKK = ( CaM ) EGFR = ( EGF AND ( ( ( NOT PKC ) ) ) ) OR ( alpha_iR AND ( ( ( Ca AND PKC ) ) ) ) OR ( alpha_qR AND ( ( ( Ca AND PKC ) ) ) ) OR ( alpha_1213R AND ( ( ( Ca AND PKC ) ) ) ) RhoGDI = ( NOT ( ( AA ) OR ( PKC ) OR ( PIP2_45 ) ) ) OR NOT ( PKC OR PIP2_45 OR AA )
Global control of cell cycle transcription by coupled CDK and network oscillators David A. Orlando1,2, Charles Y. Lin1, Allister Bernard3, Jean Y. Wang1, Joshua E. S. Socolar4, Edwin S. Iversen5, Alexander J. Hartemink3, and Steven B. Haase1,* 1Department of Biology, Duke University 2Program in Computational Biology and Bioinformatics, Duke University 3Department of Computer Science, Duke University 4Department of Physics, Duke University 5Department of Statistical Science, Duke University Abstract A significant fraction of the Saccharomyces cerevisiae genome is transcribed periodically during the cell division cycle1,2, suggesting that properly timed gene expression is important for regulating cell cycle events. Genomic analyses of transcription factor localization and expression dynamics suggest that a network of sequentially expressed transcription factors could control the temporal program of transcription during the cell cycle3. However, directed studies interrogating small numbers of genes indicate that their periodic transcription is governed by the activity of cyclin-dependent kinases (CDKs)4. To determine the extent to which the global cell cycle transcription program is controlled by cyclin/CDK complexes, we examined genome-wide transcription dynamics in budding yeast mutant cells that do not express S-phase and mitotic cyclins. Here we show that a significant fraction of periodic genes were aberrantly expressed in the cyclin mutant. Surprisingly, although cells lacking cyclins are blocked at the G1/S border, nearly 70% of periodic genes continued to be expressed periodically and on schedule. Our findings reveal that while CDKs play a role in the regulation of cell cycle transcription, they are not solely responsible for establishing the global periodic transcription program. We propose that periodic transcription is an emergent property of a transcription factor network that can function as a cell cycle oscillator independent of, and in tandem with, the CDK oscillator. The biochemical oscillator controlling periodic events during the cell cycle is centered on the activity of cyclin-dependent kinases (CDKs) (reviewed in ref. 5). The cyclin/CDK oscillator governs the major events of the cell cycle, and in embryonic systems this oscillator functions in the absence of transcription, relying only on maternal stockpiles of mRNAs and proteins. CDKs are also thought to act as the central oscillator in somatic cells and yeast, and directed *Corresponding author Mailing address: DCMB Group, Dept. of Biology Box 90338 Science Drive Durham, NC 27708-0338 Phone: 919.613.8205 Fax: 919.613.8177 shaase@duke.edu. Author Contributions D.A.O., C.Y.L., and S.B.H. designed and performed the experiments. J.Y.W. provided technical expertise. D.A.O., C.Y.L., A.B., E.S.I., and A.J.H. performed the computational analyses, with contributions from J.E.S.S and S.B.H. to the Boolean model. D.A.O. and S.B.H. prepared the manuscript with contributions from C.Y.L., A.B., E.S.I., and A.J.H. Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Author Information The microarray data discussed in this publication have been deposited in NCBI’s Gene Expression Omnibus (GEO, http://www.ncbi.nlm.nih.gov/geo/) and are accessible through GEO series accession number GSE8799. Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to S.B.H (shaase@duke.edu). NIH Public Access Author Manuscript Nature. Author manuscript; available in PMC 2009 September 2. Published in final edited form as: Nature. 2008 June 12; 453(7197): 944–947. doi:10.1038/nature06955. NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript studies suggest that they play an essential role in controlling the temporally ordered program of transcription (reviewed in refs. 4,6). However, systems-level analyses using high throughput technologies1,2,7,8 have suggested alternative models for regulation of periodic transcription during the yeast cell cycle1,3,9. By correlating genome-wide transcription data with global transcription factor binding data, models have been constructed in which periodic transcription is an emergent property of a transcription network1,3,9. In these networks, transcription factors expressed in one cell cycle phase bind to the promoters of genes encoding transcription factors that function in a subsequent phase. Thus, the temporal program of transcription could be controlled by sequential waves of transcription factor expression, even in the absence of extrinsic control by cyclin/CDK complexes. The validity and relevance of the intrinsically oscillatory transcription factor network hypotheses remain uncertain, because for the limited number of periodic genes that have been dissected in detail, periodic transcription was found to be governed by CDKs (reviewed in ref. 4). Thus, we sought to determine to what extent CDKs and transcription factor networks contribute to global regulation of the cell cycle transcription program. To this end, we investigated the dynamics of genome-wide transcription in budding yeast cells disrupted for all S-phase and mitotic cyclins (clb1,2,3,4,5,6). These cyclin mutant cells are unable to replicate DNA, separate SPBs, undergo isotropic bud growth, or complete nuclear division, indicating that they are devoid of functional Clb/CDK complexes10-12. So by conventional cell cycle measures, clb1,2,3,4,5,6 cells arrest at the G1/S border. We have previously shown that clb1,2,3,4,5,6 cells cyclically trigger G1 events10, including the activation of G1-specific transcription and bud emergence. Nevertheless, if Clb/CDK activities are essential for triggering the transcriptional program, then periodic expression of S-phase and G2/M-specific genes should not be observed. We examined global transcription dynamics in synchronized populations of both wild-type cells and cyclin mutant cells. Synchronous populations of early G1 cells were collected by centrifugal elutriation. Cell aliquots were then harvested at 16 min intervals for 270 min (equivalent to ~2 cell cycles in wild-type and ~1.5 in the cyclin mutant). Transcript levels were measured genome-wide for each time point using Yeast 2.0 oligonucleotide arrays (Affymetrix, Santa Clara, CA). Results from two independent experiments each for both wild-type and cyclin mutant cells were highly reproducible, with adjusted r2 values of 0.995 and 0.989, respectively (Supplementary Fig. 1). All statistical analyses were performed using replicate data sets, but to facilitate illustration, single data sets were used for all graphical representations. To identify periodically transcribed genes, we applied a modification of the method developed by de Lichtenberg et al.13 to data acquired from our wild-type cells. We established a set of 1271 genes that were transcribed periodically (Fig. 1a, and Supplementary Table 1). This set of periodic genes shares 510 and 577 genes with those sets previously identified as periodic by Spellman et al.2 and Pramila et al.1, respectively (Supplementary Fig. 2), with 440 consensus periodic genes identified by all three studies (Supplementary Table 2). We then examined the transcriptional dynamics of our set of 1271 periodic genes in the cyclin mutant (Fig. 1b). The behavior of many genes changed significantly in the cyclin mutant, supporting previous findings. However, despite the fact that cyclin mutant cells arrest at the G1/S border, a large fraction of periodic genes in all cell cycle phases continued to be expressed on schedule (Fig. 1b). Similar cyclin-dependent and -independent behaviors are also observed in the set of 440 consensus periodic genes (Supplementary Fig. 3). Using absolute change and Pearson correlation analyses (see Supplementary Information), we determined that 833 of the periodic genes exhibited changes in expression behavior in the cyclin mutant and thus are likely to be directly or indirectly regulated by B-cyclin/CDK. Orlando et al. Page 2 Nature. Author manuscript; available in PMC 2009 September 2. NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript Our genome-level experiments accurately reproduced previous findings regarding several well-studied B-cyclin/CDK-regulated genes (Fig. 2). We observed that a subset of late G1 transcripts (SBF-regulated genes like CLN2 but not MBF-regulated genes like RNR1) were not fully repressed (Fig. 2a and b) as expected in mitotic cyclin mutant cells 14,15. A subset of M/ G1 transcripts (including SIC1 and NIS1), are targets of the transcription factors Swi5 and Ace2, which are normally excluded from the nucleus by CDK phosphorylation until late mitosis16-19. SIC1 and NIS1 were expressed earlier in the cyclin mutant (Fig. 2c and d) presumably because nuclear exclusion of Swi5 and Ace2 is lost in cyclin mutant cells. The modest degree of shift in the timing of SIC1 and NIS1 transcription likely reflects the fact that SWI5 and ACE2 transcripts do not accumulate to maximal levels in cyclin mutant cells as expected for Clb2 cluster genes (including CDC20) (Fig. 2e and f) 14,20,21. Although a significant fraction of periodic genes exhibited changes in the amplitude of expression (increased or decreased), a statistical analysis of the dynamic range of expression across all periodic genes revealed that the majority of genes in cyclin mutant cells exhibit only modest changes, if any, with respect to wild-type cells (Supplementary Fig. 4). To identify novel subsets of co-regulated genes based on transcriptional behaviors observed in both wild-type and cyclin mutant cells, we employed the affinity propagation algorithm22 to first cluster genes based on expression in wild-type cells, and then subcluster genes based on their behavior in cyclin mutant cells (Fig. 3 and Supplementary Fig. 5). Of the 833 cyclin- regulated genes, 513 were assigned to 30 discrete clusters exhibiting similar behaviors in wild- type cells (Fig. 3a, and Supplementary Fig. 6), and were then subclustered into 56 novel clusters based on their transcription profiles in cyclin mutant cells (Fig. 3b and Supplementary Table 3). Using data from global transcription factor localization studies23, we identified subsets of transcription factors that may regulate these subclusters using an over-representation analyses (Fig. 3 and Supplementary Table 4). Based on their association with the promoters of genes in cyclin-regulated subclusters, these factors are likely to be directly or indirectly regulated by cyclins. Consistent with this hypothesis, several of these factors have already been shown to be CDK targets14,15,18,19,24-29. These findings lay the groundwork for elucidating the full range of mechanisms by which cyclin/CDKs regulate transcription during the cell cycle. Strikingly, 882 of the genes identified as periodic in wild-type cells, continued to be expressed on schedule in cyclin mutant cells despite cell cycle “arrest” at the G1/S border (Fig. 4a and b). Some of these genes (450 in total) exhibited minor changes in transcript behavior but continued to be expressed at the proper time, as shown above for ACE2. Thus, some genes that were cyclin-regulated are also included in the set of genes that maintain periodicity. Nevertheless, a statistical analysis of the dynamic range of expression of these genes in wild- type and cyclin mutant cells indicates that the amplitude changes for most of these genes is quite modest (see Supplementary Figs. 7, 8 and 9). The finding that nearly 70% of the genes identified as periodic in wild-type cells are still expressed on schedule in cyclin mutant cells demonstrates the existence of a cyclin/CDK-independent mechanism that regulates temporal transcription dynamics during the cell cycle. This observation is supported by the analysis of the set of 440 consensus periodic genes, the bulk of which maintain periodicity in the cyclin mutant (Supplementary Fig. 10). In principle, a transcription network defined by sequential waves of transcription factor expression1,3,9 might function independent of any extrinsic control by CDKs. To determine if a transcription network could account for cyclin/CDK-independent periodic transcription, we constructed a synchronously updating Boolean network model and determined that such a model can indeed explain the periodic expression patterns we observed in cyclin mutant cells (Fig. 4c). Transcription factors that maintained periodicity in the cyclin mutant were placed on a circularized cell cycle time line based on their peak time of transcription in the cyclin mutant. Connections were drawn based on documented physical interactions23,30 Orlando et al. Page 3 Nature. Author manuscript; available in PMC 2009 September 2. NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript (Supplementary Table 5) between a transcription factor and the promoter region of a gene encoding a transcription factor expressed subsequently (see Supplementary Information). The architecture of the network in cyclin mutant cells is virtually identical to that in wild-type cells (Supplementary Fig. 11), and is also remarkably similar to models based on wild-type expression data from previous studies1,3,9. When the network is endowed with Boolean logic functions (Supplementary Table 6a), synchronous updating of the model leads to a cycle that produces successive waves of transcription by progressing through five distinct states before returning to the initial state (Supplementary Fig. 12a and b). Thus, the model functions as an oscillator and produces a correctly-sequenced temporal program of transcription. To examine the robustness of the network oscillator, we evaluated outcomes when initializing the network from all possible starting states. Over 80% of the 512 starting states entered the oscillatory cycle depicted in Fig. 4c, with the remainder terminating in a steady state where all genes were transcriptionally inactive (Supplementary Table 6b and c). We also examined whether the oscillations were sensitive to the choice of the Boolean logic functions assigned to nodes with multiple inputs, specifically, the activating inputs to Cln3 and SFF, and the repressors of SBF and Cln3. For most of the logic functions, the predominant outcome was again the oscillatory cycle depicted in Fig. 4c, but in some cases, the model enters two qualitatively similar cycles (Supplementary Fig. 12c and d, and Supplementary Table 6), with the remainder again terminating in a transcriptionally inactive steady state. Several Boolean logic functions produce the same cycles (Supplementary Table 6b), so the model cannot precisely determine the true logic of the network connections. Nevertheless, the fact that the model can produce qualitatively similar cycles, and that these cycles can be reached from many initial states, suggests that robust oscillation is an emergent property of the network architecture. Previous studies proposed that a cyclin/CDK-independent oscillator could trigger some periodic events, including bud emergence10. The robust oscillating character of our model suggests that a transcription factor network may function as this cyclin/CDK-independent oscillator. Because cyclin genes are themselves among the periodic genes targeted by this network, and because cyclin/CDKs can, in turn, influence the behavior of transcription factors in the network, precise cell cycle control could be achieved by coupling a transcription factor network oscillator with the cyclin/CDK oscillator. The existence of coupled oscillators could explain why the cell cycle is so robust to significant perturbations in gene expression or cyclin/ CDK activity. Our findings also suggest that the properly scheduled expression of genes required for cell cycle regulated processes such as DNA synthesis and mitosis is not sufficient for triggering these events. The execution of cell cycle events in wild-type cells is likely to require both properly timed transcription and post-transcriptional modifications mediated by CDKs. Methods Summary Strains and cell synchronization Wild-type and cyclin mutant strains of S. cerevisiae are derivatives of BF264-15Dau, and were constructed by standard yeast methods. The clb1,2,3,4,5,6 GAL1-CLB1 mutant strain along with growth conditions and synchrony procedures was described previously10,11. RNA isolation and microarray analysis Total RNA was isolated time points (every 16 min for a total of 15 time points) as described previously10. mRNA was amplified and fluorescently labeled using GeneChip One-Cycle Orlando et al. Page 4 Nature. Author manuscript; available in PMC 2009 September 2. NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript Target Labeling (Affymetrix, Santa Clara, CA) . Hybridization to Yeast 2.0 oligonucleotide arrays (Affymetrix, Santa Clara, CA) and image collection were performed at the Duke Microarray Core Facility (http://microarray.genome.duke.edu/) according to standard Affymetrix protocols. Data analysis A workflow diagram for data analysis is depicted in Supplementary Fig. 13. Methods Strains and cell synchronization Yeast strains were grown in rich YEP medium (1% yeast extract, 2% peptone, 0.012% adenine, 0.006% uracil) containing 2% galactose. Forty-five minutes prior to elutriation, dextrose was added to YEP 2% galactose medium to terminate CLB1 expression from the GAL1 promoter. After elutriation, wild-type and clb1,2,3,4,5,6 GAL1-CLB1 cells were grown in rich YEP 2% dextrose,1M sorbitol at 30°C at a density of 107/ml. Sorbitol was added to stabilize cells with elongated buds. Aliquots of 50ml (cell density = 107/ml) were harvested every 8 min for 4hr. Budding index was determined microscopically by counting ≥ 200 cells for each time point. Data analysis CEL files from all 60 oligonucleotide arrays were normalized, and summarized using the dChip method32 as implemented in the affy package (v.1.8.1) within Bioconductor using default parameters. The output of this package is a measure of absolute expression levels for each probe in arbitrary expression units (Fig. 2). Data presented in heat maps and centroid line graphs (Figs. 1, 3, and 4, and Supplementary Figs. 3, 5, 8, 11,12, 15-18) are expressed as log2-fold change for each gene relative to its mean expression over the interval from the first G1 to the second S phase. The CLOCCS population synchrony model31 was used to temporally align expression data from our two wild-type and two cyclin mutant experiments. Briefly, the CLOCCS model allows the alignment of data from multiple synchrony/time series experiments to a common cell cycle time line using budding as a parameter measured on single cells at each time point31. Although cyclin mutant cells arrest at the G1/S border by conventional measures, G1 events, such as bud emergence, are activated periodically with a cycle time similar to wild-type cells10. Thus, the CLOCCS model can be used to temporally align cycles in wild-type and cyclin mutant cells. Because the kinetics of synchrony/release experiments can vary, and wild-type and cyclin mutant cells have marginally different cycle times, alignment is imperative for meaningful comparison of data. We used the CLOCCS parameter estimates to align all four data sets such that the population level measurements were mapped onto a common cell cycle timeline. The timeline utilizes standard cell cycle phases (as determined by measured parameters) and an additional phase (Gr) corresponding to a period of recovery from the initial synchrony procedure that overlaps with early G131. The recovery period (Gr) was eliminated from most of the data displayed, as the genes expressed in this period tend to be specific to this period and are not expressed again in the next cell cycle in either wild-type or cyclin mutant cells. The CLOCCS model was designed for wild-type yeast populations but can accommodate data from the cyclin mutant with minor modifications (see Supplementary Information). CLOCCS model fits for both the wild-type and cyclin mutant datasets are shown in Supplementary Fig. 14, and the corresponding parameter estimates are shown in Supplementary Table 7. A modification of the method described by de Lichtenberg13 was used to determine the subset of genes exhibiting periodic transcription (see Supplementary Information for details). The methods used to identify genes with altered transcriptional profiles (Fig. 3), and similar profiles Orlando et al. Page 5 Nature. Author manuscript; available in PMC 2009 September 2. NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript (Figs. 4a and b) in cyclin mutant cells with respect to wild-type cells are also described in detail in Supplementary Information. Methods for determining over-represented transcription factors in the clusters (Fig. 3) and details regarding the construction of the synchronously updating Boolean network model (Fig. 4c) can also be found in Supplementary Information. Two additional analyses similar to that performed in Fig. 3 were performed on consensus periodic genes (Supplemental Table 2) identified as changing expression as well as those identified as maintaining periodicity. Details and results of those analyses can be found in Supplementary Information (Supplementary Figs. 15-19 and Supplementary Tables 8 and 9) Supplementary Material Refer to Web version on PubMed Central for supplementary material. Acknowledgments We would like to thank D. Lew and L. Simmons Kovacs for helpful discussions and critical reading of the manuscript, and P. Benfey for helpful discussions and support. We gratefully acknowledge financial support from the American Cancer Society (to S.B.H.), Alfred P. Sloan Foundation (to A.J.H.), National Science Foundation (to A.J.H. and J.E.S.S.), and National Institutes of Health (to S.B.H., A.J.H., and J.E.S.S.). References 1. Pramila T, Wu W, Miles S, Noble WS, Breeden LL. 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NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript Figure 1. Dynamics of periodic transcripts in wild-type and cyclin mutant cells. Heat maps depicting mRNA levels of periodic genes are shown for a, wild-type and b, cyclin mutant cells. Each row in a and b represents data for the same gene (Supplementary Table 1). Transcript levels are expressed as log2-fold change vs. mean expression. Transcript levels at each point in the time series were mapped onto a cell cycle timeline31 (see Methods). The S and G2/M phases of the cyclin mutant timeline are shaded, indicating that by conventional definitions, cyclin mutant cells arrest at the G1/S-phase transition. Orlando et al. Page 8 Nature. Author manuscript; available in PMC 2009 September 2. NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript Figure 2. Transcription dynamics of established cyclin/CDK-regulated genes. Absolute transcript levels (dChip-normalized Affymetrix intensity units/1000) are shown for the SBF- and MBF- regulated genes a, CLN2 and b, RNR1; the Ace2/Swi5-regulated genes c, SIC1 and d, NIS1; and the Clb2 cluster genes e, CDC20 and f, ACE2. Wild-type cells (solid line) and cyclin mutant cells (dashed line). Orlando et al. Page 9 Nature. Author manuscript; available in PMC 2009 September 2. NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript Figure 3. Genes exhibiting altered behaviors in cyclin mutant cells. a, Clusters of genes with similar expression patterns in wild-type cells. b, Subclusters of genes with similarly altered expression patterns in cyclin mutant cells. Each row in a and b represents data for the same gene (Supplementary Table 1). Transcript levels are depicted as shown in Fig. 1. Up to five over- represented transcription factors for each cluster are shown (see Methods and Supplementary Table 4 for complete lists). Orlando et al. Page 10 Nature. Author manuscript; available in PMC 2009 September 2. NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript Figure 4. The periodic transcription program is largely intact in cyclin mutant cells that arrest at the G1/ S border. a, Genes maintaining periodic expression in cyclin mutant cells exhibit similar dynamics in b, wild-type cells. Each row in a and b represents the same gene (Supplementary Table 1). Transcript levels are depicted as shown in Fig. 1. c, Synchronously updating Boolean network model. Transcription factors are arranged based on the time of peak transcript levels in cyclin mutant cells. Arrows indicate transcription factor/promoter interaction. Activating interactions, outer rings; repressive interactions, inner rings. Coloring indicates activity in one of five successive states; SBF and YHP1 are active in two states (Supplementary Table 6). Orlando et al. Page 11 Nature. Author manuscript; available in PMC 2009 September 2. NIH-PA Author Manuscript NIH-PA Author Manuscript NIH-PA Author Manuscript	18463633	MBF = ( CLN3 ) HCM1 = ( MBF AND ( ( ( SBF ) ) ) ) SWI5 = ( SFF ) YOX1 = ( MBF AND ( ( ( SBF ) ) ) ) SFF = ( SBF AND ( ( ( HCM1 ) ) ) ) ACE2 = ( SFF ) YHP1 = ( MBF ) OR ( SBF ) SBF = ( ( ( MBF ) AND NOT ( YHP1 ) ) AND NOT ( YOX1 ) ) OR ( ( ( CLN3 ) AND NOT ( YHP1 ) ) AND NOT ( YOX1 ) ) CLN3 = ( ( ( SWI5 AND ( ( ( ACE2 ) ) ) ) AND NOT ( YOX1 ) ) AND NOT ( YHP1 ) )
BioMed Central Page 1 of 15 (page number not for citation purposes) BMC Systems Biology Open Access Research article A logic-based diagram of signalling pathways central to macrophage activation Sobia Raza1, Kevin A Robertson1,3, Paul A Lacaze1, David Page1, Anton J Enright2, Peter Ghazal1,3 and Tom C Freeman1 Address: 1Division of Pathway Medicine, University of Edinburgh, The Chancellor's Building, College of Medicine, 49 Little France Crescent, Edinburgh, EH16 4SB, UK, 2Computation and Functional Genomics Laboratory, Sanger Institute, Wellcome Trust Genome Campus, Hinxton, Cambridge, CB10 1SA, UK and 3Centre for Systems Biology, University of Edinburgh, Darwin Building, King's Building Campus, Mayfield Road, Edinburgh, EH9 3JU, UK Email: Sobia Raza - sobia.raza@ed.ac.uk; Kevin A Robertson - kevin.robertson@ed.ac.uk; Paul A Lacaze - paul.lacaze@ed.ac.uk; David Page - david.page@ed.ac.uk; Anton J Enright - aje@sanger.ac.uk; Peter Ghazal* - p.ghazal@ed.ac.uk; Tom C Freeman* - tfreeman@staffmail.ed.ac.uk * Corresponding authors Abstract Background: The complex yet flexible cellular response to pathogens is orchestrated by the interaction of multiple signalling and metabolic pathways. The molecular regulation of this response has been studied in great detail but comprehensive and unambiguous diagrams describing these events are generally unavailable. Four key signalling cascades triggered early-on in the innate immune response are the toll-like receptor, interferon, NF-?B and apoptotic pathways, which co- operate to defend cells against a given pathogen. However, these pathways are commonly viewed as separate entities rather than an integrated network of molecular interactions. Results: Here we describe the construction of a logically represented pathway diagram which attempts to integrate these four pathways central to innate immunity using a modified version of the Edinburgh Pathway Notation. The pathway map is available in a number of electronic formats and editing is supported by yEd graph editor software. Conclusion: The map presents a powerful visual aid for interpreting the available pathway interaction knowledge and underscores the valuable contribution well constructed pathway diagrams make to communicating large amounts of molecular interaction data. Furthermore, we discuss issues with the limitations and scalability of pathways presented in this fashion, explore options for automated layout of large pathway networks and demonstrate how such maps can aid the interpretation of functional studies. Background The innate immune response is executed at the molecular level by a complex series of interwoven signalling path- ways. In this context, pathways may be defined as a net- work of directional interactions between the components of a cell which orchestrate an appropriate shift in cellular activity in response to a specific biological input or event. Whilst our ability to perform quantitative and qualitative measurements on the cellular components has increased massively in recent years, as has our knowledge on how Published: 23 April 2008 BMC Systems Biology 2008, 2:36 doi:10.1186/1752-0509-2-36 Received: 23 January 2008 Accepted: 23 April 2008 This article is available from: http://www.biomedcentral.com/1752-0509/2/36 © 2008 Raza et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 2 of 15 (page number not for citation purposes) they interact with each other, we still struggle to translate these observations into graphical and computationally tractable models. However without such models we can not hope to truly understand biology at a systems level. Traditionally, representations of molecular pathways have been produced ad hoc and frequently included in reviews and original papers. Whilst they are clearly useful aids to understanding cellular events, even at their best, they are not sufficient by themselves, relying on extensive textual descriptions to explain what is shown pictorially. Recent years have seen considerable growth in the availability of public and commercial databases offering searchable access to pathways and interaction data derived from a combination of manual and automated (text mining) extraction of primary literature, reviews and large-scale molecular interaction studies. Using these tools it is pos- sible to view a range of canonical pathway views or gener- ate networks of interactions based on a given query. However, all of these efforts are let down by one or a number of key factors. The notation used in diagrams to depict one molecule's interaction with another is varied, often ambiguous and therefore limited in its ability to depict the exact nature of the relationship between com- ponents of a pathway. There is often a lack of direct access to the experimental evidence relating to the interactions depicted or to the dataset as a whole. Similarly, labelling of the pathway components often uses non-standard nomenclature or mixes protein names from one species with that of another, such that again the reader is left uncertain as to what exactly is being shown. Finally, path- way diagrams usually focus only on a small part of a bio- logical system and one which often reflects the curator's bias, such that the 'same' pathway described by different individuals may share little in common. Whatever the source of these pathways and networks they generally suf- fer from graphically poor representation with ambiguity around the precise identity of what is being shown and the exact nature of their interaction. In order to address these issues the groups of Kohn and Kitano began to devise new approaches to pathway notation using many ideas adopted from the electronics industry [1-3]. In par- ticular the MIM (molecular interaction map) notation [3] a form of entity-relationship representation and the proc- ess description notation (PDN) [1], respectively. Since then there has been an increasing interest in the systems biology community to develop a consensus view on a standard approach for representing biological pathways [4]. Whilst this process is now well advanced there is cur- rently no internationally agreed standard graphical nota- tion system for building pathway diagrams and a paucity of worked examples of this type of notation in use. Exam- ples of pathways that have been published using these notation systems include a molecular interaction map of macrophage signalling [5] and Toll-Like-Receptor signal- ling [6] which have been depicted using the PDN scheme and cell cycle control and DNA repair presented in the MIM notation [2]. Over the last four years we have been developing a nota- tion scheme for the depiction of biological pathways that borrows many of the ideas of existing notation systems but attempts to address some of their short comings. The Edinburgh Pathway Notation [26] uses a logical state- transition representation to describe biological pathways, similar to PDN. The work described here follows on from this initial publication and reports a modified version of the EPN scheme which is aligned with the developing international SBGN standard but has a number of impor- tant differences with the scheme as currently proposed. Crucially, the notation provides a logical context for inter- actions between components in the pathway, it can dis- play the temporal order of reactions and can be mapped to the machine-readable SBML (systems biology markup language) [7]. Of primary importance to this notation scheme and indeed the SBGN is the desire to develop pathway maps that are 'readable' by a biologist. Since the pathway maps are primarily produced as a tool for com- munication it is critical that they are easily understanda- ble and the notation can be applied and read by biologists with minimal training. Other objectives (of the SBGN) are that the notation should be computable, compact, show sub-cellular localization and be tolerable of incomplete knowledge. Whilst all of these objectives are valid, fulfill- ing them in practice is far from trivial and there are few worked examples of large pathway diagrams depicted in standard notations, available in the public domain. The innate immune response is orchestrated by series of signalling pathways that have evolved to elicit an appro- priate defensive response to attack by pathogenic organ- isms. Pathogen sensing involves pattern recognition receptors such as the toll-like receptors (TLR's) which in mammalian cells constitutes a family of up to 11 [8] trans- membrane receptors each responsible for distinguishing particular pathogen-associated molecular patterns (PAMPs). Detection of pathogen molecules by these receptors results in the recruitment of various adaptor pro- teins and the activation of downstream signal transduc- tion cascades [9,10]. Activation of de novo gene expression follows, which ultimately acts to recruit new proteins and augment the response to infection. Interferons (IFNs) are central to this response, as are (amongst others) interferon regulatory factors (IRFs), JAK/STAT signalling proteins and the nuclear factor-kappa B (NF-?B) family of proteins [11]. The IRF family of transcription factors bind specific DNA sequences, as do the STAT proteins, present on the promoter of target genes [12,13]. NF-?B signalling can reg- ulate transcription through a combination of NF-?B pro- tein homo- and heterodimers [14-17]. These pathways are BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 3 of 15 (page number not for citation purposes) also known to regulate components of the apoptotic path- way, thereby providing the potential for cells to undergo a programmed cell death [18], the ultimate cellular sacri- fice in defence of the organism. The TLR, IFN, NF-?B and apoptosis pathways are of central importance in defining the macrophages response to pathogens and do so in a highly inter-dependant manner [11]. Extensive literature describing the pathways and their interconnectivity, like so many others in biology, is available but only from multiple and disparate sources. In our effort to understand these events as a basis for inter- preting analyses of host-pathogen interactions and the inflammatory response in the macrophage, we have endeavoured to construct an integrated and logic-based pathway diagram of signalling cascades fundamental to macrophage activation using a current version of the EPN scheme. We present the results of these labours as an example of our on going work in this area and hope that this map will be used to supplement and contrast with the efforts of others [6] in this area. Methods Collection of Molecular Interaction Data and Biological Representation of Pathways In an effort to describe and consolidate knowledge of pathways central to macrophage activation we have con- structed a pathway diagram based on published literature. Ideally, two published papers citing protein-protein or protein-gene interactions were required for the inclusion of a given interaction on to the pathway diagram. In some circumstances we accepted one piece of published evi- dence if the paper described extensive experimental verifi- cation of the interaction. This was deemed necessary as two publications per interaction can limit inclusion of potentially interesting interactions included in other pathway resources (KEGG, Reactome etc) and newly dis- covered interactions. It is also important to note that the primary task of this exercise was to develop a 'consensus' of knowledge and information about a given pathway. A list of interactions to be mapped was compiled [see Additional file 1], including details about the nature of the interaction and source of the information. A pathway map was then drawn using the principles laid down by the EPN scheme. These include the concept that the molecu- lar components of a pathway be they proteins, protein complexes and genes (or in principle any other cellular component that plays a part in a pathway) are represented as simple shapes containing a unique and unambiguous identifying label. Attempts to depict pictorially the func- tional activity or functional domains of components have been avoided as this adds to the visual complexity of the diagram and can be misleading. For consistency compo- nents (nodes) have been named by their official human genome nomenclature (HGNC) symbol, although in cer- tain instances we have felt it necessary due to the wide- spread use of other naming conventions to supplement this with additional annotation. For example we have used the name tBID to differentiate the truncated (active) form of the protein from its precursor (BID) and similarly in order to distinguish the native (inactive) form of cas- pases we used the suffix Pro e.g. ProCASP3 from the active cleaved form (CASP3). We have also included additional naming conventions to differentiate between protein forms e.g. in the NF-?B pathway (p50, p52 etc) or included common aliases where they are prevalent in the literature, these names being placed in brackets after the official name. Whilst the use of such ad hoc naming con- ventions is in theory undesirable, they are still in common use and alternative ways to differentiate between protein forms is not supported under the HGNC and standard naming conventions for describing proteins in their vari- ous modified forms (truncated, cleaved, activated by cleavage etc) does not yet exist. Where pathway compo- nents are protein complexes, the name of the complex is given as a concatenation of the names of its constituent parts, although this has in some cases been supplemented by the inclusion of common names such as 'apoptosome' to denote the complex between CASP9, CYCS and APAF1. Components are depicted at the site of their activity and are shown only once in any given cellular compartment unless different activation states of the components are known due to phosphorylation, ubquitinisation, cleavage etc., when these molecular states may be shown as con- nected but individual entities. The state of a component may be shown as a supplement to the components name e.g. active [A], inactive [I], phosphorylated [P]. Interac- tions (edges) between components or transitions between one cellular compartment and another, are shown as arrows which either contact interacting partners via Boolean logic operators (&, OR, NOT) and/or transition/ annotation nodes that provide information as to the nature of the interaction or transition from one state to another. Attempts to depict molecular details of interac- tions and state transitions such as the exact site of a pro- tein's phosphorylation, have generally been avoided. Whilst important, if depicted on a map of this size the information quickly clutters up the diagram rendering it inaccessible to the casual reader. However, in cases where such details are necessary to differentiate one component form from another they should be added. Finally, layout of the elements and interactions that make up the path- way should be such that it is relatively easy to follow the direction and nature of flow of information from the ini- tial trigger to the eventual outcome. In an effort to achieve this, where possible interacting map components are drawn close together keeping edge lengths short and easy to follow, crossover of edges is kept to a minimum and every effort is taken to keep connecting edges separate, BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 4 of 15 (page number not for citation purposes) with a minimum number of changes in direction to get from one point to another. The pathway map was drawn using the freely available program yEd graph editor (yFiles software, Tubingen, Ger- many). yEd is a general purpose graphical tool designed for the depiction of networks. Although not specifically designed for biological pathway depiction it has been used previously for this and similar purposes [19,20] and has a range of characteristics and capabilities that make it ideally suited for the job. Initially pathways were laid out by hand. Areas of the canvas were defined as representing specific compartments of the cell e.g. plasma membrane, cytoplasm, nucleus etc., and cellular components and the interactions in which they took part were drawn in the appropriate space. A section of the overall map describing IFNG receptor signalling laid out according to the cellular location of the components has been included as an example of the notation scheme in action (Figure 1) and a list of notation symbols used here is provided in Figure 2. The combined map of macrophage activation pathways described here (Figure 3) is available for download [21] and presented in a number of image (.jpeg, .pdf) and graphical formats (.xml, .graphml). The .graphml file [see Additional file 2] can be opened in yEd graph editor [22] and in this format is available for editing or expansion. PubMed IDs supporting the interactions of the pathway are stored on appropriate edges within the .graphml ver- sion of the diagram. We have found the yEd program to be relatively intuitive to use and to require minimal or no training. Hence the pathway diagram presented here is easily accessible, distributable and can be modified by end users to suit their interests or knowledge-base. The EPN can be mapped to SBML and we are in the process of creating a SBML version of the map described here. As the complexity of maps increases and the interactions between components become evermore intertwined, manual organization of these events becomes time-con- suming and difficult. However, the pathway diagrams have been specifically drawn as directional networks. As such layout of the pathway maps can be aided by use of various automated layout algorithms. The hierarchical layout and classic-orthogonal edge routing applications within the yEd software were the most effective in terms of providing an easily interpretable view of directional flow in the diagram (Figure 4a, b). However, other layout algo- rithms such as the organic layout function (Figure 4c) can also provide different views of the pathway. Furthermore this pathway can be easily converted into a 3-D network (Figure 4d) in BioLayout Express3D [23]. Whilst 3-D path- way networks do not readily support user readability of Manual layout of Type II interferon signalling (IFNG) taken from the integrated pathway diagram (Figure 2) Figure 1 Manual layout of Type II interferon signalling (IFNG) taken from the integrated pathway diagram (Figure 2). The pathway is arranged to flow from left to right. Components are coloured according to type (protein, complex or gene) and arranged within the sub-cellular compartments in which they are active. This pathway is initiated by IFNG binding to its receptor and a subsequent phosphorylation cascade involving a number of the JAK and STAT family of proteins. Several tran- scriptionally active complexes are formed (STAT1 homodimer, ISGF3 complex, STAT1:STAT1:IRF9 complex) and the pathway culminates with the transcriptional activation of target genes. BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 5 of 15 (page number not for citation purposes) the interactions, it provides an environment where very large graphs may be plotted (15,000 nodes, 2.5 million edges) and queried. As such these tools can aid interpreta- tion of the innate structure within the network of interac- tions of large pathway diagrams and together provide a solution, albeit not necessarily a perfect one, to the issue of scalability. With these capabilities it will be possible to scale up these diagrams to the point where they may con- tain thousands of components, operators and transition nodes. Network Analysis of the Transcriptional Response of Mouse Bone Marrow Derived Macrophages to Interferon- gamma Treatment Primary mouse bone marrow derived monocytes were prepared from male balb/c mice 10–12 weeks old. Cells were washed, resuspended in DMEM-F12/10% FCS/L929 medium and counted before being plated in a 24-well plate at a concentration of 5 × 105 cells/well. To differen- tiate the cells from monocytes into primary macrophages, cells were then incubated for 7 days in DMEM-F12 growth media supplemented with 10% L929 cell suspension releasing the MCP-1 macrophage stimulating factor, with media changes on days 3 and 5. On day 7 the growth medium was replaced with DMEM-12/10%FCS medium containing 10 u/ml recombinant mouse interferon- gamma (Pierce-Thermofisher Scientific, Rockford US) and harvested 1, 2, 4 & 8 h following treatment or collected pre-treatment (0 h). Total RNA was harvested from the cells using an RNeasy Plus kit (Qiagen) according to man- ufacturer's instructions. RNA was quantified and quality controlled using a NanoDrop spectrophotometer (Nano- Symbols of the modified Edinburgh Pathway Notation Figure 2 Symbols of the modified Edinburgh Pathway Notation. Unique shapes and identifiers are used to distinguish between each element of the notation allowing its interpretation even in the absence of colour. Colour maybe used for aesthetic pur- poses and to ease identification of nodes. The notation can be broadly divided into four categories; components, boolean oper- ators, transition nodes and annotated edges. Components consist of any interacting species from proteins, complexes, genes or other molecular species (pathogens, DNA, RNA). Pathway initiators are also presented in the notation. Boolean operators are essential for capturing the dependencies of an interaction. Transition nodes provide information as to the nature of the interaction (such as cleavage, translocation, phosphorylation). Edges are directional and can be coloured for visual impact. Dis- tinctive arrow-heads are used to distinguish between the pathway inputs and outputs but are otherwise avoided. Instead in-line edge annotation is used to add a visual cue as to the meaning of an edge. Cellular compartmental information is provided by physical location and backdrop or by colouring nodes according to their sub-cellular location. BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 6 of 15 (page number not for citation purposes) Integrated pathway map of signalling in the macrophage Figure 3 Integrated pathway map of signalling in the macrophage. The diagram includes the interferon signalling, NF-?B, apop- tosis and toll-like receptor pathways, all represented as one integrated pathway due to their overlapping interactions. In gen- eral interactions of the interferon response pathway are in the top quarter of the map, with NF-?B directly below. Apoptosis is presented halfway down the map and toll-like receptor signalling is in the bottom quarter. 154 different protein or gene nodes are included in the pathway, along with 80 different complexes and 12 other molecular species (such as pathogens, DNA, RNA). The pathway diagram represents 272 different interactions. BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 7 of 15 (page number not for citation purposes) Automated layouts of the pathway diagram Figure 4 Automated layouts of the pathway diagram. (4a) a hierarchical-classic layout was applied to the entire pathway and the orientation was set to flow from left to right. Nodes are coloured according to their sub-cellular location. With this layout the flow of pathway information and biological logic is maintained, such that the inputs to pathway are placed at the left side of the diagram and these can be followed through to the outputs at the right hand side. (4b) a detailed inset of the hierarchical-classic layout of the integrated pathway taken from 4a. (4c) Organic-classic automated layout of the entire pathway generated in yEd graph editor. Although the directionality of flow in the pathway is lost, interacting partners tend to be placed in close proximity of each other in this layout. (4d) a 3-dimentional network of the apoptosis interactions in the pathway generated using BioLay- out Express3D. This network can be queried for pathway information. Unique shapes are used to identify the different pathway notation symbols; spheres denote interacting components (proteins, genes, complexes), decahedron shapes represent boolean operators or transition nodes and tetrahedron shapes correspond to the in-line edge annotation (in this case activation, or inhibition). All notation symbols are coloured to correspond to the colour scheme applied in the 2-dimentional pathway dia- gram (e.g. complexes are yellow, proteins are blue, and activation-annotations are green). Furthermore interacting compo- nents are sized according to type, such that spheres representing complexes appear larger than proteins or genes. As with the 2-dimentional diagram the colour scheme used is customisable. The 3-dimentional network retains the information captured in the 2-dimentional pathway and although spatial placement of nodes in relation to their sub-cellular location has been lost, this information can be retrieved by querying the network and/or colouring nodes according to their sub-cellular location. BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 8 of 15 (page number not for citation purposes) Drop Technologies) and BioAnalyser 2100 (Agilent). Rep- licate 150 ng samples of total RNA derived from two separate wells per time point were labelled using the Affymetrix whole transcript labelling protocol and hybrid- ized for 16 h at 45°C to Affymetrix mouse exon 1.0 ST arrays. They were then washed and scanned according to manufacturer's recommendations. Data (ArrayExpress Ac. No: E-MEXP-1490) was normal- ized using the RMA package within the Affymetrix Expres- sion Console software and annotated. Transcripts which might be considered to be differentially expressed were identified using either the Empirical Bayes function within Bioconductor [24] or using the annova function within GeneSpring (Agilent Technologies, Stockport, Cheshire) with a 1.6 fold cut-off. In total 1,678 transcripts were identified by one or both of these filters. The data corresponding to this list was then loaded into the net- work visualization tool BioLayout Express3D [23] using a Pearson correlation cut-off of 0.9 to filter edges. The resultant network graph (Figure 5a) of 1,491 nodes was clustered using the graph-based clustering algorithm MCL [25] set at an inflation value of 2.2 resulting in 26 clusters (Figure 5a & b). Clusters composed of transcripts that were up-regulated were then further collated into 3 groups; genes up-regulated at (1) 1–2 hours, (2) 2–4 hours and (3) 4–8 hours post-treatment and genes that were both differently expressed and present on the inte- grated pathway diagram were highlighted on the map. Results and Discussion We set out to use the EPN scheme as originally published [26]. However, during construction of the maps described here the notation system was found to be too limiting to convey certain biological concepts and overly compli- cated for others. A simplification of certain aspects of the notation was therefore deemed necessary in order to achieve the objectives outlined above, in particular human readability. Modifications made to the EPN were not intended to change the built in logic of the notation scheme but rather merely enhance the visual characteris- tics of the diagrams produced. One of the major modifica- a) A network graph of differentially expressed genes following Ifng treatment Figure 5 a) A network graph of differentially expressed genes following Ifng treatment. A Pearson correlation cut-off of 0.9 was set to filter edges in the network and the resultant graph was clustered using the graph-based clustering algorithm MCL set at an inflation value of 2.2. Each node represents a transcript and nodes are coloured according to the cluster to which they belong. Nodes belonging to the same cluster share a common pattern of expression over the time-course following Ifng treat- ment. b) A view of the 26 clusters defined from the network graph in 5a. The size of each sphere representing a clus- ter corresponds to the size of its node membership. Clusters are assigned a description of the co-expression pattern they present over the time course and are coloured according to whether the nodes within those clusters are up-regulated (orange) or down-regulated (green) following the Ifng treatment. a b BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 9 of 15 (page number not for citation purposes) tions we have made is in the reliance of the original EPN (and the emerging SBGN standard) on multiple types of arrow heads to infer different meaning to the interactions. We have used only one type of arrowhead and relied far more heavily on the use of transition nodes or annotation nodes to infer the nature of the transition from one molecular state to another and add information to edges. We found this system to improve the readability of the maps as well as provide greater flexibility in the range of concepts that may be depicted. The pathway diagrams cre- ated using this notation scheme function without the use of colour and do not therefore lose their semantics if viewed without it. Nevertheless, colour does provide a powerful device for increasing the visual impact of the fig- ure. Here we have generally chosen apposite or symbolic colours to represent the appropriate interaction; for exam- ple red for inhibition, green for activation. However, it must be emphasized that the exact colour scheme is not important and should be seen as customizable to suit an individuals taste or limitations in colour recognition. The pathway map described here (Figure 3) consists of a total of 295 nodes of which 140 are proteins, 99 com- plexes, 44 genes, and 12 other components (pathogens, DNA, RNA etc). A total of 272 interactions are described in the pathway map, of these 85 are binding events, 149 are various activation state modulations (67 activation of gene expression, 26 phosphorylation, 7 auto-phosphor- ylation, 1 dephosphoylation, 23 cleavage, 9 transloca- tions and 16 activation by processes not defined). There are 10 inhibition reactions, 4 of these are inhibition of gene expression, 3 are inhibition of cleavage, and 1 is an inhibition of translocation. A total of 26 translocation events occur as well as 2 protein dissociations. 282 differ- ent references support the interactions shown on the path- way [see Additional file 3]. In many circumstances the same paper may describe multiple interactions, for exam- ple Chaudhary et al., (1997) report that both TNFRSF10A and TNFRSF10B recruit the protein FADD during apopto- sis signalling [27]. A detailed description of the biological content of this pathway diagram is given in Additional file 4. In order to check the integrity of the network each input (e.g. cytokine or pathogen molecule), was highlighted in turn and the logical flow of information from this input followed through the diagram. By following the flow of information from each pathway input, a different but expected output was observed, be that the activation of transcription or a process such as apoptosis (Figure 6a & b). This suggests that although several signalling pathways have been integrated to form this diagram the specificity of connectivity has not been lost. Use of Pathway Diagram in the Interpretation of Transcriptomics Data In order to demonstrate the utility of this pathway dia- gram in the interpretation of transcriptomics data we have examined the transcriptional events following the treat- ment of mouse bone marrow derived macrophages (BMDM) with interferon-gamma (Ifng). Using the net- work analysis tool BioLayout Express3D [23] we con- structed a 3-D network of transcripts identified as being differently expressed following Ifng stimulation (Figure 5a). 1,491 transcripts were represented within the net- work, 1,274 of which grouped into 26 clusters with ? 5 members (Figure 5b). There are 154 unique proteins/ genes represented on the pathway map, 55 of which are represented within these clusters and a further 3 compo- nents were in the transcriptional network but did not fall into a cluster [see Additional file 5]. All of the genes repre- sented on the map were in clusters of up-regulated genes. Clusters of transcripts representing genes activated at dif- ferent times following treatment were then further col- lated into 3 groups of up-regulated genes; genes activated at (1) 1–2 hours, (2) 2–4 hours and (3) 4–8 hours post- treatment. Genes that were activated and included in the set of mapped genes were then highlighted on the map and the possible downstream consequences (assuming de novo protein synthesis and activity following an increase in gene transcription) were highlighted (Figure 7). In this way is has been possible for the first time to interpret these transcriptional events in the context of the possible conse- quences of these observations. During the very early phase (0–2 hours) of the response to Ifng treatment only two genes, SOC3 and IER3, corre- sponded to pathway components shown in the diagram (Figure 7a). SOCS3 (suppressor of cytokine signalling 3) is an inhibitory protein of Interferon-gamma receptor complex signalling and has also been reported elsewhere to be expressed in macrophages following interferon treat- ment [28]. The up-regulation of SOCS3 represents a clas- sical negative feedback loop required to regulate the magnitude and duration of signalling downstream of the IFNG receptor signalling, in addition to limiting the response to any subsequent cytokine stimulus [29,30]. IER3 (immediate early response 3) a stress inducible gene is a target gene of the NF-?B signalling complex NFKB1- RELA [31] and is known to be activated in response to a variety of cellular stress signals [32-35]. Although IER3 is not depicted to be directly induced by Jak-Stat signalling we understand that connectivity exists between this sig- nalling system and the NF-?B pathway. 25 components of the pathway diagram were also regulated 2–4 hours post- Ifng treatment (Figure 7b). Most noticeably members of apoptosis and TLR signalling were changing during this time and interestingly these changes occurred around the initiation or receptor signalling region of these pathways. BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 10 of 15 (page number not for citation purposes) Follow through of signalling pathways stimulated by IFNG (6a) and FASLG (6b) Figure 6 Follow through of signalling pathways stimulated by IFNG (6a) and FASLG (6b). The signalling events following the input signals of IFNG and FASLG have been highlighted on the entire map in lilac and orange, respectively. The nodes activated or directly affected by FASLG or IFN-gamma binding to their receptors are coloured and the interaction edges and gates are also highlighted. Nodes and edges not directly downstream of the FASLG or IFNG signalling are shown in grey. This figure demonstrates inputs into the pathway can clearly be followed to the expected outcome events. In the case of IFNG-input, gene transcription is the resulting event, and in the case of FASLG, apoptosis. Furthermore these examples clearly depict the inter- actions of the pathway can be followed logically and do not result in unexpected crosstalk. BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 11 of 15 (page number not for citation purposes) When observed in more detail we identified that three potential mechanisms of apoptosis induction were tar- geted; TNF, TNFRSF10 and FAS signalling. TNF, its recep- tor TNFRSF1A and an adaptor protein RIPK1 are all up- regulated, as is TNFSF10 (Trail-ligand). FAS and adaptor molecules (DAXX and CFLAR) of the FAS receptor were also increased in their expression. A similar observation was also made for TLR-signalling, as a number of key adaptors proteins (including MYD88 and IRAK2) were up-regulated in the 2–4 hour timeframe. By activating the TLR system and apoptotic machinery the cells appear to preparing themselves for contact with pathogens and priming themselves for apoptosis. One possible conse- quence of TLR signalling when followed though on the pathway diagram is the activation of the IRF5 transcrip- tion factor and indeed 5 targets of IRF5 were up-regulated at the 2–4 hour time phase (CXCL11, IFIT1, CXCL10, IFIT2, and TNFSF10). Moreover IRF5 was itself regulated at the later time points (4–8 hours) post-IFNG treatment. Another consequence of TLR-signalling is the activation of the NF-?B pathway and again the key constituents of this pathway (NFKB1 and RELA) were activated at the later time points as were some transcriptional targets of this complex. During the 4–8 hours period BID, an important amplifier of apoptotic input signals via the mitochondrial apoptotic pathway, was up-regulated (Figure 7c). BID can be cleaved and activated by any of the three aforemen- tioned apoptotic mechanisms (FASLG, TNFSF10 and TNF) [36-38] that were altered during the earlier time phase. Also up during the latter hours were members of the Jak-Stat pathway (JAK2, STAT1, STAT2, and PRKCD which phosphorylates and activates STAT1) and some tar- get genes of the Jak-Stat pathway, which could represent increased sensitivity to IFN or other cytokine signalling. The integrated pathway diagram presented at (a) 1–2 hours, (b) 2–4 hours and (c) 4–8 hours post-Ifng treatment Figure 7 The integrated pathway diagram presented at (a) 1–2 hours, (b) 2–4 hours and (c) 4–8 hours post-Ifng treat- ment. Differentially expressed genes are highlighted in red and the possible consequential downstream events resulting from the changes, (assuming de novo protein synthesis) are highlighted in blue. SOCS3 IER3 NFKBIA IL15 CXCL10 IFIT2 TNF TNFRSF1A BCL3 CXCL11 IFIT1 TNFSF10 RIPK1 DAXX CFLAR CASP4 LMNA RIPK3 MYD88 IRAK2 TLR3 TNFSF10 STAT2 STAT1 JAK2 IRF2 GBP1 TAP1 CIITA IRF2 CCL5 ICAM1 CD40 RELA NFKB1 TBK1 BIRC3 SOD2 TRAF2 TRAF1 NFKB2 IRF5 BID TLR2 TLR6 0-2 hours 2-4 hours 4-8 hours a TLR9 b c SOCS1 IRF1 IRF8 HIST2H4 FAS STAT1 PSMB9 CXCL9 PRKCD TICAM1 TRAF2 CASP1 BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 12 of 15 (page number not for citation purposes) We are acutely aware that the current pathway diagram covers only a relatively small number of the genes shown to be transcriptionally regulated following Ifng treatment. For instance none of the genes shown to be down-regu- lated by Ifng are shown in the diagram. However even with the current limited coverage we have been able to extrapolate some interesting observations by visualizing the changes and the possible downstream effect of the changes. It has been possible to appreciate the connectiv- ity and co-dependency of the changes over time and using this approach the detail of how signalling in one region may have downstream effects on another signalling sys- tem can be hypothesized and in many examples here extracted. Critical Review of Pathway In constructing this integrated map of macrophage activa- tion pathways we have attempted to represent events in a detailed, accurate and logical fashion. However, it must be emphasized that this map is by its nature a biased view of events. Its construction has been primarily driven by our interest in understanding signalling events in the macro- phage and interpretation of the literature is an unavoida- bly flawed process; determining what constitutes good evidence for an interaction and what does not, is often dif- ficult to judge especially for those who do not specifically work in the area. Furthermore, any view of what consti- tutes a given pathway is also highly subjective and is always being driven by an individual's perspective and sci- entific trends, as well as current knowledge. Even though pathway diagrams typically depict individual pathways in isolation of other systems, in reality it is well recognized that there is significant overlap in pathway membership and cross-talk between related pathways. Input from one signalling pathway can influence the outcome in another, underscoring the need to view the connections between various signalling systems. Indeed, when one searches for the known interactions of any well characterized protein using database tools such as String [39] or Ingenuity [40] one is potentially led in many directions, each interacting protein in turn leading to an ever expanding network of molecular interactions. Therefore when drawing pathway maps such as the one described here, it is impossible to include all the known interactions of any given compo- nent. We are aware there are other systems important in their regulation which have could be included, most noticeably, NOD/NALP receptor signalling, MAP kinase cascades, interleukin and other cytokine/chemokine sys- tems, many aspects of the TNF-family of proteins, antigen presentation and cell cycle pathway, to name but a few. Some of these systems are now being added to the path- way diagram but this is largely being driven by our need to interpret the results of systems-level analysis of the macrophages response to pathogens and cytokines. Indeed, the fact that this pathway is far from complete is further emphasized by its use in interpreting the transcrip- tional response to Ifng. Of the 1,141 transcripts falling into clusters of co-regulated genes following Ifng treat- ment, only 55 were represented on the map and the map so far includes only 44 genes in total as being regulated by any transcription factor. This therefore highlights the fact that there is some considerable way to go if we are to gen- erate a complete model of the potential downstream events following the interferon signalling cascade. In the case of the signalling systems described here, the interaction data is derived from the available literature and is therefore dependant on the quality of that work, the biological system from which that information was derived and as already mentioned represents a subjective view of the information available. Seldom do signalling pathways operate independently of each other therefore analyzing only a subset of nodes known to belong to a particular pathway is unlikely to be insightful as to the activity of the system as a whole. With so many of pieces of the jigsaw missing and many aspects of the activity of these large integrated molecular networks still unknown, performing meaningful analyses on relatively small sec- tions of what is otherwise an immense network of inter- acting proteins, is unlikely to deliver accurate or biologically representative predictions for some time. The current notation system used for the pathway pre- sented here arguably works well up to this size of pathway and the end result we hope will serve as a useful reference for biologists interested in these systems. However, scala- bility of pathway diagrams is an important issue especially when a compromise must be reached between presenting a human readable map with one that captures the exten- sive interaction data now available for many molecules. Although we intend to continue to consolidate and add interactions to the current map we are aware that this could prove difficult in number of respects. When new components are added, in order to place them near to the site of their interacting partners the layout of the entire graph sometimes needs to be manually altered to make space. Furthermore, as functional units of an integrated pathway network frequently share components, proteins often referred to as hubs, it is often impossible to place a component near to all its interacting partners requiring edges (interactions) to span large distances across the map. One method of reducing long edge lengths is to depict individual components more than once within a given cellular compartment. However, this in turn adds to the issue of scalability as the additional nodes consume more space, add more complexity and the visual link between components of the pathway are lost. We have therefore been exploring alternative approaches to over- come the issue of scalability in pathway depictions. One approach is to use automated layout algorithms to draw BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 13 of 15 (page number not for citation purposes) the relationships between pathway components. Certain layout algorithms are very effective at displaying connec- tivity between components with little or no need for man- ual intervention (Figure 4a & b). This allows the rendering of relatively large pathway diagrams quickly and easily, whilst retaining much of the biologist friendly aspects to the diagrams. What is lost is the spatial layout according to the cellular compartment of components. However this aspect can be retained, at least in part, by the use of colour to signify in which compartment they reside. A second approach for dealing with large interaction networks/ pathways is to visualize them in 3-dimensional space. Using the tool BioLayout Express3D recently developed by us [23] we have found it possible to render very large net- works. In this instance the shape, size and colour can all be used to distinguish between different component types and colour can be overlaid to indicate cellular compart- ment (Figure 4d). Whilst arrow heads are not supported in 3-D mode directionality is reinstated when graphs or selected portions of large graphs are converted to 2-D net- works. Conclusion With the majority of the components of life defined, at least at some level, there is an increasing desire to put the parts together in order to construct models of biological systems which can be tested and refined. In this respect, the value of logically presented pathway diagrams is becoming ever more apparent given the growing need to systematically organize and describe the interactions between the various components that make up a cell. Pathway diagrams serve several purposes; they can be used to capture a large amount of information, provide a point of reference for researchers with an interest in the pathway or particular member of that pathway, and can be used to aid the interpretation of systems level analyses. The pathway presented here is by no means a comprehen- sive view of all the pathways involved in macrophage acti- vation, but acts a worked example of how a number of key pathways might be represented in what we hope is a logi- cal and unambiguous fashion. However, with the visual modifications to the EPN scheme we believe we have ful- filled the primary objectives of providing a graphical nota- tion that is both useable by biologists and which could still serve as the basis for computational model develop- ment. So whilst others have gone some way to address the issue of human readability of their pathway diagrams we believe that we have derived an elegant yet simple nota- tion scheme that better addresses the needs of biologists. The mapping process is a continuing effort and during the next steps we aim to consolidate and expand the content of the diagram. This in turn may require refinements to the notation system as issues in depicting the relation between components and the cellular components in which they are active arise. As we enhance our under- standing of individual signalling pathways and how they integrate with others this will aid understanding of immu- nological disorders at a molecular level. Building pathway diagrams or networks of interactions from the existing knowledgebase is one of the milestones towards the appli- cation of pathway and systems biology to the field of medicine. Authors' contributions SR constructed the integrated pathway diagram, contrib- uted to the development of the notation system, partici- pated in the expression profiling and analysis, and helped to draft the manuscript. KR contributed to the pathway development efforts and standardisation of pathway data collection and storage. PL contributed to the construction of pathway, collection of molecular interaction data and development of the notation scheme. DP set up the Ifng time course study. AE developed BioLayout Express3D vis- ualisation of the pathway diagram. PG originally con- ceived the EPN scheme and has supported its continued development. TF oversaw and contributed to the pathway construction, orchestrated the development of the EPN scheme, conceived the Ifng time course study, and its analysis and drafted the manuscript. Additional material Additional file 1 Pathway interaction list. Interactions included in the pathway map are listed (in no particular order) in this data file. Official HGNC (human gene nomenclature committee) gene symbols are used to name the inter- acting components along with a brief description of the type of interaction and its cellular location. Entrez gene IDs of interacting components are also provided as are the PubMed IDs of the reference(s) supporting each interaction. Click here for file [http://www.biomedcentral.com/content/supplementary/1752- 0509-2-36-S1.xls] Additional file 2 Diagram of signalling pathways central to macrophage activation. This file can be opened, viewed and edited by users using the freely available graph-editor software yEd (yFiles software, Tubingen, Germany). This can be downloaded at [22] where full downloading instructions are described. PubMed IDs supporting the interactions of the pathway are stored on appropriate edges within this .graphml yEd file. Once an edge is selected the PubMed ID may be viewed within the descriptions tab of the properties box for that edge. Click here for file [http://www.biomedcentral.com/content/supplementary/1752- 0509-2-36-S2.zip] BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 14 of 15 (page number not for citation purposes) Acknowledgements This work was supported in part by INFOBIOMED EU FP6 programme, BBSRC and Wellcome Trust. References 1. Kitano H, Funahashi A, Matsuoka Y, Oda K: Using process dia- grams for the graphical representation of biological net- works. Nat Biotechnol 2005, 23(8):961-966. 2. Kohn KW: Molecular interaction map of the mammalian cell cycle control and DNA repair systems. Mol Biol Cell 1999, 10(8):2703-2734. 3. Kohn KW, Aladjem MI, Weinstein JN, Pommier Y: Molecular inter- action maps of bioregulatory networks: a general rubric for systems biology. Mol Biol Cell 2006, 17(1):1-13. 4. Systems Biology Graphical Notation [http://sbgn.org/] 5. 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Charles CH, Yoon JK, Simske JS, Lau LF: Genomic structure, cDNA sequence, and expression of gly96, a growth factor- Additional file 3 Bibliography of references supporting interactions on the integrated path- way diagram. Within this document a list of the 282 different references supporting the interactions on the pathway map are provided in alphabet- ical order (by author name). Click here for file [http://www.biomedcentral.com/content/supplementary/1752- 0509-2-36-S3.doc] Additional file 4 Description of the biological content of the pathway. A description of the signalling of the four pathways (Toll-like receptor, interferon, NF-?B and apoptosis) depicted on the integrated pathway diagram is provided here. The interconnectivity of these pathways and their significance in innate immune signalling is also discussed in this section. Click here for file [http://www.biomedcentral.com/content/supplementary/1752- 0509-2-36-S4.doc] Additional file 5 Interferon gamma regulated genes. A summary of the analysis of the 58 genes present on both the pathway map and in a transcriptional network of differentially expressed genes following Ifng stimulation. A transcrip- tional network of all differentially expressed genes (above 1.6 fold change) was constructed and clustered using the graph-based clustering algorithm MCL set at an inflation value of 2.2. This resulted in 26 different clusters, which were then assigned a description of the co-expression pattern they represent over the time course. The cluster numbers and the descriptions of co-expression pattern are shown in this data sheet for the genes present on the pathway diagram. 3 of these genes did not appear in any cluster. Also included in this table is a summary of the gene expression changes according to annova and Empirical Bayes calculations. RMA normalized expression values are included for each gene across the time course as are gene descriptions and GO (gene ontology) annotations for the 58 genes. Click here for file [http://www.biomedcentral.com/content/supplementary/1752- 0509-2-36-S5.xls] Publish with BioMed Central and every scientist can read your work free of charge "BioMed Central will be the most significant development for disseminating the results of biomedical research in our lifetime." Sir Paul Nurse, Cancer Research UK Your research papers will be: available free of charge to the entire biomedical community peer reviewed and published immediately upon acceptance cited in PubMed and archived on PubMed Central yours — you keep the copyright Submit your manuscript here: http://www.biomedcentral.com/info/publishing_adv.asp BioMedcentral BMC Systems Biology 2008, 2:36 http://www.biomedcentral.com/1752-0509/2/36 Page 15 of 15 (page number not for citation purposes) inducible immediate-early gene encoding a short-lived glyc- osylated protein. Oncogene 1993, 8(3):797-801. 33. 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Ingenuity Pathway Analysis Software [http://www.ingenu ity.com]	18433497	TBK1 = ( External_Activator ) IL1R1 = ( External_Activator ) APAF1gene = ( TP53nucleus ) ILIB_IL1R1_MYD88_IRAK1_IRAK4 = ( ILIB_IL1R1 AND ( ( ( IRAK4 AND IRAK1 AND MYD88 ) ) ) ) TNFRSF10B = ( External_Activator ) RELAp65_NFKB1p50cytoplasm = ( NFKBIA_RELAp65_NFKB1p50 AND ( ( ( MAP3K7 OR RPS6KA5 OR IKBKB OR CHUK OR TBK1 OR PRKCZ ) ) ) ) BAX = ( Mitochondrial_Activator ) BCL2_BAX = ( BCL2 AND ( ( ( BAX ) ) ) ) TNF_BAG4_TNFRSF1A = ( TNF AND ( ( ( BAG4_TNFRSF1A ) ) ) ) EP300 = ( External_Activator ) STAT1gene = ( IRF1_IRF1nucleus ) PARP = ( External_Activator ) BCL3_NFKB2p52_NFKB2p52 = ( BCL3 AND ( ( ( NFKB2p52_NFKB2p52nucleus ) ) ) ) TLR9_TLR9 = ( TLR9 AND ( ( ( Viral_Bacterial_CpG ) ) ) ) IRF3_IRF3cytoplasm = ( IRF3 ) ISGF3cytoplasm = ( STAT1_STAT2 AND ( ( ( IRF9 ) ) ) ) LMNA = ( External_Activator ) TNFSF10_TNFRSF10A = ( TNFSF10 AND ( ( ( TNFRSF10A ) ) ) ) GAS2 = ( External_Activator ) IFNGR1 = ( External_Activator ) IRF1gene = ( STAT1_STAT1nucleus_p2 ) TNF_TNFRSF1B = ( TNF AND ( ( ( TNFRSF1B ) ) ) ) STAT1_STAT1_IRF9cytoplasm = ( STAT1 AND ( ( ( IRF9 ) ) ) ) TICAM1 = ( External_Activator ) BIRC4gene = ( RELAp65_NFBK1p50nucleus ) cLMNA = ( LMNA AND ( ( ( CASP6nucleus ) ) ) ) TOLLIP = ( External_Activator ) TNFSF10gene = ( IRF5_IRF5nucleus ) OR ( IRF1_IRF1nucleus ) STAT1_STAT1_IRF9nucleus = ( STAT1_STAT1_IRF9cytoplasm ) FASLGgene = ( TP53nucleus ) OR ( IRF1_IRF1nucleus ) TLR1_TLR2_TIRAP_MYD88_IRAK2_IRAK1_IRAK4_TRAF6 = ( TLR1_TLR2_TIRAP_MYD88_IRAK2_IRAK1_IRAK4 AND ( ( ( TRAF6 ) ) ) ) IRF5_IRF7nucleus = ( IRF5_IRF7cytoplasm ) Apoptosis = ( Inactive_DNA_Repair ) OR ( Cell_Shrinkage ) OR ( Inactivation_of_Protein_Synthesis ) OR ( DNA_Fragmentation ) HLA_Bgene = ( IRF8 ) RELAp65_NFBK1p50nucleus = ( RELAp65_NFKB1p50cytoplasm ) TLR3 = ( External_Activator ) IRAK1 = ( External_Activator ) BID = ( External_Activator ) IRF7_IRF7cytoplasm = ( IRF7 ) BCL2A1gene = ( RELAp65_NFBK1p50nucleus ) TNFSF13B_TNFRSF17_TRAF5 = ( TNFSF13B_TNFRSF17 AND ( ( ( TRAF5 ) ) ) ) PSMB9gene = ( IRF2 ) OR ( IRF1_IRF1nucleus ) IFNGR2 = ( External_Activator ) CXCL10gene = ( CBP AND ( ( ( IRF3_IRF7nucleus OR IRF3_IRF3nucleus ) ) ) ) OR ( ISGF3nucleus ) IRF5 = ( TLR7_MYD88_TRAF6_IRF5 ) OR ( Virus ) OR ( TLR9_MYD88_TRAF6_IRF5 ) TLR5 = ( External_Activator ) PDCD8_HSPA1A = ( PDCD8cytoplasm AND ( ( ( HSPA1A ) ) ) ) Cell_Shrinkage = ( cGAS2 ) OR ( cLMNA ) CHUK_CHUK = ( CHUK AND ( ( ( MAP3K14 ) ) ) ) JAK2 = ( External_Activator ) CBP = ( EP300 AND ( ( ( CREBBP ) ) ) ) CKII = ( IRF1_IRF1_Activator ) DIABLOcytoplasm = ( DIABLOmitochondria AND ( ( ( BAK1 OR BAX OR tBID ) ) ) ) IRF5_IRF5nucleus = ( IRF5_IRF5cytoplasm ) IRF7 = ( IKBKE_TBK1 ) CCL5gene = ( IRF1_IRF1nucleus ) MYD88 = ( External_Activator ) BAG4 = ( External_Activator ) OR ( TNF_BAG4_TNFRSF1A ) CYBBgene = ( IRF8 AND ( ( ( SPI1 ) ) ) ) ILIB_IL1R1_MYD88_IRAK1_IRAK4_TRAF6 = ( ILIB_IL1R1_MYD88_IRAK1_IRAK4 AND ( ( ( TRAF6 ) ) ) ) EIF2AK2_PRKRA = ( EIF2AK2cytoplasm AND ( ( ( PRKRA ) ) ) ) STAT1 = ( IFNGR ) IFNA_IFNA = ( IFNA ) BAK1gene = ( IRF5_IRF5nucleus ) ISGF3nucleus = ( ISGF3cytoplasm ) TLR4_TICAM1_TICAM2 = ( TLR4 AND ( ( ( TICAM2 AND TICAM1 ) ) ) ) SP100gene = ( IRF5_IRF5nucleus ) RELA_p65 = ( RELA_NFKB1_Activator ) TNFSF10_TNFSF10B_FADD = ( TNFSF10_TNFSF10B AND ( ( ( FADD ) ) ) ) IPARP = ( PARP AND ( ( ( CASP3nucleus OR CASP7nucleus ) ) ) ) TLR5_MYD88_IRAK1_IRAK4_TRAF6 = ( TLR5_MYD88_IRAK1_IRAK4 AND ( ( ( TRAF6 ) ) ) ) IFNB1_IFNB1 = ( IFNB1 ) IRF3_IRF7nucleus = ( IRF3_IRF7cytoplasm ) IRF1cytoplasm = ( PKC ) OR ( PKA ) OR ( CKII ) PTP = ( External_Activator ) TRAF2gene = ( RELAp65_NFBK1p50nucleus ) NFKB1_p50 = ( RELA_NFKB1_Activator ) IRAK4 = ( External_Activator ) BIRC3gene = ( RELAp65_NFBK1p50nucleus ) CASP9 = ( CASP6_Activator ) Inactivation_of_Protein_Synthesis = ( EIF2S1 ) FAF1 = ( External_Activator ) BCL3 = ( External_Activator ) TNF_TNFRSF1A = ( TNF_BAG4_TNFRSF1A ) CASP1 = ( ProCASP1 AND ( ( ( CASP4 ) ) ) ) CFLAR = ( External_Activator ) TLR2_TLR6_TOLLIP_MYD88_IRAK1_IRAK4 = ( TLR2_TLR6 AND ( ( ( TOLLIP AND IRAK4 AND IRAK1 AND MYD88 ) ) ) ) CHUK = ( External_Activator ) TRAF6 = ( External_Activator ) TLR2 = ( External_Activator ) TRAF1gene = ( RELAp65_NFBK1p50nucleus ) TLR3_TICAM1_TICAM2 = ( TLR3_TLR3 AND ( ( ( TICAM2 AND TICAM1 ) ) ) ) TNFRSF1A = ( External_Activator ) FASgene = ( RELAp65_NFBK1p50nucleus ) FAS = ( External_Activator ) TLR1_TLR2 = ( Triacyl_Lipopeptides ) FASLG_FAS = ( FASLG AND ( ( ( FAS ) ) ) ) TLR7 = ( External_Activator ) ProCASP8 = ( External_Activator ) IRF7_IRF7nucleus = ( IRF7_IRF7cytoplasm ) NFKB2p52_NFKB2p52nucleus = ( NFKB2p52_NFKB2p52cytoplasm ) CASP3cytoplasm = ( ProCASP3 AND ( ( ( Apoptosome OR CASP4 OR CASP8 ) ) ) ) TNF_TNFRSF1A_FADD_TRADD = ( TNF_TNFRSF1A AND ( ( ( TRADD AND FADD ) ) ) ) TLR9 = ( External_Activator ) BAD = ( Mitochondrial_Activator ) BAG4_TNFRSF1A = ( BAG4 AND ( ( ( TNFRSF1A ) ) ) ) CASP4 = ( ProCASP4 ) CASP7nucleus = ( CASP7cytoplasm ) BCL2A1 = ( RELAp65_NFBK1p50nucleus ) TLR3_TICAM1_TICAM2_TBK1 = ( TLR3_TICAM1_TICAM2 AND ( ( ( TBK1 ) ) ) ) Proteasome = ( External_Activator ) PDCD8mitochondria = ( Mitochondrial_Activator ) NFKB2p100_RELB_Ub = ( NFKB2p100_RELBcytoplasm AND ( ( ( Ub ) ) ) ) PTPN2 = ( External_Activator ) IKBKE_TBK1 = ( TLR4_TICAM1_TICAM2 AND ( ( ( TBK1 AND IKBKE ) ) ) ) CYCScytoplasm = ( CYCSmytochondria AND ( ( ( BAK1 OR BAX OR tBID ) ) ) ) IRF1_IRF1cytoplasm = ( IRF1cytoplasm ) BIRC4cytoplasm = NOT ( ( DIABLOcytoplasm ) OR ( HTRA2cytoplasm ) ) TLR1_TLR2_TIRAP_MYD88_IRAK2_IRAK1_IRAK4 = ( TLR1_TLR2 AND ( ( ( IRAK4 AND IRAK1 AND IRAK2 AND MYD88 AND TIRAP ) ) ) ) TLR5_MYD88_IRAK1_IRAK4 = ( TLR5_TLR5 AND ( ( ( IRAK4 AND IRAK1 AND MYD88 ) ) ) ) IRF1_IRF1nucleus = ( IRF1_IRF1cytoplasm ) PRKCZ = ( External_Activator ) NFKB2p52_RELBcytoplasm = ( NFKB2p100_RELB_Ub AND ( ( ( Proteasome ) ) ) ) RELB = ( External_Activator ) Diacyl_Lipopeptides = ( Bacteria ) SOD2gene = ( RELAp65_NFBK1p50nucleus ) NFKB2p100_NFKB2p100_Ub = ( NFKB2p100_NFKB2p100cytoplasm AND ( ( ( Ub ) ) ) ) RPS6KA5 = ( External_Activator ) IFNAR1 = ( External_Activator ) TLR3_TICAM1_TICAM2_TRAF6 = ( TLR3_TICAM1_TICAM2 AND ( ( ( TRAF6 ) ) ) ) PDCD8cytoplasm = ( tBID AND ( ( ( PDCD8mitochondria ) ) ) ) ENDOGcytoplasm = ( tBID AND ( ( ( ENDOGmitochondria ) ) ) ) FASLG_FAS_FADD_FAF1_DAXX = ( FASLG_FAS AND ( ( ( FAF1 AND FADD AND DAXX ) ) ) ) TLR3_TICAM1_TICAM2_RIPK1 = ( TLR3_TICAM1_TICAM2 AND ( ( ( RIPK1 ) ) ) ) NFKB2p52_RELBnucleus = ( NFKB2p52_RELBcytoplasm ) TNFRSF17 = ( External_Activator ) LPS = ( Bacteria ) ENDOGnucleus = ( ENDOGcytoplasm ) DNA_Fragmentation = ( IDFFA ) OR ( Fragmented_DNAnucleus ) HSPA1A = ( External_Activator ) Flagellin = ( Bacteria ) CXCL9gene = ( STAT1_STAT1nucleus_p2 ) TLR9_MYD88_TRAF6 = ( TLR9_MYD88_IRAK1_IRAK4_TRAF6 ) NFKB2p100 = ( External_Activator ) TLR3_TLR3 = ( dsRNA AND ( ( ( TLR3 ) ) ) ) ProCASP3 = ( CASP3_Activator ) IRF3_IRF3nucleus = ( IRF3_IRF3cytoplasm ) IRAK2 = ( External_Activator ) Inactive_DNA_Repair = ( IPARP ) TAP1gene = ( IRF1_IRF1nucleus ) OR ( IRF2 ) ProCASP7 = ( CASP7_Activator ) EIF2AK2cytoplasm = ( dsRNA ) ILIB_IL1R1 = ( ILIB AND ( ( ( IL1R1 ) ) ) ) BIRC2 = ( External_Activator ) STAT1_STAT1cytoplasm = ( STAT1 AND ( ( ( PRKCD ) ) ) ) STAT1_STAT2 = ( STAT1 AND ( ( ( STAT2 ) ) ) ) TRAF5 = ( External_Activator ) IRF3 = ( TLR3_TICAM1_TICAM2_TBK1 ) OR ( IKBKE_TBK1 ) IDFFA = ( DFFA AND ( ( ( CASP3nucleus ) ) ) ) TLR6 = ( External_Activator ) IFR5gene = ( STAT1_STAT1_IRF9nucleus ) OR ( TP53nucleus ) HIST2H4gene = ( IRF2 ) OR ( IRF1_IRF1nucleus ) IL12Bgene = ( IRF1_IRF1nucleus ) TNF_TNFRSF1B_TRAF2 = ( TNF_TNFRSF1B AND ( ( ( TRAF2cytoplasm ) ) ) ) CD40 = ( External_Activator ) IFNAR2 = ( External_Activator ) PRKCD = ( External_Activator ) TYK2 = ( External_Activator ) ENDOGmitochondria = ( Mitochondrial_Activator ) PKC = ( IRF1_IRF1_Activator ) TLR9_MYD88_IRAK1_IRAK4_TRAF6 = ( TLR9_MYD88_IRAK1_IRAK4 AND ( ( ( TRAF6 ) ) ) ) cGAS2 = ( GAS2 AND ( ( ( CASP3nucleus ) ) ) ) IER3gene = ( RELAp65_NFBK1p50nucleus ) FASLG_FAS_FADD_FAF1_DAXX_CFLAR = ( FASLG_FAS_FADD_FAF1_DAXX AND ( ( ( CFLAR ) ) ) ) CREBBP = ( External_Activator ) PLSCR1gene = ( IRF5_IRF5nucleus ) CD40_CD40LG = ( CD40 AND ( ( ( CD40LG ) ) ) ) TLR2_TLR6_TOLLIP_MYD88_IRAK1_IRAK4_TRAF6 = ( TLR2_TLR6_TOLLIP_MYD88_IRAK1_IRAK4 AND ( ( ( TRAF6 ) ) ) ) CXCL11gene = ( IRF5_IRF5nucleus ) TLR7_MYD88_TRAF6_IRF5 = ( TLR7_TLR7 AND ( ( ( TRAF6 AND MYD88 ) AND ( ( ( NOT IRF5 ) ) ) ) ) ) TLR2_TLR6 = ( TLR2 AND ( ( ( Diacyl_Lipopeptides AND TLR6 ) ) ) ) BCL2L1_BAD = ( BCL2L1mitochondria AND ( ( ( BAD ) ) ) ) NFKB2p100_RELBcytoplasm = ( NFKB2p100 AND ( ( ( CHUK_CHUK AND RELB ) ) ) ) TRADD = ( External_Activator ) ssRNA = ( Virus ) TNF_TNFRSF1A_FADD_TRADD_TRAF2_RIPK1 = ( TNF_TNFRSF1A_FADD_TRADD AND ( ( ( TRAF2cytoplasm AND RIPK1 ) ) ) ) TLR5_TLR5 = ( TLR5 AND ( ( ( Flagellin ) ) ) ) TP53nucleus = ( TP53cytoplasm ) Ub = ( External_Activator ) IKBKG_CHUK_IKBKB = ( TLR3_TICAM1_TICAM2_RIPK1_RIPK3 AND ( ( ( IKBKB AND CHUK AND IKBKG ) ) ) ) OR ( IKBKG AND ( ( ( IKBKB AND MAP3K7IP1_MAP3K7IP2_MAP3K7 AND CHUK ) ) ) ) MAP3K7IP2 = ( External_Activator ) DAXX = ( External_Activator ) dsRNA = ( Virus ) BCL2 = ( Mitochondrial_Activator ) CYCSmytochondria = ( Mitochondrial_Activator ) JAK1 = ( External_Activator ) TRAF3 = ( External_Activator ) IFNAR = ( IFNA AND ( ( ( IFNAR2 AND JAK1 AND TYK2 AND IFNAR1 ) ) ) ) OR ( IFNB1 AND ( ( ( IFNAR2 AND JAK1 AND TYK2 AND IFNAR1 ) ) ) ) TNF_IKBKG_Complex = ( TNF_TNFRSF1A_FADD_TRADD_TRAF2_RIPK1 AND ( ( ( IKBKB AND CHUK AND IKBKG ) ) ) ) CASP6cytoplasm = ( ProCASP6 AND ( ( ( CASP9 ) ) ) ) CASP10 = ( ProCASP10 AND ( ( ( TNF_TNFRSF1A_FADD_TRADD ) ) ) ) STAT2 = ( IFNAR ) MAP3K7IP1 = ( External_Activator ) IRF2gene = ( IRF1_IRF1nucleus ) PRKRA = ( External_Activator ) SOCS1 = ( External_Activator ) IFIT2gene = ( CBP AND ( ( ( IRF3_IRF7nucleus OR IRF3_IRF3nucleus ) ) ) ) OR ( ISGF3nucleus ) BBC3gene = ( TP53nucleus ) OAS1gene = ( IRF8 ) OR ( IRF1_IRF1nucleus ) OR ( ISGF3nucleus ) OR ( IRF5_IRF5nucleus ) IKBKE = ( External_Activator ) CIITAgene = ( IRF2 ) OR ( IRF1_IRF1nucleus ) MDM2gene = ( TP53nucleus ) NFKB2p100_NFKB2p100cytoplasm = ( NFKB2p100 AND ( ( ( IKBKG_CHUK_IKBKB ) ) ) ) RIPK3 = ( External_Activator ) Fragmented_DNAnucleus = ( DNA AND ( ( ( ENDOGnucleus OR PDCD8nucleus ) ) ) ) CASP3gene = ( IRF5_IRF5nucleus ) OR ( CASP3cytoplasm ) CFLARgene = ( RELAp65_NFBK1p50nucleus ) IL1Bgene = ( IRF8 AND ( ( ( SPI1 ) ) ) ) TNFSF10_TNFSF10B = ( TNFSF10 AND ( ( ( TNFRSF10B ) ) ) ) SPI1 = ( External_Activator ) IRF5_IRF7cytoplasm = ( IRF5 ) MAP3K7IP1_MAP3K7IP2_MAP3K7 = ( TLR1_TLR2_TIRAP_MYD88_IRAK2_IRAK1_IRAK4_TRAF6 AND ( ( ( MAP3K7 AND MAP3K7IP2 AND MAP3K7IP1 ) ) ) ) OR ( TLR3_TICAM1_TICAM2_TRAF6 AND ( ( ( MAP3K7 AND MAP3K7IP2 AND MAP3K7IP1 ) ) ) ) OR ( TLR7_MYD88_IRAK1_IRAK4_TRAF6 AND ( ( ( MAP3K7 AND MAP3K7IP2 AND MAP3K7IP1 ) ) ) ) OR ( TLR9_MYD88_IRAK1_IRAK4_TRAF6 AND ( ( ( MAP3K7 AND MAP3K7IP2 AND MAP3K7IP1 ) ) ) ) OR ( ILIB_IL1R1_MYD88_IRAK1_IRAK4_TRAF6 AND ( ( ( MAP3K7 AND MAP3K7IP2 AND MAP3K7IP1 ) ) ) ) OR ( TLR2_TLR6_TOLLIP_MYD88_IRAK1_IRAK4_TRAF6 AND ( ( ( MAP3K7 AND MAP3K7IP2 AND MAP3K7IP1 ) ) ) ) OR ( TLR5_MYD88_IRAK1_IRAK4_TRAF6 AND ( ( ( MAP3K7 AND MAP3K7IP2 AND MAP3K7IP1 ) ) ) ) RIPK1 = ( External_Activator ) RIPK1gene = ( IRF5_IRF5nucleus ) IRF3_IRF5nucleus = ( IRF3_IRF5cytoplasm ) Fragmented_DNAcytoplasm = ( DNA_Fragmentation ) EIF2AK2gene = ( IRF1_IRF1nucleus ) OR ( ISGF3nucleus ) HTRA2mitochondria = ( Mitochondrial_Activator ) DFFA = ( External_Activator ) BAK1 = ( Mitochondrial_Activator ) ProCASP10 = ( External_Activator ) CASP7cytoplasm = ( ProCASP7 AND ( ( ( Apoptosome OR CASP8 OR CASP10 ) ) ) ) IKBKB = ( External_Activator ) IKBKG = ( External_Activator ) CASP2 = ( ProCASP2 AND ( ( ( Fragmented_DNAcytoplasm ) ) ) ) GBP1gene = ( IRF2 ) OR ( IRF1_IRF1nucleus ) TNFRSF1B = ( External_Activator ) IRF3_IRF7cytoplasm = ( IRF3 AND ( ( ( IRF7 ) ) ) ) MAP3K14 = ( CD40_CD40LG_TRAF3 ) OR ( TNFSF13B_TNFRSF17_TRAF5 ) OR ( TNF_TNFRSF1B_TRAF2 ) FADD = ( External_Activator ) Triacyl_Lipopeptides = ( Bacteria ) Apoptosome = ( APAF1_CYCS AND ( ( ( CASP9 ) ) ) ) IFIT1gene = ( IRF5_IRF5nucleus ) tBID = ( BID AND ( ( ( CASP8 OR CASP2 ) ) ) ) DNA = ( External_Activator ) IRF2 = ( IRF2_Activator ) ProCASP4 = ( External_Activator ) IFNGR = ( IFNG AND ( ( ( IFNGR2 AND IFNGR1 AND JAK2 ) ) ) ) TLR3_TICAM1_TICAM2_RIPK1_RIPK3 = ( TLR3_TICAM1_TICAM2_RIPK1 AND ( ( ( RIPK3 ) ) ) ) CD40_CD40LG_TRAF3 = ( CD40_CD40LG AND ( ( ( TRAF3 ) ) ) ) TP53cytoplasm = ( EIF2AK2_PRKRA ) ICAM1gene = ( STAT1_STAT1nucleus_p2 ) NFKB2p52_NFKB2p52cytoplasm = ( NFKB2p100_NFKB2p100_Ub AND ( ( ( Proteasome ) ) ) ) TLR9_MYD88_TRAF6_IRF5 = ( TLR9_TLR9 AND ( ( ( TRAF6 AND MYD88 ) AND ( ( ( NOT IRF5 ) ) ) ) ) ) PDCD8nucleus = ( PDCD8cytoplasm ) G1P2gene = ( CBP AND ( ( ( IRF3_IRF7nucleus OR IRF3_IRF3nucleus ) ) ) ) OR ( IRF1_IRF1nucleus AND ( ( ( IRF8 AND SPI1 AND IRF4 ) ) ) ) OR ( ISGF3nucleus ) OR ( IRF2 AND ( ( ( IRF8 AND SPI1 AND IRF4 ) ) ) ) TNFSF13B_TNFRSF17 = ( TNFSF13B AND ( ( ( TNFRSF17 ) ) ) ) ATF2 = ( External_Activator ) Viral_Bacterial_CpG = ( Virus ) OR ( Bacteria ) CASP3nucleus = ( CASP3cytoplasm ) TLR7_MYD88_IRAK1_IRAK4_TRAF6 = ( TLR7_MYD88_IRAK1_IRAK4 AND ( ( ( TRAF6 ) ) ) ) IRF4 = ( External_Activator ) ProCASP6 = ( CASP6_Activator ) TLR9_MYD88_IRAK1_IRAK4 = ( TLR9_TLR9 AND ( ( ( IRAK4 AND IRAK1 AND MYD88 ) ) ) ) TNFRSF10Bgene = ( TP53nucleus ) BCL2L1gene = ( RELAp65_NFBK1p50nucleus ) HTRA2cytoplasm = ( tBID AND ( ( ( HTRA2mitochondria ) ) ) ) EIF2S1 = ( EIF2AK2gene ) PKA = ( IRF1_IRF1_Activator ) TNFSF10_TNFRSF10A_FADD = ( TNFSF10_TNFRSF10A AND ( ( ( FADD ) ) ) ) TLR7_MYD88_IRAK1_IRAK4 = ( TLR7_TLR7 AND ( ( ( IRAK4 AND IRAK1 AND MYD88 ) ) ) ) G1P3gene = ( IRF8 ) CASP8 = ( ProCASP8 AND ( ( ( TNFSF10_TNFRSF10A_FADD OR FASLG_FAS_FADD_FAF1_DAXX OR FASLG_FAS_FADD_FAF1_DAXX_CFLAR OR TNFSF10_TNFSF10B_FADD ) ) ) ) TRAF2cytoplasm = ( External_Activator ) STAT1_STAT1nucleus_p2 = ( STAT1_STAT1nucleus_p1 ) STAT1_STAT1nucleus_p1 = ( STAT1_STAT1cytoplasm ) NFKBIA = ( NFKBIA_RELAp65_NFKB1p50 ) OR ( RELA_NFKB1_Activator ) IRF9 = ( External_Activator ) IRF8 = ( IRF2 ) OR ( IRF1_IRF1nucleus ) TLR7_TLR7 = ( TLR7 AND ( ( ( ssRNA ) ) ) ) APAF1_CYCS = ( APAF1 AND ( ( ( CYCScytoplasm ) ) ) ) PMAIPgene = ( IRF5_IRF5nucleus ) ProCASP2 = ( External_Activator ) TICAM2 = ( External_Activator ) SOCS3 = ( External_Activator ) IFNAgene = ( STAT1_STAT1_IRF9nucleus ) OR ( IRF3_IRF3nucleus ) OR ( IRF1_IRF1nucleus ) OR ( ISGF3nucleus ) OR ( IRF5_IRF5nucleus ) OR ( IRF7_IRF7nucleus ) OR ( IRF3_IRF5nucleus ) OR ( IRF3_IRF7nucleus ) TLR4 = ( LPS ) TIRAP = ( External_Activator ) IRF5_IRF5cytoplasm = ( IRF5 ) ProCASP1 = ( External_Activator ) IRF3_IRF5cytoplasm = ( IRF5 ) DIABLOmitochondria = ( Mitochondrial_Activator ) CASP6nucleus = ( CASP6cytoplasm ) NOS2Agene = ( External_Activator ) PRKRAgene = ( IRF5_IRF5nucleus ) TNFRSF10A = ( External_Activator ) APAF1 = ( External_Activator ) IL15gene = ( IRF1_IRF1nucleus ) IFNB1gene = ( STAT1_STAT1nucleus_p2 ) OR ( ISGF3nucleus ) OR ( IRF1_IRF1nucleus ) OR ( IRF3_IRF3nucleus ) OR ( IRF5_IRF5nucleus ) OR ( RELAp65_NFBK1p50nucleus AND ( ( ( CBP AND IRF3_IRF7nucleus AND IRF3_IRF3nucleus AND ATF2 ) ) ) ) BCL2L1mitochondria = ( Mitochondrial_Activator ) MAP3K7 = ( External_Activator ) NFKBIA_RELAp65_NFKB1p50 = ( TNF_IKBKG_Complex AND ( ( ( NFKB1_p50 AND RELA_p65 AND NFKBIA ) ) ) ) OR ( IKBKG_CHUK_IKBKB AND ( ( ( NFKB1_p50 AND RELA_p65 AND NFKBIA ) ) ) )
Network model of survival signaling in large granular lymphocyte leukemia Ranran Zhang†, Mithun Vinod Shah†, Jun Yang†, Susan B. Nyland†, Xin Liu†, Jong K. Yun‡, Re´ka Albert§¶, and Thomas P. Loughran, Jr.† †Penn State Hershey Cancer Institute and ‡Department of Pharmacology, The Pennsylvania State University College of Medicine, Hershey, PA 17033; and §Department of Physics, The Pennsylvania State University, University Park, PA 16802 Edited by Wayne M. Yokoyama, Washington University School of Medicine, St. Louis, MO, and approved September 4, 2008 (received for review July 5, 2008) T cell large granular lymphocyte (T-LGL) leukemia features a clonal expansion of antigen-primed, competent, cytotoxic T lymphocytes (CTL). To systematically understand signaling components that determine the survival of CTL in T-LGL leukemia, we constructed a T-LGL survival signaling network by integrating the signaling pathways involved in normal CTL activation and the known de- regulations of survival signaling in leukemic T-LGL. This network was subsequently translated into a predictive, discrete, dynamic model. Our model suggests that the persistence of IL-15 and PDGF is sufﬁcient to reproduce all known deregulations in leukemic T-LGL. This ﬁnding leads to the following predictions: (i) Inhibiting PDGF signaling induces apoptosis in leukemic T-LGL. (ii) Sphin- gosine kinase 1 and NFB are essential for the long-term survival of CTL in T-LGL leukemia. (iii) NFB functions downstream of PI3K and prevents apoptosis through maintaining the expression of myeloid cell leukemia sequence 1. (iv) T box expressed in T cells (T-bet) should be constitutively activated concurrently with NFB activation to reproduce the leukemic T-LGL phenotype. We vali- dated these predictions experimentally. Our study provides a model describing the signaling network involved in maintaining the long-term survival of competent CTL in humans. The model will be useful in identifying potential therapeutic targets for T-LGL leukemia and generating long-term competent CTL necessary for tumor and cancer vaccine development. discrete dynamic model nuclear factor kappa-B signal transduction network T box expressed in T cells T cell large granular lymphocyte leukemia C ytotoxic T lymphocyte (CTL) activation normally involves an initial expansion of antigen-specific CTL clones and their acquisition of cytotoxic activity. Subsequently, the activated CTL population undergoes activation-induced cell death (AICD), resulting in final stabilization of a small antigen-experienced CTL population (1). This process requires a delicate balance between proliferation, survival, and apoptosis. T cell large granular lymphocyte (T-LGL) leukemia is characterized by abnormal clonal expansion of antigen-primed mature CTL that successfully escaped AICD and remain long-term competent (2). Similar to normal activated CTL, leukemic T-LGL exhibit activation of multiple survival signaling pathways (3–5). How- ever, unlike normal activated CTL, leukemic T-LGL are not sensitive to Fas-induced apoptosis (6), a process essential for AICD (7). Recent molecular profiling data suggest that normal CTL activation and AICD are uncoupled in leukemic T-LGL (8), providing a unique opportunity to decipher the key medi- ators of CTL activation and AICD in humans. Network modeling has been increasingly used to better un- derstand complex and interactive biological systems (9, 10). Experimentally obtained signaling pathway information can be translated into a graph (network) by representing proteins, transcripts, and small molecules as network nodes and denoting the interactions between nodes as edges (9). The direction of edges follows the direction of the mass or information flow, from the upstream (source) node to the downstream (product or target) node. In addition, the edges are characterized by signs, where a positive sign indicates activation, and a negative sign indicates inhibition. Discrete dynamic modeling is widely used in modeling regulatory and signaling networks because of its straightforwardness, robustness, and compatibility with qualita- tive data (9–11). The simplest discrete models, called Boolean models, assume two possible states for each node in the network: ON (above threshold) and OFF (below threshold). The biolog- ical functions by which upstream regulators act on a downstream node can be readily translated into logical statements by using Boolean operators. In this study, we aimed to systematically understand the long-term survival of competent CTL in T-LGL leukemia by constructing a T-LGL survival signaling network and a Boolean model of the network’s dynamics. We found the constitutive presence of IL-15 and PDGF to be sufficient to reproduce all of the other signaling abnormalities. In addition, we studied the predicted key mediators of long-term CTL survival and their related signaling pathways. Results Constructing the T-LGL Survival Signaling Network. We performed an extensive literature search and constructed the T-LGL sur- vival signaling network (shown in Fig. 1) by adapting and simplifying a network describing the normal CTL activation– AICD process. The detailed method of network construction is described in supporting information (SI) Text. The information used to construct the network, summarized by giving the source node, target node, two qualifiers of the relationship, and refer- ences, is given in Table S1. The nomenclature of all of the nodes of the network before and after simplification is provided in Tables S2 and S3. The T-LGL survival signaling network incor- porates the most unique interactions through which all known deregulations in leukemic T-LGL are connected, in the context of normal CTL activation and AICD signaling. Proteins, mRNAs, and small molecules (such as lipids) were represented as nodes. ‘‘Cytoskeleton signaling’’, ‘‘Proliferation’’ and ‘‘Apoptosis’’ were also included as nodes to summarize the biological effects of a group of components in the signaling pathways and serve as the Author contributions: R.A. and T.P.L. designed research; R.Z., M.V.S., J.Y., and S.B.N. performed research; X.L. and J.K.Y. contributed new reagents/analytic tools; R.Z., M.V.S., J.Y., S.B.N., X.L., J.K.Y., R.A., and T.P.L. analyzed data; and R.Z., R.A., and T.P.L. wrote the paper. The authors declare no conﬂict of interest. This article is a PNAS Direct Submission. ¶To whom correspondence may be addressed at: Department of Physics, 122 Davey Labo- ratory, The Pennsylvania State University, University Park, PA 16802. E-mail: ralbert@ phys.psu.edu. To whom correspondence may be addressed at: Penn State Hershey Cancer Institute, 500 University Drive, Hershey, PA 17033. E-mail: tloughran@psu.edu. This article contains supporting information online at www.pnas.org/cgi/content/full/ 0806447105/DCSupplemental. © 2008 by The National Academy of Sciences of the USA 16308–16313 PNAS October 21, 2008 vol. 105 no. 42 www.pnas.orgcgidoi10.1073pnas.0806447105 indicators of cell fate. Because of the unknown etiology of T-LGL leukemia (2), we used ‘‘Stimuli’’ as a node to indicate antigen stimulation (12). This network contains 58 nodes and 123 edges. The biological description of the T-LGL survival signaling network is given in SI Text. Translating the T-LGL Survival Signaling Network into a Predictive, Discrete, Dynamic Model. To understand the dynamics of signaling abnormalities in T-LGL leukemia, we translated the T-LGL survival signaling network into a Boolean model. Each network node was described by one of two possible states: ON or OFF. The ON state means the production of a small molecule, the production and translation of a transcript, or the activation of a protein/process whereas the OFF state means the absence of a small molecule or transcript or the inhibition of a protein/ process. The regulation of each component in the network was described by using the Boolean logical operators OR, AND, and NOT (see Table S4). OR represents the combined effect of independent upstream regulators on a downstream node whereas AND indicates the conditional dependency of upstream regulators to achieve a downstream effect. NOT represents the effect of inhibitory regulators and can be combined with acti- vating regulations by using either OR or AND. The rules were derived from the regulatory relationships reflected in the net- work and from the literature. The detailed justification of the logical rules for all nodes in the network is provided in SI Text. As in the biological system, there is a time lag between the state change of the regulators and the state change of the targets. The kinetics of signal propagation is rarely known from experiments. Thus, we used an asynchronous updating algorithm (10, 11) that samples differences in the speed of signal propagation. The detailed algorithm is described in SI Text. To reproduce how a population of cells responds to the same signal and to simulate cell-to-cell variability, we performed multiple simulations with the same initial conditions but differ- ent updating orders (i.e., different timing). The model was allowed to update for multiple rounds until the node Apoptosis became ON in all simulations (recapitulating the death of all CTL) or stabilized in the OFF state in a fraction of simulations (recapitulating the stabilization of the long-term surviving CTL population). The state of Stimuli was set to ON at the beginning of every simulation, recapitulating the activation of CTL by antigen. The states of the other nodes were set according to their states in resting T cells, as described in the SI Text. At the end of the simulation, if the state of a node stabilized at ON even though it was OFF at the beginning of the simulation, we consider it as constitutively active. If the state of a node stabilized at OFF even though it was in the ON state at the beginning of the simulation, or it was experimentally shown to be active after normal CTL activation, we consider it as down- regulated/inhibited. During simulations, the state of a node can be fixed to reproduce signaling perturbations. Constitutive Presence of IL-15 and PDGF Is Predicted to Be Sufficient to Induce All of the Known Signaling Abnormalities in Leukemic T-LGL. Zambello et al. (13) has demonstrated the presence of mem- brane-bound IL-15 on leukemic LGL, suggesting a role of IL-15 in the pathogenesis of this disease. In the course of studying constitutive cytokine production in LGL leukemia (14), we used a protein array as an experimental method. Using this array, we had found high levels of PDGF in LGL leukemia sera (unpub- lished observation). PDGF exists in the form of homodimers or heterodimers of two polypeptides: PDGF-A and PDGF-B (15). In the current study, we examined the level of PDGF-BB level in the sera of 22 T-LGL leukemia patients and 39 healthy donors and found that PDGF-BB was significantly higher in patient serum compared with normal (P 0.005) (Fig. 2A). We subsequently incorporated this deregulation into the network model. To investigate signaling abnormalities underlying long-term survival of leukemic T-LGL, we first tested whether our model could reproduce the uncoupling of CTL activation and AICD by using all known deregulations (summarized in Table S5). We did not observe the activation of the node Apoptosis in any simu- lation. Second, we probed whether all of the deregulations have to be individually initiated or whether a subset of them can cause the others. The effect of a single signaling perturbation can be identified by keeping the state of the corresponding node according to its deregulation and tracking the states of other nodes until a stable (time-independent) state is obtained. IL-15, PDGF, and Stimuli are three nodes that have been suggested to be abnormal in T-LGL leukemia without known upstream regulators in the T-LGL survival-signaling network. To recapit- ulate the effect of their deregulations without masking the effect of the perturbation tested, the states of IL-15, PDGF, and Stimuli were randomly set at ON or OFF at every round of Fig. 1. The T-LGL survival signaling network. Node and edge color represents the current knowledge of the signaling abnormalities in T-LGL leukemia. Up-regulated or constitutively active nodes are in red, down-regulated or inhibited nodes are in green, nodes that have been suggested to be deregulated (either up-regulation or down-regulation) are in blue, and the states of white nodes are unknown or unchanged compared with normal. Blue edge indicates activation and red edge indicates inhibition. The shape of the nodes indicates the cellular location: rectangular indicates intracellular components, ellipse indicates extracellular components, and diamond indicates receptors. Conceptual nodes (Stimuli, Cytoskeleton signaling, Proliferation, and Apoptosis) are labeled orange. The full names of the node labels are provided in Table S3. Zhang et al. PNAS October 21, 2008 vol. 105 no. 42 16309 MEDICAL SCIENCES updating, i.e., in a random state, except when probing for the effect of their own deregulations. Through this analysis, we discovered a hidden hierarchy among the known deregulations in leukemic T-LGL, with up- stream deregulations as the potential cause of downstream deregulations. We present these regulatory relationships as a hierarchical network in Fig. 2B. Details of the hierarchy analysis are provided in SI Text. Surprisingly, we found that keeping the state of IL-15 at ON was sufficient to reproduce all known deregulations in leukemic T-LGL when setting a random state for PDGF and Stimuli (Fig. S1). To understand the effect of PDGF and Stimuli individually upon the constant presence of IL-15, we probed all of the possible states of PDGF and Stimuli. We determined that the presence of PDGF is needed for the long-term survival of leukemic T-LGL. In contrast, the consti- tutive presence of Stimuli is not required after its initial activa- tion (Fig. 2C). We concluded that based on the available signaling information regarding T cell activation and AICD, the minimal condition required for our model to reproduce all known signaling abnormalities in T-LGL leukemia (i.e., a T- LGL-like state) is IL-15 constantly ON, PDGF intermittently ON, and Stimuli ON in the initial condition. To test the unexpected prediction that PDGF signaling, together with IL-15, maintains leukemic T-LGL survival, we inhibited PDGF receptor by using its specific inhibitor AG 1296. As shown in Fig. 2D, AG 1296 induced apoptosis specifically in T-LGL leukemia peripheral blood mononuclear cells (PBMCs) but not in normal PBMCs (n 3–4, P 0.03). Sphingosine kinase 1 (SPHK1) Is Important for the Survival of Leuke- mic T-LGL. The next question we asked was: Can we identify the key mediators that determine the uncoupling of CTL activation and AICD in T-LGL leukemia? In our experimental system, the indication that a protein (small molecule or complex) is a key mediator in the finding that altering its amount or function can induce apoptosis in leukemic T-LGL. Accordingly, a corre- sponding network node is a key mediator if its state stabilizes once a T-LGL-like state is achieved, and altering its state increases the frequency of the ON state of Apoptosis. The detailed method to identify key mediators is provided in SI Text. As summarized in Table S6, experiments already suggested nine key mediators. We first tested whether our model could identify the corresponding nodes as key mediators. A rapid increase of apoptosis frequency was observed after resetting and maintain- ing the states of all of the known key mediators individually to their opposite states (from ON to OFF or from OFF to ON) after reproducing a T-LGL-like state. Examples of simulation results are provided in Fig. S2. Based on this result, we systematically simulated the effect of individually altering the states of all nodes that stabilize when a T-LGL-like state is achieved. A list of these nodes is provided in Table S7. In addition to PDGF and its receptor, the model predicted seven additional key mediators: SPHK1, NFB, S1P, SOCS, GAP, BID, and IL2RB, all exhibiting a similar dynamics of inducing apoptosis in the model. Fig. 3A shows the effect of inhibiting SPHK1 as an example. Recently, we found that the sphingolipid signaling is deregulated in leukemic LGL (8). Thus, we tested the effect of SPHK1 inhibition on leukemic T-LGL survival experimentally by using its chemical inhibitors, SPHK1 inhibitor-I and -II (SKI-I and SKI-II) (16, 17). As shown in Figs. 3 B and C, both SKI-I and SKI-II significantly induced apoptosis in T-LGL leukemia PBMCs in a dose-dependent manner but not in normal PBMCs (n 4–6, P 0.03). NFB Maintains the Survival of Leukemic T-LGL Through STAT3- Independent Regulation of myeloid cell leukemia sequence 1 (Mcl-1). Our model predicts that NFB is constitutively active and is a key mediator of the survival of leukemic T-LGL (Fig. 4A). Consid- ering its importance in regulating T cell proliferation, cytotox- icity, and survival (18), we studied the activity and function of NFB in T-LGL leukemia. As shown in Fig. 4B, nuclear extracts of normal PBMCs rarely exhibited NFB activity as assessed by EMSA whereas NFB activity was detected in most of the nuclear extracts of T-LGL leukemia PBMCs. Next, we examined the effect of inhibiting NFB by using its specific inhibitor BAY 11–7082 (19, 20). As shown in Fig. 4C, BAY 11–7082 inhibited the constitutive activity of NFB in T-LGL leukemia PBMCs in a dose-dependent manner as as- Fig. 2. The Boolean model of the T-LGL survival signaling network predicts that constitutive presence of IL-15, and PDGF is sufﬁcient to induce all of the known deregulations in T-LGL leukemia. (A) PDGF-BB is elevated in T-LGL leukemia patient sera compared with normal. Serum level of PDGF-BB from 39 healthy donors (gray triangles) and 22 T-LGL leukemia patients (white dia- monds) was assessed by using ELISA. The ﬁgure shows a 1.4-fold increase of mean serum level of PDGF-BB (black bar) in T-LGL leukemia patients compared with normal (, P 0.005). (B) Hierarchy among known signaling deregula- tions in T-LGL leukemia. Color code for nodes and edges is the same as in Fig. 1. (C) The effects of IL15, PDGF, and Stimuli on the frequency of apoptosis during simulation. Keeping PDGF ON does not prevent the onset of apoptosis (white triangles). While keeping IL-15 ON, keeping PDGF OFF from the ﬁrst round of updating delays but cannot prevent the onset of apoptosis (white squares). Setting Stimuli ON at the beginning of the simulation and then keeping it OFF (‘‘ONCE’’) does not alter the inhibition of apoptosis upon keeping IL-15 ON in the presence of PDGF (white circles). Results were ob- tained from 400 simulations of each initial condition. (D) 10 M AG 1296 speciﬁcally induced apoptosis in T-LGL leukemia PBMCs (white circles, n 4) after 24 h but not in normal PBMCs (gray circles, n 3, , P 0.03). Each circle represents data from one patient or healthy donor. The markers (black bars) indicate the mean apoptosis percentage. 16310 www.pnas.orgcgidoi10.1073pnas.0806447105 Zhang et al. sessed by EMSA. BAY 11–7082 (1 M) significantly induced apoptosis in T-LGL leukemia PBMCs but not in normal PBMCs (n 6, P 0.009) (Fig. 4D). Based on the Boolean logical rule for NFB (see Table S4), it can be activated by PI3K or tumor progression locus 2 (TPL2)/cancer Osaka thyroid. During simulations, however, we noticed that the ON state of NFB was only determined by the constitutive activity of PI3K because resetting the state of PI3K from ON to OFF was necessary and sufficient to induce the rapid inhibition of NFB whereas altering the state of TPL2 did not affect NFB activity (Fig. 5A). We then subjected the T-LGL leukemia PBMCs to PI3K specific inhibitor LY 294002 and tested the effect on NFB activity. LY 294002 (25 M) signif- icantly inhibited the activity of NFB as assessed by EMSA (Fig. 5B) and induced apoptosis in T-LGL leukemia PBMCs (data not shown) as reported (4). BAY 11–7082 did not inhibit the activity (phosphorylation) of v-akt murine thymoma viral oncogen ho- molog (AKT), an immediate downstream target of PI3K in T-LGL leukemia PBMCs, as assessed by Western blot assay (Fig. 5C). We found that for simulations in which we reset the state of NFB from ON to OFF, the onset of apoptosis correlated tightly with the rapid down-regulation of Mcl-1 (Fig. 4A). It has been shown that STAT3 transcriptionally regulates Mcl-1 in leukemic T-LGL (3). Interestingly, our model predicted that the initial Mcl-1 down-regulation after NFB inhibition was independent of STAT3 activity (Fig. 4A). Our experimental results confirmed this prediction. As shown in Fig. 5C, the amount of Mcl-1 after BAY 11–7082 treatment did indeed decrease correspondingly to the decreased NFB activity whereas STAT3 activity remained unchanged after NFB inhibition, as assessed by EMSA, even at the highest dose of BAY 11–7082. T box expressed in T cells (T-bet) Is Constitutively Active in Leukemic T-LGL. It has been shown that leukemic T-LGL are incapable of producing IL-2 even upon in vitro stimulation (21). It has also been shown that NFB promotes IL2 transcription (18). In our model, this apparent conflict can be resolved if T-bet is consti- Fig. 3. SPHK1 is a key mediator for the survival of leukemic T-LGL. (A) The effect of SPHK1 inhibition on Apoptosis frequency in the model. The state of SPHK1 was reset to OFF after 15 rounds of updating (white squares), or left unchanged (white diamonds) after a T-LGL-like state was achieved. A rapid increase of apoptosis was observed after SPHK1 inhibition (200 simulations). (B) 20 M and 40 M SKI-I selectively induced apoptosis in T-LGL leukemia PBMCs (n 6) after 48 h but not in normal PBMCs (n 5, , P 0.03 and , P 0.01). Each circle represents data from one patient or healthy donor. The markers (black bars) indicate the mean apoptosis percentage. (C) 5 M and 10 M SKI-II selectively induced apoptosis in T-LGL leukemia PBMCs after 48 h (white circles, n 5) but not in normal PBMCs (gray circles, n 4, , P 0.02, and *, P 0.001). Each circle represents data from one patient or healthy donor. The markers (black bars) indicate the mean apoptosis percentage. Fig. 4. NFB is constitutively active in T-LGL leukemia and mediates survival of leukemic T-LGL. (A) Model prediction of the effects of NFB inhibition (200 simulations). The state of NFB was reset from ON to OFF after 15 rounds of updating, while keeping IL-15 and PDGF ON. Apoptosis (black squares) was rapidly induced after inhibiting NFB (black diamonds). The induction of apoptosis was tightly coupled with the down-regulation of Mcl-1 (). In contrast, the state of STAT3 (white triangles) remained unchanged until the simulation was terminated. (B) NFB activity in nuclear extracts of PBMCs from healthy donors and T-LGL leukemia patients. EMSA results are representative of 16 healthy donors and 8 T-LGL leukemia patients tested. White space has been inserted to indicate realigned gel lanes. (C) BAY 11–7082 inhibits NFB activity in T-LGL leukemia PBMCs. T-LGL leukemia PBMCs were treated with vehicle DMSO or 1 M, 2 M, or 5 M BAY 11–7082 for 3 h, and the activity of NFB was assessed by EMSA. Result is representative of experiments in three patients. (D) Compared with normal PBMCs (black circles, n 6), 1 M BAY 11–7082 selectively induced apoptosis in T-LGL leukemia PBMCs (white circles, n 6) after 12h treatment (, P 0.02). Each circle represents data from one patient or healthy donor. The markers (black bars) indicate the mean of each sample group. 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 Rounds of updating Frequency of node activation Re-set PI3K from ON to OFF 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 Rounds of updating Re-set TPL2 from ON to OFF Frequency of node activation 0 25 NFκB Binding Free Probe LY 294002 (µM) p-AKT (Ser473) AKT IB EMSA GAPDH GAPDH BAY 11-7082 (µM) 0 1 2 5 p-AKT (Ser473) AKT Mcl-1 STAT3 binding Free probe IB EMSA A B C PI3K NFκB X TPL2 PI3K NFκB X TPL2 Fig. 5. NFB-mediated survival pathway in T-LGL leukemia involves PI3K and Mcl-1. (A) Analysis of the potential cause(s) of the constitutive activation of NFB. As in Table S4, the Boolean logical rule governing the state of NFB is ‘‘NFKB* [(TPL2 or PI3K) or (FLIP and TRADD and IAP)] and not Apoptosis’’. When a T-LGL-like state is achieved, the state of TRADD stabilizes at OFF (see Table S7). Thus, the node that activates NFB can only be TPL2 or PI3K, which are known to be constitutively active in T-LGL leukemia (see Table S5). Rapid inhibition of NFB (white squares) was observed after inhibiting PI3K (X) but not after inhibiting TPL2 (gray triangles) (200 simulations). (B) PI3K inhibition induced NFB inhibition in T-LGL leukemia. T-LGL leukemia PBMCs were treated with vehicle DMSO or 25 M LY 294002 for 4 h. The amount of total and phospho-AKT was assessed by Western blot assay; NFB activity was assessed by EMSA. Result is representative of experiments in three patients. (C) NFB inhibition down-regulates Mcl-1 but does not inﬂuence STAT3 activity and the PI3K pathway. T-LGL leukemia PBMCs were treated with vehicle DMSO or 1 M, 2 M or 5 M BAY 11–7082 for 3 h, and the amount of Mcl-1, total- and phospho-AKT was assessed by Western blot assay. STAT3 activity was assessed by EMSA. Result is representative of experiments in three pa- tients. GAPDH was used as a loading control for all of the Western blot assays. Zhang et al. PNAS October 21, 2008 vol. 105 no. 42 16311 MEDICAL SCIENCES tutively active. As shown in Fig. 6A, when a T-LGL-like state was achieved, the state of T-bet stabilized at ON, and there was a rapid increase of IL-2 production when the state of T-bet was reset to OFF. In agreement with the model’s prediction, T-bet was significantly elevated in T-LGL leukemia PBMCs compared with normal PBMCs at both mRNA and protein levels, as assessed by real-time PCR and Western blot assay (Figs. 6 B and C). In addition, T-LGL leukemia PBMCs exhibited high T-bet activity as assessed by EMSA whereas the T-bet activity was almost undetectable in normal PBMCs (Fig. 6D). Discussion The long-term survival of competent CTL in T-LGL leukemia offers a unique opportunity to reveal the key mediators of CTL activation and AICD in humans. In this study, we curated the signaling pathways involved in normal CTL activation, AICD, and the deregulations in leukemic T-LGL and compiled them into a T-LGL survival signaling network. By formulating a Boolean dynamic model of this network, we were able to identify the potential causes and key regulators of this abnormal survival. Signaling pathways are complex and dynamic. However, ex- perimental results are usually focused on limited interactions of the components in one pathway and neglecting the broader effects in the same or other pathways. Integrating existing pathway information to infer cross-talk among pathways is desirable, especially for studies in T-LGL leukemia where ex- perimental data are limited. Using network theory as a tool, we identified the most unique interactions among known deregu- lated components in leukemic T-LGL in the context of CTL activation and AICD and summarized these signaling events in the form of a network. This served as an innovative platform to understand the abnormal CTL survival in T-LGL leukemia. Multiple perturbations of signaling pathways in a disease can result from deregulation of only a subset of these pathways. However, identifying such a subset is difficult experimentally. In this study, we assessed this question in T-LGL leukemia by using a Boolean dynamic model. Through network simulations, we revealed the hierarchy among deregulated nodes in terms of determining other signaling abnormalities in leukemic T-LGL. The simultaneously constitutive presence of IL-15 and PDGF was shown to be sufficient to induce all know deregulations after initial T cell activation. Leukemic T-LGL are suggested to be antigen-primed (12), long-term competent CTL (22), similar to terminally differen- tiated effector memory cells (TEMRA) (23). It is worth noting that IL-15 has been shown to be important for CTL activation and generation of long-lived CD8 memory cells (24, 25). Both the CD8 cells in the IL15 transgenic mice (26) and the IL15 transduced primary human CD8 cells (27) indeed showed similar phenotypes as leukemic T-LGL. However, IL-15 alone cannot fully inhibit the onset of apoptosis in our model (Fig. 2C). Increased PDGF production occurs under inflammatory condi- tions (28), and it has been shown to exert an inhibitory effect toward CTL activation (29). We had found that LGL leukemia is characterized by production of proinflammatory cytokines (14). Here, we showed an increased level of PDGF in T-LGL patient sera. Our model and the following validation revealed that both pro- and anti-T cell activation signals are needed simultaneously to maintain the competency and survival of CTL in T-LGL leukemia. Our finding also suggests that provision of IL-15 and PDGF may be a strategy to generate long-lived CTL necessary for the development of virus and cancer vaccines. Focusing on the effect of nodes on apoptosis in leukemic T-LGL, we revealed nodes that determine the uncoupling of CTL activation and AICD. We experimentally validated two predicted key mediators: SPHK1 and NFB, the inhibition of which induces apoptosis in leukemic T-LGL. It is worth noting that although NFB has been suggested to inhibit apoptosis in CTL (30), its function in maintaining long-term CTL survival remains elusive. We validated the prediction that NFB is downstream of PI3K and prevents the onset of apoptosis in leukemic T-LGL through maintaining the expression of Mcl-1 independent of STAT3, another regulator of Mcl-1 in T-LGL leukemia (3). The confirmation of the constitutive NFB activation led to the validation of the constitutive T-bet activation in T-LGL leukemia predicted by our model. T-bet plays an important role in coupling the effector and memory CD8 T cell fate (31). It also inhibits the production of IL-2, which is known to be absent in leukemic T-LGL and in TEMRA (23, 32). T-bet has been related to multiple autoimmune diseases in humans (33–36). T-LGL leukemia has important overlaps with autoimmune disorders, particularly rheumatoid arthritis (2). The overexpres- sion and constitutive activity of T-bet in leukemic T-LGL may help to reveal the common pathogenesis between T-LGL leu- kemia and other autoimmune diseases. With the exponential increase of signaling pathway information, it is becoming more difficult to determine pathway interactions in a particular experimental system. In this study, we used network analysis and Boolean modeling to investigate the signaling abnor- malities in T-LGL leukemia. This systems biology approach was able to maximize the use of the available pathway information and to identify the key mediators of CTL survival, highlighting their importance as potential therapeutic targets for T-LGL leukemia 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 Rounds of updating Frequency of node activation 0 0.01 0.02 0.03 0.04 0.05 Normal T-LGL Relative expression * 3 4 6 9 10 11 12 13 Normal T-LGL T-bet GAPDH T-bet binding Free probe T-LGL Normal 5 6 7 8 9 6 14 15 16 17 A B C D ◊ IL-2 T-Bet Fig. 6. T-bet is overexpressed and constitutively active in T-LGL leukemia PBMCs. (A) T-bet inhibits IL-2 expression when a T-LGL-like state is achieved. Based on the Boolean logical rule ‘‘IL2* (NFKB or STAT3 or NFAT) and not (TBET or Apoptosis)’’ (Table S4), T-bet is the only negative regulator of IL-2 expression when cells are still alive. Inhibiting T-bet (white squares) after 15 rounds of updating results in IL-2 (white diamonds) expression after achieving a T-LGL-like state (200 simulations). (B) T-LGL leukemia PBMCs (white squares, n 10) express 3.3-fold higher T-bet mRNA compared with normal (black circles, n 5, *, P 0.02) as assessed by real-time PCR. (C) T-bet pro- tein expression in T-LGL leukemia and normal PBMCs. Western blot assay result is representative of samples from eight healthy donors and six T-LGL leukemia patients. White space has been inserted to indicate realigned gel lanes. (D) T-bet is constitutively active in T-LGL leukemia patients. Nuclear extract from PBMCs of ﬁve T-LGL leukemia patients and ﬁve healthy do- nors were tested for their T-bet activity by using EMSA. T-bet exhibited high activity in most T-LGL leukemia patients but not in normal. 16312 www.pnas.orgcgidoi10.1073pnas.0806447105 Zhang et al. and offering insights into CTL manipulation. This study confirms the possibility of integrating normal and disease pathway informa- tion into a single model that is powerful enough to reproduce a clinically relevant complex process, useful for therapeutic purpose, yet is constructed with only qualitative information. Materials and Methods Patient Consent. All patients met the clinical criteria of T-LGL (CD3) leukemia with increased LGL counts and clonal T cell antigen receptor gene rearrange- ment. None of the patients received treatment for LGL leukemia. Informed consents were signed by all patients and age- and sex-matched healthy individuals allowed the use of their cells for these experiments. Buffy coats were obtained from Hershey Medical Center Blood Bank according to proto- cols observed by Milton S. Hershey Medical Center, Hershey, PA. Chemicals and Reagents. All chemical reagents and LY 294002 were purchased from Sigma–Aldrich. AG 1296 and BAY 11–7082 was purchased from EMD Bioscience. LightShift Chemiluminescent EMSA Kit was purchased from Pierce Biotechnology. Human PDGF-BB Quantikine ELISA Kit was purchased from R&D systems. Annexin V-PE Apoptosis Detection Kit-I and TransFactor Extrac- tion Kit were purchased from BD Biosciences. Biotinylated and nonbiotin- ylated DNA oligonucleotides were purchased from Integrated DNA Technol- ogy. Anti-Mcl-1 and anti-T-bet antibodies were purchased from Santa Cruz Biotechnology. Anti-AKT and anti-phospho-AKT (Ser-473) antibodies were purchased from Cell Signaling Technology. Anti-GAPDH antibody was pur- chased from Chemicon and Millipore. SPHK1 inhibitor I and II (SKI-I and SKI-II) were kindly provided by Dr. Jong K. Yun. ELISA. Sera from 22 T-LGL patients and 39 age- and sex-matched healthy donors were prepared and analyzed according to manufacturer’s instruction, as described (14). Cell Culture and Apoptosis Assay. PBMCs were processed from blood samples of patients and Buffy coats of normal donors, and apoptosis assays were performed by using Annexin-V conjugated with phytoerythrocin (PE) and 7-amino-actinomycin-D staining as described (23). Each treatment was per- formed and measured three times for one blood sample. Apoptosis was calculated by using the following formula: Percentage of speciﬁc apoptosis [(Annexin-V-PE positive cells in treat- ment Annexin-V-PE positive cells in control) 100]/(100 Annexin-V-PE positive cells in control) Western Blot Assay. Cell lysates were prepared, protein concentration was determined, and Western blot assay was performed as described (3). EMSA. Nuclear and cytoplasmic extract from patient and normal PBMCs were prepared by using TransFactor Extraction Kit according to manufacturer’s instructions. Probes for NFB (5-GATCCGGCAGGGGAATCTCCCTCTC-3) (20), STAT3 (5-CTTCATTTCCCGTAAATCCCTA) (3) and T-bet (5-AAAACTTGT- GAAAATACGTAATCCTCAG-3) (34)were biotinylated at 5. Corresponding nonbiotinylated oligonucleotides were used as competition oligonucleotides. EMSA was performed by using the LightShift Chemiluminescent EMSA Kit according to manufacturer’s instructions. Real-Time PCR. Total RNA was processed as described (8). Primers speciﬁc for T-bet (forward: 5-TGTGGTCCAAGTTTAATCAGCA-3; reverse: 5-TGACAG- GAATGGGAACATCC-3) and glyceraldehyde-3-phosphate dehydro-genase (GAPDH, forward: 5-GAGTCAACGGATTTGGTCGT-3; reverse: 5-TTGATTTTG- GAGGGATCTCG-3) were used for real-time PCR and expression was quanti- ﬁed as described (8). Computational Methods. Network simpliﬁcation was performed with NET- SYNTHESIS, a signal transduction network inference and simpliﬁcation tool (37, 38). The dynamic model was implemented in custom python code. Additional details regarding computational methods are given in the SI Text. ACKNOWLEDGMENTS. We thank Nate Sheaffer and David Stanford for help with acquisition and analysis of ﬂow cytometry data and Lynn Ruiz, Kendall Thomas, and Nancy Ruth Jarbadan for help with acquiring patient samples and processing them. This work is supported by National Institutes of Health Grant R01 CA 94872. Boolean model development in R.A’s group is supported by National Science Foundation Grant CCF-0643529. 1. Klebanoff CA, Gattinoni L, Restifo NP (2006) CD8 T-cell memory in tumor immunol- ogy and immunotherapy. Immunol Rev 211:214–224. 2. Sokol L, Loughran TP, Jr (2006) Large granular lymphocyte leukemia. Oncologist 11:263–273. 3. Epling-Burnette PK, et al. (2001) Inhibition of STAT3 signaling leads to apoptosis of leukemic large granular lymphocytes and decreased Mcl-1 expression. J Clin Invest 107:351–362. 4. 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PNAS October 21, 2008 vol. 105 no. 42 16313 MEDICAL SCIENCES	18852469	FasT = ( ( NFKB ) AND NOT ( Apoptosis ) ) sFas = ( ( FasT ) AND NOT ( Apoptosis ) ) IL2 = ( ( ( STAT3 ) AND NOT ( Apoptosis ) ) AND NOT ( TBET ) ) OR ( ( ( NFAT ) AND NOT ( Apoptosis ) ) AND NOT ( TBET ) ) OR ( ( ( NFKB ) AND NOT ( Apoptosis ) ) AND NOT ( TBET ) ) NFKB = ( ( PI3K ) AND NOT ( Apoptosis ) ) OR ( ( TPL2 ) AND NOT ( Apoptosis ) ) OR ( ( FLIP AND ( ( ( IAP AND TRADD ) ) ) ) AND NOT ( Apoptosis ) ) TPL2 = ( ( PI3K AND ( ( ( TNF ) ) ) ) AND NOT ( Apoptosis ) ) OR ( ( TAX ) AND NOT ( Apoptosis ) ) A20 = ( ( NFKB ) AND NOT ( Apoptosis ) ) GPCR = ( ( S1P ) AND NOT ( Apoptosis ) ) IFNGT = ( ( TBET ) AND NOT ( Apoptosis ) ) OR ( ( STAT3 ) AND NOT ( Apoptosis ) ) OR ( ( NFAT ) AND NOT ( Apoptosis ) ) GZMB = ( ( TBET ) AND NOT ( Apoptosis ) ) OR ( ( CREB AND ( ( ( IFNG ) ) ) ) AND NOT ( Apoptosis ) ) TCR = ( ( ( Stimuli ) AND NOT ( CTLA4 ) ) AND NOT ( Apoptosis ) ) IL2RBT = ( ( ERK AND ( ( ( TBET ) ) ) ) AND NOT ( Apoptosis ) ) TRADD = ( ( ( ( TNF ) AND NOT ( IAP ) ) AND NOT ( Apoptosis ) ) AND NOT ( A20 ) ) PI3K = ( ( PDGFR ) AND NOT ( Apoptosis ) ) OR ( ( RAS ) AND NOT ( Apoptosis ) ) FYN = ( ( TCR ) AND NOT ( Apoptosis ) ) OR ( ( IL2RB ) AND NOT ( Apoptosis ) ) IL2RA = ( ( ( IL2 AND ( ( ( IL2RAT ) ) ) ) AND NOT ( IL2RA ) ) AND NOT ( Apoptosis ) ) GRB2 = ( ( IL2RB ) AND NOT ( Apoptosis ) ) OR ( ( ZAP70 ) AND NOT ( Apoptosis ) ) BID = ( ( ( ( Caspase ) AND NOT ( BclxL ) ) AND NOT ( MCL1 ) ) AND NOT ( Apoptosis ) ) OR ( ( ( ( GZMB ) AND NOT ( BclxL ) ) AND NOT ( MCL1 ) ) AND NOT ( Apoptosis ) ) Caspase = ( ( DISC ) AND NOT ( Apoptosis ) ) OR ( ( ( GZMB AND ( ( ( BID ) ) ) ) AND NOT ( Apoptosis ) ) AND NOT ( IAP ) ) OR ( ( ( TRADD AND ( ( ( BID ) ) ) ) AND NOT ( Apoptosis ) ) AND NOT ( IAP ) ) ZAP70 = ( ( ( LCK ) AND NOT ( FYN ) ) AND NOT ( Apoptosis ) ) CTLA4 = ( ( TCR ) AND NOT ( Apoptosis ) ) LCK = ( ( CD45 ) AND NOT ( Apoptosis ) ) OR ( ( ( TCR ) AND NOT ( Apoptosis ) ) AND NOT ( ZAP70 ) ) OR ( ( ( IL2RB ) AND NOT ( Apoptosis ) ) AND NOT ( ZAP70 ) ) SOCS = ( ( ( ( JAK ) AND NOT ( Apoptosis ) ) AND NOT ( IL2 ) ) AND NOT ( IL15 ) ) STAT3 = ( ( JAK ) AND NOT ( Apoptosis ) ) Apoptosis = ( Caspase ) OR ( Apoptosis ) IL2RB = ( ( IL2RBT AND ( ( ( IL2 OR IL15 ) ) ) ) AND NOT ( Apoptosis ) ) Fas = ( ( ( FasT AND ( ( ( FasL ) ) ) ) AND NOT ( sFas ) ) AND NOT ( Apoptosis ) ) Cytoskeleton_signaling = ( ( FYN ) AND NOT ( Apoptosis ) ) FLIP = ( ( ( NFKB ) AND NOT ( DISC ) ) AND NOT ( Apoptosis ) ) OR ( ( ( CREB AND ( ( ( IFNG ) ) ) ) AND NOT ( DISC ) ) AND NOT ( Apoptosis ) ) JAK = ( ( ( ( IFNG ) AND NOT ( Apoptosis ) ) AND NOT ( CD45 ) ) AND NOT ( SOCS ) ) OR ( ( ( ( RANTES ) AND NOT ( Apoptosis ) ) AND NOT ( CD45 ) ) AND NOT ( SOCS ) ) OR ( ( ( ( IL2RA ) AND NOT ( Apoptosis ) ) AND NOT ( CD45 ) ) AND NOT ( SOCS ) ) OR ( ( ( ( IL2RB ) AND NOT ( Apoptosis ) ) AND NOT ( CD45 ) ) AND NOT ( SOCS ) ) IAP = ( ( ( NFKB ) AND NOT ( Apoptosis ) ) AND NOT ( BID ) ) FasL = ( ( ERK ) AND NOT ( Apoptosis ) ) OR ( ( NFAT ) AND NOT ( Apoptosis ) ) OR ( ( NFKB ) AND NOT ( Apoptosis ) ) OR ( ( STAT3 ) AND NOT ( Apoptosis ) ) S1P = ( ( ( SPHK1 ) AND NOT ( Apoptosis ) ) AND NOT ( Ceramide ) ) SPHK1 = ( ( PDGFR ) AND NOT ( Apoptosis ) ) ERK = ( ( MEK AND ( ( ( PI3K ) ) ) ) AND NOT ( Apoptosis ) ) Ceramide = ( ( ( Fas ) AND NOT ( S1P ) ) AND NOT ( Apoptosis ) ) MCL1 = ( ( IL2RB AND ( ( ( PI3K AND NFKB AND STAT3 ) ) ) ) AND NOT ( Apoptosis ) ) P2 = ( ( ( IFNG ) AND NOT ( Stimuli2 ) ) AND NOT ( Apoptosis ) ) OR ( ( ( P2 ) AND NOT ( Stimuli2 ) ) AND NOT ( Apoptosis ) ) RANTES = ( ( NFKB ) AND NOT ( Apoptosis ) ) NFAT = ( ( PI3K ) AND NOT ( Apoptosis ) ) GAP = ( ( ( ( PDGFR AND ( ( ( GAP ) ) ) ) AND NOT ( Apoptosis ) ) AND NOT ( IL2 ) ) AND NOT ( IL15 ) ) OR ( ( ( ( RAS ) AND NOT ( Apoptosis ) ) AND NOT ( IL2 ) ) AND NOT ( IL15 ) ) SMAD = ( ( GPCR ) AND NOT ( Apoptosis ) ) IFNG = ( ( ( ( IL15 AND ( ( ( IFNGT ) ) ) ) AND NOT ( P2 ) ) AND NOT ( Apoptosis ) ) AND NOT ( SMAD ) ) OR ( ( ( ( IL2 AND ( ( ( IFNGT ) ) ) ) AND NOT ( P2 ) ) AND NOT ( Apoptosis ) ) AND NOT ( SMAD ) ) OR ( ( ( ( Stimuli AND ( ( ( IFNGT ) ) ) ) AND NOT ( P2 ) ) AND NOT ( Apoptosis ) ) AND NOT ( SMAD ) ) TNF = ( ( NFKB ) AND NOT ( Apoptosis ) ) CREB = ( ( ERK AND ( ( ( IFN ) ) ) ) AND NOT ( Apoptosis ) ) P27 = ( ( STAT3 ) AND NOT ( Apoptosis ) ) Proliferation = ( ( ( STAT3 ) AND NOT ( P27 ) ) AND NOT ( Apoptosis ) ) TBET = ( ( TBET ) AND NOT ( Apoptosis ) ) OR ( ( JAK ) AND NOT ( Apoptosis ) ) MEK = ( ( RAS ) AND NOT ( Apoptosis ) ) RAS = ( ( ( GRB2 ) AND NOT ( Apoptosis ) ) AND NOT ( GAP ) ) OR ( ( ( PLCG1 ) AND NOT ( Apoptosis ) ) AND NOT ( GAP ) ) PLCG1 = ( ( GRB2 ) AND NOT ( Apoptosis ) ) OR ( ( PDGFR ) AND NOT ( Apoptosis ) ) PDGFR = ( ( PDGF ) AND NOT ( Apoptosis ) ) OR ( ( S1P ) AND NOT ( Apoptosis ) ) BclxL = ( ( ( ( ( STAT3 ) AND NOT ( BID ) ) AND NOT ( Apoptosis ) ) AND NOT ( GZMB ) ) AND NOT ( DISC ) ) OR ( ( ( ( ( NFKB ) AND NOT ( BID ) ) AND NOT ( Apoptosis ) ) AND NOT ( GZMB ) ) AND NOT ( DISC ) ) IL2RAT = ( ( IL2 AND ( ( ( NFKB OR STAT3 ) ) ) ) AND NOT ( Apoptosis ) ) DISC = ( ( FasT AND ( ( ( Fas ) AND ( ( ( NOT FLIP ) ) ) ) OR ( ( Fas AND IL2 ) ) OR ( ( Ceramide ) ) ) ) AND NOT ( Apoptosis ) )
BioMed Central Page 1 of 14 (page number not for citation purposes) BMC Systems Biology Open Access Research article Dynamical modeling of the cholesterol regulatory pathway with Boolean networks Gwenael Kervizic* and Laurent Corcos Address: Inserm U613, Faculté de Médecine, Université de Bretagne Occidentale, 29238 Brest cedex, FRANCE Email: Gwenael Kervizic* - gwenael.kervizic@univ-brest.fr; Laurent Corcos - laurent.corcos@univ-brest.fr * Corresponding author Abstract Background: Qualitative dynamics of small gene regulatory networks have been studied in quite some details both with synchronous and asynchronous analysis. However, both methods have their drawbacks: synchronous analysis leads to spurious attractors and asynchronous analysis lacks computational efficiency, which is a problem to simulate large networks. We addressed this question through the analysis of a major biosynthesis pathway. Indeed the cholesterol synthesis pathway plays a pivotal role in dislypidemia and, ultimately, in cancer through intermediates such as mevalonate, farnesyl pyrophosphate and geranyl geranyl pyrophosphate, but no dynamic model of this pathway has been proposed until now. Results: We set up a computational framework to dynamically analyze large biological networks. This framework associates a classical and computationally efficient synchronous Boolean analysis with a newly introduced method based on Markov chains, which identifies spurious cycles among the results of the synchronous simulation. Based on this method, we present here the results of the analysis of the cholesterol biosynthesis pathway and its physiological regulation by the Sterol Response Element Binding Proteins (SREBPs), as well as the modeling of the action of statins, inhibitor drugs, on this pathway. The in silico experiments show the blockade of the cholesterol endogenous synthesis by statins and its regulation by SREPBs, in full agreement with the known biochemical features of the pathway. Conclusion: We believe that the method described here to identify spurious cycles opens new routes to compute large and biologically relevant models, thanks to the computational efficiency of synchronous simulation. Furthermore, to the best of our knowledge, we present here the first dynamic systems biology model of the human cholesterol pathway and several of its key regulatory control elements, hoping it would provide a good basis to perform in silico experiments and confront the resulting properties with published and experimental data. The model of the cholesterol pathway and its regulation, along with Boolean formulae used for simulation are available on our web site http:// Bioinformaticsu613.free.fr. Graphical results of the simulation are also shown online. The SBML model is available in the BioModels database http://www.ebi.ac.uk/biomodels/ with submission ID: MODEL0568648427. Published: 24 November 2008 BMC Systems Biology 2008, 2:99 doi:10.1186/1752-0509-2-99 Received: 11 April 2008 Accepted: 24 November 2008 This article is available from: http://www.biomedcentral.com/1752-0509/2/99 © 2008 Kervizic and Corcos; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 2 of 14 (page number not for citation purposes) Background Systems biology Systems biology is an emerging scientific field that inte- grates large sets of biological data derived from experi- mental and computational approaches. In this new paradigm, we no longer study entities of biological sys- tems separately, but as a whole. Hence, large data sets can be translated into sets of links representative of the inter- actions of species from within single or multiple path- ways. In fact, elementary functions in those systems are the result of the inherent characteristics of the specific ele- ments involved and the interactions they are engaged in within the systems [1]. In biological or biomedical mat- ters, modeling activities are strongly linked to the nature and amount of available data on the model. Furthermore, computational studies in systems biology rely on different formalisms that are intimately connected to the level of knowledge one has of a biological system. In the present study, the cholesterol synthesis pathway, including most of its associated reactions, is analyzed to address the effect of either activators or inhibitors. Hence, blockade can be attained by targeting the HMG-CoA reductase, the rate- limiting enzyme of the mevalonate pathway, with statins, widely used hypocholesterolemic drugs. Alternatively, activation of the pathway can be triggered by Sterol Response Element Binding Proteins (SREBPs), as part of a compensatory feedback mechanism. Moreover, to better analyze this pathway including both enzymatic reactions and gene regulatory networks, we will focus on the Boolean networks formalism, particularly suitable to delineate dynamic properties from qualitative informa- tion on regulatory interactions [2,3]. Boolean formalism for qualitative modeling and simulation A model or simulation of a biological network is said to be qualitative when each entity of this model is repre- sented by a variable having a finite set of possible values. We can note here that the possible values that can be taken by the variable are not necessarily linearly correlated to the concentration of the represented species. Those val- ues represent qualitative states of the entities from the net- work. In the formalism of Boolean networks, the state of a species is described by a Boolean variable, which value is either 1 if the species is active (i.e. its activity is detecta- ble, in biological terms) or 0 if inactive (its activity is undetectable). Moreover, a Boolean function allows to compute the state of a species at time t + 1, knowing the states of k other species at time t. If we denote by xi the state of species i and by bi(x(t)) the associated Boolean function, we get the following equations for the dynamics of the Boolean network: xi(t + 1) = bi(x(t)), 1 ≤ i ≤ n (1) We can note here that the Boolean formalism allows us to model various biological systems such as gene regulatory networks and metabolic networks whose entities have very different timescales. Construction of a Boolean network: modeling inhibition and activation Let us detail how inhibitions and activations should be modeled in the Boolean network formalism. • Inhibition: if A is an enzyme that produces a compound B but can be inhibited by compound C, then the Boolean function that predicts the presence of B at time t + 1 will be: B(t + 1) = A(t) AND NOT(C(t)) • Activation: if A is a precursor of B and the reaction of transformation of A to B is catalyzed by enzyme C, then the Boolean function that predicts the presence of B at time t + 1 will be: B(t + 1) = A(t) AND C(t) Here is a simple example with 4 genes (A, B, C, D) and the 4 following Boolean functions: • A(t + 1) = NOT (D(t)) • B(t + 1) = NOT (A(t)) • C(t + 1) = A(t) OR B(t) • D(t + 1) = NOT (C(t)) The graphical representation of this network can be seen in figure 1. Example of a simple regulatory network Figure 1 Example of a simple regulatory network. Graphical representation of a regulatory network with 4 genes (A, B, C, D). Its full dynamics is described in the associated Boolean functions. BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 3 of 14 (page number not for citation purposes) Synchronous and asynchronous paradigms in the Boolean formalism In Boolean simulations, there are two main paradigms where conception of time and transition between states differs. • The simplest one is the synchronous simulation. At each step of clock (time is moving discretely in Boolean simu- lations) all the decrease or increase calls are realized simultaneously. This approach is computationally effi- cient, but might lead to simulation artifacts such as spuri- ous cycles [4,5], which are cycles that do not appear in asynchronous simulation. • In asynchronous simulation, only one transition occurs at each clock step. Thus, the same reaction can occur sev- eral times before another one is completed, which enables the simulation of biological systems that contain slow and fast kinetics (equivalent to a stiff system in the Ordi- nary Differential Equations paradigm). It is worthwhile to note that the steady states, which cor- respond to some phenotypes, are the same in those two paradigms. However, some dynamic behaviors can be very different. To sum up, synchronous simulations have fewer mode- ling power but are more computationally efficient while asynchronous simulations are able to predict a wider range of biological behaviors but their exhaustive compu- tation becomes intractable for large biological systems [6,7]. In the synchronous paradigm simulation, our simple reg- ulatory network gives the results partially shown in table 1. The study of this truth table shows that {1010} is a steady state (or point attractor, or equilibrium) and that {0010, 1100, 1011} is a state cycle (or dynamic attractor, or cyclic attractor). This becomes more evident when con- verting this network into a finite state machine as shown in figure 2. The state colored in green corresponds to the steady state and the states colored in red correspond to the state cycle. In the asynchronous paradigm simulation, our simple regulatory network gives the finite state machine shown in figure 3. The state colored in green corresponds to the Table 1: Fragment of the truth table obtained from our simple regulatory network. (ABCD) t 0000 0001 0010 0011 0100 0101 ... t + 1 1101 0101 1100 0100 1111 0111 ... For each initial array of values (initial state) at time t, the new array of values, obtained by evaluating the system through the Boolean functions, is shown on the second line (t + 1). Finite state machine of our regulatory network taken as an example in synchronous simulation Figure 2 Finite state machine of our regulatory network taken as an example in synchronous simulation. The state [1010] colored in green corresponds to a steady state. It has 5 states and itself in its basin of attraction (i.e. the states whose trajectory during the simulation lead to this steady state). The 3 states [0010], [1100], [1011] colored in red correspond to a state cycle. They have 7 states and them- selves in their basin of attraction. All the state space is shown in the figure. BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 4 of 14 (page number not for citation purposes) steady state in both synchronous and asynchronous sim- ulations. We recall that steady states are obviously always the same in synchronous and asynchronous simulations. The states colored in red are the states which correspond to the state cycle in synchronous simulation. The purple arrows propose one way -among many possible- to reach cyclically those states. Note that, for some regulatory net- works, it is not possible in asynchronous simulation to reach cyclically states which form a state cycle in synchro- nous simulation. This becomes obvious when looking at the synchronous and asynchronous simulation results of a simple negative feedback loop of size 3. The synchro- nous state cycle {010, 101} does not exist in asynchro- nous simulation. These results are shown on our web site http://bioinformaticsu613.free.fr/simpleloopsn3.html. Furthermore, we can have an intuition that this purple tra- jectory is in some way unstable because while cycling through the 3 states {0010, 1100, 1011}, the system could have gone through many transitions that lead to the steady state 1010. The cholesterol biosynthesis pathway Cholesterol is an important constituent of mammalian cell membranes. It maintains their fluidity and allows other molecules playing important biological roles, like glycoproteins, to anchor to the membrane compartment. It is also the precursor of fat-soluble vitamins, including vitamins A, D, E and K and of various steroids hormones, such as cortisol, aldosterone, progesterone, the various estrogens and testosterone. It comes for about one third from the dietary intake and for about two thirds from endogenous synthesis from unburned food metabolites. Its synthesis starts from acetyl CoA, through what is often called the HMG-CoA reductase pathway. It occurs in many cells and tissues, but with higher rates in the intes- tines, adrenal glands, reproductive organs and liver. Cho- lesterol synthesis is orchestrated by a protein complex formed by the Sterol Regulatory Element Binding Protein (SREBP), the SREBP-cleavage activating protein (SCAP) and the insulin-induced gene 1 (Insig) [8-10]. This com- plex is maintained in a repressed state located in the endo- plasmic reticulum (ER). When the cholesterol level is low, Insig1 interaction with SREBP-SCAP complex is relieved allowing SREBP-SCAP to migrate to the Golgi apparatus where SREBP is cleaved by two proteases called S1P and S2P. Once SREBP is matured, it migrates to the nucleus and acts as a transcription factor upon binding to sterol regulatory elements (SRE) to activate the genes coding for the main enzymes of the HMG-CoA reductase pathway (e.g. HMG-CoA synthase, HMG-CoA reductase, FPP syn- thase, CYP51). The synthesis of cholesterol can be regu- lated by drugs such as HMG-CoA reductase inhibitors, among which the most potent belong to the statins family [11-14]. They lower cholesterol by inhibiting the enzyme HMG-CoA reductase, which is rate-limiting. Effects of statins on cancer activated pathways Therefore statins are known lipopenic drugs, but they are also drug candidates against cancer [15]. Intermediate molecules in the HMG-CoA reductase pathway undergo important biochemical reactions of prenylation whose blocking will inactivate several intracellular transduction pathways that involve Ras, Rho and small G proteins [16- Finite state machine of our regulatory network taken as an example in asynchronous simulation Figure 3 Finite state machine of our regulatory network taken as an example in asynchronous simulation. The state [1010] colored in green also corresponds to a steady state in the asynchronous simulation. (All the steady states are the same in synchronous and asynchronous simulations) The 3 states [0010], [1100], [1011] which correspond to a state cycle in the synchronous simulation are still colored in red, but this figure clearly shows that they do not correspond to a state cycle in the asynchronous simulation. Actually, even if there are several paths enabling to reach cyclically those three states (one of those paths is indicated with purple arrows), there are also several paths leading to the steady state from which there is no path back to those 3 states. BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 5 of 14 (page number not for citation purposes) 19]. Hence, statins can block Ras activation, which occurs in 30% of human tumours. Experimentally, statins can stop cell growth by blocking cells at the G1 or G2/M stages, or induce apoptosis in several cancer cell types [20]. Important results have also been obtained using rodent models where neuroblastoma, colic cancer and melanoma have regressed under the effect of lovastatin. Moreover, the combination of classical antineoplastic drugs, like DNA topoisomerase inhibitors, and statins increases tumour cell killing [21,22]. In this paper, we first focus on the synchronous formalism enabling us to compute our large model of cholesterol regulatory pathway. We next propose a methodology based on asynchronous formalism and of Markov chains to overcome one of its limitations: the appearance of spu- rious cycles. Methods Boolean modeling of the human cholesterol regulatory pathway The model shown in figure 4 has been made using data from the literature [23-25]. It is composed of the choles- terol synthesis pathway and its regulation by SREBPs. After a few simplifications aimed at reducing the state space size, our model includes 33 species (genes, mRNAs, proteins, biochemical intermediates and statins). In par- ticular, we assume the SREBP-SCAP-Insig1 complex to be always present in the membranes of the endoplasmic reticulum (ER). Therefore, in our model, the SREBP-SCAP complex can be either present in the ER if the cholesterol level is high, or absent if the cholesterol level is below the physiologically relevant threshold, a situation that occurs following its dissociation from Insig. We also assume that S1p and S2p are always present in the membranes of the Golgi apparatus. Hence, in our model, a non-fully matured SREBP protein, called here pSREBP (for precur- sor-SREBP) is automatically produced if SREBP-SCAP is present. Likewise, matured SREBP, called mSREBP, is automatically derived from pSREBP and then migrates to the nucleus to enhance transcription of the genes from the HMG-CoA reductase pathway when cholesterol levels are perceived as insufficient. Target genes will then be transcribed into their respective mRNA, which will be translated into the corresponding enzymes. The endogenous cholesterol synthesis starts with acetyl-CoA which can, in our model, be either present, or absent in case of deficiency. Acetyl-CoA com- bines with itself to give CoA-SH and acetoacetyl-CoA. Acetyl-CoA reacts then with acetoacetyl-CoA to give HMG-CoA (3-Hydroxy-3-methylglutaryl CoA). This reac- tion is catalyzed by the HMG-CoA synthase. Therefore, the Boolean formula that describes the evolution of HMG-CoA is: HMG_CoA(t+1) = Acetoacetyl_CoA(t) AND Acetyl_CoA(t) AND HMG_CoA_Synthase(t) as expressed in the formalism of equation (1). We assume that NADPH and H+ are always present and we have chosen not to represent them in our model. Thus, in the presence of HMG-CoA reductase, HMG-CoA will produce mevalonic acid. ATP is also considered to be present in sufficient amounts so that mevalonic acid will transform into mevalonyl pyrophosphate, which will then transform into isopentenyl pyrophosphate. Isopentenyl pyrophosphate will give dimethyl allyl pyro- phosphate, and then combine with its own product to form geranyl pyrophosphate. This last one will combine with isopentenyl pyrophosphate to give farnesyl pyro- phosphate. Farnesyl pyrophosphate will lose two inor- ganic phosphates and one H+ ion to give presqualene pyrophosphate that will get two hydrogens from NADPH and H+ and lose two more inorganic phosphates to trans- form into squalene. Since we assume NAPDH and H+ to be always present in enough quantity, farnesyl pyrophosphate will automati- cally give squalene and presqualene pyrophosphate which, as an intermediate of the reaction, is not men- tioned. The ring closure of squalene produces lanosterol. We have then omitted several transitions and jumped from the lanosterol to desmosterol or 7-dehydrocholesterol, which both give cholesterol. The Boolean formula that describes the formation of cholesterol from either desmosterol or 7- dehydrocholesterol is: Cholesterol(t+1) = Desmosterol(t) OR 7_dehydrocholesterol(t) Perturbations of the model such as blockade of the HMG- CoA reductase by statins, widely used hypocholestero- lemic drugs, can be readily modeled. In the case of statins and HMG-CoA reductase, the Boolean formula is: HMG_CoA_Reductase(t+1) = HMG_CoA_Reductase_RNA(t) AND NOT(Statins(t)) Encoding the model At each time of the simulation the state of the targeted biological system is represented by a Boolean vector. Each coordinate represents a species in the pathway. BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 6 of 14 (page number not for citation purposes) Cholesterol Regulatory Pathway Figure 4 Cholesterol Regulatory Pathway. The cholesterol biosynthesis pathway is shown on this figure starting by its precursor Acetyl-CoA. Several of the key enzymes of this pathway regulated by SREBPs are also shown. The genetic regulation initiated by the effect of cholesterol on the Insig-SREBP-SCAP complex can be seen on the top of this figure. The action of statins, widely used hypolipidemic drugs, on the HMG-CoA-Reductase enzyme is also captured in this graph. Species of the model are grouped into cellular compartments as nucleus, golgi apparatus and endoplasmic reticulum. Default cellular compartment is the cytosol. This graphical representation has been prepared with CellDesigner [60,61]. BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 7 of 14 (page number not for citation purposes) The evolution function takes a Boolean vector represent- ing the state of the model at time t and returns a Boolean vector representing the state of the model at time t + 1. Storing the model The study of those pathways is greatly facilitated when the models are stored in a computer-readable format allowing representation of a biological system. Such formats have already been proposed like the Systems Biology Markup Language (SBML) [26,27]. SBML files are static represen- tations of biological systems that contain species, reac- tions, kinetic laws and possible annotations. SBML implements the XML (Extensible Markup Language) standard and is now internationally supported and widely used. It allows models of biological systems to be stored in public or private databases. However, it has been designed for the purpose of ODE (Ordinary Differential Equations) simulations and thus needs some adaptations to be used for Boolean simulations, like the possibility to store Boolean formulae. For our purposes, we have used SBML files with additional <BooleanLaws> </BooleanLaws> tags which are stored within reaction tags in an annotated section to remain compatible with SBML standard. This SBML can be downloaded from the BioModels database http://www.ebi.ac.uk/biomodels/[28] and has the follow- ing submission ID: MODEL0568648427. Simulation: point and cyclic attractors In a synchronous simulation, every trajectory converges to an attractor. Indeed, as the state space is finite (its size is 2N with N the number of species in the model), if we keep the simulation running long enough it will eventually come back to an already reached state. At that point, the trajectory becomes periodic because the simulation is deterministic on a finite state space. If the periodic part of the trajectory is of size one, we call the state a point attractor. When the system loops infi- nitely through several states, we call the set of these states a cycle attractor. While non-attractor states are transient and visited at most once on any network trajectory, states within an attractor cycle or point are reached infinitely often. Thus, attractors are often identified with phenotypes [2,3]. Considering that a phenotype is an observable state, therefore stable, of an organism or a cell, real biological systems are typically assumed to have short attractor cycles [29]. The state-space explosion problem In order to fully analyze the model with a simple simula- tion approach, we would need to simulate every state of the state-space. But the size of this space grows exponen- tially with the number of species and thus the computa- tion of the trajectories starting from all possible states will rapidly become too costly. Thus, we have decided, as a first step prior to a formal analysis, to use a random gen- erator in order to choose a subset of start states signifi- cantly smaller than the whole state-space and uniformly distributed in this space. We have also taken advantage of multiple processors computing in order to cover the max- imum of the state space with a minimum of time. Algo- rithms developed for Boolean simulation are very well suited for parallel execution. For example the set of start states used for simulation can easily be divided into sub- sets and simulation can be run independently from those start subsets. However, we think that parallelization is not sufficient to overcome the combinatorial explosion. Indeed, in order to add a species to a model, the comput- ing capabilities must be multiplied by two. Relative importance of cycles: A Markovian approach based on asynchronous perturbations We propose here a methodology based on Markov proc- esses that computes the stability of cycles. Markov proc- esses have already been used for controlling and analyzing gene networks [30,31]. Our approach differs from what is done in Probabilistic Boolean Networks (PBN) by the choice of the state space: instead of classically using the state space of the system itself (i.e. the 2N possible values of the state vector), we will use the set of state cycles and equilibria which is typically much smaller [2,3]. This allows us to compute Markov chain-based algorithms on large biological systems and thus to take into account the substantial and still growing amount of data we have on those networks and pathways. However, as a price for scal- ability and unlike PBN, the framework of synchronous Boolean networks does not represent the possible stochas- ticity of state transitions. Let S be the set of results of our Boolean analysis (S is composed of point attractors and cyclic attractors). S is the state-space of the finite discrete time-homogeneous Markov chain we want to study. In order to define the transitions of this Markov chain, we apply a perturbation on each cycle C in S. C has k states (k can be 1 in the case of a point attractor), say (s1, s2, ..., sk). For each state si of the cycle (s1, s2, ..., sk) the perturbation consists in reevaluating each species by its own Boolean function triggered asynchronously. Thus we obtain N new states (si,1, si,2, ..., si,N) for each state in C. When we perturb every state with every perturbation, we obtain a new set of perturbed states of size kN. We can note here that some of the states in (si,1, si,2, ..., si,N) are equal to the perturbed state si. Those states will be taken into account similarly to the states different from si. We then simulate synchronously all the states in (si,1, si,2, ..., si,N) until they reach one of the attractors of the system (i.e. an element of S). The transition probability from a cycle to another is defined as the ratio of the number of perturbed states of the first cycle that reach the second one BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 8 of 14 (page number not for citation purposes) over the total number of perturbed states of the first cycle. We also take into account the transitions from a cycle to itself. By this mean, we add some asynchronous dynamics in our synchronous analysis. We can then compute the stationary distribution of this Markov process and inter- pret it as a measure of the relative importance of each cycle. We achieve this computation with an initial vector of size n and of value [1/n, 1/n, ..., 1/n] where n is the size of S. By this mean, we make sure that all the absorbing states are taken into consideration. The aim of this meth- odology is to provide a measure of the stability of each synchronous attractor, using an asynchronous perturba- tion. Expecting that all the resulting attractors of synchro- nous Boolean analysis are biologically relevant would mean that all the biochemical reactions in the network happened simultaneously. Yet we know that it is not the case. Furthermore, it is well known that, within a biologi- cal pathway, some reactions are triggered with higher fre- quency than others (that is why, in the ODE paradigm, a lot of systems are stiff). Thus, Boolean analysis should, in some way, take into consideration the asynchronous char- acter of biochemical reactions. Under this assumption, asynchronous perturbations seem a logical and conven- ient way to provide a hint of the biological relevance of the state cycles found. Results Dynamical synchronous analysis of the model Based on the simulations obtained from 105 random states (out of 233 . 8.6 × 109 possible states), we predict 3 equilibria or steady states: • one with the complex SREBP-SCAP-Insig1 activated but a lack of precursor (Acetyl-CoA) preventing cholesterol synthesis; • one with the presence of cholesterol precursor (Acetyl- CoA), but also the presence of statins blocking the choles- terol synthesis by inhibiting the HMG-CoA reductase enzyme; • and one with a lack of precursor and the presence of stat- ins. Furthermore, we found 4 state cycles corresponding to the physiological regulation of cholesterol synthesis: when the cholesterol level is too low (equivalent to the absence of cholesterol in a Boolean formalism) there is activation of the SREBP-SCAP complex and (enhancement of the) production of all the enzymes of the cholesterol synthesis regulated by SREBP. Then, the endogenous synthesis of cholesterol starts again and when its level becomes too high (equivalent to the presence of cholesterol in a Boolean formalism) it inhibits the release of the SREBP- SCAP complex and thus the production of the above enzymes. Among those 4 cycles one has size 29 (named cycle_0 fur- ther in this article) and the others have size 33. In the cycle of size 29 the cholesterol changes from false to true (i.e. the cholesterol gets above the threshold indicative of the activation of its synthesis by the complex SREBP-SCAP- Insig) only once per cycle, while in the cycles of size 33, the cholesterol becomes true 5 times per cycle. Results verification through a formal analysis using a SAT solver The results detailed in the previous paragraph are obtained using a start space for the simulation around 105 times smaller than the state space. This method has the advantage to quickly provide some attractors for the bio- logical system. However, when using a sample of the whole state space, there is no assurance of finding all the system attractors. Formal analysis is one way to ensure that all the attractors have been found with a computa- tional cost that could be lower than the cost of performing simulation on the whole state space. We decided to per- form such a formal analysis by running a SAT solver on our Boolean network. We recall here that the Boolean sat- isfiability problem (commonly called SAT-problem) [32] determines if there is a set of variables for which a given Boolean formula can be evaluated to TRUE and identifies this precise set if existing. This is an NP-complete problem for which some instance solvers have been developed. To achieve this formal analysis, we wrote our system of Boolean equations into a suitable dimacs file format [33] (some dimacs files used for simulation can be down- loaded at http://Bioinformaticsu613.free.fr). In that way, we were able to confirm that the only attractors of size 1, 29 and 33 were those detected by our simulation tool with a random start space of size 105. Why did we need to go further: detection of spurious cycles The simulation performed with our model results in 4 state cycles. We believe that all those cycles do not corre- spond to a phenotype. These outcomes of different simu- lations, which are not biologically relevant, are typical of the synchronous Boolean paradigm, and are called spuri- ous cycles [4,5]. Therefore, there is a need to measure the relative importance of the cycles found using the previous methods. Markov chains-based stability analysis of the previous synchronous simulation Let us use our stability analysis on the results of the syn- chronous simulation of the cholesterol regulatory path- way. We perturb the cyclic attractors found during this simulation and then simulate synchronously the states resulting from the perturbation. We interpret the ratio of BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 9 of 14 (page number not for citation purposes) the number of perturbed states of a given cyclic attractor that reach a second cyclic attractor over the total number of perturbed states of the given cyclic attractor as a transi- tion probability. Afterwards, we use all the computed transition probabilities obtained previously to build the Markov chain shown in figure 5. The stationary probability vector is [1, 0, 0, 0]. This reflects the fact that the state cycle 0 is absorbing (i.e. it has no outgoing transitions). We interpret this result as state cycles 1, 2 and 3 are spurious. Markov chains-based stability analysis of simple regulatory networks Furthermore, to validate our method of Markov chains- based stability analysis, we applied it on simple positive and negative regulatory loops of different sizes, which are well known to contain spurious cycles. In the example of a negative feedback loop of size 3, the state cycle {010, 101} is found in synchronous simulation but does not exist in asynchronous simulation. It is obviously spurious, as detected by our method. All the detailed results and graphs can be found on our web site: http:// bioinformaticsu613.free.fr/simpleloopsn3.html. Markov chain of the transition probabilities between state cycles in the cholesterol regulatory pathway Figure 5 Markov chain of the transition probabilities between state cycles in the cholesterol regulatory pathway. Let k be the number of states within an attractor (k can be 1 in the case of a point attractor) and N be the number of species in the model. For each attractor of this finite time-homogeneous Markov chain, we perturb each species of each state by triggering its own Boolean function asynchronously. Thus there are kN perturbations per attractor. In the cholesterol regulatory pathway, one cyclic attractor found by the synchronous analysis has 29 states and the three other cyclic attractors have 33 states. The number of species in the model is 33. The weight of the edge from an attractor X to an attractor Y is the ratio between the number of perturbations of X which lead to Y over the total number of perturbations of X. Cycle 0 Cycle 1 Cycle 2 Cycle 3 957/957 33/1089 78/1089 52/1089 33/1089 33/1089 26/1089 1030/1089 978/1089 971/1089 33/1089 BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 10 of 14 (page number not for citation purposes) When we perform this analysis on our example of a sim- ple regulatory network (figures 1, 2 and 3) we obtain the results shown in table 2. The transition probabilities asso- ciated to the simple regulatory network shown in table 1 allow us to build the Markov chain shown in figure 6. The resulting stationary distribution of the Markov chain shown in figure 6 is [1, 0]. Thus we interpret the state cycle of our simple regulatory network as spurious. Benchmarking of our method The lack of a common file format for qualitative analysis is an important issue for the benchmark of such methods. This is clearly stated in the article about the SQUAD soft- ware by Di Cara et al [34]: "With the increase of published signaling networks, it will be possible in the future to realize a benchmark among these software packages to compare their strengths and weaknesses. For doing that, however, it would be very useful to develop a common file format." Since Di Cara's article, this issue of a common file format for qualitative analysis is still important because the current SBML for- mat cannot encode logical models. However, work is ongoing to extend SBML such that version 3 could sup- port information for qualitative simulation. The solution we have found to overcome this current limitation was to use a proprietary annotation with a specific namespace to remain compatible with the SBML standard. This allowed us to read and write annotated SBML files from our com- putational tool. However, other software cannot use our annotated SBML to perform the qualitative analysis of a biological network, unless specific code is developed to read our annotations. SQUAD can generate SBML, but it cannot use its own generated SBML to perform qualitative analysis. All the information concerning qualitative anal- ysis is stored only in MML files (the file format used by SQUAD). This is why we could not use the current SBML version to perform the benchmark. Furthermore, except for some well-known problems which have been well formulated and thus accepted by the community (like the test for Initial Value Problems (IVPs) solvers of the Bari University [35] or the ISCAS89 benchmark for circuits [36]), any type of benchmark would be partial and its results could be seen as unfair by other authors. For example, as mentioned by Naldi et al. in [37], some methods are only suited for a subset of bio- logical problems: "Garg et al. have already represented Boolean state transition graphs in terms of BDD. They consid- ered the particular case of networks where genes are expressed provided all their inhibitors are absent and at least one of their activators is present " [7]. The Naldi et al.'s method, regard- less of its computational efficiency, is a more powerful modeling tool thanks to the use of logical evolution rules and multi-valued species. Even if it is always possible to use Boolean formalism to model multi-valued networks (by leveraging the number of Boolean species by the number of wished values, e.g. {Boolean_species_A_low_level, Boolean_species_A_middle_level, Boolean_species_A_high_level}), the use of multi-valued logical networks greatly eases the modeling process. However, despite all the restrictions discussed above, we believe that benchmarking our method is an important issue. We have then developed a program that generates a random network whose size is a user input. For the sake of simplicity, the obtained network contains species that can have 0, 1, 2 or 3 species influencing it. This means that, to compute the state of a species at time t + 1, we only Table 2: Computation of the transition probabilities associated to our simple regulatory network. Attractors Steady State (SS) State Cycle (SC) States 1010 0010 1100 1011 Perturbed states and their limit cycles 1010 → SS 1010 → SS 1100 → SC 0011 → SC 0110 → SS 1000 → SC 1011 → SC 0000 → SC 1110 → SS 1011 → SC 0010 → SC 1101 → SC 1010 → SS Resulting probability transition P(SS → SS) = 1 P(SC → SC) = 8/12 . 0.67 P(SC → SS) = 4/12 . 0.33 This table shows both the principle of our newly introduced stability analysis and its application on the simple regulatory network shown in figure 1. It has 2 main columns: the steady state column and the state cycle column. As the state cycle found during the dynamical synchronous analysis contains 3 states (see figure 2), the last column is divided into 3 sub-columns. In the line "Perturbed states and their limit cycles" we show the perturbation results of each state of each attractor by re-evaluating each species by its own Boolean function triggered asynchronously. Perturbations are done from species A to species D. There are 4 species in our simple regulatory model, therefore 4 new states are generated from 1 perturbed state. We then synchronously simulate each new state and note if their simulation leads to the attractor they are derived from or to the other attractor of the system. In other words, we watch in which basin of attraction are those new states (see figure 2). The arrows following by "SC" (state cycle) or "SS" (steady state) give those responses. For the steady state no perturbation has an effect because a steady state in synchronous analysis remains a steady state in asynchronous analysis. Thus we simplify the presentation, showing that all the perturbations applied to state [1010] leave this state unchanged. BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 11 of 14 (page number not for citation purposes) need to know the state of a maximum of 3 other species at time t. Our benchmarking tool has 3 parameters that can modify the connection density of the network : • the probability of being a "source" (i.e. the probability for a species to be influenced by no other species in the network), • the probability to be under the influence of only one other species in the network, • the probability to be under the influence of exactly two other species in the network. The complementary probability is the probability for a species to be influenced by three other species in the net- work. Then our benchmarking tool generates the files describing this network for our software as well as in MML and GINML formats for SQUAD [34,38] and GINsim [39,40], respectively. We have analyzed networks of sizes ranging from 33 (the number of species in our cholesterol regulatory pathway) up to 2500 species. The CPU times obtained with our method on a Intel® Core™ 2 Duo E6600 processor (2.4 GHz) with 2 GBytes of RAM are shown in table 3. The performance of other tested software did not compare favorably with our appli- cation. With GINsim, we were able to simulate networks as large as 1000 species, but we obtained an "out of mem- ory" error message for the network of 2500 species. When we used the SQUAD software, we were unable to simulate a network of 1000 species or above. It is however possible that the parameters used to build the automatically gener- ated networks might have an impact on the results of the benchmarking. Nevertheless, under the conditions used, our application is appropriate for the analysis of large bio- logical networks. Discussion The results reported here are in accordance with the bio- logical knowledge we have on the cholesterol biosynthe- sis pathway. The steady states found correspond to either a lack of precursor (Acetyl-CoA) or arise from the effect of statins blocking the endogenous synthesis of cholesterol, Markov chain of the transition probabilities between the steady state and the state cycle in our simple regulatory network Figure 6 Markov chain of the transition probabilities between the steady state and the state cycle in our simple regula- tory network. Let k be the number of states within an attractor (k can be 1 in the case of a point attractor) and N be the number of species in the model. For each attractor of this finite time-homogeneous Markov chain, we perturb each species of each state by triggering its own Boolean function asynchronously. Thus there are kN perturbations per attractor. In our simple regulatory network the cyclic attractor has 3 states. The number of species in the model is 4. The weight of the edge from an attractor X to an attractor Y is the ratio between the number of perturbations of X which lead to Y over the total number of perturbations of X. Steady State State Cycle 4/12 12/12 8/12 Table 3: Benchmark of our method for qualitative analysis of biological networks. number of species 33 100 250 500 1000 2500 CPU time 7.515s 15.874s 39.999s 90.295s 173.107s 569.511s This table shows the benchmarking results of our qualitative analysis methods on automatically generated networks. Its has been done on a Intel® Core™ 2 Duo E6600 processor (2.4 GHz) with 2 GBytes of RAM. BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 12 of 14 (page number not for citation purposes) and the cyclic attractor corresponds to a physiological reg- ulation of cholesterol synthesis. Based on these data, we will be able to evaluate the putative impacts of additional modifications along the pathway. For instance, we may evaluate the effect of compensatory intermediates such as farnesyl pyrophosphate or geranylgeranyl pyrophosphate, which are expected to both restore cholesterol synthesis and prevent the deleterious effects of its absence [25,41- 44]. These compounds may compensate for the lack of mevalonate, a condition that could readily be introduced in our computerized scheme and assayed experimentally at the same time. This would be particularly relevant in the field of cancer research, for defects in lipid signalling are of primary importance [19,45-47]. Hence, secondary protein modifications, including farnesylation or geranyl geranylation, which depend on the availability of farnesyl and geranyl geranyl pyrophosphate, respectively, are known to play pivotal roles in the progression of tumours that depend on Ras functional status (for review see [15]). However, it would require further studies to integrate our cholesterol regulatory pathway with oncological path- ways, like the Ras activation pathway. We believe that this would be a particularly interesting perspective, bearing in mind that signal transduction pathways with G proteins have been extensively studied [48-52] and modeling efforts have already been made [53,54]. Furthermore, the method described here to identify spurious cycles opens new routes to compute large and biologically relevant models thanks to the computational efficiency of syn- chronous simulation. An important aspect was to bench- mark our method in order to determine if its computational efficiency is comparable to those of GIN- sim and SQUAD. Our results show that our method can analyze networks containing as many as 2500 species and was time efficient. Indeed, the approach could well be applied to other regulatory pathways, either from other metabolic routes or from transduction signaling. How- ever, the current model is purely a Boolean model where a gene is either active or inactive, a protein either present or not. An obvious limitation of Boolean formalism comes, for example, from the difficulty or the impossibil- ity to model a simultaneous and antagonist influence on a species, e.g. if a gene is under the influence of a silencer and an activator. In that case, we would like to be able to model a threshold above which there is activation or inhi- bition of the targeted species, e.g. there is RNA production when there is at least twice as much activator as silencer. Boolean formalism is not suitable for this purpose. This limitation could however be alleviated by expressing the presence of a molecular species with an enumeration of values ranging from the complete lack to a highly over- expressed level such as in the generalized logical modeling approach of Thomas and D'Ari [4]. This would also ena- ble to address, with a more realistic approach, the effect of an inhibitor or the effect of an enzyme, and to predict the preponderance of one or the other species in case of antag- onistic regulation. The multi-level approach was success- fully applied to many experimentally studied biological regulatory networks (e.g. [55-58]). We can note here, that our Markov chains-based stability analysis could readily be extended on the analysis of a multilevel qualitative simulation. Other work seems to be ongoing on choles- terol on cholesterol modeling using a set of ordinary dif- ferential equations thanks to a huge effort of identification of biochemical kinetics and this should add further insights on the understanding of this pathway [59]. Those two last approaches would allow us, for exam- ple, to analyze different cholesterol levels. Conclusion To the best of our knowledge, this is the first description of a dynamic systems biology model of the human choles- terol pathway and several of its key regulatory control ele- ments. This study was designed with a formal methodology and was challenged through the use of an important biochemical pathway. To efficiently analyze this model and ensure further analysis even after its com- plexification and possible merge with other pathway models like Ras signaling cascade models, we associate a classical and computationally efficient synchronous Boolean analysis with a newly introduced method based on Markov chains, which identifies spurious cycles among the results of the synchronous analysis. The in silico exper- iments show the blockade of the cholesterol endogenous synthesis by statins and its regulation by SREPBs, in full agreement with the known biochemical features of the pathway. Furthermore, because high throughput experi- ments give rise to increased complexification of biological systems, there are major needs for new computational developments for their dynamical analysis. Our method- ology is one answer to this new challenge. Authors' contributions LC and GK conceived this study and built the model based on literature data. GK conducted the in silico experiments. Acknowledgements We wish to thank very much Dr. Claudine Chaouiya for her critical reading of the manuscript. This work was supported by grants from the Inserm, the Brittany region, the University of Brest and the Medical Faculty of Brest. Gwenael Kervizic was supported by a CIFRE contract from the ANRT. References 1. Kitano H: Computational systems biology. Nature 2002, 420(6912):206-10. 2. Kauffman SA: Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 1969, 22(3):437-67. 3. 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Sir Paul Nurse, Cancer Research UK Your research papers will be: available free of charge to the entire biomedical community peer reviewed and published immediately upon acceptance cited in PubMed and archived on PubMed Central yours — you keep the copyright Submit your manuscript here: http://www.biomedcentral.com/info/publishing_adv.asp BioMedcentral BMC Systems Biology 2008, 2:99 http://www.biomedcentral.com/1752-0509/2/99 Page 14 of 14 (page number not for citation purposes) 53. Singh A, Jayaraman A, Hahn J: Modeling regulatory mechanisms in IL-6 signal transduction in hepatocytes. Biotechnol Bioeng 2006, 95(5):850-62. 54. Maurya MR, Bornheimer SJ, Venkatasubramanian V, Subramaniam S: Reduced-order modelling of biochemical networks: applica- tion to the GTPase-cycle signalling module. Syst Biol (Steve- nage) 2005, 152(4):229-242. 55. Thomas R, Thieffry D, Kaufman M: Dynamical behaviour of bio- logical regulatory networks-I. 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Nat Biotechnol 2005, 23(8):961-6.	19025648	SREBP_SCAP = ( ( Insig_SREBP_SCAP ) AND NOT ( Statins ) ) Mevalonyl_pyrophosphate = ( Mevalonic_Acid ) mSREBP = ( pSREBP ) Farnesyl_pyrophosphate = ( ( Geranyl_pyrophosphate ) AND NOT ( FPP_Synthase ) ) Desmosterol = ( Lanosterol ) Acetyl_CoA_acetyltransferase = ( Acetyl_CoA_acetyltransferase_RNA ) HMG_CoA_Synthase_gene = ( mSREBP ) FPP_Synthase_gene = ( mSREBP ) FPP_Synthase = ( FPP_Synthase_RNA ) Statins = ( Statins ) Cyp51_RNA = ( Cyp51_gene ) Squaline = ( Farnesyl_pyrophosphate ) HMG_CoA_Synthase_RNA = ( HMG_CoA_Synthase_gene ) Dimethyl_allyl_pyrophosphate = ( Isopentenyl_pyrophosphate ) Insig_SREBP_SCAP = NOT ( ( Cholesterol ) ) HMG_CoA_Reductase = ( ( HMG_CoA_Reductase_RNA ) AND NOT ( Statins ) ) Isopentenyl_pyrophosphate = ( Mevalonyl_pyrophosphate ) pSREBP = ( SREBP_SCAP ) HMG_CoA_Synthase = ( HMG_CoA_Synthase_RNA ) Septdehydrocholesterol = ( Lanosterol ) FPP_Synthase_RNA = ( FPP_Synthase_gene ) HMG_CoA_Reductase_gene = ( mSREBP ) Geranyl_pyrophosphate = ( Dimethyl_allyl_pyrophosphate ) OR ( Isopentenyl_pyrophosphate ) HMG_CoA = ( Acetoacetyl_CoA AND ( ( ( HMG_CoA_Synthase AND Acetyl_CoA ) ) ) ) Mevalonic_Acid = ( HMG_CoA AND ( ( ( HMG_CoA_Reductase ) ) ) ) Acetyl_CoA_acetyltransferase_gene = ( mSREBP ) Acetyl_CoA = ( Acetyl_CoA ) Lanosterol = ( Squaline ) Cyp51_gene = ( mSREBP ) HMG_CoA_Reductase_RNA = ( HMG_CoA_Reductase_gene ) Cholesterol = ( Septdehydrocholesterol ) OR ( Desmosterol ) Acetoacetyl_CoA = ( Acetyl_CoA AND ( ( ( Acetyl_CoA_acetyltransferase ) ) ) ) Acetyl_CoA_acetyltransferase_RNA = ( Acetyl_CoA_acetyltransferase_gene ) Cyp51 = ( Cyp51_RNA )
BioMed Central Page 1 of 20 (page number not for citation purposes) BMC Systems Biology Open Access Research article Modeling ERBB receptor-regulated G1/S transition to find novel targets for de novo trastuzumab resistance Özgür Sahin1, Holger Fröhlich1, Christian Löbke1,2, Ulrike Korf1, Sara Burmester1, Meher Majety1,3, Jens Mattern1, Ingo Schupp1, Claudine Chaouiya4, Denis Thieffry4, Annemarie Poustka1, Stefan Wiemann1, Tim Beissbarth1 and Dorit Arlt1 Address: 1Division of Molecular Genome Analysis, German Cancer Research Center, Im Neuenheimer Feld 580, 69120 Heidelberg, Germany, 2Current address: Phadia GmbH, Munzinger Strasse 7, 79010 Freiburg, Germany, 3Current address: Roche Diagnostics GmbH, Nonnenwald 2, 82377 Penzberg, Germany and 4Technologies Avancées pour le Génome et la Clinique, INSERM U928, Université de la Méditerranée, Campus Scientifique de Luminy – Case 928, 13288 Marseille, France Email: Özgür Sahin* - oe.sahin@dkfz-heidelberg.de; Holger Fröhlich - h.froehlich@dkfz-heidelberg.de; Christian Löbke - christian.loebke@phadia.com; Ulrike Korf - u.korf@dkfz-heidelberg.de; Sara Burmester - s.burmester@dkfz-heidelberg.de; Meher Majety - meher.majety@roche.com; Jens Mattern - jens.mattern@dkfz-heidelberg.de; Ingo Schupp - i.schupp@dkfz-heidelberg.de; Claudine Chaouiya - claudine.chaouiya@univmed.fr; Denis Thieffry - thieffry@tagc.univ-mrs.fr; Annemarie Poustka - a.poustka@dkfz- heidelberg.de; Stefan Wiemann - s.wiemann@dkfz-heidelberg.de; Tim Beissbarth - t.beissbarth@dkfz-heidelberg.de; Dorit Arlt* - d.arlt@dkfz- heidelberg.de * Corresponding authors Abstract Background: In breast cancer, overexpression of the transmembrane tyrosine kinase ERBB2 is an adverse prognostic marker, and occurs in almost 30% of the patients. For therapeutic intervention, ERBB2 is targeted by monoclonal antibody trastuzumab in adjuvant settings; however, de novo resistance to this antibody is still a serious issue, requiring the identification of additional targets to overcome resistance. In this study, we have combined computational simulations, experimental testing of simulation results, and finally reverse engineering of a protein interaction network to define potential therapeutic strategies for de novo trastuzumab resistant breast cancer. Results: First, we employed Boolean logic to model regulatory interactions and simulated single and multiple protein loss-of-functions. Then, our simulation results were tested experimentally by producing single and double knockdowns of the network components and measuring their effects on G1/S transition during cell cycle progression. Combinatorial targeting of ERBB2 and EGFR did not affect the response to trastuzumab in de novo resistant cells, which might be due to decoupling of receptor activation and cell cycle progression. Furthermore, examination of c-MYC in resistant as well as in sensitive cell lines, using a specific chemical inhibitor of c-MYC (alone or in combination with trastuzumab), demonstrated that both trastuzumab sensitive and resistant cells responded to c-MYC perturbation. Conclusion: In this study, we connected ERBB signaling with G1/S transition of the cell cycle via two major cell signaling pathways and two key transcription factors, to model an interaction network that allows for the identification of novel targets in the treatment of trastuzumab resistant breast cancer. Applying this new strategy, we found that, in contrast to trastuzumab sensitive breast cancer cells, combinatorial targeting of ERBB receptors or of key signaling intermediates does not have potential for treatment of de novo trastuzumab resistant cells. Instead, c-MYC was identified as a novel potential target protein in breast cancer cells. Published: 1 January 2009 BMC Systems Biology 2009, 3:1 doi:10.1186/1752-0509-3-1 Received: 9 September 2008 Accepted: 1 January 2009 This article is available from: http://www.biomedcentral.com/1752-0509/3/1 © 2009 Sahin et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 2 of 20 (page number not for citation purposes) Background Anticancer drugs which are in clinical use show their effect by acting as non-selective anti-proliferative agents which kill also the proliferating normal cells in the tumor micro- environment [1]. The past few decades witnessed the development of targeted therapies including monoclonal antibodies, which aim at targeting certain antigens expressed on the surface of cancer cells with high specifi- city. In particular, adding trastuzumab, a recombinant humanized monoclonal antibody directed against the ectodomain of the receptor tyrosine kinase ERBB2, to reg- imens containing existing chemotherapeutic agents has significantly improved clinical outcomes for breast cancer patients. However, de novo and acquired resistance to tar- geted therapeutics are common and the next challenges for the contemporary cancer researchers [2]. The ERBB family of receptor tyrosine kinases is composed of four receptors that have the ability to form homo- and heterodimers, and couple binding of extracellular growth factors to intracellular signal transduction pathways [3,4]. ERBB2, the main player of the ERBB network, does not show any ligand binding activity, but has high dimeriza- tion affinity [5,6]. The abnormal activation of ERBB recep- tors through gene amplification, mutations, or protein overexpression has been linked to breast cancer prognosis [7]. Trastuzumab is administrated to ERBB2-overexpress- ing breast cancer patients [8,9]. The drug shows its effect by inducing antibody-dependent cellular cytotoxicity (ADCC), disrupting the downstream signaling of ERBB2 and also resulting in G1/S cell cycle arrest [10]. However, the response rate to trastuzumab is rather low, with a range from 12% to 34% having been reported for a median duration of 9 months [11,12]. Hence, at least two third of the patients are de novo resistant. On the cellular level, this might be caused by cancer cells being able to overcome cell cycle arrest despite targeting the ERBB2 receptor. Therefore, additional targets have to be identi- fied, which should avoid bypass of cell cycle arrest mech- anisms. The cell cycle of eukaryotic organisms is tightly regulated by the cyclin-dependent kinases (CDKs) and their activa- tion partners, cyclins [13], which lead cells through the well-ordered G1-, S-, G2-, and M-phases. It has been shown that ERBB2 regulates G1/S transition during cell cycle progression by modulating the activity of the Cyclin D, Cyclin E/CDK complex, the c-MYC oncogene, and the p27 kinase inhibitor [7,14]. The restriction points within different cell cycle phases represent key checkpoints, where the critical decisions are made for the cells to divide. At the G1/S restriction point of the cell cycle, cells are committed to enter S phase where DNA replication takes place [15]. This process is regulated by Cyclin D/ CDK4/6 and Cyclin E/CDK2 complexes, which phospho- rylate and thereby inactivate tumor suppressor retinoblas- toma protein pRB [16-18]. Hyperphosphorylation of pRB results in the release of the E2F transcription factor that then initiates the transcription of essential genes for DNA replication [19]. In both normal and tumor cells, pRB oscillates between an active (hypophosphorylated) state in early G1 and an inactive (hyperphosphorylated) state in the late G1, S and G2/M phases [18]. Therefore, phos- phorylation and subsequent inactivation of pRB repre- sents a key event governing cell proliferation. There have been few studies which applied systems biol- ogy approaches to identify novel markers [20] and to define drug target networks in human cancer and other pathologies [21]. In this study, we focused on the regula- tion of pRB through ERBB-receptor signaling at a network level in a de novo trastuzumab resistant cell system to iden- tify new potential perturbation points leading to cell cycle arrest. Instead of single candidate gene approach, which generally examines the role of a single protein considering it either in conjunction with a second protein or regard- less to other proteins, we applied a systems biology approach to identify the role of each component in the context of protein interaction networks. This strategy is motivated by the fact that cells react to perturbation of a single protein by taking advantage of using alternative ways to keep the system robust. In drug resistance, these alternative ways allow bypassing the inhibitory effect of drug treatment. Therefore, in order to find the uncommon perturbations to which cells cannot find an efficient way to react, we first integrated published data to build the protein network for ERBB-receptor regulated cell cycle progression, then combined qualitative dynamical mode- ling and robust experimental approaches, and finally pre- dicted suitable and efficient targets for individual or combinatorial treatments in de novo trastuzumab resist- ance in breast cancer as a model system. We used the Boolean logical framework for the dynamical modeling and analysis of the biological network. This framework simplifies the regulatory activity of proteins by considering them as all or none devices. More precisely, each protein is defined as being either active (value 1) or inactive (value 0) depending on its abundance or activity level. We selected 18 proteins connecting ERBB receptor signaling to the G1/S transition of cell cycle, and defined logical rules to describe their regulations with regard to lit- erature information. Modeling and loss of function simu- lations of the network proteins were performed using the modeling and simulation software GINsim [22,23]http:// gin.univ-mrs.fr/GINsim. Experimental perturbations of each network element using RNAi and following measurements of their effects on the output protein allowed us to compare simulations BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 3 of 20 (page number not for citation purposes) with the experimental results. Quantitative measurements of protein abundance and activation states using reverse phase protein arrays (RPPA) [24,25] enabled us to reverse engineer the interactions of proteins in the cell system we used, and to compare the experimental network data with published results of single protein analysis. Utilizing spe- cific inhibitors against potential targets alone or in combi- nation with trastuzumab, we further validated the RNAi experiments and finally defined potential future therapeu- tic strategies. Results Characterization of the de novo trastuzumab resistant cell system We first identified a suitable de novo trastuzumab resistant cell system as prerequisite for studying the ERBB-receptor regulated network. This cell system should have high ERBB2 expression but be resistant to trastuzumab treat- ment. To this end, we first analyzed several breast carci- noma cell lines and the normal epithelial MCF-12A cell line for their expression of ERBB family receptors at mRNA and protein levels, respectively (Figure 1A and 1B). HCC1954 cells, like SK-BR-3 and BT474 cells, express high levels of EGFR (ERBB1) and ERBB2 receptors, but have low levels of ERBB3. ERBB4 receptor expression was not detected in the HCC1954 cell line. Next, we examined the response to trastuzumab treatment of breast carcinoma cells with high ERBB2 expression (HCC1954 and SK-BR-3) as compared to cells with low ERBB2 level (MCF-7) in a viability assay (Figure 1C). Cells were treated with or without trastuzumab and cell viabil- ity was assayed over time to observe the effect of the drug. We further tested different concentrations of trastuzumab to rule out the possibility that the resistance of cell system could have been due to insufficient amounts of trastuzu- mab being present in the assay (Additional file 1, Figure 1A). While SK-BR-3 cells responded to trastuzumab start- ing from day two, HCC1954 cells were resistant, as they did not show any response to the drug over four days. Lastly, we verified the resistance of HCC1954 cells to tras- tuzumab in 3-D cell culture (Figure 1D). After eight days of treatment, HCC1954 cells were still growing in a large cluster-like structure that was similar to untreated HCC1954 cells, whereas SK-BR-3 cells were sensitive to trastuzumab also in 3-D culture. We could exclude that the resistance phenotype of HCC1954 cells was due to a higher or lower ERBB2 expression level compared to sen- sitive SK-BR-3 cells (Additional file 1, Figure 1B). Further- more, to rule out the potential impact of possible mutations in the ERBB2 protein on resistance phenotype of the HCC1954 cells, the ERBB2 gene sequence was veri- fied by sequencing and no mutation was found. Hence, HCC1954 cells were chosen as a de novo trastuzumab resistant model cell system in this study. Determination of experimental output Next, we characterized HCC1954 cells with regard to G1/ S progression by measuring the levels of pRB phosphor- ylation, and of cell cycle proteins by comparing MOCK (only lipofectamine transfection reagent) and CDK4 siRNA transfected cells. After synchronization, we stimu- lated the cells with EGF. Starting from "0 hour (no EGF)", cells were lysed at different time points and proteins of interest were detected with specific antibodies (Figure 2A). CDK4 knockdown was efficient, as no residual pro- tein was visible on the blot. Due to Dif-3 treatment, which degrades Cyclin D1 at both mRNA and protein levels [26], the level of Cyclin D1 was low at 0 h while it increased upon continuous EGF stimulation. After 6 h of EGF stim- ulation, Cyclin D1 expression remained constant until 24 hours in both MOCK-treated cells and after CDK4 knock- down. For the MOCK control, a gradual increase in the Cyclin E1 level was observed, starting from EGF stimula- tion (0 hour) to 18 hours. In contrast, Cyclin E1 expres- sion did not change from 0 h to 18 h after CDK4 knockdown. Surprisingly, we observed a reduction also of CDK2 in the CDK4-siRNA treated cells, starting at 6 h. This might be due to the partnering of CDK2 with Cyclin E1, whose level did not increase in case of CDK4 knock- down. We found the phosphorylation of pRB (Ser 807/811), our marker for G1/S transition, to be delayed and the pRB expression level to be decreased after CDK4 knockdown, as compared to the MOCK control. Hence, we next quan- tified the phosphorylation level of pRB (Figure 2B) in the same lysates using reverse phase protein arrays (RPPA). The phosphorylation level of pRB was found to be low in the growth-arrested cells and induction of pRB phosphor- ylation from 6 to 12 hours did not occur abruptly for CDK4 knockdown compared to MOCK. These data dem- onstrate that phosphorylation of pRB at the transition point can be quantified by RPPA as an output of EGF stim- ulation. Literature-based Boolean network of G1/S transition The initial network of G1/S transition was built by extract- ing information from the literature about interactions between proteins involved in receptor tyrosine kinase-reg- ulated cell cycle progression (Additional file 1, Table 1). The resulting network encompasses 18 proteins, includ- ing EGF as stimulus, homo- and heterodimers of ERBB family members, tyrosine kinase receptor IGF-1R, key transcription factors (ER-α and c-MYC), key signaling intermediates (AKT1 and MEK1), and G1/S transition cyc- lins, CDKs and CDK inhibitors (Figure 3). Upon activa- tion, members of the ERBB family of tyrosine kinases BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 4 of 20 (page number not for citation purposes) Characterization of breast cell lines for trastuzumab resistance/sensitivity Figure 1 Characterization of breast cell lines for trastuzumab resistance/sensitivity. A. qRT-PCR to determine ERBB recep- tor family expression at mRNA level in MCF-12A normal breast epithelial cells and in five breast carcinoma cells. B. Western blots showing the expression level of ERBB family receptors. HCC1954 cells express high levels of ERBB1 and ERBB2 recep- tors, but low level of ERBB3 and no ERBB4. β-actin was used as loading control. C. WST-1 cell viability assay to assess the resistance of breast carcinoma cells to trastuzumab (100 nM). Compared to SK-BR-3 cells, with high level of ERBB2 receptors, HCC1954 cells are resistant to trastuzumab (100 nM) over 4 days. D. Verification of resistance of HCC1954 cells to trastuzu- mab compared to sensitive SK-BR-3 cells in 3-dimensional cell culture. Photos were taken after eight days of trastuzumab treatment. BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 5 of 20 (page number not for citation purposes) form homo- and heterodimers. For HCC1954 cells, six different such dimers are possible as ERBB4 is not expressed in this cell line. The dimers ERBB1/ERBB2, ERBB1/ERBB3 and ERBB2/ERBB3 were represented as specific nodes in the network. Homodimers were implic- itly represented by the corresponding protein nodes. Since no ligand is known for ERBB2 homodimers [27] and as ERBB3 homodimers have a defective tyrosine kinase domain [28], the corresponding nodes are unable to acti- vate the ERBB targets AKT1 and MEK1. The effects of the combinations of interactions on the activity of each pro- tein was defined in terms of logical rules using the Boolean operators AND, OR, and NOT. Table 1 lists these Boolean rules for the network components, and data sup- porting the rules is provided in the Additional file 1, Table 1. We then utilized the modeling and simulation software GINsim [23] to implement these rules into a computa- tional model. Figure 3 shows the resulting logical regula- tory graph for the ERBB receptor-regulated G1/S transition protein network. Normal arrows denote positive regula- tions, which are either through phosphorylation, tran- scriptional activation, or physical interaction (e.g,. complex formation). Blunt-ended arrows denote negative regulations. The numbers associated with each edge refers to the respective publications providing experimental data in support of the corresponding regulatory interac- tion (Additional file 1, Table 1). Simulation of loss-of-functions For loss-of-function simulations, we performed in silico knockdowns of the network proteins by fixing the level of the perturbed element to "0", meaning that the corre- sponding protein was always "inactive" (Additional file 1, Figure 2). Each simulation was performed for specific ini- tial protein states, matching the biological and experi- mental conditions (for several proteins, we considered both possible values). For example, the initial states of p21 and p27, both of which being CDK inhibitors, were set to "1" because, in G0/G1 arrested cells, the expression levels of these inhibitors are high and their levels decrease (due to their degradation in proteasomes) once cells progress through S phase [29]. To represent continuous EGF simulation, the initial values of ERBB nodes were set to "1". Since the cells had been synchronized with Dif-3, which degrades Cyclin D1, the initial level of Cyclin D1 was set to "0". Using the resulting initial states, we com- puted all possible state transitions and iterated until we finally obtained a unique "stable state" in which the level of each protein was fixed (details about knockdown sim- ulations can be found in Materials and Methods section). Proof of principle experiments for the determination of G1/S transition point in trastuzumab resistant HCC1954 cells Figure 2 Proof of principle experiments for the determination of G1/S transition point in trastuzumab resistant HCC1954 cells. A. Western blots showing the expression and activation of key G1/S proteins. Cells were treated either only with Lipofectamine (MOCK) or with 20 nM CDK4 siRNA for 24 hours. Then, cells were synchronized for 24 hours and subse- quently stimulated with 25 ng/ml EGF for 6, 12, 18 or 24 hours. Cell lysates were applied to immunoblotting. B. Reverse Phase Protein Array (RPPA) showing the phosphorylation state of pRB protein (Ser 807/811). The same lysates (from A) were applied to RPPA. The upper panel shows the read-out of antibody signal at near infra-red range for phospho-pRB antibody with four replicates. The lower panel shows the graphical representation of phospho-pRB antibody signal intensity for two different conditions and for four time points. Signals were normalized to 0 hour MOCK sample. BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 6 of 20 (page number not for citation purposes) Table 2 summarizes the outcomes of the simulations. Out of 17 loss-of-function simulations, a significant decrease of pRB phosphorylation (pRB is predominantly in its hyphophosphorylated form and cells do not progress through G1/S transition: pRB = 0) was predicted for CDK4, Cyclin D1, and CDK6 loss of functions. For the ERBB1_2 and ERBB1_3 knockdowns, we obtained two possible stable states characterized by pRB = 0 and 1 that should be resolved with experimental results. The loss-of- function simulations for all other network proteins resulted in the preservation of pRB phosphorylation (pRB = 1), thus tentatively enabling G1/S transition. Furthermore, we have also simulated the loss-of-function of multiple proteins (all double and many triple knock- downs) (Additional file 2, Table 1). We have observed that if one protein knockdown gives pRB = 0, the combi- nation of any other protein knockdown with this one also gives pRB = 0 (e.g. ER-α knockdown gives pRB = 0 and ER- α+AKT1 knockdown also gives pRB = 0) and we have ver- ified this experimentally as well (Additional file 2, Table 2). We have also simulated the knockdown of all three receptors at the same time (ERBB1_2_3) and it resulted in 2 stables states with pRB = 1 or 0 (Additional file 2, Table 1). Assessment of siRNA knockdown efficiency and specificity for experimental testing of simulations In order to validate the simulations having been per- formed for various possible loss of functions, we utilized RNAi to experimentally induce knockdown of the corre- sponding proteins. First, we validated the siRNAs accord- ing to their knockdown efficiency at both mRNA and protein levels by qRT-PCR and Western blotting, respec- tively (Figure 4A and 4B). We obtained at least 70% knockdown at mRNA level for all the network proteins (Figure 4A) and for most a similar knockdown also at the protein level (Figure 4B), both in single and combinato- rial RNAi settings [24]. Because of the high level of sequence conservation among ERBB family receptors [27], it was imperative to test for a potential cross-reactiv- ity of ERBB receptor siRNAs (Figure 4C and 4D). To this end, we compared the effects of the pools of four siRNAs for every gene with those of individual siRNAs. Neither pools nor individual siRNAs were found to have cross- reactivity (Figure 4C and 4D). In the combinatorial RNAi settings, the levels of the ERBB proteins in the EGFR/ERBB2, EGFR/ERBB3, and ERBB2/ ERBB3 heterodimers were efficiently downregulated (Fig- ure 4B). While the EGFR level was drastically reduced when we applied double knockdown of EGFR/ERBB2, EGFR/ERBB3, and ERBB2/ERBB3 (Figure 4B), the EGFR protein was stable in the single knockdown with EGFR siRNA although this treatment resulted in more than 80% knockdown at the mRNA level (Figure 4A). However, knockdown of the ERBB2 receptor resulted in a substan- tial decrease of EGFR at the protein level. With respect to the qRT-PCR results, we can exclude that this effect could be due to a cross-reaction of the ERBB2 siRNA (Figure 4C). Therefore, we hypothesize an indispensable partner- ing of ERBB2 and EGFR in ERBB2 overexpressing cells (Figure 4D), and assume that the EGFR receptor protein is efficiently stabilized that way. This hypothesis was sup- ported by similar observations made in ERBB2 overex- pressing SK-BR-3 cells, but not in MDA-MB-231 having low ERBB2 expression (Additional file 1, Figure 3). Experimental validation of loss-of-function simulations Next, we designed a series of in vitro experiments using the validated conditions described above to assess the results from loss of function simulations. Lysates of three biolog- ical replicates were analyzed with RPPA using four techni- cal replicates of each. The signal intensity of phosphorylated pRB was measured in the near-infrared range (NIR) for each knockdown at two time points (0 h and 12 h). As a negative control, we utilized MOCK sam- ples which had not been stimulated with EGF. Results were compared to MOCK samples (reference sample), which had been stimulated with EGF, and the significance of the impact on pRB phosphorylation was tested using Table 1: Boolean rules for the activation of each component of the network presented in Figure 3. Target Logical rules for the activation of target ERBB1 EGF ERBB2 EGF ERBB3 EGF ERBB1_2 ERBB1 Λ ERBB2 ERBB1_3 ERBB1 Λ ERBB3 ERBB2_3 ERBB2 Λ ERBB3 IGF1R (ER-α V AKT1) Λ !ERBB2_3 ER-α AKT1 V MEK1 c-MYC AKT1 V MEK1 V ER-α AKT1 ERBB1 V ERBB1_2 V ERBB1_3 V ERBB2_3 V IGF1R MEK1 ERBB1 V ERBB1_2 V ERBB1_3 V ERBB2_3 V IGF1R CDK2 Cyclin E1 Λ !p21 Λ !p27 CDK4 Cyclin D1 Λ !p21 Λ !p27 CDK6 Cyclin D1 Cyclin D1 AKT1 V MEK1 V ER-α V c-MYC Cyclin D1* ER-α Λ c-MYC Λ (AKT1 V MEK1) Cyclin E1 c-MYC p21 ER-α Λ !AKT1 Λ !c-MYC Λ !CDK4 p27 ER-α Λ !CDK4 Λ !CDK2 Λ !AKT1 Λ !c-MYC pRB (CDK4 Λ CDK6)V (CDK4 Λ CDK6 Λ CDK2) These rules were derived from the references listed in the Additional file 1, Table 1. The refined rules for Cyclin D1 are shown with "*". Symbols "Λ": AND, "V": OR and "!": NOT BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 7 of 20 (page number not for citation purposes) ERBB receptor regulated G1/S transition network derived from published data Figure 3 ERBB receptor regulated G1/S transition network derived from published data. ERBB receptors are functional (i.e. able to transmit signal to downstream proteins) only when they form heterodimers, except for ERBB1, which is also functional as a homodimer. The number associated with each arrow indicates the reference from which the corresponding interaction was extracted (a list of these references is provided in the Additional file 1, Table 1). Normal arrows denote positive regula- tions, whereas blunt arrows denote negative regulations. These interactions correspond to transcriptional regulations, post- transcriptional modifications, or physical interaction. EGF constitutes the input and pRB protein represents the output of the network. BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 8 of 20 (page number not for citation purposes) the ANOVA method. Box plots of the knockdown effect on pRB phosphorylation are shown in Figure 5A. We clas- sified effects as "1" in cases where the knockdown of a spe- cific protein had resulted in a phosphorylation profile similar to the MOCK profile at 12 h, and no significant change of the pRB phosphorylation state had been observed. Conversely, if the knockdown resulted in a sig- nificantly lower pRB phosphorylation level compared to MOCK (FDR < 1%), the effect was classified as "0", mean- ing that a significant change of the pRB phosphorylation state was observed. The results demonstrated that knock- downs of CDK4, CDK6, Cyclin D1, Cyclin E1, ER-α, c- MYC, ERBB1, ERBB1_2, and IGF-1R indeed resulted in a significant hypophosphorylation of pRB. Simulation of loss-of-function of all three receptors (ERB1_2_3) had resulted in two stable states for pRB: "1" and "0". Experimentally, we have shown that knockdown of all three receptors resulted in pRB = 1 suggesting that combinatorial targeting of ERBB receptors may not be beneficial to overcome resistance in de novo trastuzumab resistant cells (Additional file 2, Table 2). To confirm the effect of knockdowns on G1/S transition at the DNA level, we measured incorporation of 7-AAD into the DNA of single cells by flow cytometry 18 hours after EGF stimulation (Figure 5B). The fractions of cells in G1- and in S phases were taken to calculate the G1/S ratio for each knockdown. We regarded gene knockdowns having similar effects as MOCK or p21 to be positive for G1/S transition ("value 1"), while G1/S ratios higher than MOCK or p21 were considered negative ("value 0"). For the knockdowns of CDK4, Cyclin D1, Cyclin E1, ER-α and c-MYC, we thus observed no G1/S transition (Table 2). Table 2 summarizes the simulation results for the final state of the pRB protein and the respective experimental data. Indeed, 12 out of 17 knockdown simulations were consistent with experimentally measured pRB activity lev- els (compare columns 1 and 2 of Table 2). The correlation is even slightly better with 7-AAD data, as the results of 13 out of 17 simulations were consistent with those of the p- pRB data (compare columns 1 and 3 of Table 2). How- ever, the simulations of ER-α, c-MYC and Cyclin E1 knockdowns gave results that are inconsistent with both types of the experimental data, pointing out the limits of our current model, which we will address in the next sec- tion. Altogether, our results suggest that Cyclin D1, CDK4, Cyclin E1, ER-α and c-MYC, but neither the combinatorial targeting of ERBB family receptors nor of key components of the MAPK (MEK1) and the survival pathways (AKT1) should be considered as potential targets for further test- ing in our de novo trastuzumab resistant model cell sys- tem. Table 2: Comparison of simulation results with experimental data (p-pRB protein data and 7-AAD DNA data). Simulated p-pRB data 7-AAD data Improved rules MOCK 1 1 1 1 AKT1 1 1 1 1 MEK1 1 1 1 1 CDK2 1 1 1 1 CDK4 0 0 0 0 p21 1 1 1 1 p27 1 1 1 1 Cyclin D1 0 0 0 0 ERBB2_3 1 1 1 1 ERBB1_3 0/1 1 1 0/1 ERBB1 1 0 1 1 ERBB1_2 0/1 0 1 0/1 IGF1R 1 0 1 1 CDK6 0 0 1 0 ER-α 1 0 0 0 c-MYC 1 0 0 0 Cyclin E1 1 0 0 1 The first column ("Simulated") corresponds to the results of knockdown simulations for the initial logical model, while the last column ("Improved rules") displays the results obtained with the revised model (improved logical rules for Cyclin D1 as shown in Table 1). In the "Simulated", "p-pRB data" and "Improved rules" columns, the value "1" denotes the phosphorylation of pRB (G1/S transition) and "0" denotes the lack of phosphorylation (no G1/S transition). In the "7-AAD data" column, the value "1" denotes a low ratio of G1/S (G1/S transition) and "0" denotes a high G1/S ratio (no G1/S transition). Bold numbers emphasize the knockdowns for which simulations and both experiments agree. Normal numbers correspond to the knockdowns for which experiments led to different values, one of them being met by our simulation results. In the case of ERBB1_3 knockdown, one of the two existing stable states meets the concordant experimental result. The final state depends on the choice of the initial conditions, but these are difficult to fully specify (a similar situation occurs for the ERBB1_2 knockdown). Finally, Italic numbers denote the knockdowns for which simulation data differ from the results of both experiments. BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 9 of 20 (page number not for citation purposes) Figure 4 (see legend on next page) BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 10 of 20 (page number not for citation purposes) Refinement of logical rules and network reconstruction based on quantitative protein data To find out whether the observed discrepancies between our network model and the experimental data were due to the incorporation of incorrect logical rules, missing inter- actions, or even missing components in our literature- based network, we next refined the logical rules and per- formed a network reconstruction that was based on quan- titative protein data. Extracting information about combinatorial regulatory effects of different proteins affecting a given component is much more difficult than extracting information about individual interactions from the literature. We have thus systematically evaluated modifications of the logical rule with respect to model prediction capacity. In particular, the discrepancy between the simulation results and exper- imental counterparts for c-MYC and ER-α knockdowns could be solved by changing the logical rules associated with the Cyclin D1 node. We tested several combinations for the logical rules on ER-α, c-MYC and Cyclin D1. A minor modification of the model enabled us to recover the correct behaviour for the two loss-of-functions: ER-α and c-MYC (with a stable state having pRB = 0), while conserving all the behaviour for all other proteins. The original rules assumed that the presence of one activator is sufficient (the OR connecting all 4 variables in Table 2). This is the loosest rule that can be defined for a node that is activated by several regulators. The modified rule (Cyc- lin D1 = 1 when ER-α AND c-MYC AND (AKT1 OR MEK1) is more restrictive as this states that that ER-α AND c-MYC together with AKT1 OR MEK1, are required to activate Cyclin D1. The biological implication of this change is that ER-α, c-MYC and (MEK1 or AKT1) proteins should act together to make the cells pass through S-phase and proliferate. In addition, although both transcription fac- tors are necessary at the same time, the function of the one of the signaling molecule, AKT1 or MEK1, can be compen- sated in the cell, but not of the two at the same time. So, our results may propose a more comprehensive logic for the regulation of Cyclin D1 in our model cell system. These results may hint that control of Cyclin D1 is a sequential event (AKT1 or MEK1 → ER-α → c-MYC) and can exclude the alternative edges from ER-α, MEK1 or AKT1 to Cyclin D1. We are thus left with just one knock- down simulation (Cyclin E1) disagreeing with the experi- mental data. In the next step, we wanted to test if the discrepancy observed in the case of Cyclin E1 knockdown could be attributed to some missing interactions among the regula- tory components considered in our logical model. In order to address this discrepancy and also to examine cell line specific regulations, we further quantified the activa- tion and expression levels of most of the network ele- ments for individual and combinatorial network protein knockdowns using reverse phase protein arrays. In total, we quantified the changes in expression of nine network proteins, as well as the phosphorylation levels of ERK1/2 and AKT1. Some proteins could not be included in these measurements because of the lack of antibodies suitable for RPPA. As for the pRB experiments, we examined the effect of EGF stimulation on the other network proteins for each knockdown, compared to MOCK. The heatmaps in Figure 6 show the significant changes, at the expression or activation level of the proteins before EGF stimulation (Figure 6A) and 12 h after EGF stimulation (Figure 6B). Expression and phosphorylation levels either confirmed known interactions or inferred novel ones (Figure 6B). The resulting interactions define the network presented in Figure 7. A jackknife procedure (see Methods section) was used to eliminate putative indirect edges, which could be explained by a path along other edges, and only edges having a jackknife probability greater than 50% were kept (Figure 7). In the graph, solid black arrows indicate inferred direct or indirect interactions which are also sup- ported by published data, whereas the dotted grey arrows denote novel regulations having been identified for the HCC1954 reference cellular system. As a result, we inferred most of the interactions considered in our litera- ture-based network from the experimental data for trastu- zumab resistant HCC1954 cells, although some of them have opposite directions. One should also take into account that drawing edge directions from biological liter- Determination of knockdown efficiency and specificity of siRNAs in the HCC1954 cell system Figure 4 (see previous page) Determination of knockdown efficiency and specificity of siRNAs in the HCC1954 cell system. A. qRT-PCR results showing the knockdown efficiency of 20 nM pools of four siRNAs for each gene in the network (50 nM siRNA for ESR1). ACTB and HPRT1 were used as house-keeping controls. MOCK stands for the samples which were treated only with Lipofectamine transfection reagent. B. Western blots for the determination of knockdowns for the network elements at pro- tein level. Since dimers of ERBB family members are accepted as functional units, we used combinatorial RNAi (knockdown of two genes simultaneously) to produce knockdowns of such dimers. C. qRT-PCR results showing the knockdown efficiency and effect of one member of ERBB receptor family siRNA on the other two members of the family. Both pools of four individual siRNAs per gene and only one individual siRNA per gene were used. The concentration of siRNAs was 20 nM. ACTB was used as house-keeping control. D. Western blots showing the knockdown efficiency and cross reactivity of siRNAs at protein level. β-actin was taken as loading control. BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 11 of 20 (page number not for citation purposes) ature is usually a daunting task. Indeed, edge directions, when indicated, are often not well defined or even errone- ous. Additionally, there can be cell line specific differences or thus far unknown feedback mechanisms, for example a feedback from Cyclin D1 to MEK1 or from ER-α to AKT1. It is, therefore, not really unlikely to see edges that link in the direction opposite to the expected. Hence, although this approach demonstrates the feasibility of network reverse engineering at protein level using robust and quantitative protein array data, the resulting network was no help to solve the discrepancy observed for Cyclin E1 knockdown, thereby leaving a gap in our knowledge in the regulation or regulatory effects of this component. To sum up, our network inference approach provided us with the knowledge that the most regulations which were obtained from the literature were also present in our tras- tuzumab cell system and novel regulations might have potential role in the observed phenotype of the cells. Combinatorial targeting of c-MYC or EGFR in combination with ERBB2 using small chemical inhibitors in sensitive and resistant cells In order to verify the RNAi results and to validate the potential targets in our de novo resistant cell system, we applied small chemical inhibitors against c-MYC (10058- F4) and EGFR (gefitinib), alone and in combination with trastuzumab, and examined the growth of trastuzumab resistant HCC1954 cells compared to sensitive SK-BR-3 and BT474 cells. Administration of the c-MYC inhibitor alone resulted in reduced pRB phosphorylation in all three cells lines (Figure 8A, left panel), and its application alone or in combination with trastuzumab also reduced the growth of these cell lines (Figure 8B, middle panel). The results were verified using real-time impedance meas- urements over four days (Figure 8C, right panel), provid- ing a time-lapse profile of the growth rates. The resulting data demonstrate that the reduced growth rates of cells treated with the c-MYC inhibitor was independent from trastuzumab resistance and thus support the RNAi results shown in Figure 5A and 5B. Because combinatorial targeting of ERBB receptors is already in clinical use (e.g. lapatinib), we next targeted ERBB1 and ERBB2 receptors in single and combinatorial settings and compared the outcome in the de novo resist- ant HCC1954 cell line with the trastuzumab sensitive cell lines. First, we examined the downstream effectors of ERBB receptors (ERK1/2 and AKT1) and of pRB after treat- ment with trastuzumab or gefitinib (targets ERBB1) (Fig- ure 8B, left panel). In HCC1954 cells, no reduction in the expression levels of EGFR/ERBB2 or phosphorylation lev- els of their downstream signal mediators was observed for both treatments. However, reduced pRB phosphorylation was observed in gefitinib-treated HCC1954 cells. Both, the WST-1 viability assay and real-time impedance meas- urements demonstrated that trastuzumab resistant HCC1954 cells were also resistant to gefitinib treatment alone or in combination with trastuzumab. (Figure 8B, middle and right panel). In SK-BR-3 cells, AKT1 and pRB phosphorylation levels were lower after trastuzumab treatment, and pRB phos- phorylation was reduced after incubation with gefitinib. In BT474 cells, a strong reduction in AKT and ERK1/2 phosphorylation was measured after gefitinib treatment, while no such an effect was evident for trastuzumab treat- ment (Figure 8B, left panel). Real-time impedance meas- Analysis of the effects of knockdowns on G1/S transition in trastuzumab resistant HCC1954 cells Figure 5 Analysis of the effects of knockdowns on G1/S transi- tion in trastuzumab resistant HCC1954 cells. A. Phos- phorylation state of pRB (output of the network) after 12 hour EGF stimulation (input of the network). Box plots show the quantitative phosphorylation of pRB protein for the knockdown of each network protein compared to MOCK (only transfection reagent, no siRNA). B. G1/S ratio after 18 hours of EGF stimulation for corresponding knockdowns compared to MOCK (solid line) and p21 knockdown (dotted line) using 7-AAD DNA staining. BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 12 of 20 (page number not for citation purposes) urement showed for the SK-BR-3 cells that combinatorial targeting of EGFR and ERBB2 had a strong additive effect to reduce cell proliferation (Figure 8B, right panel). This additive effect was also visible for BT474 cells although it was not as strong as in SK-BR-3 cells. These data support our RNAi results, suggesting that the combinatorial target- ing of the EGFR and ERBB2 with gefitinib and trastuzu- mab, respectively, might not be effective to sensitize the cells to trastuzumab treatment in de novo trastuzumab resistance. However, these drugs in combination might lead to an improved outcome in sensitive cells, and poten- tially also in tumors, as compared to applying them indi- vidually. Discussion In the present study, we have applied a systems biology approach to identify alternative targets in de novo trastuzu- mab resistant breast cancer. While several studies have dealt with mechanisms leading to acquired trastuzumab resistance, there has been no comprehensive study that searched for targets alternative to ERBB2 in de novo trastu- zumab resistance. Since the aim of cancer therapy is to reduce the growth rate of cancer cells, and trastuzumab resistant breast cancer cells escape cell cycle arrest during treatment, we focused on a protein network that connects ERBB signaling to G1/S phase transition, in order to deter- mine new potential targets for perturbation. In contrast to previous studies, which had focused on the involvement of an individual protein in the resistant phenotype of the cells, we aimed to examine the roles of each protein in the context of their interactions at a protein network level. Several modeling studies about the ERBB receptor-regu- lated signaling pathways have been published recently [30,31]. These studies considered the activation of key intermediates (ERK1/2 and AKT) upon EGF and HRG stimulation and proposed differential dynamical models for these pathways. Likewise, various models have been proposed for the control of the mammalian cell cycle [18,22,32]. In our study, we combined these two cellular processes into one coherent network to find novel strate- gies for breast cancer therapy. First, we derived a logical network from published data (Figure 3 and Table 1). Sys- tematic simulations of loss-of-function perturbations were performed, and the final state of pRB phosphoryla- tion (the marker for G1/S transition) was determined in each case. These computational results were then com- pared with experimental knockdowns, obtained by RNA Response of network proteins for corresponding knockdowns in trastuzumab resistant HCC1954 breast carcinoma cells (A) before and (B) after EGF stimulation Figure 6 Response of network proteins for corresponding knockdowns in trastuzumab resistant HCC1954 breast carci- noma cells (A) before and (B) after EGF stimulation. Heatmaps were drawn for a false discovery rate (FDR) of less than 1%. BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 13 of 20 (page number not for citation purposes) interference. While each network component was targeted by siRNAs in a single knockdown setting, both constitu- ents of ERBB heterodimers were repressed in a combina- torial RNAi setting (Figure 4). We quantified the effects of these knockdowns on pRB phosphorylation with reverse phase protein arrays (RPPA) (Figure 2 and Figure 5). Knockdowns of c-MYC, ER-α and Cyclin E1 resulted in a very strong reduction in pRB phosphorylation compared to ERBB1, ERBB1/ERBB2, and IGF1R knockdowns (Figure 5A). We then determined the ratio of G1/S to further ver- ify the effect of these knockdowns on G1/S transition (Fig- ure 5B). DNA staining enabled us to differentiate the strong effects of c-MYC, ER-α and Cyclin E1 knockdown as compared to weaker effects of ERBB1, ERBB1/ERBB2, and IGF1R knockdowns (Figure 5B). Consequently, Cyclin D1 and CDK4 were identified as potential targets from both simulation and experiments. This result was expected, as in response to an external stimulus, Cyclin D1 and CDK4 make a complex that Tentative regulatory interactions inferred from protein expression and activation data for trastuzumab resistant HCC1954 cells Figure 7 Tentative regulatory interactions inferred from protein expression and activation data for trastuzumab resist- ant HCC1954 cells. The heatmaps in Figure 6B were used to infer the interactions of proteins in the HCC1954 cell system with a probability higher than 50%. The numbers next to each arrow indicate the probability of each interaction. Solid black arrows denote the interactions (both direct and indirect) supported by published data, whereas dotted grey arrows denote novel interactions (compare with Figure 3). Normal arrows denote positive regulations, whereas blunt arrows denote negative regulations. BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 14 of 20 (page number not for citation purposes) Figure 8 (see legend on next page) BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 15 of 20 (page number not for citation purposes) phosphorylates pRB, and which, in turn, enables G1/S transition. Accordingly, we found knockdown of these proteins to result in a significant reduction in the phos- phorylation of pRB. In contrast, c-MYC, ER-α and Cyclin E1 were identified by experimental analyses on de novo trastuzumab resistant cells, but had not been predicted in the initial network model. After network refinement, c- MYC and ER-α were also predicted as targets from the model (Table 1 and 2). Hence, we demonstrated that this approach enables the reconstruction of phenotype-spe- cific interactions, which are essential to predict therapeu- tic strategies. In addition, missing components in the protein network can also be inferred. For example, while Cyclin E1 and CDK2 form a complex, which further phosphorylates the pRB protein, our experimental data show that only loss of Cyclin E1, but not of CDK2, significantly repressed phos- phorylation of pRB (Figure 5A). This result suggests that CDK2 could be a dispensable component for the G1/S transition in de novo trastuzumab resistant breast cancer, as it has previously been shown for colon cancer cells [33]. This observation raises the question which alternative interaction partners of Cyclin E1 could promote G1/S transition. In our study, the transcription factors c-MYC and ER-α were identified as potential targets to overcome de novo trastuzumab resistance. Park et al had previously shown that an amplification of the c-MYC gene is correlated with ERBB2 overexpression in breast cancer [34]. In trastuzu- mab sensitive cells, ERBB2-targeted antibodies can inhibit c-MYC through inhibition of the MAPK and AKT pathway which, in turn, increases the activity of p27 towards the CDK2-Cyclin E complex [35]. Here, we demonstrated that loss of c-MYC activity results in a reduction of the CDK4 level which then results in reduced pRB phosphorylation (Figure 7). Targeting c-MYC with a specific chemical inhibitor alone or in combination with trastuzumab also resulted in a strong reduction in pRB phosphorylation and cell growth, both in trastuzumab resistant and sensi- tive cells (Figure 8A). We conclude that targeting c-MYC alone or in combination with trastuzumab could be an interesting candidate for a clinical trial. Cross-talk between ERBB2 signaling and ER-α activation has been previously reported [36], and an increase in the ERBB2 expression level has been reported in tamoxifen resistant cells [37]. In this study, we have shown that ER-α is another possible target in ERBB2 overexpressing and tras- tuzumab resistant HCC1954 cells. This suggests an inter- play between ER-α and ERBB2 receptors in the context of bypassing the effects of drug treatment. Interestingly, the five novel candidates to be targeted in de novo trastuzumab resistant breast cancer have one feature in common: they all either directly (ER-α, c-MYC and CDK4) or indirectly (Cyclin D1 and Cyclin E1) regulate the p27 protein, which plays a key role also in acquired trastuzumab resistance [38]. In addition, our study indi- cated that combinatorial targeting of either of ERBB1, ERBB2 and ERRB3 may not enhance sensitivity to trastu- zumab in de novo resistant patients, although ERBB pro- teins have been previously considered as promising targets. These results let us hypothesize that these cell sur- face proteins (here: ERBB receptors or IGF1R) are decou- pled from intracellular processes (here: G1/S transition) in the de novo trastuzumab resistant cell system. Targeting EGFR alone or in combination with ERBB2 further sup- ported this notion. While trastuzumab sensitive cells (SK- BR-3 and BT474) were responding to gefitinib as well as combination of gefitinib and trastuzumab treatment in an additive manner, de novo trastuzumab resistant cells (HCC1954) did not respond at all (Figure 8B). This obser- vation suggests that combinatorial targeting of cell surface receptors might be beneficial as it is an uncommon per- turbation for cells [39], but it should be taken into consid- eration that this might be cell system- or patient specific. Effects of c-MYC inhibitor 10058-F4 and EGFR inhibitor gefitinib alone or in combination with trastuzumab on the viability of resistant (HCC1954) and sensitive (SK-BR-3 and BT474) cells Figure 8 (see previous page) Effects of c-MYC inhibitor 10058-F4 and EGFR inhibitor gefitinib alone or in combination with trastuzumab on the viability of resistant (HCC1954) and sensitive (SK-BR-3 and BT474) cells. A. Left panel: Western blot data show- ing the phosphorylation state of pRB protein after treatment with c-MYC inhibitor (10058-F4, 80 μM) for 24 hours. Middle panel: WST-1 viability assay over 4 days to determine the response of cells to c-MYC inhibitor alone and in combination with trastuzumab. DMSO is used as vehicle control. Right panel: Impedance measurement for real-time determination of cell growth before (24 hours) and after (72 hours) treatment of cells with c-MYC inhibitor, trastuzumab, and the combination of both drugs. The impedance measurements were normalized to the time point where we have added the drugs. The vertical line demonstrates the time point of normalization. B. Left panel: Western blot data showing the effect of different concentrations of trastuzumab and gefitinib (1 μM) on the expression levels of EGFR and ERBB2 and on the phosphorylation states of ERK1/2, AKT and pRB proteins. H2O is vehicle control for trastuzumab and DMSO is for gefitinib. Middle panel: WST-1 assay to deter- mine the response of cells to gefitinib and gefitinib + trastuzumab. Right panel: The impedance measurement for real-time meas- urement of cell growth before (24 hours) and after (72 hours) treatment of cells with gefitinib, trastuzumab and combination of both drugs. Normalization of cell index is as in A. BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 16 of 20 (page number not for citation purposes) According to our results, targeting EGFR with siRNAs alone resulted in an efficient knockdown at the mRNA level; however, no reduction was observed at the protein level (Figure 4). This phenomenon might be explained by the stabilization of EGFR after dimerization with the over- expressed ERBB2 receptor. Complementary to this obser- vation, knocking down ERBB2 resulted in reduced EGFR expression at the protein level, although no reduction of EGFR was observed at the mRNA level (Figure 4). These data demonstrate an explicit dependence of EGFR protein abundance on ERBB2 expression, and should be kept in mind when EGFR is targeted in cancer therapies. This observation is independent of trastuzumab sensitivity, but is highly influenced by the ERBB2 expression level (Figure 1 and Additional file 1, Figure 3). It should be noted that the logical formalism used in this work clearly caricatures subtle dose effects into all-or- none responses for all the components considered. The resulting logical model should thus be taken as a first step in the formalisation of the regulatory network involved in trastuzumab resistance. However, it is appropriate to translate qualitative information and compare the behav- iour of alternative network wirings or logical rules with data sets for unperturbed and perturbed situations. Once the regulatory wiring and the logical rules be reasonably established, it will be possible to take advantage of multi- level logical modeling extensions, or yet to translate our Boolean models into more quantitative formalisms (e.g. ordinary differential equations, or yet hybrid or stochastic Petri nets). Conclusion We constructed a literature-based protein network and combined computational simulations, validation experi- ments using RNAi, as well as chemical inhibitors, and net- work inference based on proteomic data, in order to identify novel targets with potential for individual and combinatorial therapies in breast cancer. Our concept to combine experimental and computational biology dem- onstrated the strengths and limitations of using literature- based models for simulations of therapeutic strategies. Furthermore, this study led us to select c-MYC as a candi- date to be tested in in vitro and in vivo models, regarding future treatments for breast cancer which is de novo resist- ant to trastuzumab. Our results also suggest that combina- torial targeting of key ERBB receptors might have better outcome than individual therapies in trastuzumab sensi- tive cells, but not in de novo trastuzumab resistant cells. Methods Cell Culture Five human breast cancer cell lines (HCC1954, SK-BR-3, MDA-MB-231, BT474 and MCF-7) as well as the normal breast epithelial cell line MCF-12A were obtained from ATCC (Manassas, VA). HCC1954 cells (CRL-2338) were cultured in RPMI 1640 Modified Medium (ATCC), SK-BR- 3 cells (HTB-30) in McCoy's 5a medium (GIBCO BRL), and MDA-MB-231 cells (HTB-26) in Leibovitz's L-15 medium (Sigma). BT474 cells (HTB-20) were cultured in DMEM medium, MCF-7 cells (HTB-22) in Eagle's Minim- ial essential medium, and MCF-12A cells (CRL-10782) in a medium containing a 1:2 mixture of Dulbecco's Modi- fied Eagle's Medium and Ham's F12 medium. All media were supplemented with 50 U/mL penicillin, 50 μg/mL streptomycin sulphate, 1% non-essential amino acids and 10% fetal bovine serum (all media and supplements from Gibco BRL). Additionally, 2.2 g/L sodium bicarbonate was supplemented for MDA-MB-231 cells. Media for BT474 cells were supplemented with 10% NCTC medium, 500 μl bovine insulin and 100 μl Oxalic acid, for MCF-7 cells we added 0.01 mg/mL bovine insulin, and such for MCF-12A cells were supplemented with 20 ng/ mL EGF, 100 ng/mL cholera toxin, 0.01 mg/mL bovine insulin, and 500 ng/mL hydrocortisone. The cells were incubated at 37°C with 5% CO2 and split 2–3 times per week in a 1:3 ratio for no more than 20 passages. All cell lines were validated by genotyping. 3-D cell culture HCC1954 and SK-BR-3 cells were cultured in 8-well chamber slides in order to examine the effect of trastuzu- mab on proliferation. Geltrex (Invitrogen, Carlsbad, CA) was thawed on ice and 40 μL was pipetted per well and left for 30 min at 37°C to solidify. HCC1954 and SK-BR-3 (5.000 cells/well) cells were seeded in medium supple- mented with 1:50 Geltrex and EGF (BD Biosciences), and with or without trastuzumab (100 nM) (Roche, Penzberg, Germany). The cells were incubated at 37°C and 5% CO2 for eight days, and medium was changed after 4 days. siRNA transfections and EGF stimulations HCC1954 cells were seeded at a number of 7 × 105 cells per 10 cm petri dish in antibiotic free medium. Conflu- ency of the cells was 50–60% at the day of transfection. Sequences of siRNAs are given in Additional file 1, Table 2. Twenty nM of siRNA (except ESR1 siRNA (50 nM)) (Dharmacon, Lafayette, CO) and 25 μL of Lipofectamine 2000™ (Invitrogen, Carlsbad, CA) were diluted separately in reduced-serum medium OptiMEM (Gibco BRL) and incubated for 5 minutes at RT. The two solutions were then mixed and incubated for 20 minutes at RT. The siRNA-Lipofectamine 2000™ mixture was then added to the cells and the dishes were shaken by gentle rocking. MOCK transfected cells were treated with Lipofectamine 2000, but no siRNA was added. The cells were incubated at 37°C and 5% CO2 for 24 hours. After incubation, cells were starved by Dif-3 (30 μM) (Sigma) for 22 hours in medium containing 10% FBS. Cells were further starved in 0% FBS medium for 2 hours. After 24 hours of starva- BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 17 of 20 (page number not for citation purposes) tion, cells were stimulated with EGF (25 ng/mL) for 6, 12, 18 and 24 hours. Cell lysis and Western blotting At each time point, medium was removed and cells were washed with ice-cold PBS containing 10 mM NaF and 1 mM Na4VO3. Lysis of cells was performed on ice by scrap- ing or by cold trypsinization, and shaking on over-head shaker for 15 minutes at 4°C with 70 μl M-PER lysis buffer (Pierce, Rockford, IL) containing protease inhibitor Com- plete Mini (Roche, Basel), anti-phosphatase PhosSTOP (Roche, Basel), 10 mM NaF and 1 mM Na4VO3. Protein concentrations were determined with a BCA Protein Assay Reagent Kit (Pierce, Rockford, IL). Proteins were denatur- ated with 4× Roti Load (Roth, Karlsruhe, Germany) at 95°C for 5 minutes, and 12 μg proteins were loaded in every lane. Protein samples were separated by 8% or 12% SDS PAGE, electroblotted to PVDF membranes (Amer- sham Biosciences, USA) and exposed to primary antibod- ies. A list of antibodies is given in Additional file 1, Table 3, together with their dilutions. Horseradish peroxidase conjugated anti-mouse or rabbit antibodies (Amersham Biosciences, USA) were used as secondary antibodies and signals were detected by enhanced chemiluminescence (Amersham Biosciences, USA). TaqMan (qRT-PCR) Total RNA was extracted from the cells by using the Invi- sorb Spin cell RNA mini kit (Invitek GmbH, Berlin, Ger- many), and single-stranded cDNA was transcribed with the RevertAid H Minus First Strand cDNA Synthesis kit (Fermentas, St. Leon-Rot, Germany). Ten nanograms of total RNA were used for each reaction. qRT-PCR for target genes and housekeeping genes ACTB and HPRT1 was per- formed with the ABI Prism 7900HT Sequence Detection System (Applied Biosystems, Weiterstadt, Germany), applying probes of the Universal Probe Library (Roche, Penzberg, Germany). Primers were synthesized by MWG (Ebersberg, Germany). Sequences of primers and the respective UPL probe numbers are given in Additional file 1, Table 4. Reverse Phase Protein Arrays (RPPA) Cell lysates were prepared as for Western Blotting. All lysates were adjusted to a total protein concentration of 3 μg/μl. Cell lysates were mixed 1:2 with 2× Protein Array- ing Buffer (Whatman, Brentfort, UK) to yield a final pro- tein concentration of 1.5 μg/μL. The samples were printed with a non-contact piezo spotter, sciFlexxarrayer S5 (Sci- enion, Berlin, Germany), in four replicate spots per sam- ple and subarray, and two subarrays per slide onto nitrocellulose coated ONCYTE-slides (Grace Bio Labs, Bend, USA). Twenty replicate slides were produced per run. Approximately 2.25 ng total proteins were delivered per spot. As spotting control, the total protein content of all spots was determined for two replicate slides with the FAST Green FCF assay. All antibody signals were normal- ized according to their total protein content. Slides were blocked over night and target proteins were detected with specific primary antibodies (Additional file 1, Table 3) using a protein array incubation chamber (n1-quadrat, Metecon, Mannheim, Germany). Detection of primary antibodies was carried out with near-infrared (NIR)-dye labeled secondary antibodies and visualized using an Odyssey scanner (LI-COR, Lincoln, USA). Signal intensi- ties were quantified using Odyssey 2.0 software, corrected for spot-specific background signals and normalized for their total protein concentrations. 7-AAD staining and analysis Directly after siRNA transfections, cells were synchronized for 24 hours (see above), and stimulated with EGF for 18 hours. Then, cells were trypsinized, washed once with PBS and centrifuged. Ice cold methanol was added to the cell pellets while vortexing the FACS tube. After incubation of cells at -20°C overnight, methanol was removed and 250 μl of 7-AAD (1:40 dilution) (Calbiochem, Darmstadt, Germany) was added to each tube and incubated for 1.5 hours at 4°C in the dark. The measurement was done by flow cytometry (FACS Calibur, BD Biosciences) using the FL3 channel for 7-AAD staining. Analysis of the 7-AAD results was performed using CellQuest Pro software with the histogram statistics option and a gate on the main cell population. WST-1 cell viability assay HCC1954 cells were seeded at a number of 2,500 cells/ well in 96 well format in 100 μL of 10% FBS medium without antibiotics. After 24 hours of incubation, cells were washed once with PBS and then incubated with 200 μl of either trastuzumab (100 nM) (Roche, Penzberg, Ger- many) or gefitinib (1 μM) (Biaffin, Kassel, Germany) or c- MYC inhibitor 10058-F4 (80 μM) (Sigma) containing 10% FBS medium. Cells were incubated for 24 hours and each day 20 μl of WST-1 reagent (Roche, Basel) was pipet- ted to the cells. Absorbance was measured at 450 nm after 2.5 hours with a SpectraMAX 190 (Molecular Devices, UK). The WST-1 assay was performed over four days with one measurement taken on everyday. Real-time cell-electrode impedance measurements One hundred microliters of growth medium was added to the wells of E-plates (Roche, Penzberg) for background measurements. Then, 100 μL of HCC1954, SK-BR-3 and BT474 cell suspensions were added at a number of 8,000 (for HCC1954 cells) and 10000 (for SK-BR-3 and BT474) cells/well. E-plates were incubated at room temperature for 30 minutes; then transferred to the holder and incu- bated at 37°C with 5% CO2. The continuous impedance measurement was recorded and converted to a cell index BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 18 of 20 (page number not for citation purposes) (CI). After 24 hours, the chemical inhibitors (10058-F4 (80 μM) and gefitinib (1 μM) or/and trastuzumab (100 nM) were added to the respective wells and impedance measurements were continued for 72 hours. Results were analyzed using RTCA Software 1.0 (Roche, Penzberg, Ger- many). Modeling, simulations and data analysis Logical modeling and simulations A logical model is defined by a regulatory graph, where the nodes and arcs represent the regulatory components and interactions, respectively. The dynamical behavior of each component is then defined by logical functions (also rep- resented in terms of logical parameters), which associate a target value for this component depending on the level of its regulators. The dynamics of the system is represented in terms of a state transition graph, where the nodes denote states of the system (i.e., a vector giving the levels of activity of all components), and the arcs denote state transitions (i.e., a change in the value of one or several component(s), depending on the values of the relevant logical functions or parameters). In state transition graphs, terminal nodes correspond to "stable states". Note that, for most of the conditions considered, our ERBB receptor regulated G1/S model has a single stable state. The Boolean model of ERBB signaling network was defined and analyzed using the GINsim software [22,23]. Beginning with relevant initial states, simulations using the logical rules defined in Table 1 was performed. For MOCK case, the initial levels of EGF, all ERBBs, p21 and p27 were set to 1, whereas Cyclin D1 was set to 0. The ini- tial levels of the other proteins were left undefined, mean- ing that both possible levels were considered. A knockdown can be simulated in GINsim by setting the corresponding protein's initial level and its maximal value to 0. The resulting parameterized model and all simula- tions can be downloaded from the model repository referred at the GINsim web page: http://gin.univ-mrs.fr/ GINsim/model_repository.html. Analysis of knockdown responses Statistical significance of protein expression changes and pRB phosphorylation due to knockdowns via RNA inter- ference were calculated using the ANOVA method: protein expression ~ knockdown effect + biological replicate factor + error A multiple testing correction was performed using Benjamini-Hochberg's method [40] with a false discovery rate (FDR) significance cut off of 1%. Network inference Whenever a knockdown significantly affected the expres- sion of another protein with an FDR < 1%, an edge was drawn. Then a transitive reduction of the graph was calcu- lated (i.e. eliminating putative indirect edges, which could also be explained by another path in the graph [41]. Since the transitive reduction for graphs with cycles is not unique and depends on the ordering of the nodes, we implemented a jackknife procedure, i.e. we left out each node once, estimated the network, and finally counted for each edge the frequency of the occurrence among all jack- knife samples. The corresponding jackknife probability is reported at each edge. We also performed the multiple testing corrections separately within each sample of the jackknife procedure, since the false discovery rate depends on the distribution of all raw p-values, which may change with the differing gene selection in each jackknife sample. The R source code is available from the authors upon request. Only the edges having a jackknife probability greater than 50% were kept. Abbreviations Dif-3: Dictyostelium differentiation-inducing factor-3; EGF: Epidermal Growth Factor; FDR: False discovery rate; qRT-PCR: Quantitative real-time polymerase chain reac- tion; RNAi: RNA interference; siRNA: small interfering RNA; 3-D cell culture: Three dimensional cell culture; 7- AAD: 7-Aminoactinomycin Authors' contributions ÖS, TB and DA designed the research; ÖS, CL, JM and SB performed the research; ÖS, TB, HF, CC and DT carried out computational modeling and simulations; IS and SW participated in sequence analysis; ÖS, HF, CL, UK, MM, CC, DT, TB and DA analyzed data; ÖS, HF, CC, DT, AP, SW, TB and DA wrote the manuscript. All authors read and approved the final manuscript. Additional material Additional file 1 This folder contains the following items: 1. Figure 1 and its figure leg- end (Page 1). 2. Figure 2 and its figure legend (Page 2). 3. Figure 3 and its figure legend (Page 3). 4. Table 1: List of references for Figure 3 (Page 4) 5. Table 2: List of siRNAs and their sequences (Page 5) 6. Table 3: List of antibodies (Page 6). 7. Table 4: List of primers, their sequences and probe numbers (Page 7). Click here for file [http://www.biomedcentral.com/content/supplementary/1752- 0509-3-1-S1.pdf] Additional file 2 This folder contains the following items: 1. Table 1: Stable states and pRB response for single and multiple knockdowns of network proteins (Pages 1–13). 2. Table 2: Analysis of the effects of knockdowns on G1/S transition (p-pRB response) (Page 13). Click here for file [http://www.biomedcentral.com/content/supplementary/1752- 0509-3-1-S2.pdf] BMC Systems Biology 2009, 3:1 http://www.biomedcentral.com/1752-0509/3/1 Page 19 of 20 (page number not for citation purposes) Acknowledgements The authors would like to thank Ute Ernst and Christian Schmidt for excel- lent technical assistance, as well as Dirk Ledwinka for IT support. Special thanks to Roche (Penzberg, Germany) for providing us with trastuzumab and early access to the Xcelligence screening system. This project was supported by the German Federal Ministry of Education and Research (BMBF) within National Genome Research Network Pro- gram Grants IG-Cellular Systems Genomics, and IG Prostate-Cancer. Fur- ther support was from the Helmholtz Program SB-Cancer as well as the EU FP6 TRANSFOG project (contract LSHC-CT-2004-503438). DT and CC acknowledge the support of the French Ministry of Research (ANR project JC05-53969), of the EU FP6 DIAMONDS STREP (contract LSHG-CT- 2004-503568), and of the Belgian IAP BioMaGNet project for the develop- ment of the GINsim software. This article is dedicated to the memory of Professor Annemarie Poustka, who was the founder and head of the Division Molecular Genome Analysis at the DKFZ. She was an inspiring scientist and a wonderful person. References 1. 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J Comput Biol 2007, 14(9):1217-1228.	19118495	ERa = ( MEK1 ) OR ( Akt1 ) p21 = ( ( ( ( ERa ) AND NOT ( Akt1 ) ) AND NOT ( CDK4 ) ) AND NOT ( cMYC ) ) CDK6 = ( CycD1 ) ErbB3 = ( EGF ) ErbB2_3 = ( ErbB2 AND ( ( ( ErbB3 ) ) ) ) pRB = ( CDK2 AND ( ( ( CDK4 AND CDK6 ) ) ) ) OR ( CDK4 AND ( ( ( CDK6 ) ) ) ) CDK2 = ( ( ( CycE1 ) AND NOT ( p21 ) ) AND NOT ( p27 ) ) ErbB2 = ( EGF ) Akt1 = ( ErbB1_3 ) OR ( ErbB2_3 ) OR ( ErbB1_2 ) OR ( ErbB1 ) OR ( IGF1R ) CycD1 = ( Akt1 AND ( ( ( ERa ) ) AND ( ( cMYC ) ) ) ) OR ( MEK1 AND ( ( ( cMYC ) ) AND ( ( ERa ) ) ) ) MEK1 = ( ErbB1_3 ) OR ( ErbB2_3 ) OR ( ErbB1_2 ) OR ( ErbB1 ) OR ( IGF1R ) IGF1R = ( ( Akt1 ) AND NOT ( ErbB2_3 ) ) OR ( ( ERa ) AND NOT ( ErbB2_3 ) ) ErbB1_2 = ( ErbB1 AND ( ( ( ErbB2 ) ) ) ) CycE1 = ( cMYC ) cMYC = ( Akt1 ) OR ( ERa ) OR ( MEK1 ) CDK4 = ( ( ( CycD1 ) AND NOT ( p27 ) ) AND NOT ( p21 ) ) p27 = ( ( ( ( ( ERa ) AND NOT ( CDK4 ) ) AND NOT ( cMYC ) ) AND NOT ( CDK2 ) ) AND NOT ( Akt1 ) ) ErbB1 = ( EGF ) ErbB1_3 = ( ErbB1 AND ( ( ( ErbB3 ) ) ) )
BMC Systems Biology Research article Reconstruction and logical modeling of glucose repression signaling pathways in Saccharomyces cerevisiae Tobias S Christensen†1,2, Ana Paula Oliveira†1,3 and Jens Nielsen1,4 Address: 1Center for Microbial Biotechnology, Department of Systems Biology, Technical University of Denmark, Building 223, DK-2800 Kgs. Lyngby, Denmark, 2Current address: Department of Chemical Engineering, Massachusetts Institute of Technology, Building 66, 25 Ames Street, Cambridge, MA 02139, USA, 3Current address: Institute for Molecular Systems Biology, ETH Zurich, CH-8093, Zurich, Switzerland and 4Current address: Department of Chemical and Biological Engineering, Chalmers University of Technology, SE-412 96, Gothenburg, Sweden E-mail: Tobias S Christensen - tschri@mit.edu; Ana Paula Oliveira - oliveira@imsb.biol.ethz.ch; Jens Nielsen - nielsenj@chalmers.se *Corresponding author †Equal contributors Published: 14 January 2009 Received: 9 September 2008 BMC Systems Biology 2009, 3:7 doi: 10.1186/1752-0509-3-7 Accepted: 14 January 2009 This article is available from: http://www.biomedcentral.com/1752-0509/3/7 © 2009 Christensen et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Background: In the yeast Saccharomyces cerevisiae, the presence of high levels of glucose leads to an array of down-regulatory effects known as glucose repression. This process is complex due to the presence of feedback loops and crosstalk between different pathways, complicating the use of intuitive approaches to analyze the system. Results: We established a logical model of yeast glucose repression, formalized as a hypergraph. The model was constructed based on verified regulatory interactions and it includes 50 gene transcripts, 22 proteins, 5 metabolites and 118 hyperedges. We computed the logical steady states of all nodes in the network in order to simulate wildtype and deletion mutant responses to different sugar availabilities. Evaluation of the model predictive power was achieved by comparing changes in the logical state of gene nodes with transcriptome data. Overall, we observed 71% true predictions, and analyzed sources of errors and discrepancies for the remaining. Conclusion: Though the binary nature of logical (Boolean) models entails inherent limitations, our model constitutes a primary tool for storing regulatory knowledge, searching for incoherencies in hypotheses and evaluating the effect of deleting regulatory elements involved in glucose repression. Background Signaling and regulatory cascades establish the bridge between environmental stimuli and cellular responses, and represent a key aspect of cellular adaptation to different environmental conditions. Cells can sense several stimuli, both internally and externally, and the received information will subsequently be propagated through a cascade of physico-chemical signals. The ultimate recipients of these signals will determine how the cell responds, by acting at different regulatory levels (transcriptionally, translationally, post-translationally, allosterically, etc). Contrary to metabolic networks, most signaling and regulatory pathways are relatively poorly studied and signaling properties of a protein cannot be easily derived from its gene sequence [1, 2]. Moreover, signal transduction networks operate over a wide range of time-scales, and due to the presence of feedback loops and cross talk it is difficult to discern how concurrent signals are processed. Thus, methods to analyze and model signal transduction and regulatory circuits are of prime importance in biology, medicine and cell engineering, since they can bring insights into Page 1 of 15 (page number not for citation purposes) BioMed Central Open Access the mechanistic events underlying complex cellular behavior. The availability of models for signaling and regulatory cascades represents an opportunity to expand the search space when looking for intervention targets that may lead to desired phenotypes – e.g. when looking for better drug targets in medicine, designing novel regulatory circuits in synthetic biology or finding regulatory targets that can release metabolic control in metabolic engineering. Most eukaryotic cells, including many yeasts and humans, can sense the availability of carbon sources in their surroundings and, in the presence of their favorite sugar (often glucose), trigger a cascade of signals that will repress the utilization of less-favorite sugars as well as the function of different catabolic routes [3-5]. This phenomenon is commonly termed carbon-catabolite or glucose repression. Because of its role in nutrient sensing and its industrial impact on the simultaneous utilization of different carbon sources, glucose repression has been a model system for studying signaling and regulation. In particular, glucose repression in the yeast Saccharomyces cerevisiae has been extensively studied and two main signaling pathways have been identified: a repression pathway, mediated through the protein kinase Snf1 and the transcription factor Mig1, and a glucose induction pathway, mediated through the membrane receptors Snf3 and Rgt2 and the transcription factor Rgt1 (for review see, for example, [4, 6-8]). Growing evidence suggests the existence of extensive cross talking between these two pathways. Figure 1 summarizes key aspects of the system. Besides the role of glucose repression on the utilization of alternative carbon sources, glucose repres- sion in yeast leads to the transcriptional shutdown of genes related to respiration, mitochondrial activities, and gluconeogenesis [9]. This transcriptional behavior causes the wild-type yeast to exert respiro-fermentative meta- bolism during growth on excess glucose, redirecting carbon towards by-products of metabolism such as ethanol, acetate and glycerol, at the cost of biomass formation. Despite being an extensively studied system, knowledge on yeast glucose repression is still far from complete and key questions remain, including: what exactly triggers the cascade signal(s)? How to differenti- ate between causes and consequences? How does the knowledge derived from phenotypic observations relate to mechanistic events? How does the current knowledge on glucose repression fit with available high-throughput data? In order to attempt to bring insights into these questions, we aim here at creating a mechanistic, semi- quantitative model of glucose repression signaling cascades and genetic regulatory circuits in yeast. Modeling approaches of different levels of abstraction have been proposed to analyze and simulate signal transduction and regulatory networks, ranging from purely topological to kinetic models. While attractive in principle, quantitative kinetic models based on ODEs are hampered by difficulties in determining the necessary parameters and kinetic equations. At the other extreme, strictly descriptive models have also been reported [10-12], in which the precision of the formalism proposed, based on process engineering, establish a clear and unique qualitative representation of the network interactions. Somewhere in between lie more semi-quantitative and qualitative approaches that require the topological description of signaling interac- tions and make use of well-established mathematical frameworks to analyze network structure and function- ality. Such methods include (i) stoichiometric represen- tation and extreme pathway analysis [13], (ii) Boolean (on/off) and Bayesian (probabilistic) representation of interactions [14-16], (iii) logical hypergraph representa- tion and logical steady state analyses [17], and (iv) Petri nets graph representation and simulations [18-20]. All these methods describe signal flow qualitatively within a mathematical formalism and without loss of Figure 1 Simplified representation of the main glucose repression pathways. Glucose is transported into the cell by hexose transporters with different affinities (HXT1- HXT16). Inside the cell, glucose is phosphorylated to glucose 6-phosphate by Hxk2, therefore entering into carbon metabolism. An unknown signal triggered by high glucose levels leads to inactivation of the Snf1 complex. This inactivation is regulated by the protein phosphatase Glc7- Reg1. Inactive Snf1 cannot phosphorylate Mig1, which thus remains in the nucleus under high glucose levels, exerting repression of transcription of several genes. At low glucose concentrations, when Snf1 becomes active, Mig1 is phosphorylated and translocates to the cytosol, releasing repression. Glucose is sensed by two sensors located in the cell membrane, Rgt2 and Snf3. At high glucose levels, the signal from these sensors leads to SCFGrr1 mediated ubiquitination and consequent degradation of Mth1 and Std1, which are required for Rgt1 activation. BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 2 of 15 (page number not for citation purposes) information on the network topology, allowing insight- ful computations on network structure such as evaluat- ing the degree of cross talk, determining all possible elementary 'flux' modes and calculating the number of theoretically possible positive and negative feedback loops. Moreover, logical hypergraph analyses and Petri net models also have the potential to be used for semi- quantitative simulation of network behavior, since they allow simple predictions of the state of a system in response to different stimuli. In this work, we reconstructed the signaling and transcriptional regulatory network of glucose repression in S. cerevisiae based on established knowledge reported in the literature. We converted this information into a logical hypergraph, and performed structural and func- tional analyses on the network following the framework proposed by Klamt and co-workers [17]. Next, we performed logical steady state analyses to compute the state of all nodes in the system under all possible environmental conditions (sugars availability), and for all different single gene deletions and some double gene deletions. Furthermore, we developed a framework to evaluate model predictions by comparing changes in the state of the regulatory layer against changes in gene expression data (transcriptome data was available for several knockouts of the system). Based on the results from the model evaluation, we identified main errors and discuss possible sources of discrepancies, as well as the inherent limitations to Boolean modeling. Our results point towards the existence of incoherencies between high-throughput data and literature-based knowledge related with glucose repression. To our knowledge, this represents the first attempt to mechan- istically and semi-quantitatively model glucose repres- sion signaling and regulatory pathways in the yeast S. cerevisiae. Results Reconstruction of the signaling/regulatory network and model setup Glucose repression signaling and regulatory network was reconstructed from low-throughput data reported in peer-reviewed publications. Information was gathered based on biochemical studies and physiological obser- vations, and it was included in a collection database containing: (i) list of proteins with sensor, signaling or transcription factor functions found to be related to glucose repression; (ii) list of genes known to be transcriptionally regulated by glucose repression related transcription factors; (iii) type of regulation exerted on each of the previous species by metabolites and/or regulatory proteins. The reconstructed network accounts for 72 species (corresponding to 50 genes) and 148 interactions, which cover most of the current knowledge on the Mig1/Snf1 and Snf3/Rgt2 pathways, as well as galactose and maltose regulatory systems. Transcription factors included are Rgt1, Mig1, Mig2, Mig3, Sip4, Cat8, MalR and Gal4. Regulatory targets include genes encod- ing hexose transporters and enzymes involved in maltose catabolism, gluconeogenesis and the Leloir pathway. The complete list of species and interactions considered is given as supplementary material (Additional file 1). Thereafter, the reconstructed signaling/regulatory net- work was converted into a logical hypergraph (Figure 2), representing all interactions in a logical manner (Figure 3 and Additional file 2), according to the framework proposed by Klamt et al. [17] to model signaling networks. The conversion of signaling and regulatory interactions into Boolean functions was based on described functions reported in the literature (the rationale for the choice of less obvious Boolean functions for certain interactions is explained in the Additional file 2). The resulting hypergraph consists of 77 nodes (50 genes, 22 proteins, 3 extracellular metabolites and 2 intracellular metabolites) and 118 hyperedges, and represents a logical model for glucose repression signaling and regulatory pathways. For ease of visualization, we have depicted the hypegraph into four separate sub-networks, each representing in more detail a different system: Mig1/Snf1 and Snf3/Rgt2 pathways (Figure 3A), galactose regulation (Figure 3B), maltose regulation (Figure 3C) and the Sip4/Cat8 regulatory system (Figure 3D). The model takes as input the availability of carbon sources (glucose, galactose, and maltose) and outputs the logical steady state of the network. In our model, nodes can assume one of two logical states, 1 or 0, corresponding to on or off, or in more subtle instances, higher or lower activity. For protein nodes, this can most simply be interpreted as a protein being active (1) or inactive (0), whereas in the case of gene nodes, it can be seen as a gene being expressed (1) or not (0). We used the model to analyze structural characteristics of the network and to compute logical steady states of all nodes in the network. In particular, we simulated how gene transcripts change their logical state in response to perturbations (e.g., availability of different sugars and different gene knockouts), and evaluated the predictions by using available transcrip- tional datasets for different carbon source conditions and yeast deletion mutants. During logical states simulations, although most nodes were left uncon- strained, a few nodes were assigned a default value of 1. E.g., GRR1 was set to a fix state of 1 since its regulation is not considered in the model (otherwise, no unique logical steady state would exist). Also, in the case of BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 3 of 15 (page number not for citation purposes) genes constitutively expressed at a basal level such as MALT, encoding a maltose transporter, the node state was set to a fix value of 1. Structural and functional analyses of the network Logical steady state analyses were performed for all combinations of sugar availability for the wild type, all single gene knockout mutants (24 cases), and three double gene deletion mutants of interest, in a total of 224 simulations (see Additional file 3). We notice that most of the gene nodes change their logical state in over Figure 2 Example of Boolean expressions and corresponding logical hypergraphs and truth tables. A logical hypegraph is an interaction network where each edge (or hyperarc) connects a set of start-nodes (tails) to an end-node (head), and the combination of incoming hyperarcs to an end-node represents a Boolean expression. Any Boolean expression can be written in a disjunctive normal form (only using AND, OR and NOT operators). On the disjunctive normal form, expressions are built up by literals (i.e. variables or their negation) connected by AND relations forming clauses, and clauses can then be connected by OR relationships. In the logical hypergraph, each clause is represented by a hyperarc, while separate hyperarcs linked to an end-node represents clauses connected by an OR relationship. When the value of a tail species is negated, this is marked by a repression symbol in the corresponding hyperarc (see also the symbolic explanation in Figure 3). The Boolean function determining the state of a node is thus given by all the incoming hyperedges. Figure 3 Hypergraph representation of the Boolean model for yeast glucose repression. A) Overall representation of the main glucose repression pathways, including the Snf1/ Mig1 repression pathway and the Snf3/Rgt2 induction pathway. Note how the high degree of cross talk makes it impossible to distinguish between the two pathways. B) The GAL regulatory system. C) The MAL regulatory system. MALT is set to be active by default, since MalT is assumed to be present at a basal level. D) Subset of the network controlled by Sip4 and Cat8. Signaling proteins are represented with purple rectangles, while transcription factors are represented with red rectangles. Accordingly, a post-transcriptional regulatory association is represented with a purple line, while a transcriptional regulatory interaction is represented with a red line. Gene transcripts are represented with green rectangles, and sugar metabolites are depicted by blue ellipses. The description of the representation of logical relations between species is given in the legend of Figure 2. A note about the nomenclature in the hypergraph representation: genes are denoted in uppercase (e.g., MIG1), while protein names include the suffix 'p' (e.g., Mig1p). In the main text, proteins are named similarly, but without the suffix (e.g., Mig1), and genes are in italic uppercase (e.g., MIG1) BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 4 of 15 (page number not for citation purposes) 10% of the simulations, but only few (MTH1, MALR, GAL3, GAL4 and CAT8) change in more than 15% of the simulations. The predictions for the wild type along with a subset of the deletion mutants for which transcriptome data was available were analyzed and used to evaluate the model, as will be discussed below. The capability to make semi-quantitative predictions of gene expression levels and protein activity for any combination of gene deletions and nutrient conditions is a key feature of the model. The reconstructed network contains 35 negative and 14 positive feedback loops, which is indicative of the high degree of crosstalk between pathways and complex cause-effect relationships. This is further supported by the dependency matrix of the network (Figure 4), which is based solely on the underlying network interaction graph without information on Boolean functions. In the matrix, yellow elements represent an ambivalent rela- tionship between an ordered pair of species (i,j), where i and j represents the column and the row number, respectively, in the sense that both activating and inhibiting paths exist from i to j. Dark or light green (/red) elements, Dij, indicate that species i is a total or non-total activator (/inhibitor) of species j, respectively, i.e. only activating (/inhibiting) paths from i to j exist and feedback loops are either absent (total) or present (non-total) – see Figure 4 legend for details. Examining the dependency matrix, the large number of ambivalent relationships (represented by yellow elements) as well as the prevalence of negative feedback loops in signaling paths (light green or red fields) is noteworthy. It underscores the difficulties in making predictions based on intuitive approaches and emphasizes the need for a logical modeling framework. The matrix also reveals the high degree of crosstalk between the Mig1/Snf1 and Snf3/Rgt2 pathways, since it is quickly noted that the signaling proteins in one pathway generally affect proteins in the other pathway. Model evaluation In order to evaluate the capability of the logical model to predict differential gene expression, we performed logical steady state analysis of the glucose repression regulatory response for five different gene knockouts, and compared the results with available whole-genome gene expression from DNA-microarrays. We used data from the yeast mutants Δrgt1, Δmig1, Δmig1Δmig2, Δsnf1Δsnf4, Δgrr1 and their isogenic reference strains. This type of analysis not only gives an indication of the model's predictive strength, but also hints at possible errors in the model (and eventually in the underlying hypotheses from the literature) in the cases where discrepancies between model and observation occur. Figure 4 The dependency matrix for the yeast glucose repression network. Each element in the matrix shows the relationship between an effecting species and an affected species, specified at the bottom of the column and at the end of the row, respectively. A yellow field in the intersection of the ith column and jth row signifies that the ith species is an ambivalent factor with respect to the jth species, i.e. that both activating and repressing/inhibiting paths from the ith to the jth species exist. For example, the yellow color of the first element (first column and first row) indicates that both inhibiting and activating paths exists from exterior glucose to the Sip4 protein, i.e., exterior glucose is an ambivalent factor with respect to Sip4. Similarly, a dark green field and a light green field indicate a total and a non-total activator, respectively, i.e., only activating paths exist and negative feedback loops are either absent (total) or present (non- total). Dark red and light red fields represent total and non- total repressors/inhibitors, respectively. A black field indicates that no path exists from A to B. The large number of black columns in the middle corresponds to output species (sinks), which per definition are non-affecting towards all species. Due to the directional nature of the interaction network, the matrix is not symmetric (e.g. Sip4 is non-affecting toward exterior glucose). See nomenclature note for gene and protein species in the legend of Figure 3. BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 5 of 15 (page number not for citation purposes) The best we can hope to achieve with a Boolean model is a correct prediction of the sign of the change in gene expression, i.e., the model prediction Yi mod should equal the experimental observation Yi exp when evaluating change in expression of gene i following a knockout or change in conditions. In order to assess what experi- mental results should be regarded as a change, it is necessary to make an interpretation of the gene expres- sion data that allows a comparison with the binary outputs of the Boolean model. Intuitively, the experi- mental change should be relatively large and statistically significant in order to be reflected by the discrete Boolean model. Therefore, we established a fold-change threshold ([FCmin\| = 1.5; see Methods for fold-change definition) and a Student's t-test p-value cut-off (a = 0.05) for all pairwise gene expression comparisons between a deletion mutant and its isogenic reference strain. All genes with p-value < a and FC ≥FCmin (or FC ≤ -FCmin) were assigned with a value of Yi exp = 1 (or Yi exp = -1), and 0 otherwise. Such conversion of gene expression into discrete Boolean values based on a somewhat subjective threshold may yield a number of type-2 (false negatives) and type-1 (false positives) errors. The hereby identified experimental variation, Yi exp, was then compared with the model prediction, Yi mod, for each gene i. Yi mod was determined by the difference in Boolean output for gene i between the mutant and the reference state (wildtype), at a defined external condi- tion. Thus, Yi mod can assume the values -1, 0 or 1, corresponding to a decrease, no change or increase in gene expression on transcript i in the mutant, respec- tively. Model prediction capabilities were evaluated based on the difference \|Yi mod - Yi exp\|, with a value of 0 meaning a correct prediction, a value of 1 implying a small error, and a value of 2 indicating a large error (only happening when model prediction and experimental results point towards opposite directions). A summary of the results from the comparison between model prediction and experimental up- and down- regulation for all five different knockouts evaluated is shown in Table 1. In the following, we discuss more thoroughly the results for Δrgt1, and use this to analyze common reasons for discrepancies in all the knockouts. The remaining comparisons are briefly commented afterwards. Evaluation of Δrgt1 mutant Transcriptome data for the yeast Δrgt1 mutant and its isogenic reference strain is available from [21] during shake flasks cultivations using galactose as the single carbon source. Sampling was made in the mid-exponen- tial phase, where pseudo-steady-state can be assumed (i.e., growth rate and physiological yields appear constant during the exponential phase, despite changes in the concentration of extracellular metabolites). We converted the gene expression data from this study into Yi exp according to the procedure described above, and compared it with the simulation results Yi mod (Table 1). Yi mod are derived from logical steady state analyses of the logical model assuming galactose present and all other carbon sources absent. The logical steady states were first determined for the original model without further constrains (Xi,WT). Afterwards, in order to simulate the RGT1 gene deletion, the node RGT1 of the hypergraph was set to zero, and a new logical steady state analysis was performed (Xi,RGT1). Yi mod is given by the difference between Xi,RGT1 and Xi,WT. In general, the model predictions are very good for the Δrgt1 mutant, with 82% true predictions, reflecting the fact that Rgt1 along with its regulators has been extensively studied [21-30]. Only for 6 out of the 34 genes evaluated, the experimental fold changes do not correspond to model prediction. The six genes are SNF3, MTH1, MIG2, MAL33 (which encodes a MAL regulator), SUC2 and HXT8. In the following, the causes of these discrepancies are investigated. Analysis of discrepancies in SNF3. SNF3 encodes a high- affinity glucose sensor located in the plasma membrane. Gene expression data shows no differential expression of SNF3 in the Δrgt1 mutant (p-value = 0.88, FC = 1.03). Table 1: Summary of results from the model evaluation Knockout Genotype Number of Genes Evaluated Number of true predictions Percentage of true predictions for genes changed on array Percentage of true predictions for genes changed in the model Percentage of true predictions Δrgt1 34 (25) 28 (21) 83% (83%) 71% (63%) 82% (84%) Δmig1 38 (27) 24 (20) 29% (44%) 40% (57%) 63% (74%) Δmig1Δmig2 38 (28) 24 (19) 47% (53%) 69% (80%) 63% (68%) Δsnf1Δsnf4 34 (25) 17 (14) 45% (60%) 56% (64%) 50% (56%) Δgrr1 38 (28) 15 (10) 25% (24%) 55% (100%) 39% (43%) In parentheses are the numbers when dubious genes are not included in the computations (see Discussion for details). BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 6 of 15 (page number not for citation purposes) However, in the model this gene is found to be down- regulated in the mutant relative to the wild type. The most likely explanation for this discrepancy lies in the logical equation for SNF3 applied in the model: SNF3 = NOT (Mig1 OR Mig2) = (NOT Mig1) AND (NOT Mig2) In the model, RGT1 deletion leads to an active Mig2 and consequently repression of SNF3. The most plausible explanation for this is that the model overestimates the importance of Mig2 and that, in reality, the presence of active Mig2 by itself is not enough to prevent SNF3 transcription. Nevertheless, this explanation cannot be accepted out of hand: the dependency matrix reveals that RGT1 is an ambivalent factor with regard to SNF3, i.e., both repressing and activating paths from RGT1 to SNF3 exist. It is thus possible that Mig2 is indeed a significant repressor of SNF3, but that other important, repressing pathways from RGT1 to SNF3 are also deactivated by the RGT1 deletion. A closer inspection of the signaling paths from RGT1 to SNF3 in the hypergraph reveals that, from the 8 existing possible paths, 4 are repressing paths of the form RGT1 - > Rgt1 -\| Mig2/Mig3 -\| Mig1 -\| SNF3. This means that Rgt1 represses Mig2 and Mig3, both of which repress Mig1, which then represses SNF3 (this constitutes 4 paths because two hyperedges connect RGT1 to Rgt1, either with Mth1 or Std1 as the second tail). It seems unlikely that these 4 signal flux modes play significant physiological roles since (i) no significant role of Mig3 has ever been found [31-33], and (ii) Mig2 can at most serve to attenuate Mig1 expression since the two proteins are active at basically the same conditions. Analysis of discrepancies in MTH1. Mth1 is a signaling protein intermediate between the membrane sensors Snf3/Rgt2 and the transcription factor Rgt1 [23, 24]. Gene expression of MTH1 is found to be up-regulated in the Δrgt1 mutant, whereas the model predicts the expression level of MTH1 to be unchanged. Despite the fact that Rgt1 repression of MTH1 is reported in the literature (in fact in the same paper where Δrgt1 transcriptome data is presented) [21], the repression of MTH1 by Rgt1 is ignored for logical steady state calculations for two reasons. Firstly, Kaniak et al. state that this transcriptional repression is weak (the tran- scriptome analysis was actually complemented with promotor-lacZ fusions, and it was found that MTH1, both in the wild-type and in the Δrgt1 mutant, is subject to considerable glucose repression, not glucose induc- tion as would be expected for a gene primarily regulated by Rgt1 [21]. Secondly, in terms of the Boolean model, including Rgt1 in a "NOT Rgt1 AND-relationship" would mean that Mth1 would always be inactive when Rgt1 is active, which would be somewhat incongruous consider- ing that MTH1 seems to encode a co-repressor of Rgt1. This example illustrates the difficulties in incorporating negative feedback loops in a binary Boolean model. It should also be noted that MTH1 is, according to the model at least, one of the most heavily regulated genes in the network, being transcriptionally regulated by Rgt1, Mig1, Mig2, Mig3 and Gal4. This makes a literature based determination of the Boolean function governing its expression particularly difficult. Analysis of discrepancies in MIG2 and HXT8. MIG2 encodes for a homologue of the transcription factor Mig1, while HXT8 encodes for a plasma membrane hexose transporter. MIG2 was not found to change experimentally, at least not in terms of our defined "Boolean fold change" threshold, but was found to be up-regulated in the model. This discrepancy is, most likely, due to a type-2 error in the inference of gene expression change from the transcriptome data. Even though the average fold change observed experimentally was 3.4, the p-value of this change was only 0.29. As this is above the cut-off value of 0.05, this change is deemed insignificant and the gene is attributed a "Boolean fold change" of 0. Nevertheless, the model prediction is in good agreement with the results of the continued investigation by Kaniak et al., which included promo- ter-lacZ fusions and ChIP experiments, and showed that Rgt1 is a strong (and possibly the only) transcriptional repressor of MIG2. The discrepancy for HXT8 seems to have similar reasons. Analysis of discrepancies in MAL33 (MALR). Expression of MAL33, encoding a MAL regulator, was found to be experimentally repressed in the mutant, while it remained unchanged in the model. The three genes required for maltose metabolism are mapped in various MAL loci, of which 5 are currently known [34, 35]. In the model, no distinction is made between the different complex loci. Since this is a recurrent discrepancy in all evaluations performed, we present a general discussion on the MAL regulatory system later in the Discussion section. Analysis of discrepancies in SUC2. Expression of SUC2, encoding for invertase (sucrose hydrolyzing enzyme), was not found to be significantly different between the Δrgt1 mutant and wild-type, whereas the model predicts a decrease in gene expression in the mutant. This discrepancy illustrates both the difficulties in choosing the correct logical equation for a specific species based BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 7 of 15 (page number not for citation purposes) on literature and in converting a continuous reality to a binary model. In the model it is assumed that both Mig1 and Mig2 should be absent in order for SUC2 to be expressed at high levels (SUC2 = NOT (Mig1 OR Mig2)), cf. Lutfiyya et al. who found that the single deletions had relatively low impact on SUC2 expression level, whereas Δmig1Δ- mig2 double deletion had great effect [36]. Contrary to this, Klein et al. found a large increase in SUC2 expression in a Δmig1 strain and further increase by additional disruption of MIG2 [37]. The Klein et al. observations could have been implemented in the model via a Boolean function where the absence of either one of the two repressors induces expression of SUC2 (i.e., SUC2 = NOT (Mig1 AND Mig2)) or, alternatively, by simply ignoring Mig2 in the equations. While imple- menting either of the alternatives would have led to correct model prediction for the knockout (as judged by comparison with the expression data), the actual output for SUC2 in the wild-type would have been the same regardless of the chosen equation (since absence of Mig 1 or of both Mig1 and Mig2 would always result in active SUC2). Nevertheless, the ambiguity in the literature combined with the difficulty of imposing a discrete model on a continuous reality made the choice of logical equation extremely hard in this case. The model apparently mistakenly predicts a decrease in SUC2 expression, because RGT1 deletion causes MIG2 to be expressed (i.e. Mig2 becomes active) which then leads to repression of SUC2 with the chosen Boolean equations. Based on this evaluation, and assuming that a type-2 error has not occurred, it therefore seems reason- able to say that the model overestimates the importance of Mig2 in the regulation of SUC2. Alternatively, it is possible that MIG2 transcription is induced, but that the Mig2 protein is also post-translationally regulated, some- thing that is not described in the model or, to the best of our knowledge, in the literature. This could mean that Mig2 protein activity is not increased by the deletion of RGT1, despite the eventual increase in transcript levels. Evaluation of Δmig1 and Δmig1Δmig2 mutants Transcriptome data for Δmig1 and Δmig1Δmig2 mutants, and their isogenic reference strain was available from [38] during aerobic batch cultivations using 40 g/L glucose as single carbon source. Samples were taken in the mid-exponential phase at a residual glucose con- centration of 20 g/L. Therefore, experimental observa- tions were evaluated against model predictions with only glucose present. For both knockouts, the percentage of true predictions is of 63% (Table 1). When examining the discrepancies between experimental observations and model predictions, it is particularly noticeable that model predictions for MAL and GAL regulatory genes are almost always wrong. In particular, in the Δmig1 case both MAL13 and GAL4 evaluation produces a large error (i.e., \|Yi mod - Yi exp\| = 2), meaning that the experimental direction of regulation is opposite to that predicted by the model. Whereas in the case of MAL genes this is one of several discrepancies observed in this work (see Discussion), in the case of GAL4 we find the experi- mental gene expression data from [38] to directly contradict the results of a Northern blot analysis [39]. While the former study showed a decrease in GAL4 levels upon deletion of MIG1, the second showed more than 6- fold increase in the levels of GAL4 transcripts in a Δmig1 mutant, in a medium with the same glucose concentra- tion (as cited in [40]). Evaluation of Δgrr1 mutant Transcriptome data for Δgrr1 and its isogenic reference strain were also available from [38], at conditions corresponding to high extracellular glucose concentra- tion. Evaluation of model predictions for Δgrr1 yielded the poorest results, with only 39% of true predictions (Table 1). This is probably due to the fact that, despite being an important player in a large number of cellular activities such as cell morphology, heavy metal tolerance, osmotic stress and nitrogen starvation [25, 30], Grr1 is in the model only represented as a simple regulator acting upstream of Rgt1. The highly pleiotropic nature of Grr1 is revealed in the DNA-microarray data, where 24 out of 38 evaluated genes are found to be differentially expressed (in the Boolean sense). The low percentage of correct predictions illustrates the danger of including species without properly accounting for all key func- tions. We notice that the model even fails to efficiently predict the alteration of gene expression for targets of Rgt1 (e.g. HXT2, HXT4, HXT5 and HXT8), which, according to the model, should act downstream of Grr1. However, given the scale of the perturbations caused by GRR1 deletion, it is difficult to say whether these discrepancies are caused by faults in the current hypotheses underlying the model or by secondary effects not taken into consideration, such as altered metabolism. Evaluation of Δsnf1Δsnf4 mutant Transcriptome data for Δsnf1Δsnf4 and its isogenic reference strain were available from [41], during aerobic continuous cultivations at dilution rate 0.1 h-1 and glucose (10 g/L) as single carbon source. Under these conditions, the residual glucose concentration inside the fermentor is very low, and typically no glucose repres- sion is observed. This behavior is, to some extent, similar to what happens in the absence of glucose. Thus, BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 8 of 15 (page number not for citation purposes) experimental observations were compared with model predictions for the case where all sugars were absent. The percentage of true predictions was only 50% (Table 1). A surprising discrepancy was observed for the expression levels of CAT8 and SIP4, which were predicted to decrease, but are found to be experimentally unchanged (in the Boolean sense). Nevertheless, the prediction of a down-regulatory effect on Cat8 and Sip4 gene targets (ICL1, FBP1, PCK1, MLS1, MDH2, ACS1, SFC1, CAT2, IDP2 and JEN1) is confirmed experimentally. While the observed changes for CAT8 and SIP4 are not statistically significant, they are nevertheless in the predicted direc- tion, and the occurrence of type-2 errors is therefore likely. An additional and likely explanation is that the effect of the Snf1-Snf4 complex on repression by Sip4 and Cat8 is, to a larger extent, mediated via direct posttranslational regulation rather than via indirect, Mig1 mediated transcriptional regulation. Global evaluation of predictive power Boolean models lie at the boundary between qualitative and quantitative models. For the present model of glucose repression, testing current hypotheses is at least as important as making predictions. These goals, how- ever, are connected in the sense that one way in which inconsistencies in the model (and consequently, in the hypotheses proposed in the literature) are revealed is through failure to make predictions. Therefore, evaluat- ing the predictive power of the model is an important task. Above, we looked into the capacity of the model to predict differential gene expression for individual knock- outs, and observed that the frequencies of correct predictions varied between the different knockouts (and in no case were all predictions true). What remains to be demonstrated is that the correct predictions were not obtained by chance. For the simplest random model, the probabilities that the expression of a gene is predicted to be unchanged, up-regulated or down-regulated, respectively, would all equal 1/3. Overall, the average probability of having the correct prediction in each situation would also be 1/3. Table 1 shows that, for all knockouts, the frequency of correct predictions exceeds 33%. We tested the signifi- cance of this occurrence by applying a binomial distribution test and p0 = 0.33 (cf. Methods) to all predictions (Table 2). Overall and for most knockouts, the very low p-values unambiguously show that the results were not obtained due to chance. However, for Δgrr1 it cannot be shown at 95% confidence level that the prediction rate is significantly better than with a random model. Next, we applied the same distribution to test the significance of the fraction of large errors observed (i.e., \|Yi mod - Yi exp\| = 2) in the subset of cases where differential expression was observed experimentally as well as in the model. Since in this case there would be 50% chance of a correct prediction if nothing was known a priori, we use p0 = 0.5. Out of 41 cases, only 3 cases of opposite signs predictions are observed. This is signifi- cant with a p-value less than 10-90. The three encountered large errors were in two predictions for MALR (discussed below) and one prediction for GAL4 in the Δmig1 mutant (most likely arising from the microarray experi- ment itself, as discussed above). Discussion The goal of our Boolean network modeling and analyses was dual. First, we wanted to use the model to test how the underlying biological hypotheses (for signal trans- duction and transcriptional regulation) found in litera- ture fit the observations from genome-wide gene expression studies of different signaling knockout mutants. We proposed a framework to compare simula- tion results with experimental observations and looked for discrepancies between the two. These discrepancies hinted at the identification of different types of errors, as discussed below. Second, we wanted to evaluate the model's predictive strength and investigate to what extent we could use it to simulate transcriptional responses upon deletion of various components of the glucose repression cascade. Such a model can eventually be combined with genome-scale stoichiometric meta- bolic models to further constrain the solution space during optimization problems (e.g., flux balance analy- sis). Gene expression data in the form of discrete Boolean on/off information has been previously used to constrain fluxes (or more precisely, the genes encoding the enzymes catalyzing the corresponding Table 2: Statistical evaluation of the significance of the model prediction H0: X/N = 1/3 H1: X/N > 1/3 Δrgt1 Δmig1 Δmig1Δmig2 Δsnf1Δsnf4 Δgrr1 Overall p-value 6.7 × 10-10 4.8 × 10-5 4.8 × 10-5 1.2 × 10-2 2.1 × 10-1 2.6 × 10-14 P-values for the statistical evaluation of the null hypothesis, H0, tested for whether the observed level of success was due to chance, i.e. that the average proportion of correct predictions (X/N) is 1/3, against the alternative hypothesis that the model yields a higher proportion of true predictions. The test is based on the binomial distribution (cf. Methods). BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 9 of 15 (page number not for citation purposes) reactions) in stoichiometric metabolic models, adding a layer of transcriptional regulation into this type of models [42, 43]. Our approach goes even further by also including signaling information, opening new doors to search for targets that can release metabolic control at different regulatory levels. Glucose repression is a complex and intertwined regulatory system, with extensive cross-talk among pathways, feedback loops and different levels of regula- tion responding at different time scales. This makes it difficult to decide the logical rules describing some of the species and their influence, in particular species that are heavily regulated (e.g., Mth1) or those with extensive pleiotropic effects (e.g., Grr1). Noticeably, we explicitly decided not to include hexokinase-2 (Hxk2) in the model, despite Hxk2 being hinted to be a key regulator in the Snf1/Mig1 pathway (in addition of its role as a glycolytic enzyme). This decision was based on observa- tions that changes in the activity of Hxk2 lead to an array of effects, namely altered metabolism, which may indirectly trigger other regulatory responses [38, 44]. Thus, it becomes difficult to describe the role of Hxk2 in a model of moderate size like ours. More knowledge on the exact signaling and regulatory roles of Hxk2 in glucose repression will be necessary before it can be included in our model. We performed logical steady state analyses for the wildtype, all single gene deletions and three double gene deletions under all combinations of sugar avail- ability, and observed that most nodes change their logical steady state in more than 10% of the gene deletion simulations. Thereafter, we evaluated the model predictions against available gene expression data by comparing changes in transcript levels (converted into a Boolean form) with simulations of the logical steady state of the model. Determination of the overall true prediction rate for the analyzed knockouts shows that Δrgt1 yielded the best results (82%), while true predic- tions for Δgrr1 were the weakest (only 39%). The highest prediction rate found for Δrgt1 is probably related with the fact that many of the regulatory mechanisms included in our model are originated from transcrip- tional studies on the role of Rgt1. Conversely, the very bad prediction capabilities for Δgrr1 are likely related with the pleiotropic role of Grr1 in nutrient sensing, and the fact that our model does not account for all the regulatory effects associated with Grr1. Somewhere in between, true predictions for Δmig1, Δmig1Δmig2 and Δsnf1Δsnf4 lay in the range 50%–63%. These prediction rates can be improved if we do not account for genes with dubious regulation. Namely, the genes HXT5, HXT8, YGL157W, YKR075C, YOR062C, YNL234W and the MAL loci were included in the model even tough little is known about their regulation. These genes are presumably regulated by one or two of the transcription factors in the model via a hypothesized mechanism (see Additional file 1), but may very well also be regulated via other mechanisms, possibly involving other regulators. Nevertheless, their inclusion in the model allows us to see to what extent their expression is explained by the proposed mechanism. We observed that, if these dubiously regulated genes were not included for model evaluation, the rate of correct predictions increased markedly in the case of Δmig1, Δmig1Δmig2 and Δsnf1Δsnf4 (see values in parenthesis in Table 1). Moreover, if we exclude the genes with dubious regulation mentioned above as well as the results from the highly pleiotropic knockout of GRR1, we observe an improvement in the overall success rate from 60% to 71%. This suggests that the proposed mechanisms are probably incomplete for these genes. Overall, analyses of the discrepancies between model predictions and transcriptome data hints at four main sources of errors: (i) errors arising from imprecise conversion of knowledge into logical representation, (ii) errors inherent to the Boolean formalism, (iii) errors arising from the discrete evaluation of experimental gene expression data, and (iv) situations where high-through- put data goes against literature-based knowledge. Errors arising from imprecise conversion of knowledge into logical representation. Many of the discrepancies found in the model are originated from biological ambiguities or from difficulties in translating biological behavior into logical rules. For example, during evaluation of the Δrgt1 results we saw that it was not trivial to describe in Boolean terms the regulation of SNF3 and SUC2 by Mig1 and Mig2. In both cases, the error seems to arise from an over-estimation of the importance of Mig2 repression. Although Mig1 and Mig2 are believed to have somewhat redundant roles as repressors, the Boolean formalism does not make it easy to distinguish different levels of regulation. Most notoriously, the model fails to predict the response of the MAL genes (only 1/3 of the predictions were correct, which is the same frequency expected for a random model). In S. cerevisae the MAL genes, that are required for utilization of maltose as carbon source, co-locate in telomere-associated MAL loci. Although there are five different MAL loci identified [45] there is large variations in terms of presence and activity of these loci in different strains [35]. Moreover, experimental studies suggest that different MAL loci are regulated by distinct regulatory mechanisms, and, in particular, the MAL6 locus has been reported to be regulated differently than the MAL1, MAL2 and MAL4 loci [45, 46]. In the present work, network reconstruction of the MAL system was based on investigations of the BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 10 of 15 (page number not for citation purposes) MAL6 locus [34, 45, 47]. However, during model evaluation we made no distinction between different alleles – e.g. MALR is used to represent all MAL activator encoding genes, i.e. MAL13, MAL23, MAL33, MAL43 and MAL63 (cf. [48]). This generalization may be a major reason for the very low prediction rates. Errors inherent to the Boolean formalism. Another source of discrepancies is the limited nature of the binary Boolean model itself. In some cases, very steep response curves for gene expression and protein activities are observed, corresponding well with the binary nature of the Boolean model. However, the Boolean formalism lacks the capacity to describe a continuous reality that cannot be represented in an on/off manner. For example, it is impossible to distinguish between absence, low levels and high levels of glucose, three different condi- tions that trigger different regulatory responses. Thus, a discretionary approximation that conveniently explains the biological context has to be made (e.g., for the Δsnf1Δsnf4 evaluation, low levels of glucose in a carbon- limited chemostat were approximated by a situation of absence of glucose). In other instances, the Boolean formalism may not be sensitive enough to represent different levels of expression, such as in the case of regulation of GAL1 by Mig1, Gal4 and Gal80 [49, 50]. Furthermore, when considering inducible proteins that are expressed at a basal level, a value of zero may indicate presence at basal level rather than total absence. In such instances, defining whether a gene is being expressed (1) or not (0) is somewhat subjective. A further limitation of the Boolean formalism, particularly when focusing on logical steady state analysis with no distinction between processes of different time scales, is the difficulty of incorporating negative feedback loops. As discussed above there are difficulties in representing the negative feedback loop regulating MTH1 expression, and it is also impossible to represent Mig1 repression of the MIG1 gene. Such auto-repression cannot be included by an AND-relationship, since MIG1 (and Mig1) would then never be active in a logical steady state. Errors arising from the discrete evaluation of experimental gene expression data. Conversion of gene expression changes into discrete Boolean values is a simplification, which is presumably prone to errors. Nevertheless, we used commonly accepted thresholds of fold-change and significance to decide whether a gene is changing its expression. We have also checked whether choosing different a and FCmin greatly impacts model evaluation results (results not shown), and observed that it does not. We have identified a number of discrepancies likely to be due to type-2 errors when assigning experimental variation (e.g., MIG2 and HXT8 in the Δrgt1 case, and CAT8 and SIP4 in the Δsnf1Δsnf4 case), which show a regulatory change in the expected direction although statistically is not significant. However, one must look into these errors carefully, especially when the signifi- cance of the experimental change is calculated based on a high number of replicates, since this may hint at an error in the underlying hypothesis instead of a type-2 gene expression error. Situations where high-throughput data goes against literature-based knowledge. Large errors found in the model evaluation (\|Yi mod - Yi exp\| = 2) indicate situations where model prediction and observed changes of gene expression have opposite signs. This type of error represents a situation where the hypothesis underlying the logical model needs to be reconsidered. We have found this type of error only 3 times (for GAL4 and MAL13 in Δmig1, MAL33 in Δsnf1Δsnf4). In the case of the MAL genes, we have already discussed probable sources of the wrong predictions, namely the incorrect assumption about the regulatory mechanisms control- ling the expression of the MAL loci. For the GAL4 gene, we have observed that gene expression from the Δmig1 transcriptome study directly contradicts other studies. Although more careful analysis may be advisable, it is likely this result arises from the microarray experiment itself, either due to a problem with the array hybridiza- tion or with the normalization method used at probe- sets level. Conclusion Overall, the Boolean model showed some potential as a predictive model. The overall success rate (60% for the entire model, 71% for the restricted model without genes of dubious regulation and without considering deletion of highly pleiotropic GRR1) is promising. The observed errors are most likely due to a combination of lack of knowledge on the glucose regulatory network and simplifications required by the Boolean formalism. In this regard it should be noted that the deterministic and binary approximation to reality inherent in the Boolean formalism demands careful interpretation of model outputs and limits the overall success rate, which may be achieved. Even though there is much information on glucose repression in yeast, it is clear from our analysis that there are still connections and parts that are missing. Since the model is set up rigorously based on data from the literature, these inconsistencies seem to be caused by a combination of contradictions in reported experimen- tal results and perhaps due to incorrect insights about the network topology. Future efforts in modeling of glucose repression may need to take into consideration the uncertainties concerning the connectivity of the regulatory network, as well as network dynamics. Methods to discern these regulatory uncertainties (for BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 11 of 15 (page number not for citation purposes) example, through the identification of the most probable regulatory pathway from a set of different mechanistic pathway models), moreover have the potential to be used for reverse engineering of signaling and regulatory networks. Nevertheless, the model presented here represents a condensed way of organizing regulatory information on glucose repression, and strongly facil- itates integration and evaluation of new hypotheses. It can also serve as the basis for further efforts in modeling glucose repression signaling and regulatory pathways using probabilistic and/or dynamic approaches. The model presented here is thus an important step towards a holistic understanding of glucose repression in Saccharomyces cerevisiae, and the model may further be used for design of new experiments that can lead to a better understanding of this complex regulatory system. Methods Network reconstruction and logical model representation Glucose repression signaling and regulatory network was reconstructed from low-throughput data, namely from biochemical studies and physiological observations reported in peer-reviewed, original research publications. All information found relevant regarding glucose repres- sion regulatory cascades was collected in a database specifying the species involved (genes, proteins and metabolites) and the type of regulation exerted among them. This information was then converted into a logical hypergraph, representing all interactions between species in a logical manner, according to the framework proposed by Klamt et al. [17]. In our context, a hypergraph is a generalized unipartite directed graph representation of an interaction network where each edge (also called hyperarc or hyperedge) connects a set of start-nodes (tails) to a set of end-nodes (heads). Here, we consider graphs with one or more start-nodes, but with a single end-node. Nodes represent the different species (genes, proteins or metabolites) and hyperarcs represent the signal flow between species. A logical hypergraph is a hypergraph where hyperarcs are repre- sented by Boolean (or logical) equations (Figure 2), meaning that the state of an end-node can be determi- nistically found from the state of start-nodes based on the defined Boolean function connecting these nodes. Nodes can assume one of two logical states, on (1) and off (0); a gene can be expressed (1) or not (0) (or, in a more specialized case, be upregulated (1) or expressed at a basal level (0)), a protein can be active (1) or not (0), a metabolite can be available (1) or not (0). Logical states represent a discrete approximation of a continuous reality, for example, a discrete approximation of the sigmoid curve dictated by the Hill equation used to describe both gene expression and enzyme activity. Furthermore, we notice that the hypergraph representation of a Boolean network requires all logical equations to be written in the so-called disjunctive normal form, which uses exclusively AND, OR and NOT operators [17] (Figure 2). All network interactions were therefore converted into Boolean functions written in disjunctive normal form, and logical rules were intro- duced based on literature information. The hereby reconstructed logical hypergraph can easily and unam- biguously be converted to its underlying interaction graph by splitting up hyperarcs with more than one tail. Our logical hypergraph model represents sensing events (metabolite – protein interactions), signaling cascades (protein – protein interactions) and regulatory circuits (protein – gene interactions) related with glucose repression in S. cerevisiae. For analyses purposes, we consider the sensing events (sugar availability) as the input layer of the system, while the expression levels of the gene nodes are the outputs used in the model evaluation. Thus, by properly defining an initial state of the input layer, we can determine the logical steady state of all nodes in the system given the defined set of logical rules underlying the hypergraph. Additionally, given an input node and an output node, we can also perform a number of structural analyses on the characteristics of the pathways connecting them. All our functions are time-independent, as we are only interested in logical steady state solutions. Logical steady states analyses simplify the hypergraph setup, since we do not need to take into consideration the different timescales of different processes. Moreover, it allows the model steady states solutions to be evaluated against data from steady state chemostat cultivation or from the exponential phase of a batch cultivation (where balanced growth resulting in appearance of pseudo-steady-state can be assumed). Structural and logical steady state analyses of the network We used the MATLAB toolbox CellNetAnalyzer 7.0 [17, 51] to perform structural and functional logical steady state analyses on the established network. Structural analyses (number of loops and dependency matrix) were performed on the underlying interaction graph derived from the hypergraph. We used CNA capabilities to analyze the overall number of positive and negative loops between all input nodes and output nodes. We also determined the dependency matrix, which sum- marizes the relationship between all ordered pairs of species in the network. The dependency matrix is based solely on the topology of the interaction matrix and does not incorporate information on Boolean relationships [17, 51], i.e. while the dependency matrix may tell us that A is an activator of B, it does not tell us whether BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 12 of 15 (page number not for citation purposes) species C must be present for the activation to take place. Each matrix element, Dij, tells us whether the network contains (1) only activating paths, (2) only inhibiting paths, or (3) both activating and inhibiting paths, between species i and j. In addition, it tells us whether negative feedback loops exist that may attenuate the predicted (1) activating or (2) down-regulatory effects (if this is the case, species i is referred to as a non-total activator or inhibitor). The dependency matrix thus summarizes information on network topology in a very condensed way. It was particularly helpful in setting up the underlying interaction graph, and in identifying parts of the network that were inconsistent with information in the literature. Logical steady state calculations were performed based on the logical hypergraph representation. Briefly, the logical steady state is the Boolean state that the system eventually reaches given a fixed input (see [17] for detail). We used CNA to determine the logical steady state of all nodes in the system under all logical combinations of sugars availability (glucose, galactose, and/or maltose), and for all single gene deletions and some double gene deletions. In general, all nodes (except the input layer) are by default unconstrained. A few species were given a default value of 1 (genes where no other regulation is considered and genes expressed at basal levels). Gene deletions (i.e., knockouts) were simulated by setting the state of the deleted gene to a fix value of 0. Finally, specific edges were ignored in logical steady state analysis if the corresponding regula- tory interactions were comparably weak. Model evaluation for knockouts For some of the knockouts we were able to evaluate model predictions with available gene expression data from transcriptome studies. We used the results from the logical steady state analyses for the corresponding conditions in order to calculate the changes in gene expression between the simulated wild-type and the simulated knockout mutant. For wild-type simulations we obtained, for each species i, a Boolean state Xi,WT Œ {0,1}. Similarly, each knockout simulations produces a logical state Xi,KO Œ {0,1}. The variation between these two conditions is given by the difference Yi mod = (Xi,KO - Xi,WT), with Yi mod Œ {-1,0,1}. If species i is a gene (transcript), then Yi mod can be compared with experi- mental differential gene expression data, and such comparison allow us to evaluate the predictive capability of the model. Thus, we used the available transcriptome data in order to convert experimental gene expression changes for each gene i into a discrete number Yi exp Œ {-1,0,1}, based on their significance of change (p-value from a Student's t-test) and fold change (defined as FC = "average expression of gene i in knockout"/"average expression of gene i in wild-type" if "average expression of gene i in knockout" = "average expression of gene i in wild-type", otherwise FC = -1 × "average expression of gene i in wild-type"/"average expression of gene i in knockout"). We established a fold-change threshold ([FCmin\| = 1.5) and a Student's t-test p-value cut-off (a = 0.05) for all pair-wise gene expression comparisons between a deletion mutant and its isogenic reference strain (i.e., wildtype). All genes with p-value < a and FC ≥FCmin (or FC ≤-FCmin) were assigned with a value of Yi exp = 1 (or Yi exp = -1), and 0 otherwise. Overall, the model prediction capabilites were evaluated based on the difference \|Yi mod - Yi exp\|, a value of 0 meaning a correct prediction, a value of 1 implying a small error, and a value of 2 indicating a large error (model prediction and experimental results in opposite directions). Evaluation of predictive power The capabilities of the model to make predictions were evaluated in terms of the achieved percentage of correct predictions and by testing the results against the values expected from a model making random predictions. For each knockout evaluation, the ratio of correct predictions was calculated as the ratio of the number of genes where \|Yi mod - Yi exp\| = 0, divided by the total number of genes evaluated against experimental gene expression data. In order to remove uncertainty, we also determined the percentage of correct predictions excluding dubious interactions. The model predictions were statistical evaluated in order to assess the probability of having correct predictions by chance, a high number indicating a very bad predictive model. In order to do so, our model predictions were tested against a random model using the normal approximation to the binomial distribution. Specifically, using a one-sided alternative, we tested the null hypothesis that the proportion of correct predic- tions by the model, p = X/n (X being the number of successes and n being the total sample size, i.e. the number of genes tested), is equal to that expected from the random model, p0. The statistic used is: Z X np np p = − − 0 0 1 0 ( ) which is a random variable approximated by the standard normal distribution [52]. Abbreviations ODE: ordinary differential equations; CNA: CellNetAna- lyzer (MATLAB toolbox). BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 13 of 15 (page number not for citation purposes) Authors' contributions TSC reconstructed the network, performed all the analyses, and contributed to the writing of the manu- script. APO conceived, designed and supervised the study, was involved in discussing results, and contrib- uted to the writing of the manuscript. JN designed and coordinated the study. All authors read and approved the final manuscript. Additional material Additional file 1 Commented list of regulatory species and interactions included in the Boolean model. Table containing all regulatory species considered, a description of their function, their mode of regulation and respective references, and, in some cases, additional notes. This table constitutes the basis for the Boolean associations used in the Boolean model. Click here for file [http://www.biomedcentral.com/content/supplementary/1752- 0509-3-7-S1.pdf] Additional file 2 Logical equations included in the hypergraph. Table containing all logical equations included in the computational evaluation of the hypergraph. In some cases, the logical equations are accompanied by a note. Click here for file [http://www.biomedcentral.com/content/supplementary/1752- 0509-3-7-S2.pdf] Additional file 3 Evaluation of the logical state of the system for all gene deletions and different carbon sources availability. The Excel file sheet 'KO-WT' contains the evaluation of the model prediction Yi mod (Yi mod = Xi,KO mod - Xi,WT mod) for all single gene deletions and few double deletions under all combinations of available carbon sources used in this study. The sheet 'WT_copy' contains the state of the system for the wild-type (Xi,WT mod) under all combinations of carbon sources. The sheet '2KO_Evalution' contains the state of the system for all gene deletions (Xi,KO mod) under all combinations of carbon sources. Click here for file [http://www.biomedcentral.com/content/supplementary/1752- 0509-3-7-S3.xls] Acknowledgements We thank Steffen Klamt for help regarding CellNetAnalyzer, and for providing files that accelerated our computations. We thank Kiran R. Patil for fruitful discussions throughout the work. APO was funded by Fundação para a Ciência e Tecnologia from the Portuguese Ministry of Science and Technology (grant no. SFRH/BD/12435/2003). References 1. 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Publish with BioMed Central and every scientist can read your work free of charge "BioMed Central will be the most significant development for disseminating the results of biomedical research in our lifetime." Sir Paul Nurse, Cancer Research UK Your research papers will be: available free of charge to the entire biomedical community peer reviewed and published immediately upon acceptance cited in PubMed and archived on PubMed Central yours — you keep the copyright Submit your manuscript here: http://www.biomedcentral.com/info/publishing_adv.asp BioMedcentral BMC Systems Biology 2009, 3:7 http://www.biomedcentral.com/1752-0509/3/7 Page 15 of 15 (page number not for citation purposes)	19144179	Gal3p = ( GAL3 AND ( ( ( galactose_int ) ) ) ) MIG3 = NOT ( ( Rgt1p ) ) GAL4 = NOT ( ( Mig1p ) ) SCF_grr1 = ( GRR1 ) Sip4p = ( SIP4 AND ( ( ( Snf1p ) ) ) ) Gal2p = ( GAL2 ) galactose_int = ( galactose_ext AND ( ( ( Gal2p ) ) ) ) MalRp = ( MALR AND ( ( ( maltose_int ) ) ) ) IDP2 = ( Cat8p ) HXT3 = NOT ( ( Rgt1p AND ( ( ( Mth1p ) ) ) ) ) MEL1 = ( ( Gal4p ) ) OR NOT ( Mig1p OR Gal4p ) JEN1 = ( Cat8p ) Gal1p = ( GAL1 ) Rgt2p = ( glucose_ext AND ( ( ( RGT2 ) ) ) ) GAL3 = NOT ( ( Mig1p ) ) SUC2 = NOT ( ( Mig1p ) OR ( Mig2p ) ) HXT4 = NOT ( ( Mig1p ) OR ( Rgt1p AND ( ( ( Mth1p ) ) ) ) ) Mig2p = ( MIG2 ) MALR = NOT ( ( Mig1p ) ) 4ORFs = NOT ( ( RGT1 ) ) HXT2 = NOT ( ( Mig1p ) OR ( Rgt1p ) ) Glc7Reg1 = ( GLC7 AND ( ( ( REG1 AND glucose_ext ) ) ) ) maltose_int = ( maltose_ext AND ( ( ( MalTp ) ) ) ) MTH1 = NOT ( ( Mig1p AND ( ( ( Mig2p ) ) ) ) ) MDH2 = ( Cat8p ) OR ( Sip4p ) GAL5 = ( Gal4p ) GAL10 = ( GAL4 ) MalTp = ( MALT ) Mig3p = ( ( MIG3 ) AND NOT ( Snf1p ) ) Gal4p = ( ( GAL4 ) AND NOT ( Gal80p ) ) SFC1 = ( Cat8p ) GAL7 = ( GAL4 ) GAL1 = ( ( Gal4p ) AND NOT ( Mig1p ) ) FBP1 = ( Sip4p ) OR ( Cat8p ) Gal11p = ( GAL11 ) Cat8p = ( CAT8 AND ( ( ( Snf1p ) ) ) ) Rgt1p = ( RGT1 AND ( ( ( Mth1p OR Std1p ) ) ) ) CAT8 = NOT ( ( Mig1p ) ) Mig1p = ( ( MIG1 ) AND NOT ( Snf1p ) ) Std1p = ( ( ( ( ( STD1 ) AND NOT ( SCF_grr1 ) ) AND NOT ( Rgt2p ) ) AND NOT ( Yck1p ) ) AND NOT ( Snf3p ) ) Snf1p = ( ( SNF1 AND ( ( ( SNF4 ) ) ) ) AND NOT ( Glc7Reg1 ) ) Gal80p = ( ( ( GAL80 ) AND NOT ( Gal3p ) ) AND NOT ( Gal1p ) ) HXT5 = NOT ( ( Rgt1p ) ) HXT8 = NOT ( ( Rgt1p ) ) Yck1p = ( YCK1_2 ) PCK1 = ( Cat8p ) Mth1p = ( ( ( ( ( MTH1 ) AND NOT ( SCF_grr1 ) ) AND NOT ( Snf3p ) ) AND NOT ( Rgt2p ) ) AND NOT ( Yck1p ) ) ACS1 = ( Cat8p ) HXT1 = NOT ( ( Rgt1p AND ( ( ( Mth1p OR Std1p ) ) ) ) ) Snf3p = ( glucose_ext AND ( ( ( SNF3 ) ) ) ) SIP4 = ( Cat8p ) MLS1 = ( Sip4p ) OR ( Cat8p ) ICL1 = ( Cat8p ) OR ( Sip4p ) MALS = ( ( MalRp ) AND NOT ( Mig1p ) ) MIG2 = NOT ( ( Rgt1p ) )
The Logic of EGFR/ErbB Signaling: Theoretical Properties and Analysis of High-Throughput Data Regina Samaga1, Julio Saez-Rodriguez2,3, Leonidas G. Alexopoulos2,3,4, Peter K. Sorger2,3, Steffen Klamt1* 1 Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany, 2 Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America, 3 Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America, 4 Department of Mechanical Engineering, National Technical University of Athens, Athens, Greece Abstract The epidermal growth factor receptor (EGFR) signaling pathway is probably the best-studied receptor system in mammalian cells, and it also has become a popular example for employing mathematical modeling to cellular signaling networks. Dynamic models have the highest explanatory and predictive potential; however, the lack of kinetic information restricts current models of EGFR signaling to smaller sub-networks. This work aims to provide a large-scale qualitative model that comprises the main and also the side routes of EGFR/ErbB signaling and that still enables one to derive important functional properties and predictions. Using a recently introduced logical modeling framework, we first examined general topological properties and the qualitative stimulus-response behavior of the network. With species equivalence classes, we introduce a new technique for logical networks that reveals sets of nodes strongly coupled in their behavior. We also analyzed a model variant which explicitly accounts for uncertainties regarding the logical combination of signals in the model. The predictive power of this model is still high, indicating highly redundant sub-structures in the network. Finally, one key advance of this work is the introduction of new techniques for assessing high-throughput data with logical models (and their underlying interaction graph). By employing these techniques for phospho-proteomic data from primary hepatocytes and the HepG2 cell line, we demonstrate that our approach enables one to uncover inconsistencies between experimental results and our current qualitative knowledge and to generate new hypotheses and conclusions. Our results strongly suggest that the Rac/ Cdc42 induced p38 and JNK cascades are independent of PI3K in both primary hepatocytes and HepG2. Furthermore, we detected that the activation of JNK in response to neuregulin follows a PI3K-dependent signaling pathway. Citation: Samaga R, Saez-Rodriguez J, Alexopoulos LG, Sorger PK, Klamt S (2009) The Logic of EGFR/ErbB Signaling: Theoretical Properties and Analysis of High- Throughput Data. PLoS Comput Biol 5(8): e1000438. doi:10.1371/journal.pcbi.1000438 Editor: Anand R. Asthagiri, California Institute of Technology, United States of America Received January 15, 2009; Accepted June 11, 2009; Published August 7, 2009 Copyright: 2009 Samaga et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: RS and SK are grateful to the German Federal Ministry of Education and Research (funding initiatives ‘‘HepatoSys’’ and ‘‘FORSYS’’), to MaCS (Magdeburg Centre for Systems Biology) and to the Ministry of Education of Saxony-Anhalt (Research Center ‘‘Dynamic Systems’’) for financial support. J.S.R., L.G.A. and P.K.S. acknowledge funding by NIH grant P50-GM68762 and by a grant from Pfizer Inc. to P.K.S. and D.A.L. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: klamt@mpi-magdeburg.mpg.de Introduction The epidermal growth factor receptor (EGFR) signaling pathway is among the best studied receptor systems in mammalian cells. Signaling through EGFR (ErbB1) and its family members ErbB2 (Her2/Neu2) ErbB3 and ErbB4 regulates cellular processes such as survival, proliferation, differentiation and motility and ErbB receptors are important targets for new and existing anti- cancer drugs [1,2]. Mathematical modeling of the EGFR system started more than 25 years ago with efforts to describe binding to and internalization of the receptor [3] that was followed by a variety of dynamic models that deal with different aspects of the system (reviewed in [4,5]). Whereas the first EGFR models focused on the receptor itself – internalization, ligand binding, and receptor homodimer- ization [6] – later models included downstream signaling events (e.g. [7–9]). More recent studies also address homo- and hetero- dimerization among members of the ErbB receptor family and the effects on downstream of binding to different ligands (of which 13 are known; e.g. [10–13]). All these models describe aspects of EGFR/ErbB signaling with a set of stoichiometric reactions and the dynamics of the involved species is described by a set of ordinary differential equations (ODEs). In order to simulate the model, the kinetic constants and initial concentrations of the model have to be known or, more likely, they must be estimated. Recently, a large-scale map was constructed by Kitano and colleagues to capture the current state of knowledge about interactions in the EGFR system as a stoichiometric network [14]. This model contains no information on the reaction kinetics and is thus static and cannot be used to perform dynamic simulations. Nonetheless, the Kitano map provides a reasonably comprehensive list of molecules and interactions involved in EGF signaling and represents an excellent starting point for studying its global architecture [14–16]. Existing ODE-based models cover only limited parts of the map, and parametric uncertainty present even in these smaller models suggests that it is not currently practical to build an ODE model of the entire pathway having high explanatory and predictive power. Instead, structural and qualitative (parameter-free) modeling approaches is the tool of choice. In fact, many important properties of a system rely solely PLoS Computational Biology \| www.ploscompbiol.org 1 August 2009 \| Volume 5 \| Issue 8 \| e1000438 on the often well-known network structure, including many that govern dynamic behavior; feedback loops, for example, are captured in the wiring diagram. Whereas structural (stoichiometric) analysis of metabolic networks is quite well established [17], relatively few efforts have been made thus far to study qualitatively the propagation of information in signaling networks. Efforts to date include statistical analyses of interaction graphs of large-scale protein-protein networks (e.g. [18]) and other approaches that rely on graph theory (e.g. [15,19]). Petri net theory [20,21] and constraint-based modeling [22] have also been used to unravel structural properties of signal transduction networks. Boolean (discrete logic) description of interaction networks has quite a long tradition in theoretical biology. In the past, it has been mainly applied to random networks [23] or gene regulatory networks of moderate size (e.g. [24–27]). However, we have recently developed a Boolean framework that is specifically tailored to signaling networks. In contrast to gene regulatory networks, signaling networks are usually structured into input, processing and output layers. This approach has recently been applied successfully to a large-scale model of T cell signaling [28], and used in concert with high-throughput data to analyze cell- specific network topologies (Saez-Rodriguez et al, in preparation). Within this framework, we have set-up a logical model of the main parts of the stoichiometric model of EGFR signaling [14] and additionally of signaling through ErbB2, ErbB3 and ErbB4. As mentioned above, the stoichiometric model of Oda et al [14] does not allow for dynamic simulations. Also functional issues related to network structure can be studied only to a minor extent because the stoichiometric model is limited regarding the analysis of signal flows relevant in signaling networks. By translating the stoichiometric (mass-flow based) into a logical (signal-flow based) representation, we obtain an executable model facilitating functional predictions about input-output responses of a very complex signaling cascade. Our model comprises 104 species and 204 interactions and is among the largest of a mammalian signaling network but we have recently become aware of the interesting work of Helikar et al [29] who also studied a large-scale Boolean network containing parts of the EGFR/ErbB induced signaling pathways. Their work focuses on a statistical analysis of the possible (non-deterministic) discrete behaviors of their Boolean model. In contrast, our model provides deterministic and testable predictions about responses and we have verified many using functional data. In the process, we have uncovered non-obvious functional properties of the ErbB signaling pathway that are likely to be biologically significant. This paper is organized as follows: the first part describes how we translated the stoichiometric EGFR/ErbB model of Oda et al [14] into a logical model via a set of general rules. The second part presents results from a theoretical analysis of the network including, for example, a characterization of feedback structure and identification of network components whose behavior is strongly coupled. The final section describes application of the logical model to interpret functional data in which primary human hepatocytes and hepatocarcinoma cell line HepG2 were exposed to different ErbB ligands in combination with inhibitors of intracellular signaling kinases. We show that a Boolean model of ErbB signaling can generate experimentally verifiable predictions about input-output behavior in the face of perturbation and that new hypotheses about biological function can be generated Results From a stoichiometric to a logical model for EGFR/ErbB signaling Based on a stoichiometric model of EGF receptor signaling [14] and additional information from the literature, we built a logical model that describes signaling induced by 13 members of the EGF ligand family through ErbB1-4, leading to the activation of various kinases and transcription factors that effect proliferation, growth and survival (see Figure 1 and Table S1). Ligand binding causes the formation of eight different ErbB-dimers that autophosphor- ylate and then provide docking sites for adaptor proteins such as Gab1, Grb2 and Shc, which transmit signals to the small G proteins Ras and Rac, leading to the activation of MAPK cascades. Among these, ERK1/2 is the best studied but our model also comprises the JNK and p38 cascades. Highly interconnected with the MAPKs and also downstream of the ErbB receptors is PI3K/Akt signaling, another major branch of the model. Furthermore, activation of different STATs and the PLCc/PKC pathway are included. Our model contains most parts of the stoichiometric model of Oda et al [14]. However, endocytosis, the G1/S transition of the cell cycle as well as the crosstalk with the G protein coupled receptor signaling cascade are not considered in our model as we focus here on early signaling events induced by external stimuli (EGF-type ligands). In contrast, our model considers signaling through all different ErbB dimers (in addition to EGFR homodimers), which was not part of the stoichiometric model (though a simplified diagram has been given in [14]). Finally, there are some reactions and species that are only contained in the logical model so as to use the data set (e.g. the mammalian target of rapamycin (mTOR), p70S6 kinase). Differences between the stoichiometric and the logical model regarding considered components and interactions are also explained in the model documentation (see Table S1). Translating a stoichiometric model into a logical model is not a trivial task and requires additional information. Whenever a species is only influenced by one upstream molecule, the interpretation as a Boolean function is straightforward: the downstream species is Author Summary The epidermal growth factor receptor (EGFR) signaling pathway is arguably the best-characterized receptor system in mammalian cells and has become a prime example for mathematical modeling of cellular signal transduction. Most of these models are constructed to describe dynamic and quantitative events but, due to the lack of precise kinetic information, focus only on certain regions of the network. Qualitative modeling approaches relying on the network structure provide a suitable way to deal with large-scale networks as a whole. Here, we constructed a comprehensive qualitative model of the EGFR/ErbB signaling pathway with more than 200 interactions reflecting our current state of knowledge. A theoretical analysis revealed important topological and functional properties of the network such as qualitative stimulus-response behavior and redundant sub-structures. Subsequently, we demonstrate how this qualitative model can be used to assess high-throughput data leading to new biological insights: comparing qualitative predictions (such as expected ‘‘ups’’ and ‘‘downs’’ of activation levels) of our model with experimental data from primary human hepatocytes and from the liver cancer cell line HepG2, we uncovered inconsistencies between measurements and model structure. These discrepancies lead to modifications in the EGFR/ErbB signaling network relevant at least for liver biology. The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 2 August 2009 \| Volume 5 \| Issue 8 \| e1000438 active (state 1) if and only if the state of the upstream species is 1 (vice versa if the influence is negative) (see Figure 2A). In some other cases it is clear how to code the dependency in a logical function – for example, the formation of a complex (e.g. the heterodimerization of c-Jun and c-Fos to the transcription factor AP-1 (see Figure 2B) or binding of a ligand to a receptor), where all involved proteins have to be present to trigger downstream events and are thus connected with an AND gate. Furthermore, we use an OR gate whenever a protein can be recruited through different receptors or adapter proteins (see Figure 2C). However, in many cases the stoichiometric information is not sufficient to approximate the activation level of a species as a logical function of the states of its upstream effectors and one requires additional (mainly qualitative) information, which can often be obtained from the literature. The two main cases that can arise are the following: N A species is positively influenced by two (or more) upstream molecules, for example a protein that can be phosphorylated by different kinases (see Figure 2D). Here, the decision whether both kinases are necessary or if one suffices, that is whether to use an AND or an OR, cannot be made on the basis of the information that is contained in a stoichiometric model. However, the necessary information can often be obtained from related literature (e.g. from knock-out studies where one of both effectors has been removed, or if an inhibitor is available for an upstream species). N A species is positively influenced by one species (for example a kinase) and negatively influenced by another (for example a phosphatase). In this case, we cannot be sure what happens Figure 1. Logical model of the EGF-/ErbB receptor signaling pathway represented in ProMoT. Blue circles symbolize AND connections. Inputs with default value 0 are indicated with red diamonds, inputs with default value 1 by green diamonds. Yellow diamonds stand for the outputs of the model. Gray hexagons represent the receptors (homodimers as well as heterodimers) and green hexagons stand for the 13 different ligands. Green ellipses symbolize reservoirs. The remaining species (symbolized with rectangles) are colored according to their function: red: kinases; blue: phosphatases; yellow: transcription factors; green: adaptor molecules; violet: small G proteins as well as GAPs and GEFs; black: other. The box in the upper part of the network contains binding of the ligands to the receptor and receptor dimerization, showing the high combinatorial complexity. Black arrows indicate activations, red blunt-ended lines stand for inhibitions. Dotted lines represent ‘‘late’’ interactions (with attribute t = 2) that are excluded when studying the initial network response. Dashed lines indicate connections from reservoirs. Dummy species (see Methods) are not displayed. doi:10.1371/journal.pcbi.1000438.g001 The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 3 August 2009 \| Volume 5 \| Issue 8 \| e1000438 Figure 2. Examples illustrating the translation of the stoichiometric EGFR model into a logical description. The examples are taken from the stoichiometric map of Oda et al [14]. A The activation level of MKK7 is only influenced by one upstream molecule (active MEKK1). B c-Jun and c-Fos form the transcription factor AP-1. Accordingly, both species are combined with an AND gate (denoted by ‘‘?’’ in the logical equations). C Gab1 can bind directly to EGFR homodimers or via receptor-bound Grb2. For the activation of downstream elements, the activation mechanism of Gab2 does not make a difference what results in a logical OR connection represented by two (independent) activation arrows: Grb2RGab1 OR EGFRRGab1. D In this example, we cannot immediately decide whether both Raf-1 and MEKK1 are necessary for the activation of MKK1 (in the model description we use the synonym MEK1) or if the activation of one of these two kinases suffices. Further information is required or an ITT gate can be used (in model M1 we used an OR based on facts published in the literature). doi:10.1371/journal.pcbi.1000438.g002 The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 4 August 2009 \| Volume 5 \| Issue 8 \| e1000438 when both the kinase and the phosphatase are present; it will depend on the respective strength (described as kinetic parameters in a quantitative model) and may differ in different cell types. However, the activation of phosphatases often occurs as a temporarily secondary event upon stimulating a signaling pathway (required for switching off the signal). They may therefore be neglected when considering the early events, i.e. the initial response of the network that follows upon stimulation (see below). We also have to keep in mind that, in all cases, the logical description is only a discrete approximation of a quantitative reaction. In those cases where neither an AND nor an OR is a good approximation, we can use incomplete truth tables [30]. This operator, herein after referred to as ‘‘ITT gate’’, returns 1 if and only if all positive arguments are 1 and all negative arguments are 0, and returns 0 if and only if all positive arguments are 0 and all negative arguments are 1. In all other cases, no decision can be made and the response of the molecule remains undefined. Using ITT gates may limit the determinacy of the model (when performing stimulus-response simulations it can happen that some states cannot be determined uniquely), but it allows for a safer interpretation of the results. To illustrate this concept and to discuss uncertainties in our reconstructed logical model (in the following referred to as model M1) we consider a model variant M2 where the activation mechanisms of 14 proteins are described with ITT gates reflecting the uncertainties in the logical description of M1 (see Table S2). In this way model M2 accounts explicitly for the uncertainties in the logical concatenation of different signals, however, it cannot account for uncertainties that are captured in the wiring diagram itself. Whenever we refer in the following to ‘‘the logical model’’ we refer to M1 if not stated otherwise. Once the network construction has been completed, one may start to perform discrete simulations. We will not study the transient behavior of the network; instead we propagate the signals from the input to the output layer. Mathematically, we compute the logical steady state that follows from exposing the network to a certain input stimulus (possibly in combination with network interventions; see Methods). In this way we can analyze the qualitative input-output behavior of the network. Feedback loops, which can be identified in the interaction graph underlying the logical model, may hamper this kind of analysis of the discrete behavior of logical networks (especially negative feedback loops [30]). However, herein we will focus on the initial response of the network nodes induced by external stimulations or perturbations. Assuming that the system is in a pseudo-steady state at the beginning, the initial response of a node is governed by the paths connecting the inputs with this node whereas feedback loops are secondary events that can only be activated at a later time point when each node in the loop has exhibited its initial response. Although path/cycle length is no precise measure for the velocity of signal transduction, the comparable average length of input/ output paths (19) and feedback loops (17) supports the assumption that the initial response of the network nodes is dominated by the input/output paths whereas feedback loops may overwrite the initial response of the network nodes only after a certain time period with significant length (again, feedback loops can causally not be activated before the initial response occurred). To decouple the initial response from the activity of the feedback loops, we proceed as follows: we assign to each reaction a time variable t determining whether the reaction is active/available during the initial response (i.e. is an early event; t = 1) or not (late event; t = 2). In each negative feedback loop we identify the node Z that has the shortest distance to the input layer. This node Z can be considered as the initialization point of the feedback loop and we then assign t = 2 to the ‘‘last’’ interaction of the feedback loop closing the cycle in node Z (i.e. points into Z). For example, in a causal chain InputRARBRC--\|DRB we would consider DRB as a late event. In this way we interrupt the feedback loop and the logical steady states computed in the network reflect the initial response of the nodes. Strikingly, it is sufficient to consider only four interactions as late event to break all feedback loops (see below) in the network. With this acyclic network a unique logical steady state follows for any set of input values in model M1. The assignment ‘‘late’’ was not only reasonable for selected interactions in feedback loops, but also for three interactions involved in negative feed-forward loops down- regulating the signaling after a certain time. The time variables for each reaction can be found in Table S1. Although ‘‘late’’ interactions are neglected when calculating the early signal propagation, they are nevertheless important to describe structural properties of the network that can be derived from the interaction graph representation (see below). It is also important to mention that the logical steady state computed for a given scenario (see Methods) does not necessarily reflect the activation pattern in the cell at one particular point of time. Instead, it reflects for each species the initial response to the stimulus. The time range in which this initial response takes place can differ for each molecule – typically, a species situated in the upper part of the network (e.g. a receptor) responses faster to the stimulus than a species of the output layer (e.g. a transcription factor). We set-up models M1 and M2 with ProMoT [31] and exported the mathematical description as well as the graphical representa- tion to the analysis tool CellNetAnalyzer (CNA) [32]. The results obtained with CNA have been re-imported to and visualized in ProMoT. The logical model is represented as logical interaction hypergraph (see Methods) and contains 104 nodes and 204 hyperarcs (interactions). Seven interactions are configured as late events (see Table S1), so their time scale is set to 2. Two interactions are only considered in the analysis of the interaction graph but excluded in the logical analysis as they do not change the logical function of their target node or as the exact mechanism of the interaction is unknown (see Table S1). 28 nodes are inputs of the model, i.e. their regulation is not explicitly considered in the model but can be used to simulate different scenarios. Besides ligands and receptors, these include for example some phospha- tases with unknown activation mechanism. For all input nodes, a default value is given in Table S1 (and is indicated in Figure 1) that is used for the logical analyses unless otherwise specified. Topological properties of the interaction graph A logical model in hypergraph form has a unique underlying interaction graph (see Methods) capturing merely positive and negative effects between the elements (instead of deterministic logic functions). Importantly, the usage of ITT gates in model M2 does not change the underlying interaction graph implying that all results obtained in this section are valid for both M1 and M2. A graph-theoretical analysis of the interaction graph enables us to derive important topological properties of the network, indepen- dently of the Boolean description. For example, the existence of feedback loops is necessary for inducing multistationarity (positive feedback loops) or oscillatory behavior (negative loops) of the dynamic system [33,34]. In our model, the underlying interaction graph has 236 feedback loops, thereof 139 negative. Strikingly, all positive feedback loops are composed of a negative feed-forward and a negative feedback, except one that describes the reciprocal The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 5 August 2009 \| Volume 5 \| Issue 8 \| e1000438 activation of the adaptor protein Gab1 and PIP3, a lipid of the membrane layer [35]. All negative feedback loops arise from five mechanisms: (i) the kinases ERK1/2 and p90RSK downregulate their own activation by phosphorylation of SOS1, a guanine nucleotide exchange factor (GEF) for Ras, (ii) the phosphatase SHP1 binds to the autophosphorylated ErbB1-homodimers and dephosphorylates them, (iii) Ras positively influences its GTPase activating protein RasGAP via PI3K, (iv) the ubiquitin ligase c-Cbl binds to ErbB1, leading to degradation of the receptor in the lysosome and (v) Ras potentiates the Rab5a-GEF activity of Rin1 and thus increases the formation of endocytic vesicles. Therefore, removing the species Ras and ErbB1-homodimer breaks all negative feedback loops. As described above, when considering the early response in the model the ‘‘last’’ interaction closing a feedback loop is considered as late event (see Table S1). It turned out that assigning only four interactions the ‘‘late’’ attribute t = 2 suffices not only to break all negative feedback loops, but also the positive ones, so that no feedback loop remains in the network when considering the early events. In terms of graph theory, a feedback loop is (per definition) a strongly connected subgraph, i.e. if two species A and B are part of a directed cycle it always holds that there exists a path from A to B and from B to A. In our model, all feedback loops build up one strongly connected component consisting of 34 species, meaning that all feedbacks are coupled. Figure 3 shows the participation of the different species in the feedback loops. Remarkably, the small G protein Ras is included in 98% of the loops, underlining its central role in the regulation of this network. Ras is a key regulator of cell fate [36] and a known oncogene in many human cancers [37]. However, the high number of feedbacks containing Ras in our model can also reflect the fact that Ras is one of the best studied proteins and therefore the feedback mechanisms of Ras are possibly better known than those of other proteins. Also noteworthy, RN-tre, a GTPase activating protein (GAP) for Rab5a, is only involved in positive loops, whereas the guanine nucleotide exchange factor for Rab5a, Rin1, takes only part in negative feedbacks. The large size of the network gives rise to a high number of possible signaling paths along which one node may affect another one. There are, for instance, 6786 paths (thereof 52% negative) leading from the input (ligand) EGF to the transcription factor AP- Figure 3. Species participation in the feedback loops. The darker a species is colored, the more loops it participates in. Colorless species are not part of feedback loops. All colored species build up one strongly connected component in the underlying interaction graph. doi:10.1371/journal.pcbi.1000438.g003 The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 6 August 2009 \| Volume 5 \| Issue 8 \| e1000438 1 in the output layer. Considering only the early events, 1684 paths remain being 25% of them negative, where all these negative paths include the node RasGAP. The information whether a species acts positively (activating) or/and negatively (inhibiting) on another species, i.e. whether there is any positive or/and negative path linking the two species, can be stored and visualized as dependency matrix [30]. The dependency matrix for the early events contains ambivalent dependencies (i.e. a node has positive and negative effects on other nodes) that mainly rely on the negative influence of RasGAP: as it inhibits Ras, it gives rise to a number of negative paths connecting the activated receptors with proteins downstream of Ras – in addition to the positive paths via SOS1, an activator for Ras. Not considering RasGAP leads to a matrix where only a few ambivalent interactions occur (see Figure 4): for example, the receptor ErbB2 is an ambivalent factor for almost all downstream elements as it is the preferred heterodimerization partner of the other receptors and thus prevents signaling through various different dimers (for example, ErbB1/ErbB3 formation is repressed if ErbB2 is present). When all interactions are active, Figure 4. Dependency matrix D for the early events (influence of RasGAP not considered). The color of matrix element Di j means the following: green: species i is an activator of species j (there are only positive paths connecting i with j); red: i is an inhibitor of j (there are only negative paths connecting i with j); yellow: i is an ambivalent factor for j (there are positive and negative paths connecting i with j); black: i has no influence on j (there is no path connecting i with j). (See also [32]). doi:10.1371/journal.pcbi.1000438.g004 The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 7 August 2009 \| Volume 5 \| Issue 8 \| e1000438 the dependency matrix contains more ambivalent interactions than it does when considering only the early events. Note that, except for ambivalent dependencies, the qualitative effect (up/down) of perturbations can be unambiguously predicted from the dependency matrix and we will make use of this technique when analyzing experimental data (see below). Theoretical analysis of the logical model Implementing a Boolean function in each node of the interaction graph enables us to calculate the qualitative network response to a certain stimulus or perturbation and to predict the effects of interventions. Given the binary states for the input variables and optionally for species that have a fixed value (e.g. simulating a knock-out or knock-in), one determines the resulting logical steady state by propagating the signals according to the logical function of the nodes (see Methods). Using this technique, we determined the network response in model M1 upon stimulation with the different ligands, again focusing on the early events (i.e. the interactions with t = 2 were set to zero). Due to the fact that the resulting network is acyclic (as explained above), a unique logical steady state follows for any set of input values in model M1. We found that the outputs can be divided into two groups: the majority of the output elements can be activated by all possible dimers. However, PKC, STAT1, STAT3 and STAT5 can only be activated through ErbB1-homodimers (PKC, STAT1, STAT3) or ErbB1-homodimers and ErbB2/ErbB4-dimers (STAT5). Accord- ingly, stimulation with neuregulins does not result in activation of the protein kinase PKC and the transcription factors STAT1 and STAT3, in contrast to stimulation with the other ligands that activate all output molecules except the pro-apoptotic effect of BAD which is repressed. This is due to the fact that the neuregulins, unlike the other ligands, do not bind to ErbB1 and thus cannot activate ErbB1-homodimers. Strikingly, despite of the 14 ITT gates in model M2, the logical steady state in response to ErbB1-homodimers can still be determined in model M2 and does not differ from M1. This observation reflects a high degree of redundancy in at least some parts of the network. The state of each of the different kinases phosphorylating p38 or MKK4 is for example only dependent on the activity of Rac/Cdc42 so that these kinases are always activated together (see below). Thus, the input–output behavior of the network can be uniquely predicted for all ligands except neuregulins. In contrast, model M2 fails to predict the response for some nodes if other dimers (in absence of the ErbB1-homodimer) are stimulated. This concerns in particular most of the output nodes; the states of PKC, STAT1, STAT3 and STAT5 can be determined (as in model M1, these proteins can only be activated by ErbB1-homodimers, except STAT5 that is ‘‘on’’ in response to ErbB2/ErbB4-dimers) whereas the state of the other output nodes cannot be calculated. The indeterminacy of M2 with respect to stimulations of dimers others than ErbB1-homodimers can be explained by the uncertainty (ITT gate) in the activation of Rac/ Cdc42. When performing simulations with M1, we realized that certain species in the network show strongly coupled behavior. This guided us to search systematically for equivalence classes of network nodes whose activation pattern is completely coupled: for species A and B being elements of the same equivalence class, it either holds that their states are always the same (A = 0uB = 0, A = 1uB = 1; positive coupling) or always the opposite (A = 0uB = 1, A = 1uB = 0; negative coupling) irrespective of the chosen inputs. In other words, the state of one species in the equivalence class determines the states of all other species in this class. Hence, whenever a species of a particular equivalence class is active, we can conclude that all other species of the same equivalence class must have been activated (deactivated in case of negative coupling), at least transiently. An algorithm to compute the equivalence classes efficiently is given in the Methods section. In general, equivalence classes can be computed for a given scenario (defined by a specific (possibly empty) set of fixed states, typically from input nodes). For this given scenario we test systematically for each species whether it is completely coupled with other nodes or not. This type of coupling analysis is very similar to enzyme (or reaction) subsets known from metabolic networks [38,39] and it helps to uncover functional couplings embedded in the network structure. We anticipate that the concept of equivalence classes also provides a basis for model reduction (e.g. when computing logical steady states), similar as it has been employed in metabolic networks (see e.g. [40]). Figure 5 shows the equivalence classes in the EGFR/ErbB model for early signal propagation where the states (presence) of all ligands and receptors were left open (the states of the other inputs were fixed to their default value as given in the model description (see Table S1)). We found six equivalence classes, the largest comprising 24 species. The latter includes parts of PI3K signaling as well as the Rac induced parts of the MAPK cascades reflecting the strong coupling of these two major pathways in model M1. In model M2, this equivalence class splits into three smaller ones because the ITT gates introduce uncertainties that may lead to a decoupling of the two pathways. The other equivalence classes of M2 hardly differ from the ones in M1 (see Figure S1) again indicating that alternative pathways contribute rather to a higher degree of redundancy than to a higher degree of freedom regarding the potential input-output behavior. Another concept relying on the logical description is the computation of minimal intervention sets (MIS; [30,32]). An MIS is a set of interventions that induces a certain response, whereas no subset of the MIS does (i.e. an MIS is support-minimal). One application of MIS is to determine failure modes in the network that lead to an activation of elements of the output layer without any external stimulation of the cell. In the EGFR/ErbB model we are interested in failures that stimulate proliferation and growth of the cell when no ligand is present. Regarding the early events, constitutive activation of Ras, for example, leads to activation of the transcription factors Elk1, CREB, AP-1 and c-Myc, the p70S6 kinase, the heat shock protein Hsp27 and represses apoptosis – without any external stimulus. Besides Ras, it is sufficient to permanently activate one of the species Gab1, Grb2, PI3K, PIP3 or Shc to activate/inhibit these outputs. In model M2, the minimal intervention sets to provoke the above mentioned response contain at least two elements, for example the activation of Grb2 and Vav2. These findings show that the network has fragile points where a mutated protein (e.g. one that is constitutively active) may support uncontrolled growth and proliferation. However, besides ErbB signaling, various other pathways are important for the regulation of growth and apoptosis and a failure in one pathway might be compensated by another, what makes it important to include these pathways step by step into our model. Additionally, when building up the model we did not focus on one certain cell type, but collected species and interactions that have been detected in different kinds of cells leading to a kind of ‘‘master model’’. A model that describes only one cell type would probably include less interactions (Saez-Rodriguez et al, in preparation), so that a (constitutive) signal has not such a global (network-wide) influence as in the master model. The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 8 August 2009 \| Volume 5 \| Issue 8 \| e1000438 Analyzing high-throughput experimental data One of the strengths of our model lies in the broad range of pathways it covers and in the easy simulation of the network wide response to different stimulations and interventions. It is therefore well-suited to analyze high-throughput data where various readouts are measured in response to several stimuli and to perturbations all over the network. Here we discuss the analysis of two datasets collected in primary human hepatocytes and the hepatocarcinoma cell line HepG2. In the first set of measurements - a subset of the ‘‘CSR liver compendium’’ (Alexopoulos et al, in preparation) - primary cells and HepG2 cells were stimulated with transforming growth factor alpha (TGFa) and additionally treated with seven different small-molecule drugs, whereof six inhibit the activation of nodes considered in our model. For the second data set, HepG2 cells were stimulated with different ligands of the EGF family and treated with an inhibitor for PI3K. In both cases, the phosphorylation state of 11 signaling proteins included in the ErbB model were measured after 0, 30 and 180 minutes (see Methods for a more detailed description of the experiments). Here, we only focus on the early response of the network after 30 minutes because we want to analyze which proteins become activated at all. We assume that in hepatocytes only ErbB1 and ErbB3 are expressed as it has been reported for adult rat liver [41]; thus, for the analysis of the hepatocyte data, the state values of the other two receptors (ErbB2 and ErbB4) were set to 0 in the model. As discussed earlier, our modeling framework is based on two concepts: (i) the Boolean (logical) description discretizing the kinetic behavior, and (ii) the underlying interaction graph reflecting the topology of interactions. This gives rise to two different approaches for the analysis of the data. First, using the dependency matrix of the interaction graph, we examined whether the experimental results are in accordance to the causal dependencies in our network. Second, using the logical model, we predicted the binary network response to the different experimental stimuli and compared these predictions with a discretized version of the data. Interaction graph-based data analysis In the experiments, the phosphorylation state of the readouts is measured in response to a particular set of stimuli by adding Figure 5. Equivalence classes in the EGFR/ErbB model. Each color represents one equivalence class. Species with no color are not part of any equivalence class. The states for the ligands and the four receptor monomers are left open, all other inputs are fixed to their default value (see Table S1), which is indicated by the red (0) and green (1) diamonds. Late events are excluded and therefore shown as dotted lines (see also figure 1). doi:10.1371/journal.pcbi.1000438.g005 The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 9 August 2009 \| Volume 5 \| Issue 8 \| e1000438 certain ligands and/or inhibitors and combinations thereof. For each pair of treatments it can then be checked whether the ratio of the measured responses is consistent with the causal dependencies in the network topology (as captured in the dependency matrix; Figure 4) or not. By comparing the measured phosphorylation state of a protein p under treatment A, Xp(A), with the measured value for p under treatment B, Xp(B), we can characterize the effect of the difference of both treatments on the activation level of p. We restrict ourselves here to comparing treatments that differ only in adding or removing one ligand or inhibitor, although, in principle, all possible pairwise comparisons of treatments could be considered. As an example, assume we compare the phosphorylation state Xp(A) of protein p in response to a stimulation A, where a ligand l and inhibitor i were added, with the state Xp(B) of p in response to treatment B, where only the inhibitor i was added. An increase in the phosphorylation state of protein p in response to the addition of the ligand (i.e. Xp(A)/Xp(B).1) indicates that there must be at least one positive path leading from this ligand to the protein and the respective entry in the dependency matrix (row l, column p) of the model should therefore show an activating or at least ambivalent influence. Analogously, for studying the influence of a certain inhibitor, a decrease (increase) in the data in response to inhibiting a certain protein indicates that there must be at least one positive (negative) path leading from the inhibited species to the respective readout. We decided to consider a change in the data as significant if Xp(A)/Xp(B).1.5 or if Xp(A)/Xp(B),1/1.5. Figures 6 and 7 show the comparison of the data with the dependency matrix of the model where we considered only the early events and neglected the influence of RasGAP (as discussed above). All in all, the experimental network response to the different treatments agrees reasonably well with the structure of the model, in particular in primary cells. In HepG2 cells, 10% of the analyzed dependencies are contradictory to our model: in 3% (7%) of the cases we saw a significant increase (decrease) in the activation level, although this was excluded by the model. 45% of the cases agreed explicitly with the model: in 28% (5%) of the cases, treatments that have a purely positive (negative) influence according to the dependency matrix resulted in a significant increase (decrease) in the measured activation levels and in 12% of the cases a ligand/ inhibitor causes no significant change in a measured readout as predicted in the model. In the remaining 45% of the cases (gray entries in Figure 7), the data show no significant change, although the stimulus can affect the readout in our model (many of these gray entries will be discussed below). In primary cells, 13% of the predictions were false, 74% were fully correct and for 13% we observed no significant changes, although the model contains paths between the stimulus and the readout. A discussion of specific findings is given below together with the result of the logical model. Data analysis with the logical model Whereas the dependency analysis described above is based on the raw data, a comparison of the data with the binary network response of the logical model requires a discretization of the data, the simplest being a binarization. To obtain the discretized values, we used DataRail, a recently introduced MATLAB toolbox that facilitates the linkage of experimental data to mathematical models [42]. It provides a variety of methods for data processing, including algorithms to convert continuous data into binary values and to create convenient data structures for the analysis in CellNetAnalyzer. The discretization depends on three thresholds (p1, p2, p3) which all have to be exceeded in order to discretize the measured signal to ‘‘on’’ [42]: the first threshold is for the relative significance (the ratio between the value at time 1 (in our case after 30 minutes) and the value at time 0), the second threshold ensures the absolute significance (ratio between the signal and the maximum value for this signal from all measurements) and the third threshold ascertains that the signal is above experimental noise. The choice of the thresholds is quite difficult as no reference data exist that define when a molecule is ‘‘on’’, that is when it is sufficiently activated to induce its downstream events. Most likely, the required level of activation differs from protein to protein and from cell to cell. However, since no information on these differences is available and to avoid unnecessary degrees of freedom, we decided to define the same thresholds for all molecules and both cell types (p1 = 1.5, p2 = 0.15, p3 = 100). Figure S2 shows the sensitivities of the binarization with respect to these three parameters. For each measured scenario we computed the binary network response of our model and compared it with the discretized data (Figure 8). We note that the comparison of the measured ‘‘ups and downs’’ with the dependency matrix (performed in the previous section) and the comparison of the discretized data with the predicted logical response are naturally correlated. However, they do not lead necessarily to exactly the same results. An example: assume you have an input stimulus (ligand L) which may activate a target species S via two independent pathways, one of both leading over an intermediate species A for which we have an inhibitor I. If we compare the scenario ‘‘stimulation with L and adding inhibitor I’’ against ‘‘stimulating with L’’ via dependency analysis we would expect a decrease in the (non-discretized) activation level of S since the inhibited species A is an activator for S. However, the phosphorylation state of S might show no significant change in the dependency analysis (i.e. leads to a ‘‘gray entry’’ as in Figures 6 and 7) due to the alternative pathway not affected by the inhibitor. In contrast, if the two pathways from L to S are OR-connected in the logical model, the latter would still predict S to be ‘‘on’’. Another difference in the data analysis based on dependency matrix vs. logical model is that the former compares species states obtained from two different experiments (e.g. experiment with/ without inhibitor) whereas the logical model gives for each experiment one (independent) prediction for each species. As in the case of the dependency analysis, the measured data agree reasonably well with the predictions of the model M1 (HepG2: 77% correct predictions; primary cells: 90% correct predictions). In Figure S3, the comparison of model M2 with the experimental data is shown. For primary cells, only 7% of the states cannot be determined due to the ITT gates, for HepG2 21%. 83% of the predictions for primary cells and 59% for HepG2 were correct. In all cases where a state can be predicted by M2 it naturally coincides with the prediction from M1 since the latter is only one special case of all possible behaviors in model M2. In some cases where we used an ITT gate in model M2, the logical function can be uniquely determined with the experimental results confirming some of the deterministic logic gates used in model M1: for example, the transcription factor CREB can be activated through the MEK-dependent kinase p90RSK AND/OR through the p38 dependent MK2. As CREB is still activated both with MEK inhibitor and with p38 inhibitor, this points to an OR- connection achieving a match between model predictions and data in this node. In the same way, we can verify an AND connection for the two negative modulators of Gsk3 and an OR for the phosphorylation of the auto-inhibitory domain of p70S6 kinase. Again, using ITT gates, we can only reflect uncertainties regarding the logical combination of different paths and not The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 10 August 2009 \| Volume 5 \| Issue 8 \| e1000438 whether a species influences another at all. This is why some of the discrepancies between the predictions of model M1 and the data also appear for model M2. Interpreting inconsistencies between data and model predictions Most disagreements between model predictions and experi- mental results concentrate on certain experimental conditions (rows) and readouts (columns) - in the dependency analysis as well as in the analysis with the logical model. Here we discuss such systematic inconsistencies and – using our model – we seek to provide explanations and conclusions: N A significantly increased state of phosphorylation of STAT3 in response to any of the ligands could not be found both in HepG2 and primary hepatocytes. Whether this is due to the fact that the activation of STAT3 is very transient, as it has been reported for example for the human epithelial carcinoma cell line A431 [43], or if the activation of this transcription factor through ErbB receptors plays no role in hepatocytes, has still to be clarified. N Both analysis approaches show that stimulation of HepG2 cells with amphiregulin (not measured in primary cells) did not result in activation of the measured proteins (see Figure 7, lines 34–37 and Figure 8B, lines 23/24). This is in agreement with Figure 6. Interaction graph-based comparison between experimental data and topological properties of the model (data from primary hepatocytes). Shown is the comparison between the measured and predicted changes (‘‘ups’’ and ‘‘downs’’) in the activation levels of network elements in response to ligands and inhibitors in primary human hepatocytes (data obtained from Alexopoulos et al, in preparation). Each row compares two different scenarios A and B. A dot behind the species name in the row labels indicates that, in both scenario A and scenario B, this species was added as ligand (green dot) or an inhibitor for this species was added (red dot). Species whose input values differ in both scenarios are marked with an up or down arrow, respectively. For example, the comparison of scenario A (EGF ligand, TGFa ligand, PI3K inhibitor) and scenario B (TGFa ligand, PI3K inhibitor) is labeled by TGFa N (green dot), PI3K N (red dot), EGF q, i.e. the influence of an increased level of EGF on the readouts is analyzed (under the side constraints that TGFa and a PI3K inhibitor were added as well; for further explanations see text). The readouts are shown in the columns. The color indicates whether the model predictions and the measurements are consistent or not (see color legend). doi:10.1371/journal.pcbi.1000438.g006 The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 11 August 2009 \| Volume 5 \| Issue 8 \| e1000438 Figure 7. Interaction graph-based comparison between experimental data and topological properties of the model (data from HepG2 cells). Shown is the comparison between the measured and predicted changes (‘‘ups’’ and ‘‘downs’’) in the activation levels of network elements in response to ligands and inhibitors in HepG2 cells. The horizontal line separates the first (top) from the second (bottom) dataset for HepG2 cells (see also text). For further explanations and color legend see Figure 6. doi:10.1371/journal.pcbi.1000438.g007 The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 12 August 2009 \| Volume 5 \| Issue 8 \| e1000438 Figure 8. Comparison of the discretized data with predictions from the logical model. A Primary human hepatocytes (data from Alexopoulos et al, in preparation). B HepG2 cells (the horizontal line separates the first (top) from the second (bottom) dataset for HepG2 cells; see also text). Each row represents one treatment and the readouts are shown in the columns. Light green: predicted correctly, ‘‘on’’; dark green: predicted correctly, ‘‘off’’; light red: predicted ‘‘on’’, measured ‘‘off’’; dark red: predicted ‘‘off’’, measured ‘‘on’’, black: data points where the measured species is inhibited are not considered. doi:10.1371/journal.pcbi.1000438.g008 The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 13 August 2009 \| Volume 5 \| Issue 8 \| e1000438 findings of amphiregulin being a much weaker growth stimulator than EGF in some cell types [44]. N The systematic errors in the column of p38 in the dependency analysis (for primary as well as HepG2 cells) might indicate missing edges in the model requiring further experimental studies to verify these findings. We cannot exclude that other (e.g. stress-induced) pathways not captured in our model may have caused these observations, also because some of the effects on p38 are also present without ligand stimulation. N Stimulating the HepG2 cells with both TGFa and EGF does not result in a significantly higher activation level of the readouts compared to adding only one of these ligands as can be seen from the predominantly gray entries in lines 26/27 and 44/45 in Figure 7. This finding is in accordance with the fact that both ligands are very similar and bind to the same receptor dimers (see Table S1). N One of the major differences in the behavior of the two cell types is the activation of Hsp27: whereas this heat shock protein becomes activated in response to cytokine stimulation in primary cells, no significant increase in the state of phosphorylation occurs in almost all studied scenarios in the cancer cell line (leading to many false ‘‘on’’ predictions). N Another remarkable discrepancy between the experimental data and our model predictions is the influence of the mTOR inhibitor rapamycin on phosphorylation of p70S6 kinase (see lines 14/15 in Figures 6 and 7), which is not supported by our model. Although mTOR mediates the phosphorylation of the catalytic site T389 [45], it has to the best of our knowledge not been implicated with the phosphorylation of T421 and S424, those sites, whose state of phosphorylation were measured in the analyzed data sets. However, an inhibitory effect of rapamycin on these sites has been reported earlier [46], even if the molecular mechanism that could explain this influence still has to be uncovered. N According to our model, PI3K should influence all measured readouts except STAT3. However, the data show a clear effect of the PI3K inhibitor only on the phosphorylation of Akt (see Figure 6, lines 12/13 and Figure 7, lines 50–61). Additionally, Figure 8 shows that JNK, p38 and, in primary cells also Hsp27, could be activated in the experiments in presence of PI3K inhibitor although our model predicted the phosphor- ylation to be blocked (due to the AND connections of the PI3K-dependent nodes PIP3 and PI(3,4)P2, respectively, with Vav2 and SOS1_Eps8_E3b1). We therefore searched for hypothetical changes in our model structure that could explain these experimental findings. We observed that node Rac/ Cdc42 lies on all paths connecting the inputs (ligands) with the aforementioned critical readouts (except Gsk3, see below), i.e. activation of Rac/Cdc42 is necessary in our model for phosphorylation of JNK, Hsp27 and p38. We may thus hypothesize that - in contrast to the assumption in our model - PI3K activity is not necessary for activation of the small G- proteins Rac and Cdc42 in primary hepatocytes and in HepG2 cells. N A closer look on Figure 8B (lines 19/20) reveals that the phosphorylation of JNK in response to neuregulin is – in contrast to the response to any of the other ligands – sensitive on PI3K inhibitor. This is also reflected in Figure 7 where an increase of neuregulin only increases the phosphorylation of JNK in absence of PI3K inhibitor (see lines 28–33) and decreasing the level of PI3K (i.e. adding the inhibitor) after neuregulin stimulation also leads to a decreased phosphoryla- tion state of JNK (see lines 52 and 59). Therefore, neuregulin must use a different, PI3K dependent signaling path for activating JNK than the other ligands, probably due to the fact that neuregulin only activates ErbB1/ErbB3-dimers whereas EGF, TGFa, amphiregulin and epiregulin additionally activate ErbB1-homodimers. Taking these findings together, we propose the following alternative mechanism: Vav2 is the major GEF for Rac/Cdc42 in hepatocytes and activates Rac/ Cdc42 in a PI3K-independent way. Neuregulin, which cannot bind to ErbB1-homodimers and accordingly is not able to activate Vav2 (see Table S1), provokes the activation of JNK independently of the Rac/Cdc42 induced MAPK cascade through a different, PI3K-dependent pathway. N In the model, the inhibitory phosphorylation of Gsk3 can be induced by a MEK1/2 dependent pathway (via p90RSK) and by a PI3K dependent pathway (via Akt). Figures 6 and 7 (lines 9 and 13) show that the phosphorylation of Gsk3 in response to TGFa is independent of the MEK inhibitor and the PI3K inhibitor, both in HepG2 and in primary cells. As TGFa stimulation leads to a strong phosphorylation of Gsk3 in both cell types (see Figure 8), there must be another signaling route, not involving MEK and PI3K. One possible candidate is PKC which has already been reported to inhibit Gsk3, however not in response to ligands of the EGF family [47]. N According to the data, both Gsk3 and p90RSK are influenced by JNK inhibitor after TGFa stimulation in primary hepatocytes (see Figure 6, line 18). This seems to support another possible mechanism, where JNK activates p90RSK which may then phosphorylate Gsk3. However, the JNK inhibitor affects much more proteins than expected, both in HepG2 and in primary cells. As these unexpected influences also occur in absence of ligand stimulation, this strongly suggests a minor specificity of the JNK inhibitor. N Similar as for Gsk3 phosphorylation, data analysis with our model provides useful insights into the activation mechanism of CREB in response to TGFa: the proposed effect of the p38 dependent kinase MK2 on CREB cannot be observed both in HepG2 and in primary cells (see Figures 6 and 7, line 11). The positive effect of MEK on CREB phosphorylation after TGFa stimulation can be seen in HepG2 (Figure 7, line 9), but not in primary hepatocytes (Figure 6, line 9). Together with the finding of the logical analysis that the MEK inhibitor cannot block activation of CREB in HepG2 (Figure 8), this indicates that there must be an alternative pathway for CREB activation in primary hepatocytes that is probably involving p90RSK. A summary of the above mentioned results is given in Table S3. Changing the model accordingly, we can improve the agreement of model predictions and data in the logical analysis from 90% to 97% for the primary cells and from 74% to 94% for HepG2. For the dependency analysis, the number of comparisons that agree explicitly increases from 74% to 82% for primary and from 45% to 64% for HepG2 cells. Moreover, the number of entries where we assumed a change in the data but could not detect a significant increase or decrease reduces from 13% to 4% (primary) and from 45% to 24% (HepG2), albeit at the expense of a minor increase in the number of contradictions (primary: increase from 13% to 14%, HepG2: 10% to 12%). As described above, herein we deduced the proposed changes of the model structure manually from the data analysis. More systematic approaches for network identification from combina- torial experiments are given in Saez-Rodriguez et al (in preparation) and in [48]. In general, detecting such systematic inconsistencies of the data both with respect to the dependency structure of the network and The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 14 August 2009 \| Volume 5 \| Issue 8 \| e1000438 the logical model description is a great advantage of our approach and could hardly be achieved with a model relying on differential equations (where parameter uncertainty often hampers a falsifica- tion of the model structure). Discussion In the present work, we developed a large-scale logical model of signaling through the four ErbB receptors, including the ERK, JNK and p38 MAPK cascades, Akt signaling, activation of STATs and the PLCc pathway, based on the stoichiometric pathway map of Oda et al [14]. We discussed technical problems that arise when converting a stoichiometric model into a logical one and proposed a general guideline how to deal with them. We examined several properties of the logical model charac- terizing its topology (feedback loops and network-wide interde- pendencies as derived from the underlying interaction graph) and its qualitative input-output behavior with respect to different stimuli. We also introduced the new technique of species equivalence classes revealing coupled activation patterns in the logical model providing valuable insights into the correlated behavior of network elements. One possibility to deal with uncertainties concerning the correct logical combination of different influences on a certain node is the usage of gates with incomplete truth tables (ITT gates). We replaced the (deterministic) logical gates for the activation of 14 species of our model with ITT gates and repeated all logical analyses with this modified model. Surprisingly, the predictive power of the ITT model is still high, highlighting the redundant structure of major parts of the signaling pathway and showing that many properties of the network do not rely on the assumptions we made when choosing the logical functions. Compared with a dynamic model based on differential equations, our approach for describing signaling events is certainly limited in reflecting kinetic aspects which are important to obtain a complete understanding of these processes in the cell. However, properties derived exclusively from the structure can provide insights into the transfer of signals in the cell, as the result of this and other studies have shown [28,29]. The simpler design of the qualitative models also has some advantages over complex dynamic models. First of all, the logical approach enables us to model large-scale signaling networks allowing, for example, to study the effects of crosstalk, for which a dynamic description is currently often unimaginable. An expansion of the model can easily be done, whereas adding a reaction to a model of differential equations requires usually the elaborate re-estimation of param- eters. The flexible architecture of the model also enables us to test and generate hypotheses very quickly. Another advantage is that the qualitative predictions derived with a logical model do not depend on certain parameter values except the time scales and are therefore more generally valid. There are also methods to study ODE models without parameters (e.g. [49–51]). However, these methods are currently limited to relatively small systems and study different properties. With the advances of experimental techniques, it becomes more and more essential to provide tools that allow for the analysis and exemplification of the huge amount of data that arise. We developed new techniques for the analysis of large data sets that are especially well-suited to analyze data that stem from combinatorial experiments (systematic combination of different ligands/inhibitors). The first approach, a method for comparing experimental (high-throughput) data with predictions derived from the logical model, requires a discretization of the data. Although the ‘‘on/off’’ decision is sometimes hard to take as no reference data exist and the ‘‘right’’ thresholds for the parameters are unknown, assessing the sensitivities of the data with respect to the discretization thresholds leads to a safer interpretation. Alterna- tively, the data can be assigned a relative value between 0 and 1 which can be compared to the discrete (0/1) value of the model (Saez-Rodriguez et al, in preparation). The second approach, the comparison of the data with the topological dependency structure of the model (captured in the interaction graph), requires only a significance threshold and provides an even simpler method for the falsification of qualitative knowledge as it relies on less assumptions than the logical model (only the wiring diagram is evaluated; logical combinations and discrete states are not required). Applying these new automatized techniques to analyze high- throughput phospho-proteomic data revealed some important insights into the structure of EGFR/ErbB signaling in primary hepatocytes and the HepG2 cell line. Our results strongly suggest a model where the Rac/Cdc42 induced p38 and JNK cascades are independent of PI3K, both in primary hepatocytes and in HepG2. Furthermore, we detected that the activation of JNK in response to neuregulin follows a PI3K-dependent signaling pathway that seems not to be important for activation of JNK through ErbB1- binding ligands. Additional findings concern Gsk3 and CREB where known signaling paths were excluded to provoke phos- phorylation after TGFa stimulation and new routes could be proposed. Finally, we observed no activation of STAT3 in both cell types and no activation of Hsp27 in HepG2. Besides these results on the topology of EGFR/ErbB signaling in hepatocytes, the comparison of model predictions and data could also detect side effects of the used JNK inhibitor. With our software CellNetAnalyzer (CNA; [32]) we provide a powerful tool to study structural networks. It facilitates the analysis of interaction graphs as well as logical models and also provides methods to compare model predictions with experimental data as described herein. Furthermore, CNA is now highly coupled with the tools ProMoT [31], DataRail [42] and CellNetOptimizer (Saez- Rodriguez et al, in preparation), forming an integrated pipeline for the construction, structural analysis and data interpretation of signal transduction networks. The presented model is to the best of our knowledge one of the largest existing mathematical models of the EGFR/ErbB signaling pathway. However, it is far from being complete and has to be complemented, for example by including the endocytosis of the receptors. Step by step, we want to expand the model by other important mitogenic and pro- and anti-apoptotic pathways to study crosstalk. We also think that the logical model can serve as a useful basis for the development of dynamic models. A step between both modeling frameworks could be to refine the current binary description and use multilevel activation instead, a promising approach yet it requires more detailed (semi-quantita- tive) information on the reaction kinetics and leads to more complex networks. Further refinements could be achieved by fuzzy logic description or by considering more precise time delays for the interactions. Methods Logical modeling of the EGFR/ErbB signaling network For the reconstruction and qualitative analysis of the EGFR/ ErbB signaling network we employ a logical modeling framework as introduced previously [30,32]. Signaling networks are usually structured into input, intermediate and output layer and the input signals govern the response of the network. For this characteristic network topology we introduced logical interaction hypergraphs (LIHs) The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 15 August 2009 \| Volume 5 \| Issue 8 \| e1000438 as a special representation of Boolean networks, which is well- suited to formalize, visualize and analyze logical models of signal transduction networks. As in all Boolean networks, nodes in the network represent species (e.g. kinases, adaptor molecules or transcription factors) each having an associated logical state (in the binary case as used herein only ‘‘on’’ (1) or ‘‘off’’ (0)) determining whether the species is active (or present) or not. Signaling events are encoded as Boolean operations on the network nodes. For example, the MAP kinase (MAPK) JNK can be activated (gets ‘‘on’’) if the MAPK kinase MKK7 AND the MAPK kinase MKK4 are active (see the AND connection in Figure 1). Usually, a node can be activated by more than one signaling event; all these events are then OR-connected, e.g. the MAPK p38 becomes active if MKK3 OR MKK4 OR MKK6 is active (Figure 1). In general, in LIHs we make only use of the Boolean operators AND (?), OR (+), and NOT (!), which are sufficient to represent any logical relationship. A signaling event (or interaction) in an LIH is an AND connection of nodes (negation of node values using the NOT operator are allowed) describing one opportunity how the target species of this connection can be activated. Hence, for the first example described above we would write MKK7 AND MKK4?JNK or shorter MKK7:MKK4?JNK In a graphical representation of the network (see JNK node in Figure 1), such an AND connection is displayed as a hyperarc. In contrast to arcs in graphs, a hyperarc (in hypergraphs) may have several start or end nodes. Clearly, in some cases, only one species is required to activate another, as in the example MKK3?p38: In these cases, the hyperarc is a simple arc as occurring in graphs; we will nevertheless refer to it as a hyperarc. As already mentioned, a species may be activated via several distinct signaling events (hyperarcs), i.e. all these signaling events are OR-connected. This can again be illustrated by p38, which can be activated (indepen- dently) via three different MAPKs and we therefore have three different OR-connected hyperarcs: MKK3?p38 OR MKK4?p38 OR MKK6?p38 Hence, all hyperarcs pointing into a species are OR connected. In this way we can easily interpret Figure 1, which displays graphically the interactions given in Table S1. As described in the main part, the reconstruction of our logical model of EGFR/ErbB is based on a stoichiometric model of EGF receptor signaling [14] and additional information from the literature. Some general remarks on how a stoichiometric network can be translated into a logical one are given in the main part. The logical model (for both version M1 and version M2; the latter having 14 gates with incomplete truth tables; see main text) comprises signaling of 13 members of the EGF ligand family through the EGF receptor and its heterodimerization partners ErbB2-4, leading to the activation of various transcription factors and kinases that effect proliferation, growth and survival (Figure 1). In addition to ligands and receptors, species whose regulation is not known are herein considered as members of the input layer, for example the phosphatases PTEN and SHIP2. The differentiation between ‘‘early’’ and ‘‘late’’ events (see below and main part) makes it sometimes necessary to introduce auxiliary (‘‘dummy’’) nodes that have no biological correspon- dents. Consider for example a species C that is activated by species A during the early events (t = 1) and down-regulated by another species B as a late event (t = 2). Assuming that both the presence of A and the absence of B are necessary to activate C, we use an AND connection in the LIH representation (A ? !BRC). As the two influences are combined to one hyperarc in the LIH, we can assign only one time variable to this interaction. In order to reflect the time delay of the inhibitory activity of B, we introduce an additional dummy node with t = 2. We now describe the original interaction A ? !BRC with two interactions B?B dummy t~2 ð Þ A:!B dummy?C t~1 ð Þ: An example in the ErbB model are the ErbB1-homodimers that are activated by various ligands (e.g. EGF) and dephosphorylated by SHP1 (see Table S1). To properly describe the timing of the SHP1-mediated dephosphorylation of the receptor, we introduce a dummy species shp1d that is activated by SHP1 and obtain thus two hyperarcs: shp1?shp1d t~2 ð Þ egf:erbb1:!shp1d?erbb11 t~1 ð Þ: Another type of node that is introduced for modeling purpose only is what we refer to as reservoir. It is used whenever a molecule causes different downstream events depending on how it is activated. Here, we have to use more than one compound to describe the molecule in the model. An example in our model is mTOR: associated with Rictor, it is involved in the activation of Akt, whereas the Raptor-bound form activates p70S6 kinase. However, as all these compounds represent the same biological species, we associate them with a reservoir, pointing out that they share the same pool. Inactivation of the reservoir will then affect the activation of all correspondents of this species. A full description of the model M1 with all species and interactions (hyperarcs) is given in Table S1. In model variant M2, 14 logical gates of model M1 have been configured as incomplete truth tables (ITT gates). The differences between M1 and M2 are described in Table S2. Analysis of the logical model Once an LIH has been set-up, we may start to analyze it. A typical scenario is that we apply a pattern of inputs to the network and we would like to know how the nodes in the network will respond to this stimulation. As explained in [32], by propagating input signals along the logical (hyperarc) connections (which is equivalent to computing the logical steady state resulting from the input stimuli) we obtain the qualitative response of the network. Note that the logical steady state obtained by this propagation technique is independent of the assumption of synchronous or asynchronous switching which is required when analyzing the discrete dynamics of Boolean networks [27]. It depends on the functionality of positive or negative feedback loops in the network whether we can resolve a complete and unique logical response of all nodes for a given set of input stimuli (for example, negative feedback loops may prevent the existence of a logical steady state). Feedback loops are usually present in signaling networks, however, as described in the main part, we identified one interaction in each loop that can be considered as a late event (t = 2). When considering the initial response of the network we set these late- The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 16 August 2009 \| Volume 5 \| Issue 8 \| e1000438 event connections inactive leading to an acyclic network for which always a unique network response for a given set of inputs can be computed. One can also easily perform in silico experiments, for example check how a knock-out (or inhibition) alters the network response by fixing the state of the respective species. With the idea of minimal intervention sets (MIS) one may even directly search for those interventions that enforce a desired response (e.g. activation or inactivation of a transcription factor). As described in [32], MISs can be computed by testing systematically which combinations of knockouts and knockins fulfill a specified intervention goal. Species equivalence classes in logical networks A new analysis technique for logical networks is introduced in this work: we search for equivalence classes of network nodes whose activation pattern is completely coupled in logical steady state: species A and B are elements of the same equivalence class, if it either holds that their values in steady state are always the same (A = 0uB = 0, A = 1uB = 1; positive coupling) or always the opposite (A = 0uB = 1, A = 1uB = 0; negative coupling) irrespec- tive of the chosen inputs (e.g. ligands). In other words, the state of one species in the equivalence class determines the states of all other species in this class. Again, the relation given above holds for logical steady states where both A and B are determined and where no intervention was made in the network except for the inputs. Whenever a species of a particular equivalence class is active, we can conclude that all other species of the same equivalence class must have been activated (deactivated in case of negative coupling), at least transiently. An efficient algorithm for computing the equivalence classes can be constructed as follows: 1) Equivalence classes can be computed for a given scenario, so we first define a specific (possibly empty) set of fixed states, typically from (some) input nodes. 2) For this given scenario we test systematically for each species whether it is strongly coupled with other nodes or not, independently of external stimuli. For each species A we compute (i) the logical steady states of all other species that result when fixing the state of A to 1 and (ii) the logical steady states of all other species that result when fixing the state of A to 0. A node B whose logical steady state can be determined in both cases and is 1 in one case and 0 in the other case is known to be in one equivalence class with species A: B is positively coupled with A if the two resulting logical steady states of B are 1/0 (it then holds A = 1 = .B = 1, A = 0 = .B = 0 and thus according to contraposition also B = 0 = .A = 0, B = 1 = .A = 1) and negatively coupled if the two logical steady states are 0/1 (it then holds A = 1 = .B = 0, A = 1 = .B = 0 and thus according to contraposition also B = 0 = .A = 1, B = 1 = .A = 0). The case that the logical steady state of a species B is 0/0 or 1/1 (for fixing A = 1/ A = 0) indicates that this species B can never be activated or never be inhibited, respectively, and would thus indicate a semantic problem in the model. If a species A is coupled with species B, and species B is coupled with species C, we can subsume all three species in one equivalence class (we do that systematically for all species until we reach finally the equivalence classes). Composing the equivalence classes in this way, it may also happen that species that cannot influence each other (no directed path between both exists) are in one equivalence class due to a common upstream regulator. Consider a network that only contains the interactions A R B and A R C. Fixing the state of B or C to 1/0 we cannot conclude any equivalence relations as no further states can be determined. Fixing A to 1 and 0 we find that A is equivalent to B and A is equivalent to C, thus – according to the rule given above – A, B and C form one equivalence class. Interaction graph analysis Another advantage of LIHs is that we can easily derive the (signed and directed) interaction graph underlying the logical model: we only have to split all hyperarcs that have two or more start nodes (i.e. the AND connections) into simple arcs. Interaction graphs cannot be used to give on/off predictions; however, they provide an appropriate formalism to search for signaling paths and feedback loops. Another useful feature that can be extracted from interaction graphs is the dependency matrix as introduced in [30,32] which displays network-wide interdependencies between all pairs of species. For example, a species A is an activator (inhibitor) of another species B, if at least one path leads from A to B and if all those paths are positive (negative). This kind of information can be very useful for predicting effects of perturbations. Model implementation and availability We set-up the logical EGFR/ErbB model with ProMoT [31] and exported the mathematical description as well as the graphical representation to the analysis tool CellNetAnalyzer (CNA) [32]. The results obtained with CellNetAnalyzer have been partially re- imported to and visualized in ProMoT (Figures 1, 3, 5). Data management and discretization was performed with DataRail [42]. The tools are freely available (for academic use) from the following web-sites: DataRail: http://code.google.com/p/sbpipeline/wiki/DataRail ProMoT: http://www.mpi-magdeburg.mpg.de/projects/promot/ CellNetAnalyzer: http://www.mpi-magdeburg.mpg.de/projects/ cna/cna.html After acceptance, the model will be provided in formats for ProMoT and CellNetAnalyzer. Experimental set-up and measurement data The data on primary human hepatocytes and the first part of the HepG2 data were obtained from experiments conducted by Alexopoulos et al (in preparation), while for the second part of the HepG2 data, a cue-signal-response (CSR) compendium was created for the EGFR pathway. The second dataset comprises 11 phosphoprotein measurements under 24 different perturbations generated by the combinatorial co-treatments with a diverse set of ErbB ligands and the PI3K inhibitor. For ligands we choose 5 ErbB related cytokines, namely epidermal growth factor (EGF), neuregulin 1 (NRG1; also known as heregulin), amphiregulin (AR), epiregulin (EPR), and transforming growth factor alpha (TGFa). For each stimulus, the PI3K inhibitor ZSTK-474 was added at 2 mM final concentration 30 minutes prior to any ligand treatment. Optimal inhibitor concentration was obtained for concentration-inhibition curve (data not shown) in order to achieve 95% inhibition of the downstream pAkt signal on TGFa stimulated HepG2. The dataset was created using a high- throughput method of bead-based fluorescent readings (Luminex, Austin, TX). Assays were optimized for multiplexability and checked for passage-to-passage and preparation-to-preparation variability (Alexopoulos et al, in preparation). The full dataset (first and second part) and the resulting discretization are graphically depicted in Figure S4. The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 17 August 2009 \| Volume 5 \| Issue 8 \| e1000438 Supporting Information Figure S1. Equivalence classes for model M2. Each color represents one equivalence class. The equivalence classes of model M1 are depicted by the species border color. Late interactions (t = 2) are drawn as dotted lines. The value of fixed inputs is given by the green (1) and red (0) diamonds. Found at: doi:10.1371/journal.pcbi.1000438.s001 (0.33 MB PDF) Figure S2. Sensitivities of the binarization to the chosen parameters. 2.1 Primary human hepatocytes 2.2 HepG2 cells (the horizontal line indicates the first (top) and the second (bottom) measurement set for HepG2 cells); Parameter p1 (2.1a, 2.2a): the ratio between the value at time 1 and the value at time 0 lies beneath (red) or above (green) the fixed threshold p1 = 1.5; Parameter p2 (2.1b, 2.2b): the ratio between the signal and the maximum value for this signal from all measurements lies beneath (red) or above (green) the fixed threshold p2 = 0.15; Parameter p3 (2.1c, 2.2c): the signal lies beneath (red) or above (green) the fixed threshold for experimental noise (p3 = 100). For all parameters: The darker a field is colored, the larger is the distance to the chosen threshold, i.e. the binarization is less sensitive on the parameter. Found at: doi:10.1371/journal.pcbi.1000438.s002 (0.61 MB PDF) Figure S3. Comparison of the discretized data with predictions from model M2. A Primary human hepatocytes (data from Alexopoulos et al, in preparation). B HepG2 cells (the horizontal line separates the the first (top) from the second (bottom) dataset for HepG2 cells; see also text). Each row represents one treatment and the readouts are shown in the columns. Light green: predicted correctly, ‘‘on’’; dark green: predicted correctly, ‘‘off’’; light red: predicted ‘‘on’’, measured ‘‘off’’; dark red: predicted ‘‘off’’, measured ‘‘on’’; yellow: state cannot be determined in logical steady state analysis; black: data points where the measured species is inhibited are not considered. Found at: doi:10.1371/journal.pcbi.1000438.s003 (0.21 MB PDF) Figure S4. Data plots generated with DataRail. Shown are the phosphorylation states of the proteins after 0, 30 and 180 minutes. Green: significant activation after 30 minutes (according to the chosen parameters); gray: no significant activation (cf. also Saez- Rodriguez et al, 2008). A Primary human hepatocytes (data obtained from Alexopoulos et al (in preparation)) B HepG2 cells, first set of experiments (data obtained from Alexopoulos et al (in preparation)) C HepG2 cells, second set of experiments. Found at: doi:10.1371/journal.pcbi.1000438.s004 (0.28 MB PDF) Table S1. Logical EGFR/ErbB model: list of species and interactions. Found at: doi:10.1371/journal.pcbi.1000438.s005 (0.16 MB PDF) Table S2. Incomplete truth tables (ITTs) in the model variant M2. Found at: doi:10.1371/journal.pcbi.1000438.s006 (0.01 MB PDF) Table S3. Proposed model changes to improve the fit of the model to the data. Found at: doi:10.1371/journal.pcbi.1000438.s007 (0.01 MB PDF) Acknowledgments We thank Sebastian Mirschel for his support in building and visualizing the network with ProMoT. 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The Logic of ErbB Signaling PLoS Computational Biology \| www.ploscompbiol.org 19 August 2009 \| Volume 5 \| Issue 8 \| e1000438	19662154	mkk4 = ( mlk3 ) OR ( mekk1 ) OR ( mekk4 ) mkk7 = ( mekk1 ) erbb12 = ( ( btc AND ( ( ( erbb1 AND erbb2 ) ) ) ) AND NOT ( shp1d ) ) OR ( ( tgfa AND ( ( ( erbb1 AND erbb2 ) ) ) ) AND NOT ( shp1d ) ) OR ( ( bir AND ( ( ( erbb1 AND erbb2 ) ) ) ) AND NOT ( shp1d ) ) OR ( ( hbegf AND ( ( ( erbb1 AND erbb2 ) ) ) ) AND NOT ( shp1d ) ) OR ( ( egf AND ( ( ( erbb1 AND erbb2 ) ) ) ) AND NOT ( shp1d ) ) OR ( ( epr AND ( ( ( erbb1 AND erbb2 ) ) ) ) AND NOT ( shp1d ) ) raf1 = ( ( ras AND ( ( ( csrc ) ) ) ) AND NOT ( aktd ) ) OR ( ( pak1 AND ( ( ( ras ) ) ) ) AND NOT ( aktd ) ) raccdc42 = ( vav2 ) OR ( sos1esp8e3b1 ) creb = ( p90rsk ) OR ( mk2 ) stat1 = ( erbb11 AND ( ( ( csrc ) ) ) ) mkk3 = ( mlk3 ) rntre = ( esp8r AND ( ( ( erbb11 ) ) ) ) mek12 = ( mekk1 ) OR ( raf1 ) pi3k = ( erbb13 AND ( ( ( pi3kr ) ) ) ) OR ( erbb34 AND ( ( ( pi3kr ) ) ) ) OR ( erbb23 AND ( ( ( pi3kr ) ) ) ) OR ( pi3kr AND ( ( ( gab1 ) ) ) ) OR ( ras AND ( ( ( pi3kr ) ) ) ) tsc1_tsc2 = NOT ( ( akt ) ) ship2d = ( ship2 ) vav2 = ( erbb11 AND ( ( ( pip3 ) ) ) ) OR ( pi34p2 AND ( ( ( erbb11 ) ) ) ) gab1 = ( pip3 ) OR ( erbb11 ) OR ( grb2 ) mtor_rap = ( rheb AND ( ( ( mtorr ) ) ) ) gsk3 = NOT ( ( p90rsk AND ( ( ( akt ) ) ) ) ) sos1 = ( ( sos1r AND ( ( ( grb2 ) ) ) ) AND NOT ( p90rskerk12d ) ) rheb = NOT ( ( tsc1_tsc2 ) ) ccbl = ( erbb11 ) erbb23 = ( btc AND ( ( ( erbb3 AND erbb2 ) ) ) ) OR ( nrg2b AND ( ( ( erbb3 AND erbb2 ) ) ) ) OR ( nrg1a AND ( ( ( erbb3 AND erbb2 ) ) ) ) OR ( bir AND ( ( ( erbb3 AND erbb2 ) ) ) ) OR ( epr AND ( ( ( erbb3 AND erbb2 ) ) ) ) OR ( nrg1b AND ( ( ( erbb3 AND erbb2 ) ) ) ) mekk1 = ( raccdc42 ) mlk3 = ( raccdc42 ) p70s6_2 = ( pdk1 AND ( ( ( mtor_rap AND p70s6_1 ) ) ) ) nck = ( erbb44 ) OR ( erbb11 ) OR ( erbb14 ) mkk6 = ( mlk3 ) pak1 = ( nck AND ( ( ( raccdc42 ) ) ) ) OR ( grb2 AND ( ( ( raccdc42 ) ) ) ) pro_apoptotic = ( bad ) erbb34 = ( ( nrg1a AND ( ( ( erbb3 AND erbb4 ) ) ) ) AND NOT ( erbb2 ) ) OR ( ( nrg2b AND ( ( ( erbb3 AND erbb4 ) ) ) ) AND NOT ( erbb2 ) ) OR ( ( nrg2a AND ( ( ( erbb3 AND erbb4 ) ) ) ) AND NOT ( erbb2 ) ) OR ( ( nrg1b AND ( ( ( erbb3 AND erbb4 ) ) ) ) AND NOT ( erbb2 ) ) mekk4 = ( raccdc42 ) shp1d = ( shp1 ) erk12 = ( mek12 ) limk1 = ( pak1 ) rab5a = ( ( rin1 ) AND NOT ( rntre ) ) elk1 = ( ( nucerk12 ) AND NOT ( pp2b ) ) pip3 = ( ( ( pi3k ) AND NOT ( ship2d ) ) AND NOT ( ptend ) ) erbb11 = ( ( ( btc AND ( ( ( NOT endocyt_degrad ) ) OR ( ( erbb1 ) ) ) ) AND NOT ( shp1d ) ) OR ( erbb1 AND ( ( ( NOT endocyt_degrad ) ) ) ) OR ( ( ar AND ( ( ( erbb1 ) ) OR ( ( NOT endocyt_degrad ) ) ) ) AND NOT ( shp1d ) ) OR ( ( egf AND ( ( ( erbb1 ) ) OR ( ( NOT endocyt_degrad ) ) ) ) AND NOT ( shp1d ) ) OR ( ( epr AND ( ( ( erbb1 ) ) OR ( ( NOT endocyt_degrad ) ) ) ) AND NOT ( shp1d ) ) OR ( ( tgfa AND ( ( ( NOT endocyt_degrad ) ) OR ( ( erbb1 ) ) ) ) AND NOT ( shp1d ) ) OR ( ( bir AND ( ( ( erbb1 ) ) OR ( ( NOT endocyt_degrad ) ) ) ) AND NOT ( shp1d ) ) OR ( shp1d AND ( ( ( NOT endocyt_degrad ) ) ) ) OR ( ( hbegf AND ( ( ( erbb1 ) ) OR ( ( NOT endocyt_degrad ) ) ) ) AND NOT ( shp1d ) ) ) OR NOT ( epr OR hbegf OR endocyt_degrad OR ar OR erbb1 OR shp1d OR tgfa OR egf OR btc OR bir ) erbb44 = ( btc AND ( ( ( erbb4 ) ) ) ) OR ( nrg2b AND ( ( ( erbb4 ) ) ) ) OR ( nrg1a AND ( ( ( erbb4 ) ) ) ) OR ( nrg4 AND ( ( ( erbb4 ) ) ) ) OR ( bir AND ( ( ( erbb4 ) ) ) ) OR ( nrg3 AND ( ( ( erbb4 ) ) ) ) OR ( nrg1b AND ( ( ( erbb4 ) ) ) ) pkc = ( pdk1 AND ( ( ( dag AND ca ) ) ) ) shc = ( erbb44 ) OR ( erbb11 ) OR ( erbb24 ) OR ( erbb13 ) OR ( erbb12 ) OR ( erbb23 ) OR ( erbb34 ) OR ( erbb14 ) ap1 = ( cfos AND ( ( ( cjun ) ) ) ) plcg = ( erbb11 ) erbb13 = ( ( ( nrg1a AND ( ( ( erbb3 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( tgfa AND ( ( ( erbb3 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( btc AND ( ( ( erbb3 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( nrg2a AND ( ( ( erbb3 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ar AND ( ( ( erbb3 AND erbb1 ) ) ) ) AND NOT ( shp1d ) ) OR ( ( ( egf AND ( ( ( erbb3 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( epr AND ( ( ( erbb3 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( nrg1b AND ( ( ( erbb3 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) stat5 = ( erbb24 AND ( ( ( csrc ) ) ) ) OR ( erbb11 AND ( ( ( csrc ) ) ) ) p90rskerk12d = ( p90rsk AND ( ( ( erk12 ) ) ) ) stat3 = ( erbb11 AND ( ( ( csrc ) ) ) ) aktd = ( akt ) p70s6_1 = ( jnk ) OR ( erk12 ) shp2 = ( gab1 ) cmyc = ( ( nucerk12 ) AND NOT ( gsk3 ) ) endocyt_degrad = ( ccbl AND ( ( ( rab5a ) ) ) ) grb2 = ( erbb11 ) OR ( erbb44 ) OR ( erbb13 ) OR ( erbb24 ) OR ( erbb23 ) OR ( erbb12 ) OR ( erbb34 ) OR ( erbb14 ) OR ( shc ) rin1 = ( ras ) cfos = ( ( p90rsk AND ( ( ( erk12 ) ) ) ) AND NOT ( pp2a ) ) OR ( ( jnk ) AND NOT ( pp2a ) ) akt = ( ( pdk1 AND ( ( ( pip3 AND mtor_ric ) ) ) ) AND NOT ( pp2a ) ) OR ( ( pi34p2 AND ( ( ( mtor_ric AND pdk1 ) ) ) ) AND NOT ( pp2a ) ) nucerk12 = ( ( erk12 ) AND NOT ( mkp ) ) mk2 = ( p38 ) ptend = ( pten ) rasgap = ( ( gab1 ) AND NOT ( shp2 ) ) actinreorg = ( limk1 ) p38 = ( mkk4 ) OR ( mkk3 ) OR ( mkk6 ) erbb24 = ( nrg1a AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( btc AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( nrg2b AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( nrg2a AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( nrg4 AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( nrg3 AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( egf AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( epr AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( nrg1b AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( tgfa AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( bir AND ( ( ( erbb4 AND erbb2 ) ) ) ) OR ( hbegf AND ( ( ( erbb4 AND erbb2 ) ) ) ) dag = ( plcg ) bad = NOT ( ( pak1 AND ( ( ( akt ) ) ) ) ) ip3 = ( plcg ) cjun = ( jnk ) p90rsk = ( erk12 AND ( ( ( pdk1 ) ) ) ) mtor_ric = ( mtorr ) jnk = ( mkk7 AND ( ( ( mkk4 ) ) ) ) sos1esp8e3b1 = ( sos1r AND ( ( ( pi3kr AND pip3 AND esp8r ) ) ) ) hsp27 = ( mk2 ) shp1 = ( erbb11 ) pi34p2 = ( ( ship2d AND ( ( ( pi3k ) ) ) ) AND NOT ( ptend ) ) ca = ( ip3 ) erbb14 = ( ( ( nrg2b AND ( ( ( erbb4 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( nrg1a AND ( ( ( erbb4 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( tgfa AND ( ( ( erbb4 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( nrg2a AND ( ( ( erbb4 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( nrg4 AND ( ( ( erbb4 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( egf AND ( ( ( erbb4 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( epr AND ( ( ( erbb4 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) OR ( ( ( nrg1b AND ( ( ( erbb4 AND erbb1 ) ) ) ) AND NOT ( erbb2 ) ) AND NOT ( shp1d ) ) ras = ( ( sos1 ) AND NOT ( rasgap ) )
Mathematical Modelling of Cell-Fate Decision in Response to Death Receptor Engagement Laurence Calzone1,2,3, Laurent Tournier1,2,3, Simon Fourquet1,2,3, Denis Thieffry4,5, Boris Zhivotovsky6, Emmanuel Barillot1,2,3", Andrei Zinovyev1,2,3" 1 Institut Curie, Paris, France, 2 Ecole des Mines ParisTech, Paris, France, 3 INSERM U900, Paris, France, 4 TAGC – INSERM U928 & Universite´ de la Me´diterrane´e, Marseille, France, 5 CONTRAINTES Project, INRIA Paris-Rocquencourt, France, 6 Karolinska Institutet, Stockholm, Sweden Abstract Cytokines such as TNF and FASL can trigger death or survival depending on cell lines and cellular conditions. The mechanistic details of how a cell chooses among these cell fates are still unclear. The understanding of these processes is important since they are altered in many diseases, including cancer and AIDS. Using a discrete modelling formalism, we present a mathematical model of cell fate decision recapitulating and integrating the most consistent facts extracted from the literature. This model provides a generic high-level view of the interplays between NFkB pro-survival pathway, RIP1- dependent necrosis, and the apoptosis pathway in response to death receptor-mediated signals. Wild type simulations demonstrate robust segregation of cellular responses to receptor engagement. Model simulations recapitulate documented phenotypes of protein knockdowns and enable the prediction of the effects of novel knockdowns. In silico experiments simulate the outcomes following ligand removal at different stages, and suggest experimental approaches to further validate and specialise the model for particular cell types. We also propose a reduced conceptual model implementing the logic of the decision process. This analysis gives specific predictions regarding cross-talks between the three pathways, as well as the transient role of RIP1 protein in necrosis, and confirms the phenotypes of novel perturbations. Our wild type and mutant simulations provide novel insights to restore apoptosis in defective cells. The model analysis expands our understanding of how cell fate decision is made. Moreover, our current model can be used to assess contradictory or controversial data from the literature. Ultimately, it constitutes a valuable reasoning tool to delineate novel experiments. Citation: Calzone L, Tournier L, Fourquet S, Thieffry D, Zhivotovsky B, et al. (2010) Mathematical Modelling of Cell-Fate Decision in Response to Death Receptor Engagement. PLoS Comput Biol 6(3): e1000702. doi:10.1371/journal.pcbi.1000702 Editor: Rama Ranganathan, UT Southwestern Medical Center, United States of America Received August 25, 2009; Accepted February 2, 2010; Published March 5, 2010 Copyright: 2010 Calzone et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work is supported by the APO-SYS EU FP7 project. LC, LT, SF, EB and AZ are members of the team ‘‘Systems Biology of Cancer,’’ Equipe labellise´e par la Ligue Nationale Contre le Cancer. The study was also funded by the Projet Incitatif Collaboratif ‘‘Bioinformatics and Biostatistics of Cancer’’ at Institut Curie. Work in BZ’s laboratory is supported by the Swedish and Stockholm Cancer Societies, the Swedish Childhood Cancer Foundation, the Swedish Research Council, the EC-FP-6 (Oncodeath and Chemores) programs. DT acknowledges the support from the Belgian Federal Science Policy Office: IUAP P6/25 (BioMaGNet, Bioinformatics and Modeling: from Genomes to Networks, 2007–2011). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. E-mail: Laurence.Calzone@curie.fr " These authors are joint senior authors on this work. Introduction Engagement of TNF or FAS receptors can trigger cell death by apoptosis or necrosis, or yet lead to the activation of pro-survival signalling pathway(s), such as NFkB. Apoptosis represents a tightly controlled mechanism of cell death that is triggered by internal or external death signals or stresses. This mechanism involves a sequence of biochemical and morphological changes resulting in the vacuolisation of cellular content, followed by its phagocyte- mediated elimination. This physiological process regulates cell homeostasis, development, and clearance of damaged, virus- infected or cancer cells. In contrast, pathological necrosis results in plasma membrane disruption and release of intracellular content that can trigger inflammation in the neighbouring tissues. Long seen as an accidental cell death, necrosis also appears regulated and possibly involved in the clearance of virus-infected or cancer cells that escaped apoptosis [1]. Dynamical modelling of the regulatory network controlling apoptosis, non-apoptotic cell death and survival pathways could help identify how and under which conditions the cell chooses between different types of cellular deaths or survival. Moreover, modelling could suggest ways to re-establish the apoptotic death when it is altered, or yet to trigger necrosis in apoptosis-resistant cells. The decision process involves several signalling pathways, as well as multiple positive and negative regulatory circuits. Mathematical modelling provides a rigorous integrative approach to understand and analyse the dynamical behaviours of such complex systems. Published models of cell death control usually focus on one death pathway only, such as the apoptotic extrinsic or intrinsic pathways [2,3,4]. A few studies integrate both pathways [5], some show that the concentration of specific components contribute to the decision between death and survival [6,7] while other studies investigate the balance between proliferation, survival or apoptosis in specific cell types along with the role of key components in these pathways [8], but no mathematical models including necrosis are available yet. Moreover, we still lack models properly demonstrat- ing how cellular conditions determine the choice between necrosis, PLoS Computational Biology \| www.ploscompbiol.org 1 March 2010 \| Volume 6 \| Issue 3 \| e1000702 apoptosis and survival, and how and to what extent conversions are allowed between these fates. Our study aims at identifying determinants of this cell fate decision process. The three main phenotypes considered are apoptosis, non-apoptotic cell death (which mainly covers necrosis) and survival. Although the pathways leading to these three phenotypes are highly intertwined, we first describe them separately hereafter, concentrating on the players we chose to include in each pathway. Summarised in Figure 1A, this description does not intend to be exhaustive, but rather aims at covering the most established processes participating in cell fate decision. Caspase-dependent apoptotic cell death Only the apoptotic caspase-dependent pathway downstream of FAS and TNF receptors is considered here. Upon engagement by their ligands and in the presence of FADD (FAS-Associated protein with Death Domain), a specific Death Inducible Signalling Complex (DISC-FAS or DISC-TNF in Figure 1) forms and recruits pro-caspase-8. This leads to the cleavage and activation of caspase-8 (CASP8). In the so-called type II cells, CASP8 triggers the intrinsic or mitochondria-dependent apoptotic pathway, which also responds to DNA damage directly through the p53-mediated chain of events (not detailed here). CASP8 cleaves the BH3-only protein BID (not explicitly included in the diagram), which can then translocate to the mitochondria outer membrane. There, BID competes with anti-apoptotic BH3 family members such as BCL2 for interaction with the proteins BAX or BAK (BAX will stand here for both BAX and BAK). Consequently, oligomerisa- tion of BAX results in mitochondrial outer membrane permea- bilisation (MOMP) and the release of pro-apoptotic factors. Once released to the cytosol, cytochrome c (Cyt_c) interacts with APAF1, recruiting pro-caspase-9. In presence of dATP, this enables the assembly of the apoptosome complex (referred to as ‘Apoptosome’ in Figure 1A, lumping APAF1 and pro-caspase-9), responsible for caspase-9 activation, followed by the proteolytic activation of pro-caspase-3 (CASP3) [9]. By cleavage of specific targets, the executioner caspases (CASP3 in the model) are responsible for major biochemical and morphological changes characteristic of apoptosis. SMAC/DIABLO (SMAC) is released during MOMP to the cytosol, where it is able to inactivate the caspase inhibitor XIAP [10]. CASP3 also participates in a positive circuit by inducing the activation of CASP8 [11,12]. In type I cells, CASP8 directly cleaves and activates executioner caspases such as CASP3 (not described). Non-apoptotic cell death (NonACD) Here, we consider mainly a mode of cell death with morphological features of necrosis, which occurs when apoptosis is impeded in cells treated with cytokines [13] or in some specific cell lines such as L929 cells when exposed to TNF [14]. In primary T cells, if caspases are inhibited, activation of TNFR or FAS causes necrosis via a pathway that requires the protein RIP1 and its kinase activity (RIP1K) [13]. This RIP1-dependent cytokine- induced necrotic death defines necroptosis [15,16]. A genetic screen recently identified other genes necessary for this type of cell death [17]. However, a precise description of this pathway is still lacking. Reactive oxygen species (ROS) were proposed to be involved downstream of RIP1 [18]. ROS are also thought to play a key role in the control of mitochondria permeability transition (MPT), since they are produced by damaged mitochondria and can oxidize mitochondrial components, thus favouring MPT [19,20,21]. Furthermore, the role of mitochondria in necrosis is highlighted through the involvement of MPT, which causes a fatal drop in ATP level and leads to necrotic death. Indeed, MPT results from the inhibition of ATP/ADP exchange at the level of mitochondrial membranes, or from the inhibition of oxidative phosphorylation decreasing cellular ATP level and causing energy failure [21,22]. Although there is evidence that necrosis is also triggered by TNF- and FAS-independent pathways, these are not yet considered in this study. These pathways include, for example, calpain-mediated cleavage of AIF followed by its nuclear translocation [23,24], or PARP-1-mediated NAD+ depletion [24,25]. Survival pathway NFkB represents a family of transcription factors that play a central role in inflammation, immune response to infections and cancer development [26]. The ubiquitination of RIP1 at lysine 63 by cIAP leads to the activation of IKK and ultimately that of NFkB [27]. In different cell types, especially in tumour cell lines, activation of NFkB inhibits TNF-induced cell death [28]. This effect is mediated by NFkB target genes: cFLIP inhibits recruitment of CASP8 by FADD [29]; anti-apoptotic BCL2 family members inhibit MOMP and MPT [30,31,32]; XIAP acts as a caspase inhibitor [33]; and ferritin heavy chain [34] or mitochondrial SOD2 [35] decrease ROS levels (these mechanisms are represented in Figure 1A by a direct inhibitory arrow from NFkB to ROS). For the sake of simplicity, other NFkB target genes that are known to inhibit TNF-induced apoptosis are provisionally omitted in the model (e.g., A20; cf. [36,37]). Our goal here is to provide a simplified but yet rigorous model of the mechanisms underlying cell fate selection in response to the engagement of FAS and TNF receptors. We have proceeded in several steps. First, we have assembled a regulatory network covering the main experimental data. Species and interactions were selected on the basis of an extensive literature search and integrated in the form of a diagram or ‘‘regulatory graph’’. This diagram is then translated into a dynamical model. Our analysis initially focuses on the determination of the asymptotic properties of the system for different conditions, which correspond to the possible phenotypes that the model can account for. Next, we Author Summary Activation of death receptors (TNFR and Fas) can trigger either survival or cell death according to the cell type and the cellular conditions. In other words, the same signal can have antagonist responses. On one hand, the cell can survive by activating the NFkB signalling pathway. On the other hand, it can die by apoptosis or necrosis. Apoptosis is a suicide mechanism, i.e., an orchestrated way to disrupt cellular components and pack them into specialized vesicles that can be easily removed from the environment, whereas necrosis is a type of death that involves release of intracellular components in the surrounding tissues, possibly causing inflammatory response and severe injury. We, biologists and theoreticians, have recapitulated and integrated known biological data from the literature into an influence diagram describing the molecular events leading to each possible outcome. The diagram has been translated into a dynamical Boolean model. Simulations of wild type, mutant cells and drug treatments qualitatively match current data, and predict several novel mutant phenotypes, along with general characteristics of the cell fate decision mechanism: transient activation of some key proteins in necrosis, mutual inhibitory cross-talks between the three pathways. Our model can further be used to assess contradictory data and address specific biological questions through in silico experiments. Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 2 March 2010 \| Volume 6 \| Issue 3 \| e1000702 TNF FASL TNFR DISC-TNF FADD DISC-FAS RIP1 CASP8 RIP1ub RIP1K cFLIP IKK BAX cIAP MOMP ATP CASP3 NFkB ROS BCL2 Cyt_c Apoptosome SMAC XIAP Survival NonACD Apoptosis MPT TNF FASL RIP1 CASP8 cIAP MOMP ATP CASP3 NFkB ROS Survival NonACD Apoptosis MPT A B Figure 1. Regulatory networks of cell-fate decision. (A) Master model: the molecular interactions between the main components intervening in the three pathways are described as an influence graph leading to the three cell fates: survival, non-apoptotic cell death and apoptosis. Dashed lines denote the pathway borders. (B) The corresponding reduced model. doi:10.1371/journal.pcbi.1000702.g001 Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 3 March 2010 \| Volume 6 \| Issue 3 \| e1000702 analyse the different trajectories leading to each phenotype in the wild type and mutant situations. As quantitative data are still largely lacking for this system, we use a qualitative logical formalism and its implementation in the GINsim software [38]. As we shall see, proper model analysis can assess where and when cell fate decisions are made, provide novel insight concerning the general structure of the network, in particular concerning the occurrence of cross-talks between pathways, and predict novel mutant phenotypes and component activity patterns. Results The information gathered in the literature has been integrated into a regulatory graph (Figure 1A). Our selection of molecular players (nodes of the graph) is based on our current understanding of the molecular mechanisms of cell fate decision. Documented positive or negative effects among pairs of components are repre- sented by signed arcs (Figure 1). Each node or arc is annotated and associated with bibliographical references in the model file, as well as in the accompanying documentation (cf. supplementary Text S1). Our current model encompasses three main pathways (Figure 1A): the activation of a caspase-dependent apoptosis pathway, the RIP1- kinase-dependent pathway leading to necrosis, and the activation of the transcription factor NFkB with pro-survival effects. Other pathways involved in cell death, such as growth factor receptors or other RTK (receptor tyrosine kinase), TLR (Toll-like receptor), and MAPK signalling pathways have been provisionally left out. We defined specific ‘‘markers’’ or ‘‘read-outs’’ of the three cell fates. When caspase-3 is activated, the cells are considered to be apoptotic; when MPT occurs and the level of ATP drops dramatically, the cells enter non-apoptotic cell death; finally, when NFkB is activated, we consider that cells survive. Active survival is thus monitored here by the activation of NFkB pathway, in accordance with many studies, as opposed to passive survival, which occurs when no death signals are engaged. In reality, other pathways can interact downstream of NFkB activation, which can reinforce or shut off survival. For now, passive survival will be referred to as the ‘naı¨ve’ state, i.e. the stable states with none of the three pathways activated. Cross-talks between the three pathways As mentioned before, the pathways are highly intertwined (Figure 1A). For instance, the survival pathway interacts with the apoptotic pathway at different points: cFLIP inhibits CASP8; BCL2 blocks mitochondria pore opening through inhibition of BAX (and BAK, implicitly represented in our model); and XIAP blocks the activity of both CASP9 in the apoptosome and CASP3. Conversely, the apoptotic pathway negatively regulates NFkB activity through the CASP8-mediated cleavage and inactivation of RIP1 upstream of NFkB. Because RIP1 operates upstream of the necrotic pathway, this regulation also impacts necrosis. Moreover, for the apoptosome to form, dATP (or/and ATP) is (/are) needed. Consequently, in our model, when necrosis occurs, ATP pro- duction drops, terminating apoptosis. Regarding the influence of the survival pathway on the necrotic one, NFkB tentatively stimulates the production of anti-oxidants that shuts off ROS level. Both the necrotic and the apoptotic pathways are able to interact with the survival pathway through the action of cIAP1/2, referred to as cIAP in our model. More precisely, cIAP1 and 2 are E3- ubiquitin ligases that target RIP1 for K63-linked polyubiquitina- tion. They are essential intermediates in the activation of NFkB downstream of TNF receptor [27]. Some synthetic molecules that mimic the N-terminal of SMAC IAP-interacting motif have been shown to induce cIAP1/2 auto-ubiquitination and subsequent proteasomal degradation, thus blocking TNF-dependent NFkB activation [39,40]. Tentatively, mitochondrial permeabilization in the apoptosis or necrosis pathways could block TNF-induced NFkB activation through the release of SMAC into the cytosol thereby causing the inhibition of c-IAP1/2. Initially, cIAP was not included in the model, which led to discrepancies between model simulations and published data. Indeed, in FADD or CASP8 deletion mutants, our preliminary model predicted only survival (not shown), whereas both necrotic and survival phenotypes were observed in experi- ments in the presence of TNF or FAS [41,42,43]. The consideration of the path MOMP)SMAC =\|cIAP)NFkB enabled us to eliminate the discrepancies, both necrotic and survival phenotypes were then obtained in the simulations, although it does not preclude other mechanisms. Dynamical logical model of cell fate decision To transform the static map shown in Figure 1A into a dynamical model accounting for the different scenarios or set of events leading to one of the three phenotypes, we have to define proper dynamical rules. Since there is little reliable quantitative information on reaction kinetics and cellular conditions leading to one or another phenotype, these rules must be sufficiently flexible to cover all possible scenarios following death receptor activation. The nodes encompassed in the map represent different things: simple biochemical components (receptors, ligands, proteins or metabolites): TNF, FASL, TNFR, FADD, FLIP, CASP8, RIP1, IKK, NFkB, cIAP, BCL2, BAX, Cyt_c, SMAC, ROS, XIAP, CASP3, ATP); specific modified forms of proteins: RIP1K (active RIP1 kinase), RIP1ub (K63-ubiquitinated RIP1); complexes of proteins: DISC-TNF (corresponding to TRADD, TRAF2, FADD, proCASP8), DISC-FAS (corresponding to FAS, FADD, pro- CASP8), apoptosome; cellular processes: MPT (Mitochondrial Permeability Transition) and MOMP (Mitochondria Outer Membrane Permeabilisation). A Boolean variable is associated with each of these nodes, which can take only two logical values: ‘‘0’’ (false), denoting the absence or inactivity of the corresponding component, and ‘‘1’’ (true), denoting its active state. Furthermore, a logical rule (or function) is assigned to each node, defining how the different inputs (incoming arrows) combine to control its level of activation. For example, CASP8 can be activated (its value is set to ‘‘1’’) by DISC-TNF or DISC-FAS, but only in the absence of cFLIP protein. This can be encoded into a logical rule as follows: (DISC-TNF OR DISC-FAS) AND NOT cFLIP. Several nodes correspond to simple inputs (TNF, FASL and FADD). Their initial values are kept fixed during most simulations. On the basis of the regulatory graph and the associated logical rules, we then proceeded with the exploration of the dynamical properties of our model. We first focused on the identification of all stable states and on their biological interpretation. Then, we investigated the reachability of these stable states for different initial conditions, for both wild type and mutant cases. Details on the computational methods used are provided in the Methods section and in the supplementary Text S1. The logical model has been filed in the BioModels database with the reference MODEL0912180000. Identification of stable states Analysis of the cell fate decision model (Figure 1A) led to the identification of the 27 stable states showed in Figure 2. These stable states are the sole attractors of the system under the asynchronous assumption (see Methods). They thus represent all Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 4 March 2010 \| Volume 6 \| Issue 3 \| e1000702 possible cellular asymptotical states. In other words, whatever the initial conditions, a wild type cell will end up in one of these states if we wait long enough. A closer look reveals that several stable states correspond to each cellular fate, with few differing (minor) component values. This consideration led us to address the following questions: (i) Does a cluster structure exist in the distribution of internal stable states of the network? (ii) If so, in these clusters, could the corresponding states be interpreted as slightly different realisations of the same cellular phenotype? (iii) What would be the char- acteristic signature of each cluster (conserved values of variables inside each cluster)? (iv) What is the number of independent variables defining the internal stable states of the network? Standard statistical methods and clustering algorithms are applied to group stable states. Figure 3 displays a projection of the internal (without inputs and outputs) stable values into the 2D space defined by the first two principal components of the corresponding distribution. The first two principal components explain 52% and 20% of the total variation, respectively (Table S1). The first principal component can be associated with the activity of NFkB pathway, while the second is determined mainly by ATP and MPT status. These factors do appear to determine the principal (independent) degrees of freedom for the internal state of the network. A typical trajectory starting from any set of initial conditions will thus quickly converge to the region under the influence of these three components. The 2-D graph (Figure 3) reveals a striking separation of the stable states into 4 clusters: one cluster (blue circles) devoid of significant activity, which we call the ‘naı¨ve’ state; one cluster (green rhombs) corresponding to survival, with NFkB pathway activated; and two clusters corresponding to the two different modalities of cell death, apoptosis (orange squares) and necrosis (purple triangles). K-means clustering using Euclidean and L1 distance perfectly reproduces these groupings, demonstrating that the compact groups easily distinguishable on the PCA plot indeed represent well-separated clusters in the original multidimensional space. Some interesting conclusions and predictions can be drawn just by looking at the values of each component in each phenotypical group. For instance, in the necrotic (purple) stable states, when FADD is present (i.e. normal wild type conditions), RIP1 is always OFF and CASP8 ON, even though RIP1 is required and CASP8 is dispensable for necrosis to occur. This observation suggests a transient activation of RIP1 protein when switching on the necrotic pathway in response to death receptors. However, inactivation or cleavage of RIP1 is not per se a prerequisite for necrosis, nor is CASP8 activation. Indeed, for the mutant models in which CASP8 activation is impaired, such as CASP8 or FADD deletion, there exist necrotic attractors with RIP1 = 1 (not shown). Our model thus predicts that TNF-induced necrosis could occur despite CASP8-mediated cleavage of RIP1. An attractive experimental model in which such a transient activation of RIP1 could be tested is the mouse fibrosarcoma cell line L929. Upon TNF exposure, these cells die by necrosis [44] and they have a functional CASP8 [45], which is cleaved during TNF-induced cell death [46]. Since RIP1 controls both the activation of NFkB and the level of ROS, the same transient behaviour could be expected for the survival phenotype. However, this is not observed with our model, as RIP1 = 1 in all survival (green) stable states. This can be explained by the regulatory circuit involving RIP1 and NFkB, which is not functional in necrosis. Indeed, when NFkB is active, it can mediate the synthesis of cFLIP, an inhibitor of CASP8, itself an inhibitor of RIP1. Moreover, RIP1 is part of the positive circuit that keeps NFkB ON. The model thus suggests that a sustained RIP1 activity is needed for survival. How could this hypothesis be experimentally assessed? If an experiment would reveal that RIP1 is only transiently activated upon death receptor activation, while NFkB remains activated, the model would be contradicted. In that case, one would need to look for other components capable to maintain NFkB active. Model reduction and dynamical analysis The stable state analysis described above provides a first validation of the master model presented in Figure 1A. On this basis, we performed a more detailed analysis of the dynamics of the system. We investigated which cell fates (stable states) can be reached from specific initial conditions. Given a set of reachable stable states, can we say something about their relative ‘‘attractivity’’? To avoid the combinatorial explosion of the number of states to consider, we have reduced the number of components while preserving the relevant dynamical properties of the master model (Figure 1B). Details of how this reduction is performed are provided in the Methods section. The resulting network en- compasses 11 components. The corresponding Boolean rules are listed in Table 1. The size of the transition graph (211 = 2048) is now amenable to a detailed dynamical analysis. First, the set of attractors of this reduced model is identified: 13 attractors are obtained, which are all stable states matching those found for the master model when the input variable FADD = 1. Recall that, in Figure 2. Stable states of the master model. values 0 and 1 are represented by empty and full circles, respectively.To compare these stable states to those of the simplified model, the values of FADD = 0 need to be deleted since FADD is not explicitly presented in the reduced model. The first six rows (with NonACD = 0, Apoptosis = 0, Survival = 0) correspond to the ‘‘naı¨ve’’ state. The following five rows (with NonACD = 0, Apoptosis = 0, Survival = 1) correspond to ‘survival’. The following eight rows (with NonACD = 0, Apoptosis = 1, Survival = 0) correspond to ‘apoptosis’. The last eight rows (with NonACD = 1, Apoptosis = 0, Survival = 0) correspond to ‘necrosis’. doi:10.1371/journal.pcbi.1000702.g002 Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 5 March 2010 \| Volume 6 \| Issue 3 \| e1000702 the master model, both values of FADD were considered leading to 13 stable states with FADD = 1 and 14 stable states with FADD = 0. Using the theoretical results presented in [47] (mainly Theorem 1), we can conclude that the 13 stable states of Figure 2 are the only attractors of the master model when FADD = 1. Logical definition of ‘‘mutants’’ Based on the reduced model defined in Figure 1B and Table 1, we derived 15 model variants representing biologically plausible perturbations. We will abusively use the term ‘‘mutant’’ to refer to these variants, even though they do not all technically correspond to mutations. For instance, the ‘‘z-VAD mutant’’ simulates the effect of caspase inhibitor z-VAD-fmk. Each mutant simulation consists in a local alteration of our reduced model, which can be qualitatively compared with results reported in the literature. In the Boolean framework, such alterations amount to force the level of certain variables to zero in the case of a gene deletion, or to one in the case of a component over-expression. As we are using the reduced version of the master model, some perturbed components may be hidden by the reduction process. In such cases, we change the logical rules of their (possibly indirect) targets to take into account their effects. Table 2 lists the 15 variants of the model considered, along with the modified logical rules, the expected effects on the phenotypes according to the literature, and short descriptions of simulation results. Computation of reachable attractors The references provided in Table 2 cover experiments performed on different cell types and with different experimental conditions. In contrast, our cell fate model represents mechanisms of cell fate decision in a generic cell, qualitatively recapitulating a wide variety of cellular contexts. Given a cellular system, its response to the activation of death receptors is determined by the logical rules. However, the generic model presented here considers equally all possible contexts and regulatory combinations. To evaluate the relative likelihood of having a particular response in a randomly chosen cellular system, we count the relative number of possible trajectories from the stimulated ‘naı¨ve’ state to a given phenotype. This analysis gives an idea on what is possible or forbidden in a ‘generic’ cell. Using dedicated methods and software [48], the set of reachable stable states is calculated, starting from selected physiological initial conditions, for the wild type and mutant models. The physiological state is defined by fixing the variables ATP and cIAP Figure 3. Projection of the internal stable state values onto the first two principal components. Four clusters are formed: the ‘naı¨ve’ cluster (round light blue circles) at the center; the survival cluster (green rhombs) characterised by high level of NFkB and related (see Table S1 for details); the apoptosis cluster (orange squares) characterised by high levels of MOMP, Cyt_c, SMAC and ATP; and the non-apoptotic cell death - or necrosis - cluster (purple triangles) with high levels of MPT, ROS, MOMP, Cyt_c and SMAC. In the latter three clusters, there are three subgroups of stable states which correspond to the different inputs of the system: top stable states correspond to high TNF and FAS signals, middle stable states have either one or the other signal while the lower ones have no inputs. As for the naive cluster, the two sets of stable states differ by their cIAP value. Inputs and outputs are not included in the stable state binary vector. doi:10.1371/journal.pcbi.1000702.g003 Table 1. Logical rules associated with the wild type reduced model. Node Logical update rule TNF ( INPUT NODE) FAS ( INPUT NODE) RIP19 NOT C8 AND (TNF OR FAS) NFkB9 (cIAP AND RIP1) AND NOT C3 C89 (TNF OR FAS OR C3) AND NOT NFkB cIAP9 (NFkB OR cIAP) AND NOT MOMP ATP9 NOT MPT C39 ATP AND MOMP AND NOT NFkB ROS9 NOT NFkB AND (RIP1 OR MPT) MOMP9 MPT OR (C8 AND NOT NFkB) MPT9 ROS AND NOT NFkB doi:10.1371/journal.pcbi.1000702.t001 Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 6 March 2010 \| Volume 6 \| Issue 3 \| e1000702 to ‘‘1’’ and all the other ones to ‘‘0’’. Different combinations of TNF and FASL are considered. The probability to reach each phenotype is computed as a fraction of the paths in the graph that link physiological initial conditions to each cell fate (Figure 4 for reduced model and Figure S4 for master model). As expected, the absence of TNF and FASL can only lead to the ‘naı¨ve’ state (except of course when caspase-8 or NFkB are over- expressed, for obvious reasons). This means that the inputs (TNF and FASL) are needed for the system to effectively trigger the decision process. This was expected since intracellular death signals are not yet taken into account in the model. When TNF = 1 (Figure 4, right panel), for the wild type system, we observe that three outcomes or phenotypes are reachable from the initial condition, with different probabilities: ,10% for necrosis, ,30% for active survival and ,60% for apoptosis. Although these probabilities cannot be directly compared with experimental results, they become useful when comparing different variants of the model. For instance, an increase (or decrease) of a phenotype probability between the wild type and a particular mutant can be interpreted as a gain (or a loss) of effectiveness of the corresponding pathway in that mutant. Such qualitative observa- tions can then be confronted with published experimental results, which are summarized in the last column of Table 2. In most cases, activation of FASL and TNF lead to similar effects (not shown), except in the case of the FADD deletion mutant (Figure 5). As expected, this mutant cannot lead to cell death when FASL is ON. In contrast, necrosis is still possible in the presence of TNF. Interestingly, TNF-induced apoptosis is expected to be blocked [49] whereas the qualitative analysis shows that apoptosis is actually reachable in the model. Nevertheless, the probability of this phenotype is very low (around 0.61%), which means that very few trajectories may lead to apoptosis and it would thus be difficult to obtain the corresponding cellular context. Variation of the duration of receptor activation and its effects In the reachability analysis presented above, the value of TNF and FASL are kept constant and therefore always ON (or always OFF) along all trajectories. These qualitative simulations are useful to characterize the asymptotic behaviour of the system when the death receptor is engaged for a sufficiently long time. The principle of ‘ligand removal’ experiments consists in characterizing the decision process when it is subject to a temporary pulse of TNF. Here, time is intrinsically discrete, meaning that the duration of TNF pulse denoted td is represented by an integer Table 2. Description of the different ‘‘mutant’’ versions of the reduced model. Name Modified rules Expected phenotypes Qualitative results Anti-oxidant ROS9=(RIP1 OR MPT) Prediction. Suppression of NFkB anti-oxidant effect leads to no change in the decision process. APAF1 deletion C39=0 APAF12/2 mouse thymocytes are not impaired in FAS-mediated apoptosis ([71]). Apoptosis disappears and replaced by the naı¨ve state. Necrosis and survival are close to the wild type case situations. BAX deletion MOMP9= MPT BAX deletion blocks FAS or TNF+CHX - induced apoptosis in some cell lines, such as HCT116 [72]. BAX deletion prevents apoptosis. BCL2 over- expression MOMP9= MPT MPT9=0 FAS induces the activation of NFkB pathway [29]. As expected, the survival and naive attractors are preserved while both death pathways are inhibited. CASP8 deletion C89=0 Caspase-8 deficient MEFs [41] or Jurkat cells [42] are resistant to FAS-mediated apoptotic cell death. Apoptosis disappears. Compared to the wild type, a slight increase of necrosis is observed, while survival becomes the main cell fate. constitutively activated CASP8 C89=1 Prediction. Over-expression of caspase-8 leads to a loss of NFkB activation. cFLIP deletion C89=TNF OR FAS OR C3 cFLIP2/2 MEFs are highly sensitive to FASL and TNF [73]. The increase of apoptosis is effectively observed in the cFLIP mutant; furthermore survival can no longer be sustained. cIAP deletion cIAP9= 0 NFkB activation in response to TNF is blocked [53]. NFkB activation is impaired, and only the apoptotic and necrotic attractors can be reached. FADD deletion C89=C3 AND NOT NFkB RIP19=NOT C8 AND TNF FADD2/2 mouse thymocytes are resistant to FAS mediated apoptosis [74]. FADD2/2 MEFs are resistant to FASL and TNF [75]. In Jurkat cells treated with TNF+CHX, apoptosis is turned into necrosis [43]. FASL signalling is blocked and the ‘naı¨ve’ attractor is the only reachable one. In response to TNF, apoptosis disappears. NFkB deletion NFkB9=0 TNF induces both apoptosis and necrosis in NF-kB p652/2 cells [76] or in IKKb2/2 fibroblasts [35]. This mutant shows a strong increase of necrosis (to be related with concomitant apoptosis/necrosis). constitutively active NFkB NFkB9=1 Prediction. Both death pathways are shut down in this mutant. RIP1 deletion RIP19=0 RIPK12/2 MEFs are hypersensitivity to TNF, no TNF-induced NFkB activation, [77]. Both survival and necrosis states become unreachable. The effect of RIP1 silencing leads to a complete loss of the decision process (apoptosis becoming the only outcome). XIAP deletion C39=ATP AND MOMP No effect on TNF-induced toxicity in XIAP2/2 MEFs [78]. Behaviour similar to wild type. z-VAD C39=0 FAS induced apoptosis is blocked, though cells can undergo death by necrosis [79]. FAS activates NFkB [80]. Induction of autophagic cell death observed [81]. The simulation of z-VAD mutant is similar to the silencing of caspase-8 (which implies that caspase-8 shut down in the model seems to have some priority over caspase-3 shutdown). z-VAD+RIP1 deletion C39=0 C89=0 RIP19=0 Upon TNF cells treated with z-VAD-fmk that are RIP-deficient cannot activate the NFkB pathway anymore and die by necrosis [13]. The conjugated effect of RIP1 deletion and caspase inhibition impedes the system to trigger any of the three pathways (the ‘naı¨ve’ state becomes the only possible outcome). doi:10.1371/journal.pcbi.1000702.t002 Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 7 March 2010 \| Volume 6 \| Issue 3 \| e1000702 number. In order to simulate each experiment, N trajectories were generated, starting from the ‘‘physiological’’ condition with TNF = 1. At time td, the value of TNF is forced to zero. The probabilities to reach the different phenotypes are then calculated as explained in the Methods section. The average probabilities, over the N computed trajectories, are represented in Figure 6, for the wild type and the 15 mutants. The purpose of this study is to investigate the dynamics of all the mutants and how they reach the various possible phenotypes for different lengths of TNF pulses. It provides a measurable way to assess the appearance or disappearance of certain phenotypes upon TNF induction. The curves of Figure 6 allow to link explicitly the graphs of Figure 4 when TNF is ON (right panels) and OFF (left panels) with the subjacent dynamics. Let us compare the wild type case and the deletion of cFLIP as an example of how to read these graphs. For early events, the two cases behave similarly as expected (up to event 3). As TNF pulse is prolonged, the apoptotic phenotype becomes more and more pronounced and strongly favoured over the survival one in the cFLIP mutant as opposed to the wild type conditions. This leads to the complete disappearance of survival in the mutant. This observation reinforces the role of cFLIP in the control of the apoptotic pathway. With the ‘ligand removal’ experiment, we can evaluate the number of steps, in the reduced model, that are needed for the cell to decide on its fate after TNF exposure. For almost all mutants and wild type case, the choice is made around step 4. This means that, after this point, even if TNF is removed, the cell has already committed to a specific fate. One surprise arises from the non-monotonic behaviour of mutants for which apoptosis is suppressed (APAF1, BAX, caspase- 8 and FADD deletions and z-VAD-fmk treatment), tentatively indicating a competition between components of the survival and necrotic pathways. Indeed several inhibitory cross-talks could explain this behaviour. These mutants also indicate the existence of an optimal TNF induction for which the maximum rate of necrosis is achieved (around step 2 in the corresponding mutants of Figure 6). A compact conceptual model To complete our study of cell fate decision, we reasoned on the simplest model of cell fate that can be deduced from the master model described above. The purpose here was to further simplify the network to obtain a formal representation of the logical core of the network. We have selected three components to represent the three cellular fates: NFkB for survival, MPT for necrosis and CASP3 for apoptosis. Based on reduction techniques and on the identification of all possible directed paths between these three components [50], a three-node diagram was deduced from the master model. In this compact model, each original path (including regulatory circuit) is represented by an arc whose sign denotes the influence of the source node on its target. All original paths and the corresponding arcs are recorded in Table 3. In some ambiguous cases (e.g. influence of MPT on CASP3 or of NFkB on MPT), the decision on the sign of the influence is based on the Boolean rules and not on the paths only. Indeed, two negative and one positive paths link NFkB to MPT. Therefore, the sign of the arc depends not only on the states of BCL2 and of ROS, both feeding onto MPT, but also on the rule controlling MPT value. Since the Figure 4. Reachability of phenotypes starting from ‘‘physiological’’ initial conditions. The colours correspond to the phenotypes as identified by the clustering algorithm (blue: ‘‘naı¨ve’’ survival state; green: survival through NFkB pathway; orange: apoptosis; purple: necrosis). Left panel: TNF = FAS = 0, right panel: TNF = 1 and FAS = 0. doi:10.1371/journal.pcbi.1000702.g004 NO INPUT TNF=1, FAS=0 FAS=1, TNF=0 Necrosis Survival Naive Naive Apoptosis Figure 5. FADD mutant breaks the symmetry of TNF and FAS- induced pathways. Activation of death receptors in FADD deletion mutant leads to different cell fates depending on the values of TNF and FAS. doi:10.1371/journal.pcbi.1000702.g005 Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 8 March 2010 \| Volume 6 \| Issue 3 \| e1000702 absence of BCL2 and the presence of ROS (Boolean ‘AND’ gate) participate in the activation of MPT, if BCL2 is active, then MPT is set to 0, even when ROS is ON. By extension, if NFkB is ON, then MPT is 0, justifying the choice for a negative influence. In the case of mutations eliminating all the negative influences, however, a positive arrow must be considered. The resulting molecular network is symmetrical: each node is self-activating and is negatively regulated by the other nodes (Figure 7, upper left panel). This is a conceptual picture re- presenting the general architecture of the master model that can help address specific questions. Even for this relatively simple regulatory graph, there is a finite but quite high number of possible logical rules. For now, we use a simple generic rule involving the AND and NOT operators. For example, the logical rule for CASP3 is: NOT MPT AND NOT NFkB AND CASP3. This compact model has four stable states, each corresponding to one Figure 6. Ligand removal experiments. The x-axis represents the (discrete) duration of the TNF pulse td (see text). At each discrete time point along the x-axis, the TNF signal is turned off. The different curves represent the average probabilities to reach the different attractors after the pulse (the number of trajectories N = 2000). Curves are coloured in blue for naı¨ve state, green for NFkB survival, orange for apoptosis, and purple for necrosis. doi:10.1371/journal.pcbi.1000702.g006 Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 9 March 2010 \| Volume 6 \| Issue 3 \| e1000702 cell fate, along with the ‘naı¨ve’ state (Figure 7, upper right panel). This is coherent with what was observed from the analysis of the complete model. To validate our compact model, we verified that the simulations of known mutations correspond to the published observations. Here, when a hidden component is deleted, all the paths traversing this component in the original graph are broken. If all the paths corresponding to an arc of the compact model happen to be broken, then it is removed. In the case of auto-regulation, not only the link is broken but the node is also set to zero to avoid the node to become active in the absence of death receptor activation. Let us consider the CASP8 deletion mutant to illustrate this approach (Figure 7, middle panels). For this mutant, several arrows in the compact model have to be deleted. For example, the arcs CASP3)CASP3 (paths 4+5 in Table 3) and CASP3xMPT (path 17) clearly depend on the activation of CASP8. Note, however, that CASP8 intervenes in other paths, which do not fully rely on its sole activity. In the case of the arc NFkB)NFkB, CASP8 depletion interrupts path 3, while path 2 can still enable the NFkB auto-regulation. Consistent with the results from the previous section, CASP8 depletion leads to the loss of the apoptotic fate while the ‘naı¨ve’ stable state cannot be attained. At this point, one could wonder how apoptosis could be re- established in a CASP8 mutant. The analysis of the broken paths suggests some experiments to bypass CASP8 and undergo CASP3 activation. On the basis of path 4, BAX, MOMP, SMAC and XIAP are identified as potential targets, while path 5 points to cytochrome c and apoptosome. One way to experimentally assess this possibility would be to inject exogenous cytochrome c as it was done in ‘wild type’ conditions [51], or yet provoke its release from the mitochondria by forcing the opening of the pores. This is possible only in the absence (or with low activity) of NFkB and in the presence of ATP. Again, since no quantitative information can be deduced from the path analysis proposed in this study, no prediction can be made on the concentrations of proteins needed to achieve a specific answer. In a previous section, we postulated that an inhibition of the survival pathway by the necrotic pathway is necessary to reproduce some mutant phenotype. We suggested that cIAP could play this role. Let us now test this hypothesis with our conceptual model. We build the corresponding 3-node model without cIAP. In the current version, cIAP plays two important roles, first as a mandatory intermediate in the inhibitory effect of MPT (associated with necrosis) onto NFkB (survival) (path 13), next as an obligate intermediate in the self-activation of NFkB (path 2). The simulation (Figure 7, lower right panel) shows that in the absence of cIAP, it is impossible to obtain the necrosis cell fate in the CASP8 (and FADD) mutant(s), in agreement with our previous conclusions and in support of our suggestion. A complete list of all possible gene knockouts is provided in the Table S2. This conceptual model analysis underlines the importance to simplify in order to better understand the general structure of the network and reason on it. Indeed, the simple 3-node network enables us to grasp global functional aspects and propose specific qualitative predictions. Discussion Mathematical models provide a way to test biological hypotheses in silico. They recapitulate consistent heterogeneous published results and assemble disseminated information into a coherent picture using a coherent mathematical formalism (discrete, continuous, stochastic, Table 3. List of paths corresponding to single arcs in the conceptual model of Figure 7. Arc type Arc Paths on the regulatory graph Sign of regulation Feedback circuits MPT)MPT 1) MPT)ROS)MPT (+) NFkB)NFkB 2) NFkB)cIAP)RIP1ub)IKK)NFkB (+) 3) NFkB)cFLIPxCASP8xRIP1)RIP1ub)IKK)NFkB (+) CASP3)CASP3 4) CASP3)CASP8)BAX)MOMP)SMACxXIAPxCASP3 (+) 5) CASP3)CASP8)BAX)MOMP)Cyt_c)apoptosome)CASP3 (+) Other regulatory paths CASP3xNFkB 6) CASP3)CASP8xRIP1)RIP1ub)IKK)NFkB (2) 7) CASP3)CASP8)BAX)MOMP)SMACxcIAP)RIP1ub)IKK)NFkB (2) 8) CASP3xNFkB (2) NFkBxCASP3 9) NFkB)cFLIPxCASP8)BAX)MOMP)Cyt_c)apoptosome)CASP3 (2) 10) NFkB)XIAPxCASP3 (2) 11) NFkB)XIAPxApoptosome)CASP3 (2) 12) NFkB)BCL2xBAX)MOMP)Cyt_c)apoptosome)CASP3 (2) MPTxNFkB 13) MPT)MOMP)SMACxcIAP)RIP1ub)IKK)NFkB (2) NFkBxMPT 14) NFkBxROS)MPT (2) 15) NFkB)BCL2xMPT (2) 16) NFkB)cFLIPxCASP8xRIP1)RIP1K)ROS)MPT (+) CASP3xMPT 17) CASP3)CASP8xRIP1)RIP1K)ROS)MPT (2) MPTxCASP3 18) MPT)MOMP)Cyt_c)apoptosome)CASP3 (+) 19) MPT)MOMP)SMACxXIAPxCASP3 (+) 20) MPT)MOMP)SMACxXIAPxapoptosome)CASP3 (+) 21) MPTxATP)apoptosome)CASP3 (2) doi:10.1371/journal.pcbi.1000702.t003 Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 10 March 2010 \| Volume 6 \| Issue 3 \| e1000702 hybrid, etc.), depending on the questions and the available data. Then, modelling consists of constantly challenging the obtained model with available published data or experimental results (mutants or drug treatments). After several refinement rounds, a model becomes particularly useful when it can provide counter-intuitive insights or suggest novel promising experiments. Here, we have conceived a mathematical model of cell fate decision, based on a logical formalisation of well-characterised molecular interactions. Former mathematical models only consid- ered two cellular fates, apoptosis and cell survival. In contrast, we include a non-apoptotic modality of cell death, mainly necrosis, involving RIP1, ROS and mitochondria functions. Both the master and the reduced models were constructed on the basis of an extensive analysis of the literature. The master model (Figure 1A) summarises our current understanding of the mechanisms regulating cell fate decision and identifies the major switches in this decision. However, some important interactions, components (caspase-2, calpains, AIF, etc.) or pathways (JNK, Akt, etc.) have not yet been considered. This model was built to be as generic as possible. Most of the mutants considered were analysed in Jurkat cells, T-cells, or L929 murine fibrosarcoma cells, thus in very different cellular contexts (e.g. in response to TNF, Jurkat cells are resistant to cell death, whereas L929 cell lines undergo necrosis). We are trying to account for all those phenotypes in a unique model. The next step will be to provide a model variant for each cell type in order to better match cell- specific behaviours. The reduced models can be used to simulate observed experiments and to reflect on the general mechanisms involved in apoptosis, survival or necrosis. This led us to identify the principal actors involved in the decision process. The presence of RIP1 or FADD, for example, proved to be decisive in our simulation. However, the role of cFLIP appears less obvious than previously suggested [7]. We can easily perturb the structure of the system in silico and assess the dynamical effects of such perturbations (e.g. novel knockouts). Our model can also be used to decide between antagonist results found in different publications. For instance, the inhibitory role of cIAP1/2 on the apoptotic pathway was initially attributed to a direct inhibition of caspases. However, detailed biochemical studies challenged this view [52,53]. We have tested this hypothesis by adding an inhibitory arc from cIAP onto CASP8, but simulations do not support a functional inhibitory role of cIAP1/2, since survival is favoured over apoptosis in many CASP3 NFkB MPT CASP3 NFkB MPT CASP3 NFkB MPT 111 011 101 110 010 100 001 000 111 001 101 110 100 010 000 011 111 001 101 110 010 011 000 100 Figure 7. Simplified view of the cell fate model structure. Left panels: compact regulatory graph deduced from the master model (top), along with two variants (middle and low). Right panels: state transition graphs corresponding to each regulatory graph, using generic logical rules (cf. text). Stable states are represented by ellipses (at the bottom of each state transition graph). Each stable state corresponds to one cell fate: 000 for the ‘naı¨ve’ state, 010 for survival, 001 for apoptosis, and 100 for necrosis. Top: wild type structure. Middle: CASP8 deletion mutant. Bottom: CASP8 deletion mutant in the absence of cIAP. doi:10.1371/journal.pcbi.1000702.g007 Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 11 March 2010 \| Volume 6 \| Issue 3 \| e1000702 mutants, thus making apoptosis a very improbable phenotype (Figure S1). Similarly, we tested the role of the feedback circuit involving CASP8 and CASP3. We found that the activation of CASP8 by CASP3 is not functional when TNF and FASL are constantly ON. However, when TNF or FAS signal is not sustained, CASP3)CASP8 activation becomes necessary to insure the persistence of the apoptotic phenotype. When TNF is sustained, this feedback is no longer needed (see Figures S2 and S3 for details). The in-depth analysis of model properties led us to propose several predictions or novel insights. Some concern the structure of the network, as several interactions appear to be necessary to achieve specific phenotypes. For example, our simulations of FADD and CASP8 deletion mutants underline the need for a mechanism from the necrotic pathway that would inhibit the survival one. Here, we consider a mechanism involving MPT, SMAC and cIAP. Other simulations point to different roles of proteins: RIP1 activity is transient in necrosis whereas it is sustained in survival. Similarly, our model analysis shows the role played by the duration of the TNF pulses in the cell fate decision and enlights when this decision is made. Finally, some hints about possible scenarios for forcing or restoring a phenotype in mutants are provided. Deregulations of the signalling pathways studied here can lead to drastic and serious consequences. Hanahan and Weinberg proposed that escape of apoptosis, together with other alterations of cellular physiology, represents a necessary event in cancer promotion and progression [54]. As a result, somatic mutations leading to impaired apoptosis are expected to be associated with cancer. In the cell fate model presented here, most nodes can be classified as pro-apoptotic or anti-apoptotic according to the results of ‘‘mutant’’ model simulations, which are correlated with experimental results found in the literature. Genes classified as pro-apoptotic in our model include caspases-8 and -3, APAF1 as part of the apoptosome complex, cytochrome c (Cyt_c), BAX, and SMAC. Anti-apoptotic genes encompass BCL2, cIAP1/2, XIAP, cFLIP, and different genes involved in the NFkB pathway, including NFKB1, RELA, IKBKG and IKBKB (not explicit in the model). Genetic alterations leading to loss of activity of pro- apoptotic genes or to increased activity of anti-apoptotic genes have been associated with various cancers. Thus, we can cross-list the alterations of these genes deduced from the model with what is reported in the literature and verify their role and implications in cancer. For instance, concerning pro-apoptotic genes, frameshift mutations in the ORF of the BAX gene are reported in .50% of colorectal tumours of the micro-satellite mutator phenotype [55]. Expression of CASP8 is reduced in ,24% of tumours from patients with Ewing’s sarcoma [56]. Caspase-8 was suggested in several studies to function as a tumour suppressor in neuroblas- tomas [57] and in lung cancer [58]. On the other hand, constitutive activation of anti-apoptotic genes is often observed in cancer cells. The most striking example is the over-expression of the BCL2 oncogene in almost all follicular lymphomas, which can result from a t(14;18) translocation that positions BCL2 in close proximity to enhancer elements of the immunoglobulin heavy-chain locus [59]. As for the survival pathway, elevated NFkB activity, resulting from different genetic alterations or expression of the v-rel viral NFkB isoform, is detected in multiple cancers, including lymphomas and breast cancers [60]. An amplification of the genomic region 11q22 that spans over the cIAP1 and cIAP2 genes is associated with lung cancers [61], cervical cancer resistance to radiotherapy [62], and oesophageal squamous cell carcinomas [63]. A better understanding of the pro- or anti-apoptotic roles of these genes involved in various cancers and their interactions with other pathways would set a ground for re-establishing a lost death phenotype and identifying druggable targets. The cell fate model proposed here is a first step in this direction. In the future, we will consider additional signalling cascades and their cross-talks, following the path open by other groups [64]. In parallel, we are contemplating the inclusion of other modalities of cell death such as autophagy [65], which inhibits apoptosis through BCL2 and is itself inhibited by apoptosis through Beclin1. The functioning of the intrinsic apoptotic pathway and the internal cellular mechanisms capable of triggering it could be investigated in more details, taking advantage of recent molecular analyses [66,67]. Finally, when systematic quantitative data regarding the decision between multiple cell fates will become available, our qualitative model could be used to design more quantitative models adapted to specific cellular systems in order to predict the probability for a given cell to enter into a particular cell fate depending on stimuli. Methods Boolean formalism, synchronous vs. asynchronous strategy The computation of trajectories in the state space consists in the calculation of sequences of states where each member of the sequence is a logical successor of the previous one. As we choose to use Boolean variables to encode the 25-dimensional master model, the state space is the set S = {0,1}25. Although finite, the size of this set is huge (more than 33 millions states). Furthermore, in the discrete framework, the mathematical definition of the trajectories assumes an updating rule for the variables. Two main strategies are usually considered to analyse discrete models of biological networks. The first one consists in updating all variables simultaneously, at each time step. This synchronous strategy [68] has the advantage to generate simple determinist dynamics, each state having one and only one successor. Drawing a directed arrow from each of the 225 states to its successor, one constructs the synchronous transition graph, comprising all synchronous trajectories of the system. The determinism of the synchronous transition graph is a very strong property that poorly portrays the complexity of the biochemical processes that are modelled (some processes are likely to occur faster than others). The second strategy, which is used in this paper, consists in considering that only one component is updated at each time, implying that a state may have several successors [69]. More precisely, to compute the set of asynchronous successors of a state x = (x1,…,xn)M{0,1}n, one has to follow the three steps: (1) compute the state F(x) = (f1(x),…, fn(x)), where fi is the Boolean rule of the ith variable (F(x) is thus the synchronous successor of x); (2) select the indices i such that xi?fi(x) (those are the indices of the variables that are liable to change when the system is in state x); and (3) for all such indices i, the state (x1,…,fi(x),…,xn) is an asynchronous successor of x. According to this definition, in the asynchronous approach, no a priori hypothesis is made on the order of the events: all possible orders are considered, which is much more satisfying from a modelling point of view, as it is very difficult to know the relative speeds of the different processes involved in the master model. Note that the stable states of the model are independent on the choice of the strategy (synchronous or asynchronous). Therefore, the first analysis (based on the clustering of stable states) is valid regardless the updating strategy. Drawing an arrow from each state to its asynchronous successors leads to the construction of an asynchronous transition Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 12 March 2010 \| Volume 6 \| Issue 3 \| e1000702 graph, which comprises all possible asynchronous trajectories of the system. To each arrow starting from the same state is associated an equal probability (see [70] for details). This is a strong assumption, which is the main reason why the exact values of computed probabilities (of the different phenotypes) should not be compared to experimental data in a quantitative manner. Nevertheless, the same assumption has been made for all model variants (mutants and drug treatments), thereby allowing compar- ative studies. A systematic method to assess the impact of the probability distribution is a key point towards a finer quantitative analysis (work in progress). As pointed earlier, the size of the transition graph is exponential with respect to the number of variables, which constitutes a first obstacle to the dynamical analysis. A second difficulty resides in the fact that the asynchronous graph is not deterministic, as each vertex may have more than one successor, which, given the size of the graph, makes the application of classical graph algorithms computationally heavy. Model reduction We have used a model reduction technique specifically adapted to discrete systems, which mainly consists in iteratively ‘‘hiding’’ some variables, while keeping track of underlying regulatory processes [47]. The main dynamical properties of the master model, including stable states and other attractors are conserved in the reduced model. Thanks to the computation of the reduced asynchronous transition graph, relevant qualitative dynamical properties of the model can be compared to experimental results for wild type and in different mutant cases. To reduce the number of species in the master model, each logical rule is considered. For each removed component, the information contained in its rule is included in the rules of its targets such that no effective regulation is lost. Many intermediate components could easily be replaced by a proper rewriting of the logical rules associated with their target nodes. For example, IKK has only one input (RIP1ub) and one output (NFkB). Since its role in our model merely consists in transmitting the signal from RIP1ub to NFkB, it can be easily replaced by a straightforward change in the logical rule associated with NFkB (implementing a direct activation from RIP1ub instead of IKK). We also relied on the results of the clustering of stable states and their associations with biologically plausible phenotypes to select the key components to keep in the reduced model: NFkB is the principal survival actor, while caspases-3 and -8, together with the mitochondrial membrane permeability variables (MOMP and MPT), determine apoptotic and non- apoptotic cell deaths. Let us consider the example of the removal of BAX and BCL2 (Figure 1 A and B). The regulators (or inputs) of these variables are NFkB for BCL2 and CASP8 for BAX while their regulating targets (or outputs) are MPT for BCL2 and MOMP for BAX. BCL2 is directly activated by NFkB, and has two targets: MPT and BAX. Therefore, BCL2 removal is performed by replacing BCL2 by NFkB into the rules of the two targets, leading to the two new logical rules: MPT9 = ROS AND NOT NFkB and BAX9 = C8 AND NOT NFkB. Applying the same process to remove BAX, one obtains the following new rule for MOMP: MOMP9 = MPT OR (C8 AND NOT NFkB). The variables MOMP and MPT have now as inputs the variables NFkB and CASP8. One can see that, in spite of the disappearance of variables BAX and BCL2, their regulating roles are still indirectly coded in the reduced system, ensuring that no ‘‘logical interaction’’ of the master model (i.e. activation or inhibition) is actually lost during the reduction process. Table S3 lists the variables of the master model that are removed to obtain the reduced model. Some hypotheses were made when reducing the model. First, FADD is considered to be constantly ON in wild type simulations. Second, since the two complexes TNFR and DISC-TNF have been removed together with the input FADD, the two deaths ligands TNF and L have the exact same action in the reduced model. Indeed, we consider that, in response to FAS death receptor engagement as well as that of TNF; the activations of both the survival and necrotic pathways RIP1-dependent. In this case, one could then merge these variables and consider only one input that could be called ‘‘external death receptor’’. However, we choose to keep the two variables TNF and FASL, in the FADD deletion mutant, the phenotype differs for TNF and FAS signal: actually, only for that mutant is the symmetry of TNF and FAS broken. Supporting Information Figure S1 Simulations of the reduced cell fate model incre- mented by the interaction cIAPxCASP8 with TNF = 1, FasL = 0. Found at: doi:10.1371/journal.pcbi.1000702.s001 (0.10 MB PDF) Figure S2 Simulations of the model after deletion of the interaction CASP3)CASP8 from the model with TNF = 1, FasL = 0. Found at: doi:10.1371/journal.pcbi.1000702.s002 (0.11 MB PDF) Figure S3 Ligand removal simulation for the model with the deletion of the interaction CASP3)CASP8. Found at: doi:10.1371/journal.pcbi.1000702.s003 (0.08 MB PDF) Figure S4 Comparative simulations between master model and reduced model. Found at: doi:10.1371/journal.pcbi.1000702.s004 (0.13 MB PDF) Table S1 Contribution of the different variables into the first two principal components. The colour marks relatively large contributions, positive in red and negative in green. Found at: doi:10.1371/journal.pcbi.1000702.s005 (0.01 MB PDF) Table S2 List of mutants simulated with the conceptual 3-node model. Found at: doi:10.1371/journal.pcbi.1000702.s006 (0.03 MB PDF) Table S3 List of variables hidden from the master model to generate the reduced model. Found at: doi:10.1371/journal.pcbi.1000702.s007 (0.07 MB PDF) Text S1 Supplementary Text includes 1) GINsim Report of the Annotated Model and 2) Supplementary references Found at: doi:10.1371/journal.pcbi.1000702.s008 (0.16 MB PDF) Acknowledgments We thank Luca Grieco and Brigitte Kahn-Perle`s for critical reading of the manuscript and Thomas Fink for discussions around the conceptual model. 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Mathematical Model of Cell Fate Decision PLoS Computational Biology \| www.ploscompbiol.org 15 March 2010 \| Volume 6 \| Issue 3 \| e1000702	20221256	RIP1 = ( ( DISC-FAS ) AND NOT ( CASP8 ) ) OR ( ( TNFR ) AND NOT ( CASP8 ) ) NonACD = ( NOT ( ( ATP ) ) ) OR NOT ( ATP ) XIAP = ( ( NFkB ) AND NOT ( SMAC ) ) NFkB = ( ( IKK ) AND NOT ( CASP3 ) ) RIP1ub = ( cIAP AND ( ( ( RIP1 ) ) ) ) cFLIP = ( NFkB ) BCL2 = ( NFkB ) BAX = ( ( CASP8 ) AND NOT ( BCL2 ) ) MPT = ( ( ROS ) AND NOT ( BCL2 ) ) DISC-TNF = ( TNFR AND ( ( ( FADD ) ) ) ) RIP1k = ( RIP1 ) apoptosome = ( ( Cyt_c AND ( ( ( ATP ) ) ) ) AND NOT ( XIAP ) ) survival = ( NFkB ) IKK = ( RIP1ub ) ATP = NOT ( ( MPT ) ) apoptosis = ( CASP3 ) MOMP = ( MPT ) OR ( BAX ) Cyt_c = ( MOMP ) CASP8 = ( ( DISC-TNF ) AND NOT ( cFLIP ) ) OR ( ( DISC-FAS ) AND NOT ( cFLIP ) ) OR ( ( CASP3 ) AND NOT ( cFLIP ) ) TNFR = ( TNF ) ROS = ( ( MPT ) AND NOT ( NFkB ) ) OR ( ( RIP1k ) AND NOT ( NFkB ) ) cIAP = ( ( NFkB ) AND NOT ( SMAC ) ) OR ( ( cIAP ) AND NOT ( SMAC ) ) SMAC = ( MOMP ) DISC-FAS = ( FASL AND ( ( ( FADD ) ) ) ) CASP3 = ( ( apoptosome ) AND NOT ( XIAP ) )
A Boolean Model of the Gene Regulatory Network Underlying Mammalian Cortical Area Development Clare E. Giacomantonio1, Geoffrey J. Goodhill1,2* 1 Queensland Brain Institute, The University of Queensland, St Lucia, Queensland, Australia, 2 School of Mathematics and Physics, The University of Queensland, St Lucia, Queensland, Australia Abstract The cerebral cortex is divided into many functionally distinct areas. The emergence of these areas during neural development is dependent on the expression patterns of several genes. Along the anterior-posterior axis, gradients of Fgf8, Emx2, Pax6, Coup-tfi, and Sp8 play a particularly strong role in specifying areal identity. However, our understanding of the regulatory interactions between these genes that lead to their confinement to particular spatial patterns is currently qualitative and incomplete. We therefore used a computational model of the interactions between these five genes to determine which interactions, and combinations of interactions, occur in networks that reproduce the anterior-posterior expression patterns observed experimentally. The model treats expression levels as Boolean, reflecting the qualitative nature of the expression data currently available. We simulated gene expression patterns created by all 1:68\|107 possible networks containing the five genes of interest. We found that only 0:1% of these networks were able to reproduce the experimentally observed expression patterns. These networks all lacked certain interactions and combinations of inter- actions including auto-regulation and inductive loops. Many higher order combinations of interactions also never appeared in networks that satisfied our criteria for good performance. While there was remarkable diversity in the structure of the networks that perform well, an analysis of the probability of each interaction gave an indication of which interactions are most likely to be present in the gene network regulating cortical area development. We found that in general, repressive interactions are much more likely than inductive ones, but that mutually repressive loops are not critical for correct network functioning. Overall, our model illuminates the design principles of the gene network regulating cortical area development, and makes novel predictions that can be tested experimentally. Citation: Giacomantonio CE, Goodhill GJ (2010) A Boolean Model of the Gene Regulatory Network Underlying Mammalian Cortical Area Development. PLoS Comput Biol 6(9): e1000936. doi:10.1371/journal.pcbi.1000936 Editor: Karl J. Friston, University College London, United Kingdom Received March 25, 2010; Accepted August 17, 2010; Published September 16, 2010 Copyright: 2010 Giacomantonio, Goodhill. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported by an Australian Postgraduate Award (CEG) and a Human Frontier Science Program grant RPG0029/2008-C. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: g.goodhill@uq.edu.au Introduction The mammalian cerebral cortex is a complex but extremely precise structure. In adult, it is divided into several functionally distinct areas characterised by different combinations of gene expression, specialised cytoarchitecture and specific patterns of input and output connections. But how does this functional specification arise? There is strong evidence that both genetic and activity-dependent mechanisms play a role in the development of these specialised areas, a process also referred to as arealisation. A genetic component is implicated by the spatial non-uniformity of expression of some genes prior to thalamocortical innervation, as well as the fact that altering expression of some genes early in development changes area position in adult [for review see 1–8]. On the other hand, manipulating thalamocortical inputs, and hence activity from the thalamus, can alter area size or respecify area identity [for review see 1,4,8]. These results are accommo- dated in a current working model of cortical arealisation as a multi-stage process where initial broad spatial patterns of gene expression provide a scaffold for differential thalamocortical innervation [5]. Patterned activity on thalamocortical inputs then drives more complex and spatially restricted gene expression which, in turn, regulates further area specific differentiation. This paper focuses on the earliest stage of arealisation: how patterns of gene expression form early in cortical development. Experiments have identified many genes expressed embryoni- cally that are critical to the positioning of cortical areas in adult. Although arealisation occurs in a two-dimensional field, most experiments focus on anterior-posterior patterning and hence, here we concentrate on patterning along this axis. From around embryonic day 8 (E8) in mouse, the morphogen Fgf8 is expressed at the anterior pole of the developing telencephalon (Figure 1A) [2,3,5,7–11]. Immediately after Fgf8 expression is initiated in mouse, four transcription factors (TFs), Emx2, Pax6, Coup-tfi and Sp8 are expressed in gradients across the surface of the cortex (Figure 1B) [2,3,5,8,11]. These four TFs are an appealing research target because their complementary expression gradients could provide a unique coordinate system for arealisation [5], equivalent to ‘‘positional information’’ [12,13]. Altered expression of each of Fgf8 and the four TFs shifts area positions in late embryonic stages and in adult [14–29; but see also 30]. Furthermore, during development, altered expression of each of these genes up- or down-regulates expression of some other genes in the set along the anterior-posterior axis (see Figure 2B for references). A large PLoS Computational Biology \| www.ploscompbiol.org 1 September 2010 \| Volume 6 \| Issue 9 \| e1000936 cohort of experiments has given rise to a hypothesised network of regulatory interactions between these five genes (Figure 2A). However, only one of these interactions has been directly demonstrated [24] and no analysis has been performed at the systems level. Interacting TFs are known to be able to form regulatory networks that drive differential spatial development, fulfilling a role for which morphogens are better known [31,32]. Feedback loops are the crucial feature that enable the generation of spatial (and temporal) patterns of expression of the genes in the network. Since TFs regulate the expression of other genes, local differences in expression of a set TFs are a powerful method of generating spatial patterns of growth, differentiation and expression of guidance cues (and therefore innervation), and developing more complex patterns of gene expression. The arealisation genes form a regulatory network with many feedback loops which is in principle capable of generating spatial patterns. Establishing which interactions are critical for correct arealisation is of great interest to the field, but current experimental approaches are limited in their ability to quickly assay the importance of each particular interaction. Computational modelling of gene regulatory networks is necessary because their complex behaviour is difficult to understand intuitively. In addition, it offers several other benefits. Currently, the many hypothesised interactions between arealisation genes are represented as arrow diagrams like that seen in Figure 2A. Because intuition tends to follow simple causal chains, the presence of many feedback loops makes intuition about the overall behaviour of complex systems unreliable [33–37]. Consequently, a more formal description than an arrow diagram would test the current conceptual model, and has the potential to give greater under- standing and insight, as it has done for many other regulatory networks [for review see 33–36,38–44]. The unambiguous descriptions found in mathematical and computational models offer the added benefit of making assumptions explicit and therefore allowing greater scrutiny [45]. Computational experiments can also be performed quickly and cheaply relative to laboratory experi- ments and consequently can be useful for conducting thought experiments which can then be tested experimentally [45,46]. In this way, computational modelling and experiments can spur each other on so that both are ‘‘improved in a synergistic manner’’ [36]. Here, we use the Boolean logical approach to model the arealisation regulatory network. In this approach, variables representing genes and proteins can take only two values, zero or one, representing gene and protein activity being below or above some threshold for an effect. While continuous models are more realistic, they have many free parameters which are hard to constrain from experimental data, and offer a formidable computational challenge to investigate systemati- cally. In contrast, Boolean models can be used when only qualitative expression and interaction data are available, as is the case for arealisation. In Boolean models, at each point in time, the state of a variable depends on the state of its regulators at the previous time step. A set of logic equations capture the regulatory relationships between Figure 1. Gene expression in the developing neocortex. (A) The anterior neural ridge or commissural plate (blue) is a patterning centre in the developing forebrain that secretes the morphogen Fgf8. Since the protein is secreted, it is hypothesised that it diffuses to form a gradient [5]. The directions A, P, D, V, M and L indicate anterior, posterior, dorsal, ventral, medial and lateral respectively. (B) These four transcription factors are expressed in spatial mRNA and protein gradients across the developing forebrain. Many other genes with spatial patterns of expression have also been identified [for review see 8]. (C) A schematic of the desired steady state expression levels in the anterior and posterior compartments in the discretised Boolean model. A is adapted from Figure 1A in [4] and Figure 1 in [5], B is adapted from Figure 6A in [5]. doi:10.1371/journal.pcbi.1000936.g001 Author Summary Understanding the development of the brain is an important challenge. Progress on this problem will give insight into how the brain works and what can go wrong to cause developmental disorders like autism and learning disability. This paper examines the development of the outer part of the mammalian brain, the cerebral cortex. This part of the brain contains different areas with specialised functions. Over the past decade, several genes have been identified that play a major role in the development of cortical areas. During development, these genes are expressed in different patterns across the surface of the cortex. Experiments have shown that these genes interact with each other so that they each regulate how much other genes in the group are expressed. However, the experimental data are consistent with many different regulatory networks. In this study, we use a computational model to systematically screen many possible networks. This allows us to predict which regulatory interactions between these genes are important for the patterns of gene expression in the cortex to develop correctly. Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 2 September 2010 \| Volume 6 \| Issue 9 \| e1000936 variables and dictate how the system evolves in time. The Boolean idealisation greatly reduces the number of free parameters while still capturing network dynamics and producing biologically pertinent predictions and insights [43,45,47]. In our model, we use only two spatial compartments, one representing the anterior pole and another representing the posterior pole. The anterior and posterior expression levels after Boolean discretisation are shown in Figure 1C. More than two expression levels and more than two spatial compartments would be more realistic, but would result in an explosion in the number of parameters currently unconstrained by experimental data. Having only two expression levels and only two compartments allows us to systematically screen a large number of networks, which would be impossible in a more complex model. In this paper, we simulate the dynamics of all possible networks created by different combinations in interactions between Fgf8, Emx2, Pax6, Coup-tfi and Sp8, and show that only 0:1% of these networks are able to reproduce the expression patterns observed experimentally. From this analysis, we identify structural elements common to the best performing networks, as well as elements that never appear in the networks that perform well. These results reveal important logical principles underlying the cortical area- lisation gene network, and suggest potential directions for future experimental investigations. Results Simulation of the dynamics of 224 possible networks revealed networks that reliably reproduced the experimentally observed expression gradients Experimental evidence indicates that Fgf8, Emx2, Pax6, Coup-tfi and Sp8 regulate each other’s expression, but the actual structure of the network is highly unconstrained by experimental data. Figure 2. A network created by interactions between the five genes of interest as suggested by experiments. (A) Arrows (?) indicate inductive or activating interactions, flat bars (a) indicate repressive interactions. Text in italics signifies genes while upright text signifies proteins. Only the activation of Fgf8 by Sp8 (Sp8?Fgf8) has been directly demonstrated [24]. Other interactions have generally been inferred based on altered expression patterns in mutants and therefore might be indirect. For example, the activation of Emx2 by Coup-tfi might be due to Coup-tfi repressing Pax6 which in turn represses Emx2. This panel is adapted from Figure 6B in [5]. (B) References for each of the interactions in panel A. (C) The Boolean logic equations for the network in panel A. F, E, P, C and S are the logical variables representing the genes Fgf8, Emx2, Pax6, Coup-tfi and Sp8 and F, E, P, C and S are the logical variables representing the respective proteins. For a gene to be turned on at time tz1, its inductive regulators must be present and its repressive regulators absent at time t. doi:10.1371/journal.pcbi.1000936.g002 Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 3 September 2010 \| Volume 6 \| Issue 9 \| e1000936 Hence, we performed a systematic screen of the different possible networks and then looked for common structural features in the networks that perform poorly and well. We analysed the dynamics of all networks created by different combinations of 24 possible interactions between these five genes and their respective proteins. In each network, Sp8?Fgf8 was fixed since this has been directly demonstrated [24]. We also did not consider positive interactions between species with opposing expression gradients, or negative interactions between species with the same gradient. For example, Emx2aPax6 and Fgf8?Pax6 were possible interactions, but Emx2?Pax6 and Fgf8aPax6 were not. The 24 variable interactions generated 224~1:68\|107 possible networks. The structure of each network was transformed into a set of Boolean logic functions as described in the Methods. We identified networks that proceeded from the state at the anterior pole at E8 to the state at around E10.5, as well as from the state at the posterior pole at E8 to the state at around E10.5. At E8, of our genes of interest, only Fgf8 is active due to mechanisms external to the network we are modelling [5,24,26], and only at the anterior pole. Hence, in the Boolean model with binary variables, Fgf8 gene and protein started in the active (‘1’) state in the anterior compartment and inactive (‘0’) state in the posterior compartment, while the other genes and proteins started in the inactive state in both compartments. By E10.5, the expression patterns seen in Figure 1 are present. That is, at the anterior pole, Fgf8, Pax6 and Sp8 genes are active, while Emx2 and Coup-tfi are inactive; at the posterior pole, Emx2 and Coup-tfi are active, while Fgf8, Pax6 and Sp8 are inactive. When the Boolean update functions describing a network were applied stochastically, many networks reached multiple steady states with fixed probabilities. In these cases, we calculated the average gene and protein levels, weighted by the probability of ending in a particular state, and thus each Boolean variable could be between 0 and 1. We say that a network reliably reaches a desired steady state if it does so with a greater than 50% probability. From this, it follows that networks that reliably reach both the anterior and posterior steady states from the respective starting states have differences in activity between the anterior and posterior poles than span 0.5, as in Figure 1C. We define these networks as good. A previously hypothesised regulatory network does not satisfy our criteria for reproducing the experimental observations To give a specific example, we present the dynamics of a regulatory network previously hypothesised based on experimental observations [5,8], seen in Figure 2A. The network was converted into the set of Boolean logic equations described in Figure 2C. We found that this network had a 100% chance of following the desired trajectory from the posterior starting state to the posterior steady state. In constrast, it had only a 38% chance of following the desired anterior trajectory from the anterior starting state to the anterior steady state. This poor anterior performance arises because of Fgf8 auto-induction and the Fgf8/Sp8 inductive loop, as we will explain later in more detail. While this network produced the correct activity gradients overall, as seen in Figure 3A, it does not satisfy our criteria for doing so reliably Figure 3. Performance of a previously hypothesised network, and all possible networks. (A) The average expression in the anterior and posterior compartments in the experimentally hypothesised network in Figure 2. This network does not satisfy our criteria for reliable performance because the gradients do not span 0.5. (B) Each network followed the desired anterior state trajectory and the desired posterior state trajectory with a fixed probability plotted on the two axes of this graph. We defined good networks as those with a greater than 50% chance of following both the desired anterior trajectory of states as well as the desired posterior trajectory of states. These networks lie in the upper, right quandrant of this graph (blue plusses). All other networks (black crosses) did not satisfy our criteria for reliably reproducing the experimentally observed patterns of gene expression. The point corresponding to the experimentally hypothesised network in Figure 2 is coloured green. The red plus corresponds to the two best performing networks in Figure 7B and C. The black contour lines are lines of constant network performance. doi:10.1371/journal.pcbi.1000936.g003 Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 4 September 2010 \| Volume 6 \| Issue 9 \| e1000936 because the gradients do not span 0.5; the anterior levels of Fgf8, Pax6 and Sp8 are too low (v0:5), while the anterior levels of Emx2 and Coup-tfi are too high (w0:5). The fact that this network did not reach our criteria for reproducing the experimental observations, even though all interactions have been observed indirectly, shows clearly that intuitions about the dynamics of regulatory networks with feedbacks can be unreliable. Only a small percentage of networks satisfied our criteria for reproducing the experimental observations Of all possible networks, we found that 0.1% of networks (1:00\|104) had a greater than 50% chance of proceeding from the anterior starting state to the anterior steady state, as well as a greater than 50% of proceeding from the posterior starting state to the posterior steady state. In a plot of the probability of following the desired anterior trajectory through state space against the probability of following the desired posterior trajectory, these good networks lie in the upper right quadrant (Figure 3B). To assess the similarity of the structures of the good networks, we calculated the average distance from each of the good networks to the best performing network and compared this to the average distance from all networks (Figure 4). The distance is defined as the number of different interactions [48]. The good networks differ to the best network by an average of 7:3+2:1 interactions, while all possible networks differ by an average of 12:0+2:4 interactions. This indicates that the structures of the good networks are restricted in the space of all possible networks. We then set out to understand which network interactions characterised the good and bad networks. There were many combinations of interactions that did not appear in networks that performed well Careful examination of the interactions present and absent in the good networks allowed us to identify several combinations of interactions that were never present in good networks. Networks containing nodes with no regulators obviously performed poorly. Figure 5A shows their position on the plot of probability of following the desired anterior trajectory though state space against the desired posterior trajectory. In a similar vein, networks where Fgf8 was not upstream of at least one of the four TFs also performed poorly (Figure 5B), because the starting states of the two compartments only differed in Fgf8 activity. In addition, networks with auto-inductive interactions all performed poorly (Figure 5C). This occurs because any node with auto-induction is either locked into its initial state or becomes inactive if it has other regulatory requirements that are not satisfied. Consequently, the desired trajectories cannot occur with a greater than 50% probability in both compartments. By similar reasoning, nodes with inductive loops also performed poorly (Figure 5D), as do networks with isolated repressive loops (Figure 5E). We also identified several higher order combinations of interactions that rarely appeared in networks that could produce the average expression gradients observed experimentally. For these higher order combinations, we could not deduce an intuitive explanation for why they caused networks to perform poorly. Some of these combinations are listed in Table S1. Removal of networks containing these interactions further narrowed the space of possible networks as seen in Figure 6. In total, the criteria outlined so far reject 99.96% of the networks investigated, leaving 6980 networks. Some interactions were more likely than others to occur in the networks that performed well By analysing the remaining networks, we identified certain interactions that were more likely than others. Of the remaining networks, 84% (5849 of 6980), satisfied our criteria for reliably following the desired trajectories to produce the average expression gradients observed experimentally. Surprisingly, among these good networks, no single interaction was universally present or absent, except those already identified as deterimental (Table 1, third column). In fact, among the remaining, good networks, all interactions occurred at about the frequency expected from all the remaining networks (Table 1, third column compared to second column). In general, the repressive interactions were more likely than inductive ones. The interactions Fgf8aEmx2 and Fgf8aCoup-tfi were the most likely interactions, occuring in 80% of all remaining networks that performed well. Next, Emx2aSp8 and Coup-tfiaSp8 occurred in 66% of good networks. The interactions Pax6aEmx2 and Pax6aCoup-tfi occurred in 55% of all good networks, while Emx2aPax6 and Coup-tfiaPax6 occurred in 54% of all good networks. Though many different networks performed well, we now discuss the best performing networks as an illustrative example. The two best performing networks both followed the desired anterior trajectory 74% of the time and the desired posterior trajectory 74% of the time. They are marked in red in Figure 3B and reliably produced the average expression gradients observed experimentally (Figure 7A cf. Figure 1C). Figure 7B and C show the structures of these two networks. Note that the six most likely interactions from the third column of Table 1 are present in these networks, as well as several less common interactions. However, many networks with similar structures also produced the correct average expression gradients, while some with quite different structures did too. Thus, although the networks that reproduced the experimentally observed expression gradients were constrained in structure compared to all possible structures, there was still a remarkable diversity in these networks. In general, repressive interactions were more prevalent in the networks that performed well than inductive interactions. This is evident in the probabilities of each interaction being present (Table 1, third column), as well as a set of networks that performed Figure 4. Distribution of the structural difference between the best network and the good networks, as well as the best network and all networks. The distance between two networks is the number of interactions differing between them. The good networks are constrained in their structure so that there is less difference between them and the best network than between all networks and the best network. doi:10.1371/journal.pcbi.1000936.g004 Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 5 September 2010 \| Volume 6 \| Issue 9 \| e1000936 similarly to the best performing network, that are illustrated in Figure 8A. In these 64 networks, the six most common interactions in the good networks were all required to be present. All other repressive interactions, which created reciprocal repressive loops, could be present or absent without greatly affecting network performance. The only inductive interaction appearing in this set of networks was Fgf8?Pax6, and it was present in all 64 networks. All inductive interactions between the four TFs were required to be absent along with Pax6?Fgf8, all auto-inductive loops and Fgf8?Sp8 which created an inductive loop. Discussion The roles of different genes Current experimental evidence indicates that the gene network that regulates cortical area development has multiple feedback pathways and consequently, it is difficult to understand intuitively. Using a Boolean logic model, we simulated many different possible networks and identified many structural requirements on the networks to ensure good performance. Our analysis suggests differing roles for the different genes in the network. We show that Fgf8 expression at the anterior pole, a putative cortical patterning centre, may be sufficient to drive the correct spatial patterning of the transcription factors Emx2, Pax6, Coup-tfi and Sp8, if simple interactions between these transcription factors exist. This is an example of how a transient signal, in this case Fgf8 expression initiated by external regulators, can be converted into a durable change in the developing brain [49]. In our simplified model, Emx2 and Coup-tfi, which are both expressed in high posterior–low anterior gradients, play the same role in the network. This means that if Emx2 and Coup-tfi are swapped in any network, the dynamics of the network don’t change. This is evident in the higher order interactions that rarely appear in good networks, listed in Table S1, as well as the two best performing networks in Figure 7B. In reality, Coup-tfi has a sharper anterior-posterior expression gradient than Emx2 and the two TFs Figure 5. Some combinations of interactions that never appear in good networks. Each panel shows the probability of following the desired anterior state trajectory against the probability of following the desired posterior state trajectory for all 224 networks that we considered. In each panel, we highlight in red networks that contain a particular combination of interactions. All other bad networks are marked with black crosses, all other good networks are marked with blue pluses. (A) In red are networks containing nodes with no regulators. These entered the anterior steady state or posterior steady state but not both. (B) In red are networks with Fgf8 only downstream of the four TFs (Fgf8aEmx2, Fgf8?Pax6, Fgf8aCoup-tfi and Fgf8?Sp8 all absent). Because the only difference in the starting state between the two compartments was Fgf8 activity, these networks could not enter both the anterior and posterior steady states with w50% probability. (C) Marked in red are networks with auto-induction. Networks with Emx2, Pax6, Coup-tfi or Sp8 auto-induction entered the anterior steady state or the posterior steady state but not both. Networks with Fgf8 auto- induction could reliably enter the posterior steady state but not the anterior steady state. To enter the anterior steady state, they required Sp8 to become and remain active before the state of Fgf8 was updated. Because nodes were updated asynchronously in a random order, this could not occur with w50% probability. (D) In red are networks containing inductive loops. These also could not enter the anterior steady state with w50% probability by similar reasoning to C. (E) In red are networks containing isolated repressive loops (that is, X repressing Y was the only regulation of Y and Y also repressed X). These also could not reproduce the average gradients observed experimentally. doi:10.1371/journal.pcbi.1000936.g005 Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 6 September 2010 \| Volume 6 \| Issue 9 \| e1000936 are expressed in opposing gradients along the medial-lateral axis. Experiments suggest that Emx2 promotes posterior area identity while Coup-tfi represses anterior area identity [6]. Therefore, we expect that they are not redundant as our model suggests, but play different roles through differing downstream targets. Interactions we predict are likely Our screen of possible networks identified interactions that we predict are more likely to be present in the arealisation regulatory network than others, and are therefore good experimental targets for further study. In general, we predict that repressive interactions are particularly important in this network. This is consistent with data showing that repressive cascades are important for spatial differentiation in other systems [50,51]. The interactions we predict are most likely include several interactions that have previously been hypothesised based on experiments. Our analysis predicts that Fgf8aEmx2 and Fgf8aCoup-tfi are the most likely direct interactions, consistent with many previous suggestions [20,21,27,52–54]. Since Sp8 induces Fgf8, repression of Sp8 by Emx2 has been proposed as a mechanism by which Fgf8 expression can be contained to the anterior pole [24]. Our analysis predicts that repression of Sp8 by Emx2 or Coup-tfi, or both, is quite likely. Currently, possible repression of Sp8 by Coup-tfi has not been discussed in the experimental literature. Reciprocal repression between Emx2 and Pax6 has been frequently discussed as potential regulatory interaction [5,7,11,23,55,56; but see also 2]. Our analysis predicts that these interactions are approximately equally likely. However, it also predicts that reciprocal repression loops in general are not critical for correct functioning of the network. Interactions we predict are unlikely Our screen of networks also predicts several single interactions and many combinations of interactions that are unlikely to occur in the arealisation regulatory network since they usually lead to poor performance. The lack of an intuitive explanation of why some of the combinations of interactions degrade network performance demonstrates the complexity of the network dynamics, and why computational modelling of these networks gives insights not available through intuition. Several of the interactions that we predict are unlikely have previously been hypothesised based on experiments. In particular, Fgf8?Sp8 has been proposed by Sahara et al. [24] but our simulations predict that this interaction creates an inductive loop which is detrimental to network performance. The experimental evidence for this interaction is that ectopic expression of Fgf8 in the telencephalon by in utero electroporation at E11.5 induced ectopic expression of Sp8 at E13.5 [24]. However, the target tissue contained an active regulatory network that could have indirectly initiated expression of Sp8 after perturbation by ectopic Fgf8. Direct auto-induction of any of the five genes prevented networks from being able to recreate the experimental expression patterns. Auto-induction of Fgf8 has previously been hypothesised based on experiments implanting Fgf8-coated beads in the chick midbrain [57], limbs [58] and telencephalon [52], but our model predicts the resulting induction of ectopic Fgf8 is unlikely to be direct. It could be occurring indirectly through an active regulatory network perturbed by ectopic Fgf8. For example, in the forebrain, if Emx2 does limit the region of Fgf8 expression by repressing Sp8 inducing Fgf8 (Emx2aSp8?Fgf8, [24]) and Fgf8 represses Emx2, then ectopic Fgf8 protein could induce the transcription of ectopic Fgf8 mRNA. A more definitive test of Fgf8 auto-induction would require to addition of ectopic Fgf8 the absence of Sp8 or Emx2. Changes in Fgf8 expression would need to be examined after E12.5 because Fgf8 expression in the forebrain appears to be initiated by regulators outside the network studied here and only maintained by Sp8 [26]. Relation to other modelling work To date, we are only aware of one paper modelling cortical arealisation [59]. The model starts with expression gradients of Figure 6. Some higher order combinations of interactions rarely appear in good networks. Each panel shows the probability of following the desired anterior state trajectory against the probability of following the desired posterior state trajectory for all 224 networks that we considered. In each panel, we highlight in red networks that contain particular combinations of interactions. All other bad networks are marked with black crosses, all other good networks are marked with blue pluses. (A) In red are networks containing any of the combinations of three interactions listed in Table S1. (B) In red are networks containing any of the combinations of four interactions that we found caused networks to perform badly. doi:10.1371/journal.pcbi.1000936.g006 Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 7 September 2010 \| Volume 6 \| Issue 9 \| e1000936 Fgf8, Emx2 and Pax6, which are maintained by regulation of each other. It then goes on to simulate the formation of area-specific thalamocortical connections. In contrast, this paper focuses on modelling pattern generation by the gene regulatory network, and at present does not consider the later process of thalamocortical innervation where less data are available to constrain models. This paper draws on the ideas used in other Boolean modelling papers in different systems, but a systematic analysis of possible regulatory networks is novel. Although algorithms exist for reverse engineering the Boolean expressions and hence the structure of regulatory networks [60,61], they require data on the time course of expression levels. For example, Laubenbacher and Stigler [61] tested a reverse engineering algorithm by reconstructing a well- characterised network. They showed that their algorithm only worked well when it used time series data from mutant animals, as well as wild type time series. Currently, these data are unavailable for the system we have investigated for either wild type or mutant animals. More recently, Wittmann et al. [62] used Boolean modelling to infer regulatory relationships governing the spatial patterning of genes at the midbrain-hindbrain isthmus. They were able to use a spatial, rather than temporal pattern to infer minimal Boolean equations using reverse engineering strategies from digital electronic engineering. Compared to the gene expression patterns at the isthmus however, the arealisation expression patterns are much simpler and consequently do not provide us with many constraints for the reverse engineering algorithm. In any case, for more complex modelling Wittmann et al. added additional interactions hypothesised in the literature. In contrast, our simulation of an experimentally hypothesised network gave a negative result, which led to our systematic screening all possible networks. Our goal was to explore the space of possible networks rather than identify one individual network that could produce the desired results as Wittmann et al. did, when many other sufficient networks likely exist. Albert and Othmer [63] explored a single well-characterised network (the Drosophila segment polarity network) in great detail. Using Boolean analysis, they were able to reproduce mutants and predict novel mutants. Unfortunately, mutants in the arealisation genes exhibit a phenotype of shifted expression gradients of the other genes (see Introduction). These results cannot be reproduced in the two compartment, two level model used in this paper (see Methods, Spatial Compartments for more detail). An extended model with additional spatial compartments and expression levels, or continuous expression levels would be able to incorporate the mutant data. However, these types of models have many more parameters that cannot be constrained by the qualitative experimental data available in this case. Any systematic exploration or optimisation of parameter space for the large number of possible networks we simulate in this paper would be computationally impossible. For example, an ordinary differential equation model using Michaelis-Menten kinetics has two param- eters per interaction (the Hill coefficient and the Michaelis constant), as well as a degradation rate and a constitutive activity rate for each species [35,43], none of which are constrained by experimental data. Communication between cells In this paper, we have not considered any communication between cells since we model only two compartments at the anterior and posterior poles. However, communication between cells may occur and may be useful. Although we find that many networks can produce the experimentally observed average expression patterns, we find that in most cases, each network has more than one accessible steady state from each of the starting states. We speculate that this may be resolved by cell-cell signalling of some kind, most likely by Fgf8, which is known to be a secreted molecule. Such signalling could lock the regulatory networks of nearby communicating cells into the same state. Fgf8 movement by diffusion or some other kind of transport might also generate the smooth gradients of the TFs. An investigation of the effects of Fgf8 diffusion would require a more complex model with more than two discrete expression levels and more than two compart- ments. Conclusions Overall, our exploration of the dynamical consequences of different structures of the network consistent with experimental data predicts constraints on the structure of the real network. The Boolean approach we used is well suited to the qualitative data currently available, and permitted us to screen a large number of networks. Our results may be used as a starting point for future more realistic models of the gene networks regulating cortical arealisation because the narrowed pool of possible networks may Table 1. Probability of interactions being present in all remaining networks, compared to remaining networks that perform well. Interaction P(present) in all remaining networks (%) P(present) in all remaining good networks (%) FaE 80 80 FaC 80 80 EaS 66 66 CaS 66 66 PaE 55 55 PaC 55 55 EaP 54 54 CaP 54 54 S?P 53 51 F?P 44 46 EaF 42 43 CaF 42 43 SaE 36 39 SaC 36 39 C?E 29 31 E?C 29 31 P?F 23 18 P?S 13 15 F?F 0 0 E?E 0 0 P?P 0 0 C?C 0 0 S?S 0 0 F?S 0 0 All interactions in the good networks occur at about the expected frequency, which means that it is difficult to identify any further combinations of interactions that ensured networks performed badly or well. Despite this, we can still use the probabilities of individual interactions among the remaining good networks as an indicator of which interactions are likely and unlikely to occur in the gene network regulating cortical arealisation. doi:10.1371/journal.pcbi.1000936.t001 Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 8 September 2010 \| Volume 6 \| Issue 9 \| e1000936 make it feasible to investigate parameter space systematically in a more realistic model with many more free parameters. From an experimental perspective, data on the time course of expression levels at different spatial locations, or even accurate relative protein levels would provide useful constraints to future models. We show here though that even a simple Boolean model reveals logical principals underlying the genetic regulation of cortical arealisation, and may be used to guide future experiments. Figure 7. Best performing networks. (A) In the best performing networks, the average activity of the genes and proteins of interest in the anterior and posterior compartments formed gradients in the same direction as those observed in mouse (cf Figure 1C). (B) The structure of the two best networks. The purple boxes with names in italics represent genes and the blue ellipses with names in upright text represent proteins. Each of the gene?protein interactions has been condensed into a green box to simplify the diagram and avoid intersecting edges. Each edge between the rounded green boxes indicates how the protein in the source box regulates the gene in the target box. The two best networks performed equally well. However, some other networks with quite different structures also performed nearly as well. doi:10.1371/journal.pcbi.1000936.g007 Figure 8. A selection of networks that produced the correct average expression gradients and have common structural elements. (A) The structure of the networks. The purple boxes with names in italics represent genes and the blue ellipses with names in upright text represent proteins. Each of the gene?protein interactions has been condensed into a green box to simplify the diagram and avoid intersecting edges. Each edge between the rounded green boxes indicates how the protein in the source box regulates the gene in the target box. The solid lines indicate interactions that must be present while the dashed lines indicate interactions that can be present or absent. The 6 dashed interactions means that this diagram represents 26~64 different networks. (B) The performance of these 64 networks (red pluses) on a plot of probability of following the desired anterior state trajectory against the probability of following the desired posterior state trajectory. All other good networks are marked with blue pluses, all bad networks with black crosses. doi:10.1371/journal.pcbi.1000936.g008 Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 9 September 2010 \| Volume 6 \| Issue 9 \| e1000936 Materials and Methods Networks simulated We examined the dynamics of all possible networks created by the five genes and five proteins of interest in anterior-posterior patterning of cortical areas: Fgf8, Emx2, Pax6, Coup-tfi and Sp8 and their respective proteins. The induction of Fgf8 by Sp8 has been directly demonstrated [24], and therefore, this interaction was fixed in all the simulated networks. Genes were also always fixed to induce their corresponding protein. To narrow the number of networks considered, other interactions were either inductive (?) or repressive (a), depending on the anterior-posterior expression patterns observed experimentally (shown in Figure 1). For example, because Emx2 and Pax6 are expressed in counter gradients, we considered the interactions Emx2aPax6 and Pax6aEmx2 but not the interactions Emx2?Pax6 and Pax6?Emx2. This gave 24 possible interactions, summarised in Table 2, which have not been directly demonstrated. Hence, we considered all 224~1:68\|107 networks formed by different combinations of the possible interactions. Converting a network into Boolean logic functions Each network was turned into a set of Boolean logic functions using the logical operators AND and NOT. Repressive interac- tions were incorporated with a negation (NOT operator). We assumed that if a gene has multiple regulators, all regulatory conditions must be met, and so we combined their action with a logical conjunction (AND operator). For example, the network in Figure 2A was transformed into the set of Boolean functions in Figure 2C. According to these equations, the state of a gene or protein at time tz1 is governed by the state of its regulators at time t. A protein will only be active if its corresponding gene is active at the previous time step, and a gene will only be active if the transcriptional activators of that gene are active at the previous time step and the inhibitors are inactive. Implicit in these functions are several assumptions [63]: (1) if the regulatory requirements for transcription or translation to occur are satisfied, then the mRNA or protein is synthesised in one time step, (2) mRNA decays within one time step if the necessary regulatory requirements do not continue to be satisfied, and (3) active protein decays within one time step. Albert and Othmer [63] tried relaxing these assumptions and found that it did not change the steady states. We did not consider the OR logical operator, which corresponds to the situation where only one regulatory condition (or a subset of conditions) must be satisfied to set a gene to the active state, or other logical operators. While it would obviously be possible to relax these assumptions, this would cause a large increase in the complexity of the model and a combinatorial explosion in the number of parameters to investigate, making it harder to analyse and derive conclusions from the model. Spatial compartments Since we were interested in anterior-posterior patterning, it was necessary to have a spatial dimension in the model. This was incorporated by considering two compartments, one anterior, one posterior. The regulatory networks, and therefore logic functions, operating in the two compartments were the same. The difference between the two compartments was their initial conditions (outlined later). There was no signalling between compartments. There are several reasons why signalling between compartments was not incorporated into the model. Firstly, there is currently no experimental evidence for long range communication between cells via our molecules of interest. As discussed in the Introduction, Fgf8 is a secreted protein, and it is hypothesised to diffuse, but only its mRNA expression has been characterised. Even if it does diffuse, it is unlikely to be present at high concentration at the posterior pole, represented in our model by the posterior compartment. Gradients of TF mRNA (and presumably protein) must form by some mechanism other than diffusion and here we assume the TFs act on each other independently in each compartment. Given the lack of signalling between compartments, and the fact that in Boolean models, each gene and protein can only have the state ‘0’ or ‘1’, two compartments with different initial conditions were sufficient to completely explore the system. Additional compartments between the anterior and posterior extremes would have to start with the same initial conditions as either the anterior or posterior compartment. Without communication between Table 2. Summary of all the considered interactions. Regulator Target gene or protein Fgf8 Fgf8 Emx2 Emx2 Pax6 Pax6 Coup-tfi Coup-tfi Sp8 Sp8 Fgf8 + Fgf8 z { z { z Emx2 + Emx2 { z { z { Pax6 + Pax6 z { z { z Coup-tfi + Coup-tfi { z { z { Sp8 + Sp8 + { z { z All possible combinations of these interactions form the space of networks whose dynamics were simulated. Text in italics signifies genes while upright text signifies proteins. A ‘z’ indicates an inductive interaction while a ‘{’ indicates a repressive interaction. The table is sparse because we assume that proteins can’t regulate proteins and a gene can only regulate its corresponding protein. The circled interactions (+) were present in every network because these have been directly demonstrated by experiments. These include each gene producing its respective protein and Sp8 activating Fgf8. The other 24 interactions are possible but have not been directly demonstrated. We simulated the dynamics of the 224 networks formed by all combinations of the possible interactions. doi:10.1371/journal.pcbi.1000936.t002 Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 10 September 2010 \| Volume 6 \| Issue 9 \| e1000936 compartments, these hypothetical additional interior compart- ments would follow the same dynamics as an exterior compart- ment with the same starting state. Hence, they would not provide any extra information to constrain the structures of the arealisation network. A consequence of this two-level, two-compartment model is that we cannot simulate the mutant phenotypes of shifting expression gradients (see Figure 2B for references). In the current model, an expression gradient is represented by a protein in the active state in one compartment and in the inactive state in the other compartment. The only other possible expression patterns are active–active or inactive–inactive, which are not shifted gradients. Initial states and desired steady states of each compartment The difference between the two compartments was their initial state, and we were interested in which steady state they each ended up in given the different initial states. We describe the state of the system with a ten-tuple of 1’s and 0’s representing the state of the network nodes [Fgf8, Fgf8, Emx2, Emx2, Pax6, Pax6, Coup-tfi, Coup- tfi, Sp8, Sp8]. For example, the state [1,1,0,0,0,0,0,0,0,0] denotes Fgf8 gene and protein are active, while all other genes and proteins are inactive. This corresponds to the starting state in the anterior compartment at around E8, where Fgf8 expression is thought to be initiated via a mechanism external to the regulatory network we are modelling [5,24,26]. We assume that the expression of the other four genes is controlled by the regulatory network we are modelling. In the posterior compartment, we assume that the expression of all five genes is controlled by the modelled regulatory network and so this compartment starts in the state [0,0,0,0,0,0,0,0,0,0]. The Boolean versions of the desired anterior and posterior steady states are seen in Figure 1C and are given in tuple notation as [1,1,0,0,1,1,0,0,1,1] for the anterior compartment and [0,0,1, 1,0,0,1,1,0,0] for the posterior compartment. We were interested in networks which flowed from the anterior starting state [1,1,0,0,0,0,0,0,0,0] to the anterior steady state [1,1,0,0,1,1,0,0, 1,1], as well as from the posterior starting state [0,0,0,0,0,0,0,0,0,0] to the posterior steady state [0,0,1,1,0,0,1,1,0,0]. Creating and analysing state tables The binary tuple representation of states emphasises the fact that Boolean networks are finite state machines whose steady states can be readily determined. Initially, we determined the steady states of each network by creating a state table for each network. This is a list of all possible states of the network ( [0,0,0,0,0,0,0,0,- 0,0], [0,0,0,0,0,0,0,0,0,1],…, [1,1,1,1,1,1,1,1,1,1]) and the corre- sponding next state when the Boolean rules were applied. Steady states were those that did not change under the Boolean rules. Unfortunately however, this analysis could not reveal which networks proceeded along the desired trajectories through state space. Trajectories can be traced in state tables, but such trajectories assume that all nodes update synchronously so that trajectories are deterministic. Synchronous updating has been used previously in Boolean modelling [63] but synchronous trajectories frequently end up in artefactual cyclic attractors [35,49,64]. In reality, it is highly unlikely that multiple species in a network would change their state at exactly the same time. Rather, these systems are stochastic, with nodes updated asynchronously, and this has consequences for the dynamics of the system. Simulating the networks with asynchronous updating Assuming fully asynchronous updating of nodes enabled the use of the Markov chain formalism to describe and analyse the network dynamics [65]. The transition matrix T of a Markov chain contains the probability of transition from each state to other states in state space. We used the deterministic state table described above to calculate the transition matrix, T, of each network, assuming that each individual node changed state with equal probability. For example, a deterministic transition from [1,1,0,0,0,0,0,0,0,0] to [1,1,0,0,1,1,0,0,0,0] translated to a sto- chastic transition to state [1,1,0,0,1,0,0,0,0,0] or [1,1,0,0,0,1,0, 0,0,0], each with a 50% probability. We found that most networks formed reducible Markov chains, with more than one steady state, each a part of a closed class of states. In general, the anterior and posterior starting states were transient states that could end up at more than one steady state. The probability of ending up at different steady states from a transient state could be calculated analytically [65] or by performing the simple computation: s(n)~Tns(0) ð1Þ where s(n) is the distribution of states of the system at time step n. Note that s is different to the state tuple notation used so far. Instead, it is a column vector of length 2No: nodes~210. The probability of being in state [0,0,0,0,0,0,0,0,0,0] is given by element s1, the probability of being in state [0,0,0,0,0,0,0,0,0,1] is given by element s2, and so on. The two compartments in our model each started in a single state, not a distribution of states. Hence, the anterior starting state [1,1,0,0,0,0,0,0,0,0] correspond- ed to an s-vector with a probability of one at element s769 and zero probability elsewhere, and the posterior starting state [0,0,0,0, 0,0,0,0,0,0] corresponded to an s-vector with a probability of one in element s1 and zero probability elsewhere. The element si(n) gives the probability of finding the system in state i at time step n. Since our networks always ended up in a distribution of steady states, if n was large enough, the computation of Equation 1 determined the probability of ending up at different steady states from the starting state s(0). In our analysis, since we knew the steady states of each Markov chain from the state tables, we iteratively calculated s(n)~Ts(n{1) until there was a 99.99% chance of being in the steady states. In many cases, there was a distribution of steady states. As each compartment represented many cells, the steady state probability distribution could be interpreted as the distribution of states across an inhomogeneous cell population [66]. Hence, we calculated the average amount of each species in a compartment as the sum of steady states of each compartment weighted by the probability of entering that steady state. Analysing the similarity between different groups of networks We quantified the structural difference between two networks as the number of interactions differing between them. We refer to this as the distance between networks because if the network structure is notated as a vector, then our measure of difference between two networks is the Manhattan distance between the two vectors. Because there are 24 possible interactions, the maximum distance between two networks is 24, which occurs if all interactions that are present on one network are absent in the other and vice versa. Identifying good and bad networks and good and bad combinations of interactions We were interested in networks that reliably followed a trajectory from the anterior starting state to the anterior steady state, as well as from the posterior starting state to the posterior Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 11 September 2010 \| Volume 6 \| Issue 9 \| e1000936 steady state. We defined the overall performance index of a network, P, as the minimum of the probability of following the desired anterior trajectory and the probability of following the desired posterior trajectory. If a network proceeded along each of the desired trajectories more than 50% of the time, then this was sufficient to give the average expression gradients observed experimentally. This is equivalent to Pw0:5. Graphically, we represent the performance of different networks on plots of probability of proceeding from the anterior starting state to the anterior steady state, against probability of proceeding from the posterior starting state to the posterior steady state (for example, see Figure 3B). On these plots, networks that reliably produce the experimentally observed expression gradients (Pw0:5) fall in the upper, right quadrant. Finally, we found combinations of interactions that made a network perform universally poorly or well. We did this by examining the distribution of P for networks with particular combinations of interactions. We started by looking at P for all networks with each single interaction, compared to without. We then looked at all combinations of interactions being present or absent for all combinations of two, three and four interactions. If all the networks containing a particular combination of interac- tions had Pw0:5, then that set of networks was classified as good. Conversely, if the majority of networks containing a particular combination of interactions had Pv0:6, and only a few networks with 0:5vPv0:6, then that set of networks was classified as bad. Supporting Information Table S1 Higher order combinations of interactions that rarely appear in good networks. Found at: doi:10.1371/journal.pcbi.1000936.s001 (0.04 MB PDF) Acknowledgments We thank Linda Richards and Tomomi Shimogori for their helpful feedback and comments on the manuscript. 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Gene Regulation of Brain Development PLoS Computational Biology \| www.ploscompbiol.org 13 September 2010 \| Volume 6 \| Issue 9 \| e1000936	20862356	Sp8 = ( ( Fgf8 ) AND NOT ( Emx2 ) ) Coup_fti = ( NOT ( ( Fgf8 ) OR ( Sp8 ) ) ) OR NOT ( Fgf8 OR Sp8 ) Pax6 = ( ( ( Sp8 ) AND NOT ( Coup_fti ) ) AND NOT ( Emx2 ) ) Fgf8 = ( ( Fgf8 AND ( ( ( Sp8 ) ) ) ) AND NOT ( Emx2 ) ) Emx2 = ( ( ( ( Coup_fti ) AND NOT ( Fgf8 ) ) AND NOT ( Sp8 ) ) AND NOT ( Pax6 ) )
Dynamical and Structural Analysis of a T Cell Survival Network Identifies Novel Candidate Therapeutic Targets for Large Granular Lymphocyte Leukemia Assieh Saadatpour1, Rui-Sheng Wang2, Aijun Liao3, Xin Liu3, Thomas P. Loughran3, Istva´n Albert4, Re´ka Albert2* 1 Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania, United States of America, 2 Department of Physics, The Pennsylvania State University, University Park, Pennsylvania, United States of America, 3 Penn State Hershey Cancer Institute, The Pennsylvania State University College of Medicine, Hershey, Pennsylvania, United States of America, 4 Department of Biochemistry and Molecular Biology, The Pennsylvania State University, University Park, Pennsylvania, United States of America Abstract The blood cancer T cell large granular lymphocyte (T-LGL) leukemia is a chronic disease characterized by a clonal proliferation of cytotoxic T cells. As no curative therapy is yet known for this disease, identification of potential therapeutic targets is of immense importance. In this paper, we perform a comprehensive dynamical and structural analysis of a network model of this disease. By employing a network reduction technique, we identify the stationary states (fixed points) of the system, representing normal and diseased (T-LGL) behavior, and analyze their precursor states (basins of attraction) using an asynchronous Boolean dynamic framework. This analysis identifies the T-LGL states of 54 components of the network, out of which 36 (67%) are corroborated by previous experimental evidence and the rest are novel predictions. We further test and validate one of these newly identified states experimentally. Specifically, we verify the prediction that the node SMAD is over-active in leukemic T-LGL by demonstrating the predominant phosphorylation of the SMAD family members Smad2 and Smad3. Our systematic perturbation analysis using dynamical and structural methods leads to the identification of 19 potential therapeutic targets, 68% of which are corroborated by experimental evidence. The novel therapeutic targets provide valuable guidance for wet-bench experiments. In addition, we successfully identify two new candidates for engineering long-lived T cells necessary for the delivery of virus and cancer vaccines. Overall, this study provides a bird’s-eye-view of the avenues available for identification of therapeutic targets for similar diseases through perturbation of the underlying signal transduction network. Citation: Saadatpour A, Wang R-S, Liao A, Liu X, Loughran TP, et al. (2011) Dynamical and Structural Analysis of a T Cell Survival Network Identifies Novel Candidate Therapeutic Targets for Large Granular Lymphocyte Leukemia. PLoS Comput Biol 7(11): e1002267. doi:10.1371/journal.pcbi.1002267 Editor: Yanay Ofran, Bar Ilan University, Israel Received May 18, 2011; Accepted September 22, 2011; Published November 10, 2011 Copyright: 2011 Saadatpour et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported by NSF grant CCF-0643529 to RA and by NIH grants CA98472 and CA133525 to TPL. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: ralbert@phys.psu.edu Introduction Living cells perceive and respond to environmental perturba- tions in order to maintain their functional capabilities, such as growth, survival, and apoptosis. This process is carried out through a cascade of interactions forming complex signaling networks. Dysregulation (abnormal expression or activity) of some components in these signaling networks affects the efficacy of signal transduction and may eventually trigger a transition from the normal physiological state to a dysfunctional system [1] manifested as diseases such as diabetes [2,3], developmental disorders [4], autoimmunity [5] and cancer [4,6]. For example, the blood cancer T-cell large granular lymphocyte (T-LGL) leukemia exhibits an abnormal proliferation of mature cytotoxic T lymphocytes (CTLs). Normal CTLs are generated to eliminate cells infected by a virus, but unlike normal CTLs which undergo activation-induced cell death after they successfully fight the virus, leukemic T-LGL cells remain long-term competent [7]. The cause of this abnormal behavior has been identified as dysregulation of a few components of the signal transduction network responsible for activation-induced cell death in T cells [8]. Network representation, wherein the system’s components are denoted as nodes and their interactions as edges, provides a powerful tool for analyzing many complex systems [9,10,11]. In particular, network modeling has recently found ever-increasing applications in understanding the dynamic behavior of intracel- lular biological systems in response to environmental stimuli and internal perturbations [12,13,14]. The paucity of knowledge on the biochemical kinetic parameters required for continuous models has called for alternative dynamic approaches. Among the most successful approaches are discrete dynamic models in which each component is assumed to have a finite number of qualitative states, and the regulatory interactions are described by logical functions [15]. The simplest discrete dynamic models are the so-called Boolean models that assume only two states (ON or OFF) for each component. These models were originally introduced by S. Kauffman and R. Thomas to provide a coarse- grained description of gene regulatory networks [16,17]. PLoS Computational Biology \| www.ploscompbiol.org 1 November 2011 \| Volume 7 \| Issue 11 \| e1002267 A Boolean network model of T cell survival signaling in the context of T-LGL leukemia was previously constructed by Zhang et al [18] through performing an extensive literature search. This network consists of 60 components, including proteins, mRNAs, and small molecules (see Figure 1). The main input to the network is ‘‘Stimuli’’, which represents virus or antigen stimulation, and the main output node is ‘‘Apoptosis’’, which denotes programmed cell death. Based on a random order asynchronous Boolean dynamic model of the assembled network, Zhang et al identified a minimal number of dysregulations that can cause the T-LGL survival state, namely overabundance or overactivity of the proteins platelet- derived growth factor (PDGF) and interleukin 15 (IL15). Zhang et al carried out a preliminary analysis of the network’s dynamics by performing numerical simulations starting from one specific initial condition (corresponding to resting T cells receiving antigen stimulation and over-abundance of the two proteins PDGF and IL15). Once the known deregulations in T-LGL leukemia were reproduced, each of these deregulations was interrupted individ- ually, by setting the node’s status to the opposite state, to predict key mediators of the disease. Yet, a complete dynamic analysis of the system, including identification of the attractors (e.g. steady states) of the system and their corresponding basin of attraction (precursor states), as well as a thorough perturbation analysis of the system considering all possible initial states, is lacking. Performing this analysis can provide deeper insights into unknown aspects of T-LGL leukemia. Stuck-at-ON/OFF fault is a very common dysregulation of biomolecules in various cancer diseases [19]. For example, stuck- at-ON (constitutive activation) of the RAS protein in the mitogen- activated protein kinase pathways leads to aberrant cell prolifer- ation and cancer [19,20]. Thus identifying components whose stuck-at values result in the clearance, or alternatively, the persistence of a disease is extremely beneficial for the design of intervention strategies. As there is no known curative therapy for T-LGL leukemia, identification of potential therapeutic targets is of utmost importance [21]. In this paper, we carry out a detailed analysis of the T-LGL signaling network by considering all possible initial states to probe the long-term behavior of the underlying disease. We employ an asynchronous Boolean dynamic framework and a network reduction method, which we previously proposed [22], to identify the attractors of the system and analyze their basins of attraction. This analysis allows us to confirm or predict the T-LGL states of 54 components of the network. The predicted state of one of the components (SMAD) is validated by new wet-bench experiments. We then perform node perturbation analysis using the dynamic approach and a structural method proposed in [23] to study to what extent does each component contribute to T-LGL leukemia. Both methods give consistent results and together identify 19 key components whose disruption can reverse the abnormal state of the signaling network, thereby uncovering potential therapeutic targets for this disease, some of which are also corroborated by experimental evidence. Materials and Methods Any biological regulatory network can be represented by a directed graph G = (V, E) where V = {v1, v2,…, vn} is the set of vertices (nodes) describing different components of the system, and E is the set of edges denoting the regulatory interactions among the components. The orientation of each edge in the network follows the direction of mass transfer or information propagation from the upstream to the downstream node. Each edge can be also characterized with a sign where a positive sign denotes activation and a negative sign signifies inhibition. The source nodes (i.e. nodes with no incoming edges) of this graph, if they exist, represent external inputs (signals), and one or more nodes, usually sink nodes (i.e. nodes with no outgoing edges), are customarily designated as outputs of the network. Boolean dynamic models Boolean models belong to the class of discrete dynamic models in which each node of the network is characterized by an ON (1) or OFF (0) state and usually the time variable t is also considered to be discrete, i.e. it takes nonnegative integer values [24,25]. The future state of each node vi is determined by the current states of the nodes regulating it according to a Boolean transfer function fi : f0,1gki?f0,1g, where ki is the number of regulators of vi. Each Boolean function (rule) represents the regulatory relationships between the components and is usually expressed via the logical operators AND, OR and NOT. The state of the system at each time step is denoted by a vector whose ith component represents the state of node vi at that time step. The discrete state space of a system can be represented by a state transition graph whose nodes are states of the system and edges are allowed transitions among the states. By updating the nodes’ states at each time step, the state of the system evolves over time and following a trajectory of states it eventually settles down into an attractor. An attractor can be in the form of either a fixed point, in which the state of the system does not change, or a complex attractor, where the system oscillates (regularly or irregularly) among a set of states. The set of states leading to a specific attractor is called the basin of attraction of that attractor. In order to evaluate the state of each node at a given time instant, synchronous as well as asynchronous updating strategies have been proposed [24,25]. In the synchronous method all nodes of the network are updated simultaneously at multiples of a common time step. The underlying assumption of this update method is that the timescales of all the processes occurring in a system are similar. This is a quite strong and potentially unrealistic assumption, which in particular may not be suited for intracellular biological processes due to the variety of timescales associated with transcription, translation and post-translational mechanisms [26]. To overcome this limitation, various asynchronous methods have been proposed wherein the nodes are updated based on individual Author Summary T-LGL leukemia is a blood cancer characterized by an abnormal increase in the abundance of a type of white blood cell called T cell. Since there is no known curative therapy for this disease, identification of potential thera- peutic targets is of utmost importance. Experimental identification of manipulations capable of reversing the disease condition is usually a long, arduous process. Mathematical modeling can aid this process by identifying potential therapeutic interventions. In this work, we carry out a systematic analysis of a network model of T cell survival in T-LGL leukemia to get a deeper insight into the unknown facets of the disease. We identify the T-LGL status of 54 components of the system, out of which 36 (67%) are corroborated by previous experimental evidence and the rest are novel predictions, one of which we validate by follow-up experiments. By deciphering the structure and dynamics of the underlying network, we identify component perturbations that lead to pro- grammed cell death, thereby suggesting several novel candidate therapeutic targets for future experiments. Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 2 November 2011 \| Volume 7 \| Issue 11 \| e1002267 timescales [25,27,28,29,30], including deterministic methods with fixed node timescales and stochastic methods such as random order asynchronous method [27] wherein the nodes are updated in random permutations. In a previous work [22], we carried out a comparative study of three different asynchronous methods applied to the same biological system. That study suggested that the general asynchronous (GA) method, wherein a randomly selected node is updated at each time step, is the most efficient and informative asynchronous updating strategy. This is because deterministic asynchronous [22] or autonomous [30] Boolean models require kinetic or timing knowledge, which is usually missing, and random order asynchronous models [27] are not computationally efficient compared to the GA models. In addition, the superiority of the GA approach has been corroborated by other researchers [29] and the method has been used in other studies as well [31,32]. We thus chose to employ the GA method in this work, and we implemented it using the open-source software library BooleanNet [33]. It is important to note that the stochasticity inherent to this method may cause each state to have multiple successors, and thus the basins of attraction of different attractors may overlap. For systems with multiple fixed-point attractors, the absorption probabilities to each fixed point can be computed through the analysis of the Markov chain and transition matrix associated with the state transition graph of the system [34]. Given a fixed point, node perturbations can be performed by reversing the state of the nodes i.e. by knocking out the nodes that stabilize in an ON state in the fixed point or over-expressing the ones that stabilize in an OFF state. Figure 1. The T-LGL survival signaling network. The shape of the nodes indicates the cellular location: rectangular indicates intracellular components, ellipse indicates extracellular components, and diamond indicates receptors. Node colors reflect the current knowledge on the state of these nodes in leukemic cells: highly active components in T-LGL are shown in red, inhibited nodes are shown in green, nodes that have been suggested to be deregulated are in blue, and the state of white nodes is unknown. Conceptual nodes (Stimuli, Stimuli2, P2, Cytoskeleton signaling, Proliferation, and Apoptosis) are represented by yellow hexagons. An arrowhead or a short perpendicular bar at the end of an edge indicates activation or inhibition, respectively. The inhibitory edges from Apoptosis to other nodes are not shown. The full names of the node labels are given in Table S2. This figure and its caption are adapted from [18]. doi:10.1371/journal.pcbi.1002267.g001 Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 3 November 2011 \| Volume 7 \| Issue 11 \| e1002267 Network reduction A Boolean network with n nodes has a total of 2n states. This exponential dependence makes it computationally intractable to map the state transition graphs of even relatively small networks. This calls for developing efficient network reduction approaches. Recent efforts towards addressing this challenge consists of iteratively removing single nodes that do not regulate their own function and simplifying the redundant transfer functions using Boolean algebra [35,36]. Naldi et al [35] proved that this approach preserves the fixed points of the system and that for each (irregular) complex attractor in the original asynchronous model there is at least one complex attractor in the reduced model (i.e. network reduction may create spurious oscillations). Boolean networks often contain nodes whose states stabilize in an attracting state after a transient period, regardless of updating strategy or initial conditions. The attracting states of these nodes can be readily identified by inspection of their Boolean functions. In a previous work [22] we proposed a method of network simplification by (i) pinpointing and eliminating these stabilized nodes and (ii) iteratively removing a simple mediator node (e.g. a node that has one incoming edge and one outgoing edge) and connecting its input(s) to its target(s). Our simplification method shares similarities with the method proposed in [35,36], with the difference that we only remove stabilized nodes (which have the same state on every attractor) and simple mediator nodes rather than eliminating each node without a self loop. Thus their proof regarding the preservation of the steady states by the reduction method holds true in our case. We employed this simplification method for the analysis of a signal transduction network in plants and verified by using numerical simulations that it preserves the attractors of that system. In this work, we employ this reduction method to simplify the T-LGL leukemia signal transduction network synthesized by Zhang et al [18], thereby facilitating its dynamical analysis. We also note that the first step of our simplification method is similar to the logical steady state analysis implemented in the software tool CellNetAna- lyzer [37,38]. We thus refer to this step as logical steady state analysis throughout the paper. Identification of attractors It should be noted that the fixed points of a Boolean network are the same for both synchronous and asynchronous methods. In order to obtain the fixed points of a system one can solve the set of Boolean equations independent of time. To this end, we first fix the state of the source nodes. We then determine the nodes whose rules depend on the source nodes and will either stabilize in an attracting state after a time delay or otherwise their rules can be simplified significantly by plugging in the state of the source nodes. Iteratively inserting the states of stabilized nodes in the rules (i.e. employing logical steady state analysis) will result in either the fixed point(s) of the system, or the partial fixed point(s) and a remaining set of equations to be solved. In the latter case, if the remaining set of equations is too large to obtain its fixed point(s) analytically, we take advantage of the second step of our reduction method [22] to simplify the resulting network and to determine a simpler set of Boolean rules. By solving this simpler set of equations (or performing numerical simulations, if necessary) and plugging the solutions into the original rules, we can then find the states of the removed nodes and determine the attractors of the whole system accordingly. For the analysis of basins of attraction of the attractors, we perform numerical simulations using the GA update method. A structural method for identifying essential components The topology (structure) and the function of biological networks are closely related. Therefore, structural analysis of biological networks provides an alternative way to understand their function [39,40]. We have recently proposed an integrative method to identify the essential components of any given signal transduction network [23]. The starting point of the method is to represent the combinatorial relationship of multiple regulatory interactions converging on a node v by a Boolean rule: v~(u11 AND ::: AND u1n1) OR (u21 AND ::: AND u2n2) OR ::: OR (um1 AND ::: AND umnm) where uij’s are regulators of node v. The method consists of two main steps. The first step is the expansion of a signaling network to a new representation by incorporating the sign of the interactions as well as the combinatorial nature of multiple converging interactions. This is achieved by introducing a complementary node for each component that plays a role in negative regulations (NOT operation) as well as introducing a composite node to denote conditionality among two or more edges (AND operation). This step eliminates the distinction of the edge signs; that is, all directed edges in the expanded network denote activation. In addition, the AND and OR operators can be readily distinguished in the expanded network, i.e., multiple edges ending at composite nodes are added by the AND operator, while multiple edges ending at original or complementary nodes are cumulated by the OR operator. The second step is to model the cascading effects following the loss of a node by an iterative process that identifies and removes nodes that have lost their indispensable regulators. These two steps allow ranking of the nodes by the effects of their loss on the connectivity between the network’s input(s) and output(s). We proposed two connectivity measures in [23], namely the simple path (SP) measure, which counts the number of all simple paths from inputs to outputs, and a graph measure based on elementary signaling modes (ESMs), defined as a minimal set of components that can perform signal transduction from initial signals to cellular responses. We found that the combinatorial aspects of ESMs pose a substantial obstacle to counting them in large networks and that the SP measure has a similar performance as the ESM measure since both measures incorporate the cascading effects of a node’s removal arising from the synergistic relations between multiple interactions. Therefore, we employ the SP measure and define the importance value of a component v as: ESP(v)~ NSP(Gexp){NSP(GDv) NSP(Gexp) where NSP(Gexp) and NSP(GDv) denote the total number of simple paths from the input(s) to the output(s) in the original expanded network Gexp and the damaged network GDv upon disruption of node v, respectively. This essentiality measure takes values in the interval [0,1], with 1 indicating a node whose loss causes the disruption of all paths between the input and output node(s). In this paper, we also make use of this structural method to identify essential components of the T-LGL leukemia signaling network. We then relate the importance value of nodes to the effects of their knockout (sustained OFF state) in the dynamic model and the importance value of complementary nodes to the effects of their original nodes’ constitutive activation (sustained ON state) in the dynamic model. Experimental determination of the T-LGL state of the node SMAD Patient characteristics and preparation of peripheral blood mononuclear cells (PBMC). All patients met the Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 4 November 2011 \| Volume 7 \| Issue 11 \| e1002267 clinical criteria of T-LGL leukemia with increased numbers (.80%) of CD3+CD8+ T cells in the peripheral blood. Patients received no treatment at the time of sample acquisition. Peripheral blood specimens from LGL leukemia patients were obtained and informed consents signed for sample collection according to a protocol approved by the Institutional Review Board of Penn State Hershey Cancer Institute. PBMC were isolated by Ficoll-Hypaque gradient separation, as described previously [41]. CD3+CD8+ T cells from four age- and gender-matched healthy donors were isolated by a human CD8+ T cell enrichment cocktail RosetteSep kit (Stemcell Technology). The purity of freshly isolated CD3+CD8+ T cells (26105/sample in triplicate) in each of the samples was determined by flow cytometry assay by detecting positive staining of the CD3 and CD8 T cell markers. The purity for normal purified CD3+CD8+ T cells was over 90%. Cell viability was determined by trypan blue exclusion assay with more than 95% viability in all the samples. Phospho-Smad2 and phospho-Smad3 measurement. Western blot was performed to detect Phospho-Smad2 (P- Smad2) and Phospho-Smad3 (P-Smad3) in activated normal CD3+CD8+ cells (CD3+CD8+ cells .90%) compared with PBMC (CD3+CD8+ cells .80%) from T-LGL leukemia patients. Normal CD3+CD8+ T cells were isolated by a human CD8+ T cell enrichment cocktail RosetteSep kit (Stemcell Technology) from four normal donors, then cultured in RPMI-1640 supplemented with 10% fetal bovine serum in presence of PHA (1 mg/mL) for 1 day followed by IL2 (500 IU/mL) for 3 days (lanes 1–4). The equal loading of protein was confirmed by probing with total Smad2 or Smad3. Phospho-Smad2 (Ser465/467), Smad2, Phospho-Smad3 (Ser423/425) and Smad3 antibodies were purchased from Cell Signaling Technology Inc. (Beverly, MA). Results Network simplification and dynamic analysis The T-LGL signaling network reconstructed by Zhang et al [18] contains 60 nodes and 142 regulatory edges. Zhang et al used a two-step process: they first synthesized a network containing 128 nodes and 287 edges by extensive literature search, then simplified it with the software NET-SYNTHESIS [42], which constructs the sparsest network that maintains all of the causal (upstream- downstream) effects incorporated in a redundant starting network. In this study, we work with the 60-node T-LGL signaling network reported in [18], which is redrawn in Figure 1. The Boolean rules for the components of the network were constructed in [18] by synthesizing experimental observations and for convenience are given in Table S1 as well. The description of the node names and abbreviations are provided in Table S2. To reduce the computational burden associated with the large state space (more than 1018 states for 60 nodes), we simplified the T-LGL network using the reduction method proposed in [22] (see Materials and Methods). We fixed the six source nodes in the states given in [18], i.e. Stimuli, IL15, and PDGF were fixed at ON and Stimuli2, CD45, and TAX were fixed at OFF. We used the Boolean rules constructed in [18], with one notable difference. The Boolean rules for all the nodes in [18], except Apoptosis, contain the expression ‘‘AND NOT Apoptosis’’, meaning that if Apoptosis is ON, the cell dies and correspondingly all other nodes are turned OFF. To focus on the trajectory leading to the initial turning on of the Apoptosis node, we removed the ‘‘AND NOT Apoptosis’’ from all the logical rules. This allows us to determine the stationary states of the nodes in a live cell. We determined which nodes’ states stabilize using the first step of our simplification method, i.e. logical steady state analysis (see Materials and Methods). Our analysis revealed that 36 nodes of the network stabilize in either an ON or OFF state. In particular, Proliferation and Cytoskeleton signaling, two output nodes of the network, stabilize in the OFF and ON state, respectively. Low proliferation in leukemic LGL has been observed experimentally [43], which supports our finding of a long-term OFF state for this output node. The ON state of Cytoskeleton signaling may not be biologically relevant as this node represents the ability of T cells to attach and move which is expected to be reduced in leukemic T- LGL compared to normal T cells. The nodes whose stabilized states cannot be readily obtained by inspection of their Boolean rules form the sub-network represented in Figure 2A. The Boolean rules of these nodes are listed in Table S3 wherein we put back the ‘‘AND NOT Apoptosis’’ expression into the rules. Next, we identified the attractors (long-term behavior) of the sub-network represented in Figure 2A (see Materials and Methods). We found that upon activation of Apoptosis all other nodes stabilize at OFF, forming the normal fixed point of the system, which represents the normal behavior of programmed cell death. When Apoptosis is stabilized at OFF, the two nodes in the top sub-graph oscillate while all the nodes in the bottom sub-graph are stabilized at either ON or OFF. As shown in Figure 3, the state space of the two oscillatory nodes, TCR and CTLA4, forms a complex attractor in which the average fraction of ON states for either node is 0.5. Given that these two nodes have no effect on any other node under the conditions studied here (i.e. stable states of the source nodes), their behavior can be separated from the rest of the network. The bottom sub-graph exhibits the normal fixed point, as well as two T-LGL (disease) fixed points in which Apoptosis is OFF. The only difference between the two T-LGL fixed points is that the node P2 is ON in one fixed point and OFF in the other, which was expected due to the presence of a self-loop on P2 in Figure 2A. P2 is a virtual node introduced to mediate the inhibition of interferon-c translation in the case of sustained activity of the interferon-c protein (IFNG in Figure 2A). The node IFNG is also inhibited by the node SMAD which stabilizes in the ON state in both T-LGL fixed points. Therefore IFNG stabilizes at OFF, irrespective of the state of P2, as supported by experimental evidence [44]. Thus the biological difference between the two fixed points is essentially a memory effect, i.e. the ON state of P2 indicates that IFNG was transiently ON before stabilizing in the OFF state. In the two T-LGL fixed points for the bottom sub- graph of Figure 2A, the nodes sFas, GPCR, S1P, SMAD, MCL1, FLIP, and IAP are ON and the other nodes are OFF. We found by numerical simulations using the GA method (see Materials and Methods) that out of 65,536 total states in the state transition graph, 53% are in the exclusive basin of attraction of the normal fixed point, 0.24% are in the exclusive basin of attraction of the T- LGL fixed point wherein P2 is ON and 0.03% are in the exclusive basin of attraction of the T-LGL fixed point wherein P2 is OFF. Interestingly, there is a significant overlap among the basins of attraction of all the three fixed points. The large basin of attraction of the normal fixed point is partly due to the fact that all the states having Apoptosis in the ON state (that is, half of the total number of states) belong to the exclusive basin of the normal fixed point. These states are not biologically relevant initial conditions but they represent potential intermediary states toward programmed cell death and as such they need to be included in the state transition graph. Since the state transition graph of the bottom sub-graph given in Figure 2A is too large to represent and to further analyze (e.g. to obtain the probabilities of reaching each of the fixed points), we applied the second step of the network reduction method proposed Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 5 November 2011 \| Volume 7 \| Issue 11 \| e1002267 in [22]. This step preserves the fixed points of the system (see Materials and Methods), and since the only attractors of this sub- graph are fixed points, the state space of the reduced network is expected to reflect the properties of the full state space. Correspondingly, the nodes having in-degree and out-degree of one (or less) in the sub-graph on Figure 2A, such as sFas, MCL1, IAP, GPCR, SMAD, and CREB, can be safely removed without losing any significant information as such nodes at most introduce a delay in the signal propagation. In addition, we note that although the node P2 has a self-loop and generates a new T-LGL fixed point as described before, it can also be removed from the network since the two fixed points differ only in the state of P2 and thus correspond to biologically equivalent disease states. We revisit this node when enumerating the attractors of the original network. In the resulting simplified network, the nodes BID, Caspase, and IFNG would also have in-degree and out-degree of one (or less) and thus can be safely removed as well. This reduction procedure results in a simple sub-network represented in Figure 2B with the Boolean rules given in Table 1. Our attractor analysis revealed that this sub-network has two fixed points, namely 000001 and 110000 (the digits from left to right represent the state of the nodes in the order as listed from top to bottom in Table 1). The first fixed point represents the normal state, that is, the apoptosis of CTL cells. Note that the OFF state of other nodes in this fixed point was expected because of the presence of ‘‘AND NOT Apoptosis’’ in all the Boolean rules. The second fixed point is the T-LGL (disease) one as Apoptosis is stabilized in the OFF state. We note that the sub-network depicted in Figure 2B contains a backbone of activations from Fas to Apoptosis and two nodes (S1P and FLIP) which both have a mutual inhibitory relationship with the backbone. If activation reaches Apoptosis, the system converges to the normal fixed point. In the T-LGL fixed point, on the other hand, the backbone is inactive while S1P and FLIP are active. We found by simulations that for the simplified network of Figure 2B, 56% of the states of the state transition graph (represented in Figure 4) are in the exclusive basin of attraction of the normal fixed point while 5% of the states form the exclusive basin of attraction of the T-LGL fixed point. Again, the half of state space that has the ON state of Apoptosis belongs to the exclusive basin of attraction of the normal fixed point. Notably, there is a significant overlap between the basins of attraction of the two fixed points, which is illustrated by a gray color in Figure 4. The probabilities of reaching each of the two fixed points starting from these gray-colored states, found by analysis of the corresponding Markov chain (see Materials and Methods), are given in Figure 5. As this figure represents, for the majority of cases the probability of reaching the normal fixed point is higher than that of the T-LGL fixed point. The three states whose probabilities to reach the T-LGL fixed point are greater than or equal to 0.7 are one step away either from the T-LGL fixed point or from the states in its exclusive basin of attraction. In two of them, the Figure 2. Reduced sub-networks of the T-LGL signaling network. The full names of the nodes can be found in Table S2. An arrowhead or a short perpendicular bar at the end of an edge indicates activation or inhibition, respectively. The inhibitory edges from Apoptosis to other nodes are not shown. (A) The 18-node sub-network. This sub-network is obtained by removing the nodes that stabilize in the ON or OFF state upon fixing the state of the source nodes. (B) The 6-node sub-network. This sub-network is obtained by removing the top sub-graph of the sub-network in (A) and merging simple mediator nodes in the bottom sub-graph. doi:10.1371/journal.pcbi.1002267.g002 Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 6 November 2011 \| Volume 7 \| Issue 11 \| e1002267 backbone of the network in Figure 2B is inactive, and in the third one the backbone is partially inactive and most likely will remain inactive due to the ON state of S1P (one of the two nodes having mutual inhibition with the backbone). Based on the sub-network analysis and considering the states of the nodes that stabilized at the beginning based on the logical steady state analysis, we conclude that the whole T-LGL network has three attractors, namely the normal fixed point wherein Apoptosis is ON and all other nodes are OFF, representing the normal physiological state, and two T-LGL attractors in which all nodes except two, i.e. TCR and CTLA4, are in a steady state, representing the disease state. These T-LGL attractors are given in the second column of Table 2, which presents the predicted T- LGL states of 54 components of the network (all but the six source nodes whose state is indicated at the beginning of the Results section). We note that the two T-LGL attractors essentially represent the same disease state since they only differ in the state of the virtual node P2. Moreover, this disease state can be considered as a fixed point since only two nodes oscillate in the T-LGL attractors. For this reason we will refer to this state as the T-LGL fixed point. It is expected that the basins of attraction of the fixed points have similar features as those of the simplified networks. Experimental validation of the T-LGL steady state Experimental evidence exists for the deregulated states of 36 (67%) components out of the 54 predicted T-LGL states as summarized in the third column of Table 2. For example, the stable ON state of MEK, ERK, JAK, and STAT3 indicates that the MAPK and JAK-STAT pathways are activated. The OFF state of BID is corroborated by recent evidence that it is down- regulated both in natural killer (NK) and in T cell LGL leukemia [45]. In addition, the node RAS was found to be constitutively active in NK-LGL leukemia [41], which indirectly supports our result on the predicted ON state of this node. For three other components, namely, GPCR, DISC, and IFNG, which were classified as being deregulated without clear evidence of either up- regulation or down-regulation in [18], we found that they eventually stabilize at ON, OFF, and OFF, respectively. The OFF state of IFNG and DISC is indeed supported by experimental evidence [44,46]. In the second column of Table 2, we indicated with an asterisk the stabilized state of 17 components that were experimentally undocumented before and thus are predictions of our steady state analysis (P2 was not included as it is a virtual node). We note that ten of these cases were also predicted in [18] by simulations. The predicted T-LGL states of these 17 components can guide targeted experimental follow-up studies. As an example of this approach, we tested the predicted over-activity of the node SMAD (see Materials and Methods). As described in [18] the SMAD node represents a merger of SMAD family members Smad 2, 3, and 4. Smad 2 and 3 are receptor-regulated signaling proteins which are phosphorylated and activated by type I receptor kinases while Smad4 is an unregulated co-mediator [47]. Phosphorylated Smad2 and/or Smad3 form heterotrimeric complexes with Smad4 and these complexes translocate to the nucleus and regulate gene expression. Thus an ON state of SMAD in the model is a representation of the predominance of phosphorylated Smad2 and/or phosphorylated Smad3 in T-LGL cells. In relative terms as compared to normal (resting or activated) T cells, the predicted ON state implies a higher level of phosphorylated Smad2/3 in T- LGL cells as compared to normal T cells. Indeed, as shown in Figure 6, T cells of T-LGL patients tend to have high levels of phosphorylated Smad2/3, while normal activated T cells have essentially no phosphorylated Smad2/3. Thus our experiments validate the theoretical prediction. Node perturbations A question of immense biological importance is which manipulations of the T-LGL network can result in consistent activation-induced cell death and the elimination of the dysreg- ulated (diseased) behavior. We can rephrase and specify this question as which node perturbations (knockouts or constitutive activations) lead to a system that has only the normal fixed point. These perturbations can serve as candidates for potential therapeutic interventions. To this end, we performed node perturbation analysis using both structural and dynamic methods. Structural perturbation analysis. For the structural analysis, using the T-LGL network (Figure 1) and the Boolean rules (Table S1), we constructed an expanded T-LGL survival signaling network (see Materials and Methods) as represented in Figure 3. The state transition graph corresponding to the two oscillatory nodes, CTLA4 and TCR. In this graph the left binary digit of the node identifier indicates the state of CTLA4 and the right digit represents the state of TCR. The directed edges represent state transitions allowed by updating a single node’s state; self-loops appear when a node is updated but its state does not change. doi:10.1371/journal.pcbi.1002267.g003 Table 1. Boolean rules governing the nodes’ states in the 6- node sub-network represented in Figure 2B. Node Boolean rule S1P S1P* = NOT (Ceramide OR Apoptosis) FLIP FLIP* = NOT (DISC OR Apoptosis) Fas Fas* = NOT (S1P OR Apoptosis) Ceramide Ceramide* = Fas AND NOT (S1P OR Apoptosis) DISC DISC* = (Ceramide OR (Fas AND NOT FLIP)) AND NOT Apoptosis Apoptosis Apoptosis* = DISC OR Apoptosis For simplicity, the nodes’ states are represented by the node names. The symbol * indicates the future state of the marked node. doi:10.1371/journal.pcbi.1002267.t001 Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 7 November 2011 \| Volume 7 \| Issue 11 \| e1002267 Figure S1. In order to evaluate the importance of signaling components mediating T-LGL leukemia, we introduced the complementary node of Apoptosis (denoted by ,Apoptosis in Figure S1) as an output representing the survival of the CTL cells, which is activated by the complementary node of Caspase (denoted by ,Caspase in Figure S1). The reason is that we are interested in the question of how to make this outcome (i.e., the disease state) disappear, or in graph terminology, disconnected from the inputs of the network. In order to count all the simple paths from a single (rather than multiple) input signal to the output node, we fixed the states of Stimuli and IL15 at ON and those of Stimuli2, CD45, and TAX at OFF. Once the Boolean rules were simplified, we determined all the signaling paths from PDGF to the output node ,Apoptosis. Interestingly, we found that the number of signaling paths from PDGF to ,Apoptosis is much smaller than the number of signaling paths from PDGF to Figure 4. The state transition graph of the 6-node sub-network represented in Figure 2B. It contains 64 states of which the state shown with a dark blue symbol is the normal fixed point and the state shown in red is the T-LGL fixed point. States denoted by light blue symbols are uniquely in the basin of attraction of the normal fixed point whereas the states in pink can only reach the T-LGL fixed point. Gray states, on the other hand, can lead to either fixed point. doi:10.1371/journal.pcbi.1002267.g004 Figure 5. The probabilities of reaching the normal and T-LGL fixed points when both are reachable. These probabilities are computed starting from the states that are shared by both basins of attraction (see gray-colored states illustrated in Figure 4). doi:10.1371/journal.pcbi.1002267.g005 Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 8 November 2011 \| Volume 7 \| Issue 11 \| e1002267 Table 2. A summary of the dynamic analysis results of the T-LGL survival signaling network. Node T-LGL state Ref. Fixed point the disruption leads to Size of exclusive basin of normal fixed point Ref. DISC OFF [46] Normal 100% [46] Ceramide OFF [48] Normal 100% [48] Caspase OFF [46] Normal 100% SPHK1 ON [21] Normal 100% [18] S1P ON [21] Normal 100% [21] PDGFR ON [59] Normal 100% [18] GAP OFF* Normal 100% RAS ON* Normal 100% [41]1 MEK ON [59] Normal 100% [41]1 ERK ON [50,59] Normal 100% [41]1 IL2RBT ON [60] Normal 100% IL2RB ON [60] Normal 100% STAT3 ON [49] Normal 100% [49] BID OFF [45] Normal 100% MCL1 ON [49] Normal 100% [49] SOCS OFF* Both 81% JAK ON [49] Both 81% [49] PI3K ON [50] Both 75% [50] NFkB ON [18] Both 75% [18] Fas OFF [48] Both 72% sFas ON [61] Both 72% TBET ON [18] Both 63% RANTES ON [44] Both 63% PLCG1 ON* Both 63% FLIP ON [46] Both 56% IL2 OFF [62] Both 56% IAP ON* Both 56% TNF ON* Both 56% BclxL OFF [49] Both 56% GZMB ON [63] Both 56% IL2RA OFF [62] Both 56% NFAT ON* Both 56% GRB2 ON* Both 56% IFNGT ON [44,62] Both 56% TRADD OFF* Both 56% ZAP70 OFF* Both 56% LCK ON [50] Both 56% FYN ON* Both 56% IFNG OFF [44] Both 56% SMAD ON* This study Both 56% GPCR ON [21,64] Both 56% TPL2 ON [65] Both 56% A20 ON [21] Both 56% IL2RAT OFF [62] Both 56% CREB OFF* Both 56% P27 ON* Both 56% P2 ON/OFF Both 56% FasT ON [48] T-LGL 0% FasL ON [48] T-LGL 0% Cytoskeleton signaling ON* — — Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 9 November 2011 \| Volume 7 \| Issue 11 \| e1002267 Apoptosis (78,827 versus 346,974), consistent with the finding from dynamic analysis that the exclusive basin of attraction of the T- LGL fixed point is much smaller than that of the normal fixed point. Our goal of identifying node state manipulations that lead to the apoptosis of the abnormally surviving T-LGL cells can be translated into the graph-theoretical problem of finding key nodes that mediate paths to the node ,Apoptosis. Elimination of these nodes has the potential to make ,Apoptosis unreachable, or in other words to make Apoptosis the only reachable outcome. The T-LGL fixed point determined in dynamic analysis serves as a list of candidate deletions. Accordingly, we separately deleted each node that stabilizes at ON in the T-LGL fixed point, and each complementary node whose corresponding original node stabilizes at OFF in the T-LGL fixed point (see Table 2 for the state of nodes in the T-LGL fixed point). We then calculated the importance values of these nodes by examining the cascading effects of their deletion on the number of simple paths from PDGF to the ,Apoptosis output (see Materials and Methods). The importance values of the signaling components are given in Figure 7. As we can see in this figure, several components, including ,DISC, ,Ceramide, ,Caspase, SPHK1, S1P, PDGFR, PI3K, ,SOCS, JAK, ,GAP, RAS, NFkB, MEK, and ERK have importance values of one (or very close to one). This means that blocking any of these nodes disrupts (almost) all signaling paths from the source node to ,Apoptosis, thus these nodes are candidate therapeutic targets. Dynamic perturbation analysis. To identify manipulations of the T-LGL network leading to the existence of only the normal fixed point, we first considered the following scenario. We assumed that the T-LGL network is the simplified network given in Figure 2B. We examined the following dynamic perturbation approaches as potential interventions propelling the system into the normal fixed point. In the first two approaches, it is assumed that the T-LGL fixed point has been already reached (i.e. the disease has already developed), and in the last approach, all possible initial conditions are considered. 1. Reverse the state of one node at a time in the T-LGL fixed point for only the first time step, and keep updating the system. This intervention may be accomplished by a pharmacological intervention on a T-LGL cell. 2. Reverse the state of one node in the T-LGL fixed point permanently and continue updating other nodes. This Figure 6. Experimental validation of the increased activity (ON state) of Smad2/3 in leukemic T-LGL. Western blot detection of phosphorylated Smad2 or Smad3, and total Smad2 (i.e. the sum of phosphorylated and non-phosphorylated Smad2) or Smad3 in activated normal T cells compared with peripheral blood mononuclear cells from T-LGL leukemia patients confirms that Smad2 or Smad3 is unphosphorylated (inactive) in normal T cells and predominantly phosphorylated (active) in T-LGL cells. doi:10.1371/journal.pcbi.1002267.g006 Node T-LGL state Ref. Fixed point the disruption leads to Size of exclusive basin of normal fixed point Ref. Proliferation OFF [43] — — Apoptosis OFF [66] — — TCR Oscillate* — — CTLA4 Oscillate* — — The first two columns from the left list the components of the network (except for the six source nodes) and their T-LGL states. The nodes’ states marked with a * symbol were not documented experimentally in T-LGL before and were predicted by our steady state analysis. The references for the nodes’ states documented before are given in the third column. The fixed point(s) obtained after each of the nodes’ states is reversed is given in the fourth column, while the size of the exclusive basin of attraction of the normal fixed point, expressed as a percentage of the whole relevant state space, is indicated in the fifth column. The reference of the perturbation cases for which experimental evidence exists is given in the last column. The first 19 nodes in the first column are potential therapeutic targets for T-LGL leukemia. 1Evidence in NK-LGL leukemia. doi:10.1371/journal.pcbi.1002267.t002 Table 2. Cont. Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 10 November 2011 \| Volume 7 \| Issue 11 \| e1002267 intervention may be accomplished by genetic engineering of a T-LGL cell. 3. Considering all possible initial states, fix the state of one node in the opposite of its T-LGL state and keep updating other nodes. This intervention may be accomplished by genetic engineering of a population of CTLs. For the first perturbation approach, we found that only the trivial case of flipping the state of Apoptosis to ON leads exclusively to the normal fixed point. Using the second perturbation approach, we observed that fixing S1P at OFF or Apoptosis at ON eliminates the T-LGL fixed point. In addition, fixing either Ceramide or DISC at ON results in a new fixed point which is similar to the normal fixed point of the unperturbed system, with the only difference that the disrupted node’s state is fixed at ON as long as the cell is alive. Using the last perturbation approach, we found a result identical to that of the second approach, indicating that the nodes S1P, Ceramide, and DISC are candidate therapeutic targets for the simplified sub-network. Experiments also confirm that Ceramide and DISC can serve as therapeutic targets [46,48]. We note that the third approach is superior to the second in that it provides additional information on the size of the basin of attraction of each fixed point. For example, we observed that in the case of over-expression of Fas, the exclusive basin of attraction of the normal fixed point increases significantly to 72% of the states. This suggests that although both fixed points are still reachable, the normal fixed point is more probable to be reached. This analysis revealed that the last approach leads to more detailed results than the first two approaches. Next we focused our attention to the effects of node disruptions on the whole network to make biologically testable predictions about the occurrence of the disease state under different conditions. To this end, we followed the third approach delineated above. More precisely, for each node disruption we fixed the state of that node in the opposite of its stabilized state in the T-LGL fixed point given in Table 2 (i.e. we knocked out the nodes that stabilize in the ON state in T-LGL fixed point and over-expressed the ones that stabilize in the OFF state) and considered all possible initial states for the remaining nodes (except for the six source nodes). Of the 60 nodes of the network, six are source nodes, three are output nodes and two (CTLA4 and TCR) have oscillatory behavior in the T-LGL attractor. For each of the remaining nodes, we fixed the state of that node in the opposite of its T-LGL state, initiated the six source nodes as in the unperturbed case, and identified the stabilized nodes using logical steady state analysis (see Materials and Methods). We then simplified the network of non-stabilized nodes according to the second step of our reduction method (see Materials and Methods) and obtained all possible fixed points by solving the corresponding set of Boolean equations. For some cases we needed to construct the full state transition graphs because of the possibility of oscillation (e.g. when the two oscillatory nodes, CTLA4 and TCR, were connected to other nodes in the simplified network and there was a possibility of propagating the oscillation to other nodes in the T-LGL state). We found that in the case of perturbation of TBET, PI3K, NFkB, JAK, or SOCS, five additional nodes of the network connected to CTLA4 and TCR, namely LCK, FYN, Cytoskeleton signaling, ZAP70, and GRB2, oscillate as well. Also, for the knockout of FYN, only two of these additional nodes, i.e. LCK and ZAP70 oscillate. In addition, in the case of perturbation of TBET, JAK, SOCS, or IL2, the node IL2RA shows oscillatory behavior in the T-LGL state. In general, two types of fixed points were observed, the normal fixed point with Apoptosis being ON and all other nodes being OFF, and similar-to-TLGL fixed points with Apoptosis being OFF and the state of some nodes being different from the wild-type T- LGL fixed point due to the disruption imposed on the network. We still consider these latter fixed points as the T-LGL fixed point. A summary of the node disruption results, including the fixed point(s) obtained after the disruption as well as the size of the exclusive basin of attraction of the normal fixed point in the respective reduced model, is given in the fourth and fifth columns of Table 2. Our results indicate that disruption of any of the first 15 nodes in Table 2 leads to the disappearance of the T-LGL fixed point (i.e., of the disease state). These nodes are thus predicted candidate therapeutic targets. For example, our results suggest that knockout of STAT3 or over-expression of Ceramide in deregu- lated CTLs restores their activation induced cell death. We found for the knockout of either FasT or FasL that the normal fixed point and the 50% of the state transition graph which includes the ON state of Apoptosis is separated from the rest of the state space and thus they are not accessible from the biologically relevant initial conditions. Therefore, the T-LGL fixed point is the only biologically relevant outcome in this case. For this reason, the size of the basin of attraction of the normal fixed point was indicated as 0% in Table 2. Notably, these nodes can serve as candidates for engineering of long-lived T cells, which are Figure 7. Importance values of network components in T-LGL leukemia. These values are based on the relative reduction of the number of paths from PDGF to ,Apoptosis after considering the cascading effects of node disruptions. The complementary nodes are denoted by the corresponding original nodes with a symbol ‘,’ as prefix representing ‘negation’. doi:10.1371/journal.pcbi.1002267.g007 Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 11 November 2011 \| Volume 7 \| Issue 11 \| e1002267 necessary for the delivery of virus and cancer vaccines. The remaining node disruptions still retain both disease and normal fixed points. There is corroborating literature evidence for several of the therapeutic targets predicted by our analysis. For example, it was found experimentally that STAT3 knockdown by using siRNA or down-regulation of MCL1 through inhibiting STAT3 induces apoptosis in leukemic T-LGL [49]. Furthermore, in vitro Ceramide treatment induces apoptosis in leukemic T-LGL [48]. It was also found that treatment with IL2 and TCR stimulation facilitates Fas-mediated apoptosis via induction of DISC formation [46]. In addition, SPHK1 inhibition by using chemical inhibitors signifi- cantly induces apoptosis in leukemic T-LGL [18]. These experimental results validate that perturbation of these nodes results in the normal fixed point as mentioned in Table 2. Moreover, it was reported in [41] that inhibition of RAS through introducing a dominant negative form of RAS, or inhibition of MEK or ERK through chemical inhibitors, induces apoptosis in leukemic NK-LGL, which indirectly supports our results on these three nodes. For the cases where both fixed points are still reachable, our analysis of the relative size of the basins of attraction (i.e. percentage of the whole relevant state space) of the fixed points and the probabilities of reaching the fixed points (see Materials and Methods) indicated that in most of these cases the trends are similar to the wild-type model, e.g. the size of the exclusive basin of attraction of the normal fixed point is 56%, the same as that for the unperturbed system. In a few cases, however, including JAK, PI3K, or NFkB knockout as well as SOCS over-expression, the exclusive basin of attraction of the normal fixed point increased significantly (to 75% or more). Thus, these nodes can be also considered as potential therapeutic targets. Interestingly, for three cases, namely JAK, PI3K, and NFkB, experimental data also suggest that the balance between the incidence of the two fixed points is shifted in the manipulated system compared to the original one. For example, inhibition of JAK [49], PI3K [50] or NFkB [18] through chemical inhibitors induces apoptosis in leukemic T-LGL. In summary, our analysis leads to the novel predictions that Caspase, GAP, BID, or SOCS over-expression as well as RAS, MEK, ERK, IL2RBT, or IL2RB knockout can lead to apoptosis of T-LGL cells. Comparison between structural and dynamic pertur- bation analysis. We performed the perturbation analysis using a dynamic method as well as a structural method. How do the results compare? From the dynamic analysis, a node is classified as an important mediator of the T-LGL fixed point if reversing its state from the value it achieves in the T-LGL fixed point will lead the system to have only the normal fixed point. From the structural analysis, a node can be classified as an important mediator of the T-LGL behavior if its importance value (see Materials and Methods) to the ,Apoptosis outcome is higher than a pre-specified threshold. We used different importance values as thresholds and compared the structure-based classification with the dynamics-based classification by using the latter as the standard. The sensitivity (the fraction of important components based on dynamic perturbation analysis that are recognized as important by the structural method) and specificity (the fraction of non-important components based on dynamic perturbation analysis that are recognized as non-important by the structural method) values of the structure-based classification are summarized by the red curve in Figure 8. The structural method gives the best fit to the dynamic method (namely, sensitivity of 1.00 and specificity of 0.76) if a threshold of 0.9 is used. An important feature of the structural method is its incorporation of the cascading effects of a node’s deletion. To illustrate this point, we also show the corresponding result without considering the cascading effects of nodes’ deletions represented by the green curve in Figure 8. As this figure demonstrates, the results using a pure topological measure without considering the cascading effects gives a much worse fit to the results of the dynamic method. Interestingly, for all the components whose manipulation lead the system to have only the normal fixed point according to the dynamic analysis (the first 15 components in Table 2), the reported importance values based on the structural method were larger than 0.95. For four additional cases, namely, SOCS, JAK, PI3K, and NFkB, which are identified as important for survival based on the simple path measure, the dynamic analysis results also revealed that the T-LGL outcome has a lesser probability to be reached as mentioned earlier. Therefore, they can also be considered as potential therapeutic targets. We note that there are four cases, namely, TBET, FLIP, IAP, and TNF, which were identified as important based on the structural method while their disruption maintains the existence of both fixed points based on dynamic analysis and the size of the exclusive basin of attraction of the normal fixed point is either close to or the same as that of the wild-type system. This may be partly due to the fact that in the state space analysis we consider all possible initial conditions for the system, whereas the topological analysis implicitly refers to only one initial condition, wherein three source nodes are ON and all other nodes are OFF. Another potential reason regarding the discrepancies between the structural and dynamic perturbation results might be related to the structural method’s use of the simple path measure rather than the elementary signaling modes (ESMs, see Materials and Methods). Furthermore, although the reduction method used for the dynamic analysis preserves the fixed points, it can change the state transition graph and thus may have an impact on the relative size of the basins of attraction, serving as an alternative source of inconsistencies. However, this change is not expected to be drastic as we found that the exclusive basin of attraction of the normal fixed point in the 6-node network was approximately of the same relative size as that in the 18-node network. Figure 8. Comparison of structural perturbation analysis results with and without cascading effects of node deletions. SP+CE represents the simple path measure considering cascading effects of node deletions, and SP-CE represents the simple path measure without considering cascading effects of node deletions. doi:10.1371/journal.pcbi.1002267.g008 Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 12 November 2011 \| Volume 7 \| Issue 11 \| e1002267 Discussion In this paper we presented a comprehensive analysis of the T- LGL survival signaling network to unravel the unknown facets of this disease. By using a reduction technique, we first identified the fixed points of the system, namely the normal and T-LGL fixed points, which represent the healthy and disease states, respectively. This analysis identified the T-LGL states of 54 components of the network, out of which 36 (67%) are corroborated by previous experimental evidence and the rest are novel predictions. These new predictions include RAS, PLCG1, IAP, TNF, NFAT, GRB2, FYN, SMAD, P27, and Cytoskeleton signaling, which are predicted to stabilize at ON in T-LGL leukemia and GAP, SOCS, TRADD, ZAP70, and CREB which are predicted to stabilize at OFF. In addition, we found that the node P2 can stabilize in either the ON or OFF state, whereas two nodes, TCR and CTLA4, oscillate. We have experimentally validated the prediction that the node SMAD is over-active in leukemic T-LGL by demonstrating the predominant phosphorylation of the SMAD family members Smad2 and Smad3. The predicted T-LGL states of other nodes provide valuable guidance for targeted experimen- tal follow-up studies of T-LGL leukemia. Among the predicted states, the ON state of Cytoskeleton signaling may not be biologically relevant as this node represents the ability of T cells to attach and move which is expected to be reduced in leukemic T-LGL compared to normal T cells. This discrepancy may be due to the fact that the network contains insufficient detail regarding the regulation of the cytoskeleton, as there is only one node, FYN, upstream of Cytoskeleton signaling in the network. While the network is able to successfully capture survival signaling without necessarily capturing the cytoskeleton signaling, this discrepancy suggests that follow-up experimental studies should be conducted to determine the relationship between cytoskeleton signaling and survival signaling in the T-LGL network. We note that in the case of perturbation of TBET, PI3K, NFkB, JAK, or SOCS, the node Cytoskeleton signaling exhibits oscillatory behavior induced by oscillations in TCR. At present it is not known whether this predicted behavior is relevant. Using the general asynchronous (GA) Boolean dynamic approach, we analyzed the basins of attraction of the fixed points. We found that the basin of attraction of the normal fixed point is larger than that of the T-LGL fixed point. The trajectories starting from each initial state toward the T-LGL fixed point (Figure 4) may be indicative of the accumulating deregulations that lead to the disease-associated stable survival state. Although the fixed points, being time independent, are the same for all update methods or implementations of time, the update method may affect the structure of the state transition graph of the system and the basins of attraction of the fixed points. We note that the GA method assumes that each node has an equal chance of being updated. If quantitative or kinetic information becomes available in this system, unequal probabilities may be implemented by grouping the nodes into several ‘‘priority classes’’ and assigning a weight to each class where higher weights indicate more probable transitions [51]. Incorporating such information into the state space may prune the allowed trajectories and give further insights into the accumulation of deregulations. We took one step further by performing a perturbation analysis using dynamical and structural methods to identify the interven- tions leading to the disappearance of the disease fixed point. We note that our study has a dramatically larger scope than the previous key mediator analysis of Zhang et al [18]. For the dynamical analysis, we employed the GA approach instead of the random order asynchronous method and considered all possible initial conditions as opposed to performing numerical simulations using a specific initial condition. Zhang et al only focused on the node Apoptosis, and identified as ‘‘key mediators’’ the nodes whose altered state increases the frequency of ON state of Apoptosis. An increase in Apoptosis’ ON state does not necessarily imply that apoptosis is the only possible final outcome of the system. In this work, after finding the fixed points, which completely describe the state of the whole system, we performed dynamic perturbation analysis by fixing the state of each node to its opposite state in the T-LGL fixed point and determining which fixed points were obtained and what their basins of attraction were. This way we were able to identify and distinguish the key mediators whose altered state completely eliminates the leukemic outcome, and those whose altered state reduces the basin of attraction of the leukemic outcome. Moreover, numerical simulations, as done in [18], may not be able to thoroughly sample different timing. In this study, using a reduction technique, we found the cases when timing does not matter with certainty (where there is only one fixed point), and also the cases in which timing and initial conditions may matter (where there are two reachable fixed points). For the perturbation analysis using the structural method, we used the simple path (SP) measure to identify important mediators of the disease outcome and observed consistent results with the dynamic analysis. Our dynamical and structural analysis led to the identification of 19 therapeutic targets (the first 19 nodes in the first column of Table 2), 53% of which are supported by direct experimental evidence and 15% of which are supported by indirect evidence. Multi-stability (having multiple steady states) is an intrinsic dynamic property of many disease networks [52,53], which is related to the presence of feedback loops in the network. In a graph-theoretical sense, a feedback loop is a directed cycle whose sign depends upon the parity of the number of negative interactions in the cycle. A positive/negative feedback loop has an even/odd number of negative interactions. It was conjectured that the presence of positive feedback loops in the network is necessary for multi-stability whereas the existence of negative feedback loops is required for having sustained oscillations [54]. From a biological point of view, the former dynamical property is associated with multiple cell types after differentiation while the latter is related to stable periodic behaviors such as circadian rhythms [55]. We note that the T-LGL signaling network consists of both positive and negative feedbacks and thus has a potential for both multi-stability and oscillations. Indeed, the negative feedback in the top sub-graph of Figure 2A causes the complex attractor shown in Figure 3. In contrast, the negative feedback on the node P2 of the bottom sub-graph is counteracted by the positive self- loop on the same node, thus no complex attractor is possible for the bottom sub-graph of Figure 2A. The two mutual inhibition- type positive feedback loops present in the bottom sub-graph and the self-loop on P2 generate the three fixed points, while the positive self-loop on Apoptosis maintains the normal fixed point once Apoptosis is turned ON. Negative feedback loops can be a source of oscillations [56], homeostasis [56], or excitation-adaptation behavior [57]. Espe- cially, when the activation is slower than the inhibitory interaction in the negative feedback, it can lead to sustained oscillations [56]. In the T-LGL network, the negative feedback loop between the T cell receptor TCR and CTLA4 modulates stimulus-induced activation of the receptor in such a way that CTLA4 is indirectly activated after prolonged TCR activation, whereas the inhibition of TCR by CTLA4 is a direct interaction [58]. That is, activation is slower than inhibition in the negative feedback and thus an oscillatory behavior reminiscent of that obtained by our asyn- Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 13 November 2011 \| Volume 7 \| Issue 11 \| e1002267 chronous Boolean model would also be observed in continuous modeling frameworks as well. Although no time-measurements of the T cell receptor activity in T-LGL exist, it has been reported that there is variability for TCR activation in different patients ([43] and unpublished observation by T.P. Loughran), supporting the absence of a steady state behavior. Our study revealed that both structural and dynamic analysis methods can be employed to identify therapeutic targets of a disease, however, they differ in implementation efficiency as well as the scope and applicability of the results. The structural analysis does not require mapping of the state space and thus is less computationally intensive and is more feasible for large network analysis, but it may not capture all the initial states and thus may miss or inaccurately identify some important features. The dynamic analysis method, while computationally intensive, yields a comprehensive picture of the state transition graph, including all possible fixed points of the system, their corresponding basins of attraction, as well as the relative frequency of trajectories leading to each fixed point. We demonstrated that the limitations related to the vast state space of large networks can be overcome by judicious use of the network reduction technique that we developed in our previous study [22]. We conclude that the structural method incorporating the cascading effects of node disruptions is best employed for quick exploratory analysis, and dynamic analysis should be performed to get a thorough and detailed insight into the behavior of a system. Overall, the combined analysis presented in this study opens a promising avenue to predict dysregulated components and identify potential therapeutic targets, and it is versatile enough to be successfully applied to a large variety of signal transduction and regulatory networks related to diseases. Supporting Information Figure S1 The expanded T-LGL survival signaling network. Composite nodes are represented by small gray solid circles, original nodes are represented by large ovals, and complementary nodes are represented by rectangles. The labels of complementary nodes are denoted by the labels for the corresponding original nodes with a symbol ‘,’ as prefix representing ‘negation’. (TIF) Table S1 Boolean rules governing the state of the T-LGL signaling network depicted in Figure 1. For simplicity, the nodes’ states are represented by the node names. The symbol * indicates the future state of the marked node. The Boolean rule for each node is determined based on the nature of interactions between that node and the nodes directly interacting with it. This rule can be expressed using the logical operators AND, OR and NOT. For example, if the given node has a single upstream node, the corresponding Boolean function would include only one variable. This variable will be combined with a NOT operator if the upstream node is an inhibitor. In cases where the given node has multiple upstream nodes, their effect is combined with AND or OR operators (potentially in conjunction with the NOT operator) to correctly recast the regulatory interactions. For example, the AND operator is used when the co-expression of two (or more) activating inputs is required for activating the target node, whereas, the OR operator implies that the activity of at least one of the upstream activators is sufficient to activate the target node. The type of each interaction (i.e. the logical rule) should be extracted from the relevant literature and experimental evidence. This table is adapted from [1]. The interested reader is referred to [1] for the detailed explanation of the rules. (PDF) Table S2 The full names of components in the T-LGL signaling network corresponding to the abbreviated node labels used in Figure 1. Several network nodes represent the union of a few proteins with similar roles. In such cases, a single entry in the first column corresponds to several entries in the second column. This table and its caption are adapted from [1]. (PDF) Table S3 Boolean rules governing the state of the 18- node sub-network depicted in Figure 2A. 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Dynamical and Structural Analysis of T-LGL Network PLoS Computational Biology \| www.ploscompbiol.org 15 November 2011 \| Volume 7 \| Issue 11 \| e1002267	22102804	Caspase = ( ( ( BID ) AND NOT ( IAP ) ) AND NOT ( Apoptosis ) ) OR ( ( DISC ) AND NOT ( Apoptosis ) ) Apoptosis = ( Apoptosis ) OR ( Caspase ) sFas = ( ( S1P ) AND NOT ( Apoptosis ) ) MCL1 = NOT ( ( Apoptosis ) OR ( DISC ) ) Ceramide = ( ( ( Fas ) AND NOT ( Apoptosis ) ) AND NOT ( S1P ) ) IFNG = NOT ( ( Apoptosis ) OR ( P2 ) OR ( SMAD ) ) P2 = ( ( P2 ) AND NOT ( Apoptosis ) ) OR ( ( IFNG ) AND NOT ( Apoptosis ) ) IAP = NOT ( ( Apoptosis ) OR ( BID ) ) GPCR = ( ( S1P ) AND NOT ( Apoptosis ) ) SMAD = ( ( GPCR ) AND NOT ( Apoptosis ) ) DISC = ( ( ( Fas ) AND NOT ( FLIP ) ) AND NOT ( Apoptosis ) ) OR ( ( Ceramide ) AND NOT ( Apoptosis ) ) BID = NOT ( ( Apoptosis ) OR ( MCL1 ) ) CTLA4 = ( ( TCR ) AND NOT ( Apoptosis ) ) CREB = ( ( IFNG ) AND NOT ( Apoptosis ) ) Fas = NOT ( ( Apoptosis ) OR ( sFas ) ) S1P = NOT ( ( Apoptosis ) OR ( Ceramide ) ) FLIP = NOT ( ( Apoptosis ) OR ( DISC ) ) TCR = NOT ( ( Apoptosis ) OR ( CTLA4 ) )
Network Model of Immune Responses Reveals Key Effectors to Single and Co-infection Dynamics by a Respiratory Bacterium and a Gastrointestinal Helminth Juilee Thakar1,2, Ashutosh K. Pathak1,3, Lisa Murphy4¤, Re´ka Albert1,5, Isabella M. Cattadori1,3* 1 Center for Infectious Disease Dynamics, The Pennsylvania State University, University Park, Pennsylvania, United States of America, 2 Department of Pathology, Yale University School of Medicine, New Haven, Connecticut, United States of America, 3 Department of Biology, The Pennsylvania State University, University Park, Pennsylvania, United States of America, 4 Division of Animal Production and Public Health, Veterinary School, University of Glasgow, Glasgow, United Kingdom, 5 Department of Physics, The Pennsylvania State University, University Park, Pennsylvania, United States of America Abstract Co-infections alter the host immune response but how the systemic and local processes at the site of infection interact is still unclear. The majority of studies on co-infections concentrate on one of the infecting species, an immune function or group of cells and often focus on the initial phase of the infection. Here, we used a combination of experiments and mathematical modelling to investigate the network of immune responses against single and co-infections with the respiratory bacterium Bordetella bronchiseptica and the gastrointestinal helminth Trichostrongylus retortaeformis. Our goal was to identify representative mediators and functions that could capture the essence of the host immune response as a whole, and to assess how their relative contribution dynamically changed over time and between single and co-infected individuals. Network-based discrete dynamic models of single infections were built using current knowledge of bacterial and helminth immunology; the two single infection models were combined into a co-infection model that was then verified by our empirical findings. Simulations showed that a T helper cell mediated antibody and neutrophil response led to phagocytosis and clearance of B. bronchiseptica from the lungs. This was consistent in single and co-infection with no significant delay induced by the helminth. In contrast, T. retortaeformis intensity decreased faster when co-infected with the bacterium. Simulations suggested that the robust recruitment of neutrophils in the co-infection, added to the activation of IgG and eosinophil driven reduction of larvae, which also played an important role in single infection, contributed to this fast clearance. Perturbation analysis of the models, through the knockout of individual nodes (immune cells), identified the cells critical to parasite persistence and clearance both in single and co-infections. Our integrated approach captured the within-host immuno-dynamics of bacteria-helminth infection and identified key components that can be crucial for explaining individual variability between single and co-infections in natural populations. Citation: Thakar J, Pathak AK, Murphy L, Albert R, Cattadori IM (2012) Network Model of Immune Responses Reveals Key Effectors to Single and Co-infection Dynamics by a Respiratory Bacterium and a Gastrointestinal Helminth. PLoS Comput Biol 8(1): e1002345. doi:10.1371/journal.pcbi.1002345 Editor: Rob J. De Boer, Utrecht University, Netherlands Received August 3, 2011; Accepted November 25, 2011; Published January 12, 2012 Copyright: 2012 Thakar et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This study, AKP and LM were supported by a Human Frontier Science Program grant (RGP0020/2007-C). RA was supported by NSF grant CCF-0643529. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: imc3@psu.edu ¤ Current address: Life Technologies Ltd, Paisley, United Kingdom Introduction Hosts that are immunologically challenged by one infection often show increased susceptibility to a second infectious agent, whether a micro- or a macro-parasite. Changes in the immune status and polarization of the response towards one parasite can indeed facilitate the establishment and survival of a second parasitic species [1–3]. At the level of the individual host, this can be described as an immune system that has to optimize the specificity and effectiveness of the responses against different infections while engaging in secondary but equally important functions, like tissue repair or avoiding immuno-pathology. Systemic cross-regulatory processes and bystander effects by T helper cells (Th) maintain control of these functions both at the systemic and local level [4–8]. Concurrent parasite infections are regulated by and affect these mechanisms [2,4,9–14]. They can also influence each other directly, when sharing the same tissue [15–16] or through the immune system via passive effects or active manipulation of the immune components, if colonizing different organs [4,9–14]. Empirical work on bacteria-macroparasite co-infections has often found that the development of a Th2 mediated response towards the helminth leads to a reduction of the protective Th1 cytokine response against the bacteria and a more severe bacteria- induced pathology [4,11–14], although a decrease of tissue atrophy has also been observed [17–18]. The suppression of Th1 cell proliferation acts both on the inductors and effectors and is mainly driven by the repression of the IFNc mediated inflammatory activity during the early stages of the infection. However, the degree of the T helper cell polarization and the kinetics of effectors depend on the type, intensity and duration of the co-infection, over and above the very initial immune status of the host. Since host immunity is both a major selective pressure for parasite transmission and host susceptibility to re-infections, the presence of one infection can have major consequences for the PLoS Computational Biology \| www.ploscompbiol.org 1 January 2012 \| Volume 8 \| Issue 1 \| e1002345 spread and persistence of the second infection. For example, Mycobacterium tuberculosis induces more severe disease when concurrent with intestinal helminths, suggesting increased host infectiousness and bacterial transmission compared to single infected individuals [14]. Understanding how the infection by a second parasite species can influence the network of immune processes and the polarization towards one of the infecting agents requires the quantification of the immune components both at the systemic level and at the local site of infection, and the ability to follow the kinetics of these processes over time. The immunology of co- infection often considers the Th1/Th2 paradigm a tractable simplification of the overall immune response and its main functions. Yet, this approach tells us only half of the story, namely the systemic component. Indeed, organ compartmentalization and tissue specificity create well defined host-parasite environments that contribute to, as well as are modulated by, the immune system as a whole [19–20]. This brings us to the questions: what are the key processes and components that capture the essence of immune mediated parasite interactions in co-infections? And, how do these differ from single infections? To address these questions we used a combination of laboratory experiments and network-based discrete dynamic modelling, and examined changes in the immune response against single and co- infection with the respiratory bacterium Bordetella bronchiseptica and the gastrointestinal helminth Trichostrongylus retortaeformis, two common infections of the European rabbit (Oryctolagus cuniculus). Both parasites cause persistent infections that occur with high prevalence and intensity in free-living rabbit populations [21–22]. B. bronchiseptica is a gram-negative bacterium that colonizes the respiratory tract through oral-nasal transmission and usually results in asymptomatic infections. B. bronchiseptica has been largely isolated in wildlife, pets and livestock but rarely in humans [23] where it is out-competed by the human-specific Bordetella pertussis and Bordetella parapertussis, the etiological agents of whooping cough [24]. Previous empirical and modelling work in a murine system showed that the bacterium induces anti-inflammatory responses by modulating Th regulation, thereby facilitating bacterial establish- ment and proliferation [8,25]. However, hosts successfully counteract the pathogen mediated inhibitions by activating a protective Th1 cell mediated IFNc response, which leads to bacterial clearance from the lower respiratory tract, but not the nasal cavity, via Fc receptor mediated phagocytosis [25–27]. Our recent laboratory studies of rabbits infected with B. bronchiseptica agree with the general findings of bacterial clearance from the lower respiratory tract but persistence in the nasal cavity [28]. The gastrointestinal helminth T. retortaeformis has a direct life cycle and colonizes the small intestine following ingestion of pasture contaminated with infective third stage larvae (L3). The majority of larvae settle in the duodenum where they develop into adults in about 11 days [29]. A model of the seasonal dynamics of the T. retortaeformis-rabbit interaction suggested that acquired immunity develops proportionally to the accumulated exposure to infection and successfully reduces helminth intensity in older hosts [21,30]. These results were recently confirmed by challenging laboratory rabbits with a primary infection of T. retortaeformis where the quick production of antibodies and eosinophils was associated with the consistent reduction but not complete clearance of the helminth by 120 days post challenge [31]. Based on previous studies on bacteria-macroparasite co- infections and our recent work on the rabbit system, we hypothesized that during a B. bronchiseptica-T. retortaeformis co- infection the presence of helminths will delay bacterial clearance from the respiratory tract but there will be no change in helminth abundance in the small intestine. We predicted a T. retortaeformis mediated Th2 polarization at the systemic level and a bystander effect in the distal respiratory tract. This will have suppressed IFNc, resulting in the enhancement of bacterial intensity and deferred clearance in the lower respiratory tract compared to single infection. We also expected the Th2 systemic environment to control helminth abundance but not to change the numbers compared to the single infection. To examine our hypothesis, laboratory data on single infections were used to build discrete dynamic models describing the immune processes generated in response to each infection. The two single infection models were then connected through the cross-modulation of Th cells and the cytokine network at the systemic level, and allowed to reflect changes in these interactions at the local level. The resulting co- infection model and the dynamics of the parasites were finally compared with our laboratory experiment of bacteria-helminth co-infection to confirm the correctness of the model. Lastly, we examined the robustness of the immune networks with respect to the deactivation of single immune nodes by simulated knockout laboratory experiments. In other words, we tested the role of a large number of immune components, how their knockout affected the dynamics of infection and how the system converged into a potentially novel stable state. This allowed us to elucidate the immune key mechanisms and pathways behind the observed dynamics and the relative differences between single and co-infection. Results The causal interactions between the immune components activated by B. bronchiseptica and T. retortaeformis were assembled in the form of two distinct pathogen-specific networks of immune responses. The network of interactions against B. bronchiseptica was based on the infection in the lungs, the crucial organ for bacterial clearance, and constructed following Thakar et al. [8] and the current knowledge of the dynamics of B. bronchiseptica infection in mice (Fig. 1). There is a rich literature on the immunology of gastrointestinal helminth infections and important general features can be identified despite the fact that these mechanisms are often Author Summary Infections with different infecting agents can alter the immune response against any one parasite and the relative abundance and persistence of the infections within the host. This is because the immune system is not compart- mentalized but acts as a whole to allow the host to maintain control of the infections as well as repair damaged tissues and avoid immuno-pathology. There is no comprehensive understanding of the immune respons- es during co-infections and of how systemic and local mechanisms interact. Here we integrated experimental data with mathematical modelling to describe the network of immune responses of single and co-infection by a respiratory bacterium and a gastrointestinal helminth. We were able to identify key cells and functions responsible for clearing or reducing both parasites and showed that some mechanisms differed between type of infection as a result of different signal outputs and cells contributing to the immune processes. This study highlights the impor- tance of understanding the immuno-dynamics of co- infection as a host response, how immune mechanisms differ from single infections and how they may alter parasite persistence, impact and abundance. Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 2 January 2012 \| Volume 8 \| Issue 1 \| e1002345 species-specific. The immune network against T. retortaeformis was built on the knowledge of helminth infections in mice [6–7] and focused on the duodenum (the first section of the small intestine), where the majority of T. retortaeformis colonization and immune activity was observed (Fig. 2) [29,31]. Both networks were characterized by two connected compartments: Compartment I represented the immune interactions at the local site of infection, the lungs or duodenum, while Compartment II described the systemic site of T and B cell activation and differentiation, for example, the lymph node. The networks were then developed into discrete dynamic models [32]. Discrete dynamic modelling has been proven to be a feasible and useful approach to qualitatively characterize systems where the detailed information necessary for quantitative models is lacking [32–33]. For our purpose to examine the pattern of immune responses to single and co-infection at the local and systemic level and, importantly, to highlight key interactions and cells that generated the pattern observed, the framework of the discrete dynamic Boolean model appeared to be a robust and tractable choice [34–36], given that the kinetics and timescales of many of the immune interactions is unknown in the rabbit system. Each node (e.g. immune cell) was categorized by two qualitative states, ON and OFF, which are determined from the regulation of the focal node by upstream nodes given in the network. This regulation is given by a Boolean transfer function [32,34–35] (see Materials and Methods, and Supplement Text S1). The nodes in the ON state are assumed to be above an implicit threshold that can be defined as the concentration necessary to activate downstream immune processes; below this threshold the node is in an OFF state. To follow the dynamical status of the system through time, we repeatedly applied the Boolean transfer functions for each node until a steady state (i.e. clearance of the pathogen) was found. To determine the node consensus activity over time (i.e. the time course of cell concentration or parasite numbers Figure 1. Network of immune components considered in single B. bronchiseptica infection. Ovals represent network nodes and indicate the node name in an abbreviated manner. Compartment I denotes the nodes in the lungs and Compartment II combines the nodes at systemic level. Terminating black arrows on an edge indicate positive effects (activation) and terminating red blunt segments indicate negative effects (inhibition). Grey nodes have been quantified in the single laboratory experiment. Abbreviations: Bb: B. bronchiseptica; Oag: O-antigen; IL4II: Interleukin 4 in the systemic compartment; NE: Recruited neutrophils; IL12I: Interleukin 12 in lungs; IgA: Antibody A; C: Complement; TrII: T regulatory cells in the systemic compartment; IL4I: Interleukin 4 in the lungs; Th2II: Th2 cells in the systemic compartment; TrI: T regulatory cells in the lungs; Th2I: Th2 cells in the lungs; IL10II: Interleukin 10 in the lymph nodes; TTSSII: Type three secretion system in the lymph nodes; TTSSI: Type three secretion system in the lungs; IgG: Antibody G; IL10I: Interleukin 10 in the lungs; IFNcI: Interferon gamma in the lungs; IL12II: Interleukin 12 in the systemic compartment; BC: B cells; DCII: Dendritic cells in the systemic compartment; DCI: Dendritic cells in the lungs; Th1I: T helper cell subtype I in the lungs; PIC: Pro-inflammatory cytokines; Th1II: T helper cell subtype I in the systemic compartment EC: Epithelial cells; AP: Activated phagocytes; T0: Naı¨ve T cells; AgAb: Antigen-antibody complexes; MP: Macrophages in the lungs; DNE: dead neutrophils; PH: Phagocytosis. doi:10.1371/journal.pcbi.1002345.g001 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 3 January 2012 \| Volume 8 \| Issue 1 \| e1002345 shared by multiple trajectories) we ran the simulations 100 times by randomly sampling timescales and plotted each node activity profile, defined as the proportion of simulations in which the node is in the ON state as a function of time (additional details in the Materials and Methods) [37–38]. This procedure is similar to characterizing the consensus behaviour of a population of infected hosts that exhibit individual-to-individual variation. To construct the single infection models, we formulated the Boolean transfer functions from the current knowledge of the immune regulatory processes and in case of ambiguity we iteratively modified the transfer function by comparing the simulated dynamic output with our empirical results on single infection and with immune knockout studies (a detailed example is reported in the Materials and Methods). Finally, to examine the relative importance of the immune components, we perturbed each node by setting their status to OFF and monitored parasite activity up to the time-step required for parasite clearance/ reduction in the unperturbed system. Any increase in the infection activity following the knockout of an immune node -which may cascade to the connected downstream nodes- indicated the importance of this node for parasite clearance. Nodes whose deactivation led to long term persistence, represented by parasite activity equal to 1, were classified as essential for clearance. This procedure allowed us to mimic laboratory experiments of single immune component knockouts and to follow the consequences on parasite clearance. B. bronchiseptica single infection The onset of B. bronchiseptica infection in the lungs was simulated by setting the state of the bacteria node ON and the state of the nodes of the immune response OFF (Fig. 3A). As the infection proceeded, and consistent with our empirical work [28], IFNc and IL10 expression rapidly peaked and then slowly decreased below the threshold through the course of the infection (Fig. 3B). B. bronchiseptica has been suggested to induce IL10 production by T cell subtypes, which inhibits IFNc in the lower respiratory tract [25]. By explicitly including the bacteria mediated up-regulation of IL10, through the type III secretion system (TTSS) modulation of T regulatory cells (Treg), we were able to capture the establishment of the bacteria in the lungs followed by their immune-mediated reduction and clearance. Activation of B cells by T helper cells led to the prompt increase of peripheral antibodies (serum IgG and IgA), in line with empirical data [26– 27,39]. Serum IgG reached and maintained long-lasting above- threshold saturation in all simulations whereas IgA activity dropped along with B. bronchiseptica and was turned off after 15 Figure 2. Network of immune components considered in single T. retortaeformis infection. Grey nodes have been quantified in the single laboratory experiment. Abbreviations: IS: Larvae; AD: Adult; IL4II: Interleukin 4 in the systemic compartment; NE: Recruited neutrophils; IgA: Antibody A; IL4I: Interleukin 4 in the small intestine; Th2II: Th2 cells in the systemic compartment; Th2I: Th2 cells in the small intestine; IgG: Antibody G; IgE: Antibody E; IL10I: Interleukin 10 in the small intestine; IFNcI: Interferon gamma in the small intestine; IL12II: Interleukin 12 in the systemic compartment; BC: B cells; DCII: Dendritic cells in the systemic compartment; DCI: Dendritic cells in the small intestine; Th1I: T helper cells subtype I in the small intestine; PIC: Pro-inflammatory cytokines; Th1II: T helper cells subtype I in systemic compartment EC: Epithelial cells the small intestine; T0: Naı¨ve T cells; EL2: recruited eosinophils; EL: resident eosinophils; IL13: Interleukin 13; IL5: Interleukin 5. Additional details in Figure 1. doi:10.1371/journal.pcbi.1002345.g002 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 4 January 2012 \| Volume 8 \| Issue 1 \| e1002345 time-steps (see Materials and Methods) (Fig. 3C). The rapid recruitment of peripheral neutrophils to the lungs was possible through pro-inflammatory cytokine mediated signalling (Fig. 3D), while macrophages were recruited by IFNc secreted by Th1 cells. The activation of neutrophils and macrophages by antibodies, via the antibody-antigen complex and complement nodes (see Fig. 1), led to bacterial phagocytosis and clearance from the lungs within 20 time steps, in agreement with our empirical work. The relative importance of the different immune components was then explored by knocking off single nodes and monitoring the level of bacterial intensity at the 20th time-step, the time required for B. bronchiseptica clearance from the lungs in the unperturbed system. The perturbation results reproduced the observations from B. bronchiseptica infections in the respective empirical knockout experiments (Fig. 4A) [8]. For example, it has been observed that B. bronchiseptica can persist in large numbers in mice where T0, Th1 or B cells are depleted [8]; the key role of these nodes was confirmed by our model. The simulations also highlighted the crucial role of pro-inflammatory responses, dendritic cells, macrophages and IL12 as their inactive state resulted in bacterial persistence (Fig. 4A). In contrast, knocking out IL4 or any of the 15 remaining nodes of the network did not increase the activity of the node Bordetella. T. retortaeformis single infection The infection of T. retortaeformis was simulated by setting the state of the infective larvae node ON and the immune nodes OFF (Fig. 5A). Ingested larvae were either killed by eosinophils, in a Figure 3. Results of the simulations of the time course of the single B. bronchiseptica infection. Activity profiles (the probability of the node being in an ON state at a given time-step) are reported for: A- Bacterial colonies in the lungs. B- Cytokines, IFNc, IL4 and IL10, in the lungs. C- Serum antibodies. D- Peripheral neutrophils. doi:10.1371/journal.pcbi.1002345.g003 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 5 January 2012 \| Volume 8 \| Issue 1 \| e1002345 probabilistic manner [40–41], or successfully developed into adults. Adults started to appear after 2 time-steps, mimicking the natural development of infective third stage larvae into adults. Following the infection, IFNc rapidly peaked after two time steps while IL4 and IL10 activation followed with a delay, in line with empirical findings (Fig. 5B) [31]. The initial vigorous expression of IFNc was driven by dendritic cells, probably as an inflammatory response to the infiltration of microflora and bacteria into the damaged mucosa during the establishment of larvae [31]. This was modelled by turning the activity of the local IFNc ON if sufficiently stimulated by dendritic cells; the subsequent IFNc activation occurred through a Th1 cell response. For the interpretation of Fig. 5B, the fraction of IFNc activity that occurred from 0 to 1 was due to a Th1 response while above 1 was caused by dendritic cells. Dendritic cells also activated the Th2 cell mediated expression of IL4 and as this arm of the immune response developed, IFNc decreased although remained in an active state throughout the infection (Fig. 5B). IL10 expression was relatively low and similar to IL4, as found in our experimental results. Naı¨ve T cell-initiated B cell proliferation stimulated the prompt increase of mucus IgA, IgE and IgG above the activation threshold (Fig. 5C). The consequent recruitment of neutrophils, along with IgG, led to the reduction but not clearance of adult helminths, consistent with the empirical observation that a few individuals still harboured helminths in the duodenum at 120 days post infection (Fig. 5A). Unlike IgA, whose activity followed the dynamics of T. retortaeformis abundance, IgG activity remained persistently high. In contrast to the small and short-lived neutrophil peak, the eosinophil activity was higher and lasted longer (Fig. 5D). The stability of the immune pathways and the reliability of our parsimonious model were explored by systematically knocking out network nodes and examining the effects on the activity of the adult helminth node at the 20th time-step, the time point when the unperturbed system reaches equilibrium (Fig. 4C). None of the perturbations led to an activity of the adult parasite node of less than 0.3, indicating that T. retortaeformis persists in the rabbit and this is a robust outcome of the model, which matches our empirical observations. Simulations suggested that the individual knockout Figure 4. Parasite activity at the 20th time step from simulations where network nodes were individually knocked out (from 100 replicates). A- B. bronchiseptica in single infection. B- B. bronchiseptica in co-infection. C- T. retortaeformis in single infection. D- T. retortaeformis in co-infection. Explanation of the abbreviations is reported in Figure 1, Figure 2 and Text S1. doi:10.1371/journal.pcbi.1002345.g004 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 6 January 2012 \| Volume 8 \| Issue 1 \| e1002345 of 14 nodes, including pro-inflammatory cytokines, IL13, naı¨ve T cells, dendritic cells, eosinophils and neutrophils led to helminth persistence in all the simulations (i.e. adult activity equal to 1) (Fig. 4C). Interestingly, deletion of either local or systemic IL4 (IL4I or IL4II) reduced parasite activity, as IL4 contributed to inhibit neutrophils (via the inhibition of the IL12 node). To identify the nodes that may lead to faster reduction or clearance of T. retortaeformis we constitutively turned ON single nodes. Over- expression of recruited eosinophils, IL5, neutrophils and Th2 cells in the small intestine reduced parasite activity below 0.5 (results not shown). These and the knockout simulations suggested that neutrophils and eosinophils are critically involved in the clearance of T. retortaeformis infection. B. bronchiseptica-T. retortaeformis co-infection Network modelling. To explicitly quantify the interactions between B. bronchiseptica and T. retortaeformis the two single immune networks were connected and the co-infection network simulated as a single entity without changing the Boolean rules built for the single networks, except for the adjustments necessary for assembly (Fig. 6). The link between networks was established through the cytokines, which maintain the communication between the systemic and local immune processes as well as the cross- interactions between infections. Specifically, we assumed a single unlimited pool of naive T cells and three pools of cytokines: a pool in the lungs, a pool in the small intestine (duodenum) and a systemic pool interacting with both infections. For example, we Figure 5. Results of the simulations of the time course of the single T. retortaeformis infection. Activity profiles (the probability of the node being in an ON state at a given time-step) are reported for: A- Third stage infective larvae (L3) and adults. B- Cytokines, IFNc, IL4 and IL10 in the duodenum. C- Mucus antibodies against helminth adult parasites. D- Peripheral eosinophils and neutrophils. Note that the IFNc concentration range is between 0–2 to describe additional non-immune mediated activation of that node by the tissue damage (details in the Results). doi:10.1371/journal.pcbi.1002345.g005 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 7 January 2012 \| Volume 8 \| Issue 1 \| e1002345 assumed that only one pool of IL4 and IL12 exists in the systemic compartment although antigen specific cells, polarized towards bacteria or helminths, can produce these cytokines. In other words, IL12 induced by bacterial factors can inhibit IL4 production by helminth-specific Th2 cells. Local cytokine expression can be affected by mucosal immune components, parasite intensity and the systemic cytokine response. These assumptions allowed us to take into account the compartmentalization of the infections (i.e. lungs and duodenum) as well as bystander effects of the immune response and the balance of the immune system as a whole. The dynamics of the simulated immune components and associated parasite activity were then compared with the empirical co-infection results. B. bronchiseptica. Simulations showed the switch of cytokines from the initial high expression of IFNc and IL10 to the late increase and long activity of IL4 (Fig. 7B). Antibodies quickly increased, serum IgG remained consistently high while IgA decreased below the threshold after 5 time-steps as bacterial numbers declined (Fig. 7C). The peripheral neutrophil activity was higher in co-infected compared to single infected hosts, however, their recruitment in the lungs was completely turned off after 14 time steps (Fig. 7D vs Fig. 5D). These temporal patterns resulted from the inflammatory cytokines produced in response to both T. retortaeformis and B. bronchiseptica and should be interpreted as a mixed activity against both parasites. Our simulations indicated similarities between B. bronchiseptica single and co- infection, such as the rapid increase in systemic IgA, IgG and neutrophils but also differences, namely, the higher and longer activity of IL4 in the lungs and the longer presence of peripheral neutrophils in dual compared to single infection. Overall, despite a few immunological differences the dynamics and timing of B. bronchiseptica clearance in the lungs of co-infected hosts was similar to that observed in the single infection and driven by phagocytic cells activated by antibodies and Th1 cells (Fig. 7A). The low but non-zero activity of bacteria in the co-infection steady state indicated that the infection was not cleared in a small fraction of the replicate simulations (8%) (Fig. 7A). Specifically, IL4 activated by eosinophils in response to T. retortaeformis was responsible for the persistence of bacteria in the lungs. During single bacterial infection the IL4 level was relatively low and controlled by the inhibitory effect of IL12, however, during the co-infection this suppressive effect was not observed as a Th2 environment dominated. This model prediction is supported by previous studies that showed a delayed bacterial clearance in case of persistent IL4 [42]. Knockout perturbation analysis confirmed that IL4 produced by eosinophils was responsible for this occasional bacterial persistence, since the deletion of this node led to the complete clearance of the infection in all the simulations (Fig. 4B). Bacterial persistence was also observed when Th1 cells, antibodies, pro-inflammatory cytokines or the activated phagocytes node were individually knocked out. The 15 nodes whose deletion had very little effect in the single infection had a similarly weak effect on bacterial numbers in the co-infection (Fig. 4A vs 4B). Interestingly and contrary to the single infection, the knockout of bacteria- activated epithelial cells did not influence B. bronchiseptica activity since the pro-inflammatory cytokines node, which is downstream of the epithelial cells node, was also activated by the helminths. This between-organ communication was possible by assuming a single pool of cytokines and their free movement among organs, for example via the blood system. Perturbation of any of the 17 helminth-specific nodes had a generally weak effect on bacterial activity. T. retortaeformis. The concurrent effect of B. bronchiseptica on T. retortaeformis infection dynamics was equally examined. Counter to our initial predictions, lower establishment and faster clearance of T. retortaeformis were observed in co-infected compared to single infected hosts (Fig. 8A vs 5A). The model showed high activities of IFNc and IL10 and low expression of IL4 (Fig. 8B). As observed in the single infection, the early peak of IFNc (having activity .1) was caused by an initial host-mediated inflammatory response, as an immediate-type hypersensitivity reaction of the tissue to the establishment of infective larvae. This local activation was then followed by a Th1 mediated IFNc expression, consistent Figure 6. Network of immune components considered in the B. bronchiseptica-T. retortaeformis co-infection. Bi-directional black arrows indicate the influence of components from one network on the common cytokine pool and vice a versa. doi:10.1371/journal.pcbi.1002345.g006 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 8 January 2012 \| Volume 8 \| Issue 1 \| e1002345 with the single infection model. A bystander Th1 mediated effect of B. bronchiseptica synergistically contributed to this pattern by enhancing the activity and duration of IFNc expression in the duodenum. Simulations suggested that the local IL10 expression, higher in the dual compared to the single infection, was a bystander effect induced by the type three secretion system (TTSS) of B. bronchiseptica through Treg cells. Also, the early IL4 expression was suppressed by the Th1 mediated IFNc phenotype activated both by the helminth, during the initial establishment, and the bacterial co-infection. Mucus IgG remained consistently active from time step 3 while mucus IgA was at the highest between 5 and 10 time steps but decreased thereafter (Fig. 8C). Recruited peripheral neutrophils but not eosinophils were higher in the dual infection compared to single helminth infection simulations (Fig. 8D). To provide a parsimonious mechanism that could explain the rapid helminth clearance, the immune nodes of the co-infection network were systematically knocked out and the helminth activity examined at the 20th time-step (Fig. 4D). Similar to the single infection, the deactivation of key nodes, for instance B cells, dendritic cells or T cells, resulted in helminth persistence in all the simulations (adult activity equal to 1). Unlike in the single infection, knockout of resident eosinophils or the IL12II node did not lead to helminth persistence. This was because the induction of downstream processes, such as the activation of IL4 or IFNc was now performed through the complementary effect of the bacterial nodes and their bystander effects. Interestingly, the single knockout of 92% of the nodes, including bacterium-specific nodes, increased helminth activity, compared to the unperturbed co-infection model, but did not lead to helminth persistence in Figure 7. Results of the simulations of the time course of B. bronchiseptica from the co-infection. Activity profiles (the probability of the node being in an ON state at a given time-step) are reported for: A- Bacterial colonies in the lungs. B- Cytokines, IFNc, IL4 and IL10, in the lungs. C- Serum antibodies. D- Peripheral neutrophils. doi:10.1371/journal.pcbi.1002345.g007 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 9 January 2012 \| Volume 8 \| Issue 1 \| e1002345 every simulation. From a modelling perspective, the network in Fig. 6 represents a sparse causal model of co-infection dynamics. In other words, all these nodes or nodes downstream of the targeted nodes contribute to, but are not required for, T. retortaeformis clearance. The knockout of effector nodes namely, recruited eosinophils or neutrophils and cytokines like IL5 or IL13, resulted in helminth long term persistence, supporting the hypothesis that a co-operative mechanism including leukocytes, antigen-specific antibodies (IgG and IgE) and Th2 mediated IL5 and IL13 are critical in helminth clearance [43–49]. The role of IL5 and IL13 is mostly in the recruitment of eosinophils while neutrophils are recruited by pro-inflammatory cytokines and Th1 mediated IFNc. Though antibodies recognize the helminth, in this model they do not form complexes, rather, they attract leukocytes bearing Fc-receptors leading to the recruitment of neutrophils and eosinophils. A comparison between single and dual infection offers insights into the contribution and balance of these two leukocytes to T. retortaeformis dynamics. In the single infection, when neutrophils are only transiently activated, the recruited eosinophils were relatively more important to parasite reduction, although they were not sufficient to clear the infection. In the co-infection, the robust and early activation of recruited neutrophils -which decreased following helminth reduction- and the activation of recruited Figure 8. Results of the simulations of the time course of T. retortaeformis infection from the co-infection. Activity profiles (the probability of the node being in an ON state at a given time-step) are reported for: A- Third stage infective larvae (L3) and adults. B- Cytokines, IFNc, IL4 and IL10 in the duodenum. C- Mucus antibodies against adult helminths. D- Peripheral eosinophils and neutrophils. Note that the IFNc concentration range is between 0–2 to describe additional non-immune mediated activation of that node by the tissue damage (details in the Results). doi:10.1371/journal.pcbi.1002345.g008 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 10 January 2012 \| Volume 8 \| Issue 1 \| e1002345 eosinophils -which are important in reducing the number of infecting larvae and are required for neutrophils to successfully reduce the helminths- highlighted the synergistic role of these cells in the observed fast clearance of T. retortaeformis. To explicitly study the bacterial components inducing these two leukocytes, we switched the nodes to ON one at a time and found that dendritic cells and Th1 cells, activated by bacteria, led to a significant increase in neutrophil activity (results not shown). Counter to this, no bacterial nodes significantly contributed to eosinophil produc- tion. Switching ON the type III secretion system node transiently increased eosinophil activity, compared to the unperturbed system, as expected from the role of TTSS in the induction of Th2 related cytokines [25]. However, this had a very short lived effect since TTSS was neutralized by antibodies. In summary, simulations suggest that strong inflammatory responses generated by the bacteria led to an early increase of neutrophils which contributed to a prompt and more effective helminth reduction. Empirical co-infection experiment A B. bronchiseptica-T. retortaeformis co-infection experiment was carried out and the empirical results were used to validate the co- infection dynamic model. A statistical analysis was also performed between the single and co-infection trials to further reinforce our modelling outputs. However, while the statistical findings provide an insight into the relationships among the immune components, no mechanistic understanding or dynamic outcomes can be established between these variables and parasite abundance. The network-based discrete dynamic models allowed us to establish such connections and causal interactions between the various components. Overall, we found that the parsimonious dynamic model correctly predicted the observed dynamics of concurrent B. bronchiseptica and T. retortaeformis co-infection. B. bronchiseptica. The bacterial colonization of the respiratory tract of co-infected rabbits was similar to single infection. B. bronchiseptica abundance in the lungs increased in the first 7 days post challenge and decreased thereafter, as seen in the dynamic model; by 90 days bacteria were completely cleared from the lungs and trachea but persisted in the nasal cavity (Fig. 9A). Based on the a priori measurement of optical density with a spectrophotometer, individuals received a dose similar to the single infection however, the a posteriori quantification of bacteria on blood agar plates suggested that an inoculum of 10,600 CFU/ml was administered, five times less than the single infection dose [28]. If we consider the second measure correct, the lower dose did not affect replication and the colony numbers quickly reached values comparable to single infection by 3–7 days post challenge. Specifically, the average number of bacteria in the lower res- piratory tract was analogous to the single infection but significantly higher numbers were observed in the nasal cavity during the infection (Fig. 9A, Table 1). Confirming the model simulations, IFNc quickly increased, peaked by 3 days post challenge and quickly decreased thereafter. IL10 followed a similar pattern with a small delay while IL4 slowly increased and peaked 60 days post infection (Fig. 9B). Serum antibodies showed a trend similar to that of the single infection, in accordance with our dynamic model. IgG rapidly increased and remained high throughout the experiment while IgA rapidly decreased although a second peak was observed around week twelve, this second peak was based on much fewer individuals and, probably, it was not biologically relevant (Fig. 9C). Peripheral leukocytes concentration reflected the response to both infections specifically, neutrophil numbers showed a robust peak at week three while eosinophil numbers increased between two and five weeks post-infection, both in agreement with the model (Fig. 9D and Fig. 10D). A combination of principal component analysis (PCA) and generalized linear models (GLM) indicated that B. bronchiseptica in the lungs was negatively associated with IL4, serum IgG and IgA (PCA axis 1), and peripheral eosinophils and neutrophils (PCA 2, Table S1). To compare the immune response between single and co-infected hosts, variables were scaled over the controls. Co- infected rabbits exhibited higher IL4 (coeff6S.E. = 20.87960.210, P,0.001), serum IgG (0.16660.043 P,0.001) and neutrophils (0.23360.050, P,0.0001) but lower eosinophils (21.70560.006, P,0.0001) compared to single infected individuals. It is important to note that a low or negative cytokine Ct value (cycle threshold scaled over the controls) identifies high mRNA expression and vice versa, thus in the models low Ct values are translated as high cytokine activity. The remaining variables were not significant, although this should not be interpreted as a complete lack of variability between the two infections. Indeed, as highlighted in the network model these variables play a secondary but still necessary role in generating immune differences between infections. T. retortaeformis. Helminth intensity significantly decreased with the progression of the infection and organ location (high numbers in the duodenum, SI1, and low in the ileum, SI4) however, counter to our expectation and consistent with our model simulations, lower establishment and faster clearance were observed in co-infected compared to single infected hosts (Fig. 10A, Table 2). As predicted by our dynamic model, strong and persistent IFNc expression but relatively low IL4 and IL10 were found in the duodenum of infected rabbits compared to the controls (Fig. 10B). Consistent with the single infection and the dynamic model, mucus antibody quickly increased, IgG remained relatively high for the duration of the trial while IgA declined from day 30 post challenge (Fig. 10C). The peripheral leukocyte profile has already been described in the bacteria section (Fig. 9D and Fig. 10D). Principal component analysis identified that T. retortaeformis was positively associated with the first axis (PCA 1), mainly described by the interaction among the three cytokines, and negatively related to the second axis (PCA 2) represented by eosinophils and antibodies (Table S2). Interestingly, cytokines were positively correlated (IFNc vs IL10: r = 58% P,0.001; IL4 vs IL10: r = 54%, P,0.01), indicating the co-occurrence of a specific response to the helminth, through IL4, but also a robust inflammatory/anti-inflammatory reaction probably caused by the parasite damaging the mucosal epithelium and resulting in bacterial tissue infiltration during larval establishment [31]. The comparison of immune variables between single and co-infection showed higher neutrophils (P,0.0001) and a tendency for higher IL10 (P = 0.058) in co- infected compared to single infected hosts. The overall expression of IL4 was lower in co-infected individuals (P = 0.035), however higher values were observed at 14 days post infection (interaction of IL4 with day 14 post infection P = 0.046). Discussion Co-infections affect the immune responses but how the systemic processes interact and influence the kinetics at the local sites of infection is still unclear. The majority of studies on the immunology of co-infection have focused on either one of the infecting species or a restricted class of cells or immune processes, and often concentrated on the early stage of the infection [4,9– 14,50–52]. These studies have been extremely useful in highlight- ing not only the similarities across systems but also the specificity of some of these mechanisms and how they differ from single infections. Yet, there is a need for a comprehensive understanding of these processes as a whole individual response, how systemic Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 11 January 2012 \| Volume 8 \| Issue 1 \| e1002345 and localized processes interact and how they dynamically evolve during the course of the co-infection. We used a combination of laboratory experiments and modelling to examine the dynamic network of immune responses to the respiratory bacterium B. bronchiseptica and the gastrointestinal helminth T. retortaeformis. Our aim was to identify the parsimonious processes and key cells driving parasite reduction or clearance and how they changed between single and co-infections. We confirmed the initial hypothesis of immune mediated interactions between the two parasites, however, our initial predictions were only partially supported. The most unexpected result was the faster clearance of T. retortaeformis in co-infected compared to single infected individuals, which was observed in the model simulations and confirmed in the empirical data. Neither did we expect to find that B. bronchiseptica infection in the lungs was not significantly altered by the concurrent helminth infection, despite the increase in local IL4 expression observed in both the simulations and the experiment. We found a small difference in bacterial clearance between single and co-infection (Fig. 3A vs Fig. 7A) and we were able to explain that this was driven by the differential recruitment of phagocytes, particularly macrophages induced by IFNc during co-infections, as compared to the single infection. However we found that T. retortaeformis enhanced individual variability in the immune response to B. bronchiseptica infection by occasionally reducing the overall efficacy of the Th1 immune response, through eosinophil produced IL4, and Figure 9. Summary of B. bronchiseptica intensity and immune variables from the experimental co-infection. Mean6SE during the course of the infection (days or weeks post infection) are reported. A- Bacterial intensity in the respiratory tract. For comparison, empty black circles represent the bacterial intensity in the lungs from the single infection. B- Cytokines, IFNc, IL4 and IL10 in the lungs. C- Anti-bacterial IgA and IgG in serum. D- Peripheral neutrophils. For C and D, infected hosts: full circles, controls: empty circles. doi:10.1371/journal.pcbi.1002345.g009 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 12 January 2012 \| Volume 8 \| Issue 1 \| e1002345 preventing bacterial clearance in the lungs, a pattern observed in 8% of the simulations. The helminth mediated delay or absence of bacterial clearance from the lower respiratory tract was indeed our original hypothesis and interestingly the model indicated that this is still a possible outcome of the interaction between these parasites. This implies that heterogeneities in the host immune response are not exceptional events and can have major effects on the dynamics of infection and persistence. Our model was able to capture this variability because of the large number of simulations; in other words a large group of infected individuals were examined compared to our much smaller sample tested in the laboratory. Follow-up experiments using a much larger number of animals or replication of the same experiment a few times may lead to the experimental observation of this behaviour. The empirical findings also showed that T. retortaeformis infection resulted in a significant increase of bacterial numbers in the nasal cavity compared to single infection, particularly after the initial phase of the infection. At the host population level these findings support the hypothesis that co-infections can increase individual variability to infections by altering bacterial intensity and prevalence, and this can have major consequences for the risk of transmission and disease outbreak [53]. Overall, our dynamic models indicated that the clearance of B. bronchiseptica in single and co-infection was mainly driven by phagocytosis of bacteria by macrophages and neutro- phils activated by antibodies. Deactivating nodes that affected bacterial recognition (e.g. pro-inflammatory cytokines, epithelial cells or antibodies) or phagocytosis (e.g. Ag-Ab complex or macrophages) increased bacterial abundance in single and dual infections, suggesting that these cells are necessary for controlling B. bronchiseptica. The immune network for T. retortaeformis was less detailed than that for the bacterial network, nevertheless, the model predictions of the activity pattern of the helminth and the immune variables that have been quantified were in agreement with our empirical studies. To our surprise the prediction of no effect of B. bronchiseptica on T. retortaeformis infection was proven wrong. Simulations suggested that the combined effect of neutrophils, eosinophils and antibodies (IgG and IgE) led to helminth expulsion. Neutrophils and eosinophils were activated through antigen-specific Th1 and Th2 responses, respectively. Th2- mediated differentiation of progenitor eosinophils (i.e. resident eosinophils), modulated by IL5 and IL13, also played an important role in helminth reduction in single infection, as indicated by the perturbation results. Previous studies on murine systems have shown that IL13 can complement IL4 or play an alternative or even stronger role in helminth infections [42–43]. Using our modelling approach we showed that IL5 and IL13 had complementary abilities against helminths and contributed to parasite reduction both in single and co-infection. The strategic role of neutrophils in bacteria-helminth co-infections has been previously described [44]; using a modelling approach not only we confirmed this property but also suggested a non-specific infiltration of effector cells into infected tissues. The mixed Th1/Th2 response in the duodenum was driven by different processes. The early IFNc inflammatory signal observed both in single and co-infection was a host response to the mucosa damage by helminth establishment, and probably bacteria and microflora infiltration from the lumen [31]. This was also complemented by a bystander effect of B. bronchiseptica co-infection, rather than a helminth induced up-regulation of this cytokine to facilitate tissue colonization [31]. This mechanism is supported by our recent studies on cytokine expression in different organs of single and co-infected rabbits at seven days post infection, where we showed that IFNc was remarkably reduced in the ileum, mesenteric lymph node and spleen, where fewer or no helminths were found, compared to the duodenum [54]. The Th2 cell activity was primarily focused on preventing parasite establishment and survival. These findings indicate that these two cytokines are not mutually exclusive but can simultaneously act on different tasks specifically, tissue repair, inflammatory response to micro- flora infiltration and helminth clearance. Mixed Th1/Th2 phenotypes are not new to parasite infections and the murine- Schistosoma mansoni or Trichuris muris systems are well described examples [55–57]. Model strengths and limitations The aim of this study was to develop tractable dynamic models that could capture the interactions of multi-organ, multi-species co-infection immune processes as well as single infection dynamics. We found the discrete dynamic Boolean models a feasible and reliable approach for this task since we lacked accurate spatio- temporal details on the majority of the variables and the kinetic parameters required to develop robust quantitative, differential equation-based models [34–36]. Boolean models assume that what matters the most is whether the concentration or level of expression of a node (i.e. immune cell) is higher or lower than an a priori fixed threshold. They also use a parameter-free combinatorial description for the change in status of the nodes, thus avoid the need for parameter estimation while being sufficiently flexible. Indeed, Boolean models have been successfully used in a variety of contexts, from signal transduction [38,58] to development [59–60], immune responses [8,61–62] and popula- tion-level networks [63]. Choosing a quantitative modelling approach would have forced us to drastically simplify our system, impose a large number of assumptions on the concentration, transfer function and kinetic parameter of each node, and so we would have not been able to offer robust predictions on the role of many immune components and on how they affect the dynamics of parasite infection in our system. Table 1. Summary of linear mixed effect model (LME) between B. bronchiseptica abundance (CFU/g), as a response, and infection type (single or co-infection), day post infection (DPI) and organ (lung, trachea or nose) as independent variables. Coeff±S.E., d.f. P Intercept 14.48360.745, 122 0.00001 Infection type 1.71160.895, 60 0.061 Trachea 20.25960.661, 122 0.695 Nose 0.72160.757, 122 0.343 DPI 20.11360.010, 60 0.00001 Infection typeDPI 20.04560.015, 60 0.005 TracheaDPI 20.00860.010, 122 0.425 NoseDPI 0.07660.011, 122 0.00001 Infection typeTracheaDPI 0.00460.013, 122 0.745 Infection typeNoseDPI 0.03960.015, 122 0.009 AIC 1022.895 Host ID random effect (intercept S.D.) 1.113 AR(1) 0.311 The random effect of the host identity code (ID) and the autocorrelation effect (AR-1) of sampling different organs for the same host are also reported. doi:10.1371/journal.pcbi.1002345.t001 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 13 January 2012 \| Volume 8 \| Issue 1 \| e1002345 Our models were based on the most updated knowledge of the immune components and processes during single infections to Bordetella and gastrointestinal helminths. In cases of uncertainty (e.g. whether two co-regulators were independent or synergistic) we tested a number of different assumptions (i.e. Boolean transfer functions) and selected the function that best described our single infection experiments in terms of the: timing of events, node activities and importantly, parasite steady state (see Materials and Methods for an example). To overcome the fact that timescales and duration of immune processes were unknown, we generated repeated simulations with various update orders, which essentially allowed us the sampling of various time durations and probing which model output was robust to timing uncertainties. Impor- tantly, the outputs of our simulations were not averages but the quantification of the agreement between runs, for example, the anti-B. bronchiseptica IgG activity of 1 after step 4 in Fig. 3C means that following this time point all runs show an above-threshold concentration of IgG regardless of timing variations. By compar- ing the features of the curves (e.g. saturating shape, peak occurrence and timing) with our experimental observations we were able to confirm the accuracy of the model in predicting the observed kinetics. Figure 10. Summary of T. retortaeformis intensity and immune variables from the experimental co-infection. Mean6SE during the course of the infection (days or weeks post infection) are reported. A- Helminth intensity in the small intestine sections, from the duodenum (SI-1) to the ileum (SI-4), respectively. The helminth development during the course of the infection is as follows: 4 days post infection (DPI) third stage infective larvae (L3), 7 DPI both L3 and fourth stage larvae (L4), from 14 DPI onwards adult stage only. For comparison, empty black circles represent the helminth intensity in the duodenum from the single infection. B- Expression of cytokines, IFNc, IL4 and IL10 in the duodenum. C- Mucus antibody against adult helminths, IgA (C1) and IgG (C2), from the duodenum to the ileum. D- Peripheral eosinophils. For C and D, infected hosts: full circles, controls: empty circles. doi:10.1371/journal.pcbi.1002345.g010 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 14 January 2012 \| Volume 8 \| Issue 1 \| e1002345 One of the strengths of our modelling was to make predictions on the dynamics of parasite clearance based on the perturbation of the nodes (i.e. single node knockout). These simulations followed the classical knockout lab experiments where single immune components (nodes) were turned off from the beginning of the simulation and the dynamics of the immune response, as well as parasite clearance, were examined. This approach allowed us to explore the knockout of a large number of immune variables, determine the most important components modulating the immune response and highlight how they differed between single and co-infection. These findings can be tested in the laboratory by performing knockout experiments of the crucial immune variables in different infection settings. For example, we can block neutrophil production or the cytokine IL13 and examine whether helminths persist -as predicted by our knockout simulations- or are slowly cleared in bacteria co-infected rabbits. Similarly, we can test the predicted different response of knocking out IL4 in helminth and bacteria-helminth co-infection, specifically, whether clearance is higher than in un-manipulated individuals in single helminth infection and lower than in un-manipulated co-infected hosts. We should also pay more attention to B. bronchiseptica infection in the nasal cavity and develop dynamic immune models that can explain bacterial persistence as well as possible clearance under different knockout scenarios both in single and co-infection. The most parsimonious hypotheses can then be tested in the laboratory. This is important because our recent work suggested that bacterial shedding during the long lasting chronic phase relies mainly on the infection of the upper respiratory tract, once it has been cleared from the lungs and trachea [28]. This has relevant epidemiological implications for bacterial transmission that go beyond the rabbit-parasite system. We can further refine our models and explore the dynamics of the parasite-immune network when the onset of the co-infections is lagged between the parasite species or one parasite is trickle dosed, a dynamic that resembles more closely to the natural conditions. Again, these predictions can be validated through experimental infections of naı¨ve or knockout animals. It is important to underline that our approach can be adapted to a large variety of bacteria-helminth co- infections of many host systems where organ compartmentaliza- tion, differences in the time of infection or number of parasite stages are observed. In conclusion, we showed that network-based discrete dynamic models are a useful approach to describe the immune mediated dynamics of co-infections. These models are robust as well as sufficiently tractable to qualitatively capture the complexity of the immune system and its kinetics over time. Arguably, the main limitation of our modelling approach is that it lacks a fully quantitative component. Yet, this work demonstrated that it is possible to build comprehensive qualitative dynamic models of the local and systemic immune network of single and co-infection that are validated by empirical observations. Importantly, this study is a fundamental starting point towards the future construction of quantitative models based on simplified networks that describe the kinetics and intensities of the causal relationships among key immune components identified in qualitative models. Our approach showed that we can refine the conventional approach of using the Th1/Th2 paradigm, by identifying system-specific functions or cell groups that can capture crucial immune processes during co-infections. While our parsimonious dynamical models were able to capture the patterns of single and co-infection observed in the experiments, we are aware that they are far from complete in describing the immunological complexity of the processes involved and cells activated. Nevertheless, they provide a parsimonious description of the system that can be experimentally tested. Ultimately, we showed that we cannot predict how the immune system reacts to co-infections based on our knowledge of single infection. More needs to be done to clarify the immune mechanisms involved in bacteria-helminth co-infections and how individual hosts balance the immune system as a whole. Materials and Methods Network modelling Network assembly. Interaction networks were built from the available literature and adapted to our system. Bacteria, helminth and the components of the immune system (i.e. immune cells and cytokines) were represented as network nodes; interactions, regulatory relationships and transformations among components were described as directed edges starting from the source node (regulator) and ending in the target node. We incorporated regulatory relationships that modulate a process (or an unspecified process mediator) as edges directed toward another edge. The regulatory effect of each edge was classified into activation or inhibition, visually represented by an incoming black arrow or an incoming red blunt segment. Since not all processes involved in natural B. bronchiseptica and T. retortaeformis infections are known or generally addressed in the rabbit infection model, we extended the set of known interactions following general immunological knowledge on bacterial and helminth infections. We constructed three networks: two networks that describe the respective single infections and one that links the first two and represents a co-infection network. A detailed description of each network is given below. B. bronchiseptica single infection. Infection of the lungs starts with the node Bacteria that leads to a cascade of immune Table 2. Summary of linear mixed effect model (LME) between T. retortaeformis abundance (worm/small intestine length) as a response, and infection type (single or co- infection), day post infection (DPI) and organ location (from the duodenum -SI1- to the ileum -SI4-), as independent variables. Coeff±S.E., d.f. P Intercept 3.04460.178, 207 0.00001 Infection type 20.77860.240, 68 0.002 SI-2 20.52660.103, 207 0.001 SI-3 21.76660.138, 207 0.00001 SI-4 22.53060.159, 207 0.00001 DPI 20.02960.003, 68 0.00001 Infection typeSI-2 0.04560.109, 207 0.682 Infection typeSI-3 0.24360.146, 207 0.097 Infection typeSI-4 0.52060.169, 207 0.001 Infection typeDPI 0.00560.004, 68 0.214 SI-2DPI 0.00360.001, 207 0.023 SI-3DPI 0.01660.002, 207 0.00001 SI-4DPI 0.02360.002, 207 0.00001 AIC 500.453 Host ID random effect (intercept S.D.) 0.001 AR(1) 0.773 The random effect of the host identity code (ID) and the autocorrelation effect (AR-1) of sampling different organs of the same host are also reported. doi:10.1371/journal.pcbi.1002345.t002 Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 15 January 2012 \| Volume 8 \| Issue 1 \| e1002345 interactions (Fig. 1, Text S1). This node includes generic virulence factors of the bacteria such as the lipopolysaccharide chain (LPS) required for tissue adherence following recognition of bacteria by epithelial cells. Other bacterial virulence factors, particularly O-antigen and type III secretion system (TTSS), are explicitly included as separate nodes in the network and are involved in the initial immune recognition of the bacteria node. Upon detection, epithelial cells activate pro-inflammatory cyto- kines, which in turn activate dendritic cells, often the most important antigen presenting cells. Dendritic cells are also activated by IFNc. Dendritic cells induce differentiation of naı¨ve T cells (T0) by producing IL4 and IL12. The cytokine profile along with the antigen leads to the activation of T cell subtypes including helper and regulatory T cells. T helper cells are activated in the lymph nodes (Compartment II) and subsequently tran- sported to the site of infection (Compartment I). IL4 is also produced by differentiated Th2 cells; IL4 and IL12 inhibit each other and IL4 also inhibits IFNc. T regulatory (Treg) cells are stimulated by the type III secretion system of B. bronchiseptica to produce IL10. Th1 cells produce IFNc which along with pro- inflammatory cytokines activates neutrophils and macrophages. A different subtype of T cells, follicular T helper cells, is known to stimulate B cell activation. To simplify the network we assumed that naı¨ve T cells could play this role. Antigen-specific B cell proliferation leads to the production of antibodies, namely IgG and IgA. IgA production occurs only in the direct presence of antigen unlike IgG that persists after bacterial clearance [28]. IgG and bacteria complexes also induce complement fixation along with bacteria themselves. Activation of complement by bacteria is inhibited by O-antigen. The node ‘‘activated phagocytic cells’’ represents the outcome of the stimulation of neutrophils and macrophages by antibody-antigen complex and complement. These cells induce the node phagocytosis that depletes bacteria. T. retortaeformis single infection. The network starts with infective larvae that develop into adults with no delay in the larval- adult development, adults appear 2 time steps post infection (Fig. 2, Text S1). Both parasite stages activate epithelial cells that lead to the production of pro-inflammatory cytokines which then activate dendritic cells and neutrophils, with the latter able to inhibit adult helminths. Infective larvae stimulate IL13 production by resident eosinophils and these recruit additional eosinophils from the progenitor cells in the peripheral blood [63]. Eosinophils can kill larvae through a stochastic process described by a uniform distribution [64]. IL5 secreted by Th2 cells is required for the recruitment of additional eosinophils. Infective larvae also directly activate IFNc by damaging the mucosa tissue and causing a host inflammatory response. This process does not include Th1 cells. Pro-inflammatory cytokines activate dendritic cells that stimulate naı¨ve T cells (T0). As described for B. bronchiseptica, dendritic cells interact with naı¨ve T cells (T0) leading to the activation of T cell subtypes Th1 and Th2 through the production of IL12 and IL4. IL4 is also produced by Th2 cells and IL4 and IL12 inhibit each other. Consistent with the bacteria network, the activation of T helper cells occurs in the lymph nodes (Compartment II) and subsequently transported to the site of infection (Compartment I). In compartment I, IFNc is produced by Th1 cells and dendritic cells. IL4 and IL10, produced by Th2 cells, have anti- inflammatory properties and inhibit pro-inflammatory cytokines and neutrophils. Naive T cells stimulate clonal expansion of B cells and these lead to the production of antibodies such as IgG. While B cells can secrete IgG much longer after antigen removal, IgA production is assumed to be in response to larval establishment and development. The IgE isotype is produced upon signalling from either IL4 or IL13. Among these antibodies IgG inhibits adult helminths while IgE and IgA are involved in activating eosinophils and inhibiting pro-inflammatory cytokines respectively. B. bronchiseptica-T. retortaeformis co-infection. The co- infection immune network was developed by combining the two single infection networks together (Fig. 6, Text S1). This network is characterized by three compartments, representing the lungs, the small intestine (duodenum) and the systemic compartment (e.g. the lymphatic system). The connection of the networks and the immune mediated interactions between parasites were represented through the cytokines produced as a single pool. Local cells activated by bacteria and helminths can contribute to cytokine production, which are then transported through the blood and disseminate to other organs [63]. For example, pro-inflammatory cytokines are systematically detectable when any one of the parasites activates epithelial cells. Similarly, IL4 or IL12 can be produced by B. bronchiseptica- or T. retortaeformis-specific T subtypes or dendritic cells. For the co-infection network, Tregs are induced by bacteria which produce IL10 that can ultimately affect the helminth, since IL10 is not an antigen-specific node. Moreover, there is only a single pool of naı¨ve T cells that induces T cell subtypes against either the bacteria or the helminths, depending on the antigen-specific dendritic cells. Discrete dynamic model implementation. The immune- parasite interaction networks were developed into discrete dynamical models by characterizing each node with a variable that can take the ON state, when the concentration or activity is above the threshold level necessary to activate downstream immune processes, or the OFF state when activity is below this threshold. The evolution of the state of each node was described by a Boolean transfer function (Text S1) [32]. Target nodes with a single activator and no inhibitors follow the state of the activator with a delay. The operator AND was used to describe a synergistic or conditional interaction between two or more nodes that is necessary to activate the target node. When either of the nodes were sufficient for the activation of the target node we used the operator OR. An inhibitory effect was represented by an AND NOT operator. In cases where prior biological information did not completely determine the transfer functions (e.g. there was no information whether two coincident regulatory effects are independent or synergistic), different alternative transfer functions were tested. The transfer functions that reproduced the qualitative features of the single infection experimental time courses, such as the parasite clearance profile, the relative peaks of different cytokines or the saturating behaviour of IgG as compared to IgA, were selected. For example, IL4 is produced by T helper cells during T helper cell differentiation as well as by eosinophils in response to stimulation by nematode antigens or allergens. While IL12 is known to inhibit the production of IL4, there are two possible ways this cytokine may interact with IL4: IL12 can inhibit IL4 produced by T helper cells or IL12 can suppress IL4 production by blocking both the T helper and eosinophil signal. The inhibitory effect of IL4 on the activation of neutrophils is known. The two transfer functions were then examined by comparing the temporal pattern for neutrophils and IL4 from the single T. retortaeformis infection model with the experimental observations. The second transfer function did not reproduce the observed low activity of IL4 -compared to the other cytokines- in the duodenum at day 14 post infection and it also led to higher neutrophil activity, compared to the other leukocytes, than the empirical data. Since the first transfer function did not lead to such deficiencies, we chose the first over the second rule. The transfer functions used in the co-infection model were the same as, or the relevant composites of, transfer functions used in each individual infection. Thus, the Boolean transfer functions applied in our Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 16 January 2012 \| Volume 8 \| Issue 1 \| e1002345 model provide a mechanistic understanding of the interactions leading to bacterial or helminth clearance. The status of the system across time was simulated by repeatedly applying the Boolean rules for each node until a stationary state (e.g. clearance of the parasite) was found. Since the kinetics and timescales of the individual processes represented as edges are not known, a random order asynchronous update was selected wherein the timescales of each regulatory process were randomly chosen in such a way that the node states were updated in a randomly selected order during each time-step [32]. The asynchronous algorithm was: X t i ~Fi(X ta a ,X tb b ,X tc c ,:::), where F is the Boolean transfer function, ta, tb, tc represent the time points corresponding to the last change in the state of the input nodes a, b, c and can be in the previous or current time-step. The time-step (time unit) of our model approximately corresponds to nine days. The randomized asynchronicity of the model does not alter the steady states of the dynamical system but causes stochasticity in the trajectory between the initial conditions and the equilibria (attractors) [32,37], thus it can sample more diverse behaviours as the traditionally used synchronous models. To determine the node consensus activity over time (i.e. shared by trajectories with different update orders) we ran the simulations 100 times and presented the fraction of simulations in which the node was in an ON state at a given time-step in the node activity profile. We confirmed that running the simulations for more than 100 times did not change the activity profiles. Our approach of using discrete dynamic modelling allowed us to sample the timescales of interactions and perform replicate simulations as well as provide continuously varying activities of the network nodes over time, which ranged between the lower limit of 0 (below-threshold concentration in all runs) and upper limit of 1 (above-threshold concentration in all runs). However, notice the exception for IFNc expression higher than one in the helminth infections. While these activities cannot be directly compared to quantitative concentrations, we could compare the qualitative features of the time courses and ask: are they saturating? Do they show single or multiple peaks? We could also compare the relative trends of similar variables. It is important to stress that the empirical data on B. bronchiseptica-T. retortaeformis co-infection were not used as inputs to the co-infection model but only to validate the simulated course and intensity of immune responses during co- infection. Laboratory experiments The primary single infections of naı¨ve rabbits with B. bronchiseptica strain RB50 and T. retortaeformis have been described in detail in Pathak et al. [28] and Murphy et al. [31]. The co- infection of naı¨ve rabbits with a primary dose of B. bronchiseptica RB50 and T. retortaeformis followed similar procedures. Here, we report a concise description of the experimental design, quanti- fication of the immune variables and parasite intensities. Ethics statement. All listed animal procedures were pre- approved by the Institutional Animal Care and Use Committee of The Pennsylvania State University. Co-infection study design. Out-bred 60 days old New Zealand White male rabbits were intra-nasally inoculated with 1 ml of PBS solution containing 2.56104 B. bronchiseptica RB50 and simultaneously orally challenged with a 5 ml mineral water solution of 5,500 infective third stage T. retortaeformis larvae (L3). Control individuals were treated with 1 ml of PBS or 5 ml of water, respectively. Groups of 6 individuals (4 infected and 2 controls) were euthanized at days 3, 7, 14, 30, 60, 90, 120 post challenge and both the respiratory tract and small intestine were removed to quantify: parasite abundance, cytokine expression in the lungs and small intestine (duodenum) and mucus-specific anti- helminth antibody levels (IgA and IgG) from the duodenum to the ileum (Section SI-1 to SI-4). Blood samples were collected weekly and used for serum-specific antibody quantification against both parasites and leukocyte cells count [28,31]. Parasite quantification. A fixed amount of lungs (15 ml), trachea (5 ml) and nasal cavity (15 ml), homogenized in PBS, was serial diluted onto BG blood agar plates supplemented with streptomycin and incubated at 37uC for 48 hours for bacteria quantification (Colony forming units, CFU) [28]. The four sections of the small intestine (SI-1 to SI-4) were washed over a sieve (100 mm) and helminths collected and stored in 50 ml tubes. Parasites were counted in five 2.5 ml aliquots and the mean number, developmental stage and sex (only for adults) estimated in the four sections [31]. Local cytokine gene expression. The expression of IFNc, IL-4 and IL-10 in the lung and duodenum was determined using Taqman qRT- PCR. RNA isolation, reverse transcription and qRT-PCR quantification were performed following protocols we have developed [28,31]. Antibody detection: Antibody IgA and IgG against B. bronchiseptica and adult T. retortaeformis were quantified using Enzyme-Linked Immunosorbance Assay (ELISA) [28,31]. Optimal dilutions and detector antibody against the two parasites were selected by visually identifying the inflection point from the resulting dilution curves. For B. bronchiseptica serum dilutions were: 1:10 for IgA and 1:10,000 for IgG, secondary detection antibody: IgA 1:5,000 and IgG 1:10,000. For T. retortaeformis mucus dilution was: 1:10 both for IgA and IgG and 1:5,000 for the secondary antibody. We found cross-reactivity at the antibody level between the somatic third stage infective larvae (L3) and the adults both in the serum and the mucus [31]. As such and for simplicity, the empirical data and the network models were based on the antibody response to the adult helminth stage. Haematology. Blood in anti-coagulated EDTA tubes was processed using the Hemavet 3 haematology system (Drew Scientific, USA) and the general haematological profile quantified [28]. Statistical analysis. Linear mixed effect models (LME- REML) were applied to identify changes in the immune variables during the course of the co-infection and between single and co-infection. The individual identification code (ID) was included as a random effect and an autoregressive function of order 1 (AR-1) was integrated to take into account the non- independent sampling of the same individual through time or the monitoring of different parts of the same organ from the same individual. To identify the combination of immunological variables that mainly affected parasite abundance a principal component analysis (PCA singular value decomposition) was used [31]. Briefly, the strongest linear combination of variables along the two main PC axes was identified; generalized linear models (GLM) were then used to examine how parasite abundance was influenced by each PC axis. To compare the immune variables between single and co-infection, data from infected animals were initially scaled over the controls as: Xij* = Xij-Xc, where Xij is an immune variable for individual i at time j and Xc is the total average of the controls across the infection for that variable. Supporting Information Table S1 Relationship between B. bronchiseptica abundance (CFU/g) and immune variables from the co-infection experiment. A- Summary of the Principal Component Analysis (PCA) based on the most representative immune variables; only the first two PCA Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 17 January 2012 \| Volume 8 \| Issue 1 \| e1002345 axes are reported. Note that the cytokine Ct values are inversely related to the level of expression. B- Summary of the generalized linear model (GLM) between bacteria abundance and PCA axis 1 and axis 2. (DOC) Table S2 Relationship between T. retortaeformis abundance (worm/duodenum length) and immune variables from the co- infection experiment. A- Summary of the Principal Component Analysis (PCA) based on the most representative immune variables; only the first two PCA axes are reported. Note that the cytokine Ct values are inversely related to the level of expression. B- Summary of the generalized linear model (GLM) between helminth abundance and PCA axis 1 and axis 2. (DOC) Text S1 Transfer functions for every node of each network: A- Single B. bronchiseptica infection; B- single T. retortaeformis infection; C- B. bronchiseptica-T. retortaeformis co-infection. In the functions we depict the nodes in the intestine with the suffix ‘t’ and the nodes in the lungs with the suffix ‘b’. Abbreviations: Oag: O-antigen; IL4II: Interleukin 4 in systemic compartment; DNE: Dead neutrophils; NE: Recruited neutrophils; IL12I: Interleukin 12 in lungs/intestine; IgA: Antibody A; C: Complement; TrII: T regulatory cells in systemic compartment; IL4I: Interleukin 4 in lungs/small intestine; Th2II: Th2 cells in systemic compartment; TrI: T regulatory cells in lungs/small intestine; Th2I: Th2 cells in lungs/small intestine; IL10II: Interleukin 10 in systemic com- partment; TTSSII: Type three secretion system in systemic compartment; TTSSI: Type three secretion system in lungs; IgG: Antibody G; IgE: Antibody E; IL10I: Interleukin 10 in lungs/ small intestine; IFNcII: Interferon gamma in systemic compart- ment; IFNcI: Interferon gamma in lungs/small intestine; IL12II: Interleukin 12 in systemic compartment; BC: B cells; DCII: Dendritic cells in systemic compartment; DCI: Dendritic cells in lungs/small intestine; Th1I: T helper cells subtype I in lungs/ small intestine; PIC: Pro-inflammatory cytokines; Th1II: T helper cells subtype I in systemic compartment EC: Epithelial cells lungs/ intestine; AP: Activated phagocytes; T0: Naı¨ve T cells; AgAb: Antigen-antibody complexes; MP: Macrophages in lungs; EL2: recruited eosinophils; EL: resident eosinophils; IL13: Interleukin 13; IL5: Interleukin 5; TEL: total eosinophils; TNE: total neutrophils; TR: T. retortaeformis, Bb: B. bronchiseptica DNE: dead neutrophils; IS: T. retortaeformis Larvae; AD: T. retortaeformis Adults; PH: Phagocytosis. (DOC) Acknowledgments We are grateful to Ashley Ruscio for her technical support with the laboratory co-infection experiment. Author Contributions Conceived and designed the experiments: IMC. Performed the experi- ments: AKP LM IMC. Analyzed the data: JT RA IMC. Contributed reagents/materials/analysis tools: AKP LM IMC. Wrote the paper: IMC JT RA. Conceived the immune network models: JT, RA, IMC. Performed the simulations: JT and RA. References 1. Cox FE (2001) ‘‘Concomitant infections, parasites and immune responses’’. Parasitology 122: S23–38. 2. Cattadori IM, Albert R, Boag B (2007) Variation in host susceptibility and infectiousness generated by co-infection: the myxoma-Trichostrongylus retortaeformis case in wild rabbits. J R Soc Interface 4: 831–40. 3. Graham AL (2008) Ecological rules governing helminth-microparasite coinfec- tion. Proc Natl Acad Sci U S A 105: 566–70. 4. 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Immuno-network in Single and Co-infections PLoS Computational Biology \| www.ploscompbiol.org 19 January 2012 \| Volume 8 \| Issue 1 \| e1002345	22253585	MPI_Bacterium = ( IFNg_Bacterium AND ( ( ( Bb ) ) ) ) OR ( PIC AND ( ( ( Bb ) ) ) ) Th2I_Bacterium = ( Th2II_Bacterium ) Oag = ( Bb ) Th1II_TRetortaeformis = ( DCII_TRetortaeformis AND ( ( ( T0 ) ) AND ( ( DCII_TRetortaeformis ) ) AND ( ( IL12II ) ) ) ) Bb = ( ( Bb ) AND NOT ( PH ) ) PIC = ( ( ( EC_TRetortaeformis ) AND NOT ( IL10I ) ) AND NOT ( IgA_TRetortaeformis ) ) OR ( ( ( EC_Bacterium ) AND NOT ( IL10I ) ) AND NOT ( IgA_TRetortaeformis ) ) OR ( ( ( AD ) AND NOT ( IL10I ) ) AND NOT ( IgA_TRetortaeformis ) ) OR ( ( ( AP ) AND NOT ( IL10I ) ) AND NOT ( IgA_TRetortaeformis ) ) IFNgI = ( Th1I_TRetortaeformis ) OR ( IFNg_Bacterium ) OR ( DCI_TRetortaeformis ) Th2I_TRetortaeformis = ( Th2II_TRetortaeformis ) DCII_Bacterium = ( DCI_Bacterium ) IL12II = ( ( DCII_Bacterium AND ( ( ( T0 ) ) ) ) AND NOT ( IL4II ) ) OR ( ( DCII_TRetortaeformis AND ( ( ( T0 ) ) ) ) AND NOT ( IL4II ) ) EC_Bacterium = ( Bb ) AD = ( ( ( IgG AND ( ( ( IS OR AD ) ) ) ) AND NOT ( MPI_Bacterium ) ) AND NOT ( NE_TRetortaeformis ) ) IL5 = ( Th2II_TRetortaeformis ) OR ( EL2 ) IL10I = ( IL10I_Bacterium ) OR ( Th2I_TRetortaeformis ) IgG = ( BC_TRetortaeformis ) Th1I_TRetortaeformis = ( Th1II_TRetortaeformis ) NE_Bacterium = ( PIC ) IL4I = ( IL4II ) Th2II_TRetortaeformis = ( ( DCII_TRetortaeformis AND ( ( ( T0 ) ) ) ) AND NOT ( IL12II ) ) DP = ( NE_Bacterium AND ( ( ( TTSSI ) ) ) ) AP = ( AgAb_Bacterium AND ( ( ( Th1I_Bacterium AND MPI_Bacterium ) ) AND ( ( Bb ) ) ) ) OR ( IgG_Bacterium AND ( ( ( Cb ) ) AND ( ( Th1I_Bacterium AND MPI_Bacterium ) ) AND ( ( Bb ) ) ) ) TTSSI = ( ( ( Bb ) AND NOT ( IgA_Bacterium ) ) AND NOT ( IgG_Bacterium ) ) DCI_Bacterium = ( IFNg_Bacterium AND ( ( ( Bb ) ) ) ) OR ( PIC AND ( ( ( Bb ) ) ) ) IL4II = ( EL2 ) OR ( ( ( Th2II_Bacterium ) AND NOT ( IL12II ) ) AND NOT ( IFNgI ) ) OR ( ( ( Th2II_TRetortaeformis ) AND NOT ( IL12II ) ) AND NOT ( IFNgI ) ) OR ( ( ( DCII_Bacterium AND ( ( ( T0 ) ) ) ) AND NOT ( IL12II ) ) AND NOT ( IFNgI ) ) OR ( ( ( DCII_TRetortaeformis AND ( ( ( T0 ) ) ) ) AND NOT ( IL12II ) ) AND NOT ( IFNgI ) ) EL2 = ( IgE AND ( ( ( IL5 ) ) ) ) OR ( IL13 AND ( ( ( IL5 ) ) ) ) IgE = ( IL4II AND ( ( ( BC_TRetortaeformis ) ) ) ) OR ( IL13 AND ( ( ( BC_TRetortaeformis ) ) ) ) TTSSII = ( TTSSI ) TNE = ( NE_TRetortaeformis ) OR ( NE_Bacterium ) IFNg_Bacterium = ( DCI_Bacterium ) OR ( MPI_Bacterium ) OR ( ( ( Th1I_Bacterium ) AND NOT ( IL10I_Bacterium ) ) AND NOT ( IL4I ) ) BC_Bacterium = ( T0 ) OR ( BC_Bacterium ) EL = ( ( IS ) AND NOT ( EL2 ) ) IL10I_Bacterium = ( TrI_Bacterium ) OR ( Th2I_Bacterium AND ( ( ( TTSSI ) ) ) ) OR ( MPI_Bacterium ) T0 = ( DCII_Bacterium ) OR ( DCII_TRetortaeformis ) Th2II_Bacterium = ( ( DCII_Bacterium AND ( ( ( T0 ) ) ) ) AND NOT ( IL12II ) ) IFNgII = ( IFNg_Bacterium ) OR ( IFNgI ) EC_TRetortaeformis = ( IS ) OR ( AD ) Th1II_Bacterium = ( DCII_Bacterium AND ( ( ( T0 AND IL12II ) ) ) ) PH = ( AP AND ( ( ( Bb ) ) ) ) DCI_TRetortaeformis = ( PIC ) Cb = ( AgAb_Bacterium AND ( ( ( IgG_Bacterium ) ) ) ) OR ( ( Bb ) AND NOT ( Oag ) ) IgA_Bacterium = ( BC_Bacterium AND ( ( ( Bb ) ) ) ) OR ( IgA_Bacterium AND ( ( ( Bb ) ) ) ) BC_TRetortaeformis = ( BC_TRetortaeformis ) OR ( T0 ) Th1I_Bacterium = ( Th1II_Bacterium ) TrI_Bacterium = ( TrII ) IL13 = ( Th2I_Bacterium ) OR ( Th2I_TRetortaeformis ) OR ( EL2 ) OR ( EL AND ( ( ( IS ) ) ) ) IgG_Bacterium = ( BC_Bacterium ) OR ( IgG_Bacterium ) DCII_TRetortaeformis = ( DCI_TRetortaeformis ) AgAb_Bacterium = ( IgA_Bacterium AND ( ( ( Bb ) ) ) ) OR ( IgG_Bacterium AND ( ( ( Bb ) ) ) ) NE_TRetortaeformis = ( ( ( IFNgI ) AND NOT ( IL4I ) ) AND NOT ( IL10I ) ) OR ( PIC AND ( ( ( AD ) ) ) ) TEL = ( EL2 ) OR ( EL ) TrII = ( DCII_Bacterium AND ( ( ( TTSSII ) ) AND ( ( T0 ) ) ) ) IgA_TRetortaeformis = ( IS AND ( ( ( BC_TRetortaeformis ) ) ) )
Helikar et al. BMC Systems Biology 2012, 6:96 http://www.biomedcentral.com/1752-0509/6/96 SOFTWARE Open Access The Cell Collective: Toward an open and collaborative approach to systems biology Tom´aˇs Helikar1, Bryan Kowal2, Sean McClenathan2, Mitchell Bruckner1, Thaine Rowley1, Alex Madrahimov1, Ben Wicks2, Manish Shrestha2, Kahani Limbu2 and Jim A Rogers1,3 Abstract Background: Despite decades of new discoveries in biomedical research, the overwhelming complexity of cells has been a signiﬁcant barrier to a fundamental understanding of how cells work as a whole. As such, the holistic study of biochemical pathways requires computer modeling. Due to the complexity of cells, it is not feasible for one person or group to model the cell in its entirety. Results: The Cell Collective is a platform that allows the world-wide scientiﬁc community to create these models collectively. Its interface enables users to build and use models without specifying any mathematical equations or computer code - addressing one of the major hurdles with computational research. In addition, this platform allows scientists to simulate and analyze the models in real-time on the web, including the ability to simulate loss/gain of function and test what-if scenarios in real time. Conclusions: The Cell Collective is a web-based platform that enables laboratory scientists from across the globe to collaboratively build large-scale models of various biological processes, and simulate/analyze them in real time. In this manuscript, we show examples of its application to a large-scale model of signal transduction. Background The immense complexity in biological structures and pro- cesses such as intracellular signal transduction networks is one of the obstacles to fully understanding how these systems function. As understanding of these biochemical pathways increases, it is clear that they form networks of astonishing complexity and diversity. This means that the complex pathways involved in regulation of one area of the cell (so complex that a researcher could spend their entire career working in that area alone) are so interconnected to other, equally complex areas that all of the diﬀerent path- way systems must be studied together, as a whole, if any of the individual components are to be understood. How- ever, the large scale and minute intricacy of each of the individual networks makes it diﬃcult for cell biologists or biochemists working in one area of a cell’s biochemistry to be aware of, let alone relate their results to, ﬁndings obtained from the various diﬀerent areas. So how will all Correspondence: thelikar@unomaha.edu 1Department of Mathematics, University of Nebraska at Omaha, Omaha, NE, USA Full list of author information is available at the end of the article of these individually complex systems be possible to study in an integrated biochemical “mega-system?” In order to address this problem, the concept of systems biology study has emerged [1-8]. However, with i) data being generated by laboratory scientists at a staggering rate in the course of studying the individual systems, ii) the fact that these individual systems are so complicated that scientists rarely have detailed knowledge about areas outside those that they study, there is a huge imped- iment to implementing a systems approach in cellular biochemistry, and iii) for laboratory scientists to fully embrace systems biology computational tools must lend themselves to usage without requiring advanced mathe- matical entry or programming. Several signiﬁcant advancements in the systems biology ﬁeld have been made as a response to the sea of data being generated at ever increasing rates. For example, in the area of biochemical signal transduction, several community-based projects to organize information about signal transduction systems such as the Alliance for Cellu- lar Signaling [9], the former Signal Transduction Knowl- edge Environment [10], UniProt [11], or the WikiPathways project [12] have been created. These resources provide a © 2012 Helikar et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Helikar et al. BMC Systems Biology 2012, 6:96 Page 2 of 14 http://www.biomedcentral.com/1752-0509/6/96 way to organize and store important laboratory-generated data and information such as gene sequences, protein characteristics, interaction partners, etc.; these are then easily accessible via the Internet to the scientiﬁc commu- nity. Building on these resources and advancements has been the development of tools to visualize and analyze these data and, speciﬁcally, the entities that make up the complex, network-like structures of biological processes. Amongst the most widely used tools to visualize biological networks is the open-source software, Cytoscape [13]. The information contained in the above database resources (and visualized via Cytoscape) is limited in that it is mostly static; biological systems however are dynamic in nature. Hence to fully understand the under- lying mechanisms (and those of corresponding diseases), the dynamics of these processes need to be considered. Computational modeling and simulation has been suc- cessfully adopted in a number of ﬁelds to dramatically reduce development costs. The use of these modern tools to organize and probe biological structure and function has a high potential to provide the basis for new break- throughs in both basic understanding of cell function and the development of disease therapies. The ability to observe the actual dynamics of large scale biolog- ical systems increases the probability that, out of the tens of thousands of combinations of interactions, unex- pected points of intervention might be deciphered. The Cell Collective aims at providing an environment and resource where the biomedical community, as a whole, can more eﬀectively bring these exciting new computa- tional approaches to bear on cellular systems. The inte- gration of computational and laboratory research has the potential to lead to improved understanding of biological processes, mechanisms of disease, and drug development. If a “systems approach” is to be successful, then there must be a “system” into which the thousands of labora- tory scientists all over the world can incorporate their detailed local knowledge of the pathways to create a global model of biochemical pathways. With such a systems plat- form, all local information would be far more accurate if laboratory scientists would contribute their specialized expertise into a system that enables the integration of the currently dispersed knowledge. Hence, a collabora- tive modeling platform has the potential to substantially impact and move forward biomedical research. This is precisely the purpose of The Cell Collective. The Cell Collective is an environment to model biolog- ical processes. The platform allows scientists to deposit and track dynamical information about biological pro- cesses and integrate and interrogate this knowledge in the context of the biological process as a whole. Laboratory scientists can directly simulate large-scale models in real time to not only help test and form new hypotheses for their laboratory research, but also to make research more easily reproducible (through sharing their models with collaborators). Furthermore, the creation and simulation of models in The Cell Collective doesn’t require direct use of mathematics or programming – a substantial advance- ment in the ﬁeld [14]; this tool has been developed to bring modeling into the hands of mainstream laboratory scientists. The role of The Cell Collective in the current landscape of systems biology technology As a result of the constant ﬂow of data from laborato- ries, the success of biomedical research relies now, more than ever, on computational and computer technologies. While a number of diﬀerent technologies have already been developed and succeeded in their purpose, The Cell Collective further builds on the successes of these eﬀorts to provide a novel technology to exploit the full potential of systems biology. In this section, a discussion of some of these technologies follows. Note that, the following is not an extensive review, rather we aim to illustrate how The Cell Collective ﬁts within the landscape of systems biology resources. For better understanding, these resources have been categorized according to their function. A) Biological databases (as mentioned in the Background section, Alliance for Cellular Signaling [9], STKE [10], UniProt [11], the WikiPathways project [12], KEGG [15], UniProt [16], Reactome [17], Pathway Commons [18], etc.) were developed as one of the ﬁrst steps to deal with the sea of biological data being produced with high-throughput technologies. The information contained in these biological databases focuses on static cell “parts lists.” In other words, the data focuses on the description of the individual entities rather than the dynamical relationship between the individual parts. Conversely, The Cell Collective, and speciﬁcally its Knowledge Base component (discussed in the Results section) extends static knowledge and data into dynamical models; hence the information contained in the Knowledge Base (which is purely qualitative) is dynamical in nature; it takes into account the dynamical relationship between all of the interacting partners. B) Software for dynamical models (which employ mathematical frameworks similar to the ones used in The Cell Collective – i.e., rule-based formalisms) also already exist (e.g., GINsim [19], BooleanNet [20], CellNetOptimizer [21], or BoolNet [22]). These tools have been built and used mainly for individual groups to study networks of a conﬁned size. They also rely on the users’ training in computer programming and/or mathematics (and hence are ﬁrst and foremost tools developed for modelers); this makes it diﬃcult for laboratory scientists to incorporate these tools into Helikar et al. BMC Systems Biology 2012, 6:96 Page 3 of 14 http://www.biomedcentral.com/1752-0509/6/96 their experimental studies. The Cell Collective provides a novel tool in the area of large-scale, whole cell models, while extending the use of computational modeling to laboratory scientists. C) Model repositories such as the CellML repository [23] or the BioModels Database provide a central location to store models developed by the community. These models are then available to others for download and further analyses using other tools. The BioModels Database is primarily a model repository, however, it does provide simulation capabilities via the JWS simulator [24]. In addition, the PathCase systems biology tool [25,26] provides a central place for kinetic models from the BioModels Database and KEGG pathways to be queried, visualized, and simulated side-by-side. Similar to these resources, The Cell Collective provides the ﬁrst repository (with simulation capabilities) for models based on a qualitative mathematical formalism. D) Model exchange standards such as the Systems Biology Markup Language (SBML, [27,28]) or CellML [29] make it easier for models to be exchanged between diﬀerent groups and simulated/analyzed by diﬀerent simulation tools. For example, when a research group wants to simulate a model deposited to the BioModels Database, the model’s description in SBML or CellML ensures that the model truly corresponds to the same model used by a diﬀerent group, and hence the generated data can be easily reproduced. While users can share their models with other users of The Cell Collective directly, without the need to import/export model ﬁles, the platform currently provides SBML export features based on the most recent version of SBML L3 qualitative package [30]. E) Visualization and analysis tools for static interaction networks, such as the aforementioned Cytoscape [13], but also others including VisANT [31] or Gephi (http://gephi.org), have been used extensively to visualize and analyze the graph properties of networks of various types and sizes. As a complement to existing graph analyses, The Cell Collective deals with dynamical models – ones that can be put in motion via computer simulations – and hence focuses on the visualization of the dynamics of these models via simulations, and susbsequent analyses (e.g., input-output relationships). Together, The Cell Collective is a platform that not only provides a unique combination of successful systems biology and modeling approaches, but also oﬀers signiﬁcant innovations to these technologies. In this manuscript, discussed are the various components and features of the platform, and exempliﬁed on a previously published large-scale network model of signal transduction [32]. Implementation The Cell Collective is a server-based software imple- mented in Java and powered by MySQL database. The simulation engine is based on ChemChains which was implemented in C++ [33]. The user interface of The Cell Collective was implemented primarily using JavaServer Faces (http://www.javaserverfaces.org) and Primefaces (http://www.primefaces.org). Computational framework and simulations Models in The Cell Collective are based on a qualita- tive, rule-based mathematical framework. In this frame- work, each species can assume either an active or inac- tive state. Which state a species assumes at any given time point depends on a set of rules that take into account the activation state of all immediate upstream regulators. The Bio-Logic Builder provides the user interface for users to enter qualitative information about the regula- tory mechanism of each species in a model, and sub- sequently converts this information into an appropriate mathematical (algebraic) expression (manuscript submit- ted). Before the simulation engine (ChemChains) can simulate a model, the mathematical expressions of indi- vidual species are converted into C++ (.cpp) ﬁles, which are subsequently compiled into a single dynamical library (.so ﬁle). This dynamical library encodes the entire model which is subsequently simulated by ChemChains (see Figure 1). Though a discrete (active/inactive) mathematical framework is used to represent the modeled biological processes, ChemChains has been developed to enable simulations of discrete models while using continuous input/output data. In general, the activity levels of the models’ individual constituents is measured as %ON. Depending on the context of the biological process being simulated, this measure corresponds, for example, to concentration or the fraction of biological species being active at any given time. In the case of real-time simulations, %ON of a species represents its moving average activity, and is calculated as the fraction of the active/inactive states over a slid- ing window. For simulations using the Dynamical Analysis feature, the activity levels of the individual species (or %ON) also corresponds to the ratio of active/inactive states, but is calculated once the dynamics of the model settle in a steady behavior (or an attractor as described in great detail in [33]). In both the real time simula- tions and dynamical analysis, %ON is used as a semi- quantitative way to measure the dynamics of the modeled biological processes. Helikar et al. BMC Systems Biology 2012, 6:96 Page 4 of 14 http://www.biomedcentral.com/1752-0509/6/96 Figure 1 Construction of models prior to their simulations via built-in ChemChains. The bio-logic for each species (deﬁned by users) is converted (automatically) to a mathematical (Boolean) expression. Each species’ expression is encoded to a C++ ﬁle, and all ﬁles are subsequently compiled into a single dynamic library (.so ﬁle) which can be read and executed by ChemChains for simulations. Simulation performace We analyzed the perfomance of individual simulations for randomly generated models of diﬀerent sizes and diﬀerent complexities (in terms of network connectivity). Speciﬁ- cally, we considered models with 10, 100, 500, and 1,000 nodes and network connectivities of 2, 5, 10, 20, and 100. Note that for biological application, relatively small (low single digit) connectivity is most realistic [32,34,35]. As can be seen Table 1, simulations in The Cell Collec- tive are relatively eﬃcient as the required computational resources are in a linear relationship with the increasing parameters of the generated networks. Results and discussion The Cell Collective is a web-based platform (accessible at http://www.thecellcollective.org) in which laboratory sci- entists can collaboratively build mathematical models of Table 1 Simulation performance for models with ranging complexity # of nodes/ connectivity 2 5 10 20 100 10 0.88s 0.94s 0.85s 0.99s 0.93s 100 4.82s 4.98s 5.55s 5.95s 9.8s 500 26.99s 29.42s 32.11s 37.31s 68.73s 1,000 60.89s 64.61s 70.95s 79.59s 149.34s Simulations consisted of 10,000 time steps and were performed on a computer with a single core, 2GHz processor and 2GB of RAM. biological processes by utilizing existing laboratory data, and subsequently simulate the models to further guide their laboratory experiments. Conceptually, the platform can be broken up into three parts (Figure 2) that form the basis for the core functionality of the software: 1) inte- grated Knowledge Base of protein dynamics generated from laboratory research in a single repository, 2) integra- tion of this knowledge into mathematical representation that allows visualization of the dynamics of the data (i.e., put it in motion via simulations), and 3) simulations and analyses of the model dynamics. As can also be seen in the ﬁgure, these three parts form a loop that is closed by laboratory experimentation. The ﬁrst model in The Cell Collective (available in for all users to simulate and build upon) is one of the largest models of intracellular signal transduction [32]. Features available in the current version of The Cell Collective are described in more detail in the following sections. Knowledge Base of interaction dynamics When laboratory scientists produce new results, for example regarding the role of one protein interacting with another protein, these results are usually published along with thousands of other results generated by the scien- tiﬁc community. The publication of individual results in isolation means that separate ﬁndings are not necessarily absorbed, veriﬁed, analyzed, and integrated into the existing knowledge. With the invention of various high- throughput technologies, the gap between the amount of knowledge produced and the ability of the scientiﬁc community to fully utilize this knowledge has grown [36]. The ﬁrst major component of The Cell Collective (as highlighted in Figure 2) is a Knowledge Base which enables laboratory scientists to contribute to the integra- tion of knowledge about individual biological processes at the most local level which includes, for example, the identiﬁcation of direct protein-protein interactions. How- ever, the goal of The Cell Collective is not to duplicate other well-established resources by providing extensive parts lists that make up various biological processes and cells. Instead, the aim of the platform is to extend static knowledge and data into dynamical models; hence the information provided in the Knowledge Base needs to be dynamical in nature. This means that the information (which is purely qualitative – see the Methods section) contained in The Cell Collective Knowledge Base takes into account the dynamical relationship between all of the interacting partners. For example, let’s assume, there are two positive regulators (X and Y) of a hypothetical species Z. While in the context of a parts list, information about the above species and interactions would be suﬃcient, in order to abstract the biological process to a dynami- cal model, one needs to know the dynamical relationship between the interacting partners. For instance, are both X Helikar et al. BMC Systems Biology 2012, 6:96 Page 5 of 14 http://www.biomedcentral.com/1752-0509/6/96 Figure 2 Overview of the ﬂow of knowledge about biological processes, and the role of The Cell Collective in integrating and understanding this knowledge in the context of the biological processes as a whole. and Y necessary for the activation, or is either one of them suﬃcient to activate Z? This is the type of information that is used to construct dynamical models in The Cell Collective. Based on a widely known wiki-like concept, the Knowl- edge Base module of the platform was developed to allow laboratory scientists to contribute – collabora- tively – their knowledge to the complete regulatory mechanisms of individual biological species. Because all of the regulatory information forms the basis of the modeled biological/biochemical process, and hence has to be correct for the model to exhibit similar behav- iors as seen in the laboratory, this process of aggre- gating all known information about a species into one place can also serve as a mechanism to identify pos- sible contradictions or holes in the current knowledge about the regulatory mechanism of a particular species. Using the previous hypothetical example, let’s assume laboratory scientist A discovers that proteins X and Y are both necessary to activate species Z, but scientist B’s laboratory results suggest either protein X or Y can suﬃciently activate Z (Figure 3). The process of inte- grating all known information on species Z becomes crucial in discovering such discrepancies (or additional missing information), which may have not been found otherwise. Because the goal of The Cell Collective is to also integrate this information into dynamical mod- els, simulations of the large-scale model (which might have hundreds or thousands of additional components in it) can suggest whose data is more likely to be correct. Assume that scientist A adds his informa- tion into the model and the model exhibits phenom- ena similar to the ones seen in the laboratory, whereas when the model is built with the data from scientist B’s experiments, the simulation dynamics of the over- all model fails to resemble the known actions of the real system. In such a case, new laboratory experiments would be warranted, with a potential to produce more insights into the regulatory mechanism of protein Z (Figure 3). The sea of biological information has made it dif- ﬁcult for the data to be veriﬁed on such an inte- grated basis. We fully understand how some of the most complex biological systems work only when the experimental data is re-integrated into and seen in the context of the entire system; a platform for inte- gration of data is exactly what The Cell Collective provides. Dynamical information Each species in The Cell Collective’s Knowledge Base has a dedicated page where laboratory scientists can directly deposit their knowledge regarding the species’ regulatory mechanisms. While the wiki-like format of the Knowl- edge Base gives users the ability to input their data in a free form which can be also interactively discussed, each page is structured to help users organize and review their data more eﬃciently. Because the wiki format is Helikar et al. BMC Systems Biology 2012, 6:96 Page 6 of 14 http://www.biomedcentral.com/1752-0509/6/96 Figure 3 Integration of laboratory results via modeling. The diﬀerent relationships between hypothetical interactions of X and Y with Z as discovered by scientists A and B. Solid lines depict the necessity of the interaction for species Z to be activated, whereas dashed lines correspond the optional nature of the interaction. Because scientist B’s results suggest an “OR” relationship between the regulators, there are two graphical representations of Z’s regulatory mechanism. an easy medium for collecting knowledge from a large number of individuals, a number of scientiﬁc eﬀorts have successfully adopted a variation of this technology (e.g., [12][32][33][34]). First, the Regulation Mechanism Summary section describes the general mechanism of the activa- tion/deactivation of the species. This section, found at the top of the page of a given species, is most important from a systems perspective as the information therein takes into an account the role of all immediate upstream regulators (see below). The Upstream Regulators section contains the list of key players that have a role in the regulation of the species, as well as any evidence (as found in the laboratory) sup- porting those roles. Using the earlier example involving the regulatory mechanism of species Z, this section would include proteins X and Y as upstream regulators, and the ﬁndings of laboratory scientists A and B suggest- ing the role of these regulators in the activation of the species (Figure 4). On the other hand, the Regulation Mechanism Summary section (discussed above) would contain the overall dynamical information as to how Z is regulated in the context of both X and Y (i.e., are both regulators required for the activation, or only one of them?). Model-speciﬁc Information section: Because a number of molecular species can be regulated diﬀerently based on the type of the cell, this section allows users to enter such cell type-speciﬁc information. For example, an intracellular species can be regulated either by dif- ferent players, or the same players but with diﬀerent dynamical relationships in, say, a T cell and a mammary epithelial cell. This section enables users to diﬀerenti- ate between the regulatory mechanisms of the species in the two (or more) diﬀerent types of cells (i.e., mod- els). Hence, this section can be utilized by users to deﬁne upstream regulators and the regulation mecha- nism summary that is speciﬁc to users’ diﬀerent mod- els. For example, the regulation mechanism summary of species Z in scientist A’s model would describe his ﬁnd- ings that both upstream regulators of Z are necessary for its activation, whereas scientist B’s regulation mech- anism summary on wiki page for Z would indicate that either one of the upstream regulators can activate Z (Figure 4). Finally, References is a section that users can use to record any published works that support information entered in any of the above sections. Users can enter ref- erences by simply entering the Pubmed ID (pmid) of the article of interest and The Cell Collective will automati- cally import all of the bibliographical information about the works. As a starting point, we have deposited all biological knowledge describing one of the largest dynamical models of signal transduction built and published as part of our previous research [32]. This model consists of around 400 biochemical interactions between 130 species, comprising a number of main signaling pathways such as the Epi- dermal Growth Factor, Integrin, and G-Protein Coupled Receptor pathways. The dynamical information about the hundreds of local interactions, collected manually from published biochemical literature, is available in the Knowledge Base module. Expert scientists in the ﬁeld may begin contributing to it, as well as discovering Helikar et al. BMC Systems Biology 2012, 6:96 Page 7 of 14 http://www.biomedcentral.com/1752-0509/6/96 Figure 4 Visualization of the ﬂow of data generated by laboratory scientists through The Cell Collective Knowledge Base and Bio-Logic Builder. For example scientists A and B identify diﬀerent upstream regulators (protein X and Y, respectively) of protein Z. This knowledge is subsequently recorded in the Upstream Regulators section on the page of protein Z. Then both scientists A and B determine what the relationship is between the two upstream regulators of Z. Once the overall regulation mechanism is agreed upon, the scientists use Bio-Logic Builder to add the regulatory mechanism of Z to an actual model. The mathematical representation of the species bio-logic is generated in the background, so the user never has to deﬁne any mathematical equations nor expressions. discrepancies and gaps in the biological knowledge that might have been included in the model. Once the dynamical information about the individual interactions is added in the platform Knowledge Base, the next step is to convert this knowledge into a dynam- ical model; a discussion on where this piece ﬁts into the overall concept of The Cell Collective follows in the next section. Building computational models While the Knowledge Base component of The Cell Collec- tive serves as the knowledge aggregator for the dynamical regulatory mechanisms of individual biological species, the next step (#2 in Figure 2) is to convert this knowl- edge into a dynamical computational model that can be simulated and analyzed on the computer. Perhaps one of the biggest challenges in transforming biological knowledge into a computational model is the conceptual gap between the mathematical and biological sciences. Thus far, the creation of mathematical models has been limited to scientists who are well versed in com- puter science and mathematics. To address this issue, we have developed Bio-Logic Builder (manuscript submit- ted), a component of The Cell Collective, which allows laboratory scientists to build computational models based purely on the logic of the species’ regulatory mechanisms as discovered in the laboratory. The step of transforming biological knowledge into its model representation is aided by the information pro- vided in the Knowledge Base component of the software platform (Figure 4). Speciﬁcally, as discussed above, the information recorded for the corresponding local interac- tions by individual scientists amounts to the overall regu- lation mechanism which represents the blueprint of each species’ bio-logic. While the local interactions (concerning a hypothetical protein Z in Figure 4) are discovered in the laboratory by individual scientists (for example scientists A and B as shown in the ﬁgure), the species overall reg- ulation mechanism should take into an account all of the local knowledge (and hence should be determined in a collaborative fashion). Bio-Logic Builder was developed in such a way that all that is necessary to construct the com- putational representation of the regulatory mechanism of each species is the same qualitative data provided in the Knowledge Base component. Scientists deﬁne each species’ bio-logic in a modular fashion by simply deﬁn- ing activators and inhibitors (i.e., upstream regulators) of the species of interest, as well as the logical relation- ship between the upstream regulators (e.g., whether or not a set of activators is required for activation, as dis- cussed in an example above). Because models in The Cell Collective utilize a qualitative, rule-based mathemat- ical framework, no kinetic parameters are necessary to construct the models. (A quick tutorial on how to use the Bio-Logic Builder to construct models is available at http://www.thecellcollective.org) Once the bio-logic is deﬁned for all species in a given model, in silico simulations and analyses can be conducted (step #3 in Figure 2). How this can be done with The Cell Collective is the focus of the next section. Simulations and analyses of model dynamics The idea behind abstracting biological processes as com- putational models is to be able to visualize the dynamics of these processes on the computer, and to conduct in silico experiments that can provide i) new insights into laboratory experiments and ii) additional basis for the- oretical computational research to further elucidate the complexity governing these biological processes. With its simulation and analysis component, The Cell Collective has been designed to provide exactly these features. Helikar et al. BMC Systems Biology 2012, 6:96 Page 8 of 14 http://www.biomedcentral.com/1752-0509/6/96 Speciﬁcally, in the current version of the platform, two tools for simulations and analyses (discussed below) are available. Real-time simulations Perhaps the most unique and novel innovation to com- putational modeling is the real-time simulation feature in the platform, which allows users to visualize the dynamics of any model interactively and in real time. Similar to the rest of the platform, the simulation features have been designed with simplicity and intuitiveness in mind. All modeled biological/biochemical processes in The Cell Collective, represented by species that make up the internal machinery of the cell, are simulated in exter- nal environments which drive the dynamics of the sys- tem. In our example of signal transduction, this environ- ment is represented by external species corresponding to various extracellular signals such as growth hormones, stress, etc. Using a simple slider, users can change the amount of each extracellular signal (measured in %ON on a scale of 0 to 100 – see the Methods section for more detail) and visualize the eﬀects of the changes on the dynamics of the cell while the simulation is running. Similarly, users can introduce biological mutations to sim- ulate loss-of-function and gain-of-function experiments while watching the dynamics of the cell change as a result of the mutations. For users’ convenience, real time sim- ulations can be also paused and resumed at any time. Figure 5 shows a screen-shot of the real time simulation tool. A short video demonstration of real time simulations using the previously mentioned large-scale model of sig- nal transduction is also available as a Additional ﬁle 1. Dynamic Analysis Laboratory studies to identify functional relationships between extracellular stimuli and various components of the cell involve a number of experiments that can be both time consuming and resource demanding. For example, a laboratory study [37] that suggests that Akt (a ser- ine/threonine kinase involved in the regulation of a variety of cellular responses such as apoptosis, proliferation, etc.) is activated in response to the Epidermal Growth Factor Figure 5 Screen-shot of a real-time simulation. Users can change the activity level of the extracellular species via simple sliders (boxed in red). Each tracing in the graph corresponds to an activity level of a species speciﬁed in the legend by the user. Any eﬀects of the change of activity of the external species is then reﬂected in the dynamics of the species’ graph; as the user moves the slider, the activity patterns of the selected species change in real time. In addition, by using the “Mutate” button, users can simulate the eﬀects of gain/loss-of-function mutations on the dynamics the modeled biological process. Helikar et al. BMC Systems Biology 2012, 6:96 Page 9 of 14 http://www.biomedcentral.com/1752-0509/6/96 (EGF), the activity of Akt is measured and compared in untreated cells and cells treated with EGF. Such studies usually involve the construction of a number of protein constructs, cell cultures, assays, etc, amounting to the use of many resources. While Akt has been known for many years to be activated in response to EGF, there are many areas of the cell that are not as well understood. Laboratory experiments in such areas can be sometimes based on less sound hypotheses that may lead to the waste of many resources. But what if one had the ability to pre-test laboratory hypotheses on the computer, using a com- putational model, in a matter of minutes? This would allow laboratory scientists to weed out weak hypotheses while focusing on the ones that have a better chance of being proven correct, and hence resulting in more eﬃcient studies. This is where the Dynamic Analysis simulation fea- ture of The Cell Collective plays an important role. This tool allows users to conduct in silico experiments that closely resemble the way laboratory experiments are per- formed, with the advantage that in these computational studies researchers can perform more simulations and experiments in a much shorter time-frame. For example, models in The Cell Collective can be simulated and their dynamics visualized and analyzed in hundreds or thou- sands of extracellular environments (as opposed to the limited number of scenarios possible in the laboratory) in a manner of minutes. As an example, we will demonstrate how the soft- ware can be used to study the relationship between EGF and Akt. The dynamical analysis studies are done in two parts. First, on the main page of the simulation tool (Figure 6), users deﬁne the extracellular environ- ment under which the study will be done. This is anal- ogous to the preparation of cell media in the laboratory. Similar to laboratory experiments with real cells, diﬀer- ent studies using computational models (or virtual cells) Figure 6 Dynamical analysis page. Dynamical analysis page. For each in silico experiment, users can use the dual sliders to deﬁne the ranges of activity levels of each extracellular species. Users can also set additional properties of the experiment including the number of simulations as well as mutations (gain/loss-of-function). Helikar et al. BMC Systems Biology 2012, 6:96 Page 10 of 14 http://www.biomedcentral.com/1752-0509/6/96 also require the set up of optimal extracellular condi- tions. As visualized in the ﬁgure, this can be done easily by setting the ranges of the activity (from 0 to 100%) of the individual extracellular (external) species via the dual sliders (or by just typing the activity levels in the appropriate text boxes). Because in this example exper- iment, we are interested in the eﬀects of EGF on the network model, the activity of EGF (boxed in red) is set to range on the full scale between 0 and 100% ON. On the other hand, the activity ranges of the remaining external species are selected for optimal results based on our previous research [32], and supported by laboratory- generated data. For example, the Extracellular Matrix (ECM) is set to higher activity levels, varying between 56 and 100% (boxed in blue); this corresponds to a biological ﬁnding that EGF-induced growth (as well as other cellu- lar processes) is dependent on cell anchorage via ECM [38]. (Note that, from our experience with large-scale models, while optimal conditions should be determined, the simulations and results are not sensitive to exact values.) While in this example, 100 simulations are performed, users can specify the number of simulations to be run within the study (Figure 6). During each simulation, an activity level for each extracellular species is selected ran- domly by the software such that the activity falls into the speciﬁed range. As a result, the user is able to simulate what would amount to 100 diﬀerent laboratory experi- ments, with each experiment corresponding to a diﬀerent external condition. Once the in silico experiment has completed, users can analyze the dynamics of the model. Currently, the Dynamic Analysis tool allows users to generate dose- response curves to investigate qualitative (input-output) relationships between external cellular signals and vari- ous components of the model, such as the one between EGF and Akt as visualized in Figure 7. As can be seen in the graph, there is indeed a positive correlation between EGF and Akt, similar to the phenomenon seen in the laboratory. An additional signiﬁcant advantage of com- putational experiments using this tool is that users can generate a number of analyses without re-running the entire experiment. For instance, in addition to examining the functional relationship of Akt and growth, one can generate similar dose-response curves for any species in the model using a single 100-simulation experiment. This Figure 7 An example of a dose-response curve visualizing the functional relationship between Akt and EGF. Users can generate a number of graphs that are saved and can later be retrieved from the table at the top of the page. Generated graphs can also be saved on the computer and used directly in a manuscript. Helikar et al. BMC Systems Biology 2012, 6:96 Page 11 of 14 http://www.biomedcentral.com/1752-0509/6/96 is done by specifying the appropriate extracellular sig- nal and output species (i.e., any species of interest) from drop-down menus available on the page. On the generated graph, the selected external species is represented on the x-axis whereas the output species is represented on the y-axis. Furthermore, similar to the real time simulation feature, mutations to any of the cellular species can easily be speciﬁed which allows users to simulate gain/loss-of- function in an intuitive fashion. In the current version of the software, users can generate the dose-response graphs for all species in the model by selecting the appro- priate input-output species. While we are in the course of adding additional means of visualizing the simulation results, users can also download all generated (raw) simu- lation data, which can subsequently be analyzed by users according to their needs. The Dynamical Analysis feature can be used not only to generate new hypotheses, but also to test the correct- ness of the model. Because the models are built using local knowledge of the individual interactions, how do we know that all of this local information adds up to a system that represents what is seen in the laboratory? Hence the correctness of the model needs to be tested on global phenomena of the system. The above exam- ple demonstrates how the model of signal transduction in a ﬁbroblast cell can be tested to ensure that species associated with apoptosis and growth (such as Akt) appro- priately respond to a growth signal (EGF). If, for example, the dose-response curve for Akt and EGF suggested a negative correlation, one would have to go back and inves- tigate which of the local interaction data resulted in the contradictory result. Seed models In addition to the signal transduction model of a ﬁbroblast cell created and previously published by our group [32], as part of our most recent research eﬀorts, we have con- structed additional models of the budding yeast cell cycle [39] and host cell infection by Inﬂuenza A, including the viral replication cycle (manuscript submitted). We have also re-created a model of ErbB signaling and regulation of the G1/S transition in the cell cycle during breast cancer. This model was initially created by the authors to study trastuzumab resistance and predict possible drug targets in breast cancer [40]. All of these models are now avail- able and published in The Cell Collective, hence available to the scientiﬁc community as seed models for further contributions and/or simulations and analyses. Collaboration and accessibility As discussed in the Background section, collaboration amongst laboratory scientists working in diﬀerent areas of complex biological processes and the accessibility to modeling frameworks is key to new discoveries using the systems approach. These two properties were strictly kept in mind when designing the software, and provide the main framework for The Cell Collective. First, motivated by this framework was the use a wiki- like format to keep track of the knowledge concern- ing the dynamical properties of biological process. This framework was also applied to the way users interact with the actual computational models. Perhaps the most important feature in the context of accessibility is the concept of “Published Models” (Figure 8). These models created by the community are freely accessible to all registered users, fostering the idea of open science. All users can view the bio-logic as well as the information in the knowledge base, and perform real time simulations on these models directly. To make changes to these models and see how these modiﬁca- tions aﬀect the dynamics of the model, users can create personal copies of published models. Once a copy of a published model is created, the copy will be available and visible only to the one user until shared under “My Models” as seen in Figure 8. (As mentioned earlier, a number of models are now available under Published Models for all users to access and simulate.) My Models is a collection of models created by any given user. Users have an additional ability to share and collaborate on any of these models with a select group of colleagues. The degree to which such a collabora- tion can take place is guided with the choice of three types of permission a user can specify when sharing his/her model. First, models can be shared such that other users can simulate the shared models and view the model’s bio-logic. A second way of model shar- ing also allows other users to contribute to the mod- els and directly edit them. Finally, models can be also shared so that other users become model administrators and have the same rights as the creator of the model, including the ability to share the model with additional collaborators. Many biomedical research software tools (especially the commercial ones) tend to limit users in such a way that once the user commits to the tool, it becomes diﬃcult to move their data to a diﬀerent platform. This is exactly the opposite with The Cell Collective. In addition to being able to share models with any and every user of the plat- form, features to export models in formats that can work with other modeling tools are also available. In the most recent version, users can export all mathematical expres- sions for each model (including the available published models) in the form of ﬂat text ﬁles as well as SBML (SBML [28]). Finally, a forum is available as part of The Cell Collective modeling suite. This will aﬀord users additional means of communication with the scientiﬁc community as well as with the platform’s development team. Helikar et al. BMC Systems Biology 2012, 6:96 Page 12 of 14 http://www.biomedcentral.com/1752-0509/6/96 Figure 8 Main model panel. The ﬁlter in the top left corner allows the user to switch between the diﬀerent types of models (discussed in text). The majority of the space in the right section of the panel is dedicated to the model’s controls (boxed in) and more general information about the model (e.g., creator and description). Users can also navigate from this panel to the simulation page as well as a page containing all model constituents by using the Simulate and Model Bio-Logic buttons, respectively. As indicated in the right upper corner, users can also initiate the creation of new models from this page. Conclusions Because of the inherent size and complexity of biochem- ical networks, it is extremely diﬃcult for a single person or group to eﬃciently transfer the vast amount of labo- ratory data into a mathematical representation; this fact applies to any modeling technique. One way to address this issue is to engage the community of laboratory sci- entists that have generated these data and, hence, have ﬁrst-hand knowledge of the local protein-protein regula- tory mechanisms. If the community of laboratory scien- tists had a mechanism by which they could collaborate and contribute their intimate knowledge of local inter- actions into a large-scale global model, the creation of these models would be greatly enhanced in terms of both size and accuracy. As most laboratory scientists commu- nicate their data in qualitative terms, rule-based models which utilize such qualitative information provide an ideal candidate for that platform. Although qualitative models do not require an under- standing of high level mathematics, it does assume that users dealing with these models are familiar with rule- based (e.g., Boolean) formalisms. At ﬁrst, this may seem a subtle issue (as most qualitative information generated in laboratories is practically generated and interpreted in Boolean terms; e.g., protein x AND y activate protein z), however, the Boolean truth tables (and expressions) get more complex as the size of the model increases. This complexity eﬀectively creates another challenge in build- ing large-scale models. The Cell Collective and its major component, Bio-Logic Builder (manuscript submitted), aims at bridging this gap by enabling users to create these dynamical models without having to directly interact with the model’s mathematical complexities. The collaborative nature of The Cell Collective also opens doors to more open and reproducible science. By integrating biological knowledge, currently dispersed Helikar et al. BMC Systems Biology 2012, 6:96 Page 13 of 14 http://www.biomedcentral.com/1752-0509/6/96 across hundreds of scientiﬁc papers, scientists will be able to test the integrity of this knowledge in the context of the b/iological processes as a whole. The model building process will make it easier to identify published results that contradict each other, as well as ﬁnd gaps in cur- rent knowledge that may have not been realized. Using a modeling platform such as The Cell Collective has the potential to generate new hypotheses that can be further veriﬁed in the laboratory. Furthermore, the non-technical and easy-to-use nature of building and simulating computational models in The Cell Collective, the platform has a potential as a great edu- cational tool for undergraduate and graduate biology stu- dents with diverse mathematical/computer science skills. Rather than studying biochemical pathways presented in current textbooks as “static” and isolated components of the cell, students can easily visualize and start understand- ing cells as complex, dynamical systems – precisely as is the case with real cells. Large models available in The Cell Collective allow for the instruction of experimen- tal design – because modeled biological processes have (the complex) properties of the real counterparts, students can learn how to design experimental studies, including the concepts of controls. Students can also create simple cellular models and study the dynamical properties of a wide range of molecular subsystems such as positive and negative feedback loops. We are actively developing new features and making The Cell Collective even more intuitive for users to inter- act with it. We are also working on implementing a plug-in system to allow the community to be directly involved in the development of additional features. Availability and requirements The Cell Collective is platform independent, and can be accessed through any modern web browser (Firefox and Chromium are recommended). Data made public in The Cell Collective are governed with GNU GPL v.3. The platform is free for academic use. Additional ﬁle Additional ﬁle 1: Real time simulation example. Video example of a real time simulation of a large-scale model of intracellular signal transduction. Competing interests The authors declare that they have no competing interests. Authors contributions TH and JAR conceived the platform. TH designed the software and led the development. BK, MS, SM, and KL developed the software. TH, JAR, KB, MS, SM, KL, and AM tested the software. TH and JAR wrote the manuscript. All authors read and approved the ﬁnal manuscript. Acknowledgements This project was supported and funded by the College of Arts and Sciences at the University of Nebraska at Omaha, the University of Nebraska Foundation, and Patrick J. Kerrigan and Donald F. Dillon Foundations. Author details 1Department of Mathematics, University of Nebraska at Omaha, Omaha, NE, USA. 2College of Information Science and Technology, University of Nebraska at Omaha, Omaha, NE, USA. 3Department of Pathology and Microbiology, University of Nebraska Medical Center, Omaha, NE, USA. Received: 27 March 2012 Accepted: 16 July 2012 Published: 7 August 2012 References 1. Coveney PV, Fowler PW: Modelling biological complexity: a physical scientist’s perspective. 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Sahin O, Fr¨ohlich H, L¨obke C, Korf U, Burmester S, Majety M, Mattern J, Schupp I, Chaouiya C, Thieﬀry D, Poustka A, Wiemann S, Beissbarth T, Arlt D: Modeling ERBB receptor-regulated G1/S transition to ﬁnd novel targets for de novo trastuzumab resistance. BMC Syst Biol 2009, 3:1. [http://view.ncbi.nlm.nih.gov/pubmed/19118495]. doi:10.1186/1752-0509-6-96 Cite this article as: Helikar et al.: The Cell Collective: Toward an open and collaborative approach to systems biology. BMC Systems Biology 2012 6:96. Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color ﬁgure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit	22871178	STAT1 = ( Jak1 ) OR ( IL27 AND ( ( ( NFAT ) ) ) ) IL23R = ( ( IL23 AND ( ( ( STAT3 ) ) ) ) AND NOT ( Tbet ) ) OR ( STAT3 ) Foxp3 = ( ( ( ( TGFbR ) AND NOT ( GATA3 ) ) AND NOT ( IL6R AND ( ( ( STAT3 ) ) ) ) ) AND NOT ( IL21R ) ) OR ( ( ( ( STAT5 ) AND NOT ( GATA3 ) ) AND NOT ( IL6R AND ( ( ( STAT3 ) ) ) ) ) AND NOT ( IL21R ) ) IL4 = ( ( GATA3 AND ( ( ( NFAT ) ) ) ) AND NOT ( STAT1 ) ) IL12R = ( ( STAT4 ) AND NOT ( GATA3 ) ) OR ( ( TCR ) AND NOT ( GATA3 ) ) OR ( Tbet ) OR ( IL12 AND ( ( ( NFAT ) ) ) ) RORgt = ( ( ( ( TGFbR AND ( ( ( STAT3 AND IL6R ) ) OR ( ( IL21R AND STAT3 ) ) ) ) AND NOT ( GATA3 ) ) AND NOT ( Tbet ) ) AND NOT ( Foxp3 ) ) SOCS1 = ( Tbet ) OR ( STAT1 ) IL2 = ( ( NFAT AND ( ( ( NFkB ) ) ) ) AND NOT ( Tbet ) ) NFAT = ( ( TCR ) AND NOT ( Foxp3 ) ) IFNgR = ( IFNg AND ( ( ( NFAT ) ) ) ) OR ( IFNg_e AND ( ( ( NFAT ) ) ) ) Tbet = ( ( ( STAT4 ) AND NOT ( RORgt ) ) AND NOT ( Foxp3 ) ) OR ( ( ( STAT1 ) AND NOT ( RORgt ) ) AND NOT ( Foxp3 ) ) OR ( ( ( Tbet AND ( ( ( NOT IFNg AND NOT IL12 ) ) ) ) AND NOT ( RORgt ) ) AND NOT ( Foxp3 ) ) STAT3 = ( IL21R ) OR ( IL6R ) OR ( IL23R ) IL2R = ( IL2 AND ( ( ( NFAT ) ) ) ) GATA3 = ( ( ( ( ( STAT5 ) AND NOT ( Tbet ) ) AND NOT ( RORgt ) ) AND NOT ( TGFb ) ) AND NOT ( Foxp3 ) ) OR ( ( ( ( ( STAT6 AND ( ( ( NFAT ) ) ) ) AND NOT ( Tbet ) ) AND NOT ( RORgt ) ) AND NOT ( TGFb ) ) AND NOT ( Foxp3 ) ) OR ( ( GATA3 ) AND NOT ( Tbet ) ) IL6R = ( IL6 ) OR ( IL6_e ) IL17 = ( ( RORgt ) AND NOT ( STAT1 ) ) OR ( ( ( STAT3 AND ( ( ( IL17 ) ) AND ( ( IL23R ) ) ) ) AND NOT ( STAT5 ) ) AND NOT ( STAT1 ) ) TGFbR = ( TGFb AND ( ( ( NFAT ) ) ) ) IL4R = ( ( IL4 ) AND NOT ( SOCS1 ) ) OR ( IL4_e ) IRAK = ( IL18R ) IFNg = ( ( ( STAT4 AND ( ( ( NFkB ) ) AND ( ( NFAT ) ) ) ) AND NOT ( STAT6 ) ) AND NOT ( STAT3 ) ) OR ( ( Tbet ) AND NOT ( STAT3 ) ) OR ( NFkB ) IL21 = ( STAT3 AND ( ( ( NFAT ) ) ) ) STAT5 = ( IL2R ) NFkB = ( ( IRAK ) AND NOT ( Foxp3 ) ) IL18R = ( ( IL18 AND ( ( ( IL12 ) ) ) ) AND NOT ( STAT6 ) ) STAT4 = ( ( IL12R AND ( ( ( IL12 ) ) ) ) AND NOT ( GATA3 ) ) STAT6 = ( ( ( IL4R ) AND NOT ( SOCS1 ) ) AND NOT ( IFNg ) ) IL21R = ( IL21 ) IL6 = ( RORgt ) Jak1 = ( ( IFNgR ) AND NOT ( SOCS1 ) )
BIOINFORMATICS Vol. 28 ECCB 2012, pages i495–i501 doi:10.1093/bioinformatics/bts410 Boolean approach to signalling pathway modelling in HGF-induced keratinocyte migration Amit Singh1,2,†, Juliana M. Nascimento1,2,†, Silke Kowar1,2, Hauke Busch1,2,‡,∗ and Melanie Boerries1,2,‡,∗ 1Freiburg Institute for Advanced Studies, LifeNet, Albert-Ludwigs-University of Freiburg, Albertstrasse 19 and 2Center for Biological Systems Analysis, Albert-Ludwigs-University of Freiburg, Habsburger Strasse 49, 79104 Freiburg, Germany ABSTRACT Motivation: Cell migration is a complex process that is controlled through the time-sequential feedback regulation of protein signalling and gene regulation. Based on prior knowledge and own experimental data, we developed a large-scale dynamic network describing the onset and maintenance of hepatocyte growth factor- induced migration of primary human keratinocytes. We applied Boolean logic to capture the qualitative behaviour as well as short- and long-term dynamics of the complex signalling network involved in this process, comprising protein signalling, gene regulation and autocrine feedback. Results: A Boolean model has been compiled from time-resolved transcriptome data and literature mining, incorporating the main pathways involved in migration from initial stimulation to phenotype progress. Steady-state analysis under different inhibition and stimulation conditions of known key molecules reproduces existing data and predicts novel interactions based on our own experiments. Model simulations highlight for the ﬁrst time the necessity of a temporal sequence of initial, transient MET receptor (met proto- oncogene, hepatocyte growth factor receptor) and subsequent, continuous epidermal growth factor/integrin signalling to trigger and sustain migration by autocrine signalling that is integrated through the Focal adhesion kinase protein. We predicted in silico and veriﬁed in vitro that long-term cell migration is stopped if any of the two feedback loops are inhibited. Availability: The network ﬁle for analysis with the R BoolNet library is available in the Supplementary Information. Contact: melanie.boerries@frias.uni-freiburg.de or hauke.busch@frias.uni-freiburg.de Supplementary information: Supplementary data are available at Bioinformatics online. 1 INTRODUCTION Cell migration and wound healing are complex cellular processes that involve keratinocytes, ﬁbroblasts, blood vessels and inﬂammatory cells (Xue et al., 2007). Keratinocyte migration plays an important role in re-epithelialization and wound healing (Hunt et al., 2000), which is a multistep cellular process by the †The authors wish it to be known that, in their opinion, the ﬁrst two authors should be regarded as joint First Authors. ‡The authors wish it to be known that, in their opinion, the last two authors should be regarded as joint Last Authors. ∗To whom correspondence should be addressed. coordination of extra- and intracellular signals (Muyderman et al., 2001; Werner et al., 2007). The precise regulation of cell migration in its temporal sequence, activation and de-activation is crucial for tissue homeostasis. In its aberrant form, it can lead to scar formation (Heng, 2011) and has critical implications to cancer metastasis formation (Schäfer and Werner, 2008). Different growth factors such as hepatocyte growth factor (HGF), epidermal growth factor (EGF), transforming growth factor-beta (TGF-β), keratinocyte growth factor (KGF) and ﬁbroblast growth factor (FGF) that activate and regulate cell migration have been extensively studied in many cell types (Birchmeier et al., 2003; Hudson and McCawley, 1998; Jaakkola et al., 1998; Pastore et al., 2008; Tsuboi et al., 1993). These growth factors have been found to overlap with mitogen-activated protein kinase (MAPK) pathways (Cho and Klemke, 2000; Kain and Klemke, 2001; Klemke et al., 1997). HGF interacts and activates MET receptor (Bottaro et al., 1991) to induce context-dependent several cellular processes such as proliferation, cell movement or morphogenic differentiation (Brinkmann et al., 1995; Clague, 2011; Jeffers et al., 1996; Medico et al., 1996). Herein, we focus on HGF-induced migration of primary normal human keratinocytes (NHK). Although there is vast literature concerning HGF-induced keratinocyte migration and MET receptor dynamics, the dynamic interplay of initial MET receptor regulation and subsequent autocrine regulation that initiate, sustain and control cell migration remain poorly understood. Based on time-resolved transcriptome data of NHK after HGF stimulation, we have previously inferred a gene regulatory model describing the decision process of NHK cells towards migration (Busch et al., 2008). From the model analysis it was evident that several pathways coordinate their action to initiate and sustain cell migration upon initial HGF stimulation: migration is started through the AP-1 system and maintained after MET receptor internalization (Clague, 2011) by autocrine signalling through EGF receptor (EGFR) and urokinase plasminogen activator surface receptor (uPAR) (Schnickmann et al., 2009). The model predicted qualitatively how the temporal sequence of transient MET receptor activation and subsequent long-term EGF receptor activity sustained the migratory phenotype. However, as the model was based on transcriptome data alone, there was no mechanistic explanation of the observed processes. A model combining transcriptome data with mechanistic protein signalling has been missing so far. A major obstacle in building such a model lies in the different time scales involved in the process of cell migration. In general, the transcriptome response changes over several hours, while protein signalling pathways become active within minutes upon receptor © The Author(s) 2012. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A.Singh et al. HGF EGFR DAG PKC AKAP12 cMYC EGR1 CRKL IP3 Ca2+ RSK CREB ATF2 CCL20 HBEGF CTGF IL8 DOCK1 C3G RAP1 FAK Integrins MMP1/10 ECM Plasmin uPA AKT CDC42/ RAC1 MEKK1 MEKK7 JNK PAK2 PAK3 PAK1 MEKK4 MKK4 MLK3 MKK3 MKK6 p38 cFOS PTGS2 cJUN Cell Migration ELK1 ETS STAT3 CyclinD CDK2 CDKN2A CDKN1A Proliferation uPAR PAI-1 PLC PI3K PTEN MET SHC GRB2 RAS RAF MEK ERK SOS AP1 DUSP1 PTGS2 cJUN Gene Protein Drain Input Activation Inhibition "AND" Gate PLC/PKC MAPK uPA/uPAR AP-1 System PI3K Jnk/p38 Rac1/CDC42 Fig. 1. Boolean network model of the HGF-induced keratinocyte migration. Nodes are connected by directed edges, where black and red connections denote activating and inhibitory interactions, respectively. Red nodes represent transcriptionally regulated proteins, yellow nodes are endpoints of the network. ‘AND’ ‘gates are denoted by blue dots and ‘OR’ gates are found where more than one edge connects to single node. Dashed edges denote interactions that have not been considered, when calculating the steady state and are shown for completeness stimulation (Mesecke et al., 2011). Capturing all necessary and sufﬁcient events on the protein signalling level, including kinetic parameters, is close to impossible by current biological technology. To link our prior transcriptome-based model with protein signalling pathways, we present a Boolean network model of HGF- induced keratinocyte migration. The Boolean approach allows to derive important functional properties and predictions without the need for detailed quantitative kinetic data and parameters. In the past, the approach has been successfully applied for diverse systems such as gene regulatory networks (Albert and Othmer, 2003; Chaves et al., 2005), models of ﬂoral morphogenesis (Mendoza et al., 1999), mammalian cell cycle (Mendoza, 2006), EGFR signalling (Samaga et al., 2009) or apoptosis (Schlatter et al., 2009). To our knowledge, this is the ﬁrst model for HGF-induced keratinocyte migration that incorporates protein signalling, gene regulation and autocrine feedback, following cellular dynamics from initial stimulation to the execution of the phenotype. To obtain the dynamical behaviour reproducing literature knowledge and our own experimental data, we include several time scales in the model mimicking the fast activation of downstream signalling of MET, MAPK/ERK and p38/JNK pathways, as well as the slow transcriptome response and subsequent autocrine activation of EGFR and uPA receptors, all of which are necessary to sustain cell migration after MET receptor internalization. Speciﬁcally, from a logical steady-state analysis, we show that priming of the HGF– MET receptor system is necessary for continued autocrine regulation i496 Boolean modelling of keratinocyte migration through EGFR and integrins, sustaining the MAPK/ERK activity. More importantly, we predicted and showed experimentally, that the inhibition of the plasminogen activator inhibitor-1 (PAI-1), or serpin E1, a serine protease inhibitor, stops cell migration only beyond 1 h of stimulation, when autocrine signalling loops through uPA/uPAR become important and after the ﬁrst wave of protein signalling and transcriptional response. 2 METHODS 2.1 Reconstruction of the NHK migration model A Boolean network, comprising protein signalling pathway, gene expression dynamics and autocrine feedback was constructed based on our previous gene regulatory model for keratinocyte migration (Busch et al., 2008). There, time-resolved gene expression data of NHK were recorded at t = [0h,1h,2h,3h,4h,6h,8h] after stimulation with HGF (ArrayExpress ID: E-TABM-440). As a basis for our HGF-induced cell migration network, we chose genes that have either a large differential response after HGF stimulation or genes that are known to be functionally related to cell migration. Genes ﬁnally included in the model are depicted in Figure 2A. To link immediate early and late responding genes to initial MET receptor signalling and subsequent protein pathways, respectively, we integrated differentially expressed genes with signalling pathways known from literature. Additional pathways for the HGF migration network were identiﬁed through the commercial IPA (Ingenuity Systems; www. ingenuity.com) software. A dataset containing gene identiﬁers and corresponding expression values was uploaded into the application. Each gene kinetic was mapped to its corresponding object in the Ingenuity Knowledge Base. The above identiﬁed molecules were overlaid onto a global molecular network developed from information contained in the application. This generated a score with meaningful and signiﬁcant networks, biological functions and the canonical pathways based on the Fisher exact test. 2.2 The NHK migration model as a dynamic Boolean model We used a Boolean model framework to construct a dynamic, temporally discrete model for NHK migration. Each node y can take the values 0 or 1, representing either the present/absent or inactive/active, i.e. phosphorylated, state of the protein or gene. The network state is represented by the vector with the set of Boolean variables Y ={y1,y2,...,yn}, where yi denotes the state of the ith node. The state of activation of each node changes according to the transition function F ={f1,f2,...,fn}. The next state of the network Y(t+1) changes in discrete time steps according to yi(t+1)=fi{x(t)}. We simulated the Boolean network under synchronous update using the R BoolNet library (Müssel et al., 2010). As we consider both protein signalling and gene regulation, two time scales were included in the model. Rapid protein modiﬁcations such as phosphorylation can thereby be separated from long-term effects, transcriptional changes, protein synthesis and autocrine signalling. Time-scale separation was done by ﬁrst introducing a reference time through the transcriptome kinetics and equating the time of maximal fold change of the respective genes with their switching-on time. Consequently, our model contains two time scales: 0–1 and 1–3 h (marked as 1 and 3, respectively), denoting the time intervals after HGF stimulation, during which the reactions can be switched on the earliest. These represent the early HGF downstream signalling and ﬁrst transcriptional response as well as the autocrine feedback, which are both necessary to trigger and sustain cell migration. The reference publications from which the interactions have been inferred as well as their Boolean transition functions and time windows are listed in the Supplementary Table S1. 2.3 Cell culture Normal human skin keratinocytes (NHK) were derived from foreskin epidermis and cultivated in keratinocyte serum free medium (KSFM; Invitrogen, Carlsbad, CA, USA) as previously described (Busch et al., 2008). Cells were kept under a humidiﬁed environment with 5% CO2 and 37◦C. NHK up to Passages 4–5 were used in all experiments of this study. Cells were treated as described bellow and collected after 1, 2, 3, 4, 6 and 8 h treatment for expression proﬁling. 2.4 Scratch assay Monolayer scratch assays were used to evaluate migration of NHK as described before (Busch et al., 2008). Brieﬂy, cells were grown to conﬂuence in ibidi μ-dish containing culture inserts (ibidi, Munich, Germany) and treated with mitomycin c 10 μg/mL (Sigma-Aldrich, St. Louis, MO, USA) for 3 h before stimulation. Cells were stimulated with 10 ng/mL HGF (Sigma-Aldrich) and/or 25 μM Tiplaxtinin, a PAI-1 inhibitor (Axon Medchem, Groningen, Netherlands). Time-lapse microscopy of cell migration was recorded using the Perfect Focus Systems , every 30 min up to 24 h, on a Nikon Eclipse Ti microscope with a Digital Sight DS-QiMc (Nikon Instruments Inc., Tokyo, Japan), coupled to an ibidi-heating chamber. 2.5 Cell migration assay Keratinocyte migration was analysed with an independent second technique, so-called xCELLigence Real-Time Cell Analyzer DP (Roche Diagnostics). The speciﬁc migration CIM-plates were ﬁlled with medium and the respective stimulus/inhibitor as described above. NHK were seeded (6×104 cells/well) into the top chamber wells of the CIM-plate according to the manufacturer instructions. Cell migration was monitored every 15 min for up to 24 h by changes of the impedance signal of the cells that crossed the membrane from the top to the bottom chamber. For analysis of migration, the area under the curve was measured for the ﬁrst 8 h. The data were expressed as the mean ± SD of quadruplicates in three independent experiments. Differences were assessed by the Student t-test for unpaired samples and a P-value <0.05 was considered to be signiﬁcant. 2.6 Western blot NHK were lysed in RIPA buffer containing protease inhibitor cocktail (Roche), and later diluted in Laemmli buffer. Proteins were electrophoresed on 12.5% sodium dodecyl sulphate (SDS)-polyacrylamide gels, transferred to polyvinylidene diﬂuoride membranes, and immunoblotted with antibodies to total p44/42 MAPK (ERK1/2) (Cell Signalling #9102), phospho p44/42 MAPK (pERK1/2) (Cell Signalling #9101), total FAK (Cell Signalling #3285), phospho-FAK (Tyr925) (Cell Signalling #3284) overnight at 4◦C. Membranes were visualized with chemiluminescence after using Table 1. Predicted network steady states under different network perturbations HGF EGF Inhibition Over-expression Cell migration Conﬁrmed 1 0 — — 1 Own data 0 1 — — 0 Predicted 0 1 FAK — 0 Predicted 1 1 EGFR — 0 Own data 1 0 uPAR — 0 19020551 1 0 PAI-1 — 0 Own data 1 0 PTGS2 — 0 Own data 1 0 IL8 — 0 Own data 1 0 — AKAP12 0 21779438, Own data 1 0 — PTEN 0 16246156 The last column lists the PubMed IDs of the respective publication. i497 A.Singh et al. 0h 1h 2h 3h 4h 6h 8h egr1 0h 1h 2h 3h 4h 6h 8h il8 0 1 2 3 4 0h 1h 2h 3h 4h 6h 8h fos 0 1 2 3 4 0h 1h 2h 3h 4h 6h 8h ptgs2 0 1 2 3 4 0h 1h 2h 3h 4h 6h 8h pak3 0h 1h 2h 3h 4h 6h 8h hbegf 0 1 2 3 4 0h 1h 2h 3h 4h 6h 8h dusp1 0 1 2 3 4 0h 1h 2h 3h 4h 6h 8h ctgf 0 1 2 3 4 0h 1h 2h 3h 4h 6h 8h ccl20 0h 1h 2h 3h 4h 6h 8h akap12 0 1 2 3 4 0h 1h 2h 3h 4h 6h 8h mmp10 0 1 2 3 4 0h 1h 2h 3h 4h 6h 8h mmp1 0 1 2 3 4 0h 1h 2h 3h 4h 6h 8h itga2 0h 1h 2h 3h 4h 6h 8h serpine1/PAI-1 0 1 2 3 4 0h 1h 2h 3h 4h 6h 8h plaur/uPAR 0 1 2 3 4 HGF MET SHC GRB2 SOS RAS RAF MEK ERK PLCG IP3 DAG CA PKC CRKL DOCK1 PI3K AKT RAP1 C3G PAK1 PAK2 PAK3 CDC42RAC1 MLK3 RSK CREB CMYC EGR1 ELK1 ETS CDK2 CDKN1A CDKN2A CYCLIND PROLIFERATION STAT3 CFOS CJUN AP1 CCL20 COX2 IL8 CTGF ATF2 HBEGF EGFR MKK3 MKK4 MKK6 P38 JNK MEKK7 MEKK1 MEKK4 UPAR UPA PAI1 PLASMIN MMP ECM INTEGRIN FAK CELL_MIGRATION 4 Time 0h 1h 3h a b c d MAPK/ERK PLC/PKC PI3K CDC42/RAC1 Proliferation AP-1 Transcriptome Response e JNK/p38 uPA/uPAR HGF/MET egr1 il8 fos ptgs2 ctgf dusp1 hbegf pak3 ccl20 akap12 mmp10 mmp1 plaur/uPAR serpine1/ PAI-1 itga2 Time [h] Fold Change [log2] 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 s.s. EGFR Inhibition PAI-1 Inhibition A B Fig. 2. (A) Transcriptome time series of differential regulation with respect to 0 h time point for genes included in the Boolean cell migration network. (B) Network simulation of time sequential pathway activation. (a) Path to attractor upon HGF stimulation up to 1 h after stimulation. (b) Change in network state after autocrine signalling through uPA and integrin signalling up to 3 h after stimulation, initializing the network using the network state after 1 h and setting PAI-1 activity to 1. (c) Switching off MET receptor signalling after 3 h. Cell migration sustains in steady state (s.s.). (d) and (e) Inhibition of EGFR and PAI-1, respectively, in both cases leading to a stop in cell migration. Time increases in arbitrary units from left to right until a logical steady state is reached. Absolute times correspond to the maximal fold induction of the corresponding transcriptome data. Pathway-based grouping of network nodes (cf. Fig. 1) is indicated in colour and named on the left the appropriate horseradish peroxidase-linked secondary antibody (Sigma- Aldrich). Immunoblots were quantiﬁed using Multi Gauge v3.1 (Fujiﬁlm) software. Values obtained for both p44 and p42 ERK bands were added together and phospho p44/42 values were normalized to total p44/42. Values of phospho-FAK (Tyr925) were normalized to total FAK. 3 RESULTS AND DISCUSSION Upon stimulation with HGF keratinocytes start to migrate collectively. Several points of interference that modulate keratinocyte migration have been previously identiﬁed. However, time sequential orchestration of the whole-cell signalling remains unclear so far. Our goal is to understand how downstream signalling of the HGF-activated MET receptor is translated into a sustained migratory behaviour. To accomplish this, we developed a Boolean network model of the combined MAPK signalling pathways, gene regulation and autocrine feedback, which links known interactions of downstream protein and gene targets of MET with subsequent changes in the cellular homeostasis. 3.1 Boolean network model properties The keratinocyte migration model is a logical interaction hypergraph connected by logic gates. It comprises 66 nodes, excluding the drain nodes and 66 interactions (Fig. 1), integrating the main pathways and genes known to be involved in HGF-induced keratinocyte migration. For detailed information about the biological processes and context from which the model was derived, please confer to Supplementary Table S1. There are two input nodes, the MET receptor, stimulated through HGF, as well as EGFR, stimulated by HBEGF. Both receptors have been shown to be involved in keratinocyte migration in a time-sequential manner (Busch et al., 2008). Four further nodes are included to applying external interventions: PAI-1, AKAP12, DUSP1 and PTEN. AKAP12 and DUSP1 are not included in the calculation of the steady-state below. Despite the fact that they are found to be up-regulated on the transcriptome level, the respective proteins seem to exert a stabilizing negative feedback function (Legewie et al., 2008), not completely inhibiting their speciﬁc targets, but allowing for a rapid protein induction (Blüthgen, 2010). In line with this, we ﬁnd akap12 strongly up-regulated in HGF-induced keratinocyte migration (Fig. 2A), although over- expression of akap12 has been associated with reduced motility (Gelman, 2010).ABoolean representation of such negative feedback behaviour is not straight forward and will often lead to — a biologically questionable — oscillatory steady state. Hence, we included the proteins for completeness, yet excluded it from steady- state analysis. 3.2 Dynamics of the Boolean network model for migration To search for steady-state attractors of the Boolean network model, we randomly initialized all network nodes, except for HGF/PAI-1 and AKAP12/PTEN with either 0 or 1 and performed synchronous state transitions until a simple attractor was reached. Activating the nodes HGF and PAI-1 to 1 mimicked HGF stimulation and allowed for autocrine feedback through uPAR signalling. Setting AKAP12 and PTEN to zero excluded their inhibitory effects. Sampling over n=107 random initialization of the network we ﬁnd only one attractor of the network with the node CELL MIGRATION switched on. Although only a minor fraction of all possible i498 Boolean modelling of keratinocyte migration 0h 1h 3h 8h HGF HGF/PAI-1 inhibitor Control HGF HGF + Inhibitor 0 1 2 3 * * AUC (8h) Control HGF HGF + Inhibitor 0 2 4 6 8 0.8 1.0 1.2 1.4 1.6 1.8 Time (h) Delta Cell Index ERK p-ERK C H H+I C H H+I C H H+I C H H+I 1h 2h 3h 8h C H H+I C H H+I C H H+I C H H+I 0.0 0.5 1.0 1.5 2.0 1h 2h 3h 8h * * * * pERK/ERK A B C Fig. 3. Keratinocyte migration analysis under HGF and PAI-1 inhibition. (A) Life-time imaging microscopy of NHK up to 8 h. HGF stimulation increases migration of NHK (upper panel), addition of PAI-1 inhibitor, Tiplaxtinin, decreases strongly the HGF effect (lower panel). Bar: 20 μm. (B) Increased HGF migration is signiﬁcantly reduced with PAI-1 inhibitor (25 μM) addition after a short time period (left plot). Migration response is calculated as area under the curve (AUC; right plot). (C) Determination of pERK level under HGF and inhibition conditions. Original western blot of pERK and ERK for different time points reveals a continuous activation of pERK under HGF (H) stimulation over time comparing to control (C). In contrast under PA1-1 inhibition (H+I) the pERK level decrease signiﬁcantly over time. ∗denote a t-test P-value <0.05, data points obtained in triplicate. The ratio of pERK/ERK is shown for the respective time points (right plot) network initializations (n=262) has been sampled, this result is still suggestive of a robust response irrespective of the initial network state, i.e. cell migration follows upon MET receptor activation and subsequent autocrine signalling. In detail node and pathway activity moves along the following steps after transient MET receptor signalling: (i) the ﬁrst and necessary input into the network towards migration is the stimulation with HGF, which immediately and speciﬁcally activates the MET receptor. Within the ﬁrst hour, the signal activates three different downstream pathways, PLC/PKC, MAPK/ERK and PI3K (grey boxes, Fig. 1); (ii) ERK phosphorylation activates transcriptional responses, leading to the down-regulation of proliferation and activates, together with p38/JNK, essential cytokines and transcription factors for migration within the ﬁrst hour, such as HBEGF, IL8 and ATF2, as well as cJUN and cFOS, respectively. HBEGF has been shown to mediate the subsequent autocrine activation of EGFR (Busch et al., 2008); (iii) The activation of cJUN and cFOS nodes leads to an initiation of the AP-1 system, which in turn stimulates the uPA/uPAR signalling pathway by activation of the uPAR, triggering the formation from plasminogen activator to plasmin. According to the transcriptome kinetics, the uPA/uPAR pathway becomes active 2 h after HGF stimulation, being controlled by PAI-1. Plasmin is a major factor for induction of metalloproteinases 1 and 10 (MMP1/MMP10), linking degradation of the extracellular matrix (ECM) with integrin signalling; (iv) The integrins transmit the extracellular signalling back into the cell through the focal adhesion kinase (FAK). Together with activated EGFR this protein sustains PLC/PKC, MAPK and PI3K activity similar to the initial HGF/MET activation. It is known that the MET receptor undergoes rapid internalization, possibly switching off its signalling in favour of EGFR activity. In fact, we have shown previously that HGF/MET i499 A.Singh et al. activity is not required for keratinocyte migration beyond 1.5 h after stimulation (Busch et al., 2008). Accordingly, the model suggests that continued PI3K up-regulation can only occur through the combined activity of integrin and EGFR signalling in the presence of FAK. Signalling continues through AKT, DOCK1 and RAS to sustain RAC1/CDC42 activity, which result in the downstream activity of p21 protein (CDC42/RAC)-activated kinases (PAKs), mitogen-activated kinase kinases (MKK) and ﬁnally activation of JNK/p38. This closes the autocrine loop through time sequentially activated external receptors. This late response of the keratinocyte migration network through activation of uPAR, integrins and EGFR triggers similar pathways as the MET signalling, but furthermore results in the prolonged activation of PLC/PKC, MAPK/ERK, PI3K, RAC1/CDC42 and JNK/p38 pathways to sustain the long-term migration response. Figure 2B shows a simulation of the network dynamics after HGF stimulation up to 3 h, as marked by the white vertical gaps, having initialized all network nodes, except for HGF with 0 for clarity. The transitions towards the ﬁnal steady states are indicated in arbitrary time units. Clearly, an activation wave of the three downstream pathways PLC/PKC, MAPK/ERK and PI3K is evident, resulting in the up-regulation of the respective target genes (Fig. 2A), the AP-1 system and starting cell migration within 1 h. In the following 2 h, autocrine signalling loops activate EGFR and integrin signalling through HBEGF and uPAR, respectively. Switching off the MET receptor has no inﬂuence on the steady state at this time, and cell migration continues. Switching off either uPA/uPAR signalling through PAI-1 or inhibiting EGFR stops migration through subsequent switching off all pathways. Table 1 lists the steady states of the Boolean network under different input settings and/or different scenarios. Interestingly, the model predicts that cells will migrate only when HGF signalling primes the cells, followed by EGFR and integrin signalling. This is in line with our previous ﬁndings, which now can be explained on the causal level of protein signalling. Lastly, we note that our model still has limitations predicting the correct long-term behaviour for transiently activated genes such as egr1, il8, ctgf or ccl20. Although the model captures the long- term cell migration response and upstream pathway activity, it does not yet include a negative feedback down-regulating of these genes (compare Fig. 2A and B). Although the biological consequences of the transient gene activation remain unclear so far, this divergence between the model steady-state behaviour and experimental data beyond 3 h need to be addressed in more detail in the future. Model simulation clearly reﬂects the necessity for the time sequential pathway activation, shown by the early and late steady state after 1 and 3 h, respectively. Initial HGF/MET receptor signalling triggers, while subsequent integrin/EGF receptor signalling sustains MAPK/ERK, PI3K, PLC/PKC and JNK/p38 signalling (Fig. 3C). Model simulations further predict that continued migration depends on both EGFR and integrin signalling. Failure of either one causes the down-regulation of the FAK protein and subsequent PI3K, MAPK/ERK and p38/JNK pathways (Fig. 2, Columns d and e). Indeed, we have previously shown the dependency of cell migration on sustained EGFR activity after MET signalling pathway activation (Busch et al., 2008). To experimentally validate the long-term dependency of NHK on the FAK protein-mediated integrin signalling, we interrupt the uPA/uPAR signalling pathway through inhibition of PAI-1. In line with previous ﬁndings (Providence and Higgins, 2004) and predicted from our network simulation, long-term, but not immediate cell migration should be decreased. A scratch assay (Fig. 3A) shows a signiﬁcant decrease with the usage of the PAI-1 inhibitor (Tiplaxtinin) in migration when compared with control conditions. While under HGF stimulation, the scratch is almost closed after 8 h, hardly any cell movement is detected under additional PAI-1 inhibitor treatment. The delayed impact of PAI-1 inhibition becomes evident from a real-time analysis of keratinocyte migration using the xCELLigence Cell Analyzer (Fig. 3B). Clearly, the migration speed becomes strongly reduced after 2.5 h, in line with the suggested role for ‘late’uPA/uPAR signalling pathway involvement, activating FAK through integrin/EGFR signalling for sustained migration. This time point also coincides with the start of transcriptional activation of PAI-1 (Fig. 2A), furthermore supporting the late involvement of this pathway. Interestingly, MET receptor and integrin/FAK pathways both activate MAPK/ERK, PI3K and PLC/PKC, RAC1/CDC42 and JNK/p38. However, while the former primes the cells towards migration, the impact of the latter on downstream pathways seems to be much more pronounced. Analysing the phosphorylation state of ERK (pERK) we observe an immediate and sustained increase of pERK under HGF treatment in line with our simulation. Differences in pERK level under simultaneous PAI-1 inhibition become most apparent at late time points beyond 2 h, conﬁrming the model predictions of late impact of integrin signalling on ERK. Looking at FAK as an up-stream effector of ERK (Sawhney et al., 2006), we ﬁnd similar activity for pFAK under HGF stimulation and PAI-1 inhibition. We observe a strong, but late increase in FAK activity as determined from phosphorylation of the Y925 site of FAK (pFAK (Y925)). Simultaneous stimulation of HGF and PAI-1 inhibition decreases pFAK (Y925) when compared with HGF alone (Supplementary Fig. S1). Immediate increase of pFAK (Y925) suggests a possible role of FAK in the beginning of migration. Previous work has shown two distinct phases in FAK involvement for wound healing in rat keratinocytes (Providence and Higgins, 2004). There, the effect of PAI-1 inhibition became evident only after 6 h and more into migration. Herein, we can possibly explain the importance of FAK for prolonged migration through the time sequential regulation of uPA/uPAR, integrin and EGFR signalling pathways, which were predicted from network simulation and have been — in part — experimentally validated. Further studies for a better understanding of this complex pathway orchestration of HGF-induced migration will be necessary, of course. 4 CONCLUSIONS We have shown for the ﬁrst time a comprehensive model for HGF-induced keratinocyte migration. The model comprises two time scales and incorporates various signalling pathway critically involved in the initiation, sustaining and controlling of keratinocyte migration. Being mostly compiled from prior knowledge and vast literature, it will lend itself to rapid hypothesis testing of key points of interference. We are aware that the above model cannot capture the entire complexity of this process. Most of the simulation results are suggestive about the underlying process and further experiments will need to be conducted to study the complex orchestration of pathways leading to keratinocyte migration. However, our model makes several important and experimentally testable predictions i500 Boolean modelling of keratinocyte migration about putative targets and time of intervention to control this process. It underscores the temporal sequence of events from initial trigger to execution, allowing for a fail-safe mechanism of migration under wild-type and inhibition conditions. It is in line with previous ﬁndings from literature and captures the short- and long-term feedback regulation of protein signalling and gene expression. In particular, the order of events becomes evident, how MET receptor activity primes the cell for subsequent EGFR and integrin signalling, leading sustained migration. Exchanging the order of stimulation (ﬁrst EGFR followed by MET receptor activation), keratinocytes will not migrate, which is explained in the model and supported by our ﬁrst experimental results from the altered role of the FAK proteins at late time points. Indeed, MET receptor deregulation is a hallmark for cancer metastasis (Gherardi et al., 2012). If MET is constitutively activated, it would need only additional EGFR activity to induce cellular spread, according to the network model. Apparently, this by-passes the fail-safe mechanism for cells to migrate only within the correct context.Asynergistic action of EGFR and MET have been found before (Brusevold et al., 2012; Zhou et al., 2007), yet the causal relationship between them remained unclear so far. Beyond further experimental validation, the need for model extensions to multiple logical states or even continuous representation of the variables using ordinary differential equation approach is evident. Our current approach cannot account for the multiple negative feedback regulations of either AKAP12 or DUSP1. Such negative feedback seems to be a recurrent regulatory motif (Becskei and Serrano, 2000; Blüthgen, 2010), and it should be interesting to study its biological implications. Taken together, the Boolean model approach lends itself to a better mechanistic understanding of the process of keratinocyte migration, wound healing, cancer metastasis and/or impaired wound healing from stimulation to phenotype development and will help in the prediction of cellular control targets in wild type and disease. ACKNOWLEDGEMENT A.S. acknowledges fruitful discussions with Jeremy Huard. M.B., H.B. and A.S. thank the MedSys consortium for fruitful discussions. Funding: This work was supported by the Excellence Initiative of the German Federal and State Governments. 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Endocrinology, 148, 5195–5208. i501	22962472	EGFR = ( HBEGF ) OR ( EGF ) CDKN2A = ( Elk1 ) OR ( ETS ) DAG = ( PLC_g ) PAK3 = ( Cdc42_Rac1 ) uPA = ( uPAR ) Mkk4 = ( Mekk4 ) OR ( Mekk1 ) OR ( MLK3 ) p38 = ( ( Mkk3 AND ( ( ( Mkk6 ) ) ) ) AND NOT ( DUSP1 ) ) OR ( PAK1 ) PTGS2 = ( ATF2 ) OR ( cFOS AND ( ( ( cJUN ) ) ) ) JNK = ( Mekk7 AND ( ( ( Mkk4 ) ) ) ) OR ( PAK2 ) Mekk7 = ( Mekk1 ) CDKN1A = ( STAT3 ) Integrins = ( ECM ) CREB = ( RSK ) PAK2 = ( Cdc42_Rac1 ) Akt = ( ( PI3K ) AND NOT ( PTEN ) ) CCL20 = ( Erk ) RSK = ( Erk ) DOCK180 = ( CRKL ) SOS = ( Grb2 ) Mkk3 = ( MLK3 ) CyclinD = ( Elk1 ) OR ( ATF2 ) EGR1 = ( Erk ) Erk = ( Mek ) IP3 = ( PLC_g ) Mekk4 = ( Cdc42_Rac1 ) Proliferation = ( CDK2 AND ( ( ( CyclinD ) ) ) ) Plasmin = ( uPA AND ( ( ( PAI-1 ) ) ) ) Ca = ( IP3 ) AP1 = ( cFOS AND ( ( ( cJUN ) ) ) ) CRKL = ( Grb2 ) Ras = ( SOS ) STAT3 = ( Erk ) CellMigration = ( IL8 AND ( ( ( PTGS2 AND CTGF AND CCL20 ) ) ) ) PAK1 = ( Cdc42_Rac1 ) Cdc42_Rac1 = ( Akt AND ( ( ( Ras AND DOCK180 ) ) ) ) Mek = ( Raf ) OR ( Mekk1 ) PLC_g = ( EGFR ) OR ( MET ) Mekk1 = ( Cdc42_Rac1 ) Fak = ( ( Integrins AND ( ( ( Rap1 ) ) ) ) AND NOT ( PTEN ) ) Elk1 = ( JNK ) OR ( Erk ) PI3K = ( EGFR AND ( ( ( Fak ) ) ) ) OR ( MET ) cMYC = ( Erk ) Mkk6 = ( MLK3 ) uPAR = ( AP1 ) ECM = ( MMP1_10 ) cFOS = ( Erk ) cJUN = ( JNK AND ( ( ( p38 ) ) ) ) MLK3 = ( Cdc42_Rac1 ) Grb2 = ( Shc ) MET = ( HGF ) Raf = ( Ras AND ( ( ( PKC AND PAK3 ) ) ) ) HBEGF = ( p38 ) OR ( Erk ) Shc = ( Fak ) OR ( MET ) OR ( EGFR ) Rap1 = ( C3G ) PKC = ( ( DAG AND ( ( ( Ca ) ) ) ) AND NOT ( AKAP12 ) ) IL8 = ( p38 ) OR ( Erk ) CTGF = ( p38 ) OR ( Erk ) ATF2 = ( JNK AND ( ( ( p38 ) ) ) ) CDK2 = ( CyclinD AND ( ( ( NOT CDKN2A ) ) OR ( ( NOT CDKN1A ) ) ) ) ETS = ( Erk ) MMP1_10 = ( Plasmin ) C3G = ( CRKL )
Ergodic Sets as Cell Phenotype of Budding Yeast Cell Cycle Robert G. Todd, Toma´sˇ Helikar Department of Mathematics, University of Nebraska at Omaha, Omaha, Nebraska, United States of America Abstract It has been suggested that irreducible sets of states in Probabilistic Boolean Networks correspond to cellular phenotype. In this study, we identify such sets of states for each phase of the budding yeast cell cycle. We find that these ‘‘ergodic sets’’ underly the cyclin activity levels during each phase of the cell cycle. Our results compare to the observations made in several laboratory experiments as well as the results of differential equation models. Dynamical studies of this model: (i) indicate that under stochastic external signals the continuous oscillating waves of cyclin activity and the opposing waves of CKIs emerge from the logic of a Boolean-based regulatory network without the need for specific biochemical/kinetic parameters; (ii) suggest that the yeast cell cycle network is robust to the varying behavior of cell size (e.g., cell division under nitrogen deprived conditions); (iii) suggest the irreversibility of the Start signal is a function of logic of the G1 regulon, and changing the structure of the regulatory network can render start reversible. Citation: Todd RG, Helikar T (2012) Ergodic Sets as Cell Phenotype of Budding Yeast Cell Cycle. PLoS ONE 7(10): e45780. doi:10.1371/journal.pone.0045780 Editor: Jean Peccoud, Virginia Tech, United States of America Received May 1, 2012; Accepted August 24, 2012; Published October 1, 2012 Copyright: 2012 Todd, Helikar. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: The authors have no support or funding to report. Competing Interests: The authors have declared that no competing interests exist. E-mail: rtodd@unomaha.edu Introduction Complex network structures can be found across the biological spectrum, and growing evidence indicates that these biochemical networks have evolved to perform complex information processing tasks in order for the cells to appropriately respond to the often noisy and contradictory environmental cues [1]. While reduction- ist techniques focus on the local interactions of biological components, the systems approach aims at studying properties of biological processes as a result of all components and their local interactions working together [2]. A wide spectrum of modeling techniques ranging from continuous frameworks utilizing differential equations to discrete (e.g., Boolean) techniques based on qualitative biological relation- ships exist [3–5]. Each modeling technique is based on different assumptions and hence comes with different advantages and disadvantages. Differential equation models can depict the dynamics of biological systems in great detail, but depend on a large number of difficult-to-obtain biological (kinetic) parame- ters. On the other hand, discrete modeling frameworks, namely Boolean networks, are qualitative and parameter-free, which makes them more suitable to study the dynamics of large-scale systems for which these parameters are not available. Further- more, probabilistic Boolean networks (PBN) enhance the discrete framework by allowing for uncertainty and stochasticity (e.g., [6,7]). It has been proposed that the irreducible sets of states (i.e., ergodic sets) of the corresponding Markov chain in probabilistic Boolean network models (PBNs) are the stochastic analogue of the limit cycle in a standard Boolean network, and should thus represent cellular phenotype [8]. However, often PBNs with perturbations are studied to include internal noise, rendering the search for the irreducible sets trivial (as the whole state space constitutes a single irreducible component). Furthermore, this makes the determination of the limiting distribution of the corresponding Markov chain and the interpretation of those results in light of the biology challenging even for moderately sized models [9–11]. Using the idea from [1] to introduce stochasticity to Boolean models via control nodes, herein we determine and examine the nature of ergodic sets of a regulatory network governing each phase of the cell cycle of budding yeast, Saccharomyces cerevisiae. The budding yeast cell cycle has been modeled previously using Boolean approaches (e.g., [5,12,13]) and probabilistic Boolean approaches (e.g., [7,14,15]). We expand on previous works by considering each phase of the cell cycle as an individual evolving system. The logic of the model used in this study was developed from the description of the yeast cell cycle interactions given in [12]. Using this model we show that as suggested in [8], irreducible sets of states can correspond to cellular phenotype. This approach enables us to model and visualize richer dynamical properties of each phase and the cell cycle as a whole. In particular, we show that under stochastic external signals the continuous oscillating waves of cyclin activity and the opposing waves of CKIs that form the cell cycle engine can emerge from the logic of a relatively simple regulatory network without the need for specific bio- chemical/kinetic parameters. Furthermore, by considering each phase of the cell cycle as an individual system represented by an ‘‘ergodic set’’, we are able to more directly and precisely compare the model dynamics with experimental studies. Specifically, results of [16] as interpreted graphically at cyclebase.org reveal relatively precise similarities. We also observe good agreement between our oscillating cyclin activities and recently published analyses of cyclin activities using fluorescent microscopy in [17]. The improved approach to the modeling of the yeast cell cycle enables us to visualize other qualitative features of the system: the secondary PLOS ONE \| www.plosone.org 1 October 2012 \| Volume 7 \| Issue 10 \| e45780 activation of a number of G1-cyclins later in the cell cycle [16] and the renewed reversibility of Start upon the removal of the Cln2- SBF-Whi5 feedback loop [18]. We also capture the same robustness to internal perturbations as described in [5], however we extend this result and conclude that each phase of the yeast cell cycle (and thus as the cell cycle as a whole) is robust in the face of the variable behavior of the cell size. Within the model, this results in the post-Start commitment to the cell cycle and the ability to complete a single round of division under deprived nutrition conditions [19]. Results Modeling the Cell Cycle The budding yeast cell cycle involves hundreds of species and interactions [20]. In order to keep the mathematical analyses manageable, we consider a much smaller network consisting of some key players (see Methods for a narrative description of the cell cycle). The logic of our network was constructed based on the descriptions of the cell cycle interaction as given in section 3.1 of [12], which is an expansion of the network found in [5]. All nodes, the species they represent and the logic associated to each node, are available in The Cell Collective (www.thecellcollective.org). Figure 1 shows the static interaction graph of the model. The model used in this study has four external inputs: cell size signal (CSS) to model cell growth, the Start checkpoint (Start), the budding (or morphogenic) checkpoint (BuddingCP) and the spindle assembly checkpoint (SpindleCP). Each of these external inputs plays a different role. First consider Start, BuddingCP, and SpindleCP. Each external input is incorporated into the logic of an internal node(s) so as to mimic the biological behavior of a checkpoint. Activating one of these external inputs (setting it to 1) indicates that the corresponding checkpoint has been satisfied. In pre-Start cells, Cln3 cannot inhibit Whi5 nor can Cln2 be activated unless the critical size threshold has been reached; hence Start is integrated into the logic of Whi5 and Cln2 as follows: if Start~0 then Whi5~1 and Cln2~0 [21–24]. The external input BuddingCP corresponds to the correct formation of the bud neck and the localization and subsequent degradation of Swe1 [25–27]. As such, we say that if BuddingCP~0 then Swe1~1. Lastly, SpindleCP corresponds to the spindle assembly checkpoint which modulates the activation of Cdc20: if SpindleCP~0 then Cdc20~0 [28,29]. Finally, CSS is a signal representing cell size. It is known that cell size regulates the cell cycle via its correlation with Cln3 levels. The mechanism governing this regulation involves a complex network of biochemical interactions [30,31], and has been omitted for simplicity. Unlike the external nodes representing cell cycle checkpoints, which are binary in nature (either satisfied or not), the CSS external input is inherently continuous (cell size varies continuously over time). To represent this continuous signal passed from the cell and its environment to activate Cln3 at a given moment, a probability (q) that CSS is active is defined: p(CSS~1)~q[(0,1). This signal is relative as p(CSS~1)~1 indicates Cln3 is receiving the strongest activation signal. The cell cycle was modeled as a sequential activation of the checkpoints. In other words, the pre-start or G1 phase was modeled by setting all checkpoints to 0. The G1/S phase is modeled by setting Start to 1. For the G2/M phase, BuddingCP is set to 1; finally, the M/G1 phase is modeled via the activation of the SpindleCP checkpoint. Hence, the cell cycle as a whole results in a sequence of probabilistic Boolean control networks (PBCNs) (see the Methods section for detailed discussion of PBCNs) as follows: (CSS,Start,BuddingCP,SpindleCP)~ (q1(t),0,0,0)?(q2(t),1,0,0)?(q3(t),1,1,0)?(q4(t),1,1,1) Call these PBCN1, PBCN2, PBCN3, PBCN4, where each qi(t) is the control function governing CSS during each modeled phase. The question is then: does each PBCN behave in accordance with the phase assigned to it by the status of its checkpoints? In the next section, the results of our analyses of the dynamics of these PBCNs are presented. Cyclin Activity Profiles Correspond to Ergodic Sets To demonstrate how PBCNs can be used to visualize and analyze the dynamics of biological systems, we first show that ergodic sets correspond to cell phenotypes; i.e., cyclin activity patterns of the individual cell cycle phases, in our case. Each PBCN was analyzed, and ergodic sets were calculated. The question we then asked: Do the cyclin activity functions of the individual ergodic sets (and hence the modeled cell cycle phases) correspond to the cyclin activity profiles during the cell cycle as seen in the laboratory? In other words, does our model represent the biological reality? In fact, the results of our analyses (discussed below) indicate that the presented model accurately captures many of the features of the species’ expected behavior (i.e., their activity levels) during each cell cycle phase. In Figure 2 the ergodic sets associated with each PBCN and the corresponding activity functions of key cyclins as a function of q~CSS are summarized. For each of the PBCNs exactly one ergodic set was found (ES1-4, Figure 2A). For (ES1) the cyclin activity functions (column 1 in Panel C) is consistent with pre-start G1 cells. The cyclin activity functions of ergodic sets for PBCN2 and PBCN3 are consistent with the G1/S and G2/M phase of the cell cycle, respectively (columns 2 and 3 in Figure 2A and B). Finally, during the last stage, the cyclin activity functions of PBCN4 is consistent with M/G1 phase when CSS is decreasing. That is, the cyclin dependent kinases (e.g., Cln1{3, Clb2, etc.) deactivate while the cyclin kinase inhibitors (e.g., Sic1 and Cdh1) reactivate. Thus we see that in fact each PBCN does behave according the phase assigned to it by the status of its checkpoints. In order to model the dynamics of the cell cycle as a whole we must consider how CSS is changing over time. Choosing an appropriate qi(t) for i~1,2,3,4 as the control functions for CSS for each corresponding phase we may see the behavior of each species across the cell cycle as a whole. As time is arbitrary in our model, we chose qi(t) to have the ith quarter of the unit interval as its domain, and thus the modeled cell cycle to take one unit of time. To organize the transition from one phase to the next we suppose that if one concatenates those functions into a single function q(t)~qi(t) if t[½i{1 4 , i 4 the overall behavior of CSS should mimic cell size; i.e., it should grow for the majority of the cell cycle and drop at the end. Furthermore, we assume that Cln3 peaks when it is receiving the maximum signal. It has been shown that the level of Cln3 rises and falls over the cell cycle and peaks sometime during M phase [16,32]. Thus we let qi(t)~ 4 3 t with domain ½i{1 4 , i 4 for i~1,2,3 and q4(t)~{4tz4 with domain ½3 4 ,1. (Note that the dynamical properties of the model are highly robust to variations of the function, and thus our choice of the control functions, as discussed in the Robustness section. ). Consequently for each species, a piecewise function that governs its activity across the cell cycle was constructed by composing each node’s activity function with qi(t) during each corresponding phase of the cell cycle. In Figure 3, one can see the control Ergodic Sets for BYCC PLOS ONE \| www.plosone.org 2 October 2012 \| Volume 7 \| Issue 10 \| e45780 function for CSS over the whole cell cycle on the left and the corresponding activity of selected cyclins across the whole cell cycle on the right. It is clear that we are able to reproduce the general structure of the cell cycle. Cyclin kinase inhibitors are active in G1, followed by their deactivation and the activation of the G1 cyclins Clb5 and Cln2. Then the G1 cyclins deactivate and Clb2 activates. Finally Clb2 deactivation correlates with Cdc20 activation as the cell progresses through M phase, and the reactivation of the CKIs. (See Methods for a narrative description of the cell cycle.) Direct comparison of the shape of the calculated activity profiles to experimental studies in [16] (via cyclebase.org) revealed a strong correspondence (Figure 4). Exceptions to this correspondence with results from [16] were the dynamics of Cdc14 and Cdh1. Our model predicts that Cdc14 is activated late in the M phase (while inactive during the previous phases). This behavior appears however to be consistent with another study that suggested that Cdc14 activation occurs in late mitosis [33]. Also, while the activation profile of Cdh1 predicted by our model doesn’t agree with the results in [16], it appears to be consistent with the activation profile described in Figure 2 in [4] (as well as all other species common to each model). Thus not only does our model’s results compare to laboratory results but also to the results of a differential equation model. Note that the activity levels of Whi5, Sic1, Cln2, Clb2, and Cdc20 also qualitatively correspond to the combination of activity and localization measured in the cell (see Figure 3 in [17]). Together, these data suggest that, in fact, ergodic sets can model cell phenotypes. Furthermore, as visualized in Figure 3 and Figure 4, a secondary peak of the G1 Cyclins (Cln2 and Clb5 in particular) was found as the cell transitions from PBCN3 to PBCN4. In fact, this phenomenon was also observed in the laboratory [16]. This is also a feature of the cyclin activity profiles of the respective ergodic sets. Notice also that this peak is not purely a result of the function that we chose for CSS. While the shape of the peak may change, its existence is intrinsic to the Figure 1. Regulatory Graph for Budding Yeast. doi:10.1371/journal.pone.0045780.g001 Ergodic Sets for BYCC PLOS ONE \| www.plosone.org 3 October 2012 \| Volume 7 \| Issue 10 \| e45780 logic of the network; that is, so long as CSS does not drop instantly to zero when the spindle assembly checkpoint has been satisfied, there will be some sharp rise and fall of Cln2 and Clb5. Start, Irreversibility, and Commitment to the Cell Cycle The irreversible nature of the Start signal was explored in [18] by investigating the positive feedback loop that exists between Cln2, SBFo (‘‘SMBF’’ in our model) and Whi5 (see Figure 1). As can be seen in Figure 3B, the bi-stability of Cln2 is clearly represented in the transition from the G1 ergodic set (ES1) where Cln2 is inactive to the S-phase ergodic set (ES2) where Cln2 is active. Notice that in PBCN1, the Whi5-Cln2-SMBF feedback loop cannot be initiated, as Whi5 is active and Cln2 is inactive until the Start signal has been received. On the other hand, in the post-Start phase (i.e., PBCN2), Whi5 is now inhibiting itself as a result of the Start-activated feedback loop. This suggests that the feedback loop is inherent to the irreversibility of Start. In the aforementioned work [18], the authors showed that removing Cln2 from the feedback loop allows the reactivation of Whi5 following an exogenous pulse of Cln2, rendering Start reversible. To perform an analogous inquiry on our model, and to investigate the role of the feedback loop, we eliminated Cln2 as an upstream regulator of Whi5 and re-analyzed PBCN2. A single ergodic set was found, whose cyclin activity profile is pictured in Figure 5A. The functions from the activity profiles of ES1 and ES2, that govern Cln2 when the feedback loop is present are constant functions, and thus have no dependence on CSS. In contrast, Cln2o and Whi5 activities are now a function of CSS (Figure 5A). In other words, if the CSS stimulus is removed from Cln3, Cln2 becomes inactive and Whi5 reactivates, indicating a return to G1 phase and a renewed possibility of G1 arrest due to mating pheromone [34]. The transition to S phase is now reversible. Though the context of our model and what was done in [18] are different, the result is the same – the irreversibility of the G1/S transition is dependent on the positive feedback loop. That the functions for the cyclins in the G1, S, and G2 phases are constant has another implication for our model. Specifically, once the Start signal has been received, the typical (oscillating) activity profiles of the key cyclins will ensue even when stimulus of Cln3 by cell size is incoherent, so long as the checkpoints are satisfied. In other words, once the cell receives the Start signal, it commits to a round of cell division. Robustness Robustness of biological systems is critical to the proper function of processes such as the cell cycle. Within our modeling regime Figure 2. Analysis of each PBCN. A) Ergodic sets (consisting of network states) for the individual PBCNs corresponding to individual cell cycle phases. Each PBCN was constructed by changing the combination of satisfied checkpoints; the ‘‘activity’’ of the Cell Size Signal (CSS) external node is defined by a probability q. Ergodic sets are visualized as nodes corresponding to network states (represented by their binary number +1) connected by arrows illustrating the flow of these states. Red arrows correspond to q~1, blue arrows correspond to q = 0. Discussion of the individual ergodic sets and their biological meaning can be found in the main text. B) Activity profiles (‘‘signatures’’) of cyclins during each modeled cell cycle phase. C) Plots of cyclin activity functions as found by computing stationary distribution analytically using Maple 15, as discussed in the main text. doi:10.1371/journal.pone.0045780.g002 Ergodic Sets for BYCC PLOS ONE \| www.plosone.org 4 October 2012 \| Volume 7 \| Issue 10 \| e45780 noise is interpreted as the systems’ sensitivity to the control function, and the robustness of the ergodic sets to random perturbations, respectively. To consider the system’s sensitivity to the control function, we considered the activity functions of the ergodic sets. As noted in the previous section, the activity functions governing most of the key species in the system are constant, and hence independent of CSS during the first three phases of the cell cycle. In particular, Cln2, Clb5, and Clb2, which drive bud formation, DNA replication, and mitosis, respectively, have their activities governed by constant functions. This indicates that so long as the checkpoints are appropriately activated (i.e., the environment is stable enough for the successful completion of the current phase), the modeled cell will progress through the cell cycle independently of CSS (i.e., cell size). Therefore our model is robust to the variable behavior of the cell growth. Furthermore, this is also consistent with the findings in [19] that a cell deprived of nitrogen will proceed through one round of division and arrest in G1. We modeled this scenario by removing the cell size signal (CSS) right after Start has been satisfied. Consistent with [35], as a control function we chose q1(t)~(4=3)t for t[½0,1=4 and qi(t)~1=100 for t[( i{1 4 , i 4, i~1,2,3. The dynamics of modeled cyclins are depicted in Figure 5B. During the first three phases, the activities of the species are the same as the normal cell cycle (Figure 2). The activities of the species during the last phase are also consistent with a cell in the G1 phase. That is, the modeled cell has completed a round of division and arrested in G1. This may suggest that the phenomenon of completing a cell cycle without appreciable growth is a consequence of the robustness of the cell cycle to variable external environments, and is inherent to the logic of the biological regulatory network governing the yeast cell cycle. In addition to being able to represent cellular phenotypes, the calculated ergodic sets (and the number thereof) in the previous section have another implication. Similar to attractors in Boolean network, ergodic sets can provide insights into the robustness of the modeled biological systems. A standard approach to analyze robustness is to consider the basins of attractions of each attractor and interpret its relative size as a measure of stability (e.g., [5]). The concept of a basin of attraction for an ergodic set in a PBCN is not well defined; this is due to the fact that a random walk initiated from a single state in the state space may arrive at different ergodic sets. However, each of the PBCNs have a single ergodic set which means that any perturbation will eventually return to the ergodic set (and can be modeled by its associated cyclin activity functions). As such, we see that the modeled G1, G1/S, G2/M and M/G1 phases of the cell cycle are highly robust in the face of perturbations. Together, our results suggest that each phase of the modeled cell cycle is robust as well as the cell cycle as a whole. Discussion Results presented herein are twofold. First, as suggested in [8], we show that it is possible to model cellular phenotype as ergodic sets in the context of probabilistic Boolean control networks. In contrast to previous works utilizing Boolean models, our approach centers around understanding not only the cell cycle as a whole, but also its individual phases. Specifically, we modeled the cell cycle as a sequence of models, each representing an individual phase in the cycle. This approach has significant implications as to how the dynamics of the modeled cell cycle are interpreted and are compared with experimental studies. Specifically, in previous works the yeast cell cycle was modeled as a single system where the phases were represented as transient states leading to a (fixed point) attractor corresponding to the G1 phase [5], or as consecutive states in a cyclic attractor [12,13]. Considering each phase as an evolving system of its own enabled us to capture continuous dynamics of key species during each phase and compare them to laboratory studies. Modeling each phase separately and transitioning between models via the activation of checkpoints is also consistent with the biological observations that it is not only kinase activity that causes phase transitions, but the completion of each phases task [36]. Figure 3. The cell cycle in relative time. The left hand side depicts the control function for CSS along with the points in time where checkpoints are activated. The right hand side depicts the concatenated activity profiles of the corresponding ergodic sets composed with CSS control function. All species appear during each phase, though several my take on the same value, including 0. doi:10.1371/journal.pone.0045780.g003 Ergodic Sets for BYCC PLOS ONE \| www.plosone.org 5 October 2012 \| Volume 7 \| Issue 10 \| e45780 Figure 4. Comparison between our analytically calculated results (red) and the experimental results in [16] (green) via cyclebase.org. Each node in the network may represent several species. In the case that a node represents more than one species its calculated activity profile is compared to the experimental activation of the species to which it most clearly correlates. For example, the node Yhp1 in our model represents the species YHP1 and YOX1. We thus compare the calculated profile of the node Yhp1 to YOX1, as they appear to have the best correspondence. Numbered peaks and valleys identify our interpretation of the correlation between plots. The species corresponding to each node can be found at thecellcollective.org. doi:10.1371/journal.pone.0045780.g004 Ergodic Sets for BYCC PLOS ONE \| www.plosone.org 6 October 2012 \| Volume 7 \| Issue 10 \| e45780 Similar to [5,12,13] we find that each phase of the cell cycle and thus the cell cycle as a whole is robust as measured by basin size, i.e. the existence of a single ergodic set for each phase. Stability of the yeast cell cycle has also been considered in the framework of probabilistic Boolean networks, concluding the cell cycle attractor is robust to internal noise [7,15,37]. However, this approach is incompatible with our goal of exploring the relevance of ergodic sets as it renders the entire state space a single ergodic set. Modeling extracellular signals as continuous variables (i.e., cell size) allowed us show the stability of the yeast cell cycle network under different choices of control functions, a question precluded by previous modeling techniques. Lastly, taking the perspective of qualitative activity introduced in [1] we are able to directly incorporate the role of cell size into our model. The further correlation of cell size with time also allows us to escape the discrete time of other Boolean network models. Evidence is increasing that biological processes possess complex properties that emerge from the dynamics of the system working as a whole (e.g., [1,30,38–41]). To better understand these emergent properties, large-scale computational models of the complex biological interactions will be needed. The size of the budding yeast cell cycle network in this work is relatively small and makes the analytic calculations manageable. Larger and more compre- hensive models will be key in systems biology. For example, understanding how the cell controls checkpoints via additional regulatory network pathways, and how to incorporate this understanding into current models is of paramount importance. Thus the question of how to approach large networks is important in extending these results to truly life-size scales. To deal with such scales simulation techniques and software (such as The Cell Collective; http://www.thecellcollective.org) will be an important part of extending these results to large models. Methods Budding Yeast Cell Cycle Newborn cells begin in the G1 phase of the cell cycle, where they start growing. It isn’t until the cell reaches a critical size that a round of division begins [42]. This transition point is referred to as Start, and is irreversible; that is, once the Start signal is received, the cell is no longer susceptible to G1 arrest due to mating pheromone, and the cell has committed to a round of division, [18,42,43]. The activity profile of the biochemical network underlying the cell cycle during the initial G1 phase is characterized by the increasing activity of the Cln3 cyclin in response to the cell’s increasing size, and the activity of the cyclin kinase inhibitor (CKI) Sic1 [42]. The transition to S phase occurs once the critical size has been reached, i.e. Start has occurred, and Cln1, 2 has become active and Sic1 has been inactivated. The inactivity of Sic1 allows the activation of Clb5. Having transi- tioned to S phase, the cells characteristic cyclin activity pattern is the activity of Cln1, 2 and Clb5 and the inactivity of Sic1. During S phase, Cln1, 2 allow bud and spindle-pole body formation, while the activity of Clb5 allows DNA replication [18,23]. In G2 phase, Clb2 (the primary mitotic cyclin) accumulates [44], and Swe1 is degraded in the newly formed bud neck [25–27]. In fact, bud formation (along with other nuclear events) constitutes another quality control point: a morphogenic checkpoint [27]. The activity of Clb2 is sustained into early M phase [44,45]. Thus one may say that active Clb2 (and inactive Sic1) characterizes the G2/M phase of the cell cycle. Further progression through M phase is governed by another checkpoint: the spindle assembly checkpoint. Once the chromosomes are correctly aligned on the mitotic spindle, Cdc20, a co-factor of the ubiquitin ligase anaphase-promoting complex/ cyclosome (APC/C), is released from inhibition. The cell then will progress through the rest of M phase and divide into a mother and daughter cell in G1 phase, awaiting another round of division. Figure 5. Irreversibility and commitment to cell cycle. A) Cln2 becomes inactive and Whi5 reactivates when CSS stimulation is removed. Thus breaking Whi5-SMBF-Cln2 feedback loop makes Start reversible. B) Modeled cell cycle under nitrogen deprivation. CSS is linear during the G1 phase and drops to.01 there after. doi:10.1371/journal.pone.0045780.g005 Ergodic Sets for BYCC PLOS ONE \| www.plosone.org 7 October 2012 \| Volume 7 \| Issue 10 \| e45780 Thus, the activation and deactivation of Cdc20 and the corresponding recovery of the Sic1 and Cdh1 and characterize the M/G1 phase of the cell cycle [29,46]. It is this oscillating activity of cyclin-dependent kinases that ‘‘act as the master regulator for cell cycle progression’’ [47]. The complete model is freely available for download and further modifications in The Cell Collective software at http://www. thecellcollective.org; [48]. Modeling Framework As noted in the Introduction section, the modeling framework herein was suggested by [1]. The essential perspective of this framework is to suppose that at every moment of time, our biological system is being modeled by the stationary distribution of an irreducible Markov chain, whose states are an irreducible subset of the state space for a probabilistic Boolean network (which itself is a reducible Markov chain). Consider a collection of n nodes fx1, . . . xng, representing biological entities, each taking a value in f0,1g, and n{m Boolean functions fi : f0,1gn?f0,1g, i~1, . . . ,n{m, where the function fi is the logical rule governing xmzi. Call the nodes xmz1, . . . ,xn internal nodes and call nodes x1, . . . xm external inputs, as they are not governed by a Boolean function. Decompose the state space of the original n nodes as the direct sum f0,1gm+f0,1gn{m so that for v+w[f0,1gm+f0,1gn{m v represents the state of the external inputs and w represents the state of the internal nodes. Notice that for each v[f0,1gm we may define Fv : f0,1gn{m?f0,1gn{m by Fv(w)~(f1(v+w), . . . ,fn{m(v+w)) (we suppress the notation for the standard inclusion of the direct sum). Thus we have defined a family of 2m Boolean networks consisting of the internal nodes, one for each vector in f0,1gm. Suppose that to each external input xi we associate a function qi(t) taking values in (0,1) with t[D, some arbitrary domain representing time. Call qi(t) a control function. We suppose that this probability represents the qualitative activation of the species represented by xi at time t. Let t[D be fixed and consider the probability distribution nt on f0,1gm given by nt(v)~ Pm i~1 qi(t)vi(1{qi(t))1{vi. Using this construct PBNt, a probabilistic Boolean network where the probability that Fv is chosen to update the network is nt(v). Abusing notation so that Fv Figure 6. An example calculation. A) A diagram of a sample network with one external input. The logic of the internal nodes is represented with Boolean truth tables. B) The state space associated with the network. Nodes are labeled by (bz1) where b is the binary number corresponding to the activity of (N1,N2,N3,N4). Supposing that the probability that EI is active is q, the state space is traversed on dashed arrows with probability q and solid arrows with probability 1{q. Nodes labeled with an underline constitute the ergodic set. C) On the left is the probabilistic transition matrix that governs the system once it has reached the ergodic set. With the matrix is associated a unit modulus eigenvector that provides the invariant distribution for the system. D) Each state of the ergodic set gives the activities of the internal nodes. Taking the sum of these binary vectors weighted by the invariant distribution gives the likelihood that a particular node is active. Thus on the right of this expression is the activity function of each node in the ergodic set. Note that the activity function is continuous for q[(0,1). E) In the left graph, the activity function of each node is plotted as a function of q. In the middle graph, an arbitrary function for q (or the activity level of EI) is plotted as a function of time. In the graph on the right side, the activities of the network nodes is plotted as a function of the composite function for EI in time (as designed in the middle graph). doi:10.1371/journal.pone.0045780.g006 Ergodic Sets for BYCC PLOS ONE \| www.plosone.org 8 October 2012 \| Volume 7 \| Issue 10 \| e45780 also stands for the state transition matrix of the associated Boolean network, the state transition matrix of the corresponding Markov chain is A 0 t~ P v[f0,1gm nt(v)Fv. It is important to point out that we may not assume that this Markov chain is irreducible, as we are not considering any arbitrary perturbations of nodes. However, within the state space f0,1gn{m there are recurrent communicat- ing classes of states, and any random walk corresponding to this Markov chain will arrive at one of these sets. Suppose then that W~fw1, . . . ,wkg5f0,1gn{m is a recurrent communicating class. Restricting the state transition matrix to W, let At~A 0 tDW. At is an irreducible Markov chain. As we have no guarantee that the resulting transition matrix is aperiodic we consider pt, the stationary distribution on W associated to the Markov chain At. We define the activity profile of the W at time t, a recurrent communicating class of the original Markov chain, by Pt~ Pk i~1 pt(wi) wi. We then interpret the ith entry of Pt as the qualitative activation of the species represented by node xi at time t. It is important to note that the recurrent communicating classes of PBNt are the same for all times t[D. (Thus, as above, we do not need to index W by t.) This can be seen by understanding that the recurrent communicating classes are determined by the semigroup generated by the maps fFvDv[f0,1gmg, and not by the probabil- ities associated to each Fv [49]. This is why we take care to assume that each qi(t) takes values in (0,1)o since if at some time t, qi(t)~0 or 1, then the semigroup associated to the Markov chain has changed and thus the recurrent communicating classes at that moment may be different. We will refer to this infinite family of PBNs, fPBNtDt[Dg, associated to the semigroup S~fFvDv[f0,1gmg as a probabilistic Boolean control network. Calculating Pt is aided by the fact that it can computed in two steps. First we consider each qi as a formal variable instead as a function of t. The matrix A is still stochastic, but its entries are now 0’s, 1’s or polynomials in qi,i~1, . . . ,m. As such application of the Perron-Frobenious theorem allows us to compute the stationary distribution for this irreducible Markov chain as a function which is continuous for all qi[(0,1). We call these the activity functions for each ergodic set. We then compose these functions with the control function for each qi rendering the stationary distribution a function of t. Thus we have continuous functions of t that give activity profile for the ergodic set at time t. This procedure is demonstrated in a smaller example in Figure 6. We used GAP (Groups, Algorithms, Programming) along with the package Monoid written by James Mitchell in order to compute the recurrent communicating classes for each PBCN. Maple 15 was used to compute the associated stationary distributions. For further mathematical details see [49] and [50]. Model Construction via The Cell Collective The Cell Collective (www.thecellcollective.org; [48]), is a collab- orative modeling platform for large-scale biological systems. The platform allows users to construct and simulate large-scale computational models of various biological processes based on qualitative interaction information. The platform’s Bio-Logic Builder was used to create this yeast cell cycle models truth tables by specifying the biological qualitative data (adopted from [12]). The Cell Collective’s Knowledge Base component was also used to catalog and annotate all biochemical/biological information for the yeast cell cycle. Acknowledgments We thank Dr. Jim Rogers for his useful conversations and comments, and Drs. Dora Matache and John Konvalina for their helpful comments on the manuscript. Author Contributions Conceived and designed the experiments: RT TH. Performed the experiments: RT TH. Analyzed the data: RT TH. Contributed reagents/materials/analysis tools: RT TH. 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Ergodic Sets for BYCC PLOS ONE \| www.plosone.org 10 October 2012 \| Volume 7 \| Issue 10 \| e45780	23049686	Cdc14 = ( MEN AND ( ( ( FEAR ) ) ) ) Whi5 = ( NOT ( ( Cln3 AND ( ( ( Start ) ) ) ) OR ( Cln2 AND ( ( ( Start ) ) ) ) ) ) OR NOT ( Start OR Cln2 OR Cln3 ) Swi5 = ( ( Cdc14 AND ( ( ( NOT Swi5 ) ) AND ( ( SFF ) ) ) ) AND NOT ( Clb2 ) ) Cdh1 = ( ( Cdc14 ) ) OR NOT ( Cdc14 OR Clb2 OR Cln2 OR Clb5 ) Sic1 = ( ( ( ( ( Swi5 ) AND NOT ( Clb2 AND ( ( ( NOT Cdc14 ) ) ) ) ) AND NOT ( Clb5 AND ( ( ( NOT Cdc14 ) ) ) ) ) AND NOT ( Cln2 AND ( ( ( NOT Cdc14 ) ) ) ) ) OR ( ( ( ( Sic1 ) AND NOT ( Clb2 AND ( ( ( NOT Cdc14 ) ) ) ) ) AND NOT ( Clb5 AND ( ( ( NOT Cdc14 ) ) ) ) ) AND NOT ( Cln2 AND ( ( ( NOT Cdc14 ) ) ) ) ) ) OR NOT ( Swi5 OR Cdc14 OR Sic1 OR Clb2 OR Clb5 OR Cln2 ) FEAR = ( Cdc20 ) Clb2 = ( ( ( ( ( SFF ) AND NOT ( Cdh1 AND ( ( ( Cdc20 ) ) ) ) ) AND NOT ( Cdc20 AND ( ( ( Cdh1 ) ) ) ) ) AND NOT ( Swe1 ) ) ) OR NOT ( Cdc20 OR SFF OR Cdh1 OR Sic1 OR Swe1 ) Cln3 = ( ( Size ) AND NOT ( Yhp1 ) ) Clb5 = ( ( ( SMBF ) AND NOT ( Sic1 ) ) AND NOT ( Cdc20 ) ) Yhp1 = ( SMBF ) Swe1 = ( NOT ( ( BuddingCP ) ) ) OR NOT ( BuddingCP ) MEN = ( FEAR AND ( ( ( Clb2 ) ) ) ) Cdc20 = ( SpindleCP AND ( ( ( Clb2 ) ) AND ( ( SFF ) ) ) ) Cln2 = ( SMBF AND ( ( ( Start ) ) ) ) SMBF = ( NOT ( ( Whi5 ) OR ( Clb2 ) ) ) OR NOT ( Clb2 OR Whi5 ) SFF = ( Clb2 )
A Boolean Model of the Cardiac Gene Regulatory Network Determining First and Second Heart Field Identity Franziska Herrmann1,2,3., Alexander Groß1,3., Dao Zhou1, Hans A. Kestler1, Michael Ku¨ hl2 1 Research Group Bioinformatics and Systems Biology, Institute for Neural Information Processing, Ulm University, Ulm, Germany, 2 Institute for Biochemistry and Molecular Biology, Ulm University, Ulm, Germany, 3 International Graduate School in Molecular Medicine, Ulm University, Ulm, Germany Abstract Two types of distinct cardiac progenitor cell populations can be identified during early heart development: the first heart field (FHF) and second heart field (SHF) lineage that later form the mature heart. They can be characterized by differential expression of transcription and signaling factors. These regulatory factors influence each other forming a gene regulatory network. Here, we present a core gene regulatory network for early cardiac development based on published temporal and spatial expression data of genes and their interactions. This gene regulatory network was implemented in a Boolean computational model. Simulations reveal stable states within the network model, which correspond to the regulatory states of the FHF and the SHF lineages. Furthermore, we are able to reproduce the expected temporal expression patterns of early cardiac factors mimicking developmental progression. Additionally, simulations of knock-down experiments within our model resemble published phenotypes of mutant mice. Consequently, this gene regulatory network retraces the early steps and requirements of cardiogenic mesoderm determination in a way appropriate to enhance the understanding of heart development. Citation: Herrmann F, Groß A, Zhou D, Kestler HA, Ku¨hl M (2012) A Boolean Model of the Cardiac Gene Regulatory Network Determining First and Second Heart Field Identity. PLoS ONE 7(10): e46798. doi:10.1371/journal.pone.0046798 Editor: Robert Dettman, Northwestern University, United States of America Received April 16, 2012; Accepted September 10, 2012; Published October 2, 2012 Copyright: 2012 Herrmann et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: The work was supported by the German Federal Ministry of Education and Research within its joint research project SyStaR and by the International Graduate School in Molecular Medicine Ulm, funded by the Excellence Initiative of the German Federal and State Governments. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: michael.kuehl@uni-ulm.de; hans.kestler@uni-ulm.de . These authors contributed equally to this work. Introduction The heart is the first functional organ to develop in mammals. After the end of gastrulation, cardiogenic progenitor cells constitute the cardiac crescent in the anterior mesoderm of the murine embryo. At this stage the cardiogenic mesoderm splits from a common cardiovascular progenitor cell population [1,2] into two areas of differential gene expression: the so-called first heart field (FHF) and the second heart field (SHF). Cells of the FHF build the primary heart tube and later mainly contribute to the left ventricle, most of the atria and provide a minority of cells of the right ventricle. Cells of the SHF mainly contribute to the right ventricle, the outflow tract and the atria [3,4]. Underlying regulatory factors control these differentiation processes. The induction of mesoderm depends on canonical Wnt signaling [5]. After mesoderm formation cardiogenic precursor cells are characterized by the expression of the transcription factor Mesp1 [6]. Endodermal signals such as Bmp2 were also described as being crucial for cardiogenesis [7,8,9]. These signals activate a variety of transcription factors of the cardiogenic mesoderm like Nkx2.5 or GATA factors [7,8,10]. Some of the cardiac transcription factors can be assigned to one of the two heart fields. The transcription factors Isl1, Foxc1/2, Tbx1 and the ligand Fgf8 determine the area of the SHF, while the transcription factor Tbx5 is only expressed in the FHF [11,12,13,14]. It is thought that intrinsic wiring among these cardiac factors determines the progression of cardiac differentia- tion and the division into subdomains of differential gene expression. Heart development can severely be impaired in case a regulatory factor of cardiogenesis is missing. Several studies analyzed specific interactions within gene regulation of early mammalian heart development using knock out or knock down approaches of individual factors. A deeper understanding of the cardiac gene regulatory network requires the implementation of this network as a computational model and its subsequent analysis by computational simulations. Expression of a gene is regulated by input signals given by transcription factors binding to the regulatory region of the gene. The strength of transcription, e.g. the amount of primary transcript, can be depicted as a function depending on the concentration of these regulatory transcription factors. This function often follows a sigmoidal behaviour, which is governed by cooperativity in a first stage and controlled by saturation at later stages resulting in a switch-like behavior. This property ensures defined levels of gene expression for a wide range of concentration levels. This sigmoidal function of gene expression can be approximated as a step function [15]. A common approximation of the possible states of a gene is therefore to consider a gene to be active or inactive [15]. These two states PLOS ONE \| www.plosone.org 1 October 2012 \| Volume 7 \| Issue 10 \| e46798 of a gene correspond to a present and to an absent gene product and can be encoded as Boolean logical values: true (1) and false (0). Dependencies between genes, e.g. whether a transcription factor acts as a transcriptional activator, repressor or both, can then be captured by Boolean functions which map the state of a gene regulatory network to a succeeding state. These functions allow a Boolean model to exhibit dynamical behavior in simulations. Boolean logic network models have been used to model e.g. endomesodermal territories in the sea urchin [16], the hrp regulon of Pseudomonas syringae [17], and the bistable lac operon in E. coli [18]. Every Boolean model has a finite number of states, as the state of each gene is represented by one of two possible values. For k genes this results in 2k possible state combinations. It follows, that starting a simulation from an initial state and following synchronous state transitions according to the Boolean functions, the model eventually ends up in recurring states, a cycle. A degenerated cycle may consist of a single Boolean state. These recurring states are called attractors. They can correspond to observed expression profiles or phenotypes in gene regulatory networks [19,20,21]. We here introduce a Boolean model for the early cardiac gene regulatory network of the mouse, containing known core genes required for cardiac development and FHF/SHF determination. The model is based on published temporal and spatial expression patterns of relevant transcription factors and growth factors and includes known regulatory interactions taking into account whether a transcription factor acts as an activator or repressor on a given target gene. We are able to show that this computational model is able to reproduce different states observed during cardiac development. Model simulations demonstrate that stable states of gene expression representing either the FHF or the SHF are encoded within the wiring of gene interactions. Thereby, we provide an insight into the functional properties of the cardiac gene regulatory network. This will be an important basis for further enlargements of the network and for in-silico predictions of genetic interactions. Results A Gene Regulatory Network for Early Murine Cardiogenesis For constructing a gene regulatory network of early cardiac development we collected published data. An overview of cardiac genes and their interactions is provided in Figure 1 and Table S1. The expression of genes and their interactions take place in a temporal and spatial frame, as marked by colored boxes in Figure 1. The network is characterized by early signaling events during gastrulation resulting in cardiac specification and subse- quent signaling activities at the cardiac crescent stage which separate the cardiac progenitor cell population into the territories of the FHF and the SHF lineages. Furthermore, signaling from the endoderm was also included into our model. Early canonical Wnt signaling is required for the activation of the pan-mesodermal transcription factor Brachyury [5,22] and for the cardiac specific expression of the transcription factor Mesp1 [10]. Mesp1 subsequently activates various cardiac factors, initiating the cardiac crescent stage. Mesp1 upregulates the expression of genes of both heart fields, e.g. Nkx2.5, GATA4, Tbx1 and Tbx5 [8,10]. At the same time, Mesp1 inhibits expression of genes of other developmental fates (not included into the model), e.g. endodermal genes and the mesodermal gene Brachyury which later supports posterior mesoderm formation and axial development [10,23,24]. In the FHF, cardiac transcription factors like Nkx2.5, GATAs and Tbx5 build an intertwined positive feedback circuit to stabilize their expression. They activate downstream regulatory genes like Hand genes or myocardin. Finally, regulatory factors upregulate a set of differentiation genes. Genes being specific for terminal differentiation such as myosin light chain genes (MLC) or myosin heavy chain genes (MHC) code for structural proteins and constitute the end of the developmental processes described by the regulatory network (Figure 1, FHF area). Similarly, a network of molecular interactions exists in the SHF (Figure 1, SHF area). Furthermore, the endoderm has been shown to influence cardiogenesis, especially by the signaling factors Bmp2 and Dkk1. In addition, in the heart looping stage the regulatory factors Isl1, Tbx1 and Fgf8 are also expressed in the pharyngeal endoderm. There, Shh activates Tbx1 through the Forkhead transcription factor Foxa2. Shh might also signal to the SHF and regulate gene expression during later stages [12]. A Boolean Model of the Cardiac Regulatory Network We implemented the core cardiac genes and their interactions (Fig. 2A) as a Boolean model. The interactions of the involved genes and signaling factors were gained from published data and are enlisted in detail in Table S2. The corresponding Boolean functions are given in Figure 2B. This computational model represents the core regulatory interactions of the gene regulatory network of cardiogenesis as presented in Figure 1. As introduced, cardiac development also depends on signals derived at particular time points of development from other tissues such as the endoderm and thus are not included in the core cardiac gene regulory network. Those are represented in our model by four genes: exogen BMP2 I, exogen BMP2 II, exogen CanWnt I, exogen CanWnt II. Bmp2 signaling for example from the endoderm is important for the induction of cardiogenic mesoderm. In order to represent the required activation of Bmp2 at the correct time point, the cardiac progenitor cell state, we modeled a temporal delay by the two genes exogen BMP2 I and exogen BMP2 II. Similarly, exogen CanWnt I and exogen CanWnt II are used to activate canonical Wnt signaling at the cardiac crescent state in the SHF. This represents the described canonical Wnt signaling in the SHF at E7.5 [25]. Expectations of the Boolean Model Simulations of the computational Boolean model are expected to reproduce gene expression profiles as closely as possible and in the same temporal sequence as they appear during cardiogenesis in vivo. Therefore, the temporal and spatial expression patterns of genes included in the model were collected from publications (Table S3). According to the collected data, expected attractors representing the FHF and SHF as well as the expectations for transient states were defined (Figure 3). Furthermore, as genes are stably expressed in a certain area the model should not only reproduce a gene expression profile, but exhibit also stability of these states. Thus, we expect the expression profiles of the FHF and of the SHF to be represented in attractors of the network model. The expected gene expression profiles for a FHF attractor and for a SHF attractor are given in Figure 3A and Figure 3B, respectively. In the FHF the genes Bmp2, Nkx2.5, Gatas and Tbx5 are expected to be active, while genes which usually only appear in the SHF are inactive. In the SHF canWnt, Tbx1, Fgf8, Foxc1/2, Gatas, Nkx2.5 and Isl1 are active, while Tbx5 is expected to be inactive. Figure 3C summarizes the initial states, transition states and the attractors of the FHF and the SHF. Boolean Model of Cardiac Regulatory Network PLOS ONE \| www.plosone.org 2 October 2012 \| Volume 7 \| Issue 10 \| e46798 The Network Model Exhibits Stable States for the FHF and the SHF and Reproduces Temporal Development To analyze the cardiac network, we simulated all possible initial state combinations (215 = 32768 states for all genes) with the cardiac network model. This analysis detects all possible Boolean attractors of the Boolean model (Figure 4A). Our simulations lead to three attractors. One attractor appears only for 1% of the initial states and contains no active cardiac genes. Another attractor appears in 49% of the cases. In this state the genes Bmp2, Tbx5, GATA and Nkx2.5 are active, while other genes are inactive. This attractor resembles the gene expression in FHF cells (compare with Figure 3A) and will be called the FHF attractor from now on. An additional attractor appears for 50% of all initial states and corresponds to the SHF gene expression state (as specified in Figure 3B). We call this the SHF attractor. This finding indicates that the wiring of the network determines gene expression in the first and second heart field. Next, we analyzed the temporal sequence of network states leading to the FHF and the SHF attractors. For this purpose we included relevant biological information to define an appropriate initial setting of the network. At the beginning of gastrulation, canonical Wnt signaling is active and initiates the determination of the mesodermal and cardiac cell lineage [26]. None of the other cardiac specific genes included in our network are active at that time. Therefore, we defined an initial state in which only canonical Wnt signaling is active for further simulations with our network model (compare expectation for the initial state in Figure 3C). Furthermore, both heart fields are induced by endodermal Bmp signaling after the induction of mesoderm. We modeled this by the external signals exogen BMP2 I and exogen BMP2 II which initiate Bmp signaling at the appropriate time point. The initial state with active cardiac canWnt and exogen (endodermal) BMP2 leads to a FHF attractor (Figure 4B, left panel). After gastrulation, the SHF receives additional canonical Wnt signaling while the FHF is unaffected. Therefore, we additionally specified this external signal by exogen CanWnt I and II for the setup which re-activates canonical Wnt signaling at the cardiac crescent state. The initial state with active canWnt, exogen BMP2 and exogen CanWnt leads to a SHF attractor (Figure 4B, right panel). Setups giving rise to both FHF and SHF contain an initial state with active canWnt signaling and active exogen BMP2 I. The difference between both setups is the additional activation of exogen CanWnt I in the setup leading to the SHF. The use of external signals allows us to compare the intrinsic states of the network during the simulations to a temporal developmental process in the developing organism, which integrates signals from non-cardiac tissues. The state transitions of the network, which occur during the simulation, can be compared to a temporal process in the developing organism. From the initial state on (marked by time point t = 1) we follow the state transitions towards the final attractors for the two setups differing in exogen CanWnt I activation (Figure 4B). There are three state transitions leading to the FHF attractor. Following an active canonical Wnt signaling Mesp1 and Dkk1 are expressed at time point t = 2. Transient Mesp1 expression is described in cardiac precursor cells during gastrulation [6,27,28]. Mesp1 activates a variety of cardiac regulatory factors [8,29]. The network state at t = 2 of the simulation resembles the gastrulation stage in vivo (compare transit 1 in Figure 3C). Cardiac regulatory genes Nkx2.5, GATAs, Isl1 and Tbx5 are activated at t = 3 of the simulation. Active genes of this state resemble the expression in the common cardiovascular progenitor cell population where Isl1, Tbx5, GATAs and Nkx2.5 are present [1,2,30]. The expected expression for this state is defined in transition state 2 in Figure 3C. After one additional transition the FHF resembling attractor appears (Figure 4B, without exogen CanWnt I, t = 4). In the setup with active exogen CanWnt I, cardiac canonical Wnt signaling is reactivated at the state of the common cardiovascular progenitor cell (Figure 4B, with exogen CanWnt Figure 1. Gene regulatory network during early murine cardiac development. The overview comprises published gene regulations in early heart precursor cells, focussing on two areas with different gene expression, the first heart field (FHF) and the second heart field (SHF). A differentiation of the two heart fields happens around E7.5. Signaling of the endoderm which influences cardiac progenitors was included in this overview as well as early mesodermal signals. Genes are represented by their regulatory region and their transcriptional start site. Information from other genes is processed within the regulatory region. The transcriptional start site of a gene indicates expression and influences gene transcription of other genes. Arrow heads indicate activation and bar heads inhibition of gene transcription. Broken lines represent intercellular signaling with an integrated signal transduction cascade. doi:10.1371/journal.pone.0046798.g001 Boolean Model of Cardiac Regulatory Network PLOS ONE \| www.plosone.org 3 October 2012 \| Volume 7 \| Issue 10 \| e46798 I, t = 3). States leading to the common cardiovascular progenitors are identical in comparison to the setup without exogen CanWnt I. Canonical Wnt signaling leads to the activation of SHF genes and thereby to the inhibition of the FHF transcription factor Tbx5. The SHF attractor is constituted at time points t = 4 and t = 5. In summary, the tracing of state transitions in the simple Boolean model substantiates the literature derived expectations. To verify that canonical Wnt signaling is the signaling event that drives cells towards a SHF fate, we eliminated the influence of exogen CanWnt II in the model by keeping exogen CanWnt II = 0 throughout the simulation. This is in line with investigations by Klaus et al. [31] and Lin et al. [25] which showed that Wnt/aˆ- catenin dependent transcription is upregulated at E7.5 in the second heart field. For both initial setups the network attains a FHF attractor, passing the same transition states as for the wildtype without exogen canWnt (Figure 4B, left side). It demonstrates that in our network model cardiac canonical Wnt signaling which is induced from non cardiac tissue is sufficient to establish the SHF attractor. The Boolean Model Reproduces Knock-out and Overexpression Phenotypes For most of the genes involved in the presented cardiac network, knock-out mice have been studied with respect to cardiac development. To analyze whether our model will produce attractors comparable to knock-out phenotypes, the corresponding gene was kept off at all time points of simulation. Figure 2. Boolean model of the cardiac gene regulatory network. (A) Only genes included into the model and their regulations are shown. Regulations are based on published data. (B) Boolean transition functions of the network in (A). All genes of the network are listed on the left side. A new state for each gene is derived from the value of the Boolean function on the right side based on the preceding states of genes. Input variables are combined by Boolean functions: ! = NO, \| = OR or & = AND. Brackets determine the order of evaluation, starting with the innermost. Exogen BMP2 I+II: inputs for non cardiac BMP2 signaling; exogen CanWnt I+II: inputs for non cardiac canonical Wnt signaling. doi:10.1371/journal.pone.0046798.g002 Boolean Model of Cardiac Regulatory Network PLOS ONE \| www.plosone.org 4 October 2012 \| Volume 7 \| Issue 10 \| e46798 Without Wnt signaling no mesoderm is formed, which is the prerequisite for cardiogenesis [5]. For this, we set canWnt = 0, simulating the ablation of cardiac canonical Wnt signaling (Figure 5A). In the simulations of both setups Mesp1 is not activated resulting in absence of cardiac mesoderm at time t = 2 and thus further cardiac factors are not activated. The predictions of the model simulations are consistent with knock-out experi- ments in mice, where upon ablation of canonical Wnt signaling no mesoderm forms [5]. We also simulated overexpression of cardiac canonical Wnt signaling by constantly activating Wnt signaling (canWnt = 1) (Figure 5B). It is known that a sequence of different levels of canonical Wnt signaling are required for proper heart development [26]. In both initial setups, mesoderm is induced upon Wnt overexpression as indicated by Mesp1 activation (Figure 5B, t = 2). In the setup without exogen canonical Wnt signaling, some of the cardiac genes are activated after expression of Mesp1, but no defined heart field is established, leading to an attractor without activated cardiac genes. In contrast, starting by the setup with non-cardiac canonical Wnt signaling, the simulation soon reaches the SHF attractor. In our model a FHF attractor is not formed, while the SHF attractor is reached one time step earlier. Conditional overexpression of b-catenin (a key transducer of canonical Wnt signaling) disrupts primary heart tube formation, a FHF derived structure and leads to an expanded Isl1 expression in the SHF [25,31]. The mesodermal gene Mesp1 induces the expression of many cardiac genes. In the mouse embryo Mesp2 can compensate for some Mesp1 functions. Since Mesp2 is not an explicit part of the network model, but merely is represented by Mesp1, model simulations switching off Mesp1 (Mesp1 = 0) resembles a double knock-out of Mesp1 and Mesp2 in the mouse embryo [28]. These double knock-out mutant embryos do not form cardiac mesoderm. In our model, switching of Mesp1 leads for the setup without exogen canonical Wnt signaling to an attractor without any expression of cardiac genes. For the setup with exogen CanWnt signaling, no cardiac genes are active in the appropriate time frame when a common cardiac progenitor cell should be established (Figure 5C, with exogen CanWnt I, t = 3). If the time window for differentiation of the cells passes, some other fate will be adopted. In our simulations, the network reaches the SHF attractor after a number of further state transitions due to a lack of genes for alternative fates and a lack of further signaling input from other tissues. Since our model does not exhibit cardiac gene expression within two time steps past the gastrulation state, it is in accordance with the reported in vivo results. Dkk1 has been demonstrated to induce cardiac marker genes together with Mesp1. Without Mesp1, Dkk1 inhibits their expression [8]. The knock-out simulation of Dkk1 in the presented cardiac gene regulatory network model exhibited a delay of Nkx2.5 activation by one transition state. Besides this, the attractors and state transitions are are identical in comparison to the undisturbed network (Figure 5D). This simulation result demonstrates that in our model Dkk1 is not important for the correct specification and differentiation of cardiac mesoderm into FHF and SHF lineages. As shown in [32], Dkk1 and Dkk2 double mutant mice have no immediate effect on heart development. Figure 3. Expected network states. Literature derived state descriptions are expected to appear in simulations, presented by a defined set of genes to be active. In (A) a state defined as FHF state with the according gene activity and in (B) the expected SHF state are presented. Colored genes are active, while gray genes are inactive. In (C) states are listed which are expected to appear during a simulation course. In the initial state of the network which corresponds to early mesoderm development, only canonical Wnt signaling is expected to be present, while genes for differentiation of cardiogenic precursor cells are still inactive. A simulation of the network model is expected to pass transition steps one and two. These correspond to transient states of early cardiogenic mesoderm expressing Mesp1 and to the common cardiac progenitor cell population. Finally, the simulation is expected to result in either the FHF or the SHF state. Genes which are expected to be expressed at a certain state are listed in green, and genes which should not appear in a state are shown red. On the right side, the same information as in the table on the left is shown in a manner similar to the results in Figures 4 and 5. In this table, white color indicates that no expectation for the gene activity is specified. doi:10.1371/journal.pone.0046798.g003 Boolean Model of Cardiac Regulatory Network PLOS ONE \| www.plosone.org 5 October 2012 \| Volume 7 \| Issue 10 \| e46798 Later, these double mutant mice exhibit defects in proliferation and hypertrophy in the heart. These defects affect the heart later than it is displayed in our network model and may result from a later impact of Dkks on heart development. Furthermore, genes regulating proliferation are not integrated into the network model and can not be detected in our simulations. The consistency between the biological phenotypes described in the literature and our corresponding simulations demonstrate that our Boolean model closely incorporates the molecular mechanisms underlyingcardiacdevelopmentastheyhavebeeninvestigatedsofar. Discussion In the presented model of the cardiac gene regulatory network we collected and integrated knowledge about major regulatory factors required for heart development and their interactions. The construction of a Boolean model of the cardiac regulatory network allowed us to show that the interactions within the network lead to stable regulatory states representing the FHF and SHF lineages at E7.5 of murine development and indicates a robustness within the network wiring. Figure 4. Results of network model simulations. Gene activity for all genes of the model is presented at distinct network states. A green box indicates activation whereas a red box denotes inactivation of a gene. (A) Summary of the analysis starting simulations from all possible initial states. All runs resulted in one of the three attractors shown. 49% of the simulations resulted in an attractor for the FHF (indicated in purple), 50% in an attractor mimicking the SHF state (indicated in blue) and 1% of the simulations yield an attractor without activation of core cardiac genes. (B) Simulation of time courses from expected initial states of the cardiac gene regulatory network model. Initial state setups differ only in the activation of canonical Wnt signaling at t = 3 (with exogen CanWnt I or without exogen CanWnt II). State transitions match expectations of intermediate state expressions and end in the attractors for FHF and SHF lineages. doi:10.1371/journal.pone.0046798.g004 Boolean Model of Cardiac Regulatory Network PLOS ONE \| www.plosone.org 6 October 2012 \| Volume 7 \| Issue 10 \| e46798 Boolean Model of Cardiac Regulatory Network PLOS ONE \| www.plosone.org 7 October 2012 \| Volume 7 \| Issue 10 \| e46798 The Boolean Model Describes Early Cardiac Development We show that the computational model presented here is sufficient to describe basic regulations of early heart development in mice. Simulations of this model reproduce temporal behavior of heart developmental processes reflecting important stages as the canonical Wnt expression phases [26], a common cardiac progenitor cell stage [1,2] and the FHF and SHF phenotypes [3]. The model furthermore predicts the behaviour of the network upon particular disturbance. Switching off initial canonical Wnt signaling for example (Figure 5A; Wnt = 0) leads into a ’’no heart field‘‘ attractor. This simulation result is consistent with the complete ablation of b-catenin in mice, when mesoderm is not formed [5]. Moreover, the transcription factor Mesp1 marks cardiac progenitor cells. Upon switching off Mesp1 in our model, either no heart field is developed or after activation of some cardiac factors and six state transitions a SHF phenotype is reached. After gastrulation, at about t = 3 or t = 4 cardiac genes are not expressed in the simulation. At this stage usually a cardiac fate is established. As Mesp1 expression, which is required for cardiogenic induction, is not present and further network wiring which could direct the network towards another attractor were not included in the network the simulation ends in a SHF attractor. Nevertheless, these results indicate that cardiac formation is impaired upon Mesp1 ablation. This corresponds to the finding that Mesp1 ablation in mouse leads to severe defects of the formation of cardiogenic mesoderm. Upon ablation of Mesp1 and Mesp2 no cardiac mesoderm is detected at all [27,28]. Further- more, Dkk1 knock-out in our network model revealed no defect in differentiation towards FHF and SHF fates and has barely an impact on the activation of other cardiac factors. This is comparable to Dkk1/Dkk2 double mutant mice, which do not show defects in heart fate decision at the early stages of development which the presented cardiac gene regulatory network model covers [32]. Therefore, known in-vivo knock-out experi- ments can be reproduced with the here presented mathematical network model. The stable state of the FHF is an example of intertwined positive feedback regulation, as the factors involved activate each other`s expression. The stabilization of the SHF is less clear. In our computational model, it is mediated by canonical Wnt signaling. Canonical Wnt signaling has been shown to act in the SHF from E7.5 [25]. A conditionally ablated b-catenin (a mediator of canonical Wnt signaling) mutant mouse leads to shortened SHF derived right ventricle and outflow tract. Furthermore, SHF specific gene expression, especially Isl1, is diminished in the outflow tract and in the splanchnic mesoderm [25,31]. Analyses of a Mesp1-induced gain-of-function mutant of b-catenin [31] shows that the formation of the linear heart tube (usually promoted by FHF cells) was disrupted and the expression of Isl1 was expanded. This observation is in agreement with the overexpression study in our Boolean model (Figure 5B; Wnt = 1) which lacks the formation of a FHF state. Together, these results indicate that canonical Wnt signaling is a major regulator of SHF identity. Wiring within the Network Results in Robustness Our analyses demonstrate an important property of the network wiring: robustness. Robustness ensures that aberrations in the temporal appearance or in amounts of transcription factor expression between cells do not alter the cell’s next stable regulatory state. Our simulations show that there are stable states of the network, which resemble the gene expression patterns of the FHF and SHF, respectively. This analysis investigated all possible initial states and all transitions towards the attractors. The simulation of all possible initial states has limited biological relevance, because most of these initial states will not appear in a mouse embryo in vivo. Nevertheless, the experiment shows that these attractors are an intrinsic property of the Boolean network. The results can serve as a measure of the stability against random fluctuations in gene expression. Thus, most possible aberrations in states will eventually lead to a FHF or SHF attractor through a self-stabilizing mechanism contained in the wiring of the Boolean network. Afterwards, for the progression of differentiation to a succeeding stable regulatory state this robustness needs to be overruled e.g. by a signalfromexternaltissue.Thissignalcanbetransmittedbysignaling ligands for example. The cardiac network model e.g. contains canonicalWntsignalingstartingtosignalfromnon-cardiactissueina defined time frame. This signal affects the target cells to arrive at a stable state, resembling the SHF. This state is only stable as long as canonical Wnt signaling is present. If the canonical Wnt signal discontinues, differentiation is directed to some other stable regulatory state. Thus, robustness of a stable regulatory state is required within the network, but also needs to be disabled by defined signals in order to assure directed development. Suitability of the Choosen Model to Simulate Cardiac Development Commonly, time dependent processes are modeled with differential equations, which relate the change of a compound to its value. These models describe networks of genes and require the knowledge of concentrations for each involved species and kinetic rates for each specified interaction [33,34,35]. Changes in time and space further require additional parameters and can be modeled using partial differential equations [36,37] or stochastic approaches for low molecule numbers [38]. Differential equations and stochastic approaches can accurately represent biological systems if the quantitative data is available, which is rarely the case for large systems [39]. In contrast, many approaches for modeling gene regulatory networks are based on Boolean networks. Boolean models were used for describing the cell cycle [40] or regulation of segment polarity genes in Drosophila melanogaster [41]. Even small Boolean networks with only a few genes show dynamic behavior, which resembles experiments [42]. Another example for a Boolean representation is the lac operon [18]. It demonstrates activation and repression of gene transcription with bistability by Boolean logic. These examples for Boolean models of gene regulatory networks allow for a qualitative investigation and are suitable for the analysis of larger networks [43,44]. Figure 5. Knock-down or overexpression simulations of canonical Wnt signaling, Mesp1 and Dkk1. For knock-down or overexpression a gene is set to 0 or 1, respectively, throughout the simulation. Apart from that, the simulation is performed as in Figure 4B, starting from the defined initial state and receiving signals as in the setup without non-cardiac canonical Wnt signaling or as in the setup with non-cardiac canonical Wnt signaling. (A) Canonical Wnt signaling is switched off (canWnt = 0). This leads in both setups to attractors lacking active cardiac genes. (B) Upon canonical Wnt overexpression (canWnt = 1), no FHF but a SHF forms. (C) If Mesp1 is switched off (Mesp1 = 0), no FHF builds. In the SHF setup, major cardiac regulator genes are inactive after three state transitions. (D) Upon Dkk1 knock-out, attractors and transitions states stay the same. Activation of Nkx2.5 is delayed by one step compared to the undisturbed simulation. doi:10.1371/journal.pone.0046798.g005 Boolean Model of Cardiac Regulatory Network PLOS ONE \| www.plosone.org 8 October 2012 \| Volume 7 \| Issue 10 \| e46798 The specified Boolean model represents states of single entities by two values. This is a simplification of gene expression since in vivo all factors can occur in more than two concentration levels. The Boolean model is supported by the available data as in many expression profiles discrete values are used describing either the presence or absence of a transcription factor. The presence of factors in embryonic tissue is mostly assessed by in-situ hybridisa- tions or immunostainings and thereby provides qualitative data. Additionally, the dependencies in the expression of factors are often given just as positive or negative regulations. Some interactions are measured by RT-PCR and stainings. This qualitative data on states and relations can be translated without many further considerations or interpretations into Boolean values and functions. Nevertheless, the model integrates the different findings on the cardiac gene regulatory network found in the literature without inconsistencies. All input data used to model the Boolean network is solely derived from literature. No estimations of mechanisms and kinetic parameters or concentrations from the available data were needed which would have been required for a more complex model such as one based on differential equations. The cardiac network model fulfills all conditions, which were derived from various experimental studies found. Based on these temporal and spatial expression and interaction data, the network model attains a high validity. In order to fully validate the network model, the expression pattern for all genes at all temporal stages in the specific subset of cells would need to be determined. Furthermore, knock-out or overexpression of these factors and non cardiac signals in the respective developmental area would help to test defined knock-out or overexpression situations of the cardiac regulatory network. These data compared to the simulation of the Boolean network model would in the end fully clarify whether the model completely displays and predicts developmental processes or not. Only a limited amount of such experimental data is available. Known results have been compared to the results of the simulated Boolean model of the core cardiac gene regulatory network and confirm our model. Future Extensions of the Boolean Model Beyond the regulations presented in the network, many more factors, which are known to be expressed during cardiac development, were not yet integrated into the model. Including these factors and further interactions might refine the current model. As new data on these relations become available the computational model of the cardiac gene regulatory network will be expanded to incorporate the new knowledge. This data might be derived by multiple methods. These include time series of gene expression data in cardiac tissue, prediction of transcription factor binding sites in regulatory regions of cardiac genes, monitoring whole genome transcription factor binding sites of factors of interest by chromatin IP as well as by gene expression profiling upon loss or gain of function of cardiac specific transcription factors in geneticaly modified mice or differentiating murine ES cells. Recently developed tools that allow for binarization of gene expression data [45] and reverse engineering approaches [46,47] will be of relevance for these purposes. Furthermore, logical models using more than two states can provide an extension to Boolean models [48,49]. In these models intermediate values for gene states are needed requiring appropriate biological observa- tions [50]. These and other extensions, like stochastic updates, spatial dependency, or the restriction to certain subclasses of models can then bridge the gaps as more data becomes available. In summary, our here established initial model of the gene regulatory network covering early cardiac development fulfills all specified expectations and reproduces temporal and spatial gene expression in early murine cardiogenesis. Thereby it helps to deepen the picture of gene regulation dynamics during early cardiogenesis including the consequences of misregulation as is shown by the knock-out simulations. Furthermore, this Boolean model will be the foundation for a growing gene regulation model and further targeted experiments. Materials and Methods To generate the cardiac gene regulatory network, we collected literature data about temporal and spatial expression of key genes regulating cardiogenesis and their regulatory relations. These were gained from experimental studies in mice, murine ES cells and in two cases in a human cell line. A core set of genes was selected for implementation as a Boolean model. Network components of the model were chosen by their significance for heart development. This is given by an expression between embryonic day 6.0 and 8.5 of heart development in mouse, and a sufficient amount of data available concerning the regulation of expression. To concentrate on core regulatory effects, genes integrated into the network contain input as well as output relations. Furthermore, the functional importance of genes involved has been shown by impairment of cardiogenesis upon their knock-out in mice. Network figures were drawn with Biotapestry (www.biotapestry. org). Simulations of the Boolean network were performed with the R package BoolNet [51] in R (www.r-project.org). Our model contains four external signals (non cardiac BMP2 (exogen BMP2 I+II), non cardiac CanWnt (exogen CanWnt I+II). They do not correspond to genes within the cardiac gene regulatory network, but represent regulation input from non- cardiac tissues as this has been described for cardiogenic cells. The exogen BMP2 I and exogen BMP2 II represent a Bmp2 signal from the endoderm while exogen CanWnt I and exogen CanWnt II are required to reactivate cardiac canonical Wnt signaling in the SHF at E7.5. Both external signals are represented by two non- cardiac inputs in order to convey a temporal delay of two time steps of the non-cardiac signals into the Boolean model of the cardiac gene regulatory network. Supporting Information Table S1 Regulations of cardiac factors as depicted in Figure 1 and their literature references. (DOC) Table S2 Regulatory interactions used in the cardiac regulatory network model. (PDF) Table S3 Spatial and temporal expression pattern of cardiac factors involved in the computational cardiac network model. (DOC) Author Contributions Conceived and designed the experiments: HAK MK. Wrote the paper: AG FH MK HAK. Reviewed the literature and specified the model equations: FH. Implemented the model: DZ. Carried out the simulations: AG DZ FH. Analyzed the results, prepared the figures and supplements AG FH. Boolean Model of Cardiac Regulatory Network PLOS ONE \| www.plosone.org 9 October 2012 \| Volume 7 \| Issue 10 \| e46798 References 1. Moretti A, Caron L, Nakano A, Lam JT, Bernshausen A, et al. (2006) Multipotent embryonic isl1+ progenitor cells lead to cardiac, smooth muscle, and endothelial cell diversification. Cell 127: 1151–1165. 2. Yang L, Soonpaa MH, Adler ED, Roepke TK, Kattman SJ, et al. 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Boolean Model of Cardiac Regulatory Network PLOS ONE \| www.plosone.org 10 October 2012 \| Volume 7 \| Issue 10 \| e46798	23056457	Bmp2 = ( ( exogen_BMP2_II ) AND NOT ( canWnt ) ) GATAs = ( Nkx2_5 ) OR ( Tbx5 ) OR ( Mesp1 ) Isl1 = ( Mesp1 ) OR ( Tbx1 ) OR ( Fgf8 ) OR ( canWnt AND ( ( ( exogen_canWnt_II ) ) ) ) exogen_canWnt_II = ( exogen_CanWnt_I ) canWnt = ( exogen_canWnt_II ) Nkx2_5 = ( Tbx1 ) OR ( Mesp1 AND ( ( ( Dkk1 ) ) ) ) OR ( Bmp2 AND ( ( ( GATAs ) ) ) ) OR ( Tbx5 ) OR ( Isl1 AND ( ( ( GATAs ) ) ) ) Tbx1 = ( Foxc1_2 ) exogen_BMP2_II = ( exogen_BMP2_I ) Foxc1_2 = ( canWnt AND ( ( ( exogen_canWnt_II ) ) ) ) Mesp1 = ( ( canWnt ) AND NOT ( exogen_BMP2_II ) ) Tbx5 = ( ( ( ( Nkx2_5 ) AND NOT ( Dkk1 AND ( ( ( NOT Mesp1 AND NOT Tbx5 ) ) ) ) ) AND NOT ( Tbx1 ) ) AND NOT ( canWnt ) ) OR ( ( ( ( Tbx5 ) AND NOT ( Dkk1 AND ( ( ( NOT Mesp1 AND NOT Tbx5 ) ) ) ) ) AND NOT ( Tbx1 ) ) AND NOT ( canWnt ) ) OR ( ( ( ( Mesp1 ) AND NOT ( Dkk1 AND ( ( ( NOT Mesp1 AND NOT Tbx5 ) ) ) ) ) AND NOT ( Tbx1 ) ) AND NOT ( canWnt ) ) Dkk1 = ( Mesp1 ) OR ( ( canWnt ) AND NOT ( exogen_BMP2_II ) ) Fgf8 = ( ( Foxc1_2 ) AND NOT ( Mesp1 ) ) OR ( ( Tbx1 ) AND NOT ( Mesp1 ) ) exogen_CanWnt_I = ( exogen_CanWnt_I )
RESEARCH Open Access Boolean modeling and fault diagnosis in oxidative stress response Sriram Sridharan1, Ritwik Layek1, Aniruddha Datta1, Jijayanagaram Venkatraj2 From IEEE International Workshop on Genomic Signal Processing and Statistics (GENSIPS) 2011 San Antonio, TX, USA. 4-6 December 2011 Abstract Background: Oxidative stress is a consequence of normal and abnormal cellular metabolism and is linked to the development of human diseases. The effective functioning of the pathway responding to oxidative stress protects the cellular DNA against oxidative damage; conversely the failure of the oxidative stress response mechanism can induce aberrant cellular behavior leading to diseases such as neurodegenerative disorders and cancer. Thus, understanding the normal signaling present in oxidative stress response pathways and determining possible signaling alterations leading to disease could provide us with useful pointers for therapeutic purposes. Using knowledge of oxidative stress response pathways from the literature, we developed a Boolean network model whose simulated behavior is consistent with earlier experimental observations from the literature. Concatenating the oxidative stress response pathways with the PI3-Kinase-Akt pathway, the oxidative stress is linked to the phenotype of apoptosis, once again through a Boolean network model. Furthermore, we present an approach for pinpointing possible fault locations by using temporal variations in the oxidative stress input and observing the resulting deviations in the apoptotic signature from the normally predicted pathway. Such an approach could potentially form the basis for designing more effective combination therapies against complex diseases such as cancer. Results: In this paper, we have developed a Boolean network model for the oxidative stress response. This model was developed based on pathway information from the current literature pertaining to oxidative stress. Where applicable, the behaviour predicted by the model is in agreement with experimental observations from the published literature. We have also linked the oxidative stress response to the phenomenon of apoptosis via the PI3k/Akt pathway. Conclusions: It is our hope that some of the additional predictions here, such as those pertaining to the oscillatory behaviour of certain genes in the presence of oxidative stress, will be experimentally validated in the near future. Of course, it should be pointed out that the theoretical procedure presented here for pinpointing fault locations in a biological network with feedback will need to be further simplified before it can be even considered for practical biological validation. Introduction The control of gene expression in eukaryotic organisms is achieved via multivariate interactions between different biological molecules such as proteins and DNA [1]. Consequently, in recent years, various genetic regulatory network modeling approaches such as differential equa- tions and their discrete-time counterparts, Bayesian networks, Boolean networks (BNs) and their probabilistic generalizations, the so-called probabilistic Boolean networks (PBNs) [2] have been proposed for capturing the holistic behavior of the relevant genes. Some of these approaches such as differential equations involve finer models and require a lot of data for inference while others such as Boolean networks yield coarse models with lower data requirements for model inference. On the other hand, historically biologists have focused on experimen- tally establishing marginal cause-effect relationships between different pairs of genes, which when concatenated Correspondence: datta@ece.tamu.edu 1Texas A & M University, Electrical and Computer Engineering, College Station, TX, 77843-3128, USA Full list of author information is available at the end of the article Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 © 2012 Sridharan et al.; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. together leads to what is known as pathway information. Biological pathways are used by biologists to represent complex interactions occurring at the molecular level inside living cells [3]. Pathway diagrams describe how the biological molecules interact to achieve their biological function in the presence of appropriate stimuli [4]. At a very simple level, biological pathways represent the graphi- cal interactions between different molecules. However, as already noted, the pathways give only a marginal picture of the regulations (up-regulation or down-regulation) of the different genes/RNAs/proteins by other genes/RNAs/ proteins. The complexity of biological signaling and the preve- lance of prior information in the form of pathway knowl- edge demand that genetic regulatory network models consistent with pathway information be developed. Motivated by this, we developed an approach to generate Boolean network models consistent with given pathway information and applied it to studying the p53-mediated DNA damage stress response [5]. In addition, we used a signaling diagram of the MAP-Kinase pathways to predict possible location(s) of the single signaling breakdowns, based on the cancer-causing breakdown signature [6]. Moreover, we also made theoretical predictions of the effi- cacy of different combination therapies involving six anti- cancer drugs, which we plan to validate in the near future. In this paper, we first develop a Boolean network model consistent with oxidative stress response pathway informa- tion from the biological literature. Thereafter this model is linked with the PI3k/Akt pathway and the composite model is used to pinpoint the possible fault locations based on the observed deviations in the apoptotic signa- ture over different time windows. The paper is organized as follows. Section contains a brief general description of Stress Response Pathways while Section presents a discus- sion specific to the case of oxidative stress. The Boolean network model for oxidative stress response is developed in Section. The role of mitochondria as the site in a cell where the oxidative stress is generated is discussed in Sec- tion. In Section, we develop an integrated network linking oxidative stress response to the phenomenon of apoptosis via the PI3k/Akt pathways. Section presents an approach for pinpointing fault locations in the integrated network by observing the apoptotic signature in response to certain test stress input sequences. Finally, Section contains some concluding remarks. Stress response pathways Adaptive stress response pathways are the first responders to chemical toxicity, radiation, and physical insults. The different stress response pathways share a very similar architecture. This architecture has three main compo- nents: a transducer, a sensor and a transcription factor (TF) [7]. The transcription factor (TF) is a DNA-binding protein that interacts with the promoter regions of its target genes via its canonical DNA-binding sites, known as ‘response elements’ (REs), to activate the expression of the target genes. The sensor is a protein that physically inter- acts with the transcription factor in the cytosol, sequester- ing the transcription factor from the nucleus under normal cellular conditions. In addition to its role in cyto- plasmic sequestration of the TF, the sensor may direct TF degradation, providing an additional layer of regulatory control. The result of the sensor-TF complexation is to maintain inactivity of the TF under normal cellular condi- tions, while providing a mechanism that permits activation in response to an appropriate insult to the cell. The trans- ducer is an enzymatic protein, such as a kinase, that con- veys a biochemical change from a signaling pathway upstream of the sensor/TF complex in the event of cellular stress. The transducer may directly modify the transcrip- tion factor, providing the activating signal or modify the sensor which in turn, destabilizes the sensor/TF complex. Liberated, stabilized, and activated, the transcription factor relocates to the nucleus where it activates its target genes. Generally the sensor and TF are unique for a given stress response pathway unlike transducers which can be shared between different stress response pathways, leading to what is commonly referred to as ‘crosstalk’ between the pathways. A schematic diagram showing the general archi- tecture of a stress response pathway is shown in Figure 1. Oxidative stress response pathways Oxidative stress is caused by exposure to reactive oxygen intermediaries/species (ROS). The stress induced on the cells by electrophiles and oxidants gives rise to a variety of chronic diseases. The outcome of interactions between the cell and oxidants is determined largely by the balance between the enzymes that activate the reactive intermedi- aries and the enzymes that detoxify these reactive interme- diaries [8]. For example, oxidative stress contributes to aging and age-related diseases such as cancer, cardiovascu- lar disease, chronic inflammation, and neurodegenerative disorders. The body has developed a variety of counterac- tive measures for combating oxidative stress. At elevated concentrations of electrophiles the complex Keap1-Nrf2 (made up of the transcription factor Nrf 2 and sensor Keap1) is broken and Nrf2 is liberated and transported into the nucleus. Keap1 has been known to sequester Nrf2 in the cytoplasm and also leads to the proteasomal degra- dation of Nrf2. Once the complex is broken, Nrf2 is phos- phorylated and transported to the nucleus. Inside the nucleus, Nrf2 forms heterodimers with small Maf proteins (SMP) which then binds to the anti-oxidant response element (ARE) and leads to the translation of antioxidant genes, which produces Phase II detoxifying enzymes. The purpose of this is to detoxify the electrophiles to water soluble components. Thus in response to elevated Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 2 of 16 concentrations of electrophiles, various antioxidant pro- teins are activated [9-13]. The schematic diagram for Nrf2 activation is shown in Figure 2. In the rest of this paper, the term ARE will be interchangeably used to represent either the antioxidant response element cis enhancer sequence that is upstream of the gene promoters for the antioxidant proteins or the antioxidant genes/proteins themselves. The context will make it clear whether we are referring to the regulatory sequence or to the resulting gene/protein. We next focus on the procedure by which Nrf 2 is deactivated. This is carried out by other proteins that stop translation of the antioxidant genes once the elec- trophiles have been neutralized. For instance, the Bach1-SMP complex has been known to bind to the same region on the ARE as the Nrf 2-SMP complex. Similarly, small Maf proteins are known to form homo- dimers or heterodimers with other small Maf proteins. These protein complexes are known to bind to the same location on the ARE as the Nrf2-SMP complex. So, once the electrophiles have been eliminated, these protein complexes bind to the ARE and displace Nrf 2 which is then transported back to the cytoplasm. In the cytoplasm, it binds with Keap1, which directs its Figure 1 General scheme of stress response pathways. This figure explains the general flow of information in stress response pathways. Figure 2 Nrf2 Activation. Explains how Nrf2 is activated and how it is able to neutralize the free radicals. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 3 of 16 proteosomal degradation [14-17]. The schematic dia- gram for Nrf2 deactivation is shown in Figure 3. One of the byproducts of normal metabolism is the production of a large number of free radicals. Oxidative stress is caused by the production of free radicals in quanti- ties beyond those that can be handled by the cellular antioxidant system. Indeed, oxidative stress has been impli- cated in the development of many age-related diseases, including neurodegenerative ones, such as Alzheimer’s and Parkinson’s, and in aging itself. In addition, excess free radicals react with the nucleotides in the DNA resulting in mutations in the long run. Although there are cellular mechanisms to sense and repair the oxidative DNA damage, mutations can accumulate over a period of time and result in a major disease like cancer. In the next section, we develop a Boolean network model for oxidative stress response pathways. This network will be later utilized to analyze different failure modes that can supress apopto- sis and possibly lead to cancer. Boolean network modeling of oxidative stress response pathways Before proceeding to the actual modeling of the specific oxidative stress response pathways, we first formally define the general terms ‘pathway’ and ‘Boolean Network’ following the detailed development in [5]. Given two genes/proteins A and B and binary values a, b Î {0, 1}, we define the term pathway segment A t:a,b →B to mean that if gene/protein A assumes the value a then gene/protein B transitions to b in no more than t subsequent time steps. A pathway is defined to be a sequence of pathway segments of the form A t1:a,b →B t2:b,c →C. A Boolean Network (BN), ϒ = (V, F ), on n genes is defined by a set of nodes/genes V = {x1, ..., xn}, xi Î {0, 1}, i = 1, ..., n, and a list F = (f1, ..., fn), of Boolean functions, fi: {0, 1}n ® {0, 1}, i = 1, ..., n [18]. The expression of each gene is quantized to two levels, and each node xi repre- sents the state/expression of the gene i, where xi = 0 means that gene i is OFF and xi = 1 means that gene i is Figure 3 Nrf2 Deactivation. Explains how after neutralizing free radicals Nrf2 is transported back to cytoplasm from mitochondria. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 4 of 16 ON. The function fi is called the predictor function for gene i. Updating the states of all genes in ϒ is done syn- chronously at every time step according to their predictor functions. At time t, the network state is given by x(t) = (x1(t), x2 (t), ..., xn(t)), which is also called the gene activity profile (GAP) of the network. The modeling approach that we will follow here involves using the biological pathway knowledge from the literature and applying Karnaugh map reduction techniques to it to obtain an update equation for each node of the Boolean network [5]. The details specific to the oxidative stress response pathway are discussed next. The pathway segments relevant to the oxidative stress response are given below [9,10,12,15,19,20]: ROS 1:1,0 →K eap1 (1) ROS 1:1,1 →PKC (2) ROS 1:a,¯a →Bach 1 (3) Keap 1 1:b,¯b →Nrf2 (4) Nrf2, ROS 1:(1,0),1 → Keap1 (5) PKC 1:1,1 →Nrf2 (6) Bach1, SMP 1:(1,1),0 → ARE (7) Nrf2, SMP 1:(1,1),1 → ARE (8) SMP, SMP 1:(1,1),0 → ARE (9) ARE 1:1,1 →SMP (10) ARE 1:1,0 →ROS (11) ARE 1:1,0 →PKC (12) In these pathways ARE represents the family of antioxi- dant genes in the sense that if the correct complexes bind to ARE it leads to the up-regulation/down-regulation of the appropriate antioxidant gene. These pathway interac- tions are pictorially represented in Figure 4. In this figure we have used square boxes without making any distinction between whether they represent proteins/genes or a bio- chemical entity. ROS stands for reactive oxidative species which is a biochemical entity. The other entities like PKC, Keap1, Nrf2, Bach1 are all proteins and ARE (Antioxidant Response Element) is a cis enhancer sequence that is upstream of the gene promoters for the antioxidant pro- teins or the antioxidant genes/proteins themselves. Also the merged activation (Nrf2/SMP) or inhibition (Bach1/ SMP) corresponds to dimers formed between these com- ponents. The Karnaugh-maps for the genes/proteins are shown in Figure 5. From the pathways described above and using the Karnaugh-map reduction techniques, the Boolean update equations for each node of the network are deduced. Some logical reasoning has been used for determining the equations: 1) the maximum number of predictors for updating a variable is fixed to be 3; 2) Small Maf Protein is assumed to be ubiquitously expressed and the pathway given by Eqn.(10) only increases the concentration of SMP, which in conjunction with Eqn.(9), binds to ARE and down-regulates the antioxidant gene; 3) a gene being turned on implies that the corresponding protein is being produced although, in reality, this is not necessarily true; and 4) in the case of a conflict in the Karnaugh map, bio- logical knowledge has been used to assign either a 0 or a 1. This last point is demonstrated by a specific example. For instance, in the case of ARE, the entry shown with a grey circle around it says that when both Bach1 and Nrf2 are upregulated and antioxidant gene is downregulated, then at the next time step antioxidant gene will be upregu- lated. The biological explanation for such an update is that it corresponds to the situation where, in the presence of Stress, Nrf2 has been activated and is relocating to the nucleus while the inhibitor Bach1 is simultaneously relo- cating to the cytoplasm prior to the activation of antioxi- dant gene at the next time step. Such intuitive reasoning has been used to model the system here. One might use a different reasoning which could lead to a different set of update equations. However, since we are concerned only about the final steady-state behavior, such reasoning can be justified as long as the overall system behavior, defined by the update equations, matches the steady-state. As an example, the final update equation for ARE is derived as follows. In the K-maps, the ones are grouped up in pairs of 2,4,8 and so on and each group should have at least one variable staying constant. So for this case there are two groups whose equations correspond to Nrf2 · (ARE) and Nrf2 · (Bach1). The final update equation for ARE is the sum of these two equations. Please refer to Additional file 1 for some additional details. Indeed, by working with dif- ferent sets of update equations, we determined that all bio- logically plausible ones led to the same/similar attractor behavior. From the set of possible Boolean networks we chose the ones that appealed most to our biological under- standing and the resulting update equations are given below: ROSnext = Stress · ARE (13) Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 5 of 16 Keap1next = ROS · (Nrf2 + Keap1) (14) PKCnext = ROS · ARE (15) Nrf2next = PKC + Keap1 (16) Bach1next = ROS (17) Figure 4 Oxidative Stress Response Pathways. The major pathways involved in oxidative stress response. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 6 of 16 SMPnext = 1 (18) AREnext = Nrf2 · (ARE + Bach1). (19) An equivalent digital circuit with logic gates is shown in Figure 6. Here the lines in bold represent feedback paths. The state transition diagrams resulting from Eqns. (13)-(19) for the two cases Stress = 0 and Stress = 1 are shown in Figures 7 and 8 respectively. In these transition diagrams, the genes in the binary state representation are ordered as [ROS Keap1 PKC Nrf2 Bach1 ARE] and the binary states are compactly represented by their decimal equivalents. For instance, the binary state (111100) would be represented by the decimal number 60. The states of particular interest are the attractors as they give rise to the steady-state properties of the network. In Figure 7, the state of interest is the singleton attractor 18(010010). On the other hand, in Figure 8, the states of interest are the seven states forming the attractor cycle. These states are: 18(010010), 50(110010), 40(101000), 44(101100), 45(001101), 5(000101) and 23(010111) traversed in that order. They would lead to cyclical/oscillatory behavior in the time domain response. It is clear from the preceding discussion that some kind of oscillatory behavior of the genes will be observed when the external Stress input equals 1. On the other hand, when the Stress input equals 0, the system will rest in only one state meaning that there will be no oscillation. Time domain simulation results The network obtained was simulated using MATLAB by giving an external stress input signal for a duration of 50 timesteps, and both the input signal and the responses are shown in Figure 9. The signal ROS is a biological manifes- tation of the external input signal, Stress being applied to the network. The biological purpose of this network is to counteract the effect of ROS produced in response to the Stress input. As we can see from Figure 9, in the absence Figure 5 Karnaugh Maps for Deriving the Oxidative Stress Response Boolean Network. K-map simplification for all the elements involved in the system. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 7 of 16 Figure 6 Equivalent Boolean Network for Oxidative Stress Response. Boolean network model for oxidative stress response based on the equations derived using K-maps. Figure 7 The Boolean State Transition Diagram when the Stress input is 0. The state transition diagram for the Boolean network with no stress on the system. This gives us an idea of the attractor states of the system. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 8 of 16 of any Stress signal, the system reaches the singleton attractor 18(010010). Once Stress signals are applied, there are oscillations as theoretically expected from the exis- tence of an attractor cycle. In Reichard et al. [14], the cells were treated with Arsenite, a well known activator of Nrf2 and an out-of-phase relationship was observed between Nrf2 and Bach1. Shan et al. [17] also showed a similar out of phase relationship. In Katsuoka et al. [16]DEM (an Figure 8 The Boolean State Transition Diagram when the Stress input is 1. The state transition diagram for the Boolean network with stress on the system. This gives us an idea of the attractor states of the system. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 9 of 16 activator of Nrf2) also leads to increased expression of NQO1 which is a known anti-oxidant response element. Such an in-phase relationship between Nrf2 and the anti- oxidant gene is also seen in Figure 9. Thus the theoretical predictions made by our Boolean network model for oxi- dative stress response appear to be consistent with experi- mental observations from the published literature. Note, however, that these experiments consider only two genes/ proteins at a time and therefore, there is a need for experi- mentally studying the simultaneous activities of ROS, Keap1, Nrf2, PKC, Bach1 and ARE in the time domain. Mitochondria and free radical generation Mitochondria play an important role in cellular energy metabolism, free radical generation and apoptosis. It has long been suspected that mitochondrial functions con- tribute to the development and progression of cancer [21-23]. Over 70 years ago, Otto Warburg proposed that a key event in carcinogenesis is a defect in the respira- tory mechanism, leading to increased glycolysis even in the presence of oxygen;this is known as the Warburg effect [24]. The well known function of mitochondria is to generate Adenosine Triphosphate (ATP) molecules providing energy for the survival of the cell through oxi- dative phosphorylation (OXPHOS), which is collectively accomplished by proteins encoded both by nuclear and mitochondrial DNA. Oxidative phosphorylation is a metabolic process, which takes place in mitochondria in which ATP is formed as a result of the transfer of elec- trons from NADH or FADH2 to O2 by a series of elec- tron carriers. OXPHOS is the major source of ATP as well as free radical generation in aerobic organisms. For example, oxidative phosphorylation generates 26 of the 30 molecules of ATP that are formed when a molecule of glucose is completely oxidized to CO2 and H2O, although 1 to 2% of the electrons are lost during trans- fer through the chains leading to free radical generation [25]. Figure 10 [26] shows a schematic representation of the whole process along with free radical generation. The points shown with red stars correspond to the loca- tions where free radicals are generated. Even though it has been long recognized that increased ROS production in mitochondria leads to genetic instabil- ity and progression of cancer, there remain several unan- swered questions regarding the complex signalling capacity of this organelle [27]. The DNA is highly suscep- tible to free radical attacks. Free radicals can break DNA strands or delete bases. These mutations can prove to be carcinogenic. It has been estimated that more than 10,000 hits of oxidative stress occur each day. So it is important to tackle these free radicals at the source of their genera- tion, which is why the mitochondria is also a very rich source of anti-oxidants. Although cellular mechanisms can tackle this stress, damage accumulates with age. At present Figure 9 Time response behaviour of the system in Fig.4. Time response simulation of the Boolean network to observe oscillations of the proteins in the system. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 10 of 16 altered energy metabolism is considered to be an addi- tional hall mark of cancer progression [28] and these metabolic pathways have been investigated as targets for cancer therapy. In this paper, we will specifically focus on the PI3k/Akt pathway which is one such pathway and is described in the following section. An integrated network for oxidative stress response and apoptosis Cancer is an umbrella term for diseases that are associated with loss of cell-cycle control, leading to uncontrolled cell proliferation and/or reduced apoptosis. It is often caused by genetic alterations leading to malfunctioning in the bio- logical pathways [1,29,30]. One of the possible cellular responses resulting from oxidative stress is the induction of apoptosis. Thus it is important to develop a network model linking the oxidative stress input to the fate of the cell. In this section, we will do precisely that by consider- ing the oxidative stress response pathways alongside other downstream pathways capable of inducing apoptosis. Spe- cifically, we will focus on the PI3k/Akt pathway. The PI3k/ Akt pathway is downstream of the Ras gene which is known to play an important role in many cancers. In addi- tion, other genes in the PI3k/Akt pathways are found mutated in many cases of cancer. Oxidative stress often upregulates many of the genes in the PI3k/Akt pathway. The detailed interactions between the oxidative stress response pathway and the PI3k/Akt pathway are shown in Figure 11 [1,31-33]. Starting with this pathway diagram and utilizing the procedure developed earlier in Section, an equivalent digital circuit in terms of logic gates can be implemented as shown in Figure 12. The above circuit is modeled with two output genes which effectively control the final fate of the cell. Bad and Bcl2 are known to have pro-apoptotic and anti-apoptotic functions respectively and thus can serve as biomarkers of apoptosis induction. Indeed, it is the delicate balance between the activity of these two genes that dictates the ultimate fate of the cell [34-36]. The purpose of the Nrf 2-ARE pathway in this integrated network is to reduce the average value of ROS present in the system, in response to the oxidative stress. This is clear from the plot in Figure 9: between the time instants from the 25th timestep to the 75th timestep when there is a continuous Stress present in the system, the ROS present in the system is oscillating between 0 and 1 which implies that its average value is less than ‘1’, which is the value that we would have otherwise had in the absence of the Nrf 2-ARE pathway. Classification of faults in the integrated network In the integrated pathway diagram of Figure 11, the two genes namely Bad and Bcl2 are instrumental in deciding the fate of the cell. The preferred status of the two genes, when oxidative stress is not being neutralized, are 1 and 0 respectively since it corresponds to the situation where the pro-apoptotic factor is turned ON and the anti-apoptotic factor is turned OFF. Although a devia- tion from this state may not signal that the cell is turn- ing cancerous, there is a higher possiblity of the cell exhibiting aberrant behaviour. Depending on the final resting status of these two genes, one may be able to characterize the degree of invasiveness of the disease especially if it is being caused by apoptosis supression. Once it has been determined that a cell is Figure 10 Stages of Oxidative Phosphorylation producing free radicals. Explains Krebs cycle and how and where free radicals are produced in the mitochondria. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 11 of 16 exhibiting abberant behavior, one would like to pinpoint the location of the fault/error so that the necessary thera- peutic intervention(s) can be applied. Since the digital cir- cuit model of Figure 12 uses logic gates, it should be possible to use the fault detection techniques from the Digital Logic literature [37,38] to pinpoint the fault loca- tions. This will be carried out in this section. An important difference between the results obtained in Layek et al. [6] for pinpointing the fault locations in the MAPKinase path- ways and the results to be presented here is that the digital circuit in Figure 12 involves feedback and its behaviour is, therefore, much more complicated to analyze. However, it should be pointed out that the simpler fault pinpointing methodology presented in Layek et al. [6] is much more amenable to biological validation via appropriately designed experiments while the same cannot be said about the results to be presented here. Indeed, the results to be presented here show that the pinpointing of the fault loca- tions is theoretically possible even in this case, although the biological feasibility of the methods required is open to question. We note that the faults in a digital circuit are mainly of two types [37]: • Stuck-at Faults: As the name implies, this is a fault where a particular line l is stuck at a particular value a Î {0, 1}, denoted by line l,s-a-a (s-a-a means stuck-at-a). This means that the value at that line is always going to be a regardless of the inputs coming in. This can be thought of as something similar to a mutation in a gene, where a particular gene is either permanently turned ON or OFF. • Bridging Faults: This is the type of fault where new interconnections are introduced among elements of the network. This can be thought of as new pathways being created in the cell. This type of fault is not con- sidered in the current paper due to the lack of biologi- cal knowledge about new pathways being introduced. Here, it is appropriate to mention that the biological relevance of each of these two types of faults has been discussed in Layek et al. [6]. Figure 11 Pathway Diagram of Oxidative Stress along with PI3k/Akt. Inclusion of PI3k/Akt pathways along with oxidative stress pathways and study how they can lead to aberrant be-haviour in cells. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 12 of 16 The digital circuit in Figure 12 has feedback (shown in bold lines) and is, therefore, a sequential circuit. To detect a fault in a sequential circuit we need a test sequence. Let T be a test sequence and let R(q,T) be the response of the fault-free sequential system N starting in the intial state q. Now let the faulty sequential circuit be denoted by Nf where f is the fault. Let us denote by Rf (qf,T) the response of Nf to T starting in the initial state qf. A test sequence T detects a fault f iff (if and only if or equivalently this condition is both necessary and suf- ficient) for every possible pair of initial states q and qf, the output sequences R(q,T) and Rf (qf ,T) are different for some specified vector ti Î T. The output being observed is the status of [Bad, Bcl2]. Once this output shows a deviation from a desired value, it becomes imperative to pinpoint the possible fault loca- tions which can give rise to the aberrant behaviour. To do so, one can represent the digital circuit of Figure 12 as in Figure 13. The Primary Input(PI) is Stress which is the only external signal which the experimenter has control over. The Primary Output’s (PO’s) are the status of Bad and Bcl2, which are the only outputs available to the experimenter. The Secondary Output’s and Secondary Input’s are [ARE, Keap1, Mdm2], which are being fed back into the system. The states of these 3 genes ARE, Keap1 and Mdm2 determine the internal state of the system. These 3 elements can be considered as memory elements of the system as their previous state is retained by the system and fed back. The input sequence consists of two parts namely a Homing sequence and a Test sequence, denoted by H and T respectively. The purpose of this procedure is to pinpoint the possi- ble locations for the fault f in Nf, given the output sequence of Bad and Bcl2 for the normal and faulty cir- cuits. It is assumed that we have no knowledge about the initial status of any of the genes. Knowledge of the initial status of the internal states is important as all future computations are based on these values. The Homing sequence is an initial input sequence that brings the net- work to a known internal state. So, once the Homing Sequence is given to N and Nf, N will come to a known internal state. Note that a similar claim cannot be made about Nf as the fault f is not known apriori. For the cir- cuit in Figure 13, a possible Homing sequence is [0 0 0 0 0 0 0 0], which brings the internal state of the system to [0 1 0]. This means that if the Stress input is zero for eight time steps, then at the end of that period, the inter- nal state of the system becomes [0 1 0], regardless of the initial status of any of the genes in the network. A reason for choosing this Homing sequence is that it implies that no input needs to be given to the system and it evolves to the indicated internal state. In future when we are trying to validate these results experimentally this will be of immense help. If we refer back to Figure 7, we see that regardless of the initial state, within four time steps the trajectory reaches the state (’010010’) where ARE = 0 and Figure 12 Boolean Network modeling of Fig. 11. A Boolean network model of the network along with PI3k/Akt pathways. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 13 of 16 Keap1 = 1. This is consistent with the conclusion that we are getting from the Homing sequence here with the only difference that a slightly longer sequence is required here as the state transition diagram has a higher cardinality than that in Figure 7. Once the Homing sequence has done its job, the Test sequence(T) is fed into N and Nf, and by comparing the output states of the normal and faulty networks, we can pinpoint the location of the fault in the network, assuming that a single stuck-at-fault has occurred. This can be car- ried out using the time-frame expansion method which is briefly discussed next. The block in Figure 13 is replicated n times with the feedback loops cut-off. The Secondary Output of the kth stage is fed as the Secondary Input for the (k + 1)th stage. The Primary Outputs of the first (n - 1) stages are neglected. The Primary Outputs of the nth stage of the normal and faulty circuits will be different as the network configurations are different for both. The Primary Input sequence has to be derived so that the error in a line is propagated to the primary output in n time steps, so that a difference is observed at the primary outputs of the normal and faulty circuits [37,38]. The situation is picto- rially represented in Figure 14. Please refer to Additional file 1 for to y example. From the preceding discussion in this section, we know that there are 15 possible genes (this is the total number of genes in Figure 11, excluding the output genes Bad and Bcl2) where there could be a mutation. This means that there are 30 cases of faults as a single gene can be mutated as a s-a-0 or as a s-a-1. We consider all possible cases of single mutation, because in the presence of mutation, the normal and faulty system cannot produce the same output unless, of course, the mutated gene is not a critical one. Based on the methods described earlier in this section, we came up with a list of test sequences for the detection of each gene fault. It is to be noted that the Test Sequences generated here are only for the Hom- ing Sequence considered earlier. For a different Homing Sequence the Test Sequence will also be different. The different test sequences and their ability to detect differ- ent single stuck-at faults are tabulated in Figure 15. Here, truncated versions of the same test sequence can be used to detect different faults appearing in the same row. For detecting any particular fault, one would apply the test sequence from the same row truncated at the bit whose color matches that of the particular fault. The mismatch between the outputs of the normal and faulty systems, characterized by the vector [Bad, Bcl2] would then result in the detection of that fault. Thus we have developed a method to pinpoint the possible fault locations in a Boo- lean network with feedback. The algorithm will work with multiple fault cases too with minor modifications. Concluding remarks In this paper, we have developed a Boolean network model for the oxidative stress response. This model was developed based on pathway information from the cur- rent literature pertaining to oxidative stress. Where applicable, the behaviour predicted by the model is in agreement with experimental observations from the published literature. It is our hope that some of the additional predictions here, such as those pertaining to Figure 13 Block Diagram Representation of Fig.12. A simple description of the system showing clearly the feedback lines in the system. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 14 of 16 the oscillatory behaviour of certain genes in the pre- sence of oxidative stress, will be experimentally validated in the near future. We have also linked the oxidative stress response to the phenomenon of apoptosis via the PI3k/Akt pathway. An integrated model based on collectively considering the PI3k/Akt pathways and the oxidative stress response pathways was developed and then used to pinpoint pos- sible fault locations based on the Bad-Bcl2 apoptotic signatures in response to ‘test’ oxidative stress inputs. The approach used to achieve this differs significantly from the earlier results in Layek et al. [6] since the Boo- lean network of this paper has feedback. The approaches used here and in Layek et al. [6] could potentially have a significant effect on cancer therapy in the future as pinpointing the possible fault location(s) in cancer could permit the choice of the appropriate combination of drugs (such as kinase inhibitors) for maximum thera- peutic effectiveness. Of course, it should be pointed out that the theoretical procedure presented here for pin- pointing fault locations in a biological network with feedback will need to be further simplified before it can be even considered for practical biological validation. Additional material Additional file 1: Explains the algorithms discussed in the manuscript with toy examples. Acknowledgements Based on “Modelling oxidative stress response pathways”, by Sriram Sridharan, Ritwik Layek, Aniruddha Datta and Jijayanagaram Venkatraj which appeared in Genomic Signal Processing and Statistics (GENSIPS), 2011 IEEE International Workshop on. © 2011 IEEE [39]. This work was supported in part by the National Science Foundation under Grants ECCS-0701531 and and ECCS-1068628 and in part by the J. W. Runyon, Jr. ‘35 Professorship II Endowment Funds at Texas A & M University. This article has been published as part of BMC Genomics Volume 13 Supplement 6, 2012: Selected articles from the IEEE International Workshop Figure 14 Fault Detection using Time-Frame Expansion. Fault detection in the boolean(digital) network using time-frame expansion method. Figure 15 Test Sequences for detecting single stuck-at-faults. The test sequence which can be given to system to find out single stuck-at- faults based on output signature. Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 15 of 16 on Genomic Signal Processing and Statistics (GENSIPS) 2011. The full contents of the supplement are available online at http://www. biomedcentral.com/bmcgenomics/supplements/13/S6. Author details 1Texas A & M University, Electrical and Computer Engineering, College Station, TX, 77843-3128, USA. 2Texas A & M University, Vet Integrative Biosciences, College Station, TX, 77843-4458, USA. Authors’ contributions Sriram Sridharan did most of the theoretical work on this paper with some assistance from Ritwik Layek. Aniruddha Datta provided overall direction and supervision while Jijayanagaram Venkatraj provided the relevant supporting biological domain knowledge. Competing interests The authors declare that they have no competing interests. Published: 26 October 2012 References 1. Weinberg RA: The Biology of Cancer. Garland Science, Princeton;, 1 2006. 2. Datta A, Dougherty E: Introduction to Genomic Signal Processing with Control Boca Raton: CRC Press; 2007. 3. Viswanathan GA, Seto J, Patil S, Nudelman G, Sealfon SC: Getting Started in Biological Pathway Construction and Analysis. PLoS Comput Biol 2008, 4: e16. 4. 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Genomic Signal Processing and Statistics (GENSIPS), 2011 IEEE International Workshop on: 4-6 December 2011 2011, 166-169. doi:10.1186/1471-2164-13-S6-S4 Cite this article as: Sridharan et al.: Boolean modeling and fault diagnosis in oxidative stress response. BMC Genomics 2012 13(Suppl 6): S4. Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color ﬁgure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit Sridharan et al. BMC Genomics 2012, 13(Suppl 6):S4 http://www.biomedcentral.com/1471-2164/13/S6/S4 Page 16 of 16	23134720	ARE = ( ( ( ( Nrf2 ) AND NOT ( GSK3b ) ) AND NOT ( Bach1 ) ) AND NOT ( ARE ) ) Ras = ( ROS ) PTEN = NOT ( ( ROS ) ) Akt = ( PIP3 ) p53 = ( ( ATM ) AND NOT ( Mdm2 ) ) Bad = NOT ( ( Akt ) ) PI3K = ( Ras ) Nrf2 = ( ( Akt ) OR ( PKC ) ) OR NOT ( Akt OR Keap1 OR PKC ) Keap1 = ( ( Keap1 ) AND NOT ( Bach1 ) ) OR ( ( Nrf2 ) AND NOT ( Bach1 ) ) PIP3 = ( ( PIP2 ) AND NOT ( PTEN ) ) Mdm2 = ( ( Akt ) AND NOT ( ATM ) ) OR ( ( p53 ) AND NOT ( ATM ) ) ROS = ( ( Stress ) AND NOT ( ARE ) ) GSK3b = NOT ( ( Akt ) ) Bach1 = NOT ( ( ROS ) ) PIP2 = ( PI3K ) PKC = ( ROS AND ( ( ( NOT ARE ) ) OR ( ( NOT ARE ) ) ) ) Bcl2 = NOT ( ( Bad ) OR ( p53 ) ) ATM = ( ROS )
ORIGINAL RESEARCH ARTICLE published: 10 December 2012 doi: 10.3389/fphys.2012.00446 Boolean model of yeast apoptosis as a tool to study yeast and human apoptotic regulations Laleh Kazemzadeh1,2, Marija Cvijovic 1,3* and Dina Petranovic 1* 1 Department of Chemical and Biological Engineering, Chalmers University of Technology, Gothenburg, Sweden 2 Digital Enterprise Research Institute, National University of Ireland, Galway, Ireland 3 Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden Edited by: Matteo Barberis, Humboldt University Berlin, Germany; Max Planck Institute for Molecular Genetics, Berlin, Germany Reviewed by: Ioannis Xenarios, SIB Swiss Institute of Bioinformatics, Switzerland Abhishek Garg, Harvard University, USA Correspondence: Marija Cvijovic, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Chalmers tvärgata 3, Göteborg 412 96, Sweden. e-mail: marija.cvijovic@chalmers.se; Dina Petranovic, Department of Chemical and Biological Engineering, Chalmers University of Technology, Kemivägen 10, Göteborg SE-412 96, Sweden. e-mail: dina.petranovic@chalmers.se Programmed cell death (PCD) is an essential cellular mechanism that is evolutionary con- served, mediated through various pathways and acts by integrating different stimuli. Many diseases such as neurodegenerative diseases and cancers are found to be caused by, or associated with, regulations in the cell death pathways.Yeast Saccharomyces cerevisiae, is a unicellular eukaryotic organism that shares with human cells components and pathways of the PCD and is therefore used as a model organism. Boolean modeling is becoming promising approach to capture qualitative behavior and describe essential properties of such complex networks. Here we present large literature-based and to our knowledge ﬁrst Boolean model that combines pathways leading to apoptosis (a type of PCD) in yeast. Analy- sis of the yeast model conﬁrmed experimental ﬁndings of anti-apoptotic role of Bir1p and pro-apoptotic role of Stm1p and revealed activation of the stress protein kinase Hog propos- ing the maximal level of activation upon heat stress. In addition we extended the yeast model and created an in silico humanized yeast in which human pro- and anti-apoptotic reg- ulators Bcl-2 family andValosin-contain protein (VCP) are included in the model.We showed that accumulation of Bax in silico humanized yeast shows apoptotic markers and that VCP is essential target of Akt Signaling. The presented Boolean model provides comprehen- sive description of yeast apoptosis network behavior. Extended model of humanized yeast gives new insights of how complex human disease like neurodegeneration can initially be tested. Keywords: apoptosis, Boolean modeling, Stm1, Bir1, Hog1,VCP, Bcl-2 family INTRODUCTION Apoptosis is a complex process which is strictly under control of several regulatory networks. Any kind of malfunctioning in these controlling systems due to insufﬁcient or excessive apoptosis sig- nal can potentially lead to threatening diseases such as various types of cancer and neurodegenerative disorders. Therefore keep- ing this process tightly regulated is important for the cell. Even though apoptosis is often studied in multicellular organisms, the discovery of yeast apoptosis in 1997 (Madeo et al., 1997) attracted the attention of the wide research community (Frohlich et al., 2007; Owsianowski et al., 2008; Madeo et al., 2009; Carmona- Gutierrez et al., 2010b). As in other multicellular organisms the apoptosis in yeast is triggered by both internal and external sig- nals. In yeast,the external signals can include acetic acid (Ludovico et al., 2001, 2002), salts, metal ions, ethanol, osmotic stress, heat stress (Madeo et al., 2009), lipids (Aerts et al., 2008; Low et al., 2008; Garbarino et al., 2009), mating pheromone (Zhang et al., 2006), different pharmacological molecules, and drugs (Almeida et al., 2008). Internal signals can include, ammonium, NO, ROS (that can be generated within the cell by mitochondria and the ER, and also induced by H2O2 addition (Madeo et al., 1999) and other factors), damage (proteins, lipids, nucleic acids) as a consequence of aging and mutations (Mazzoni et al., 2005; Wein- berger et al., 2005; Hauptmann et al., 2006), as well as expression of heterologous proteins, such as human pro-apoptotic proteins (Eisenberg et al., 2007). Many proteins residing in the cytoplasm, nucleus,mitochondria,ER,peroxisomes,and lysosomes have been identiﬁed as the regulators of apoptosis. For example, proteoly- sis is one of the main steps that leads to execution of cell death and, a yeast metacaspase Yca1p has been shown to be central for most (but not all) cell death scenarios (Madeo et al., 2002, 2009). Besides degradation of proteins, degradation of nucleic acids is also carried out during apoptotic death and one of the two important caspase-independent mediators is Nuc1p (homolog of endonuclease G; Buttner et al., 2007). The second is Aif1p (apoptosis-inducing factor; Wissing et al., 2004) that is together with Nuc1p released from the mitochondrion and translocated to the nucleus during the initiation and execution of apopto- sis. The regulation of apoptosis in the nucleus, is achieved via pro-apoptotic factor Nma111p (nuclear mediator of apoptosis; Fahrenkrog et al., 2004) a serine protease that cleaves an anti- apoptotic factor (inhibitor of apoptosis, IAP) Bir1p, which is the only known IAP in yeast, and its anti-apoptotic mechanisms (known to beYCA1-independent) are not well characterized (Wal- ter et al., 2006). To understand how large and complex network of apoptosis process is regulated it should be studied as a whole allowing identiﬁcation of the properties essential for biological function (Janes et al., 2005). To complement experimental studies www.frontiersin.org December 2012 \| Volume 3 \| Article 446 \| 1 Research Topic: From structural to molecular systems biology: experimental and computational approaches to unravel mechanisms of kinase activity regulation in cancer and neurodegeneration Kazemzadeh et al. Boolean model of yeast apoptosis mathematical models are often use permitting systematic analysis of the network components either individually or jointly (Wolken- hauer,2002; Stelling,2004). In Boolean networks (BN) introduced by Kauffman (1969) these assumptions are made based on activa- tion/inhibition effects of one node on another downstream node. The Boolean “on” state (or 1 state or “true” state) can be translate to biological active state of speciﬁc species, while “off” state (or 0 state or “false” state) corresponds to inactive state. With sim- ple logical rules (AND, OR, and NOT) it is possible to capture system’s behavior in a discrete manner without being dependent on experimental measurements such as molecular concentration or kinetic rates. This type of model implementation is becom- ing more common in biology (Handorf and Klipp, 2012) and examples include various model organisms and processes, rang- ing from cell cycle models of simple ﬁssion yeast (Davidich and Bornholdt, 2008), to complex dynamic analysis of mammalian cell cycle (Fauré et al., 2006), study of mammalian neurotrans- mitter signaling pathway (Gupta et al., 2007), investigation of irreversible mammalian apoptosis and stable surviving (Mai and Liu, 2009), and model of apoptosis in human (Schlatter et al., 2009). In each of these studies different extensions of Boolean modeling is implemented giving clear indication of the grow- ing application of logic based modeling in qualitative studies of biological networks where there is not much quantitative data available. We describe here a model based on Boolean network approach that consists of two parts: in the ﬁrst part construction and the evaluation of the yeast apoptosis Boolean model is intro- duced and in the second part we propose the use of established model for study of human apoptotic proteins in yeast. Simplic- ity of BN allowed us to construct the model that integrates vast amount of heterogeneous knowledge that currently exists for yeast apoptosis. The major purpose of this study is to understand the emergence of systems properties. Extensive analysis of the state space in combination of different input signals generated series of in silico experiments. Simulating knock out experiments we were able to test the function of speciﬁc feedback structures in apoptotic network. The results were compared with the exist- ing experimental data and the model was used to explore several hypotheses in order to better understand certain apoptotic mech- anisms and to suggest new strategies for further experimental studies. RESULTS NETWORK TOPOLOGY The constructed yeast apoptosis network contains 73 species and 115 reactions (Table 1). Six species do not have succes- sor (Sink/Output) or predecessor (Source/Input; Table 2). In the schematic diagram (Figure 1) species are represented as nodes and reactions as edges. Species include: processes, proteins, and small molecules (metabolites or signals) and Reactions include activa- tion (green arrow) and inhibition (red arrow). Nine nodes depict inputs to the model and are colored blue. Seventeen elements are active in nucleus and are shown in gray, 12 mitochondria species are shown in yellow, and 34 orange boxes represent species resid- ing in cytoplasm. System has only one output node which is called “Apoptosis” and it is in dark blue. Filled blue circles are used as an “AND” gates between two or more reactions to indicate the necessity of presence of two species for activation or inhibition of a reaction (Figure 1). Network is activated via input signals corresponding to the fol- lowing species: Acetic Acid, Heat, H2O2, Adozelesin, Mg2+, Cu2+, Salt (NaCl), mating, and osmotic stress. MODEL PROPERTIES Like many molecular mechanisms in living cells, apoptosis can be approximated as an outcome of sequential regulation steps which do not occur all at the same time. As a result, upon induction, the state of the cell changes with passing time. In order to cap- ture this feature, each reaction was assigned activation time scale implicating occurrences of different scenarios in sequential order. By introducing time delays to the logical function, it is possible to describe dynamic behavior of the given process using logical networks (Thomas and D’Ari, 1990). For this study we used Cell Net Analyser (CNA; Klamt et al., 2006) which provides the function to capture signal propagation in a time series to get a snapshot of the network and discrim- ination of signaling events. This approach has been successfully used to model human apoptotic network revealing new feedback loops (Schlatter et al., 2009). To describe dynamic behavior of the yeast apoptosis ﬁve timescales t = [0, 2, 4, 5, 6] are assigned. These timescales are constants and indicate at which timescale each node gets activated or inhibited. Simulation of the network at t = x comprises of all interactions with timescale t ≤x but not interactions with t ≥x. This gives the possibility of separation of different functional groups such as different signaling pathways or feedback loops. It should be noted that speciﬁed timescales do not refer to real time but are only indicators of sequential regu- latory steps (difference between timescale t = 0 and t = 2 is equal to difference between timescales t = 2 and t = 4 or t = 4 and t = 5 or between t = 5 and t = 6). Timescales are not assigned based on speed of reactions (how fast or slow reactions are), they are assigned based on the sequence of events. To allow ﬂexibility in our model and facilitate changes and insertions of new events timescales 1 and 3 are reserved and not used in the current net- work structure. First timescale t = 0 is assigned to genes which are already present and constantly active in cell (27 reactions). Values for all input arcs to stimuli species are set to 1 at second timescale t = 2 (53 reactions). Further interactions are activated at time t = 4 (17 reactions). Although yeast apoptosis does not contain any feedback loops time point t = 5 is reserved for feed- back loops which get activated in response to osmotic and heats shock and will lead to apoptosis. Considering impact of feed- back loops on system behavior it is reasonable to assign them a separate timescale. Finally interaction occurring at the very end are assigned timescale t = 6 (18 reactions). Details on each reac- tion, their time points and species involved in reactions are in Table 3. The model simulated the induction of apoptosis both in the independent mode (assessing each individual stimulus separately) as well as in the additive mode, where the activation of all inputs were set at the same time (Table 4). Frontiers in Physiology \| Systems Biology December 2012 \| Volume 3 \| Article 446 \| 2 Kazemzadeh et al. Boolean model of yeast apoptosis Table 1 \| List of species in yeast Boolean model. ID Species Type Name description 1 ABNORMALTELOMERASE Change ABNORMALTELOMERASE 2 ACETIC ACID Input Chemical 3 ADENYLATECYCLASE Enzyme Lyase enzyme 4 ADOZELESIN Input Drug 5 AIF-MT Protein Apoptosis-inducing factor in mitochondria 6 AIF-NUC Protein Apoptosis-inducing factor in nucleus 7 APOPTOSIS Output Cell death 8 BIR1 Protein Baculoviral IAP repeat-containing protein 1 9 CAMP Protein Cyclic adenosine monophosphate 10 CDC48 Protein Cell division cycle 11 CDC6 Protein Cell division cycle 12 CPR3 Protein Cyclosporin-sensitive proline rotamase 13 CU2 Input Ion 14 DesCYCLINCCDK8 Change Destruction of cylinC/CDCk8 15 CYTC-CYT Protein CytochromC in cytososl 16 CYTC-MT Protein CytochromC in mitochondria 17 DNA-FRAG Change DNA fragmentation 18 DRE2/TAH18 Change Dre2-TAH18 complex 19 EMC4 Protein ER membrane protein complex 20 ESP1 Protein Separase 21 FIS1 Protein Mitochondrial FISsion 22 FYV10 Protein Function required for yeast viability 23 H2B Protein Histon 2B 24 H2O2 Input Hydroxide peroxide 25 HEAT Input Event 26 HK – House keeping function* 27 HOG1 Protein High osmolarity glycerol response 28 HOG1-DEP Protein HOG1 dependent genes 29 HOS3 Protein Hda one similar 30 KAP123 Protein KAryoPherin 31 MAPK Protein Map kinase cascade 32 MATING Input Mating pheromone 33 MCD1-MT Protein Mitotic chromosome determinant in mitochondria 34 MCD1-NUC Protein Mitotic chromosome determinant in nucleus 35 MDV1 Protein Mitochondrial DiVision 36 MEC1 Protein Mitosis entry checkpoint 37 MG2 Input Ion 38 MMI1 Protein Translation machinery associated 39 MSN2-4 Protein Multicopy suppressor of SNF1 mutation 40 MT-ALT Change Mitochondria alteration 41 MT-FRAG Change Mitochondria fragmentation 42 NDI1 Protein NADH dehydrogenase internal 43 NMA111-CYT Protein Nuclear mediator of apoptosis in cytososl 44 NMA111-NUC Protein Nuclear mediator of apoptosis in nucleus 45 NUC1-MT Protein NUClease 1 in mitochondria 46 NUC1-NUC Protein NUClease 1 in nucleus 47 PKA Protein Protein kinase A 48 POR1-2 Protein PORin 49 PROTOSOM Complex PROTOSOM 50 PTP2 Protein Protein tyrosine phosphatase (Continued) www.frontiersin.org December 2012 \| Volume 3 \| Article 446 \| 3 Kazemzadeh et al. Boolean model of yeast apoptosis Table 1 \| Continued ID Species Type Name description 51 PTP3 Protein Protein tyrosine phosphatase 52 RAS2 Protein Homologous to RAS proto-oncogene 53 RedActinDyn Change Reduced actin dynamic 54 RLM1 Protein Resistance to lethality of MKK1P386 overexpression 55 ROS-CYT Molecule Reactive oxygen species in cytososl 56 ROS-MT Molecule Reactive oxygen species in mitochondria 57 RPD3 Protein Reduced potassium dependency 58 SALT Input – 59 SDP1 Protein Stress-inducible dual speciﬁcity phosphatase 60 SLT2 Protein SYNtaxin (SYN8) 61 SNO1 Protein SNZ proximal open reading frame 62 SOD1 Protein Superoxide dismutase 63 SOD2 Protein Superoxide dismutase 64 SRO7 Protein Suppressor of rho3 65 STE20-CYT Protein Sterile in cytosol 66 STE20-NUC Protein Sterile in nucleus 67 STM1-CYT Protein Translation initiation factor (TIF3) in cytososl 68 STM1-NUC Protein Translation initiation factor (TIF3) in nucleus 69 STRESS Input Event 70 SVF1 Protein SurVival factor 71 TAT-D Protein 3′ →5′ exonuclease and endonuclease 72 TOR1 Protein Target of rapamycin 73 YCA1 Protein MetaCAspase Table includes name, type, and description of each species involved in yeast apoptosis. Species refers to all types of nodes that are depicted in the network map and are color coded based on their location or activity in cell. *Housekeeping function refers to those genes which are present and give snapshot of state of the cell before applying any kind of treatment. Table 2 \| Summary of the interactions without successor (Sink/Output) and predecessor (Source/Input). Species Type of connection Number of connections Ros-MT Sink/output 1 MCD1-NUC Sink/output 1 H2B Sink/output 5 CAMP Sink/output 2 RedActinDyn Source/input 3 AbnormalTelomer Source/input 1 HK Source/input 18 Table contains species without successor (there are no edges coming out of these nodes) and predecessor (there are no edges going to these nodes). PREDICTIONS WITH THE CONTINUOUS MODEL Based on qualitative knowledge we have constructed a discrete Boolean model of yeast apoptosis. While it can capture its essen- tial behavior,the question remained how this model can be used to predict the qualitative behavior of the system. In order to address this question we expanded the model by transforming the discrete Boolean model into a continuous model using Odefy (Wittmann et al., 2009; Krumsiek et al., 2010; see Materials and Methods). In order to test the continuous model and its predictive capac- ity, we performed three independent case-studies: (i) induction of apoptosis by activation of Hog1p by heat stress, (ii) inhibition by Bir1p of acetic acid-induced apoptosis, and (iii) induction of apoptosis with H2O2 by activation of Stm1p. We show here that the behavior that emerges from speciﬁc interactions in the model is in agreement with published experimental data. ACTIVATION OF HEAT STRESS-INDUCED APOPTOSIS WITH Hog1p We simulated the activation of the mitogen-activated protein kinase that is a key component of the HOG pathway (Albertyn and Hohmann, 1994; Van Wuytswinkel et al., 2000; Hohmann, 2002; de Nadal et al., 2004), which is an osmoregulatory sig- nal transduction cascade (Hohmann, 2009). Upon stress, Hog1p (encoded by HOG1/YLR113W) regulates the expression of almost 600 genes by phosphorylating several different transcription fac- tors (Hohmann, 2002; Westfall et al., 2004). The activity and nuclear localization of Hog1p is regulated by its phosphorylation state,and that in turn is regulated by the kinase MAPKK Pbs2p and the phosphatases Ptc1p, Ptc2p, Ptc3p, Ptp2p, and Ptp3p (Brewster et al., 1993; Ferrigno et al., 1998; Warmka et al., 2001; Young et al., 2002). Besides the induction by osmotic stress, the HOG path- way can be induced by heat stress, via a Sho1p-dependent sensory mechanism (Winkler et al., 2002), thus we used heat stress as an input to activate the HOG pathway and simulate the cell death response. Heat stress activates Slt2 which then activates Rlm1. Consequently Rlm1 triggers expression of Slt2 and PTP2 form- ing a feedback loop. On the other hand heat shock inhibits activity Frontiers in Physiology \| Systems Biology December 2012 \| Volume 3 \| Article 446 \| 4 Kazemzadeh et al. Boolean model of yeast apoptosis FIGURE 1 \| Schematic representation ofYeast Apoptosis network. Blue boxes depict input nodes, yellow nodes are placed in mitochondria, orange nodes reside in cytosol and grey nodes belong to nucleus. Green arrows show activation effect and red arrows show inhibition effect. Blue circles depict “AND” gate. of PKA leading to release the inhibition effect of PKA on MSN2- 4. MSN2-4 activates Sdp1 which then along with PTP2 inhibit Slt2. We started by setting all other stimuli to zero and then by transforming the Boolean apoptosis model into Hill Cube contin- uous model we performed the simulations. Steady states predicted from continuous Hill Cube (Figure 2) and synchronous Boolean (Figure 3) model are in perfect agreement with each other for all nodes apart from the nodes corresponding to the feedback loops in response to heat and osmotic stress. Feedback loop in heat acti- vated pathway includes activation of Rlm1 by Slt2 and expression of Slt2 by Rlm1. Osmotic shock induced Hog1 activates Rlm1 to regulate Slt2 which was inhibited by osmotic shock and PTP2. Unknown Hog1 dependent transcription factor triggers transcrip- tion of PTP3 and PTP2 resulting in dephosphorylation of Hog1 phosphotyrosine which inhibits Hog1 activities. All nodes in our model were connected to activation of apoptosis via the heat shock pathway and were indeed activated in our simulation and are col- ored in red; other pathways are colored in blue indicating that they are not activated during the simulation (Figure 2). Model predicts that upon heat induction, concentration of Hog1p changes trough time never reaching its maximum level of concentration and as an intensity of stimulus decreases level of Hog1p also decreases. Our simulations also proposed that the maximal level of activation of Hog1p during heat stress is 70% of the total activation and as the heat stimulus continues over time its activity decreases and reaches a plateau at 40% of total activation (Figure 4). This model prediction is in agreement with an experimental measurement performed by Winkler et al. (2002) which shows the induced activity of Hog1p upon heat induction (Figure 4). The difference between the maximal activity values and the lag phase of the activation is due to the fact that we did not use any quantitative data as input to the model. INHIBITION OF ACETIC ACID-INDUCED APOPTOSIS WITH Bir1p Even though there are several genes and pathways that are involved in yeast pro-apoptotic response, there are only few anti-apoptotic genes. For many years Bir1p (encoded by BIR1/YJR089W) was thought to be the only apoptotic inhibitor in yeast, but recently a TSC22-protein family was found and two of the proteins with TSC22-motif have been shown to have anti-apoptotic roles Sno1p and Fvy10p (Khoury et al., 2008). Bir1 belongs to the IAP family and phylogenetic analysis (Uren et al., 1998) showed similarity to Schizosaccharomyces pombe BIR1, human survivin, and Caenorhabditis elegance BIR-1 and BIR-2 proteins. Yeast’s www.frontiersin.org December 2012 \| Volume 3 \| Article 446 \| 5 Kazemzadeh et al. Boolean model of yeast apoptosis Table 3 \| List of logical interactions in yeast Boolean model. ID Interaction Function Time scale Reference 1 HK =AIF1-MT Housekeeping 0 2 HK = DRE2/TAH18 Housekeeping 0 3 HK = EMC4 Housekeeping 0 4 HK = SVF1 Housekeeping 0 5 HK = FVY10 Housekeeping 0 6 HK = SOD2 Housekeeping 0 7 HK = SNO1 Housekeeping 0 8 HK = NDI1 Housekeeping 0 9 HK = POR1-2 Housekeeping 0 10 HK = MMI1 Housekeeping 0 11 HK = MCD1-MT Housekeeping 0 12 HK = SRO7 Housekeeping 0 13 HK = CDC48 Housekeeping 0 14 HK = FIS1 Housekeeping 0 15 HK = MDV1 Housekeeping 0 16 HK = STM1-CYT Housekeeping 0 17 =AceticAcid Input 2 18 =Adozelesin Input 2 19 =CU2 Input 2 20 =H2O2 Input 2 21 =Mating Input 2 22 =MG2 Input 2 23 =Salt Input 2 24 =Heat Input 2 25 =Stress Input 2 26 !SOD2 + NDI1 = ROS-MT 4 Li et al. (2006) 27 AceticAcid = CytC-MT 4 Ludovico et al. (2002) 28 CDC48 = CytC-CYT 4 Eisenberg et al. (2007) 29 CytC-CYT =YCA1 4 Eisenberg et al. (2007) 30 CytC-MT = CytC-CYT 4 Eisenberg et al. (2007) 31 MCD1-MT = CytC-MT 4 Yang et al. (2008) 32 MEC1 =YCA1 4 Weinberger et al. (2005) 33 MT-Frag = MT-ALT 4 Wissing et al. (2004) 34 !FYV10 =Apoptosis 4 Khoury et al. (2008) 35 2 CDC48 = ROS-CYT 4 – 36 CU2 + CPR3 =Apoptosis 4 Liang and Zhou (2007) 37 DNA-Frag =Apoptosis 4 Madeo et al. (2009) 38 ESP1 = ROS-CYT 4 Yang et al. (2008) 39 MT-Frag =YCA1 4 Eisenberg et al. (2007) 40 NMA111-CYT = NMA111-NUC 4 Walter et al. (2006) 41 NUC1-MT = KAP123 4 Buttner et al. (2007) 42 RAS2 =AdenylateCyclase 4 Wood et al. (1994) 43 RAS2 = ROS-CYT 4 Kataoka et al. (1984) 44 RedActinDyn = ROS-CYT 4 Eisenberg et al. (2007) 45 RedActinDyn =YCA1 4 Madeo et al. (2009) 46 ROS-CYT =Apoptosis 4 Eisenberg et al. (2007) 47 ROS-CYT =YCA1 4 Madeo et al. (2002) 48 Salt = ROS-CYT 4 Wadskog et al. (2004) 49 SOD1 = ROS-CYT 4 Eisenberg et al. (2007) 50 STE20-NUC = H2B 4 Madeo et al. (2009) (Continued) Frontiers in Physiology \| Systems Biology December 2012 \| Volume 3 \| Article 446 \| 6 Kazemzadeh et al. Boolean model of yeast apoptosis Table 3 \| Continued ID Interaction Function Time scale Reference 51 Stress = RPD3 4 Ahn et al. (2006) 52 Tat-D = DNA-Frag 4 Qiu et al. (2005) 53 !SNO1 =Apoptosis 4 Khoury et al. (2008) 54 AbnormalTelomer = MEC1 4 Weinberger et al. (2005) 55 AdenylateCyclase = CAMP 4 Schmelzle et al. (2004) 56 Adozelesin = CDC6 4 Blanchard et al. (2002) 57 AIF1-MT =AIF1-NUC 4 Wissing et al. (2004) 58 AIF1-NUC = H2B 4 Wissing et al. (2004) 59 Apoptosis = Output 4 – 60 CDC6 = Protosom 4 Blanchard et al. (2002) 61 ESP1 = MCD1-NUC 4 Yang et al. (2008) 62 H2O2 = NUC1-MT 4 Buttner et al. (2007) 63 H2O2 = ESP1 4 Yang et al. (2008) 64 H2O2 = HOS3 4 Carmona-Gutierrez et al. (2010a) 65 Heat = NMA111-CYT 4 Walter et al. (2006) 66 HOS3 = H2B 4 Carmona-Gutierrez et al. (2010a) 67 KAP123 = NUC1-NUC 4 Buttner et al. (2007) 68 MAPK = STE20-CYT 4 Carmona-Gutierrez et al. (2010a) 69 MatingPheromone = MAPK 4 Carmona-Gutierrez et al. (2010a) 70 Mg2+ =Tat-D 4 Qiu et al. (2005) 71 MMI1 = MT-ALT 4 Eisenberg et al. (2007) 72 MT-ALT = MT-FRAG 4 – 73 NUC1-NUC = H2B 4 Buttner et al. (2007) 74 PKA = MT-ALT 4 Carmona-Gutierrez et al. (2010a) 75 RAS2 = MT-ALT 4 Eisenberg et al. (2007) 76 RAS2 = PKA 4 Carmona-Gutierrez et al. (2010a) 77 RedActinDyn = RAS2 4 Eisenberg et al. (2007) 78 RPD3 = H2B 4 Ahn et al. (2006) 79 STE20-CYT = STE20-NUC 4 Carmona-Gutierrez et al. (2010a) 80 Stress =AdenylateCyclase 4 Schmelzle et al. (2004) 81 TOR1 = CAMP 4 Schmelzle et al. (2004) 82 TOR1 = RAS2 4 Schmelzle et al. (2004) 83 Heat = SOD1 4 84 2 NDI1 = ROS-CYT 4 – 85 Stress =TOR1 4 Schmelzle et al. (2004) 86 !PTP2 = SLT2 5 Hahn and Thiele (2002) 87 !PTP2 = HOG1 5 Hahn and Thiele (2002) 88 HOG1 = HOG1-Dep 5 Hahn and Thiele (2002) 89 !PTP3 = HOG1 5 Hahn and Thiele (2002) 90 !SDP1 = SLT2 5 Hahn and Thiele (2002) 91 !SLT2 = DesCyclinCCDK8 5 Krasley et al. (2006) 92 !Stress = SLT2 5 Hahn and Thiele (2002) 93 DesCyclinCCCDK8 = ROS-CYT 5 Krasley et al. (2006) 94 Heat = PKA 5 Hahn and Thiele (2002) 95 Heat = SLT2 5 Hahn and Thiele (2002) 96 Hog1 = RLM1 5 Hahn and Thiele (2002) 97 HOG1-Dep = PTP3 5 Hahn and Thiele (2002) 98 MSN2-4 = SDP1 5 Hahn and Thiele (2002) 99 PKA = MSN2-4 5 Hahn and Thiele (2002) 100 RLM1 = PTP2 5 Hahn and Thiele (2002) 101 RLM1 = SLT2 5 Hahn and Thiele (2002) (Continued) www.frontiersin.org December 2012 \| Volume 3 \| Article 446 \| 7 Kazemzadeh et al. Boolean model of yeast apoptosis Table 3 \| Continued ID Interaction Function Time scale Reference 102 SLT2 = RLM1 5 Hahn and Thiele (2002) 103 Stress = HOG1 5 Hahn and Thiele (2002) 104 !SRO7 + Salt =YCA1 6 Wadskog et al. (2004) 105 !STM1-NUC = DNA-Frag 6 Ligr et al. (2001) 106 AceticAcid + !SVF1 = ROS-CYT 6 Vander Heiden et al. (2002) 107 H2O2 + !EMC4 = ROS-CYT 6 Ring et al. (2008) 108 H2O2 + !SVF1 = ROS-CYT 6 Vander Heiden et al. (2002) 109 !FIS1 + MDV1 = MT-Frag 6 Eisenberg et al. (2007) 110 !POR1-2 +AceticAcid =Apoptosis 6 Pereira et al. (2007) 111 !POR1-2 + H2O2 =Apoptosis 6 Pereira et al. (2007) 112 H2O2 + !DRE2/TAH18 = MT-Frag 6 Vernis et al. (2009) 113 YCA1 + !BIR1 =Apoptosis 6 Walter et al. (2006) 114 !NMA111-NUC = BIR1 6 Walter et al. (2006) 115 STM1-CYT + !Protosom = STM1-NUC 6 Ligr et al. (2001) Table includes involved species in each interaction, logical rule for each interaction and time scale in which interaction takes place. Note: the interactions of the model are given in the notation of the Cell Net Analyser: a logical NOT is represented by “!”; a logical AND is represented by “+” and interaction on right hand side of “=” gives the value of node on left hand side or equation. Table 4 \| Predicted states of relevant species at steady state. Species t = 0 t = 4 t = 5 t = 6 Acetic acid 1 1 1 1 Adozelesin 1 1 1 1 AIF1-MT 1 1 1 1 AIF1-NUC 0 1 1 1 Apoptosis 0 0 0 1 BIR1 0 0 0 0 DNA-FRAG 0 1 1 1 H2O2 1 1 1 1 Heat 1 1 1 1 NMA111-NUC 0 1 1 1 ROS-CYT 0 1 1 1 STE20-CYT 0 1 1 1 STM1-CYT 1 1 1 0 STM1-NUC 0 0 0 1 YCA1 0 1 1 1 Table includes time scale scenario upon induction of all stimuli.T stands for differ- ent time steps. As an example if Acetic Acid is inducted to the cell at time point 0 it is expected to cause DNA Fragmentation at next time step and eventually ends to apoptosis in last step. Bir1p has been previously intensively studied in chromosome seg- regation (as a component of the Aurora kinase complex (chromo- some passenger complex, CPC; Ruchaud et al., 2007) but recently studies of its role as a negative regulator of apoptosis have gained momentum. It has been shown that Bir1p is a target for degrada- tion by Nma111p (Owsianowski et al., 2008), an apoptotic serine protease and yeast cells lacking Bir1 are more sensitive to apopto- sis, while overexpression of Bir1 reduces apoptosis (Walter et al., 2006). When building the model we assumed that addition of acetic acid induces cytochrome c release from mitochondria and its translocation to the cytosol. Another assumption is that the execution of apoptosis is Yca1p-dependent (encoded by YCA1/MCA1/YOR197W) in this context and that the activation of the caspase is downstream from the cytochrome c transloca- tion (Ludovico et al., 2001, 2002). Thus, taking these assumptions into account acetic acid was used as an inducer in the simula- tions with direct induction of apoptosis. The model conﬁrmed experimental evidence that Bir1 is indeed apoptosis inhibitor in yeast (Walter et al., 2006) and as acetic acid is applied as a pulse stimulus (that is then decreasing over time) and cytochrome c present in the cytosol increases, the decrease of Bir1p due to Nma111p degradation promotes apoptosis that then reaches the maximum (Figure 5A). We then performed an artiﬁcial and bio- logically irrelevant simulation: after apoptosis has occurred and no more inducer was present (acetic acid is not added again and the previously added amount has been “used”) the eventual the- oretical accumulation of Bir1p did inhibit apoptosis and revert it to zero. Obviously this scenario is biologically implausible, since once the cell has undergone apoptosis it cannot be revived, but has a purpose to show mathematical correctness of the developed model. Additionally, we have converted discreet apoptosis model to continuous model with constant presence of Bir1 in order to test if this type of model would predict the same outcome as the experimental approach in which Bir1p is overexpressed and provides protection from induction of apoptosis. The continu- ous model was created taking into account translocation effect of each element from one compartment to another. This effect has been applied to translocation of Nuc1 from mitochondria to nucleus, MCD1 from nucleus to mitochondria, Stm1 from cytosol to nucleus Aif1 (from mitochondria to nucleus, NMA111 from cytosol to nucleus, Ste20 from cytosol to nucleus, and cytochrome Frontiers in Physiology \| Systems Biology December 2012 \| Volume 3 \| Article 446 \| 8 Kazemzadeh et al. Boolean model of yeast apoptosis HillCube Heat H202 Mg2 Adozelesin Acetic Acid CU2 Salt Mating Stress AIF1-MT CYTC-MT MMI1 CPR3 DRE2-Tah18 FIS1 MDV1 SOD2 ROS-MT NUC1-MT SVF1 CDC6 EMC4 POR1-2 NMA111-CYT NMA111-NUC PROTOSOM STM1-CYT STM1-NUC DNA-FRAG Tat-D SNO1 CYTC-CYT KAP123 NUC1-NUC CDC48 ROS-CYT YCA1 SOD1 NDI1 MEC1 MAPK PKA STE20-CYT MT-FRAG MT-ALT TOR1 Adelynatecyclase RAS2 RedActionDyn RPD3 STE20-NUC ESP1 MCD1-NUC AIF1-NUC HOS3 FVY10 H2B BIR1 Apoptosis AbnormalTelomer MCD1-MT SRO7 CAMP HK MSN2-4 SDP1 SLT2 RLM1 PTP2 PTP3 HOG1_Dep HOG1 DesCyclinCCDK8 Species Time [arbitrary units] 0 FIGURE 2 \| Continuous Hill Cube transformation. All species in apoptosis network are mapped on vertical axis. Dark blue color indicates those nodes that are not activated (value = 0) while dark red refers to nodes which are completely activated (value = 1). Each color in between indicates the level of activation between 0 and 1. c from mitochondria to cytosol. Initially, in this model, translo- cation of each species is modeled as one node in order to rep- resent the re-localization which introduced self-regulatory loops to the system which is impossible since to our knowledge yeast apoptosis regulatory network does not have such loops. One solution implies intuitive approach in deﬁning single variable for single species to mimic the effect of transferring from one compartment to another. Technically this was solved by intro- ducing two variables for a single species representing both com- partments they can belong to. This approach, also, conﬁrmed experimental ﬁnding (Walter et al., 2006) that constant pres- ence of Bir1, inhibits apoptosis, validating Bir1 anti-apoptotic role (Figure 5B). ACTIVATION OF H2O2-INDUCED APOPTOSIS WITH Stm1p It has been shown that degradation of short-lived pro-apoptotic proteins via proteasomal – ubiquitine pathway plays important role in mammalian apoptosis (Drexler, 1997). One of the yeast proteasomal substrates – Stm1 (YLR150W) was identiﬁed in the study by Ligr et al. (2001) as an activator of the cell death process. Conservedorthologsof Stm1aredetectedinseveralspecies(highly conserved ortholog in Schizosaccharomyces pombe and a putative ortholog in Drosophila melanogaster (Nelson et al., 2000) suggest- ingthatregulationof apoptosisviathisproteincanbeevolutionary conserved process. We have in silico tested two scenarios conﬁrming the role of Stm1 in apoptosis (Ligr et al., 2001). Accumulation of Stm1 will induce apoptotic behavior followed by DNA fragmentation which is a known marker of cell death, while the Stm1 knock out will promote survival and consequently deterring DNA fragmentation (Figures 6A,B). IN SILICO HUMANIZED YEAST APOPTOSIS S. cerevisiae is a model organism that has conserved genes, pro- teins and pathways that are similar to the ones in the human cells. This allows for using yeast as a host in which human genes can be expressed, so called “humanized yeast” (Winderickx et al., 2008) and subsequently the physiological roles and molecular mecha- nisms can be studied. In order to test if our system could be used in a similar way (in silico humanized yeast) and provide reliable simulations and predictions, we inserted three human genes with complete downstream pathways into our initial yeast apoptosis www.frontiersin.org December 2012 \| Volume 3 \| Article 446 \| 9 Kazemzadeh et al. Boolean model of yeast apoptosis Heat H202 Mg2 Adozelesin Acetic Acid CU2 Salt Mating Stress AIF1-MT CYTC-MT MMI1 CPR3 DRE2-Tah18 FIS1 MDV1 SOD2 ROS-MT NUC1-MT SVF1 CDC6 EMC4 POR1-2 NMA111-CYT NMA111-NUC PROTOSOM STM1-CYT STM1-NUC DNA-FRAG Tat-D SNO1 CYTC-CYT KAP123 NUC1-NUC CDC48 ROS-CYT YCA1 SOD1 NDI1 MEC1 MAPK PKA STE20-CYT MT-FRAG MT-ALT TOR1 Adelynatecyclase RAS2 RedActionDyn RPD3 STE20-NUC ESP1 MCD1-NUC AIF1-NUC HOS3 FVY10 H2B BIR1 Apoptosis AbnormalTelomer MCD1-MT SRO7 CAMP HK MSN2-4 SDP1 SLT2 RLM1 PTP2 PTP3 HOG1_Dep HOG1 DesCyclinCCDK8 Time [arbitrary units] 1 Boolean (synchronous) Species FIGURE 3 \| Synchronous Boolean model. All species in apoptosis network are mapped on vertical axis. Dark blue indicates those nodes that are not activated (value = 0) while dark red refers to nodes which are totally activated (value = 1). Boolean model. Yeast apoptotic network was “humanized” by in silico insertion of genes belonging to Bcl-2 protein family and Valosin-contain protein (VCP) – distinctive representatives of human apoptosis (Figure 7). INSERTION OF Bcl-2 FAMILY PROTEINS: ANTI-APOPTOTIC Bcl-xL AND PRO-APOTOTIC BAX This protein family consists of apoptotic agonist and anti-agonist proteins. Among members of Bcl-2 family Bax as an apoptotic inducer and Bcl-xL as an anti-apoptotic factor were included in our extended model. Bax is located in cytosol in mammalian cells and has vital role in mitochondria morphogenesis. Heterologously expressed Bax causes growth arrest and rapid cell death in S. cere- visiae (Sato et al., 1994; Greenhalf et al., 1996). Also expression of Bax has been linked to the release of cytochrome c from mito- chondria (Manon et al., 1997). Yeast cells with Bax expression accumulate ROS and show other apoptotic hallmarks such as DNA fragmentation (Madeo et al., 1999). Since members of this protein family were previously success- fully expressed in yeast, we ﬁrst validate the “humanized” yeast model by inserting Bcl-xL, Bax, Bad, and Bcl-2 genes (Sato et al., 1994; Greenhalf et al., 1996; Madeo et al., 1999). As an input signal human Akt signaling was used (Akt Signaling), as an extrinsic regulatory switch (since this signaling cascade is not present in yeast). The Akt Serine/Threonine-kinase promotes cell survival by phosphorylating the pro-apoptotic protein BAD (member of the Bcl-2 family), which is the cause of dissociation of BAD from the Bcl-2/Bcl-X complex, and promotion of cell survival (Datta et al., 1997). Besides cell survival,Akt signaling is related to the cell cycle, metabolism,and angiogenesis and therefore a target for anticancer drug development (Falasca, 2010; Hers et al., 2011). Upon activation of Akt Signaling at the ﬁrst time step (t = 0, node value Akt Signaling = 1), Bcl-2 and Bcl-xL are activated in the following step (t = 4, node value Bcl-xL = 1 and Bcl-2 = 1) and remain active throughout the simulation and as the inhibitors of apoptosis promote the survival (node value Apoptosis = 0; Table 5). Simulation results suggest the anti-apoptotic role of two Bcl-2 family members: Bcl-2 and Bcl-xL which is consistent with experimental ﬁndings (Kharbanda et al., 1997). DUAL FUNCTIONALITY OF VCP IN SURVIVAL AND APOPTOSIS The evolutionary conserved Valosin-containing protein (VCP) is a mammalian ortholog of yeast Cdc48, which is the ﬁrst apoptotic mediator found in S. cereivisae (Braun and Zischka, 2008). VCP is Frontiers in Physiology \| Systems Biology December 2012 \| Volume 3 \| Article 446 \| 10 Kazemzadeh et al. Boolean model of yeast apoptosis the member AAA-ATPase family which is ubiquitously expressed (Braun and Zischka,2008). It consists of four domains:N-terminal domain, two ATPase domains D1 and D2 and C-terminal domain (Wang et al., 2004). The major ATPase activity of VCP is carried FIGURE 4 \| Hog1 study. Comparison of experimental and simulation study. Black curve shows activity of wild type Hog1 upon induction of heat (Winkler et al., 2002) and red curve illustrates Hog1 activation level in continues simulation. on by D2 domain (Wang et al., 2004; Song et al., 2003). VCP is involved in different cellular process such as protein degradation, membrane fusion and chaperone activity (Braun and Zischka, 2008). Role of VCP/Cdc48 in ﬂuctuating number of death cell in various types of disease naming cancer and protein deposition diseases is not well understood. Increase in expression of VCP is correlated to the development of cancer and metastasis there- fore detecting the level of VCP expression is proposed as cancer progression marker. Also VCP is known as detector of aggregated proteins causing neurodegenerative disease such as Parkinson and Alzheimer (Hirabayashi et al., 2001; Mizuno et al., 2003; Ishigaki et al., 2004). It has been observed that yeast cell carrying mutation of Cdc48 is showing morphological markers of apoptosis (Madeo et al., 1997) and that depletion of this protein has apoptotic effect in other organisms as well (Imamuraab et al., 2003). It had been shown that VCP can both promote or inhibit apop- tosis (Braun and Zischka,2008). Deletion of VCP triggers ER stress which is followed by unfolded protein response and cell death via ER-associated degradation (ERAD) pathway – a highly conserved pathway between mammalian and yeast cells (Braun and Zischka, 2008). Wild type VCP has pro-apoptotic role in the cells undergo- ing apoptosis upon ER stress which in turn triggers ER-associated apoptotic pathway. Finally VCP can trigger survival pathway in response to NFkB which is a pro-survival molecule in cells with over expressed level of VCP/Cdc48(Braun and Zischka, 2008). The dual functionality of VCP in survival and apoptosis mech- anism makes it an attractive candidate to be inserted in initial yeast apoptosis Boolean network. Since VCP includes expression of a handful of heterologous proteins, its in vivo insertion to yeast plasmid would be difﬁcult to perform and thus represents a FIGURE 5 \| Bir1 study. (A) Acetic acid (green) is applied as a pulse stimulus (that is then decreasing over time) and cytochrome c (yellow) present in the cytosol increases, the decrease of Bir1p (red) promotes apoptosis (B) Constant presence of Bir1p (red) inhibits apoptosis (black), validating Bir1 anti-apoptotic role. www.frontiersin.org December 2012 \| Volume 3 \| Article 446 \| 11 Kazemzadeh et al. Boolean model of yeast apoptosis FIGURE 6 \| Stm1 study. (A) Presence of Stm1p (blue) promotes apoptosis (yellow; B) Knock out of Stm1p (blue) prevents apoptosis (yellow) and DNA fragmentation (red) and consequently promotes survival. FIGURE 7 \| In silico “humanized yeast apoptosis network”. Human apoptotic pathways BCL-2 protein family and VCP dependent genes inserted into the yeast apoptosis network (due to simplicity we show only human pathways). Frontiers in Physiology \| Systems Biology December 2012 \| Volume 3 \| Article 446 \| 12 Kazemzadeh et al. Boolean model of yeast apoptosis Table 5 \| Summary of simulations upon insertion of Bcl-2 pathway. Species t = 0 t = 4 t = 5 t = 6 UV 0 0 0 0 Akt signaling 1 1 1 1 BCL-XL 0 1 1 1 P53 0 0 0 0 BAD 0 0 0 0 BAX 0 0 0 0 BCL-2 0 1 1 1 Apoptosis 0 0 0 0 Table includes simulation results of heterologous expression of BCL-2 in yeast apoptosis model.T stands for different time steps. Upon activation of Akt Signal- ing pathway at ﬁrst time step BCL-2 gets activated in following step and as an inhibitor of apoptosis prevents apoptosis till end point. good candidate for further investigation and exploration of model capabilities. In our model, yeast Cdc48 was replaced with human VCP gene and its downstream pathway effector caspases (caspases 3, 6 and 7), initiator caspases (caspase9 and 12), IAP family, IkB-alpha inhibitory protein which when degraded by proteasome cause the release, and nuclear translocation of active NFkB (represented in the model as NFkB_Cyt and NFkB_Nuc) and gp130/Stat3 pathway (represented as a single node). Upon activation of Akt Signaling pro-survival role of VCP is observed (node Survival = 1 at t = 6, Table 3). This is achieved when IkBα is dissociated from NFkB (node NFkB/IkBα = 1 at t = 4), which in turn gets activated (node NFkB = 1, t = 5) and is translocated to the nucleus (nodes NFkB_Cyt = 1 and NFkB_Nuc = 1, t = 6) inducing survival of the cell (node Sur- vival = 1, t = 6). Simultaneously, activation of NFkB, promotes activity of IAP family of proteins which inhibits the activity of both effector and initiator caspases (nodes c-3-6-7 = 0 and c-9-12 = 0, t = [0,4,5,6],thusdisablingapoptosis-dependentcaspasepathway. As an independent, but parallel process, activation of VCP via Akt Signaling activates gp130-Stat3 (node gp130-Stat3 = 1, t = 4) pathway and consequently leads to survival (Table 6). This result suggests that yeast carrying mammalian VCP gene exhibits the same behavior as it is known from the human apoptotic model (Vandermoere et al., 2006). DISCUSSION In this work we have constructed a Boolean model for the bio- chemical network that controls apoptosis pathway in budding yeast Saccharomyces cerevisiae. Firstly, we presented the Boolean model describing only yeast pro and anti-apoptotic genes and val- idated the model by further analyzing the role of Stm1p, Bir1p, and Hog1p. Even though construction of the yeast apoptosis net- work involved certain simpliﬁcations (nodes have only two states and rules are describing network dynamics) we were able to model more complex network than using dynamic modeling approach that requires knowledge of kinetic parameters for all molecular processes. This approach was able to suggest general design prin- cipals of yeast apoptosis. One of the advantages of constructing mathematical models in biology is that we are able to simulate Table 6 \| Summary of simulations upon insertion of VCP pathway. Species t = 0 t = 4 t = 5 t = 6 Akt signaling 1 1 1 1 GP130-STAT3 0 1 1 1 NFkB-CYT 0 1 1 1 NFkB-NUC 0 1 1 1 NFkB/IkBα 0 1 1 1 VCP 1 1 1 1 C-3-6-7 0 0 0 0 C-9-12 0 0 0 0 IkBα 0 1 1 1 IAP 0 1 1 1 Survival 0 0 0 1 Apoptosis 0 0 0 0 Table includes simulation results of humanized yeast apoptosis model by inser- tion of VCP. T stands for different time steps. VCP in presence of Akt Signaling is expected to prevent apoptosis and promote survival at last time point. scenarios that are not feasible in real experiments. In the case of Bir1 p we were able to in silico revive a cell already reaching apoptosis. These examples are important to understand general mechanisms of the constructed network. A study of proteasomal substrate Stm1p suggested that Stm1p seems to be an effector of H2O2 and the presence of Stm1p with an inducer leads to apopto- sis in our model,and in Stm1p knock out survival is promoted and DNA fragmentation is avoided, irrespective of the presence of the inducer. Despite the limitation of BN in terms of giving quanti- tative predictions of the system dynamics they allow investigation of the large networks and their systematic exploration resulting in better understanding of cellular processes. Example of Hog1p study showed that our model was capable of reproducing the pat- tern of Hog1p activation,but was not able to quantitatively predict the maximal Hog1p activity. In the second stage, we extended the initial model by inserting two pathways of human apoptosis (VCP and Bcl-2 family), hereby creating a“humanized”in silico yeast. Humanized yeast strains are used in experimental molecular biology where the human proteins (causing, or associated with diseases) are expressed and studied in vivo (in yeast in this case). Conservation of many apoptotic mediators and mechanisms among the Eukarya provides the possibility of inserting genes from other organisms into yeast (in vivo) or in the yeast apop- totic network (in silico). We validated constructed humanized yeast model by insertion of Bcl-2 family which have been pre- viously successfully expressed in yeast. The model was able to reproduce well-known pro and anti-apoptotic phenotypes con- ﬁrming that yeast expressing Bax accumulated ROS and showed other apoptotic markers like DNA fragmentation. To test whether or not speciﬁc pathways playing role in neurodegeneration and cancer can be elucidated by our Boolean model and can we con- sequently take advantage of a simple system like yeast to explore hypothesis generated for higher organisms, we in silico expressed evolutionary conserved VCP and its downstream components in existing yeast apoptosis network. VCP is important player in can- cer cell survival and can be used as a target for cancer therapy. It www.frontiersin.org December 2012 \| Volume 3 \| Article 446 \| 13 Kazemzadeh et al. Boolean model of yeast apoptosis also serves as detector of aggregated proteins that are known to be cause of neurodegenerative diseases such as Parkinson’s and Alzheimer’s. Our model showed that cell survival is mediated by VCP via the degradation of IkBα that leads to translocation of NFkB to nucleus. This result is in agreement with experi- mental ﬁndings that VCP is an essential target in the Akt sig- naling pathway suggesting that presented model in combination with experimental approach would represents a promising plat- form to study complex cellular processes involved in cancer and neurodegeneration. Exploiting the advantages of BN models that enables extrac- tion of system level properties of large networks and extensive state exploration and converting discrete model to continuous model our results suggested that in contrast to human apoptotic network yeast apoptosis is linear process whose regulation does not involve any complex feedback loops. Analysis of the second model showed that with certain adjustments Boolean model of yeast apoptosis can be adapted for studies of apoptosis in higher organisms. Our results show that even without kinetic and qualitative data, it is possible to build models that can simulate relevant states of yeast physiology and regulations and can contribute to further understanding of biology. Since yeast is a preferred model organ- ism for many studies of fundamental processes in a Eukaryal cell, we argue that in silico studies of yeast will be an important contrib- utor to the understanding of complex cellular regulations, such as cell death pathways and that the applications will extend toward study of regulations or causes of human diseases such as cancer and neurodegeneration. MATERIALS AND METHODS APOPTOSIS NETWORK SETUP Based on the extensive literature study and databases search (Sac- charomyces Genome Database-SGD; Cherry et al.,2011) the apop- tosis network consisting of 73 nodes and 115 edges is constructed. These nodes are selected based on their interactions and their sub- strates involved in apoptosis. Cell Designer (Funahashi et al.,2003) was used to visualize genes and their connection. Cell Designer allowed us to represent network using comprehensive graphical notation. Moreover, Cell Designer is able to connect to online data bases such as KEGG (Kanehisa and Goto, 2000), BioModels (Li et al., 2010) and PubMed which expands its connectivity, visual- izationandmodelbuilding.Themostprominentadvantageof Cell Designer is its ability to support SBML (Systems Biology Markup Language; Hucka et al., 2003) format. Creating SBML ﬁle avoids creating logic rule ﬁle which is more error prone when rules have to be deﬁned by user in simple text and it is not in form of easily drawing boxes. Heat H202 Mg2 Adozelesin Acetic Acid CU2 Salt Mating Stress AIF1-MT CYTC-MT MMI1 CPR3 DRE2-Tah18 FIS1 MDV1 SOD2 ROS-MT NUC1-MT SVF1 CDC6 EMC4 POR1-2 NMA111-CYT NMA111-NUC PROTOSOM STM1-CYT STM1-NUC DNA-FRAG Tat-D SNO1 CYTC-CYT KAP123 NUC1-NUC CDC48 ROS-CYT YCA1 SOD1 NDI1 MEC1 MAPK PKA STE20-CYT MT-FRAG MT-ALT TOR1 Adelynatecyclase RAS2 RedActionDyn RPD3 STE20-NUC ESP1 MCD1-NUC AIF1-NUC HOS3 FVY10 H2B BIR1 Apoptosis AbnormalTelomer MCD1-MT SRO7 CAMP HK MSN2-4 SDP1 SLT2 RLM1 PTP2 PTP3 HOG1_Dep HOG1 DesCyclinCCDK8 Heat H202 Mg2 Adozelesin Acetic Acid CU2 Salt Mating Stress AIF1-MT CYTC-MT MMI1 CPR3 DRE2-Tah18 FIS1 MDV1 SOD2 ROS-MT NUC1-MT SVF1 CDC6 EMC4 POR1-2 NMA111-CYT NMA111-NUC PROTOSOM STM1-CYT STM1-NUC DNA-FRAG Tat-D SNO1 CYTC-CYT KAP123 NUC1-NUC CDC48 ROS-CYT YCA1 SOD1 NDI1 MEC1 MAPK PKA STE20-CYT MT-FRAG MT-ALT TOR1 Adelynatecyclase RAS2 RedActionDyn RPD3 STE20-NUC ESP1 MCD1-NUC AIF1-NUC HOS3 FVY10 H2B BIR1 Apoptosis AbnormalTelomer MCD1-MT SRO7 CAMP HK MSN2-4 SDP1 SLT2 RLM1 PTP2 PTP3 HOG1_Dep HOG1 DesCyclinCCDK8 FIGURE 8 \| Interaction Matrix ofYeast Apoptosis Network. Each row corresponds to single species and each column corresponds to reactions. A red matrix element eij indicates an inhibition inﬂuence of species ion reaction j. In contras a green ﬁled shows an activation inﬂuence of species i on reaction j while a blue box indicates species i gets activated in reaction j and as it is expected the black cells indicates that species i does not participate in reaction j. Number of interactions where the species is involved is mentioned at the end of each row as connectivity number of each species. Number of reactions that activates/inhibits is mentioned in brackets (Color coding: red – inhibition, green – activation and black – no interaction inﬂuence). Frontiers in Physiology \| Systems Biology December 2012 \| Volume 3 \| Article 446 \| 14 Kazemzadeh et al. Boolean model of yeast apoptosis Heat H202 Mg2 Adozelesin Acetic Acid CU2 Salt Mating Stress AIF1-MT CYTC-MT MMI1 CPR3 DRE2-Tah18 FIS1 MDV1 SOD2 ROS-MT NUC1-MT SVF1 CDC6 EMC4 POR1-2 NMA111-CYT NMA111-NUC PROTOSOM STM1-CYT STM1-NUC DNA-FRAG Tat-D SNO1 CYTC-CYT KAP123 NUC1-NUC CDC48 ROS-CYT YCA1 SOD1 NDI1 MEC1 MAPK PKA STE20-CYT MT-FRAG MT-ALT TOR1 Adelynatecyclase RAS2 RedActionDyn RPD3 STE20-NUC ESP1 MCD1-NUC AIF1-NUC HOS3 FVY10 H2B BIR1 Apoptosis AbnormalTelomer MCD1-MT SRO7 CAMP HK MSN2-4 SDP1 SLT2 RLM1 PTP2 PTP3 HOG1_Dep HOG1 DesCyclinCCDK8 5 ( 4/0/1) 8 ( 7 /0/1) 2 (1/0/1) 2 (1/0/1) 4 ( 3/0/1) 2( 1/0/1) 3 ( 2/0/1) 2 ( 1/0/1) 6 ( 4/1/1) 2 (1/0/1) 3 (1/0/2) 2 (1/0/1) 2 (1/0/1) 2 (0/1/1) 2 (0/1/1) 2 (1/0/1) 2 (0/1/1) 1 (0/0/1) 2 (1/0/1) 3 (0/2/1) 2 (1/0/1) 2 (0 /1/ 1) 3 (0/2/1) 2 (1/0/1) 2 (0/1/1) 2 (0/1/1) 2 (1/0/1) 2 (0/1/1) 3 (1/0/2) 2 (1/0/1) 2 (0/1/1) 3 (1 /0/2) 2 (1/0/1) 2 (1/0/1) 3 (2/0/1) 13 (2/0/11) 7 (1/0/6) 2 (1/0/1) 3 (2/0/1) 2 (1/0/1) 2(1/0/1) 4 (2/0/2) 2 (1/0/1) 4 (1/0/3) 4 (1/0/3) 3 (2/0/1) 3 (1/0/2) 6 (4/0/2) 3 (3/0/0) 2 (1/0/1) 2 (1/0/1) 3 (2/0/1) 1 (0/0/1) 2 (1/0/1) 2 (1/0/1) 2 (0/1/1) 5 (0/0/5) 2 (0/1/1) 9 (1/0/8) 1 (1/0/0) 2 (1/0/1) 2 (0/1/1) 2 (0/0/2) 16 (16/0/0) 2 (1/0/1) 2 (0/1/1) 7 (1/1/5) 4 (2/0/2) 3 (0/2/1) 2 (0/1/1) 2 (1/0/1) 5 (2/0/3) 2 (1/0/1) Ace!cAcid= CytC-MT MCD1-MT = CytC-MT CytC-MT = CytC-CYT CytC-CYT =YCA1 !SRO7 + Salt =YCA1 MEC1=YCA1 MT-Frag =YCA1 ROS-CYT =YCA1 RedAc!nDyn =YCA1 ESP1 = ROS-CYT SOD1 = ROS-CYT 2 NDI1 = ROS-CYT Salt = ROS-CYT RAS2 = ROS-CYT RedAc!nDyn = ROS-CYT H2O2 + !EMC4 = ROS-CYT H2O2 + !SVF1 = ROS-CYT Ace!cAcid + !SVF1 = ROS-CYT !SOD2 + NDI1 = ROS-MT MT-ALT = MT-FRAG !FIS1 + MDV1 = MT-Frag H2O2 + !DRE2/TAH18 = MT-Frag !SNO1 = apoptosis !FYV10 = apoptosis YCA1 + !BIR1 = apoptosis ROS-CYT = Apoptosis DNA-Frag = apoptosis !STM1-NUC = DNA-Frag !POR1-2 + H2O2 = apoptosis !POR1-2 + Ace!cAcid = apoptosis CPR3 = apoptosis RedAc!nDyn = RAS2 TOR1 = RAS2 RAS2 = adenylatecyclase Stress = AdenylateCyclase AdenylateCyclase = CAMP RAS2 = PKA TOR1 = CAMP PKA=MT-ALT RAS2 = MT–ALT MMI1 = MT-ALT Adozelesin = CDC6 CDC6 = PROTOSOM STM1-CYT + !Protosom = STM1-NUC Heat = NMA111-CYT NMA111-CYT = NMA111-NUC !NMA111-NUC = BIR1 Ma!ng = MAPK MAPK = STE20-CYT STE20-CYT = STE20-NUC Abnormal Telomer = MEC1 Stress = RPD3 HOS3 = H2B RPD3 = H2B NUC1-NUC = H2B STE20-NUC = H2B AIF1 -NUC = H2B H2O2 = HOS3 ESP1 = MCD1-NUC H2O2 = ESP1 H2O2 = NUC1-MT NUC1-MT = KAP123 KAP123 = NUC1-NUC AIF1-MT = AIF1-NUC Tat-D = DNA-Frag Mg2+=Tat-D =Ace!cAcid = Heat =H2O2 =Adozelesin =MG2 =CU2 =Salt =Ma!ng =Stress Apoptosis= Cu2 = CPR3 Heat = PKA PKA = MSN2-4 MSN2-4 = SDP1 Heat = SLT2 !SDP1 = SLT2 SLT2 = RLM1 RLM1 = SLT2 RLM1 = PTP2 !PTP2 = SLT2 Stress = HOG1 Hog1 = RLM1 !PTP2 = HOG1 !PTP3 = HOG1 HOG1-Dep = PTP3 !Stress = SLT2 !SLT2 = DesCyclinCCDK8 DesCyclinCCCDK8 = ROS-CYT HK = SVF1 HK = DRE2/TAH18 HK = EMC4 HK = POR1-2 HK = SNO1 HK=FVY10 HK = SRO7 HK = STM1-CYT HK = MMI1 HK = NDI1 CDC48 = CytC-CYT 2 CDC48 = ROS-CYT HK = CDC48 HK = FIS1 HK = MDV1 HK = MCD1-MT HK = AIF1-MT HOG1 = HOG1-Dep HK = SOD2 Heat = SOD1 Stress =TOR1 FIGURE 9 \| Dependency Matrix forYeast Apoptosis Network. In the dependency matrix each element mij represent the relation between an affecting and an affected species. Former is speciﬁed at the bottom of each column and later is shown at the beginning of each row. At intersection of i th column and j th row there are three possibilities. A yellow box indicates species iis an ambivalent factor meaning both activating and inhibiting path exist from species i to species j. Similarly a dark green and or light green cell shows a total and a non-total activator respectively. Another possibility is having dark or light red indicates species i is a total inhibitor or non-total inhibitor of species j. whenever there is no path from spices i to species j the intersection cell is ﬁeld by black. The hyper graph underlying the network is a directed graph and consequently the dependency matrix is non-symmetric. (Color coding: light and dark green – complete and incomplete activation, dark and light red – complete and incomplete inhibitor, yellow indicates an ambivalent factor and black indicates that there is no dependency between two species). COMPUTATION OF LOGICAL STEADY STATES Identiﬁcation of Logical Steady States (LSSs) in a Boolean net- work is an important task as they comprise the states in which a gene-regulatory network resides most of the time. Strong biolog- ical implication can be carried out by LSSs of the network. LSSs can even be linked to phenotype (Kauffman, 1969). CNA (Klamt et al., 2006) is used to calculate all possible LLSs based on speciﬁed initial value for each gene and signal ﬂow in network. LSSs are used to evaluate the network behavior under perturbation and changes in network structure. IDENTIFYING NETWORK WIDE DEPENDENCY Considering a pair of nodes (a, b) dependency is deﬁned as the inﬂuence of node a on node b and vice versa, node a inﬂuences node b as follow: a is a total activator of b if there is an activat- ing path between a and b, a is a total inhibitor of b is there is an inhibition path from a to b or a is an ambivalent effecter of b meaning that there is an intermediate node which is involved in a negative feedback loop. Using CNA the interaction matrix and dependency matrix were drawn from the network (Figures 8 and 9). CONVERSION OF DISCRETE TO CONTINUOUS MODEL USING SQUAD In order to convert the schematic network into Boolean model we used SQUAD (Mendoza and Xenarios, 2006), a user friendly graphical software which is suitable for modeling signaling net- work where kinetic reactions are not available. Simulation in SQUAD consists of three steps: (1) the network is ﬁrst loaded from the SBML ﬁle. Components of the network are presented as nodes and value of each node represents the state of that node. SQUAD converts the network to discrete dynamic model. Using Boolean algorithms all steady sates in network are calculated. (2) network is converted to a continues dynamic model generating sets of ordinary differential equations (ODEs) and steady states achieved in pervious step. (3) SQUAD allows perturbation in order to understand the role of each node within the network. Using Reduced Order Binary Decision Diagram (ROBDD), it is possible to calculate steady states (Di Cara et al., 2007). ROBDD is a memory efﬁcient data structure which is widely used in elec- tronic ﬁeld and has been proven to work for large binary networks. Moreover, ROBDD computes steady states for large networks (n > 50) in matter of seconds.Another advantage of this algorithm is its ability to identify the cyclic steady states. These oscillating www.frontiersin.org December 2012 \| Volume 3 \| Article 446 \| 15 Kazemzadeh et al. Boolean model of yeast apoptosis states are reachable when system identiﬁes a cyclic pattern instead of one single state. In the ﬁrst step, schematic network is supplied to SQUAD resulting in a discrete network, generating a set of either cyclic or single steady states. These steady states are then used to convert discrete model to continues. Given all calculated steady states or cycles we examined all possible outcomes for each input. Depend- ing on the desire form of output,discrete to continuous conversion can be carried out either as a complete or progressive mode. Our simulations are performed in the complete mode since cell under- going apoptosis should die after certain time and it is expected to maintain a constant level of apoptosis or survival (in case when apoptosis is not activated) at the end of each run. As an opposite to complete mode, the progressive model allows the user to stop the simulation at any time even before reaching the steady states. CONVERSION OF DISCRETE TO CONTINUOUS MODEL USING ODEFY Reconstructing Boolean model of yeast apoptosis from qualitative knowledge never gives details about concentration of molecules in different time points. For this purpose the discrete Boolean model is transformed to continuous model using Odefy. Odefy uses the multivariate polynomial interpolation in order to trans- form the logical rules into sets of ODEs. Yeast apoptosis Boolean model is converted to continuous model using Hill Cube and nor- malized Hill Cube where the Hill function is normalized to the unit interval. Behavior of biochemical reactions can be seen as a sigmoid Hill function represented as f (¯¯x) = ¯¯xn/(¯¯xn + kn). 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This is an open- access article distributed under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in other forums, pro- vided the original authors and source are credited and subject to any copy- right notices concerning any third-party graphics etc. Frontiers in Physiology \| Systems Biology December 2012 \| Volume 3 \| Article 446 \| 18	23233838	SDP1 = ( MSN2-4 ) CDC48 = ( HK ) NDI1 = ( HK ) MT-ALT = ( MMI1 ) OR ( RAS2 ) OR ( MT-Frag ) OR ( PKA ) MEC1 = ( AbnormalTelomer ) YCA1 = ( ( Salt ) AND NOT ( SRO7 ) ) OR ( MEC1 ) OR ( MT-Frag ) OR ( RedActinDyn ) OR ( ROS-CYT ) OR ( CytC-CYT ) DesCyclinCCDK8 = NOT ( ( SLT2 ) ) Apoptosis = ( ( POR1-2 AND ( ( ( NOT AceticAcid OR NOT BIR1 OR NOT H2O2 OR NOT FVY10 ) AND ( ( ( NOT SNO1 ) ) ) ) ) ) OR ( CU2 AND ( ( ( CPR3 ) ) OR ( ( NOT POR1-2 OR NOT AceticAcid OR NOT BIR1 OR NOT H2O2 ) AND ( ( ( NOT FVY10 AND NOT SNO1 ) ) ) ) ) ) OR ( CPR3 AND ( ( ( NOT POR1-2 OR NOT AceticAcid OR NOT BIR1 OR NOT H2O2 OR NOT FVY10 ) AND ( ( ( NOT SNO1 ) ) ) ) ) ) OR ( ROS-CYT AND ( ( ( NOT POR1-2 OR NOT AceticAcid OR NOT BIR1 OR NOT H2O2 OR NOT FVY10 OR NOT SNO1 ) ) OR ( ( POR1-2 AND AceticAcid AND BIR1 AND H2O2 ) ) ) ) OR ( ( YCA1 AND ( ( ( NOT POR1-2 OR NOT AceticAcid OR NOT BIR1 OR NOT H2O2 OR NOT FVY10 OR NOT SNO1 ) ) ) ) AND NOT ( BIR1 AND ( ( ( FVY10 AND SNO1 ) ) ) ) ) OR ( DNA-Frag AND ( ( ( NOT POR1-2 OR NOT AceticAcid OR NOT BIR1 OR NOT H2O2 OR NOT FVY10 OR NOT SNO1 ) ) OR ( ( POR1-2 AND AceticAcid AND BIR1 AND H2O2 AND FVY10 ) ) ) ) OR ( BIR1 AND ( ( ( NOT POR1-2 AND NOT AceticAcid AND NOT H2O2 AND NOT FVY10 AND NOT SNO1 ) ) ) ) OR ( FVY10 AND ( ( ( NOT POR1-2 OR NOT AceticAcid OR NOT BIR1 OR NOT H2O2 ) AND ( ( ( NOT SNO1 ) ) ) ) ) ) OR ( SNO1 AND ( ( ( H2O2 AND FVY10 ) AND ( ( ( NOT POR1-2 AND NOT DNA-Frag AND NOT ROS-CYT ) ) ) ) OR ( ( NOT POR1-2 OR NOT AceticAcid OR NOT BIR1 OR NOT H2O2 ) AND ( ( ( NOT FVY10 ) ) ) ) ) ) OR ( H2O2 AND ( ( ( NOT POR1-2 OR NOT AceticAcid OR NOT BIR1 OR NOT FVY10 ) AND ( ( ( NOT SNO1 ) ) ) ) ) ) OR ( AceticAcid AND ( ( ( FVY10 AND SNO1 ) AND ( ( ( NOT POR1-2 AND NOT YCA1 AND NOT DNA-Frag AND NOT ROS-CYT AND NOT BIR1 AND NOT H2O2 ) ) ) ) OR ( ( NOT POR1-2 OR NOT BIR1 OR NOT H2O2 OR NOT FVY10 ) AND ( ( ( NOT SNO1 ) ) ) ) OR ( ( POR1-2 AND BIR1 AND H2O2 ) AND ( ( ( NOT FVY10 OR NOT SNO1 ) ) ) ) OR ( ( BIR1 AND FVY10 AND SNO1 ) AND ( ( ( NOT POR1-2 AND NOT H2O2 ) ) ) ) ) ) ) OR NOT ( POR1-2 OR AceticAcid OR DNA-Frag OR YCA1 OR ROS-CYT OR BIR1 OR H2O2 OR CU2 OR FVY10 OR SNO1 OR CPR3 ) SVF1 = ( HK ) PTP3 = ( HOG1-Dep ) SOD2 = ( HK ) POR1-2 = ( HK ) BIR1 = NOT ( ( NMA111-NUC ) ) DRE2_TAH18 = ( HK ) STM1-NUC = ( ( STM1-CYT ) AND NOT ( Protosom ) ) RLM1 = ( HOG1 ) OR ( SLT2 ) SLT2 = ( ( RLM1 ) OR ( Heat ) OR ( PTP2 AND ( ( ( NOT SDP1 OR NOT Stress ) ) ) ) OR ( SDP1 AND ( ( ( NOT PTP2 OR NOT Stress ) ) ) ) OR ( Stress AND ( ( ( NOT SDP1 OR NOT PTP2 ) ) ) ) ) OR NOT ( SDP1 OR PTP2 OR Stress OR Heat OR RLM1 ) MCD1-MT = ( HK ) FIS1 = ( HK ) DNA-Frag = ( ( Tat-D ) ) OR NOT ( Tat-D OR STM1-NUC ) CAMP = ( AdenylateCyclase ) OR ( TOR1 ) KAP123 = ( NUC1-MT ) STE20-CYT = ( MAPK ) SOD1 = ( Heat ) HOG1 = ( ( Stress ) OR ( PTP3 AND ( ( ( NOT PTP2 ) ) ) ) OR ( PTP2 AND ( ( ( NOT PTP3 ) ) ) ) ) OR NOT ( PTP3 OR PTP2 OR Stress ) AdenylateCyclase = ( Stress ) OR ( RAS2 ) ROS-CYT = ( Salt ) OR ( CDC48 ) OR ( RAS2 ) OR ( DesCyclinCCDK8 ) OR ( NDI1 ) OR ( RedActinDyn ) OR ( ( ( H2O2 ) AND NOT ( SVF1 ) ) AND NOT ( EMC4 ) ) OR ( ( AceticAcid ) AND NOT ( SVF1 ) ) OR ( ESP1 ) OR ( SOD1 ) Tat-D = ( MG2 ) HOS3 = ( H2O2 ) FVY10 = ( HK ) MDV1 = ( HK ) NMA111-NUC = ( NMA111-CYT ) PTP2 = ( RLM1 ) CytC-MT = ( MCD1-MT ) OR ( AceticAcid ) EMC4 = ( HK ) H2B = ( RPD3 ) OR ( AIF1-NUC ) OR ( STE20-NUC ) OR ( HOS3 ) OR ( NUC1-NUC ) ROS-MT = ( NDI1 AND ( ( ( NOT SOD2 ) ) ) ) PKA = ( Heat ) OR ( RAS2 ) CytC-CYT = ( CDC48 ) OR ( CytC-MT ) MT-Frag = ( ( H2O2 ) AND NOT ( DRE2_TAH18 ) ) OR ( MT-ALT ) OR ( ( MDV1 ) AND NOT ( FIS1 ) ) MSN2-4 = ( PKA ) STM1-CYT = ( HK ) NUC1-NUC = ( KAP123 ) ESP1 = ( H2O2 ) RAS2 = ( TOR1 ) OR ( RedActinDyn ) MMI1 = ( HK ) HOG1-Dep = ( HOG1 ) NMA111-CYT = ( Heat ) NUC1-MT = ( H2O2 ) RPD3 = ( Stress ) AIF1-MT = ( HK ) TOR1 = ( Stress ) MCD1-NUC = ( ESP1 ) AIF1-NUC = ( AIF1-MT ) CDC6 = ( Adozelesin ) Protosom = ( CDC6 ) MAPK = ( Mating ) STE20-NUC = ( STE20-CYT ) SNO1 = ( HK ) SRO7 = ( HK )
Canalization and Control in Automata Networks: Body Segmentation in Drosophila melanogaster Manuel Marques-Pita1,2, Luis M. Rocha1,2 1 Instituto Gulbenkian de Cieˆncia, Oeiras, Portugal, 2 Indiana University, Bloomington, Indiana, United States of America Abstract We present schema redescription as a methodology to characterize canalization in automata networks used to model biochemical regulation and signalling. In our formulation, canalization becomes synonymous with redundancy present in the logic of automata. This results in straightforward measures to quantify canalization in an automaton (micro-level), which is in turn integrated into a highly scalable framework to characterize the collective dynamics of large-scale automata networks (macro-level). This way, our approach provides a method to link micro- to macro-level dynamics – a crux of complexity. Several new results ensue from this methodology: uncovering of dynamical modularity (modules in the dynamics rather than in the structure of networks), identification of minimal conditions and critical nodes to control the convergence to attractors, simulation of dynamical behaviour from incomplete information about initial conditions, and measures of macro-level canalization and robustness to perturbations. We exemplify our methodology with a well-known model of the intra- and inter cellular genetic regulation of body segmentation in Drosophila melanogaster. We use this model to show that our analysis does not contradict any previous findings. But we also obtain new knowledge about its behaviour: a better understanding of the size of its wild-type attractor basin (larger than previously thought), the identification of novel minimal conditions and critical nodes that control wild-type behaviour, and the resilience of these to stochastic interventions. Our methodology is applicable to any complex network that can be modelled using automata, but we focus on biochemical regulation and signalling, towards a better understanding of the (decentralized) control that orchestrates cellular activity – with the ultimate goal of explaining how do cells and tissues ‘compute’. Citation: Marques-Pita M, Rocha LM (2013) Canalization and Control in Automata Networks: Body Segmentation in Drosophila melanogaster. PLoS ONE 8(3): e55946. doi:10.1371/journal.pone.0055946 Editor: Luı´s A. Nunes Amaral, Northwestern University, United States of America Received September 10, 2012; Accepted January 3, 2013; Published March 8, 2013 Copyright: 2013 Marques-Pita, Rocha. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: Funding provided by Fundac¸a˜o para a Ciencia e a Tecnologia (Portugal) grant PTDC/EIA-CCO/114108/2009. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors declare that LMR is a PLOS ONE Editorial Board member and that this does not alter the authors’ adherence to all the PLOS ONE policies on sharing data and materials. * E-mail: marquesm@indiana.edu (MMP); rocha@indiana.edu (LMR) Introduction and Background The notion of canalization was proposed by Conrad Waddington [1] to explain why, under genetic and environmental perturba- tions, a wild-type phenotype is less variable in appearance than most mutant phenotypes during development. Waddington’s fundamental hypothesis was that the robustness of wild-type phenotypes is the result of a buffering of the developmental process. This led Waddington to develop the well-known concept of epigenetic landscape [2,3], where cellular phenotypes are seen, metaphorically, as marbles rolling down a sloped and ridged landscape as the result of interactions amongst genes and epigenetic factors. The marbles ultimately settle in one of the valleys, each corresponding to a stable configuration that can be reached via the dynamics of the interaction network. In this view, genetic and epigenetic pertur- bations can only have a significant developmental effect if they force the natural path of the marbles over the ridges of the epigenetic landscape, thus making them settle in a different valley or stable configuration. Canalization, understood as the buffering of genetic and epigenetic perturbations leading to the stability of phenotypic traits, has re-emerged recently as a topic of interest in computational and systems biology [4–10]. However, canalization is an emergent phenomenon because we can consider the stability of a phenotypic trait both at the micro-level of biochemical interactions, or at the macro-level of phenotypic behaviour. The complex interaction between micro- and macro-level thus makes canalization difficult to study in biological organisms – but the field of complex systems has led to progress in our understanding of this concept. For instance, Conrad [3] provided a still-relevant treatment of evolvability [11] by analysing the tradeoff between genetic (micro-level) instability and phenotypic (macro-level) stability. This led to the concept of extra- dimensional bypass, whereby most genetic perturbations are buffered to allow the phenotype to be robust to most physiological perturbations, but a few genetic perturbations (e.g. the addition of novel genetic information) provide occasional instability necessary for evolution. Conrad highlighted three (micro-level) features of the organization of living systems that allows them to satisfy this tradeoff: modularity (or compartmentalization), component redundancy, and multiple weak interactions. The latter two features are both a form of redundancy, the first considering the redundancy of components and the second considering the redundancy of interactions or linkages. Perhaps because micro-level redundancy has been posited as one of the main mechanisms to obtain macro-level robustness, the term canalization has also been used – especially in discrete mathematics – to characterize redundant properties of automata functions, particularly when used to model micro-level dynamical PLOS ONE \| www.plosone.org 1 March 2013 \| Volume 8 \| Issue 3 \| e55946 interactions in models of genetic regulation and biochemical signalling. An automaton is typically defined as canalizing if there is at least one state of at least one of its inputs that is sufficient to control the automaton’s next state (henceforth transition), regardless of the states of any other inputs [12]. Clearly, this widely used definition refers to micro-level characteristics of the components of multivariate discrete dynamical systems such as automata networks, and not to canalization as the emergent phenomenon outlined above. Nonetheless, using this definition, it has been shown that (1) canalizing functions are widespread in eukaryotic gene-regulation dynamics [13]; (2) genetic regulatory networks modelled with canalizing automata are always stable [14,15]; and (3) realistic biological dynamics are naturally observed in networks with scale-free connectivity that contain canalizing functions [16]. These observations suggest that the redundancy captured by this micro-level definition of canalization is a mechanism used to obtain stability and robustness at the macro-level of phenotypic traits. Since the proportion of such ‘strictly’ canalizing functions drops abruptly with the number of inputs (k) [17], it was at first assumed that (micro-level) canalization does not play a prominent role in stabilizing complex dynamics of gene regulatory networks. However, when the concept of canalization is extended to include partially canalizing functions, where subsets of inputs can control the automaton’s transition, the proportion of available canalizing automata increases dramatically even for automata with many inputs [18]. Furthermore, partial canalization has been shown to contribute to network stability, without a detrimental effect on ‘evolvability’ [18]. Reichhardt and Bassler, point out that, even though strictly canalizing functions clearly contribute to network stability, they can also have a detrimental effect on the ability of networks to adapt to changing conditions [18] – echoing Conrad’s tradeoff outlined above. This led them to consider the wider class of partially canalizing functions that confer stable network dynamics, while improving adaptability. A function of this class may ignore one or more of its inputs given the states of others, but is not required to have a single canalizing input. For example, if a particular input is on, the states of the remaining inputs are irrelevant, but if that same input is off, then the state of a subset of its other inputs is required to determine the function’s transition. In scenarios where two or more inputs are needed to determine the transition, the needed inputs are said to be collectively canalizing. Reichhardt and Bassler [18] have shown that the more general class of partially canalizing functions dominates the space of Boolean functions for any number of inputs k. Indeed, for any value of k, there are only two non-canalizing functions that always depend on the states of all inputs. Other classes of canalizing functions have been considered, such as nested canalizing functions [14], Post classes [19] and chain functions [20]. All these classes of functions characterize situations of input redundancy in automata. In other words, micro-level canalization is understood as a form of redundancy, whereby a subset of input states is sufficient to guarantee transition, and therefore its complement subset of input states is redundant. This does not mean that redundancy is necessarily the sole – or even most basic – mechanism to explain canalization at the macro-level. But the evidence we reviewed above, at the very least, strongly suggests that micro-level redundancy is a key mechanism to achieve macro-level canaliza- tion. Other mechanisms are surely at play, such as the topological properties of the networks of micro-level interactions. Certainly, modularity, as suggested by Conrad, plays a role in the robustness of complex systems and has rightly received much attention recently [21]. While we show below that some types of modularity can derive from micro-level redundancy, other mechanisms to achieve modularity are well-known [21]. Here, we explore partial canalization, as proposed by Reich- hardt and Bassler [18], to uncover the loci of control in complex automata networks, particularly those used as models of genetic regulation and signalling. Moreover, we extend this notion to consider not only (micro-level) canalization in terms of input redundancy, but also in terms of input-permutation redundancy to account for the situations in which swapping the states of (a subset) of inputs has no effect on an automaton’s transition. From this point forward, when we use the term canalization we mean it in the micro-level sense used in the (discrete dynamical systems) literature to characterize redundancy in automata functions. Nonetheless, we show that the quantification of such micro-level redundancy uncovers important details of macro-level dynamics in automata networks used to model biochemical regulation. This allows us to better study how robustness and control of phenotypic traits arises in such systems, thus moving us towards understanding canaliza- tion in the wider sense proposed by Waddington. Before describing our methodology, we introduce necessary concepts and notations pertaining to Boolean automata and networks, as well as the segment polarity gene-regulation network in Drosophila melanogaster, an automata model we use to exemplify our approach. Boolean Networks This type of discrete dynamical system was introduced to build qualitative models of genetic regulation, very amenable to large- scale statistical analysis [22] – see [23] for comprehensive review. A Boolean automaton is a binary variable, x[f0,1g, where state 0 is interpreted as false (off or unexpressed), and state 1 as true (on or expressed). The states of x are updated in discrete time-steps, t, according to a Boolean state-transition function of k inputs: xtz1~f it 1,:::,it k . Therefore f : f0,1gk?f0,1g. Such a function can be defined by a Boolean logic formula or by a look-up (truth) table (LUT) with 2k entries. An example of the former is xtz1~f (x,y,z)~xt ^ (yt _ zt), or its more convenient shorthand representation f ~x ^ (y _ z), which is a Boolean function of k~3 input binary variables x,y,z, possibly the states of other automata; ^, _ and : denote logical conjunction, disjunction, and negation respectively. The LUT for this function is shown in Figure 1. Each LUT entry of an automaton x, fa, is defined by (1) a specific condition, which is a conjunction of k inputs represented as a unique k-tuple of input-variable (Boolean) states, and (2) the automaton’s next state (transition) xtz1, given the condition (see Figure 1). We denote the entire state transition function of an automaton x in its LUT representation as F:ffa : a~1,:::,2kg. A Boolean Network (BN) is a graph B:(X,E), where X is a set of n Boolean automata nodes xi[X,i~1,:::,n, and E is a set of directed edges eji[E : xi,xj[X. If eji[E, it means that automaton xj is an input to automaton xi, as computed by Fi. Xi~fxj[X : eji[Eg denotes the set of input automata of xi. Its cardinality, ki~jXij, is the in-degree of node xi, which determines the size of its LUT, jFij~2ki. We refer to each entry of Fi as fi:a, a~1:::2ki. The input nodes of B are nodes whose state does not depend on the states of other nodes in B. The state of output nodes is determined by the states of other nodes in the network, but they are not an input to any other node. Finally, the state of inner nodes depends on the state of other nodes and affect the state of other nodes in B. At any given time t, B is in a specific configuration of node states, xt~Sx1,x2,:::,xnT. We use the terms state for individual automata (x) and configuration (x) for the collection of states of the set of automata of B, i.e. the collective network state. Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 2 March 2013 \| Volume 8 \| Issue 3 \| e55946 Starting from an initial configuration, x0, a BN updates its nodes with a synchronous or asynchronous policy. The dynamics of B is thus defined by the temporal sequence of configurations that ensue, and there are 2n possible configurations. The transitions between configurations can be represented as a state-transition graph, STG, where each vertex is a configuration, and each directed edge denotes a transition from xt to xtz1. The STG of B thus encodes the network’s entire dynamical landscape. Under synchronous updating, configurations that repeat, such that xtzm~xt, are known as attractors; fixed point when m~1, and limit cycle – with period m – when mw1, respectively. The disconnected subgraphs of a STG leading to an attractor are known as basins of attraction. In contrast, under asynchronous updating, there are alternative configuration transitions that depend on the order in which nodes update their state. Therefore, the same initial configuration can converge to distinct attractors with some probability [24,25]. A BN B has a finite number b of attractors; each denoted by Ai : i~1,:::,b. When the updating scheme is known, every configuration x is in the basin of attraction of some specific attractor Ai. That is, the dynamic trajectory of x converges to Ai. We denote such a dynamical trajectory by s(x) Ai. If the updating scheme is stochastic, the relationship between configu- rations and attractors can be specified as the conditional probability P(Aijx). The Segment Polarity Network The methodology introduced in this paper will be exemplified using the well-studied Boolean model of the segment polarity network in Drosophila melanogaster [26]. During the early ontogenesis of the fruit fly, like in every arthropod’s development, there is body segmentation [27,28]. The specification of adult cell types in each of these segments is controlled by a hierarchy of around forty genes. While the effect of most of the genes in the hierarchy is only transient, a subset of segment polarity genes remains expressed during the life of the fruit fly [29]. The dynamics of the segment polarity network was originally modelled using a system of non-linear ordinary differential equations (ODEs) [30,31]. This model suggested that the regulatory network of segment polarity genes is a module largely controlled by external inputs that is robust to changes to its internal kinetic parameters. On that basis, Albert and Othmer later proposed a simpler discrete BN model of the dynamics of the segment polarity network (henceforth SPN) [26]. This was the first Boolean model of gene regulation capable of predicting the steady state patterns experimentally observed in wild-type and mutant embryonic development with significant accuracy, and has thus become the quintessential example of the power of the logical approach to modelling of biochemical regulation from qualitative data in the literature. Modelling with ODEs, in contrast, is hindered by the need of substantial quantitative data for parameter estimation [32–37]. The SPN model comprises fifteen nodes that represent intra- cellular chemical species and the genes engrailed (en); wingless (wg); hedgehog (hh); patched (ptc) and cubitus interruptus (ci) [29–31]. These genes encode a number of proteins such as the transcription factors Engrailed (EN), Cubitus Interruptus (CI), CI Activator (CIA), and CI repressor (CIR); the secreted proteins Wingless (WG) and Hedgehog (HH); and the transmembrane protein Patched (PTC). Other proteins included in the SPN model are Sloppy-Paired (SLP) – the state of which is previously determined by the pair-rule gene family that stabilizes its expression before the segment polarity genes – as well as Smoothened (SMO) and the PH complex that forms when HH from neighbouring cells binds to PTC. Figure 2 shows the topology and Table 1 lists the logical rules of the nodes in every cell of the SPN. This model consists of a spatial arrangement of four interconnected cells, a parasegment. While the regulatory interactions within each cell are governed by the same network, inter-cellular signalling affects neighbouring cells. That is, regulatory interactions in a given cell depend on the states of WG, hh and HH in adjacent cells. Therefore, six additional (inter-cellular) ‘spatial signals’ are included: hhi+1, HHi+1 and WGi+1, where i~1,:::,4 is the cell index in the four- cell parasegment. In a parasegment, the cell with index i~1 corresponds to its anterior cell and the cell with index i~4 to its posterior cell (see Figure 3). In simulations, the four-cell parasegments assume periodic boundary conditions (i.e. anterior and posterior cells are adjacent to each other). Since each parasegment has 4\|15~60 nodes, four of which are in a fixed state (SLP), there are 256 possible configurations – a dynamical landscape too large for exhaustive analysis. Even though the original model was not fully synchronous because PH and SMO were updated instantaneously at time t, rather than at tz1, here we use the fully equivalent, synchronous version. Specifically, since PH is an output node, synchronizing its transition with the remaining nodes at tz1 does not impact the model’s dynamics. The state of SMO influences the updating of CIA and CIR; but since the update of SMO is instantaneous, we can include its state- transition function in the state-transition functions of CIA and CIR (which update at tz1) with no change in the dynamics of the model as described in [38]. The initial configuration (IC) of the SPN, depicted in Figure 3, and which leads to the wild-type expression pattern is known [26]: wg4~en1~hh1~ptc2,3,4~ci2,3,4~1 (on or expressed). The re- maining nodes in every cell of the parasegment are set to 0 (off, or not expressed). Overall, the dynamics of the SPN settles to one of ten attractors – usually divided into four qualitatively distinct groups, see Figure 4: (1) wild-type with three extra variations (PTC mutant, double wg bands, double wg bands PTC mutant); (2) Broad-stripe mutant; (3) No segmentation; and (4) Ectopic (with the same variations as wild-type). Albert and Othmer estimated that the number of configurations that converge to the wild-type attractor is approximately 6\|1011 – a very small portion of the total number of possible configurations (&7\|1016) – and that the broad-stripe mutant attractor basin contains about 90% of all possible configurations [26]. Figure 1. (A) LUT for Boolean automaton f ~x ^ (y _ z) and (B) components of a single LUT entry. doi:10.1371/journal.pone.0055946.g001 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 3 March 2013 \| Volume 8 \| Issue 3 \| e55946 The inner and output nodes of each cell in a parasegment – that is, every node except the input node SLP – that has reached a stable configuration (attractor) are always in one of the following five patterns. N I1: all nodes are off except PTC, ci, CI and CIR. N I2: same as I1 but states of ptc, PH, SMO, CIA and CIR are negated. N I3: all nodes are off except en, EN, hh, HH and SMO. N I4: same as I3 but PTC and SMO are negated. N I5: negation of I4, except PTC and CIR remain as in I4. Figure 2. Connectivity graph of the SPN model. The fifteen genes and proteins considered in the SPN model are represented (white nodes). The incoming edges to a node x originate in the nodes that are used by x to determine its transition. Shaded nodes represent the spatial signals (states of WG, HH and hh in neighbouring cells). Note that SLP – derived from an upstream intra-cellular signal – is an input node to this network. The self-connection it has represents the steady-state assumption: SLPtz1 i ~SLPt i. Notice also that this graph represents the fully synchronous version of the model, where modifications concerning PH and SMO have been made (see main text for details). doi:10.1371/journal.pone.0055946.g002 Figure 3. A parasegment in the SPN model. Cells are represented horizontally, where the top (bottom) row is the most anterior (posterior) cell. Each column is a gene, protein or complex – a node in the context of the BN model. The specific pattern shown corresponds to the wild-type initial expression pattern observed at the onset of the segment polarity genes regulatory dynamics (xini); Black/on (white/off) squares represent expressed (not expressed) genes or proteins. doi:10.1371/journal.pone.0055946.g003 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 4 March 2013 \| Volume 8 \| Issue 3 \| e55946 For example, the wild-type configuration corresponds – from anterior to posterior cell – to the patterns I3, I2, I1 and I5. Thus the pattern I4 is only seen in mutant expression patterns. The patterns I1 to I5 can be seen as attractors of the inner- and output-node dynamics of each cell in a parasegment. Besides the fact that the SPN is probably the most well-known discrete dynamical system model of biochemical regulation, we chose it to exemplify our methodology because (1) it has been well- validated experimentally, despite the assumption that genes and proteins operate like on/off switches with synchronous transitions and (2) the model includes both intra-cellular regulation and inter- cellular signalling in a spatial array of cells. The intra and inter- cellular interactions in the SPN model result in a dynamical landscape that is too large to characterize via an STG, while adding also an extra level of inter-cellular (spatial) regulation. The ability to deal with such multi-level complexity makes our methodology particularly useful. As we show below, we can uncover the signals that control collective information processing in such (spatial and non-spatial) complex dynamics. Methodology and Results Micro-level Canalization via Schemata In previous work, we used schema redescription to demonstrate that we can understand more about the dynamical behaviour of automata networks by analysing the patterns of redundancy present in their (automata) components (micro-level), rather than looking solely at their macro-level or collective behaviour [39]. Here we relate the redundancy removed via schema redescription with the concept of canalization, and demonstrate that a characterization of the full canalization present in biochemical networks leads to a better understanding of how cells and collections of cells ‘compute’. Moreover, we show that this leads to a comprehensive characterization of control in automata models of biochemical regulation. Let us start by describing the schema redescription methodology. Since a significant number of new concepts and notations are introduced in this, and subsequent sections, a succinct glossary of terms as well as a table with the mathematical notations used is available in Data S1. From the extended view of canalization introduced earlier, it follows that the inputs of a given Boolean automaton do not control its transitions equally. Indeed, substantial redundancy in state-transition functions is expected. Therefore, filtering redun- dancy out is equivalent to identifying the loci of control in automata. In this section we focus on identifying the loci of control in individual automata by characterizing the canalization present in their transition functions. First, we consider how subsets of inputs in specific state combinations make other inputs redundant. Then we propose an additional form of canalization that accounts for input permutations that leave a transition unchanged. Later, we use this characterization of canalization and control in individual automata to study networks of automata; this also allows us to analyse robustness and collective computation in these networks. Wildcard schemata and enputs. Consider the example automaton x in Figure 5A, where the entire subset of LUT entries in F with transitions to on is depicted. This portion of entries in F can be redescribed as a set of wildcard schemata, F’:ff ’ug. A wildcard schema f ’u is exactly like a LUT entry, but allows an additional wildcard symbol, # (also represented graphically in grey), to appear in its condition (see Figure 5B). A wildcard input means that it accepts any state, leaving the transition unchanged. In other words, wildcard inputs are redundant given the non-wildcard input states specified in a schema f ’u. More formally, when the truth value of an input Boolean variable i in a schema f ’u is defined by the third (wildcard) symbol, it is equivalent to stating that the truth value of automaton x is unaffected by the truth value of i given the conditions defined by f ’u: (xjf ’u,i)~(xjf ’u,:i). Each schema Table 1. Boolean logic formulae representing the state-transition functions for each node in the SPN (four-cell parasegment) model. Index Node State{TransitionFunction 1 SLPtz1 i /0 if i~1 _ i~2; 1 if i~3 _ i~4; 2 wgtz1 i /(CIAt i ^ SLPt i ^ :CIRt i) _ (wgt i ^ (CIAt i _ SLPt i) ^ :CIRt i) 3 WGtz1 i /wgt i 4 entz1 i /(WGt i{1 _ WGt iz1) ^ :SLPt i 5 ENtz1 i /ent i 6 hhtz1 i /ENt i ^ :CIRt i 7 HHtz1 i /hht i 8 ptctz1 i /CIAt i ^ :ENt i ^ :CIRt i 9 PTCtz1 i /ptct i _ (PTCt i ^ :HHt i{1 ^ :HHt i{1) 10 PHt i /PTCt i ^ (HHt i{1 _ HHt iz1) 11 SMOt i /:PTCt i _ (HHt i{1 _ HHt iz1) 12 citz1 i /:ENt i 13 CItz1 i /cit i 14 CIAtz1 i /CIt i ^ (:PTCt i _ hht i{1 _ hht iz1 _ HHt i{1 _ HHt iz1) 15 CIRtz1 i /CIt i ^ PTCt i ^ :hht i{1 ^ :hht iz1 ^ :HHt i{1 ^ :HHt iz1 The subscript represents the cell index; the superscript represents time. Note that every node has a numerical index assigned to it, which we use for easy referral throughout the present work. The extra-cellular nodes, hh,HH and WG in adjacent cells are indexed as follows: 16 to 21 denote hhi{1, hhiz1, HHi{1, HHiz1, WGi{1 and WGiz1 in this order. doi:10.1371/journal.pone.0055946.t001 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 5 March 2013 \| Volume 8 \| Issue 3 \| e55946 redescribes a subset of entries in the original LUT, denoted by Uu:ffa : fa f 0 ug ( means ‘is redescribed by’). Wildcard schemata are minimal in the sense that none of the (non-wildcard) inputs in the condition of a schema can be ‘raised’ to the wildcard status and still ensure the automaton’s transition to the same state. Because wildcard schemata are minimal, Uu6(Uw ^ Uw6(Uu, Vf ’u, f ’w[F’. In other words, a wildcard schema is unique in the sense that the subset of LUT entries it redescribes is not fully redescribed by any other schema. However, in general Uu\Uw=1. This means that schemata can overlap in terms of the LUT entries they describe. In Figure 5, U1:ff1,f5,f9,f13g and U9:ff4,f5,f6,f7g, therefore U1\U9:ff5g. The set of wildcard schemata F’ is also complete. This means that for a given LUT F there is one and only one set F’ that contains all possible minimal and unique wildcard schemata. Since wildcard schemata are minimal, unique and they form a complete set F’, they are equivalent to the set of all prime implicants obtained during the first step of the Quine & McCluskey Boolean minimization algorithm [40]. Typically, prime implicants are computed for the fraction of the LUT that specifies transitions Figure 4. The ten attractors reached by the SPN. These attractors are divided in four groups: wild-type, broad-stripe, no segmentation and ectopic. More specifically: (a) wild-type, (b) variant of (a), (c) wild-type with two wg stripes, (d) variant of (c), (e) broad-stripe, (f) no segmentation, (g) ectopic, (h) variant of (g), (i) ectopic with two wg stripes, and (j) variant of (i). The wild-type attractor (a) is referred to as Awt in the results and discussion sections. doi:10.1371/journal.pone.0055946.g004 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 6 March 2013 \| Volume 8 \| Issue 3 \| e55946 to on. Then a subset of the so-called essential prime implicants is identified. The set of essential prime implicants is the subset of prime implicants sufficient to describe (cover) every entry in the input set of LUT entries. However, to study how to control the transitions of automata we use the set of all prime implicants, since it encodes every possible way a transition can take place. The set F’ may also contain any original entry in F that could not be subsumed by a wildcard schema. Although the upper bound on the size of F’ is known to be O(3k= ﬃﬃﬃ k p ) [41], the more input redundancy there is, the smaller the cardinality of F’. The condition of a wildcard schema can always be expressed as a logical conjunction of literals (logical variables or their negation), which correspond to its non-wildcard inputs. Since a wildcard schema is a prime implicant, it follows that every literal is essential to determine the automaton’s transition. Therefore, we refer to the literals in a schema as its essential input states, or enputs for short. To summarize, each enput in a schema is essential, and the conjunction of its enputs is a sufficient condition to control the automaton’s transition. It also follows that the set F’ of wildcard schemata can be expressed as a disjunctive normal form (DNF) – that is, a disjunction of conjunctions that specifies the list of sufficient conditions to control automaton x, where each disjunction clause is a schema. The DNF comprising all the prime implicants of a Boolean function f is known as its Blake’s canonical form [42]. The canonical form of f always preserves the input-output relationships specified by its LUT F. Therefore, the basic laws of Boolean logic – contradiction, excluded middle and de Morgan’s laws – are preserved by the schema redescription. Schema redescription is related to the work of John Holland on condition/action rules to model inductive reasoning in cognitive systems [43] and to the general RR framework proposed by Annette Figure 5. Schema redescription. (A) Subset of LUT entries of an example automaton x that prescribe state transitions to on (1); white (black) states are 0 (1). (B) Wildcard schema redescription; wildcards denoted also by grey states. Schema f ’9 is highlighted to identify the subset of LUT entries U9:ff4,f5,f6,f7g it redescribes. (C) Two-symbol schema redescription, using the additional position-free symbol; the entire set F’ is compressed into a single two-symbol schema: f ’’1. Any permutation of the inputs marked with the position-free symbol in f ’’1 results in a schema in F’. Note that f ’’1 redescribes the entire set of entries with transition to on and thus jHhj~14. Since there is only one set of marked inputs, the position-free symbol does not require an index. Although this figure depicts only the schemata obtained for the subset of LUT entries of x that transition to on, entries that do not match any of these schemata transition to off (since x is a Boolean automaton). doi:10.1371/journal.pone.0055946.g005 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 7 March 2013 \| Volume 8 \| Issue 3 \| e55946 Karmiloff-Smith to explain the emergence of internal representa- tions and external notations in human cognition [44]. Our methodology to remove redundancy from automata LUTs also bears similarities with the more general mask analysis developed by George Klir in his ‘reconstructability’ analysis, which is applicable to any type of variable [45]. In addition, prime implicants have been known and used for the minimization of circuits in electrical engineering since the notion was introduced by Quine & McCluskey [40]; similar ideas were also used by Valiant [46] when introducing Probably Approximately Correct (PAC) learning. Two-symbol schemata. We now introduce a different and complementary form of redundancy in automata, which we consider another form of canalization. Wildcard schemata identify input states that are sufficient for controlling an automaton’s transition (enputs). Now we identify subsets of inputs that can be permuted in a schema without effect on the transition it defines [39]. For this, a further redescription process takes as input the set of wildcard schemata (F’) of x to compute a set of two-symbol schemata F’’:ff ’’hg (see Figure 5C). The additional position-free symbol (0 m) above inputs in the condition of a schema f ’’ means that any subset of inputs thus marked can ‘switch places’ without affecting the automaton’s transition. The index of the position-free symbol, when necessary, is used to differentiate among distinct subsets of ‘permutable’ inputs. A two-symbol schema f ’’h redescribes a set Hh:ffa : faf 00 h g of LUT entries of x; it also redescribes a subset H’h(F’ of wildcard schemata. A two-symbol schema f ’’h captures permutation redundancy in a set of wildcard schemata H’h. More specifically, it identifies subsets of input states whose permutations do not affect the truth value of the condition, leaving the automaton’s transition unchanged. In group theory, a permutation is defined as a bijective mapping of a non- empty set onto itself; a permutation group is any set of permutations of a set. Permutation groups that consist of all possible permutations of a set are known as symmetric groups under permutation [47]. For Boolean functions in general, the study of permutation/symmetric groups dates back to Shannon [48] and McCluskey [49] (see also [50]). Two-symbol schemata identify subsets of wildcard schemata that form symmetric groups. We refer to each such subset of input states that can permute in a two-symbol schema – those marked with the same position-free symbol – as a group-invariant enput. Note that a group-invariant enput may include wildcard symbols marked with a position-free symbol. More formally, a two-symbol schema f ’’ can be expressed as a logical conjunction of enputs – literal or group-invariant. Let us denote the set of literal enputs on the condition of f ’’ by X‘(X – the non-wildcard inputs not marked with the position-free symbol. For simplicity, n‘~ X‘ j j. A group-invariant enput g is defined by (1) a subset of input variables Xg(X that are marked with an identical position-free symbol, and (2) a permutation constraint (a bijective mapping) on Xg defined by the expression ng~n0 gzn1 gzn# g , where ng~ Xg , n0 g is the number of inputs in Xg in state 0 (off), and n1 g is the number of inputs in Xg in state 1 (on). We further require that at least two of the quantities n0 g,n1 g and n# g are positive for any group-invariant enput g. We can think of these two required positive quantities as subconstraints; in particular, we define a group-invariant enput by the two subconstraints n0 g,n1 g, since n# g is always derivable from those two given the expression for the overall permutation constraint. This precludes the trivial case of subsets of inputs in the same state from being considered a valid group-invariant enput – even though they can permute leaving the transition unchanged. A two-symbol schema f ’’ has n‘ literal enputs and g group-invariant enputs; each of the latter type of enputs is defined by a distinct permutation constraint for g~1,:::,g. An input variable whose truth value is the wildcard symbol in a given schema is never a literal enput (it is not essential by definition). However, it can be part of a group-invariant enput, if it is marked with a position-free symbol. Further details concerning the computation of wildcard and two-symbol schemata are available in Data S2. In our working example, the resulting two-symbol schema (see Figure 5C) contains n‘~2 literal inputs: X‘~fi2~0,i3~1g. It also contains one (g~1) group-invariant enput Xg~fi1,i4,i5,i6g with size ng~4 and subconstraints n0 g~1 ^ n1 g~1. This rede- scription reveals that the automaton’s transition to on is determined only by a subset of its six inputs: as long as inputs 2 and 3 are off and on, respectively, and among the others at least one is on and another is off, the automaton will transition to on. These minimal control constraints are not obvious in the original LUT and are visible only after redescription. We equate canalization with redundancy. The more redundancy exists in the LUT of automaton x, as input-irrelevance or input- symmetry (group-invariance), the more canalizing it is, and the more compact its two-symbol redescription is, thus jF’’jvjFj. In other words – after redescription – input and input-symmetry redundancy in F is removed in the form of the two symbols. The input states that remain are essential to determine the automaton’s transition. Below we quantify these two types of redundancy, leading to two new measures of canalization. Towards that, we must first clearly separate the two forms of redundancy that exist in 2-symbol schemata. The condition of a two-symbol schema f ’’ with a single group-invariant enput g – such as the one in Figure 5C – can be expressed as: ^ ij[X0 ‘ :ij ^ ij[X1 ‘ ij ^ X ij[Xg :ij§n0 g 0 @ 1 A ^ X ij[Xg ij§n1 g 0 @ 1 A ð1Þ where X 0 ‘ is the set of literal enputs that must be off, and X 1 ‘ is the set of literal enputs that must be on (thus X‘~X 1 ‘ \|X 0 ‘ ). This expression separates the contributions (as conjunctions) of the literal enputs, and each subconstraint of a group-invariant enput. Since we found no automaton in the target model (see below) with schemata containing more than one group-invariant enput, for simplicity and without lack of generality, we present here only this case (g~1). See Data S3 for the general expression that accounts for multiple group-invariant enputs (gw1). All possible transitions of x to on are described by a set F1’’ of two-symbol schemata. This set can also be expressed in a DNF, where each disjunction clause is given by Expression 1 for all schemata f ’’[F1’’: Transitions to off are defined by the negation of such DNF expression: F0’’: :f ’’,Vf ’’[F1’’ f g. Canalization of an automaton x is now characterized in terms of two-symbol schemata that capture two forms of redundancy: (1) input-irrelevance and (2) input-symmetry (group-invariance). We next describe the procedure to compute 2-symbol schemata for a an automaton x. Readers not interested in the algorithmic details of this compu- tation can safely move to the next subsection. The procedure starts with the set of wildcard schemata F’ obtained via the first step of the Quine & McCluskey algorithm [40] (see above). The set F’ is then partitioned into subsets H’i such that, F’~ [ i H’i: Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 8 March 2013 \| Volume 8 \| Issue 3 \| e55946 where each H’i contains every schema x’[F’ with equal number of zeroes (n0), ones (n1), and wildcards (n#), with n0zn1zn#~k. In other words, the H’i are equivalence classes induced on F’ by n0, n1, and n#. This is a necessary condition for a set of wildcard schemata to form a symmetric group. The algorithm then iterates on each H’i, checking if it contains a symmetric group; i.e. if it contains wildcard schemata with all the permutations of the largest set of inputs variables possible. If it does, it marks those input variables as a group-invariant enput in H’i and moves to another subset H’j. If it does not, then it checks for symmetric groups in smaller sets of input variables within each set H’i. It does this by iteratively expanding the search space to include all subsets of H’i with cardinality jH’ij{1. The procedure is repeated, if no symmetric groups are found, until the subsets contain only one wildcard schema. Although several heuristics are implemented to prune the search space, the algorithm is often not suitable for exhaustively searching symmetric groups in large sets of schemata. However, the individual automata found in models of biochemical regulation and signalling networks typically have a fairly low number of inputs. Therefore, schema redescription of their LUT leads to manageable sets of wildcard schemata, which can be exhaustively searched for symmetric groups. Indeed, as shown below, all automata in the SPN model have been exhaustively redescribed into two-symbol schemata. For additional details on the compu- tation of schemata see Data S2. Quantifying Canalization: Effective Connectivity and Input Symmetry Schemata uncover the ‘control logic’ of automata by making the smallest input combinations that are necessary and sufficient to determine transitions explicit. We equate canalization with the redundancy present in this control logic: the smaller is the set of inputs needed to control an automaton, the more redundancy exists in its LUT and the more canalizing it is. This first type of canalization is quantified by computing the mean number of unnecessary inputs of automaton x, which we refer to as input redundancy. An upper bound is given by, kr(x)~ P fa[F max h:fa[Hh n# h jFj ð2Þ and a lower bound is given by: kr(x)~ P fa[F min h:fa[Hh n# h jFj ð3Þ These expressions compute a mean number of irrelevant inputs associated with the entries of the LUT F. The number of irrelevant inputs in a schema f ’’h is the number of its wildcards n# h . Because each entry fa of F is redescribed by one or more schemata f ’’h, there are various ways to compute a characteristic number of irrelevant inputs associated with the entry, which is nonetheless bounded by the maximum and minimum number of wildcards in the set of schemata that redescribe fa. Therefore, the expressions above identify all schemata f ’’h whose set of redescribed entries Hh includes fa. The upper (lower) bound of input redundancy, Equation 2 (Equation 3), corresponds to considering the maximum (minimum) number of irrelevant inputs found for all schemata f ’’h that redescribe entry fa of the LUT – an optimist (pessimist) quantification of this type of canalization. Notice that input redundancy is not an estimated value. Also, it weights equally each entry of the LUT, which is the same as assuming that every automaton input is equally likely. Here we use solely the upper bound, which we refer to henceforth simply as input redundancy with the notation kr(x). This means that we assume that the most redundant schemata are always accessible for control of the automaton. We will explore elsewhere the range between the bounds, especially in regards to predicting the dynamical behaviour of BNs. The range for input redundancy is 0ƒkr(x)ƒk, where k is the number of inputs of x. When kr(x)~k we have full input irrelevance, or maximum canalization, which occurs only in the case of frozen-state automata. If kr(x)~0, the state of every input is always needed to determine the transition and we have no canalization in terms of input redundancy. In the context of a BN, if some inputs of a node x are irrelevant from a control logic perspective, then its effective set of inputs is smaller than its in-degree k. We can thus infer more about effective control in a BN than what is apparent from looking at structure alone (see analysis of macro-level control below). A very intuitive way to quantify such effective control, is by computing the mean number of inputs needed to determine the transitions of x, which we refer to as its effective connectivity: ke(x)~k(x){kr(x) ð4Þ whose range is 0ƒke(x)ƒk. In this case, ke(x)~0 means full input irrelevance, or maximum canalization, and kr(x)~k, means no canalization. The type of canalization quantified by the input redundancy and effective connectivity measures does not include the form of permutation redundancy entailed by group-invariant enputs. Yet this is a genuine form of redundancy involved in canalization, as in the case of nested canalization [14], since it corresponds to the case in which different inputs can be alternatively canalizing. The two-symbol schema redescription allows us to measure this form of redundancy by computing the mean number of inputs that participate in group-invariant enputs, easily tallied by the occurrence of the position-free symbol (0) in schemata. Thus we define a measure of input symmetry for an automaton x, whose upper-bound is given by ks(x)~ P fa[F max h:fa[Hh n0 h jFj ð5Þ and a lower-bound by, ks(x)~ P fa[F min h:fa[Hh n0 h jFj ð6Þ where n 0 h is the number of position-free symbols in schema f ’’h. The upper bound of input symmetry (Equation 5) corresponds to considering an optimist quantification of this type of canaliza- tion. Here we use solely the upper bound, which we refer to henceforth simply as input symmetry and denote by ks(x). Again, the assumption is that the most redundant schemata are always accessible for control of the automaton. The range for input symmetry is 0ƒks(x)ƒk. High (low) values mean that permuta- Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 9 March 2013 \| Volume 8 \| Issue 3 \| e55946 tions of input states are likely (unlikely) to leave the transition unchanged. Canalization in automata LUTs – the micro-level of networks of automata – is then quantified by two types of redundancy: input redundancy using kr(x) and input symmetry with ks(x). To be able to compare the canalization in automata with distinct numbers of inputs, we can compute relative measures of canalization: k r (x)~ kr(x) k(x) ; k s (x)~ ks(x) k(x) ð7Þ the range of which is ½0,1: Automata transition functions can have different amounts of each form of canalization, which allows us to consider four broad canalization classes for automata: class A with high kr(x) and high ks(x), class B with high kr(x) and low ks(x), class C with low kr(x) and high ks(x), and class D with low kr(x) and low ks(x). We will explore these classes in more detail elsewhere. Below, these measures are used to analyse micro-level canalization in the SPN model and discuss the type of functions encountered. Before that, let us introduce an alternative repre- sentation of the canalized control logic of automata, which allows us to compute network dynamics directly from the parsimonious information provided by schemata. Network Representation of a Schema Canalization in an automaton, captured by a set of schemata, can also be conveniently represented as a McCulloch & Pitts threshold network – introduced in the 1940s to study computation in interconnected simple logical units [51]. These networks consist of binary units that can transition from quiescent to firing upon reaching an activity threshold (t) of the firing of input units. To use this type of network to represent two-symbol schemata we resort to two types of units. One is the state unit (s-unit), which represents an input variable in a specific Boolean state; the other is the threshold unit (t-unit) that implements the condition that causes the automaton to transition. Two s-units are always used to represent the (Boolean) states of any input variable that participates as enput in the condition of an automaton x: one fires when the variable is on and the other when it is off. To avoid contradiction, the two s-units for a given variable cannot fire simultaneously. Directed fibres link (source) units to (end) units, propagating a pulse – when the source unit is firing – that contributes to the firing of the end unit. The simultaneous firing of at least t (threshold) incoming s-units into a t-unit, causes the latter to fire. In the example automaton in Figure 5, the set of schemata F’’ contains only one schema. This schema can be directly converted to a (2-layer) McCulloch & Pitts network. This conversion, which is possible due to the separation of subconstraints given by Expression (1), is shown in Figure 6 and explained in its caption. Note that in the McCulloch & Pitts representation, the transition of the automaton is determined in two steps. First, a layer of threshold units is used to check that the literal and group-invariant constraints are satisfied; then, a second layer – containing just one threshold unit – fires when every subconstraint in Expression (1) has been simultaneously satisfied, determining the transition. This means that in this network representation each schema with literal enputs and at least a group-invariant enput requires two layers and three t-units. Since in McCulloch & Pitts networks each threshold unit has a standard delay of one time step, this network representation of a schema takes two time steps to compute its transition. We introduce an alternative threshold network representation of a two-symbol schema f ’’ that only requires a single t-unit and takes a single time delay to compute a transition. We refer to this variant as the Canalizing Map of a schema or CM for short. A CM is essentially the same as a McCulloch and Pitts network, with the following provisos concerning the ways in which s-units and t-units can be connected: 1. Only one fibre originates from each s-unit that can participate as enput in f ’’ and it must always end in the t-unit used to encode f ’’. 2. The fibre that goes from a s-unit to the t-unit can branch out into several fibre endings. This means that if the s-unit is firing, a pulse propagates through its outgoing fibre and through its branches. Branching fibres are used to capture group-invariant enputs, as we explain later. 3. Branches from distinct s-units can fuse together into a single fibre ending – the fused fibre increases the end t-unit’s firing activity by one if at least one of the fused fibres has a pulse. 4. A fibre that originates in a t-unit encoding a schema f ’’ must end in a s-unit that corresponds to the automaton transition defined by f ’’. Figure 7 depicts the elements of a single schema’s CM. Table 2 summarizes the rules that apply to the interconnections between units. Transitions in CMs occur in the same way as in standard McCulloch & Pitts networks. Once sufficient conditions for a transition are observed at some time t, the transition occurs at tz1. The firing (or not) of t-units is thus assumed to have a standard delay (one time-step), identical for all t-units. Note that in CMs, s-units can be regarded as a special type of t-unit with threshold t~1 that send a pulse through their outgoing fibres instantaneously. Next we describe the algorithm to obtain the CM representation of a schema. Readers not interested in the algorithmic details of this computation can safely bypass the next subsection. Algorithm to obtain the canalizing map of a schema. Given a 2-symbol schema f ’’, there are two steps involved in producing its CM representation. The first is connecting s-units to the t-unit for f ’’ in such a way that it fires, if and only if, the constraints of f ’’ – defined by Expression (1) – are satisfied. The second step is determining the appropriate firing threshold t for the t-unit. If the schema does not have group- invariant enputs, the conversion is direct as for the standard McCulloch & Pitts network – see Figure 6: The s-units corresponding to literal enputs ij[X‘ are linked to the t-unit using a single fibre from each s-unit to the t-unit, which has a threshold t~n‘. If the schema has a group-invariant enput, its subcon- straints are implemented by branching and fusing fibres connect- ing the s-units and the t-unit. In cases such as our example automaton x (Figures 5 and 6) where the subconstraints n0 g~n1 g~1, the solution is still simple. To account for subcon- straint n0 g, it is sufficient to take an outgoing fibre from each of the s-units ij[Xg : ij~0 and fuse them into a single fibre ending. Therefore, if at least one of these s-units is firing, the fused fibre ending transmits a single pulse to the t-unit, signalling that the subconstraint has been satisfied. Increasing the t-unit’s threshold by one makes the t-unit respond to this signal appropriately. The same applies for subconstraint n1 g, using a similar wiring for s-units ij[Xg : ij~1. The final threshold for the t-unit that captures the example schema of Figure 5 is thus t~n‘zn0 gzn1 g~2z1z1~4, as shown in Figure 8C. The case of general group-invariant constraints is more intricate. Every literal enput ij[X‘ is linked to the t-unit via a single fibre exactly as above. Afterwards, the subconstraints n0 g and n1 g of a group-invariant enput g are treated separately and Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 10 March 2013 \| Volume 8 \| Issue 3 \| e55946 consecutively. Note that for every input variable ij in the set Xg of symmetric input variables, there are two s-units: one representing ij in state 0 and another in state 1. To account for subconstraint n0 g on the variables of set Xg, let S(Xg be the set of s-units that represent the variables of the group-invariant enput that can be in state 0, where jXgj~ng. Next, we identify all possible subsets of S, whose cardinality is ng{(n0 g{1). That is, S~ Si : Si f x5S ^ jSij~ng{(n0 g{1)g. For each subset Si[S, we take an outgoing fibre from every s-unit in it and fuse them into a single fibre ending as input to the schema t-unit. After subconstraint n0 g is integrated this way, the threshold of the t-unit is increased by, jSj~ ng ng{(n0 g{1) ! ~ ng n0 g{1 ! ð8Þ This procedure is repeated for the subconstraint n1 g on Xg. The final threshold of the t-unit is, t~n‘z ng n0 g{1 ! z ng n1 g{1 ! ð9Þ This algorithm is illustrated for the integration of two example subconstraints in Figure 9; in Figure 8, the case of the only schema describing the transitions to on of running example automaton x is shown. Further details concerning this procedure are provided in Data S3. The canalizing map of an automaton. The algorithm to convert a single schema f ’’ to a CM is subsequently used to produce the CM of an entire Boolean automaton x as follows: Each schema f ’’[F’’ is converted to its CM representation. Each state of an input variable is represented by a single s-unit in the resulting threshold network. In other words, there is a maximum of two s-units (one for state 0 and one for state 1) for each input variable that is either a literal enput or participates in a group- invariant enput of x. The resulting threshold network is the canalizing map of x. The connectivity rules of automata CMs include the following provisos: 1. Every s-unit can be connected to a single t-unit with a single outgoing fibre, which can be single or have branches. 2. Therefore, the number of outgoing fibres coming out of a s-unit (before any branching) corresponds to the number of schemata f ’’[F’’ in which the respective variable-state participates as an enput. If such a variable is included in a group-invariant enput, then the fibre may have branches. 3. Any subset set of t-units with threshold t~1 for the same automaton transition (x~0 or x~1) are merged into a single t- Figure 6. McCulloch & Pitts representation of Expression (1). The conjunction clauses in Expression (1) for the example automaton x are directly mapped onto a standard McCulloch & Pitts network with two layers. On one layer the two literal enputs are accounted for by a threshold unit (at the top) with threshold t~n‘~2. There is also a group-invariant enput with permutation subconstraints on both Boolean states. Two threshold units on the same layer are used to capture these. The threshold unit on the left accounts for the permutation subconstraint n1 g~1. It thus has as incoming s-units the inputs xi[Xg : xi~1 and threshold t~n1 g~1. In a similar way, the threshold unit on the right accounts for the subconstraint n0 g~1. When all the constraints (literal and group-invariant) are satisfied, the last threshold unit (second layer) ‘fires’ causing the transition to on. doi:10.1371/journal.pone.0055946.g006 Figure 7. Elements of a Canalizing Map. Every s-unit is a circle, labelled according the automaton’s input it represents and coloured according to its state: black is on and white is off (here we use light-blue for a generic state). The t-unit (schema) is represented using a larger circle. One of its halves is coloured, and the other labelled with the t- unit’s threshold t. Fibres can be single, or branched. In this example there are branching fibres only, where fibre fusions represent all possible combinations of two out of the three s-units. doi:10.1371/journal.pone.0055946.g007 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 11 March 2013 \| Volume 8 \| Issue 3 \| e55946 unit (also with t~1), which receives all incoming fibres of the original t-units. In such scenario, any fused branches can also be de-fused into single fibres. Note that this situation corresponds to schemata that exhibit nested canalization, where one of several inputs settles the transition, but which do not form a symmetric group. The CM of x can be constructed from the subset of schemata F1’’ (the conditions to on), or F0’’ (the conditions to off). When the conditions are not met for convergence to on, one is guaranteed convergence to off (and vice-versa). However, since we are interested in exploring scenarios with incomplete information about the states of variables in networks of automata rather than a single automaton (see below), we construct the CM of a Boolean automaton x including all conditions, that is using F’’:F1’’\|F0’’. This facilitates the analysis of transition dynamics where automata in a network can transition to either state. Figure 10 depicts the complete CM of the example automaton x described in Figure 5– now including also its transitions to off. By uncovering the enputs of an automaton, we gain the ability to compute its transition with incomplete information about the state of every one of its inputs. For instance, the possible transitions of the automaton in Figure 5 are fully described by the CM (and schemata) in Figure 10; as shown, transitions can be determined from a significantly small subset of the input variables in specific state combinations. For instance, it is sufficient to observe i3~0 to know that automaton x transitions to off. If x was used to model the interactions that lead a gene to be expressed or not, it is easy to see that to down-regulate its expression, it is sufficient to ensure that the regulator i3 is not expressed. This is the essence of canalization: the transition of an automaton is controlled by a small subset of input states. In the macro-level canalization section below, we use the CM’s ability to compute automata transitions with incomplete information to construct an alternative portrait of network dynamics, which we use in lieu of the original BN to study collective dynamics. Let us first apply our micro-level methodology to the SPN model. Micro-level Canalization in the SPN Model The automata in the SPN fall in two categories: those that have a single input (k~1), the analysis of which is trivial, namely, SLP, WG, EN, HH, ci and CI, and those with kw1. The two-symbol schemata and canalization measures for each automaton in the SPN model are depicted in Figure 11; Figure 12 maps the automata to their canalization classes. Schemata easily display all the sufficient combinations of input states (enputs) to control the transitions of the automata in this model, which represent the inhibition or expression of genes and proteins. Indeed, the resulting list of schemata allows analysts to quickly infer how control operates in each node of the network. Wildcard symbols (depicted in Figure 11 as grey boxes) denote redundant inputs. Position-free symbols (depicted in Figure 11 as circles), denote ‘functionally equivalent’ inputs; that is, sets of inputs that can be alternatively used to ensure the same transition. For example, for wg to be expressed, SLP, the previous state of wg (reinforcing feedback loop) and CIA can be said to be ‘functionally equivalent’, since any two of these three need to be expressed for wg to be expressed. The several schemata that are listed for the expression or inhibition of a specific node (genes and gene products), give experts alternative ‘recipes’ available to control the node according to the model – and which can be experimentally tested and validated. Let us now present some relevant observations concerning micro-level canalization in the SPN model: 1. The inhibition of wg can be attained in one of two ways: either two of the first three inputs (SLP, wg, CIA) are off (unexpressed), or CIR is on (expressed). The expression of wg – essential in the posterior cell of a parasegment to attain the wild-type expression pattern (Figure 3)– is attained in just one way: CIR must be off (unexpressed), and two of the other three inputs (SLP, wg, CIA) must be on (expressed). Note the simplicity of this control logic vis a vis the 24~16 possible distinct ways to control wg specified by its LUT, given that it is a function of 4 inputs. This control logic is also not obvious from the Boolean logic expression of node wg, as shown in Table 1; at the very least, the schemata obtained for wg provide a more intuitive representation of control than the logical expression. Moreover, schema redescription, unlike the logical expression, allows us to directly quantify canalization. The control logic of this gene shows fairly high degree of both types of canalization: even though there are k~4 inputs, on average, only ke~1:75 inputs are needed to control the transition, and ks~2:25 inputs can permute without effect on the transition (see Figures 11 and 12); wg is thus modelled by an automaton of class A. 2. The inhibition of CIR can be attained in one of two simple, highly canalized, ways: either one of its first two inputs (PTC, CI) is off (unexpressed), or one of its four remaining inputs (hh and HH in neighbouring cells) is on (expressed); all other inputs can be in any other state. The expression of CIR can be attained in only one specific, non-canalized, way: the first two inputs must be on (expressed), and the remaining four inputs must be off (unexpressed) – a similar expression behaviour is found for hh and ptc. Note the simplicity of this control logic vis a vis the 26~64 possible distinct ways to control CIR specified by its LUT, given that it is a function of 6 inputs. While, in this case, the control logic is also pretty clear from the original Boolean logic expression of node CIR (in Table 1), the schemata obtained for CIR provide a more intuitive representation of control and allows us to directly quantify canalization. CIR is a protein with a very high degree of both types of canalization: even though there are k~6 inputs, on average, only ke~1:08 inputs are needed to control the transition, and ks~5:25 inputs can permute without effect on Table 2. Connectivity rules in canalizing maps. s-units t-units incoming fibres one or more one or more outgoing fibres one per schema of which is enput one for the transition it causes branching out Yes no fusing in No yes doi:10.1371/journal.pone.0055946.t002 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 12 March 2013 \| Volume 8 \| Issue 3 \| e55946 the transition (see Figures 11 and 12). This high degree of both types of canalization, which is not quantifiable directly from the logical expression or the LUT, is notable in Figure 12, where CIR emerges very clearly as an automaton of class A. 3. The control logic of CIA entails high canalization of the input redundancy kind. For instance, its inhibition can be achieved by a single one of its six inputs (CI off) and its expression by two inputs only (PTC off and CI on). On the other hand, there is low canalization of the input symmetry kind, therefore CIA is modelled by an automaton in class B. 4. The expression of en – essential in the anterior cell of a parasegment to achieve the wild-type phenotype – depends on the inhibition of (input node) SLP in the same cell, and on the expression of the wingless protein in at least one neighbouring cell. Figure 8. Canalizing map of example automaton x character- ized by a single schema. (A) Since f ’’ (shown on top) has n‘~2, the corresponding s-units for literal enputs xi[X‘ are directly linked to the t- unit for f ’’ with single fibres; t~n‘~2. (B) Adding the subconstraint n0 g~1 of the group-invariant enput Xg~fi1,i4,i5,i6g. In this case, ng{(n0 g{1)~ng~4, so there is only one subset Si(S and thus a single branch from each s-unit in the group-invariant, fused into a single ending. The threshold becomes t~n‘z ng n0 g{1 ~2z 4 0 ~3. (C) Finally, we add the second subconstraint n1 g~1 of the group-invariant enput Xg, which has the same properties as the subconstraint integrated in (B). The final threshold of the t-unit is given by (9), therefore t~n‘z ng n0 g{1 z ng n1 g{1 ~2z 4 0 z 4 0 ~4. Notice that only the input-combinations that satisfy the constraints of Expression (1) for f ’’ can lead to the firing of the t-unit; in other words, the canalizing map is equivalent to schema f ’’. doi:10.1371/journal.pone.0055946.g008 Figure 9. Procedure for obtaining the canalizing map of a group-invariant subconstraint. (A) subconstraint defined by n0 g~2, where ng~4. The first step is to consider the s-units (in state 0) for the four input variables in the group invariant enput Xg~fi1,i2,i3,i4g. Next we identify all the subsets Si of these s-units containing ng{(n0 g{1)~3 s-units: fi1,i2,i3g,fi1,i2,i4g,fi1,i3,i4g,fi2,i3,i4g (shown with dotted ar- rows). From every s-unit in each such subset Si, we take an outgoing fibre to be joined together into a single fibre ending as input to the t- unit. Finally, we increase the threshold of the t-unit by the total number of subsets, that is tA~ ng n0 g{1 ~ 4 4 ~4. (B) An example of the same procedure but for n0 g~3 and ng~4: tB~ ng n0 g{1 ~ 4 2 ~6. doi:10.1371/journal.pone.0055946.g009 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 13 March 2013 \| Volume 8 \| Issue 3 \| e55946 5. Most automata in the model fall into canalization class B described above. CIR and wg discussed above display greatest input symmetry, and fall in class A (see Figure 12). 6. Looking at all the schemata obtained in Figure 11, we notice a consistent pattern for all spatial signals, hhi+1, HHi+1 and WGi+1. Whenever they are needed to control a transition (when they are enputs in the schemata of other nodes), either they are off in both neighbouring cells, or they are on in at least one of the neighbouring cells. For instance, for a given cell i, HH in neighbouring cells is only relevant if it is unexpressed in both cells (HHi+1~0), or if it is expressed in at least one of them (HHi{1~1 _ HHiz1~1). This means that the six nodes corresponding to spatial signals affecting a cell in a paraseg- ment can be consolidated into just three neighbour nodes, a similar consolidation of spatial signals was used previously by Willadsen & Wiles [52] to simplify the spatial model into a single-cell non-spatial model. In what follows, we refer to these spatial signals simply as nhh, nHH and nWG. If such a node is off it means that the corresponding original nodes are off in both adjacent cells; if it is on it means that at least one of the corresponding original nodes in an adjacent cell is on. 7. Only PTC and wg have feedback loops that are active after schema redescription, both for their inhibition and expression; these are self-reinforcing, but also depend on other enputs (see also Figures 13 and 14). Because this is a relatively simple model, some of the observations about control, especially for nodes with fewer inputs, could be made simply by looking at the original transition functions in Table 1, since they are available as very simple logical expressions – this is the case of CIR, but certainly not wg above. However, the quantification of canalization requires the additional symbols used in schema redescription to identify redundancy, which are not available in the original automata logical expressions or their LUTs. Moreover, the transition functions of automata in larger Boolean models of genetic regulation and signalling are rarely available as simple logical expressions, and nodes can be regulated by a large number of other nodes, thus making such direct comprehension of control-logic difficult. In contrast, since redescription uncovers canalization in the form of input redundancy and symmetry, the more canalization exists, the more redundancy is removed and the simpler will be the schemata representation of the logic of an automaton. This makes canalizing maps (CM) particularly useful, since they can be used to visualize and compute the minimal control logic of automata. The CMs that result from converting the schemata of each node in the SPN to a threshold-network representation are shown in Figure 13 and Figure 14. For a biochemical network of interest, such as the SPN or much larger networks, domain experts (e.g. biomedical scientists and systems and computational biologists) can easily ascertain the control logic of each component of their model from the schemata or the corresponding CMs. In summary, there are several important benefits of schema redescription of Boolean automata vis a vis the original Boolean logic expression or the LUT of an automaton: (1) a parsimonious and intuitive representation of the control logic of automata, since redundancy is clearly identified in the form of the two additional symbols, which gives us (2) the ability to quantify all forms of canalization in the straightforward manner described above; finally, as we elaborate next, the integration of the schema redescription (or CMs) of individual automata in a network (micro- level) allows us to (3) characterize macro-level dynamics parsimoniously, uncovering minimal control patterns, robustness and the modules responsible for collective computation in these networks. Macro-level Canalization and Control in Automata Networks After removing redundancy from individual automata LUTs in networks (micro-level), it becomes possible to integrate their canalizing logic to understand control and collective dynamics of automata networks (macro-level). In other words, it becomes feasible to understand how biochemical networks process infor- mation collectively – their emergent or collective computation [39,53–56]. Dynamics canalization map and dynamical modularity. The CMs obtained for each automaton of a BN, such as the SPN model (see Figures 13 and 14), can be integrated into a single threshold network that represents the control logic of the entire BN. This simple integration requires that (1) each automaton is represented by two unique s-units, one for transition to on and another to off, and (2) s-units are linked via t-units with appropriate fibres, as specified by each individual CM. Therefore a unique t-unit represents each schema obtained in the redescrip- tion process. This results in the Dynamics Canalization Map (DCM) for the entire BN. Since the DCM integrates the CMs of its constituent automata, it can be used to identify the minimal control conditions that are sufficient to produce transitions in the dynamics of the entire network. Notice that when a node in the original BN undergoes a state-transition, it means that at least one t-unit fires in the DCM. When a t-unit fires, according to the control logic of Figure 10. Canalizing Map of automaton x. (A) complete set of schemata F’’ for x, including the transitions to on shown in Figure 5 and the transitions of off (the negation of the first).(B) canalizing map; t-units for schemata f ’’2 and f ’’3 were merged into a single t-unit with threshold t~1 (see main text). (C) effective connectivity, input symmetry and input redundancy of x. doi:10.1371/journal.pone.0055946.g010 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 14 March 2013 \| Volume 8 \| Issue 3 \| e55946 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 15 March 2013 \| Volume 8 \| Issue 3 \| e55946 the DCM, it can cause subsequent firing of other t-units. This allows the identification of the causal chains of transitions that are the building blocks of macro-level dynamics and information processing, as explained in detail below. Another important feature of the DCM is its compact size. While the dynamical landscape of an automata network, defined by its state-transition graph (STG), grows exponentially with the number of nodes – 2n in Boolean networks – its DCM grows only linearly with 2n units plus the number of t-units needed (which is the number of schemata obtained from redescribing every automaton in the network): 2nz Pn i~1 jF’’ij. Furthermore, the computation of a DCM is tractable even for very large networks with thousands of nodes, provided the in-degree of these nodes is not very large. In our current implementation, we can exhaustively perform schema redescription of automata with kƒkmax&20; that is, LUTs containing up to 220 entries. It is very rare that dynamical models of biochemical regulation have molecular species that depend on more than twenty other variables (see e.g. [57]). Therefore, this method can be used to study canalization and control in all discrete models of biochemical regulation we have encountered in the literature, which we will analyse elsewhere. It is important to emphasize that the integration of the CMs of individual automata into the DCM does not change the control logic encoded by each constituent CM, which is equivalent to the logic encoded in the original LUT (after removal of redundancy). Therefore, there is no danger of violating the logic encoded in the original LUT of any automaton in a given BN. However, it is necessary to ensure that any initial conditions specified in the DCM do not violate the laws of contradiction and excluded middle. This means, for instance, that no initial condition of the DCM can have the two (on and off) s-units for the same automaton firing simultaneously. The DCM for a single cell in the SPN model is shown in Figure 15. The spatial signals from adjacent cells are highlighted using units with a double border (nhh,nHHandnWG). For the simulations of the spatial SPN model described in subsequent sections, we use four coupled single-cell DCMs (each as in Figure 15) to represent the dynamics of the four-cell parasegment, where nodes that enable inter-cellular regulatory interactions are appropriately linked, as defined in the original model. Also, as in the original model, we assume periodic boundary conditions for the four-cell parasegment: the posterior cell is adjacent to the anterior cell. When making inferences using the DCM, we use signal to refer to the firing of a s-unit and the transmission of this information through its output fibres. When a s-unit fires in the DCM, it means that its corresponding automaton node in the original BN transitioned to the state represented by the s-unit. We also use pathway to refer to a logical sequence of signals in the DCM. We highlight two pathway modules in the DCM of the SPN in Figure 15: M1 and M2. The first is a pathway initiated by either the inhibition of WG in neighbour cells, or the expression of SLP upstream in the same cell. That is, the initial pattern for this module is M0 1~:nWG _ SLP. The initiating signal for M2 is defined by the negation of those that trigger the first: M0 2~:M0 1~nWG ^ :SLP. Both modules follow from (external or upstream) input signals to a single cell in the SPN; they do not depend at all on the initial states of nodes (molecular species) of the SPN inside a given cell. Yet, both of these very small set of initial signals necessarily cause a cascade of other signals in the network over time. M1 is the only pathway that leads to the inhibition of en Figure 11. Micro-level canalization for the Automata in the SPN model. Schemata for inhibition (transitions to off) and expression (transitions to on) are shown for each node (genes or proteins) in model. In-degree (k), input redundancy (kr), effective connectivity (ke), and input symmetry (ks) are also shown. doi:10.1371/journal.pone.0055946.g011 Figure 12. Quantification of canalization in the SPN automata. Relative input redundancy is measured in the horizontal axis (k r ) and relative input symmetry is measured in the vertical axis (k r ). Most automata in the SPN fall in the class II quadrant, showing that most canalization is of the input redundancy kind, though nodes such as CIR and wg display strong input symmetry too. doi:10.1371/journal.pone.0055946.g012 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 16 March 2013 \| Volume 8 \| Issue 3 \| e55946 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 17 March 2013 \| Volume 8 \| Issue 3 \| e55946 (and EN) as well as the expression of ci (and CI). It also causes the inhibition of hh and HH, both of which function as inter-cellular signals for adjacent cells – this inhibition can be alternatively controlled by the expression of CIR, which is not part of neither M1 nor M2. Since M0 1 is a disjunction, its terms are equivalent: either the inhibition of nWG or the upstream expression of SLP control the same pathway, regardless of any other signals in the network. M2 is the only pathway that leads to the expression of en (and EN) as well as the inhibition of ci (and CI); It also causes the inhibition of CIA, ptc and CIR – these inhibitions can be alternatively controlled by other pathways. If the initial conditions M0 2 are sustained for long enough (steady-state inputs), the downstream inhibition of CIA and sustained inhibition of SLP lead to the inhibition of wg (and WG); likewise, from sustaining M0 2, the downstream expression of EN and inhibition of CIR lead to the expression of hh (and HH). Since M0 2 is a conjunction, both terms are required: both the expression of nWG and the upstream inhibition of SLP are necessary and sufficient to control this pathway module, regardless of any other signals in the network. M1 and M2 capture a cascade of state transitions that are inexorable once their initiating signals (M0 1 and M0 2) are observed: M1~f:en,:EN, :hh, : HH, ci, CIg and M2~f:ci, :CI, :CIA, :wg, :WG, :CIR, :ptc, en, EN, hh, HHg. Further- more, these cascades are independent from the states of other nodes in the network. As a consequence, the transitions within a module are insensitive to delays once its initial conditions are set (and maintained in the case of M2 as shown). The dynamics within these portions of the DCM can thus be seen as modular; these pathway modules can be decoupled from the remaining regulatory dynamics, in the sense that they are not affected by the states of any other nodes other than their initial conditions. Modularity in complex networks has been typically defined as sub-graphs with high intra- connectivity [21]. But such structural notion of community structure does not capture the dynamically decoupled behaviour of pathway modules such as M1 and M2 in the SPN. Indeed, it has been recently emphasized that understanding modularity in complex molecular networks requires accounting for dynamics [58], and new measures of modularity in multivariate dynamical systems have been proposed by our group [59]. We will describe methods for automatic detection of dynamical modularity in DCMs elsewhere. Collective computation in the macro-level dynamics of autom- ata networks ultimately relies on the interaction of these pathway modules. Information gets integrated as modules interact with one another, in such a way that the timing of module activity can have an effect on downstream transitions. For instance, the expression of CI via M1 can subsequently lead to the expression of CIA, provided that nhh is expressed – and this is controlled by M2 in the adjacent cells. The expression of CI can also be seen as a necessary initial condition to the only pathway that results in the expression of CIR, which also depends on the inhibition of nhh and n HH and the expression of PTC, which in turn depends on the interaction of other modules, and so on. As these examples show, pathway modules allow us to uncover the building blocks of macro-level control – the collective computation of automata network models of biochemical regulation. We can use them, for instance, to infer which components exert most control on a target collective behaviour of interest, such as the wild-type expression pattern in the SPN. Indeed, modules M1 and M2 in the SPN model, which include a large proportion of nodes in the DCM, highlight how much SLP and the spatial signals from neighbouring cells control the dynamical behaviour of segment polarity gene regulation in each individual cell. Particularly, they almost entirely control the expression and inhibition of EN and WG; as discussed further below. The behaviour of these proteins across a four-cell parasegment mostly define the attractors of the model (including wild-type). The transitions of intra-cellular nodes are thus more controlled by the states of ‘external’ nodes than by the initial pattern of expression of genes and proteins in the cell itself. This emphasizes the well-known spatial constraints imposed on each cell of the fruit fly’s developmental system [60,61]. We next study and quantify this control in greater detail. Dynamical unfolding. A key advantage of the DCM is that it allows us to study the behaviour of the underlying automata network without the need to specify the state of all of its nodes. Modules M1 and M2 are an example of how the control that a very small subset of nodes exerts on the dynamics of SPN can be studied. This can be done because, given the schema redescription that defines the DCM, subsets of nodes can be assumed to be in an unknown state. Since the schema redescription of every automaton in the DCM is minimal and complete (see micro-level canalization section), every possible transition that can occur is accounted for in the DCM. By implementing the DCM as a threshold network, we gain the ability to study the dynamics of the original BN by setting the states of subsets of nodes. This allows us study convergence to attractors, or other patterns of interest, from knowing just a few nodes. More formally, we refer to an initial pattern of interest of a BN B as a partial configuration, and denote it by ^x. For example, M0 1 is a partial configuration ^x~M0 1~SLP _ :nWG, where the states of all other nodes is #, or unknown. We refer to dynamical unfolding as the sequence of transitions that necessarily occur after an initial partial configuration ^x, and denote it by s(^x) P, where P is an outcome pattern or configuration. From the DCM of the single-cell SPN model (Figure 15), we have s(M0 1) M1 and s(M0 2) M2. An outcome pattern can be a fully specified attractor A, but it can also be a partial configuration of an attractor where some nodes remain unknown – for instance, to study what determines the states of a specific subset of nodes of interest in the network. In the first case, it can be said that ^x fully controls the network dynamics towards attractor A. In the second, control is exerted only on the subset of nodes with determined logical states. The ability to compute the dynamical unfolding of a BN from partial configurations is a key benefit of the methodology introduced here: it allows us to determine how much partial configurations of interest control the collective dynamics of the network. For instance, in the SPN model it is possible to investigate how much the input nodes to the regulatory network of each cell control its dynamics. Or, conversely, how much the initial configuration of the intra-cellular regulatory network is irrelevant to determining its attractor. The nodes within each cell in a parasegment of the SPN are sensitive to three inter-cellular (external) input signals: nWG, nhh and nHH, and one intra- cellular (upstream) input, SLP. Given that the formation of parasegment boundaries in D. melanogaster is known to be tightly Figure 13. Canalizing Maps of individual nodes in the SPN model (part 1). The set of schemata for each automaton is converted into two CMs: one representing the minimal control logic for its inhibition, and another for its expression. Note that nX denotes the state of node X in both neighbour cells: :nXu:Xi{1 ^ :Xiz1 and nXuXi{1 _ Xiz1, where X is one of the spatial-signals hh, HH, or WG (see text). doi:10.1371/journal.pone.0055946.g013 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 18 March 2013 \| Volume 8 \| Issue 3 \| e55946 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 19 March 2013 \| Volume 8 \| Issue 3 \| e55946 spatially constrained [60,61], it is relevant to investigate how spatio-temporal control occurs in the SPN model. We already studied the control power of SLP and nWG, which lead to modules M1 and M2. We now exhaustively study the dynamical unfolding of all possible states of the intra- and inter-cellular input signals. We assume that SLP (upstream) and the (external) spatial signals are in steady-state to study what happens in a single cell. Since the state of nHH is the same as nhh after one time step, we consolidate those input signals into a single one: nhh. We are left with three input signals to the intra-cellular regulatory network: nodes SLP, nWG and nhh. Each of these three nodes can be in one of two states (on, off) and thus there are eight possible combinations of states for these nodes. Such simplification results in a non-spatial model and this was done previously by Willadsen & Wiles [52]. Setting each such combination as the initial partial configuration ^x, and allowing the DCM to compute transitions, yields the results shown in Figure 16. We can see that only two of the outcome patterns reached by the eight input partial configurations are ambiguous about which of the final five possible attractors is reached. Each individual cell in a parasegment can only be in one of five attractor patterns I1{I5 (see } background). This is the case of groups G2 and G4 in Figure 16. For all the other input partial configurations, the resulting outcome pattern determines the final attractor. We also found that for almost every input partial configuration, the states of most of the remaining nodes are also resolved; in particular the nodes that define the signature of the parasegment attractor – Engrailed (EN) and Wingless (WG) – settle into a defined steady-state. Notice also that for two of the input partial configurations (groups G3 and G5 in Figure 16), the states of every node in the network settle into a fully defined steady-state. The picture of dynamical unfolding from the intra- and inter-cellular inputs of the single-cell SPN network also allows us to see the roles played by modules M1 and M2 in the dynamics. The six input configurations in groups G1, G2, and G3 depict the dynamics where M1 is involved, while the two input configurations in G4 and G5 refer to M2 (node-states of each module in these groups appear shaded in Figure 16). By comparing the resulting dynamics, we can see clearly the effect of the additional information provided by knowing if nhh is expressed or inhibited; we also see that the dynamics of the modules is unaffected by other nodes, as expected. Figure 14. Canalizing Maps of individual nodes in the SPN model (cont). The set of schemata for each automaton is converted into two CMs: one representing the minimal control logic for its inhibition, and another for its expression. Note that nX denotes the state of node X in both neighbour cells: :nXu:Xi{1 ^ :Xiz1 and nXuXi{1 _ Xiz1, where X is one of the spatial-signals hh, HH, or WG (see text). doi:10.1371/journal.pone.0055946.g014 Figure 15. Dynamics Canalization Map for a single cell of the SPN Model. Also depicted are pathway modules M1 (pink) and M2 (blue), whose initial conditions depend exclusively on the expression and inhibition of input node SLP and of WG in neighbouring cells (the nWG spatial- signals). M1~:nWG _ SLP, M2~:M1 (see details in text). doi:10.1371/journal.pone.0055946.g015 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 20 March 2013 \| Volume 8 \| Issue 3 \| e55946 It is clear from these results that (single-cell) cellular dynamics in the SPN is almost entirely controlled from the inputs alone. We can say that extensive micro-level canalization leads the macro- level network dynamics to be highly canalized by external inputs – a point we explore in more detail below. For the dynamical unfolding depicted in Figure 16 we assumed that the three input signals to the intra-cellular regulatory network are in steady-state, focusing on a single cell. This is not entirely reasonable since inter- cellular signals are regulated by spatio-temporal regulatory dynamics in the full spatial SPN model. We thus now pursue the identification of minimal partial configurations that guarantee convergence to outcome patterns of interest in the spatial SPN model, such as specific (parasegment) attractors. Minimal configurations. To automate the search of min- imal configurations that converge to patterns of interest, we rely again on the notion of schema redescription, but this time for network-wide configurations rather than for individual automata LUTs. Notice that the eight input partial configurations used in the dynamical unfolding scenarios described in Figure 16 are wildcard schemata of network configurations: the state of the 14 Figure 16. Dynamical unfolding of the (single-cell) SPN with partial input configurations. The eight initial partial configurations tested correspond to the combinations of the steady-states of intra- and inter-cellular inputs SLP, nWG and nhh (and where nHH and nhh are merged into a single node, nhh). The specific state-combinations of these three variables is depicted on the middle (white) tab of each dynamical unfolding plot. Initial patterns that reach the same target pattern are grouped together in five groups G1 to G5 (identified in the top tab of each plot). The six input configurations in groups G1, G2, and G3 depict the dynamics where pathway module M1 is involved (nodes involved in this module are highlighted in pink.) The two input configurations in G4 and G5 depict the dynamics where pathway module M2 is involved (nodes involved in this module are highlighted in blue.) Three of the eight combinations are in G1 because they reach the same final configuration which, although partial, can only match the attractor I1. There are five possible attractor patterns of the SPN model for a single cell, shown in bottom right inset: I1 to I5 (see } background). Attractors reached by each group are identified in the bottom tab of each plot. Groups G2 and G4 both unfold to an ambiguous target pattern that can end in I2 or I5 for G2, and I3 or I4 for G4. Finally, the initial partial configurations in groups G3 and G5 are sufficient to resolve the states of every node in the network. doi:10.1371/journal.pone.0055946.g016 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 21 March 2013 \| Volume 8 \| Issue 3 \| e55946 inner nodes is unknown (wildcard), and only three (input) nodes (SLP, nWG,nhh) are set to a combination of Boolean states. Each of these eight schemata redescribes 214 possible configurations of the single-cell SPN. Six of the eight input schemata converge to one of the five possible attractors for inner nodes in a single cell of the SPN model (Figure 16). We can thus think of those six schemata as minimal configurations (MCs) that guarantee conver- gence to patterns (e.g. attractors) of interest. More specifically, a MC is a 2-symbol schema x’’ that redescribes a set of network configurations that converge to target pattern P; when the MC is a wildcard schema, it is denoted by x’. Therefore, s(x0’) P. MC schemata, x’’ or x’, are network configurations where the truth value of each constituent autom- aton can be 0, 1, or # (unknown); symmetry groups are allowed for x’’ and identified with position-free symbols 0m (see Micro-level canalization section). An MC schema redescribes a subset H of the set of configurations X: H:fx[X : x x00g. A partial config- uration is a MC if no Boolean state in it can be raised to the unknown state (#) and still guarantee that the resulting partial configuration converges to P. In the case of a two-symbol schema, no group-invariant enput can be enlarged (include additional node-states) and still guarantee convergence to P. Finally, the target pattern P can be a specific network configuration (e.g. an attractor), or it can be a set of configurations of interest (e.g. when only some genes or proteins are expressed). After redescription of a set of configurations X of a BN – a subset or its full dynamical landscape – we obtain a set of two-symbol MCs X’’; a set of wildcard MCs is denoted by X’. Similarly to micro-level schemata, we can speak of enputs of MCs. In this context, they refer to individual and sets of node-states in the network that are essential to guarantee convergence to a target pattern. The dynamical unfolding example of the single-cell SPN model shows that to converge to the attractor I1 (Figure 16, G1), only the states of the three input nodes need to be specified, in one of three possible Boolean combinations: 000,100 or 110 for the nodes SLP, nWG and nhh; all other (inner) nodes may be unknown (#). Moreover, these three initial patterns can be further redescribed into two schemata: X’~ff#,0,0g,f1,#,0gg. This shows that to guarantee converge to I1, we only need to know the state of two (input) nodes: either nWG ~nhh~0, or SLP = 1 and nhh~0. All other nodes in the single-cell model can remain unknown. Therefore, the MCs for attractor pattern I1 are: X0~f###############00,##############1#0g ð10Þ where the order of the inner nodes is the same as in Figure 16, and the last three nodes are SLP, nWG and nhh in that order. Notice that in this case there is no group-invariance, so X’’~X’. Any initial configuration not redescribed by X’, does not converge to pattern I1. Therefore, these MCs reveal the enputs (minimal set of node-states) that control network dynamics towards attractor I1: nhh must remain unexpressed, and we must have either SLP expressed, or nWG unexpressed. However, as mentioned above, this example refers to the case when the three input nodes are in steady-state. For the single-cell SPN, the steady-state assumption is reasonable. But for the spatial SPN, with parasegments of four cells, we cannot be certain that the spatial signals (nWG and nhh) have reached a steady-state at the start of the dynamics. Therefore, we now introduce a procedure for obtaining MCs, without the steady-state assumption, which we apply to the spatial SPN network model. It was discussed previously that individual automata in BN models of biochemical regulation and signalling very rarely have large numbers of input variables. This allows tractable computa- tion of two-symbol schema redescription of their LUTs (see micro- level section). In contrast, computing MCs for network configu- rations easily becomes more computationally challenging. Even for fairly small networks with n&20, the size of their dynamical landscape becomes too large to allow full enumeration of the possible configurations and the transitions between them. As shown above, it is possible to identify pathway modules, and to compute dynamical unfolding on the DCM, without knowing the STG of very large BNs, but it remains not feasible to fully redescribe their entire dynamical landscape. One way to deal with high-dimensional spaces is to resort to stochastic search (see e.g. [62]). We use stochastic search to obtain MCs that are guaranteed to converge to a pattern of interest P. We start with a seed configuration known to converge to P. Next, a random node in a Boolean state is picked, and changed to the unknown state. The resulting partial configuration is then allowed to unfold to determine if it still converges to P. If it does, the modified configuration becomes the new seed. The process is repeated until no more nodes can be ‘raised’ to the unknown state and still ensure convergence to P. Otherwise, the search continues picking other nodes. The output of this algorithm (detailed in Data S4) is thus a single wildcard MC. Afterwards, the goal is to search for sets of MCs that converge to P. We do this in two steps: first we search for a set of MCs derived from a single seed, followed by a search of the space of possible different seeds that still converge to P. We use two ‘tolerance’ parameters to determine when to stop searching. The first, d, specifies the number of times a single seed must be ‘reused’ in the first step. When the algorithm has reused the seed d consecutive times without finding any new MCs, the first step of the MC search stops. The second tolerance parameter, r, is used to specify when to stop searching for new seeds from which to derive MCs. When r consecutively generated random (and different) seeds are found to be already redescribed by the current set of MCs, the algorithm stops. Both parameters are reset to zero every time a new MC is identified. These two steps are explained in greater detail in Data S4. The two-step stochastic search process results in a set of wildcard schemata X’ that redescribe a given set of configurations X guaranteed to converge to pattern P. We next obtain a set of two-symbol MCs X’’ from X’, by identifying group-invariant subsets of nodes using the same method described in the micro- level canalization section. Since X’ can be quite large (see below), this computation can become challenging. In this case, we restrict the search for symmetric groups in X’ that redescribe a minimum number b of wildcard MCs x’. Notice that it is the DCM, implemented as a threshold network, that allows us to pursue this stochastic search of MCs. With the original BN, we cannot study dynamics without setting every automaton to a specific Boolean truth value. With the DCM, obtained from micro-level canalization, we are able to set nodes to the unknown state and study the dynamical unfolding of a partial configuration (see previous subsection) to establish convergence to a pattern of interest. Therefore, the DCM helps us link micro-level canalization to macro-level behaviour. Let us exemplify the approach with the SPN model. We started our study of MCs in the spatial SPN model, with a set of seed configurations Xbio that contains the known initial configuration of the SPN (shown in Figure 3), the wild-type attractor (Figure 4a), and the five configurations in the dynamic trajectory between them. When searching for MCs using these seed configurations we set d~105. This resulted in a set containing 90 wildcard MCs X’bio (available in data S7). Using the set X’bio, we performed the two-step stochastic search with r~106 and (10) Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 22 March 2013 \| Volume 8 \| Issue 3 \| e55946 d~105. This resulted in a much larger set of 1745 wildcard MCs (available in data S8) which guarantee convergence to wild-type: X’wt6X’bio. The number of literal enputs in each MC contained in this set varies from 23 to 33 – out of the total 60 nodes in a parasegment. In other words, from all configurations in X’wt we can ascertain that to guarantee convergence to the wild-type attractor, we need only to control the state of a minimum of 23 and a maximum of 33 of the 60 nodes in the network. Equivalently, 27 to 37 nodes are irrelevant in steering the dynamics of the model to the wild-type attractor – a high degree of canalization we quantify below. We chose to study two further subsets of X’wt separately: X’noP and X’min. The first (available in data S9) is the subset of MCs that do not have enputs representing expressed (on) proteins, except SLP3,4 – since SLP in cells 3 and 4 is assumed to be present from the start, as determined by the pair-rule gene family (see [26] and introductory section). This is a subset of interest because it corresponds to the expected control of the SPN at the start of the segment-polarity dynamics, including its known initial configura- tion (Figure 3); thus X’noP5X’wt. The second, X’min5X’wt is the subset of MCs with the smallest number of enputs (available in data S10. This corresponds to the set of 32 MCs in X’wt that have only 23 enputs each. This is a subset of interest because it allows us to study how the unfolding to wild-type can be guaranteed with the smallest possible number of enputs. Notice that X’min redescribes a large subset of configurations in Xwt because it contains the MCs with most redundant number of nodes. These sets of wildcard MCs are available in data S7,S8, S9 and S10; Table 3 contains their size. There are severe computational limitations to counting exactly the number of configurations redescribed by each set of MCs, since it depends on using the inclusion/exclusion principle [63] to count the elements of intersecting sets (MCs redescribe overlap- ping sets of configurations). See Data S6 for further details. We can report the exact value for jX’noPj~8:35\|1010, which is about 14% of the number of configurations – or pre-patterns – estimated by Albert & Othmer [26] to converge to the wild-type attractor (6\|1011). Using the inclusion/exclusion principle, it was also computationally feasible to count the configurations redescribed by a sample of 20 of the 32 MCs in X’min : 9:6\|1011. Since this sample of 20 MCs is a subset of X’min, which is a subset of X’wt, we thus demonstrate that jXwtj§jXminj§9:6\|1011, which is 1:6 times larger than the previously estimated number of pre-patterns converging to the wild-type attractor [26]. This means that the wild-type attraction basin is considerably (at least 1.6 times) larger than previously estimated, with a lower bound of at least 9:6\|1011 network configurations. Although it was not computa- tionally feasible to provide exact counts for the remaining MC sets, it is reasonable to conclude that the set X’wt redescribes a significant proportion of the wild-type attractor basin, given the number of configurations redescribed by 20 of its most canalized MCs in comparison to the previous estimate of its size. Indeed, we pursued a very wide stochastic search with large tolerance parameters, arriving at a large number (1745) MCs, each of which redescribes a very large set of configurations. For instance, each MC with the smallest number of enputs (23) alone redescribes 1:37\|1011 configurations, which is about 23% of the original estimated size of the wild-type attractor basin, and 14% of the lower bound for the size of the attractor basin we computed above. Given the large number of MCs in the X’wt set, even with likely large overlaps of configurations, much of the attractor basin ought to be redescribed by this set. From X’wt, we derived two-symbol MC sets using b~8. That is, due to the computational limitations discussed previously, we restricted the search to only those two-symbol MCs x’’ that redescribe at least b~8 wildcard MCs x’. Given that configura- tions of the spatial SPN are defined by 60 automata states, the group-invariance enputs we may have missed with this constraint are rather trivial. For instance, we may have missed MCs with a single group-invariant enput of 3 variables (any group-invariant enput with 4 variables would be found), or MCs with 2 distinct group-invariant enputs of 2 variables each (any MCs with 3 group- invariant enputs would be found.) With this constraint on the search for two-symbol MCs, we identified only the pair of two- symbol MCs depicted in Figure 17: fx’’1,x’’2g – each redescribing 16 wildcard MCs – the MCs redescribed are available in data S13. These two MCs redescribe 1:95\|1011 configurations; that is, about 32% of the wild-type attraction basin as estimated by [26], or 20% of the lower bound for the size of the attractor basin we computed above – a very substantial subset of the wild-type attractor basin. No other two-symbol MCs redescribing at least eight wildcard MCs were found in the set X’wt. Therefore, X’’wt is comprised of the wildcard MCs in X’wt with the addition of fx’’1,x’’2g and removal of the wildcard MCs these two schemata redescribe. Table 3 contains the size of all MC sets. Moreover, fx’’1,x’’2g have no intersecting schemata with the additional three subsets of X’’wt we studied. This means that the two-symbol redescription (with b~8) is equal to the wildcard redescription of the sets of configurations Xbio, XnoP and Xmin. The pair of two-symbol MCs identified denote two very similar minimal patterns that guarantee convergence to the wild-type attractor. In both MCs, the pairs of nodes wg2,4, HH2,4 as well as ci4 and CI4 are marked with distinct position-free symbols. In other words, they have three identical group-invariant enputs. For x’’1 a fourth group-invariant enput comprises the nodes hh1,3, while for x’’2 the fourth group-invariant enput contains the nodes HH1,3. For x’’2 there is an extra literal enput: ptc4~0 (ptc gene in fourth cell is unexpressed). The Table 3. Macro-level canalization in the wildcard MC sets converging to wild-type in the SPN. MC set jX’’j e (min) e (max) ne nr ns X’wt 1745 23 33 24:01+0:08 35.99 +0:17 0:98+0:03 X’min 32 23 23 23+0 37 +0 0 X’bio 90 25 28 25:75+0:11 34.25 +0:11 0 X’noP 24 26 30 26:2+0:04 34.8 +0:04 0 The table lists for every set of MCs reported in the main text: cardinality, minimum number of enputs, maximum number of enputs, estimated canalization. Canalization measures were obtained, for each MC set, from 10 independent samples of 104 configurations, thus j^Xj~105. Values shown refer to the mean plus 95% confidence intervals for the 10 independent measurements. doi:10.1371/journal.pone.0055946.t003 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 23 March 2013 \| Volume 8 \| Issue 3 \| e55946 remaining literal enputs are identical to those of x’’1. The group- invariance in these MCs is not very surprising considering the equivalent roles of neighbouring hedgehog and Wingless for intra- cellular dynamics – as discussed previously when the SPN’s DCM was analysed. Notice that most group-invariance occurs for the same genes or proteins in alternative cells of the parasegment; for instance, wg expressed in either cell 2 or cell 4. Nonetheless, both two-symbol MCs offer two minimal conditions to guarantee convergence to the wild-type attractor, which includes a very large proportion of the wild-type attractor basin. Therefore, they serve as a parsimonious prescription for analysts who wish to control the macro-level behaviour (i.e. attractor behaviour) of this system. Finally, the MCs obtained observe substantial macro-level canalization which we quantify below. Quantifying Macro-level Canalization In the micro-level canalization section, we defined measures of input redundancy, effective connectivity and input symmetry to quantify micro-level canalization from the schema redescription of individ- ual automata. Since we can also redescribe configurations that produce network dynamics, leading to the minimal configurations (MCs) of the previous section, we can use very similar measures to quantify macro-level canalization and control. At the macro-level, high canalization means that network dynamics are more easily controllable: MCs contain fewer necessary and sufficient node- states (enputs) to guarantee convergence to an attractor or target pattern P. Similarly to the micro-level case, we first define upper and lower bounds of node redundancy computed from the set of MCs X’’ for a target pattern: nr(X,P)~ P x[X max h:x[Hh n# h jXj ð11Þ nr(X,P)~ P x[X min h:x[Hh n# h jXj ð12Þ These expressions tally the mean number of irrelevant nodes in controlling network dynamics towards P for all configurations x of a set of configurations of interest X (e.g. a basin of attraction). The number of irrelevant nodes in a given MC x’’h is the number of its wildcards n# h . Because each configuration x is redescribed by one or more MCs, there are various ways to compute a characteristic number of irrelevant nodes associated with the configurations, which is nonetheless bounded by the maximum and minimum number of wildcards in the set of MCs that redescribe x. Therefore, the expressions above identify all MCs whose set of redescribed configurations Hh includes x. The upper (lower) bound of node redundancy, Equation 11 (Equation 12), corresponds to considering the maximum (minimum) number of irrelevant nodes found for all MCs that redescribe configuration x of the interest set – an optimist (pessimist) quantification of this type of macro-level canalization. Here we use solely the upper bound, which we refer to henceforth simply as node redundancy with the notation nr(X,P). Similarly to the micro-level case, the assumption is that the most redundant MCs are always accessible for control of the network towards pattern P. The range for node redundancy is 0ƒnrƒn, where n is the number of nodes in the network. When nr(X,P)~n we have full node irrelevance, or maximum canalization, which occurs only in the case of networks where the state of every node is not dependent on any input (that is, when kr~k for every node). If nr(X,P)~0, the state of every node is always needed to determine convergence to P and we have no macro-level canalization. Figure 17. Two-Symbol schemata with largest number of position-free symbols, obtained from redescription of Xwt. The pair fx’’1,x’’1g were the two-symbol schemata obtained in our stochastic search; both include 4 pairs of symmetric node-pairs, each denoted by a circle and a numerical index. doi:10.1371/journal.pone.0055946.g017 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 24 March 2013 \| Volume 8 \| Issue 3 \| e55946 If some nodes of a network are irrelevant to steer dynamics to P, from a control logic perspective, we can say that P is effectively controlled by a subset of nodes of the network with fewer than n nodes. In other words, by integrating the micro-level control logic of automata in a network into the DCM, we are able to compute MCs and infer from those the macro-level effective control, which is not apparent from looking at connectivity structure alone: ne(X,P)~n{nr(X,P) ð13Þ whose range is 0ƒneƒn. If ne(X,P)~0 it means full node irrelevance, or maximum canalization. When ne(X,P)~n, it means no canalization i.e. one needs to control all n nodes to guarantee converge to P. Macro-level canalization can also manifest alternative control mechanisms. The two-symbol schema redescription allows us to measure this form of control by computing the mean number of nodes that participate in group-invariant enputs, easily tallied by the number of position-free symbols (n 0 h) in MC schemata x’’h that characterize convergence to target pattern P. Thus, we quantify the upper and lower bounds of node symmetry in a set of configurations of interest X related to target pattern P (e.g. a basin of attraction). ns(X,P)~ P x[X max h:x[Hh n0 h jXj ð14Þ ns(X,P)~ P x[X min h:x[Hh n0 h jXj ð15Þ Here we use solely the upper bound, which we refer to henceforth simply as node symmetry and denote by ns(X,P); its range is ½0,n. Again, the assumption is that the most canalized MCs are always accessible for control of the network towards pattern P. High (low) values mean that permutations of node- states are likely (unlikely) to leave the transition unchanged. Macro-level canalization in network dynamics is then quantified by two types of redundancy: node redundancy (or its counterpart, effective control) and node symmetry. To be able to compare macro-level control in automata networks of different sizes, we can compute relative measures of canalization: n r(X,P)~ nr(X,P) n ; n e(X,P)~ ne(X,P) n ; n s(X,P)~ ns(X,P) n ð16Þ whose range is ½0,1: Network dynamics towards a pattern of interest P can have different amounts of each form of canalization, which allows us to consider four broad classes of control in network dynamics – just like the micro-level canalization case (see above). The two MCs identified above for the single-cell SPN model (Eq. 10), redescribe the full set of configurations that converge to I1. Since these MC schemata do not have group-invariant enputs, node symmetry does not exist: ns(X,I1)~0. Node redundancy and effective control is nr(X,I1)~15 and ne(X,I1)~2, respec- tively. In other words, even though the network of the single-cell SPN model comprises n~17 nodes, to control its dynamics towards attractor I1, it is sufficient to ensure that the states of only two nodes remain fixed; the initial state of the other 15 nodes is irrelevant. More concretely, nhh must remain off and either SLP remains on or nwg remains off. The relative measures become: n r(X,I1)~15=17 (&88% of nodes are redundant to guarantee convergence to attractor I1) n e(X,I1)~2=17 (one only needs to control &12% of nodes to guarantee convergence to attractor I1), and n s(X,I1)~0 (there is no node symmetry in these MCs). This means that there is a large amount of macro-level canalization of the node redundancy type – and thus higher controllability – in the basins of attraction of the SPN model where pattern I1 is present. The macro-level canalization measures above assume that the interest set of configurations X can be enumerated. Moreover, schema redescription of network configurations itself assumes that X can be sufficiently sampled with our stochastic search method (see previous sub-section). The node symmetry measure addition- ally assumes that the set of wildcard MCs obtained by stochastic search is not too large to compute symmetric groups. While these assumptions are easily met for micro-level analysis, because LUT entries of individual automata in models of biochemical regulation do not have very large number of inputs, they are more challenging at the macro-level. Certainly, canalization in the single-cell SPN model can be fully studied at both the micro- and macro-levels – see Figures 11 and 12 for the former as well as example above for the latter. But quantification of macro-level canalization of larger networks, such as the spatial SPN model, needs to be estimated. Therefore, in formulae 11, 12, 14, and 15, the set of configurations X is sampled: ^X. Configurations for ^X are sampled from each MC in the set X’’, proportionally to the number of configurations redescribed by each MC – i.e. roulette wheel sampling. Configurations from a selected MC are sampled by ascribing Boolean truth values to every wildcard in the MC schema; the proportion of each of the truth values is sampled from a uniform distribution. If a selected MC is a 2-symbol schema, the truth-values of group-invariant enputs are also sampled from a uniform distribution of all possible possibilities. Naturally, the same configuration x can be redescribed by more than one MC h. In summary, macro-level canalization for larger networks is quantified with the estimated measures: ^nr, ^ne, and ^ns, as well as their relative versions. Tables 3 and 4 summarize the quantification of macro-level canalization estimated for the four MC sets obtained above: X’’wt, X’’min, X’’bio, and X’’noP. Effective control (ne) ranges between 23 and 26:2 nodes (out of 60) for the four sets of MCs; this means (see n e) that only 38 to 44% of nodes need to be controlled to guarantee convergence to wild-type. This shows that there is substantial macro-level canalization in the wild-type attractor basin; from n r, we can see that 56 to 62% of nodes are, on average, redundant to guarantee convergence to wild-type. On the other hand, macro-level canalization in the form of alternative (or symmetric) control mechanisms is not very relevant on this attractor basin, as observed by the low values of ns and n s: in the wild-type attractor basin, on average, only approximately 1 out 60 nodes, or 1:6% can permute. Enput Power and Critical Nodes Every MC is a schema, and hence comprises a unique set of enputs, not entirely redescribed by any other MC. As defined in the micro-level canalization section, an enput e can be literal – a single node in a specific Boolean state – or a group-invariant enput: a set of nodes with a symmetry constraint. Every enput e in Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 25 March 2013 \| Volume 8 \| Issue 3 \| e55946 a given MC is essential to ensure convergence to a pattern P, e.g. an attractor A. Consequently, if the state or constraint of e is disrupted in the MC, without gaining additional knowledge about the configuration of the network, we cannot guarantee conver- gence to P. How critical is e in a set of configurations X redescribed by an MC set X’’ – such as the set of MCs that redescribe a basin of attraction? Since there are usually alternative MCs that redescribe the possible dynamic trajectories to P, the more e appears in X’’, the more critical it is in guaranteeing convergence to P. For instance, in the two MCs shown in Equation 10, the enput e:(nhh~0) is common to both. Therefore, disrupting it, without gaining additional knowledge about the state of other nodes, would no longer guarantee convergence to the attractor pattern I1 in the single-cell SPN dynamics. Similarly, for the two-symbol MC set of the spatial SPN model, shown in Figure 17, enputs e:(hh2,4~0) and group-invariant enput e:(wg2~1 _ wg4~1) appear in both MCs. Disrupting them, would no longer guarantee convergence to wild-type attractor in the spatial SPN dynamics. Let us quantify the potential disruption of target dynamics by perturbation of enputs in an MC set. The power of an enput e in a set of configurations X X00 : s(x) P, Vx[X, is given by: (e,X00,P)~ jXej jXj ð17Þ where Xe(X is the subset of configurations redescribed by X’’ that contain enput e: Xe:fx[X : xx00 ^ e[x00g. Thus, this measure yields the proportion of configurations in X redescribed by the MCs in which e is an enput; its range is ½0,1. If an enput appears in every MC, as in the examples above, then E~1 – in which case e is said to have full power over X’’. For the analysis of the SPN model below when 0:5ƒEv1, e is a high power enput, when 0vev0:5 it is a low power enput, and when E~0 it is a null power enput. The larger the power of e, the more its perturbation is likely to disrupt convergence to the target pattern P. When X is too large, we estimate ^ – similarly to the canalization measures discussed in the previous subsection. We studied the wild-type attractor basin of the spatial SPN model using the four MC sets of interest: X’’wt, X’’min, X’’bio, and X’’noP (see Minimal configurations subsection above) focusing on the power of literal enputs only. It is also possible to compute the enput power of group-invariant enputs. For example, the two- symbol MC x’’1 in Figure 17, has one of its four group-invariant enputs defined by ci~1 _ CI~1. The power of this enput would tally those MCs in which this condition holds. Nonetheless, here we only measure the power of literal enputs and present the study of the power of group-invariant enputs elsewhere. The enput power computed for these four sets is depicted in Figure 18, where the output nodes PH and SMO are omitted because they are never input variables to any node in the SPN model, and therefore have null power. For the discussion of these results, it is useful to compare them to the known initial condition, xini depicted in Figure 3, and the wild-type attractor, Awt depicted in Figure 4 (a). Enput power in X’’wt (see Figure 18A). The enputs with full power (E~1) are: SLP1,2~0, SLP3,4~1, hh2,4~0 and ptc1~0. This is not entirely surprising since all of these genes and proteins are specified as such in both xini and Awt. However, these values show that these enputs must remain in these states in the entire (sampled) wild-type basin of attraction. In other words, these enputs are critical controllers of the dynamics to the wild-type attractor. Indeed, the wild-type is not robust to changes in these enputs, which are likely to steer the dynamics to other attractors, as discussed further in the next section. Therefore, the spatial SPN model appears to be unable to recover the dynamic trajectory to the wild-type attractor when either the hedgehog gene is expressed in cells two and four; or the patched gene is expressed in the anterior cell, as well when the initial expression pattern of SLP determined upstream by the pair-rule gene family is disrupted in any way. There are also enputs with high power to control wild-type behaviour: wg1,3~WG1,3~0, en1~1, PTC1~0, en2,4~0, ptc3~1, CI3~0 and CIR3~1. Again, these are the states of these genes and proteins in the known initial configuration of the SPN xini, and most of them, except for ptc3~1, CI3~0 and CIR3~1 correspond to their final states in Awt. In Figure 18A every node in the SPN – except the omitted nodes PH and SMO – appear as an enput, in at least one Boolean state, in many cases with very low values of . Thus, while macro- level dynamics is significantly canalized (see above), especially by SLP and the spatial signals for each cell, control of wild-type can derive from alternative strategies, whereby every node can act as an enput in some context. Nonetheless, most nodes ultimately do not observe much power to control wild-type behaviour, thus interventions to disturb wild-type behaviour are most effective via the few more powerful controllers (see also next section). We can also compare the enput power computed for X’’wt (Figure 18A), with the two-symbol MCs x’’1 and x’’2 in Figure 17. These two MCs redescribe a significant portion of the wild-type attractor basin – 20% of our lower bound count of this basin. Because they only appear in X’’wt and not in any of the other MC sets we studied, the portion of the wild-type attractor basin they redescribe is unique to Xwt, and can be analysed via x’’1 and x’’2. Most of the literal enputs specified in x’’1 and x’’2 have high power in X’’wt, except for WG2~wg4~CIR1,2,4~1, which are enputs in these two-symbol MCs that have low power. Conversely, there are literal enputs with high-power in X’’wt that are not enputs in these two-symbol MCs: EN2,4~0 and PTC1~0. A key distinguishing feature of x’’1 and x’’2 is the expression of CIR across the entire parasegment as well as of the wingless protein in the second cell, both of which are different from the trajectory between the known initial condition of the SPN and the wild-type attractor. Therefore, x’’1 and x’’2 redescribe a (large) portion of the attractor basin outside of the more commonly studied dynamical trajectories. Enput power in X’’min (see Figure 18B). We found an unexpected expression of CIR2~1 (now with full power) as well as wg2~WG2~1 (high power). Other enputs whose expression is in opposition to both xini and Awt appear with low power: HH2,4~1 and CIR1~1. This again suggests that there is a substantial subset of the wild-type attractor basin, controlled by these and other Table 4. Macro-level canalization in the wildcard MC sets converging to wild-type in the SPN. MC set ne nr ns X’wt 0.4 +0:001 0.6 +0:001 0.016 +0:002 X’min 0.38 0.62 0 X’bio 0.43 +0:001 0.57 +0:001 0 X’noP 0.436 +0:0007 0.564 +0:0007 0 The table lists the relative canalization measures for every set of MCs reported in the main text. Canalization measures were obtained, for each MC set, from 10 independent samples of 104 configurations, thus j^Xj~105. Values shown refer to the mean plus 95% confidence intervals for the 10 independent measurements. doi:10.1371/journal.pone.0055946.t004 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 26 March 2013 \| Volume 8 \| Issue 3 \| e55946 enputs, distinct from the trajectory that results from the known (biologically plausible) initial configuration. We can also see that there is a significant number of nodes that do not play the role of enput in any MC – nodes with null power, depicted as small grey circles – as well as many more enputs with full power. X’’min redescribes wild-type dynamics with the smallest number (23) of enputs; this set contains only 32 MCs out of the 1731 in X’’wt. However, these are the most macro-canalizing MCs that guarantee convergence to wild-type. Indeed, because of their parsimony, they redescribe a very large subset of the wild-type attractor basin with at least 1.6 times more configurations than what was previously estimated for this basin (see above). Therefore, X’’min provides a solid baseline for the understanding of control in the wild-type attractor basin. This means that the genes and proteins with full power in this set are critical controllers of wild-type behaviour. Enput power in X’’bio (see Figure 18C). Because this MC set only redescribes configurations in the dynamic trajectory from xini to Awt, the transient dynamics observed in X’’wt and X’’min, e.g. wg2~1 and CIR2~1, disappear. There are, however, other enputs with full power: wg1,3~WG1,3~0, en2,4~EN2,4~0, ptc1~PTC1~0. These critical enputs are particularly important Figure 18. Enput power in the wild-type basin of attraction of the spatial SPN model. Enput power is shown for each of the four sets of MCs considered in our analysis: (A) X’’wt, (B) X’’min, (C) X’’bio and (D) X’’noP. A parasegment is represented by four rounded rectangles, one for each cell, where the anterior cell is at the top, and posterior at the bottom. Since enput power is computed for every node in each of its two possible states, every cell rectangle has two rows of circles. The bottom row (marked on the sides with a white circle on the outside) corresponds to enput power of the nodes when off, while the top row is the enput power when the same nodes are on (marked on the sides with a dark circle). Each circle inside a cell’s rectangle corresponds to the power of a given enput in the corresponding subset of MCs identified by the letters A to D. Full power is highlighted in red, other values in blue and scaled, while null power is depicted using small grey circles. Full power occurs only for enputs that are present in every MC (and configurations) of the respective set, whereas null power identifies nodes that are never enputs in any MC – always irrelevant for the respective dynamical behaviour. doi:10.1371/journal.pone.0055946.g018 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 27 March 2013 \| Volume 8 \| Issue 3 \| e55946 for restricting analysis to a better-known portion of the wild-type attractor basin, for which the model was especially built. Enput power in X’’noP (see Figure 18D). This set of MCs is useful to understand the beginning of the segment polarity regulatory dynamics, with no proteins expressed. The set of critical genes that must be expressed (on) are ptc3 and wg4, which appear with full power; moreover, en1~hh1~ptc2~ci2~1 appear with high power. As shown in the figure, most other enputs with full or high power correspond to genes and proteins that must be inhibited (off), except, of course, SLP3,4 that are assumed to be always on in the SPN model. We compared these results with previous work on identifying critical nodes in the SPN model. Chaves et al. [38] deduced, from the model’s logic, minimal ‘pre-patterns’ for the initial configura- tion of the SPN that guarantee convergence to wild-type attractor. More specifically, two necessary conditions and one sufficient condition were deduced, which we now contrast with the enput power analysis. The first necessary condition for convergence to the wild- type attractor is: ptc3~1, assuming that all proteins are unexpressed (off ) initially, and the sloppy pair gene rule is maintained constant (i.e. SLP1,2~0 ^ SLP3,4~1.) Of the MC sets we analysed, only X’’noP obeys the (biologically plausible) assumptions for this necessary condition. As we can see in Figure 18D, the enput ptc3~1 has full power on this MC set, which confirms this previous theoretical result. However, since every enput with full power is a necessary condition for the set of configurations described by its MC set, we can derive other necessary conditions for this set of configurations (with the same assumptions), such as ptc1~0, wg3~0, or wg4~1 (see below). We can also see that not all assumptions for the first necessary condition are necessary; while the sloppy pair rule appears as four enputs with full power, not all proteins are required to be unexpressed: the expression of HH is irrelevant in every cell of the parasegment, as is the expression of PTC2,3, WG2,4, CIA4, and CIR1,2,3. Moreover, the enput power analysis allows us to identify ‘degrees of necessity’; some enputs may not be necessary, but almost always necessary. This is the case of the expression of en1, which has high power in X’’noP, but is not a necessary condition as a few MCs can guarantee convergence to wild-type with en1~0 (which also appears as enput with low power). Naturally, if we relax the assumptions for condition ptc3~1, it may no longer be a necessary condition. This can be see when we look at the enput power analysis of the entire (sampled) wild-type basin X’’wt (Figure 18A) or the smaller X’’bio (Figure 18C). In these cases, which still preserve the sloppy pair rule assumption, ptc3~1 is no longer an enput with full power. This means that, according to this model, if some proteins are expressed initially, ptc3~1 is no longer a necessary condition. Interestingly, we found that in the most macro-canalizing subset of the attractor basin, X’’min (Figure 18B) – which assumes the sloppy pair rule constraint but is not constrained to initially unexpressed proteins – ptc3~1 does appear as an enput with full power again. This means that in the most parsimonious means to control convergence to wild-type attractor, ptc3~1 is a necessary condition too. It is noteworthy that in this case, not only can some proteins be expressed, but the expression of CIR2 is also a necessary condition (enput with full power). The second necessary condition for convergence to the wild-type attractor is: wg4~1 _ en1~1 _ ci4~1, assuming that all proteins are unexpressed (off) initially, and the sloppy pair gene rule is maintained constant (i.e. SLP1,2~0 ^ SLP3,4~1) [38]. Again, only X’’noP obeys the (biologically likely) assumptions for this necessary condition. As we can see in Figure 18D, the enput wg4~1 has full power, therefore it is a necessary condition. However, the enput en1~1 has high power, and the enput ci4~1 has no power. This means that they are not necessary, though en1~1 is most often needed. These results suggest that this necessary condition could be shortened to wg4~1, because in our sampling of the wild-type attractor basin, in the subset meeting the assumptions of the condition, we did not find a single configura- tion where wg4~0. Even though our stochastic search was very large, it is possible that there may be configurations, with no proteins expressed, where wg4~0 ^ (en1~1 _ ci4~1), thus maintaining the original necessary condition. However, our enput power analysis gives a more realistic and nuanced picture of control in the SPN model under the same assumptions. While the necessary condition may be wg4~1 _ en1~1 _ ci4~1, the individual enputs have strikingly different power in controlling for wild-type behaviour: ci4~1 was never needed (no power), en1~1 has high power, and wg4~1 has full power. Naturally, if we relax the assumptions for this condition, it may no longer be a necessary condition. For instance, if we allow proteins to be expressed initially (still preserving the sloppy pair constraint), we can find MCs that redescribe configurations where wg4~en1~ci4~0. We found 171 MCs in X’’wt (available in data S14 where this condition is not necessary, one of them depicted in Figure 19. The sufficient condition for convergence to the wild-type attractor is: wg4~1 ^ ptc3~1, assuming that the sloppy pair gene rule is maintained constant (i.e. SLP1,2~0 ^ SLP3,4~1). A variation of this sufficient condition assumes instead (maintaining the sloppy pair gene rule): wg4~1 ^ PTC3~1 In their analysis, Chaves et al. [38] assume that all proteins are unexpressed and that many other genes are initially inhibited (off ). Even though in Chaves et al. [38] the initial condition itself only requires ptc1~ci1,3~0, the argument hinges on propositions and facts that require knowing the state of additional genes such as en2~wg3~hh2,4~0. While Chaves et al. [38] concluded rightly from this minimal pre-pattern, that convergence to the wild-type pattern has a remarkable error correcting ability to expression delays in all other genes, the condition does not really describe robustness to premature expression of genes and proteins. It is interesting to investigate sufficient conditions that do require the states of most variables to be specified, giving us the ability to study robustness to both delays and premature expression of chemical species. The MC schemata we obtained with our macro-level analysis allows us to investigate such sufficient conditions directly. We searched the entire MC set X’’wt to retrieve the MCs with the fewest number of enputs specified as on. The 10 MCs (available in S11) we retrieved contain only 26 literal enputs, where in six MCs the two nodes in the sufficient condition above (wg4,ptc3), plus the nodes from the sloppy pair rule (SLP3,4) are on, 24 are off and the remaining 32 are wildcards, and thus irrelevant. In the remaining MCs, instead of ptc3~1, we found PTC3~1 to be an enput. In those MCs ptc3~#. Converting all wildcards to off in one of these MCs, confirms the sufficient condition, as can be seen from Figure 20A, where SLP3,4~wg4~ptc3~1, and everything else is off. This can be seen as an ‘extreme’ condition to wild-type attractor, with a minimum set of genes expressed. We also searched for the opposite extreme scenario, retrieving all MCs with the largest number of on nodes, that still converges to the wild-type pattern (available in data S12. By replacing all wildcards in such MCs to on, we obtained the configuration in which only 16 nodes must be inhibited (off ), while the remaining 44 are expressed (on), depicted in Figure 20B. Interestingly, in this extreme configuration, hh must remain off across the whole parasegment. Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 28 March 2013 \| Volume 8 \| Issue 3 \| e55946 Robustness to Enput Disruption The power measure introduced in the previous subsection allows us to predict critical nodes in controlling network dynamics to a pattern of interest P. A natural next step is to investigate what happens when the critical controllers are actually disrupted. We can disrupt an enput e in an MC set with a variety of dynamic regimes. Here, we adopt the approach proposed by Helikar et al. [64], where a node of interest flips its state at time t with a probability f, which can be seen to represent noise in regulatory and signalling events, as well as the ‘concentration’ of a gene (its corresponding mRNA) or protein – thus making it possible to use Boolean networks to study continuous changes in concentration of biochemical systems (see [64]). We start from an initial set of configurations of interest: X 0. This can be a single configuration, such as the known initial configuration of the SPN X 0:fxinig (as in Figure 3A), where the enput e is in a specific (Boolean) value. Next, we set the value of noise parameter f, which is the probability that e momentarily flips from its state in X 0 at time t. This noise is applied at every time step of the simulated dynamics; when a state-flip occurs at time t, the node returns to its original state at tz1 when noise with probability f occurs again. Noise is applied to e from t~0 to t~m. At time step t~mz1 no more noise is applied to e (f~0) and the network is allowed to converge to an attractor. This process is repeated for M trials. Finally, we record the proportions of the M trials that converged to different attractors. Since in this paper we only computed enput power for literal enputs (see previous subsection), we also only study literal enput disruption. It is straightforward to disrupt group-invariant enputs; for instance, the group-invariant enput defined by ci~1_ CI ~1 from the two-symbol MC x’’1 in Figure 17, can be perturbed by making ci~0^ CI ~0. Nonetheless, for simplicity, we present the study of the disruption of group-invariant enputs elsewhere. The enput power analysis in the previous subsection, revealed that in the wild-type attractor basin (Xwt) of the spatial SPN model there are the following critical nodes (or key controllers): across the parasegment, SLP proteins must be inhibited in cells 1 and 2 (SLP1,2~0) and expressed in cells 3 and 4 (SLP3,4~1), as determined by the pair-rule gene family; hedgehog genes (spatial signals) in cells 2 and 4 must be inhibited (hh2,4~0); the patched gene in the anterior cell must also be inhibited (ptc1~0). With the stochastic intervention procedure just described, we seek to answer two questions about these key controllers: (1) how sensitive are they to varying degrees of stochastic noise? and (2) which and how many other attractors become reachable when they are disrupted? In addition to the seven full power enputs, for comparison purposes, we also test the low power enput CI4~0. In the original SPN model the states of SLP1,2,3,4 are fixed (the sloppy gene constraints). Because these naturally become enputs with full power (see Figure 18), it is relevant to include them in this study of enput disruption. However, by relaxing the fixed-state constraint on SLP1,2,3,4, by inducing stochastic noise, the dynamical landscape of the spatial SPN model is enlarged from 256 to 260 configurations. This means that more attractors than the ten identified for the SPN Boolean model (depicted in Figure 4) are possible, and indeed found as explained below. We used X 0:fxinig as the initial state of the networks analysed via stochastic interventions, because of its biological relevance. The simulations where performed with the following parameters: f[½0:05,0:95, swept with D(f)~0:05, plus extremum values f~0:02 and f~0:98; m~500 steps; M~104. The simulation results are shown in Figure 21. The first striking result is that disruption of SLP1~0 makes it possible to drive the dynamics away from wild-type into one of five other attractors (one of which a variant of wild-type). For fw0:15 no further convergence to wild-type is observed, and at f~0:05 the proportion of trials that converged to wild-type was already very small. We also found phase transitions associated with the values of f. For fƒ0:15 most trials converged to wild-type, wild- type (ptc mutant), broad-stripes or no-segmentation, and a very small proportion to two variants of the ectopic mutant. When f~0:15 the proportion of trials converging to broad-stripes reaches its peak, and decreases, so that no trial converged to this mutant expression pattern for f§0:55. Finally, for f§0:55 convergence to the ectopic variants reaches its peak and decreases steadily but does not disappear, while convergence to the no- segmentation mutant increases becoming almost 100% when f~0:98. We thus conclude that SLP1~0 is a wild-type attractor enput which is very sensitive to noise. In the case of SLP3~1, we observed convergence to an attractor that is not any of the original ten attractors – characterized by having two engrailed bands in cells 1 and 3 (see Data S5). The proportion of trials converging to wild-type and to the new attractor decrease and increase respectively, reaching similar proportions when f~0:5. When f~0:98, almost every trial converged to the new attractor. We conclude that SLP3~1 is a wild-type attractor enput whose robustness is proportional to noise. Disruption of SLP4~1 resulted in a behaviour similar to SLP1, but with fewer possible attractors reached. As f is increased, fewer trials converge to wild-type and growing proportions of trials converge to the wild-type ptc mutant pattern (reaching a peak at f~0:5) and the no-segmentation mutant. For more extreme values of f, the majority of trials converged to the no-segmentation mutant. However, an important difference with respect to SLP1 was observed: for fƒ0:5 the majority of trials converged to wild- type, and convergence to this attractor is observed for the whole range of f. Thus the wild-type phenotype in the SPN model is much more robust to perturbations to the expression of SLP in the posterior cell (SLP4~1), than to perturbations to its inhibition in the anterior cell (SLP1~0). With the parameters chosen, the disruption of SLP2~0 leads to a remarkable similar behaviour: any disruption (any amount of noise) leads to the same wild-type variant attractor pattern with two wingless stripes (c). Therefore, SLP2~0 is not robust at all – though the resulting attractor is always the same and a variant of wild-type. In this case, convergence to a single attractor for all values of f is the result of setting m~500 in our experiments. When we lower the value of m enough in our simulations, for low values of f, there are trials that are not perturbed and thus maintain convergence to the wild-type attractor. But any Figure 19. A MC not requiring wg4~1 _ en1~1 _ ci4~1 in wild- type attractor basin. When proteins are allowed to be expressed initially, the second necessary condition, reported in [38], ceases to be a necessary condition, as discussed in the main text; in the MC shown, wg4, en1 and ci4 can be in any state and the network still converges to the wild-type attractor. doi:10.1371/journal.pone.0055946.g019 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 29 March 2013 \| Volume 8 \| Issue 3 \| e55946 perturbation of SLP2~0 that occurs leads the dynamics to the wild-type variant. Disruption of hh2,4~0 increasingly drives dynamics to the broad-stripes mutant. However, disruption of hh2 reveals greater robustness since a large number of trials still converges to wild-type for fƒ0:15, and residual convergence to wild-type is observed up to f~0:75. In contrast, any disruption of hh4 above f~0:05 leads to the broad-stripes mutant, and even very small amounts of disruption lead to a large proportion of mutants. Similarly, disruption of e:ptc1~0 drives the dynamics to one – and the same – of the wild-type variants. Yet, when f~0:02 there is a minute proportion of trajectories that still converge to the wild- type attractor. Therefore, as expected, the wild-type attractor in the SPN model is not very robust to disruptions of the enputs with full power. Finally, and in contrast, no disruption of low-power enput CI4~0 is capable of altering convergence to the wild-type attractor. Discussion We introduced wildcard and two-symbol redescription as a means to characterize the control logic of the automata used to Figure 20. ‘Extreme’ configurations converging to wild-type in the SPN model. (A) A configuration with the minimal number of nodes expressed that converges to wild-type, and its corresponding MC: 32 nodes are irrelevant, 24 must be unexpressed (off), and only 4 must be expressed (on). (B) The opposite extreme condition where 16 genes and proteins are unexpressed and all other 44 are expressed. doi:10.1371/journal.pone.0055946.g020 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 30 March 2013 \| Volume 8 \| Issue 3 \| e55946 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 31 March 2013 \| Volume 8 \| Issue 3 \| e55946 model networks of biochemical regulation and signalling. We do this by generalizing the concept of canalization, which becomes synonymous with redundancy in the logic of automata. The two- symbol schemata we propose capture two forms of logical redundancy, and therefore of canalization: input redundancy and symmetry. This allowed us to provide a straightforward way to quantify canalization of individual automata (micro-level), and to integrate the entire canalizing logic of an automata network into the Dynamics Canalization Map (DCM). A great merit of the DCM is that it allows us to make inferences about collective (macro-level) dynamics of networks from the micro-level canaliz- ing logic of individual automata – with incomplete information. This is important because even medium-sized automata models of biochemical regulation lead to dynamical landscapes that are too large to compute. In contrast, the DCM scales linearly with number of automata – and schema redescription, based on computation of prime implicants – is easy to compute for individual automata with the number of inputs typically used in the literature. With this methodology, we are thus providing a method to link micro- to macro-level dynamics – a crux of complexity. Indeed, in this paper we showed how to uncover dynamical modularity: separable building blocks of macro-level dynamics. This an entirely distinct concept from community structure in networks, and allows us to study complex networks with node dynamics – rather than just their connectivity structure. The identification of such modules in the dynamics of networks is entirely novel and provides insight as to how the collective dynamics of biochemical networks uses these building blocks to produce its phenotypic behaviour – towards the goal of explaining how biochemical networks ‘compute’. By basing our methodology on the redescription of individual automata (micro-level), we also avoid the scaling problems faced by previous schemata approaches which focused solely on redescription of the dynamical landscape (macro-level) of networks [52]. By implementing the DCM as a threshold network, we show that we can compute the dynamical behaviour of the original automata network from information about the state of just a few network nodes (partial information). In its original formulation, the dynamic unfolding of an automata network cannot be computed unless an initial state of all its nodes is specified. In turn, this allows us to search for minimal conditions (MCs) that guarantee convergence to an attractor of interest. Not only are MCs important to understand how to control complex network dynamics, but they also allow us to quantify macro-level canalization therein. From this, we get a measurable understanding of the robustness of attractors of interest – the greater the canalization, the greater the robustness to random perturbations – and, conversely, the identification of critical node-states (enputs) in the network dynamics to those attractors. We provided a measure of the capacity of these critical nodes to control convergence to an attractor of interest (enput power), and studied their robustness to disruptions. By quantifying the ability of individual nodes to control attractor behaviour, we can obtain a testable understanding of macro-level canalization in the analysed biochemical network. Indeed, we can uncover how robust phenotypic traits are (e.g. robustness of the wild-type attractor), and which critical nodes must be acted upon in order to disrupt phenotypic behaviour. We exemplified our methodology with the well-known segment polarity network model (in both the single-cell and the spatial versions). Because this model has been extensively studied, we use it to show that our analysis does not contradict any previous findings. However, our analysis also allowed us to gain new knowledge about its behaviour. From a better understanding of the size of its wild- type attractor basin (larger than previously thought) to uncovering new minimal conditions and critical nodes that control wild-type behaviour. We also fully quantified micro- and macro-level canalization in the model, and provided a complete map of its canalization logic including dynamical modularity. Naturally, our results pertain to this model; we do not claim that our results characterize the real Drosophila segment polarity gene network. However, our results, should they be found to deviate from organism studies, can certainly be used to improve the current model, and thus improve our understanding of Drosophila development. Thus a key use of our methodology in systems biology should be to help improve modelling accuracy. With the methodology now tested on this model, in subsequent work we will apply it to several automata network models of biochemical regulation and signalling available in the systems biology literature. The pathway modules we derived by inspection of the DCM for the segment polarity network revealed a number of properties of complex networks dynamics that deserve further study. For instance, the dynamical sequence that occurs once each such module is activated is independent of the temporal update scheme utilized. Therefore, if the dynamics of a network is captured exclusively by such modules, its intra-module behaviour will be similar for both synchronous and asynchronous updating – denoting a particular form of robustness to timing. We will explore this property in future work, but as we showed here, the dynamics of the single-cell version of the SPN model is very (though not fully) controlled by only two pathway modules. This explains why its dynamical behaviour is quite robust to timing events as previously reported [38]. Research in cellular processes has provided a huge amount of genomic, proteomic, and metabolomics data used to characterize networks of biochemical reactions. All this information opens the possibility of understanding complex regulation of intra- and inter- cellular processes in time and space. However, this possibility is not yet realized because we do not understand the dynamical constraints that arise at the phenome (macro-) level from micro- level interactions. One essential step towards reaching these ambitious goals is to identify and understand the loci of control in the dynamics of complex networks that make up living cells. Towards this goal, we developed the new methodology presented in this paper. Our methodology is applicable to any complex network that can be modelled using binary state automata – and easily extensible to multiple-state automata. We currently focus only on biochemical regulation with the goal of understanding the possible mechanisms of collective information processing that may be at work in orchestrating cellular activity. Supporting Information Data S1 Glossary and mathematical notation. (PDF) Data S2 Details about the computation of wildcard and two-symbol schemata. (PDF) Figure 21. Wild-type enput disruption in the SPN model. Each coordinate (x,y) in a given diagram (each corresponding to a tested enput) contains a circle, depicting the proportion of trials that converged to attractor y when noise level x was used. Red circles mean that all trajectories tested converged to y. doi:10.1371/journal.pone.0055946.g021 Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 32 March 2013 \| Volume 8 \| Issue 3 \| e55946 Data S3 Details about the conversion of schemata into a single threshold network. (PDF) Data S4 Algorithms for the computation of minimal configurations. (PDF) Data S5 Further details concerning the minimal con- figurations found for the segment polarity network model. (PDF) Data S6 Basic notions of the inclusion/exclusion prin- ciple. (PDF) Data S7 Minimal configurations for the segment polar- ity network model obtained from biologically-plausible seed configurations. (CSV) Data S8 Entire set of minimal configurations obtained for the segment polarity network model. (CSV) Data S9 Minimal configurations for the segment polar- ity network where no protein is on. (CSV) Data S10 Minimal configurations for the segment polarity network with the smallest number of nodes that need to be specified in a Boolean state. (CSV) Data S11 Minimal configurations for the segment polarity network with the fewest number of on nodes. (CSV) Data S12 Minimal configurations for the segment polarity network with the largest number of on nodes. (CSV) Data S13 (Wildcard) minimal configurations for the segment polarity network that were redescribed as two- symbol schemata. (CSV) Data S14 Minimal configurations for the segment polarity network that do not satisfy wg4~1 _ en1~1 _ ci4~1. (CSV) Acknowledgments We thank the FLAD Computational Biology Collaboratorium at the Gulbenkian Institute of Science (Portugal) for hosting and providing facilities used for this research. We also thank Indiana University for providing access to its computing facilities. 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Canalization and Control in Automata Networks PLOS ONE \| www.plosone.org 34 March 2013 \| Volume 8 \| Issue 3 \| e55946	23520449	HH_protein = ( hh ) EN_protein = ( en ) WG_protein = ( wg ) CIR = ( ( CI_protein AND ( ( ( PTC_protein ) ) ) ) AND NOT ( hh_external ) ) PTC_protein = ( ptc ) OR ( ( PTC_protein ) AND NOT ( hh_external ) ) ci = NOT ( ( EN_protein ) ) en = ( ( WG_external ) AND NOT ( SLP ) ) PH = ( PTC_protein AND ( ( ( hh_external ) ) ) ) wg = ( ( wg AND ( ( ( CIA OR SLP ) ) ) ) AND NOT ( CIR ) ) OR ( ( CIA AND ( ( ( SLP ) ) ) ) AND NOT ( CIR ) ) ptc = ( ( ( CIA ) AND NOT ( CIR ) ) AND NOT ( EN_protein ) ) hh = ( ( EN_protein ) AND NOT ( CIR ) ) SMO = ( ( hh_external ) ) OR NOT ( hh_external OR PTC_protein ) CI_protein = ( ci ) CIA = ( ( CI_protein ) AND NOT ( PTC_protein ) ) OR ( hh_external AND ( ( ( CI_protein ) ) ) )
A Comprehensive, Multi-Scale Dynamical Model of ErbB Receptor Signal Transduction in Human Mammary Epithelial Cells Toma´sˇ Helikar1, Naomi Kochi1, Bryan Kowal2, Manjari Dimri3, Mayumi Naramura4,5,6, Srikumar M. Raja4,5, Vimla Band4,5,6, Hamid Band4,5,6,7, Jim A. Rogers1,6* 1 Department of Mathematics, University of Nebraska at Omaha, Omaha, Nebraska, United States of America, 2 College of Information Technology, University of Nebraska at Omaha, Omaha, Nebraska, United States of America, 3 George Washington University School of Medicine, Washington, D. C., United States of America, 4 The Eppley Institute for Research in Cancer and Allied Diseases, Omaha, Nebraska, United States of America, 5 University of Nebraska Medical Center-Eppley Cancer Center, Omaha, Nebraska, United States of America, 6 University of Nebraska Medical Center, Department of Genetics, Cell Biology and Anatomy, College of Medicine, Omaha, Nebraska, United States of America, 7 University of Nebraska Medical Center, Departments of Biochemistry and Molecular Biology; Pathology and Microbiology; and Pharmacology and Experimental Neuroscience, College of Medicine, University of Nebraska Medical Center, Omaha, Nebraska, United States of America Abstract The non-receptor tyrosine kinase Src and receptor tyrosine kinase epidermal growth factor receptor (EGFR/ErbB1) have been established as collaborators in cellular signaling and their combined dysregulation plays key roles in human cancers, including breast cancer. In part due to the complexity of the biochemical network associated with the regulation of these proteins as well as their cellular functions, the role of Src in EGFR regulation remains unclear. Herein we present a new comprehensive, multi-scale dynamical model of ErbB receptor signal transduction in human mammary epithelial cells. This model, constructed manually from published biochemical literature, consists of 245 nodes representing proteins and their post-translational modifications sites, and over 1,000 biochemical interactions. Using computer simulations of the model, we find it is able to reproduce a number of cellular phenomena. Furthermore, the model predicts that overexpression of Src results in increased endocytosis of EGFR in the absence/low amount of the epidermal growth factor (EGF). Our subsequent laboratory experiments also suggest increased internalization of EGFR upon Src overexpression under EGF-deprived conditions, further supporting this model-generated hypothesis. Citation: Helikar T, Kochi N, Kowal B, Dimri M, Naramura M, et al. (2013) A Comprehensive, Multi-Scale Dynamical Model of ErbB Receptor Signal Transduction in Human Mammary Epithelial Cells. PLoS ONE 8(4): e61757. doi:10.1371/journal.pone.0061757 Editor: Nikos K. Karamanos, University of Patras, Greece Received September 29, 2012; Accepted March 12, 2013; Published April 18, 2013 Copyright: 2013 Helikar et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported by the National Institutes of Health (NIH) grants CA105489, CA87986, CA99163, CA116552 and NCI 5U01CA151806-02 and Department of Defense grant W81WH-11-1-0167 to H.B; the NIH grants CA96844 and CA144027 and Department of Defense grants W81XWH-07-1-0351 and W81XWH-11-1-0171 to V.B; Department of Defense grant W81 XWH-10-1-0740 to M.N.; the NCI Core Support Grant to UNMC-Eppley Cancer Center; by the College of Arts and Sciences at the University of Nebraska at Omaha, the University of Nebraska Foundation, and Patrick J. Kerrigan and Donald F. Dillon Foundations. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: jrogers@unomaha.edu Introduction EGF receptor (ErbB1) and other members of the ErbB family of receptor tyrosine kinases (RTKs) play essential physiological roles in development and maintenance of epithelial tissues by generat- ing cell proliferation, survival, differentiation and migration signals in response to specific ligands and via the stimulation of several signaling pathways including PI3K/Akt, MAPK, Src, as well as STAT pathways [1,2]. Activation of ErbB receptors is also linked to the initiation and progression of human cancers. Thus, elucidating signaling pathways that play critical roles in physio- logical and oncogenic signaling by the ErbB family of receptors is of substantial clinical significance [2–5]. Despite substantial progress through experimental studies, in depth mechanistic analyses of the signaling mechanisms of ErbB receptor family have been quite challenging due to the multiple interactions between members of the family, the number of associated effector pathways, and the complexity of regulatory mechanisms [6]. In addition to a multitude of positive signaling pathways triggered by ErbB receptor activation, ErbB receptor signaling is also under regulation by negative feedback mechanisms via receptor endo- cytosis and recycling/degradation, and this mechanism is critical for normal function [7]. The level of intricacy of the ErbB signaling system is further multiplied by the fact that ErbB signaling pathways are closely intertwined with a number of other signaling pathways such as those downstream of integrins and G- Protein-coupled Receptors [8]. Together, these complexities have hampered our basic understanding of ErbB receptor signaling and our ability to develop treatments for diseases, such as breast cancer, lung cancer, gliomas and others, associated with aberrant ErbB receptor signaling. An example of the complex biology of ErbB receptor signaling that is highly relevant to their role in oncogenesis involves the non- receptor tyrosine kinase c-Src. The c-Src kinase is overexpressed or hyperactive in a range of human tumors, including breast cancer where as many as 70% cases have been reported with c-Src overexpression along with EGFR/ErbB1 or ErbB2, leading to conjectures of possible synergy between Src and the ErbBs in PLOS ONE \| www.plosone.org 1 April 2013 \| Volume 8 \| Issue 4 \| e61757 breast cancer [9]. Indeed, in rodent fibroblasts [9,10] and more importantly in untransformed human mammary epithelial cells [11] the overexpression of c-Src promotes ErbB1/EGFR-depen- dent oncogenic transformation. In particular, c-Src is a critical component in the regulation of cell survival, proliferation as well as migration, invasion and metastasis via the regulation of a number of signaling pathways including PI3K/Akt, MAPK, as well as focal adhesion kinase (FAK) [12]. However, the interconnectivity of pathways associated with c-Src and the ErbB signaling has hindered the determination of the mechanisms of ErbB-c-Src synergy in cancer. These difficulties represent an ideal example of the need for a systems biology approach to ErbB receptor signaling. Because ErbB1/EGFR has been extensively studied over the last several decades, it is perhaps one of the best understood receptor tyrosine kinase systems; this makes it a good candidate for computational modeling [13]. Thus far, several EGFR-based computational models have been created; these have been used in studies focusing on receptor trafficking and endocytosis [14–17], ErbB dimeriza- tion [18–20], as well as the relationships between physiological responses and the receptor activation dynamics [21–23]. Several modeling efforts have also been made to better understand the signaling events downstream of EGFR [18,24–28]. In addition, recent efforts also utilized a logical modeling approach to analyze the topology and dynamics of an ErbB signaling network in human liver cells [29], and to identify a potential new drug target, c-MYC, in a model of ErbB receptor-mediated G1/S cell cycle transition [30]. In this work, a new comprehensive, multi-scale logical model of signal transduction in a human mammary epithelial cell (hMEC) is presented. This large-scale dynamical model consists of 245 cellular components and about 1,100 biochemical interactions, and encompasses all ErbB receptor family members, including individual receptor phosphorylation sites, as well as integrin, G- protein-coupled receptor, and stress signaling pathways. The model was constructed manually by collecting and integrating biochemical information from over 800 published papers. One of the main advantages of logical models lies in their scalability; first, they are based on qualitative information available for many cellular components across many cell types and do not depend on kinetic parameters (that are only sparsely available), and second, simulations of logical models are relatively efficient [31,32], making this approach appropriate for large systems. Simulations of the model indicate a relatively accurate depiction of the complexities of ErbB signaling by integrating a number of other signaling pathways such as G-protein-coupled receptors (GPCR) and integrins. Following its validation, the model was used to generate predictions about the role of c-Src in EGFR signaling, which were verified experimentally in the laboratory. Finally, the model (including its governing logical expressions as well as all annotations) is available on-line in The Cell Collective software (www.thecellcollective.org; [32]) not only for download in multiple open formats (e.g., SBML; [33]) , but also for live simulations. Results 1. The hMEC model The hMEC model for EGFR signaling networks in a human mammary epithelial cell was created by manually collecting information on local biochemical interactions (e.g., protein- protein) from the primary literature (using the same methods as described in [34]). All interactions and logical expressions have been cataloged and annotated, and are available in the Cell Collective software [32]. In addition, all representing logical expressions are available in Supporting Information S1. The model contains a number of integrated signaling pathways at the level of protein-protein as well as -post-translational (namely phosphorylation) site interactions. These pathways include E- cadherin, ErbB (1–4), ErbB1 (EGFR) endocytosis, G-protein- coupled Receptor, integrin, and stress signaling pathways (Figure 1). Detailed description of some of these follows below. ErbB receptors. All known individual ErbB receptors (ErbB1–4), as well as the major ErbB receptor dimers were included in the model. Moreover, the hierarchy of the dimeriza- tion process [35] was also captured via the logical functions associated with each receptor node in the model (see the Model Validation section). Furthermore, this model goes into an even greater detail; all major (auto) phosphorylation sites of the ErbB receptors were included. This allows for a range of mutational studies at the phosphorylation site level in future studies; for example, this multi-scale property of the mode will enable in silico simulations and analyses of system-wide effects of all theoretically possible combinations of virtual knock-out studies of the main phosphorylation sites in a single receptor as well as across all ErbB receptors. EGFR endocytosis. EGFR endocytosis as a potential mech- anism of negative regulation through lysosomal degradation is extremely important in relation to oncogenic signaling by ErbB receptors [6]. Modeling receptor endocytosis is not trivial as the same receptor can localize into different areas of the cell (e.g., clathrin-coated (CC) pits, CC vesicles, endosome, etc.), depending on its stage of the endocytic trafficking. The way these multiple localizations are handled using our modeling framework is to represent EGFR with multiple nodes depicting the receptor in the different locations during endocytic traffic. Specifically, the locations included in the model are the following: the plasma membrane, clathrin-coated pits, clathrin-coated vesicles, early endosome, late endosome/multivesicular bodies (MVBs), and the lysosome. The node representing EGFR in the lysosome denotes the degradation process of EGFR. Because results from these models do not attempt to predict exact measurements such as concentrations of ligands used in laboratories, during a simulation, the activity level associated with, for example, the node representing EGFR in the lysosome corresponds to the degree of EGFR being degraded in a semi-quantitative fashion. Further- more, the type of ligand which activates EGFR has an effect on whether the receptor is recycled back to cell surface or degraded upon its internalization. To be able to simulate these effects in addition to the nodes representing the different localizations of the receptor during endocytosis, nodes depicting the receptor being activated by different types of ligands (using EGF or TGFa as prototypes) were added. Thus there is a node that represents EGFR on the plasma membrane activated by EGF and a node for EGFR activated by TGF-alpha. While these differentiations add complexity to the model, they allow the visualization and study of the dynamics of the model in greater detail. Drugs and Antibodies. Therapeutic agents that impact ErbB receptor signaling and/or traffic, such as humanized anti- ErbB2 monoclonal antibodies Herceptin and Pertuzumab, as well as small molecular inhibitors are included in the presented model. These components allow the simulation of mutations known to cause cancer while at the same time introducing a number of different levels and combinations of drugs and observing their effects on the dynamics of the system. In summary, the initial version of the new model of signal transduction in human MEC comprises 240+ biological species and 1,100+ biochemical interactions. The amount of detail A Dynamical Model of Signal Transduction in hMEC PLOS ONE \| www.plosone.org 2 April 2013 \| Volume 8 \| Issue 4 \| e61757 accomplished by including individual phosphorylation sites, various localizations, as well as dimers of ErbB receptors, and the scale in terms of the number of the different pathways included makes this model, to our best knowledge, the most comprehensive dynamic model of signal transduction available to date. 2. Model Validation The model was constructed using only information from the primary literature about local interactions. In other words, during the construction phase of the model there was no attempt to determine the local interactions based on any other larger phenotypes or phenomena. However, after the model was completed, verification of the accuracy of the model involved testing it for the ability to reproduce complex input-output phenomena that have been observed in the laboratory. To do this, The Cell Collective’s ‘‘Dynamical Analysis’’ simulation feature was used [32]. This simulation component allows users to simulate virtual cells under tens of thousands of cellular conditions, and analyze and visualize the results in terms of input-output dose- response curves that make it easy to determine whether the virtual cell behaves as expected. The presented hMEC model was interrogated to ensure that it is able to reproduce some of the known global biological phenomena as previously observed experimentally (Figure 2), including EGF-induced activation of Figure 1. Graph representation of the model. The purpose of this graph is to visualize the complexity of the model, rather than to read the individual interactions. This graph representation of the model was generated in Gephi (www.gephi.org). doi:10.1371/journal.pone.0061757.g001 A Dynamical Model of Signal Transduction in hMEC PLOS ONE \| www.plosone.org 3 April 2013 \| Volume 8 \| Issue 4 \| e61757 Akt and Erk, EGF-independent regulation of Erk via activated Ras, integrin-dependent stimulation of Erk, Rac, and Cdc42, G- protein Coupled Receptor activation of adenylyl cyclase, as well as ErbB receptor dimerization hierarchy. Clearly, one cannot expect that all phenomena will be replicated by the virtual cell due to the fact that the model does not represent the entire cell. Hence, the reproducibility of certain phenomena by the model only indicates that the model is on the right track. 3. Use of the model to form laboratory-testable predictions Once a functional model of hMEC signaling was completed, we used it to generate predictions about the system that could be subsequently tested in the laboratory. In this work, the conjecture of possible synergy between Src and the ErbBs in breast cancer (described in the introduction) was explored using the model. Specifically, the question examined was whether the internaliza- tion of EGFR increases as a result of Src overexpression; this was based on studies done in fibroblasts that showed increased EGFR Figure 2. Validation of the MEC model against known cellular phenomena. A) EGF-dependent stimulation of survival signals via activation of Akt. B) Activation of Erk by EGF [52]. Although a positive relationship between Erk and the ligand can be seen, the activation Erk by EGF seems to exhibit a more complex dynamics than the ones seen in the other diagrams (i.e., the positive relationship is exhibited when EGF activity levels are 0– 40%). This is, however, not surprising given the complex interactions and cross-communication within the ErbB signaling family. C) Activating mutations of known protooncogenes such as Ras result in growth factor-independent activation of Erk [53]. D) Erk dependency on signaling via integrins by extracellular matrix (ECM) [54]. E and F) Activation of Rac and Cdc42 by ECM [55]. G) Positive relationship between Adenylyl Cyclase (AC) and the G-Protein Coupled Receptor ligand alpha-s [56,57]. H) Hierarchy of ErbB receptor dimerization. The panel on the left represents a system with EGFR expression alone and, thus, the formation of EGFR homodimers. The expression of ErbB2 (middle panel) results in the shift of the formation (activity) from EGFR homodimers (EGFR-EGFR) to the formation of EGFR-ErbB2 heterodimers. Furthermore, the expression of ErbB 1–3 results in the dominant formation of ErbB2–3 heterodimers [13,35]. Note that the references refer to classical, qualitative input-output relationships (not necessarily quantitative dose–response curves), and the dose-response curves presented here are intended to demonstrate how the computational model qualitatively reproduces the referenced input-output relationships over a range of stimulus signals. doi:10.1371/journal.pone.0061757.g002 A Dynamical Model of Signal Transduction in hMEC PLOS ONE \| www.plosone.org 4 April 2013 \| Volume 8 \| Issue 4 \| e61757 internalization in response to sub-saturating levels of EGF when Src was overexpressed [36], but this phenomenon has not been investigated in the more relevant MECs nor has it been tested at low levels/in the absence of added EGF. To test whether the level of Src activity affects EGFR endocytosis, the node representing c-Src was constitutively activated in the model, using the Cell Collective’s Dynamical Analysis feature. The model was then simulated in The Cell Collective, and the activity levels of EGF- activated EGFR homodimer on i) the plasma membrane, ii) in clathrin-coated pits, iii) clathrin-coated vesicles, and iv) the endosome were measured. The experiment was first conducted with high levels of EGF to ensure that the model could predict the known increase in internalization of EGFR under that condition. The model was then simulated with low levels of EGF activity (randomly ranging from 0–5%ON). As can be seen in Figure 3, under both high and low levels of EGF, the overexpression of Src (i.e., mutating Src to be constitutively-active) leads to the decrease of the activity levels of the node representing EGFR homodimers on the plasma membrane, while increasing the % ON levels of nodes representing the receptor during the internalization process. Thus the model indicates that Src overexpression will lead to increased internalization of EGFR even in the absence (or low levels) of EGF, a result that we assessed and confirmed experimentally as discussed in the next section. 4. Verification of model-generated predictions We sought to verify whether the predicted enhancement of the intracellular (endocytosed) EGFR pools is seen in an actual human MEC model in laboratory experiments. The overall levels of ectopically expressed EGFR and Src in 76NTERT human MEC lines retrovirally transuced with EGFR or EGFR plus Src (using retroviral infection) [37] were assessed using Western blotting. As is clear in Figure 4, increased Src and EGFR levels are observed in the appropriate transductants. As expected, both the EGFR alone transduced as well as the EGFR plus Src transduced cell lines showed higher EGFR levels compared to the parent 76NTERT cell line (Figure 4; results further explained in the caption). Notably, the total levels of biochemically detected EGFR in the EGFR plus Src transductant (lane 3) exceed the levels of EGFR detectable in the EGFR alone transductant. In contrast, Fluores- cence-activated cell sorting (FACS) based analysis that was designed to selectively measure the levels of EGFR on the cell surface (FACS analysis was done on live cells without permabiliz- ing them; under these conditions, the staining antibody is excluded from endocytosed pools of EGFR) demonstrated that, in the absence of added EGF, there is dramatically reduced expression of EGFR on the surface of MECs overexpressing Src (Figure 5, third panel of the second row; indicated by the lower median fluorescence channel values along the X-axis – MFI = 276) compared to EGFR-only transduced MEC controls (Figure 5, second panel of the second row, which expectedly shows a markedly higher median channel value of 528 compared to112 in untransduced control in the first panel). Thus, the prediction from the hMEC model, that higher levels of Src introduced into MECs will lead to a lower proportion of EGFR at the cell surface even in the absence of EGF, i.e., EGFR is internalized, is fully verified by experimental analyses of an actual mammary epithelial cell system. Discussion The critical roles of ErbB receptors in physiological processes and the importance of their overexpression and/or hyperactivity in the initiation and progression of cancers makes analyses of these receptor tyrosine kinases extremely significant. EGFR is also the most highly studied prototype of receptor tyrosine kinase signaling. Therefore, predictive computational modeling of signaling down- stream of these receptors in the context of positive and negative loops and cross-talk with other receptor systems are likely to greatly enhance our fundamental knowledge of cellular signaling in health and disease. These models can also provide a more informed platform for therapeutic targeting of aberrant ErbB signaling in cancer to reduce treatment failures and to stem the emergence of resistance. Here, we present a new and most comprehensive computational model of ErbB receptor signaling in a human mammary epithelial cell, use simulations to make a specific prediction on the biological behavior of a hMEC under experimental conditions that model the overexpression of EGFR and Src as seen in human cancers, and then use laboratory experiments to fully verify the prediction. It is well-established that EGFR and c-Src tyrosine kinase are co-overexpressed in human cancers, and experimental modeling of their co-overexpression in untransformed hMECs in the laboratory leads to their collaborative promotion of oncogenesis [11]. Studies in such systems will be greatly enhanced by generating hypotheses on the interactions of the two oncogenic proteins that can be experimentally tested. As RTK signaling is spatio-temporally regulated in part by the subcellular location of activated receptors in different endocytic compartments which serves as a critical determinant of the level and diversity of their Figure 3. EGFR internalization effects by Src overexpression. Experiments were conducted under conditions for which the expression of ErbB2–4 was turned off and the virtual cell stimulated with EGF. A) Stimulation of the virtual cell with low levels of EGF (0–5%). B) EGF was introduced to the model in randomly selected high activity levels (60– 70% ON). * p,0.05 (Student’s t-test; n = 300; error bars represent the standard error of the mean). Note: PM corresponds to EGFR homodimers on the plasma membrane, CCP represents the homodimer in clathrin-coated pits, CCV – clathrin-coated vesicles, and MVB – EGFR homodimer in late endosome/multivescicular bodies. doi:10.1371/journal.pone.0061757.g003 A Dynamical Model of Signal Transduction in hMEC PLOS ONE \| www.plosone.org 5 April 2013 \| Volume 8 \| Issue 4 \| e61757 signaling outputs [37,38]. Therefore, we used the computational model that we have developed to specifically address questions of endocytic localization of EGFR under the influence of Src. It is remarkable that the model could make an accurate de novo prediction that the elevated Src activity will promote the localization of EGFR in internal compartments of the endocytic pathways even in the absence of added ligand. We used a cell system in which we utilized an externally-introduced EGFR (under a viral promoter) to test this prediction. Even though the total levels of EGFR are substantially higher in the cell line that co- overexpresses Src (Figure 4), the levels of EGFR on the cell surface are dramatically reduced (Figure 5); thus, a vast majority of EGFR in these cells is predicted to be in endocytic compartments even without an added ligand. Under normal conditions, ligands such as EGF cause rapid internalization of EGFR and its rapid degradation in the lysosome while other ligands such as TGFalpha or amphiregulin promote less degradation with more recycling [39]. Notably, increased internal pools of EGFR are a feature of oncogenic mutants of EGFR; we have recently shown that human non-small cell lung cancer cell lines harboring EGFR mutants with activating kinase domain mutations show increased levels of active EGFR within intracellular endocytic compartments when cultured without external EGF [40]. Remarkably, the internalized pool of oncogenic EGFR co-localized with active Src [40] and the interaction of mutant EGFR and Src was required for efficient oncogenic transformation of fibroblasts [41]. Thus, our current model-based prediction followed by experimental verification in a relevant cell model in the laboratory should open a productive lead to further experimentation towards understanding how Src and EGFR cooperate in oncogenesis. Importantly, the verified experimental findings can then be incorporated back into our computational model to enhance its ability to make further predictions and efforts along these lines are underway. The use of computational models to generate experimentally testable hypotheses in an information flow cycle from laboratories to computational models and back to laboratories [42] is an important dynamic that will define the future of computational systems biology. However, the sheer size and complexity of biochemical and biological processes poses a barrier for one person or group to create and/or expand in an effective way large- scale dynamical models of these systems. While the presented model is one of the largest computational models created, it merely represents a small fraction of the cell. Similar to Wikipedia and open source software – both of which are centered around large amounts of knowledge that could not have originated from one single person or group, one way to create larger computational models of biological process, ones that have the potential to eventually lead to whole-cell models, is to engage the scientific community in a collaborative fashion. Hence, the presented hMEC model has been made available in The Cell Collective software which was designed precisely to enable such a collabo- rative and collective approach to systems biology [32]. The model is available to the entire scientific community via the software for further expansion, refinements, as well as simulations and analyses. The user-friendly interface of the software allows users to make changes to the model without any need to enter complex mathematical equations or computer code, making it accessible to experimental scientists who have the most intimate knowledge of the local data to improve and grow this model (and others available in the software platform; e.g., [30,43,44]). Materials and Methods 1. Model construction via The Cell Collective The presented model is based on a common qualitative (discrete) modeling technique where the regulatory mechanism of each node is described by a Boolean expression (for more comprehensive information on Boolean modeling see for example [45,46]). The construction of the model was accomplished using The Cell Collective (www.thecellcollective.org; [32]), a collabora- tive modeling platform for large-scale biological systems. The platform allows users to construct and simulate large-scale computational models of various biological processes based on qualitative interaction information using the platform’s Bio-Logic Builder which converts the entered qualitative biochemical information into Boolean expressions in the background [47]. (Though the Boolean expressions for any model created in the platform can be downloaded from the website.) This non-technical creation and representation of the individual interactions in the model make it especially easy for experimental biologists to contribute to the creation of the model without the need for training in the underlying mathematical formalisms. The model has been exported and is also available as part of this manuscript in a SBML format for qualitative models (Supporting Information S2). The Cell Collective’s Knowledge Base component was also used to catalog and annotate all biochemical/biological information for signaling in hMECs as mined from the primary literature. Each Figure 4. Src overexpression does not affect total EGFR levels. Parental 76N-TERT cells or its EGFR or EGFR + Src transductants were EGF deprived by culture in the EGF-deficient D3 medium for 48 hrs and cell lysates were prepared. 50 mg aliquots of cell lysate protein were run on an 8% SDS PAGE gel and immunoblotted with anti-EGFR (top panel) or anti-Src (middle panel). Membrane was re-probed with anti-beta actin (bottom panel) to ensure equal loading. doi:10.1371/journal.pone.0061757.g004 A Dynamical Model of Signal Transduction in hMEC PLOS ONE \| www.plosone.org 6 April 2013 \| Volume 8 \| Issue 4 \| e61757 model species in the Knowledge Base has its own wiki-like page where information on the individual interactions is stored, including references. 2. Model Simulations and Analysis In addition to the model building and cataloging process, The Cell Collective platform was also used to perform all computa- tional simulations of the hMEC model. While the dynamical model is based on a discrete (i.e., Boolean) formalism, as can be seen in the results, the simulation input and output data are continuous. This was accomplished by converting the digital output of the model simulations to % activity (% ON) which ranges (for each model component) from 0 to 100 [31,34]. It is important to note that the % ON doesn’t directly correspond to the biological concentration or any other measurable property, rather the % ON provides a semi-quantitative measure to describe the relative activity level of a particular protein. As such, the model output (species activity levels) is compared to previously published experimental findings as well as the experimental results presented herein by assessing the directionality of the changes (up-/down- regulation) of species activity relative to the wild-type. All simulations were conducted using a biologically relevant initial condition as discussed in [34]; this condition is also accessible via The Cell Collective software. All in silico experiments were performed under external conditions (Table 1) that were optimized for the particular experiment [34]. 3. Establishment of mammary epithelial cell lines overexpressing EGFR or EGFR plus Src Human telomerase reverse transcriptase (TERT) immortalized 76N normal human MEC line 76N-TERT has been previously described [48,49]. These cells were cultured in DFCI-1 medium and the human EGFR or EGFR plus c-Src were overexpressed in these cells using retroviral infection as described previously [50]. 4. Assessment of Src overexpression and EGFR levels using Western blotting Parental 76NTERT cell line or its EGFR or EGFR + Src transductants were growth factor deprived for 48 h (with medium change each day) in EGF-deficient D3 medium (DFCI-1 medium lacking insulin, hydrocortisone, EGF and bovine pituitary extract) Figure 5. Surface expression of EGFR is reduced in Src-transfected cells. FACS analysis of the cell surface expression of EGFR in MEC transductants shows (in row 2) that Src overexpression leads to a reduction in the level of EGFR at the cell surface despite higher total EGFR levels detected biochemically (shown in Figure 3). Cells were EGF-deprived by culture in D3 medium for 48 h, after which single cell suspensions were prepared with trypsin/EDTA. Live cells were stained with isotype-matched control monoclonal antibodies or with anti-EGFR monoclonal antibody for 1 hr.., washed and incubated with the secondary antibody (PE-conjugated) for 45 min., and analyzed by FACS to determine cell surface levels of EGFR. Numbers in the right top corner of each FACS panel indicate median fluorescence channel intensity (higher numbers indicating higher levels and vice versa). Initial experiments (not shown) established the specificity of antibodies. doi:10.1371/journal.pone.0061757.g005 A Dynamical Model of Signal Transduction in hMEC PLOS ONE \| www.plosone.org 7 April 2013 \| Volume 8 \| Issue 4 \| e61757 [51], Cell lysates were prepared in a Triton X-100-based lysis buffer, and 50 mg aliquots of cell lysate protein were run on an 8% SDS PAGE gel and immunoblotted with anti-EGFR, anti-Src and anti-beta actin antibodies, as described [50]. 5. Assessment of surface expression of EGFR Cells were cultured under EGF-deprivation conditions as above for 48 h, and single cell suspensions were prepared by releasing cells from tissue culture plates with trypsin/EDTA. Live cells were stained on ice with isotype-matched control monoclonal antibodies or with anti-EGFR monoclonal antibody (clone 528; ATCC) for 1 h, washed and incubated with the secondary antibody (PE- conjugated anti-mouse IgG) for 45 min followed by FACS analysis (using a FACSCalibur instrument) to determine the relative cell surface EGFR levels. Supporting Information Supporting Information S1 A comprehensive, multi-scale dynamical model of ErbB receptor signal transduction in human mammary epithelial cells (DOC) Supporting Information S2 SBML model representation of signal transduction epithelial cells (SBML) Author Contributions Conceived and designed the experiments: TH JAR HB MN SMR VB MD. Performed the experiments: TH NK JAR HB MN SMR VB MD. Analyzed the data: TH JAR HB MN SMR VB MD. Contributed reagents/materials/analysis tools: TH BK JAR HB MN SMR VB MD. Wrote the paper: TH JAR HB. References 1. 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A Dynamical Model of Signal Transduction in hMEC PLOS ONE \| www.plosone.org 9 April 2013 \| Volume 8 \| Issue 4 \| e61757	23637902	Grb2 = ( EGFR_Y1068 ) OR ( EGFR_Y1086 ) OR ( ErbB2_Y1139 ) OR ( Src AND ( ( ( Fak ) ) ) ) OR ( Shc ) ILK = ( PIP3_345 ) PIP2_45 = ( PTEN AND ( ( ( PIP3_345 ) ) ) ) OR ( PI4K AND ( ( ( PI5K ) ) ) ) OR ( ( PIP2_45 ) AND NOT ( PI3K AND ( ( ( PIP2_45 ) ) ) ) ) PKC = ( ( AA AND ( ( ( PKC_primed ) ) AND ( ( Ca ) ) ) ) AND NOT ( Trx AND ( ( ( PKC ) ) ) ) ) OR ( ( PKC AND ( ( ( NOT PP2A ) ) AND ( ( NOT Trx ) ) ) ) AND NOT ( Trx AND ( ( ( PKC ) ) ) ) ) OR ( ( DAG AND ( ( ( Ca ) ) AND ( ( PKC_primed ) ) ) ) AND NOT ( Trx AND ( ( ( PKC ) ) ) ) ) Cdc42 = ( ( Cdc42 AND ( ( ( NOT p190RhoGAP AND NOT Graf AND NOT RalBP1 ) ) AND ( ( IQGAP1 ) ) ) ) AND NOT ( RhoGDI AND ( ( ( Src ) ) ) ) ) OR ( ( Pix_Cool AND ( ( ( PAK AND Gbg_i ) AND ( ( ( NOT Rac ) ) ) ) OR ( ( Cdc42 ) ) ) ) AND NOT ( RhoGDI AND ( ( ( Src ) ) ) ) ) ErbB2_Y1221_22 = ( EGFR_ErbB2 ) OR ( ErbB2_ErbB3 ) OR ( ErbB2_ErbB4 ) ARF = ( ARNO AND ( ( ( NOT PIP2_45 ) ) ) ) OR ( ARF AND ( ( ( NOT PIP2_45 ) ) ) ) OR ( PIP3_345 AND ( ( ( NOT PIP2_45 ) ) ) ) OR ( PIP2_45 AND ( ( ( PIP3_345 OR ARNO ) AND ( ( ( NOT ARF ) ) ) ) ) ) Talin = ( PIP2_45 AND ( ( ( NOT Talin ) ) ) ) OR ( Talin AND ( ( ( NOT Src ) ) ) ) Mekk4 = ( Rac ) OR ( Cdc42 ) ErbB4_Y1242 = ( ErbB4_ErbB4 ) OR ( ErbB3_ErbB4 ) OR ( EGFR_ErbB4 ) OR ( ErbB2_ErbB4 ) RKIP = ( PKC ) Ga_1213 = ( Ga_1213 AND ( ( ( NOT p115RhoGEF ) ) AND ( ( Gbg_1213 ) ) ) ) OR ( alpha_1213R AND ( ( ( NOT Ga_1213 AND NOT Gbg_1213 ) ) ) ) CaMKK = ( CaM ) Cbl_RTK = ( ( ( Grb2 AND ( ( ( Src ) ) ) ) AND NOT ( EGFR_T654 ) ) AND NOT ( CIN85 AND ( ( ( Spry2 ) ) ) ) ) OR ( ( ( EGFR_Y1045 AND ( ( ( Src ) ) ) ) AND NOT ( EGFR_T654 ) ) AND NOT ( CIN85 AND ( ( ( Spry2 ) ) ) ) ) RGS = ( CaM AND ( ( ( PIP3_345 ) ) ) ) EGFR_Y1148 = ( EGFR_ErbB3 ) OR ( EGFR_ErbB2 ) OR ( EGFR_ErbB4 ) OR ( EGFR_EGFR ) OR ( EGFR_EGFR_EGF_PM ) OR ( EGFR_EGFR_TGFa_PM ) Tiam = ( PKC AND ( ( ( Ras OR Rap1 OR PIP2_45 ) ) AND ( ( PIP3_345 OR PIP2_34 ) ) ) ) OR ( Src AND ( ( ( Ras OR Rap1 OR PIP2_45 ) ) AND ( ( PIP3_345 OR PIP2_34 ) ) ) ) OR ( CaMK AND ( ( ( PIP3_345 OR PIP2_34 ) ) AND ( ( Ras OR Rap1 OR PIP2_45 ) ) ) ) Hsp90 = ( ( EGFR_ErbB2 ) AND NOT ( CHIP AND ( ( ( Hsp90 ) ) ) ) ) OR ( ( ErbB2_ErbB3 ) AND NOT ( CHIP AND ( ( ( Hsp90 ) ) ) ) ) OR ( ( ErbB2_ErbB4 ) AND NOT ( CHIP AND ( ( ( Hsp90 ) ) ) ) ) ErbB3_ErbB4 = ( ( NRG AND ( ( ( ErbB4_Free AND ErbB3_Free ) ) ) ) AND NOT ( ErbB2_Free ) ) PA = ( PLD ) RhoK = ( Rho ) GAK = ( GAK AND ( ( ( EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_EGF_CCV ) ) ) ) OR ( EGFR_EGFR_EGF_CCP AND ( ( ( Clathrin OR Dynamin OR AP2 ) ) ) ) OR ( EGFR_EGFR_TGFa_CCP AND ( ( ( Clathrin OR Dynamin OR AP2 ) ) ) ) EGFR_EGFR_EGF_Lysosome = ( EGFR_EGFR_EGF_MVB AND ( ( ( VPS4 OR Eps15 ) ) AND ( ( Rab7 ) ) AND ( ( Alix ) ) ) ) OR ( ESCRT_III AND ( ( ( VPS4 OR Eps15 ) ) AND ( ( Rab7 ) ) AND ( ( Alix ) ) ) ) EGFR_ErbB2 = ( Pertuzumab AND ( ( ( EGFR_ErbB2 ) ) ) ) OR ( ( ( EGFR_ErbB2 ) AND NOT ( Trastuzumab ) ) AND NOT ( ErbB2Deg_Contr AND ( ( ( EGFR_ErbB2 ) ) ) ) ) OR ( ( EGF AND ( ( ( NOT NRG OR NOT ErbB3_Free ) ) AND ( ( NOT EGFR_ErbB2 ) ) AND ( ( NOT EGFR_ErbB2 ) ) AND ( ( ErbB2_Free AND EGFR_Free ) ) AND ( ( NOT EGFR_T654 ) ) ) ) AND NOT ( Pertuzumab ) ) EGFR_Y1173 = ( EGFR_ErbB3 ) OR ( EGFR_ErbB2 ) OR ( EGFR_ErbB4 ) OR ( EGFR_EGFR ) OR ( EGFR_EGFR_EGF_PM ) OR ( EGFR_EGFR_TGFa_PM ) alpha_catenin = ( B_catenin ) SAPK = ( ( ( MKK7 ) AND NOT ( MKPs AND ( ( ( SAPK ) ) ) ) ) AND NOT ( PP2A AND ( ( ( SAPK ) ) ) ) ) OR ( ( ( Sek1 ) AND NOT ( MKPs AND ( ( ( SAPK ) ) ) ) ) AND NOT ( PP2A AND ( ( ( SAPK ) ) ) ) ) ErbB2_ErbB3 = ( ( ErbB2_ErbB3 ) AND NOT ( ErbB2_Lysosome AND ( ( ( ErbB2_ErbB3 ) ) ) ) ) OR ( ( ( NRG AND ( ( ( ErbB2_Free AND ErbB3_Free ) ) ) ) AND NOT ( Pertuzumab ) ) AND NOT ( ErbB2_Lysosome AND ( ( ( ErbB2_ErbB3 ) ) ) ) ) Cortactin = ( Fer ) OR ( Src ) OR ( Actin ) OR ( Rac ) OR ( Dynamin ) OR ( Hip1R ) OR ( PAK ) OR ( Erk ) Hip1R = ( Clathrin ) OR ( CIN85 ) PIP2_34 = ( PIP2_34 AND ( ( ( NOT PI5K ) ) AND ( ( NOT PTEN ) ) ) ) OR ( PI4K AND ( ( ( NOT PIP2_34 ) ) AND ( ( PI3K ) ) ) ) EGFR_ErbB4 = ( EGF AND ( ( ( NOT EGFR_T654 ) ) AND ( ( NOT ErbB3_Free ) ) AND ( ( ErbB4_Free ) ) AND ( ( NOT ErbB2_Free ) ) AND ( ( NRG ) ) AND ( ( EGFR_Free ) ) ) ) p120RasGAP = ( ( ( EGFR_Y992 ) AND NOT ( Src ) ) AND NOT ( Fak ) ) OR ( ( ( PIP3_345 ) AND NOT ( Src ) ) AND NOT ( Fak ) ) OR ( ( ( PIP2_45 ) AND NOT ( Src ) ) AND NOT ( Fak ) ) OR ( ( ( PIP2_34 ) AND NOT ( Src ) ) AND NOT ( Fak ) ) p90RSK = ( Erk AND ( ( ( PDK1 ) ) AND ( ( NOT p90RSK ) ) ) ) EGFR_EGFR_EGF_MVB = ( ( EGFR_EGFR_EGF_MVB ) AND NOT ( EGFR_EGFR_EGF_Lysosome ) ) OR ( EGFR_EGFR_EGF_End ) Spry2 = ( ( EGFR_ErbB3 ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_ErbB2 ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_EGFR_TGFa_CCV ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_EGFR_EGF_End ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_ErbB4 ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_EGFR_EGF_CCP ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_EGFR_EGF_CCV ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_EGFR_TGFa_CCP ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_EGFR_EGF_MVB ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_EGFR ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_EGFR_EGF_PM ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_EGFR_TGFa_End ) AND NOT ( Cbl_RTK ) ) OR ( ( EGFR_EGFR_TGFa_PM ) AND NOT ( Cbl_RTK ) ) ESCRT_I = ( ESCRT_0 ) VPS4 = ( ESCRT_III ) UBPY = ( Alix ) OR ( ESCRT_III ) OR ( ESCRT_I ) MLK1 = ( Cdc42 ) OR ( Rac ) cAMP = ( ( cAMP ) AND NOT ( PDE4 ) ) OR ( ( AC ) AND NOT ( PDE4 ) ) PLD = ( Rho AND ( ( ( Actin ) AND ( ( ( PIP3_345 ) ) OR ( ( PIP2_45 ) ) ) ) AND ( ( NOT ARF ) ) ) ) OR ( PKC AND ( ( ( Actin ) AND ( ( ( PIP3_345 ) ) OR ( ( PIP2_45 ) ) ) ) AND ( ( NOT ARF ) ) ) ) OR ( ARF AND ( ( ( PIP2_45 ) ) OR ( ( PIP3_345 ) ) ) ) OR ( Rac AND ( ( ( NOT ARF ) ) AND ( ( Actin ) AND ( ( ( PIP2_45 ) ) OR ( ( PIP3_345 ) ) ) ) ) ) OR ( Cdc42 AND ( ( ( NOT ARF ) ) AND ( ( Actin ) AND ( ( ( PIP2_45 ) ) OR ( ( PIP3_345 ) ) ) ) ) ) Fak = ( ( Integrins AND ( ( ( Talin ) ) ) ) AND NOT ( PTEN AND ( ( ( Fak ) ) ) ) ) OR ( ( Src AND ( ( ( Fak ) ) ) ) AND NOT ( PTEN AND ( ( ( Fak ) ) ) ) ) Nck = ( EGFR_ErbB3 ) OR ( EGFR_EGFR_TGFa_CCV ) OR ( EGFR_ErbB2 ) OR ( EGFR_EGFR_EGF_End ) OR ( EGFR_ErbB4 ) OR ( Cas ) OR ( EGFR_EGFR_EGF_CCP ) OR ( EGFR_EGFR_EGF_CCV ) OR ( EGFR_EGFR_TGFa_CCP ) OR ( EGFR_EGFR_EGF_MVB ) OR ( EGFR_EGFR ) OR ( EGFR_EGFR_TGFa_End ) OR ( EGFR_EGFR_EGF_PM ) OR ( EGFR_EGFR_TGFa_PM ) ErbB2_Ub = ( Cbl_ErbB2 AND ( ( ( NOT Hsp90 ) ) ) ) OR ( CHIP ) EGFR_Y1101 = ( Src ) EGFR_ErbB3 = ( EGF AND ( ( ( NRG ) ) AND ( ( NOT ErbB2_Free ) ) AND ( ( NOT EGFR_T654 ) ) AND ( ( EGFR_Free ) ) AND ( ( ErbB3_Free ) ) ) ) PTPPEST = ( ( ( Integrins AND ( ( ( ECM ) ) ) ) AND NOT ( PKA ) ) AND NOT ( PKC ) ) Ral = ( CaM ) OR ( AND_34 ) OR ( RalGDS ) Gai = ( Gbg_i AND ( ( ( NOT RGS ) ) AND ( ( Gai ) ) ) ) OR ( alpha_iR AND ( ( ( NOT Gai AND NOT Gbg_i ) ) ) ) OR ( PKA AND ( ( ( NOT Gbg_i ) ) AND ( ( NOT Gai ) ) AND ( ( alpha_sL ) ) AND ( ( NOT alpha_sR ) ) ) ) PAK = ( ( Rac AND ( ( ( Grb2 ) ) OR ( ( Nck ) AND ( ( ( NOT Akt ) ) ) ) ) ) AND NOT ( PKA ) ) OR ( ( ( Src AND ( ( ( PAK ) AND ( ( ( Cdc42 OR Rac ) ) ) ) ) ) AND NOT ( PTP1b ) ) AND NOT ( PKA ) ) OR ( ( Cdc42 AND ( ( ( Grb2 ) ) OR ( ( Nck ) AND ( ( ( NOT Akt ) ) ) ) ) ) AND NOT ( PKA ) ) EGFR_T669 = ( Erk ) ErbB3_Free = ( ErbB3_Contr ) OR ( ( ( ( ErbB3_Free ) AND NOT ( EGFR_ErbB3 ) ) AND NOT ( ErbB2_ErbB3 ) ) AND NOT ( ErbB3_ErbB4 ) ) NIK = ( TAK1 ) OR ( Nck ) MLCK = ( ( ( CaM AND ( ( ( NOT PKA ) ) AND ( ( NOT PAK ) ) ) ) AND NOT ( PAK ) ) AND NOT ( PKA ) ) OR ( ( ( Erk AND ( ( ( NOT PKA ) ) AND ( ( NOT PAK ) ) ) ) AND NOT ( PAK ) ) AND NOT ( PKA ) ) PLC_g = ( AA ) OR ( EGFR_Y1068 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR EGFR_EGFR_EGF_End ) ) ) ) OR ( EGFR_Y992 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR EGFR_EGFR_EGF_End ) ) ) ) OR ( EGFR_Y1173 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR EGFR_EGFR_EGF_End ) ) ) ) Ras = ( RasGRF_GRP ) OR ( SHP2 ) OR ( Sos ) p115RhoGEF = ( Ga_1213 AND ( ( ( PIP3_345 ) ) ) ) Rho = ( Rho AND ( ( ( NOT p190RhoGAP AND NOT Graf AND NOT PKA ) ) ) ) OR ( p115RhoGEF AND ( ( ( NOT Rho AND NOT RhoGDI ) ) AND ( ( p120_catenin ) ) ) ) Integrins = ( Src AND ( ( ( NOT Integrins AND NOT Talin AND NOT ECM AND NOT ILK AND NOT PP2A ) ) ) ) OR ( Talin AND ( ( ( ECM ) ) AND ( ( NOT Integrins AND NOT ILK ) ) ) ) OR ( PP2A AND ( ( ( Talin AND ECM AND ILK ) ) AND ( ( NOT Integrins ) ) ) ) OR ( Integrins AND ( ( ( NOT ILK AND NOT Src ) ) ) ) GRK = ( ( ( Gbg_q AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( Erk ) ) AND NOT ( RKIP ) ) OR ( ( ( Gbg_i AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( Erk ) ) AND NOT ( RKIP ) ) OR ( ( ( B_Arrestin AND ( ( ( Src ) ) ) ) AND NOT ( Erk ) ) AND NOT ( RKIP ) ) OR ( ( ( Gbg_1213 AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( Erk ) ) AND NOT ( RKIP ) ) OR ( ( ( Gbg_s AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( Erk ) ) AND NOT ( RKIP ) ) PIP3_345 = ( ( PI5K AND ( ( ( PIP2_34 ) ) ) ) AND NOT ( PTEN AND ( ( ( PIP3_345 ) ) ) ) ) OR ( ( PI3K AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( PTEN AND ( ( ( PIP3_345 ) ) ) ) ) EGFR_EGFR_TGFa_PM = ( ( ( EGFR_Free AND ( ( ( NOT EGFR_T654 ) ) AND ( ( TGFa ) ) ) ) AND NOT ( ErbB2_Free ) ) AND NOT ( EGFR_EGFR_TGFa_CCP ) ) OR ( ( EGFR_EGFR_TGFa_PM ) AND NOT ( EGFR_EGFR_TGFa_CCP ) ) MKK7 = ( Mekk4 AND ( ( ( ASK1 ) ) ) ) OR ( MLK1 AND ( ( ( ASK1 ) ) ) ) OR ( MLK2 AND ( ( ( ASK1 ) ) ) ) OR ( MLK3 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk1 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk2 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk3 AND ( ( ( ASK1 ) ) ) ) ErbB2_Y1248 = ( EGFR_ErbB2 ) OR ( ErbB2_ErbB3 ) OR ( ErbB2_ErbB4 ) WASP = ( ( Src AND ( ( ( PIP2_45 OR Nck OR Grb2 ) ) AND ( ( Cdc42 AND Crk ) ) ) ) AND NOT ( PTPPEST ) ) OR ( ( Fak AND ( ( ( Cdc42 AND Crk ) ) AND ( ( PIP2_45 OR Nck OR Grb2 ) ) ) ) AND NOT ( PTPPEST ) ) OR ( ( Cdc42 AND ( ( ( Src OR Fak ) ) AND ( ( NOT PTPPEST AND NOT Crk ) ) AND ( ( PIP2_45 OR Nck OR Grb2 ) ) ) ) AND NOT ( PTPPEST ) ) PTPa = ( PKC ) IQGAP1 = ( NOT ( ( CaM AND ( ( ( Ca ) ) ) ) ) ) OR NOT ( Ca OR CaM ) Eps15 = ( EGFR_Ub ) OR ( EGFR_EGFR_EGF_PM ) OR ( EGFR_EGFR_TGFa_PM ) ErbB2_Y1196 = ( EGFR_ErbB2 ) OR ( ErbB2_ErbB3 ) OR ( ErbB2_ErbB4 ) IP3R1 = ( ( ( ( Gbg_i ) AND NOT ( Ca AND ( ( ( IP3R1 ) ) AND ( ( NOT IP3 ) ) ) ) ) AND NOT ( CaM AND ( ( ( Ca ) ) AND ( ( IP3R1 ) ) ) ) ) AND NOT ( IP3R1 AND ( ( ( NOT Ca AND NOT IP3 AND NOT PKA AND NOT PP2A ) ) AND ( ( CaM AND Gbg_i ) ) ) ) ) OR ( ( ( IP3 AND ( ( ( Ca ) ) ) ) AND NOT ( Ca AND ( ( ( IP3R1 ) ) AND ( ( NOT IP3 ) ) ) ) ) AND NOT ( CaM AND ( ( ( Ca ) ) AND ( ( IP3R1 ) ) ) ) ) OR ( ( ( ( PKA ) AND NOT ( Ca AND ( ( ( IP3R1 ) ) AND ( ( NOT IP3 ) ) ) ) ) AND NOT ( PP2A AND ( ( ( IP3R1 ) ) ) ) ) AND NOT ( CaM AND ( ( ( Ca ) ) AND ( ( IP3R1 ) ) ) ) ) GCK = ( Trafs ) TAK1 = ( Tab_12 ) EGFR_EGFR_TGFa_CCV = ( ( EGFR_EGFR_TGFa_CCV ) AND NOT ( EGFR_EGFR_TGFa_End ) ) OR ( EGFR_EGFR_TGFa_CCP AND ( ( ( GAK OR Clathrin ) ) AND ( ( Dynamin AND Actin ) ) AND ( ( PIP2_45 AND AP2 ) ) ) ) EGFR_EGFR_EGF_CCV = ( ( EGFR_EGFR_EGF_CCV ) AND NOT ( EGFR_EGFR_EGF_End ) ) OR ( ( EGFR_EGFR_EGF_CCP AND ( ( ( Dynamin AND Actin ) ) ) ) AND NOT ( EGFR_EGFR_EGF_End ) ) Rab5 = ( ( p120RasGAP ) AND NOT ( Rab7 AND ( ( ( Rab5 ) ) ) ) ) OR ( ( Rab5 ) AND NOT ( Rab7 AND ( ( ( Rab5 ) ) ) ) ) OR ( ( Rabex_5 ) AND NOT ( Rab7 AND ( ( ( Rab5 ) ) ) ) ) OR ( ( EGFR_EGFR_EGF_PM ) AND NOT ( Rab7 AND ( ( ( Rab5 ) ) ) ) ) OR ( ( RIN ) AND NOT ( Rab7 AND ( ( ( Rab5 ) ) ) ) ) OR ( ( EGFR_EGFR_TGFa_PM ) AND NOT ( Rab7 AND ( ( ( Rab5 ) ) ) ) ) CHIP = ( AG AND ( ( ( Hsp90 ) ) ) ) DOCK180 = ( Crk AND ( ( ( Cas ) ) AND ( ( PIP3_345 ) ) ) ) RhoGDI = ( NOT ( ( AA ) OR ( PKC ) OR ( PIP2_45 ) ) ) OR NOT ( AA OR PIP2_45 OR PKC ) Raf_DeP = ( PP2A AND ( ( ( Raf_Rest ) ) AND ( ( NOT Raf_DeP ) ) ) ) OR ( Raf_DeP AND ( ( ( NOT Raf_Loc ) ) ) ) Clathrin = ( GAK ) OR ( Hip1R ) OR ( CALM AND ( ( ( PIP2_45 ) ) ) ) OR ( AP2 ) OR ( Epsin AND ( ( ( PIP2_45 ) ) ) ) OR ( Src ) OR ( ESCRT_0 ) Graf = ( Fak AND ( ( ( Src ) ) ) ) ErbB2_ErbB4 = ( NRG AND ( ( ( ErbB4_Free AND ErbB2_Free ) AND ( ( ( NOT ErbB3_Free ) ) ) ) ) ) Crk = ( ( Cas AND ( ( ( Src OR Fak ) ) ) ) AND NOT ( PTPPEST ) ) Trx = ( Stress ) OR ( Trafs ) Sek1 = ( Mekk4 AND ( ( ( ASK1 ) ) ) ) OR ( MLK1 AND ( ( ( ASK1 ) ) ) ) OR ( MLK2 AND ( ( ( ASK1 ) ) ) ) OR ( MLK3 AND ( ( ( ASK1 ) ) ) ) OR ( TAK1 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk1 AND ( ( ( ASK1 ) ) ) ) OR ( Tpl2 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk2 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk3 AND ( ( ( ASK1 ) ) ) ) Palpha_1213R = ( alpha_1213R AND ( ( ( GRK ) ) ) ) PDK1 = ( p90RSK ) OR ( Src ) PI4K = ( Rho ) OR ( PKC ) OR ( ARF ) OR ( Gai ) OR ( Gaq ) EGFR_Y891 = ( Src ) MLK3 = ( IL1_TNFR ) OR ( Rac ) OR ( Cdc42 ) PKA = ( ( PKA AND ( ( ( cAMP ) ) ) ) AND NOT ( PP2A AND ( ( ( PKA ) ) ) ) ) OR ( ( PDK1 AND ( ( ( cAMP ) ) ) ) AND NOT ( PP2A AND ( ( ( PKA ) ) ) ) ) Rab7 = ( Rab5 ) Rac = ( ( RasGRF_GRP AND ( ( ( Integrins AND ECM ) ) ) ) AND NOT ( RalBP1 AND ( ( ( Rac ) ) ) ) ) OR ( ( Rac AND ( ( ( NOT RalBP1 ) ) ) ) AND NOT ( RalBP1 AND ( ( ( Rac ) ) ) ) ) OR ( Pix_Cool AND ( ( ( NOT PAK ) AND ( ( ( Cdc42 ) ) AND ( ( Integrins AND ECM ) ) AND ( ( NOT Tiam AND NOT Rac AND NOT RasGRF_GRP AND NOT DOCK180 ) ) ) ) OR ( ( PAK AND Gbg_i ) AND ( ( ( Integrins AND ECM ) ) AND ( ( NOT Rac ) ) ) ) OR ( ( NOT Gbg_i ) AND ( ( ( Cdc42 ) ) AND ( ( NOT Rac ) ) AND ( ( Integrins AND ECM ) ) ) ) ) ) OR ( ( Tiam AND ( ( ( Integrins AND ECM ) ) ) ) AND NOT ( RalBP1 AND ( ( ( Rac ) ) ) ) ) OR ( ( DOCK180 AND ( ( ( Integrins AND ECM ) ) ) ) AND NOT ( RalBP1 AND ( ( ( Rac ) ) ) ) ) ESCRT_0 = ( EGFR_EGFR_EGF_End AND ( ( ( PIP3_345 ) ) ) ) Gbg_i = ( Gai ) OR ( alpha_iR AND ( ( ( NOT Gbg_i ) ) AND ( ( NOT Gai ) ) ) ) CaMK = ( CaMKK AND ( ( ( CaM ) ) ) ) ErbB4_Y1188 = ( ErbB4_ErbB4 ) OR ( ErbB3_ErbB4 ) OR ( ErbB2_ErbB4 ) OR ( EGFR_ErbB4 ) Raf_Loc = ( Raf_Loc AND ( ( ( NOT Raf ) ) ) ) OR ( Ras AND ( ( ( NOT Raf_Loc ) ) AND ( ( Raf_DeP ) ) ) ) Gbg_q = ( alpha_qR AND ( ( ( NOT Gbg_q ) ) AND ( ( NOT Gaq ) ) ) ) OR ( Gaq ) Shc = ( ( EGFR_Y992 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR ErbB3_ErbB4 OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR ErbB2_ErbB4 OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( PTEN ) ) OR ( ( Fak ) AND NOT ( PTEN ) ) OR ( ( EGFR_Y1173 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR ErbB3_ErbB4 OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR ErbB2_ErbB4 OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( PTEN ) ) OR ( ( ErbB2_Y1196 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR ErbB3_ErbB4 OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR ErbB2_ErbB4 OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( PTEN ) ) OR ( ( Src ) AND NOT ( PTEN ) ) OR ( ( ErbB4_Y1242 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR ErbB3_ErbB4 OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR ErbB2_ErbB4 OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( PTEN ) ) OR ( ( ErbB4_Y1188 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR ErbB3_ErbB4 OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR ErbB2_ErbB4 OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( PTEN ) ) OR ( ( ErbB2_Y1221_22 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR ErbB3_ErbB4 OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR ErbB2_ErbB4 OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( PTEN ) ) OR ( ( ErbB3_Y1309 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR ErbB3_ErbB4 OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR ErbB2_ErbB4 OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( PTEN ) ) OR ( ( ErbB2_Y1248 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR ErbB3_ErbB4 OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR ErbB2_ErbB4 OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( PTEN ) ) OR ( ( EGFR_Y1148 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR ErbB3_ErbB4 OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR ErbB2_ErbB4 OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( PTEN ) ) DGK = ( EGFR_ErbB3 ) OR ( EGFR_ErbB2 ) OR ( EGFR_EGFR_TGFa_CCV ) OR ( EGFR_EGFR_EGF_End ) OR ( EGFR_ErbB4 ) OR ( Src AND ( ( ( Ca AND PA ) ) ) ) OR ( EGFR_EGFR_EGF_CCP ) OR ( EGFR_EGFR_EGF_CCV ) OR ( PKC AND ( ( ( DAG ) ) ) ) OR ( EGFR_EGFR_TGFa_CCP ) OR ( EGFR_EGFR_EGF_MVB ) OR ( EGFR_EGFR ) OR ( EGFR_EGFR_TGFa_End ) OR ( EGFR_EGFR_EGF_PM ) OR ( EGFR_EGFR_TGFa_PM ) AND_34 = ( Cas ) Rabaptin_5 = ( Rab5 ) RalBP1 = ( Ral ) Cbl_ErbB2 = ( Trastuzumab AND ( ( ( ErbB2_ErbB4 ) ) OR ( ( ErbB2_ErbB3 ) ) OR ( ( EGFR_ErbB2 ) ) ) ) Actin = ( Arp_23 AND ( ( ( alpha_catenin ) ) AND ( ( NOT IQGAP1 ) ) AND ( ( Myosin ) ) ) ) OR ( IQGAP1 AND ( ( ( Myosin ) ) ) ) MKPs = ( p38 AND ( ( ( cAMP ) ) ) ) OR ( Erk AND ( ( ( cAMP ) ) ) ) OR ( SAPK AND ( ( ( cAMP ) ) ) ) Fer = ( E_cadherin AND ( ( ( p120_catenin ) ) ) ) Rap1 = ( CaMK AND ( ( ( NOT Gai OR NOT Rap1 ) ) AND ( ( cAMP AND Src ) ) ) ) OR ( PKA AND ( ( ( NOT Gai OR NOT Rap1 ) ) AND ( ( cAMP AND Src ) ) ) ) RasGRF_GRP = ( CaM AND ( ( ( Cdc42 ) ) ) ) OR ( DAG AND ( ( ( Cdc42 ) ) ) ) ErbB2_Y1139 = ( EGFR_ErbB2 ) OR ( ErbB2_ErbB3 ) OR ( ErbB2_ErbB4 ) IP3 = ( PLC_B AND ( ( ( PIP2_45 ) ) ) ) OR ( PLC_g AND ( ( ( PIP2_45 ) ) ) ) Dynamin = ( Grb2 ) OR ( Endophilin ) OR ( EGFR_EGFR_EGF_PM ) OR ( PIP2_45 ) OR ( EGFR_EGFR_TGFa_PM ) Akt = ( CaMKK AND ( ( ( PIP3_345 OR PIP2_34 ) ) AND ( ( ILK AND Src ) ) AND ( ( NOT Akt ) ) ) ) OR ( Akt AND ( ( ( NOT PP2A ) ) ) ) OR ( PDK1 AND ( ( ( ILK AND Src ) ) AND ( ( NOT Akt ) ) AND ( ( PIP3_345 OR PIP2_34 ) ) ) ) Tpl2 = ( Trafs ) E_cadherin = ( ( ( B_catenin AND ( ( ( ExtE_cadherin ) ) ) ) AND NOT ( IQGAP1 AND ( ( ( NOT Cdc42 AND NOT Rac ) ) ) ) ) AND NOT ( Hakai AND ( ( ( NOT p120_catenin ) ) ) ) ) p38 = ( ( ( MKK6 ) AND NOT ( PP2A ) ) AND NOT ( MKPs ) ) OR ( ( ( MKK3 ) AND NOT ( PP2A ) ) AND NOT ( MKPs ) ) OR ( ( ( Sek1 ) AND NOT ( PP2A ) ) AND NOT ( MKPs ) ) Raf_Rest = ( ( Raf_Rest AND ( ( ( NOT Raf_DeP ) ) ) ) OR ( Raf_DeP AND ( ( ( NOT Raf_Rest AND NOT Raf ) ) ) ) ) OR NOT ( Raf_DeP OR Raf_Rest OR Raf ) EGFR_Ub = ( ( ( EGFR_EGFR_EGF_PM AND ( ( ( Cbl_RTK ) ) ) ) AND NOT ( EGFR_EGFR_EGF_CCP ) ) AND NOT ( EGFR_EGFR_TGFa_CCP ) ) OR ( ( ( EGFR_EGFR_TGFa_PM AND ( ( ( Cbl_RTK ) ) ) ) AND NOT ( EGFR_EGFR_EGF_CCP ) ) AND NOT ( EGFR_EGFR_TGFa_CCP ) ) Cbp = ( ( Src ) AND NOT ( SHP2 ) ) MKK6 = ( Mekk4 AND ( ( ( ASK1 ) ) ) ) OR ( MLK3 AND ( ( ( ASK1 ) ) ) ) OR ( PAK AND ( ( ( ASK1 ) ) ) ) OR ( TAK1 AND ( ( ( ASK1 ) ) ) ) OR ( Tpl2 AND ( ( ( ASK1 ) ) ) ) OR ( TAO_12 AND ( ( ( ASK1 ) ) ) ) Rabex_5 = ( Rabaptin_5 ) TAO_12 = ( Stress ) alpha_qR = ( ( alpha_qL ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_iR AND NOT alpha_qL AND NOT alpha_qR ) ) OR ( ( Palpha_iR ) ) ) ) ) OR ( ( Palpha_iR AND ( ( ( NOT B_Arrestin ) ) ) ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_iR AND NOT alpha_qL AND NOT alpha_qR ) ) OR ( ( Palpha_iR ) ) ) ) ) OR ( ( alpha_qR ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_iR AND NOT alpha_qL AND NOT alpha_qR ) ) OR ( ( Palpha_iR ) ) ) ) ) p120_catenin = ( EGFR_ErbB3 ) OR ( EGFR_EGFR_TGFa_CCV ) OR ( EGFR_ErbB2 ) OR ( EGFR_EGFR_EGF_End ) OR ( EGFR_ErbB4 ) OR ( Src ) OR ( EGFR_EGFR_EGF_CCP ) OR ( ( Rho ) AND NOT ( Fer ) ) OR ( EGFR_EGFR_EGF_CCV ) OR ( EGFR_EGFR_TGFa_CCP ) OR ( EGFR_EGFR_EGF_MVB ) OR ( EGFR_EGFR ) OR ( EGFR_EGFR_TGFa_End ) OR ( EGFR_EGFR_EGF_PM ) OR ( EGFR_EGFR_TGFa_PM ) Arp_23 = ( WASP ) Cas = ( ( Src AND ( ( ( Fak ) ) ) ) AND NOT ( PTPPEST AND ( ( ( Cas ) ) ) ) ) p190RhoGAP = ( Src AND ( ( ( NOT p190RhoGAP ) ) OR ( ( NOT p120RasGAP ) ) OR ( ( Fak ) ) ) ) OR ( Fak AND ( ( ( Src ) ) ) ) Csk = ( Cbp AND ( ( ( Gbg_1213 OR PKA OR Gbg_q OR Gbg_i ) ) OR ( ( NOT SHP2 AND NOT Gbg_1213 AND NOT PKA AND NOT Gbg_q AND NOT Gbg_i ) ) ) ) OR ( ( Fak AND ( ( ( Cbp AND Src ) ) ) ) AND NOT ( SHP2 ) ) ESCRT_II = ( ESCRT_I ) CIN85 = ( Cbl_RTK ) Raf = ( Ras AND ( ( ( Raf ) ) ) ) OR ( Src AND ( ( ( NOT Raf ) ) AND ( ( PAK AND Raf_Loc AND RKIP ) ) ) ) OR ( Raf AND ( ( ( NOT Akt AND NOT PKA AND NOT Erk ) ) ) ) OR ( PAK AND ( ( ( Raf ) ) AND ( ( NOT Ras AND NOT Akt AND NOT Erk ) ) ) ) ErbB2_Y1023 = ( EGFR_ErbB2 ) OR ( ErbB2_ErbB3 ) OR ( ErbB2_ErbB4 ) Palpha_iR = ( alpha_iR AND ( ( ( GRK ) ) ) ) IL1_TNFR = ( IL1_TNF ) alpha_1213R = ( ( alpha_1213L ) AND NOT ( B_Arrestin AND ( ( ( NOT alpha_1213R AND NOT alpha_1213L AND NOT Palpha_1213R ) ) OR ( ( Palpha_1213R ) ) ) ) ) OR ( ( Palpha_1213R AND ( ( ( NOT B_Arrestin ) ) ) ) AND NOT ( B_Arrestin AND ( ( ( NOT alpha_1213R AND NOT alpha_1213L AND NOT Palpha_1213R ) ) OR ( ( Palpha_1213R ) ) ) ) ) OR ( ( alpha_1213R ) AND NOT ( B_Arrestin AND ( ( ( NOT alpha_1213R AND NOT alpha_1213L AND NOT Palpha_1213R ) ) OR ( ( Palpha_1213R ) ) ) ) ) MKK3 = ( Mekk4 AND ( ( ( ASK1 ) ) ) ) OR ( MLK1 AND ( ( ( ASK1 ) ) ) ) OR ( MLK2 AND ( ( ( ASK1 ) ) ) ) OR ( MLK3 AND ( ( ( ASK1 ) ) ) ) OR ( TAK1 AND ( ( ( ASK1 ) ) ) ) OR ( Tpl2 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk2 AND ( ( ( ASK1 ) ) ) ) OR ( Mekk3 AND ( ( ( ASK1 ) ) ) ) OR ( PAK AND ( ( ( ASK1 ) ) ) ) OR ( TAO_12 AND ( ( ( ASK1 ) ) ) ) PTP1b = ( NOT ( ( EGFR_ErbB3 ) OR ( EGFR_ErbB2 ) OR ( EGFR_EGFR_TGFa_CCV ) OR ( EGFR_EGFR_EGF_End ) OR ( EGFR_ErbB4 ) OR ( EGFR_EGFR_EGF_CCP ) OR ( EGFR_EGFR_EGF_CCV ) OR ( EGFR_EGFR_TGFa_CCP ) OR ( EGFR_EGFR_EGF_MVB ) OR ( EGFR_EGFR ) OR ( EGFR_EGFR_EGF_PM ) OR ( Stress ) OR ( EGFR_EGFR_TGFa_PM ) ) ) OR NOT ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR Stress OR EGFR_ErbB4 OR EGFR_EGFR OR EGFR_EGFR_EGF_End ) AMSH = ( Alix ) OR ( ESCRT_0 ) OR ( ESCRT_I ) Trafs = ( IL1_TNFR ) AC = ( Integrins AND ( ( ( ECM ) AND ( ( ( Gas ) ) AND ( ( Gbg_i ) ) ) ) ) ) EGFR_EGFR_EGF_CCP = ( ( Eps15 AND ( ( ( EGFR_EGFR_EGF_PM ) ) AND ( ( Rab5 ) ) AND ( ( PIP2_45 ) ) AND ( ( Cbl_RTK ) ) AND ( ( Clathrin ) ) ) ) AND NOT ( EGFR_EGFR_EGF_CCV ) ) OR ( ( Epsin AND ( ( ( Cbl_RTK ) ) AND ( ( EGFR_EGFR_EGF_PM ) ) AND ( ( Rab5 ) ) AND ( ( PIP2_45 ) ) AND ( ( Clathrin ) ) ) ) AND NOT ( EGFR_EGFR_EGF_CCV ) ) OR ( ( AP2 AND ( ( ( Rab5 ) ) AND ( ( Clathrin ) ) AND ( ( EGFR_EGFR_EGF_PM ) ) AND ( ( Cbl_RTK ) ) AND ( ( PIP2_45 ) ) ) ) AND NOT ( EGFR_EGFR_EGF_CCV ) ) OR ( ( EGFR_EGFR_EGF_CCP ) AND NOT ( EGFR_EGFR_EGF_CCV ) ) EGFR_Y1086 = ( EGFR_ErbB3 ) OR ( EGFR_ErbB2 ) OR ( EGFR_ErbB4 ) OR ( EGFR_EGFR ) OR ( EGFR_EGFR_EGF_PM ) OR ( EGFR_EGFR_TGFa_PM ) EGFR_EGFR = ( alpha_qR AND ( ( ( EGFR_Free ) ) AND ( ( Ca ) ) AND ( ( EGFR_T654 ) ) ) ) OR ( alpha_iR AND ( ( ( Ca ) ) AND ( ( EGFR_Free ) ) AND ( ( EGFR_T654 ) ) ) ) OR ( alpha_1213R AND ( ( ( Ca ) ) AND ( ( EGFR_Free ) ) AND ( ( EGFR_T654 ) ) ) ) Gab1 = ( ( Gab1 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR EGFR_EGFR_EGF_End ) ) AND ( ( PIP3_345 ) ) ) ) AND NOT ( SHP2 ) ) OR ( ( Grb2 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR EGFR_EGFR_EGF_End ) ) AND ( ( NOT Gab1 ) ) ) ) AND NOT ( SHP2 ) ) Palpha_sR = ( alpha_sR AND ( ( ( GRK ) ) ) ) EEA1 = ( Rab5 AND ( ( ( PIP3_345 ) ) ) ) CALM = ( PIP2_45 ) PTEN = ( ( Stress ) AND NOT ( PTEN_I ) ) OR ( ( Pix_Cool AND ( ( ( Rho ) ) AND ( ( Cdc42 ) ) AND ( ( PI3K ) ) ) ) AND NOT ( PTEN_I ) ) B_Arrestin = ( Palpha_iR ) OR ( Palpha_qR ) OR ( Palpha_1213R ) OR ( Palpha_sR ) ErbB4_Y1056 = ( ErbB4_ErbB4 ) OR ( ErbB3_ErbB4 ) OR ( EGFR_ErbB4 ) OR ( ErbB2_ErbB4 ) SHP2 = ( Gab1 ) ErbB3_Y1257 = ( EGFR_ErbB3 ) OR ( ErbB3_ErbB4 ) OR ( ErbB2_ErbB3 ) Palpha_qR = ( alpha_qR AND ( ( ( GRK ) ) ) ) ErbB4_ErbB4 = ( ( NRG AND ( ( ( ErbB4_Free ) ) ) ) AND NOT ( ErbB2_Free ) ) EGFR_Y1045 = ( EGFR_ErbB3 ) OR ( EGFR_ErbB2 ) OR ( EGFR_ErbB4 ) OR ( EGFR_EGFR ) OR ( EGFR_EGFR_EGF_PM ) OR ( EGFR_EGFR_TGFa_PM ) EGFR_Y845 = ( EGFR_Free AND ( ( ( Cas AND Integrins AND Src ) ) ) ) OR ( Src AND ( ( ( EGFR_EGFR_EGF_PM ) ) ) ) Gbg_s = ( Gas ) OR ( alpha_sR AND ( ( ( NOT Gbg_s ) ) AND ( ( NOT Gas ) ) ) ) ErbB3_Y1243 = ( EGFR_ErbB3 ) OR ( ErbB3_ErbB4 ) OR ( ErbB2_ErbB3 ) EGFR_Y1068 = ( EGFR_ErbB3 ) OR ( EGFR_ErbB2 ) OR ( EGFR_ErbB4 ) OR ( EGFR_EGFR ) OR ( EGFR_EGFR_EGF_PM ) OR ( EGFR_EGFR_TGFa_PM ) ESCRT_III = ( ESCRT_II ) OR ( ESCRT_I ) AA = ( PLA2 ) PLA2 = ( PIP3_345 AND ( ( ( PIP2_45 ) ) AND ( ( CaMK ) ) ) ) OR ( PIP2_45 AND ( ( ( Erk ) ) AND ( ( PIP3_345 ) ) ) ) OR ( Erk AND ( ( ( Ca ) ) ) ) OR ( CaMK AND ( ( ( Ca ) ) ) ) EGFR_EGFR_EGF_SR = ( EGFR_EGFR_EGF_MVB AND ( ( ( AMSH ) ) ) ) Cbl_FA = ( ( Src AND ( ( ( Pix_Cool ) ) AND ( ( Cdc42 ) ) ) ) AND NOT ( Cbl_RTK ) ) EGFR_Free = ( ( EGFR_EGFR_TGFa_End ) AND NOT ( EGFR_Free AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_PM OR EGFR_ErbB3 OR EGFR_EGFR OR EGFR_EGFR_EGF_PM ) ) ) ) ) OR ( ( EGFR_Free ) AND NOT ( EGFR_Free AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_PM OR EGFR_ErbB3 OR EGFR_EGFR OR EGFR_EGFR_EGF_PM ) ) ) ) ) OR ( ( EGFR_Contr ) AND NOT ( EGFR_Free AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_PM OR EGFR_ErbB3 OR EGFR_EGFR OR EGFR_EGFR_EGF_PM ) ) ) ) ) alpha_iR = ( ( alpha_iL ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_iR AND NOT alpha_iL AND NOT alpha_iR ) ) OR ( ( Palpha_iR ) ) ) ) ) OR ( ( Palpha_iR AND ( ( ( NOT B_Arrestin ) ) ) ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_iR AND NOT alpha_iL AND NOT alpha_iR ) ) OR ( ( Palpha_iR ) ) ) ) ) OR ( ( alpha_iR ) AND NOT ( B_Arrestin AND ( ( ( NOT Palpha_iR AND NOT alpha_iL AND NOT alpha_iR ) ) OR ( ( Palpha_iR ) ) ) ) ) Vinc = ( Actin AND ( ( ( Talin AND Vinc ) ) AND ( ( NOT PIP2_45 ) ) ) ) OR ( Talin AND ( ( ( Src ) ) ) ) Ca = ( ( IP3R1 ) AND NOT ( ExtPump ) ) ErbB3_Y1203_05 = ( EGFR_ErbB3 ) OR ( ErbB3_ErbB4 ) OR ( ErbB2_ErbB3 ) Erk = ( Mek ) OR ( ( ( Erk ) AND NOT ( MKPs ) ) AND NOT ( PP2A ) ) PP2A = ( ( ( EGFR_ErbB3 ) AND NOT ( PP2A ) ) OR ( ( EGFR_ErbB2 ) AND NOT ( PP2A ) ) OR ( ( EGFR_EGFR_TGFa_CCV ) AND NOT ( PP2A ) ) OR ( ( EGFR_EGFR_EGF_End ) AND NOT ( PP2A ) ) OR ( ( EGFR_ErbB4 ) AND NOT ( PP2A ) ) OR ( ( EGFR_EGFR_EGF_CCP ) AND NOT ( PP2A ) ) OR ( ( EGFR_EGFR_EGF_CCV ) AND NOT ( PP2A ) ) OR ( PP2A AND ( ( ( NOT EGFR_ErbB2 AND NOT EGFR_EGFR_TGFa_CCV AND NOT EGFR_EGFR_TGFa_PM AND NOT EGFR_EGFR_EGF_CCV AND NOT EGFR_ErbB3 AND NOT EGFR_EGFR_TGFa_End AND NOT EGFR_EGFR_EGF_PM AND NOT EGFR_EGFR_EGF_MVB AND NOT EGFR_EGFR_TGFa_CCP AND NOT EGFR_EGFR_EGF_CCP AND NOT EGFR_ErbB4 AND NOT EGFR_EGFR AND NOT EGFR_EGFR_EGF_End ) ) ) ) OR ( ( EGFR_EGFR_TGFa_CCP ) AND NOT ( PP2A ) ) OR ( ( EGFR_EGFR_EGF_MVB ) AND NOT ( PP2A ) ) OR ( ( EGFR_EGFR ) AND NOT ( PP2A ) ) OR ( ( EGFR_EGFR_EGF_PM ) AND NOT ( PP2A ) ) OR ( ( EGFR_EGFR_TGFa_End ) AND NOT ( PP2A ) ) OR ( ( EGFR_EGFR_TGFa_PM ) AND NOT ( PP2A ) ) ) OR NOT ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_TGFa_End OR PP2A OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_EGFR OR EGFR_EGFR_EGF_End ) ErbB2_Free = ( ( ErbB2_Contr ) AND NOT ( Trastuzumab ) ) OR ( ( ( ( ( ErbB2_Free ) AND NOT ( Trastuzumab ) ) AND NOT ( EGFR_ErbB2 ) ) AND NOT ( ErbB2_ErbB3 ) ) AND NOT ( ErbB2_ErbB4 ) ) PI5K = ( PA ) OR ( PI5K AND ( ( ( Talin ) ) ) ) OR ( RhoK ) OR ( ARF ) OR ( Src AND ( ( ( NOT Talin ) ) AND ( ( NOT PI5K ) ) AND ( ( Fak ) ) ) ) PIP_4 = ( ( ( PTEN AND ( ( ( NOT PIP_4 ) ) AND ( ( PIP2_34 ) ) ) ) AND NOT ( PI5K AND ( ( ( PIP_4 ) ) ) ) ) AND NOT ( PI3K AND ( ( ( PIP_4 ) ) ) ) ) OR ( ( ( PIP_4 AND ( ( ( NOT PI5K ) ) AND ( ( NOT PI3K ) ) ) ) AND NOT ( PI5K AND ( ( ( PIP_4 ) ) ) ) ) AND NOT ( PI3K AND ( ( ( PIP_4 ) ) ) ) ) OR ( ( ( PI4K AND ( ( ( NOT PIP_4 ) ) ) ) AND NOT ( PI5K AND ( ( ( PIP_4 ) ) ) ) ) AND NOT ( PI3K AND ( ( ( PIP_4 ) ) ) ) ) PKC_primed = ( PKC_primed AND ( ( ( NOT PKC ) ) ) ) OR ( PKC AND ( ( ( NOT PKC_primed ) ) AND ( ( PDK1 ) ) ) ) OR ( PDK1 AND ( ( ( NOT PKC ) ) ) ) ErbB2_Lysosome = ( ErbB2_ErbB3 AND ( ( ( ErbB2Deg_Contr ) ) ) ) OR ( ErbB2_Ub AND ( ( ( NOT ErbB2Deg_Contr ) ) ) ) ErbB3_Y1309 = ( EGFR_ErbB3 ) OR ( ErbB3_ErbB4 ) OR ( ErbB2_ErbB3 ) CaM = ( Ca ) Pix_Cool = ( PIP3_345 AND ( ( ( B_Parvin ) ) ) ) OR ( PIP2_34 AND ( ( ( B_Parvin ) ) ) ) PLC_B = ( ( Gbg_i AND ( ( ( PLC_B ) ) ) ) AND NOT ( PKA AND ( ( ( NOT Gaq ) ) ) ) ) OR ( Gaq ) Alix = ( ESCRT_III ) OR ( ESCRT_I ) Gas = ( Gbg_s AND ( ( ( Gas ) ) AND ( ( NOT RGS ) ) ) ) OR ( alpha_sR AND ( ( ( NOT Gas ) ) AND ( ( NOT Gbg_s ) ) AND ( ( NOT PKA ) ) ) ) Hsc70 = ( GAK ) OR ( Dynamin ) Tab_12 = ( ( Trafs ) AND NOT ( p38 ) ) Mek = ( ( PAK AND ( ( ( Tpl2 ) ) ) ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) OR ( ( Mekk1 AND ( ( ( Raf ) ) ) ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) OR ( ( Tpl2 ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) OR ( ( Mekk2 AND ( ( ( Raf ) ) ) ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) OR ( ( Raf AND ( ( ( Tpl2 ) ) ) ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) OR ( ( Mekk3 AND ( ( ( Raf ) ) ) ) AND NOT ( PP2A AND ( ( ( Mek ) ) ) ) ) alpha_sR = ( ( alpha_sR ) AND NOT ( B_Arrestin AND ( ( ( Palpha_sR ) ) OR ( ( NOT alpha_sR AND NOT Palpha_sR AND NOT alpha_sL ) ) ) ) ) OR ( ( alpha_sL ) AND NOT ( B_Arrestin AND ( ( ( Palpha_sR ) ) OR ( ( NOT alpha_sR AND NOT Palpha_sR AND NOT alpha_sL ) ) ) ) ) OR ( ( Palpha_sR AND ( ( ( NOT B_Arrestin ) ) ) ) AND NOT ( B_Arrestin AND ( ( ( Palpha_sR ) ) OR ( ( NOT alpha_sR AND NOT Palpha_sR AND NOT alpha_sL ) ) ) ) ) RalGDS = ( ( ( alpha_sR AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( PKC ) ) AND NOT ( Ras AND ( ( ( PIP3_345 ) ) AND ( ( PDK1 ) ) ) ) ) OR ( ( ( alpha_iR AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( PKC ) ) AND NOT ( Ras AND ( ( ( PIP3_345 ) ) AND ( ( PDK1 ) ) ) ) ) OR ( ( ( alpha_qR AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( PKC ) ) AND NOT ( Ras AND ( ( ( PIP3_345 ) ) AND ( ( PDK1 ) ) ) ) ) OR ( ( ( alpha_1213R AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( PKC ) ) AND NOT ( Ras AND ( ( ( PIP3_345 ) ) AND ( ( PDK1 ) ) ) ) ) MLCP = ( ( ( ( ( ( PKA AND ( ( ( RhoK ) ) ) ) AND NOT ( ILK ) ) AND NOT ( PAK ) ) AND NOT ( Raf ) ) AND NOT ( PKC ) ) ) OR NOT ( PAK OR ILK OR PKC OR PKA OR RhoK OR Raf ) ErbB3_Y1270 = ( EGFR_ErbB3 ) OR ( ErbB2_ErbB3 ) OR ( ErbB3_ErbB4 ) EGFR_T654 = ( PKC ) Mekk3 = ( ( Trafs ) AND NOT ( Gab1 ) ) OR ( ( IL1_TNFR ) AND NOT ( Gab1 ) ) OR ( ( Rac ) AND NOT ( Gab1 ) ) Rabenosyn_5 = ( Rab5 AND ( ( ( PIP3_345 ) ) ) ) MLK2 = ( Rac AND ( ( ( SAPK ) ) ) ) OR ( Cdc42 AND ( ( ( SAPK ) ) ) ) Mekk1 = ( Rho AND ( ( ( Grb2 ) ) OR ( ( Shc ) ) ) ) OR ( NIK AND ( ( ( Shc ) ) OR ( ( Grb2 ) ) ) ) OR ( Grb2 AND ( ( ( Shc ) ) ) ) OR ( Ras ) OR ( Trafs ) OR ( Rac ) OR ( GCK ) OR ( Cdc42 ) RIN = ( Ras ) EGFR_Y920 = ( Src AND ( ( ( EGFR_EGFR_EGF_PM ) ) ) ) ErbB3_Y1241 = ( EGFR_ErbB3 ) OR ( ErbB2_ErbB3 ) OR ( ErbB3_ErbB4 ) ARNO = ( PIP2_45 ) Myosin = ( ( ILK AND ( ( ( NOT MLCP ) ) OR ( ( NOT Myosin ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) OR ( ( PAK AND ( ( ( NOT Myosin ) ) OR ( ( NOT MLCP ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) OR ( ( MLCK AND ( ( ( CaM ) ) AND ( ( NOT MLCP ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) OR ( ( RhoK AND ( ( ( NOT MLCP ) ) OR ( ( NOT Myosin ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) OR ( ( CaM AND ( ( ( MLCK ) ) AND ( ( NOT Myosin ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) OR ( ( Myosin AND ( ( ( NOT MLCP ) ) ) ) AND NOT ( MLCP AND ( ( ( Myosin ) ) ) ) ) ErbB4_Free = ( ( ( ( ( ErbB4_Free ) AND NOT ( ErbB2_ErbB4 ) ) AND NOT ( ErbB4_ErbB4 ) ) AND NOT ( ErbB3_ErbB4 ) ) AND NOT ( EGFR_ErbB4 ) ) OR ( ErbB4_Contr ) ErbB3_Y1035 = ( EGFR_ErbB3 ) OR ( ErbB3_ErbB4 ) OR ( ErbB2_ErbB3 ) EGFR_EGFR_TGFa_CCP = ( Eps15 AND ( ( ( EGFR_EGFR_TGFa_PM ) ) AND ( ( PIP2_45 AND Clathrin ) ) AND ( ( Rab5 ) ) ) ) OR ( Epsin AND ( ( ( PIP2_45 AND Clathrin ) ) AND ( ( EGFR_EGFR_TGFa_PM ) ) AND ( ( Rab5 ) ) ) ) OR ( AP2 AND ( ( ( EGFR_EGFR_TGFa_PM ) ) AND ( ( Rab5 ) ) AND ( ( PIP2_45 AND Clathrin ) ) ) ) OR ( ( EGFR_EGFR_TGFa_CCP ) AND NOT ( EGFR_EGFR_TGFa_CCV ) ) EGFR_EGFR_TGFa_End = ( ( EGFR_EGFR_TGFa_End ) AND NOT ( EGFR_Free ) ) OR ( EGFR_EGFR_TGFa_CCV AND ( ( ( Hsc70 AND PIP3_345 AND EEA1 AND Rab5 ) AND ( ( ( GAK OR Rabaptin_5 ) ) ) ) ) ) B_Parvin = ( ILK ) Endophilin = ( Eps15 ) OR ( Epsin ) OR ( Endophilin AND ( ( ( PIP2_45 ) ) ) ) OR ( CIN85 ) PDE4 = ( B_Arrestin AND ( ( ( NOT Erk ) ) ) ) OR ( PKA AND ( ( ( B_Arrestin ) ) ) ) ASK1 = ( Trx ) Mekk2 = ( ( PI3K AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCV OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( Mekk2 ) ) OR ( ( Src AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCV OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( Mekk2 ) ) OR ( ( PLC_g AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCV OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( Mekk2 ) ) OR ( ( Grb2 AND ( ( ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_TGFa_CCP OR EGFR_EGFR_EGF_CCV OR EGFR_EGFR_EGF_CCP OR EGFR_ErbB4 OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_EGF_End ) ) ) ) AND NOT ( Mekk2 ) ) DAG = ( ( PLC_B AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( DGK AND ( ( ( DAG ) ) ) ) ) OR ( ( PLC_g AND ( ( ( PIP2_45 ) ) ) ) AND NOT ( DGK AND ( ( ( DAG ) ) ) ) ) OR ( DAG AND ( ( ( NOT DGK ) ) ) ) AP2 = ( Hip1R ) OR ( PIP3_345 ) OR ( Eps15 ) OR ( Epsin ) OR ( EGFR_EGFR_EGF_PM ) OR ( PIP2_45 ) OR ( EGFR_EGFR_TGFa_PM ) OR ( CIN85 ) Gbg_1213 = ( Ga_1213 ) OR ( alpha_1213R AND ( ( ( NOT Ga_1213 ) ) AND ( ( NOT Gbg_1213 ) ) ) ) Epsin = ( EGFR_Ub ) OR ( PIP2_45 ) OR ( EGFR_EGFR_EGF_PM ) OR ( EGFR_EGFR_TGFa_PM ) Hakai = ( Src AND ( ( ( NOT Ca ) ) AND ( ( E_cadherin ) ) ) ) Sos = ( Crk AND ( ( ( Grb2 ) ) AND ( ( NOT PIP2_45 AND NOT Nck AND NOT Erk ) ) AND ( ( PIP3_345 ) ) ) ) OR ( ( Grb2 AND ( ( ( PIP3_345 ) ) ) ) AND NOT ( Cbl_RTK ) ) OR ( Nck AND ( ( ( Crk ) ) AND ( ( PIP3_345 ) ) ) ) Src = ( ( PTPa AND ( ( ( NOT Src ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( EGFR_Y992 ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( Fak AND ( ( ( PTP1b ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( EGFR_Y1086 ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( Cas AND ( ( ( PTP1b ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( Gas AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( alpha_sR AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( EGFR_Y1148 ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) OR ( ( Gai AND ( ( ( B_Arrestin ) ) ) ) AND NOT ( Csk AND ( ( ( Src ) ) ) ) ) ErbB3_Y1178 = ( EGFR_ErbB3 ) OR ( ErbB3_ErbB4 ) OR ( ErbB2_ErbB3 ) EGFR_Y992 = ( ( EGFR_ErbB3 ) AND NOT ( SHP2 AND ( ( ( EGFR_Y992 ) ) ) ) ) OR ( ( EGFR_Y992 ) AND NOT ( SHP2 AND ( ( ( EGFR_Y992 ) ) ) ) ) OR ( ( EGFR_ErbB2 ) AND NOT ( SHP2 AND ( ( ( EGFR_Y992 ) ) ) ) ) OR ( ( EGFR_ErbB4 ) AND NOT ( SHP2 AND ( ( ( EGFR_Y992 ) ) ) ) ) OR ( ( EGFR_EGFR ) AND NOT ( SHP2 AND ( ( ( EGFR_Y992 ) ) ) ) ) OR ( ( EGFR_EGFR_EGF_PM ) AND NOT ( SHP2 AND ( ( ( EGFR_Y992 ) ) ) ) ) OR ( ( EGFR_EGFR_TGFa_PM ) AND NOT ( SHP2 AND ( ( ( EGFR_Y992 ) ) ) ) ) Gaq = ( alpha_qR AND ( ( ( NOT Gaq ) AND ( ( ( NOT Gbg_q ) ) ) ) ) ) OR ( Gaq AND ( ( ( Gbg_q ) ) AND ( ( NOT RGS AND NOT PLC_B ) ) ) ) B_catenin = ( ( Fer AND ( ( ( NOT EGFR_ErbB2 AND NOT EGFR_EGFR_TGFa_CCV AND NOT EGFR_EGFR_TGFa_PM AND NOT EGFR_EGFR_EGF_CCV AND NOT EGFR_ErbB3 AND NOT EGFR_EGFR_TGFa_End AND NOT EGFR_EGFR_EGF_PM AND NOT EGFR_EGFR_EGF_MVB AND NOT EGFR_EGFR_TGFa_CCP AND NOT EGFR_EGFR_EGF_CCP AND NOT Src AND NOT EGFR_ErbB4 AND NOT EGFR_EGFR AND NOT EGFR_EGFR_EGF_End ) ) OR ( ( PTP1b ) ) ) ) OR ( PTP1b AND ( ( ( NOT EGFR_ErbB2 AND NOT EGFR_EGFR_TGFa_CCV AND NOT EGFR_EGFR_TGFa_PM AND NOT EGFR_EGFR_EGF_CCV AND NOT EGFR_ErbB3 AND NOT EGFR_EGFR_TGFa_End AND NOT EGFR_EGFR_EGF_PM AND NOT EGFR_EGFR_EGF_MVB AND NOT EGFR_EGFR_TGFa_CCP AND NOT EGFR_EGFR_EGF_CCP AND NOT Src AND NOT EGFR_ErbB4 AND NOT EGFR_EGFR AND NOT EGFR_EGFR_EGF_End ) ) ) ) ) OR NOT ( EGFR_ErbB2 OR EGFR_EGFR_TGFa_CCV OR PTP1b OR EGFR_EGFR_TGFa_PM OR EGFR_EGFR_EGF_CCV OR EGFR_ErbB3 OR EGFR_EGFR_TGFa_End OR EGFR_EGFR_EGF_PM OR EGFR_EGFR_EGF_MVB OR EGFR_EGFR_TGFa_CCP OR Fer OR EGFR_EGFR_EGF_CCP OR Src OR EGFR_ErbB4 OR EGFR_EGFR OR EGFR_EGFR_EGF_End ) EGFR_EGFR_EGF_PM = ( ( EGFR_EGFR_EGF_PM ) AND NOT ( EGFR_EGFR_EGF_CCP ) ) OR ( ( ( EGFR_Free AND ( ( ( EGF ) ) AND ( ( NOT EGFR_T654 ) ) ) ) AND NOT ( EGFR_EGFR_EGF_CCP ) ) AND NOT ( ErbB2_Free ) ) EGFR_EGFR_EGF_End = ( ( EGFR_EGFR_EGF_End ) AND NOT ( EGFR_EGFR_EGF_MVB ) ) OR ( ( EGFR_EGFR_EGF_CCV AND ( ( ( Hsc70 AND GAK AND PIP3_345 AND Rabaptin_5 AND EEA1 AND Rab5 ) ) ) ) AND NOT ( EGFR_EGFR_EGF_MVB ) ) ErbB3_Y1180 = ( EGFR_ErbB3 ) OR ( ErbB2_ErbB3 ) OR ( ErbB3_ErbB4 ) PI3K = ( ( Gbg_i ) AND NOT ( PI3K_I ) ) OR ( ( Fak ) AND NOT ( PI3K_I ) ) OR ( ( E_cadherin ) AND NOT ( PI3K_I ) ) OR ( ( ErbB3_Y1257 ) AND NOT ( PI3K_I ) ) OR ( ( Ras ) AND NOT ( PI3K_I ) ) OR ( ( Src AND ( ( ( Cbl_RTK ) ) ) ) AND NOT ( PI3K_I ) ) OR ( ( EGFR_Y920 ) AND NOT ( PI3K_I ) ) OR ( ( ErbB4_Y1056 ) AND NOT ( PI3K_I ) ) OR ( ( ErbB3_Y1203_05 ) AND NOT ( PI3K_I ) ) OR ( ( Gab1 ) AND NOT ( PI3K_I ) ) OR ( ( ErbB3_Y1270 ) AND NOT ( PI3K_I ) ) OR ( ( EGFR_Y845 ) AND NOT ( PI3K_I ) ) OR ( ( Crk ) AND NOT ( PI3K_I ) ) OR ( ( ErbB3_Y1178 ) AND NOT ( PI3K_I ) ) OR ( ( ErbB3_Y1035 ) AND NOT ( PI3K_I ) ) OR ( ( ErbB3_Y1241 ) AND NOT ( PI3K_I ) )
Integrative Modelling of the Influence of MAPK Network on Cancer Cell Fate Decision Luca Grieco1,2,3,4,5,6, Laurence Calzone6,7,8, Isabelle Bernard-Pierrot6,9, Franc¸ois Radvanyi6,9, Brigitte Kahn-Perle`s2, Denis Thieffry2,3,4,5,10 1 Aix-Marseille Universite´, Marseille, France, 2 TAGC – Inserm U1090, Marseille, France, 3 Institut de Biologie de l’Ecole Normale Supe´rieure (IBENS), Paris, France, 4 UMR 8197 Centre National de la Recherche Scientifique (CNRS), Paris, France, 5 Inserm 1024, Paris, France, 6 Institut Curie, Paris, France, 7 Inserm U900, Paris, France, 8 Ecole des Mines ParisTech, Paris, France, 9 UMR 144 Centre National de la Recherche Scientifique (CNRS), Paris, France, 10 INRIA Paris-Rocquencourt, Rocquencourt, France Abstract The Mitogen-Activated Protein Kinase (MAPK) network consists of tightly interconnected signalling pathways involved in diverse cellular processes, such as cell cycle, survival, apoptosis and differentiation. Although several studies reported the involvement of these signalling cascades in cancer deregulations, the precise mechanisms underlying their influence on the balance between cell proliferation and cell death (cell fate decision) in pathological circumstances remain elusive. Based on an extensive analysis of published data, we have built a comprehensive and generic reaction map for the MAPK signalling network, using CellDesigner software. In order to explore the MAPK responses to different stimuli and better understand their contributions to cell fate decision, we have considered the most crucial components and interactions and encoded them into a logical model, using the software GINsim. Our logical model analysis particularly focuses on urinary bladder cancer, where MAPK network deregulations have often been associated with specific phenotypes. To cope with the combinatorial explosion of the number of states, we have applied novel algorithms for model reduction and for the compression of state transition graphs, both implemented into the software GINsim. The results of systematic simulations for different signal combinations and network perturbations were found globally coherent with published data. In silico experiments further enabled us to delineate the roles of specific components, cross-talks and regulatory feedbacks in cell fate decision. Finally, tentative proliferative or anti-proliferative mechanisms can be connected with established bladder cancer deregulations, namely Epidermal Growth Factor Receptor (EGFR) over-expression and Fibroblast Growth Factor Receptor 3 (FGFR3) activating mutations. Citation: Grieco L, Calzone L, Bernard-Pierrot I, Radvanyi F, Kahn-Perle`s B, et al. (2013) Integrative Modelling of the Influence of MAPK Network on Cancer Cell Fate Decision. PLoS Comput Biol 9(10): e1003286. doi:10.1371/journal.pcbi.1003286 Editor: Satoru Miyano, University of Tokyo, Japan Received January 16, 2013; Accepted September 2, 2013; Published October 24, 2013 Copyright: 2013 Grieco et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement nu HEALTH-F4-2007-200767 for APO-SYS(http://cordis.europa.eu/fp7/). It has been further supported by the Agence Nationale de la Recherche, France (project MI2 iSA). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: grieco@tagc.univ-mrs.fr (LG); thieffry@ens.fr (DT) Introduction Mitogen-activated protein kinase (MAPK) cascades can be activated by a wide variety of stimuli, such as growth factors and environmental stresses. They affect diverse cellular activities, including gene expression, cell cycle machinery, apoptosis and differentiation. A recurrent feature of a MAPK cascade is a central three-tiered core signalling module, consisting of a set of sequentially acting kinases. MAPK kinase kinases (MAPKKKs) are activated follow- ing upstream signals. For instance, they can be phosphorylated by small G-proteins belonging to the Ras/Rho family in response to extracellular stimuli. Their activation leads to double phosphor- ylation and activation of downstream MAPK kinases (MAPKKs), which in turn double phosphorylate MAPKs. Once activated, MAPKs act on their target substrates, which include other kinases and transcription factors [1]. To date, three main cascades have been extensively studied, named after their specific MAPK components: Extracellular Regulated Kinases (ERK), Jun NH2 Terminal Kinases (JNK), and p38 Kinases (p38). These cascades are strongly interconnected, forming a complex molecular network [1–4]. MAPK phosphorylation level is regulated by the opposing actions of phosphatases. As the effects of MAPK signalling have been shown to depend on the magnitude and duration of kinase activation, phosphatase action might play an important functional role [5]. Moreover, scaffold proteins bring together the compo- nents of a MAPK cascade and protect them from activation by irrelevant stimuli, as well as from negative regulators (such as phosphatases) [6]. The involvement of MAPK cascades in major cellular processes has been widely documented [1,7,8]. However, the wide range of stimuli and the large number of processes regulated, coupled with the complexity of the network, raises the fundamental and debated question of how MAPK signalling specificity is achieved [9]. Several interrelated mechanisms have been proposed: opposing action of phosphatases; presence of multiple components with different roles at each level of the cascade (e.g. different isoforms of a protein); interaction with scaffold proteins; distinct sub-cellular localisations of cascade components and/or targets; feedback PLOS Computational Biology \| www.ploscompbiol.org 1 October 2013 \| Volume 9 \| Issue 10 \| e1003286 mechanisms; great variety of molecular signals, as well as distinct durations and strengths; cross-talks among signalling cascades that are activated simultaneously [4,10]. All these factors contribute to the complexity of the MAPK network and presumably act together to determine signalling specificity. Deregulations of the MAPK cascades are often observed in cancer [11,12]. Several components of the network have already been proposed as targets in cancer therapy, such as p38, JNK, ERK, MEK, RAF, RAS, and DUSP1 [12–23], but the intricacy of the underlying mechanisms still hinders the conception of effective drugs [24]. A deeper understanding of the regulatory mechanisms involved is crucial to clarify the roles of MAPKs in cancer onset and development, as well as to delineate therapeutic strategies. During the last decades, mathematical modelling has been widely used to study different aspects of the MAPK cascades [25] (Table S1). Quantitative models (based on Ordinary Differential Equations – ODE) have been proposed to explain the main dynamical properties of the MAPK cascades in relation with their particular structural features (double phosphorylation events, phosphatase effects, feedback loops, role of scaffold proteins, etc.) [26–32]. Other modelling studies investigated the behaviour of specific cascades (mainly ERK) leading to MAPK activation in response to external stimuli [33–42]. More recently, comprehen- sive qualitative dynamical models have been developed. Samaga et al. [43] built a large logical model of the signalling network (including MAPKs) responding to Epidermal Growth Factor Receptor (EGFR) stimuli, which was largely derived from the reaction map published by Oda et al. [44]. This model accurately covers the early response of the MAPK cascades to signalling stimuli, with a particular reference to primary and transformed hepatocytes. Also focusing on cancer (in particular, epithelial tumours), the logical model proposed by Poltz and Naumann recapitulates the response of a cell to DNA damaging agents (DNA repair versus apoptotic cell death), and was used to identify candidate target molecules to design novel therapies [45]. In this study, we aimed at better understanding how MAPK signalling deregulations can interfere with tissue homeostasis, leading to imbalance between cell proliferation, on the one hand, and cell growth arrest, possibly followed by apoptotic cell death, on the other hand. The choice between these phenotypes (cell fate decision) is of vital importance in cancer progression: transformed cells receive external and/or autocrine growth stimuli pushing towards cell proliferation (i.e. tumour growth); but they also receive external and/or internal anti-proliferative signals, which coupled with apoptotic stimuli trigger transformed cell clearance from the organism [46]. Our goal was to build a predictive dynamical model able (i) to recapitulate the response of the entire MAPK network to selected stimuli, along with its specific contribution to cell fate decision, and (ii) to assess novel hypotheses about poorly documented mechanisms involved in specific cancer cell types. We focused on urinary bladder cancer, where MAPK network deregulations have been associated with specific pheno- types. Bladder cancer is the fourth most common cancer among men in Europe and America. Two main types of early stage bladder carcinoma have been delineated so far: (i) non-invasive papillary carcinomas (Ta) are usually mildly aggressive and rarely progress towards higher stages, whereas (ii) carcinomas in situ (Cis) often develop into invasive tumours (T1 to T4 stages) [47]. Activating mutations of Fibroblast Growth Factor Receptor 3 (FGFR3) have been found in 70–75% of Ta tumours, but they are absent in Cis and less frequent (15–20%) in invasive tumours [47,48]. Oncogenic FGFR3 gene fusions have also been recently identified in a small percentage of invasive bladder tumours [49]. In contrast, over-expression of EGFR has been recurrently associated with higher probability of tumour progression [50]. The mechanisms underlying the cellular response of cancer cells to these signalling stimuli are still poorly understood. Alterations of p53 and retinoblastoma (RB) pathways are presumably involved in tumour progression [51]. These pathways are major controllers of the cell cycle, and the MAPK network presumably regulates their activation by responding to growth factor stimuli. For instance, ERK phosphorylation leads to MYC activation, which can inhibit cell cycle progression through the p14/p53 pathway [52], or activate Cyclin/CDK complexes leading to RB phosphorylation and subsequent E2F-dependent gene transcrip- tion [51]. Both EGFR and FGFR3 pathways can activate the MAPK cascades. Although the two signalling pathways largely overlap, the presence of specificity factors might contribute to tune the final cellular response. To tackle these questions, we first compiled published data to build a comprehensive generic reaction map using CellDesigner software [53–55]. This map takes into account signals propagating from major stimuli, such as growth factors, cytokines, stress, leading to the activation of MAPKs and their downstream targets, and consequently to cell fate decision. We considered three main cell fates: proliferation, apoptosis, growth arrest. Next, we used the resulting reaction map to design a qualitative dynamical model with GINsim software [56,57], which relies on a logical formalism [58–60]. To cope with the relatively high number of components, we applied a semi- automatic model reduction procedure to lower the computa- tional cost of dynamical analyses, without losing the main dynamical properties of the system. We then performed logical simulations to check the behaviour of the model in specific documented situations, as well as to predict the behaviour in novel situations. We further investigated the role of positive and negative regulatory circuits in cell fate decision. Altogether, these analyses provided novel insights into the mechanisms differen- tiating the response of urinary bladder cancer cells to EGFR versus FGFR3 stimuli. Author Summary Depending on environmental conditions, strongly inter- twined cellular signalling pathways are activated, involving activation/inactivation of proteins and genes in response to external and/or internal stimuli. Alterations of some components of these pathways can lead to wrong cell behaviours. For instance, cancer-related deregulations lead to high proliferation of malignant cells enabling sustained tumour growth. Understanding the precise mechanisms underlying these pathways is necessary to delineate efficient therapeutical approaches for each specific tumour type. We particularly focused on the Mitogen-Activated Protein Kinase (MAPK) signalling network, whose involve- ment in cancer is well established, although the precise conditions leading to its positive or negative influence on cell proliferation are still poorly understood. We tackled this problem by first collecting sparse published biological information into a comprehensive map describing the MAPK network in terms of stylised chemical reactions. This information source was then used to build a dynamical Boolean model recapitulating network responses to characteristic stimuli observed in selected bladder cancers. Systematic model simulations further allowed us to link specific network components and interactions with prolif- erative/anti-proliferative cell responses. Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 2 October 2013 \| Volume 9 \| Issue 10 \| e1003286 Methods Logical modelling We built our dynamical model using the logical formalism originally proposed by Thomas [58,59]. Implemented in GINsim, our logical modelling approach initially requires the delineation of a regulatory graph, where each vertex (node) represents a model component and each arc (signed, directed edge) represents an interaction (activation or inhibition) between two components. Here, all components are associated with Boolean variables, meaning that they can take two possible levels, 0 or 1, denoting the absence/inactivation or the presence/activition of the modelled entities (protein activation level, gene expression level, activation of a cellular process, etc.). The model definition is completed by assigning a logical rule to each component. This logical rule specifies the target value of the component depending on the presence/absence of its regulators, using the classical Boolean operators AND, OR and NOT. Logical simulations The dynamical behaviour of the model can be computed starting from any initial state, step by step, updating the current state according to the logical formulae (logical simulations) [60]. Updating policy. Two updating policies are mainly used. According to the synchronous policy, all components are updated simultaneously at each step; consequently, each state has at most one successor. In contrast, according to the asynchronous policy, only one variable can be updated at each step and all the possible successors of a state are computed. Mixed policies based on the notion of priority classes can also be defined using GINsim [61], where subsets of components are ranked. At each step, highest rank variables are then updated in a synchronous or asynchronous way. In this work, we have used the fully asynchronous updating policy, which usually generates more realistic behaviours [58]. State transition graphs and attractors. The dynamics of a logical model can be represented in terms of a state transition graph (STG), in which nodes denote different states of the system (represented by a Boolean vector encompassing the values of all the components), whereas arcs represent enabled transitions between pairs of states. Of particular interest are the states forming attractors, i.e. (groups of) states from which the system cannot escape, which represent potential asymptotical behaviours. Attractors can be ranged into two main classes: – stable states, corresponding to fixed points (i.e. states without successors); – cyclic attractors, corresponding to terminal cycles or to more complex terminal strongly connected components, comprising several intertwined cycles. Leaning on a representation of the logical rules in terms of Multi-valued Decision Diagrams (MDD), an algorithm enables the computation of all the stable states of a logical model (indepen- dently of the initial conditions) [62]. The efficiency of the algorithm (which does not require to compute the state transition graph) makes this tool particularly useful when dealing with large logical models. However, other means are needed to assess the reachability of the stable states from specific initial states, or yet to identify cyclic attractors. Deeper dynamical analyses imply the computation of the state transition graph. GINsim user can define a set of initial states and an updating strategy; the software then computes the state transition graph, highlighting stable states and cyclic attractors. GINsim further eases the definition of perturbations, which are simulated by forcing the level of a subset of components to fixed values (or value intervals). For instance, in the Boolean case, we can reproduce a loss-of-function by setting a component to 0, whatever the levels of its regulators, whereas a gain-of-function can be simulated by forcing the corresponding component to 1. More subtle perturbations can be simulated by rewriting relevant logical rules. As the size of the model considered increases, we are facing the well known problem of the exponential growth of the state transition graph. To cope with this problem, we used two methods that amount to compress the model before simulation or to compress the resulting state transition graph on the fly. These two methods are briefly described hereafter, along with a complemen- tary method enabling the identification of regulatory circuits playing crucial dynamical roles. Model reduction To deal with large models, GINsim enables their reduction by ‘‘hiding’’ selected components [63]. In practice, the user selects the components to hide, and the software hides each of them iteratively, while recomputing the logical rules of their targets. Provided that no functional regulatory circuit is eliminated in the process, this reduction preserves all attractors. For example, the stable states are all conserved, in the sense that each stable state of the reduced model is the projection (on the reduced state space) of a stable state of the original model [63]. This tool is particularly useful when the high dimensionality impedes the computation of the full STG. Hierarchical transition graph representation The analysis of the paths from initial states to attractors can be done directly on the STG when it is small (tens of states), but becomes quickly intractable as the size of STG increases. To cope with this difficulty, we use a novel feature of GINsim, which iteratively clusters the state transition graph into groups of states (components or hyper-nodes) sharing the same set of successors [64]. The resulting hierarchical state transition graph (HTG) displays all the reachable attractors (components at the bottom of the graph), while the other clusters of states represent their basins of attractions (including strict basins with a single outgoing arc targeting a specific attractor, or non-strict basins grouping states that can reach a specific set of HTG components). HTG computation is done on the fly, i.e. without having to store the whole STG, which often leads to strong memory and CPU usage shrinking. Furthermore, this functionality eases the identification of the key commutations (changes of component levels) underlying irreversible choices between the different reachable attractors. Altogether, the HTG representation is very compact (often much more compact than the more classical graph of strongly connected components, as HTG further compacts linear/non circular pathways) and very informative regarding the organisation of the original STG. Regulatory circuit analysis Rene´ Thomas proposed generic rules linking the presence of regulatory circuits (simple oriented regulatory cycles) in biological networks with dynamical properties. The first rule states that the existence of a positive circuit (involving an even number of negative regulatory interactions) is a necessary condition for multi- stationarity. The second rule states that the existence of a negative regulatory circuit (involving an odd number of negative regulatory interactions) is a necessary condition for the generation of sustained oscillations [65]. More recently, Remy et al. [66] Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 3 October 2013 \| Volume 9 \| Issue 10 \| e1003286 translated these rules into theorems in the case of asynchronous Boolean dynamical systems (which is the case of our MAPK model). However, when embedded in a more complex network, specific constraints on the values of the external components acting on circuit components have to be fulfilled in order to allow a regulatory circuit to produce the expected behaviour (‘‘circuit functionality constraints’’) [67]. The concept of circuit function- ality has been formalised for logical models and implemented into GINsim [62]. GINsim allows to compute all the functional positive and negative circuits of a model. For each of them, the software also provides the corresponding functionality context, defined as a set of constraints on the values of its external regulators. This tool enables the identification of the regulatory circuits playing key dynamical roles within a complex network. Results MAPK reaction map Based on published data, we have built and annotated a comprehensive reaction map using CellDesigner (supplementary Dataset S1). This map encompasses 232 species (proteins, genes, complexes, other molecules) and 167 reactions involved in the three most extensively documented MAPK cascades (ERK, JNK, p38). The CellDesigner version of the map (XML format) is provided as supplementary Dataset S2. The MAPK map has been further integrated into the Atlas of Cancer Signalling Networks developed by the group of Emmanuel Barillot at Institut Curie in Paris (https://acsn.curie.fr), where it can be explored using a web browser. Our reaction map takes into account signals propagating from different major stimuli, such as growth factors, cytokines, stress, which lead to the activation of MAPKs and their downstream targets. It covers feedbacks and cross-talks among the MAPK cascades, as well as the roles of the best documented phosphatases and scaffold proteins. The main cellular compartments are also represented (plasma membrane, cytoplasm, nucleus, mitochon- dria, endosomes, etc.), showing the localisation of reactions within the cell. When compartmentalisation has not been fully char- acterised yet, reactions have been provisionally assigned to the cytoplasm. Proteins are coloured to emphasise relevant families. Figure 1 shows a map excerpt reporting two different mechanisms of ERK activation (see map annotations for more details). We considered two compartments named ‘‘Genes’’ and ‘‘Phenotypes’’ at the bottom of the map, which include representative genes activated by the MAPK cascades, as well as phenotypes (proliferation, apoptosis, growth arrest) enabled by selected readouts. We considered information concerning different human and mouse cell types, implying that the MAPK map should be considered as generic. Indeed, at this stage, information is lacking to build a detailed map based exclusively on data for a specific cell type. However, we selected biological events explicitly considered to be cell type independent. When applicable, information concerning cell types is provided through links to relevant database entries (mainly PubMed). Because the precision of the information retrieved from the literature varies, our map represents different pathways with different levels of details. For instance, we could find detailed information about the scaffold proteins intervening in the ERK cascade and on the sub-cellular localisation of the correspond- ing protein complexes; in contrast, such information is still largely lacking for the JNK and p38 cascades. This is why the map currently reaches its greatest level of detail for the ERK cascade. Furthermore, the level of detail represented could also be dictated by readability considerations. For instance, the RTK (receptor tyrosine kinase) component in the map represents several different receptors (e.g. EGFR, FGFR, VEGFR, etc.): all these receptors share common features that are related to MAPK activation. However, their mechanisms of action may differ in some subtle ways, which are not fundamental for our purpose here. The detailed representation of all these pathways would have made the map very difficult to read, and we thus decided to simplify the graphical representation, while keeping track of relevant variations in the annotations of the corresponding species or reactions. The resulting CellDesigner map constitutes a comprehensive and integrated source of information concerning the roles of the MAPK network in cell fate decision, taking into account specificity factors. This map can be directly used by biologists and modellers to get information about the reported phenomena. It can also be used for visualisation of high-throughput data (e.g. by automat- ically colouring components based on expression levels) derived from different cell conditions, for example in order to identify differentially expressed components. This can also give insights into cell type-dependent mechanisms. MAPK logical model Hereafter, we focus on the impact of the MAPK network in urinary bladder cancer, with particular emphasis on the differen- tial behaviour between EGFR over-expression and FGFR3 activating mutation. Scope of the MAPK logical model. In order to study the response of the MAPK network to specific stimuli, and its influence on cell fate decision, we built a dynamical model covering the mechanisms reported in the MAPK map. We derived a regulatory graph using the MAPK reaction map as an information source, as detailed in supplementary Text S1. In particular, we considered the following subset of stimuli in our model: EGFR stimulus, FGFR3 stimulus, TGFbR stimulus, and DNA damage. With reference to the latter stimulus, please notice that we did not consider explicitly here the DNA repair process following DNA damage, but we only account for the triggering of growth arrest and apoptosis following sustained DNA damage [68]. In our dynamical model, DNA damage thus corresponds to sustained stress or to the effects of therapies involving DNA- damaging agents. The regulatory graph shown in Figure 2 covers the activation of MAPK targets that influence the choice between proliferation, growth arrest, and apoptosis. In particular, we consider MYC and p70 (in the absence of p21) as markers of cell cycle enablement, p21 as a marker of growth arrest, FOXO3 and p53 as markers of apoptosis, whereas ERK and/or BCL2 indicate apoptosis disablement. To ease the interpretation of phenotypes, we defined three output nodes denoting proliferation, growth arrest, and apoptosis, respectively. These nodes represent enablement/ disablement of the corresponding processes, depending on the MAPK network state, but not necessarily all requirements for this phenotype. For instance, when proliferation is enabled (by the interplay of MYC, p70 and p21), we assume that Cyclin/CDK complexes are activated. In this context, the node ‘‘Proliferation’’ denotes entry into the cell cycle and does not account for alterations of later stages of the cell cycle. Similar considerations are applicable for the other phenotypes modelled. This simplifi- cation is justified by our focus on the specific contributions of the MAPK network to cell fate decision. Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 4 October 2013 \| Volume 9 \| Issue 10 \| e1003286 Each of the 52 components of the regulatory graph is modelled by a Boolean variable along with a logical rule (Table S2) specifying how the component activity depends on its regulators. Reduced model versions. To cope with the relatively high dimension (52 components) of our model, we took advantage of the model reduction function implemented in GINsim (see Methods). Indeed, it is difficult to perform simulations with the original model version, as it entails 252 states. The choice of components to hide depends on the simulation performed. For instance, if we plan to simulate a p53 loss-of-function and observe its effects on p21, we better conserve p53 (otherwise we cannot define the perturbed version) and p21 (otherwise, we cannot explicitly observe its value). However, as we wanted to test several situations, almost half of the MAPK model components were needed to be observable. Consequently, we designed several reduced versions of the original MAPK model, each of which dedicated to a subset of simulations. This strategy enabled us to drastically reduce the computational cost of our in silico experiments (the dimension of the reduced models ranged from 16 to 18 components). Altogether, we defined three different reduced model versions, whose component lists are reported in supplementary Table S3. These definitions are enclosed in the comprehensive model file (supplementary Dataset S4) and enable the generation of reduced versions according to simulation needs. Figure 3 shows the regulatory graph corresponding to one reduced version, namely, ‘‘red1’’. Supplementary Dataset S3 lists the simulations performed for each reduced version. The three model reductions were found equivalent in terms of attractors and main dynamical properties. Briefly, reduction ‘‘red1’’ was used to obtain the results discussed in the sections ‘‘Coherence with well established bladder cancer deregulations’’ and ‘‘Predictions generated with the MAPK logical model’’, while reductions ‘‘red2’’ and ‘‘red3’’ were used to obtain the results discussed in the section ‘‘Coherence with additional cancer-related facts’’. Coherence of the logical model behaviour with published data The logical rules assigned to model components were inferred from information about a broad range of experiments and cellular conditions. To check the coherence of the global behaviour of the resulting model with current biological knowledge, we systemat- ically compared its dynamical properties with published data concerning different tumoural cell types, with particular attention to bladder cancer. More specifically, we first assessed the dynamical behaviour of the model under well established perturbations observed in the bladder cancer subtypes of interest. We further checked the coherence of the model behaviour with an additional list of biological facts, not necessarily involved in bladder cancer. These analyses were carried out by performing asynchronous simulations for selected initial conditions (initial states, input signals, potentially in the presence of perturbations), and observing the attractors reached by the system. Figure 1. Molecular map for ERK regulation and sub-cellular localisation. After RAS activation, ERK cascade can be recruited and activated on plasma membrane with the help of KRS1 scaffold protein (upper part of the figure); activated ERK is then released (in complex with MEK and KSR1) into the cytoplasm, where it can activate some of its cytoplasmic targets (e.g. PLA2G4A protein). Alternatively, activated receptor complex can translocate to late endosomes (left part of the figure), where ERK cascade can be triggered with the help of MP1 scaffold protein; in this case, activated ERK monomers are released into the cytoplasm, from where they can translocate into the nucleus and exert other effects (e.g. induction of DUSP1 phosphatase). This map is a small fraction of the detailed MAPK network built with the software CellDesigner (www.celldesigner.org) and provided in png and cell formats (supplementary Datasets S1 and S2). doi:10.1371/journal.pcbi.1003286.g001 Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 5 October 2013 \| Volume 9 \| Issue 10 \| e1003286 In practice, the entire process from reaction map construction to model simulations is iterative, requiring several rounds of literature searches and in silico experiments. Whenever the model disagreed with established facts, we went back to the literature to seek complementary information and refined our modelling hypotheses. The reaction map and the logical model where systematically and consistently completed with relevant informa- tion during this process. Coherence with well established bladder cancer deregulations. As we build our model around the comparison between EGFR over-expression and FGFR3 activating mutation in bladder cancer, our first simulations were dedicated to the assessment of the model behaviour in these circumstances. Figure 4a reports a simplified view of the model dynamics following EGFR over-expression, obtained by setting EGFR to 1 throughout the simulation, in the absence of additional stimuli (see supplementary Dataset S3 for precise simulation settings). In response to EGFR over-expression, the asynchronous state transition graph encompasses two sets of trajectories: one characterised by p53 activation and ERK silencing, leading to an apoptotic stable state (i.e. Apoptosis = Growth_Arrest = 1, Proliferation = 0); the other characterised by p53 silencing and ERK activation, leading to a PI3K/AKT-dependent proliferation stable state (i.e. Apoptosis = Growth_Arrest = 0, Proliferation = 1) (cf. simulation provided in the supplementary Text S2). Alterations in the p53 pathway have been associated with more aggressive and invasive bladder cancers [50]. The fundamental role of p53 in the model can be observed by simulating a p53 loss-of-function (second row of Figure 4c). In this case, the proliferative attractor is kept, while the apoptotic attractor is lost. In contrast, still in presence of EGFR over-expression, when the system is also subjected to persistent DNA damage (third row of Figure 4c), we obtain a single apoptotic attractor. This behaviour is in agreement with the fact that when damage is moderate (i.e. absence of DNA damage stimulus), the cell is still able to escape apoptotic cell death by down-regulating p53 signalling (i.e. possible switch between the two attractors of Figure 4a), but p53 eventually induces apoptosis in cells subjected to extensive DNA damage [69]. A similar response is also predicted in the case of TGFBR stimulus, in line with the typical anti-proliferative role played by this pathway [70]. In this respect, TGFBR has also been shown to induce proliferation in tumours, in some circumstances, but the conditions (especially in relation with MAPK network) under which this occurs are still poorly understood [70]. Strong activation of PI3K/AKT pathway has also been associated with enhanced bladder tumour proliferation [50]. Accordingly, in our model, PI3K/AKT gain-of-functions counteract p53 pathway effects (fifth row of Figure 4c), impairing the apoptotic phenotype. Two other important loss-of-function known to be associated with poorer prognosis in bladder cancers have been simulated. Deletions of either PTEN or p14 in our model are associated with a more aggressive phenotype (sixth and seventh row of Figure 4c). The former is a tumour suppressor shown to inhibit AKT Figure 2. Regulatory graph of the MAPK logical model. Each node denotes a model component. Model inputs, phenotypes and MAPK proteins (ERK, p38, JNK) are denoted in pink, blue and orange, respectively. Green arrows and red T-arrows denote positive and negative regulations, respectively. A comprehensive documentation is provided in the Table S4, which includes a summary of all modelling assumptions, references (PubMed links) and the specification of the logical rule associated with each component. The source file is further provided as supplementary Dataset S4, which can be opened, edited, analysed and simulated with the softare GINsim (www://www.ginsim.org/beta). doi:10.1371/journal.pcbi.1003286.g002 Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 6 October 2013 \| Volume 9 \| Issue 10 \| e1003286 expression [71]. The latter is induced by MYC and is able to enhance p53 activity by inhibiting MDM2 [51]. According to our model, p14 loss-of-function abrogates apoptosis, which accounts for the observed dual role of MYC [72]: on the one hand, MYC contributes to proliferation (MYC is a read-out for proliferation in the model); on the other hand, it is involved in p53-dependent apoptosis. The behaviour of our model in the case of FGFR3 activating mutation is depicted in Figure 4b (cf. Text S2 for a complete simulation). We find again the ‘‘p53 versus ERK’’ pattern accounting for the fundamental role of p53 in cell fate decision. Interestingly, the non-apoptotic branch of the asynchronous state transition graph is now characterised by two different behaviours. On the one hand, similarly to EGFR over-expression, when PI3K is active, the system will eventually reach a proliferative attractor. On the other hand, a p53-independent PI3K/AKT pathway leads to an attractor characterised by all phenotypes set to 0, that we interpret as ‘‘no cell fate decision taken’’ at the level of MAPK network. This is coherent with the contention that FGFR3 mutations, mainly characterising non-invasive bladder carcino- mas, relatively mildly induce proliferation due to the action of ERK cascade [47,51,73]. Indeed, the coexistence of these outcomes (proliferation versus no cell fate decision) tentatively explain the less aggressive phenotype generally observed in FGFR3-mutated bladder carcinomas, in comparison with urothe- lial tumours over-expressing EGFR (associated only with a proliferative attractor). The underlying mechanisms are further analysed below. By and large, the simulations of FGFR3 mutation correctly recapitulate the effects of the major bladder cancer deregulations listed in Figure 4c (left column), producing results that are qualitatively coherent with those described for EGFR over-expression. Coherence with additional cancer-related facts. To further assess the consistency of the behaviour of our model with current knowledge, we selected a list of established facts regarding the effects of perturbations on (human/mouse) cancer cells, not necessarily bladder-related. Based on this list, we defined a series of in silico experiments, combining relevant initial states and virtual perturbations (loss-of-functions and/or gain-of-functions of select- ed model components, as defined in Methods). This analysis mainly consisted in cross-checking the attractors obtained in our simulations with the qualitative information retrieved from the literature, without focusing on the full dynamics of the system. A summary of the results obtained is provided in Table 1 (for more details, see the supplementary Dataset S3). Additionally, all the simulations performed can be easily reproduced using the model files available as supplementary Dataset S4. Briefly, the involvement of MAPKs in cell fate decision was assessed through perturbations of relevant components. The model accounts for the pro-apoptotic role of p38 and JNK, as well as for the promotion of growth arrest by p38, and for the proliferative role of ERK. The model also recapitulates the p21-mediated tumour suppressor function of p53, along with the impairment of this function due to epigenetic silencing of GADD45. Additionally, we were also able to reproduce (i) the positive effects of EGFR/FGFR3/RAS/RAF over-expressions on ERK activation; (ii) the negative effects of HSP90-inhibitors on cell proliferation; (iii) the role of ERK against anti-proliferative TGFb signalling; and (iv) the role of JNK against RAS-induced proliferation. These simulations cover the most Figure 3. Regulatory graph of a reduced version of the MAPK model. The regulatory graph corresponds to the ‘‘red1’’ reduced model version (cf. supplementary Table S3, column 1). To obtain this version, the preservation of pink and blue nodes was imposed, along with that of {EGFR, FGFR3, p53, p14, PI3K, AKT, PTEN, ERK}, in order to investigate the effects of perturbations affecting these components. The remaining nodes {FRS2, MSK} were maintained by the reduction algorithm because of the occurrence of auto-regulatory loops during the reduction process. Green arrows and red T-arrows denote positive and negative regulations, respectively, whereas blue arrows denote dual interactions. doi:10.1371/journal.pcbi.1003286.g003 Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 7 October 2013 \| Volume 9 \| Issue 10 \| e1003286 Figure 4. Coherence of the logical model with well established bladder cancer deregulations. a) Simplified representation of the model dynamics following EGFR over-expression (EGFR = 1 throughout the simulation and all inputs set to 0 throughout the simulation). If p53 is activated first (right branch), an apoptotic attractor is reached, characterised by inactivation of ERK and AKT. If ERK and PI3K are activated first (left branch), then p53 is inactivated and AKT is activated, leading to a proliferative attractor. b) Simplified representation of the model dynamics following FGFR3 activating mutation (FGFR3 = 1 and all inputs set to 0 throughout the simulation). When p53 is activated first (right branch), an apoptotic attractor is reached, characterised by inactivation of ERK and AKT. If ERK is activated first (left and central branches), then p53 is inactivated. When PI3K is also activated (central), a proliferative attractor is reached, characterised by activated AKT. In contrast, when PI3K is not activated (left), the cell fails to make a clear decision at the level of the MAPK network. c) Attractors reached by the model in presence of receptor alterations, coupled with additional common deregulations observed in bladder cancer. Coloured circles denote the phenotypes characterising the attractors reached in each situation (we used the same colour code as in panels a and b, while empty spaces denote the loss of the corresponding branch in the state transition graph). Identifiers in rectangles (e.g.. r3, r4, etc.) point to simulation results reported in more details in Dataset S3 and Text S2. doi:10.1371/journal.pcbi.1003286.g004 Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 8 October 2013 \| Volume 9 \| Issue 10 \| e1003286 salient behaviours of the model, showing a remarkable coherence with published data. Predictions generated with the MAPK logical model Having shown that our MAPK model is consistent with published data, we designed additional simulations to explore novel mechanistic hypotheses. ERK-related feedback mechanisms. So far, we have described the behaviour of our model in presence of tumoural deregulations of growth factor receptors. Let us consider now what happens when the expression of such receptors is not altered (i.e. unperturbed logical rules for either EGFR or FGFR3 variables), in presence of sustained growth factor stimulation (i.e. either EGFR_stimulus or FGFR3_stimulus set to 1 throughout the simulations). The attractor reached from normal EGFR stimulation is characterised by oscillations (between 0 and 1) of the values of EGFR, ERK and p53, thus leading to oscillations of phenotype variables, in particular for ‘‘Proliferation’’ (Dataset S3 – r1). This behaviour contrasts with the well defined phenotypes obtained following EGFR over-expression (Figure 4a). It can be interpreted as the impossibility to obtain sustained activation (or inactivation) of the considered actors in presence of sustained growth factor stimuli. In other words, ERK oscillations in our state transition graph correspond to the transient ERK activation in the ODE-based model from Orton et al. [38]. Similar results are obtained for FGFR3 stimulation (Figure 4b and Dataset S3 – r2), in agreement with literature [74]. The main negative feedbacks underlying such responses are acting directly on the receptors (Figure 2): one accounting for GRB2-dependent ubiquitination and degradation of the receptors Table 1. Coherence of model simulations with published experimental evidence. Reduction Simulation Biological data Model behaviour red2 r17, r18 * RAF or RAS over-expressions can lead to constitutive activation of ERK. [11] In absence of inputs, constitutive activity of any one among RAF or RAS can lead to permanent ERK activation, associated with proliferation. red2 r19 * HSP90-inhibitor disrupts RAF, AKT and EGFR, leading to successful cancer treatment [86]. Concomitant RAF, AKT, EGFR deletions abrogate the proliferative stable states observed in the unperturbed model, both in the case of EGFR over-expression (obvious – simulation not performed) and in the case of FGFR3 activating mutation. red2 r20, r21, r22, r23 * Patients with p53-altered/p21-negative tumors demonstrated a higher rate of recurrence and worse survival compared with those with p53-altered/ p21-positive tumors [87]. Following either EGFR over-expression or FGFR3 activating mutation, concomitant p21 and p53 loss-of-functions correspond to a phenotype characterised by apoptosis escape (Apoptosis = Growth_Arrest = 0), with the possibility to attain proliferation. Association of p53 loss-of-function and p21 gain-of-function leads to growth arrest attractors, all characterised by no proliferation. red3 r25 p38 and JNK play important roles in stress responses, such as cell cycle arrest and apoptosis [7,69]. In presence of either DNA_damage or TGFBR_stimulus, growth arrest/apoptosis stable states are all lost in the p38/ JNK-deleted model. red3 r26 p38 and JNK, especially in the absence of mitogenic stimuli, have been shown to induce apoptotic cell death [7,69]. When p38/JNK are constitutively active, apoptotic attractors (Growth_Arrest = Apoptosis = 1, Proliferation = 0) are obtained in the absence of other stimuli. red3 r27 p38 plays its tumour suppressive role by promoting apoptosis and inhibiting cell cycle progression [11]. Under JNK constitutive activation, p38 loss-of-function determines loss of apoptotic attractors obtained in r26. red3 r28 JNK may contribute to the apoptotic elimination of transformed cells by promoting apoptosis [11,88]. Under p38 constitutive activation and JNK loss-of-function, all apoptotic attractors obtained in r26 become growth arrest attractors (Growth_Arrest = 1, Apoptosis = 0, Proliferation = 0), thus determining loss of apoptotic attractors obtained in r26. red3 r29 Epigenetic gene silencing of GADD45 family members has been frequently observed in several types of human cancers [69]. In presence of DNA_damage (main GADD45 activator), Growth_Arrest and Apoptosis components permanently oscillate when GADD45 is silenced, suggesting less propensity to cell death. Apoptotic stable states are still reached in presence of TGFBR_stimulus red3 r30 ERK increases transcription of the cyclin genes and facilitates the formation of active Cyc/CDK complexes, leading to cell proliferation [89]. ERK gain-of-function always leads to proliferative attractors (Proliferation = 1, Growth_Arrest = Apoptosis = 0), in the absence of other stimuli. red3 r31 ERK disrupts the anti-proliferative effects of TGFb [11]. Whereas TGFBR_stimulus leads to an apoptotic stable state (r24), coupling of TGFBR_stimulus with ERK gain-of-function only leads to permanent growth arrest (Growth_Arrest = 1, Apoptosis = 0). red3 r32 JNK might reduce RAS-dependent tumour formation by inhibiting proliferation and promoting apoptosis [88]. In absence of other stimuli, JNK constitutive activation completely abrogates RAS-dependent proliferation following RAS over-expression (r18). Instead, apoptotic attractors are always reached. Asterisks denote facts explicitly related to bladder cancer, whereas unmarked entries correspond to generic or loosely specified mechanisms. Full simulation results can be found in Dataset S3, with the help of the identifiers provided in the first two columns. doi:10.1371/journal.pcbi.1003286.t001 Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 9 October 2013 \| Volume 9 \| Issue 10 \| e1003286 [75]; the other accounting for PKC-mediated negative effects [74,76]. Concomitant disruptions of these feedbacks in our model lead to simulation results equivalent to those obtained with receptor gain-of-function (cf. Figure 2 and Table S2), whereas disruption of any other downstream negative feedback does not qualitatively influence the outcome (data not shown). This is also in agreement with the results obtained by Orton et al., who proposed that the degradation of receptors (e.g. rather than SOS inhibition by RSK) could be the main mechanism determining a transient activation of ERK pathway in response to growth factors. Role of Sprouty-mediated feedbacks. According to our model simulations (Figure 4a), when EGFR is over-expressed (e.g. in the presence of an autocrine signal), in the absence of p53 activation, the outcome is proliferation. In contrast, when FGFR3 stimulus is present, two possible outcomes are observed in the absence of p53: a proliferative stable state and a non-proliferative stable state, the later with all phenotype variables set to 0. General hypotheses involving the interplay between the p53, RB and ERK pathways have been proposed to explain the different phenotypes experimentally observed in bladder carcino- mas [50,73], but the precise mechanisms have not been elucidated yet. A closer analysis of the regulatory graph shown in Figure 2 reveals several feedbacks. Interestingly, ERK exerts a positive feedback on EGFR but a negative feedback on FGFR3-activated FRS2, through Sprouty (SPRY in the model). Intuitively, this suggests that ERK strengthens EGFR stimulus but weakens FGFR3 stimulus, potentially explaining the different phenotypes observed. Additionally, GRB2 exerts a negative feedback on FRS2, which is in turn specifically activated by FGFR3. Disruption of EGFR activation by SPRY does not play an important role in the case of EGFR over-expression (which indeed corresponds to setting EGFR to 1 independently of its regulators). FRS2 inhibition by SPRY, but not by GRB2, tentatively plays an important role in the response of the MAPK network to FGFR3 activating mutation. Indeed, disrupting the latter inhibition (Figure 5) does not affect significantly the model behaviour. On the contrary, comparison of Figures 4a–b and Figure 5 indicates that SPRY-dependent inhibition of FRS2 might be the key to explain the difference between the responses to EGFR and FGFR3 stimulations (i.e. in the absence of this inhibition, the model behaves equivalently in the two cases). To further clarify these mechanisms, we considered the role of functional positive circuits, which are known to promote multi- stable behaviours (cf. Methods). According to our model analysis, the GAB1-PI3K-GAB1 circuit underlies the coexistence of the two stable states found in the presence of FGFR3 activating mutation, but in the absence of p53 activation. We thus propose that this circuit plays a fundamental role in FGFR3 signalling, constituting a switch between proliferative and non-proliferative phenotypes. The underlying mechanisms can be further clarified by a careful analysis of Figure 2. On the one hand, following FGFR3 stimulus, when PI3K activation is faster/stronger than ERK activation, cell proliferation is enabled, because PI3K is definitively activated (due to the action of GAB1-PI3K-GAB1 positive circuit) and can then inhibit p21 through the PDK1/AKT pathway. ERK is then also activated, enhancing proliferation together with PI3K. On the other hand, upon ERK activation (coming from a rapid GRB2 and/or PKC mediated signalling), if the inhibition of GRB2 through the SPRY/FRS2 feedback is faster/stronger than PI3K activation, then PI3K cannot be activated anymore. In this scenario, ERK would rather contribute to disable cell prolifera- tion. Our model thus predicts that the strength/rapidity of PI3K activation versus SPRY-mediated ERK negative feedback could underly the less aggressive phenotypes observed in FGFR3- mutated bladder carcinomas. Figure 5. FGFR3 activating mutation and role of SPRY. Simulations were performed under FGFR3 gain-of-function (FGFR3 = 1 and all inputs set to 0, throughout the simulations). Simplified model dynamics are shown as in Figure 4a–b. Results are shown for the wild type model (red1 model reduction), as well as for perturbed model versions obtained by disrupting the inhibition of interest. doi:10.1371/journal.pcbi.1003286.g005 Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 10 October 2013 \| Volume 9 \| Issue 10 \| e1003286 MAPK cross-talk mechanisms. Using our logical model, we further addressed the roles of cross-talks between the different MAPK cascades, in particular those involving phosphatases. We first analysed the negative cross-talks from p38/JNK cascades towards ERK cascade, which involve MEK inhibition by AP1 and the phosphatase PPP2CA [2]. In the context of either EGFR over-expression or FGFR3 activating mutation (Figure 6a), the disruption of these inhibitions mainly lead to the loss of apoptotic attractors (compare Figure 6a with Figure 4a–b). The lost attractors are ‘‘replaced’’ by new attractors characterised by growth arrest alone. These two cross-talks are thus presumably important for the triggering of apoptotic responses in the presence of growth factor receptor alterations. Indeed, in the absence of such cross-talks, p53 pathway is only able to induce growth arrest, but not apoptosis, precluding a complete anti-proliferative response. This is also true in the concomitant presence of DNA damage stimulus (data not shown). Finally, we examined the roles of p38 and JNK inhibitions by DUSP1 [77]. Following receptor (either EGFR or FGFR3) alteration, disruption of any of these two inhibitions results in a persistent silencing of ERK and a persistent activation of p53, as well as an activation of PI3K and an inactivation of AKT, which ultimately lead the system towards an apoptotic attractor (compare Figure 6b with Figure 4a–b). DUSP1-mediated cross-talks between the MAPK cascades thus tentatively underly proliferative responses in presence of growth factor receptor alterations, presumably via the inhibition of p53 pathway. Discussion We have presented a bottom-up modelling approach to gain insights into the influence of the complex MAPK signalling network on cancer cell fate decision. We started by collecting pieces of information from the literature and assembling them into a detailed reaction map, which served as source of information for further dynamical modelling. The resulting map is generic, meaning that it was drawn by using information coming from different experimental models. Based on specific biological questions, our dynamical logical modelling involved the abstraction of relevant information from the map and the drawing of a qualitative influence network (regulatory graph). Next, we assigned consistent logical rules to each component to enable logical simulations. In order to perform detailed analyses at reasonable computational costs, we derived reduced model versions preserving the main dynamical properties of the original model. The reduced versions can be considered as further abstractions of the MAPK network, explaining its qualitative behaviour in terms of selected molecular actors. Despite the fact that we made no use of quantitative data, and that we finally represented an extremely complex signalling network through a limited number of Boolean components, we were able to recapitulate its behaviour for diverse documented biological conditions. These results set the background to investigate the roles of poorly documented regulatory mechanisms. In this modelling study, we particularly focused on bladder cancer. Importantly, our simulations qualitatively recapitulated salient phenotypic differences observed in invasive versus non- invasive carcinomas, and allowed us to formulate reasonable hypotheses concerning the mechanisms determining such differ- ences. These hypotheses are readily amenable to experimental validation. Our MAPK network model can be considered as a module for the assembly of more comprehensive cancer-related network. From this point of view, it will be interesting to merge our model with other logical models implementing other aspects of cell fate decision, in particular the model proposed by Calzone et al. [78], Figure 6. Analysis of MAPK cross-talks by disruptions of specific interactions. a) Effects of the disruptions of the inhibitions of MEK by AP1 and the phosphatase PPP2CA. b) Effects of the disruption of the inhibition of p38 or of JNK by the phosphatase DUSP1. These simulations were performed after removing the corresponding interactions and blocking the level of the perturbed receptor to level 1 (with all inputs set to 0, throughout the simulation). doi:10.1371/journal.pcbi.1003286.g006 Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 11 October 2013 \| Volume 9 \| Issue 10 \| e1003286 which covers the interplays between NFkB pro-survival pathway, RIP1-dependent necrosis, and extrinsic/intrinsic apoptosis path- ways. In the Introduction, we highlighted the importance of specificity factors in determining signal specificity of the MAPK network and took this into consideration in the construction of the reaction map. However, given the heterogeneity of available information among the different MAPK cascades, we could not include all these factors in our logical model. Nonetheless, we considered some of them, including several feedbacks, cross-talks, phospha- tases and input stimuli. These allowed us to focus on interesting aspects and identify mechanisms potentially underlying the different responses of bladder cancer cells to different growth factor receptors (EGFR versus FGFR3). The role of SPRY-dependent down-regulation of FGFR3 signalling seems to be determinant for the decision between proliferative and non-proliferative response. Moreover, the model also suggests that the presence of PI3K/AKT, but not ERK, positively correlates with the presence of a proliferative phenotype. Nevertheless, ERK-related mechanisms (fastness/strength of ERK activation and activation of SPRY) seem to be determinant for driving the switch. Such different responses provide a striking example of how signals transduced by largely overlapping pathways can produce opposite effects. To explain this behaviour, we analysed the roles of specific model circuits, which are presumably extremely important in the phenotype choice. Our data further highlight the contribution of cross-talks among the MAPK cascades to cell fate decision. Other specificity factors, including scaffold proteins and sub-cellular localisation, should also be taken into consider- ation in the near future, as novel data on these factors will be gathered. This will require a regular updating of our MAPK reaction map, by including new findings related to cell fate decision. We interpreted the p53-independent response of the MAPK network to FGFR3 stimulus as a sort of balance between proliferative and non-proliferative phenotype. A decreased rate of cell proliferation might indeed explain the less aggressive phenotypes frequently observed in FGFR3-mutated bladder carcinomas, in comparison with EGFR over-expression cases. Interestingly, this behaviour can be further related with opposite effects of FGFR3 activation in other cell types. In particular, activating FGFR3 mutations have been associated with growth arrest in chondrocytes, whereas they enhance proliferation and/or transformation in several cancer types and skin disorders (e.g. bladder cancer, multiple myeloma, seborrheic keratosis, etc.) [79]. Tentatively, proper modifications (e.g. concerning the introduction of STAT-dependent pathways and tuning of AKT response to growth factors [80]) may enable our MAPK model to account for these observations. Finally, we are currently assessing a potential proliferative role of p38 in FGFR3-mutated bladder carcinomas (unpublished preliminary data), which might lead to further model refinement. To wrap up, the present study demonstrates how Boolean modelling can recapitulate salient dynamical properties of an extremely complex biological network. As further details are uncovered, our logical model could be refined and eventually translated into a more quantitative framework (e.g. using ODEs or stochastic equations). In a first step towards more quantitative simulations, a continuous time Boolean framework could be used to explicitly represent time dependencies [81]. Tentatively, this approach would allow us to recapitulate more precisely the differential effects of transient versus sustained ERK activation [33,37,82]. Combining the delineation of a detailed reaction map and that of a predictive logical model, this study can serve as a basis to develop (semi-)automatic tools to derive logical models from reaction maps. Indeed, the manual derivation of a logical model from a complex reaction map presents risks of misinterpretations of either map symbols or map annotations. Errors are particularly likely to happen when the model is not built by the author of the map. In this respect, recent rule-based languages used to derive more quantitative models could be used to systematically derive predictive logical models, although potentially at the cost of additional efforts to build reaction maps in a more rigorous fashion [83–85]. Supporting Information Dataset S1 MAPK reaction map. The png (map) and txt (annotations) files were directly exported from the corresponding CellDesigner file (Dataset S2). Map components are coloured to emphasise relevant classes of proteins. The default protein colour is light green, whereas the default gene colour is yellow. MAPK cascades are coloured with different blue gradations (from light to dark blue going down the cascade). Scaffold proteins are coloured in darker green; phosphatases are coloured in red. Complete graphical notations can be found at www.celldesigner.org. (ZIP) Dataset S2 CellDesigner file (xml format) of the MAPK reaction map. Species and reactions are annotated and identifiers of the corresponding sources of information (PubMed IDs) are provided. (XML) Dataset S3 Summary of the results of the main simulations performed in this work. The xls file includes three sheets, erresponding to a model reduction. For each simulation, we report here the simulation ID (referenced in the main text and in the model files provided in Dataset S4), the perturbations performed (e.g. ‘‘EGFRgain; p53loss’’ indicates that EGFR was set to 1 and p53 was set to 0 throughout the simulation), the inputs considered and the initials states (asterisks denote all possible combinations of initial states). The attractor types (along with the number of corresponding states within parentheses, in the case of cyclic attractors) are further reported, as well as the corresponding component values in the attractor: 1 or 0 for stable values; asterisks for oscillating values. (XLS) Dataset S4 GINsim model files. For each model version (the original large model, and the three reduced versions), a file is provided in the format (zginml) that can be opened with the software GINsim (http://ginsim.org/beta). Simulation parameters have been encoded to ease the reproduction of the experiments referenced in the main text. (ZIP) Table S1 Selected MAPK modelling studies. (PDF) Table S2 Logical rules for the MAPK comprehensive model. & = AND; \| = OR; ! = NOT. More details about modelling assumptions and references are provided in Table S4 (model documentation). (PDF) Table S3 Reduced MAPK models. We considered three alternative reductions of the MAPK model (columns), each preserving the input and phenotype components. Additional components (Selected observables) were kept depending on the simulations performed. The last row lists components that were Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 12 October 2013 \| Volume 9 \| Issue 10 \| e1003286 conserved because they turned out to be auto-regulated at some point during the reduction procedure. Such auto-regulations arise from the compression of longer circuits. (PDF) Table S4 MAPK model documentation. Following a brief general description, all the components of the MAPK model (comprehensive version) are reported, along with their corre- sponding logical rules and annotations, including modelling hypotheses and links to the main sources of information (PubMed and HGNC databases). (PDF) Text S1 Supplementary text encompassing two sections. The first one describes how we derived the logical model from the reaction map. The second one demonstrates how we checked that all cyclic attractors obtained for the MAPK model reductions indeed correspond to attractors of the original comprehensive model. (PDF) Text S2 Hierarchical transition graphs associated with receptor alterations. Model dynamics following either EGFR over-expres- sion or FGFR3 activating mutation (with all inputs set to 0, throughout the simulations) are depicted in two separated graphs, which were obtained using the reduced model version red1. For sake of simplicity, simulations were performed by using a single initial state with all the remaining variables set to 0 (the salient dynamics were preserved in these cases – cf. Dataset S3). The resulting hierarchical transition graphs (see Methods) are com- posed by different classes of nodes, emphasising strongly connected components (blue), and linear (non circular) pathways (pink). The attractors reached are represented at the bottom of the figures. Attractor colours refer to the corresponding phenotypes: red for proliferation, green for apoptosis, grey for no decision. Stables states are denoted by rectangles, while cyclic attractors are denoted by circles. The accompanying tables give the composition of each node of the corresponding HTG. For instance, the node cc1 of the HTG obtained for FGFR3 activating mutation corresponds to a strongly connected component of the state transition graph. The number of states belonging to it (i.e. 24), as well as the list of these states are listed in the table (asterisks denote all possible values for the corresponding variable). (PDF) Acknowledgments We thank Emmanuel Barillot, Claudine Chaouiya, Adrien Faure´, Je´roˆme Feret, Abibatou Mbodj and Aure´lien Naldi for many insightful discussions. We further thank Ozgu¨r Sahin and Andrei Zinovyev for their critical reading of earlier versions of this manuscript. Author Contributions Conceived and designed the experiments: LG LC FR DT. 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Physiology 17: 62–67. Modelling of MAPK Influence on Cell Fate Decision PLOS Computational Biology \| www.ploscompbiol.org 15 October 2013 \| Volume 9 \| Issue 10 \| e1003286	24250280	PDK1 = ( PI3K ) FRS2 = ( ( ( FGFR3 ) AND NOT ( SPRY ) ) AND NOT ( GRB2 ) ) MAX = ( p38 ) GAB1 = ( GRB2 ) OR ( PI3K ) PI3K = ( GAB1 ) OR ( RAS AND ( ( ( SOS ) ) ) ) AKT = ( ( PDK1 ) AND NOT ( PTEN ) ) p70 = ( PDK1 AND ( ( ( ERK ) ) ) ) ERK = ( MEK1_2 ) SOS = ( ( GRB2 ) AND NOT ( RSK ) ) JNK = ( TAK1 AND ( ( ( MAP3K1_3 ) ) ) ) OR ( MAP3K1_3 AND ( ( ( MTK1 ) ) ) ) OR ( MTK1 AND ( ( ( NOT DUSP1 ) ) ) ) OR ( TAOK AND ( ( ( NOT DUSP1 ) ) ) ) EGFR = ( ( ( SPRY ) AND NOT ( GRB2 ) ) AND NOT ( PKC ) ) OR ( ( ( EGFR_stimulus ) AND NOT ( GRB2 ) ) AND NOT ( PKC ) ) p53 = ( p38 AND ( ( ( NOT MDM2 ) ) ) ) OR ( ATM AND ( ( ( p38 ) ) ) ) RAF = ( ( ( PKC ) AND NOT ( AKT ) ) AND NOT ( ERK ) ) OR ( ( ( RAS ) AND NOT ( AKT ) ) AND NOT ( ERK ) ) RAS = ( SOS ) OR ( PLCG ) GRB2 = ( EGFR ) OR ( FRS2 ) OR ( TGFBR ) MSK = ( p38 ) OR ( ERK ) SPRY = ( ERK ) MYC = ( MSK AND ( ( ( MAX ) ) ) ) RSK = ( ERK ) FOXO3 = ( ( JNK ) AND NOT ( AKT ) ) MEK1_2 = ( ( ( RAF ) AND NOT ( PPP2CA ) ) AND NOT ( AP1 ) ) OR ( ( ( MAP3K1_3 ) AND NOT ( PPP2CA ) ) AND NOT ( AP1 ) ) PPP2CA = ( p38 ) DUSP1 = ( CREB ) PLCG = ( EGFR ) OR ( FGFR3 ) FOS = ( ERK AND ( ( ( RSK ) AND ( ( ( ELK1 OR CREB ) ) ) ) ) ) TGFBR = ( TGFBR_stimulus ) ATM = ( DNA_damage ) JUN = ( JNK ) Proliferation = ( ( p70 AND ( ( ( MYC ) ) ) ) AND NOT ( p21 ) ) GADD45 = ( SMAD ) OR ( p53 ) p21 = ( ( p53 ) AND NOT ( AKT ) ) FGFR3 = ( ( ( FGFR3_stimulus ) AND NOT ( PKC ) ) AND NOT ( GRB2 ) ) MAP3K1_3 = ( RAS ) TAOK = ( ATM ) AP1 = ( JUN AND ( ( ( ATF2 OR FOS ) ) ) ) ELK1 = ( p38 ) OR ( JNK ) OR ( ERK ) PKC = ( PLCG ) BCL2 = ( CREB AND ( ( ( AKT ) ) ) ) PTEN = ( p53 ) p38 = ( TAK1 AND ( ( ( NOT DUSP1 ) ) ) ) OR ( MAP3K1_3 AND ( ( ( NOT DUSP1 ) ) ) ) OR ( MTK1 AND ( ( ( NOT DUSP1 ) ) ) ) OR ( TAOK AND ( ( ( MTK1 ) ) ) ) Apoptosis = ( ( ( FOXO3 AND ( ( ( p53 ) ) ) ) AND NOT ( ERK ) ) AND NOT ( BCL2 ) ) Growth_Arrest = ( p21 ) MDM2 = ( ( AKT ) AND NOT ( p14 ) ) OR ( ( p53 ) AND NOT ( p14 ) ) CREB = ( MSK ) TAK1 = ( TGFBR ) MTK1 = ( GADD45 ) ATF2 = ( p38 ) OR ( JNK ) p14 = ( MYC ) SMAD = ( TGFBR )
Boolean ErbB network reconstructions and perturbation simulations reveal individual drug response in different breast cancer cell lines von der Heyde et al. von der Heyde et al. BMC Systems Biology 2014, 8:75 http://www.biomedcentral.com/1752-0509/8/75 von der Heyde et al. BMC Systems Biology 2014, 8:75 http://www.biomedcentral.com/1752-0509/8/75 RESEARCH ARTICLE Open Access Boolean ErbB network reconstructions and perturbation simulations reveal individual drug response in different breast cancer cell lines Silvia von der Heyde1, Christian Bender2, Frauke Henjes3, Johanna Sonntag4, Ulrike Korf4 and Tim Beißbarth1* Abstract Background: Despite promising progress in targeted breast cancer therapy, drug resistance remains challenging. The monoclonal antibody drugs trastuzumab and pertuzumab as well as the small molecule inhibitor erlotinib were designed to prevent ErbB-2 and ErbB-1 receptor induced deregulated protein signalling, contributing to tumour progression. The oncogenic potential of ErbB receptors unfolds in case of overexpression or mutations. Dimerisation with other receptors allows to bypass pathway blockades. Our intention is to reconstruct the ErbB network to reveal resistance mechanisms. We used longitudinal proteomic data of ErbB receptors and downstream targets in the ErbB-2 amplified breast cancer cell lines BT474, SKBR3 and HCC1954 treated with erlotinib, trastuzumab or pertuzumab, alone or combined, up to 60 minutes and 30 hours, respectively. In a Boolean modelling approach, signalling networks were reconstructed based on these data in a cell line and time course specific manner, including prior literature knowledge. Finally, we simulated network response to inhibitor combinations to detect signalling nodes reflecting growth inhibition. Results: The networks pointed to cell line specific activation patterns of the MAPK and PI3K pathway. In BT474, the PI3K signal route was favoured, while in SKBR3, novel edges highlighted MAPK signalling. In HCC1954, the inferred edges stimulated both pathways. For example, we uncovered feedback loops amplifying PI3K signalling, in line with the known trastuzumab resistance of this cell line. In the perturbation simulations on the short-term networks, we analysed ERK1/2, AKT and p70S6K. The results indicated a pathway specific drug response, driven by the type of growth factor stimulus. HCC1954 revealed an edgetic type of PIK3CA-mutation, contributing to trastuzumab inefficacy. Drug impact on the AKT and ERK1/2 signalling axes is mirrored by effects on RB and RPS6, relating to phenotypic events like cell growth or proliferation. Therefore, we additionally analysed RB and RPS6 in the long-term networks. Conclusions: We derived protein interaction models for three breast cancer cell lines. Changes compared to the common reference network hint towards individual characteristics and potential drug resistance mechanisms. Simulation of perturbations were consistent with the experimental data, confirming our combined reverse and forward engineering approach as valuable for drug discovery and personalised medicine. Keywords: ErbB, RPPA, Network reconstruction, Boolean model, Breast cancer cell line, Drug resistance *Correspondence: tim.beissbarth@ams.med.uni-goettingen.de 1Statistical Bioinformatics, Department of Medical Statistics, University Medical Center Göttingen, Humboldtallee 32, 37073 Göttingen, Germany Full list of author information is available at the end of the article © 2014 von der Heyde et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 2 of 21 http://www.biomedcentral.com/1752-0509/8/75 Background Longitudinal time course data are the basis for modelling signalling networks in a holistic systems biology approach in order to uncover mechanisms of signal transduction dynamics [1,2]. Network models provide novel insight [3,4] and allow us to perform efficiently simulations to predict systems behaviour or evaluate certain hypotheses [5]. Furthermore, combining perturbation experiments with the measurements of system dynamics seems to be even more efficient than time series data on their own [6-8]. Knock-outs or stimuli as directed perturba- tions support the systematic identification of regulatory relationships. Quantitative models, based on differential equations, require explicit knowledge on the kinetics of the sys- tem of interest [9-12]. In contrast, the qualitative Boolean abstraction considers the components’ states as binary variables, being either active (1) or passive (0), but nev- ertheless encompasses the essential functionality [13,14]. Wang et al. stressed, that Boolean models have already been successfully applied in reverse engineering of pro- teomic signalling networks, and their reduced complexity is considered to be especially advantageous for large- scale systems [15]. To avoid the drawbacks of purely data- or literature-driven algorithms regarding completeness, generalisation or interpretability, combined approaches become more and more prominent in the area of net- work reconstruction [6,16,17]. Some reverse engineering approaches, like ddepn [6] or CellNOptR [18], ideally join perturbed time course input data and literature prior knowledge in network reconstruction, while preserving the simplicity of Boolean logic at the same time. Forward engineering methods allow subsequent analysis of the sta- ble states of the reconstructed system. Hence, this may allow to deduce possible long-term behaviour of compo- nents activity under perturbations. Such approaches are integrated and freely available in the open source Python software package BooleanNet [19] or in the R [20] pack- age BoolNet [21], for example. As reviewed by Samaga and Klampt [22], several software tools can be applied for the dynamic modeling of logical signal transduction net- works. Among others, they exemplarily mentioned GIN- sim [23], SQUAD [24], BooleanNet [19], ChemChains [25], Odefy [26], and BoolNet [21]. Here we focus on protein signalling networks in breast cancer, representing the most common cancer type among women [27]. Breast cancer, as a heterogeneous disease, can be divided into subgroups, which differ in cellular properties as well as in prognosis. This requires individual therapy approaches, which are in the focus of current research and have partially already been realised. Here we are interested in the ‘HER2-positive’ subtype of breast cancer, overexpressing the human epidermal growth factor receptor 2 (HER2, also termed ErbB-2). ErbB-2 is a receptor tyrosine kinase (RTK) and mem- ber of the epidermal growth factor (EGF) receptor family, consisting of three further RTKs, namely ErbB-1, ErbB-3 and ErbB-4. These receptors cooperatively function as homo- or heterodimers after activation via growth fac- tors like EGF for ErbB-1 or heregulin (HRG) for ErbB-3 [28]. This initialises signalling cascades, pathologically contributing to tumourigenesis and tumour progression. Interestingly, different dimer formations induce different signalling pathways, like PI3K and MAPK, also with dif- fering signalling strengths [29]. The role of the orphan receptor ErbB-2 in dysregulation of the ErbB network is of major interest, due to its overexpression in 10- 20% of breast tumours, diagnosed as HER2-positive. Furthermore, its role as favoured dimerisation part- ner independent on ligand-activation implies oncogenic potential [30-32]. The therapeutic antibodies trastuzumab and pertuzumab have especially been designed to target ErbB-2 [33]. However, frequently occurring therapy resistance reduces the efficiency of targeted therapeutics [34-36]. This resistance is often associated with deregulated path- way activity [37,38] or bypasses via other RTKs, especially ErbB family members [39]. Mainly ErbB-1 expression has been anticipated as molecular cause to overcome impact of ErbB-2 targeting drugs. Small-molecule inhibitors such as erlotinib are already in use against non-small cell lung cancer [40] and pancreatic cancer [41]. Here we aim as a first step at the identification of individual drug response patterns and insights into drug resistance in HER2-positive breast cancer. ErbB-2 ampli- fied cell lines were therefore subjected to short- and long-term drug treatment with erlotinib, pertuzumab and trastuzumab, alone or in combinations. Samples were analysed by reverse-phase protein arrays (RPPA) [42]. We were interested in synergistic benefits of combining erlotinib, pertuzumab or trastuzumab in ErbB-1 express- ing, ErbB-2 amplified tumours with differing resistance phenotypes. Therefore three representative breast cancer cell lines were selected as model systems, namely BT474, SKBR3 and HCC1954, of which the latter is known to be trastuzumab resistant due to a PIK3CA mutation, while BT474 exhibits wild type behaviour [43]. The SKBR3 cell line is supposed to be pertuzumab resistant [44]. ErbB dimers predominantly activate the MAPK and PI3K pathway [29]. Therefore, we concentrated on the involved key regulators in fast downstream signalling. Among those were ERK1/2 and AKT, and also p70S6K, which is upstream influenced by both of the signalling axes. Phosphorylation of RPS6 and RB was used as long- term indicator for proliferation, cell cycle or tumour progression [28]. Prior literature knowledge on ErbB sig- nalling was used as input for protein network reconstruc- tion per cell line via ddepn. Beyond that, we inferred von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 3 of 21 http://www.biomedcentral.com/1752-0509/8/75 combined therapies that target ErbB family members, cus- tomised to the topology of the different subtypes. BoolNet was applied to compute stable cycles of protein activ- ity states, so-called attractors, incorporating all possible treatment combinations. This way, optimal drug treat- ment to deactivate oncogenic proteins was identified. Methods Data Protein abundance and phosphorylation measurements in BT474, SKBR3 and HCC1954 cells were carried out as described by Henjes et al. [28]. In principle, the RPPA pro- tein array technology works as follows. Minimal amounts (1 nl volume) of cell lysate are spotted along with a serial dilution of control samples on nitrocellulose-coated glass slides using a printing robot (Aushon 2470 arrayer). Sam- ples are organised as ordered subarrays so that they are addressable during the data analysis procedure, and a sin- gle slide can accommodate one or more subarrays. Each subarray is analysed using a highly specific detection anti- body to measure the abundance of a certain protein or its phosphorylation rate. For each spot, the ratio of bound detection antibody is visualised using secondary antibod- ies labelled with near infrared (NIR) fluorescent dyes. Slides are scanned using the Odyssey scanner (LiCor Bio- sciences). Spot intensities are determined using a microar- ray image analysis software (GenePix). Apart from the quantitative character, another advan- tage of the technology is the handling of large sample sets which protein abundance can be detected simultaneously in a high throughput fashion. 20-200 identical slides can be produced in parallel in a single print run. In order to normalise the data spot-wise for deviant total protein concentrations due to spotting variance, staining with Fast Green FCF dye was employed [42]. There- fore, one slide was stained with the dye to determine the total protein content of each lysate spot and correspond- ing signal intensity correction factors. The spots on the remaining slides were divided by these correction factors and afterwards multiplied by the median value to scale the data back to the native range. The RPPA data used here include data presented in Henjes et al. [28]. Additionally, further targets have been measured and were used for network reconstruction. The complete data set has been submitted to the Gene Expres- sion Omnibus (GEO) with accession number GSE50109. Short-term measurements In the short-term measurements, trastuzumab, per- tuzumab and erlotinib were added to the cells in starva- tion medium one hour before stimulation with the growth factors EGF and HRG. All possible 24 combinations of drugs and stimuli were measured. Application of the stim- uli was defined as time point zero in the measurements. The growth factors were chosen to activate explicitly the MAPK and PI3K pathway. Lysate preparation was per- formed at ten time points, namely after 0, 4, 8, 12, 16, 20, 30, 40, 50 and 60 minutes. The drug treatment exper- iments comprised three biological replicates, whereas the inhibitor-free experiments incorporated five biological replicates. The experiments for the SKBR3 cell line com- prised only two biological replicates of HRG stimulated cells under the triple drug combination. Each biological replicate was spotted in triplicate on the RPPA slides. To obtain short-term signal intensities, eleven antibodies for specific phosphorylation sites were selected according to quality checks, including inspection of corresponding dilution series and comparison to signals arising from sec- ondary antibodies only. The chosen target proteins and respective antibodies are listed in Additional file 1. Long-term measurements For long-term measurements, no explicit ligand stimu- lation was performed. Instead, cells were incubated in full growth medium for 24 hours prior to adding the three mentioned therapeutics in double combinations or as triplet. Single drug treatment was just conducted with erlotinib. Full growth medium was used to avoid con- founding effects of nutrient deficiency. Protein abundance was also quantified without any drug application. The measuring points included 0, 1, 2, 4, 6, 8, 12, 18, 24 and 30 hours with three biological and technical replicates each. At time point 18, only two biological replicates were avail- able. Additional file 1 displays the 21 targets of interest for long-term signalling. Statistical inference of drug effects To determine, whether a specific drug treatment revealed an inhibiting effect on the signal intensities of the proteins, we applied the following method. Firstly, for each protein and (combinatorial) drug treatment we linearly modelled the signal intensities as depending on the factors time and group, i.e. no drug treatment versus drug treatment. If the interaction of both factors showed a significant (p-value < 0.05) influence on the signal intensity, we further applied a Wilcoxon rank sum test for the measurements at time point 60 minutes for the short-term data, or at time point 30 hours for the long-term data. Thereby, we tested for significantly (p-value < 0.05) smaller intensity values in the drug treated group. The drug treatments with a sig- nificant test result were considered as efficient inhibitors. The therapeutic (combination) with the smallest p-value was defined as the optimal one. Literature prior knowledge We manually determined two reference networks, i.e. one for each time course, as initial joint hypotheses for all of the three breast cancer cell lines. Because emphasis von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 4 of 21 http://www.biomedcentral.com/1752-0509/8/75 was put on phosphoproteomic signalling, this was mainly based on PhosphoSitePlus® [45]. Several publications con- firm these assumptions, as depicted in Additional file 2. Network reconstruction For Boolean network reconstruction, we chose the method of dynamic deterministic effects propagation net- works (DDEPN) [6]. This method was particularly tailored to perturbed longitudinal protein phosphorylation data. It is based on the DEPN approach [46], which stands for deterministic effects propagation networks. The deter- minism is related to the way of perturbation effect prop- agation in the networks from parent to child nodes, implying transitively closed graphs. The dynamic version of Bender et al. [6,47] differs with respect to the integra- tion of perturbed time course measurements. While the DEPN approach requires many perturbations, like knock- downs, but only few time points, which are regarded as independent measurements, ddepn is designed for longer time series without the necessity of many or all network nodes being perturbed. The latter situation, i.e. few per- turbations by drug interventions, reflected the design of the RPPA experiments under consideration here, hence leading to the application of ddepn. Most network recon- struction algorithms have been designed for gene expres- sion data from microarray measurements [7], which differ from (phospho-)protein data regarding the amount of involved network nodes. Many current methods are tai- lored to the inference of gene regulatory networks based on static measurements at one time point, reflecting the steady state of the system under consideration [48]. The longitudinal time course data used here require a suitable method, as provided by ddepn. The method of Bender et al. was shown to outperform two dynamical Bayesian network approaches, and to be capable of inferring known signalling cascades in the ErbB pathway [47]. A further advantage was the public availability of ddepn as an R [20] package. The reconstruction procedure is depicted in Additional file 3, and the core elements are described according to [6,47] in the following. The protein interaction net- works are modelled as directed, possibly cyclic, graphs, with nodes V = {vi : i ∈1, . . . , N} representing proteins and edges representing interactions. Also the external per- turbations, i.e. the drugs and growth factors in our case, are modelled as nodes. The edge types can be either acti- vating or inhibiting, denoted by 1 and -1, respectively, in the adjacency matrix = V × V →{0, 1, −1} of the network. An entry of zero indicates no edge between two nodes. So each edge incorporates a pair of nodes φij : i, j ∈1, . . . , N . The measurement data, which form the basis for the reconstruction, are stored in a matrix D = {ditr : i ∈1, . . . , N, t ∈1, . . . , T, r ∈1, . . . , R}, consid- ering T time points and R replicates. For the inference of a network structure, optimally fitting to the data, we applied the stochastic Markov Chain Monte Carlo (MCMC) approach of ddepn, called inhibMCMC, in which the space of possible networks is sampled, based on posterior probabilities. It extends a Metropolis-Hastings type of MCMC sampler by the capability of sampling two edge types directly, i.e. acti- vation and inhibition. The posterior distribution of a network given the data D, is defined as P(\|D) = P(D\|)P() P(D) ∝P(D\|)P(), with P() as the prior prob- ability distribution and P(D\|) as the likelihood of the data given the network. The latter is defined in [47] as p(D\|) = p(D\| ˆ∗, ˆ) = T t=1 N i=1 R r=1 p(ditr\| ˆθi ˆγ ∗ itr), where ∗= γ ∗ itr : i ∈1, . . . , N, t ∈1, . . . , T, r ∈1, . . . , R denotes the optimized system state matrix, containing active and passive states per protein and time point. It is estimated in the following way. Assuming that the pro- teins can be either active (1) or inactive (0), signalling dynamics are modelled by Boolean signal propagation for a given network. All nodes, except the permanently active perturbations, are therefore initialised with inactive states. The transition rule is that children nodes get acti- vated if at least one activating parent node is active and all inhibiting ones are inactive. In this way, all reachable system states are computed and stored in a matrix = {γik ∈{0, 1} : i ∈1, . . . , N, k ∈1, . . . , M}, holding column- wise the activation states of all proteins at transition step k. The amount of transitions is limited by 0 < M ≤2N. This state matrix has to be optimized, as it is not related to the measured time points yet. The true unknown state sequence over time is represented by ∗, which is esti- mated by a hidden Markov model (HMM). The resulting ˆ∗indicates whether a data point ditr has an underlying active (1) or passive (0) normal distribution ditr ∼ N (μi0, σi0), if ˆγ ∗ itr = 0 N (μi1, σi1), if ˆγ ∗ itr = 1. The distribution parameters are for each protein esti- mated as empirical mean and standard deviation of all measurements for the considered protein in the cor- responding class, yielding the parameter matrix ˆ = ˆθi0, ˆθi1 = ( ˆμi0, ˆσi0), ( ˆμi1, ˆσi1) ∀i ∈1, . . . , N. The prior probability distribution P() includes penali- sation of differences between the network structure and a user-defined prior belief B = V × V →[−1, 1], where the absolute value correlates with the confidence in an edge. Here we chose B = V × V →{0, 1, −1}, assum- ing in advance specific activating, inhibiting or missing edges with maximum confidence. We made use of the Laplace prior model (laplaceinhib), accounting for both edge types, i.e. activation and inhibition. The prior belief von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 5 of 21 http://www.biomedcentral.com/1752-0509/8/75 for an edge is defined as P(φij\|bij, λ, γ ) = 1 2λe − ij λ , includ- ing a weighted difference term ij = \|φij −bij\|γ with a weight exponent γ ∈R+. As the edge probabilities are assumed to be independent, the prior belief for a net- work structure is derived as the product of those, i.e. P(\|B, λ, γ ) = i,j P(φij\|bij, λ, γ ), i, j ∈{1, . . . , N}. The individual edge probabilities lie between 0 and 1 2λ ∀λ, γ ∈ R+. The protein interactions corresponding to our cho- sen prior are displayed in Additional file 2. The prior’s impact strength was emphasised in such a way, that only strongly deviating data influence the network structure, because the ErbB wiring as well as the MAPK and PI3K pathways are well examined in literature. This prioritisa- tion is reflected in the hyperparameter λ set to 0.0001. For the parameter γ we chose one, neglecting extra penali- sation of deviation from the prior. These settings should preserve robustness, but at the same time allow enough impact strength of strongly differing data values. The network inference via inhibMCMC spanned 50,000 iterations with the first 25,000 iterative steps as burn-in phase. To ensure convergence, ten parallel MCMC chains were run, each initialised with a starting network. Con- vergence was validated via Gelman diagnostic [49]. Nine of the initial ten networks were randomly generated, i.e. for the defined nodes activating, inhibiting or no edges were sampled. The remaining network assumed no con- nections between the nodes. These initial networks were pruned to the following constraints. Firstly, the nodes related to the growth factors and drugs must not have any ingoing edges. Above that, the indegree of all nodes was limited to four. Finally, no self-loops were allowed. To find significantly occurring edges among the indepen- dent runs, merging into a consensus network, a Wilcoxon rank sum testing procedure was used. In detail, in each run the amount of sampled activations and inhibitions per edge was counted and divided by the total number of sam- pled edges. Subsequently the null-hypothesis was tested, whether the means of these ten edge-specific confidence values equal the same for activation and inhibition. In case of not rejecting the null-hypothesis, coming along with an adjusted p-value exceeding the significance level α = 0.05, no edge was assumed. Otherwise, the respective alter- native determined the type of interaction. Adjustment for multiple testing followed the method of Benjamini and Hochberg, controlling the false discovery rate [50]. The whole procedure was embedded into a leave-one- out cross-validation approach. So each of the ten MCMC chains was left out once, and the testing algorithm was applied to the remaining runs. An edge was included in the final consensus network if it occurred in all of the cross validation runs. Finally, to prevent excessive spuri- ous or obsolete connections ascribable to transitivity, as argued by Bo Na Ki et al. [51], newly reconstructed edges were successively added to the prior network according to ddepn significance and fit of resulting attractor states to the observations of Henjes et al. [28]. Perturbation simulations To figure out which input of drug combination leads to a certain attractor state of the reconstructed network system, the R package BoolNet [21] was applied. The moti- vation was based on the assumption that attractors, rep- resenting cycles of states, comprise the stable states of cell function. In those states networks mostly reside. Hence, they mirror system phenotypes, dependent on the pertur- bation context. To the best of our knowledge, apart from BoolNet, there are hardly any R packages offering attractor calculations for Boolean networks. This package supports import of networks in form of files containing Boolean formulas. So it could be easily integrated in our workflow as subsequent analysis step after network reconstruction. We used its functionality to identify attractors in a syn- chronous and an asynchronous way. The resulting attrac- tors were steady-state attractors. These consist of only one state, in which all transitions from this state result. These attractors are identical for synchronous and asyn- chronous updates. We focused on the steady-states, as these should reflect the homoeostatic system state of the cell lines. Intermediate transition states would be interest- ing as well, but due to the large amount of the involved targets, it would have been too complex to analyse those here in detail. The search started from predefined initial states of the network nodes. The drug and growth factor nodes were fixed to specific values, reflecting the conducted experiment to be simulated. For short-term signalling, perturbations included all possible combinations of the therapeutics under the combined stimulus of EGF and HRG. Although the data of separate stimulation with EGF and HRG was used for network reconstructions, here we focused on the combined treatment, representing a more natural tumour environment than a single growth factor alone. Two possible binary states, i.e. active (1) or pas- sive (0), to the power of three different drugs led to eight possible combinations. These were used as fixed input conditions, as the effect was assumed to be continuously valid. Analogously, the growth factors were permanently fixed to one. The remaining protein activity start states were initialised with zero. These components were flexi- ble towards updates. In the long-term measurements, no growth factors were involved but full growth medium. This was defined as one stimulating input S, initially acti- vating the ErbB receptors. This also led to eight fixed input combinations. BoolNet expects network representation in form of log- ical interaction rules as input. In contrast, ddepn deliv- ers network reconstruction output in terms of adjacency von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 6 of 21 http://www.biomedcentral.com/1752-0509/8/75 matrices. Therefore, we incorporated an interface func- tion into the ddepn package, called adjacencyMa- trix_to_logicalRules. In detail, the loadNetwork function of BoolNet requires a file containing row-wise logical acti- vation rules of each network node. Each row looks like ‘target node, (activator_1 \| activator_2) & !(inhibitor_1 \| inhibitor_2)’, here exemplary for a node with two ingo- ing activating and inhibiting edges each. The logical OR operator is encoded by ‘\|’, the logical AND is encoded by ‘&’, and logical negation is represented by ‘!’. Accord- ingly, all of the A inferred activating nodes V+ = {va : a ∈1, . . . , A, A < N} of a target node vj, represented by an adjacency matrix entry φaj = 1, and vj itself were connected via OR operators. This ensured that at least one of the activators or the target protein itself had to be active to activate the target node. Analogously, the I inhibiting nodes V−= {vi : i ∈1, . . . , I, I < N} with φij = −1 were connected via OR operators. A logical negation opera- tor was attached to ensure that the activity of one of the nodes vi would result in an inactive node vj. Both sets of activators and negated inhibitors were then connected via a logical AND operator. After conversion of the adja- cency matrices to logical rules, those were implemented in BoolNet into a computational model, to perform per- turbation simulations per cell line and time course as well as subsequent analyses of the resulting attractor states. Results and discussion The complete workflow, holding for both, short- and long-term analysis, is depicted in Figure 1. For a better understanding of the discussion on MAPK and PI3K sig- nalling, Figure 2 displays the interactions between the main MAPK and PI3K targets of the ErbB prior net- works. It shows the preferred pathway activations by all possible homo- and heterodimers formed upon ligand binding to the ErbB-1 and ErbB-3 receptors [9,29,52-54]. The confidence values, representing the likeliness of the reconstructed network edges, are shown in Additional file 4. Short-term signalling network reconstruction The short-term signalling networks, reconstructed by the ddepn algorithm, are depicted in Figure 3. The equivalent Boolean logical interaction rules are listed in Additional file 5. In comparison to the prior network, newly inferred edges were specific for each cell line, and all of them were activating. For HCC1954 and BT474, seven addi- tional edges were reconstructed, while in SKBR3 only two new edges were reconstructed. No prior edge deletion or type reversal took place. HCC1954 is driven by the PI3K as well as the MAPK pathway In HCC1954, the new edges contributed to both, PI3K and MAPK, signalling. The interaction ErbB-1→ErbB-2 reflected a dominant role of heterodimerisation of both receptors, as described by Henjes et al. [28]. The fact that it was specifically inferred for HCC1954, pointed to hyperactive ErbB-1/2 heterodimers here. These are known to trigger the MAPK but also, to a lesser extent, the PI3K pathway. The link PDK1→MEK1/2, supported by Sato et al. [55], stressed crosstalk between these path- ways, placing PDK1 into a key position in the PI3K pathway, and MEK1/2 in the MAPK pathway, respec- tively. Two of the new edges in HCC1954, PDK1→ErbB-2 and p70S6K→AKT, contributed to feedback loops, which were not present in the other two cell lines. Such a topological network element could stabilise the known trastuzumab resistance by boosting the oncogenic effect of ErbB-2 and the mutant hyperactive PI3K pathway. Evi- dence for the feedback mechanism involving PDK1 was provided by Maurer et al. [56] and Tseng et al. [57]. Vega et al. noted an indirect activation of AKT by p70S6K via mTOR [58]. BT474 is driven by the PI3K pathway, while SKBR3 is driven by the MAPK pathway Comparably to HCC1954, in BT474 an edge indicat- ing hyperactive heterodimers was found, namely ErbB- 3→ErbB-2, here interestingly with a strong impact on AKT [28]. BT474 is known to contain a rare type of PIK3CA mutation [43]. Pathway crosstalk was also observed in BT474, but here MEK1/2 activated PDK1, and not vice versa like in HCC1954. This edge was supported by Frödin et al. [59], underlining dominant PI3K signalling in this cell line. The newly detected interactions in SKBR3 started from ErbB-3 and PDK1, and both activated ERK1/2. This reflected a dominant MAPK pathway, in which ErbB- 3→ERK1/2 was interpretable as indirect stimulation of ERK1/2 via MEK1/2, activated by ErbB-2/3 dimers [55]. Perturbation simulations on short-term networks Perturbations included all possible combinations of the therapeutics erlotinib, pertuzumab and trastuzumab under combined stimulation of EGF and HRG. All inferred attractors were simple and consisted of one steady-state. This means that all transitions from this state result in the state itself. Table 1 summarises all simula- tion outcomes for the attractors of the AKT and ERK1/2 proteins, as those are key players in the PI3K (AKT) and MAPK (ERK1/2) pathways. Additionally, the results for p70S6K are listed there, as both pathways regulate this protein [60]. Stimulation with EGF and HRG should result in acti- vation of ErbB-1 and ErbB-3, followed by dimerisation amongst ErbB members. This should initialise signalling cascades in the MAPK and PI3K pathways (Figure 2). Indeed, AKT, ERK1/2 and p70S6K got activated in von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 7 of 21 http://www.biomedcentral.com/1752-0509/8/75 Figure 1 Modelling workflow. The figure summarises the applied modelling approach. RPPA data of three individual breast cancer cell lines were generated under short- and long-term drug treatment. They constituted the basis for network reconstruction in combination with prior literature knowledge about protein wiring. The reconstructed networks per cell line and time course in turn underwent Boolean perturbation simulations to reveal optimal drug treatments. all cell lines, which was revealed by simulations as well as observations in graphical analyses (Table 1, Figures 4, 5, 6). As we were interested in identifying optimal drug treat- ments, Table 2 summarises the corresponding statistical results. Most of them were supported by the perturbation von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 8 of 21 http://www.biomedcentral.com/1752-0509/8/75 Figure 2 Scheme of ErbB dimers related MAPK and PI3K pathway activation. The figure depicts the different homo- and heterodimers of ErbB receptors, induced upon activation via the ligands EGF or HRG. The active dimers then initialise the MAPK and PI3K signalling cascades. The orange (PI3K) and green (MAPK) arrows denote, which dimer activates which pathway. simulation results, corresponding to attractor states of AKT, ERK1/2 and p70S6K being zero. Four main con- clusions were drawn from these results, which will be discussed in detail in the following subsections. Firstly, inhibition of PI3K signalling, reflected by downregulated AKT, required the combined treatment with erlotinib, pertuzumab and trastuzumab. Secondly, inhibition of the MAPK pathway, represented by ERK1/2, was reached with erlotinib alone in SKBR3 and HCC1954. BT474 addi- tionally needed pertuzumab. Thirdly, the protein activity of p70S6K was influenced by both, PI3K and MAPK, pathways. The drug response differed between cell lines, indicating both pathways contribute to a different extent. Finally, the drug effect on PI3K signalling was much better in SKBR3 than in HCC1954, pointing to resistance in the latter cell line. Inhibition of PI3K signalling requires drug combinations In SKBR3, the triple drug combination was most effec- tive in inhibiting AKT (Figure 4, Table 2). In BT474, pertuzumab combined with erlotinib was most effi- cient, but AKT signalling was not fully suppressed as in SKBR3 (Figure 5). Statistically, we did not infer any significant positive drug effect in this cell line. Obvi- ously, erlotinib in synergistic combination with at least pertuzumab was needed to block the ErbB-2 receptor and its heterodimerisation, mainly with ErbB-1, but also ErbB-3. The HRG activated ErbB-2/3 heterodimers and PI3K pathway in BT474, as revealed by the network reconstructions, might have prevented a potent drug efficacy. Interestingly, BT474 and SKBR3 required pertuzumab. This drug was especially designed to prevent het- erodimerisation with ErbB-2. The stimuli EGF and HRG together activate PI3K signalling by ErbB-2/3, ErbB- 1/2 and ErbB-1/3 dimers (Figure 2). The need for pertuzumab combined with erlotinib indicated an impor- tant role of ErbB-1/2 dimers. This was supported by the fact, that in HCC1954 with dominant heterodimers of this type, as revealed by network reconstructions, none von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 9 of 21 http://www.biomedcentral.com/1752-0509/8/75 Figure 3 Reconstructed short-term signalling networks. The figure displays the reconstructed short-term signalling networks coloured according to the preserved prior reference network (black) and newly inferred (added) individual edges per cell line. Target proteins are represented as rectangles with stimuli and drugs coloured in red. The three drug names erlotinib, trastuzumab and pertuzumab are abbreviated via their first letters. Solid arrows denote activating interactions while dashed ones represent inhibitions. Table 1 Attractor states of short-term perturbation simulations BT474 HCC1954 SKBR3 Simulation AKT ERK1/2 p70S6K AKT ERK1/2 p70S6K AKT ERK1/2 p70S6K A E A E A E A E A E A E A E A E A E X 1 1 1 1 1 1 1 1 1 E 0 1 1 0 1 0 1 0 1 0 1 0 0 1 P 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 T 1 1 1 1 1 1 1 1 1 E, P 1 1 0 1 0 1 0 0 1 0 0 0 0 1 E, T 0 1 1 0 1 1 0 1 1 0 1 0 0 1 P, T 1 1 1 0 1 0 0 1 0 0 0 1 E, P, T 1 1 0 1 0 1 0 0 1 0 0 0 The therapeutics erlotinib, trastuzumab and pertuzumab, abbreviated by first letters, that were permanently active besides EGF and HRG in the simulated perturbation conditions are stored in the column Simulation. No simulated drug treatment is denoted by ‘X’. The A columns hold the attractor states of the proteins AKT, ERK1/2 and p70S6K, associated with the perturbations. The E columns contain the protein activity status, statistically deduced from the experimental data. In case of a significant (p-value < 0.05) combined influence of both, drug treatment and time, on the protein signal intensity, a Wilcoxon rank sum test was conducted for the measurements at time point 60 minutes. The drug treatments leading to significantly (p-value < 0.05) smaller intensity values compared to the control measurement ‘X’ were considered as efficient inhibitors, resulting in a table entry of zero. Consistency between simulations and experimental observations is printed in bold. von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 10 of 21 http://www.biomedcentral.com/1752-0509/8/75 Figure 4 SKBR3 short-term time courses of AKT, ERK1/2 and p70S6K. The figure shows splines and related standard error bars of the measured RPPA data for AKT, ERK1/2 and p70S6K after combined EGF and HRG stimulation in the SKBR3 cell line. The measurements included ten time points up to 60 minutes. The different drug treatments are marked by different colours with ‘X’ denoting no drug treatment. of the drugs was likewise efficient in inhibiting AKT (Figure 6). However, the optimal effect was revealed for the triple drug combination (Table 2). The simulations suggested pertuzumab alone or a combination of both monoclonal antibodies (Table 1). It has to be kept in mind, that the attractor states resembled a long-term steady state, which can differ from observations up to 60 minutes. The perturbation simulations in BT474 did not lead to inactive AKT upon combined pertuzumab and erlotinib treatment. Instead, erlotinib alone or combined with trastuzumab was efficient (Table 1). Nevertheless, this supported the need for the small molecule inhibitor and a monoclonal antibody to suppress ErbB-2 induced PI3K signalling. In SKBR3, the attractor states con- firmed the described optimal drug treatment to deactivate AKT. Trastuzumab, when applied alone, was the only treatment without a positive effect in the simulations (Table 1). Inhibition of MAPK signalling requires erlotinib Signalling through the MAPK pathway, represented by ERK1/2 activation, was efficiently inhibited by erlotinib alone in both, HCC1954 (Figure 6, Table 2) and SKBR3 (Figure 4, Table 2), cell lines. EGF activates the MAPK pathway via ErbB-1 homodimers and ErbB-1/2 het- erodimers (Figure 2). Both are prevented by ErbB-1 inhibi- tion via erlotinib, which was especially designed to target this receptor. In BT474, pertuzumab plus erlotinib was required (Figure 5, Table 2). This was analogous to the situation in PI3K signalling. HRG activates the MAPK pathway via ErbB-2/3 het- erodimers (Figure 2). Obviously, BT474 needed the addition of the monoclonal antibody due to dominant ErbB-2/3 formation and activity. On the contrary, the other two cell lines just needed erlotinib alone. Here, in addition to the ErbB-1 dimers, the ligand-independent ErbB-2 homodimers might have driven ERK1/2 activation von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 11 of 21 http://www.biomedcentral.com/1752-0509/8/75 Figure 5 BT474 short-term time courses of AKT, ERK1/2 and p70S6K. The figure shows splines and related standard error bars of the measured RPPA data for AKT, ERK1/2 and p70S6K after combined EGF and HRG stimulation in the BT474 cell line. The measurements included ten time points up to 60 minutes. The different drug treatments are marked by different colours with ‘X’ denoting no drug treatment. and could be inhibited by the small molecule inhibitor. Efficacy of erlotinib towards ErbB-2 dimers was previ- ously mentioned by Schaefer et al. [61]. In BT474, the simulations resulted in active ERK1/2 states, resisting drug treatment (Table 1). In HCC1954 and SKBR3, the positive effect of erlotinib was supported by the simulations. The attractor states were additionally inactive for all other (combinatorial) drug treatments, but not trastuzumab alone. p70S6K is influenced by both, PI3K and MAPK, pathways The target p70S6K is upstream influenced by the PI3K as well as the MAPK pathway (Figure 2). Hence, p70S6K merges both pathways, leading to activation of RPS6 [60]. The three cell lines showed different pathway prefer- ences. BT474 required the combination of pertuzumab and erlotinib to suppress p70S6K (Figure 5). On the con- trary, in SKBR3 the triple drug combination was shown to be optimal (Table 2). Obviously, the effect was driven by erlotinib (Figure 4), which was supported by the attractor states of p70S6K (Table 1). This resembled the drug response of ERK1/2 and reflected a stronger influence by the MAPK pathway. In HCC1954, deactivation of p70S6K was reached via application of erlotinib combined with pertuzumab (Table 2). The treatment with erlotinib alone had a similar effect (Figure 6), while the simulations just confirmed a positive effect of pertuzumab (Table 1). Thus, this cell line seemed to be influenced by both, PI3K and MAPK, pathways. These results were in line with the newly inferred edges in the network reconstructions. They pointed to a strong influence of PI3K in BT474 in contrast to a dominant MAPK pathway in SKBR3. HCC1954 was influenced by both pathways to a similar extent. To follow up on the hypothesis that different path- ways contribute to a different extent in individual cell lines, we tested correlation between the p70S6K time course and the ones of AKT and ERK1/2, respectively. In BT474, p70S6K correlated positively with AKT (p- value 0.01, Kendall’s τ estimate 0.64). In HCC1954, von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 12 of 21 http://www.biomedcentral.com/1752-0509/8/75 Figure 6 HCC1954 short-term time courses of AKT, ERK1/2 and p70S6K. The figure shows splines and related standard error bars of the measured RPPA data for AKT, ERK1/2 and p70S6K after combined EGF and HRG stimulation in the HCC1954 cell line. The measurements included ten time points up to 60 minutes. The different drug treatments are marked by different colours with ‘X’ denoting no drug treatment. p70S6K correlated positively with both, AKT (p-value < 2.22 · 10−16, Kendall’s τ estimate 0.69) and ERK1/2 (p-value < 2.22 · 10−16, Kendall’s τ estimate 0.87). In SKBR3, p70S6K also correlated positively with both, AKT (p-value 0.05, Kendall’s τ estimate 0.51) and ERK1/2 (p-value 0.02, Kendall’s τ estimate 0.6), with a stronger tendency towards MAPK signalling. The correlation was not as convincing as in the other two cell lines. One could speculate, that the dominance of the MAPK pathway in SKBR3 cells was not as strong as the domi- nance of the PI3K pathway in BT474. This was supported by the reconstructed networks. They revealed down- Table 2 Optimal drug treatment in short-term signalling Cell line AKT ERK1/2 p70S6K BT474 - PE PE HCC1954 PTE E PE SKBR3 PTE E PTE The table summarises the optimal drug treatments for the short-term data, leading to inactive AKT, ERK1/2 and p70S6K, respectively. In case of a significant (p-value < 0.05) combined influence of both, drug treatment and time, on the protein signal intensity, a Wilcoxon rank sum test was conducted for the measurements at time point 60 minutes, testing for significantly (p-value < 0.05) smaller intensity values under the drug treatment compared to the control measurement. The drug treatment with the smallest p-value was considered as the optimal inhibitor. No inferred significant positive drug effect is denoted by ‘-’. The therapeutics erlotinib, trastuzumab and pertuzumab are abbreviated by their first letters. More than one letter denotes drug combinations. The growth factors EGF and HRG were added in combination to the cell lines and permanently active in the simulated perturbation conditions. The column Cell line holds the cell lines under consideration. The columns AKT, ERK1/2 and p70S6K hold the optimal drug combinations for each target. If those were confirmed by the attractor states (0) of perturbation simulations, they are printed in bold. von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 13 of 21 http://www.biomedcentral.com/1752-0509/8/75 stream effects of MAPK signalling in SKBR3, while they revealed hyperactive ErbB-2/3 dimers in BT474. The dimers drive PI3K already at the receptor layer, and espe- cially ErbB-2/3 dimers are regarded as the most potent heterodimer [29]. Drug resistance in HCC1954 regarding the PI3K pathway In HCC1954, the inferred optimal treatment against AKT signalling with the triple drug combination was not con- vincing (Figure 6). Analogously, Henjes et al. did not monitor any positive drug effect on AKT under EGF appli- cation alone [28]. However, the simulations suggested pertuzumab alone or a combination of both monoclonal antibodies to inhibit AKT phosphorylation. In principle, divergence of simulations from experimental observations can be expected, as the simulated steady state of the sys- tem does not necessarily have to be reached after the measured period of time. Anyhow, the apparent resis- tance here pointed to a hyperactive PI3K pathway which was explainable by the newly inferred HCC1954 edges described in the previous subsection. They represented feedback loops, hyperactive ErbB-1/2 heterodimers and pathway crosstalk. On the contrary, in SKBR3, the triple drug combination worked well, as described before. The simulations even predicted efficacy of every other drug (combination) apart from trastuzumab alone. The drug efficacy towards AKT in this cell line could be explained by the fact that the two reconstructed interactions in SKBR3 mainly promoted the MAPK instead of the PI3K pathway. The regulation of AKT activity under drug influence, highly diverging in HCC1954 and SKBR3, attracted our attention. Therefore we intended testing for edgetic muta- tions, as discussed by Zhong et al. [62], leading to AKT gain-of-function in HCC1954. Such mutations, perturb- ing not a node but an edge of a network, are speculated to have deeper impact on phenotypic manifestation of a dis- ease. In detail, we removed each of the AKT stimulating edges outgoing from p70S6K, PDK1, mTOR and ErbB- 3, alone or in all possible eleven combinations. We then computed the attractor states for the modified networks in HCC1954. Removal of the connections of mTOR, PDK1 and ErbB-3 alone or combined had no influence on improving drug effects, i.e. AKT just got inactive under pertuzumab treat- ment. Involvement of p70S6K→AKT in the withdrawal process led to much better results. Removed alone or in double combinations with the aforementioned edges, as well as in the two triple combinations containing mTOR, AKT was deactivated under all drug treatments, but not yet trastuzumab alone. Finally, simultaneous removal of the outgoing connections from p70S6K, ErbB-3 and PDK1 with or without mTOR, turned out as the only combina- tion enabling potency of all possible drug combinations, including trastuzumab alone. This hinted at a less strong impact of mTOR on AKT here, but indicated synergistic drug resistance potential of p70S6K, ErbB-3 and PDK1, also due to the newly inferred edges. Long-term signalling network reconstruction The reconstructed long-term signalling networks per cell line are displayed in the Additional file 6. Additional file 5 lists the equivalent Boolean logical interaction rules. Compared to the prior network, most of the newly inferred edges were individual for each cell line, but HCC1954 shared ErbB-1→ERK1/2 with SKBR3, for example. This seemed to be an indirect edge via cRAF, as represented in the prior network. Besides activat- ing connections, also inhibiting ones and edge deletions occurred. For HCC1954, ten new interactions were recon- structed, while two were deleted. In BT474, nine new links were added, and one edge was deleted. In SKBR3, we inferred 20 new connections and one deletion, namely the removal of p53 activation via p38, bearing oncogenic risk [63,64]. In contrast to the short-term networks, new feedback loops were reconstructed in every cell line, not exclu- sively in HCC1954. In HCC1954, the mutual activation between p53 and RB established such a feedback mecha- nism. For SKBR3 we even inferred two edges, each form- ing feedback loops. Contrary to HCC1954, p53 inhibited RB. The second loop connection was inhibition of ErbB- 3 by AKT, pointing to a negative feedback against PI3K signalling [65-67]. In HCC1954, the newly inferred edges Cyclin B1→AKT and ErbB-3→ErbB-1 contributed to PI3K signalling, of which the latter was explainable as heterodimers. The newly inferred edge cJUN→ErbB-1 in HCC1954 also indicated raised activity of ErbB-1. Interestingly, in SKBR3 we conducted an inhibiting edge from Cyclin B1 to AKT but instead an activating one to ERK1/2, contributing to MAPK signalling, which was also stated by Abrieu et al. [68]. Another new edge in HCC1954 involved a cell cycle player, i.e. activation of Cyclin D1 by p70S6K [69]. Accord- ingly, we inferred RPS6→Cyclin D1 in BT474, with RPS6 as downstream target of p70S6K. In SKBR3, the edge p70S6K→Cyclin B1 was reconstructed. A further inter- esting new activating edge in HCC1954 led from RB to TSC2, while we inferred a reversed inhibition in SKBR3. Searle et al. discussed targeting RB deficient cancers by deactivating TSC2 [70]. Two novel interactions in BT474 activated Cyclin B1, arising from ErbB-1 and ErbB-3, respectively, which meant that mitosis was driven by ErbB-1/3 dimers in this cell line. This indicated a hyperactive PI3K pathway, as revealed in the short-term case. In SKBR3, we reconstructed an outgoing edge from the artificial network stimulus S, representing full growth von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 14 of 21 http://www.biomedcentral.com/1752-0509/8/75 medium, activating AKT. This could be explained as strong activation of AKT, driving PI3K signalling in this cell line. The new edges ErbB-2→TSC2 and ErbB- 3→PRAS had to be interpreted as indirect effects, too. They pointed to activity of ErbB-2/3 dimers, feeding into both, MAPK and PI3K, pathways. The edge ErbB- 2→TSC2 could imply an oncogenic role of TSC2. Liu et al. discussed a context dependent functionality of TSC2 [71]. Perturbation simulations on long-term networks Similarly to the perturbation simulations for the short- term networks, we performed those for the long-term networks under all eight initial state combinations of the therapeutics erlotinib, pertuzumab and trastuzumab. Also here, all inferred attractors were simple and consisted of one steady-state. Table 3 contains the simulation results for the attractors of the RPS6 and RB proteins, as those are key players in cell growth and proliferation and mainly comparable to the experimental results of Henjes et al. [28] for HCC1954 and SKBR3. We analysed the attractor states of AKT and ERK1/2, too, but the results are not explicitly listed, since they mostly resembled the ones of RPS6. The control measurements without any drug treatment should result in activation of ErbB members and dimeri- sation events, promoting cell growth and proliferation. In fact, this was expressed as reasonable activation of AKT, ERK1/2 and RPS6 in all cell lines, which held for simu- lations as well as experimental observations. In contrast, the attractor states of RB were inactive in all cell lines (Table 3). Actually, a continuously rising stimulation effect over 30 hours was not observed for HCC1954 and SKBR3 by Henjes et al. [28] either. The attractor states of RPS6 and RB were identical in all cell lines (Table 3). All drugs, except trastuzumab under stimulation alone, led to inactive attractor states of RPS6. This was also the case for ERK1/2 in all cell lines, as well as AKT in BT474 and HCC1954. In SKBR3, the attractor states of AKT were just inactive without the stimulus. All therapeutics, including trastuzumab, resulted in deacti- vated attractor states of RB. The statistically inferred drug effects for AKT, ERK1/2, RB and RPS6 were slightly differ- ent. Table 4 summarises the optimal drug combinations, confirming and extending the observations of Henjes et al. [28]. Most of them were supported by the perturba- tion simulation results, corresponding to attractor states of AKT, ERK1/2, RB and RPS6 being zero. The optimal long-term drug response for AKT and ERK1/2 confirms short-term observations As shown in Figure 7, the best drug response in BT474 and HCC1954 regarding AKT was yielded for a combina- tion of trastuzumab and erlotinib. Statistically, we inferred no positive effect in BT474 at all, which is explainable by the fact that we just considered a combined effect of drug treatment and time. Although the time courses of AKT signalling with and without the drug treatment were differing in the intensity strength, the signalling profiles were similar. This parallel shift indicated no time effect. Instead, the group effect was significant (p-value < 2 · 10−16). This was also the explanation, why we detected erlotinib, but not the combination with trastuzumab, as the optimal treatment in HCC1954 (Table 4). In SKBR3, we inferred the triple drug combination as the optimal one, but the combination of both monoclonal antibodies alone also had a significant effect over time (Figure 7). Table 3 Attractor states of long-term perturbation simulations BT474 HCC1954 SKBR3 Simulation RPS6 RB RPS6 RB RPS6 RB A E A E A E A E A E A E X 1 0 1 1 0 1 1 0 1 E 0 1 0 0 1 0 0 1 0 P 0 - 0 - 0 - 0 - 0 - 0 - T 1 - 0 - 1 - 0 - 1 - 0 - E, P 0 1 0 0 1 0 0 1 0 E, T 0 1 0 0 1 0 0 0 P, T 0 0 0 1 0 1 0 0 E, P, T 0 1 0 0 1 0 1 0 0 The therapeutics erlotinib, trastuzumab and pertuzumab, abbreviated by first letters, that were permanently active in the simulated perturbation conditions besides the stimulus S, standing for the full growth medium, are stored in the column Simulation. No simulated drug treatment is denoted by ‘X’. The A columns hold the attractor states of the proteins RPS6 and RB associated with the perturbations. The E columns contain the protein activity status, statistically deduced from the experimental data. In case of a significant (p-value < 0.05) combined influence of both, drug treatment and time, on the protein signal intensity, a Wilcoxon rank sum test was conducted for the measurements at time point 30 hours. The drug treatments leading to significantly (p-value < 0.05) smaller intensity values compared to the control measurement ‘X’ were considered as efficient inhibitors, resulting in a table entry of zero. Lacking comparable experiments is labelled as ‘-’, while consistency between simulations and experimental observations is printed in bold. von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 15 of 21 http://www.biomedcentral.com/1752-0509/8/75 Table 4 Optimal drug treatment in long-term signalling Cell line AKT ERK1/2 RB RPS6 BT474 - TE E TP HCC1954 E TE E - SKBR3 PTE TE TE TE The table summarises the optimal drug treatments for the long-term data, leading to inactive AKT, ERK1/2, RB and RPS6, respectively. In case of a significant (p-value < 0.05) combined influence of both, drug treatment and time, on the protein signal intensity, a Wilcoxon rank sum test was conducted for the measurements at time point 30 hours, testing for significantly (p-value < 0.05) smaller intensity values under the drug treatment compared to the control measurement. The drug treatment with the smallest p-value was considered as the optimal inhibitor. No inferred significant positive drug effect is denoted by ‘-’. The therapeutics erlotinib, trastuzumab and pertuzumab are abbreviated by their first letters. More than one letter denotes drug combinations. The column Cell line holds the cell lines under consideration. The columns AKT, ERK1/2, RB and RPS6 hold the optimal drug combinations for each target. If those were confirmed by the attractor states (0) of perturbation simulations, they are printed in bold. Hence, like in the short-term results, a drug combination was required to suppress PI3K signalling, here with an obvious need for trastuzumab. For BT474 and HCC1954, this was supported by the simulation results, in which trastuzumab alone had no effect, but was efficient within drug combinations. In HCC1954, even the best drug response was not convincing (Figure 7), pointing to a dominant PI3K pathway, as revealed in the short-term analysis. Interestingly, SKBR3 showed a strong activation peak of AKT phosphorylation between 8 and 18 hours (Figure 7), which was just suppressed under combined application of trastuzumab and pertuzumab. We revealed a positive cor- relation with ERK1/2 (p-value 0.02, Kendall’s τ estimate 0.6) and RPS6 (p-value 0.01, Kendall’s τ estimate 0.64). The reconstructed edges S→AKT and ErbB-1→ERK1/2 in SKBR3 indicated strong activation of AKT and ERK1/2. In addition to the prior network, in which AKT and ERK1/2 fed into RPS6 phosphorylation via p70S6K, some of the novel edges pointed to a positive feedback from p70S6K or RPS6 to ERK1/2. The feedback from p70S6K via Cyclin B1, for example, was expressed by the edges p70S6K→Cyclin B1 and Cyclin B1→ERK1/2. Compared to the short-term results, indicating a dominant MAPK pathway, this long-term observation indicated strong sig- nalling via both, PI3K and MAPK, pathways in SKBR3. As displayed in Figure 8, erlotinib alone or in combina- tion with trastuzumab showed the optimal effect against ERK1/2 in all of the three cell lines. This was in line with the short-term observations, and confirmed by the Figure 7 Long-term time courses of AKT for all cell lines. The figure shows splines and related standard error bars of the measured RPPA data for AKT in all cell lines. The measurements included ten time points up to 30 hours. The different drug treatments are marked by different colours with ‘X’ denoting no drug treatment. von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 16 of 21 http://www.biomedcentral.com/1752-0509/8/75 Figure 8 Long-term time courses of ERK1/2 for all cell lines. The figure shows splines and related standard error bars of the measured RPPA data for ERK1/2 in all cell lines. The measurements included ten time points up to 30 hours. The different drug treatments are marked by different colours with ‘X’ denoting no drug treatment. perturbation simulations. Statistically, the most potent drug effect was yielded with the combination of erlotinib and trastuzumab (Table 4). Quick drug response for RPS6 and delayed response for RB As shown in Figure 9, in BT474, the simulation based predicted efficacy of erlotinib alone to counteract RPS6 (Table 3) was not as convincing as in case of drug combi- nations. A combination of pertuzumab and trastuzumab worked best (Table 4). For RB, the simulated drug effects in BT474 resembled the observed ones (Table 3, Figure 10), with a positive effect of all measured drug treatments. Erlotinib was inferred as the optimal treat- ment (Table 4). Though, the drug impact unfolded not before 18 hours. In HCC1954, it was the combination of both mon- oclonal antibodies, that failed in deactivating RPS6 (Figure 9), while the simulations predicted trastuzumab alone to fail (Table 3). The graphical observations were similar for RB (Figure 10). The newly inferred edges ErbB- 3→ErbB-1 and cJUN→ErbB-1 in HCC1954 explained the necessity for erlotinib against ErbB-1 dimers. The positive impact of erlotinib, the optimal treatment against RB sig- nalling (Table 4), was supported by simulations. However, it did not unfold before 12-18 hours, in case of RB as well as RPS6. Regarding RPS6, no significant effect was detected for HCC1954 (Table 4). According to Henjes et al. [28], in SKBR3 erlotinib and all therapeutic combinations helped to suppress RPS6, which was supported by the simulations (Table 3). As shown in Figure 9, the combination of trastuzumab and erlotinib was the only one, that revealed its continuous inhibiting effect already after one hour. This combined treatment was also statistically inferred as the optimal one (Table 4). The same combination was optimal with respect to RB activity, which was also in line with the simulations. Here, analogously to BT474 and HCC1954, the drug effect did not appear before 18 hours (Figure 10). As the combination of trastuzumab and erlotinib was efficient in all of the three cell lines against RPS6 as well as RB phosphorylation, we further analysed target correla- tions under this drug combination to explain the different rapidness of drug responses. In BT474, RB positively correlated with Cyclin B1 (p- value 0.02, Kendall’s τ estimate 0.6), while RPS6 positively correlated with ERK1/2 (p-value 0.02, Kendall’s τ esti- mate 0.6). Obviously, RPS6 was mainly stimulated by the MAPK pathway, which was efficiently inhibited by the combination of trastuzumab and erlotinib in a fast manner. On the contrary, RB seemed to be influenced von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 17 of 21 http://www.biomedcentral.com/1752-0509/8/75 Figure 9 Long-term time courses of RPS6 for all cell lines. The figure shows splines and related standard error bars of the measured RPPA data for RPS6 in all cell lines. The measurements included ten time points up to 30 hours. The different drug treatments are marked by different colours with ‘X’ denoting no drug treatment. by Cyclin B1. The newly reconstructed edges ErbB- 1→Cyclin B1 and ErbB-3→Cyclin B1 supported hyper- activity of Cyclin B1, driven by ErbB-1/3 heterodimers. In SKBR3, RB negatively correlated with PRAS (p-value 0.05, Kendall’s τ estimate -0.51) and TSC2 (p-value 0.03, Kendall’s τ estimate -0.56), while RPS6 positively corre- lated with AKT (p-value 0.03, Kendall’s τ estimate 0.56) and ERK1/2 (p-value 0.02, Kendall’s τ estimate 0.6). Obvi- ously, like in BT474, RPS6 was mainly activated through the MAPK pathway. Interestingly, RB seemed to require inhibition via PRAS or TSC2. The latter was confirmed via one of the novel edges in SKBR3, namely inhibition of RB by TSC2. In addition, PRAS as well as TSC2 seemed to be especially active in this cell line with regard to the new edges ErbB-3→PRAS and ErbB-2→TSC2. In HCC1954, the drug response was not only delayed for RB, but also for RPS6, which was in line with the posi- tive correlation with RB (p-value < 2.22 · 10−16, Kendall’s τ estimate 0.73). Like in BT474, Cyclin B1 seemed to be a driving force, since both, RPS6 (p-value 0.03, Kendall’s τ estimate 0.56) and RB (p-value < 2.22 · 10−16, Kendall’s τ estimate 0.82) positively correlated with this target. The new edge Cyclin B1→AKT supported special activation of RPS6 via PI3K signalling, leading to a delayed drug response. Interestingly, we revealed negative correlations, as observed for SKBR3. In HCC1954, RPS6 and RB corre- lated with BAX (p-value 0.03, Kendall’s τ estimate -0.56) and FoxO1/3a (p-value 0.05, Kendall’s τ estimate -0.51), pointing to a delayed inhibition of RPS6 and RB via BAX or FoxO1/3a. Conclusions Using a combination of reverse and forward engineer- ing techniques, we focused on deregulated protein inter- actions in the ErbB network in a Boolean modelling framework. The reconstructed hypothetical networks revealed individual protein interactions contributing to signalling pathway preferences as well as drug resistance via feedback loops, pathway crosstalk or hyperactive het- erodimers. While this reverse engineering focused on the network edges, we concentrated in the subsequent forward engineering step on the network nodes. The per- turbation simulations for AKT, ERK1/2, RB and RPS6 mainly confirmed our graphical and statistical analy- ses as well as the observations of Henjes et al. [28] regarding (combinatorial) drug efficacy. However they have to be interpreted as an independent, more prospec- tive investigation, because stable system states do not necessarily have to be reached in temporally limited observations. von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 18 of 21 http://www.biomedcentral.com/1752-0509/8/75 Figure 10 Long-term time courses of RB for all cell lines. The figure shows splines and related standard error bars of the measured RPPA data for RB in all cell lines. The measurements included ten time points up to 30 hours. The different drug treatments are marked by different colours with ‘X’ denoting no drug treatment. In the first step, the combined Boolean modelling approach revealed the mechanisms underlying individual drug response. In the second step, it predicted the net- work propagation effects on protein activity, and hence the drug response itself. One major finding is, that different breast cancer pheno- types seem to be driven by specific pathway preferences in the ErbB network. This leads to individual drug response, requiring different therapeutic treatments. The perturba- tion simulations revealed a more diverse drug response in short-term than in long-term signalling, which stresses the importance of early intervention at the top level layer of the signalling network. Another interesting aspect is to combine edge and node perturbations in Boolean network models to reveal edgetic mutations, as we did in the HCC1954 cell line for AKT. Basic molecular research, embedded in a Boolean mod- elling framework here, composes a first step to gain insight into individual mechanisms of drug response or resistance mechanisms in breast cancer. Especially, the proteomic signalling interplay directly effects tumour development and represents a promising target in cancer therapy, which has to be understood in more detail in the future. Additional files Additional file 1: Proteins and phosphorylation sites involved in RPPA measurements. The tables show the proteins and phosphorylation sites involved in RPPA short- and long-term measurements. The antibody catalogue numbers and providing companies are mentioned in brackets. For BT474, no experimental short-term data under EGF or HRG stimulation were available for PDK1. In case of total protein measurements, the column Phosphosite remains empty (‘-’) apart from the antibody number and supplier name. Additional file 2: Literature references for the prior networks of short- and long-term signalling. The interactions between proteins are listed line by line in the tables. The column Protein denotes the source of the connection with the sink called Target. The interaction (Type) is encoded numerically, i.e. activation is marked by 1, while inhibition is labelled with 2, e.g. AKT activates mTOR. The column Reference specifies the supportive publication. Additional file 3: Workflow of MCMC-based network structure inference. The inhibMCMC procedure of the ddepn package was run with maxIter = 50, 000 in 10 parallel runs. The results of the 25,000 iterations after the burn-in phase were merged into one consensus network. It was applied for short- and long-term data separately per cell line, leading to six consensus networks. The figure is based on [6,47]. Additional file 4: Edge confidences for the reconstructed networks of the three cell lines per time course. In each of the ten MCMC runs, activation and inhibition edges were sampled. The percentage, i.e. the confidence, of sampled activation (red) and inhibition (blue) edges in the 25,000 iterations after the burn-in phase are depicted in the boxes. The sink nodes are displayed in each panel, while the activating, inhibiting or von der Heyde et al. BMC Systems Biology 2014, 8:75 Page 19 of 21 http://www.biomedcentral.com/1752-0509/8/75 missing influence of the source nodes is shown column-wise in the red, blue or missing boxes. The source node names are displayed at the x-axis with additional indicators, where ‘-’ refers to an inhibiting influence and ‘+’ is related to activation. The x-axis of the short-term plots is labelled as ‘AKT, E, EGF, ERBB1, ERBB2, ERBB3, ERK1/2, HRG, MEK1/2, mTOR, P, p70S6K, PDK1, PKCα, PLCγ , T’. The x-axis of the long-term plots is labelled as ‘AKT, BAX, cJUN, cRAF, CyclinB1, CyclinD1, E, ERBB1, ERBB2, ERBB3, ERK1/2, FOXO1/3a, GSK3α/β, NF-κB, P, p38, p53, p70S6K, PRAS, PTEN, RB, S, RPS6, T, TSC2’. An activating edge in the consensus network, as described in Additional file 3, means that the sampled activating edges have a significantly higher confidence value than the inhibiting ones. As self-loops and ingoing edges to the drug or growth factor nodes were not allowed during inference, the respective confidences are zero. Additional file 5: Boolean interaction rules for the components of the short- and long-term signalling networks. The tables contain the rules that arose from network reconstructions based on short- and long-term RPPA data of BT474, HCC1954 and SKBR3. The three drug names erlotinib, trastuzumab and pertuzumab are abbreviated via their first letters. For the long-term networks, the stimulus is denoted by S. Symbols are interpretable in the following way: & ≡AND, ∨≡OR and ! ≡NOT. Additional file 6: Reconstructed long-term signalling networks. The figure displays the reconstructed long-term signalling networks for BT474, HCC1954 and SKBR3. Target proteins are represented as rectangles with stimulus and drugs coloured in red. The three drug names erlotinib, trastuzumab and pertuzumab are abbreviated via their first letters. Stimulation via full growth medium is denoted by S. Solid arrows denote activating interactions while dashed ones represent inhibitions. Abbreviations DDEPN: Dynamic deterministic effects propagation networks; EGF: Epidermal growth factor; EGFR: Epidermal growth factor receptor; GEO: Gene expression omnibus; HER2: Human epidermal growth factor receptor 2; HMM: Hidden Markov model; HRG: Heregulin; MAPK: Mitogen-activated protein kinase; MCMC: Markov chain Monte Carlo; NIR: Near infrared; PI3K: Phosphoinositide 3-kinase; RPPA: Reverse phase protein array; RTK: Receptor tyrosine kinase. Competing interests The authors declare that they have no competing interests. Authors’ contributions FH performed the RPPA measurements under supervision of UK and was mainly involved in target selection for the modelling approach. JS was involved in discussing the conducted RPPA experiments. CB and TB developed the applied network reconstruction algorithm and participated in planning the modelling procedure. TB and SvdH initiated the simulation study concepts. SvdH carried out the literature research, network reconstructions, perturbation simulations followed by associated analyses, and finally drafting the manuscript. All authors edited, read and approved the final manuscript. Acknowledgements Pertuzumab, trastuzumab and erlotinib were provided by Roche Diagnostics GmbH, Penzberg, Germany. This work was supported by a grant from the German Federal Ministry of Education and Research (BMBF) within the Medical Systems Biology programme BreastSys. We also acknowledge support by the Open Access Publication Funds of the Göttingen University. Author details 1Statistical Bioinformatics, Department of Medical Statistics, University Medical Center Göttingen, Humboldtallee 32, 37073 Göttingen, Germany. 2TRON - Translational Oncology at the University Medical Center Mainz, Langenbeckstraße 1, 55131 Mainz, Germany. 3Science for Life Laboratory, School of Biotechnology, KTH - Royal Institute of Technology, Box 1031, 17121 Solna, Sweden. 4Division of Molecular Genome Analysis, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 580, 69120, Heidelberg, Germany. Received: 20 December 2013 Accepted: 10 June 2014 Published: 25 June 2014 References 1. Hill SM, Lu Y, Molina J, Heiser LM, Spellman PT, Speed TP, Gray JW, Mills GB, Mukherjee S: Bayesian inference of signaling network topology in a cancer cell line. Bioinformatics (Oxford, England) 2012, 28(21):2804–2810. PMID: 22923301. 2. Park Y, Bader JS: How networks change with time. Bioinformatics (Oxford, England) 2012, 28(12):40–48. PMID: 22689777. 3. 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Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color ﬁgure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit	24970389	p70S6K = ( ( ( ( ERK1_2 ) AND NOT ( TSC2 ) ) AND NOT ( Nfkb ) ) AND NOT ( PRAS ) ) OR ( ( ( ( p70S6K ) AND NOT ( TSC2 ) ) AND NOT ( Nfkb ) ) AND NOT ( PRAS ) ) Nfkb = ( Nfkb ) FoxO1_3a = ( ( FoxO1_3a ) AND NOT ( AKT ) ) AKT = ( ( ERBB3 ) AND NOT ( PTEN ) ) OR ( ( AKT ) AND NOT ( PTEN ) ) OR ( ( ERBB1 ) AND NOT ( PTEN ) ) OR ( ( ERBB2 ) AND NOT ( PTEN ) ) BAX = ( BAX ) p53 = ( CyclinB1 ) OR ( PTEN ) OR ( RB ) OR ( p38 ) OR ( stimulus ) OR ( p53 ) CyclinB1 = ( ( ERBB3 ) AND NOT ( p53 ) ) OR ( ( CyclinB1 ) AND NOT ( p53 ) ) OR ( ( ERBB1 ) AND NOT ( p53 ) ) ERBB1 = ( ( ( ERBB1 ) AND NOT ( pertuzumab ) ) AND NOT ( erlotinib ) ) OR ( ( ( stimulus ) AND NOT ( pertuzumab ) ) AND NOT ( erlotinib ) ) cRAF = ( ( cRAF ) AND NOT ( ERK1_2 ) ) OR ( ( ERBB1 ) AND NOT ( ERK1_2 ) ) OR ( ( ERBB2 ) AND NOT ( ERK1_2 ) ) p38 = ( AKT ) OR ( p38 ) RPS6 = ( p70S6K ) OR ( RPS6 ) ERBB2 = ( ( ( ( stimulus ) AND NOT ( pertuzumab ) ) AND NOT ( trastuzumab ) ) AND NOT ( erlotinib ) ) OR ( ( ( ( ERBB2 ) AND NOT ( pertuzumab ) ) AND NOT ( trastuzumab ) ) AND NOT ( erlotinib ) ) RB = ( ( RB ) AND NOT ( CyclinD1 ) ) OR ( ( Nfkb ) AND NOT ( CyclinD1 ) ) ERBB3 = ( ( ( ( ERBB3 ) AND NOT ( PTEN ) ) AND NOT ( erlotinib ) ) AND NOT ( pertuzumab ) ) OR ( ( ( ( RPS6 ) AND NOT ( PTEN ) ) AND NOT ( erlotinib ) ) AND NOT ( pertuzumab ) ) OR ( ( ( ( stimulus ) AND NOT ( PTEN ) ) AND NOT ( erlotinib ) ) AND NOT ( pertuzumab ) ) GSK3a_b = ( CyclinD1 ) OR ( GSK3a_b ) OR ( p53 ) cJUN = ( ( cJUN ) AND NOT ( GSK3a_b ) ) CyclinD1 = ( ( AKT ) AND NOT ( GSK3a_b ) ) OR ( ( CyclinD1 ) AND NOT ( GSK3a_b ) ) OR ( ( ERK1_2 ) AND NOT ( GSK3a_b ) ) OR ( ( RPS6 ) AND NOT ( GSK3a_b ) ) TSC2 = ( ( ( ( TSC2 ) AND NOT ( AKT ) ) AND NOT ( ERK1_2 ) ) AND NOT ( GSK3a_b ) ) PRAS = ( ( PRAS ) AND NOT ( AKT ) ) ERK1_2 = ( ERK1_2 ) OR ( cRAF ) PTEN = ( ( PTEN ) AND NOT ( GSK3a_b ) )
ORIGINAL RESEARCH ARTICLE published: 05 December 2014 doi: 10.3389/ﬁmmu.2014.00599 Design, assessment, and in vivo evaluation of a computational model illustrating the role of CAV1 in CD4+ T-lymphocytes Brittany D. Conroy 1†,Tyler A. Herek 1†,Timothy D. Shew 1†, Matthew Latner 1, Joshua J. Larson1, Laura Allen1, Paul H. Davis 1,Tomáš Helikar 2 and Christine E. Cutucache1* 1 Department of Biology, University of Nebraska at Omaha, Omaha, NE, USA 2 Department of Biochemistry, University of Nebraska at Lincoln, Lincoln, NE, USA Edited by: Sergio Quezada, University College London Cancer Institute, UK Reviewed by: Carlos Alfaro, Clínica Universidad de Navarra, Spain Haidong Dong, Mayo Clinic, USA *Correspondence: Christine E. Cutucache, Department of Biology, University of Nebraska at Omaha, Allwine Hall 413, 6001 Dodge Street, Omaha, NE 68182, USA e-mail: ccutucache@unomaha.edu †Co-ﬁrst authors of this manuscript Caveolin-1 (CAV1) is a vital scaffold protein heterogeneously expressed in both healthy and malignant tissue. We focus on the role of CAV1 when overexpressed in T-cell leukemia. Previously, we have shown that CAV1 is involved in cell-to-cell communication, cellular proliferation, and immune synapse formation; however, the molecular mechanisms have not been elucidated. We hypothesize that the role of CAV1 in immune synapse formation contributes to immune regulation during leukemic progression, thereby warranting stud- ies of the role of CAV1 in CD4+ T-cells in relation to antigen-presenting cells. To address this need, we developed a computational model of a CD4+ immune effector T-cell to mimic cellular dynamics and molecular signaling under healthy and immunocompromised conditions (i.e., leukemic conditions). Using the Cell Collective computational modeling software, the CD4+ T-cell model was constructed and simulated under CAV1+/+, CAV1+/−, and CAV1−/−conditions to produce a hypothetical immune response. This model allowed us to predict and examine the heterogeneous effects and mechanisms of CAV1 in silico. Experimental results indicate a signature of molecules involved in cellular proliferation, cell survival, and cytoskeletal rearrangement that were highly affected by CAV1 knock out. With this comprehensive model of a CD4+ T-cell, we then validated in vivo protein expres- sion levels. Based on this study, we modeled a CD4+ T-cell, manipulated gene expression in immunocompromised versus competent settings, validated these manipulations in an in vivo murine model, and corroborated acute T-cell leukemia gene expression proﬁles in human beings. Moreover, we can model an immunocompetent versus an immunocom- promised microenvironment to better understand how signaling is regulated in patients with leukemia. Keywords: caveolin-1, CD4+ T-lymphocyte, the cell collective, adult T-cell leukemia, immunosuppression, immunotherapy, computational biology, logical models INTRODUCTION Caveolae are cave-like invaginations comprised mostly of the pro- tein caveolin-1 (CAV1). In addition to the traditional roles of CAV1 in endocytosis, CAV1 has been implicated in processes ranging from signal transduction (1, 2), to both oncogenesis (3– 5), and tumor suppression (6–8). Recently, three new roles for CAV1 emerged, including regulating immune synapse formation, T-cell receptor (TCR) activation, and mediating actin polymer- ization (9–11). Caveolin-1 knockout studies show an attenuated immunesynapseformationasobservedbydecreasedF-actinstain- ing and dysregulation of RAC1 and ARP2/3 pathways (9). When T-cells engage with antigen-presenting cells (APCs), decreased TCR-dependent T-cell proliferation isobserved when CAV1ispro- hibited from interacting with CD26 (12). Downstream signaling pathways affected by CAV1 knockdown include the organization of the KSR1 mediated Raf/MEK/ERK signal cascade (13) and ZAP70, p56lck, and TCRζ phosphorylation (14). This mechanism has been shown to be distinct from CD3/CD28 stimulation (15), where no proliferation defects were observed in Cav1−/−T-cells. CAV1 acts as a scaffolding molecule thereby likely contributing to diverse events in the cell through CAV1-mediated recruit- ment of signaling complexes to the plasma membrane. More- over, T-cell activation through the TCR and competent immune synapse formation are necessary for a healthy immune response. Misregulation of these processes can lead to deleterious effects, including cancer progression and a phenotype known as tumor- induced immunosuppression (16, 17). As CD4+ T-cells are vital for proper adaptive immune function, and CAV1 plays a role in immune synapse formation, we chose to further investigate the CAV1-mediated pathways in a CD4+ T-cell. To better understand the intricate biology of CAV1 signaling in CD4+ T-cells, the development of a comprehensive in silico model is warranted. Through such a model, further identiﬁcation of molecules associated with CAV1 signaling can occur. www.frontiersin.org December 2014 \| Volume 5 \| Article 599 \| 1 Conroy et al. Role of CAV1 in CD4+ T-lymphocytes Importantly, such a model allows for real-time simulations using computer software in an effort to identify speciﬁc mech- anisms in the cell. In order to generate such a comprehensive and dynamic model, a systems biology approach is required (18). This approach provides a potentially greater understanding of the com- plex cellular functions that occur in living systems, allowing the use of computer models to conduct thousands of virtual experi- ments as well as make methodical predictions regarding proteins of interest (18–21). Herein, we describe the construction and validation of a fully functional in silico CD4+ T-cell model using the Cell Collec- tive, a web-based, open-source dynamic modeling platform that allows scientists to construct computational models in a non- mathematical fashion (20,22). From this in silico starting position, comprehensive simulations were performed, allowing for predic- tions and hypotheses to be drawn for further in vitro/in vivo experimentation. To our knowledge,this is the ﬁrst time a dynamic model of a CD4+ T-cell has been created to observe the down- stream effects of CAV1+/+ (wild type), CAV1+/−(heterozygous), and CAV1−/−(knock down) upon cell signaling and intracel- lular networks as validated by in silico simulations and in vivo investigations. MATERIALS AND METHODS COMPUTATIONAL MODEL CONSTRUCTION WITH CELL COLLECTIVE The presented model was constructed using Cell Collective – a collaborative and interactive platform for modeling biologi- cal/biochemical systems (20, 22). The mathematical framework behind Cell Collective is based on a common qualitative (discrete) modeling technique where the regulatory mechanism of each node isdescribedwithalogicalfunction[formorecomprehensiveinfor- mation on logical modeling, see Ref. (23, 24)]. Cell Collective allows users to construct and simulate large-scale computational models of various biological processes based on qualitative inter- action information extracted from previously published literature. The initial version of the model was structured after the previously published models (25, 26). The individual components and local interactions in the presented ﬁnal model were retrieved manually from published literature. The model was subsequently validated against well-known experimentally demonstrated T-cell dynam- ics (see Model Validation), as well as new experiments presented in this paper. The Cell Collective’s Knowledge Base was used to catalog and annotate every interaction and regulatory mechanism (e.g., tyrosine phosphorylation on Y316) as mined from the pri- mary literature. The model is freely available for simulations and furthercontributionsbyothers directlyintheplatform. Themodel can be also downloaded in the SBML format (24) to be used within other software tools. MODEL VALIDATION Themodel was constructed usinglocal (e.g.,protein–protein inter- action) information from the primary literature. In other words, during the construction phase of the model, there was no attempt to determine the local interactions based on any other larger phe- notypes or phenomena. However, after the model was completed, veriﬁcation of the accuracy of the model involved testing it for the ability to reproduce complex input–output phenomena that have been observed in the laboratory. To do this, the T-cell model was simulated under a multitude of cellular conditions and ana- lyzed in terms of input–output dose–response curves to determine whether the model behaves as expected [Figure 2; Ref. (27–33)], including various downstream effects as a result of activation of the TCR,G-protein-coupled receptor,cytokine,and integrin path- ways. A total of 20 phenomena were used for the validation phase (data not shown). IN SILICO SIMULATIONS The Cell Collective platform was utilized to perform all sim- ulations for the CD4+ T-cell model. Virtual extracellular envi- ronments, composed of 20 CD4+ T-cell stimuli, were optimized for each in silico experiment based on immunocompetent versus immunocompromised (diseased) settings [Table 1; Ref. (9, 13, 30, Table 1 \| A summary of the experimental conditions simulated. External stimulus Tissue (WT) Tissue (Disease A) Tissue (Disease B) Alpha_13L Med High High GalphaS_L Med High High APC Med High High CGC Med Med-High Med-High ECM High High High GP130 0 0 0 IFNB Med Med Med IFNG Med Med Med IFNGR1 Med Med Med IFNGR2 Med Med Med IL10 Med High 0–100 IL10RA Med High High IL10RB Med Med Med IL12 Med High High IL15 Med High High IL15RA Med High High IL18 Med High High IL21 Med High High IL22 Med High High IL23 Med High High IL27 Med High High IL27RA Med Med Med IL2 Med High High IL2RB Med High High IL4 Low Low Low IL6 Low Low Low IL6RA Low Low Low IL9 Low Low Low TGFB Low Low Low Speciﬁcally, these conditions included (1) a wild-type condition (i.e., healthy bio- logical levels of cytokines), (2) an immunosuppressive disease condition (i.e., Disease A), and (3) a scenario with varying degrees of immunosuppression (i.e., Disease B) with CAV1+/+, CAV1+/−, and CAV1−/−. Low, 0–20 activity level; Med, 21–60 activity level; High, 61–100 activity level (Note that the activity levels do not directly correspond to concentrations, rather the activity levels provide a semi-quantitative measure to describe the relative activity of a particular component of the model.). Frontiers in Immunology \| Tumor Immunity December 2014 \| Volume 5 \| Article 599 \| 2 Conroy et al. Role of CAV1 in CD4+ T-lymphocytes FIGURE 1 \| In silico modeling of a CD4+ T-cell. (A) Nodal representation of CD4+ T-cell signaling pathways constructed using the Bio-Logic builder inclusive within the Cell Collective. Linkages represent protein–protein, protein–phosphorylation, and kinase interactions. (B) Osprey modeling of predicted CAV1 protein–protein interactions and functions. Linkages are categorized by function and centrality to CAV1. (C) Graphical depiction of CAV1-associated interactions. Major pathway end-points include cell survival, cytoskeletal rearrangement, and cellular proliferation. 31, 34, 35)]. For each experiment, these values were analyzed and used to compare proteins most affected by CAV1+/+, CAV1+/−, and CAV1−/−in an immunocompetent (i.e., WT) versus varying degrees of immunosuppression (i.e., Diseases A versus B) condi- tion. The model was simulated under hypothetical disease-causing environments in order to observe the changes, if any, in CAV1 reg- ulatory activity. Disease A mimics an immunosuppressive disease condition, and disease B simulates varying degrees of immuno- suppression, as controlled by varying IL-10 levels. Each experi- ment consisted of 1,000 simulations, with different activity levels randomly selected between 0 and 100 for the external stimuli representing the extracellular environment. Each simulation con- sisted of 800 iterations and activity level of the model species was calculated over the last 300 iterations using methods previously www.frontiersin.org December 2014 \| Volume 5 \| Article 599 \| 3 Conroy et al. Role of CAV1 in CD4+ T-lymphocytes FIGURE 2 \|The Cell Collective accurately models complex cellular phenomena. (A–F) Certiﬁcation of Bio-Logic built local interactions executing in accordance with primary literature ﬁndings. (A) Activation of the mitogen-activated protein kinase (MAPK) pathway via APC stimulation (27). (B) Positive relationship between ﬁlamentous actin polymerization in response to stimulation with extracellular matrix (ECM) components (28). (C) PI3-Kinase activation via binding of ligand to G protein-coupled receptor, GαQ (29). (D) Activation of the MAPK pathway via integrin-dependent ECM stimulation (9, 30). (E) Activation of the MAPK pathway via stimulation with interleukin-2 (IL2) (31, 32). (F) Activation of the small GTPase Cdc42 via binding of ligand to the G protein-coupled receptor, Gα12/13 (33); these results not shown in the graphic. Each dose–response curves appears to demonstrate a positive correlation with the stimulus. described (36). The aforementioned simulations were run under six separate conditions including wild-type tissue, diseased tissue (diseasesA and B),wild-type blood,and diseased blood (diseasesA and B).Wild-type and diseased blood simulations are not included duetoinconclusivedata. Eachexperimentalenvironmentwassim- ulated under (1) healthy cellular conditions, (2) CAV1 knocked out, (3) CAV1 activated 50% of the time (CAV1+/−) and (4) CAV1 activated at random levels between 0 and 100. (To be able to arti- ﬁcially control the activity levels of CAV1 under environments 3 and 4, an external species, “CAV1 Activator,” was built into the model to activate CAV1 independently of the activity levels of its direct upstream regulators). MOUSE MAINTENANCE Animals were housed in pathogen-free animal facilities, and all experimental protocols were reviewed and approved per the Institutional Animal Care and Use Committee at the University of Nebraska Medical Center/University of Nebraska at Omaha (IACUC# 13-056-08-EP). C57Bl/6J and B6.Cg-Cav1tm1Mls/J mice were purchased from the Jack-son Laboratory (Bar Harbor, ME, USA). Post-natal day 54 (±5 days) mice were used for all experiments. HISTOLOGICAL STAINING Spleen and lymph node tissues were sectioned and stained at the University of Nebraska Medical Center’s Tissue Science Facility. Spleen and lymph node tissues were sectioned, preserved in 10% formalin, and embedded onto slides in parafﬁn. Speciﬁcally, all tissues were sectioned after at least 48 h in ﬁxative and stained with hematoxylin and eosin using standard protocol. For immunohistochemical staining (IHC), tissues were depar- raﬁnized in xylene for 3 min and rehydrated in decreasing concen- trations of ethanol (100–50%). Antigen retrieval was performed by boiling sections in a solution of Sodium Citrate with 0.05% Tween-20. Blocking against non-speciﬁc binding and endoge- nous peroxidases was performed by incubation with 5% bovine serum albumin (BSA; Invitrogen) and 0.3% hydrogen perox- ide, respectively. Primary antibody incubation was conducted for 90 min at room temperature in phosphate buffered saline (PBS; DIBCO). The following antibodies were used: Rac1 (Merck KGaA, Darmstadt, Germany); CD28 (BD Pharmingen); GATA3 (BD Pharmingen); CD26 (Abcam); BCL10 (Cell Applications, Inc.). Horse radish peroxidase-conjugated secondary antibodies (Cell Signaling Technology; BD Pharmingen; Abcam) were incubated for 1 h at room temperature. Slides were developed with a working solution 3,3-diaminobenzidine for 10 min at room temperature, followedbyrinsing withdistilledwaterand mountingthecoverslip with Permount (Thermo Fisher Scientiﬁc). GENE EXPRESSION PROFILING Microarray data were downloaded from the Gene Expression Omnibus, accession number GSE55851 (37). Data contained whole genome expression proﬁling of CD4+ T-cells, sorted based on a CADM1/CD7 phenotype. Samples were collected from Frontiers in Immunology \| Tumor Immunity December 2014 \| Volume 5 \| Article 599 \| 4 Conroy et al. Role of CAV1 in CD4+ T-lymphocytes FIGURE 3 \| In silico predictions for translation into in vitro/in vivo experimentation. Following 1,000 iterations of simulation as described in Table 1, the most affected proteins (either up or downregulated) were compiled by the Cell Collective and ranked based on activity% ON. Speciﬁcally, those described were the top 15 most differentially expressed molecules in the (A) CAV1+/+, (B) Cav1+/−, (C) CAV1−/−genotype. These proteins were selected for further investigation with in vitro/in vivo veriﬁcation. patients diagnosed with Adult T-cell leukemia-lymphoma (ATL) subtypes: asymptomatic (n = 2), smoldering (n = 2), chronic (n = 1), acute (n = 2), and healthy controls (n = 3). A mini- mum of two samples were taken from each patient for microar- ray analyses. Molecules of interest, as established utilizing the Cell Collective, were selected within the microarray data and analyzed by fold-change from normal controls between ATL subtypes. Fold-change values were subjected to uncentered, average-linkage correlation using Cluster 3.0, and Java Tree- View as described previously (9). Further, Pearson regression analyses were conducted to discern correlation among mole- cules of interest in relation to CAV1 expression across ATL subtypes. RESULTS IN SILICO MODELING OF A CD4+ T-CELL The completed CD4+ T-cell model consists of 188 nodes representing components of various signaling pathways and corresponding protein-to-protein, protein-phosphorylation, and kinase interactions (Figure 1A). These interactions correlate with preliminary data generated using Osprey software used to model CAV1 protein-to-protein interaction types (Figure 1B). Each method of analysis (both the Cell Collective and Osprey) impli- cates a role for CAV1 in phosphorylation, signal transduction, transport, and cytoskeletal arrangement. The regulation of these events by CAV1 is highly complex and dynamic, as illustrated in Figure 1C. To verify that the local interactions built into the model were able to accurately mimic complex phenomena that have been produced in the laboratory,20 validations were conducted via sim- ulations in Cell Collective (six representative validations are shown in Figures 2A–F). As an example, simulated TCR activation by an APC leads to Erk activation,and the subsequent downstream effect of cellular proliferation as represented by the literature (Figure 2A, Figure S1 in Supplemental Material). IDENTIFICATION OF MOST AFFECTED PROTEINS IN SILICO Experiments were simulated using the in silico model (as described in Table 1) to make rational predictions about how the sys- tem would function in the laboratory. Following 1,000 iterations, www.frontiersin.org December 2014 \| Volume 5 \| Article 599 \| 5 Conroy et al. Role of CAV1 in CD4+ T-lymphocytes we observed the protein products most affected by CAV1+/+, CAV1+/−, and CAV1−/−in immounocompetent versus immuno- compromised conditions (Figures 3A–C). In order to test the validity of the model, we chose to investigate expression levels of the proteins most affected in the knock down genotype as com- pared to a wild-type system. Speciﬁcally proteins disregulated by CAV1−/−across all three conditions (WT, Disease A, and Disease B) included CD26, CARMA1, FYN, SHC1, SOS, SHP2, NOS2A, BCL10, and GRB2 (Figure 3C). Based on ﬁndings from the model as well as preliminary in vitro data, we hypothesized that CAV1 expression regulates Ras-related C3 botulinum toxin substrate 1 (RAC1), B-cell lymphoma/leukemia 10 (BCL10), GATA-binding protein 3 (GATA3), CD26, and CD28 (Figures 1C and 3C). The abovementioned results are indicative of CAV1-mediate regulation of a variety of cellular functions, notably those that are downstream of TCR and integrin pathways of which CAV1 serves as the scaffold. Given these results, we were able to make predic- tions about protein expression in relation to CAV1 and test them in the laboratory using in vitro and in vivo experiments. For exam- ple, we observed that CAV1 is involved in the integrin signaling pathway that ultimately activates the mitogen-activated protein kinase (MAPK) cascade (Figure 2); therefore, we can predict that cellular proliferation will be decreased if CAV1 is knocked down. VERIFICATION OF IN SILICO PREDICTIONS IN VIVO To determine differences in morphology between CAV1−/−and wild-type mice, we examined tissues (including lymph nodes and spleen) stained with hematoxylin and eosin and observed no differences were observed in tissue architecture. Lymphoid organs (lymph nodes and spleen) were selected for their robust- ness of CD4+ T-cells, and liver was used as a control for tis- sue histology (i.e., to ensure mice were disease free). Further- more, immunohistochemistry was utilized to biologically validate in silico predictions from our CD4+ T-cell model. Top hit proteins: GATA3, RAC1, CD26, and BCL10 were selected for IHC to validate the model (Figure 4). RAC1 and GATA3 showed upregulation in the lymph node tissue of the CAV1−/−mice. We observed CD26 and BCL10 to be upregu- lated in both the lymph node and spleen tissues of the CAV1−/− mice. We also stained for CD28, as it is a well-characterized co- stimulatory protein involved in T-cell activation. CD28 showed no differential expression between the wild-type and CAV1−/− mice. Based on predictions from the model (Figure 3C), we investi- gated the differential expression,hierarchal clustering (Figure 5A), and regression analyses (Figure 5B) of top hit proteins using microarray data from ATL cases (GSE55851). Comparison of ATL subtypes for identiﬁcation of potential molecular signa- tures in relation to CAV1 expression reveal seven molecules, including CAV1, clustered together based upon gene expression proﬁles following hierarchal clustering (Figure 5A). We observed a positive correlation (R = 0.78), with distinct signatures dis- played between healthy, asymptomatic, smoldering, chronic, and acute patients (Figure 5B). Pearson regression analyses were con- ducted between each molecule of interest in relation to CAV1 expression across ATL subtypes (Figure 5B). Speciﬁcally, we FIGURE 4 \| Immunohistochemistry from murine model validation of in silico-predicted differentially expressed molecules with CAV1 knockout. Molecules downstream of CAV1 that were predicted to be affected with CAV1 knockout using the Cell Collective were validated using lymphoid tissue histology from wild-type (WT) C57Bl/6 mice and CAV1−/− mice.The corresponding hematoxylin and eosin preparations are included in the top panel for morphological orientation; all tissues were sectioned subsequently. Frontiers in Immunology \| Tumor Immunity December 2014 \| Volume 5 \| Article 599 \| 6 Conroy et al. Role of CAV1 in CD4+ T-lymphocytes FIGURE 5 \| Veriﬁcation and comparison of in silico results with gene expression proﬁling from adultT-cell leukemia-lymphoma (ATL). (A) Uncentered average-linkage correlation of fold-change values from top affected proteins in ATL patients. The yellow-boxed region represents a CAV1-associated molecular signature (R = 0.78). Healthy (n = 3), asymptomatic (ASYM) (n = 2), smoldering (SMLD) (n = 2), chronic (CHRN) (n = 1), and acute (ACUT) (n = 2) cases are shown. A minimum of two samples were taken from each patient for microarray analyses. (B) Pearson regression analyses of top affected proteins in relation to CAV1 expression across ATL subtypes. observed strong correlations between CAV1 and the follow- ing molecules: BCL10 (R = 0.947), DEC2/BHLHB3 (R = 0.782), SHP2/PTPN11 (R = 0.742), and GATA3 (R = 0.694). Conversely, SOS1 (R = −0.981), FYN (R = −0.949), SOS2 (R = -0.825), and CD26 (R = −0.740) were most negatively correlated to CAV1 expression. These data corroborate those described and simu- lated in the model (Figure 3); therefore, it is translated to in vivo, leukemic conditions. DISCUSSION Herein, we present a comprehensive, computational model of a CD4+ T-cell, including CAV1 regulatory pathways. This model incorporates experimentally validated interactions to posit the role of CAV1 in healthy CD4+ cells and CD4+ cells in the context of T-cell leukemia/lymphoma (i.e., when the immune response is skewed). CD4+ T-cells are a vital component of the immune system, as they protect against cancer, infection, and play a role in autoimmunity. CAV1 has been shown to be upregulated in numerous types of malignancies. Consequently, we built a CD4+ T-cell model to better understand basic T-cell biology and to address the role(s) of CAV1 within immunocompetent versus immunocompromised conditions. Inclusively, we investigated the role of CAV1 in the regulation of cellular processes, including cell cycle progression, cell proliferation, actin polymerization, and immune synapse formation. This model was successfully con- structed using the Cell Collective platform that allows users to build cellular models capable of mimicking actual cellular sys- tems in the laboratory (19–22, 38). The accuracy of the model was then successfully validated through the comparison of simu- lations with well-established, global input–output relationships as previously observed experimentally. Most importantly, new in silico predictions were validated in vitro/in vivo using both murine models and gene expression proﬁles from patients with a T-cell leukemia due to the previously observed role of Cav1 in lymphocytes (39–46). Using Cell Collective, we were able to perform virtual experi- ments in order to make predictions as to how a CD4+ T-cell would behave when the expression levels of CAV1 were altered and when CAV1 was knocked down. These experiments provided insight as to which proteins, and ultimately which cellular functions, might be regulated by CAV1. Based on in silico results, we observed that BCL10, CD26, FYN, CARMA1, SHC1, SOS, SHP2, NOS2A, GRB2, and GATA3 are strongly inﬂuenced by CAV1 expression (Figure 3C). Consequently, the expression of these molecules in vivo was investigated using cluster analyses of microarray data to measure gene expression (Figure 5). Finally,four key proteins were selected for further veriﬁcation of the predictions of the model using immunohistochemistry on mouse tissue with and without Cav1 (Figure 4). In addition to the four key proteins, CD28 was chosen because it is known to regulate T-cell activation independent of CAV1 expression (15). RAC1 and GATA3 expression were upregulated in the lymph node tissue of the CAV1−/−mice. These results were expected based on studies showing the role of CAV1 in lymphoid tissue (9). We observed both CD26 and BCL10 upregulation,espe- cially in the germinal centers of the lymph node and spleen tissue of the CAV1−/−mice. These validations of the in silico predictions show that the CD4+ T-cell model is biologically relevant. These validations of the in silico predictions show that the CD4+ T-cell model is biologically relevant. Therefore, we suggest that based on www.frontiersin.org December 2014 \| Volume 5 \| Article 599 \| 7 Conroy et al. Role of CAV1 in CD4+ T-lymphocytes the validations in vivo the T-cell in silico model is predictive of biological processes. We then translated the in silico predictions to gene expression proﬁles of patients with a T-cell malignancy (i.e., ATL). Of the top 15 most differentially expressed molecules in CAV1-mediated pathways, the top 4 most highly correlated molecules to CAV1 expression were BCL10,DEC2,SHP2,and GATA3 (R value > 0.74; Figure 5B). Obstinately, SOS1, FYN, SOS2, and CD26 were neg- atively correlated with CAV1 (R < 0.74; Figure 5B). Additionally, we observed unique clustering of these 15 conserved molecules across subtypes of ATL patients. Interestingly, there was a distin- guishable differential expression of MALT1 in asymptomatic ATL cases as compared with healthy individuals (Figure 5A). There- fore, further investigation into the plausibility of these correlated molecules being used for diagnostic purposes is warranted. We hope that our other ongoing studies will shed light as to their role in ATL. In short, our data regarding the role of CAV1 in cell signaling (as demonstrated using an in silico software and subse- quently validated experimentally) corroborate that of the existing literature. Speciﬁcally, CAV1 participates in processes including actin polymerization, cell proliferation, and cell survival (9, 12, 15, 47–49). The usefulness of the in silico approach combined with that of in vivo/in vitro approaches provide rapid information as to the cell signaling networks in healthy and leukemic cells. There are currently many therapies being used to treat leukemia that tar- get speciﬁc proteins in order to inhibit cellular pathways. These treatment modalities are advanced when comprehensive, molecu- lar models allow the researcher to observe the direct mechanism of action of gene targeting as well as downstream consequences of gene/protein knockdown. The CD4+ T-cell model will hopefully be able to provide insight to for both T-cell biology (as demon- strated herein) as well as possible targets for lymphocytic leukemia treatments. The importance of in silico approaches combined with immunoinformatics as well as in vivo validation cannot be under- stated (18). With the often-prohibitive cost of drug design, it is imperative to use computational approaches to derive and test hypotheses. Current therapy regimens for T-cell malignancies can bemodeledinsilico initiallyinanefforttounderstandmechanisms and potential outcomes. A comprehensive model of the CD4+ cells has the potential to providesubstantialinsightintocancertreatment,immunotherapy, and cellular biology. This twofold approach incorporating in silico and in vivo investigations has the potential to translate diagnostics and therapeutic targets from bench to bedside. AUTHOR CONTRIBUTIONS Brittany D. Conroy, Tyler A. Herek, and Timothy D. Shew are equally contributing ﬁrst authors. Brittany D. Conroy wrote the paper, built the model, and did the simulations and veriﬁcations. Timothy D. Shew and Tyler A. Herek did bioinformatics studies, immunohistochemistry, veriﬁcations, and wrote the paper. Joshua J. Larson assisted in bioinformatics studies and mouse work. Laura Allen and Matthew Latner built the model, ran validations, and performed data analyses. Paul H. Davis provided suggestions for experimental design and helped implement experiments. Chris- tine E. Cutucache and Tomáš Helikar conceptualized and designed the experiment, assisted in implementation, oversaw evaluation, and wrote the paper. ACKNOWLEDGMENTS We thank Andrew Pulfer for his work in helping to construct the initial CD4+ T-cell model. Thanks to the Tissue Core Facility at the University of Nebraska Medical Center for assistance with his- tology. Additionally, we thank Nebraska NASA for Fellowships (Brittany D. Conroy and Christine E. Cutucache), the University of Nebraska at Omaha’s Sponsored Programs Ofﬁce for internal funding through an UCRCA grant (Tomáš Helikar and Christine E. Cutucache),and thanks to Dr. George Haddix and the Nebraska University Foundation. 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Mechanism of recruitment of WASP to the immunological synapse and of its activation following TCR ligation. Mol Cell (2002) 10(6):1269–81. doi:10.1016/S1097-2765(02)00728-1 49. Thome M. CARMA1, BCL-10 and MALT1 in lymphocyte development and activation. Nat Rev Immunol (2004) 4(5):348–59. doi:10.1038/nri1352 Conﬂict of Interest Statement: Tomáš Helikar is a founder and scientiﬁc advisor to Discovery Collective, Inc. Discovery Collective holds a license to use the Cell Collective software. All other authors declare no conﬂict of interest. Received: 25 August 2014; accepted: 07 November 2014; published online: 05 December 2014. Citation: Conroy BD, Herek TA, Shew TD, Latner M, Larson JJ, Allen L, Davis PH, Helikar T and Cutucache CE (2014) Design, assessment, and in vivo evaluation of a computational model illustrating the role of CAV1 in CD4+ T-lymphocytes. Front. Immunol. 5:599. doi: 10.3389/ﬁmmu.2014.00599 This article was submitted to Tumor Immunity, a section of the journal Frontiers in Immunology. Copyright © 2014 Conroy, Herek, Shew, Latner, Larson, Allen, Davis, Helikar and Cutucache. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. www.frontiersin.org December 2014 \| Volume 5 \| Article 599 \| 9	25538703	FYN = ( CAV1_scaffold ) OR ( CD3 AND ( ( ( TCR ) ) ) ) PKA = ( cAMP ) MEK3 = ( MEKK4 ) FOXP3 = ( ( ( SMAD3 AND ( ( ( STAT5 AND NFAT ) ) ) ) AND NOT ( STAT1 ) ) AND NOT ( STAT3 AND ( ( ( RORGT ) ) ) ) ) OR ( NFAT AND ( ( ( FOXP3 AND STAT5 ) ) ) ) IL17 = ( ( ( ( NFAT AND ( ( ( proliferation AND STAT3 AND NFKB AND RORGT ) ) ) ) AND NOT ( STAT5 AND ( ( ( FOXP3 ) ) ) ) ) AND NOT ( STAT6 AND ( ( ( FOXP3 ) ) ) ) ) AND NOT ( STAT1 AND ( ( ( FOXP3 ) ) ) ) ) Lck = ( CD28 ) OR ( JAK3 AND ( ( ( IL2RB ) ) ) ) OR ( CD4 ) IL4 = ( IRF4 ) OR ( ( ( ( GATA3 AND ( ( ( proliferation AND NFAT ) ) ) ) AND NOT ( FOXP3 ) ) AND NOT ( TBET AND ( ( ( RUNX3 ) ) ) ) ) AND NOT ( IRF1 ) ) IL23 = ( NFAT AND ( ( ( proliferation AND STAT3 ) ) ) ) TGFB = ( FOXP3 AND ( ( ( proliferation AND NFAT ) ) ) ) Vav = ( SLP-76 ) IL4R_HIGH = ( IL4 AND ( ( ( IL4RA_HIGH AND CGC ) ) ) ) OR ( IL4_e AND ( ( ( IL4RA_HIGH AND CGC ) ) ) ) GSK-3b = ( NOT ( ( AKT ) ) ) OR NOT ( AKT ) was = ( Src ) IL2 = ( ( ( NFAT AND ( ( ( NOT FOXP3 ) ) ) ) AND NOT ( TBET AND ( ( ( NFKB ) ) ) ) ) AND NOT ( STAT5 AND ( ( ( STAT6 ) ) ) ) ) OR ( ( ( NFKB ) AND NOT ( TBET AND ( ( ( NFKB ) ) ) ) ) AND NOT ( STAT5 AND ( ( ( STAT6 ) ) ) ) ) C3G = ( Crk ) IL9R = ( IL9_e ) OR ( JAK3 ) Nck = ( SLP-76 ) FAK_Tyr397 = ( Bintegrin ) PDK1 = ( PIP3_345 ) MKK7 = ( TAK1 ) STAT3 = ( IL21R ) OR ( IL27R ) OR ( IL6R ) OR ( IL23R ) OR ( IL10R ) SMAD3 = ( TGFBR ) Profilin = ( RIAM ) Calcineurin = ( Ca2+ ) IFNBR = ( IFNB_e ) IL2RA = ( FOXP3 AND ( ( ( NFAT ) ) ) ) OR ( STAT5 AND ( ( ( NFAT ) ) ) ) OR ( SMAD3 AND ( ( ( NFAT ) ) ) ) OR ( NFKB AND ( ( ( NFAT ) ) ) ) HLX = ( TBET ) Shc1 = ( FYN ) OR ( IL2RB AND ( ( ( IL2R ) ) ) ) Cdc42 = ( C3G ) OR ( RhoGEF ) IL4RA = ( NOT ( ( STAT5_HIGH ) ) ) OR NOT ( STAT5_HIGH ) Tyk2 = ( IL12RB1 AND ( ( ( IL12RB2 ) ) ) ) IL2R_HIGH = ( IL2 AND ( ( ( IL2RB AND CGC AND IL2RA ) ) ) ) OR ( IL2_e AND ( ( ( IL2RB AND CGC AND IL2RA ) ) ) ) N_WASP = ( Cdc42 ) OR ( Nck AND ( ( ( Vav ) ) ) ) IL22 = ( STAT4 ) OR ( STAT5 ) OR ( STAT1 ) OR ( STAT3 ) RhoA = ( CAV1_scaffold ) OR ( RhoGEF ) PKC = ( DAG ) JAK3 = ( IL2R ) CD28 = ( APC ) OR ( B7 ) IL4RA_HIGH = ( STAT5_HIGH ) NFKB = ( NOT ( ( FOXP3 ) OR ( IKB ) ) ) OR NOT ( IKB OR FOXP3 ) IL12RB2 = ( IL12_e ) F_Actin = ( Arp2_3 AND ( ( ( G_Actin ) ) ) ) ROCK = ( RhoA ) MEKK4 = ( GADD45B AND ( ( ( GADD45G ) ) ) ) CARMA1 = ( CD26 ) OR ( PKC ) ERM = ( STAT4 ) Galpha_Q = ( Galpha_QL ) IL10 = ( NFAT AND ( ( ( GATA3 OR STAT3 ) AND ( ( ( proliferation ) ) ) ) ) ) ATF2 = ( P38 ) IKB = ( NOT ( ( IKKcomplex ) ) ) OR NOT ( IKKcomplex ) MEK1_2 = ( RAF1 ) OR ( BRAF ) OR ( PAK ) GalphaS_R = ( GalphaS_L ) GATA3 = ( ( STAT6 ) AND NOT ( TBET ) ) OR ( Dec2 ) rac1 = ( was ) OR ( Crk AND ( ( ( Paxillin ) ) ) ) OR ( NOS2A ) OR ( Vav ) CD4 = ( TCR AND ( ( ( MHC_II AND CD3 ) ) ) ) Src = ( Bintegrin ) OR ( FAK_Tyr397 ) IL23R = ( IL23 AND ( ( ( GP130 AND STAT3 AND IL12RB1 AND RORGT ) ) ) ) OR ( IL23_e AND ( ( ( GP130 AND STAT3 AND IL12RB1 AND RORGT ) ) ) ) NOS2A = ( CAV1_scaffold ) TRAF6 = ( IRAK1 ) GFI1 = ( TCR ) OR ( STAT6 ) Dec2 = ( GATA3 ) Cas = ( FAK_576_577 AND ( ( ( Bintegrin ) ) ) ) Arp2_3 = ( WAVE-2 ) OR ( N_WASP ) SLP-76 = ( ZAP-70 ) OR ( Gads ) Gads = ( LAT ) IFNGR = ( IFNG_e AND ( ( ( IFNGR2 AND IFNGR1 ) ) ) ) OR ( IFNG AND ( ( ( IFNGR2 AND IFNGR1 ) ) ) ) Grb2 = ( Shc1 ) OR ( LAT ) IL4R = ( IL4 AND ( ( ( IL4RA AND CGC ) ) ) ) OR ( IL4_e AND ( ( ( IL4RA AND CGC ) ) ) ) PI3K = ( CD28 AND ( ( ( ICOS ) ) ) ) OR ( SHP2 ) OR ( IL2R ) OR ( GAB2 ) OR ( Ras ) OR ( FAK_576_577 ) LIMK = ( PAK ) OR ( ROCK ) SOCS1 = ( STAT6 ) OR ( STAT3 ) ERK = ( MEK1_2 ) SOCS3 = ( STAT3 ) RASgrp = ( DAG ) NFAT = ( CD28 AND ( ( ( TCR ) ) ) ) OR ( ( Calcineurin AND ( ( ( P38 ) ) ) ) AND NOT ( GSK-3b ) ) OR ( TCR AND ( ( ( CD28 ) ) ) ) IL21R = ( IL21 AND ( ( ( GP130 AND CGC ) ) ) ) OR ( IL21_e AND ( ( ( GP130 AND CGC ) ) ) ) IL6R = ( GP130 AND ( ( ( IL6_e AND IL6RA ) ) ) ) AKT = ( PDK1 ) RAF1 = ( Ras ) Paxillin = ( FAK_576_577 ) LAT = ( ZAP-70 ) ITAMS = ( Lck ) PIP3_345 = ( PI3K ) Sos = ( Grb2 ) CAV1_scaffold = ( Src ) OR ( CAV1_ACTIVATOR ) OR ( Bintegrin ) MEK4 = ( MEKK4 ) BCL10_Malt1 = ( CARMA1 ) STAT4 = ( ( JAK2 ) AND NOT ( GATA3 ) ) OR ( ( P38 AND ( ( ( Tyk2 ) ) ) ) AND NOT ( GATA3 ) ) G_Actin = ( Profilin ) JNK = ( rac1 AND ( ( ( Crk ) ) ) ) OR ( MEK4 ) OR ( MKK7 ) CD26 = ( CAV1_scaffold ) ITK = ( SLP-76 ) IRF4 = ( GATA3 ) adenyl_cyclase = ( GalphaS_R ) GAB2 = ( Shc1 AND ( ( ( Grb2 ) ) ) ) proliferation = ( proliferation ) OR ( STAT5_HIGH ) IRSp53 = ( rac1 ) IL21 = ( NFAT AND ( ( ( proliferation AND STAT3 ) ) ) ) PAK = ( rac1 ) OR ( Cdc42 ) OR ( Nck ) MEK6 = ( MEKK4 ) FAK_576_577 = ( FAK_Tyr397 AND ( ( ( Src ) ) ) ) Galpha_iR = ( Galpha_iL ) IL12RB1 = ( IRF1 ) OR ( IL12_e ) GADD45G = ( IL12_e ) OR ( CD3 ) IFNG = ( ( ( STAT4 AND ( ( ( proliferation AND NFAT ) ) ) ) AND NOT ( FOXP3 ) ) AND NOT ( STAT3 ) ) OR ( ( ( ATF2 ) AND NOT ( FOXP3 ) ) AND NOT ( STAT3 ) ) OR ( ( ( AP1 AND ( ( ( STAT4 ) ) ) ) AND NOT ( FOXP3 ) ) AND NOT ( STAT3 ) ) OR ( ( ( RUNX3 AND ( ( ( proliferation AND TBET AND NFAT ) ) ) ) AND NOT ( FOXP3 ) ) AND NOT ( STAT3 ) ) OR ( ( ( HLX ) AND NOT ( FOXP3 ) ) AND NOT ( STAT3 ) ) IL15R = ( CGC AND ( ( ( IL2RB AND IL15RA AND IL15_e ) ) ) ) TBET = ( ( TBET ) AND NOT ( GATA3 ) ) OR ( ( STAT1 ) AND NOT ( GATA3 ) ) EPAC = ( cAMP ) RhoGEF = ( Galpha12_13R ) OR ( FAK_576_577 ) IL2R = ( IL2 AND ( ( ( IL2RB AND CGC ) AND ( ( ( NOT IL2RA ) ) ) ) ) ) OR ( IL2_e AND ( ( ( IL2RB AND CGC ) AND ( ( ( NOT IL2RA ) ) ) ) ) ) STAT6 = ( IL4R ) STAT5_HIGH = ( IL4R_HIGH ) OR ( IL2R_HIGH ) TCR = ( APC AND ( ( ( CD28 ) ) ) ) STAT1 = ( ( IFNBR ) AND NOT ( SOCS1 ) ) OR ( ( IFNGR ) AND NOT ( SOCS1 ) ) OR ( ( IL27R ) AND NOT ( SOCS1 ) ) DAG = ( PLCb ) OR ( PLCg ) JAK1 = ( ( IL2R ) AND NOT ( SOCS3 ) ) OR ( ( JAK3 ) AND NOT ( SOCS3 ) ) OR ( ( IL9R ) AND NOT ( SOCS3 ) ) OR ( ( IL22R ) AND NOT ( SOCS3 ) ) IL10R = ( IL10 AND ( ( ( IL10RB AND IL10RA ) ) ) ) OR ( IL10_e AND ( ( ( IL10RB AND IL10RA ) ) ) ) Ras = ( Sos ) OR ( RASgrp ) IP3 = ( PLCg ) BRAF = ( Rap1 ) RIAM = ( Rap1 ) Ca2+ = ( IP3 ) IRAK1 = ( IL18R1 ) Cofilin = ( NOT ( ( LIMK ) ) ) OR NOT ( LIMK ) IL18R1 = ( IL18_e ) ZAP-70 = ( ITAMS AND ( ( ( CD3 ) ) ) ) Rap1 = ( EPAC ) OR ( C3G AND ( ( ( Crk ) ) ) ) OR ( PKA ) IRF1 = ( STAT1 ) AP1 = ( STAT4 ) OR ( JNK ) OR ( ERK ) Bintegrin = ( ECM ) OR ( TCR ) PLCb = ( Galpha_Q ) MLC = ( ROCK ) cAMP = ( adenyl_cyclase ) SYK = ( IL2R ) ICOS = ( APC ) RUNX3 = ( ( TBET ) AND NOT ( GATA3 ) ) RORGT = ( RORGT AND ( ( ( STAT3 OR TGFBR ) ) ) ) OR ( TGFBR AND ( ( ( STAT3 ) ) ) ) Galpha12_13R = ( alpha_13L ) PLCg = ( ZAP-70 ) OR ( ITK ) OR ( LAT ) NIK = ( TRAF6 ) CD3 = ( TCR ) WAVE-2 = ( IRSp53 AND ( ( ( rac1 ) ) ) ) Bcl10_Carma1_MALTI = ( BCL10_Malt1 AND ( ( ( CARMA1 ) ) ) ) GADD45B = ( IL12_e AND ( ( ( TCR ) ) ) ) IL27R = ( GP130 AND ( ( ( IL27_e AND IL27RA ) ) ) ) JAK2 = ( IL12RB1 AND ( ( ( IL12RB2 ) ) ) ) IL22R = ( IL22_e ) Crk = ( Cas ) OR ( Paxillin ) P38 = ( MEK3 ) OR ( MEK6 ) IKKcomplex = ( Bcl10_Carma1_MALTI ) OR ( NIK ) OR ( TCR ) SHP2 = ( GAB2 ) OR ( IL2RB ) STAT5 = ( IL2R ) OR ( IL4R ) OR ( SYK ) OR ( IL15R ) OR ( Lck ) OR ( JAK1 ) TAK1 = ( TRAF6 ) TGFBR = ( TGFB ) OR ( TGFB_e )
EDUCATION Integrating Interactive Computational Modeling in Biology Curricula Tomáš Helikar1, Christine E. Cutucache2, Lauren M. Dahlquist2, Tyler A. Herek2, Joshua J. Larson2, Jim A. Rogers3 1 Department of Biochemistry, University of Nebraska–Lincoln, Lincoln, Nebraska, United States of America, 2 Department of Biology, University of Nebraska–Omaha, Omaha, Nebraska, United States of America, 3 Department of Mathematics, University of Nebraska–Omaha, Omaha, Nebraska, United States of America thelikar2@unl.edu Abstract While the use of computer tools to simulate complex processes such as computer circuits is normal practice in fields like engineering, the majority of life sciences/biological sciences courses continue to rely on the traditional textbook and memorization approach. To address this issue, we explored the use of the Cell Collective platform as a novel, interactive, and evolving pedagogical tool to foster student engagement, creativity, and higher-level think- ing. Cell Collective is a Web-based platform used to create and simulate dynamical models of various biological processes. Students can create models of cells, diseases, or pathways themselves or explore existing models. This technology was implemented in both under- graduate and graduate courses as a pilot study to determine the feasibility of such software at the university level. First, a new (In Silico Biology) class was developed to enable stu- dents to learn biology by “building and breaking it” via computer models and their simula- tions. This class and technology also provide a non-intimidating way to incorporate mathematical and computational concepts into a class with students who have a limited mathematical background. Second, we used the technology to mediate the use of simula- tions and modeling modules as a learning tool for traditional biological concepts, such as T cell differentiation or cell cycle regulation, in existing biology courses. Results of this pilot application suggest that there is promise in the use of computational modeling and software tools such as Cell Collective to provide new teaching methods in biology and contribute to the implementation of the “Vision and Change” call to action in undergraduate biology edu- cation by providing a hands-on approach to biology. Introduction The enormous complexity that recent research has revealed in biological and biochemical sys- tems has resulted in the emergence of mathematical modeling and computer simulations as an integral part of biomedical research. This provides researchers with new tools to understand the role of emergent properties in healthy and diseased cells, to generate new hypotheses, and even screen potential pharmaceuticals for cross-reactivity and potential targets [1–3]. PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004131 March 19, 2015 1 / 9 a11111 OPEN ACCESS Citation: Helikar T, Cutucache CE, Dahlquist LM, Herek TA, Larson JJ, Rogers JA (2015) Integrating Interactive Computational Modeling in Biology Curricula. PLoS Comput Biol 11(3): e1004131. doi:10.1371/journal.pcbi.1004131 Editor: Joanne A. Fox, University of British Columbia, CANADA Published: March 19, 2015 Copyright: © 2015 Helikar et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: Office of Sponsored Programs at the University of Nebraska at Omaha via University Committee on Research and Creative Activity grants to TH, CC, TAH, and LD. National Institutes of Health (#5R01DA030962) to JAR. University of Nebraska– Lincoln to TH. The funders had no role in the preparation of the manuscript. Competing Interests: Tomáš Helikar and Jim A Rogers are or have served as scientific advisors and/ or consultants to Discovery Collective. Given the fact that the field is undergoing a shift in the basic way the functions of these dy- namical systems/networks are understood, it is essential for biology education to evolve in order to reflect these changes [4,5]. It is vital for students to learn about these structures and the resultant emergent properties that are not obvious from looking at static pictures in text- books. Furthermore, the National Science Foundation and the American Association for the Advancement of Science have initiated a call to action, “Vision and Change” [6], that aims to transform undergraduate biology education by incorporating computational methods and by introducing key core competencies including simulation and modeling. A number of efforts have already been initiated in this direction, including problem-based learning in the under- graduate setting [7], translational approaches (i.e., having students serve as researchers in the classrooms to investigate biological problems and identify solutions), as well as those led by Carl Wieman of the Carl Wieman Institute [8] and other leaders in foundational learning (e.g., [9,10]). Our group has also attempted to address this issue using our recently developed and re- leased modeling platform called Cell Collective [11,12]. The platform enables scientists to cre- ate, simulate, and analyze large-scale computational models of various biological systems without the need to enter/modify any mathematical expressions and/or computer code. Be- cause accessibility to modeling for a wide audience is the key ingredient of the technology, the platform lends itself to application in a classroom setting. Specifically, students can create, sim- ulate, and analyze then break and re-create and re-analyze dynamical models to understand major biological processes. The collaborative nature of the Web-based environment enables students to easily collaborate inside and outside of the classroom in a meaningful way. The types of biological processes that can be explored with Cell Collective are virtually unlimited; students can model biological processes including, but not limited to, cellular development, cel- lular differentiation, cell-to-cell interactions, disease pathogenesis, the effects of various treat- ments on disease, etc. Herein, we discuss two different applications of the Cell Collective’s interactive technology as a tool to facilitate hands-on, creative learning in the classroom and allow students to apply their knowledge in real-time. The first is using Cell Collective in a dedicated course (In Silico Biology) designed around the use of the technology, and the second involves introducing the technology as a supplement to existing, traditional biology courses. Both applications have been subjected to initial testing in a variety of undergraduate settings, and the results indicate that both methods were successful in increasing both understanding of and enthusiasm for complex biological systems in undergraduate student populations. A New Course Designed for Integrated Learning of Biological and Computational Concepts In Silico Biology is a course that was designed de novo to use Cell Collective as the central tool for teaching students complex biochemical systems by recreating them in silico. The individual objectives of the course include helping students to expand their analytical skills and become interested in computational sciences, learn to actively read primary journal articles, critically analyze and interpret data, and use interactive computational models to learn about biological networks. This is facilitated throughout the course via three major topics and strategies incor- porated into the course: 1. Introduction of biological concepts from a systems perspective The focus of the biological component of the In Silico Biology course is on complex networks found in biological systems. A series of lectures at the beginning of the semester provide PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004131 March 19, 2015 2 / 9 students with the foundation of molecular biology of the cell, including the principles of intra- and intercellular signal transduction. During this session, students also learn to think about biochemical protein regulatory mechanisms from a holistic perspective; that is, rather than fo- cusing on individual protein–protein interactions, students are expected to research and under- stand the overall regulatory mechanism of a given protein while taking into account most known interaction partners. For example, students are required to go beyond the traditional representation of the regula- tion of the Raf protein (Fig. 1). Raf is a key component of the mitogen activated protein kinase (MAPK) pathway, which regulates numerous cellular functions (e.g., growth, apoptosis, etc.). Students learn that Ras is only one of many components required to successfully activate, as well as deactivate, Raf via a combination of biochemical events (Fig. 1B) [13,14]. In the final part of this session, students are expected to research (from published literature) and describe the complete regulatory mechanism of an enzyme of their choice, as a system of multiple inter- action components. In this session, students are also introduced to Cell Collective, and are ex- pected to create and simulate a simple pathway model such as the one illustrated in Fig. 1A, as well as to model the regulatory dynamics of the researched enzyme. Importantly, with this ap- proach, the students learn how to read and critically analyze primary journal articles. (Fig. 1 adapted from [14]) 2. Introduction to the dynamics of biological systems via computational modeling In this part of the course, students learn the principles of the technology and modeling frame- work on which Cell Collective is based (Section 1 in S1 Text) [15–20]. This includes the differ- ent types of representation of Boolean functions, as well as concepts of state transition graphs, feedback loops, attractors, attractor stability, etc. All of these concepts are tied to and demon- strated in the Cell Collective platform and applied to biological examples. Students also learn about nonlinear dynamics such as bistability and oscillations associated with positive and nega- tive feedback loops, respectively. By the end of this session, students are able to represent com- plex biological regulatory mechanisms as Boolean functions and create and simulate the dynamics of their corresponding models (by hand, as well as in Cell Collective). An example of a biological system well-suited to the approach is bacterial chemotaxis (Section 2 in S1 Text). 3. Blurring the line between education and research: incorporating meaningful undergraduate research experiences into the classroom A large part of the course is devoted to a hands-on project during which students learn about a biological system by integrating the biological and computational concepts they learned in the course. Specifically, students select a biological network process of interest that they research, construct a computational model representation of, and study the dynamics of the process by simulating the model in Cell Collective. From our experience, it is the learning-by-building approach that enables students to learn and appreciate the diversity and complexities of biological systems. This method fosters curios- ity from the students, which keeps them motivated and active in the project. Reading the litera- ture with an objective to create a functional computer model forces the student to truly parse and analyze the information contained in published papers in order to distill the underlying logic of the system. Section 3 in S1 Text provides an example of how students learn by reading the literature and performing virtual research. PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004131 March 19, 2015 3 / 9 Incorporating Computational Modeling in Existing Life Sciences Courses As it is not always possible or practical to create a complete course de novo, the Cell Collective platform has also been used to aid in various existing undergraduate and graduate courses. These include undergraduate/graduate (online) cancer biology, undergraduate microbiology, and graduate (online) immunology courses. In order to facilitate the introduction of modeling into existing courses, a series of modeling modules were created; these modules are currently available in a new problem-based workbook [21] focused on cancer biology. Students utilized the models that comprise the various modules to simulate and analyze the dynamics of the biological processes as a way to visualize and rein- force the content discussed during regular lectures. The interactive nature of the technology en- ables students to alter any component or pathway of the process and, via instant feedback, observe the effects of the change made to the system. The modules are complementary to the traditional method of teaching as an interactive, dy- namic process with learning objectives that match the covered topic. For example, from the ex- ercises used in the cancer biology course, learning objectives focused on 1) determining the Fig 1. Comparison of linear and systems representation of Raf regulation. A) Traditional (linear) representation of MAPK signaling [13]. B) Detailed regulatory mechanism of Raf regulation that takes into account the role of most Raf interaction partners. doi:10.1371/journal.pcbi.1004131.g001 Table 1. List of developed modeling modules. Example Biological Concept Taught Course Type/Topic Malaria lifecycle Microbiology Positive feedback loops Cancer biology Negative feedback loops Cancer biology Cell cycle regulation Cancer biology DNA damage Cancer biology CD4+ T cell differentiation Cancer biology, immunology Cell communication networks Cancer biology doi:10.1371/journal.pcbi.1004131.t001 PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004131 March 19, 2015 4 / 9 dynamic, complex signaling processes that regulate tumor development and tumor regression and 2) the ability to illustrate feedback loops that contribute to tumor progression and regres- sion after use of the Cell Collective. Learning objectives of the computational module used in the microbiology course centered on the life cycle of Plasmodium spp., which leads to the de- velopment of malaria. Specifically, after dynamically modeling and manipulating developmen- tal processes of the Plasmodium lifecycle, students should be able to 1) draw and describe the complex life cycle and 2) define “vector,” “reservoir,” and “transmission.” Table 1 provides a list of modeling modules developed so far. As an example, one of these modeling modules used for more effective learning is discussed next. T cell differentiation and response to pathogen T cell differentiation is an important concept taught in many immunology courses. Precise reg- ulation of the differentiation process of naive CD4+ T cells (a subset of T-lymphocytes) to one of the helper T cells or regulatory T cells (Tregs) is critical for the proper functioning of the im- mune system. At the intracellular level, the differentiation process is regulated via a wide varie- ty of types of signaling receptors and pathways that are mutually cross-linked and form highly interconnected biochemical networks. Additionally, cytokines produced by each cell further modulate the activation and behavior of neighboring cells, as well as the entire immune system [22,23]. Hence, the complex network structures and nonlinear dynamics governing this pro- cess, via both intra- and intercellular paths, make T cell differentiation a great candidate for an interactive modeling approach. As such, a modeling module that mimics concepts and rela- tionships (Fig. 2) was created and used to aid the learning of T cell differentiation in Cell Collective. An advantage to the availability of a tool such as Cell Collective is that students can alter ex- ternal and internal conditions of the cell and observe real-time “output” or consequences at the molecular and/or cellular level. For example, students are asked to simulate the model by first activating antigen presenting cells (APCs) and naive T cells by introducing a “pathogen.” Path- ogens can be introduced by changing a simple activity slider on the user interface (Fig. 3A). As illustrated in Fig. 3B (left), the dynamical response to the change of the environment is imme- diate. Students can subsequently simulate Th2 differentiation by introducing IL4 (Fig. 3B mid- dle), as well as the effects of regulatory T cells (Treg) by activating TGF beta (Fig. 3B right). In addition to the time-series, real-time simulation output, students can view the dynamics of the entire model in a network representation in which each component of the model interactively assumes different colors based on the activity level of the component (Fig. 3C). Students are assigned a number of similar exercises to better understand the dynamics gov- erning T cell regulation during the activation of the immune system, including positive feed- back loops and associated bistable behaviors. Note that this model is one of many possible computational model representations of T cell differentiation. Other logical models that in- clude greater detail as to specific molecular interactions have been previously published by oth- ers [24–26], and some of these are also available in Cell Collective for simulations. Outcomes and Discussion A number of efforts to incorporate computation into life science courses have been established. For example, BioQuest consortium (http://www.bioquest.org) provides access to software tools, datasets, and other materials developed by educators and developers engaged in educa- tion and research in science. Another example includes NetLogo, a programming environment for agent-based modeling that has been used to study dynamics of complex systems, as well as for teaching of complex systems in many settings (middle schools, high schools, and PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004131 March 19, 2015 5 / 9 universities) [27]. Our approach provides a novel take on the implementation of problem- based methods in life sciences in that it offers a Web-based, systems- and network-focused, interactive, and real-time simulation-driven environment without the need for computer pro- gramming or manipulation of complex mathematical equations. We have used a Cell Collective “learning by modeling” approach both as a stand-alone class and as a supplement to complement existing classes. In both cases, student outcomes were highly positive (Section 5 in S1 Text). Future studies will include a comprehensive study using both quasi-experimental and randomized control groups to determine the effect that use of Cell Collective has on student understanding, long-term retention, critical thinking, applica- tion, and overall mastery of material. In addition to directly addressing the challenging problem of teaching students about com- plex, highly connected networks, there is an additional benefit; it provides these students with an opportunity to become interested in additional training in computational methods, some- thing that is critical for the current and the next generation of biomedical researchers. Making the class accessible for students with a wide range of skills such as biology, computer science, mathematics, etc., creates an ample environment for learning from one another, resulting in cross-pollination across disciplines. Fig 2. CD4+ T Cell differentiation as modeled for classroom use. doi:10.1371/journal.pcbi.1004131.g002 PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004131 March 19, 2015 6 / 9 Furthermore, one of the major components of utilization of Cell Collective was blurring the line between learning and research. This is a non-trivial aspect of this teaching method and, in- deed, it is in some ways the most exciting—for both the students and potentially the instruc- tors. In the course of their learning, students have the opportunity to be constructing the very first model of the system they are studying or, if working on an existing model, they have the opportunity to add information from recent literature to significantly update an existing model. This means that students, while learning, are engaging in real research. In our applica- tion of this teaching method, we have had a number of student-created and/or student- initiated modeling projects that led to research findings, some of which were subsequently presented by the students at an external research conference [28], and even accepted for publi- cation in a peer-reviewed journal [29]. A positive consequence of this is that it is possible for faculty to further their own research during the course of teaching the material. We have had several experiences of students who had no knowledge of what they might be interested in studying being assigned a project in the class that aligned with a research interest of our group. In several cases, the results were ulti- mately useful to the group, and in subsequent semesters new students were assigned to either re-create, significantly update, or provide fresh analysis of the model. All students that made significant contributions to the models were included as authors on all publications using that information. This result is a true win-win situation; faculty responsi- ble for teaching a course have the possibility of actually furthering their research, while stu- dents have the possibility to perform and be recognized for research participation. Real Fig 3. Interactive simulation of a T cell differentiation model. A) Simple sliders can be used to change the activity levels of various stimuli. B) Example of an interactive, real-time simulation. Left: Activation of Pathogen results in the stimulation of Antigen Presenting Cells and Naive T Cells. Middle: Stimulation with IL4 results in the activation of Th2 cells. Right: Addition of TGF beta stimulates Tregs, resulting in the suppression of Th2 cells. C) Network view of the changing dynamics during a real-time simulation. (Color range from bright red [inactive components] to bright green, which denotes full activity.) doi:10.1371/journal.pcbi.1004131.g003 PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004131 March 19, 2015 7 / 9 undergraduate research is not only a major goal for many universities, it is also very important for any undergraduate looking for entry into graduate programs. Supporting Information S1 Text. Integrating interactive computational modeling in biology curricula. (PDF) Acknowledgments We would like to thank Denis Thieffry for his feedback on the manuscript. We also thank all of the student participants for providing feedback to help make the novel teaching approach and software an exciting, high-quality learning tool. References 1. Kitano H (2002) Computational systems biology. Nature 420: 206–210. PMID: 12432404 2. Arkin AP, Schaffer DV (2011) Network News: Innovations in 21st Century Systems Biology. Cell 144: 844–849. doi: 10.1016/j.cell.2011.03.008 PMID: 21414475 3. 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Iron acquisition and oxidative stress response in aspergillus fumigatus Brandon et al. Brandon et al. BMC Systems Biology (2015) 9:19 DOI 10.1186/s12918-015-0163-1 Brandon et al. BMC Systems Biology (2015) 9:19 DOI 10.1186/s12918-015-0163-1 RESEARCH ARTICLE Open Access Iron acquisition and oxidative stress response in aspergillus fumigatus Madison Brandon1,2, Brad Howard3,4, Christopher Lawrence3,4 and Reinhard Laubenbacher2,5,6 Abstract Background: Aspergillus fumigatus is a ubiquitous airborne fungal pathogen that presents a life-threatening health risk to individuals with weakened immune systems. A. fumigatus pathogenicity depends on its ability to acquire iron from the host and to resist host-generated oxidative stress. Gaining a deeper understanding of the molecular mechanisms governing A. fumigatus iron acquisition and oxidative stress response may ultimately help to improve the diagnosis and treatment of invasive aspergillus infections. Results: This study follows a systems biology approach to investigate how adaptive behaviors emerge from molecular interactions underlying A. fumigatus iron regulation and oxidative stress response. We construct a Boolean network model from known interactions and simulate how changes in environmental iron and superoxide levels affect network dynamics. We propose rules for linking long term model behavior to qualitative estimates of cell growth and cell death. These rules are used to predict phenotypes of gene deletion strains. The model is validated on the basis of its ability to reproduce literature data not used in model generation. Conclusions: The model reproduces gene expression patterns in experimental time course data when A. fumigatus is switched from a low iron to a high iron environment. In addition, the model is able to accurately represent the phenotypes of many knockout strains under varying iron and superoxide conditions. Model simulations support the hypothesis that intracellular iron regulates A. fumigatus transcription factors, SreA and HapX, by a post-translational, rather than transcriptional, mechanism. Finally, the model predicts that blocking siderophore-mediated iron uptake reduces resistance to oxidative stress. This indicates that combined targeting of siderophore-mediated iron uptake and the oxidative stress response network may act synergistically to increase fungal cell killing. Keywords: Boolean network, Discrete dynamic model, Invasive aspergillosis, Siderophores, Stochastic discrete dynamical system Background Aspergillus fumigatus is a ubiquitous airborne fungus which has become an increasingly dangerous pathogen of humans worldwide, causing invasive infections, severe asthma and sinusitis [1]. The most severe form of A. fumi- gatus infection, called invasive aspergillosis (IA), occurs when inhaled A. fumigatus spores germinate into hyphae and invade lung tissue. IA is a major cause of mortality in immunocompromised human hosts [2-6]. In immuno- competent individuals A. fumigatus may trigger allergic Correspondence: mbrandon@uchc.edu 1Center for Cell Analysis and Modeling, University of Connecticut Health Center, 400 Farmington Ave, 06030 Farmington, USA 2Center for Quantitative Medicine, University of Connecticut Health Center, 195 Farmington Ave, 06030 Farmington, USA Full list of author information is available at the end of the article reactions and is a major cause of fungal keratitis, an inflammation of the cornea [7]. Our focus on A. fumigatus oxidative stress response and iron acquisition is motivated by the following three arguments. First, several studies show that deletion of genes involved in either A. fumigatus oxidative stress response or iron acquisition leads to attenuated virulence in vivo [5,8-10]. Impairment of the corresponding host defense mechanisms, e.g. defective ROS production or inability to sufficiently deplete available iron, also leads to an increased susceptibility to A. fumigatus infection [4,10,11]. Second, recent publications present proof of concept that targeting either A. fumigatus oxidative stress response or iron acquisition systems may be an effective treatment strategy [10,12]. Thus oxidative stress response © 2015 Brandon et al.; licensee BioMed Central. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Brandon et al. BMC Systems Biology (2015) 9:19 Page 2 of 17 and iron acquisition are important systems contribut- ing to A. fumigatus pathogenicity, and both systems are feasible targets for therapeutic intervention. Third, iron uptake and oxidative stress response networks are known to interact, and hence more can be learned about the molecular mechanisms underlying these networks if they are studied together. In fact, a connection between iron uptake and oxidative stress response has been described in both A. fumigatus and S. cerevisiae [13-15]. These motivating points will now be discussed in greater detail. Several lines of evidence point to the A. fumigatus ROS- detoxifying enzymes as key virulence factors and potential drug targets. Firstly, on the host side, the activation of the enzymatic complex NADPH oxidase (NOX) and sub- sequent production of cytotoxic ROS by host phagocytic cells is a critical mechanism for host defense against fun- gal pathogens such as A. fumigatus [16-18]. Noteably, a mouse model of fungal keratitis in the cornea using mice that do not express a functional NOX complex showed that neutrophil NOX expression was required for inhibiting A. fumigatus growth [10]. From a fun- gal perspective, genes encoding oxidative stress response enzymes are known to be among the most differentially expressed genes of A. fumigatus hyphae following expo- sure to human neutrophils from healthy individuals [19]. Furthermore, A. fumigatus antioxidant enzymes and the ROS-sensing transcription factor deletion strains show a heightened sensitivity to ROS in vitro [9,10,20]. Other evidence suggests that the adeptness of A. fumi- gatus to acquire iron from the host is a major basis of its pathogenicity. Both the fungus and host require iron for important cellular functions including respiration, gene regulation, DNA synthesis, and oxidative stress response [21]. Iron deprivation of invading pathogens by the host is a crucial host defense mechanism [22-24]. To combat this, fungi secrete siderophores, low-molecular-mass iron binding compounds that sequester iron from host pro- teins. [25]. A significant body of evidence suggests that the victor of this battle for iron is a key determinant of whether infection will persist or be cleared [25-28]. Notably, a mutant A. fumigatus strain unable to produce both extra- and intracellular siderophores was avirulent in a mouse model of IA [5]. Any advantage A. fumigatus has in the battle for iron can be dangerous. For instance, increased iron in bone marrow is a risk factor for IA in high-risk patients [11]. Similarly, the heightened suscep- tibility to fungal infections in neutropenic patients may be in part due to increased extracellular iron due to the absence of host cells which mediate iron sequestration [29]. Leal et al. show that the use of topical drugs to tar- get either A. fumigatus oxidative stress response or iron acquisition systems is effective for treating A. fumiga- tus infection in mice cornea [10,12]. The fungal iron acquisition system is a particularly promising target for therapeutic intervention because the fungal proteins which import ferri-siderophores are one of the few protein families that are unique to fungi [30]. This might make it possible to design drugs which specifically target the fun- gus without affecting the host, perhaps by a “Trojan horse” approach [31,32]. Furthermore, the iron acquisition and oxidative stress response networks are connected. Indeed it was found in A. fumigatus that deletion of a key iron regulatory protein, sreA, caused increased sensitivity to superoxide [13]. Also in A. fumigatus deletion of an intracellular siderophore led to decreased expression of conidial, but not hyphal, catalase [33]. Similarly, in A. nidulans oxidative stress was shown to increase the accu- mulation of an intracellular siderophore [14]. Finally, a yeast mutant with deletion of genes that regulate the tran- scription of high-affinity iron transport genes also showed several phenotypes related to oxidative stress such as hypersensitivity to hydrogen peroxide [15]. The role of mathematical modeling The purpose of the present work is to gain a deeper understanding of the molecular mechanisms underly- ing the systems that most contribute to A. fumigatus pathogenicity, the iron acquisition and oxidative stress response networks. For this purpose, we have constructed a novel dynamic mathematical model of key molecu- lar interactions defining these networks. Mathematical modeling of complex molecular interaction networks allows for the encoding of dynamic interactions among molecules, and thus enables the simulation of global net- work behavior based on information known about indi- vidual interactions. Recently, the first computational model of A. fumiga- tus iron regulation was proposed [34]. Taking a top-down approach, Linde et al. used gene expression time series data to reverse engineer a regulatory network and pre- dict new interactions between transcription factors and target genes. The authors constructed a system of differ- ential equations to model changes in gene expression as a function of other genes in the network. A major challenge to building differential equations models is that many of the required parameters are either unknown or unmea- surable, and so parameters must be estimated by fitting equations to experimental time series data, which is lim- ited for A. fumigatus iron regulation and oxidative stress response. However, there is a wealth of qualitative data for these networks, for example the interaction between a tran- scription factor and a gene, from high-throughput tran- scriptomic experiments such as microarrays [13,29,35]. In contrast to the Linde et al. computational study, we take a bottom-up approach to investigate both iron regula- tion and oxidative stress response, and we apply a discrete Brandon et al. BMC Systems Biology (2015) 9:19 Page 3 of 17 dynamic modeling framework. Discrete models make use of the available qualitative data by encapsulating the reg- ulatory logic driving a network, and they do not require kinetic parameters. Simulation of discrete models pro- vides coarse-grained information as the network evolves over an arbitrary unit of time in response to broad changes in some physiological condition. Qualitative observations generated by these models are extremely useful for inves- tigating the ability of known or proposed information to explain current experimental results, studying how per- turbations may alter global behavior, and for pinpointing productive future experiments. Discrete models, in particular Boolean network mod- els, are routinely used to investigate biological systems such as gene regulatory networks, signaling pathways, and metabolic pathways [36-41]. Discrete models have contributed insights into host-pathogen interactions for several pathogenic bacteria [42-44]. To our knowledge, discrete models have not yet been used to study A. fumi- gatus biology, yet many aspects of yeast biology have been explored via discrete models [45-47]. This includes a Boolean network model of metabolic adaptation to oxygen in relation to iron homeostasis and oxidative stress [48]. Results and discussion Description of model species The model contains an oxidative stress response mod- ule and a larger iron acquisition module which is made up of five submodules: siderophore biosynthesis (SB), iron uptake, iron storage, iron usage, and iron regulation. Figure 1 is a graphical representation of all model species (nodes), their interactions (edges), and the sign of the interaction. Siderophore biosynthesis A. fumigatus produces four siderophores, low molecular mass ferric iron-specific chelators [33]. Two extracellu- lar siderophores are excreted from the cell to sequester iron from the extracellular space [8]. And two intracel- lular siderophores are used for intracellular iron storage [14,49]. For simplicity, our model considers only one extracellular siderophore, triacetylfusarinine C (TAFC), and one intracellular siderophore, ferricrocin (FC), which have been shown to be the two most abundant and active A. fumigatus siderophores [50]. The first step in the biosynthesis of all four siderophores is the hydrox- ylation of ornithine catalyzed by SidA, an ornithine monooxygenase. Iron uptake Iron uptake is believed to be the main iron homeostasis control mechanism used by A. fumigatus, in part because mechanisms of iron excretion have not been found in fungi [51]. A. fumigatus has three known mechanisms of iron uptake: low affinity ferrous iron uptake, which has not yet been characterized at the molecular level, and two high affinity ferric iron uptake systems, namely siderophore- mediated iron uptake and reductive iron assimilation (RIA) [8]. RIA involves the reduction of ferric iron to fer- rous iron by the ferric reductase FreB and subsequently the import of ferrous iron by a protein complex consisting of the ferroxidase FetC and the iron permease FtrA [52]. For simplicity, these three proteins are modeled as a single species called RIA. Siderophore-mediated iron uptake is represented in the model by nodes TAFC, MirB, and EstB. TAFC is released into the extracellular space to steal ferric iron from host proteins such as transferrin [53]. A protein fam- ily called siderophore-iron transporters (SIT) recognizes and retrieves specific ferri-siderophores. After binding to Fe3+, the ferri-TAFC complex is taken back up by the TAFC-specific SIT MirB [54]. After import into the cell the ferri-TAFC complex is degraded by a TAFC-specific esterase called EstB [55]. Subsequently, breakdown prod- ucts are recycled, and iron is released into the cell for transfer to intracellular siderophores or the iron vacuole [56]. Iron storage Unlike bacteria, plants and animals, most fungi lack ferritin-mediated iron storage [51]. Instead, A. fumigatus relies on siderophore-mediated iron storage via the intra- cellular siderophore FC and a siderophore-independent iron storage unit, the iron vacuole [49,56]. Import of iron into the vacuole is in part mediated by the protein CccA which is localized in the vacuolar membrane [56]. The labile iron pool, a pool of redox-active iron, is also mod- eled as a transitory state between the release of iron from ferri-TAFC and the transfer of iron to FC or the vacuole. Again, since fungi lack mechanisms for iron excretion, iron storage plays a crucial role in avoiding iron-induced toxicity. In A. nidulans, FC deficiency was shown to cause an increase in LIP and a decrease in the oxidative stress resistance of hyphae [57]. Iron usage All iron consuming pathways, for example heme biosyn- thesis, TCA cycle, respiration, and ribosome biogenesis, are modeled as a single species named ICP. Regulation Iron is toxic in excess; thus tight regulatory mechanisms are required to maintain iron homeostasis. Iron regulation in A. fumigatus is controlled by two central transcrip- tion factors: the bZip CCAAT-binding transcription fac- tor HapX and the GATA transcription factor SreA [13,29]. HapX and SreA are postulated to sense intracellular iron Brandon et al. BMC Systems Biology (2015) 9:19 Page 4 of 17 Iron Regulation Iron Storage Iron Usage Oxidative Stress Response Iron Uptake Siderophore Biosynthesis sreA hapX SreA HapX RIA EstB MirB TAFC SidA LIP VAC thioredoxin pathway Fe3+ CccA O2 - ROS SOD2/3 Yap1 Cat1/2 ICP FC-Fe FC+Fe Figure 1 Model interaction diagram of A. fumigatus iron regulation and oxidative stress response. Rectangles represent genes. Ovals represent other molecules. Fe3+ and O− 2 are external parameters to describe the physiological state of a fungal cell. A →B represents activation. A ⊣B represents inhibition. levels through a posttranslational mechanism similar to the mechanism employed by a closely related species, the fission yeast Schizosaccharomyces pombe [27]. In S. pombe, orthologs of HapX and SreA physically interact with a monothiol glutaredoxin Grx4 which is localized along the nuclear rim [58-60]. When intracellular iron lev- els are low Grx4 maintains SreA in an inactive state [59]. When intracellular iron levels are high, Grx4 inactivates HapX by directing its export from the nucleus [58]. Hence, intracellular iron blocks HapX function while activating SreA function at the posttranslational level. Furthermore, SreA represses transcription of hapX when intracellular iron levels are high, while HapX represses transcription of sreA when intracellular iron levels are low. Both tran- scriptional and posttranslational regulatory mechanisms are modeled. SreA transcriptionally represses genes coding for pro- teins involved in iron uptake, including sidA, mirB, estB, and those involved in RIA [13]. HapX activates siderophore biosynthesis, in part by upregulating the pro- duction of the precursor ornithine, and activates the transcription of mirB [29]. HapX indirectly activates the transcription of sidA, estB, and the genes involved in RIA through its repression of sreA. Additionally, HapX represses iron consuming pathways, cat1, and cccA at the transcriptional level. Oxidative stress response NOX expressed by host phagocytic cells catalyzes the con- version of oxygen to the the extremely reactive superox- ide anion, O− 2 . Contact between neutrophils and hyphae triggers a respiratory burst, the targeted release of O− 2 from the neutrophil into the extracellular space where it diffuses into nearby hyphal cells. The A. fumigatus ROS- sensing transcription factor Yap1 is believed to be the main regulator of antioxidant defense against O− 2 and hydrogen peroxide, H202 [61,62]. Yap1 typically resides in the cytoplasm, yet under oxidative stress conditions Yap1 localizes to the nucleus and from there controls, directly or indirectly, the expression of key ROS-detoxifying enzymes including superoxide dismutases (SODs), cata- lases, and thioredoxin peroxidases (peroxiredoxins) [61]. Elevated free iron levels (high LIP) in the cell also con- tribute to the formation of ROS [63]. SODs catalyze the conversion of O− 2 to less reac- tive H2O2 which can then be converted to non-reactive Brandon et al. BMC Systems Biology (2015) 9:19 Page 5 of 17 H2O by either catalases or peroxiredoxins. A. fumigatus produces four SODs, yet only the mitochondrial SOD2 and cytoplasmic SOD3 are modeled here since both are most strongly expressed in hyphae, the tissue invasive form of this pathogen, as opposed to in conidia [20]. A. fumigatus hyphae produce two catalases, Cat1 and Cat2, which break down hydrogen peroxide [9]. The thiore- doxin pathway in A. fumigatus is not well characterized; however, two putative peroxiredoxins and five putative thioredoxins have been identified [10,61]. Briefly, per- oxiredoxins reduce H202 and by doing so become oxi- dized, a non-functional state. Thioredoxins then reduce the oxidized peroxiredoxins back to their functional state so that more H202 can be reduced [64]. In the model the thioredoxin pathway is modeled as a single vari- able. Note that in Figure 1 the ROS species has a self- activating arrow. The purpose of this interaction is to enforce “memory” in the system, i.e. if ROS is high at the current time step and antioxidant enzymes are not expressed or inactive, then the ROS variable should “remember” to remain high until antioxidant enzymes are active. Building and simulating the mathematical model The model presented in this paper is discrete. This means species can take on only a finite number of states, and the state of each species is iteratively updated at discrete time steps according to logical rules. The discrete model presented here is a Boolean network model, meaning that each species can take on only two states (e.g. low expressed or high expressed; low active or high active), which may be represented numerically by either a 0 or a 1. Furthermore, the rules determining how species are updated are Boolean functions. We conducted an extensive literature survey to iden- tify key species involved in the A. fumigatus iron reg- ulatory and oxidative stress response networks as well as the interactions of each species with other species in the networks (Figure 1). Table 1 gives a biological description of each species and the meaning assigned to its states. Note that for different species we may assign different meanings to their states. Importantly, the two species iron and superoxide should be thought of as external parameters since they are meant to distinguish between different physiological conditions that are reflec- tive of the host-pathogen interaction. Iron and superox- ide have no regulators (incoming arrows) (see Figure 1) and so, unlike other species, a fixed state is chosen at the start of a simulation and this state will never be updated. Next we integrated all identified interactions into a dynamic framework by specifying, through logical rules called update rules, how each species transitions between its two states based upon the states of its inputs. Table 2 Table 1 List of species, their biological type, and their model states Species Type Model states 0 1 hapX Gene Low expressed High expressed sreA Gene Low expressed High expressed HapX Protein; bZip CCAAT-binding TF Low active High active SreA Protein; GATA TF Low active High active RIA Enzyme complex; reductive iron assimilation Low active High active EstB Enzyme; TAFC-specific esterase Low active High active MirB Protein; TAFC-specific importer Low active High active SidA Enzyme; ornithine monooxygenase Low active High active TAFC Extracellular siderophore Low synthesized High synthesized ICP Iron consuming pathways Low active high active LIP Labile iron pool Low iron High iron CccA Protein; iron importer to vacuole Low active High active FC+Fe Intracellular siderophore w/ bound iron Low iron High iron FC−Fe Intracellular siderophore w/o bound iron Low synthesized High synthesized VAC Vacuole Low iron High iron ROS Reactive oxygen species Low ROS High ROS Yap1 Protein; bZip TF Low active High active SOD2/3 Enzyme; superoxide dismutase Low active High active Cat1/2 Enzymes; hyphal catalases Low active High active Thioredoxin P. Enzyme pathway Low active High active Iron Physiological state Low iron High iron Superoxide Physiological state Low superoxide High superoxide lists the update rule for each species as a Boolean function along with a summary of experimental support for each rule. The model is available in SMBL qual format, a stan- dard language for representation of qualitative models of biological networks [65], see Additional file 1. Brandon et al. BMC Systems Biology (2015) 9:19 Page 6 of 17 Table 2 Update rules of model species and supporting literature citations Update rules Literature support 1 hapX(t+1) = NOT SreA Transcription of hapX is repressed by SreA [13,29]. 2 sreA(t+1) = NOT HapX Transcription of sreA is repressed by HapX [13,29]. 3 HapX(t+1) = hapX AND (NOT LIP) An ortholog of HapX is inactivated by intracellular iron [58]. 4 SreA(t+1) = sreA AND LIP An ortholog of SreA is activated by intracellular iron [59,60]. 5 RIA(t+1) = NOT SreA SreA transcriptionally represses RIA genes [13]. 6 EstB(t+1) = NOT SreA SreA transcriptionally represses estB [13]. 7 MirB(t+1) = HapX AND (NOT SreA) HapX transcriptionally activates mirB [29]. SreA transcriptionally represses mirB [13]. 8 SidA(t+1) = HapX AND (NOT SreA) HapX up regulates the SidA substrate ornithine [29]. SreA transcriptionally represses sidA [13]. 9 TAFC(t+1) = SidA SidA catalyzes the first step in siderophore biosynthesis [5,8] 10 ICP(t+1) = (NOT HapX) AND (VAC OR FC+Fe) HapX represses consumption of intracellular iron [29]. 11 LIP(t+1) = (TAFC AND MirB AND EstB) OR (Iron AND RIA) TAFC sequesters iron from the extracellular space [8]. MirB imports ferri- TAFC [54]. EstB degrades ferri-TAFC bonds and releases free iron [55]. RIA compensates for a lack of siderophores when grown in high iron media [33]. 12 CccA(t+1) = NOT HapX HapX transcriptionally represses cccA [29]. 13 FC−Fe(t+1) = SidA SidA catalyzes the first step in siderophore biosynthesis [5,8] 14 FC+Fe(t+1) = LIP AND FC−Fe FC is involved in intracellular iron storage [14,49]. 15 VAC(t+1) = LIP AND CccA CccA mediates import of intracellular iron into the vacuole [56]. 16 ROS(t+1) = LIP OR Elevated free iron levels catalyze the formation of ROS [63]. Superoxide AND NOT (SOD3 AND ThP AND Cat1/2) OR SODs convert O− 2 to H2O2 [20]. Either catalases or thioredoxin ROS AND NOT SOD3 AND (ThP OR Cat1/2) convert H2O2 to non-reactive H2O [9,64]. 17 Yap1(t+1) = ROS Yap-1 is activated by superoxide [61,62]. 18 SOD2/3(t+1) = Yap1 Yap-1 activates transcription of sod2/3 [61]. 19 Cat1/2(t+1) = Yap1 AND (NOT HapX) Yap-1 activates transcription of cat1/2 [61]. HapX transcriptionally represses cat1 [29]. 20 ThP(t+1) = Yap1 Yap-1 activates transcription of thioredoxin peroxidases [61]. 21 Iron(t+1) = Iron External parameter. 22 Superoxide(t+1) = Superoxide [= NOT Superoxide, Figure 5 only] External parameter. Species that appear on the right side of the = represent states at time t. In general, the dynamic behavior of discrete models is simulated by starting from an initial state and then enumerating the changing state space as each species is updated over a specified number of iterations called time steps. The result of deterministic simulations, when all species are updated simultaneously at each time step, is shown in Figure 2. This system has no steady state solu- tion for any of the four external conditions. All long term behavior is oscillatory, i.e. the stable states form a limit cycle and 100% of the 1048576 states converge to the limit cycle displayed. Many biological processes such as gene expression have been found to exhibit a high degree of stochasticity [66-69]. Furthermore, protein levels can differ signif- icantly among cells in a population [70,71]. To our knowledge no single cell gene expression or protein level measurements are available for A. fumigatus. Hence in order to make comparisons to experimental data possible, we needed to account for the variability that one observes in a population of cells. We accounted for this variabil- ity by simulating randomness in the update of species. At each time step, rather than updating all species, some species are randomly selected to be updated, while the unselected species are left in their current state. We assume that the average of many of these stochastic simu- lations represents a population level measurement. Brandon et al. BMC Systems Biology (2015) 9:19 Page 7 of 17 State: Low High Low Fe3+ High Fe3+ Extracellular Fe3+ & O2 - Levels hapX sreA HapX SreA RIA EstB MirB SidA TAFC ICP LIP CccA FC-Fe FC+Fe VAC ROS Yap1 SOD2/3 Cat1/2 ThP O w o L 2 - Low Fe3+ High Fe3+ O h gi H 2 - Wildtype Figure 2 Stable states of A. fumigatus iron regulatory and oxidative stress response networks. This figure shows the cyclic attractor for each of the four possible external conditions. States transition from top to bottom. Under both low iron conditions ICP is in state 0 (low) the majority of the cycle. Under both high superoxide conditions ROS is in state 1 (high) the majority of the cycle. Linking model simulation results to phenotype predictions For the results presented in this paper, we ran 100 inde- pendent stochastic simulations (initialized in the same state) and, for each species, calculated the average state at each time step. From there, we counted the number of times a species took on any average state throughout the simulation period. We can plot a histogram of these counts to visualize a distribution of species’ average state across 100 simulations, as in Figure 3. To characterize long-term behavior, we introduce a measure called the sta- ble distribution mean (SDM) for a given species under a given set of initial conditions. The SDM is simply the mean of the distribution of the average states from time steps 100 to 200. Excluding the first 100 time steps from the calculation gives the model time to settle into a stable configuration. We first simulated the Boolean network model of wild type A. fumigatus under each of the four possible condi- tions: (1) low iron and low superoxide, (2) high iron and low superoxide, (3) low iron and high superoxide, and (4) high iron and high superoxide. Figure 3 (A) - (C) show the distributions of average states across 100 wild type sim- ulations for six selected species under three of the four conditions. Wild type distributions are not shown for the remaining condition; instead Figure 4(B) and (D) show trajectories, the average state at each time step, for eight selected species. For both low iron conditions, we observed that HapX, the transcription factor activating iron uptake and repressing iron consumption, is more active than SreA, the transcription factor repressing iron acquisition. This leads to strong activity of proteins related to siderophore- mediated iron uptake (MirB) and reductive iron assim- ilation (RIA). Conversely, for the high iron conditions we observe that SreA is more active than HapX. Conse- quently, activity of both MirB and RIA are significantly reduced as compared to the low iron, low superoxide condition. These results recapitulate experimental obser- vations [29,72]. ROS-detoxifying enzymes, SOD2/3 and Cat1/2, are moderately active in the low iron, low superoxide con- dition. As expected, since free iron and superoxide con- tribute to ROS, the activity of SOD2/3 and Cat1/2 are elevated in high iron and high superoxide conditions. Fur- ther, we observed that in low iron conditions Cat1/2 is less active than SOD2/3. This makes sense because catalases Brandon et al. BMC Systems Biology (2015) 9:19 Page 8 of 17 Low growth High growth Minimal growth Overwhelming cell death High cell death Low cell death A B C D 0 5 10 Count Low Fe3+, High O2 - High Fe3+, High O2 - Phenotype Reference Cat1/2 HapX MirB RIA SOD2/3 SreA Variable State State Count Count 10 5 0 15 10 5 0 0.0 0.25 0.5 0.75 1.0 0.0 0.25 0.5 0.75 1.0 0.0 0.25 0.5 0.75 1.0 State Condition O2 -=0, Fe3+=0 Average state 0.0 0.25 0.5 0.75 1.0 O2 -=0, Fe3+=1 O2 -=1, Fe3+=0 O2 -=1, Fe3+=1 ICP ROS Variable Low Fe3+, Low O2 - Figure 3 Summary of model wild type phenotypes. (A)-(C) Histogram of average states of six species from time steps 100-200 (i.e., the model reaches a stable configuration before counting begins). Vertical dashed lines mark stable distribution means (SDM). (D) The SDM of ICP and ROS for a wild type fungal cell under each of the four conditions overlayed with a depiction of the phenotype reference. If the SDM of ICP is 0, then we interpret the model observation as minimal or no growth. An ICP SDM in (0, 0.33) is interpreted as low growth. Otherwise, an ICP in [0.33, 1] signifies a high growth phenotype. If the ROS SDM falls in [0.66,1] we interpret this as high cell death. When the SDM of ROS is 1, we assume the ROS is so overwhelming that the entire population dies. Otherwise, for an ROS SDM in [0, 0.66) the interpretation is low cell death. require heme as a cofactor whereas SODs instead require copper, zinc or manganese [20]. Based on experimental results of wild type A. fumiga- tus growth under each of the four conditions [8,20,33], we used the stable distribution mean (SDM) of model variables ROS and ICP to establish a phenotype refer- ence according to the following rules (see Figure 3). If the SDM of ICP is 0, then we interpret the model observa- tion as minimal or no growth. An ICP SDM in (0, 0.33) is interpreted as low growth. Otherwise, an ICP in [0.33, 1] signifies a high growth phenotype. If the ROS SDM falls in [0.66,1] we interpret this as high cell death. When the SDM of ROS is 1, we assume ROS is so overwhelming that the entire population dies. Otherwise, for an ROS SDM in [0, 0.66) the interpretation is low cell death. These rules bin wild type model behavior to match what we observe experimentally. We then used this set of rules to infer the severity of model knockouts. Stochastic simulations reproduce in vitro time course data We validated the model on the basis of its ability to repro- duce transcriptional time course data from a previously published study and data generated in this study. In both experiments, A. fumigatus is grown in iron depleted min- imal media (low iron, low superoxide conditions). After an incubation period, iron is added to the media (high iron, low superoxide conditions) and gene expression is measured over a period of hours either using microarrays (Schrettl et al., 2008 [13]) or by qRT-PCR (this study, see Methods). To mimic the switch from low iron to high iron con- ditions, all simulations were initialized from a state of iron starvation (Figure 4G). Iron and superoxide were fixed at 1 and 0, respectively, throughout model simula- tions. Experimental results are displayed alongside model simulation results in Figure 4. From the Schrettl et al. study, we plot all time course data for genes which corre- spond to species in the model. For knockout simulations, the state of the corresponding species is fixed at 0. To distinguish between model and experimental knockouts, using sreA as an example, we write sreA=0 to refer to model knockouts and sreA to refer to experimental knockouts. The model provides a good qualitative reproduction of changes in gene expression over time. Additionally the model captures the relative differences in degrees of up- Brandon et al. BMC Systems Biology (2015) 9:19 Page 9 of 17 Figure 4 Model simulation results and experimental time course data following a switch from low iron, low superoxide to high iron, low superoxide conditions. (A) Gene expression from a qRT-PCR experiment conducted in this study. (C), (E) Gene expression from a microarray experiment by Schrettl et al., 2008 for a wild type and sreA strain, respectively [13]. (B), (D), (F), (H) Simulated trajectories for corresponding model species plotted as the average state at each time step across 100 stochastic simulations. (G) All simulations were initialized from this state representing iron starvation. In (H) trajectories are generated by a model with post-translational regulation of HapX and SreA by iron (PTL) and an altered model with transcriptional regulation of hapX and sreA by iron (TS). Brandon et al. BMC Systems Biology (2015) 9:19 Page 10 of 17 or down-regulation among genes. For ease of exposition, we discuss the following results in the syntax of model species even though some model species refer to amount of protein while the experimental results refer to amount of transcript. Wild type results For wild type A. fumigatus, the experimental and model simulation results show the same expression patterns. Following the switch from low to high iron, catalases Cat1/2, the vacuolar iron importer CccA, and sreA were quickly up-regulated, then slowly decreased and leveled off. After the addition of iron, the expression of hapX, siderophore biosynthesis enzyme SidA, ferri-siderophore importer MirB, ferri-siderophore esterase EstB, and reductive iron assimilation RIA (ftrA in the experimen- tal data) were quickly down-regulated and remained low. Moreover, the model recapitulates experimental observations that among species contributing to iron uptake, SidA and MirB were less active under high iron conditions, as compared to the activity of RIA and EstB. sreA results Experimental and model simulation results are also in agreement for the sreA deletion strain, except for SidA and MirB which we discuss shortly. As in the wild type case, expression of CccA and Cat1/2 increased sharply after the addition of iron. However in the sreA knock- out, expression of CccA and Cat1/2 remained high over time. This can be attributed to the fact that iron uptake mechanisms were depressed in a sreA mutant. Indeed, in contrast to the wild type case, both experimental and model simulation results showed no change in the expres- sion of hapX, EstB, or RIA despite being exposed to high iron over a long period of time. In the sreA deletion experimental data the amount of sidA transcript remained the same, whereas the amount of SidA enzymatic activity in the model simulation plum- meted to very low. This in fact is not a discrepancy and serves to illustrate an important point. Although both HapX and SreA ultimately activate and respectively repress SidA enzymatic activity, only SreA directly tran- scriptionally regulates sidA [13,29]. Instead, HapX up- regulates the production of ornithine, the SidA substrate. This explains the derepression of sidA in the experimental data yet the lack of SidA activity in the model simula- tion. A difference between amount of sidA transcript and SidA enzymatic activity is not visible in the wild type data because HapX indirectly regulates the transcription of sidA through repression of sreA; this feature is lost in a sreA mutant. The discrepancy between gene expression of mirB in the experiment and activity of MirB in the model is unexpected since MirB is known to be regulated transcriptionally by both HapX and SreA [13,29]. This may suggest that MirB is in fact not regulated transcrip- tionally by HapX. Or alternatively, since MirB is known to transport other siderophores it may have additional regulators [54]. Regulation of HapX and SreA by iron The post-translational regulation of S. pombe orthologs of HapX and SreA by iron has been investigated [58-60]. A. fumigatus HapX and SreA are postulated to sense intra- cellular iron levels through a similar post-translational mechanism, but the corresponding mechanism has not yet been identified [27]. We included in the model both the known transcriptional regulation of hapX and sreA, by SreA and HapX respectively, and the proposed but not yet verified post-translational regulation of HapX and SreA by intracellular iron. Additionally, we analyzed a modified model whereby hapX and sreA were regulated transcriptionally by iron, and all other interactions are the same. Both versions of the model were consistent with gene expression data for the wild type. However, the model with HapX and SreA regulated by iron at the post-transtlational level, but not the modified model, agreed with the Schrettl et al. hapX gene expression data for the sreA mutant strain (see Figure 4H). This pro- vides support for the hypothesis that, as in S. pombe, a post-translational regulation of the iron regulatory proteins HapX and SreA by iron is in fact employed by A. fumigatus. Model knockout simulations recapitulate experimental gene deletion results. Next, we systematically analyzed the effect of all single and double knockouts on model predicted phenotypes under each of the four external conditions. Key observations from wild type and knockout simulations are summarized in Table 3. Iron regulation knockouts For the low iron conditions, the SidA = 0 knockout led to minimal or no growth (SDM of ICP = 0). However, no growth defects were observed when RIA = 0 under the same conditions. In high iron conditions, the SidA = 0 knockout did not deviate from the wild type high growth phenotype. However, in high iron conditions, a double RIA = SidA = 0 knockout led to minimal or no growth. These results are consistent with experimental results showing: (1) a sidA but not ftrA mutant is avirulent in a mouse model of aspergillosis [5,8], and (2) that RIA can compensate for a lack of siderophores in high iron but not low iron conditions [33]. Also in agreement with experiments, under low iron conditions the TAFC = 0 knockout led to more severe growth defects than the FC−Fe =0 knockout [33]. Knocking Brandon et al. BMC Systems Biology (2015) 9:19 Page 11 of 17 Table 3 Summary of observations from model wild type and knockout simulations Condition Strain Long term model behavior Cell Cell Support Conflicts ICP ROS Other interesting behavior Growth Death O− 2 = 0 wt 0.29 0.44 • TAFC = FC−Fe = 0.52; high siderophore production − − [5,8] • Cat1/2 = 0.29; SOD2/3 = ThP = 0.44 prediction • FC−Fe/FC+Fe =1.7 [14] Fe3+ = 0 hapX = 0 0 0 • SidA = 0 − − [29] SidA = 0 or TAFC = 0 0 0 − − [5,8,33,52] FC−Fe = 0 0.11 0.43 − − [14,33] EstB = 0 or MirB = 0 0 0 • TAFC = FC−Fe = 1; accumulation of siderophores − − [55] Yap1 = 0 or SOD2/3 = 0 0.29 1 − + [10,20] O− 2 = 0 wt 0.48 0.62 • TAFC = FC = 0.18; low siderophore production + − [5,8] • Cat1/2 = 0.54, SOD2/3 = ThP = 0.61 [13] • FC−Fe/FC+Fe = 1 [14] Fe3+ = 1 sreA = 0 1 1 • Derepression of hapX, RIA, CccA, & Cat1/2 + + [13,52] • LIP = VAC = 1; iron overload [13] SidA = 0 0.42 0.61 + − [5,8,33] RIA = 0 0.29 0.45 • SidA = 0.52; increased siderophore production − − [8,33] SidA = RIA = 0 0 0 − − [8,33] Yap1 = 0 or SOD2/3 = 0 0.49 1 • Decreased resistance to Fe3+ + + [10,20] O− 2 = 1 wt 0.28 0.78 • SOD2/3 = ThP = 0.76; Cat1/2 = 0.40 − + [20,33,61] hapX = 0 0 0.58 • Derepressed Cat1/2 and increased resistance to O− 2 − − prediction Fe3+ = 0 SidA = 0, TAFC = 0, 0 1 • Decreased resistance to O− 2 − + prediction MirB = 0 or EstB = 0 Yap1 = 0, SOD2/3 = 0, 0.29 1 • Decreased resistance to O− 2 − + [9,10,20,61] Cat1/2 = 0 or ThP = 0 O− 2 = 1 wt 0.49 0.73 • FC−Fe/FC+Fe = 1 + + [14,20,33] • SOD2/3 = ThP = 0.73; Cat1/2 = 0.63 prediction Fe3+ = 1 sreA = 0 1 1 • Decreased resistance to Fe3+ + + [13] Yap1 = 0, SOD2/3 = 0, 0.47 1 • Decreased resistance to Fe3+ and O− 2 + + [9,20,61] Cat1/2 = 0 or ThP = 0 Numerical values in the ‘Long Term Model Behavior’ column represent SDMs. A −denotes low cell growth or low cell death, while a + denotes high cell growth or high cell death. Citations for supporting and conflicting literature are provided. out any part of the siderophore iron uptake system under low iron conditions (TAFC = 0, MirB = 0, or EstB = 0) resulted in a minimal growth phenotype. Interestingly, we observed an accumulation of siderophores for either MirB = 0 or EstB = 0 under low iron conditions, a behav- ior which has been observed experimentally in an estB mutant [55]. The hapX = 0 knockout displayed a minimal growth phenotype under low iron conditions, but had no defects under high iron conditions. Conversely, the sreA = 0 knockout led to iron overload (SDM of LIP = 1) and cell death by overwhelming ROS (SDM of ROS = 1) under high iron conditions, but had no defects under low iron conditions. This recapitulates experimental results show- ing that growth defects of a hapX mutant are confined to low iron conditions while growth defects of a sreA mutant are confined to high iron conditions [13,29]. Oxidative stress response knockouts As expected, wild type ROS-detoxifying enzyme activity was lowest under the low iron, low superoxide condition. The SDM of Cat1/2 was less than that of SOD2/3 and the thioredoxin pathway (abbreviated to ThP in Table 3) whenever iron was low. Under low superoxide conditions the model predicted a Yap1 = 0 or SOD2/3 = 0 knockout, but not a Cat1/2 = 0 or Thp = 0 knockout, to be fatal. This observation demonstrates that the model accounts for the redundancy that both catalases and peroxiredoxins reduce H2O2. Under high superoxide conditions, model knockouts of any of the four oxidative stress-related Brandon et al. BMC Systems Biology (2015) 9:19 Page 12 of 17 species had a high cell death phenotype due to over- whelming ROS. The observation that Yap1 or SOD2/3 deletion is more severe than deletion of Cat1/2 or blocking of the thioredoxin pathway is consistent with experimental results from Leal et al. which show that yap1 and sod1/2/3 mutant strains are sensitive to neutrophil- mediated oxidative stress, whereas a cat1/2 strain is not [10]. Yet the observation is inconsistent with a result from the same study which showed that blocking the thioredoxin pathway results in a reduction of in vivo hyphal growth similar to deletion of either yap1 or sod2/3 [10]. An earlier study, which demonstrated that a cat1/2 mutant showed increased sensitivity to H2O2 in vitro and delayed growth during infection in a rat model of aspergillosis, further conflicts with the Leal et al. study and provides support for the model predicted phenotype of a Cat1/2 = 0 knockout [9]. Overall, the severity of experimental knockout results seem to be exaggerated by some model predictions. In particular, deletion of either yap1 or sod2/3 should not result in high cell death in the absence of oxidative stress, yet under low superoxide conditions the model predicted knockouts a high cell death phenotype for Yap1 = 0 and SOD2/3 = 0 knockouts. Discrepancies between experimental results and model predictions indicate that important species or interactions may be missing from the model. This may reflect that our understanding of A. fumigatus oxidative stress response is still not complete. For instance, there may be uniden- tified redundancy, some of which could be attributed to LaeA-controlled secondary metabolites which inhibit neutrophil production of NOX [73]. Yet knockout exper- iments of several of these metabolites as well as laeA suggest they may play no role in protecting A. fumiga- tus from neutrophil-mediated oxidative stress [10]. Since model-predicted phenotypes of Yap1 and Yap1-regulated species knockouts are most overstated in low superox- ide conditions, it is possible that the model lacks some constitutively active or baseline antioxidants which may be useful for neutralizing ROS produced during normal cellular activities but may not necessarily be helpful in combating oxidative stress. As more research is done to characterize new players in the A. fumigatus oxidative stress response network, the oxidative stress response module of this model can be improved and new insights may be gained. Model suggests combined blocking of iron uptake and oxidative stress response Of the four conditions in Table 3, the low iron and high superoxide condition most resembles the environment that A. fumigatus cells experience inside a mammalian host. Under this condition, model knockouts which impaire siderophore-mediated iron uptake increased A. fumigatus sensitivity to oxidative stress. A similar rela- tionship between high-affinity iron uptake and sensitivity to oxidative stress has been observed in yeast [15]. This observation led us to wonder what the model would pre- dict for ROS levels if combined blocking of siderophore- mediated iron uptake and oxidative stress response were simulated under less rigid external conditions. Several experimental studies have investigated target- ing either siderophore-mediated iron uptake or oxidative Sample O2- Trajectories Time steps 0 1 0 10 20 30 40 50 0 1 State State ROS Stable Distributions State Count 0 5 10 0.0 0.25 0.5 0.75 1.0 Treatment Both Drug 1 Drug 2 No Drug A B Figure 5 Model results comparing the application of two hypothetical anti-fungal drugs to treat a simulated A. fumigatus infection. Iron is fixed at low (0) while superoxide is allowed to randomly toggle between low (0) and high (1). (A) Two representative superoxide trajectories. (B) ROS stable distributions for no drug, either drug individually, or both drugs together. Vertical dashed lines represent ROS SDMs. Drug 1 targets siderophore- mediated iron uptake. Drug 2 targets oxidative stress response. Simulations are initialized from the state in row 2 of the low iron, high superoxide block in Figure 2. Brandon et al. BMC Systems Biology (2015) 9:19 Page 13 of 17 stress response, but none have investigated any potential therapeutic gain by combined targeting. TAFC and MirB are promising drug targets since they are easily acces- sible and unique to fungi [30]. Leal et al. demonstrate proof of concept that using lipocalin-1 to sequester TAFC improves the treatment of topical A. fumigatus infection [12]. An anti-cancer drug, PX-12, which is known to block the thioredoxin pathway also shows promise as an anti-A. fumigatus drug [10]. To investigate the effects of simultaneously inhibiting siderophore-mediated iron uptake and oxidative stress response, we simulated treatment with two hypothetical drugs loosely based on lipocalin-1 and PX-12. Hypotheti- cal drug 1 binds and inactivates TAFC from 50% of fungal cells. Hypothetical drug 2 blocks the thioredoxin pathway in 50% of fungal cells. For these simulations, we held iron fixed at 0 but allowed superoxide to randomly toggle between 0 and 1. This setup recapitulates host defense mechanisms of sustained iron witholding and intermittent respiratory bursts. Figure 5(A) shows two representative superoxide trajectories when random toggling is allowed. Figure 5(B) shows ROS stable distributions from the aver- age of 100 stochastic simulations for treatment with Drug 1, Drug 2, both drugs or neither drug. To simulate the drug treatments with 50% efficacy, we fixed either TAFC, ThP, or both at 0 for 50 of the 100 simulations. Drug 1 alone has no effect, Drug 2 alone increases the ROS SDM from 0.64 to 0.74, and the combination of Drug 1 and Drug 2 further increases the ROS SDM to 0.83. This result sug- gests that combined targeting of siderophore-mediated iron uptake and the oxidative stress response network may act synergistically to increase fungal cell killing. Conclusions In this study we introduce a stochastic Boolean model of the iron regulatory and oxidative stress response net- works in A. fumigatus. Model simulations of a population of A. fumigatus cells reproduces gene expression patterns in experimental time course data when A. fumigatus is switched from a low iron to a high iron environment. In addition, the model is able to accurately represent the phe- notypes of many knockout strains under varying iron and superoxide conditions. We drew three main observations from model analysis. First, the model provides support for the hypothesis that A. fumigatus iron regulatory proteins, HapX and SreA, are regulated by iron at the post-translational level. Second, based on discrepancies between model knockout sim- ulations and experimental observations of A. fumigatus oxidative stress response related mutants, it is likely that important enzymes or pathways involved in A. fumigatus ROS-detoxification remain uncharacterized. And third, impairment of siderophore-mediated iron uptake mecha- nisms reduces A. fumigatus resistance to oxidative stress. This fact could be exploited when designing a treatment strategy. Deterministic simulation (as well as individual stochas- tic simulations, data not shown) of the model predicts sustained oscillations under each of the four external con- ditions (Figure 2). On the other hand when a population of cells is modeled by averaging many stochastic simula- tions, the model converges to a steady state distribution (Figure 3). Without single cell data, it is unclear how to interpret discrepancies between an individual (determin- istic or stochastic) simulation and the average of many stochastic simulations. It is conceivable that, in agree- ment with individual model simulations, expression of iron homeostasis and oxidative stress response genes in a single A. fumgatus cell may continually oscillate, perhaps always overshooting and undershooting ideal intracellu- lar iron levels. A recent study in E coli reported damped oscillations in the expression of genes involved in iron homeostasis in a single E. coli cell undergoing a switch from high iron to low iron conditions [21]. Future single cell experiments of A. fumigatus could shed light on how stochasticity arises in fungal iron regulatory and oxidative stress response networks. The intended future application of this model is to incorporate it into a multi-scale systems biology model of invasive aspergillosis in the lung. The ultimate goal of the proposed multi-scale model is to capture the effect of the initial inoculum on disease outcome and to allow for the investigation of a variety of therapeutic interventions. Methods Computational methods Discrete modeling framework In order to translate the network interactions depicted in the diagram of Figure 1 into a dynamic discrete model, namely a time- and state-discrete dynamical system, the state transitions for each species must be specified by assigning an update rule that describes how the species’s state will be updated at the next time step based upon the states of its inputs at the current time step. Since this is a Boolean model, each species can take on only two states and update rules are Boolean functions. It is convenient to encode update rules in an object called a transition table. As an example, consider the iron-sensing transcrip- tion factor SreA. From the literature we know that when intracellular iron levels are low, SreA is kept in an inac- tive state [59,60]. Based on this we decide the update of SreA should depend on two inputs, its gene sreA and the labile iron pool LIP. These interactions are represented in Figure 1 as the two edges incident on SreA. Based on the state descriptions assigned to SreA, sreA, and LIP listed in Table 1, we obtain the following table which determines which state SreA will transition to at time step t + 1 based on the states of sreA and LIP at the current time step, t. Brandon et al. BMC Systems Biology (2015) 9:19 Page 14 of 17 Using Table 1 to translate the state descriptions into 0’s and 1’s, we obtain the following transition table. This table encodes the AND function. Both sreA AND LIP must be in state 1 at the time t for SreA to be in state 1 at time t + 1. Any Boolean function can be written using only AND, OR, and NOT gates (see Table 2). For ease of computation, we prefer to work with a math- ematical object rather than transition tables or Boolean functions. Any discrete dynamical system can be rep- resented as a system of polynomial equations over a finite field. A model in this form is called a polynomial dynamical system (PDS) and can be analyzed using theory and tools from computational algebra [74,75]. Since each species in a Boolean network model can take on only two states, the finite field for our model is F2 ∼= Z/2Z, i.e., the set of integers {0, 1} where addition and multiplication is modulo 2. The polynomial dynamical system for our model (cor- responding to the update rules listed in Table 2) is: F = ( f1, . . . , f22) : F22 2 →F22 2 where the variables xi, i = 1, . . . , 22 are the species and the fi, i = 1, . . . , 22 are the update functions written as the following polynomials over F2. x1 = hapX x2 = sreA x3 = HapX x4 = SreA x5 = RIA x6 = EstB x7 = MirB x8 = SidA x9 = TAFC x10 = ICP x11 = LIP x12 = CccA x13 = FC−Fe x14 = FC+Fe x15 = VAC x16 = ROS x17 = Yap1 x18 = SOD2/3 x19 = Cat1/2 x20 = ThP x21 = Fe3+ x22 = O− 2 f1 = x4 + 1 f2 = x3 + 1 f3 = x11 · x1 + x1 f4 = x11 · x2 f5 = x4 + 1 f6 = x4 + 1 f7 = x3 · x4 + x3 f8 = x3 · x4 + x3 f9 = x8 f10 = x3 · x14 · x15 + x3 · x14 + x3 · x15 + x14 · x15 + x14 + x15 f11 = x21 · x5 · x9 · x7 · x6 + x9 · x7 · x6 + x21 · x5 f12 = x3 + 1 f13 = x8 f14 = x11 · x13 f15 = x11 · x12 f16 = x16 · x11 · x22 · x18 · x19 · x20 + x16 · x11 · x22 · x18 · x19 + x16 · x11 · x22 · x18 · x20 + x16 · x11 · x18 · x19 · x20 + x16 · x22 · x18 · x19 · x20 + x11 · x22 · x18 · x19 · x20 + x16 · x11 · x18 · x19 + x16 · x22 · x18 · x19 + x16 · x11 · x18 · x20 + x16 · x22 · x18 · x20 + x16 · x18 · x19 · x20 + x22 · x18 · x19 · x20 + x16 · x11 · x22 + x16 · x18 · x19 + x16 · x18 · x20 + x16 · x11 + x16 · x22 + x11 · x22 + x16 + x11 + x22 f17 = x16 f18 = x17 f19 = x3 · x17 + x17 f20 = x17 f21 = x21 f22 = x22 Incorporating stochasticity In this study, we use a random update schedule to simulate dynamic behavior. The basic idea behind this approach is to change the deterministic update of each species into a probability of being updated. The stochastic discrete dynamical systems (SDDS) framework was used to gen- erate stochastic simulations [76]. An SDDS is a time- and state-discrete dynamical system which models stochas- ticity at the functional level by introducing two update probabilities that, together with the update function, spec- ify a probability of transition of a given species at each time step. Let pin↑be the probability that species xi will be updated given that the corresponding update func- tion fi specifies an increase in state at the next time step. Let p↓ i be the probability xi will be updated given that fi specifies a decrease in state at the next time step. Then a stochastic discrete dynamical system in n variables is a collection of triplets fi, p↑ i , p↓ i n i=1 where we may repre- sent the update functions fi as polynomials over a finite field. Thus a SDDS can be represented as a PDS along with propensity parameters. The probabilities p↑ i , p↓ i ∈[ 0, 1] for all i ∈{1, . . . , n} are called the activation propensity and degradation propen- sity, respectively, of the i-th species. If p↑ i = p↓ i = 1 for all i = 1, . . . , n then all species are updated simultaneously at every time step, and the simulation is deterministic. To implement a random update schedule, we let p↑ i = p↓ i = 0.5 for all i = 1, .., n, meaning that at each time step each species has an equal probability of either being updated or remaining in its current state. Hence at each time step, some species are randomly selected to be updated whereas others are not. Updating of selected species is done simultaneously at each time step. A “time step” in this model refers to a single round of updates in which the Brandon et al. BMC Systems Biology (2015) 9:19 Page 15 of 17 state of any given species can be updated only once. The unit of time step is arbitrary, yet based on comparisons with experimental time course data (Figure 4), we deter- mined each time step of our model corresponds to about 6 minutes of real time. Analysis of Dynamic Algebraic Models (ADAM), a free web-based software tool which analyzes the dynamics of discrete models using Gröbner bases calculations, was used to generate the above PDS from transition tables and to simulate dynamic behavior using the SDDS framework [77]. ADAM is available at http://adam.plantsimlab.org/. Experimental methods A. fumigatus strain and growth conditions The A. fumigatus strain used was wild-type AF293. A. fumigatus was cultured on glucose minimal media plus agar plates at 37°C for 7 to 10 days until fully conidiated. Spores were harvested by flooding the culture plates with endotoxin-free phosphate-buffered saline solution con- taining 0.05% Tween-20 and swabbing with a sterile inoc- ulation loop to obtain spore suspension. The spores were vortexed and concentrations of spores were determined by counting with a hemacytometer. Incubation and harvesting A. fumigatus was grown in a liquid shaker under iron depleted conditions. 25 × 106 A. fumigatus condia were added to standard glucose minimal media plus 0.05% Tween-20 but without iron in the trace elements to a final volume of a 25 mL for a final concentration of 1 million spores per mL. Flasks were incubated at 37°C and 200 rpm for 72 hours. Glass flasks were rinsed prior to inoc- ulation with a 0.1 M HCL solution followed by a rinse with double distilled water to remove residual traces of iron. After 72 hours, A. fumigatus was shifted from iron depleted to iron replete conditions by adding FeSO4 to a final concentration of 10μM FeSO4. A. fumigatus was then incubated for another 9 hours. Mycelia were harvested from triplicate samples at 0 (control), 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, and 360 minutes after the addition of iron. Mycelia were filtered through gauze and immediately flash frozen in liquid nitrogen and stored at -80°C. Frozen mycelia were subsequently ground to a fine powder using a mortar and pestle in the presence of liquid nitrogen. RNA extraction and cDNA synthesis Total RNA was isolated using a Qiagen RNeasy plant mini-kit. “Protocol: Purification of Total RNA from Plant Cells and Tissues and Filamentous Fungi” was used along with optional on-column DNase digestion step. Extracted RNA was stored at -80°C. RNA integrity was assessed by gel electrophoresis. Concentrations of RNA in each sample were determined by spectrophotometry on a Table 4 Primers used for real-time qRT-PCR Gene Primer sequence (5’-3’) melting Product Tm (°C) size(bp) β-tubuliln FP CTGCTCTGCCATTTTCCGTG 56.8 119 RP CGGTCTGGATGTTGTTGGGA 57.3 sidA FP TGACGACTCGCCTTTTGTGAA 57.0 474 RP TTGCTCGGGTCCATCTCAAC 57.3 sreA FP CTCAGTACGATCGCTTCCCC 57.3 297 RP GTCCCACAATTACTGCACGA 55.2 ftrA FP GGCATGATCGGAGCGTTCTA 57.1 411 RP GGCTTGGTTTCCTCCTCGAT 57.2 cccA FP GAGCCAAGAGTGAGGCAGAA 57.0 448 RP TGCACACCACCCTTGATACC 57.4 NANODROP 1000 Spectrophotometer. Next, cDNA was synthesized following manufacturer’s instructions (Tetro cDNA Synthesis Kit, Bioline). All incubations were car- ried out in a thermacycler. Following synthesis, cDNA was stored at -20°C. qRT-PCR Real time reverse transcription polymerase chain reaction (qRT-PCR) was performed using the cDNA as a template. The constitutively expressed gene β-tubulin of A. fumi- gatus was used as the house-keeping gene. See Table 4 for a list of primers for target genes. Real time qRT-PCR was carried out in 20 μL reaction volumes on a BIO- RAD iQTM5 Multicolor Real-Time PCR Detection System machine. The real time qRT-PCR consisted of the follow- ing a 3-step protocol: (95°C denaturation for 10 s, 55°C annealing period for 30 s, 72°C extension for 45 s) × 40 cycles. Cycling involved an initial denaturing/polymerase activation step (95°C for 3 min) and a final melting curve analysis (+0.5°C ramping × 81 cycles; 30 second incu- bation between each cycle). SYBR Green (Bioline) was used as the fluorescent reporter molecule in all reactions. Real time qRT-PCR mixes consisted of 1 μL template cDNA to 19 μL master mix. Relative gene expression (fold change from the addition of iron) was quantified using the Pfaffl method and normalized to β-tubulin [78]. Results were collected from biological triplicates, and qRT-PCR for each biological replicate was carried out in techni- cal duplicates. Standard errors were calculated to ensure statistical accuracy. Additional file Additional file 1: Brandon2015_Aspergillus_iron_superoxide. The Boolean network model of Aspergillus fumigatus iron acquisition and oxidative stress response is provided in SBML qual format. Brandon et al. BMC Systems Biology (2015) 9:19 Page 16 of 17 Competing interests The authors declare that they have no competing interests. Authors’ contributions Conceived the study: RL and CL. Performed construction and analysis of mathematical model: MB. Designed the qRT-PCR experiment: CL, BH, and MB. Performed wet lab work: MB, BH. Performed data analysis: MB. Interpreted results: MB, CL, RL. Wrote the manuscript: MB. Reviewed and edited manuscript: BH, CL, and RL. All authors have read and approved the final manuscript. Acknowledgements We would like to acknowledge Drs. R. Cramer and H. Haas for meaningful discussions. This work was supported in part by NIH/NIAID grant number 1R21AI101619 to RL and CL. 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RESEARCH Open Access Proteins interaction network and modeling of IGVH mutational status in chronic lymphocytic leukemia María Camila Álvarez-Silva1†, Sally Yepes2†, Maria Mercedes Torres2 and Andrés Fernando González Barrios1* * Correspondence: andgonza@uniandes.edu.co †Equal contributors 1Grupo de Diseño de Productos y Procesos (GDPP), Departamento de Ingeniería Química, Universidad de los Andes, Bogotá, DC, Colombia Full list of author information is available at the end of the article Abstract Background: Chronic lymphocytic leukemia (CLL) is an incurable malignancy of mature B-lymphocytes, characterized as being a heterogeneous disease with variable clinical manifestation and survival. Mutational statuses of rearranged immunoglobulin heavy chain variable (IGVH) genes has been consider one of the most important prognostic factors in CLL, but despite of its proven value to predict the course of the disease, the regulatory programs and biological mechanisms responsible for the differences in clinical behavior are poorly understood. Methods: In this study, (i) we performed differential gene expression analysis between the IGVH statuses using multiple and independent CLL cohorts in microarrays platforms, based on this information, (ii) we constructed a simplified protein-protein interaction (PPI) network and (iii) investigated its structure and critical genes. This provided the basis to (iv) develop a Boolean model, (v) infer biological regulatory mechanism and (vi) performed perturbation simulations in order to analyze the network in dynamic state. Results: The result of topological analysis and the Boolean model showed that the transcriptional relationships of IGVH mutational status were determined by specific regulatory proteins (PTEN, FOS, EGR1, TNF, TGFBR3, IFGR2 and LPL). The dynamics of the network was controlled by attractors whose genes were involved in multiple and diverse signaling pathways, which may suggest a variety of mechanisms related with progression occurring over time in the disease. The overexpression of FOS and TNF fixed the fate of the system as they can activate important genes implicated in the regulation of process of adhesion, apoptosis, immune response, cell proliferation and other signaling pathways related with cancer. Conclusion: The differences in prognosis prediction of the IGVH mutational status are related with several regulatory hubs that determine the dynamic of the system. Keywords: CLL, PPI network, Boolean network, Topological analysis Background Chronic lymphocytic leukemia (CLL), the most common type of adult leukemia in de- veloped countries, is an incurable malignancy of mature B lymphocytes, characterized by accumulation of mature B cells in the blood, bone marrow, and secondary lymphoid organs such as the lymph nodes (LN) [1, 2]. Patients with CLL show a highly variable © 2015 Alvarez-Silva et al. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/ publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 DOI 10.1186/s12976-015-0008-z disease evolution and different response to therapy. This variability may be related to evolutionary dynamics of sub-clonal mutations [3]. Investigations of the B cell receptor (BCR) indicate that 60–65 % of CLLs carry immunoglobulin heavy chain variable (IGHV) genes with evidence of somatic hypermutation and this may modify BCR affinity for antigens. Conversely, 35–40 % of CLLs are devoid of IGHV somatic mutations [4]. Understanding the pathological mechanisms of CLL has helped to divide the disease into two risk categories that have a strong impact on prognosis and treatment: 1) patients with minimal clinical manifestations and 2) an aggressive form characterized by high mortality, whose IGHV genes can be somatically mutated or unmutated, respectively. Due to the importance of IGVH status in the determination of the course of the disease, several expression studies have focused on the comparison of CLL type mutated IGVH vs. IGVH unmutated. Nevertheless, these studies have identified genes that are not functionally related and therefore cannot elucidate biological mechanisms to distinguish between risk categories. The interactions of proteins are essential to execute biological functions in different contexts [5]. Since cancer is a complex and multi-factorial disease involving diverse anomalies, the representation and analysis of a malignant cell as a protein-protein interaction (PPI) network can provide insights into its behavior. It has been postulated that proteins with high connectivity within a PPI network could represent meaningful biological information, despite non-being differentially expressed [6]. Thus, the inte- grated analysis of gene expression data with PPI networks could be valuable method to provide knowledge into molecular mechanisms of diseases. The analyses of PPI networks have varied applications such as identification of drug targets, functional protein modules and disease candidate genes [7, 8]. On the other hand, dynamic network modeling can be used to gain insight into the functionality of biological processed and made possible simulations to predict models behavior [9]. Modeling of regulatory networks as dynamical systems includes modeling based on ordinary differential equations [10, 11], Bayesian framework [12] and Boolean rules [13, 14]. Given the limitation of quantitative models that need knowledge on the kinetics and mechanistic parameters of the system, in addition of a wealth of qualitative and interaction data obtained from the experimental literature and high-throughput technologies, the qualitative approaches such as Boolean modeling become an ex- tremely useful resource [15]. The Boolean modeling considers the genes as binary variables being either active or passive, but encompassing the essential functionality of the system, the general building blocks that have been identified in Boolean networks constitute different types of robust switching elements [16]. This type of approach is already successfully applied in complex models as the FA/BRCA pathway in Fanconi anemia [17], the survival process of in large granular lymphocyte leukemia [18], process of T-helper lymphocytes [19] and the control of the mammalian cell cycle [20]. In this study, we constructed a simplified PPI network of the IGVH mutational status in CLL and analyzed its structure and critical genes. We used the topology of the network to develop a Boolean model, infer regulatory mechanisms and perform simulations to analyze the network in dynamic state. The modeling of the PPI network led to identify regulatory elements of the disease, contributing to understand the prog- nostic differences and the dynamic behavior under different perturbations over time. Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 2 of 15 Results We inquired into the impact of differentially expressed genes (DEG) between the IGVH statuses by mapping them onto the PPI network. The initial data set of 502 DE genes was reduced to 90 genes with the software STRING and exhaustive literature reviewed. The PPI network reconstructed contains 90 nodes and 120 regulatory edges (Fig. 1). An additional table shows the functions of all genes implicated in the network (Additional file 1: Table S1). The resulting simplified network made evident that DEG between IGVH statuses are not always represented by highly connected nodes. The main topological characteristic of the network is the degree distribution P(k), which tells us the probability that a select node has exactly k links. The degree distribution P(k) allows us to distinguish between different types of biological networks. We obtained a power-law degree distribution which characterize scale free networks (Fig. 2), where the probability that a node displays k links follows P(k) ∼k−γ, where γ is the degree exponent that describes the role of the hubs in the system [21]. In the PPI network we obtained values of γ between 2 and 3, indicating that there exist a hierarchy of hubs, i.e. there are a large number of nodes with few connections while highly connected nodes are scarce [21]. The following genes showed the highest values in degree evaluation: in-degree (PTEN, FOS, and EGR1) and out-degree (TNF, TGFBR3, and IFGR2). Values of γ between 2 and 3 refer also to the small-world property [22], characterized by a small value of diam- eter, which increase the network efficiency. However, we obtained a value of diameter of 8, greater-than-expected for networks with the small-world property. To explain the values of diameter higher to the expected, Zhang et al. [22] made a comparison between the values of diameter reported for real biological networks regarding to diameters ob- tained for networks with the same features in which the connections between nodes are randomized. Specifically, they evaluated the diameter of protein-protein interaction Fig. 1 Protein-protein interaction network. Pink edges: inhibition. Green edges: activation. Purple nodes: low expression. Blue nodes: high expression Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 3 of 15 networks of biological organisms in contrast to the obtained in randomized networks. Their simulation showed that an increment of the diameter in the real networks allows a significant increase of the network modularity, suggesting an adjustment between network efficiency and the benefits obtainable by modularity [22]. This analysis was completed by other centralities measures such as closeness and be- tweenness, which provide a characterization of nodes that are relevant for the network structure. Closeness is defined by the inverse of the average length of the shortest paths to all other nodes [23]. We found TNF, TGFBR3, and IFGR2 as proteins with the high- est closeness values in the PPI network. A protein with high closeness, compared to the average closeness of the network, will be easily central to the regulation of other proteins but with some proteins not influenced by its activity [24]. Implying that those proteins are the closest to all other nodes and have an extent of influences on the entire Number of nodes Number of nodes In-degree Out-degree a b Fig. 2 a. Power-law in-degree distribution b. Power-law out-degree distribution Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 4 of 15 network. This parameter can also be considered a measure of how long it will take in- formation to spread from a given node to others [25]. Betweenness is defined by the number of shortest paths that pass through a node [26]. The betweenness index favors nodes that join communities rather than nodes that lie inside a community [27, 28]. FOS, TNF and LPL exhibited the highest values, implying a role as linkers in the control of interactions between proteins. Selected genes, reported above, can be seen in Fig. 3. The overall parameters that characterized the network are shown in the Additional file 2: Table S2, and the topological parameters for each one of the nodes are shown in the Additional file 3: Table S3. We saw that centrality measures in the PPI network shown some degrees of overlap, stressing the importance of the implicated proteins in the system structure. According to Yu et al. [29], as a complementary notion of highly connected proteins known as hubs proteins, it is possible to define bottlenecks proteins as proteins with high be- tweenness values, bottlenecks proteins are essential connectors with surprising func- tional and dynamic properties. Therefore, to develop a Boolean model and evaluate the genes with influence in the behavior of the network over time, we focused on those that were at the center of the major structural hubs and simultaneously exhibited the highest values in the topological centralities evaluated. The selected nodes were: FOS, PTEN, TGFBR3, and TNF. The dependencies between the genes obtained from the literature re- view were translated to rule sets. The biological events for activation or inhibition were qualitatively represented by Boolean functions, that is, combinations of AND, OR, and NOT operations, that determine the evolution of a node through time and their relation to the other components of the system (Additional file 4: Table S4). Starting from an initial condition, the Boolean model evolved over time to finally stabilizes in a recurrent state known as attractor, representing the long-term behavior of the system [15]. We found a simple attractor for the PPI network for CLL consisting of one state. The model obtained achieves the fixed point (steady state) after six time steps. The state of transition and its successor attractor (starting from the initial state determined by microarray analysis) are shown in Fig. 4. Starting from 50 random initial states, the system had both the single-state attractors and cycle attractors. The major cycle attractors displayed four states (Fig. 5). This showed important dependency of the achieved attractor according to the initial system state. Given the relevance of signaling pathways as triggers of processes associated with cancer oncogenesis and progression, the activated proteins in the attractor were subjected to modular functional enrichment to determine annotations from KEGG and Panther pathways simultaneously. The associated annotations involved various pathways related to cancer with statistical significance for focal adhesion (corrected p value = 0.000231747). Other signaling pathways detected in the attractor included: B cell receptor, T cell receptor, cytokine-cytokine, integrin, and cadherin, among others. Processes related with cell proliferation and regulations of transcription were also present. Given the overriding importance attributed to FOS and TNF in cancer biology and their high topological measures in the PPI network, we chose these genes to performed perturbation simulations of knockout and overexpression in the system. Furthermore, we analyzed the effect of different initial conditions that can lead the system to different steady states (attractors). The two initial conditions that were taken into account were: i) Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 5 of 15 initial condition determined by microarray analysis and ii) an initial state in which all nodes were active. The overexpression of FOS produced activation of genes related with multiples sig- naling pathways. When comparing activated genes under the FOS overexpression re- gardless of activated genes in the original attractor, the modular functional analysis found the MAPK signaling pathway with the most significant value, (p = 4.37211e-05). Other pathways involved were: apoptosis (p = 7.34148e-05), PDGF (p = 0.000100226), JAK-STAT (p = 0.0001216), angiogenesis (p = 0.0001216) and cytokine-cytokine inter- action (p = 0.000500178). Similarly, activated genes under TNF overexpression were involved in multiple signaling pathways associated with cancer: focal adhesion (p = 7.05488e-07), angiogenesis (p = 8.39556e-07), JAK-STAT (p = 1.39118e-06), tight junc- tion (p = 5.76719e-06), MAPK (p = 7.60619e-06), Wnt (p = 0.000105245), among others. Under both initial conditions the effect of knocking out of any gene did not display an effect, since the same attractor was obtained when no gene was knocked out. Never- theless, the path length to achieve the attractor varies significantly, that is, depending on the initial conditions, the system takes more or less steps of evolution in time to stabilize in a recurrent state, known as attractor. From this behavior of the system, it can be concluded that the attractor achieved is the most stable state of the network, because although there are perturbations involving the system, the network returns to the same steady state after different steps of time evolution. On the other hand, when constantly maintaining the major nodes active under the two initial conditions studied, we found that the selected gene displayed an effect on the attractor achieved and therefore on the behavior of the system, affecting evolution Percentage Percentage Percentage Percentage FOS TNF PTEN TGFBR3 OutDegree InDegree Closeness Betweenness centrality value average min max OutDegree InDegree Closeness Betweenness OutDegree InDegree Closeness Betweenness OutDegree InDegree Closeness Betweenness Fig. 3 Measure of centralities of FOS, TNF, PTEN and TGFBR3 Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 6 of 15 of the network. These changes in the behavior are important to determine its relation to the evolution of the disease. Under both conditions of perturbation, the overexpression of the gene FOS and TNF showed important influence in the evolution over time of the system (Fig. 6). In both cases the system reaches complex attractors in which the network oscillates among a set of four states, i.e., the attractor of the network is a cycle. In these states the nodes involved in regulation of CLL oscillate under states of OFF or ON, which affects the course of the disease. Discussion We applied a system approach by linking proteins interaction data with differentially expressed genes of the IGVH status, the reconstructed PPI network allowed identified critical genes, and given the stringent parameters applied, they represent only relation- ships based on strong protein interactions. The topology of the reconstructed PPI net- work followed the power-law of node degree distribution, a feature of true complex biological networks. Therefore, the obtained network is a scale-free biological entity ra- ther than a random network, indicating the presence of few nodes having a very high degree measure [21]. On the other hand, it is recognized that high values of degree cen- trality are associated with proteins that are interacting with several others suggesting a central regulatory role [23]. The degree index highlighted some important proteins with regulatory functions and considered interactions hubs in the PPI network: PTEN, FOS, EGR1, TNF, TGFBR3, and IFGR2. According to the lethality and centrality rule, the highly connected nodes are biologically relevant, representing vulnerable and essential Inactive Active a b t= 1 2 3 4 5 6 steady state Fig. 4 Visualization of a sequence of states. a. The columns of the table represent consecutive states of the time series. b. Steady-state attractor of the network from initial state determined by microarray analysis. Genes are encoded in the following order: AEBP1 AFF1 AICDA AKAP12 AKT3 ALOX5 ANXA2 APLP2 APOBEC3G APP BLNK BMI1 CASP3 CAV1 CCL5 CCND2 CD27 CD63 CD69 CD70 CD79A CD81 CD86 CHST2 CNR1 CREM CSDA CSNK2A2 CTSB CUL5 DPP4 EED EGR1 EZH2 FCER2 FGFR1 FOS FRK FYN GSK3B H2AFX HDAC9 HIST1H3H HIST2H2AA3 HSP90AA1 HSP90B1 IFNGR2 IGF1R IL10RA IL7 ILK INPP5D JAK1 LGALS1 LIG1 LMNA LPL MAP2K6 MAP4K4 MARCKS MGAT5 MIF MYL9 MYLK NAB1 NCOR2 NFE2L2 NOTCH2 OGT PAX3 PCNA PLD1 PRF1 PRKCA PTCH1 PTEN RFC5 RPS6KA5 RRM1 RUNX3 SELL SELP SIAH1 SKI TCF3 TNF TNFRSF1B VDR CD74 ADM TGFBR3. Active genes in this attractor state were: AFF1, APLP2, APP, BMI1, CD27, CD81, CD86, CREM, CUL5, EED, EZH2, FYN, GSK3B, HIST2H2AA3, HSP90B1, IL10RA, ILK, MARCKS, MGAT5, RRM1, SKI Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 7 of 15 points to system viability [30, 31], supporting this argument the establishment and stability of cancer cells through these hubs. It was noted that highly connected proteins in the PPI network are not necessarily represented for highly DEG. Consequently, genes with a central role in cancer not detected for high-throughput approaches could be identified by networks based analysis [6]. This was the case for PTEN, FOS, EGR1 and TNF, whose p values were significant but they were not among the lowest in the meta-analysis. Several genes with known prognostic implications in CLL were present in the list of DEG; additionally, the top DEG obtained were consistent with other studies [32–34], validating these findings the microarray meta-analysis approach to produce robust conclusions. LPL is one for the strongest prognostic markers to predict outcome in CLL [35, 36]. It was one of the genes with high betweenness index, reflecting the large amount of control exerted by this node over the interactions between the other nodes, in this way, LPL may function as bridge between sub-graphs. According to Kolset and Salmivirta [37] LPL facilitate the contact between monocytes and endothelial cell through its union with heparan sulfate proteoglycans, serving as a bridging protein between cell surface proteins and lipoproteins. On the other hand, LPL may influence CLL behavior for its relation with functional pathways involved in fatty acid degradation and signaling [38]. All genes found with high centralities have central roles in cancer and are involved in major, diverse and sometimes interrelated signaling pathways. They have roles as tumor suppressors or oncogenes, engaging central role in cancer progression. PTEN has phosphatase catalytic function that antagonizes the PI3K/AKT signaling pathway and Inactive Active 2.99% 2.45% 2.99% 2.72% 2.72% 2.99% Fig. 5 Major attractors obtained from 50 random initial states. The columns of the table represent consecutive states of the attractor. On top, the percentage of states leading to the attractor is supplied. Genes are encoded in the following order: AEBP1 AFF1 AICDA AKAP12 AKT3 ALOX5 ANXA2 APLP2 APOBEC3G APP BLNK BMI1 CASP3 CAV1 CCL5 CCND2 CD27 CD63 CD69 CD70 CD79A CD81 CD86 CHST2 CNR1 CREM CSDA CSNK2A2 CTSB CUL5 DPP4 EED EGR1 EZH2 FCER2 FGFR1 FOS FRK FYN GSK3B H2AFX HDAC9 HIST1H3H HIST2H2AA3 HSP90AA1 HSP90B1 IFNGR2 IGF1R IL10RA IL7 ILK INPP5D JAK1 LGALS1 LIG1 LMNA LPL MAP2K6 MAP4K4 MARCKS MGAT5 MIF MYL9 MYLK NAB1 NCOR2 NFE2L2 NOTCH2 OGT PAX3 PCNA PLD1 PRF1 PRKCA PTCH1 PTEN RFC5 RPS6KA5 RRM1 RUNX3 SELL SELP SIAH1 SKI TCF3 TNF TNFRSF1B VDR CD74 ADM TGFBR3 Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 8 of 15 suppresses cell survival as well as cell proliferation [39]. TNF gene encodes a multifunc- tional proinflammatory cytokine that belongs to the tumor necrosis factor (TNF) super- family, can induce a wide range of intracellular signal pathways including apoptosis and cell survival as well as inflammation and immunity. TNF has two receptors (TNFR1, TNFR2), TNFR1 signaling induces activation of many genes, primarily controlled by two distinct pathways, NF-kappa B pathway and the MAPK cascade, or apoptosis and necrosis. TNFR2 signaling activates NF-kappa B pathway, including PI3K-dependent NF-kappa B pathway and JNK pathway leading to survival [40]. FOS gene family encodes leucine zipper proteins that can dimerize with proteins of the JUN family, thereby forming the transcription factor complex AP-1. As such, the FOS proteins have been implicated as regulators of cell proliferation, differentiation, and transformation. In some cases, expression of the FOS gene has also been associated with apoptotic cell a b t= 1 2 3 4 t= 1 2 3 4 Inactive Active Fig. 6 Genes are encoded in the following order: AEBP1 AFF1 AICDA AKAP12 AKT3 ALOX5 ANXA2 APLP2 APOBEC3G APP BLNK BMI1 CASP3 CAV1 CCL5 CCND2 CD27 CD63 CD69 CD70 CD79A CD81 CD86 CHST2 CNR1 CREM CSDA CSNK2A2 CTSB CUL5 DPP4 EED EGR1 EZH2 FCER2 FGFR1 FOS FRK FYN GSK3B H2AFX HDAC9 HIST1H3H HIST2H2AA3 HSP90AA1 HSP90B1 IFNGR2 IGF1R IL10RA IL7 ILK INPP5D JAK1 LGALS1 LIG1 LMNA LPL MAP2K6 MAP4K4 MARCKS MGAT5 MIF MYL9 MYLK NAB1 NCOR2 NFE2L2 NOTCH2 OGT PAX3 PCNA PLD1 PRF1 PRKCA PTCH1 PTEN RFC5 RPS6KA5 RRM1 RUNX3 SELL SELP SIAH1 SKI TCF3 TNF TNFRSF1B VDR CD74 ADM TGFBR3. a. Visualization of states under overexpression of FOS b. Visualization of states under overexpression of TNF Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 9 of 15 death [41]. Studies about EGR1 have been suggested that it is a cancer suppressor gene and a transcriptional regulator. The products of target genes it activates are required for differentiation and mitogenesis [42]. TGFBR3 is a membrane proteoglycan that functions as a co-receptor with other transforming growth factors receptors. Soluble TGFBR3 may inhibit TGFB signaling. Decreased expression of this receptor has been observed in various cancers [41]. When the attractors found in the analysis of Boolean model are analyzed, several key proteins associated with specific signaling pathways related with cancer are found, it became clear that the phenotype depends upon multiple and interrelated signaling pathways. We underscore the importance of MAPK signaling pathway, identified by enrichment analysis, under FOS overexpression in the Boolean model. Belonging to the MAPK/ERK signaling cascade were found activated: CASP3, FGFR1, AKT3, FOS, MAP2K6, MAP4K4, PRKCA, RPS6KA5, and TNF. Aberrations in the MAPK/ERK pathway have been identified in human cancers in high frequency including hematologic malignancies [42]. In the context of CLL, the MAPK signaling pathway has been recently implied in the disease based on clustering of RNA sequencing data [43]. Similarly, working with gene co-expression subnetworks associated with disease progression, it has been proven association of MAPK pathway with higher expression levels in patients at early stages of the disease [44]. The regulatory hubs determine the behavior of the disease over time. The dynamics of the network is controlled by attractors involved of diverse signaling pathways, which may suggest a variety of mechanisms controlling the difference in CLL behavior. “The 2 distinct disease” hypothesis in CLL could be challenged; it is an interesting approach to speculate that the CLL disease transcriptome evolves over time to reach a state associated with disease requiring treatment [44]. These results have implications for understanding transcriptional dynamic in the evolution of the disease. Conclusion The PPI network and a Boolean model of IGVH mutational status in CLL allowed iden- tified regulatory proteins and generated insight about processes associated with the mani- fest differences in prognosis. The perturbation in the network through overexpression of important regulatory proteins, such as FOS and TNF, determine the dynamic of the network and activate genes involved in different signaling pathways that play important roles in cancer. Methods Differential expression analysis between the IGVH mutational statuses To ensure reliability and generalization of results, we combined information from different and independent microarray expression cohorts. It is well known that integra- tion of expression data allow the discovery of new biological insights by increasing the statistical power [45]. We retrieved CLL cohorts from the Gene Expression Omnibus (GEO) of the National Center for Biotechnology Information (NCBI). The cohorts selected (GSE2466, GSE16746, GSE9992 and GSE38611) had raw data available, were originally processed with different microarray platforms and had at least 60 CLL patients with information about the IGVH statuses, in total were processed 356 CLL Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 10 of 15 patients (174 mutated/umutated status). Each study was normalized independently using the VSN method implemented in R [46]. For filtering non-expressed and non- informative genes, matching genes among different microarray platforms and merging among studies, we used MetaDE package in R [47]. To combining the information of cohorts and avoid batch effect we followed a meta-analysis approach, the moderated-t statstics with permutations was used for individual analysis and Fisher P-value combin- ation method for combine the individual p values [48]. For meta-analysis we used the “MetaOmics” software suite [47]. Reconstruction of protein–protein interaction network The reconstruction of the protein–protein interaction network was based on data from differential expression analysis between IGVH mutational statuses. The list of 502 DE genes obtained was used to retrieve interacting partners from curated databases and current literature. The protein–protein interaction network was constructed based on the current litera- ture and, through the STRING—Search Tool for the Retrieval of Interacting Genes/ Proteins—web source [49]. The STRING database contains information from several sources, including experimental data, computational prediction methods, public text collection and an recompilation of predicted protein interactions of databases such as EXPASY [50], BIND [51], BioGRID [52], DIP [53], IntAct MINT [54], and HPRD [55] and with interactions from the pathway databases such as PID [56], Reactome [57], KEGG [58], and EcoCyc [59]. In order to reduce the amount of data while maintaining the main gene relations, the parameters of confidence for STRING were restricted for obtain more reliable associa- tions. Furthermore, the active prediction methods taken into account for STRING pre- dictions were: co-expression, experiments, databases, and text mining. From the protein-protein interactions predicted by STRING, with the restrictions mentioned above, only the genetic relationships causing the activation or inhibition of the compo- nents of the network were considered. In this way we reduced the number of network nodes from 502 to 90. Is important to state that the database predictive methods could reduce the overall confidence of network. Network topology analysis Topological analysis of the protein–protein interaction network was carried out by plugin Network Analysis [60] of the open source program Cytoscape 3.1.0 [61]. A topological evaluation of the network was carried out by evaluating structural parameters such as the clustering coefficient and degree distributions, to evaluate the number of interactions among one node and its neighbors, normalized by the maximum number of possible interactions, and to determine the number of nodes directly connected (first neighbors) to a given node v, respectively. In the network evaluation we distinguished in-degree distribution, when the edges target the node v, and out-degree distribution, when the edges target the adjacent neighbors of v [62, 60]. The evaluation of the relevance of a protein in the PPI network was also made through measurements of network centrality parameters, for this purpose, were used the betweenness, closeness and degree metrics. On the other hand, to analyze the Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 11 of 15 “compactness” of the network, we evaluate the average path length and the network diameter, parameters that indicate how distant are the two most distant nodes, showing the overall proximity between nodes in the interaction network analyzed [21]. Boolean network model In a Boolean network model, each node i = 1, 2, …, N represents a protein of the net- work that can assume only binary states θi. When θi = 1 the protein is functionally ac- tive (TRUE), on the other hand, when θi = 0 the protein is functionally inactive (FALSE). Thus, a network with N nodes will have 2 N possible states [21]. In this model, edges represent regulatory relationships between elements; their orientation in the network follows the direction of regulation process from the upstream to the downstream node. As time passes, the state of each node is determined by the states of its neighbor, through Boolean transfer functions based on evidence from the literature [63, 64]. The exponential behavior of the possible states in a Boolean network makes it com- putationally unsuitable for large networks, where it is necessary to reduce the network size, restricting the protein–protein interactions to the relationships of activation or inhibition of any of the components of the system. In this study, the Boolean synchronous algorithm proposed by Stuart Alan Kauffman in 1969 [13] was implemented. The synchronous pattern is the most simple update mode, where the states of all nodes are updated simultaneously according to the last state of the network [15]. We used the package BoolNet [65] to construct Boolean synchronous networks from knowledge of the dependencies of genes, based on evidence from the current literature. Starting from an initial condition, the model evolves over time to finally stabilize in a recurrent state known as attractor, representing the long-term behavior of the system [15]. Different initial conditions for the model may lead the system to different attrac- tors, whereby the Boolean model should start from previously known biological infor- mation; in this model the initial states of the network were determined from results supplied for microarray analysis of up and down regulation states (Additional file 4: Table S4). Aiming to prove the sensitivity of the Boolean model, we assayed 50 random initial states, and demonstrated that the constructed model shows changes in the struc- ture of the attractor achieved in the steady state under different initial states. To determine critical proteins for structure and behavior of the system, we examined the changes in network attractors if a certain component is knocked out (fixed in the OFF state in the Boolean model) or overexpressed (fixed in the ON state in the Boolean model). If knocking out or overexpressing a component leads to changes in network dynamic response, it can be concluded that this component is implicated in the biological regulation processes [15]. Functional enrichment analysis Significant concurrent annotations from KEGG and Panther pathways were searched with GeneCodis software [66–68]. Additional files Additional file 1: Table S1. Summary of genes functions. Álvarez-Silva et al. Theoretical Biology and Medical Modelling (2015) 12:12 Page 12 of 15 Additional file 2: Table S2. Topological properties of the CLL network. Additional file 3: Table S3. Topological parameters for the individual nodes. Additional file 4: Table S4. Boolean transfer functions and initial conditions of the Boolean network. Abbreviations CLL: Chronic lymphocytic leukemia; IGVH: Immunoglobulin heavy chain variable; PPI: Protein-protein interaction; DEG: Differentially expressed genes. Competing interests The authors declare that they have no competing interests. Authors’ contributions MCAS performed the Boolean model, topological analysis of the network, drafted the manuscript and analyzed data. SY participated in the conception and design of the study, performed statistical analysis of microarrays, analyzed data, and drafted the manuscript. AFGB participated in the design, coordination of the study, drafted the manuscript and analyzed data. MMTC participated in the design and coordination of the study. All authors read and approved the final manuscript. Acknowledgements Vicerectoria de Investigaciones and Facultad de Ciencias, Universidad de los Andes, supported this work. Author details 1Grupo de Diseño de Productos y Procesos (GDPP), Departamento de Ingeniería Química, Universidad de los Andes, Bogotá, DC, Colombia. 2Departamento de Ciencias Biológicas, Facultad de Ciencias, Universidad de los Andes, Bogotá, DC, Colombia. Received: 12 March 2015 Accepted: 8 June 2015 References 1. Murray F, Insel PA. Targeting cAMP in chronic lymphocytic leukemia: a pathway-dependent approach for the treatment of leukemia and lymphoma. Expert Opin Ther Targets. 2013;17(8):937–49. 2. Gaidano G, Foà R, Dalla-Favera R. Molecular pathogenesis of chronic lymphocytic leukemia. J Clin Invest. 2012;122(10):3432–8. 3. Landau DA, Carter SL, Stojanov P, McKenna A, Stevenson K, Lawrence MS, et al. Evolution and impact of subclonal mutations in chronic lymphocytic leukemia. Cell. 2013;152(4):714–26. 4. Chiorazzi N, Ferrarini M. Cellular origin(s) of chronic lymphocytic leukemia: cautionary notes and additional considerations and possibilities. Blood. 2011;117(6):1781–91. 5. 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Theoretical Biology and Medical Modelling (2015) 12:12 Page 15 of 15	26088082	MAP2K6 = ( CCL5 ) ILK = NOT ( ( FOS ) ) RUNX3 = NOT ( ( EZH2 ) ) HSP90AA1 = ( HSP90AA1 ) CCND2 = ( ( ANXA2 ) AND NOT ( PTEN ) ) CD81 = ( CD81 ) PTEN = ( ( ( ( ( ( FRK AND ( ( ( INPP5D AND BMI1 AND ILK AND IFNGR2 AND RRM1 AND EGR1 AND TNF ) ) ) ) AND NOT ( ADM ) ) AND NOT ( BMI1 ) ) AND NOT ( TGFBR3 ) ) AND NOT ( CSNK2A2 ) ) AND NOT ( AEBP1 ) ) OR ( ( ( ( EGR1 AND ( ( ( FRK AND INPP5D AND BMI1 AND ILK AND RRM1 ) ) ) ) AND NOT ( BMI1 ) ) AND NOT ( TGFBR3 ) ) AND NOT ( AEBP1 ) ) BLNK = ( CD79A ) MAP4K4 = ( TNF ) AICDA = ( HSP90AA1 ) OR ( ( CD27 AND ( ( ( HSP90AA1 ) ) ) ) AND NOT ( CD79A ) ) CREM = ( CREM ) TNF = ( LPL ) FGFR1 = ( FGFR1 ) CHST2 = ( CHST2 ) CD79A = ( TCF3 AND ( ( ( CD86 ) ) ) ) TNFRSF1B = ( TNFRSF1B ) LIG1 = ( PCNA ) DPP4 = ( TNF ) FCER2 = ( NOTCH2 ) CD86 = NOT ( ( TNFRSF1B ) ) AKAP12 = ( TNF ) CD70 = ( TNF ) FOS = ( ( ADM AND ( ( ( LMNA AND MAP2K6 AND TNF ) ) ) ) AND NOT ( JAK1 ) ) OR ( ( ( CNR1 AND ( ( ( LMNA AND MAP2K6 AND ADM AND PCNA AND TNF ) ) ) ) AND NOT ( CREM ) ) AND NOT ( JAK1 ) ) AKT3 = ( IGF1R AND ( ( ( NOT PTEN ) ) ) ) GSK3B = ( GSK3B ) FRK = ( FRK ) OGT = ( IGF1R ) NFE2L2 = ( ( TNF ) AND NOT ( GSK3B ) ) CAV1 = ( PRKCA ) OR ( TGFBR3 AND ( ( ( PRKCA ) ) ) ) APLP2 = ( APP ) HSP90B1 = NOT ( ( IFNGR2 ) ) SIAH1 = ( SIAH1 ) NOTCH2 = ( TNF ) HDAC9 = ( ( NCOR2 ) AND NOT ( SKI ) ) MIF = ( CD74 AND ( ( ( IFNGR2 AND TNF ) ) ) ) CD27 = NOT ( ( PRF1 ) ) RPS6KA5 = ( TNF ) PAX3 = ( ( PTCH1 ) AND NOT ( TGFBR3 ) ) EED = ( EED ) PTCH1 = ( FGFR1 ) APP = ( ( ( FYN ) AND NOT ( CD74 ) ) AND NOT ( CD74 ) ) OR ( IFNGR2 AND ( ( ( TNF ) ) ) ) AEBP1 = ( TGFBR3 ) H2AFX = ( CASP3 ) BMI1 = ( BMI1 ) EZH2 = ( ( ( EED ) AND NOT ( HDAC9 ) ) ) OR NOT ( EED OR HDAC9 ) CUL5 = ( CUL5 ) PLD1 = ( PRKCA AND ( ( ( APP ) ) ) ) MYLK = ( TNF ) JAK1 = ( ( IFNGR2 AND ( ( ( IL7 AND IL10RA ) ) ) ) AND NOT ( HDAC9 ) ) PRKCA = ( TGFBR3 AND ( ( ( AKAP12 ) ) ) ) HIST2H2AA3 = NOT ( ( HDAC9 ) ) CCL5 = ( ( IFNGR2 ) AND NOT ( FOS ) ) LMNA = ( LMNA ) IL10RA = ( IL10RA ) AFF1 = NOT ( ( SIAH1 ) ) RFC5 = ( RFC5 ) CNR1 = ( CNR1 ) ALOX5 = ( TGFBR3 AND ( ( ( EGR1 ) ) ) ) OR ( EGR1 ) TCF3 = ( TCF3 ) RRM1 = ( RRM1 ) SELL = ( CHST2 AND ( ( ( IFNGR2 ) ) ) ) FYN = ( FYN ) CD63 = ( SELP ) MYL9 = ( MYLK ) CD74 = ( CD74 ) ANXA2 = ( ANXA2 ) HIST1H3H = NOT ( ( HIST2H2AA3 ) ) LPL = ( ( FOS ) AND NOT ( TNF ) ) PRF1 = ( TNF AND ( ( ( RUNX3 ) ) ) ) OR ( RUNX3 ) CD69 = ( TNF AND ( ( ( CD81 ) ) ) ) ADM = ( HSP90AA1 ) OR ( TNF AND ( ( ( HSP90AA1 ) ) ) ) IFNGR2 = ( TNF ) PCNA = ( ( CSDA AND ( ( ( HSP90AA1 ) ) ) ) AND NOT ( RFC5 ) ) MARCKS = NOT ( ( PRKCA ) ) LGALS1 = ( TGFBR3 ) IL7 = ( IFNGR2 AND ( ( ( TNF ) ) ) ) OR ( TNF ) VDR = ( ( PRKCA ) AND NOT ( NCOR2 ) ) SELP = ( MGAT5 AND ( ( ( TNF ) ) ) ) CSDA = ( CSDA ) MGAT5 = NOT ( ( LGALS1 ) ) CTSB = ( CAV1 ) APOBEC3G = ( ( ( IFNGR2 ) AND NOT ( CUL5 ) ) ) OR NOT ( CUL5 OR IFNGR2 ) IGF1R = ( EGR1 AND ( ( ( CAV1 ) ) ) ) NCOR2 = ( TNF ) CASP3 = ( TNF AND ( ( ( NOT CTSB AND NOT IGF1R ) ) ) ) NAB1 = ( EGR1 ) SKI = ( SKI ) CSNK2A2 = ( CSNK2A2 ) TGFBR3 = ( TGFBR3 ) EGR1 = ( ( ( CNR1 AND ( ( ( TGFBR3 AND AEBP1 ) ) ) ) AND NOT ( NAB1 ) ) AND NOT ( HDAC9 ) ) INPP5D = ( TGFBR3 ) OR ( IGF1R AND ( ( ( TGFBR3 ) ) ) )
RESEARCH ARTICLE A Minimal Regulatory Network of Extrinsic and Intrinsic Factors Recovers Observed Patterns of CD4+ T Cell Differentiation and Plasticity Mariana Esther Martinez-Sanchez1,2, Luis Mendoza3, Carlos Villarreal2,4, Elena R. Alvarez- Buylla1,2* 1 Departamento de Ecología Funcional, Instituto de Ecología, Universidad Nacional Autónoma de México, Coyoacán, México Distrito Federal, México, 2 Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Coyoacán, México Distrito Federal, México, 3 Departamento de Biología Molecular y Biotecnología, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, México Distrito Federal, México, 4 Departamento de Física Teórica, Instituto de Física, Universidad Nacional Autónoma de México, México Distrito Federal, México * eabuylla@gmail.com Abstract CD4+ T cells orchestrate the adaptive immune response in vertebrates. While both experi- mental and modeling work has been conducted to understand the molecular genetic mech- anisms involved in CD4+ T cell responses and fate attainment, the dynamic role of intrinsic (produced by CD4+ T lymphocytes) versus extrinsic (produced by other cells) components remains unclear, and the mechanistic and dynamic understanding of the plastic responses of these cells remains incomplete. In this work, we studied a regulatory network for the core transcription factors involved in CD4+ T cell-fate attainment. We first show that this core is not sufficient to recover common CD4+ T phenotypes. We thus postulate a minimal Boolean regulatory network model derived from a larger and more comprehensive network that is based on experimental data. The minimal network integrates transcriptional regulation, sig- naling pathways and the micro-environment. This network model recovers reported configu- rations of most of the characterized cell types (Th0, Th1, Th2, Th17, Tfh, Th9, iTreg, and Foxp3-independent T regulatory cells). This transcriptional-signaling regulatory network is robust and recovers mutant configurations that have been reported experimentally. Addi- tionally, this model recovers many of the plasticity patterns documented for different T CD4 + cell types, as summarized in a cell-fate map. We tested the effects of various micro-envi- ronments and transient perturbations on such transitions among CD4+ T cell types. Inter- estingly, most cell-fate transitions were induced by transient activations, with the opposite behavior associated with transient inhibitions. Finally, we used a novel methodology was used to establish that T-bet, TGF-β and suppressors of cytokine signaling proteins are keys to recovering observed CD4+ T cell plastic responses. In conclusion, the observed CD4+ T cell-types and transition patterns emerge from the feedback between the intrinsic PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 1 / 23 OPEN ACCESS Citation: Martinez-Sanchez ME, Mendoza L, Villarreal C, Alvarez-Buylla ER (2015) A Minimal Regulatory Network of Extrinsic and Intrinsic Factors Recovers Observed Patterns of CD4+ T Cell Differentiation and Plasticity. PLoS Comput Biol 11(6): e1004324. doi:10.1371/journal.pcbi.1004324 Editor: Josep Bassaganya-Riera, Virginia Tech, UNITED STATES Received: December 5, 2014 Accepted: May 7, 2015 Published: June 19, 2015 Copyright: © 2015 Martinez-Sanchez et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Additionally, the models presented can be found at BioModels Database (acession numbers: MODEL1411170000 and MODEL1411170001). URL: https://www.ebi.ac.uk/biomodels/reviews/ MODEL1411170000-1/ Funding: This work was supported by grants from: Consejo Nacional de Ciencia y Tecnología México (www.conacyt.mx): 180380 to CV and ERAB, and 180098 to (ERAB). Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica or intracellular regulatory core and the micro-environment. We discuss the broader use of this approach for other plastic systems and possible therapeutic interventions. Author Summary CD4+ T cells orchestrate adaptive immune responses in vertebrates. These cells differenti- ate into several types depending on environmental signals and immunological challenges. Once these cells are committed to a particular fate, they can switch to different cell types, thus exhibiting plasticity that enables the immune system to dynamically adapt to novel challenges. We integrated available experimental data into a large network that was for- mally reduced to a minimal regulatory module with a sufficient set of components and in- teractions to recover most CD4+ T cell types and reported plasticity patterns in response to various micro-environments and transient perturbations. We formally demonstrate that transcriptional regulatory interactions are not sufficient to recover CD4+ T cell types and thus propose a minimal network that induces most observed phenotypes. This model is robust and was validated with mutant CD4+ T phenotypes. The model was also used to identify key components for cell differentiation and plasticity under varying immunogenic conditions. The model presented here may be a useful framework to study other plastic systems and guide therapeutic approaches to immune system modulation. Introduction The immune system protects organisms against external agents that may cause various types of diseases. As the immune system mounts specialized responses to diverse pathogens, it relies on plastic responses to changing immunological challenges. At the same time, the immune system must maintain homeostasis and avoid auto-immune responses. Therefore, the immune system relies on resilience mechanisms that enable it to return to basal conditions once pathogens or immunogenic factors are no longer present [1–3]. CD4+ T cells, also known as T helper (Th) cells, are key in the response to infectious agents and in the plasticity of the immune system. Naive CD4+ T cells (Th0) are activated when they recognize an antigen in a secondary lymphoid organ. Depending on the cytokine milieu and other signals in their micro-environment, CD4+ T cells attain different cell fates [2,4–7]. None- theless, we still do not have a complete understanding of the dynamic mechanisms underlying CD4+ T cell differentiation and plasticity [5]. Each CD4+ T cell type is associated with specific cytokines, receptors, transcription factors and functions (Fig 1). Th1 cells express T-bet, secrete interferon-γ (IFN-γ) and are associated with cellular immunity [8]. Th2 cells express GATA3, secrete interleukin (IL)-4 and are associ- ated with immunity to parasites [8]. Th17 cells express RORα and RORγt, secrete IL-17 and IL-21, and are associated with neutrophil activation [9–10]. Follicular helper CD4+ T cells (Tfh) express Bcl6 and CXCR5, secrete IL-21 and are associated with B cell maturation in ger- minal centers [11,12]. Th9 cells secrete IL-9 and exert anticancer activity [13,14]. Induced regu- latory T cells express Foxp3, secrete TGF-β and/or IL-10, and are associated with immune tolerance [15,16]. There is also considerable overlap among the expression profiles of different CD4+ T cells. For example, IL-9 and IL-10 can be secreted by Th1, Th2, Th17, iTreg cells and a variety of other immune cells [17–19]. T regulatory cells can also express IL-17 [20]. CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 2 / 23 Universidad Nacional Autónoma de México (dgapa. unam.mx/html/papiit/papit.html): IN203113; IN204011; IN226510-3 and IN203814 to ERAB. Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica Universidad Nacional Autónoma de México (dgapa.unam.mx/html/papiit/papit.html): IN200514 to LM. MEMS acknowledges support from the graduate program “Doctorado en Ciencias Biomédicas, de la Universidad Nacional Autónoma de México”. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. CD4+ T cells are highly plastic, switching from one type to another in response to environ- mental challenges (Fig 1) [1,21–23]. Th17 cells can transform into Th1 cells [24–25], and iTregs differentiate into Th17 in the presence of IL-6 [26]. Th2 cells can become IL-9 produc- ing cells but may not easily become Th1 cells [27]. iTreg and Tfh cells can independently devel- op into other CD4+ T cell types, and they can be derived from Th1, Th2 or Th17 cells [28–30]. The differentiation and plasticity of CD4+ T cells depends on the interactions among the cyto- kines produced by other immune cells, epithelial cells, adipocytes, or by the CD4+ T cells themselves; the transduction of those signals and the regulation of this signaling by suppressors of cytokine signalling (SOCS) proteins; the set of transcription factors expressed inside the cells; epigenetic regulation; certain metabolites; and also microRNAs [4,6,31–33]. Given the Fig 1. Differentiation and plasticity of CD4+ T cell types. CD4+ T cell types are characterized by their unique cytokine production profiles, transcription factors and biological functions. The main cell types are Th0, Th1, Th2, Th17, iTreg and Tfh. Other possible cell types have been described such as IL-9 (Th9), IL-10+Foxp3-(Tr1) and TGF-β+Foxp3-(Th3) producing cells. doi:10.1371/journal.pcbi.1004324.g001 CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 3 / 23 complexity of CD4+ T cell transitions and the difficulty of classifying a particular expression pattern as a subset or a lineage, we will refer to the different stable expression patterns of CD4 + T cells as “cell-types”. A mechanistic, integrative and system-level understanding of CD4+ T cell differentiation and plasticity requires dynamic regulatory network models that consider the concerted action of many components. These models can be used to prove whether the known biological inter- actions are necessary and sufficient to recover attractors that correspond to experimentally ob- served configurations in different CD4+ T cell types. Additionally, such models may be used to address whether the considered components and interactions also restrict and explain the ob- served patterns of transition among cell types. Finally, this type of model can be used to test the role of different network components in cell differentiation and plasticity. In such regulatory network models, the nodes correspond to the regulatory components of the network such as genes, proteins or signals, while the links correspond to the interactions among components. The state of each node is determined by the expression level of its regula- tors, and the logical functions describe the dynamic evolution of the node states. The attractors, the states to which such regulatory networks converge, can be interpreted as the profiles char- acterizing different cell types (see reviews in: [34–36]). Previous studies have used regulatory network models to study CD4+ T cell differentiation and plasticity [37–40]. These models captured the dynamic and non-linear regulation of CD4 + T cells and recovered the attractors corresponding to the Th0, Th1, Th2, iTreg and Th17 cell types. They have also been useful for preliminary studies of CD4+ T cell plasticity in the pres- ence of different cytokines in the micro-environment [38] and fir studies of the effect of a spe- cific molecule (PPARγ) in the Th17/iTreg switch [40]. However, as new T CD4+ cell types such as Tfh, regulatory Foxp3-independent, Th9, and Th22 cells are described, it is necessary to develop an updated regulatory network that is able to recover the configurations that charac- terize such novel cell subsets. Additionally, to date no minimal model that incorporates the necessary and sufficient set of interactions to also recover the reported patterns of transitions among Th cells has been reported. Here, we specifically address whether CD4+ cell types and their transition patterns emerge as a result of the feedback between a minimal regulatory core of intra-cellular transcription fac- tors and cytokines produced by the CD4+ T cell together with cytokines produced by other cells present in the micro-environment. Our results confirm that a regulatory network model that only considers the interactions among the master transcription factors is not sufficient to recover configurations that characterize the different CD4+ T cell types. Therefore, we then in- tegrated a minimal network of master transcriptional factors with cytokine signaling pathway, including the cytokines produced by the cell and those present in the micro-environment, to integrate a network with the necessary and sufficient set of components to recover documented CD4+ T cell differentiation and plasticity patterns. The observed configurations of CD4+ T cells (Th0, Th1, Th2, Th17, iTreg, Tfh, Th9 and Foxp3-independent T regulatory cells) emerge from the feedback and cooperative dynamics among the multiple levels of regulation consid- ered in the minimal model. In addition, this system is able to recover the plastic transition pat- terns and stability behavior that have been described for the different cell types in response to transitory perturbations and different micro-environments. Interestingly, our model predicts that transitions from particular cell types to others are caused by transient activations, while transient inhibitions usually cause cells to remain in their original cell types. Additionally, we show that T-bet, TGF-β and SOCS proteins are keys to recovering observed CD4+ T cell plastic responses. Finally, we discuss the relevance of our models for a system-level understanding of mammalian immunological responses and eventual biomedical interventions. CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 4 / 23 Results CD4+ T cell regulatory network Boolean networks are capable of integrating qualitative interactions (molecular, physical, chemical, etc.) into a coherent picture and are useful ways to explore the minimal set of restric- tions that are necessary and sufficient to produce emergent biological patterns and behaviors [41–43]. The regulatory interactions considered in the present model are grounded on experi- mental data. In the proposed regulatory network, the nodes represent the regulatory compo- nents of the network and the links the interactions among them (S1 Table and S1 Fig). Given the complexity of the network, we simplified the model by removing intermediate components along a network path (S1 File) following a method proposed in [44] and checked the consisten- cy of the reduced network using GINsim [45]. The predicted cell phenotypes arising from the steady states of the network are consistent with the available experimental data [2,4–7]. The model assumes that all interactions are syn- chronous, that all cytokine receptors are present, and that the TCR and its cofactors are activat- ed (being unable to model unactivated and anergic CD4+ T cells). The model ignores weak interactions, low levels of expression, and epigenetic regulation (S1 File). A core of master transcriptional regulators is not sufficient to explain CD4+ T cell differentiation To address whether a minimal transcriptional regulatory core could recover the observed con- figurations that characterize the main CD4+ T cell types that have been described up to now, we extracted from the general network under study a minimal regulatory module consisting only of transcriptional regulators (Fig 2A, S2 Table, BioModels Database: MODEL1411170000). Our aim was to test whether this minimal module contained a sufficient set of interactions to predict the observed configurations for the transcription factors included in the model that characterize different CD4+ T cell types. The nodes of the transcriptional Fig 2. Minimal network of master transcriptional regulators CD4+ T (CD4+ T TRN). Based on published experimental data we constructed a CD4+ T cell regulatory network that includes the master transcriptional regulators and the interactions among those regulators (CD4+ T TRN). (A) Graph of the CD4+ T TRN. Node colors correspond to cell types: Th1 (yellow), Th2 (green), Th17 (red), iTreg (blue) and Tfh (purple). Activations among elements are represented with black arrows and inhibitions with red dotted arrows. (B) Attractors of the CD4+ T TRN: Each column corresponds to an attractor. Each node can be active (green) or inactive (red). The attractors correspond to configurations that characterize the Th0, Th1, Th2, iTreg, T-bet +Foxp3+ and GATA3+Foxp3+ types. The attractors corresponding to the Th17 and Tfh types could not be recovered. doi:10.1371/journal.pcbi.1004324.g002 CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 5 / 23 regulatory network (TRN) correspond to the five “master” transcription factors associated with CD4+ T cell types: T-bet for Th1, GATA3 for Th2, RORγt for Th17, Foxp3 for iTreg, and Bcl6 for Tfh. The dynamic analysis of this TRN recovered attractors corresponding to different CD4+ T cell types (Fig 2B): Th0, Th1, Th2, iTreg and the hybrid states T-bet+Foxp3+ [46] and GATA3 +Foxp3+ [47]. However, this TRN did not converge to configurations that characterize the Th17 and Tfh cell types, implying that the expression of RORγt and Bcl6 is not sufficient to maintain such cell types. This result may be caused by the lack of feed-forward loops in the TRN. RORγt has no positive interactions with any of the transcription factors considered in the TRN and lacks a feedback loop mediated by transcription factors [48]. The mode of self- regulation of Bcl6 remains unclear, as it has been reported to either activate or inhibit its own expression in B cells [49–50]. CD4+ T cell differentiation patterns emerge from feedback between the transcriptional regulatory network, cytokines and signaling pathways The above result reveals which T CD4+ cell types rely only on the postulated TRN and which require extrinsic signals. To formally test this hypothesis, we extended the TRN network by in- troducing key components of signaling pathways and their regulators, as well as cytokines that have been shown to be fundamental in CD4+ T cell type attainment. This T CD4+ cell tran- scriptional-signaling regulatory network (TSRN) was then simplified (S1 File, S1 Fig) to obtain a minimal network. To reduce the number of nodes in the network, we assumed that the TCR signal was present and that the cytokine receptors were present in sufficient amounts to trans- duce a signal. This network lacks many important inflammatory cytokines (such as IL-1, TNFα), because while these cytokines are crucial for the immune response, they are dispens- able for CD4+ T cell differentiation. The model analyzed in this paper also lacks extrinsic cyto- kines produced by other immune system cells and other cell types such as IL-12 and IL-18. The network also lacks some transcription factors and cytokines associated with newly reported Th types such as IL-22, as detailed experimental information linking them to the network model under analysis is not yet available. The nodes of the simplified TSRN represent (Fig 3A, S3 Table, BioModels Database: MODEL1411170001) transcription factors, signaling pathways and extrinsic cytokines. The nodes corresponding to cytokine pathways are active if the signal is transduced; this means that if the cytokine is present, it forms a complex with the receptor that can activate a messen- ger molecule (for example a STAT protein), which is then translocated to the nucleus. Cyto- kines can be produced by both CD4+ T cells (intrinsic) and by other cells of the immune system and the organism (extrinsic). To resolve this ambiguity we added nodes representing the extrinsic cytokines produced by other cells and tissues of the immune system (IL_e). This extended TSRN includes 18 nodes: the transcription factors (Tbet, GATA3, RORγt, Foxp3, Bcl6), the effector cytokines and their signaling pathways (IFN-γ, IL-2, IL-4, IL-21, IL-9), the regulatory cytokines (TGF-β and IL-10) and the extrinsic cytokines (IFN-γe, IL-2e, IL-4e, IL- 21e, TGF-βe and IL-10e). While IL-10, IL-6 and IL-21 all signal using STAT3, IL-6 and IL-21 cause inflammation, while IL-10 suppresses inflammation. To analyze this network, we assume that IL-10 signaling was mediated by a different pathway than IL-6/IL-21, even though they share STAT3 as a messenger molecule. The production of these external cytokines is indepen- dent of regulation inside the CD4+ T cell, but their signaling can be blocked (for example by SOCS proteins [51]). The resulting network includes two levels of regulation, the regulation in the nucleus by mutually inhibiting transcription factors and the regulation among the receptors and their signal transduction pathways mediated by SOCS proteins. CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 6 / 23 Fig 3. CD4+ T cell transcriptional-signaling regulatory network (TSRN). We constructed a regulatory network using available experimental data. The network includes transcription factors, signaling pathways, and intrinsic and extrinsic cytokines. (A) Graph of the TSRN. The nodes include transcription factors (rectangles), intrinsic cytokines and their signaling pathways (ellipses) and extrinsic cytokines (ellipses). Node colors correspond to cell type: Th1 (yellow), Th2 (green), Th17 (red), iTreg (blue), Tfh (purple), and Th9 (brown). Activations between elements are represented with black arrows, and inhibitions with red dotted arrows. The dotted lines represent inhibition mediated by SOCS proteins. (B) Attractors of the TSRN. Each column corresponds to an attractor. Each node can be active (green) or inactive (red), extrinsic cytokines may be active or inactive (yellow). The following attractors were found in the network: Th0, Th1, Th2, Th17, iTreg, Tfh, Th9 producing T cells, Foxp3-independent T regulatory cells (TrFoxp3-), T-bet+ T regulatory cells (Th1R), GATA3+ T regulatory cells (Th2R) and GATA3+IL-4- cells. Attractors where labeled according to the active transcription factors and intrinsic cytokines. doi:10.1371/journal.pcbi.1004324.g003 CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 7 / 23 The dynamic analysis of the TSRN yields stable configurations that correspond to: Th0, Th1, Th2, Th17, iTreg, Tfh, T regulatory Foxp3-independent cells, Th1R, Th2R and GATA3 +IL4- cells (Fig 3B). As this biological patterns can be obtained in the presence of various ex- trinsic cytokines, we labeled each attractor according to the active transcription factors and intrinsic cytokines. Resting CD4+ T cells (labeled Th0) were defined as expressing no tran- scription factors or regulatory cytokines. Th1 was defined as Tbet and IFN-γ active [8], Th2 as GATA3 and IL-4 active [8] and GATA3+ (a Th2-like cell type) as GATA3+IL4-[38]. Th17 was defined based on RORγt and STAT3 signaling mediated by IL-6 or IL-21, all of which require the presence of TGF-βe [9–10]. iTreg expressed Foxp3 and TGF-β, IL-10 or both, all of which require the presence of IL-2e [16]. Interestingly, the TSRN model also predicts a novel set of steady states that had not been predicted by previous models but that correspond to reported biological cell types (Fig 3B); for example, Tfh cells with Bcl6 and STAT3 signaling mediated by IL-21 [12]; Th9 cells with IL-9, requiring the presence of TGF-β and extrinsic IL-4 [27]; T regulatory cells, as Foxp3-independent CD4+ T cells (TrFoxp3-) with TGF-β, IL-10 or both, but not Foxp3 [52]; Th1 regulatory cells (Th1R) expressing a regulatory cytokine and T-bet [46]; and Th2 regulatory cells (Th2rR) expressing a regulatory cytokine and GATA3 [47]. The model does not consider the Th22 cell type [53] because IL-22 was not included in the network due to the lack of experimental data on this molecule. To validate the model with experimental data, we simulated loss and gain of function alter- ations for some nodes. In general, the results agree with the available experimental data, except in the case of the IL-2 knock-out. IL-2- causes the loss of iTreg cells as these cells require con- tinuous IL-2 signaling [54,55], but this differs from the actual IL-2 KO mutants, which lose most CD4+ T cell types because IL-2 is also critical for the activation and survival of CD4+ T cells. This model also allows us to predict the behavior of the Tr Foxp3-, Th1R and Th2R cell types in response to various knock-out and over-expression simulations for several transcrip- tion factors or signaling pathways where no experimental data are available. We performed a functional robustness analysis in which the logical functions of the network were altered (S2 Fig) to verify the construction of the functions and the structural properties of the model and to avoid over-fitting. Altering one of the functions of the network resulted in 1.389% of the initial states attaining a different final attractor than the original final state, and only 0.219% of the initial states arrived at an attractor that was not in the original set of attrac- tors of the non-altered network. To further verify that the results of the Boolean network are not an artifact due to the dis- crete nature of the model and to further assess the robustness of the attractors to variations in the node values, we approximated the discrete step-like functions of the Boolean model with continuous interaction functions [44] (S2 File). The continuous model recovers the same at- tractors as the Boolean regulatory network. Furthermore, these attractors are stable in response to small perturbations in the value of the nodes as predicted by the robustness analyses of the Boolean version of the model. CD4+ T cell differentiation in response to the micro-environment Cytokines can be produced by the cell (intrinsic) or by other cells of the immune system (ex- trinsic). These extrinsic cytokines constitute the micro-environment for CD4+ T cell differenti- ation. The role of polarizing micro-environments in CD4+ T cell differentiation was assessed using the TSRN model. In this network, the values of the extrinsic cytokines were fixed at a given expression level and the network response was analyzed again (Fig 4). Th0, Th1, Th2 and Tfh can be maintained in the absence of extrinsic cytokines or in the presence of effector cyto- kines such as IFN-γ, IL-2, IL-4 or IL-21. Th17, iTreg and Th9 cells require extrinsic TGF-β, IL- CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 8 / 23 2 and IL-4, respectively, to maintain their homeostatic states [13,56]. TrFoxp3- states can be maintained in most polarizing micro-environments [57,58]. The recovered behaviors agree with the experimental data and also with previous models [38]. The importance of the extrinsic cytokines present in the micro-environment can be further analyzed when the system is studied under polarizing conditions. The presence of extrinsic sig- nals for a given cell type increases the number of initial states that differentiate into that cell type, while the absence of extrinsic signals may lead to the loss of a cell type, as is the case with Th17, iTreg and Th9 cells (Fig 4). The presence of the regulatory cytokines IL-10 and TGF-β inhibits most effector CD4+ T cells, except for Th17. This finding may explain the presence of Th17 cells in regulatory micro-environments [59] and provides important insight concerning the relationship between Th17 and iTreg. Thus, this type of modeling framework and analysis may prove useful for finding therapeutic approaches to chronic inflammation. The polarization of the micro-environment towards a particular cell type increases the size of the basin of attraction and its resistance to transient perturbations. Basin size and attractor stabil- ity are not identical (S3 Fig). In this way, the environmental signals promote specific cell types and increase their stability, which likely affects the population dynamics of CD4+ T cells. None- theless, different CD4+ T cell types coexist during immune responses. Even if the signals in the micro-environment promote a specific cell type, attractors corresponding to other cell types can still appear in this micro-environment, but their basin sizes and stability tend to be smaller. CD4+ T cell plasticity in response to the micro-environment The ability of the immune system to dynamically respond to environmental challenges de- pends on its plastic responses. CD4+ T cells are phenotypically plastic, and once differentiated, Fig 4. Effect of the micro-environment on CD4+ T cell differentiation as determined using the TSRN model. The values of the extrinsic signals of the TSRN were fixed according to different polarizing micro- environments. The basins of attraction of the resulting attractors were plotted on a logarithmic scale. The following micro-environments were studied: combinations of all extrinsic cytokines, no extrinsic cytokines (Th0), IFN-γe (Th1), IL-4e and IL-2e (Th2), IL-21e and TGF-βe (Th17), TGF-βe and IL-2e (iTreg), IL-10e (IL10), IL-21e (Tfh), and IL-4e and TGF-βe (Th9). doi:10.1371/journal.pcbi.1004324.g004 CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 9 / 23 their expression patterns can be altered depending on internal and external cues. This cell plas- ticity seems to be important for the overall plasticity of immune system responses [1]. To analyze CD4+ T cell plasticity, we transiently perturbed the attractors of the system. For each attractor we altered the value of one of its nodes and then evaluated the system until an at- tractor was reached. If the original attractor was reached, we considered the corresponding cell type as stable towards that perturbation. If a new cell-type was reached, we considered that the transition from one cell type to another corresponded to phenotypic plasticity. This analysis was repeated for every node and every attractor. This methodology allowed us determine all the transitions between cell types, the specific perturbation that caused the transition, and the path from one cell-type to another. These transient perturbations in the values of the nodes are equivalent to developmental noise or temporal changes in the micro-environment of the cell. The result is a cell-fate map where the nodes represent CD4+ T cell types recovered by the TSRNand the connections represent the possible transitions between pairs of differentiated cell types (Fig 5, S3 File). The model recovers the reported transitions corresponding to the polarization of naïve CD4 + T cells into canonical CD4+ T cell types, as well as various events of trans-differentiation be- tween canonical CD4+ T cell types. Most of the predicted transitions are to or from Th0 or to- wards TrFoxp3-. It is important to clarify that the TCR complex was not included in the minimal model. Thus, in our model, the Th0 attractor represents resting CD4+ T cells. There are few direct transitions among the Th1, Th2, and Th17 cell types. The few direct transitions found towards iTreg and Tfh can only be achieved in polarizing micro-environments. It is also possible to transition from one of the main cell types to another one through the Th0, TrFoxp3-, Th1R, Th2R or GATA3+IL4- attractors. This ability raises multiple questions about the signals necessary for plasticity in vivo. It is possible that in order to transition from one cell type to another, some signals have to be maintained for a certain period of time, or that more than one perturbation is necessary. Further studies are required to determine which conditions are necessary and sufficient for CD4+ T cell type transitions to further understand CD4+ T cell plasticity. Therefore, in the context of this study, we define plasticity as the potential of a given differ- entiated cell to attain other fates in response to alterations in the expression patterns of their in- trinsic components and/or of the extrinsic micro-environment. Of the total of 121 possible transitions between cell types arising from those alterations, the TSRN network yielded 66 cell- type transitions. Thus, the topology or set of regulatory interactions proposed in this network generates restrictions in terms of cell types but also in terms of the patterns of cell-fate transitions. CD4+ T cells are typically under the influence of particular micro-environments, with spe- cific cytokines affecting the dynamics of these cells. Depending on the combination of cyto- kines, some cell types are lost, and transitions among the remaining cell types are also restricted. To simulate polarizing micro-environments, we fixed the value of the cytokines as- sociated with pro-Th1 (IFGγe), pro-Th2 pro-(IL-4e, IL-2e), pro-Th17 (IL-21e, TGF-βe), pro- iTreg (TGF-βe, IL-2e), pro-Tr (IL-10,) pro-Tfh (IL-21e) and pro-Th9 (IL-4 and TGF-βe). In general, the polarizing micro-environment increases the size of the attraction basin, the stabili- ty and the transition into the attractor. The biological nature of the polarizing signal affects the nature of the resulting transition. In response to regulatory signals (IL-10e, TGF-βe), the ma- jority of the transitions are towards TrFoxp3-, while inflammatory signals lead to more transi- tion signals towards Th1 and Th2. All of these results represent interesting predictions that could be tested experimentally. Activation of specific CD4+ T transcriptional-signaling regulatory network nodes in- duces cell type plasticity while inhibitions induce stability. The nature of the perturbation CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 10 / 23 Fig 5. Cell fate map in response to the micro-environment and perturbations of the TSRN model. The values of the extrinsic signals of the TSRN were fixed according to different polarizing micro-environments, and the resulting attractors were transiently perturbed. The nodes represent CD4+ T cell types, and the node sizes correspond to the size of the basin of attraction. The edges represent transitions between cell types, the width of the edges corresponds to the number of times the transition occurred in logarithmic scale, and self-loops correspond to perturbations where the network returned to the original cell type. The following micro-environments were studied: combinations of: (A) all extrinsic cytokines, (B) IFN-γe (Th1), (C)IL-4e and IL-2e (Th2), (D) IL-21e and TGF-βe (Th17), (E) TGF-βe and IL-2e (iTreg), (F) IL-10e (IL10), (G) IL-21e (Tfh), (H) IL-4e and TGF-βe (Th9), (I) no extrinsic cytokines (Th0). doi:10.1371/journal.pcbi.1004324.g005 CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 11 / 23 is also important for CD4+ T cell plastic responses or stability (Fig 6). If an inactive node is ac- tivated (0!1), there is a high probability that a transition from one cell type to another is in- duced. In contrast, if an active node is inactivated (1!0), there is a high probability that the system remains in the original cell-type. This pattern may be caused by the topology of the net- work and, in particular, may depend on the functional feedback loops of the system that are al- tered. The positive feedback loops of a cell type may increase the stability of an attractor and help to recover a transiently inactive node, thus stabilizing a given differentiated state. We hy- pothesize that the activation of a previously inactive node may induce more transitions, as this alteration likely affects the positive and negative functional circuits of the system [60], thus in- creasing the chances that the system leads to a new attractor. Further simulations should be used to exhaustively test how specific regulatory circuits react to transient activations and inhi- bitions. In any case, the analysis presented in this study enables us to postulate that CD4+ T cells are expected to be able to react to activation signals and environmental alterations but are stabilized in response to the transient loss of signals. Thus, the proposed model for CD4+ T cell dynamics implies that these cells are under an unstable equilibrium between cell-fate stability and plasticity. Key nodes for CD4+ T transcriptional-signaling regulatory network plasticity While all the elements of the TSRN have previously been shown to be necessary for the differ- entiation of CD4+ T cells, we wished to address their relative importance in cell plasticity re- sponses. To evaluate this question, we perturbed each node of all the attractors and measured how many times the perturbed state changed to a new attractor (Fig 7) and to which new cell type the system converged (S4 Fig). This process is equivalent to the temporal activation or in- activation of a transcription factor or an element of the signaling pathway in response to noise. Alterations of T-bet and TGF-β usually caused the perturbed state to change from one attractor to another, while RORγt and IL-9 had the least effect on cell-fate transitions. In general, the system is more sensitive to perturbations in the master transcriptional regulators than to alter- ations of the cytokines. Fig 6. Cell fate map in response to activating or inhibitory signals of the TSRN model. The attractors of the network were transiently perturbed in all possible micro-environments. Perturbations were considered activations (0 ! 1) when a previously inactive element was turned on, and inhibitions (1 ! 0) when a previously active element was turned off. The nodes represent CD4+ T cell types, and the node sizes correspond to the size of the basin of attraction. The edges represent transitions between cell types, the width of the edges correspond to the number of times the transition occurred on the logarithmic scale. The number of transitions towards a different or the original cell type were counted for both activations and inactivations. doi:10.1371/journal.pcbi.1004324.g006 CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 12 / 23 In contrast to previously published T CD4+ network models that only included SOCS1 [37–40], several SOCS-type proteins were considered in the TSRN presented and analyzed here. SOCS proteins are important for the differentiation and plasticity of CD4+ T cells. SOCS1 is commonly silenced in inflammatory diseases, and over-expression of SOCS3 corre- lates with allergies [31,51]. To explore the role of SOCS proteins and the impact of alterations in these proteins on CD4+ T type transitions, we generated a network lacking the inhibitions mediated by these proteins (Fig 8). This altered system recovers the original attractors includ- ing Th0, Th1, Th2, Th17, iTreg, Tfh, TrFoxp3-, and Th9, but it also predicts novel attractors expressing RORγt+IL-10+ (Th17R) and GATA3+IL-10+IL-9+ (Th2RIL9+), thus confirming the importance of SOCS proteins for attaining the Th17 and Th9 cell types. The importance of IL-10 for CD4+ T cell plasticity dramatically increased in the altered network, while the impor- tance of the rest of the molecular elements decreased. This result suggests that SOCS proteins play an important role in stabilizing effector cell types and regulating the Th0 and TrFoxp3- cell types. SOCS proteins inhibit signal transduction; IL-10 in particular acts through these pro- teins to regulate CD4+ T cells. This regulation is important to buffer the effect of extrinsic cyto- kines in the TSRN network model. When SOCS proteins are absent, the network is more sensitive to changes in extrinsic cytokines and IL-10. Further analyses of the effects of SOCS proteins on CD4+ T cells and the possibility of updates to the model based on experimental work should enable the evaluation of more subtle alterations in and combinations of SOCS proteins. Fig 7. Role of different network nodes in the plasticity of the TSRN model. The proportion of transitions between attractors in response to transient perturbations in the value of each node. On average, 37.76% of the perturbations result in transitions to another cell type, with 47.12% of perturbations of intrinsic components resulting in transitions, compared with 24.43% of perturbations of extrinsic cytokines. doi:10.1371/journal.pcbi.1004324.g007 CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 13 / 23 Discussion This model provides a mechanistic description of the way in which CD4+ T cell types and plas- ticity emerge from the interactions among the intrinsic and extrinsic components of the im- mune response. The study formally shows that, as expected, the interactions among master transcription factors considered in the TSRN are not sufficient to recover the configurations characteristic of CD4+ T cell types, nor the reported transition patterns. Furthermore, these re- sults clearly demonstrate the necessity to include the feedback from signaling pathways in re- sponse to cytokines to recover most of the range of CD4+ T cell types (Th0, Th1, Th2, Th17, Tfh, Th9, iTreg and T regulatory Foxp3 independent cells) and their transition pathways. As noted above, CD4+ T cell differentiation does not arise solely from the regulatory action of the core of the reported "master" transcription factors (TF): T-bet, GATA3, Foxp3, RORγt and Bcl6. This may be due to the lack of feedforward loops mediated by the transcription fac- tors RORγt [48] and Bcl6 [49,50]. These results show that the transcriptional regulatory core of CD4+ T cell differentiation is necessary, but not sufficient for CD4+ T cell differentiation. The emergence of the different CD4+ T cell types and their transition patterns, requires the feed- back from cytokine signaling pathways and external cues. This model provides a formal test for the emergence of different CD4+ T cell types from feedback or cooperative dynamics among master transcriptional factors, signaling pathway, cy- tokines produced by the cell and those present in the micro-environment. The proposed model recovers the observed configurations for the following CD4+ T cell types: Th0, Th1, Th2, Th17, Tfh, Th9, iTreg and T regulatory Foxp3 independent cells [2,4–7]. The model also yields Fig 8. Role of SOCS proteins in the differentiation and plasticity of the TSRN model. The interactions mediated by SOCS proteins were removed to study their role. (A) Cell fate map of CD4+ T cell types when the SOCS protein interactions are removed from the TSRN model. The nodes represent CD4+ T cell types and the node sizes correspond to the size of the basin of attraction. New attractors corresponding to GATA3+IL9+IL10+ (Th2RTh9) and RORγt+IL- 10+ (Th17R) appeared. The edges represent transitions between cell types, the width of the edges corresponds to the number of times the transition occurred on logarithmic scale, and self-loops correspond to perturbations where the network returned to the original cell type. (B) Proportion of transitions between cell types in response to transient perturbations in the value of each node. On average, 21.65% of the perturbations result in transitions to another cell type, with 17.55% of perturbations of the intrinsic components of the network resulting in transitions, compared with 27.51% of perturbations of extrinsic cytokines. doi:10.1371/journal.pcbi.1004324.g008 CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 14 / 23 the cell types Tfh, Th9 and T regulatory Foxp3 independent cells that had not been previously incorporated into such models [37–40]. CD4+ T cell types depend on signals from other cells for their differentiation and mainte- nance. The cytokines in the micro-environment restrict which cell types and transitions can be attained. A cytokine micro-environment that promotes a particular cell type increases its at- traction basin size, stability and increases the number of transitions towards the promoted cell type. Nonetheless, different CD4+ T cell types can coexist in micro-environments that do not promote all the present cell types. For example, the presence of pro-regulatory cytokines IL-10 and TGF-β inhibits most effector cells, except for Th17. This finding may explain the presence of Th17 cells in regulatory micro-environments [59] and provides important insights concern- ing the relationship between Th17 and iTreg cells and the paradoxical role of TGF-β in inflam- mation [61]. Thus, the type of modeling framework and analyses presented here may prove to be useful for efforts to find therapeutic approaches to address chronic inflammation. The model was also used to analyze the plasticity of CD4+ T cells by systematically testing how transient perturbations affect the transition patterns among cell types under various micro-environments. Previous studies focused on cell plasticity in response to different micro- environments [38] or on the role of specific molecules [40], rather than studying these phe- nomena as consequences of the global properties of the system. For example, the TSRN faith- fully captures the polarization of resting CD4+ T cells into Th1, Th2, Th17, iTreg and Foxp3-independent T cells, but the predicted cell-fate maps lack direct transitions from iTreg to Th17 and Th17 to Th1 [23–25]. The TSRN model may lack components, interactions or epi- genetic mechanisms of regulation that are important to enabling such direct transitions [33]. An additional possibility is that signals must be combined during particular lengths of time to enable some transitions. Further theoretical and experimental research is required to under- stand the mechanisms underlying CD4+ T cell plasticity. However, the qualitative model pro- posed here can serve as a framework to incorporate additional details involved in CD4+ T plasticity. Our model shows that the activation of specific CD4+ T cell transcriptional-signaling regu- latory network nodes generally induce cell type plasticity while inhibitions induce stability. The observed response patterns may be caused by the feedback loops and mutual inhibitions molec- ular network. These findings are coherent with the fact that the immune system generates a specific immunological response to particular challenges, maintains this response while the challenge remains present, and finally downregulates the immune response once the challenge has passed, thus maintaining homeostasis [3,61]. Our model suggests that T-bet, TGF-β and SOCS proteins are key network components to recover the observed CD4+ T cell plasticity. Although T-bet is a key transcription factor for Th1, it also inhibits other transcription factors regulating the differentiation into different cell types [4]. TGF-β is a critical regulator of the immune response but also plays a key role during chronic inflammatory responses [61]. SOCS proteins regulate the phosphorylation of STAT proteins, playing a key role in modulating the signal transduction among different cell types [31,51]. Determining the key elements enabling cell-type plasticity has possible therapeutic im- plications, as these findings can help to identify therapeutic targets for modulating the immune response while predicting and avoiding secondary effects[3,62]. Given the complexity of CD4+ T cell expression patterns and transitions, it remains unclear whether cytokine expression profiles correspond to lineages or subsets [1–3,22]. The term line- age implies the stability of the cellular phenotype and that the cell has committed to an expres- sion pattern and will maintain it in a fairly robust manner, regardless of environmental alterations. On the other hand, the term subset implies that the cell has a specified expression pattern but that extrinsic signals are required to maintain that pattern [1,22]. Cell types Th1, CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 15 / 23 Th2, Tfh and TrFoxp3- can be considered lineages, as they exhibit commitment under different cytokine milieus, even if the extrinsic signals change, although environmental alterations can still affect their stability. However, Th17, iTreg and Th9 cells, which require TGF-βe, IL-2e or IL-4e respectively, are potentially subsets. Th17 and iTreg cells also have small basins of attrac- tion, low stability, and require extrinsic signals, exhibiting a lack of commitment. Th9 has a larger basin of attraction than Th17 or iTreg, but is less stable and susceptible to environmental alterations. Based on our analyses, we propose that the degree of dependence on extrinsic sig- nals and the stability in response to changes in the micro-environment can provide clearer and more objective criteria to distinguish between CD4+ T cell subsets and lineages. CD4+ T cell differentiation and plasticity arises from the feedback among multiple levels of regulation: transcriptional regulation, signaling pathways and the micro-environment. Study- ing the molecular network as a dynamic system allows us to understand how the interactions among the components, the topology of the network, and the dynamic functions of the nodes give rise to the biological behavior. However, further theoretical and experimental research is required to understand CD4+ T cells. As our understanding of these cells improves, it will be possible to incorporate more detailed molecular information, such as the effect of relative ex- pression levels and the characteristic time courses of expression in the system. This will, in turn, allow us to recover novel cell types and their relationship with other CD4+ T cell types and other cells of the immune system. The present model can now be extended to incorporate multiple cells and their population dynamics [39], relationships with other cells of the immune system, and the formation of specialized niches that result from the dynamic interaction with the micro-environment. This approach will allow us to differentiate between CD4+ T cell sub- sets and lineages, to understand the developmental dynamics between the different cell types, and to propose approaches to immune system reprogramming that can be used in the clinic. Methods Logical modeling formalism: Boolean networks CD4+ T cell differentiation results from interactions among cytokines, signaling pathways and transcription factors. These interactions were modeled using Boolean networks that enabled us to integrate the qualitative nature of complex regulatory systems. A Boolean network is com- posed of nodes that represent the system´s molecular components (i.e., cytokines, signaling pathways or transcription factors). In a Boolean network, each node represents a component (gene, protein, phenomenological signal) that can be associated with a discrete variable denot- ing its current functional level of activity. If the node is functional its value is 1, and if it is not functional, then its value is 0 (see S1 File). Some nodes required special considerations concern- ing their activation states in the Boolean model. For example, in the case of GATA3, which is continuously expressed during T-cell-lineage development and is necessary for lineage com- mitment and maintenance, GATA3low is set to 0. As GATA3 is upregulated in Th2 differentia- tion [63], we set GATA3high to 1. Another example concerns STAT proteins, which are activated when the protein is phosphorylated, forming a dimer that translocates to the nucleus, where it activates its target genes. In this case, the value for STAT protein activation was only set to 1 when all the required conditions were met. The value of a node xi at a time t depends on the value of the input nodes (including itself), referred to as its regulators. This value can be expressed with a logical function that describes the behavior of the node through time: xiðtÞ ¼ ϕιðτ; ξ1; ξ2; ξ2; …; ξι; …; ξνÞ: CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 16 / 23 Weak interactions that are not necessary or sufficient, but only modulate a target factor, were not included in the input regulators of the truth tables (S1 File). Such is the case for Foxp3, which positively modulates the expression of IL-2Rα, which can be activated and func- tional in the absence of Foxp3 [64]. An input is a node that affects the values of the network but is independent of the network. The state of the network S can be represented by a vector that specifies the value of each node. The state of the network can be represented by a vector S composed of the values of all the nodes of the system. The state of the network corresponds to the expression patterns of a cell. Inference of the regulatory functions. Boolean functions were defined based on the avail- able experimental data for the reported interactions among a network of 85 components (S1 Table). A transcription factor regulates another factor if it binds to the regulatory region of the latter factor and inhibits or activates is transcription. A cytokine is present if it is either secreted by the cell (intrinsic) or produced by other cells of the immune system (extrinsic). To separate the effects of the cytokines produced by the immune system from those of the cytokines pro- duced by the CD4+ T cell, we label extrinsic cytokines as ILe. Receptors are considered to be ac- tive when the cytokine is stably bound to a receptor, enabling it to transduce a signal. STAT proteins are considered active when they are phosphorylated and capable of translocating to the nucleus. The activation of a STAT protein depends on the presence of interleukin, its cor- rect binding to the receptor, and subsequent phosphorylation. SOCS proteins inhibit the phos- phorylation of STAT by competing for the phosphorylation site. Model reduction To facilitate the analysis of the network and determine which components were necessary and sufficient to recover observed profiles and their patterns of transition, we reduced the extended regulatory network consisting of 85 nodes to one with 18 nodes, including 5 transcription fac- tors, 7 signaling pathways and 6 extrinsic cytokines. To simplify the network, we assumed that the signal produced by the TCR and its co-factors was constitutive and ignored weak interac- tions as well as input and output nodes. Considering that the expression level of node xi at time t is represented by xi(t), the attractors (steady states) that represent different phenotypes are de- termined by: xi(t+1) = xi(t). In that case, the mapping becomes a set of coupled Boolean algebraic equations. The explicit expressions of the attractors are then obtained by performing the algebraic operations accord- ing to the axioms of Boolean algebra [44]. Self-regulated nodes were not removed. If a node was removed, then the logical rules of its targets were modified, maintaining the regulatory logic and indirect regulation. To verify that we did not remove a necessary node, we recovered the attractors of the network and ensured that the configurations corresponding to the Th0, Th1, Th2, Th17 and iTreg states could still be attained (see the details of the reduction methods used in S1 File). The reduction was verified using the GINsim[45] software. GINsim uses decision diagrams to iteratively remove regulatory components and updates the components to maintain the indi- rect effects. This method preserves the dynamic properties of the original model. The simplifi- cation with GINsim returned a similar network to the one that we obtained with the Boolean logic reduction method proposed by Villareal et al. ([44];S1 File). Dynamic analysis After inferring and simplifying the network, we studied its dynamic behavior. A regulatory net- work is a dynamic system. The state of a network will change over time depending on the CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 17 / 23 logical functions associated with each node. When the values of a state vector S at t+1 are the same as those at time t, the system has attained an attractor: S(t) = S(t + n), n 1. An attractor is interpreted as a stable expression phenotype of a cell, representing a cell type. All the states that lead to a solution S constitute the basin of attraction of such an at- tractor. We determined the attractors and basins of attraction of the network using the R li- brary BoolNet. Attractors were classified depending on the expression of both the master transcription factors and the main cytokine. Th0 was defined as expressing no transcription factors or regulatory cytokines. Th1 was defined as Tbet and IFN-γ active [8], Th2 as GATA3 and IL-4 active [8] and GATA3+ (a Th2-like cell type) as GATA3+IL4-[38]. Th17 was identi- fied by RORγt and STAT3 signaling mediated by IL-6 or IL-21, all of which require the pres- ence of TGF-βe [9–10]. The iTreg type was defined by Foxp3 and TGF-β, IL-10 or both, all of which require the presence of IL-2e [16]. Tfh cells were defined by Bcl6 and STAT3 signaling mediated by IL-21 [12]. Th9 cells express IL-9, requiring the presence of TGF-β and extrinsic IL-4 [27]. T regulatory Foxp3-independent CD4+ T cells (TrFoxp3-) featured TGF-β, IL-10 or both, without expressing Foxp3 [52]. Th1 regulatory cells (Th1R) express a regulatory cytokine and T-bet [46]. Th2 regulatory cells (Th2rR) express a regulatory cytokine and GATA3 [47]. Network validation. The network was validated by comparing it with reported knock-out and over-expression profiles. To simulate loss of function mutations (knock-out) and inhibi- tions of the signaling pathway, we set the value of the corresponding node to 0 throughout the complete simulation. To simulate over-expression, the value of the node was set to 1. The functional robustness of the network was characterized by altering the logical functions of the network. Functional robustness refers to the invariance of the attractors in response to noise or perturbations [44]. In this case, to verify that the results of the model did not depend on over-fitting the logical functions, we perturbed the latter and verified the stability of the re- sulting attractors and their basins. To achieve this, we randomly selected a large number of en- tries and flipped their values from 0 to 1 or vice versa, one by one (bit flip). The basins and attractors were obtained for the altered networks and compared the original basins and attractors. To further evaluate the robustness of the network to small changes in the values of the nodes and interaction functions, we approximated the Boolean step functions as continuous functions [44]. We replaced the logical functions f(xi) with a set of continuous functions that satisfy Zadeh's rules of fuzzy propositional calculus. Using this approach for each state variable, we derived a continuous function, wi(q). The latter functions correspond to step-like (differen- tiable) activation functions. The continuous system can then be described by: dqi dt ¼ 1 e½−2bðwiðqÞ−wthr i Þþ1 18 where wi is the input function for node i, wi thr is a threshold level, b is the input saturation rate, and αi is its relaxation rate. In particular, for b >>1, the activation function becomes a Heavi- side step function. Plasticity The attractors of the network correspond to cell types. A multi-stable system can have multiple attractors and switch between them in response to alterations in the state of the system [65]. To study the plasticity and robustness of the system we transiently perturbed the attractors of the network and then evaluated the functions until we arrived at an attractor. This methodolo- gy enabled us to obtain all the transitions between cell types, the specific perturbations that caused those transitions, and the path from one cell-type to another. We define an attractor as CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 18 / 23 stable when the system remains in the same attractor in the presence of perturbations. The sta- bility of each attractor in response to changes in the micro-environment and signaling path- ways was analyzed by characterizing the evolution of the network in response to pulses of activation or inhibition of specific nodes. To quantify the stability of the attractors of the net- work, we perturbed the state vector of the solutions for one time step. Then, we counted how many of the perturbed state vectors stayed in the same attractor to quantify its stability. A sys- tem is plastic when it can transition from one state to another in response to alterations of the system. More specifically, the network was said to be plastic when a transition occurred from a given attractor to another in response to a transient perturbation in the value of one of its nodes. Supporting Information S1 Table. T CD4+ lymphocyte extended regulatory network references. (XLS) S2 Table. T CD4+ lymphocyte transcriptional regulatory network model. (XLS) S3 Table. T CD4+ lymphocyte transcriptional-signaling regulatory network model. (XLS) S1 File. T CD4+ lymphocyte extended regulatory network simplification. (PDF) S2 File. T CD4+ lymphocyte transcriptional-signaling continuous regulatory network model. (PDF) S3 File. Transitions in response to transient perturbations in the nodes of the T CD4+ lym- phocyte transcriptional-signaling regulatory network. (PDF) S1 Fig. T CD4+ lymphocyte extended regulatory network. (EPS) S2 Fig. Validation of the T CD4+ lymphocyte transcriptional-signaling regulatory network. (A) To validate the TSRN model, we simulated loss of function or null mutations (KO) and over-expression experiments and compared the results with the available experimental data. The values of the nodes were set to “0” for simulations of loss-of-function or knock-out experi- ments and to “1” for over-expression. The color corresponds to the basin size of each attractor on the logarithmic scale. '—-' represents attractors that were not attained in the original wild type (WT) network. The attractors marked with (red) "X" correspond to incorrect predictions. (B) To verify the construction of the functions and the structural properties of the model, we performed a robustness analysis altering the update rules. Networks with perturbed functions of the TSRN were generated to test the robustness of the structural properties of the networks to noise, mis-measurements and incorrect interpretations of the data. After altering one of the functions of the network, 1.389% of the possible initial states changed their final attractor (yel- low), and only 0.219% of the possible initial states arrived at an attractor not present in the original network (red). (EPS) S3 Fig. Effect of the environment on the stability of the T CD4+ lymphocyte transcription- al-signaling regulatory network. The values of the extrinsic signals of the TSRN were fixed CD4+ T Lymphocyte Minimal Regulatory Network PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004324 June 19, 2015 19 / 23 according to different polarizing micro-environments. Each attractor was transiently per- turbed, and the proportion of transitions that stayed in the same cell type was plotted on a loga- rithmic scale. The following micro-environments were studied here: combinations of all extrinsic cytokines, no extrinsic cytokines (Th0), IFN-γe (Th1), IL-4e and IL-2e (Th2), IL-21e and TGF-βe (Th17), TGF-βe and IL-2e (iTreg), IL-10e (IL10), IL-21e (Tfh), and IL-4e and TGF-βe (Th9). (EPS) S4 Fig. Effect of transient perturbations on the state of the nodes of the T CD4+ lymphocyte transcriptional-signaling regulatory network. Number of transitions to an attractor in re- sponse to transient perturbations in the value of each node. The states of the node were per- turbed during one time step from 1 to 0 (-) or 0 to 1 (+), depending on its state in the original attractor. 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RESEARCH ARTICLE Inference of Network Dynamics and Metabolic Interactions in the Gut Microbiome Steven N. Steinway1,2☯, Matthew B. Biggs3☯, Thomas P. Loughran Jr2, Jason A. Papin3, Reka Albert4 1 College of Medicine, Pennsylvania State University, Hershey, Pennsylvania, United States of America, 2 University of Virginia Cancer Center, University of Virginia, Charlottesville, Virginia, United States of America, 3 Department of Biomedical Engineering, University of Virginia, Charlottesville, Virginia, United States of America, 4 Department of Physics, Pennsylvania State University, University Park, Pennsylvania, United States of America ☯These authors contributed equally to this work. * papin@virginia.edu (JAP); ralbert@phys.psu.edu (RA) Abstract We present a novel methodology to construct a Boolean dynamic model from time series metagenomic information and integrate this modeling with genome-scale metabolic network reconstructions to identify metabolic underpinnings for microbial interactions. We apply this in the context of a critical health issue: clindamycin antibiotic treatment and opportunistic Clostridium difficile infection. Our model recapitulates known dynamics of clindamycin anti- biotic treatment and C. difficile infection and predicts therapeutic probiotic interventions to suppress C. difficile infection. Genome-scale metabolic network reconstructions reveal met- abolic differences between community members and are used to explore the role of metab- olism in the observed microbial interactions. In vitro experimental data validate a key result of our computational model, that B. intestinihominis can in fact slow C. difficile growth. Author Summary The community of bacteria that live in our intestines (called the “gut microbiome”) is im- portant to normal intestinal function, and destruction of this community has a causative role in diseases including obesity, diabetes, and even neurological disorders. Clostridum difficile is an opportunistic pathogenic bacterium that causes potentially life-threatening intestinal inflammation and diarrhea and frequently occurs after antibiotic treatment, which wipes out the normal intestinal bacterial community. We use a mathematical model to identify how the normal bacterial community interacts and how this community changes with antibiotic treatment and C. difficile infection. We use this model to identify bacteria that may inhibit C. difficile growth. Our model and subsequent experiments indi- cate that Barnesiella intestinihominis inhibits C. difficile growth. This result suggests that B. intestinihominis could potentially be used as a probiotic to treat or prevent C. difficile infection. PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 1 / 25 OPEN ACCESS Citation: Steinway SN, Biggs MB, Loughran TP Jr, Papin JA, Albert R (2015) Inference of Network Dynamics and Metabolic Interactions in the Gut Microbiome. PLoS Comput Biol 11(6): e1004338. doi:10.1371/journal.pcbi.1004338 Editor: Costas D. Maranas, The Pennsylvania State University, UNITED STATES Received: February 18, 2015 Accepted: May 13, 2015 Published: June 23, 2015 Copyright: © 2015 Steinway et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: The code generated for this paper is publicly available in this repository: https://bitbucket.org/gutmicrobiomepaper/ microbiomenetworkmodelpaper/src. Funding: SNS and MBB were funded by The Jefferson Trust/ University of Virginia Data Science Institute Collaborative Research Award in Big Data: http://gradstudies.virginia.edu/bigdata. MBB and JAP were funded by R01 GM108501 National Institute of General Medical Sciences, National Institutes of Health: http://www.nigms.nih.gov/Research/ Mechanisms/Pages/ResearchProjectGrants.aspx. MBB was funded by University of Virginia Introduction Human health is inseparably connected to the billions of microbes that live in and on us. Cur- rent research shows that our associations with microbes are, more often than not, essential for our health [1]. The microbes that live in and on us (collectively our “microbiome”) help us to digest our food, train our immune systems, and protect us from pathogens [2,3]. The gut microbiome is an enormous community, consisting of hundreds of species and trillions of indi- vidual interacting bacteria [4]. Microbial community composition often persists for years with- out significant change [5]. When change comes, however, it can have unpredictable and sometimes fatal consequences. Acute and recurring infections by Clostridium difficile have been strongly linked to changes in gut microbiota [6]. The generally accepted paradigm is that antibiotic treatment (or some other perturbation) significantly disrupts the microbial community structure in the gut, which creates a void that C. difficile will subsequently fill [7–10]. Such infections occur in roughly 600,000 people in the United States each year (this number is on the rise), with an associated mortality rate of 2.3% [11]. Each year, healthcare costs associated with C. difficile infection are in excess of $3.2 billion [11]. An altered gut flora has further been identified as a causal factor in obesity, diabetes, some cancers and behavioral disorders [12-17]. What promotes the stability of a microbial community, or causes its collapse, is poorly understood. Until we know what promotes stability, we cannot design targeted treatments that prevent microbiome disruption, nor can we rebuild a disrupted microbiome. Studying the sys- tem level properties and dynamics of a large community is impossible using traditional micro- biology approaches. However, network science is an emerging field which provides a powerful framework for the study of complex systems like the gut microbiome [18–23]. Previous efforts to capture the essential dynamics of the gut have made heavy use of ordinary differential equa- tion (ODE) models [24,25]. Such models require the estimation of many parameters. With so many degrees of freedom, it is possible to overfit the underlying data, and it is difficult to scale up to larger communities [26,27]. Boolean dynamic models, conversely, require far less param- eterization. Such models capture the essential dynamics of a system, and scale to larger systems. Boolean models have been successfully applied at the molecular [28,29], cellular [20], and com- munity levels [30]. Here we present the first Boolean dynamic model constructed from metage- nomic sequence information and the first application of Boolean modeling to microbial community analysis. We analyze the dynamic nature of the gut microbiome, focusing on the effect of clindamy- cin antibiotic treatment and C. difficile infection on gut microbial community structure. We generate a microbial interaction network and dynamical model based on time-series data from metagenome data from a population of mice. We present the results of a dynamic network analysis, including steady-state conditions, how those steady states are reached and main- tained, how they relate to the health or disease status of the mice, and how targeted changes in the network can transition the community from a disease state to a healthy state. Furthermore, knowing how microbes positively or negatively impact each other—particularly for key microbes in the community—increases the therapeutic utility of the inferred interaction net- work. We produced genome-scale metabolic reconstructions of the taxa represented in this community [31], and probe how metabolism could—and could not—contribute to the mecha- nistic underpinnings of the observed interactions. We present validating experimental evidence consistent with our computational results, indicating that a member of the normal gut flora, Barnesiella, can in fact slow C. difficile growth. Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 2 / 25 Biotechnology Training Grant: http://faculty.virginia. edu/biotech/Home.html. SNS was funded by F30 DK093234 National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health: http://grants.nih.gov/grants/guide/contacts/ parent_F30.html. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. Methods Data Sources Buffie et al. reported treating mice with clindamycin and tracking microbial abundance by 16S sequencing [32]. Mice treated with clindamycin were more susceptible to C. difficile infection than controls. The collection of 16S sequences corresponding to these experiments was ana- lyzed by Stein et al. [24]. First, Stein et al. aggregated the data by quantifying microbial abun- dance at the genus level. Abundances of the ten most abundant genera and an “other” group were presented as operational taxonomic unit (OTU) counts per sample. We use the aggre- gated abundances from Stein et al. as the starting point for our modeling pipeline (Fig 1). This processed dataset consisted of nine samples and three treatment groups (n = 3 replicates per treatment group). The first treatment group (here called “Healthy”) received spores of C. dif- ficile at t = 0 days, and was used to determine the susceptibility of the native microbiota to inva- sion. The second treatment group (here called “clindamycin treated”) received a single dose of clindamycin at t = -1 days to assess the effect of the antibiotic alone, and the third treatment group (here called “clindamycin+ C. difficile treated”) received a single dose of clindamycin (at t = -1 days) and, on the following day, was inoculated with C. difficile spores (S1A Fig). Under the clindamycin+ C. difficile treatment group conditions, C. difficile could colonize the mice and pro- duce colitis; however this was not possible under the first two treatment group conditions. Interpolation of Missing Genus Abundance Information The gut bacterial genus abundance dataset included some variation in terms of time points in which genera were sampled. That is, genus abundances were measured between 0 to 23 days; however, not all samples had measurements at all the time points (S1A Fig). Particularly, the healthy population only included time points at 0, 2, 6, and 13 days and Sample 1 of clindamycin + C. difficile treated population was missing the 9 day time point. Missing abundance values for these 4 points were estimated using an interpolation approach (S1B Fig). For healthy samples, the 16 and 23 day time points could not be interpolated as the last experimentally identified time point for these samples is at 13 days. The assumption of the approximated polynomial for these samples is that extrapolated data points are linear using the slope of the interpolating curve at the nearest data point. Because genera abundances are fairly stable across time in this treatment group (i.e. the slope of most of the genera abundances is approximately zero), extrapolating two time points was deemed reasonable. A principal component analysis was completed on the inter- polated data (Fig 2A) and shows that the interpolated time series bacterial genus abundance data clusters by experimental treatment group in the first two principal components. Furthermore, the results of the binarization for the healthy population suggest that interpolation did not have any concerning effects on the 16 and 23 day time points (S2 Fig). Natural cubic spline interpolation was used to estimate genus abundances at missing time points in some samples. A cubic spline is constructed of piecewise third order (cubic) polyno- mials which pass through the known data points and has continuous first and second deriva- tives across all points in the dataset. Natural cubic spline is a cubic spline that has a second derivative equal to zero at the end points of the dataset [33]. Natural splines were interpolated such that all datasets had time points at single day intervals through the 23 day time point (S1B Fig). Network Modeling Framework We use a Boolean framework in which each network node is described by one of two qualita- tive states: ON or OFF. We chose this framework because of its computational feasibility and Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 3 / 25 capacity to be constructed with minimal and qualitative biological data [34]. The ON (logical 1) state means an above threshold abundance of a bacterial genus whereas the OFF (logical 0) state means below-threshold genus absence. The putative biological relationships among gen- era are expressed as mathematical equations using Boolean operators [29,34]. We inferred putative Boolean regulatory functions for each node, which are able to best capture the trends in the bacterial abundances. These rules, (edges in the interaction network) can be assigned a direction, representing information flow, i.e. effect from the source (upstream) node to the tar- get (downstream) node. Furthermore, edges can be characterized as positive (growth promot- ing) or negative (growth suppressing). An additional layer of network analysis is the dynamic Fig 1. Dynamic analysis workflow. Time course genus abundance information was acquired from metagenomic sequencing of mouse gastrointestinal tracts under varying experimental conditions. Missing time points from experimental data were estimated such that genus abundances existed at the same time points across all treatment groups. Next, genus abundances were binarized such that Boolean regulatory relationships could be inferred. A dynamic Boolean model was constructed to explore gut microbial dynamics, therapeutic interventions, and metabolic mediators of bacterial regulatory relationships. doi:10.1371/journal.pcbi.1004338.g001 Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 4 / 25 model, which is used to express the behavior of a system over time by characterizing each node by a state variable (e.g., abundance) and a function that describes its regulation. Dynamic mod- els can be categorized as continuous or discrete, according to the type of node state variable used. Continuous models use a set of differential equations; however, the paucity of known kinetic details for inter-genus and/or inter-species interactions makes these models difficult to implement. Binarization Genus abundance data was binarized (converted to a presence-absence dataset) to enable infer- ence of Boolean relationships for modeling applications. We adapted a previously developed approach called iterative k-means binarization with a clustering depth of 3 (KM3) for this pur- pose [35]. This approach was employed because binarized data is able to maintain complex Fig 2. Construction of a network model of the gut microbiome from time course metagenomic genus abundance information. Principal component analysis coefficients associated with each sample in the metagenomic genus abundance dataset was completed for A) interpolated genus abundances and B) binarized interpolated genus abundances. ‘’ = Healthy; ‘^’ = clindamycin treated; ‘#’ = clindamycin+ C. difficile treated. C) Consensus binarization of genus abundance information. Each heatmap represents the consensus binarization for each treatment group. The horizontal axis represents the day of the experiment that the sample came from. The vertical axis represents the specific genera being modeled. Each genus was binarized to a 1 (ON; above activity threshold) or 0 (OFF; below activity threshold). D) Interaction rules were inferred from the binarized data. The interaction rules were simplified for visualization (compound rules were broken into simple one-to-one edges). doi:10.1371/journal.pcbi.1004338.g002 Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 5 / 25 oscillatory behavior in Boolean models constructed from this data, whereas other binarization approaches fail to maintain these features [35]. Briefly, this approach uses k-means clustering with a depth of clustering d and an initial number of clusters k = 2d. In each iteration, data for a specific genus G are clustered into k unique clusters C1 G,. . .,Ck G, then for each cluster, Cn G, all the values are replaced by the mean value of Cn G. For the next iteration, the value of d is decreased and clustering is repeated. This methodology is repeated until d = 1. This approach, with d = 3 (called here as KM3 binariza- tion) has previously been demonstrated as a superior binarization methodology to other binari- zation approaches for Boolean model construction because it conserves oscillatory behavior [35]. These analyses were performed using custom Python code based on a previously written algorithm [35] and is available in the supplemental materials. Because KM3 binarization has a stochastic component (the initial grouping of binarization clusters), we employed KM3 binarization on the entire bacterial genus abundance time series dataset 1000 times. The average binarization for each sample (S2 Fig) was used to determine the most probable binarized state of each genus in each sample at each time point (S3 Fig). A principal component analysis of the most probable binarized genus abundances for each sam- ple demonstrates that as with the continuous time series abundances (Fig 2A), binarized bacte- rial genus abundance data cluster by experimental treatment group (Fig 2B). For inference of Boolean rules from the binarized genus abundances (S3 Fig), the consensus of two of three samples for each treatment population was used as the binarized state of each genus at each time point in each sample (Fig 2C). Inference of Boolean Rules from Time Series Genus Abundance Information The Best-fit extension was applied to learn Boolean rules from the binarized time series genus abundance information [36]. For each variable (genus) Xi in the binarized time series genus abundance data, Best-fit identifies the set of Boolean rules with k variables (regulators) that explains the variable’s time pattern with the least error size. The algorithm uses partially defined Boolean functions pdBf (T, F), where the set of true (T) and false vectors (F) are defined as T = {X0 2 {0, 1}k: Xi (t + 1) = 1} and F = {X0 2 {0, 1}k: Xi (t + 1) = 0}. Intuitively, the partial Boolean function summarizes the states of the putative regulators that correspond to a turning ON (T) or turning OFF (F) of the target variable. The error size ε of pdBf(T,F) is defined as the minimum number of inconsistencies within X0 that best classifies the T and F values of the dataset. The Best-Fit extension works by identifying smallest size X0 for Xi. For more detailed information refer to [36]. In line with this, we considered the most parsimonious representation of the rules with the smallest ε. If the most parsimonious rule was self-regulation, we also considered rules with the same ε that included another regulator. If multiple rules fit these criteria for a given Xi, it implied that they can independently represent the inferred regulatory relationships. In cases where the alternatives had the same value of (non-zero) ε, we explored combinations (such as appending them by an OR rule) and used the combination that best described the experimentally observed final (steady state) outcomes. For example, we combined the two alternative rules for Blautia with an OR relationship. In the case of Barnesiella, we chained three rules ("Other", "Lachnospiraceae_other", "Lachnospiraceae") by an OR relationship, and "not Clindamycin" by an AND relationship to incorporate the loss of Barnesiella in the presence of clindamycin (Fig 2C). This was also done for rules for “Lachnospiraceae”, “Lachnospiraceae_other” and “Other” and all four nodes attained the same rule. There are six nodes with multiple inferred (alternative) rules: “Barnesiella”,”Blautia”,”Enterococcus”,”Lachnospiraceae”,”Lachnospiraceae_other”, and”- Other” had 4, 2, 5, 4, 4, and 4 rules, respectively. The six other nodes had a single inferred rule. Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 6 / 25 The network in Fig 2C represents the union of all of the alternative rules produced by Best-Fit, or in other words,–it is a super-network of all alternative rules. Any alternative networks would be a sub-network of what we show. A strongly connected component between the nodes inhib- ited by clindamycin is a feature of the vast majority of these sub-networks. We used the imple- mentation of Best-Fit in the R package BoolNet [37]. Dynamic Analysis Dynamic analysis is performed by applying the inferred Boolean functions in succession until a steady state is reached. Boolean models and discrete dynamic models in general focus on state transitions instead of following the system in continuous time. Thus, time is an implicit vari- able in these models. The network transitions from an initial condition (initial state of the bac- terial community) until an attractor is reached. An attractor can be a fixed point (steady state) or a set of states that repeat indefinitely (a complex attractor). The basin of attraction refers to the set of initial conditions that lead the system to a specific attractor. For the network under consideration, the complete state space can be traversed by enumerating every possible combi- nation of node states (212) and applying the inferred Boolean functions (or “update rules”) to determine paths linking those states. The state transition network describes all possible com- munity trajectories from initial conditions to steady states, given the observed interactions between bacteria in the community. We made use of two update schemes to simulate network dynamics: synchronous (deter- ministic) and asynchronous (stochastic). Synchronous models are the simplest update method: all nodes are updated at multiples of a common time step based on the previous state of the sys- tem. The synchronous model is deterministic in that the sequence of state transitions is definite for identical initial conditions of a model. In asynchronous models, the nodes are updated indi- vidually, depending on the timing information, or lack thereof, of individual biological events. In the general asynchronous model used here, a single node is randomly updated at each time step [38]. The general asynchronous model is useful when there is heterogeneity in the timing of network events but when the specific timing is unknown. Due to the heterogeneous mecha- nisms by which bacteria interact, we made the assumption of time heterogeneity without spe- cifically known time relationships. Synchronous and asynchronous Boolean models have the same fixed points, because fixed points are independent of the implementation of time. How- ever, the basin of attraction of each fixed point (i.e. the initial conditions that lead to each fixed point) may differ between synchronous and asynchronous models (S2 Table). For identifica- tion of all of the fixed points in the network (the attractor landscape), the synchronous updat- ing scheme was used. However, for the perturbation analysis, the asynchronous updating scheme was used because it more realistically models the possible trajectories in a stochastic and/or time-heterogeneous system. The simulations of the gut microbiome model were per- formed using custom Python code built on top of the BooleanNet Python library, which facili- tates Boolean simulations [39]. Our custom Python code is available in the supplemental materials. Perturbation Analysis To capture the effect of removal (knockout) or addition (probiotic; forced over abundance) of genera, modification of the states/rules to describe removal or addition states were performed. These modifications were implemented in BooleanNet by setting the corresponding nodes to either OFF (removal) or ON (addition) and then removing the corresponding updating rules for these nodes for the simulations. By examining many such forced perturbations, we can identify potential therapeutic strategies, many of which may not be obvious or intuitive, Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 7 / 25 particularly as network complexity increases. We used asynchronous update when simulating the effect of perturbations on the microbial communities. In each case we performed 1000 sim- ulations and report the percentage of simulations that achieve a certain outcome. Generating Genus-Level Genome-Scale Metabolic Reconstructions To generate draft metabolic network reconstructions for each of the ten genera in the paper, we first obtained genome sequences for representative species by searching the “Genomes” database of the National Center for Biotechnology Information (NCBI). Complete genomes for the first ten (or if less than ten, all) species within the appropriate genus were downloaded. During the process of reconstructing genus-level metabolic reconstructions, some genera were underrepresented (fewer than 10 species genomes) in the NCBI Genome database, including Akkermansia, Barnesiella and Coprobacillus (S3 Table). The search result order is based on record update time, and so it is quasi-random. Genomes were uploaded to the rapid annota- tions using subsystems technology (RAST) server for annotation [40]. Draft metabolic network reconstructions were generated by providing the RAST annotations to the Model SEED service [41]. Metabolic network reconstructions were downloaded in “.xls” format. Genus-level meta- bolic reconstructions were produced by taking the union of all species-level reconstructions corresponding to each genus, as has been done previously [42]. The one exception was C. diffi- cile, which was produced by taking the union of three strain-level reconstructions. Subsystem Enrichment Analysis Subsystems were defined as the Kyoto Encyclopedia of Genes and Genomes (KEGG) map with which each reaction was associated [43,44]. These associations were determined based on annotations in the Model SEED database [41]. To quantify enrichment, the complete set of unique reactions from all genus-level reconstructions was pooled, and the subsystem annota- tions corresponding to those reactions were counted. To determine enrichment for a given sub- set of the community (either a single genus-level reconstruction, or a set of reconstructions corresponding to a subnetwork), the subsystem occurrences were counted within the subset. The probability of a reconstruction containing N total subsystem annotations, with M or more occurrences of subsystem I, was determined by taking the sum of a hypergeometric probability distribution function (PDF) from M to the total occurrences of subsystem I in the overall popu- lation. Enrichment analysis was performed in Matlab [45]. Identifying Seed Sets and Defining Metabolic Competition and Mutualism Scores To quantify metabolic interactions, we started by utilizing the seed set detection algorithm developed by Borenstein et al. [46,47]. The algorithm follows three steps: 1. The genome-scale metabolic network reconstruction is reduced into simple one-to-one edges, such that for each reaction, each substrate and product pair forms an edge (e.g. A + B ! C would become A ! C and B ! C). 2. The network is divided into strongly connected components, those groups of nodes for which two paths of opposite directions (e.g. A ! B and B ! A) exist between any two nodes in the group. 3. Nodes (and strongly connected components with five or fewer nodes) for which there are exclusively outgoing edges are defined as “inputs” to the model, or seed metabolites. Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 8 / 25 The rationale is that metabolites that feed into the network, but cannot be produced by any reactions within the network, must be obtained from the environment. Competition metrics were generated following the process of Levy and Borenstein [46]. For a given pair of genera, the competition score is defined as: CompScoreij ¼ jSeedSeti \ SeedSetjj jSeedSetij ð1Þ Here SeedSeti is the set of obligatory input metabolites to the metabolic network reconstruc- tion for genus i, and \|SeedSeti\| is the number of metabolites contained in SeedSeti. The competi- tion score indicates the fractional overlap of inputs that genus i shares with genus j, and so ranges between zero and one. The higher the score, the more similar the metabolic inputs to the two networks, making competition more likely. For a given pair of genera, the mutualism score is defined as: MutualismScoreij ¼ jSeedSeti\:SeedSetjj jSeedSetij ð2Þ Here ¬SeedSetj is the set of metabolites that can be produced by the metabolic network for species j (i.e. all non-seed metabolites). The mutualism score indicates the fractional overlap of inputs that genus i consumes which genus j can potentially provide. The mutualism score ranges between zero and one. The higher the score, the more potential there is for nutrient sharing between species. While the score does not measure “mutualism” per se (it cannot nec- essarily distinguish between other interactions such as commensalism or amenalism [48]), for simplicity, we will refer to these scores as the competition and mutualism scores. All metabolic reconstructions, seed sets, competition scores and mutualism scores are avail- able in the supplemental materials. Seed set generation was performed using custom Matlab scripts, which are available in the supplement. [45]. Statistical tests were performed in R [49]. Co-culture and Spent Media Experiments Barnesiella intestinihominis DSM 21032 and Clostridium difficile VPI 10463 were grown anaer- obically in PRAS chopped meat medium (CMB) (Anaerobe Systems, Morgan Hill, CA) at 37 C. To prepare B. intestinihominis spent medium, B. intestinihominis was grown in CMB until stationary phase (44 hours). The saturated culture was centrifuged, and the supernatant was fil- ter sterilized (0.22 μM pore size). Growth curves were obtained by inoculating batch cultures in 96-well plates and gathering optical density measurements (870 nm) using a small plate reader that fits in the anaerobic chamber [50]. Single cultures were inoculated from overnight liquid culture to a starting density of 0.01. The co-cultures were started at a 1:1 ratio, for a total start- ing density of 0.02. Optical density was measured every 2 minutes for 24 hours, and the result- ing growth curves were analyzed in Matlab [45]. Maximum growth rates were calculated by fitting a smooth line to each growth curve, and finding the maximum growth rate from among the instantaneous growth rates over the whole time course: [log(ODt+1)—log(ODt)] / [t+1-t]. The achieved bacterial density—area under the growth curve (AUC)—in a culture was calcu- lated by integrating over the growth curve in each experiment using the “trapz()” function in Matlab. It can be thought of as representing the total biomass produced over time. The simply additive null model was calculated by fitting a Lotka-Volterra model [24] to the single cultures for both B. intestihominis and C. difficile. The null model of co-culture (assuming zero interac- tion between species) was simulated by using the parameters from single culture, and summing the predicted OD870 values. Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 9 / 25 All scripts used to analyze the data are available at https://bitbucket.org/ gutmicrobiomepaper/microbiomenetworkmodelpaper/wiki/Home. Results Processing of a Microbial Genus Abundance Dataset for Network Inference To capture the dynamics of inter-genus interactions in the intestinal tract we employed a pipe- line (Fig 1) which translates metagenomic genus abundance information into a dynamic Bool- ean model. This approach involves three steps: 1) discretization (binarization) of genus abundances, 2) learning Boolean relationships among genera, and 3) translation of genus asso- ciations into a Boolean (discrete) dynamic model. Construction of a Dynamic Network Model from Binarized Time Series Microbial Genus Abundance Information Boolean rules (S1 Table) were inferred from the time series binarized genus abundances using an implementation of the Best-fit extension [36] in the R Boolean network inference package BoolNet [37](see Methods). A network of 12 nodes and 33 edges was inferred (Fig 2D). The inferred interaction network has a clustered structure: the cluster (subnetwork) containing the two Lachnospiraceae nodes and Barnesiella is strongly influenced by clindamycin whereas the other subnetwork is largely independent of the first, except for the single edge between Barne- siella and C. difficile (Fig 2D). In fact, Lachnospiraceae nodes, Barnesiella and the group of “Other” genera form a strongly connected component; that is, every node is reachable from every other node. Most nodes of the second subnetwork are positively influenced by C. difficile, with the exception of Coprobacillus, for which no regulation by other nodes was inferred, and Akkermansia, which is inferred to be regulated only by Coprobacillus. These latter two genera are transiently present (around day 5) in the clindamycin treatment group, but they do not appear in the final states of any of the treatment groups (see S1 Fig). This network structure is consistent with published data in which the dominant Firmicutes (Lachnospiraceae) and Bac- teroidetes (Barnesiella) are devastated by antibiotic administration [51,52]. Furthermore, the clustered structure (Fig 2D) supports the established mechanism of C. difficile colitis: loss of normal gut flora, which normally suppresses opportunistic infection (clindamycin cluster), and the presence of C. difficile at a minimum inoculum (C. difficile cluster) [10,53]. The network clusters have a single route of interaction between Barnesiella and C. difficile. The negative influence of Barnesiella on C. difficile is in agreement with recently published findings in which Barnesiella was strongly correlated with C. difficile clearance [54]. The role of Barnesiella as an inhibitor of another pathogen (vancomycin-resistant Enterococci (VRE)) has been shown in mice [55], which is also visible in the network model as an indirect relationship between Barnesiella and Enterococcus (Fig 2D). Related species of Bacteroidetes have been shown to play vital roles in protection from C. difficile infection in mice [56]. Furthermore, the network structure shows that Lachnospiraceae positively interacts with Barnesiella, leading to an indirect suppression of C. difficile. Interestingly, the two Lachnospiraceae nodes and the “Other” node form a strongly connected component, suggesting a similar role in the network, particularly in promoting growth of Barnesiella, which directly suppresses C. difficile. In sup- port of this finding, Lachnospiraceae has been shown to protect mice against C. difficile coloni- zation [52,57]. Therefore, the structure of the network is both a parsimonious representation of the current data set, and is supported by literature evidence. Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 10 / 25 We applied dynamic analysis using the synchronous updating scheme (see Methods) to determine all the possible steady states of the microbiome network model. In a 12 node net- work, there are 212 possible network states. We employed model simulations using the syn- chronous updating scheme to visit all possible network states and identify all fixed points of the model. Exploration of the steady states of this network reveals 23 possible fixed point attractors (S4 Fig). Three of the identified attractors (Fig 3A) are in exact agreement with the experimentally identified terminal time points of binarized genus abundances (Fig 2C). These attractors make up a small subset of the entire microbiome network state space (S2 Table). The attractor landscape can be divided into six groups based on abundance patterns they share (S4 Fig). Group 1 is made up of a single attractor wherein all genera are absent (OFF). The second group attractor consists of the experimentally defined healthy state (Attractor 2) and gen- era in the C. difficile subnetwork which can be abundant (ON) independent of the clindamycin subnetwork. The third grouping has the clindamycin treated steady state (Attractor 7) and gen- era in the C. difficile subnetwork that can survive in the presence of the clindamycin. Group 4 contains the clindamycin plus C. difficile steady state (Attractor 12) and its subsets in which one or both of the source nodes Mollicutes and Enterobacteriaceae are absent. Group 5 contains attractors in which clindamycin is absent and C. difficile is present. Even if clindamycin is absent, our model suggests that C. difficile can thrive if Lachnospiraceae and Barnesiella are absent, i.e. these states represent a clindamycin-independent loss of Lachnospiraceae and Barnesiella. Lastly, group 6 attractors have both clindamycin and C. difficile as OFF. Blautia and Enterococcus are always abundant in these attractors. Indeed, because of the mutual activation between Blautia and Enterococcus they always appear together. Attractors in this group may also include the abundance (ON state) of the source nodes Mollicutes and Enterobacteriaceae. Perturbation Analysis We next explored the perturbation of genera in the gut microbiome network model. We con- sidered the clinically relevant question of which perturbations might alter the microbiome steady states produced by clindamycin or clindamycin+C. difficile treatment after clindamycin treatment was removed. Thus, we considered the clindamycin-treated steady state (Attractor 7 in S3 Fig) and the clindamycin+C. difficile treated steady state (Attractor 12) as initial condi- tions and assumed that clindamycin treatment was stopped. Our simulations, employing asyn- chronous update (see Methods), indicate that for both initial conditions, only the state of clindamycin changes after the treatment is stopped; these steady states become Attractor 1 and Attractor 19, respectively (S4 Fig). In other words, the steady states remain identical in the absence of clindamycin. We next explored the effect of addition (overabundance; Fig 3B, left column) and removal (knockout; Fig 3B, right column) of individual genera, simultaneously with the stopping of clindamycin treatment, on the model predicted steady states. For the per- turbation analysis, the model was initialized from the clindamycin treated steady state (Fig 3B, top row) or the clindamycin+C. difficile steady state (Fig 3B, bottom row). From the clindamy- cin treated state, addition of Lachnospiraceae or “Other” nodes restores the healthy steady state; however, no removal restore the healthy steady state (Fig 3B). From the clindamycin+C. difficile state, addition of Barnesiella, Lachnospiraceae, or “Other” nodes lead to a shift toward the healthy steady state (suppression of C. difficile). Generating Genus-Level Metabolic Reconstructions Species-level reconstructions from the genus Enterobacteriaceae contained the most reactions on average (1335), while those from Mollicutes contained the least (485) (S3 Table). The Barne- siella and Enterococcus reconstructions contained the most unique reactions (S4 Table) and, Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 11 / 25 interestingly, also displayed more overlap in reaction content between each other (503 reac- tions) than was observed between any other pair of reconstructions (S5 Table). Lachnospira- ceae and Barnesiella had the next highest degree of overlap (424 reactions). Mollicutes and Coprobacillus had the least degree of overlap (363 reactions) (S5 Table). Note that the meta- bolic reconstructions produced by the SEED framework are draft quality, and as such, may lack the predictive power of well-curated metabolic reconstructions. Subsystem Enrichment Analysis Enrichment analysis was performed for the 99 unique subsystem annotations that were observed in the community. 22 subsystems displayed interesting enrichment patterns with respect to the structure of the interaction network (Fig 4). The subsystems for glycolysis/gluconeogenesis and nucleotide sugars metabolism are enriched in all taxa, highlighting the fact that all taxa contain Fig 3. Steady states and node perturbations in the gut microbiome model. A) Heatmap of the three steady states in the gut microbiome model. These steady states are identical to steady states identified in the three experimental groups. B) The effect of node perturbations represented by four heatmaps. On the Y-axis of each of the four heatmaps are nodes (genera) in each steady state. On the x-axis of each of the four heatmaps are the steady states found under normal model conditions (i.e. no node perturbations) and also the specific perturbation of a single network node. The two heatmaps in the left column of the figure demonstrate the effect of addition (forced overabundance) of individual genera, and the two heatmaps in the right column of the figure demonstrate the effect of removal (knockout) of individual genera. The top row heatmaps show the effect of node perturbations on the clindamycin treated group and the bottom row heatmaps show the effect of node perturbations on the clindamycin+ C. difficile treatment group. Genus abundance of 0 means present in 0% of asynchronous simulations and is indicated in blue; Genus abundance of 1 means present in all (100%) of asynchronous simulations, shown in yellow. n = 1000 simulations were applied for all Boolean model simulations. doi:10.1371/journal.pcbi.1004338.g003 Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 12 / 25 relatively full complements of reactions within those subsystems. Interestingly, C. difficile is highly enriched for reactions in cyanamino acid metabolism compared to all other genera. Lipopolysaccharide (LPS) biosynthesis and cyanoamino acid metabolism subsystems are differ- entially enriched between C. difficile and both Barnesiella and Lachnospiraceae. Between Barne- siella and Enterococcus, Barnesiella is more highly enriched for d-glutamine and d-glutamate metabolism, pantothenate and CoA biosynthesis, LPS biosynthesis. With respect to Enterococ- cus, Barnesiella is less highly enriched in pyrimidine metabolism, and phenylalanine, tyrosine, and tryptophan biosynthesis. Fig 4. Subsystem enrichment analysis highlights metabolic differences between taxa. The p-values from the enrichment analysis are log-transformed and negated, such that darker regions indicate greater enrichment. The enrichment analysis quantifies the likelihood that a given subsystem (row) would be as highly abundant as observed within a given metabolic reconstruction (column) by chance alone. A subset of 22 interesting subsystems is shown here. Subsystems of interest include those for which all taxa are enriched, such as glycolysis, and nucleotide sugars metabolism, highlighting the fact that all taxa contain relatively full compliments of reactions within those subsystems. Similarly, subsystems for which a single genus differs from the remaining genera are interesting, such as cyanoamino acid metabolism, where C. difficile is highly enriched for reactions in that subsystem. Some subsystems are differentially enriched between Barnesiella and Lachnospiraceae, and C. difficile such as lipopolysaccharide biosynthesis and cyanoamino acid metabolism. doi:10.1371/journal.pcbi.1004338.g004 Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 13 / 25 Generating Metabolic Competition and Mutualism Scores The metabolic reconstructions were used to explore the potential metabolic underpinnings of the inferred interaction network. Competition scores were generated for all pairwise relation- ships between the genera considered in the model (self-edges were excluded). The two Lachnos- piraceae genera were treated as metabolically identical, and the “Other” group was excluded. We grouped pairs of genera into five groups based on being connected by a positive or negative edge, a negative or positive path (meaning an indirect relationship), or no path. A positive relationship was found between competition score and edge type in the interaction network (i.e. positive edges tend to have a higher competition score), which was not statistically significant, perhaps due to the small sample size (p-value = 0.058 by one-sided Wilcoxon rank sum test) (S5A Fig). The mutualism score did not display any obvious trends with respect to the network structure (S5B Fig). All pairs with inferred edges exhibited relatively high competition scores and low mutualism scores (S5C Fig). Barnesiella, a key inhibitor of C. difficile in the interaction network, holds the second smallest competition score with C. difficile (see Fig 5A). Barnesiella and C. diffi- cile also have the highest mutualism score among all interacting pairs in the network (S5C Fig). The positive relationship between edge type and competition score suggests that more meta- bolic similarity between genera tends to foster positive interaction. The converse is also true, where less metabolic similarity tends to foster negative interactions (S5A Fig). Here, “positive/ negative interaction” is derived from the Boolean model, where a positive edge between species A and B indicates that if A is ON at time t, then B is likely to turn ON at t+1. Co-culture and Spent Media Experiments Barnesiella intestinihominis was chosen as a representative species for the genus Barnesiella for the in vitro experiments. C. difficile grew more slowly in B. intestinihominis spent media (n = 16, p- value < 0.005, by one-sided Wilcoxon rank sum test) (Fig 5B). The co-culture with both B. intesti- nihominis and C. difficile grew more slowly than C. difficile alone (n = 16, p-value < 0.05, by one- sided Wilcoxon rank sum test) (Fig 5B). C. difficile area under the growth curve (AUC), a measure of the achieved bacterial density over the experiment, was not statistically different between growth in fresh media and B. intestinihominis spent media (n = 16, p-value = 0.22 by one-sided Wilcoxon rank sum test). However, the co-culture displayed a much lower AUC than expected under a null model of interaction (in which the two species do not interact) (Fig 5C). Examining the co-culture growth curve, it maintained a consistently lower density than a null model (Fig 5D). Discussion Here we have developed a novel strategy for generating a dynamic model of gut microbiota com- position by inferring relationships from time series metagenomic data (Fig 1). To our knowledge, this is the first Boolean dynamic model of a microbial interaction network and the first Boolean model inferred from metagenomic sequence information. Metagenomic sequencing is a power- ful tool that tells us the consequences of microbial interaction—changes in bacterial abundance. Bacterial interactions are, in fact, mediated by the many chemicals and metabolites the bacteria use and produce. In a network sense these relationships are a bipartite graph; bacterial genera produce chemicals/metabolites, which have an effect on other bacteria. Because there is no com- prehensive source for the bacterial metabolites and their effect on other bacterial genera, we infer the effects of genera on each other from the relative abundances of genera in a set of microbiome samples, and we employ genome-scale metabolic reconstructions to gain insight into these rela- tionships (Fig 6B). Binarization of the microbial abundances clarifies these relationships and is the starting point for the construction of a dynamic network model of the gut microbiome. Inter- estingly, principal component analysis demonstrates that the time series data clusters by Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 14 / 25 experimental treatment group, suggesting that our initial assumption of binary relationships does not lead to significant information loss (Fig 2A and 2B). Fig 5. Metabolic competition scores and in vitro data indicate a non-metabolic interaction mechanism. A) Competition scores for all pairs of genera with C. difficile. Notice that Barnesiella has nearly the lowest competition score. B) Maximum growth rates for all growth conditions. C. difficile grew more slowly in B. intestinihominis spent media (n = 16, p-value < 0.005, by one-sided Wilcoxon rank sum test). The co-culture with both B. intestinihominis and C. difficile grew more slowly than C. difficile alone (n = 16, p-value < 0.05, by one-sided Wilcoxon rank sum test). C) Area under the curve (AUC) was not significantly different for C. difficile in fresh media or B. intestinihominis spent media (n = 16, p-value = 0.22 by one-sided Wilcoxon rank sum test). D) The experimental (red, solid line) and simulated (blue, dashed line) co-culture growth curves. “Binte” indicates B. intestinihominis, while “Cdiff” stands for C. difficile. On average, the experimental co-culture growth curves maintained a lower density than the simply additive null model. Error bars represent the standard error of the mean from 16 independent replicates. doi:10.1371/journal.pcbi.1004338.g005 Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 15 / 25 We analyze the topological and dynamic nature of the gut microbiome, focusing on the effect of clindamycin antibiotic and C. difficile infection on gut microbial community structure. We generate a microbial interaction network and dynamic model based on time-series data from a population of mice. We validate a key edge in this interaction network between Barne- siella and C. difficile through an in vitro experiment. Consistent with the literature, our model affirms that solely inoculating a healthy microbiome with C. difficile is insufficient to disrupt the healthy intestinal tract microbiome. Additionally, our results demonstrate that clindamycin treatment has a tremendous effect on the microbiome, greatly reducing many microbial genera, and that during the time C. difficile is present, a certain subset of bacteria come to dominate the microbiome (S1 and S2 and 2C Figs). Our dynamic network model reveals the steady state conditions attainable by this microbial system, how those steady states are reached and maintained, how they relate to the health or disease status of the mice, and how targeted changes in the network can transition the Fig 6. Computational models can bring us closer to true interaction networks. A) Potential inhibitory mechanisms include direct inhibition of C. difficile by Barnesiella (e.g. via competition for scarce resources, or toxin production), or indirect inhibition (e.g. through a host antimicrobial response). B) A great deal has been published on the topic of network inference from complex data sets, and more can be done to improve inference methods. Particularly for microbial interaction networks, it is essential to identify, not only the nature of the interactions, but also the underlying mechanisms. Metagenomic genus abundance information can be used to infer causal relationships between bacteria; however, other information sources are required to determine the exact nature of these interactions. Each individual network edge may have very different underlying causes (metabolic, physical interaction, toxin-based, etc.). Including more tools in the pipeline, such as metabolic network reconstructions, bioinformatics tools, etc., will help elucidate these mechanisms, allowing far more rapid hypothesis generation, leading to a more focused effort in the wet lab. doi:10.1371/journal.pcbi.1004338.g006 Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 16 / 25 community from a disease state to a healthy state. Furthermore, we examine genome-scale metabolic network reconstructions of the taxa represented in this community, examine broad metabolic differences between the taxa in the community, and probe how metabolism could— and could not—contribute to the mechanistic underpinnings of the observed interactions. Network Structure The first feature that stands out in the inferred interaction network is its clustered structure. Clindamycin has a strong influence on the subnetwork containing the two Lachnospiraceae nodes and Barnesiella. The other subnetwork contains C. difficile and other genera that become abundant during C. difficile infection (Fig 2D). Also worth noticing are the two contradicting edges in the network, between Coprobacillus and Blautia, and the self-edges for Blautia (Fig 2D). These arise from rules in the Boolean model that are context-dependent. Such context- dependent rules can manifest as opposite edge types, depending on the state of other nodes in the network. Context-dependent interactions have been demonstrated in many microbial pair- ings, and nutritional environments can even be designed to induce specific interaction types [58]. It is possible that subtle environmental changes over the course of the experiment altered conditions in a way that flipped the Coprobacillus-Blautia interaction. Because the interaction network is derived from time-series data, it is possible to estimate causality, and therefore, derive a directed graph. A directed network with clear, causative interactions can be used to study community dynamics. This is in contrast with association networks, which are often derived from independent samples, and cannot determine direction of causality [48,59–61]. Such networks are more limited in utility because they cannot be used to predict system behav- ior over time, or system responses to perturbations [24,62]. Note that the inferred network structure represents a set of hypotheses as to potential interactions among genera. Determining whether or not the interactions truly occur requires further experimentation, similar to the experimentation completed to validate the edge between Barnesiella and C. difficile. Experimental Validation of Barnesiella Inhibition of C. difficile We experimentally validated a key edge in the interaction network, and showed that Barnesiella can in fact slow C. difficile growth. C. difficile was grown alone, in co-culture with B. intestini- hominis, and in B. intestinihominis spentmedia. C. difficile grew more slowly in both co-culture and spent-media conditions. Though moderate, the effect was statistically significant (Fig 5B). The fact that C. difficile growth rate was inhibited under spent-media conditions indicates that B. intestinihominis-mediated inhibition does not require B. intestinihominis to “sense” the presence of C. difficile. Further, C. difficile growth on B. intestinihominis spent media demon- strates that the two species have different nutrient requirements. Whether the reduction in growth rate is a result of nutritional limitations (e.g. C. difficile resorts to a less preferred carbon source) is unknown, but unlikely given the AUC data. The AUC—a summation of the OD over the entire time course—is a measure of the total bacterial density achieved over the course of the experiment. It can be thought of as a single metric combining growth rate and biomass production over time. Examining the AUC for all conditions showed that C. difficile AUC did not significantly change between fresh media and spent media (Fig 5C). Thus, C. difficile was able to produce comparable overall biomass despite a reduction in growth rate, further demonstrating that nutrient availability was sufficient in the spent media condition. The AUC for the co-culture was much lower than expected in a simu- lated null model (Fig 5C). Apparently, in co-culture, the total community biomass production capacity is reduced from what would be expected in a scenario without species interaction. Thus, there is a measurable negative interaction between B. intestinihominis and C. difficile in Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 17 / 25 co-culture that impacts biomass production. This can be observed over the full time-course of the co-culture, where the overall density is consistently lower than what would be expected in a null model (Fig 5D). Network Dynamics and Perturbation Analysis Computational perturbation analysis showed that forced overabundance of Barnesiella led to a shift from the “disease” state (clindamycin+ C. difficile treatment group) to a state highly simi- lar to the original healthy state (loss of C. difficile). This result is particularly interesting from a therapeutic design standpoint. In this case, the model results indicate that Barnesiella may serve as an effective probiotic. Model-driven analysis can be used to identify candidate organ- isms for probiotic treatments. Recent work by Buffie et al. performed a proof-of-concept study in which they used statistical models to identify candidate probiotic organisms, which were then tested on a murine model of C. difficile infection [54]. This model-driven approach can be favorably contrasted with the brute-force experimental approach in which successive combina- tions of microbes are tested until a curative set is found [56]. The model-driven approach requires far fewer experiments, and saves time and resources. While the computational model presented here differs from that used by Buffie et al., the integration of computational models in probiotic design has been shown to be a feasible, effective approach. Improved tools, such as the perturbation analysis presented here, will surely accelerate the probiotic design process and shorten the path to the clinic. Metabolic Competition Scores Point towards a Non-metabolic Interaction Mechanism Genome-scale metabolic network reconstructions can be used to estimate the interactions between microbes in a complex community based purely on genome sequence data. Our use of genus-level metabolic network reconstructions (a union of several species-level reconstruc- tions) may not reflect the unique, species-level interactions and heterogeneity within a commu- nity. This higher-level model will only capture broad trends and the possible extent of metabolic capacity within a genus. Furthermore, the draft status of these models precludes the effective application of flux balance analysis (FBA) to estimate interactions among genera. This is due to the established lack of precision in draft reconstructions in predictions of growth rates and substrate utilization patterns [63], and the sensitivity of interaction models to metabolic environment and model structure [58,64]. Future efforts to infer metabolic interactions using FBA and well-curated metabolic networks could provide deeper insights into specific metabo- lites that are shared (or competed for) between specific microbial pairs. The application of competition scores demonstrated here (S5A Fig) could potentially be used to quickly establish a rough expectation (notice the spread of competition scores for the species pairs not connected by a path through the network) for community structure—based solely on genomic information—that can then be tested experimentally. Interestingly, the fact that higher competition score is associated with more positive interactions inferred from the Boolean model relates to previous work that demonstrates that higher competition scores were associated with habitat co-occurrence [46]. In this same work, the authors suggest that this effect is due to habitat filtering; that is, microbes with similar metabolic capabilities tend to thrive in similar environments. It has been shown experimentally that microorganisms from the same environment tend to lose net productivity in batch co-culture, indicating similar met- abolic requirements [65]. Thus, it appears that metabolically similar organisms tend to co- locate to similar niches, and over evolutionary time, co-localized organisms tend to develop positive relationships with each other. Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 18 / 25 Understanding this relationship between competition score and interaction type leads to the conclusion that negative interactions are probably not caused by metabolic competition. Of all the genus competition scores with C. difficile, Barnesiella showed the second lowest (Fig 5A). In other words, Barnesiella is among the least likely to share a similar metabolic niche with C. diffi- cile, which fits with the broad trend mentioned above. The fact that the competition score between C. difficile and Barnesiella is so low strongly suggests that the negative interaction between them is due, not to competition for scarce resources (although it does not completely exclude the possibility), but rather to some non-metabolic mechanism. The similarity in reaction content between Barnesiella and Enterococcus indicates similar network structure (S5 Table), and yet, Enterococcus does not inhibit C. difficile in the inferred interaction network (Fig 2D). Either the differences that are present between Barnesiella (65 unique reactions) and Enterococ- cus (36 unique reactions) are hints at the mechanism of interaction, or metabolism does not play a significant role in C. difficile inhibition in the environment of the gut. For example, enrichment analysis showed that that, with respect to Enterococcus, Barnesiella is more highly enriched for d-glutamine and d-glutamate metabolism, pantothenate and CoA biosynthesis and LPS biosyn- thesis. With respect to Enterococcus, Barnesiella is less enriched in pyrimidine metabolism, and phenylalanine, tyrosine, and tryptophan biosynthesis. The possible role of LPS is discussed fur- ther on. The possible roles of these other metabolic pathways in C. difficile inhibition is unclear. There is experimental evidence that Barnesiella (and other normal flora) may combat path- ogen overgrowth through non-metabolic mechanisms. As a first step, it has been shown that VRE can grow in sterile murine cecal contents—indicating the presence of sufficient nutrition to support VRE—but is inhibited in saline-treated cecal contents—indicating that live flora are needed to suppress VRE growth, and that this suppression is not through nutrient sequestra- tion [66]. Further, the presence of B. intestinihominis has been demonstrated to prevent and cure VRE infection in mice [55], and is strongly correlated with resistance to C. difficile infec- tion in mice [54]. Clearly, Barnesiella plays a key role in pathogen inhibition, and pathogen inhibition can be caused by mechanisms other than nutrient competition. This non-metabolic mechanism may be direct or indirect (Fig 6A). We demonstrated in vitro that B. intestinihominis can inhibit C. difficile growth rate (Fig 5C and 5D). The fact that C. difficile grows on B. intestinihominis spent media at all indicates that the metabolic require- ments of the two species are different, which is consistent with our computational results sup- porting the hypothesis that C. difficile and Barnesiella do not compete metabolically (Fig 5B). Further, C. difficile is moderately inhibited both in co-culture with B. intestinihominis and in B. intestinihominis-spent media, indicating a direct mechanism of inhibition. In further support of a direct mechanism, it has been shown that Clostridium scindens inhibits growth of C. diffi- cile through the production of secondary bile acids [54]. Perhaps Barnesiella works through an analogous mechanism in vivo, enhancing the moderate inhibition observed in vitro. In support of an additional indirect mechanism of bacterial interaction, Buffie and Pamer, in a recent review, hypothesized that the normal flora (of which Barnesiella is a member) may prevent pathogen overgrowth by stimulation of a host antimicrobial response [67] (Fig 6A). Specifically, they point out that Barnesiella can activate host toll-like receptor TLR signaling, which activates host antimicrobial peptide production. For example, LPS and flagellin have been shown to stimulate the host innate immune response through toll-like receptor (TLR) sig- naling and production of bactericidal lectins [68,69]. Barnesiella shows enrichment for LPS biosynthesis pathways (Fig 4). However, this mechanism did not seem to be responsible for inhibition of VRE by Barnesiella [55]. An indirect, host-mediated mechanism is further sup- ported by the fact that members of the normal gut flora can interact differently with pathogens depending on the host organism [54]. Regardless, any indirect mechanism is in addition to the direct inhibitory mechanism observed in vitro. Both direct and indirect mechanisms may play Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 19 / 25 a role in vivo, and further work is needed to clearly discern the underlying process that allows Barnesiella to play this protective role. We demonstrate that dynamic Boolean models capture key microbial interactions and dynamics from time-series abundance data in a murine microbiome. We show that this computational approach enables exhaustive in silico perturbation, which leads to fast candidate selection for probiotic design. We further describe the use of genome-scale metabolic network reconstructions to explore the metabolic potential attributed to community members, and to estimate metabolic competition and cooperation between members of the microbiome com- munity. Analysis of genome-scale metabolic network reconstructions indicates that Barnesiella likely inhibits C. difficile through some non-metabolic mechanism. We present empirical in vitro evidence that B. intestinihominis does in fact inhibit C. difficile growth, likely by a non- metabolic mechanism, and our findings are in good agreement with published results. We present this work as a demonstration of the use of dynamic Boolean models and genome-scale metabolic reconstructions to explore the structure, dynamics, and mechanistic underpinnings of complex microbial communities. Supporting Information S1 Fig. Bacterial genera abundances over time in response to clindamycin treatment and/ or C. difficile inoculation. A) Genera abundance information for the nine samples. The “Healthy” population received spores of C. difficile (at t = 0 days) and did not undergo observ- able microbial changes, Population 2 received a single dose of clindamycin (at t = -1 days), and Population 3 received a single dose of clindamycin (at t = -1 days) and, on the following day, was inoculated with C. difficile spores (at t = 0 days). Genus abundances were measured at 0, 2, 3, 4, 5, 6, 7, 9, 12, 13, 16, and 23 days; however, not all samples had measurements at all the time points. B) Cubic spline interpolation of data points was performed such that all the same time point measurements of bacterial abundance occurred in all samples and that single day intervals were present in all datasets. (TIF) S2 Fig. Averaged binarized genera abundances using iterative k-means binarization. Itera- tive k-means binarization was completed on all the samples 1000 times and average binariza- tion is shown for each genus at each time point in each of the nine samples. If a node (genus) is binarized as 0 (OFF) at a time step, then it is colored blue, and if a node (genus) is binarized as 1 (ON) at a time step, then it is colored yellow. This figure represents the average of 1000 repli- cates of IKM binarization. Intermediate cell colors represent cases where a genus abundance at a time point was binarized to 1 (ON) in a fraction of the replicates. (TIFF) S3 Fig. Averaged binarized genera abundances using iterative k-means binarization were rounded to the most probable binarized state. The most probable binarized state of each genus at each time point. If the average genus abundance binarization (S2 Fig) was greater than 0.5 (ON in over 500 of 1000 replicates), then that genus abundance was assumed to be 1 (ON) for downstream analysis. If the average genus abundance binarization was less than 0.5 (ON in less than 500 of 1000 replicates) then that genus abundance was assumed to be 0 (OFF) for downstream analysis. (TIFF) S4 Fig. All possible steady states of the Boolean model of the gut microbiome. There are 23 predicted steady states in the Boolean model of the gut microbiome. Each attractor is a column in the heatmap and is made up of the state of each genus in the network model (rows). Each Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 20 / 25 genus can be present above an activity threshold (yellow; ON) or below an activity threshold (blue; OFF). The steady states in the model are grouped based on their similarities to other steady states in the same group. The first steady state of group 2 (Attractor 2) is the healthy steady state, the first steady state of group 3 (Attractor 7) is the clindamycin treated steady state, and the first steady state of group 4 (Attractor 12) is the clindamycin + C. difficile steady state. These three steady states are directly corroborated by experimental metagenomic data. (TIFF) S5 Fig. Competition and mutualism scores by edge and path type in Boolean network. A) Competition score values for all classes of paths through the network, including direct edges, directed paths, and no directed path. A positive relationship was found between competition score and direct edge type in the dynamic network (self-edges were excluded), which was not statistically significant, perhaps due to the small sample size (p-value = 0.058 by one-sided Wil- coxon rank sum test), but is worthy of note. B) Mutualism score values for all classes of paths through the network, including direct edges, directed paths, and no directed path. C) Competi- tion and mutualism score plot for the interaction edges in the network. All the interactions reflect moderate to high competition scores and relatively low mutualism scores. All the inter- actions have a higher competition score than mutualism score. The two negative interactions (red circles) do not have higher competition scores, nor lower mutualism scores, than the posi- tive interactions. In fact, the negative interaction between Barnesiella and C. difficile corre- sponds to the highest mutualism score. (TIF) S1 Table. Boolean update rules for the gut microbiome network. The ruleset inferred from metagenomic sequencing information using Boolnet. (DOCX) S2 Table. Basin size as % of total state space (unique basin size) for experimentally realized network attractors. (DOCX) S3 Table. Genus-level genome-scale metabolic network reconstruction characteristics. In this table we characterize the genus-level metabolic network reconstructions. Average model size refers to the average number of reactions in the component species reconstructions within each genus. Akkermansia is represented by a single species-level reconstruction, while several genera are represented by 10 species-level reconstructions. The average network overlap within a genus refers to the average number of shared reactions between any two pairs of species within the genus. Similarly, the average fraction of unique reactions refers to the average subset of reactions in a given species that are unique within the genus. (DOCX) S4 Table. Unique reactions within genera. The genus in each row has n reactions that the genus in the columns do not have. For example, the genus-level reconstruction for Barnesiella contains 167 reactions that the reconstruction for C. difficile does not. Conversely, the recon- struction for C. difficile only contains 30 unique reactions that the reconstruction for Blautia does not already contain. (DOCX) S5 Table. Reaction overlap between genera. The upper portion of the table contains the num- ber of shared reaction content between all genus-level metabolic network reconstructions. (DOCX) Network Model of the Gut Microbiome PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004338 June 23, 2015 21 / 25 Acknowledgments The authors thank Dr. Glynis Kolling (University of Virginia) for help obtaining bacterial iso- lates and carrying out in vitro experiments. The authors further thank Dr. David J. Feith (Uni- versity of Virginia) for helpful comments/suggestions. Author Contributions Conceived and designed the experiments: SNS MBB JAP RA. Performed the experiments: SNS MBB. Analyzed the data: SNS MBB TPL JAP RA. Contributed reagents/materials/analysis tools: SNS MBB JAP RA. Wrote the paper: SNS MBB TPL JAP RA. References 1. 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1521-0103/354/3/448–458$25.00 http://dx.doi.org/10.1124/jpet.115.224766 THE JOURNAL OF PHARMACOLOGY AND EXPERIMENTAL THERAPEUTICS J Pharmacol Exp Ther 354:448–458, September 2015 U.S. Government work not protected by U.S. copyright Logic-Based and Cellular Pharmacodynamic Modeling of Bortezomib Responses in U266 Human Myeloma Cellss Vaishali L. Chudasama, Meric A. Ovacik, Darrell R. Abernethy, and Donald E. Mager Department of Pharmaceutical Sciences, University at Buffalo, State University of New York, Buffalo, New York (V.L.C., M.A.O., D.E.M.); and Office of Clinical Pharmacology, Food and Drug Administration, Silver Springs, Maryland (D.R.A.) Received March 28, 2015; accepted July 9, 2015 ABSTRACT Systems models of biological networks show promise for in- forming drug target selection/qualification, identifying lead com- pounds and factors regulating disease progression, rationalizing combinatorial regimens, and explaining sources of intersubject variability and adverse drug reactions. However, most models of biological systems are qualitative and are not easily coupled with dynamical models of drug exposure-response relation- ships. In this proof-of-concept study, logic-based modeling of signal transduction pathways in U266 multiple myeloma (MM) cells is used to guide the development of a simple dynamical model linking bortezomib exposure to cellular outcomes. Bortezomib is a commonly used first-line agent in MM treatment; however, knowledge of the signal transduction pathways regulating bortezomib-mediated cell cytotoxicity is incomplete. A Boolean network model of 66 nodes was con- structed that includes major survival and apoptotic pathways and was updated using responses to several chemical probes. Simulated responses to bortezomib were in good agreement with experimental data, and a reduction algorithm was used to identify key signaling proteins. Bortezomib-mediated apoptosis was not associated with suppression of nuclear factor kB (NFkB) protein inhibition in this cell line, which contradicts a major hypothesis of bortezomib pharmacodynamics. A pharmacody- namic model was developed that included three critical proteins (phospho-NFkB, BclxL, and cleaved poly (ADP ribose) polymer- ase). Model-fitted protein dynamics and cell proliferation profiles agreed with experimental data, and the model-predicted IC50 (3.5 nM) is comparable to the experimental value (1.5 nM). The cell-based pharmacodynamic model successfully links bortezomib exposure to MM cellular proliferation via protein dynamics, and this model may show utility in exploring bortezomib-based combination regimens. Introduction The fields of systems biology and pharmacokinetic (PK)/ pharmacodynamic (PD) modeling have evolved largely in parallel, and there is an emerging consensus that an effective integration of these disciplines is needed to fully realize the promise of each in bringing new therapeutic molecules and combination regimens to the bedside (http://www.nigms.nih. gov/Training/Documents/SystemsPharmaWPSorger2011.pdf). Traditional PK/PD models of drug action use compartmen- tal structures to integrate the time course of drug exposure, pharmacological properties (capacity, sensitivity, and transduc- tion of drug-target interactions), and (patho)physiological turn- over processes (Mager et al., 2003). Such semimechanistic models contain a minimal number of identifiable parameters to describe temporal profiles of macroscale therapeutic and adverse drug effects. When coupled with nonlinear mixed- effects modeling of relatively large clinical trials, a covariate analysis can be used to identify patient-specific characteristics (e.g., genetic polymorphisms) that explain the interindividual variability in model parameters (Pillai et al., 2005). Although a major component of model-informed drug development and therapeutics (Milligan et al., 2013), this approach can be limited by specific study designs and is rarely sufficient for recapitu- lating multiple, complex genotype-phenotype relationships. Significant insights have been realized from the recognition that both drugs and disease processes give rise to complex and dynamic clinical phenotypes by altering natural intercon- nected biochemical networks and support the emergence of systems pharmacology models of drug action (Zhao and Iyengar, 2012; Huang et al., 2013; Jusko, 2013). Multiscale models that combine PK/PD principles and signaling net- works can serve as a platform for integrating genomic/ proteomic factors that regulate drug effects and clinical out- comes—so-called enhanced PD (ePD) models (Iyengar et al., 2012). Two major challenges to the development of ePD models include the lack of complete mathematical models of signal transduction networks (e.g., concentrations and re- action rate constants) and unknown quantitative relationships This work was supported by the National Institutes of Health National Institute of General Medical Sciences [Grant R01-GM57980] (to D.E.M.); the University at Buffalo-Pfizer strategic alliance (D.E.M.); an unrestricted training grant from Daiichi Sankyo Pharma Development (to D.E.M.); and an American Foundation for Pharmaceutical Education predoctoral fellowship (to V.L.C.). dx.doi.org/10.1124/jpet.115.224766. s This article has supplemental material available at jpet.aspetjournals.org. ABBREVIATIONS: ePD, enhanced pharmacodynamics; FBS, fetal bovine serum; IkBi, inhibitor of kB inhibitor; IKKi, inhibitor of kB kinase inhibitor; JAK, janus kinase; JNK, c-Jun N-terminal kinase; MM, multiple myeloma; NFkB, nuclear factor kB; PARP, poly (ADP ribose) polymerase; PD, pharmacodynamics; pIkBa, phosphor-IkBa; PK, pharmacokinetics; pNFkB, phospho–nuclear factor kB; pStat3, phospho–signal transducer and activator of transcription 3; RIP, receptor-interacting protein; STAT, signal transducer and activator of transcription. 448 between individual genomic/proteomic differences and model parameters. Mechanistic network models are preferred over empirical structures (Birtwistle et al., 2013); however, such models may not be defined or calibrated to specific pharmaco- logical and/or disease systems. Logic-based modeling tech- niques provide a global perspective of system properties in the absence of kinetic parameters through the integration of qualitative a priori knowledge of network connections (Albert and Wang, 2009). In this proof-of-concept study, a reduction algorithm is applied to a mathematical network to guide the development of a small signaling model for bortezomib, a potent proteasome inhibitor, which may ultimately serve as an ePD model for its use in multiple myeloma (MM). Multiple myeloma is a B cell neoplasm associated with several comorbidities, including hypercalcemia, renal insuffi- ciency, anemia, and bone lesions (Caers et al., 2008; Blade et al., 2010). The prognosis for advanced stages of MM is poor despite multiple treatment options, with a median survival of advanced-stage patients of less than 10 months (Richardson et al., 2003, 2005). Bortezomib is commonly prescribed alone or in combination with other antimyeloma agents (Oancea et al., 2004), and the addition of bortezomib has significantly improved overall survival of MM patients (Caers et al., 2008). However, almost all patients relapse and become refractory to all treatment options (Richardson et al., 2005; San Miguel et al., 2008), and a better understanding of MM disease progression and mechanisms of drug action is critical for improving the treatment of MM. Bortezomib modulates both survival and apoptotic cellular pathways in MM cells (Fig. 1), and multiple mechanisms of action are proposed for inducing cell death, including the inhibition of proteasome and the phospho–nuclear factor kB (pNFkB) pathway (Hideshima et al., 2001, 2002, 2003a,b). However, recent reports suggest that bortezomib stimulates receptor-interacting protein (RIP; a signaling protein up- stream of the NFkB pathway), leading to activation of pNFkB protein expression (Hideshima et al., 2009). Despite extensive qualitative information on bortezomib-induced intracellular signaling, mathematical models linking bortezomib exposure to intracellular protein dynamics have not been established. Systems-level modeling may facilitate the rational design of single and combinatorial dosing regimens, approaches to overcome drug resistance, and prevent suboptimal dosing (Berger and Iyengar, 2011; Zhao and Iyengar, 2012). Mecha- nistic models are emerging in which chemotherapy exposure is connected to ultimate responses through target occupancy and biomarker signal transduction (Yamazaki et al., 2011; Harrold et al., 2012; Kay et al., 2012; Kirouac et al., 2013). The purpose of this study is to integrate network systems analysis and PK/PD modeling principles to study bortezomib effects on signal trans- duction in MM cells. Although the current study is conducted in U266 cells, the strategic framework may be extended to other cell lines and applied to other therapeutic areas. Materials and Methods Tissue Culture Materials. The human myeloma cell line U266 (TIB-196) was purchased from American Type Culture Collection (Manassas, VA). Inhibitor of kB kinase inhibitor (IKKi) (PS-1145) and Janus kinase (JAK) inhibitor I (JAKi) were purchased from Santa Cruz Biotechnology (Dallas, TX). IkBi (BAY11-7085) was purchased from Sigma-Aldrich (St. Louis, MO). The clinically available formula- tion of bortezomib was used for all experiments (Millennium Phar- maceuticals, Cambridge, MA). The primary monoclonal antibodies to phospho-p65, phosphor-IkBa (pIkBa), phospho–signal transducers and activator of transcription 3 (pStat3), Bcl-xL, poly (ADP ribose) polymerase (PARP), p65, Stat3, IkBa, and b-actin were purchased from Cell Signaling Technology (Danvers, MA). a-Tubulin primary and rabbit and mouse secondary antibodies were purchased from Santa Cruz Biotechnology. WST-1 reagent assay kit was purchased from Roche (Basel, Switzerland). Horseradish peroxidase conjugate was purchased from Bio-Rad (Hercules, CA), and enhanced chemiluminescence sub- strate was purchased from Thermo Scientific (Pittsburgh, PA). Fig. 1. Signal transduction pathways in multiple my- eloma disease pathology. Cyt-c, cytochrome c; DR4/5, death receptor 4/5; FasL, TNF receptor superfamily member 6 ligand; MAPK, mitogen-activated protein kinase; NIK, NFkB-inducing kinase. Mathematical Modeling of Cellular Responses to Bortezomib 449 RPMI 1640 and fetal bovine serum (FBS) were purchased from American Type Culture Collection. Cell Culture Experimental Design. All experiments were con- ducted in U266 myeloma cells. Cells were cultured in RPMI 1640 medium supplemented with 15% FBS and 1% penicillin/streptomycin antibiotics. Treatment protocols included 1) IKKi (10 mM), 2) JAKi (10 mM), 3) IkBi (10 mM), 4) IKKi and JAKi (10 mM each), 5) IkBi and JAKi (10 mM each), 6) bortezomib (20 and 2 nM), and 7) dimethylsulf- oxide vehicle control. All treatments were continuous for 48 hours, with the exception of IkBi experiments (10 hours). A transient exposure to bortezomib (20 nM) was also conducted, in which cells were incubated for either 1 or 2 hours followed by removal of drug from the culture media and subsequent incubation with vehicle control for up to 48 hours. WST-1 Cell Proliferation Assay. Approximately 10,000 cells per well were incubated with a range of concentrations (0.001–100 mM) of JAKi, IKKi, or a combination of IKKi and JAKi. Incubation experi- ments with bortezomib alone ranged from 0.001 to 100 nM. Cell viability was measured at 0, 24, 48, 72, and 96 hours according to manufacturer instructions. Absorbance was measured at 450 and 690 nm after 2-hour incubation with WST-1 reagent with a Microplate spectrophotometer (Molecular Devices, Sunnydale, CA). Western Blot Analysis. Relative protein expression levels of pStat3, pNFkB, pIkBa, cleaved PARP, and BclxL were measured following treatment regimens as specified in Supplemental Table 1. Cells (5 106/10 ml culture media) were incubated in 10-cm2 culture dishes. Cells were collected at the end of the treatment duration, washed with ice-cold phosphate-buffered saline, and lysed at 4°C in radio- immunoprecipitation assay RIPA buffer (Cell Signaling Technology) supplemented with protease and phosphatase inhibitor cocktail (Bio- Rad) and phenylmethylsulfonyl fluoride (Bio-Rad). Protein lysates were stored at 280°C until used. Equal amounts of proteins were separated on SDS-PAGE gels and transferred to nitrocellulose membranes. Immunoblotting was performed according to manufacturer instruc- tions, and the relative intensity of bands was assessed by densito- metric analysis of digitized images using ImageJ software (NIH, Bethesda, MD). All experiments were conducted in at least duplicate. Drug Stability. Bortezomib degradation in cell culture was assessed at different time points (0, 12, 24, 48, and 72 hours). Bortezomib concentrations were measured after incubation (20 nM) at 37°C in culture medium (RPMI 1640 supplemented with 15% FBS and 1% penicillin/streptomycin) using a liquid chromatography–tandem mass spectrometry assay previously validated in our laboratory (un- published). Bortezomib degradation kinetics were fit with a monoexpo- nential (l) decay model, and the half-life was calculated as ln(2)/l. Boolean Network Assembly and Simulations. The Boolean network model (Supplemental Fig. 1) was drawn with SmartDraw software (http://www.smartdraw.com) and was implemented in Odefy (http://www.helmholtz-muenchen.de/cmb/odefy) (Wittmann et al., 2009), a toolbox compatible with MATLAB (MathWorks, Natick, MA). Odefy converts Boolean relationships into a continuous frame- work using a Hill-type function. In the hypothetical case in which node B stimulates A, the relationship can be described by dA=dt 5 1=t½Bn=ðBn 1 knÞ 2 A : Default parameter values for k (0.5), n (3), and t (1) were used for all nodes. All model simulations were performed using the “HillCubeNorm” option within Odefy (MATLAB model code is provided in the Data Supplement). Each node in the model was initialized as ON (1) or OFF (0) based on baseline activity in the cell. For example, if the state is constitutively active in the cell, it was initialized as 1. Boolean transfer functions and initial state values are summarized in Supplemental Table 2. Examples of ordinary differential equations corresponding to each node, which were generated using Odefy, are listed in Supplemental Eqs. 1–5. Three specific probes, JAKi, IkBi, and IKKi, were used to develop and update the network model. The effect of the JAKi was added such that it inhibits nodes JAK1 and JAK2. The IkBi inhibitor was added by direct inhibition of pIkB node activation. Similarly, the IKKi effect was added such that it inhibits node IKK. Model simulations were performed to predict bortezomib outcomes, and drug effect was in- corporated as direct inhibition of the proteasome node and stimulation of the RIP node. For simulations of transient bortezomib exposure, the bortezomib node was activated for only one or two iterations. Network Reduction. The final full Boolean network model de- veloped for U266 cells (Supplemental Fig. 1) was reduced using a model reduction algorithm (Veliz-Cuba, 2011) to identify critical proteins involved in bortezomib-mediated signal transduction. Figure 2 shows examples of the steps taken to reduce the network. First, nodes with only one input and one output are eliminated and the pathways are reconnected (Fig. 2A). For example, RAF was removed and RAS and MEK1 were directly connected (Fig. 2B). In another network reduction rule, nonfunctional edges are identified and re- moved based on the Boolean relationships (algorithm S from Veliz-Cuba, 2011). For example, Fig. 2C shows nodes A, B, and C, with the following Boolean functions: f(A) 5 B OR (B AND NOT C), f(B) 5 (A AND C), and f(C) 5 A. Hence, node C is nonfunctional in f(A) because of the “OR” relationship, and the B node is sufficient to elicit the same effect without invoking C. The resulting diagram is shown (block arrow, Fig. 2C) with the Boolean relationships: f(A) 5 B, f(B) 5 (A AND C), and f(C) 5 A. p21 is an example of nonfunctional edges (Fig. 2D), and Boolean relationships for p21 [f(p21) 5 p53 AND (NOT AKT OR NOT MDM OR NOT MYC OR NOT CKD4)] were refined using step 2 to f(p21) 5 p53 AND NOT AKT to remove nonfunctional edges. AKT is the sole connection to BAD; therefore, the p21 connection to AKT is retained (Fig. 2D). Finally, nonfunctional nodes are identified and removed from the network (algorithm R from Veliz-Cuba, 2011). Before applying this rule, the network is rewired and the first rule is reapplied. Nodes that do not have any impact on other nodes are considered nonfunctional and are removed. In Fig. 2E, node C is regulating node B, but at the same time node A is regulating node C. Therefore, the connection from node C to B can be removed, and consequently node C can be removed. As an example, the only node modulated by MYC is CYCE, as the MYC connection to CYCD can be removed because of the AKT connection to CYCD (Fig. 2F). pStat3, mitogen-activated protein kinase, and extracellular signal-regulated kinase stimulate MYC independently, and mitogen-activated protein kinase was removed following the first network reduction rule (Fig. 2A). Similarly, extracellular signal- regulated kinase was removed as it does not modulate any other node besides MYC. pStat3 modulates several other nodes (e.g., BclxL and XIAP) and stimulates MYC. MYC can be removed following the one input–one output rule, and therefore, CYCE is directly modulated by pStat3 (Fig. 2F), resulting in four final nodes. This entire process was repeated until no further nodes could be removed from the Boolean network. Boolean simulations of the final reduced network were compared with simulations of the full network using Odefy (Wittmann et al., 2009). Dynamical Model Development. Several critical proteins iden- tified using the model reduction algorithm were incorporated into a reduced cellular PD model based on mechanisms of bortezomib action and signal transduction pathways. The reduced dynamic model of bortezomib is depicted in Fig. 3. In brief, bortezomib stimulates protein expression of pNFkB and cleaved PARP (following delays) and inhibits expression of BclxL. A transit compartment (M1B) was added to account for the slight delay in stimulation of pNFkB protein expression (Mager and Jusko, 2001). Bortezomib stimulates the synthesis rate of M1B (ksyn_M1B) via a linear stimulation coefficient (Sm_M1B), and the rate of change in expression of M1B is defined as follows: dðM1BÞ dt 5 ksyn M1B× 1 1 Sm_M1B×CB 2 kdeg_M1B×M1B; M1Bð0Þ 5 1 (1) where CB is the concentration of bortezomib, and kdeg_M1B is a first- order degradation rate constant of M1B. pNFkB protein expression 450 Chudasama et al. increases but returns toward the baseline after 24 hours of continuous bortezomib exposure. To capture this trend, a precursor-dependent indirect response model was proposed (Sharma et al., 1998), with stimulation of the first-order transfer rate constant from the precursor pool (pre_pNFkB) to the pNFkB compartment (ktr_NFkB). The rate of change of pre_pNFkB and pNFkB is described by the following equations: d pre pNFkB dt 5 ksyn_NFkB 2 ktr_NFkB × pre_pNFkB × M1B; pre_pNFkBð0Þ 5 ksyn NFkB ktr NFkB (2) dðpNFkBÞ dt 5 ktr_NFkB × pre_pNFkB × M1B 2 kdeg_NFkB × pNFkB; pNFkBð0Þ 5 1 (3) where ksyn_NFkB is a zero-order production rate constant of pre_pNFkB, and kdeg_NFkB is a first-order degradation rate constant of pNFkB. Changes in cleaved PARP expression follow a significant delay, and the protein expression profile was best characterized using a time- dependent transduction model (Mager and Jusko, 2001), with negative feedback from the last compartment to the synthesis rate of first cleaved PARP compartment to characterize the downward phase of protein expression. Bortezomib stimulates the synthesis rate (ksyn_PARP) of the first cleaved PARP compartment (cPARP1) with a linear stimulation coefficient (Sm_PARP): dðcPARP1Þ dt 5 ksyn_PARP cPARP4 × 1 1 Sm_PARP_B × CB 2 ktr_PARP × cPARP1; cPARP1ð0Þ 5 1 (4). The three subsequent transit compartments are described by the following general equation: dðcPARPnÞ dt 5 ktr_PARP × ðcPARPn 2 1 2 cPARPnÞ; cPARPnð0Þ 5 1 (5) with n representing the compartment number (n 5 2–4). pNFkB is a prosurvival transcription factor that upregulates antiapoptotic proteins (e.g., BclxL), whereas PARP is a proapoptotic factor that results in apoptosis when activated (cleaved PARP) and stimulates Fig. 2. Boolean network reduction steps. (A) Removal of nodes with one input and one output (see node Y). (B) Specific example of removing nodes with one input and one output, in which nodes RAS and MEK1 are connected after removing RAF. (C) General example of identification and removal of nonfunctional edges in a network, in which the edge from node C to node A is identified as a nonfunctional edge and removed. (D) Specific subnetwork example of removing a nonfunctional edge for p21. (E) General example of identification and removal of nonfunctional nodes, in which node C is removed after applying the rule in panel (A). (F) Specific subnetwork example for removing nonfunctional nodes (e.g., MYC). Block arrows indicate the final network after applying the specific rule. “OR” relationship is represented by ‖, “AND” by &&, and “NOT” by ∼. ERK, extracellular signal-regulated kinase; MEKK, mitogen-activated protein kinase. Mathematical Modeling of Cellular Responses to Bortezomib 451 the degradation of BclxL. The rate of change of BclxL is defined as follows: dðBclxLÞ dt 5 ksyn_Bcl × pNFkB 2 kdeg_Bcl × cPARPl 4 ×BclxL; BclxLð0Þ 5 1 (6) where ksyn_Bcl is a zero-order synthesis rate constant of BclxL, kdeg_Bcl is a first-order degradation rate constant of BclxL, and l is a power coefficient for the cleaved PARP effect on BclxL. Cell proliferation is dependent on the balance between apoptotic and antiapoptotic signals. Therefore, cell proliferation (N) was modulated by BclxL and cleaved PARP expression profiles, with the first-order natural cell death rate constant (kd) inhibited by BclxL and stimulated by cleaved PARP. N represents cell proliferation: dðNÞ dt 5 N × kg 2 kd×cPARP4 ð2-BclxLÞ ; Nð0Þ 5 1 (7) with kg representing a first-order growth rate constant. Secondary equations defining zero-order production rate constants are listed in Supplemental Eqs. 6–9. Data Analysis. The dynamical model (Fig. 3) was first fitted to mean pNFkB and cleaved PARP data, followed by pooling of all relative changes in these protein expression patterns (naïve pooled data approach). Initially, pNFkB and cleaved PARP protein dynamics were fit separately. BclxL data were subsequently included, and all of the data including BclxL, pNFkB, and cleaved PARP protein dynamics were fitted simultaneously. Next, cell proliferation was introduced to the existing cellular dynamic model, and all of the data (three biomarkers and cell proliferation) were fitted simultaneously. The in vitro degradation half-life of bortezomib was included for all model runs. Parameters were estimated using MATLAB (fminsearch func- tion, maximum likelihood algorithm, and ode23s) and a model devel- opment framework (Harrold and Abraham, 2014). All protein dynamics were described using a proportional error variance model (Yobs 5 Ypred×s), and cell proliferation was fitted using an additive plus proportional error variance model (Yobs 5 Ypred×s 1 «), where Yobs is the observation at time t, Ypred is the model-predicted value at time t, and s and « are estimated variance model parameters. Model Qualification. The final cell-based model and parameter estimates were used to simulate protein dynamics and cell pro- liferation after continuous exposure to a 10-fold-lower bortezomib concentration (2 nM). Simulations were compared with the experi- mentally measured cell proliferation and protein expression profiles. Only parameters associated with natural cell proliferation (kg and kd) were estimated. Cell proliferation was measured at 0, 24, 48, and 72 hours, and protein expression measurements were made at 0, 1, 4, 6, 8, 11, 24, 33, and 48 hours. The final model was also used to predict cell proliferation at 48 hours for a range of bortezomib concentrations (0.001–100 nM). The experimentally estimated IC50 value was compared with the IC50 obtained from the simulated data. Results Network Development with IKK and JAK Inhibitors. The final Boolean network model incorporates major survival and apoptotic pathways in U266 cells (Supplemental Fig. 1), and Supplemental Table 2 summarizes all node descriptions, Boolean internodal relationships, and initial values. The green connections in Supplemental Fig. 1 indicate how the initial network was updated based on cellular responses to the pathway probes. Nodes that are constitutively active under baseline cell conditions were set as being active (1) or other- wise inactive (0) in the network. An initial Boolean network was constructed, and the performance of the initial model was tested with two pathway-specific probes, IKKi and JAKi, to inhibit the NFkB and JAK/STAT pathways. In the Boolean network, the effect of each inhibitor was added such that IKKi inhibits node IKK, and JAKi inhibits nodes JAK1 and JAK2. Simulations of the initial Boolean network show that nodes representing pIkBa, pNFkB, pStat3, and BclxL expression decrease gradually upon inhibition of node IKK (Supplemen- tal Fig. 2A, black dash-dotted lines). Inhibition of pStat3 expression appears to be due to interleukin-6 inhibition (major stimulus of JAK/STAT3 pathway) via pNFkB expression. However, in vitro Western blot experiments show that expressions of pNFkB, pStat3, and BclxL remained un- changed after 48-hour exposure to the IKKi, whereas pIkBa expression decreased (Supplemental Fig. 2B, black symbols and dotted lines). In contrast, simulations of the same proteins using the initial model following JAKi exposure (Supplemen- tal Fig. 2A, green dashed lines) were comparable to observed experimental profiles over 48 hours (Supplemental Fig. 2B, green symbols and dashed lines). To account for the observed trend in pNFkB expression, the initial network was modified such that pStat3 also stimulates pNFkB (Supplemental Fig. 1). Although not yet confirmed in U266 or other MM cell lines, studies suggest cross-talk between NFkB and STAT3 signaling in tumors (Squarize et al., 2006; Lee et al., 2009; Saez-Rodriguez et al., 2011). To further test this hypothesis, model simulations were compared for the combination of IKKi and JAKi treatment with measured temporal expression profiles of pNFkB. Simu- lations of pNFkB following combination treatment with JAKi and IKKi using the initial Boolean network showed a steady decrease over time (data not shown). However, pNFkB expres- sion measured by Western blot analysis only transiently de- creased with a return to baseline values (Supplemental Fig. 2B, blue symbols and dash-dot lines). A detailed evaluation of pNFkB is described in the next section. Overall, cellular protein dynamic simulations using the final model (Supplemental Fig. 2C) reasonably agree with the experimental results (Supple- mental Fig. 2B). Fig. 3. Signal transduction model of bortezomib effects in multiple myeloma. Bortezomib compartment represents bortezomib concentration in vitro with a degradation half-life of 144 hours. M1B is a signaling compartment for stimulating the conversion of the precursor compart- ment (pre_NFkB) to pNFkB, which represents relative pNFkB protein expression. cPARPn represents transit compartment n for cleaved PARP. The Bcl-xL compartment represents relative BclxL protein expression, and N is cell proliferation in vitro. Yellow highlighted boxes are compartments for which experimental data are measured. Open and closed rectangles represent stimulation and inhibition processes. 452 Chudasama et al. NFkB Dynamics. As the expression of pNFkB was not suppressed by the IKKi, either as a single agent or in combination with the JAKi, cellular responses to another NFkB pathway inhibitor (IkBi) were evaluated alone or in combination with the JAKi. Using the initial Boolean net- work, inhibition of node pIkBa by IkBi resulted in simulations showing inhibition of pNFkB expression (data not shown). However, continuous IkBi exposure to U266 cells for up to 10 hours (alone and in combination with JAKi) maintained pIkBa expression below baseline values (Supplemental Fig. 3A), whereas pNFkB expression transiently decreased fol- lowed by a steady increase above the baseline (Supplemental Fig. 3A). Based on the lack of pNFkB suppression with either the IKKi or IkBi, alone or in combination with JAKi, additional factors were assumed to govern pNFkB expression in U266 cells outside of IKK, pIkBa, and pStat3 signaling. This phenomenon was emulated by incorporating a dummy node “X” to constantly stimulate pNFkB in the final network (Supplemental Fig. 1). The addition of this factor stabilized the Boolean network and reconciled simulations (Supplemen- tal Fig. 2, C, D, and F) with all experimental data (Supple- mental Fig. 2, B, E, and G). These results highlight the need to inhibit NFkB activity directly rather than through upstream pathways. Both final model simulations and experimental data confirm inhibition of pIkBa expression following contin- uous 48-hour exposure to the IKKi (10 mM), as well as the lack of suppression of pNFkB and BclxL expression levels (Sup- plemental Fig. 2, B and C, black symbols and dotted lines). Analogously, continuous exposure to the JAKi (10 mM) sup- pressed expression of pStat3, whereas pNFkB and BclxL expression levels remained unchanged (Supplemental Fig. 2, B and C, green symbols and dashed lines). In addition, final model simulations of U266 cellular proliferation and apoptosis agreed well with experimental cellular responses (Supple- mental Fig. 2, D–G). A range of IKKi and JAKi concentrations (0.001–100 mM) was used to evaluate cell viability, and neither induction of apoptosis nor decreased cell viability was observed after 72-hour continuous exposure alone or in combination (Supplemental Fig. 2, E and G). Bortezomib Pharmacodynamics. Once the final Bool- ean network model was updated using protein dynamics and cellular responses after exposures to probe inhibitors, the model was used to evaluate bortezomib pharmacodynamics. Bortezomib effect was introduced into the network such that it directly inhibits the “proteasome” node and stimulates the “RIP” node (Supplemental Fig. 1). Stimulation of RIP acti- vates a downstream cascade, leading to activation of pIkBa followed by pNFkB. In the Boolean network, a state initialized as 1 (active) cannot be further stimulated; therefore, pIkBa and pNFkB signal intensities remain unchanged (Supplemen- tal Fig. 4A, blue dash-dot line). However, our immunoblot analysis revealed transient increases in pNFkB and pIkBa expression levels, followed by a gradual return to baseline values (Supplemental Fig. 4B, blue symbols and lines), which is in agreement with published profiles (Hideshima et al., 2009). Comparing steady-state values for pNFkB and pIkBa before and after treatment suggests no change in expression levels, which is in agreement with Boolean network simula- tions (Supplemental Fig. 4A). Furthermore, inhibition of proteasome results in accumulated cellular stress that acti- vates the c-Jun N-terminal kinase (JNK) pathway as well as the apoptotic pathway. The mitochondrial apoptotic pathway activates caspase-3, leading to activation of p53 followed by p21, resulting in the inhibition of the Bcl-2 family proteins (e.g., BclxL and Bcl-2) (Supplemental Fig. 4B, blue symbols and lines). The activated JNK pathway inversely regulates pStat3, leading to downregulation of pStat3 expression (Sup- plemental Fig. 4B, blue symbols and lines). Simulations using the final Boolean network model correctly predicted the inhibition of pStat3 and BclxL in U266 cells after bortezomib exposure (Supplemental Fig. 4A, blue symbols and lines). In addition, final model simulations of U266 cellular outcomes to bortezomib exposure were in good agreement with in vitro measurements of cell viability and apoptosis measured via cleaved PARP expression (Fig. 4). To further test the fidelity of the Boolean network model to predict bortezomib pharmacodynamics, we compared Boolean network simulations with experimental results of cellular responses upon transient bortezomib exposures. Simulations of transient drug exposure were achieved by maintaining the Bortezomib node as active (1 5 ON) for a limited number of iterations, and the dynamics and steady states of protein and cellular response nodes were monitored. Transient experi- ments were conducted in which U266 cells were briefly exposed (i.e., for 1 and 2 hours) to bortezomib. Interestingly, some nodes (e.g., proteasome) returned to baseline values once bortezomib was removed from the system, whereas other nodes (e.g., cleaved PARP or Cl. PARP) achieved a new steady state even after drug was removed. Furthermore, steady-state outcomes for several nodes varied depending on the duration of simulated bortezomib exposure. For example, a relatively short duration of proteasome suppression produces a transient induction of apoptosis, whereas longer durations of bortezomib exposure resulted in steady states of apoptosis induction and inhibited cell growth that are similar to simulated outcomes Fig. 4. Comparison of model-simulated and observed U266 cellular outcomes with continuous bortezomib exposure. (A) Cell proliferation over 96 hours after bortezomib (20 nM) exposure in U266 cells. (B) Time course of apoptosis as measured by cleaved PARP protein expression under constant exposure to bortezomib (20 nM) in U266 cells. (C) Final Boolean model (Supplemental Fig. 1) simulations of cell proliferation. (D) Apoptosis under control conditions (red, solid) and after constant exposure to bortezomib (blue, dash-dot line). Symbols are the mean observed data, and error bars represent the standard deviation. Mathematical Modeling of Cellular Responses to Bortezomib 453 following continuous drug exposure. A shorter duration of bortezomib exposure was associated with a delay in apoptosis induction as compared with continuous drug exposure (Supple- mental Fig. 5A), and similar trends were observed experimen- tally (Supplemental Fig. 5B). Western blot analysis of BclxL and cleaved PARP expression shows a reduced magnitude in changes from baseline values between transient and continu- ous bortezomib exposure. The magnitude of cleaved PARP induction was reduced from 22- to 6-fold after 24 hours of bortezomib treatment. Model simulations of selected proteins were comparable with experimental results (Supplemental Fig. 5, A and B). However, stimulation of cleaved PARP is associated with apoptosis induction, downregulation of total NFkB ex- pression, and subsequent suppression of pNFkB expression. In contrast, incubation of U266 cells with bortezomib (20 nM) for 2 hours failed to inhibit pNFkB expression (Supplemental Fig. 5C, bottom), despite activation of cleaved PARP for over 48 hours (Supplemental Fig. 5B, apoptosis, black triangles). A specific threshold of cleaved PARP activation might be required to inhibit NFkB expression, which is not incorporated into the current network model, and further studies are needed to test this hypothesis. Network Reduction. A Boolean network reduction ap- proach (Veliz-Cuba, 2011) identified eight critical nodes (Supplemental Fig. 6A), five of which are survival pathway nodes (AKT, pNFkB, BclxL, proteasome, and pRB) and three are apoptotic pathway nodes (caspase-3, JNK, and p21). Boolean simulations of the reduced network are identical to the steady-state values of the full network, which further supports the reduction algorithm (Supplemental Fig. 6B). Although caspase-3 was identified as a critical protein through the Boolean network reduction, cleaved PARP expression was measured as a marker for apoptosis due to caspase-3 assay limitations. Bortezomib Cellular Pharmacodynamic Model. Three critical proteins (i.e., pNFkB, BclxL, and cleaved PARP) were selected from the reduced Boolean network model (Supplemen- tal Fig. 6A) for measurement and inclusion in the cellular pharmacodynamic model. The final cellular model (Fig. 3) integrates the time courses of bortezomib exposure, protein dynamics, and cell proliferation. Bortezomib elicits its effects on pNFkB via stimulation of upstream proteins in the pNFkB pathway and on cleaved PARP via stress accumulation due to proteasome inhibition. Upon continuous exposure of U266 cells to bortezomib, pNFkB protein expression is stimulated after a slight delay with a return toward the baseline (Fig. 5A). The slight delay in the stimulation of pNFkB was well characterized by adding a simple transit compartment (M1B; Eqs. 1 and 2). pNFkB expression was well described by a precursor model, in which the delayed signal (M1B) stimulates the first-order transfer from the precursor to the pNFkB compartment (Eqs. 2 and 3). Parameters associated with M1B and pNFkB (kdeg_M1B and Sm_M1B) were not estimated with good precision; therefore, M1B-associated parameters were fixed to the estimates during an initial model run. This had no impact on model performance (i.e., model fits were not compromised and parameter values did not change substantially), but precision of the estimated parameters was significantly improved (Table 1). A relatively long delay was observed before cleaved PARP expression increased (Fig. 5B), and a transit-compartment model was selected to describe this delay. Four transit compartments were found to be adequate, and the total transit time was well estimated at 26.8 hours (Table 1, ktr_parp). BclxL expression starts decreasing after 12 hours (Fig. 5C), and this delay was also well characterized by the proposed model. The initial phase of BclxL was maintained at steady state by pNFkB, and the eventual decrease in BclxL expression was successfully de- scribed using cleaved PARP stimulation of the BclxL degrada- tion rate constant. An exponential growth model well captured the natural cell proliferation under control conditions (Fig. 5D, triangles). The final signal transduction model reasonably captured the delay in cell death, and parameters were esti- mated with good precision (Table 1). Overall, the pharmacody- namic model well characterized the time courses of protein expression and cell proliferation profiles after exposure to bortezomib at 20 nM. Sensitivity to Dose and Model Qualification. The final pharmacodynamic model (Fig. 3) was developed using several cellular biomarkers after continuous exposure to a single, relatively high concentration of bortezomib (20 nM). Simu- lations of protein expression profiles and cell proliferation following exposure to different bortezomib concentrations (0.1–20 nM) were performed to evaluate the role of bortezomib dose in cellular outcomes (Supplemental Fig. 7). As bortezomib concentration is increased, the magnitude of pNFkB expression is also increased, and the time to peak response is decreased (Supplemental Fig. 7A). The extent of induced cleaved PARP is also increased (Supplemental Fig. 7B), along with greater suppression of BclxL expression (Supplemental Fig. 7C) as bortezomib concentration increases. For cell proliferation, cell growth is suppressed up to 2 nM (Supplemental Fig. 7D, red line), but greater concentrations result in cell death (Supple- mental Fig. 7D). As an external predictive check, protein ex- pression profiles and cell proliferation after low-dose bortezomib exposure (2 nM) were measured and compared with model simulations, which were obtained using the final model (Fig. 3) and parameter estimates (Table 1) from the high-dose bortezomib (20 nM) experiments. The low concentration of bortezomib (2 nM) was chosen, as it is close to its IC50 value (1.5 nM) from the in vitro exposure-response relationship at 48 hours. Thus, the selected concentration is relatively low but should still elicit a pharmacological response. Model- predicted pNFkB, cleaved PARP, and BclxL profiles and cell proliferation dynamics are in good agreement with the experimental data (Supplemental Fig. 8). The final model was also used to predict the IC50 for bortezomib after 48 hours of continuous exposure. Although the model was developed based on temporal profiles after a single concentration of bortezomib, the model-predicted IC50 was comparable to that obtained from the in vitro concentration- effect experiments (3.5 versus 1.5 nM; Fig. 6). Discussion Network-based approaches are increasingly used in drug discovery and development (Csermely et al., 2013; Harrold et al., 2013). Pharmacological networks are now commonly used for target identification (Sahin et al., 2009), evaluating signaling networks between normal and diseased conditions (Saez-Rodriguez et al., 2011), and understanding interactions among pathways (Thakar et al., 2007; Ge and Qian, 2009; Mai and Liu, 2009). For example, a Boolean network was used to identify novel targets to overcome trastuzumab resistance in breast cancer cell lines (Sahin et al., 2009), in which c-MYC 454 Chudasama et al. was identified as a potential therapeutic target. In another example, Boolean network modeling was used to analyze immune responses due to the presence of virulence factors in lower respiratory tract infection (Thakar et al., 2007). Three distinct phases of Bordetellae infection were identified, which was not possible using traditional experimental methods (i.e., biochemical and molecular biology techniques). A similar approach is used in the present analysis, in which a Boolean network model is applied for evaluating bortezomib signal transduction pathways in U266 cells. Our initial Boolean network model was developed based on the literature; however, available studies focus on either NFkB (Bharti et al., 2003b) or JAK/STAT3 (Bharti et al., 2003a; Park et al., 2011) pathways independently, and joint effects of these pathways have not been previously evaluated in U266 cells (e.g., apoptosis and cell proliferation). In addition, cellular protein dynamics and outcomes following exposure to specific probe compounds were also unavailable. Therefore, in vitro experiments and computational modeling were combined with pathway-specific inhibitors to evaluate Fig. 5. Time course of cellular protein dynamics and cell proliferation after continuous bortezomib exposure (20 nM). Relative protein expression profiles are shown for pNFkB (A), cleaved PARP (B), and BclxL (C). Protein expression was measured using Western blot in whole- cell lysate. (D) Cell proliferation measured using WST-1 assay kit. Measurements following bortezomib treat- ment and vehicle control are represented by circles and triangles. Solid lines are model-fitted profiles. TABLE 1 Final Bortezomib parameter estimates in U266 cells Parameter Unit Definition Value %CV Protein dynamic parameters ktr_NFkB h21 pNFkB transit rate constant 0.000429a — kdeg_NFkB h21 pNFkB degradation rate constant 0.54 52.0 kp_NFkB h21 pNFkB precursor transfer rate constant 0.034 5.76 Sm_NFkB nM21 pNFkB stimulatory coefficient 24.8a — ktr_parp h21 cPARP transit rate constant 0.149 4.11 Sm_parp nM21 cPARP stimulatory coefficient 6.72 11.4 Ybcl — BclxL power coefficient 0.949 14.6 kdeg_bcl h21 BclxL degradation rate constant 7.72E-03 58.4 «NFkB — pNFkB proportional error coefficient 0.097 11.4 «bcl — BclxL proportional error coefficient 0.163 11.1 «parp — cPARP proportional error coefficient 0.229 11.7 In vitro cell dynamic parameters kg h21 Cell growth rate constant 0.021 3.74 kd h21 Cell death rate constant 2.56E-03 9.81 C0cell Initial cell density 1a — scell — Cell additive error coefficient 0.031 32.9 «cell — Cell proportional error coefficient 0.157 21.7 %CV, percent coefficient of variation. aFixed value. Mathematical Modeling of Cellular Responses to Bortezomib 455 the roles of both pathways individually and simultaneously. The Boolean network model confirmed that stress accumula- tion due to proteasome inhibition is a major pathway of myeloma cell death despite the activation of pNFkB protein expression, which contradicts a major proposed hypothesis of bortezomib effects. Whereas logic-based models provide qualitative insight into network connectivity and drug-induced signal transduction, a quantitative dynamical model that includes important cellular biomarkers allows for the integration of critical factors responsible for cell death upon chemotherapy exposure (Yamazaki et al., 2011; Kay et al., 2012; Zhang et al., 2013). It is not yet practical to quantify all components in cellular signaling pathways; therefore, it is necessary to identify critical proteins for dynamical model development. A Boolean network reduction algorithm (Veliz-Cuba, 2011) identified critical factors regulating bortezomib cell death that guided development of a reduced PD model. Among the biomarkers (Supplemental Fig. 6), two antiapoptotic proteins and one proapoptotic protein (pNFkB, BclxL, and cleaved PARP) were integrated into a reduced pharmacodynamic model (Fig. 3). pNFkB was integrated in the model as bortezomib increases its expression, contradictory to proposed mechanisms. BclxL was selected as a major antiapoptotic protein that inhibits apoptosis, and cleaved PARP is a primary proapoptotic marker. The factor p21 was not incorporated in the current model as Boolean simulations suggest that bortezomib effects on apoptosis precede cell growth arrest. The final cellular PD model (Fig. 3) was successfully qualified using the external data set following a low concen- tration of bortezomib (2 nM). Despite the fact that the cellular model was developed based on a single bortezomib concentra- tion (20 nM) and linear coefficients, the final model reasonably predicted responses to the lower bortezomib exposure (Sup- plemental Fig. 8) and the dose-response curve for bortezomib at 48 hours (Fig. 6). Although there is a slight misfit for BclxL and cleaved PARP profiles (Supplemental Fig. 8, B and C), overall simulated profiles reasonably agree with experimental data. Most commonly, exposure-response relationships of protein expression data are sigmoidal in nature (Bharti et al., 2003a,b; Park et al., 2008, 2011). For example, the inhibition of pNFkB activity by curcumin is 10% at 1 mM and 40% at 10 mM (Bharti et al., 2003b). Similarly, cleaved PARP activation is about 1% at 10 mM curcumin but 100% at 50 mM curcumin (Park et al., 2008). It is therefore interesting that, although our model was developed using a single drug concentration and simple linear coefficients (e.g., Sm_M1B and Sm_PARP in Eqs. 1 and 4), it reasonably predicts profiles at a lower bortezomib concentration (Supplemental Fig. 8) and a sigmoidal concentration-effect relationship (Fig. 6). Further- more, the predicted exposure-response relationship for BclxL can be overlaid with observed cell proliferation at 48 hours (Supplemental Fig. 9). This suggests that BclxL could serve as a potential biomarker to predict efficacy in MM and warrants further study. However, a potential limitation is that the proteins measured in this study reflect relative fold change and not absolute values of protein concentrations. Grounding on relative changes in protein expression maintains a degree of modularity, but more advanced proteomic methods are needed to quantitatively measure low-abundance signaling proteins. Cell growth and death parameters were also com- pared with available values from the literature. Natural cell growth and death were modeled using first-order growth rate constants (kg and kd). The estimated net growth rate constant (kg – kd) in the final model (0.00490 h21) is comparable to net growth rate constants from U266 xenografts at 0.00487 h21 (Siveen et al., 2014) and 0.00450 h21 (Rhee et al., 2012) that were obtained by fitting an exponential model to digitized control curves (data not shown). Preliminary experiments were conducted to measure pNFkB in the nucleus and cytoplasm of U266 cells after bortezomib exposure. Both cellular fractions showed a similar trend of increased relative pNFkB expression (data not shown); therefore, total cellular pNFkB was measured by Western blot analysis of cell lysates, revealing transient increased expression (Fig. 5A). Despite the stimulation of pNFkB protein expression, apoptosis is induced and the model is able to well capture this phenomenon. The NFkB pathway is one of the major cell survival pathways and is deregulated in many types of cancer (Karin, 2009). Bortezomib stimulates the upstream cascade of the NFkB pathway (Hideshima et al., 2009) leading to activation of pNFkB protein expression. Apoptosis is still induced through cellular stress resulting from the inhibition of proteasome (Fig. 4D) (Hideshima et al., 2001). The cellular model was able to well describe both mechanisms. Aberrant expression of pNFkB is responsible for the lack of efficacy and resistance in some cases of MM (Hideshima et al., 2002; Bharti et al., 2004). Greater expres- sion of pNFkB results in greater expression of antiapoptotic proteins (e.g., BclxL) (Karin and Lin, 2002), with cross-talk between survival and apoptotic pathways determining cellu- lar fate. Hence, greater drug concentrations are required to activate the apoptotic pathway. Initially, BclxL inhibition of cleaved PARP activation and cleaved PARP stimulation on removal of BclxL was incorporated. However, since BclxL exerts a negative feedback on cell death, as incorporated in the model, the BclxL effect on cleaved PARP was removed to simplify the model and reduce model redundancy. In summary, systems pharmacology is an emerging field that seeks to couple systems biology and PD modeling, which could promote the discovery, development, and effective use of drugs based upon first principles. Computational tools based on graph theory (Liu et al., 2013), discrete dynamic relation- ships (Albert and Wang, 2009), and others can be used to identify critical system components within networks at mul- tiple organizational levels, thus providing guidance for Fig. 6. Comparison of model-predicted (Pred) and observed (Obs) bortezomib concentration-effect profiles at 48 hours. Circles represent mean observed data (error bars are S.D.) at 48 hours. Lines represent either a fitted curve to observed data using a Hill-type function (red) or the model-predicted data at 48 hours (blue). 456 Chudasama et al. multiscale model construction and evaluation. We have used an integrated approach to investigate bortezomib signal transduction and exposure-response relationships in MM cells. A cell-based model of bortezomib in U266 human myeloma cells was developed that incorporates one of the major survival pathway proteins (pNFkB), antiapoptotic pro- tein BclxL, and an apoptotic marker (cleaved PARP) to link bortezomib exposure to cell proliferation. The final model- predicted in vitro IC50 for bortezomib reasonably agrees with the experimental IC50 at 48 hours. Although the Boolean and dynamical models are relatively simple and specific to U266 cells and bortezomib, the overall strategic approach can be easily extended with slight modification to other myeloma cell lines (e.g., MM.1S and RPMI 8226) or bortezomib-based combination regimens (e.g., histone deacetylase inhibitors). This model may serve as a basis for studying bortezomib combinations with antimyeloma agents and to optimize xenograft combination studies, which is a focus of current research and will be reported separately. In addition, the model structure can be easily extended to describe responses in other cancer types that share similar pathways. Acknowledgments The authors thank Dr. John M. Harrold (University at Buffalo, SUNY) for developing MATLAB code for this project. Authorship Contributions Participated in research design: Design and execution of experi- ments: Chudasama. Conducted experiments: Chudasama. Performed data analysis: Chudasama, Ovacik, Mager. 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E-mail: dmager@buffalo.edu 458 Chudasama et al.	26163548	FLIP = ( pNFKB ) Apo = ( Cl_PARP ) cJun = ( JNK ) Prot = NOT ( ( Bort ) ) MEK1 = ( RAF ) XIAP = ( ( ( pSTAT3 ) AND NOT ( p53 ) ) AND NOT ( Smac ) ) OR ( ( ( pNFKB ) AND NOT ( p53 ) ) AND NOT ( Smac ) ) CYCE = ( MYC ) DNAdam = ( STRESS ) OR ( Cas3 ) BCL2 = ( ( ( pSTAT3 ) AND NOT ( p53 ) ) AND NOT ( BAD ) ) OR ( ( ( pNFKB ) AND NOT ( p53 ) ) AND NOT ( BAD ) ) p27 = ( ( ( ( p53 ) AND NOT ( AKT ) ) AND NOT ( MYC ) ) AND NOT ( CDK4 ) ) CYCD = ( AKT ) OR ( MYC ) OR ( ERK ) IKK = ( AKT ) OR ( RIP AND ( ( ( NIK ) ) ) ) pSTAT3 = ( ( JAK2 AND ( ( ( JAK1 AND STAT3 ) AND ( ( ( NOT IKK ) ) ) ) ) ) AND NOT ( JNK ) ) OR ( JAK1 AND ( ( ( STAT3 AND JAK2 ) ) ) ) CDK4 = ( ( ( CYCD ) AND NOT ( p27 ) ) AND NOT ( p21 ) ) Bclxl = ( ( ( ( pSTAT3 ) AND NOT ( p53 ) ) AND NOT ( BAD ) ) AND NOT ( BAX ) ) OR ( ( ( ( pNFKB ) AND NOT ( p53 ) ) AND NOT ( BAD ) ) AND NOT ( BAX ) ) JAK1 = ( gp130 AND ( ( ( IL6 ) ) ) ) BAD = NOT ( ( AKT ) ) CDK2 = ( ( CYCE ) AND NOT ( p21 ) ) MYC = ( pSTAT3 ) OR ( MEKK ) OR ( ERK ) ERK = ( MAPK ) PIP3 = ( ( PIP3 ) AND NOT ( PTEN ) ) MITO = ( BAX ) MEKK2 = ( RAC ) JAK2 = ( ( IL6 AND ( ( ( gp130 ) ) ) ) AND NOT ( SHP1 ) ) PI3K = ( IL6 AND ( ( ( gp130 ) ) ) ) JNK = ( ( MKK4 ) AND NOT ( Prot ) ) Cas3 = ( ( Cas8 ) AND NOT ( XIAP ) ) OR ( ( Cas9 ) AND NOT ( XIAP ) ) Cytc = ( MITO ) pRB = ( CDK2 AND ( ( ( CDK6 AND CDK4 ) ) ) ) OR ( CDK4 AND ( ( ( CDK6 ) ) ) ) Fas = ( FasL ) OR ( p53 ) gp130 = NOT ( ( Cas3 ) ) MKK4 = ( MEKK2 ) STRESS = ( ( DNAdam ) ) OR NOT ( DNAdam OR Prot ) IL6 = ( pNFKB ) RAC = ( STRESS ) MDM = ( ( AKT ) AND NOT ( ATM ) ) OR ( ( p53 ) AND NOT ( ATM ) ) pNFKB = ( pSTAT3 ) OR ( X ) OR ( pIKB ) OR ( Prot AND ( ( ( pIKB ) ) ) ) TRAF3 = NOT ( ( CIAP ) ) AKT = ( PIP3 ) CIAP = ( TNFAR ) Smac = ( MITO ) MAPK = ( MEK1 ) pIKB = ( IKK ) Cas8 = ( ( Fas AND ( ( ( FasL ) ) ) ) AND NOT ( FLIP ) ) GROWTH = ( pRB ) STAT3 = NOT ( ( Cas3 ) ) NIK = NOT ( ( TRAF3 ) ) p21 = ( ( ( ( ( p53 ) AND NOT ( MYC ) ) AND NOT ( AKT ) ) AND NOT ( CDK4 ) ) AND NOT ( MDM ) ) RAS = ( SHP1 ) OR ( IL6 AND ( ( ( gp130 ) ) ) ) ATM = ( DNAdam ) OR ( Cas3 ) p53 = ( ( JNK ) AND NOT ( MDM AND ( ( ( Prot ) ) ) ) ) OR ( ( DNAPK ) AND NOT ( MDM AND ( ( ( Prot ) ) ) ) ) BID = ( ( ( STRESS ) AND NOT ( BCL2 ) ) AND NOT ( Bclxl ) ) OR ( ( ( Cas8 ) AND NOT ( BCL2 ) ) AND NOT ( Bclxl ) ) OR ( ( ( Fas ) AND NOT ( BCL2 ) ) AND NOT ( Bclxl ) ) RIP = ( Bort ) OR ( TNFAR AND ( ( ( TNFA ) ) ) ) BAX = ( ( ( BID ) AND NOT ( Bclxl ) ) AND NOT ( BCL2 ) ) OR ( ( ( p53 ) AND NOT ( Bclxl ) ) AND NOT ( BCL2 ) ) FasL = ( cJun ) OR ( Fas ) RAF = ( RAS ) Cl_PARP = ( Cas3 ) CDK6 = ( CYCD ) MEKK = ( MEK1 ) PTEN = ( p53 ) DNAPK = ( ATM ) Cas9 = ( ( ( Cytc ) AND NOT ( XIAP ) ) AND NOT ( AKT ) )
RESEARCH ARTICLE Predicting Variabilities in Cardiac Gene Expression with a Boolean Network Incorporating Uncertainty Melanie Grieb2,5☯, Andre Burkovski2,3,5☯, J. Eric Sträng2☯, Johann M. Kraus2, Alexander Groß1, Günther Palm3, Michael Kühl4, Hans A. Kestler1,2,3 1 Leibniz Institute for Age Research, Fritz-Lipmann Institute, Jena, Germany, 2 Core Unit Medical Systems Biology, Ulm University, Ulm, Germany, 3 Neural Information Processing, Ulm University, Ulm, Germany, 4 Institute for Biochemistry and Molecular Biology, Ulm University, Ulm, Germany, 5 International Graduate School of Molecular Medicine, Ulm University, Ulm, Germany ☯These authors contributed equally to this work. * michael.kuehl@uni-ulm.de (MK); hkestler@fli-leibniz.de (HAK) Abstract Gene interactions in cells can be represented by gene regulatory networks. A Boolean net- work models gene interactions according to rules where gene expression is represented by binary values (on / off or {1, 0}). In reality, however, the gene’s state can have multiple val- ues due to biological properties. Furthermore, the noisy nature of the experimental design results in uncertainty about a state of the gene. Here we present a new Boolean network paradigm to allow intermediate values on the interval [0, 1]. As in the Boolean network, fixed points or attractors of such a model correspond to biological phenotypes or states. We use our new extension of the Boolean network paradigm to model gene expression in first and second heart field lineages which are cardiac progenitor cell populations involved in early vertebrate heart development. By this we are able to predict additional biological pheno- types that the Boolean model alone is not able to identify without utilizing additional biologi- cal knowledge. The additional phenotypes predicted by the model were confirmed by published biological experiments. Furthermore, the new method predicts gene expression propensities for modelled but yet to be analyzed genes. Introduction Specialization of cells during development and differentiation is driven by transcription or growth factors. These are interconnected in gene regulatory networks. The temporary regu- lated interaction of these factors are finally resulting in terminally differentiated, specialized cells which are characterized by the expression of a certain set of genes. Thus, development and function of a certain cell type is largely reflected by the expression of selected genes in a cell. Gene regulatory networks describe the interactions between those genes in the cell [1–3]. During embryonic development, these gene regulatory networks evolve over time towards a stable state, finally reflecting the terminally differentiated cell [1], i.e., biological phenotypes. PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 1 / 15 OPEN ACCESS Citation: Grieb M, Burkovski A, Sträng JE, Kraus JM, Groß A, Palm G, et al. (2015) Predicting Variabilities in Cardiac Gene Expression with a Boolean Network Incorporating Uncertainty. PLoS ONE 10(7): e0131832. doi:10.1371/journal.pone.0131832 Editor: Lars Kaderali, Technische Universität Dresden, Medical Faculty, GERMANY Received: March 5, 2015 Accepted: June 6, 2015 Published: July 24, 2015 Copyright: © 2015 Grieb et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: This work was funded in part by the German federal ministry of education and research (BMBF) within the framework GERONTOSYS II (Forschungskern SyStaR, Project ID 0315894A to MK and HAK), European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 602783 (to HAK), and the International Graduate School in Molecular Medicine at Ulm University (GSC270). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. A gene regulatory network can be visualized as a static map that describes the interaction of these genes and reflects the activation or inactivation of genes by other factors in the network. Such a gene regulatory network can be implemented as a Boolean network if one assumes that a gene can be either active or inactive in a cell and thus can be represented by a Boolean value (on / off or {1,0}). Interaction between genes can then be mathematically modeled by Boolean functions. A set of such logical rules or functions, more exactly one Boolean function per con- sidered gene defines a Boolean network (BN) [4, 5]. Given some initial expression pattern, a BN computes the evolution of gene expression in discrete time steps. Of particular importance are states which are invariant or lead to periodic sequences of expression patterns, so called attractors. For finite sized BNs any initial state will converge to one of these attractors in finite time [6] In a Boolean network representing a gene regulatory network, these attractors are the equivalent to the stable state of gene expression reflecting the differentiated biological pheno- type of the cell. BNs are useful as a first approach when it comes to model complex networks with many genes and their interactions [7]. Often the BN is modeled from known regulatory interactions that are manually derived from qualitative wet-lab experiments [8] or computationally deter- mined with BN reconstruction methods [9, 10]. Additionally, simulated Boolean states of genes from the simulation allow an intuitive interpretation of the results. Recently, BN models have been used to capture the essence of gene regulation in several biological processes such as the mammalian cell cycle [11], the guard cell abscisic acid signaling [12], or the oxidative stress response pathway [13]. Modelling of gene regulatory networks and their simulation, however, is hampered by dif- ferent drawbacks. In practice, for example, absolute data for gene expression activities are mea- sured indirectly, e.g., by quantifying the relative amounts of the corresponding transcripts. These measurements are inherently noisy. Furthermore, some notion of activity/inactivity has to be inferred in order to infer the state of the gene. To this effect binarization schemes are used in order to differentiate between active and inactive genes in time series data [14]. Here, one also has to consider that effective thresholds are gene dependent [8]. Finally, one has to take into account that gene expression can vary between different cells of an apparently homoge- neous population of cells as previously shown for the common cardiac progenitor cell popula- tion that gives rise to the heart [15]. Here, we implement a novel extension of the Boolean network paradigm and illustrate the procedure on a Heart Field Development model. We also illustrate the utility of the method on the Mammalian Cell Cycle [11] (see Section G in S1 Supplementary Information File). Our pri- mary focus is the evolutionary conserved core cardiac regulatory network that drives early car- diac development and that predicts the dynamic behaviour of gene expression during early development [16]. In this process a common cardiac progenitor cell population splits into two populations of cells called first (FHF) and second heart field (SHF), that are characterized by the selective expression of typical transcription factors such as Isl1, Tbx1, Tbx5, and Nkx2.5. Cells of the FHF develop to the primary heart tube and later to the left ventricle and the atria, whereas cells of the SHF mainly develop into the right ventricle and the outflow tract [17]. Activation of these genes during cardiac development is regulated among others through growth factors of the Wnt family [18]. The BN model of this gene regulatory network correctly predicts the general pattern of gene expression in general, work in Xenopus [19] and in mouse ES cells [15] albeit suggests that during cardiac development on a single cell level a much more complex variability in gene expression exists. In an attempt to include the variability of single cell gene expression in an otherwise homog- enous cell population, our goal was to describe gene expression levels with multiple values, extending the binary values of a BN. Previously, transformations of BNs have also been A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 2 / 15 Competing Interests: The authors have declared that no competing interests exist. considered by others [20, 21]. An overview over these approaches can be found in [22, 23]. These transform the Boolean rules into a system of ordinary differential equations which describe the dynamics of gene concentrations. As opposed to the analysis of behaviour and evolution of concentration levels we use an approach to model continuous intervals of gene expression values in order to potentially find new fixed points using only the original BN. In our model, we call continuous values attributed to genes “propensities” of gene expression and do not need additional parameters that are otherwise required for modelling concentrations. The corresponding interactions are derived from the Boolean functions of the BN. The opera- tions AND, OR, and NOT are replaced by their arithmetic counterparts based on fuzzy logic product sum rules [24]. This extends the BN into a discrete-time, non-linear, dynamical model that is represented by a system of difference equations, namely, a BN extension (BNE). Natu- rally, fixed points of this new model also represent possible expression patterns or phenotypes of cells. Interestingly, this novel method is able to predict variabilities in gene expression during cardiac development and cell cycle (see Figs M and N in S1 Supplementary Information File). For cardiac development the extension predicts additional phenotypes that are in agreement with published results and novel gene expression pattern for yet to be analyzed genes. Methods Since we intertwine biological and mathematical terms we shortly present an overview of the important terminology that we use in the following: • Boolean fixed point: A fixed point of the BN. It takes values Bn 2 {0,1}n with n being the number of variables in the BN. • BNE fixed point: A fixed point of the BNE. It takes values In 2 [0, 1]n. • biological phenotype: A phenotype that describes a binarized gene expression of measure- ments. It takes values in Bn, i.e., in form of binary gene expression. • hypothetical phenotype: A pattern of gene expression. Hypothetical phenotypes are used in order to map the extension fixed points to their nearest neighbouring pattern. In our particu- lar case we consider binary gene expression patterns with values in Bn (a set of 2n binary patterns). The extension and analysis of the BN is conducted in several steps drafted in Fig 1 and are described in detail below. Given a BN, using the canonical Disjunctive Normal Form (DNF), each term is then transformed into a sum of products. The extended model is then simulated to find BNE fixed points of the model. These fixed points can be interpreted by a mapping the fixed points to the nearest hypothetical phenotypes. The meaning of the nearest hypothetical phenotype must then be further interpreted in biological context. Boolean Networks (BN) BN were pioneered by Kauffman in 1969 [25, 26] to model gene interactions in a cell. BNs are based on the assumption that a cell regulates its function in a time-dependent manner by switching genes on (active) or off (inactive). The regulatory mechanism is described by logical rules where the state of a gene is defined by logic rules based on the previous gene states. Here, we denote by B = {0, 1} the set of Boolean values in binary representation. Formally, a BN is defined by n Boolean variables x = (x1, . . ., xn) 2 Bn and a vector of n Boolean transition functions F = (f1, . . ., fn), which describe the interaction between variables. A transition function fi is a map fi:Bn ! B. In that way that the discrete time evolution gen- erated by a BN is defined by sequential application of the vector valued function F = (f1, . . ., fn) A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 3 / 15 on an initial state x at time 0. A state transition is thus formally described by the map xðt þ 1Þ ¼ FðxðtÞÞ; t 2 N0; ð1Þ given the state x(t) at time t. Bn is ﬁnite and discrete and there are 2n unique states. Each is a Fig 1. Phenotype analysis using the Boolean Network Extension (BNE). The application of the BNE to a given Boolean network (BN) can be divided into three basic steps: Model extension (top), identification of stable structures (middle) and mapping to phenotypes (bottom). In the model extension step (top) the rules of the BN are transformed to the rules of the BNE by converting the rules of the BN to canonical disjunctive normal form (DNF) and then to product-sum fuzzy logic (DNF product-sum extension, details see section Extension of Boolean networks). In the “identification of stable structures”-step (middle) the extended BNE is simulated for a large number of random inputs. The resulting approximated attractors can either be fixed points approximated by point clouds, fixed points depending on one or multiple parameters or different dependencies. Finally, new phenotypes are identified step (bottom) by mapping the fixed points to their nearest hypothetical phenotype. doi:10.1371/journal.pone.0131832.g001 A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 4 / 15 priori allowed as BN initial value. It follows that evolution of an initial state will converge to a cyclic sequence of states in ﬁnite time. Such sequences are called attractors. Attractors are usu- ally categorized in • fixed points (attractors of period 1) and • periodic sequences (attractors of period T > 1). In the following synchronous BN will be considered. In synchronous BN, each Boolean func- tion is executed once at each time step. In a Boolean network any variable may interact with any subset of variables in the network. Additionally, variables with constant values may be considered in order to parametrize external inputs, e.g., influences of exogenous factors. Discrete time delays may also be modeled by intro- ducing a chain of “dummy” variables which consecutively take the value of the chain’s first var- iable value. Such a chain of n additional “dummy” variables result in a time delay of n steps of the considered variable. Boolean Network Extension (BNE) By I we denote the interval [0, 1]. The new model extends the state space from Bn to In. We do so by adapting the logical rules of the original BN. In general one has to find a mapping from the Boolean operators AND (^), OR (_), and NOT (¬) to continuous operators (functions) on In. For the sake of consistency, these operators should render the same results as their corre- sponding Boolean analogue when restricting the values to {0, 1}. A common approach is to treat the Boolean transition functions as fuzzy logic functions [24, 27]. In the fuzzy logic literature, there are mainly two approaches. The first approach is the min–max fuzzy logic. The second approach, product–sum fuzzy logic, replaces the Boolean algebraic operators on Bn (_, ^,¬) with their arithmetic counterparts on In, namely, (+, ×) and negation by (1 −x). Constant values of the BN are translated to constant functions of the BNE from I. Contrarily to the min–max fuzzy logic, the product–sum fuzzy logic are differentiable functions. Additionally, product–sum allows a smooth evolution and interaction between the variables which correspond the idea that interactions in cells depend on the concentration lev- els of products. In contrary, in min–max variables that are not minimal or maximal do not influence the resulting value. In the following, we will only consider the product–sum fuzzy logic. Formally, the extension of a Boolean function fi : Bn ! B ð2Þ a7!bi ð3Þ is the function ^f i : In ! I ð4Þ ^a 7! ^bi; ð5Þ i.e., we consider the extensions of the Boolean domains and functions given by the operationb. A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 5 / 15 The product–sum fuzzy logic results in the following properties c :xi ¼ 1 ^xi; ð6Þ b xi ^ xj ¼ ^xi ^xj; ð7Þ b xi _ xj ¼ ^xi þ ^xj ^xi ^xj: ð8Þ Eq 8 can be derived from Eqs 6 and 7 using DeMorgan’s law. The Boolean formulae are trans- formed into a unique representation using the canonical disjunctive normal form (DNF) which can be directly derived from the truth table. Then, given a Boolean formula in DNF, we directly extend it into the continuous version by applying the product-sum rules. The resulting formula have values in I since DNF encodes a truth table for every possible term with n vari- ables [28]. It is easily veriﬁed that the BN and its extension coincide for variable values in Bn when applying the DNF/product–sum extension (DNFPS). Example: sequence of transformations for the Boolean function f(a, b, c) = (a_b)^c, Booleanfunction ! DNF ! DNFPS ða _ bÞ ^ c ! ð:a ^ b ^ cÞ _ ða ^ :b ^ cÞ _ ða ^ b ^ cÞ ! ð^a þ ^b ^a ^bÞ ^c Extension fixed points As in the case of BN, its extension will have fixed points. Fixed points of the model are meant to represent biological states since both are stable and time-invariant. Firstly, we defined the extension procedure in such a way that a BN and its extension are consistent when restricting to values in Bn. Hence, the BN fixed points are fixed points of its extension as well. Secondly, an extension may have non–Boolean fixed points. One crucial point of the extension is the fact that the variables of the system, i.e., variables which are considered as constant input, may now take values in I. If these parameters are uncertain, unknown, or the behavior of the system is to be examined, one would have to inves- tigate the variations of the fixed points as the input variables are changed. Compared to the BN case, two new aspects need to be taken into account. It is a priori not possible to predict the number of fixed points of a BNE nor is it possible to conduct an exhaustive search. Addition- ally, the iteration of a BNE can only be (practically) carried out numerically. Thus the values of the fixed points given by iteration are not exact. The same would be true if the fixed points were found by numerically solving ^f ^x ð Þ ¼ ^x. Any attempt to systematically ﬁnd the set of extension ﬁxed points of an extension would hence result in a numerical approximation of ﬁxed points gained by sweeping the initial values of the respective search through In. Amongst those found, several may correspond to a single actual ﬁxed point. A proper identiﬁcation of the true ﬁxed point is therefore necessary. They can, e.g., be grouped into ﬁxed point proto- types by using k-means. The ﬁxed points of the BNE would typically describe surfaces over the investigated parameter space (see Fig 2). Numerical considerations BN were simulated with the help of the BoolNet package [29]. Fixed points were investigated in two manners A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 6 / 15 • iteration with initial data taken from uniform distributions over In. The criteria for termina- tion were met if the last k = 2 function evaluations of the iteration were below a threshold ε = 10−8 (j^F tð^sÞ ^F t1ð^sÞj < ε) with ^s 2 In being the propensity vector. The maximal number of iterations for the heart field model and cell cycle model was 100 since a typical conver- gence was achieved after 20–30 function evaluations. • numerically solving In ∍^s? : ^Fð^sÞ ¼ ^s ð9Þ using the nleqslv R-package [30]. More speciﬁcally, we used the Broyden secant method [31] which is a heuristic for the Newton method. The global strategy uses the dbldog argument which is a the trust region method using a double dogleg method [32]. Both methods yielded similar results up to solver tolerance. Graphics were generated with R [33]. Fig 2. Parametric fixed points. An example of parametric dependency of fixed points is shown. Table 1 shows the BNE. doi:10.1371/journal.pone.0131832.g002 Table 1. Boolean Network Extension. For a given parameter ^A, the BNE converges towards a single ﬁxed point. The gene expression values ^B and ^C of the ﬁxed point depend on this parameter. The x-axis corresponds to the parameter ^A and the y-axis shows the value of the ﬁxed point for the variables ^B and ^C, respectively. E.g., the ﬁxed point for ^A ¼ 0:5 is (^B ¼ 0:6; ^C ¼ 0:8). Boolean Network Boolean Network Extension A constant parameter ^A constant parameter B(t+1) A_¬C(t) ^Bðt þ 1Þ ^A þ ð1 ^AÞ ð1 ^CðtÞÞ C(t+1) ¬A_B(t) ^Cðt þ 1Þ ð1 ^AÞ þ ^A ^BðtÞ doi:10.1371/journal.pone.0131832.t001 A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 7 / 15 Association of BNE fixed points with putative biological phenotypes Whether considering prototypes or actual fixed points of the extension, the actual predictive value of the model is given by its capacity to describe and predict biological phenotypes. As mentioned above, we expect our model to reflect the properties of a Boolean state under pertur- bation. It would hence be expected that only stable fixed points may be of interest biologically since stable states correspond to biological states in equilibrium. Also, in simulations, unstable fixed points are unlikely to be found numerically. However, known Boolean fixed points may turn out to be unstable under the extension. Thus the BNE is able to additionally characterize the stability of the Boolean fixed points. Conversely, new stable fixed points may be found by the BNE. The values of the fixed points do require a scheme to determine expression levels of each specific gene to enable comparison with measured binary biological phenotypes. In practice this would mean that we would need a binarization scheme to extract the gene expression in terms of a set of a priori unknown critical values. For this reason we employ a more absolute scheme for the identification by mapping fixed points and hypothetical phenotypes which lie nearest to each other in In, in a subset of SI In, or a fuzzy description of hypothetical pheno- types in {0, 1}n. We call this identification nearest neighbor matching (NNM). In general, using a distance measure results in a specific ordering of the considered elements. Typically we use the Euclidean distance since it is widely known and has an intuitive interpretation. In order to assess the mapping approach we also applied it in context of the cell cycle network [11] (see Section G in S1 Supplementary Information File). Interpretation of the values of a BNE The BNE uses fuzzy logic product-sum transformation of the Boolean rules to compute a value for each variable. The main property of the extension is that it inherits the interaction patterns of the BN. The defined operations corresponding to the Boolean operations are also t–norms and corresponding associated co-norms, which ensure that the formalism is a consistent fuzzy logic [34, 35]. Furthermore, the extension is conducted in such a way that the transition of the DNFPS to the Boolean limit is differentiable. We wish to emphasize that the assumption we make is that the approximation also yields plausible results for larger perturbations over the entire In and that the intermediate values will be in a monotonic relation to measurements of gene expression, i.e, the larger the value xi the larger the expression of the corresponding gene product. The assertions of the BNE values are in no way absolute but do reflect the corresponding expression of genes in a relational way, i.e., place the corresponding expressions on an ordinal scale. We can state, a gene has a “higher” or “lower” expression values when comparing two values. This however does not give any conclusive answer to whether a gene is expressed or not. The values only reveal an ordering of gene expressions. From the Boolean case we expect that 0 corresponds to certainly unexpressed and 1 to certainly expressed. An actual quantifica- tion for values in between 0 and 1 may hence only be carried with some a priori knowledge, i.e., by comparison with actual measurements. As the BNE attributes numbers to genes, it might also be natural to interpret those as con- centrations. An example would be to associate the outputs of the BNE as the gene transcript products over time. However, it is very unlikely that, what in effect is a system of kinetic reac- tions may be described without the addition of any kinetic parameters. Such attempts have been carried out in the past and do require additional parameters to describe the dynamics of the underlying chemical molecules [20, 21]. Since the values are neither concentrations nor probabilities we call them propensities for gene expression. A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 8 / 15 Results Previous results for early cardiac development Herrmann et al. [16] analyzed the gene regulatory network of early cardiac development by use of a BN and found a correspondence between biological measurements and mathematically simulated attractors. The model simulates the interaction between intracellular genes (Bmp2, canonical Wnt, Dkk1, Fgf8, Foxc1.2, GATAs, Mesp1, Isl1, Nkx2.5, Tbx1, Tbx5) and extracellu- lar factors (exogenous Bmp2 and canonical Wnt) that form gradients (Table 2). When considering all possible binary initial values, two fixed points were reached in 99% of the cases. The gene expression values corresponding to these two fixed points are similar to the gene expression in the FHF and SHF that was extracted from literature. In 49% of the initial values, the network converges to attractors corresponding to the FHF (49% of cases) and in 50% to the SHF. In the remaining 1% the simulation converged towards a fixed point with no activated cardiac genes. This was thought to correspond to a biological phenotype where no heart field is formed, like if canonical Wnt signaling is not activated during development. The BN fixed point that resembles the FHF is characterized by the expression of the FHF specific genes Bmp2, GATAs, Nkx2.5, and Tbx5 to be active. Accordingly, the fixed point for the SHF shows activation of the SHF genes, Isl1, Foxc1/2, Tbx1 and Fgf8. In the following we name the phenotypes predicted by the Boolean model FHF_BOOL and SHF_BOOL, respectively. We apply the BNE to this cardiac development model in order to investigate new phenotypes that are outside of the Boolean pradigm. Biological phenotypes are described in terms of present or absent gene expression. In our case we wanted to compare the gene expression of the four genes Isl1, Nkx2.5, Tbx1, and Tbx5 for FHF and SHF differentiation to the single cell RT-PCR analysis of Gessert and Kühl [19]. The phenotypes previously identified are given in Fig 3. In the following we name these pheno- types as SHF1, SHF2, SHF3 and SHF4, as these are determined as second heart field Table 2. Genes, proteins and model variables to BN model of cardiac development. The first column shows the variables used in the BN model. The second column, function, describes the type and location of the expressed protein or the purpose of the variable in the BN. Variable (Gene/Protein) Function Intracellular factors Bmp2 (Bmp2) Signaling factor canWnt (canonical Wnt) canonical Wnt signaling Dkk1 (Dkk1) Signaling factor Fgf8 (Fgf8) SHF transcription factor Foxc1.2 (Foxc1, Foxc2) SHF transcription factor GATAs (GATA4, GATA5, GATA6) transcription factor, cardiogenic mesoderm Isl1 (Isl1) SHF transcription factor Mesp1 (Mesp1, Mesp2) transcription factor, early cardiogenic mesoderm development Nkx2.5 (Nkx2.5) transcription factor, cardiogenic mesoderm Tbx1 (Tbx1) SHF transcription factor Tbx5 (Tbx5) FHF transcription factor Extracellular factors exogen_Bmp2_I Bmp2 derived from neighboring tissue exogen_Bmp2_II Time delay of Bmp2 derived from neighboring tissue exogen_CanWnt_I Canonical Wnt derived from neighboring tissue exogen_CanWnt_II Time delay of canonical Wnt derived from neighboring tissue doi:10.1371/journal.pone.0131832.t002 A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 9 / 15 phenotypes by the expression of the SHF marker gene Isl1, and the phenotypes representing the first heart field FHF5, FHF6, FHF7. Simulation results for the BNE Given the continuous model of early cardiac development we computed fixed points for 104 different initial values of the genes. The values for each gene were drawn from a uniform distri- bution U(0,1). We additionally performed simulations that were aimed at initial inactivation (value 0) of all genes with the exogen_canWnt_I as controlling parameter in order to examine its influence to the formation of the phenotypes. As the cardiac model is parametrized by the exogen_canWnt_I parameter, we ordered the identified fixed points accordingly. The linear increase of the propensity of the exogen_canWnt_I causes a continuous transition in propen- sity for the remaining genes (see Fig B in S1 Supplementary Information File). Prediction of additional phenotypes for FHF and SHF The structure provided by the BN is sufficient enough to allow a prediction of previously unknown biological phenotypes through the extension. In order to characterize the phenotypes in the BNE we compared all 11 genes that are effec- tively modeled by the BN (Bmp2, canonical Wnt, Dkk1, Fgf8, Foxc1.2, GATAs, Mesp1, Isl1, Nkx2.5, Tbx1, Tbx5). This allows prediction of gene expression propensity of genes for which no expression information is available. In order to evaluate our results we computed the dis- tances between all hypothetical phenotypes and the continuous fixed points for each parameter value of exogen_canWnt_I in the simulation. The 11 genes give rise to 211 = 2048 different qualitative expression patterns that are compared and the phenotype with the minimal distance Fig 3. Schematic drawing of cardiac tissue in Xenopus laevis at stage 24—Expression of genes in heart fields (left) and RT–PCR analysis of selected genes (right). Panels adapted from Gessert and Kühl [19]. The left panel shows the genes expressed in different domains of the first heart field (FHF) and second heart field (SHF). The SHF is shown at the top and the FHF is shown at the bottom. Common genes expressed in all regions of the FHF and SHF, respectively, are shown on the left. Genes expressed in particular domains are shown on the right. Colors indicate different domains and corresponding expressed genes. The right figure shows the results of single cell RT–PCR analysis of gene expression for the four genes Nkx2.5, Isl1, Tbx1, and Tbx5. Values (0 and 1) and colors red/green represent inactive or active genes. The panel shows the gene expression of different single cell samples (numbered and named at the bottom). FHF and SHF are distinguished by the expression of the Isl1. doi:10.1371/journal.pone.0131832.g003 A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 10 / 15 to a fixed point is then considered to be the phenotype of this fixed point. In order to distin- guish the hypothetical phenotypes we use the naming scheme “PH-X” where X is the decimal number encoding the binary expression pattern of the corresponding phenotype. Fig 4 shows the 7 nearest hypothetical phenotypes that are mapped to the computed fixed points of the BNE. For the genes Isl1, Nkx2.5, Tbx1, and Tbx5 we see the same expression pro- pensity pattern that is referenced in the RT-PCR analysis. The phenotypes FHF6 and SHF4 also correspond to the fixed points of the BN model FHF_BOOL and SHF_BOOL, respectively. The NO_CARDIAC fixed point of the BNE also corresponds to the “no-cardiac” fixed point of the BN. For the remaining phenotypes BNE predicts expression pattern for the FHF7 via PH- 1060 and additionally three new phenotypes. These phenotypes, PH-1076, PH-564, and PH- 692, correspond to the SHF1 based on the four genes measured by RT-PCR [19], however, the data shows that the SHF1 phenotype may have different gene expression propensities for the genes Bmp2, canonical Wnt, and Fgf8 (Fig 4). Stability of fixed points of the BN The Boolean phenotypes predicted by the BN model correspond to the FHF6 and SHF4 pheno- types (Figs 3 and 4). In the BNE these phenotypes correspond to values close to 0 and 1 of the exogen_canWnt_I expression propensity. Consistently, our extension can predict the same phenotypes of the BN model and it shows that under the perturbation of exogen_canWnt_I Fig 4. Phenotypes predicted by the BNE. The phenotype profile used for the mapping is based on the 11 genes present in both the Boolean model and the Xenopus analysis. The figure in the left panel shows the distance curves for the nearest phenotypes and fixed points. The x-axis denotes the values of the parameter exogen_canWnt_I and the phenotypes to which the fixed points were mapped. The y-axis shows the actual distance. The phenotypes are ordered by increasing exogen_canWnt_I expression propensity (right panel). Activated genes are shown in green and deactivated genes are shown in red. The framed box shows the gene expression propensity pattern for the four genes Isl1, Nkx2.5, Tbx1, and Tbx5 that corresponds to the the RT–PCR phenotypes of the FHF and SHF from the Fig 3. The FHF_BOOL and SHF_BOOL phenotypes correspond to the phenotypes found in the Boolean model [16]. The SHF1 phenotype is split in three sub-phenotypes PH-1076, PH-564, and PH-692 that differ by the gene expression propensity of canWnt, Bmp2, and Fgf8. The expression of the Fgf8 gene was not reported in Xenopus. Its activation pattern is a prediction of the BNE. doi:10.1371/journal.pone.0131832.g004 A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 11 / 15 parameter the results remain close to the phenotypes found by the BN model. The 1% attractor, which was assumed not to correspond to any of the heart fields, is also a fixed point of the BNE. In our simulation we additionally analyzed the BN fixed points for stability. In particular, the 1% attractor reported in the Boolean Network model. Any perturbations added to this fixed point resulted in the fixed point corresponding to FHF4 for the given value of exogen_- canWnt_I. This fixed point is thus unstable in the BNE. Discussion We extended the Boolean network model of early cardiac development and identified the bio- logical phenotypes that were previously predicted by the Boolean model as well as additional biological phenotypes that represent a more detailed differentiation of the FHF and SHF in terms of gene expression propensities. These additional phenotypes were confirmed by experi- ments in Xenopus laevis[19]. There are several advantages of the proposed method. Essentially, it helps to characterize the gene expression propensity of phenotypes from the structure given by the BN alone. It cor- responds to the BN model in case of binary inputs. The complexity of the extension can be seen as an intermediate representation between the BN and ODE models. It can cope with con- tinuous values but does not need additional kinematic parameters that are required, e.g., in an ODE model for concentration levels. Considering the possibility theory approach [36], the BNE does not use fuzzy sets and thus is not representable as a possibility. In our case, the fuzzy logic approach is used to extend the Boolean function on the intervals [0, 1]. Different approaches exist that transform a BN into a system of ordinary differential equa- tions. Mendoza and Xenarios [21] partition the genes into activating and inhibiting subsets. Each subset is postulated to activate or inactivate a considered gene in a sigmoid manner add- ing the corresponding terms to the ODE vector field. They do not directly transform the logical rules of the BN, but rather construct the rules according to the activator and inhibitor subsets. They identify fixed points in the system by perturbing the Boolean attractors. By focusing on activation and inhibition of the genes they limit the BN to only a subset of possible Boolean rules for state transition. Conversely, the approach of Wittmann et al. [20] directly transforms the rules of a BN into continuous functions. They include production and decay rates into the rules, thereby introducing additional parameters into the model. Transformation of the contin- uous input variables to continuous switch-like values is done with Hill functions [37–39]. Both approaches have in common that they require additional knowledge either from biological experiments or expert opinion to determine the values for the different parameters. The state space of BN is discrete and finite. The attractors can be exactly determined by sim- ulating the network in an exhaustive manner. In this respect, the BNE has the same limitation as an ODE model. In general, the complete exploration of the search space for identification of fixed points is infeasible and we cannot determine the number of fixed points in the system a priori. Fixed points of the model can only be found numerically by sweeping through the search space. The BNE behaviour resembles that of the Boolean model for small perturbations in the Boolean input. When the Boolean input is perturbed and the functions are evaluated for a sin- gle step, the resulting values of the BNE deviate slightly from the values of the successor state of the corresponding BN. The BNE functions reflect the Boolean rules of the Boolean Network which regulate the expression of genes. The BNE models the influence of genes on other genes in a continuous manner. The resulting values of BNE can be seen as propensity for gene expression. As genes interact with each other via the concentration of gene products, a propen- sity is similar to concentration levels. A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 12 / 15 Similarly to the fixed points of the BN, we relate the resulting fixed points to biological phe- notypes. We use a distance based approach to map fixed points to phenotypes. In order to compare the fixed points we compute Euclidean distances to the biological phenotypes. The hypothetical phenotype which has the shortest distance to a fixed point corresponds to the phe- notype of the fixed point. In case of perfect agreement between the fixed point and the pheno- type the distance is 0. In order to find the best corresponding phenotype to a fixed point it is necessary to exhaustively test the set of all hypothetical phenotypes. Since the values of genes of the fixed points represent only gene expression propensities, one could choose a threshold for which a certain gene propensity becomes either an activation or inactivation of a gene. However, this requires additional knowledge about the property of the gene. Usually, the threshold is not easily determined and the choice may be arbitrary. We avoid choosing a threshold by using the proposed distance based approach. The fixed points of the BNE for the cardiac development are parametrized by the exogen_- canWnt_I parameter. This parameter influences all core genes of the model except for exogenous Bmp2 parameters. This means that the fixed points of the cardiac model are not just single points, but the values of the fixed point are continuous curves that depend directly on the gene expres- sion propensity of the exogenous canonical Wnt. Further, the cardiac model directly encodes the exogen_Bmp2_I as a constant in the model. If we allow interval values for the exogen_Bmp2_I, it would directly influence the interaction of the core genes. This would result in fixed points that depend on two independent parameters and form a plane of fixed points. Here, however, we want to remain faithful to the original Boolean model for cardiac development where the exo- gen_Bmp2_I parameter is needed to be “on” in order to start the FHF and SHF formation [40]. The additional phenotypes, that are described by the fixed points of the BNE, are not found in the BN due to its discrete nature. However, these phenotypes are found to be biologically rel- evant to the early cardiac development. In general, the examination of BN attractors in pertur- bative manner with the BNE makes it possible to further characterize any Boolean model. The attractors of the cardiac development BN model are per definition fixed points in the BNE. In case of the 1% attractor from the Boolean Model, we found that this fixed point is unstable. Any perturbation of this fixed point leads to the FHF phenotype of the BN. In our approach we use the nearest neighbor method to map fixed points to phenotypes. We do so by only considering a subset of genes that are know from the literature. However, once we have mapped the phenotypes, we can explore genes for which no information is avail- able. The gene expression propensity of the additional genes is given by the fixed points of the simulated model. We thus can predict what a phenotype would look like by inspecting the complete set of genes for the nearest hypothetical phenotype as has been shown in the simula- tion of the BNE for the 11 core genes for early cardiac development. Supporting Information S1 Supplementary Information File. Detailed description of the cardiac and cell cycle BN and BNE. Additional information regarding parametric dependency and biological relevance for the subset of modelled genes, simulations with varying exogen_Bmp2_I parameter, and min–max operator. 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Development. 2005; 132:5601–5611. doi: 10.1242/dev.02156 A Boolean Network Model Incorporating Uncertainty PLOS ONE \| DOI:10.1371/journal.pone.0131832 July 24, 2015 15 / 15	26207376	Tbx1 = ( Foxc1.2 ) Fgf8 = ( ( Tbx1 ) AND NOT ( Mesp1 ) ) OR ( ( Foxc1.2 ) AND NOT ( Mesp1 ) ) Tbx5 = ( ( ( ( Tbx5 ) AND NOT ( Tbx1 ) ) AND NOT ( Dkk1 AND ( ( ( NOT Mesp1 AND NOT Tbx5 ) ) ) ) ) AND NOT ( canWnt ) ) OR ( ( ( ( Nkx2.5 ) AND NOT ( Tbx1 ) ) AND NOT ( Dkk1 AND ( ( ( NOT Mesp1 AND NOT Tbx5 ) ) ) ) ) AND NOT ( canWnt ) ) OR ( ( ( ( Mesp1 ) AND NOT ( Tbx1 ) ) AND NOT ( Dkk1 AND ( ( ( NOT Mesp1 AND NOT Tbx5 ) ) ) ) ) AND NOT ( canWnt ) ) exogen_CanWnt_II = ( exogen_CanWnt_I ) Nkx2.5 = ( Tbx1 ) OR ( GATAs AND ( ( ( Bmp2 ) ) ) ) OR ( Tbx5 ) OR ( Isl1 AND ( ( ( GATAs ) ) ) ) OR ( Mesp1 AND ( ( ( Dkk1 ) ) ) ) Foxc1.2 = ( canWnt AND ( ( ( exogen_CanWnt_II ) ) ) ) Bmp2 = ( ( exogen_BMP2_II ) AND NOT ( canWnt ) ) GATAs = ( Tbx5 ) OR ( Nkx2.5 ) OR ( Mesp1 ) Mesp1 = ( ( canWnt ) AND NOT ( exogen_BMP2_II ) ) canWnt = ( exogen_CanWnt_II ) exogen_CanWnt_I = ( exogen_CanWnt_I ) Isl1 = ( Tbx1 ) OR ( Mesp1 ) OR ( Fgf8 ) OR ( canWnt AND ( ( ( exogen_CanWnt_II ) ) ) ) Dkk1 = ( Mesp1 ) OR ( ( canWnt ) AND NOT ( exogen_BMP2_II ) ) exogen_BMP2_II = ( exogen_BMP2_I )
RESEARCH ARTICLE An Extended, Boolean Model of the Septation Initiation Network in S. pombe Provides Insights into Its Regulation Anastasia Chasapi1☯, Paulina Wachowicz2☯, Anne Niknejad1, Philippe Collin2¤, Andrea Krapp2, Elena Cano2, Viesturs Simanis2, Ioannis Xenarios1,3 1 Vital-IT Group, Swiss Institute of Bioinformatics (SIB), Lausanne, Switzerland, 2 Cell cycle control laboratory, Ecole Polytechnique Fédérale de Lausanne (EPFL), SV-ISREC, Lausanne, Switzerland, 3 Swiss-Prot Group, Swiss Institute of Bioinformatics (SIB), Geneva, Switzerland ☯These authors contributed equally to this work. ¤ Current address: Horizon Discovery Group, Campbridge Research Park, Cambridge, United Kingdom * viesturs.simanis@epfl.ch (VS); ioannis.xenarios@isb-sib.ch (IX) Abstract Cytokinesis in fission yeast is controlled by the Septation Initiation Network (SIN), a protein kinase signaling network using the spindle pole body as scaffold. In order to describe the qualitative behavior of the system and predict unknown mutant behaviors we decided to adopt a Boolean modeling approach. In this paper, we report the construction of an extended, Boolean model of the SIN, comprising most SIN components and regulators as individual, experimentally testable nodes. The model uses CDK activity levels as control nodes for the simulation of SIN related events in different stages of the cell cycle. The model was optimized using single knock-out experiments of known phenotypic effect as a training set, and was able to correctly predict a double knock-out test set. Moreover, the model has made in silico predictions that have been validated in vivo, providing new insights into the regulation and hierarchical organization of the SIN. Introduction Schizosaccharomyces pombe, commonly referred as fission yeast, has long been used as a model organism for the study of conserved, essential functions in the eukaryotic cell. It has proved highly informative in the study of the cell cycle, particularly the control of the G2/M transition. Like many somatic higher eukaryotic cells, it divides by binary fission. Cytokinesis in fission yeast is controlled by the Septation Initiation Network (SIN), a protein kinase signaling net- work, which uses the spindle pole body (SPB; the functional counterpart of the centrosome in yeast), as a scaffold from which to initiate signaling. Elements of the SIN signaling architecture have been conserved throughout evolution. In Saccharomyces cerevisiae the corresponding pathway is known as the mitotic exit network (MEN), and controls both cytokinesis and mitotic exit. In higher eukaryotes the equivalent signaling network is the hippo pathway, which regulates cell growth and proliferation [1,2]. PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 1 / 22 OPEN ACCESS Citation: Chasapi A, Wachowicz P, Niknejad A, Collin P, Krapp A, Cano E, et al. (2015) An Extended, Boolean Model of the Septation Initiation Network in S. pombe Provides Insights into Its Regulation. PLoS ONE 10(8): e0134214. doi:10.1371/journal. pone.0134214 Editor: Takashi Toda, Cancer Research UK London Research Institute, UNITED KINGDOM Received: July 3, 2015 Accepted: July 9, 2015 Published: August 5, 2015 Copyright: © 2015 Chasapi et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: This work was funded by a SINERGIA grant from the Swiss National Science Foundation (CRSII3_132392), a Swiss National Science Foundation grant to VS (31003A_138176) and PC (109454) and State Secretariat for Research and Innovation (SEFRI) for IX and AN. PC contributed to the study while being affiliated to VS's research group, before his association with his current affiliation with the Horizon Discovery Group. The Horizon Discovery Group had no funding role, and no The SIN comprises a group of protein kinases and their regulators that induce cytokinesis when CDK activity drops in anaphase [3–5]. Signaling failure results in multinucleated cells, as cytokinesis fails while growth and the nuclear cycle continue [6], which is referred to as the SIN phenotype. Failure to turn off SIN signaling produces multiseptated cells that remain uncleaved and contain one or two nuclei [7]. Ppc89p, Cdc11p and Sid4p form the scaffold upon which signaling proteins are assembled at the SPB [8–11]. SIN signaling requires the action of three kinase complexes. The association properties of SIN proteins with the SPB differ in early and late mitosis (see [12], and references for each protein cited below). The kinase Cdc7p associates with the signaling GTPase Spg1p [13,14], Sid1p associates with its regulatory subunit Cdc14p [4,15] and the kinase Sid2p associates with its regulator Mob1p [16–18]. Asso- ciation of the SIN kinase modules with the SPB during mitosis is considered to indicate that the kinase in question is active (reviewed by [19,20]). The nucleotide status of Spg1p is regu- lated by a bipartite GAP, composed of a catalytic subunit (Cdc16p), which interacts with Spg1p in the context of a scaffold, Byr4p [21,22]. Etd1p regulates the nucleotide status of Spg1p, per- haps by modulating Rho1p signaling [23–26]. Plo1p acts upstream of the SIN [27,28] and coor- dinates SIN activity with other mitotic events. The SIN controls many aspects of cytokinesis including the assembly of the contractile ring and synthesis of the division septum [29]. Our goal is to describe the qualitative behavior of the system, investigate the role of each SIN regulator and potentially predict unknown mutant behaviors. Towards this end we adopted a Boolean modeling approach. The choice of qualitative modeling was based on their suitability to simulate systems with restricted kinetic data, as well as their computational effi- ciency, that permits large numbers of in silico experiments even in networks with hundreds of nodes. Computational models find their origins in engineering science, and have proved to be useful tools with which to analyze complex biological systems (for example [30–32]). The different types of modeling techniques can vary from qualitative Boolean models, to quantitative kinetic- based models; which of them is chosen depends on the type and amount of knowledge and experimental data available for the specific system, as well as the size of the network [33,34]. The cell cycles of fission and budding yeast have long been popular fields of research and several modeling strategies have been employed to understand them [30,35–40]. Models focused on the fission yeast SIN have already been generated by Csikasz-Nagy et al. (2007) and Bajpai et al. (2013) [41,42]. In the study by Csikasz-Nagy et al. the timing of septation in wild type and mutant cells was described using a minimal, continuous model. The SIN components were treated as two groups, the “Top of SIN” and “Bottom of SIN”, with Sid1p localization to the SPB being the pivotal event that differentiates the two groups [42]. In the subsequent model [41], the asymmetric distribution of molecules at the SPBs was analyzed using a simple, non-linear model of two antagonistic molecules. The model was also extended to incorporate key regulators of the SIN [41]. In this work, we present an extended, Boolean model of the SIN, comprising most known SIN components and regulators as individual, experimentally testable nodes. The Boolean framework allows us to perform in silico knock-out and “constant activation” experiments for every combination of molecules present in the model, and to assess phenotypic predictions that could be subsequently validated experimentally. Our model provided useful insights for several aspects of SIN regulation such as the role of Fin1p, the inhibitory function of Nuc2p in interphase, as well as an in silico, counter-intuitive, double mutant phenotypic prediction. The model predicted that Sid4p mutant cells would septate if they express Cdc7p in high levels. The prediction has been experimentally confirmed. This work serves as a good example of the use of qualitative modeling in hypotheses generation and prediction of experimental outcomes in otherwise complicated and long experiments. Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 2 / 22 input into the design or execution of the study. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors declare that they have no conflicts of interest. Results Model construction through expert biocuration An overview of the workflow used for the model construction, optimization and use is pre- sented in Fig 1. For the gene regulatory network construction of the SIN we chose an expert biocuration approach [43,44], taking advantage of the long-term expertise in the Swiss-Prot group. Experimentally determined interactions specific to the SIN, were retrieved, structured, curated and annotated from the literature and from available knowledge databases (for exam- ple Pubmed, iHOP, UniProtKB/Swiss-Prot, ChEBI). To generate the model, we started by add- ing the main SIN signaling regulators such as the GTPase Spg1p, its effector kinase Cdc7p and the GAP Byr4p and Cdc16p [13,21,45]. We then added the SPB scaffold for the SIN, which is comprised of Ppc89p, Sid4p and Cdc11p [10,45]. Subsequently, additional regulators were added to this core unit, to complete a first working model. The collected knowledge was stored in a structure formed of pairwise interactions and regulations that include information about participating components, the origin of publications (PMID), the evidence used to evaluate the interaction was mentioned and a confidence assessment as an evidence tag from the biocurator (a full interaction table provided in S1 Table). The constructed prior knowledge network (PKN) consists of 50 nodes (gene products, pro- teins and complexes) and 124 directed edges (Fig 2A). The regulatory information is the result of the curation of 67 published scientific papers (S1 table). The most recently published interac- tion contained in this model is the inhibitory regulation of CDK and Plo1p upon Byr4p recently published by [46]. The model interactions were classified as activations or inhibitions and they were repre- sented in the network as a combination of Boolean functions that can include AND, OR and NOT [40,47–51]. Qualitative model simulation Despite the intensive study of the SIN over the past decades, there is little kinetic data for the protein interactions described in the literature that form the basis for our model. Obtaining such spatiotemporal data is experimentally difficult and represents one of the major challenges in systems biology research. For the simulation of the SIN model we adopted a qualitative Bool- ean approach, which has been successfully used in several other contexts [30,40,52–62]. In Boolean formalism, each node is characterized by an activation state that can take the val- ues 1 for “active” or 0 for “inactive”, corresponding to the logical values TRUE and FALSE. The activation state can refer to transcription, localization, phosphorylation or other post-transla- tional modifications. For the construction of the SIN model we assumed that for scaffold pro- teins “TRUE” corresponds to a state that permits the assembly of signaling complexes. The state of each node depends on the state of the nodes regulating it, that is, the state of all the incoming edges, and the rules that govern their interaction. The state of all the nodes at a given moment defines the network state. The network transitions from state to state are dic- tated by the underlying Boolean functions, until it reaches a steady state or a cyclic attractor [48]. The possible trajectories in the state space can be represented by the state transition graph [34,63,64]. In Boolean modeling, time is abstract and can be simulated using diverse strategies such as in a continuous manner, with discrete updates or using probabilistic transitions. In the case of discrete time representation, two main updating schemes can be used during model simulation; synchronous and asynchronous update. The former assumes that all biological events in the system have similar timescales, and all functions are updated simultaneously. In the latter, one Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 3 / 22 function is updated at each time step, which can be deterministic (deterministic asynchronous) or randomly selected (stochastic asynchronous) [65,66]. The asynchronous behavior can be controlled by setting additional rules for time delays and priorities [67,68]. Alternatively, all possible transitions can be generated [33,34,67,69]. Fig 1. Model construction and optimization workflow. The Prior Knowledge Network (PKN) is constructed after collecting relevant information from various sources, including network databases and literature. The PKN is translated into logical functions, describing the regulatory relations among gene products. The logical model is simulated under the preferred conditions, resulting in one or more steady states, where all logical rules are satisfied. The model goes then through an optimization procedure, where the goal is to fit the resulting steady states with available experimental data by altering regulatory rules. The optimization typically includes removing outdated / low confidence links, adjusting their representation and adding new regulatory rules. The process is iterated until the simulation fits the available data. The model can then be used as a predictive tool, by performing in silico perturbations. Validation of the predictions can lead to discovery of missing regulatory links that are then added to the PKN. doi:10.1371/journal.pone.0134214.g001 Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 4 / 22 Fig 2. The extended Boolean SIN model. (A) The initial, prior knowledge network, manually re-constructed from the literature. Purple nodes represent proteins and complexes that take part in the regulation of the SIN, and pink nodes represent AND gates. Blue arrows indicate activation events and orange Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 5 / 22 Asynchronous deterministic updating was chosen for the SIN model simulation in this study, since it assumes non-synchronous regulatory events, which is likely to reflect the in vivo situation. However, the challenge in asynchronous update lies in interpreting the simulation trajectories; in stochastic asynchronous simulations, the same initial state can lead to different trajectories in the state space, due to the stochasticity of the updating scheme [34]. The simula- tion algorithm used was based on genysis, a tool for synchronous and asynchronous modeling of gene regulatory networks, based on reduced ordered binary decision diagrams (ROBDDs) [69]. The algorithm identifies all steady states / attractors that can be reached, by efficiently investigating all possible asynchronous state transitions. The use of nodes representing CDK levels as input nodes for SIN activity modeling Cdc2p/CDK1 influences the SIN both positively and negatively. Active Cdc2p inhibits the SIN early in mitosis; its inactivation is required for septum formation and to establish SIN protein asymmetry [3,4,70–72]. Furthermore, Cdc2p and the Byr4p-Cdc16p GAP may cooperate to prevent septation in interphase [73]. However, Cdc2p and Plo1p also collaborate positively to ensure removal of Byr4p from the SPBs and facilitate SIN signaling in anaphase [46]. Failure to increase CDK levels during early mitosis will block cytokinesis, since the cells do not enter mitosis. However, constant, high CDK levels through mitosis will block cytokinesis. Thus, CDK levels need to increase to permit entry into mitosis, after which cytokinesis will occur. However, this will only happen once CDK activity decreases to a very low level, and cells exit mitosis. The model must therefore accommodate these CDK-dependent regulatory events. Towards this goal, we introduced three independent nodes for CDK, representing the CDK levels before, during and after mitosis. CDK-L corresponds to the low CDK levels during inter- phase; these prevent re-replication of DNA, but are insufficient for entry to mitosis [74,75], CDK-H represents the high level of CDK activity found in early mitosis. Finally, CDK-0 repre- sents the very low CDK activity in late mitosis as cells undergo the M-G1 transition. This multi-node representation of CDK allows us to describe the SIN-related phenotypes corre- sponding to several stages of the cell cycle, using the CDK nodes as inputs. For example, setting CDK-L constantly on, indicates that we are simulating the events during interphase, while, CDK-H on represents early mitosis and CDK-0 on represents late mitosis (Fig 2B). It should be stressed that the 3 CDK nodes are not regulated themselves, but are rather used as control (i.e. input) nodes for the system’s simulation. For this reason, there are no incoming regulatory links towards the CDK nodes (CDK-L, CDK-H and CDK-0) (Fig 2B). Model refinement and simulation results This model configuration that uses CDK levels as control nodes for the simulation of cell cycle events, allowed us to clearly define the expected steady states of the system and set our refine- ment strategy. First, we attributed the PKN interactions involving CDK to the correct CDK node. For example, an activation link from CDK-H was added towards Plo1p (Fig 2B), which in turn will reinforce the activity of CDK in a positive feedback loop [28,76]. Following the attribution step, the model was evaluated using a number of well characterized in silico circles inhibition events. Other logical functions, such as AND, OR and NOT regulatory gates are also encoded in the model. SAC: spindle assembly checkpoint, APC: anaphase-promoting complex, PP: protein phosphatase. (B) The final, optimized model, which uses a 3-node representation of CDK activity. Nodes in green are used as switches, and they are turned on to represent different stages of the cell cycle: interphase, early mitosis and late mitosis. Pink nodes represent AND gates. In the case of the Cdc42p regulatory link towards Byr4p, the regulatory rule can be phrased as “NOT Cdc42p activates Byr4p”. doi:10.1371/journal.pone.0134214.g002 Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 6 / 22 perturbations whose phenotypic consequences are known; knock-out of cdc11, spg1, cdc16, byr4, and cdc7. For the evaluation, the above 5 knock-out perturbations were simulated, by set- ting the corresponding node to 0 throughout simulation. A fixed set of nodes, with activation states indicative of the expected phenotype was selected to score the model’s ability to correctly reproduce the mutation outcomes. The scoring set includes sid4, cdc11, byr4-cdc16, spg1, cdc7, sid2-mob1 and sid1-cdc14. For each in silico perturbation, the resulting steady states were eval- uated according to the number of the scoring set nodes that had the expected activation state (see S1 Fig for a list of the scoring set expected states). We proceeded by refining the connections within the network. A refinement cycle consisted of altering an edge of the network, perturbing the model and evaluating the simulation out- come of the perturbations test set. The alterations could involve additions and deletions of reg- ulatory edges, or modifications of the existing regulatory rules. The reasoning behind each change of the model’s regulatory rules was based on several factors, such as the confidence level of each interaction, coupled with information from the published literature, as well as forming alternative logical rules of the given information to better represent the biological real- ity of the interaction. For example, “A inhibits B” can be alternatively encoded as “NOT A acti- vates B”, and is more suited for cases where the inhibition is not dominant. During this process we maintained the known, required connections of the model and minimized the model’s com- plexity by removing nodes that no longer served any regulatory role in the model. An example of the latter is the removal of cell cycle regulatory elements such as Cdc25p, Wee1p, Slp1p and Rum1p, to simplify the cell cycle representation by using multi-node CDK. The final, opti- mized network is presented in Fig 2B. A full list of the edges comprising the final network, together with the justification for the inclusion of each edge, can be found at the supplementary material (S2 Table), as well as the model in genYsis and SBML-Qual format (S1 and S2 Files respectively) [77]. The optimized model was used for in silico experiments in which a combination of nodes was perturbed and the phenotypic outcome in the interphase, early mitosis and late mitosis CDK-states were determined. A simulation of the wild type model, where no perturbation is introduced, is presented in Fig 3. To simulate interphase, CDK-L is set to 1, and Ppc89p is set to 1 as well, to permit “binding” of scaffold proteins to the SPB. In interphase, the model simulation results in a steady state where Byr4p and Cdc16p are present and able to form the GAP complex, therefore active. The scaffold proteins Sid4p and Cdc11p are also present (therefore “active” according to our initial assumption for scaffold molecules), but no SIN signaling occurs due to the inhibitory effect of the Byr4p-Cdc16p GAP. Early mitosis is simulated by setting CDK-H and Ppc89p to 1. The SIN scaffold is still formed, as expected. Cdc16p is absent from the SPBs in early mitosis, preventing formation of the GAP. This allows SIN signaling to initiate, and we observe that all the main components of the SIN are active (Plo1p, Spg1p, Cdc7p, Sid2p-Mob1p), apart from Cdc14p-Sid1p, which is inhibited by high CDK activity [4,70]. Late mitosis is represented by setting CDK-0 and Ppc89p to 1 during the simulation. There are 2 resulting steady states of the system simulation. In one state, the SIN signaling scaffold is present, the Byr4p-Cdc16p complex is formed, and all SIN components, except Plo1p are inac- tive. In the other state, Byr4p-Cdc16p is not active, and all proteins of the SIN scaffold and sig- naling including Cdc14p-Sid1p are active. Intriguingly, these resemble the asymmetric constellation of proteins observed at the old and new SPBs in late anaphase B (see [19,20,29] for review), with the exception of Sid2p-Mob1p, which is present on both SPBs, but only active in one of the two states of the model. Setting GAP function to 0 abolishes the state that resem- bles the old SPB. Though it is often assumed to be the case, there is scant evidence to support Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 7 / 22 the view that localization of SIN proteins to the SPB is a faithful readout of their in vivo activity. There is no data addressing whether Sid2p signals from one or two SPBs in late anaphase. Fig 3. In silico steady states of the SIN, in wild type and mutated cells. Steady states deriving from simulations performed on the final model. The boxes on the left indicate the experiments performed, which can be knock-out (KO) or over-expression (OE). When there is more than one gene in the box, it is a double perturbation. For each perturbation, 3 experiments were performed: interphase simulation (indicated as i), early mitosis (eM) and late mitosis (lM, with suffixes new and old when there are 2 resulting steady states, indicative of late mitosis asymmetry). Blue boxes correspond to active proteins, white to inactive and light blue to proteins that can be either active or inactive at the resulting steady states of the system. doi:10.1371/journal.pone.0134214.g003 Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 8 / 22 Future experiments will investigate this. A detailed heatmap showing the activation state of all nodes of the model for all experiments presented herein can be found in the supplementary material (S2 Fig). Assessing experimentally validated in silico perturbations for the model evaluation The optimized model can describe the SIN related events during interphase, early and late mitosis. In order to evaluate the model’s ability to describe current knowledge regarding S. pombe mutants, we performed a series of in silico knock-out and constant activation experi- ments mimicking those described in the literature that have an established phenotype. Fig 3 summarizes the steady states yielded after simulating interphase, early and late mitosis behav- ior of core gene mutants. Interestingly, in all the in silico experiments we obtained steady states where the nodes displayed, overall, the expected activation state. More specifically, cdc11 knock-out completely blocks septation. Both, byr4 knock-out and cdc16 knock-out have the same effect, which is failure to inhibit SIN signaling, and therefore SIN triggering in interphase. In a knock-out of either spg1 or cdc7, signaling fails, with Spg1p still getting activated in cdc7 deletion, indicating that Spg1p acts upstream of Cdc7p, as experimentally proven. Apart from the experiments that were used as training set for the model refinement, we per- formed double mutant experiments towards which the model had not been optimized (test set). These experiments assess the predictive value of the model, as the in silico predictions are in accordance with the expected results. Specifically, the double deletion of cdc11 and cdc16 simulation predicts that cells should not septate, as shown in Fig 3, with supporting evidence from the literature [78]. A Cdc7p over-expression in an spg1 deletion mutant will septate, in agreement with in vivo studies [13]. Moreover, Cdc7p over-expression will produce septation in the absence of Cdc11p (Fig 4A), as confirmed by the literature [79]. In this project, setting a node to 1 throughout the simulation has been used to simulate over-expression in silico, except in cases where it is known that the over-expression phenotype results from an indirect effect, such as the titration of another protein. Other in silico experiments performed during the optimization provided us with great insights into potential knowledge gaps regarding SIN regulation, as well as the limitations of our model. One such example was a prediction that a byr4-null sid4-null should septate. When this was tested in vivo, the double mutant cells did not septate. This allowed us to refine the model, by identifying regulatory links that would permit this state to be achieved and target them as candidates for edge deletion. Moreover, the nuc2 inhibitory links that were present in the PKN revealed our limitation of describing events that occur at the end of septation and the incomplete regulatory inputs to cdc16 helped us discover a potential link with fin1. The nuc2 and fin1 cases are discussed in detail below. Does Nuc2p have a role in interphase? Increased expression of the APC/C component nuc2 blocks septation, while incubation of nuc2-663 at low restrictive temperature results in cutting of the cell [82,83]. Analysis of how the SIN is reset at the end of mitosis revealed an APC/C-independent role for Nuc2p [84]. Nuc2p interferes with formation of the Cdc7p-Spg1p complex, possibly by stimulating the GAP activity of Byr4p-Cdc16p. Since our current model does not include resetting of the SIN, we tested whether the inhibitory link of nuc2 towards the Cdc7p-Spg1p complex should be maintained. If it is required, then it might indicate a role for Nuc2p in regulating septation in interphase, once the cell has completed the M-G1 transition. We therefore modeled the effect of inactivating Nuc2p in silico upon SIN behavior in interphase. The predicted outcome when Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 9 / 22 including the Nuc2p inhibitory link was two steady states; one with inactive SIN and one with cells that septate in interphase. To test whether this could be the case in vivo, the strain nuc2-663 atb2-mCherry leu1-32 was arrested in S-phase by growth in medium containing 12mM hydroxyurea (HU). After 5h at 25°C, cells were shifted to 36°C to inactivate Nuc2p, and samples were analyzed at hourly inter- vals. Before shift to 36°C nuc2-663 (97%; N = 403 cells) and nuc2+ cells (97%; N = 480) were mononucleate with no septum; the interphase arrest was confirmed by the presence of an inter- phase array of microtubules (data not shown). Following shift of the cultures to 36°C, the majority of nuc2+ cells remained in interphase for three hours, as judged by the continued pres- ence of interphasic microtubules and the absence of a spindle (97%; N = 498, and 90%; N = 400 Fig 4. Cdc7p over-expression in a sid4 mutant will result in septation. (A) Steady states of in silico, double mutation experiments. The model predicts that in the absence of SIN scaffold proteins (Cdc11p or Sid4p) and over-expression of Cdc7p, the cell will septate. (B) sid4-SA1 leu1-32 was transformed with a REP1-based plasmids [80] expressing cdc7; empty vector served as a control. Cells were grown to exponential phase in EMM2 medium at 25°C containing 2mM thiamine. Expression was induced by washing with EMM2 and growth for 16h at 25°C; cells were then shifted to 36°C for 5h, fixed, and stained with DAPI and Calcofluor as described [81]. Note that the cells carrying empty vector have become elongated and multinucleated, while 75% of cells expressing cdc7 have one or more septa. The scale bar represents 10 μm. (C) The strain leu1::pADH1-cdc7 was grown to exponential phase in YE medium at 19°C. A sample was taken and cells were fixed and stained with DAPI and Calcofluor. The remainder of the culture was incubated for 5h at 36°C before fixation. Note the elevated percentage of septated cells. The scale bar represents 10 μm. (D) The indicated strains were grown to exponential phase in YE medium, counted, and diluted to 106 ml-1. 10 μl of serial 5-fold dilutions were spotted on plates, allowed to dry and then incubated at the indicated temperature until the wild-type control had formed colonies. doi:10.1371/journal.pone.0134214.g004 Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 10 / 22 at, 1 and 2h respectively;). The nuc2-663 cells maintained the hydroxyurea arrest less effi- ciently, (89%; N = 319, and 86%; N = 636 at 1, and 2h, respectively). When nuc2-663 cells entered mitosis, they arrested with a mitotic spindle (not shown). A fraction of both nuc2+ and nuc2-663 cells septated in the first two hours, but this did not exceed 5%. In contrast, previous studies from this lab [73] and the Hagan lab [85] showed that activation of the SIN in inter- phase-arrested cells by incubation of the cdc16-116 mutant at 36°C produced >50% of type II (mononucleated, septated cells; defined by Minet et al. [7]) within 100 minutes. The levels of septation observed in this experiment are far lower, and, given the similar levels in nuc2+ and nuc2-663, most likely reflect slippage of the hydroxyurea arrest. This leads us to conclude that Nuc2p does not play a major role in preventing septation in interphase, once the M-G1 transi- tion has been completed. Contrary to traditional studies, where models are constructed from available data and are then used for the experimental design of predictive simulations, our modeling approach is bidi- rectional: in vivo experiments were performed to choose among refinement strategies during model optimization, as well as the model was used to predict experimental outcomes (Fig 1). The case of nuc2 regulation is an example of the former. Keeping all nuc2 SIN-related prior knowledge in the multi-node CDK level model required the presence of a dual inhibitory con- trol of the SIN in interphase by both Byr4p-Cdc16p and Nuc2p. In vivo experiments were per- formed to identify the events that can be described by the model and, consequently, guide its refinement strategy. The in vivo data argue against a post START role for Nuc2p, in addition to that ascribed to it at the M-G1 transition. Therefore, nuc2 was removed from the final, model presented here, which does not describe the M-G1 transition in its current form. Fin1p over-expression may contribute to inactivation of the GAP for Spg1p at mitotic onset Fission yeast has a single orthologue of the conserved never-in-mitosis (nimA) kinase, called fin1 [86]. Fin1p is not essential, but is important for spindle formation and regulates the affin- ity of Plo1p to the SPB [87]. Fin1 mutant cells are delayed in the G2-M transition and Fin1p is in part regulated by Sid2p [88]. This link between fin1 and the SIN prompted us to include fin1 in the SIN regulatory circuit. In the PKN of the model there were no negative regulators targeting GAP components dur- ing early mitosis, which resulted in suboptimal outcomes during the simulations of early mito- sis; i.e. the simulation would produce a steady state where the GAP remained active in early mitosis. Since removal of the SIN GAP from the SPB is an early step in the activation of the SIN after entry into mitosis [12,74,89], we modeled whether GAP components could be regu- lated by fin1. Since Cdc16p contains several sites matching the established consensus for mam- malian Nek2 (one of the orthologues of nimA), the effect of increased expression of fin1 on Cdc16p localization was investigated by in vivo experiments. Expression of fin1 from the medium strength nmt-41 promoter [80] resulted in partial displacement of Cdc16p-GFP from SPBs in interphase cells (Fig 5A). Quantification of the SPB-associated signal of Cdc16p-GFP in interphase cells revealed that it was significantly decreased upon expression of fin1 (Fig 5B). This was not due to a significant alteration of the steady state level of Cdc16p (Fig 5C). Interestingly, the decreased level of Cdc16p-GFP at the SPB resulted in 24% of REP41-fin1 cells forming one or more septa in interphase, compared to <1% in the empty-vector control. This is consistent with previous studies [73,85], which demonstrated that inactivation of cdc16- 116 in interphase cells promotes septation in interphasic cells. Therefore, the reduced level of Cdc16p-GFP at the SPB may decrease the extent to which the SIN is inhibited by lowering the amount of GAP available to inhibit Spg1p signaling. Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 11 / 22 Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 12 / 22 Previous studies have shown that in the absence of GAP function, Fin1p acts as an inhibitor of the SIN [85]. This study suggests that increased levels of Fin1p result in the reduction of Cdc16p levels at the SPB, and therefore potentially to the activation of the SIN at the entry into mitosis. This may point to a dual role of Fin1p in SIN regulation, which will be addressed in future studies. Fin1p is implicated both in mitotic commitment, and in SIN regulation [85,88]. Expression of fin1 promotes recruitment of Plo1p to the SPB in interphase cells [87], and Plo1p is involved in the displacement of Byr4p from the SPB in anaphase [46]. Future studies will examine the mechanism by which Fin1p contributes to the decrease in Cdc16p at the SPB. An unexpected prediction: cells overexpressing Cdc7p will septate in the absence of Cdc11p or Sid4p The final, optimized model describes the existing knowledge of the SIN, in wild type and known mutants. One of the main goals of developing this Boolean model was to use it predictively by performing in silico perturbations of interesting and/or experimentally challenging mutants. The regulatory relationships described in this model predict that increased expression of Cdc7p should produce septation in the absence of Cdc11p and Sid4p (Fig 4A). Previous studies have shown that Spg1p overexpression will induce septation and permit colony formation in a cdc11 mutant [13], but not a sid4 mutant [91]. Moreover, increased expression of Cdc7p will permit cdc11 mutants to form colonies [79]. In contrast to the situation with Spg1p overexpression, induction of Cdc7p expression from the very strong nmt1 promoter in sid4-SA1 at 36°C did not permit colony formation, but septa were formed in the cells (Fig 4B). To test whether increased expression of Cdc7p would permit growth of a sid4 mutant, cdc7 was expressed from the ADH1 promoter, integrated at leu1. The leu1::pADH1-cdc7 strain has a very high septation index at 19°C (>90%) and is barely capable of colony formation at 25°C and above (Fig 4D), with cells dying multiseptated at higher temperatures (Fig 4C). The strain sid4-SA1 leu1::pADH1-cdc7 was capable of colony formation at 27°C and 29°C (Fig 4D), where neither parental strain could do so. Previous studies have shown that increased expression of cdc7 increases the level of kinase activity in immunoprecipitates of Cdc7p [79]. This shows that septation can occur if the function of the scaffold proteins is compromised, provided the expression of Cdc7p is sufficiently elevated. This raises the intriguing possibility that SIN signaling in this case originates in the cytoplasm, bypassing the need for assembly on a SPB-associated scaffold. The nature of the SIN protein sig- naling complexes present in these cells will be the subject of future studies. Discussion In this paper we use qualitative Boolean modeling to represent and explore the regulatory rela- tionships of genes participating in the Septation Initiation Network of fission yeast. Qualitative Fig 5. Fin1p over-expression results in Cdc16p disassociation from the SPB. (A) Cells expressing the labeled tubulin marker leu1::m-Cherry-atb2 and cdc16-GFP were induced to express fin1 from the medium strength nmt41 promoter [80]. Cells transformed with empty vector served as control. Cells were grown in medium without thiamine for 27h at 25°C. Cells were imaged and the intensity of SPB associated cdc16-GFP signal was analyzed as described in [12]. The panel shows m-Cherry-atb2 leu1::cdc16-GFP(ura4+) cells bearing REP41 or REP41-fin1. The scale bar is 10 μm. (B) The SPB associated signal was determined in interphase cells in each strain. Since REP41-fin1 eventually leads to a mitotic arrest [87] interphase cells were identified by the presence of an interphasic microtubule array. The box shows 25%-75% range for the population, the line indicates the median. The bars indicate 10% and 90% range for the population, and dots indicate more extreme individual values. The y-axis shows fluorescence intensity on an arbitrary scale. (C) Cells bearing the leu1::cdc16-HA allele were induced to express fin1 (ON) by growing them in defined minimal medium [81] in the presence (OFF) or absence (ON) of 2mM thiamine. Protein extracts were prepared 27h after induction and analyzed by western blotting using monoclonal antibody 12CA5. The anti-α- tubulin monoclonal antibody TAT-1 [90] was used as a control. doi:10.1371/journal.pone.0134214.g005 Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 13 / 22 modeling is a powerful method for systems with restricted kinetic information and it is compu- tationally efficient, allowing for thousands of in silico experiments in a short time, even in net- works with hundreds of nodes. Moreover, it can be used predictively, to test combination of mutations that would otherwise be time consuming, expensive and/or experimentally challeng- ing to undertake. The value of such models increases significantly when the model is coupled with in vivo experiments. Such experiments can be used to evaluate the regulatory rules, help the optimization procedure and test the predictions of the model (Fig 1). We report the construction of an extended, Boolean model of the SIN network that uses CDK levels as control nodes to simulate SIN related events in interphase, early mitosis and late mitosis. The prior knowledge network was manually curated, providing a trustworthy initial framework that could then be further optimized (Fig 1). Information reported in literature (and used in network databases) can be conflicting, outdated, incomplete or based on in vitro knowledge only. Therefore, expert biocuration provides a significant advantage in order to fil- ter the available information and construct a comprehensive network. We optimized the model using in silico experiments with well-established outcomes based on in vivo data, in order to recapitulate the SIN state in different stages of the cell cycle (Fig 1). A challenging aspect of qualitative modeling, and especially of asynchronous update, is to interpret the resulting steady states of the simulations. This is because the simulation might result in a number of steady states that are theoretically possible but never reached in vivo. Our approach was to use CDK levels as an initial condition for the simulation, indicating the stage of the cell cycle that the simulation corresponds, to reduce unrealistic simulation outcomes. We further restricted the simulation space by taking as a fact that the scaffold has the potential to be constructed at all times by setting the SIN-SPB linker protein Ppc89p to 1. The optimization process under the controlled environment of CDK switches provided important insights into SIN regulation during the cell cycle. In the case of the fin1, the incorrect simulation results that were obtained in early mitosis helped us locate a potential missing link in the PKN. Increased expression of fin1 removes Cdc16p from the SPB. At present we do not know whether this is by direct phosphorylation of Cdc16p or an indirect effect; this will be the subject of future analysis. However, the important point in this context is that the modeling revealed the requirement for an additional control point to turn off the GAP in early mitosis. The optimization strategy was also useful in evaluating the limitations of our model. An exam- ple of this is the role of Nuc2p in SIN regulation. In the PKN there were several inhibitory links from Nuc2p to SIN kinases, indicating the events in SIN resetting, after septation [84]. The use of CDK switches restricts the cell cycle events that can be modeled, and our model does not presently incorporate resetting of the SIN at the M-G1 transition. Our modeling predicted that if Nuc2p continued to activate the GAP in interphase, extending the role proposed for it at the M-G1 transition [84], then its inactivation in post-START cells could result in septum forma- tion; in vivo analysis showed this was not the case. Thus, the modeling was useful in this case to define the possible limits of the extent of the time-window in which Nuc2p is active towards the SIN. The great value of creating an optimized qualitative model is that it can then be used predic- tively to perform difficult or iconoclastic experiments in silico. We focused on testing whether an over-expression of SIN kinases would rescue SIN scaffold mutants. The model’s prediction was that over-expression of Cdc7p in a cdc11 or sid4 knock-out will still septate, a prediction that was experimentally validated. The model can be used in the future for any combination of gene mutants, and hopefully provide interesting hypotheses that can be tested experimentally. Future studies will aim to model the M-G1 transition, and to incorporate spatial components into the model (protein localization to one or both SPB, cytoplasm or division site). This will be facilitated by the incorporation of the cell cycle Boolean module of fission yeast, by Davidich Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 14 / 22 & Bornholdt [30]. We will also incorporate multivariate nodes to simulate the effect of changes in the post-translational modifications of SIN proteins during the cell cycle [41,92,93]. This should allow modeling of the role of the asymmetry of SPBs with regard to SIN protein associa- tion, building upon the analysis performed by Bajpai et al. [41]. Future versions of the model will attempt to incorporate Etd1p. Though its effects upon SIN signaling are clear, the pub- lished analyses do not provide a sufficiently clear, direct link to SIN components to permit its unequivocal incorporation into the model presented here. Our extended, Boolean model of the SIN can be used by the scientific community for testing various hypotheses in silico, including multiple gene perturbations that can be experimentally challenging. The model can be reduced to a minimum number of nodes and still capture the system steady states (see S3 File). Though a reductive approach can be a useful aid in under- standing the information flow in the system, the greater complexity of the extended model sys- tem increases the predictive value of the model, as we can use the model nodes for testing the desired experimental scenarios. Finally, it is worth noting that qualitative models such as the one presented here are over- simplifications of the actual regulatory processes; in our case of the regulation of the SIN. With advances in live monitoring of cell division and development of new fluorescent probes, we should be able to generate more accurate quantitative models for such a system. Our approach is nevertheless an important step towards a more comprehensive model that recapitulates known biology of the SIN and can be used as a hypothesis generator for complex experimental design. Materials and Methods Literature database construction For the construction of the PKN, several online resources were curated to retrieve SIN relevant information, such as Pathguide, Pubmed, iHOP, iRefWeb, Scholar Google, PriME and Uni- ProtKB/Swiss-Prot. The collected information was stored in a structure formed of pairwise interactions and regulations that includes information about participating components, the origin of publications (PMID) where the interaction was mentioned and a confidence level as an evidence tag from the biocurator. In detail, the database contains the following columns: 1. Node 1: The name of the first element of the interaction, the one that acts as activator or inhibitor 2. Action: A symbol characterizing the type of interaction as activation (->) or inhibition (-\|) 3. Node 2: The name of the second element of the interaction, the one that gets activated or inhibited 4. Node 1 type: The type of node 1. Can be protein, complex or miRNA 5. Node 2 type: The type of node 2. Can be protein or miRNA 6. UniProt ID 1: Reference of node 1 7. UniProt ID 2: Reference of node 2 8. PMID: Literature reference of the interaction 9. Class: A letter characterizing the confidence level of the interaction. It can be one of the following: Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 15 / 22 Sure (S), when the interaction is confirmed or known in textbook, and/or already in the Uni- Prot general annotation lines. Sure interactions are generally associated with many PMIDs. Unsure (U), when the interaction is shown once and/or not confirmed by others, or when the authors are not confident about the results. Inferred (I), when there are no results for the network in question, but the interaction was found in different cell types and/or organisms. It may also refer to cases where the informa- tion is inferred to all protein isoforms of a gene without confirmed results. Inferred interac- tions might be associated with more than one PMIDs. Contradictory (C), when the interaction is based on contradictory results. 10. Evidence tag: Short extract from the publication where the interaction is mentioned. GenYsis Boolean modeling toolbox All Boolean simulations of the SIN model, including the identification of wild type attractors and in silico perturbation experiments, we performed using the genYsis Boolean modeling tool- box. GenYsis uses reduced ordered binary decision diagrams (ROBDDs) in order to efficiently compute attractors and steady states of large networks. ROBDDs are directed acyclic graphs that can represent Boolean functions efficiently, and are computationally suitable for complex Boolean operations. To map gene regulatory networks on ROBDDs the network has to be transformed into Boolean functions that represent the dynamics of the model. All the opera- tions that can be performed on Boolean functions can also be performed on their correspond- ing ROBDD representations [69]. The simulation modes available with genYsis include synchronous and asynchronous updating. In both cases, the user has the possibility of perform- ing in silico perturbations by fixing the activation state of one or multiple components during simulation. The perturbation possibilities comprise (a) knock-out experiments, were the selected components are set to be inactive during the whole simulation, (b) over-expression experiments, were the selected components are set to be active during the whole simulation, and (c) initial state experiments, where the selected components have a fixed activation state at the beginning of the simulation that is thereafter allowed to change according to the regulatory rules. The software binaries of genYsis are available for Linux (64 bits gcc version 4.4.5, Debian 4.4.5–8) and Mac OS X (64 bits gcc version 4.2.1, Mac OS X 10.8.5) at http://www.vital-it.ch/ software/genYsis. Fission yeast techniques (A) Media. Growth and manipulation of S. pombe was performed according to standard protocols [81]. Defined medium was EMM2 with supplements at 100 mg/l as required, and complete medium was YE [81]. Cell number was determined using a hemocytometer. For the induction of nmt1 regulated genes, cells were grown to exponential phase (approx. 2-3x 106 ml-1) in EMM2 containing 2 μM thiamine with additional supplements as required. Cells were washed twice in medium without thiamine, and then grown for the time indicated in the Fig legends. (B) Molecular and Genetic analyses. Strains were constructed by standard genetic meth- ods. Vectors [80,94] and cdc7 plasmids [79] have been described previously. (C) Imaging and image analysis. Living cells were imaged using a U-Plan-S-Apo 60× N. A. 1.42 objective lens mounted on an Olympus IX-81 spinning disc confocal microscope. The temperature was maintained using a custom-built heating system. Fixed cells were photo- graphed on a Zeiss Axiophot microscope using a Zeiss 100x NA 1.4 PLAN-apochromat lens. Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 16 / 22 Images were captured on a Nikon Coolpix camera. Level adjustment and cropping were per- formed using Adobe Photoshop CS6. DAPI and Calcofluor staining was performed on cells that had been harvested by centrifu- gation, washed, and fixed with cold 70% (v/v) ethanol, as described previously [95]. Micros- copy analysis of living cells was performed as described in [12], using the RodcellJ imageJ plugin [96]. Data were plotted using GraphPad Prism v6. In the whisker plots the box shows 25%-75% range for the population, the line indicates the median. The bars indicate 10% and 90% range for the population, and dots indicate more extreme individual values. Supporting Information S1 File. The SIN model in genYsis format. The final model in genYsis format can be used for any combination of in silico experiments using the genYsis software. (ZIP) S2 File. The SIN model in SMBL qual format. The final model in SBML qual format can be used to perform additional analyses in most qualitative modeling platforms. (ZIP) S3 File. Model reduction analysis. A reduction analysis performed using GINsim [97], highlighting the information flow that is necessary for the maintenance of the system’s steady states. (PDF) S1 Fig. The model optimization scoring set. The experiments used to score the model candi- dates during the optimization phase are represented in the y axis and the proteins used for scoring in the x axis. The table uses the same color coding as the article figures: blue for Bool- ean state 1, white for Boolean state 0 and light blue for oscillation or, in this case, two alterna- tive steady states with different activation states of the given protein. (TIF) S2 Fig. Detailed in silico results of final model simulations. A detailed heatmap showing the activation state of all nodes of the final model for all experiments presented in this paper. (TIF) S1 Table. Prior Knowledge Network interaction table. A complete list of the interactions included in the Prior Knowledge Network of the SIN. (PDF) S2 Table. Final model interaction list. The list of interactions comprising the final, optimized model, together on comments justifying their alteration / addition. (PDF) Acknowledgments We thank Iain Hagan (Paterson institute for Cancer Research, Manchester, UK) for the fin1 expression plasmids and Keith Gull (Oxford, UK), for TAT-1. A special thanks to Julien Dorier (SIB Swiss Institute of Bioinformatics, Lausanne, Switzerland) for the constructive discussions all along this project. Boolean Model of the S. pombe SIN PLOS ONE \| DOI:10.1371/journal.pone.0134214 August 5, 2015 17 / 22 Author Contributions Conceived and designed the experiments: IX VS. Performed the experiments: AC PW AN VS PC AK EC. Analyzed the data: AC PW PC. Wrote the paper: AC VS PW IX. References 1. Bardin AJ, Amon A (2001) Men and sin: what's the difference? Nat Rev Mol Cell Biol 2: 815–826. PMID: 11715048 2. Seshan A, Amon A (2004) Linked for life: temporal and spatial coordination of late mitotic events. 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RESEARCH ARTICLE A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle Elizabeth Ortiz-Gutiérrez1,2, Karla García-Cruz1, Eugenio Azpeitia1,2¤, Aaron Castillo1,2, María de la Paz Sánchez1, Elena R. Álvarez-Buylla1,2* 1 Instituto de Ecología, Universidad Nacional Autónoma de México, 3er Circuito Exterior, Junto a Jardín Botánico Exterior, México, D.F. CP 04510, México, 2 Centro de Ciencias de la Complejidad-C3, Universidad Nacional Autónoma de México, Ciudad Universitaria, Apartado Postal 70–275, México, D.F. 04510, México ¤ INRIA project-team Virtual Plants, joint with CIRAD and INRA, UMR AGAP, Montpellier, France * eabuylla@gmail.com Abstract Cell cycle control is fundamental in eukaryotic development. Several modeling efforts have been used to integrate the complex network of interacting molecular components involved in cell cycle dynamics. In this paper, we aimed at recovering the regulatory logic upstream of previously known components of cell cycle control, with the aim of understanding the mechanisms underlying the emergence of the cyclic behavior of such components. We focus on Arabidopsis thaliana, but given that many components of cell cycle regulation are conserved among eukaryotes, when experimental data for this system was not available, we considered experimental results from yeast and animal systems. We are proposing a Boolean gene regulatory network (GRN) that converges into only one robust limit cycle attractor that closely resembles the cyclic behavior of the key cell-cycle molecular compo- nents and other regulators considered here. We validate the model by comparing our in sil- ico configurations with data from loss- and gain-of-function mutants, where the endocyclic behavior also was recovered. Additionally, we approximate a continuous model and recov- ered the temporal periodic expression profiles of the cell-cycle molecular components involved, thus suggesting that the single limit cycle attractor recovered with the Boolean model is not an artifact of its discrete and synchronous nature, but rather an emergent con- sequence of the inherent characteristics of the regulatory logic proposed here. This dynam- ical model, hence provides a novel theoretical framework to address cell cycle regulation in plants, and it can also be used to propose novel predictions regarding cell cycle regulation in other eukaryotes. Author Summary In multicellular organisms, cells undergo a cyclic behavior of DNA duplication and deliv- ery of a copy to daughter cells during cell division. In each of the main cell-cycle (CC) PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 1 / 28 a11111 OPEN ACCESS Citation: Ortiz-Gutiérrez E, García-Cruz K, Azpeitia E, Castillo A, Sánchez MdlP, Álvarez-Buylla ER (2015) A Dynamic Gene Regulatory Network Model That Recovers the Cyclic Behavior of Arabidopsis thaliana Cell Cycle. PLoS Comput Biol 11(9): e1004486. doi:10.1371/journal.pcbi.1004486 Editor: Reka Albert, UNITED STATES Received: February 27, 2015 Accepted: August 3, 2015 Published: September 4, 2015 Copyright: © 2015 Ortiz-Gutiérrez et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: This study was financed with the following grants: CONACyT:180098 and 180380 (ERAB), 152649 (MPS); and UNAM-DGAPA-PAPIIT: IN203113 (ERAB) and IN203814 (MPS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. stages different sets of proteins are active and genes are expressed. Understanding how such cycling cellular behavior emerges and is robustly maintained in the face of changing developmental and environmental conditions, remains a fundamental challenge of biol- ogy. The molecular components that cycle through DNA duplication and citokinesis are interconnected in a complex regulatory network. Several models of such network have been proposed, although the regulatory network that robustly recovers a limit-cycle steady state that resembles the behavior of CC molecular components has been recovered only in a few cases, and no comprehensive model exists for plants. In this paper we used the plant Arabidopsis thaliana, as a study system to propose a core regulatory network to recover a cyclic attractor that mimics the oscillatory behavior of the key CC components. Our analy- ses show that the proposed GRN model is robust to transient alterations, and is validated with the loss- and gain-of-function mutants of the CC components. The interactions pro- posed for Arabidopsis thaliana CC can inspire predictions for further uncovering regula- tory motifs in the CC of other organisms including human. Introduction The eukaryotic cell cycle (CC) in multicellular organisms is regulated spatio-temporally to yield normal morphogenetic patterns. In plants, organogenesis occurs over the entire lifespan, thus CC arrest, reactivation, and cell differentiation, as well as endoreduplication should be dynamically controlled at different points in time and space [1]. Endoreduplication is a varia- tion of the CC, in which cells increase their ploidy but do not divide. Normal morphogenesis thus depends on a tight molecular coordination among cell proliferation, cell differentiation, cell death and quiescence. These biological processes share common regulators which are influ- enced by environmental and developmental stimuli [1–3]. It would not be parsimonious to depend on different regulatory circuits to control such interlinked cellular processes, CC behaviors and responses. Thus we postulate that a common network is deployed in all of them. Such overall conserved CC network may then connect to different regulatory networks under- lying cell differentiation in contrasting tissue types or to signal transduction pathways elicited under different conditions, and thus yield the emergence of contrasting cellular behaviors in terms of cycling rate, entrance to endocycle, differentiation, etc. Furthermore, the overall CC behaviors are widely conserved and robust among plants and animals. Hence, we aim at further investigating the collective behavior of the key upstream reg- ulators and studied CC components to understand the mechanisms involved in the robustness of CC regulation under changing developmental stages and environmental conditions faced by plants along their life-cycles. Previous studies, that have shown the oscillatory behavior of sev- eral transcription factors, that had not been associated as direct regulators of the CC, support our proposed hypothesis [4]. We thus propose to uncovering the set of necessary and sufficient regulatory interactions underlying the core regulatory network of plant CC, including some key upstream transcriptional regulators. Computational tools are essential to understanding the collective and dynamical behavior of these components within the regulatory networks involved. As a means of uncovering the main topological and architectural traits of such networks, we propose to use Boolean formal- isms that are simple and have proven to be useful and powerful to follow changes in the activity of regulators of complex networks in different organisms and biological processes [5, 6]. Although the key CC components have been described in different organisms, the complex- ity and dynamic nature of the molecular interactions that are involved in CC regulation and Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 2 / 28 the emergence of the cyclic behavior of the CC molecular components are not well understood yet. The use of systemic, dynamic and mathematical or computational approaches has been useful towards this already. Previous models have focused mainly on yeast and animal systems and have been useful to analyze many traits of CC behavior such as robustness, hysteresis, irre- versibility and bistability [7–11]. The latter two properties have been validated with experimen- tal data [12–14]. We herein summarize the main traits and components of the eukaryotic CC. The molecular CC regulators have been described and they are well conserved across distantly related organ- isms [15, 16]. CC progression is regulated by Cyclin-Dependent Kinases (CDKs) [17] that asso- ciate with different cyclins to confer substrate specificity [18]. CDK-cyclin complexes trigger the transition from G1 (Gap 1) to synthesis phase (S phase) in where the genome is duplicated, and from G2 (Gap 2) to mitotic phase (M phase) for the delivery of the newly duplicated DNA to the two daughter cells [19] (see for a review [17, 20]). The CDK-cyclin activity also regulates the cell transit between G and S phases during the endoreduplication process [21, 22]. Two CDKs (CDKA and CDKB) are involved in CC regulation. CDKA;1-CYCDs and CDKA;1-CYCA3 complexes regulate G1/S and S phase progression [23–25]; while CDKB-CYCA2 and CDKB-CYCBs regulate G2/M phase and M progression [26–28]. Thus CDK-cyclin activity is finely-tuned by phosphorylation, interactions with CDK inhibitors such as Kip-related proteins (KRPs), and degradation of cyclins and KRPs by Skp1/Cullin/F- box (SCF), as well as by the anaphase-promoting complex/Cyclosome (APC/C) [29–31]. Besides these components, plant CC machinery has a greater number of CC regulators than other eukaryotes and some of those components such as the CDKB are plant-specific. Several key transcriptional regulators participate in the G1/S and G2/M transitions [32]. The E2F/RBR pathway regulates G1/S transition by transcriptional modulation of many genes required for CC progression and DNA replication [33, 34]. While E2Fa and E2Fb with their dimerization partner (DP) activate transcription of a subset of S phase genes, E2Fc-DP represses transcription [35]. The function of E2Fa and E2Fb is inhibited by their interaction with RBR [36]; in G1/S transition CDKA;1-CYCD-mediated RBR hyperphosphorylation, releases E2Fa/b-DP heterodimers allowing transcriptional activation of E2Fa and E2Fb targets. Simultaneously the E2Fc-DP transcriptional inhibitor is degraded [37]. Little is known about the regulation of G2/M transition in plants, however a class of con- served transcription factors belonging to the MYB family has been described, that seem to have key roles in CC regulation. MYB transcription factors have a prominent role during G2/M transition, by regulating, for example, CYCB1;1 which is determinant in triggering mitosis [38–43]. For the mitosis exit, APC/C mediates degradation of the mitotic cyclins as CYCB1;1 and CYCA2;3, inactivating CDK-cyclin complexes. CCS52A2, an activator subunit of APC/C, is transcriptionally inhibited by E2Fe [44]. Some previous models have recovered the limit cycle attractor as well for CC components [45–48]. A pioneer model of the CC focused on mitotic CDK-cyclin heterodimer and a cyclin protease oscillatory behavior [49]. On the other hand, Novak and Tyson incorporated addi- tional nodes and interactions to model the G1/S and G2/M transitions of the S. pombe CC [50, 51]. They also analyzed evolutionary roles of CC regulators [52], mutant phenotypes [53], sta- ble steady states [7] and the role of cues such as cell size or pheromones in CC progression [54, 55]. Additionally, comprehensive CC continuous models [45] and generic modules for eukary- otic CC regulation [56, 57] have been proposed. In addition to continuous formalisms, CC models have used discrete approaches as Boolean models for yeast and mammalian systems [46–48, 58–61], and more recently, hybrid models for mammalian cells have been published [62]. Subsequently, time-delayed variables [63] and variables defining CC events [47, 48] were incorporated. Time robustness was improved with Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 3 / 28 specifications of the temporal order with which each component is activated [60]. Recent pub- lished reports on CC dynamics use steady state probability distributions and potential land- scapes, and highlight the enormous potential of CC models to characterize normal and altered regulation of mammalian CC [64, 65]. Yeast CC Boolean models with summatory thresholds [58, 59], incorporated self-degrada- tion for proteins, but did not incorporate several negative regulators explicitly. In a later work [61], nodes were kept active when the summatory effect of their regulators was greater than the activation threshold, which implies self-degradation of the protein, when such summatory is equal to or below the threshold. Fauré and Thieffry have transformed CC Boolean models, that use threshold functions, to models with a combinatorial scheme, and they have also presented a broader discussion about these two approaches to logical frameworks [66]. Two Boolean models of budding yeast CC and another one of mammalian CC recover cyclic attractors [46–48]. The mammalian CC model [46] also recovers a fixed-point attractor corre- sponding to G0. In another study, Fauré and collaborators integrated three modules to yield a comprehensive model for the budding yeast CC GRN [47]. The components included variables to represent cellular growth, citokinesis, bud formation, DNA replication and the formation of the spindle. The yeast CC model by Irons also included variables of CC events (e.g. bud forma- tion or DNA replication) as well as time delays [48]. In contrast to other eukaryotes, in Arabi- dopsis thaliana (A. thaliana herein) very few attempts have been made to integrate available experimental data on CC regulators using mechanistic models. Only a study that considers the G1/S transition has been proposed and contributed to show some additional conserved features of this CC control point among eukaryotes [67]. We integrated available experimental data on 29 A. thaliana regulatory interactions involved in CC progression into a Boolean discrete model, that recovers key properties of the observed plant CC. The regulatory network, that we put forward, also incorporates three uncovered inter- actions, based on animal systems (E2Fb ! SCF, CDKB1;1-CYCA2;3 a E2Fa, APC/C a SCF), as well as 16 interactions based on bioinformatic analyses. Therefore, the latter proposed interac- tions constitute new predictions that should be tested experimentally. The use of yeast or animal data is supported by the fact that main CC components or regulatory motifs are conserved among eukaryotes [16]. In our model, we include solely molecular components and avoid artifi- cial self-degradation loops, which have been used for recovering the limit cycle attractor. We vali- dated the model simulating loss- and gain-of-function lines, and hence demonstrate that the Boolean network robustly implements true dynamical features of the biological CC regulatory network under wild type and genetic alterations. Possible artifacts due to the discrete dynamical nature of the model used, and of its synchronous updating scheme, were discarded by comparing the Boolean model results to those of a continuous approximation model. The continuous model indeed recovers the robust limit cycle that mimics the dynamical behavior of CC components under a wide range of parameters tested. Finally, we provide novel predictions that can be tested against biological experimental measurements in future studies. The model put forward consti- tutes a first mechanistic and integrative explanation to A. thaliana CC. Materials and Methods Boolean model We proposed a Boolean approach to integrate and study the qualitative complex logic of regu- lation of the molecular components underlying the CC dynamics. We formalized available experimental data on logical functions and tables of truth that rule how the state of a particular component is altered as a function of the states of all the components that regulate it. In a Bool- ean model each node state can be 0, when the expression of a gene or other type of molecular Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 4 / 28 component or complex of such components is unexpressed or “OFF”, or 1 when it is expressed, or “ON”. Nodes states are updated according to the function: Xi(t+1) = Fi(Xi1(t), Xi2(t), . . ., Xik(t)), where Xi(t+1) is the state of Xi gene at time t+1 and Xi1(t), Xi2(t), . . ., Xik(t) is the set of its regulators at time t. The set of logical rules for all the network components defines the dynamics of the system. By applying the logical rules to all nodes for several iterations, the dynamics of the whole network can be followed until it reaches a steady state; a configuration or set of configurations that does not change any more or are visited in a cyclical manner, respectively. Such state is called an “attractor”. Single-point attractors only have one GRN con- figuration, or cyclic attractors with period n, which have n configurations that are visited indef- initely in the same order. In this paper we propose a GRN model that converges to a single limit cycle attractor that recovers the CC molecular components’ states of presence (network configuration) in a cyclic pattern that mimics the pattern observed for the molecular compo- nents included in the model along the different CC phase. Model assumptions A. thaliana CC Boolean model has the following assumptions: 1. Nodes represent mRNA, proteins or protein complexes involved in CC phase transitions. Node state “ON” is for the presence of regulator, and “OFF” is for absence; in the latter case, it may also indicate instances in which a component may be present but non-functional due to a post-translational modification. 2. The state of the RBR (RETINOBLASTOMA-RELATED) node corresponds to a 1 or “ON” when this protein is in its hypo-phosphorylated form and therefore is ready to inhibit E2F transcription factors. 3. When a particular CDK is not specified, a cyclin can form a complex with CDKA;1, a kinase that is always present because it is expressed in proliferative tissues [68] during the complete CC. 4. E2Fa, E2Fb and E2Fc need dimerization partner proteins (DPa or DPb) for its DNA-bind- ing. Given that DP expression does not change drastically in CC [69], we assumed that the state of these heterodimers is given only by the presence of E2F factors. 5. The Boolean logical functions integrate and formalize experimental data available mainly for the A. thaliana root apical meristem, however some data from leaves were considered, and we assumed that these are also valid for CC regulation in the root meristem. Also, data from other systems and data obtained by sequence promoter analysis were considered as indicated in each case [27, 39, 40, 67, 70–85] (summarized in Table 1). 6. The dynamics of complex formation (such as CDK-cyclin and KRP1, or RBR and E2F fac- tors) are specified directly in the Boolean function of their target genes. For instance, the logic rule for E2Fb is E2Fa & !RBR, indicating that E2Fb state is “ON” when it is transcrip- tionally activated by E2Fa free of RBR. All E2Fa targets also included in their logical rules RBR, as is shown in S1 Text. Then, the presence of KRP1 or RBR in a logical rule does not imply that they are regulators acting directly on the corresponding target. 7. The updating scheme for the node states was synchronous. Periodic expression and promoter sequence analysis Most regulatory interactions and logical rules were obtained from the A. thaliana data [20, 21, 25–27, 29, 30, 35, 37, 38, 40, 43, 44, 78–80, 85–103] (detailed in Table 2). A. thaliana CC- Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 5 / 28 dependent expression data for validation was obtained from: [72–74]. The consensus site used for MYB77 was CNGTTR, according to: [75, 76], while that for MYB3R4 was AACGG accord- ing to: [43]. The motifs were searched in the regulatory sequences of all network nodes using Pathmatch tool (http://arabidopsis.org/cgi-bin/patmatch/nph-patmatch.pl) of TAIR. Regula- tory sequences in TAIR10 Loci Upstream Sequences-1000bp and TAIR10 5’ UTRs datasets were used. Software for robustness analysis and mutant simulation We used BoolNet [104] (a library of R language [105]) and Atalia(Á. Chaos; http://web. ecologia.unam.mx/achaos/Atalia/atalia.htm) to simulate the CC GRN dynamics and perform robustness, and mutant analyses. Systematic alterations in Boolean functions for robustness Table 1. Hypothetical Interactions for the A. thaliana CC Network. Regulator Target Data supporting the proposition of the interaction Refs. E2Fb ! SCF F-box protein Skp2 is part of the SCF complex and is transcriptionally regulated by E2F1 in humans. In A. thaliana, it has only been reported that E2F factors regulate FBL17, another F-box protein. [67, 70] E2Fb ! MYB77 Direct regulation between E2F and MYB factors has been reported in budding yeast and mammals, but in plants it could include at least one intermediary; A. thaliana could have a similar regulation because its CC also presents transcriptional waves in G1/S and G2/M transitions as yeasts and mammals. After analyzing the two main families of transcription factors involved in CC regulation: TCP and MYB, we propose MYB77 as a mediator between E2F and MYB regulation. Using available microarray analyses, we found that MYB77 shows CC-dependent expression with a peak in M phase. In addition to having binding sites for E2F, with the identiﬁcation of the binding site recognized by MYB77, we can hypothesize that MYB77 regulates MYB3R1/4 and other CC genes. [39, 71–74] MYB77 ! E2Fe, KRP1, MYB3R1/4, CYCB1;1, CYCA2;3, CDKB1;1, CCS52A2 The sequence CNGTTR identiﬁed as a consensus site recognized by MYB77 was used to ﬁnd its possible targets among CC core genes. Several of them are expressed just before G2 to M phase transition. [75–77] MYB3R1/4 ! SCF, RBR, CDKB1;1, CYCA2;3, APC/C, E2Fc, MYB3R1/4, KRP1 The consensus site of MYB3R4 was found in SKP2A, RBR, CDKB1;1, CYCA2;3, CCS52A2, KRP1, E2Fc, MYB3R1/4 and CYCB1;1 by in silico analysis described in the Materials and Methods section. In tobacco, NtmybA1 and NtmybA2 genes have the MSA sequence and they can regulate themselves. MYB3R1/4 might promote the expression of KRP1, since KRP1 has a peak of expression in G2/M and has eight putative MSA elements. CYCB1;1 regulation by MYB3R1/4 also has experimental support. [40, 78] CDKB1;1-CYCA2;3 a E2Fa It has been hypothesized that a cause of low levels of E2Fa could be due to its high turnover rate as result of CDKB1;1 phosphorylation. This E2F factor has putative CDK-phosphorylation sites in its N-terminal end, and a high CDK activity inversely correlates with its DNA binding ability in vitro. This hypothesis is supported by observations in mammalian cells. [27, 79–81] APC/C a SCF It was proposed that APC/C and SCF functions are mutually exclusive during CC progression, which led to the identiﬁcation of the relationship amongst them. In proliferating mammal cells, levels of Skp2, a SCF subunit, oscillate under the pattern of APC/C substrates. Furthermore, the APC/C subunit Cdh1 participates in the degradation of Skp2 and the reduction of Cdh1 expression stabilizes Skp2. A. thaliana SCF and APC/C seem have the same roles during CC as their animal counterparts. [82–85] A summary of the data led us to propose interactions that have not been previously described for A. thaliana CC. a stands for negative regulation and ! for positive regulation. doi:10.1371/journal.pcbi.1004486.t001 Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 6 / 28 analyses were done with Atalia, while stochastic perturbations in random networks to compare attractor’s robustness were done with BoolNet. For random perturbations made in transitions between network configurations or in Boolean functions, the “bitflip” method was applied. To validate the GRN model proposed here, we used BoolNet and simulated loss- and gain-of-func- tion mutations for each node, by skipping the node’s logical rule and setting the respective gene to “0” and “1”, respectively. Table 2. Experimental Interactions for the A. thaliana CC Network and their Evidence. Regulator Target Description of the interaction Refs. CDKA;1-CYCD3;1 a RBR Studies suggest that complexes formed by CDKA;1 and D-type cyclins phosphorylate RBR. [20, 86–89] CDKA;1-CYCD3;1 a RBR– E2Fb E2Fb–RBR complex diminishes in CYCD3;1 overexpressor line. [90] CDKA;1-CYCD3;1 a E2Fc CDKA;1 bound to D-type cyclin affects formation of E2Fc-DPb complex and its binding to DNA. The recognition of E2Fc by the SCF complex depends on phosphorylation mediated by CDKA;1. [35, 37, 91] SCF a CYCD3;1 SCF is involved in the ubiquitination required for CYCD3;1 degradation. [92] SCF a KRP1 SCF ubiquitinates KRP1 to be degraded. [85, 93] SCF a E2Fc E2Fc shows the accumulation in skp2a mutant (subunit of SCF); the overexpression of SKP2A reduces levels of E2Fc. [35, 91] RBR a E2Fa/b RBR is a negative regulator of E2Fa/b transcriptional activity. [90] E2Fa ! E2Fb E2Fb transcription is induced in E2Fa overexpressor line. [94] E2Fa ! E2Fc E2Fc has binding sites for E2F and it is induced in E2Fa-DPa overexpressors. [80, 94] E2Fa ! RBR Transcriptional control of RBR is under E2Fa transcriptional activity. [95] E2Fa ! APC/C CCS52A2, a component of APC/C, is induced when RBR-free E2Fa is overexpressed. [90] E2Fb ! CYCB1;1 CYCB1;1 expression is induced when RBR-free E2Fb increases; targets of E2Fb are genes needed for G2/M transition. [79, 80, 90] E2Fb ! CDKB1;1 Inducible expression of E2Fb promotes CDKB1;1 expression. [79] E2Fb ! E2Fe E2Fb induces transcription of E2Fe. [96] E2Fc a CDKB1;1 The effect of E2Fb can be countered by E2Fc; with E2Fc destabilization increments CDKB1;1. [96, 97] E2Fc a CYCB1;1 CYCB1;1 expression increases when E2Fc expression is silenced; E2Fc overexpression reduces CYCB1;1 level. [37] E2Fc a E2Fa E2Fa messengers increase when E2Fc expression is silenced. [37] E2Fc a E2Fe E2Fc counteracts the positive effect that E2Fb has in the expression of E2Fe. [96] E2Fe a APC/C Expression of CCS52A, a subunit of APC/C, is downregulated by E2Fe. [44] MYB3R1/4 ! CYCB1;1 MYB3R1/4 recognizes the sequence AACGG required for CYCB1;1 expression; other regulators seem to drive its G2/M-speciﬁc expression. [38, 43] CDKB1;1 – CYCA2;3 CYCA2;3 interacts with CDKB1;1 to form a functional complex. [25, 27] CDKB1;1-CYCA2;3 a KRP1 In complex with CYCA2;3, CDKB1;1 could promote KRP1 proteolysis as promotes KRP2 proteolysis; both KRPs could have similar roles in mitosis entry, since both interact with CDKA;1 and are expressed in G2/M. [21, 27, 78] CDKB1;1, CDKA;1 – CYCB1;1 B-type cyclins interact with B-type and A-type CDKs. [25, 26] CDKA;1-CYCB1;1 ! MYB3R1/ 4 The overexpression of MYB3R4 enhances the 2-fold activity of its target promoters in comparison to WT, and the co-expression of MYB3R4 and CYCB1;1 enhances them 4-fold; CycB1 and other mitotic cyclins enhances the activity of NtmybA2 factors in tobacco. [40, 98, 99] KRP1 a CYCD3;1 KRP1 is able to interact with CDKA;1 and CYCD3;1. [29, 93, 100, 101] KRP1 a CYCB1;1 KRP1 binding to CDKA;1 inhibits the activity of CDKA–CYCB1;1. [30, 100] APC/C a CYCB1;1 The APC/C complex ubiquitinates CYCB1;1 to be degraded. [102] APC/C a CYCA2;3 CYCA2;3 is stabilized with loss-of-function mutations in APC/C subunits or with mutations in its D- box. [27, 103] Summary of experimental evidence supporting interactions of A. thaliana CC GRN. a represents negative regulation, ! is for positive and — represents the formation of functional complex. doi:10.1371/journal.pcbi.1004486.t002 Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 7 / 28 Continuous model For the continuous model, we followed [106, 107]. In the continuous version of the model the rate of change for each xi node is represented by a differential equation that comprises produc- tion as well as decay rates: dxi dt ¼ e0:5h þ ehðoiÞ ð1 e0:5hÞ ð1 þ ehðoi0:5ÞÞ gixi ð1Þ The parameter h determines the form of the curve; when h is very close to 0, the curve becomes a straight line, while with values close to 100, the curve approximates a step function. The parameter ωi is the continuous form of Fi(Xi1(t), Xi2(t), . . ., Xik(t)) used in the Boolean model, and γi is its degradation rate. Detailed information about the continuous model can be found in S2 Text. Results The regulatory network recovers a dynamical model of A. thaliana CC The CC model proposed here integrates and synthesizes published data for A. thaliana CC components interactions, as well as some molecular data from other organisms (mammal and yeast), that we propose as predictions for A. thaliana CC regulation, and assume to be con- served among all eukaryotes. The whole set of interactions and nodes included in the model and detailed in Tables 1 and 2 are shown in Fig 1. Four types of molecular interactions can be distinguished: (i) transcriptional regulation, (ii) ubiquitination, (iii) phosphorylation and (iv) physical protein-protein interactions. Additionally, an in silico analysis of transcription factors and promoters was carried out, in order to further substantiate 16 predicted interactions in the GRN (these are: E2Fb ! MYB77; MYB77 ! E2Fe, MYB3R1/4, KRP1, CYCB1;1, CYCA2;3, CDKB1;1 and CCS52A2; MYB3R1/4 ! SCF, RBR, CDKB1;1, CYCA2;3, APC/C, KRP1, E2Fc and MYB3R1/4). The logical rules are available in S1 Text. Our results show that the nodes and interactions considered are sufficient to recover a single robust cyclic steady state, and thus the cyclic behavior of the components considered. Such behavior closely resembles the periodic patterns observed during actual CC progression, Fig 2. The first two columns or network configurations match a G1 state, given that during the early G1 phase, the CDKA;1-CYCD3;1 complex is absent or inactive by the presence of KRP1 [92, 93, 108]. The CDKA;1-CYCD3;1 state is given only by the presence of CYCD3;1 since CDKA;1 is always expressed in proliferative cells [68]. To facilitate understanding, in Fig 2 the complex CDKA;1-CYCD3;1 is shown instead of only CYCD3;1. The absence of mitotic cyclins (CYCA2;3 and CYCB1;1) at this stage [28, 38], as well as the APC/C presence until the early G1 phase, which is needed for the mitosis exit, also coincides with experimental observations [44, 109, 110]. The presence of the RBR protein in G1-phase implies an inactive state of the E2F, as expected [33, 111, 112]. Then, the third column resembles G1/S transition, where the presence of CDKA;1-CYCD3;1 complex would be inducing RBR phosphorylation and its inac- tivation [32]. In the fourth configuration, the S-phase is represented by RBR inactivation and E2Fa/b transcriptional activation [113]. In the fifth and sixth configuration, E2Fc state returns to “ON” but RBR state is kept in “OFF”, which indicates that transcription driven by E2Fa and E2Fb can still happen. Indeed, the E2Fb factor appears from the fifth configuration and it is consistent with their function regulating the expression of genes needed to achieve the G2/M transition. In the sixth configuration, MYB77 is turned on, although in synchronization experi- ments it has been observed to be on until the beginning of mitosis [73]. During G2-phase the MYB transcription factors and KRP1 are expressed [31, 73, 93], the former would maintain Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 8 / 28 dimers of CDKA;1 and mitotic cyclins inactive; and together, this data is consistent with what is observed in the seventh configuration of the CC attractor. In the eighth column, KRP1 is lost because it was phosphorylated by CDKB1;1-CYCA2;3, which is active in the G2/M transition and the onset of mitosis [27]. The phosphorylation of KRP1 drives its degradation and poste- rior activation of mitotic complexes such as CDKA;1-CYCB1;1 to trigger mitosis [21, 78] (con- figuration 9 and 10 in Fig 2). The lack of APC/C at the onset of mitosis is determinant for the accumulation of the mitotic cyclins, but APC/C presence is necessary for the mitosis exit [110], which occurs in the eleventh configuration of the attractor (Fig 2). Thus, our CC GRN model recovers a unique attractor of eleven network configurations (Fig 2), which shows a congruent Fig 1. Regulatory network of the A. thaliana CC. The network topology depicts the proteins included in the model as well as the relationship among them. Nodes are proteins or complexes of proteins and edges stand for the existing types of relationships among nodes. The trapezoid nodes are transcription factors, the circles are cyclins, the squares are CDKs, the triangle represent stoichiometric CDK inhibitor, the hexagons are E3-ubiquitin ligase complexes and the octagon is a negative regulator of E2F proteins. Edges with arrow heads are positive regulations and edges with flat ends illustrate negative regulations. The red edges indicate regulation by phosphorylation while blue ones indicate ubiquitination, the green ones show physical protein-protein interactions and the black edges transcriptional regulation. Only CDK-cyclin interactions are not represented with a line. Interactions to or from rhombuses stand for interactions that involve the CDK as well as the cyclin. A solid line indicates that there is experimental evidence to support such interaction and dotted lines represent proposed interactions grounded on evidence from other organisms or in silico analysis. doi:10.1371/journal.pcbi.1004486.g001 Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 9 / 28 cyclic behavior of its components with that observed experimentally. This result validates that the proposed set of restrictions converge to a single cyclic behavior, which is independent of the initial conditions. A further validation of the proposed CC model, would imply that the recovered cyclic attractor is robust to permanent alterations, as is the case for real CC behavior that is highly robust to external and internal perturbations [14, 58, 114, 115]. The CC Boolean model is robust to alterations To provide further validation for the proposed CC regulatory network, we performed robust- ness analyses of the attractor to four types of alterations in the logical functions of the model. First, we altered the output of each logical rule by systematically flipping one by one, each one of their bits. We found that 87.47% of the perturbed networks recovered the original attractor, while 1.77% of the altered networks maintained the original attractor and produced new ones (see supplementary material S3 Text for details). In contrast, the remaining 10.76% of alter- ations reduced the number of network configurations of the original attractor. In the second robustness analysis, after calculating the transitions between one network configuration to the next one, one bit (i.e. the state of a node) of this next configuration is randomly chosen and its value changed. Then, the network is reconstructed and its attractors recovered again. This pro- cedure was repeated 100 times, thus we found that in 88.2 ± 3.2 out of the 100 perturbations (mean ± SD) the original attractor was reached. These results suggest that the proposed GRN for A. thaliana CC is robust to alterations as expected and in coincidence with previous GRN models proposed for other developmental processes [116, 117]. To confirm that the robustness recovered in these two types of analyses is a specific property of the network under study, we performed robustness analyses of randomly generated Fig 2. Attractor corresponding to a dynamic network of CC in A. thaliana. 100% of the whole set of network configurations converges to a unique attractor composed by 11 configurations. Each column is a network configuration (state of each network component) and the rows represent the state of each node during CC progression. The squares in green indicate components that are in an “ON” state and the ones in red are nodes in an “OFF” state. doi:10.1371/journal.pcbi.1004486.g002 Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 10 / 28 networks with similar structures (same number of input interactors for the logical functions) to the one proposed here for the A. thaliana CC regulatory network, and compared the above robustness analyses results to those recovered for equivalent analyses for the random networks. We generated 1000 random networks. Then, 100 copies of the random and of our network were done. In each copy we randomly flipped the value of one bit in one logical function (to confirm the first robustness analysis), or in one next configuration (for the second robustness analysis). When perturbations are made in logical functions, the A. thaliana CC GRN recovers its attractor in 68% of perturbations, while the median of percentage of cases in which such attractor was recovered in the random networks was only 18.55% (mean 19.12% ± 13.86 SD, Fig 3A). The difference between the 68% of this latter analysis and the 87.47% of the first robustness analysis could be due to sampling error. If transitions between network configura- tions are perturbed, the median of original attractors recovered in random networks is 24.2% (mean 24.6% ± 18.2 SD). In contrast, the original attractor of A. thaliana CC GRN was found in 88% of perturbed networks starting with that grounded on experimental data (Fig 3B). These results confirm that the CC GRN proposed here is much more robust than randomly generated networks with similar topologies and suggests that its robustness is not due to overall structural properties of the network. Boolean models can produce cyclic dynamics as an artifact due to their discrete nature and the time delays implied. To address this issue we approximated the Boolean model to a contin- uous system of differential equations following [106, 107, 118, 119]. To recover steady states of such continuous system, the continuous versions of the GRN were evaluated for 1000 different randomly picked initial conditions (See S2 Text). In all cases and independently of the method- ology (i.e. [106, 107] or [118, 119]), we recovered the same limit cycle steady state. In the con- tinuous model, key cyclins for the main phase transitions, CYCD3;1 and CYCB1;1, have an oscillatory behavior that is not attenuated with time (Fig 4). Importantly, this result is robust to changes in the decay rates or alterations of the h parameter that affects the shape of activation function (see details in S2 Text); the limit cycle was recovered in 92.86% of the cases. The results of the continuous model corroborate that the limit cycle attractor recovered by the Bool- ean version, is not due to an artifact associated to the discrete and synchronous nature of the Boolean model, but is rather an emergent property of the underlying network architecture and topology. In addition, the recovery of the cyclic behavior of the continuous model constitutes a further robustness test for the Boolean model. Previous studies have also tested asynchronous updating schemes [46]. In this study we have used a continuous form of the model to discard that the recovered cyclic attractor is due to an artifact owing to the discrete and synchronous nature of the model used. Future studies could approach analyses of asynchronous behavior of the model by devising some priority classes dis- tinguishing fast and slow processes, and thus refining the asynchronous attractor, under a plausi- ble updating scheme. On the other hand, biological time delays may be involved in CC progression, but they are not enough for irreversibility. The CC unidirectionality has been pro- posed to be a consequence of system-level regulation [120], here we hypothesize that the ordered transitions of A. thaliana CC are an emergent property of network architecture and dynamics. Simulated loss- and gain-of-function mutants recover observed patterns: normal CC and endocycle An additional validation analysis for the proposed A. thaliana CC model implies simulating loss- and gain-of-function mutations and comparing the recovered attractors with the expres- sion profiles documented experimentally for each mutant tested. We simulated mutants by fix- ing the corresponding node to 0 or 1 in loss- and gain-of-functions mutations, respectively. Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 11 / 28 Fig 3. Attractor robustness analysis. Random networks with similar structure to A. thaliana CC GRN were less tolerant to perturbations than original CC GRN. The frequency of perturbations that recovered the original attractor after a perturbation in the Boolean functions, is shown in: (A), where the red line indicates that A. thaliana CC GRN recovers its original attractor in 68% of perturbations (the median of random networks was 18.55% and mean 19.12% ± 13.86 SD). When transitions between network configurations are perturbed (B), A. thaliana CC GRN recovers its original attractor in 88% (vertical red line) of perturbations, while the median of random networks that recover the original attractor was 24.2% (mean 24.6% ± 18.2 SD). Vertical blue line indicates the 95% quantile. 1000 random networks were analyzed. doi:10.1371/journal.pcbi.1004486.g003 Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 12 / 28 The recovered altered configurations are summarized in S4 Text, and in Table 3 as well as in Table 4 for gain- and loss-of-function mutants, respectively. The simulated mutant attractors are coherent with experimental data in most cases [2, 21, 23, 30, 35, 37, 43, 44, 76, 79, 80, 88, 90–93, 103, 108, 109, 111, 113, 114, 121–129]. In Fig 5 we show a representative example of attractors recovered by simulations of CDKB1;1 and KRP1 loss-of-function and APC/C and E2Fa gain-of-function mutants. It is noteworthy that several simulated mutants, such as mitotic cyclins or B-type CDK loss-of-function, converge to a cyclic attractor that corresponds to the configuration observed under an endoreduplicative cycle (e.g. Fig 5A). In such attractors, endoreduplication inductors, such as APC/C, KRP1 and E2Fc [37, 78, 130] are present, at least in some network configurations (Fig 5A, 5C and 5D-right). Another outstanding feature of these mutant attractors is that, although mitotic CDK-cyclin complex may be present, it is inhibited by KRP1, therefore there is no CDK-cyclin activity to trigger the onset of mitosis. These data are coincident with the reported regulation during the onset of endoreduplication [21]. In the attractors where E2Fa coincides with alternating states of RBR, it suggests that DNA replication may occur (Fig 5). Likely due to plant redundancy, some mutations do not produce an obvious impaired phenotype. Such is the case of KRP1 loss-of-function, in which loss-of-function simulation, a cyclic attractor identical to the original one is recovered, as is expected (see Table 4), because such mutants do not show an evident altered CC behavior (Fig 5B) [93]. Interestingly, the simulation of a constitutively active APC/C also converges to a single cyclic attractor, which corresponds to an endoreduplication cycle, since it has Gap and S phases, but lacks an M-phase configuration. This coincides with the experimental observation that the overexpression of one of the APC/C subunits (CCS52A) promotes entry to an endo- cycle [44] (see Table 3). Another interesting example is the gain-of-function mutation of E2Fa that yields two cyclic attractors, one corresponding to the normal CC cycle and the other one Fig 4. Continuous version of the A. thaliana CC Boolean model. In this graph we show the activity of the CDKA;1-CYCD3;1 and the CDKA;1-CYCB1;1 complexes as a function of the amount of cyclins, and KRP1 inhibitor. The CDK-cyclin activity is the limiting factor to pass the G1/S and the G2/M checkpoints. A little more than two complete CC are shown (upper horizontal axis) to confirm that oscillations are maintained. doi:10.1371/journal.pcbi.1004486.g004 Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 13 / 28 to an endocycle (Table 3). It has been shown that this gene is required for both processes [111] that are apparently exclusive, although in both processes the DNA replication occurs and among E2Fa targets there are genes required for S-phase. Thus our model suggests that the reg- ulation of E2Fa at the end of G2 phase is decisive for CC exit and transition to endoreduplica- tion. In this E2Fa gain-of-function simulation, we found an inconsistency with APC/C because this E3 ubiquitin ligase is decisive for endoreduplication, while in the simulated attractor is only present in one network configuration (Fig 5D-right). Such behavior observed in the endoreduplication attractor for E2Fa gain-of-function leads to unstable activity in the CDK- cyclin complex (Fig 5D), thus suggesting that the increase in APC/C is required for endoredu- plication entry as well as its progression. In the attractor of the simulated APC/C gain-of-func- tion, the states of the CYCD3;1, SCF, E2Fb, E2Fc and MYB nodes are more stable than in Table 3. Phenotypes of gain-of-function mutations in CC components. Node Phenotypes of gain of function Recovered attractor(s) Refs. Model CYCD3;1 Inhibition of CC exit, increases division zones and ectopic divisions. Decreases G1 phase duration and increases G2 duration. Delays expression of G2/M genes. Fixed-point attractor of G2-phase. [108, 121] PA SCF SKP2A gain-of-function enhances proliferation, and increases number of cells in G2/M and ploidy levels decrease. Oscillates between G1 and S. [122, 123] NR RBR CC arrest, cells in root apical meristem lose CYCB1;1 expression; in rice, the number of cells synthesizing DNA decrease. Fixed-point attractor characterizing G1 arrest. [2, 88] A E2Fa Mitosis and endoreduplication are promoted. One attractor comprising 40.48% of initial conditions that is a WT CC. The other closely resembles an endocycle but APC/C activity is lower (59.52% of conﬁgurations). [111, 113] A E2Fb Cell division is induced but endoreduplication is suppresed; CC duration and cells are shorter, and the amount of S- phase transcripts increases. Similar to WT but with a shorter S phase. [79, 80] A E2Fc Overexpression of a non-degradable form of E2Fc leads to larger cells or a lack of division. Fixed-point attractor where only E2Fc and CYCD3;1 are present, congruent with a CC-arrest. [35] PA E2Fe Reduces ploidy levels. CC arrest in M phase. [44] PA MYB77 Plants are stunted but there is no information about how CC could be affected. CC arrest in a mitotic state. [76] - MYB3R1/ 4 No available data about how it could alter cell division. Two ﬁxed-point attractors of CC arrest at early G1 phase, state of E2Fa varies among them. - - CYCB1;1 Root growth enhanced, slightly small cells. WT CC [124] A CDKB1;1 Does not seem to affect CC behavior. WT CC [125] A CYCA2;3 Not enough to produce multicellular trichomes but the proportion of polyploid cells is less. WT CC [103] A KRP1 CC arrest and inhibition of cell proliferation, G2 phase is longer; a weak overexpression of KRP2 led to an increment in DNA ploidy. Attractor with period 2 oscillating between G1 and G1/S transition. [21, 30, 126] PA APC/C Gain-of-function of APC/C subunit CCS52A2 enhanced endoreduplication entry; more cells with increased DNA ploidy. Cyclic attractor pointing to endocycle. [44] A Summary of mutant phenotypes and recovered attractors simulating that mutation. A means that the result of simulation is in Agreement with the data available in the reference(s). PA means it is Partially Agrees with evidence, because not all expected traits were reproduced by the attractor but this does not contradict the mutant phenotype. NR are attractors that do not make sense with expected behavior and therefore, the model did Not Recover the mutant phenotype. doi:10.1371/journal.pcbi.1004486.t003 Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 14 / 28 endoreduplication attractors of CDKB1;1 loss-of-function or E2Fa gain-of-function, where E2Fb, E2Fc and MYB factors expression states alternate between “ON” and “OFF” (Fig 5). We highlight APC/C gain-of-function simulations, as it provides a possible mechanism for plant hormones action over the CC machinery and, thus how such key morphogens regulate cell proliferation patterns. Recently, Takahashi and collaborators reported a direct connection between cytokinins and CC machinery in A. thaliana root [131]. The authors showed that ARR2, a transcriptional factor of cytokinins signaling, induces expression of APC/C activator protein CCS52A1. Our simulated APC/C gain-of-function is congruent with that observation, since it reproduces the configuration attained by a cell entering an endocycle when APC/C activity is enhanced (Fig 5C), as it happens at the elongation zone of A. thaliana root. There- fore, our model is able to recover the attractors of loss- and gain-of-function mutant pheno- types reported experimentally, and it thus provides a mechanistic explanation for observed patterns of expression in both normal CC and during endoreduplication cycles or endocycle. Table 4. Phenotypes of loss-of-function mutations in CC components. Node Phenotypes of loss of function Recovered attractor(s) Refs. Model CYCD3;1 When this cyclin is depleted by sucrose starvation, cells are arrested in G1 phase; in adult leaves, triple mutant of cycd3;1–3 led to a diminished number of cells. Period 2 oscillating between G1 and G1/S transition. [23, 92] A SCF Plants with a diminished level of SKP2 do not show obvious affected development but KRP1 is accumulated. Similar to a normal CC but endoreduplication would be favored by the KRP1 stabilization. [93] A RBR Proliferation is promoted and cell differentiation is impaired; downregulation of RBR in rice promotes an increase of cells in S-phase. One attractor of a normal CC (includes 81.98% of possible conﬁgurations) and other attractor oscillates among G2-S-G2 (18.02% of conﬁgurations). [127] A E2Fa Expression of E2Fb, RBR and other CC regulators decrease; more cells in G1 and G2 with respect to WT. Fixed-point attractor with E2Fe and CYCD3;1 present suggesting an arrest in a Gap phase. [90] PA E2Fb Without information. Fixed-point attractor representing the G1/S transition. - - E2Fc Mitotic proteins such as CYCB1;1 have increased expression, ploidy is reduced. Fixed-point attractor of M phase arrest. [37, 91] PA E2Fe Increased endoreduplication. Attractor of endoreduplication (period 7). [44] A MYB77 Lower density of lateral roots, inconclusive data to evaluate simulation. CC of seven conﬁgurations. [76] - MYB3R1/ 4 Lower levels of G2/M transcripts, incomplete cell division, some embryos only have one cell with multiple nuclei. 2 attractors, the ﬁrst seems a three-conﬁgurations endocycle, and the second is a CC of seven conﬁgurations where APC/C is always absent. [43] A CYCB1;1 Cyclin widely used as a marker of cell proliferation, its absence is associated with differentiated cells. Attractor characterizing endocycle (period 8), intriguingly APC/C is never present. [128] - CDKB1;1 Overexpression of a dominant negative allele leads to enhanced endoreduplication. Attractor of endoreduplication (period 11). [129] A CYCA2;3 In null mutants, cells with 2C DNA content decreases before than in WT, endocycles begin before and are faster than in WT. Attractor which is an endocycle (period 7). [103] PA KRP1 No evident phenotypic effects observed but relative kinase activity increases to 1.5 in relation to WT. A CC without alterations. [114] A APC/C Loss of CCS52A2 function (activator subunit of APC/C) produces a decrement in the number of meristematic cells without affecting endoreduplication index; cells in quiescent center become mitotically active. Fixed-point attractor of a CC arrest previous to conclude mitosis. [109] PA Summary of mutant phenotypes and recovered attractor when that mutation was simulated. Abbreviations in Model column are as in Table 3. doi:10.1371/journal.pcbi.1004486.t004 Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 15 / 28 Plant E2Fc and KRP1: validation of A. thaliana CC GRN We test if the CC GRN recovers the periodic patterns observed in synchronization experiments of A. thaliana CC molecular components. Interestingly, the E2Fc repressor and KRP1 are regu- lators that have two short lapses of expression in the attractor recovered in the continuous model (Fig 6), and experimentally they also show two peaks of expression when synchronized with aphidicolin [74]. In such synchronization experiments, the expression of E2Fc increases Fig 5. Attractors recovered by simulations of loss- or gain-of-function mutants of four CC components. (A) The simulation of loss of CDKB1;1 function produced only one cyclic attractor with period 7 that resembles G1 ! S ! G2 ! G1 cycle, whereas in (B) with simulation of loss of KRP1 function, one cyclic attractor was attained, which has period 11 and comprises 100% of the initial conditions. This attractor is almost identical to WT phenotype but without KRP1. With the simulation of APC/C gain-of-function, a single attractor with period 7 was recovered, which is shown in (C) and is consistent with an endoreduplication cycle. Attractors obtained with the simulation of E2Fa overexpression are shown in (D). Two attractors were found, one of them has period 10 and the 40.48% of the initial conditions converge to that cycle that is closely similar to the WT CC attractor. The second attractor that correspond to E2Fa overexpression has period 8 and it is very similar to the endoreduplication attractor of loss of CDKB1;1 function, which comprises 59.52% of possible network configurations. doi:10.1371/journal.pcbi.1004486.g005 Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 16 / 28 from late S to middle G2, but then it decreases dramatically in late G2. In the model, E2Fc appears from S to G2 phase, and then a second increment of E2Fc expression in G2/M is observed. The latter correspondence is a further validation of the CC GRN model proposed here. Furthermore, synchronization experiments using sucrose have shown that KRP1 is expressed previous to G1/S transition and before mitosis [132], in a similar way that occurs in the model. More recently it has been proposed that KRP1 has a role during G1/S and G2/M transitions [93]; the latter should be important for endoreduplication control [78]. Once again, such roles and expression profiles are consistent with the recovered active state of KRP1 in our model. In contrast with the consistent behaviors of E2Fc and KRP1 components to recovered results with our model, E2Fe results do not coincide with previous observations. In our model this E2F factor presents only one peak from S to early M phase, but according to synchroniza- tion experiments [69], E2Fe has two peaks of expression. One of its peaks is due to regulation by other E2F family factors during S phase, while the G2/M peak could be due to MSA ele- ments. Indeed, when the regulatory motifs for E2F binding are deleted from E2Fe, it can still be expressed although at lower levels [96], suggesting that additional transcription factors regulate its expression. Such factors could belong to the MYB family as suggested for the A. thaliana CC GRN proposed here. Discussion The canonical cyclic behavior of eukaryotic cells as they go from DNA duplication to cytokine- sis suggests that a conserved underlying mechanism with shared molecular components and/ or regulatory logic should exist. While yeast and animal CC have been thoroughly studied and modelled, plant CC is less studied and no comprehensive model for it has been proposed. In this study we put forward a Boolean model of the A. thaliana CC GRN. We show that this model robustly recovers a single cyclic attractor or steady state with 11 network configura- tions. Such configurations correspond to those observed experimentally for the CC compo- nents included here at each one of the CC stages. In addition, the canonical order of sequential transitions that is recovered also mimics the observed temporal pattern of transition from one Fig 6. Dynamical behavior of E2Fc and KRP1 according to the continuous model. These nodes were chosen by their peculiar pattern of expression, which was qualitatively recovered by the Boolean and continuous models. doi:10.1371/journal.pcbi.1004486.g006 Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 17 / 28 configuration to another one along the CC (Fig 2). The fact that the 16,384 initial conditions of the proposed system converge to this single cyclic attractor already suggests that the GRN com- prises a robust module that integrates the necessary and sufficient set of components and inter- actions to recover molecular oscillations experimentally observed. The proposed GRN is also robust to alterations, being similarly robust to previously published models for other cell differ- entiation or developmental modules [116, 117, 133]. The model is validated because it recovers A. thaliana wild type and altered (in gain- and loss-of-function) configurations and cycling behaviors. The comparison between experimentally observed and recovered gene configura- tions is summarized in Tables 3 and 4. Some cyclins such as CYCD3;1 and CYCB1;1, important components during G1/S and G2/ M transitions, show a mutually exclusive regulation, as occurs in a predator-prey Lotka-Vol- terra dynamical system [134], even though they do not interact directly. Their mutual exclu- sion is achieved thanks to the coordinated expression of genes with specific proteolytic degradation capacity. Our cyclic attractor shows two transcriptional periods, one of them in S- phase regulated by E2F-RBR pathway, and the second one operating at a time previous to M- phase and regulated by MYB transcription factors. The SCF and APC/C ubiquitin ligases work during G2-to-M phases, and during mitosis exit, respectively. Therefore, the fourteen nodes and their interactions proposed in the CC GRN constitute a necessary and sufficient set of restrictions to recover the oscillations of node states characteristic of CC phases. Two alternative possibilities could drive CC progression in actual organisms. The first would imply that transitions from one CC state to the next would require external cues, like the cell size. The alternative possibility is that CC progression and the temporal pattern of tran- sitions among stages are both emergent consequences of an underlying complex regulatory network, and do not require external cues, or these only reinforce such temporal progression emergent from complex underlying regulatory interactions. Our CC GRN model supports the latter. This does not imply that several internal or external signals or molecules, such as hor- mones or other types of cues could alter the CC. Therefore, the two alternative possibilities are not exclusive but they likely complement or enhance each other. Indeed, A. thaliana CC is reg- ulated by plant hormones, light, sucrose, osmotic stress [135] or oxidative stress [136]. These could now be modelled as CC modulators. In the model proposed here we avoided redundancy. For instance, the KRP1 node repre- sents the KRP family members that share several functions. Also the metaphase-anaphase tran- sition could be added to the model when more data about APC/C regulation (i.e. negative feedback loop comprising CDK-cyclin complexes, or the regulation of Cdc20 homologues) becomes available in plants. Apparently, these simplifications did not disrupt the main features of the A. thaliana CC, since the cyclic behavior distinctive of the CC components was correctly recovered. A mechanistic model for the A. thaliana CC: novel predictions Our proposed GRN model suggests some predictions regarding the regulation of certain CC components in A. thaliana. Such predictions can be classified into two types. The first type per- tains to those recovered by in silico promoter analysis. The predictions of the second type were inferred from data of other eukaryotes, because they seem to imply conserved components and some evidence from A. thaliana suggested that these interactions are part of the CC GRN in A. thaliana. Three interactions belong to the second type, E2Fb ! SCF, CDKB1;1-CYCA2;3 a E2Fa and APC/C a SCF (see Table 1 for a synthesis of hypothetical interactions). Although some evidence supports the idea that these interactions could exist in A. thaliana, they should be corroborated with additional experimental examination. Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 18 / 28 Our model provides a dynamic explanation to the cyclic behavior of certain transcription factors and predicts a novel interaction for E2F and MYB regulators; they connect waves of periodic expression that seem to be key for the robust limit cycle attractor that characterizes CC behavior. Interestingly, previous studies have shown that such periodic transcription can be maintained even in the absence of S-phase and mitotic cyclins [4], which underpin the role of a transcription factor network oscillator for the correct CC progression [137]. A regulatory interaction between E2F and MYB factors (or among the equivalent regulators) may be con- served among other eukaryotes (e.g. mammals and yeast), but there is no experimental support yet for it in A. thaliana. After looking for the same direct evidence in A. thaliana and not find- ing it, we thought about an alternative regulatory mechanism that consists in transcription fac- tors acting between E2F and MYB. Hence, we decided to analyze the important transcription factor families known so far, to find out if one of their members could be mediating the regula- tion between E2F and MYB. The TCP (for Teosinte branched 1, Cycloidea, PCF) and the MYB family were chosen because they have been reported to be involved in CC regulation [42]. Based on their gene expression patterns and promoter sequence analysis, MYB77 was our best candidate: it is expressed at the beginning of M phase, and could be regulated by E2F and regu- lator of MYB (see Table 1). A second possibility might be that several tissue-specific transcrip- tion factors are involved in E2F-MYB genetic regulation (e.g. GL3, MYB88, SHR/SCR [17], MYB59 [138] or even members of the MADS box gene family could be implied). Indeed, we have recently documented that a MADS-box gene, XAL1, encodes a transcription factor that regulates several CC components (García-Cruz et al., in preparation). A. thaliana CC in comparison to animal and yeast CC Differences among eukaryotic CCs allow us to recognize or characterize alternative mecha- nisms for the regulation of CC. The first difference between GRN of A. thaliana CC and that of other eukaryotes, concerns the number of duplicates of some key regulators. A. thaliana has up to ten copies of some of the genes that encode for CC regulators (e.g. families of cyclins or CDK), while yeast, mammals or the algae Ostreococcus tauri, have much fewer duplicates [20, 139–141]. The only exception concerns the homologues of Retinoblastoma protein, of which there are three members in humans and mouse, and only one copy in A. thaliana [127]. Future models should address the explicit role of CC duplicated components in the plastic response of plant development to environmental conditions. Being sessile, such developmental adjust- ments, as plants grow under varying environments, are expected to be more important, com- plex and dynamic than in motile yeast and animals. One possibility is that different members of the same gene family are linked to different transduction pathways of signals that modulate CC dynamics. The second difference among A. thaliana and other CC was regarding the transcriptional regulation throughout the GRN underlying it. For instance, S. cerevisiae does not have RBR or E2F homologues, but instead has Whi5, Swi4,6 and Mbp1 proteins which perform equivalent regulatory functions to the former CC components [142, 143]. S. cerevisiae does not have any MYB transcription factors but it presents other transcriptional regulators, such as Fkh1/2, Ndd1 and Mcm1 [142, 144, 145], which regulate the G2/M transition in a similar way to MYBs in mammals. Contrary to the conservation in G1/S transition [15, 67], molecular components controlling G2/M transition seem to vary among different eukaryotes. It seems that molecules such as WEE1 kinase and CDC25 phosphatase are not conserved. In A. thaliana, CDC25-like has phosphatase and arsenate-reductase functions [146], while A. thaliana WEE1 phosphorylates monomeric CDKA;1 in vitro [147], and Nicotiana tabacum WEE1 inhibits CDK activity in Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 19 / 28 vitro [148]. However the lack of any obvious mutant phenotype of CDC25 or WEE1 loss-of- function mutants predicts that these genes are not involved in the regulation of a normal CC. Additionally, although WEE1 has a role during DNA damage [146, 149], does not seem to have a CDKA;1 recognition domain [150]. CDC25-like does not have the required sites for CDKA;1 recognition [150]. In summary, the positive regulatory feedback between CDKA;1 and CDC25-like, as well as the mutual-inhibitory feedback loop between CDKA;1 and WEE1, seem not to be conserved in A. thaliana. Given all that evidence for G2/M regulation, we integrated the regulatory interactions between stoichiometric CDK inhibitor (KRP1), B-type plant specific CDK and MYB transcrip- tional factors. It is not surprising that there are clear differences between plant G2 phase regula- tion and that of other organisms, because variations in this control point could define cell fate. Although differences among the A. thaliana CC GRN uncovered here and that of yeasts and animals have now become clear, we think that the basic regulatory CC module reported here, will be a useful framework to incorporate and discover new components of the CC GRNs in plants and also in other eukaryotes. Despite the fact that our CC GRN model recovers observed CC stage configurations and their canonical pattern of temporal transitions, it did not recover an alternative attractor that corresponds to the endocycle. We hypothesize that the same multi-stable GRN underlies both states, and additional components yet to be connected to the CC GRN will ensure a cyclic attractor corresponding to the complete CC, and another one with shorter period correspond- ing to the endocycle. In its present form, our model suggests that CYCD3;1 function, which has been associated with the proliferative state [108] and with a delay in the endocycle onset [23], is important to enter the endocycle. Besides, it also has been reported that CYCD3;1 plays a role in G1/S transition [121] and regulates RBR protein during DNA replication [89]. Fur- thermore, the endoreduplication attractor obtained in some of our mutant simulations (e.g. Fig 5A, 5C and 5D-right) also supports the role of CYCD3;1 in entering an endocycle. The GRN model of A. thaliana CC could help to identify physiological or developmental interactions involved in the tight relationship between proliferation and differentiation observed during different stages of development [1, 88, 108, 109, 126]. Previous to cell division, the cell senses its intracellular and environmental conditions to arrest or promote CC progress. Such cues directly affect the CC machinery, which does not depend on a master or central regulator. CC control is the result of a network formed by feedback and feedforward loops between complexes of CDK-cyclin and its regulators. It is not evident how complex dynamical processes such as CC progression emerge from simple interactions among components acting simulta- neously. The proposed CC GRN will be very helpful to study how cell proliferation/differentia- tion decisions and balance keeps a suitable spatio-temporal control of CC during plant growth and development. Supporting Information S1 Text. Logical rules of A. thaliana CC Boolean model. (PDF) S2 Text. Equations, parameters, analysis of parameters and initial conditions of the contin- uous version of A. thaliana CC model. (PDF) S3 Text. New recovered attractors by robustness analysis. Additional attractors yielded by making alterations in each bit of logical functions. (PDF) Dynamic Gene Regulatory Network Model of A. thaliana Cell Cycle PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004486 September 4, 2015 20 / 28 S4 Text. Attractors obtained in the simulation of mutant phenotypes. (PDF) Acknowledgments The present manuscript is part of EOG’s PhD thesis in the Graduate Program in Biomedical Sciences of the Universidad Nacional Autónoma de México (UNAM). EOG acknowledges the scholarship and financial support provided by Consejo Nacional de Ciencia y Tecnología of Mexico (CONACyT). This work greatly benefited from input provided by Dr. Joseph G. Dubrovsky. 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Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 DOI 10.1186/s12976-015-0011-4 RESEARCH ARTICLE Open Access Fanconi anemia cells with unrepaired DNA damage activate components of the checkpoint recovery process Alfredo Rodríguez1,2, Leda Torres1, Ulises Juárez1, David Sosa1, Eugenio Azpeitia3,4,5, Benilde García-de Teresa1, Edith Cortés6, Rocío Ortíz6, Ana M. Salazar7, Patricia Ostrosky-Wegman7, Luis Mendoza4,7 † and Sara Frías1,7† Correspondence: sarafrias@biomedicas.unam.mx †Equal contributors 1Laboratorio de Citogenética, Departamento de Investigación en Genética Humana, Instituto Nacional de Pediatría, D.F., México 7Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, D.F., México Full list of author information is available at the end of the article Abstract Background: The FA/BRCA pathway repairs DNA interstrand crosslinks. Mutations in this pathway cause Fanconi anemia (FA), a chromosome instability syndrome with bone marrow failure and cancer predisposition. Upon DNA damage, normal and FA cells inhibit the cell cycle progression, until the G2/M checkpoint is turned off by the checkpoint recovery, which becomes activated when the DNA damage has been repaired. Interestingly, highly damaged FA cells seem to override the G2/M checkpoint. In this study we explored with a Boolean network model and key experiments whether checkpoint recovery activation occurs in FA cells with extensive unrepaired DNA damage. Methods: We performed synchronous/asynchronous simulations of the FA/BRCA pathway Boolean network model. FA-A and normal lymphoblastoid cell lines were used to study checkpoint and checkpoint recovery activation after DNA damage induction. The experimental approach included flow cytometry cell cycle analysis, cell division tracking, chromosome aberration analysis and gene expression analysis through qRT-PCR and western blot. Results: Computational simulations suggested that in FA mutants checkpoint recovery activity inhibits the checkpoint components despite unrepaired DNA damage, a behavior that we did not observed in wild-type simulations. This result implies that FA cells would eventually reenter the cell cycle after a DNA damage induced G2/M checkpoint arrest, but before the damage has been fixed. We observed that FA-A cells activate the G2/M checkpoint and arrest in G2 phase, but eventually reach mitosis and divide with unrepaired DNA damage, thus resolving the initial checkpoint arrest. Based on our model result we look for ectopic activity of checkpoint recovery components. We found that checkpoint recovery components, such as PLK1, are expressed to a similar extent as normal undamaged cells do, even though FA-A cells harbor highly damaged DNA. Conclusions: Our results show that FA cells, despite extensive DNA damage, do not loss the capacity to express the transcriptional and protein components of checkpoint recovery that might eventually allow their division with unrepaired DNA damage. This might allow cell survival but increases the genomic instability inherent to FA individuals and promotes cancer. Keywords: DNA damage, Checkpoint recovery, Boolean network model © 2015 Rodríguez et al. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http:// creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 2 of 22 Introduction The molecular basis of the DNA damage response (DDR) has been largely elucidated through the study of the rare chromosome instability syndromes (CIS) [1] which are cytogenetically characterized by the spontaneous appearance of chromosome aberrations (CA) as well as hypersensitivity to specific DNA damaging agents [2–4]. The best-known CIS include Bloom syndrome (BS) which appears due to mutations in BLM helicase [5, 6] and results in increased sister chromatid exchanges [7], Ataxia Telangiectasia (AT) that shows particular clonal chromosome rearrangements as a consequence of mutations in the checkpoint kinase ATM gene[8–11], and Fanconi anemia (FA) [12] whose phenotype results from mutations in any of the genes that conform the FA/BRCA pathway [13–19] and consists of chromatidic breaks, iso-chromatidic breaks and radial exchange figures among chromosomes. Even if these breaks and radials are predominantly seen in FA, they can also be observed in BS and AT [4, 20]. Although patients affected by CIS display phe- notypic similarities, such as growth defects, compromised immunological system and an increased risk to develop cancer [1, 20], each syndrome presents particular phenotypes and pivotal data. Namely, BS shows sun sensitivity [5], AT presents progressive cerebel- lar ataxia and oculo-cutaneous telangiectases [8], while FA is characterized by congenital malformations and progressive bone marrow failure [21]. The products of these genes interact in the cell’s DNA damage response [1], and thus the deficiency of any of these proteins diminishes the efficiency of a cell to cope with DNA damage, leading to their accumulation. Given the critical role that these proteins have in the protection of the human genome, certain authors have speculated that survival of CIS patients is an oddity and that cells escaping apoptotic death do so by constitutively inducing alternative replication or DNA damage tolerance pathways, which might contribute to the characteristic mutator phenotypes observed in the CIS [22]. In the particular case of FA, cells are hypersensitive to agents that create DNA inter- strand crosslinks (ICL), such as mitomycin C (MMC) or diepoxybutane (DEB) [21]. The treatment of FA cells with MMC or DEB induces a blockage during the G2 phase of the cell cycle and exacerbates the frequency of CAs, including double strand breaks (DSBs) and radial exchange figures [23]. Biallelic mutations in at least one of 18 distinct FANC genes can generate FA. The products of these genes interact in the so-called Fan- coni Anemia/Breast Cancer (FA/BRCA) pathway [13–18], involved in the repair of the DNA damage generated by intrinsic acetaldehydes and extrinsic ICL inducing agents. Therefore, a deficiency in this pathway results in DNA damage accumulation that might originate congenital malformations, uncontrolled hematopoietic cell death and cancer in FA patients [24–27]. Over the years, the FA diagnosis assays and experimental approaches have shown that a great proportion of FA cells succumb to DNA damage due to their inherent repair defi- ciencies. However, some cells are able to tolerate high levels of DNA damage and progress into mitosis despite a great amount of CAs. The mechanisms that allow the cells with CAs to omit the DNA damage integrity checkpoints remain uncertain because the more obvious candidate, the G2/M checkpoint, is considered to be properly activated in FA cells [28–30]. Thus, the idea of a malfunctioning checkpoint in FA cells has been ruled out and it is presumed that some other mechanisms are responsible for the checkpoint override in FA cells with unrepaired DSBs. Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 3 of 22 In recent times, an attenuated G2 checkpoint phenotype, characterized by low levels of CHK1 (NP_001107594.1) and p53 (NP_000537.3), absence of the G2 phase arrest, and arrival to metaphase with a large number of MMC-induced CAs has been described in cells from adult FA individuals [31]. It has been suggested that the G2 checkpoint attenuation could be an important contributor for the increased life expectancy of these FA patients, and that the release of cells with unrepaired DSBs could promote neoplas- tic transformation [31]. Nevertheless, since non-attenuated FA cells carrying unrepaired DNA damage achieve a correct G2/M checkpoint activation [28–30], the aforementioned mechanism seems to be a particular scenario rather than a general mechanism to enable the resolution of the G2 checkpoint blockage. Network modeling has been previously used with success to study the dynamics of biological systems [32–37]. Particularly, we developed a Boolean network model (BNM) for the FA/BRCA pathway [38], in which we observed that the inclusion of the check- point recovery (CHKREC) node is crucial for the network correct function. In our model, the CHKREC node represents the process that relieves the inhibition of the checkpoint machinery over the mitosis-promoting factor (Cyclin B/CDK1) after a complete DNA damage repair to allow further cell division [39–42]. This node comprises the G2 tran- scriptional program that activates the expression of genes driving the G2/M transition and the protein program that inactivates the γ H2AX histone (NP_002096.1) and check- point kinases [43]. We presumed that CHKREC activation might be releasing cells with unrepaired DNA damage in FA mutants. To test this possibility, as well as to validate the inclusion of the node itself in the FA/BRCA network, we used a simplified version of our previously published FA/BRCA pathway BNM and experimentally determined if CHKREC components become activated in FA cells during G2/M during MMC-induced arrest. Materials and methods Model and simulations The simplification of the FA/BRCA network was done by reorganizing the existing 28 nodes and 122 interactions [38], resulting in a deterministic BNM with 15 nodes and 66 interactions (Fig.1 and Table 1) that vastly simplifies the computational analysis while maintaining the qualitative dynamical behavior of the original FA/BRCA network. The simplification was made by collapsing the network components that share functions or belong to a single pathway into one single node. We were careful to preserve all the impor- tant functional categories of the network and made sure to recover the behavior of the wild type and mutant networks. The modifications and simplification criteria are listed in Table 2. Simulations were performed for the wild type and all possible gain of function or null mutants of the model with synchronous and asynchronous update regimes. Here we report the simulations exploring checkpoint and CHKREC function in wild type and FA core mutants. These null mutants were simulated fixing to zero the node of interest. In these mutants we simulated the response to ICLs, whose presence is dependent on the time that the system requires to turn it off. With our model we simulated two biolog- ically relevant conditions, a short exposure to ICLs, which is supposed to be repaired fast and efficiently by the FA/BRCA pathway (Fig. 2b) and a persistent exposure to damaging agents, which is more difficult to face given the accumulation of damage and saturation Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 4 of 22 Fig. 1 (See legend on next page) Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 5 of 22 (See figure on previous page) The latest FA/BRCA network. In response to an ICL, the FA/BRCA network responds by blocking the cell cycle through the ATR and ATM checkpoint kinases and their downstream target p53. Similarly, the FA core complex (FAcore) becomes activated and ubiquitinates FANCD2I complex, which in turn recruits DNA endonucleases (NUC1 and NUC2). These endonucleases unhook the ICL generating a DNA adduct (ADD) and a double strand break (DSB). Translesion synythesis (TLS) takes over the ADD while the DSB can be rejoined either by FA/BRCA-dependent Homologous Recombination (FAHRR), FA/BRCA-independent Homologous Recombination (HRR2), or by the error prone Non-Homologous End-Joining (NHEJ) pathways. Finally, we predict that the CHKREC node, composed by the G2/M transcriptional program and checkpoint recovery proteins, turns off the checkpoint and DNA repair proteins. Rectangles represent proteins or protein complexes, pointed arrows are positive regulatory interactions, and dashed lines with blunt arrows are negative regulatory interactions. Readers may refer to [38] for a more detailed description of the FA/BRCA pathway of the DNA repair pathway (Fig. 2c). The response to short ICL exposure was simulated in both the wild type (Fig. 2b) and FAcore mutant (Fig. 2d) with the ICL value ON only at the starting time step; whereas a continuous exposure to DNA damage was simulated fixing the ICL value to 1 during the entire simulation. We performed exhaustive searches of all possible trajectories and attractors in the system. Implementation The current FA/BRCA network is available through the supplementary file FAnetwork.r this file has been tested using R (v3.1.1) package BoolNet (v1.63) [66]. Additionally, the SBML-qual implementation of the model obtained by using the toSBML() function of BoolNet is provided as the supplementary file FAnetwork.sbml. The generated file was validated using the online service at http://sbml.org/Facilities/Validator/. Table 1 Boolean functions for the nodes in the FA/BRCA network RULES REFERENCES ICL ←ICL ∧¬ DSB [38] FAcore ←ICL ∧(ATR ∨ATM) ∧¬ CHKREC [14, 16, 44–46] FANCD2I ←FAcore ∧((ATR ∨ATM) ∨((ATR ∨ATM) ∧DSB)) ∧ [47–49] ¬ (CHKREC) NUC1 ←ICL ∧FANCD2I [50]; [38] NUC2 ←(ICL ∧(ATR ∨ATM) ∧¬ (FAcore ∧FANCD2I)) ∨ [51]; [38] (ICL ∧NUC1 ∧p53 ∧¬(FAcore ∧FANCD2I)) ADD ←(NUC1 ∨NUC2 ∨(NUC1 ∧NUC2)) ∧¬ (TLS) [47, 50, 51] DSB ←(NUC1 ∨NUC2) ∧¬ (NHEJ ∨FAHRR ∨HRR2) [50, 52] TLS ←(ADD ∨(ADD ∧FAcore)) ∧¬ (CHKREC) [53, 54] FAHRR ←DSB ∧FANCD2I ∧¬ (NHEJ ∧CHKREC) [53, 54] HRR2 ←(DSB ∧NUC2 ∧NHEJ ∧ICL ∧¬ (FAHRR ∨CHKREC)) ∨ [38] (DSB ∧NUC2 ∧TLS ∧¬ (NHEJ ∨FAHRR ∨CHKREC)) NHEJ ←(DSB ∧NUC2 ∧¬ (FAHRR ∨HRR2 ∨CHKREC)) [49, 52, 55–57] ATR ←(ICL ∨ATM) ∧¬ CHKREC [58–60] ATM ←(ATR ∨DSB) ∧¬ CHKREC ∨FAcore [61, 62] P53 ←((ATR ∨ATM) ∨NHEJ) ∧¬ CHKREC [58, 63, 64] CHKREC ←((TLS ∨NHEJ ∨FAHRR ∨HRR2) ∧¬ DSB ) ∨ [52, 53]; ((¬ ADD) ∧(¬ ICL) ∧(¬ DSB) ∧¬ (CHKREC)) [38, 65] Key references are included. Full discussion of interactions can be found in [38] Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 6 of 22 Table 2 Network model simplification criteria Node in the Nodes in the Simplification criteria original BNM simplified BNM ICL ICL Unchanged node FANCM, FAcore FAcore ICL recognition proteins working together in the upstream FA/BRCA pathway FANCD2I FANCD2I Unchanged node MUS81 NUC1 Nuclease mediated ICL incision XPF, FAN1 NUC2 Nuclease mediated ICL incision ADD ADD Unchanged node DSB DSB Unchanged node ATR, CHK1, H2AX ATR These proteins act in the Checkpoint pathway ATM, CHK2, H2AX ATM These proteins act in the Checkpoint pathway p53 p53 Unchanged node PCNATLS TLS This is only a change in name FANCJMLH1, MRN, BRCA1, FAHRR These proteins act in the FANCD1N, RAD51, HRR, Homologous Recombination ssDNARPA Repair pathway —— HRR2 New node representing the alternative Homologous Recombination Repair Pathway KU, DNAPK, NHEJ NHEJ These proteins act in the Non-Homologous End-Joining DNA repair pathway USP1, CHKREC CHKREC Global negative regulators of the FA/BRCA pathway Cell culture and treatments Lymphoblastoid cell lines from FA-A VU817 (kindly donated by Dr. Hans Joenje, VU University Medical Center) and normal NL-49 (generated in our institution under writ- ten informed consent) were maintained in RPMI 1640 medium supplemented with 10 % fetal calf serum, 1 % non-essential aminoacids and 1 % sodium pyruvate (all from GIBCO, Waltham, Massachusetts, USA). During experiments 300,000 cell/ml were exposed to 10 ng/ml of MMC (Sigma-Aldrich Co, St. Louis MO, USA) for 24 h and harvested to evaluate different markers. All the experiments were run by triplicate. Chromosome aberration and nuclear division index analysis For chromosome aberration analysis, colchicine (Sigma-Aldrich Co, St. Louis MO, USA) (final concentration of 0.1 μg/ml) was added to cell cultures one hour before harvesting with the conventional method. Twenty five metaphases per experimental condition were scored by recording the number of chromatid breaks, chromosome breaks and radial figures. A cytokinesis block assay, using 3 μg/ml of cytochalasin B (Sigma-Aldrich Co, St. Louis MO, USA), was implemented to obtain binucleated and tetranucleated cells: after exposing the cells to MMC for 24 h, they were washed, reincubated with fresh Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 7 of 22 A B C D E Fig. 2 FA network simulations. a The current information regarding the FA/BRCA pathway have not uncovered the mechanism that allows the resolution of the G2/M checkpoint after DNA damage and further cell division. b Trajectories and attractor of the wild type FA/BRCA network under an ICL pulse. In this simulation wild type cells repair DNA damage through the FA/BRCA pathway and arrive to CCP attractor after activating the CHKREC node once the damage has been fixed. The inclusion of the CHKREC node, as a checkpoint negative regulator, allows to explore the mechanisms behind cell division after checkpoint resolution. c In response to a continuous ICL DNA damage, wild type cells arrive to a CCA attractor with activation of the checkpoint and DNA damage repair nodes,the CHKREC node becomes eventually activated in this attractor. d Under and ICL pulse FAcore mutant cells activate the NHEJ pathway to repair DNA damage and arrive to a CCP attractor. e In response to a continuous ICL DNA damage, FAcore mutant cells concomitantly activate the checkpoint and the CHKREC nodes. Node names are indicated at the topmost row. The leftmost column indicates simulation time steps in arbitrary units. Time steps corresponding to trajectories are indicated and time steps corresponding to attractors are indicated by shaded gray and “ATT”. For illustrative purpose cyclic attractors are represented twice cytochalasin B for another 24 h and harvested using a 7:1 methanol:acetic acid fixative. Five hundred cells were scored to quantify the number of micronuclei, mononucleated, binucleated and tetranucleated cells in every experimental condition [67]. Flow cytometry analysis To determine cell cycle distribution and mitotic index the cells were fixed with 70 % ice-cold ethanol, washed twice with PBS (GIBCO, Waltham, Massachusetts, USA) and permeabilized with 0.1 % PBS 1X + Triton X100. The MPM2 antibody (CellSignaling, Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 8 of 22 Boston MA, USA) was used to determine the number of cells in M phase. The antibody was marked with the labeling anti-mouse Alexa-Fluor 488 fluorophore from the Zenon Tricolor Mouse IgG Labeling Kit # 1 (Invitrogen, Carlsbad, CA, USA) according to man- ufacturer instructions. The cells were incubated during 1 h with the antibody, washed with PBS/NGS 10 % and counterstained with propidium iodide (Sigma-Aldrich Co, St. Louis MO, USA). A total of 20,000 events were scored in a FACSCan (Beckton Dickinson, Ontario, CA) cytometer and the analysis was performed using the CellQuest program version 3.2.1. RNA extraction and quantitative real-time PCR (qRT-PCR) Total RNA was obtained employing the combined method of TRIzol (Invitrogen, Carlsbad, CA, USA) followed by RNeasy mini procedure (Qiagen, Valencia, CA, USA), according to manufacturer instructions. Before retro-transcription, 1 μg of total RNA was treated with 0.1 U RNase-free DNase I (Invitrogen, Carlsbad, CA, USA) in 20 mM Tris-HCl, pH 8.3, 50 mM KCl, and 1 mM MgCl2 for 15 min at room tempera- ture. The enzyme was inactivated by adding EDTA to a final concentration of 1 mM followed by incubation at 65°C/10 min. Total RNA was retro-transcribed into cDNA using the Transcriptor First Strand cDNA Synthesis Kit (Roche Diagnostics, GmbH, Mannheim, Germany) using anchored-oligo (dT) 18 primer (50-pmol/μL) and Random hexamer primer (600 pmol/μL), protector RNase Inhibitor (20 U), and Transcriptor Reverse Transcriptase (10 U). Total RNA and cDNA were quantified using a Nanodrop ND 1000 spectrophotometer (Nanodrop Technologies, Wilmington, DE, USA). Real-time quantitative-PCR (qRT-PCR) was performed by duplicate for each cell line, treatment and biological repeat using 2 μg of cDNA per reaction with the Universal Probes sys- tem (Roche Diagnostics, GmbH, Mannheim, Germany) and the Light Cycler Taq Man Master kit (Roche Diagnostics, GmbH, Mannheim, Germany). 7SL (NR_002715.1), β2 microglobulin (NM_004048.2) and β-actin (NM_001017992.3) gene expression were used as reference. Primers for each gene were designed on-line with the ProbeFinder Software (http://www.universalprobelibrary.com) and manufactured by the Sequencing and Synthesis Unit (IBT, UNAM). The qRT -PCR was carried out in a Light Cycler 2.0 Carousel Roche equipment. Protein extraction and immunoblot Cells were harvested in TLB lysis buffer supplemented with the Complete C protease and phosphatase inhibitors mix (Roche, Mannheim, Germany). Quantification was made with Bradford ready to use reagent (Biorad, Hercules, CA). Total cell protein (10μg) was separated by 12 % SDS- PAGE, transferred to nitrocellulose membrane (Biorad, Hercules, CA) and incubated with primary antibodies overnight at 4°C followed by incubation with goat-anti-mouse (Invitrogen, Carlsbad, CA, USA) or goat-anti-rabbit (Invitrogen, Carls- bad, CA, USA) HRP tagged secondary antibodies. Bands were visualized with Lumigen on Amersham Hyperfilm (GE Healthcare, Fairfield, CT, USA). Primary antibodies used are listed below: anti-WEE1 (NP_001137448.1) (Abcam, Cambridge, UK), anti-WIP1 (NP_003611.1 ) (Abcam, Cambridge, UK), anti-pCHK1 Ser345 (Cell Signaling, Boston MA, USA), anti-γ H2AX (Genetex, Irvine, CA), anti-p21 (NP_000380.1) (Genetex, Irvine, CA), anti-MYT1 (NP_004526.1) (Genetex, Irvine, CA), anti-Aurora A (NP_003591.2) (Abcam, Cambridge, UK), anti-CDC25B (NP_001274445.1) (Genetex, Irvine, CA) and Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 9 of 22 anti-PLK1 (NP_005021.2) (Abcam, Cambridge, UK); anti-GAPDH (NP_001243728.1) was used as loading control (Genetex, Irvine, CA). Statistical analysis Experimental groups were compared using two way ANOVA, followed by Tukey’s post- hoc test. A difference was considered significant if p < 0.05. Results FA/BRCA network analyses show that CHKREC promotes cell division in FA mutants with DNA damage Appropriate function of the FA/BRCA pathway guarantees the complete repair of ICLs and correct checkpoint activation impedes cell division upon DNA damage detection [68]. Therefore an accurate model of the FA/BRCA pathway should show cell division after complete DNA damage repair in wild-type cells. In our previous work [38], we demonstrated that the inclusion of the CHKREC node is crucial to reproduce correctly the DNA repair behavior. Without CHKREC, as a negative regulator of the checkpoint nodes, the network remains in a permanent arrest after DNA repair (Fig. 2a). Hence, CHKREC provides a mechanism that allows the cell to resolve the checkpoint (Fig. 2b). We performed synchronous and asynchronous simulations with the updated and sim- plified version of the FA/BRCA network and observed that the simplified model is able to reproduce all the previously reported results (Fig. 2b and data not shown). Only synchronous simulations are shown given that asynchronous update results in complex trajectories, while preserving the attractors of the original model [38]. Hence, we decided to use our new version of the network model to deeply study the role of CHKREC in the abnormal behavior of FA cells. Ninety percent of FA patients carry mutations in one of the components of the FA core complex, including FANCA (NP_000126.2), FANCB (NP_001018123.1), FANCC (NP_000127.2), FANCE (NP_068741.1), FANCF (NP_073562.1), FANCG (NP_004620.1), FANCL (NP_001108108.1) and FANCM (NP_001295063.1) [21]. Hence, to study the role of CHKREC in FA cells, we simulated the FA core complex mutant, represented in our model by the FA core node, and compared its dynamic behavior to a wild type network. Our simulations recapitulate two cellular behaviors relevant to DNA damage that are represented by two specific attractors. We denominated them as the cell cycle progression attractor (CCP), and the cell cycle arrest attractor (CCA). The CCP attractor is charac- terized by the CHKREC-mediated inactivation of every checkpoint node, namely ATM, ATR and p53, followed by CHKREC oscillations. It has been experimentally proven that CHKREC is required for the activation of the genes and proteins that release the G2/M checkpoint to allow cell cycle progression [39, 41–43]. Hence, the cyclic behavior of the CHKREC node in the CCP attractor represents the periodical transition into the cell cycle, and should ideally be reached when DNA damage has been repaired. In our simu- lations both wild type and FA core mutant reach the CCP attractor after an ICL pulse of damage (Fig. 2b,d). On the other hand, CCA is a cyclic attractor that represents a checkpoint mediated cell cycle arrest that is reached when DNA damage persists and the cell is engaged in a DNA repair process. Once the system has reached CCA there is recurrent activation of the DNA damage repair and the checkpoint nodes, accompanied by CHKREC node Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 10 of 22 activation, thus CHKREC activation might occur during an ongoing CCA but the cell would not divide unless the checkpoint nodes are turned off, which in turn would not occur until the DNA damage has been completely removed. Although more than one combination of node activation patterns can be interpreted as a CCA attractor, all such patterns share the activation of the DNA damage and the checkpoint nodes followed by activation of CHKREC. In our simulations with a constant ICL damage the wild type (Fig. 2c) and FA core mutant (Fig. 2e) networks reach a CCA attractor with checkpoint and CHKREC activa- tion. In the wild-type simulation we observe that the checkpoint components are never completely down-regulated in presence of DSBs or during the ICL stimulus, however the FA core mutants have a transient state in which DSBs are activated and the checkpoint components are inactivated, as a response to CHKREC activation in the previous step. This result suggests that FA cells might overcome, through CHKREC activation, the cell cycle arrest despite unrepaired DNA damage. Our modeling approach has advanced many interesting predictions about the effect of FA mutations during the DNA repair process. In the next section we focused on the one that we considered more general and important. Namely, that CHKREC inhibition over the checkpoint components might allow the division of FA cells even if DNA has not been completely repaired. Hence, we verified if CHKREC activation might occur in FA cells after DNA damage induction allowing their eventual cell division, even in the presence of unrepaired DNA damage. CHKREC components are activated in FA cells with unrepaired DNA damage Cells should divide only after successful and thorough DNA repair [68, 69], which is achieved through efficient DNA repair and accurate G2/M checkpoint activation. FA core mutants are DNA repair deficient but G2/M checkpoint proficient, therefore the fact that they are able to divide despite a strong G2/M checkpoint activation and carrying unrepaired DNA damage is remarkable. Our BNM anticipates that turning off a DNA damage-induced G2/M checkpoint might occur through CHKREC activation, thus allow- ing cell division. We verified this prediction by following the transit through G2 and M phases in the presence of DNA damage in wild type (NL49) and FA-A (VU817) cell lines exposed to MMC. First, we evaluated checkpoint activation using several markers. Using PI cell cycle flow cytometry analysis we observed that treatment with MMC induces an over time increase in the number of FA-A cells arrested in G2 when compared to normal cells (Fig. 3a, left panel), as well as a reduction in the number of mitotic cells (MPM2+ cells in Fig. 3a, right panel), accompanied by a lag of approximately 6–12 hours in the peak of MPM2+ cells in both MMC-treated FA and normal cells, compared to their respective untreated controls (see 24 and 30 hrs of MMC treatment). However normal MMC treated cells have the highest peak as they deliver a bigger number of cells into M phase. This lag might indicate that, while repairing the MMC-induced DNA damage, the cells postpone the resolution of the G2 checkpoint. This arrest is shorter in normal cells given that they repair in a more efficient way thus having a more prominent contribution to the mitotic index when compared to FA cells. The highest percentage of MPM2+ cells of MMC treated normal cells might indicate a sharp delivery of previously G2 arrested cells, contrary to a smooth delivery of untreated normal cells. Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 11 of 22 A B C Fig. 3 FA cells arrest at G2 phase in response to MMC. a Flow cytometry analysis showing accumulation of FA cells in G2 in response to MMC (left panel) and diminished number of FA mitotic cells compared to normal cells (right panel). b FA cells activate CHK1 kinase in response to MMC treatment. c FA cells increase the expression of p21 mRNA as showed by qRT-PCR analysis (n = 3 independent experiments, p < 0.05) In FA-A cells treated with MMC we also observed increased CHK1 phosphoryla- tion (Fig. 3b), a classical checkpoint activation marker, along with increased p21 mRNA expression (Fig. 3c). p21 is the main p53 target and is an important player for cell cycle arrest. The expression of this gene shows that the cell is committed to cell cycle arrest and its continuous expression is necessary to prevent cell division in cells that carry unre- paired chromosomes [68, 69]. These experiments show that FA-A cells are able to activate mechanisms that halt cell cycle progression at the G2 phase upon DNA damage induction. We then evaluated if FA-A and normal cells were able to divide despite unrepaired DNA damage. We quantified the cell division capacity after MMC treatment by performing a cytokinesis block assay with cytochalasin B (CB). Meanwhile, the DNA damage was eval- uated by recording the frequency of micronuclei in multinucleated cells and the frequency of CAs in metaphase spreads. CB experiments showed that treatment with MMC increased the proportion of mononucleated cells (cells that still do not divide due to G2 halt) (Fig. 4a upper panel), while the number of binucleated cells irrespective of the cell type (NL49 or VU817) or the addition or not of MMC remained the same (Fig. 4a middle panel). Remarkably, MMC treatment reduced significantly the number of tetranucleated FA cells (Fig. 4a bottom panel). On the other hand, the analysis of metaphase spreads showed that FA-A cells reached mitosis with a significantly higher frequency of CAs (Fig. 4b upper panel) than normal cells, and were able to divide despite unrepaired DNA damage, i.e. micronuclei (Fig. 4b bottom panel). These experiments show that FA-A cells first arrest in response to DNA damage but eventually reach cell division regardless of CA. As suggested by our model, CHKREC activation could be relieving cell cycle arrest mediators, leading the cell to divide. To determine if the CHKREC components became Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 12 of 22 A B Fig. 4 FA cells divide despite MMC treatment and cell cycle arrest. a The number of mononucleated cells (upper panel), binucleated cells (middle panel) and tetranucleated cells (bottom panel) was quantified after exposure to MMC (24 h) and Citochalasin B (48 h). The number of basal binucleated and tetranucleated cells was counted without Citochalasin B treatment and rested from the total number (data not shown). b Despite G2 arrest FA cells arrive to mitosis and divide with unrepaired DNA damage as demonstrated by two independent DNA damage analyses, increased chromosome aberrations (upper panel) and increased micronuclei in cells that have reached one division (bottom panel) (n = 3 independent experiments, p < 0.05) active in MMC treated FA cells, thus allowing their eventual division, we evaluated some molecular markers relevant for CHKREC and cell division. We analyzed by qRT-PCR the expression of the G2 transcriptional program, whose protein products are necessary for the G2/M transition; namely, Cyclin A2 (CCNA2, NM_001237.3 ), Cyclin B1 (CCNB1, NM_031966.3), WIP1 (PPM1D, NM_003620.3), FOXM1 (NM_001243088.1) and PLK1 (NM_005030.4) [16, 27, 70]. Our results show that the expression levels of these genes remain unaffected in FA-A cells, compared to wild type cells (Fig. 5a–e). Importantly, these genes are expressed in a cell cycle-dependent manner and are necessary for G2 phase completion [43], thus if they remain unchanged after MMC treatment, suggests Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 13 of 22 A D B C E Fig. 5 FA cells have a gene expression pattern compatible with checkpoint resolution despite DNA damage. Gene expression analysis of the genes belonging to the G2 transcriptional program did not show differences in the expression of these genes despite MMC treatment. Cyclin A2 (a), Cyclin B1 (b), WIP1 (c), FOXM1 (d) and PLK1 (e) (n = 3 independent experiments). No statistically significant differences were found in the gene expression patterns among groups that this program remains poised for resolution of the G2 cell cycle blockage in FA cells, even with incomplete DNA repair. Our BNM and these experimental results indicate that FA-A cells are able to block the cell cycle progression in G2 but eventually recover. Simulations with the BNM showed also that co-activation of G2 checkpoint and CHKREC components might occur in arrested FA cells, therefore, additional to CHK1, we evaluated other protein markers to asses key G2 checkpoint and CHKREC activation 24 h after MMC treatment. The G2 checkpoint markers included: WEE1, MYT1, p21 and γ H2AX; while CHKREC activation markers consisted of: WIP1, Aurora A, PLK1 and CDC25B. We observed that CHK1 activity is increased after MMC treatment in FA-A cells (See Fig. 3b), but other checkpoint components, namely WEE1, p21 and γ H2AX (Fig. 6a), have reduced levels. Remarkably, we also observed concomitant activation of CHKREC proteins PLK1, CDC25B and Aurora A (Fig. 6b) in damaged FA cells. Thus indicating Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 14 of 22 A B Fig. 6 FA and normal cells co-express checkpoint and CHKREC proteins. a Western Blot analysis of checkpoint proteins. b Western blot analysis of CHKREC proteins. FA cells increase the amount of some G2 blockage proteins, but have a reduction in others. Although CHK1 (Fig. 4b) and MYT1 show increased signal, WEE1, γ H2AX and p21 protein appear as diminished in FA cells, this weakens the checkpoint blockage, which is eventually overwhelmed by CHKREC signaling (n = 3 independent experiments, see also Fig.7) that despite a strong CHK1 signal that leads to cell cycle progression blockage, FA-A cells co-express the components that might dampen the DNA damage signaling and allow an eventual CHKREC despite an elevated amount of CA. In agreement, we observed in FA-A cells reduced levels of the histone γ H2AX, a DNA damage signaler and WIP1 phos- phatase target. Notably, we also observed weakening of p21 protein signaling, which has also been correlated with CHKREC activation [71]. These results suggest that signaling of DSBs might be weakened at this time-point, triggering full CHKREC activation and cell division despite a strong CHK1 signaling and high levels of CAs (relative protein amount for all the markers can be seen in Fig. 7). These experimental results show that the CHKREC is being activated in FA cells car- rying CA to a similar extent as normal undamaged cells, this CHKREC induction might allow the escape of G2 with unrepaired DNA damage and cell division. The correlation between the nodes of the network and the experiments performed can be seen in Table 3. Discussion Several methods are used to model and analyze biological systems [72–74]. These meth- ods analyze the topology of the network or the kinetics of the system specifying the flux of information through a continuous model or a logical model [74]. Continuous models represent the temporal dynamics of biochemical processes with considerable detail, but are highly dependent on the values of free parameters (initial protein concentrations and rate constants), whose estimation might be challenging as networks get larger [73, 75]. Logical models rely on qualitative knowledge [72]. Logical BNM are the minimal computational model necessary to obtain a meaningful idea about the dynamics of a regulatory network and are useful when detailed enzymatic informa- tion is missing [75, 76]. Many molecular regulatory systems show binary behaviors or act like bistable switches [77], thus the binary or discrete representation of BNM can adjusts to them and predict sequence patterns of proteins and gene activities with less Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 15 of 22 A B D C E F H G I Fig. 7 Western Blot densitometry analysis. Checkpoint proteins (a–e) and CHKREC proteins (f–i). (n = 3 independent experiments). No statistically significant differences were found in the protein expression patterns among groups parameters than a continuous model. Although BNM have been used for modeling sev- eral systems [32–37], they might not be appropriate if the system has continuous values or if knowledge on the network architecture is lacking [75]. We have developed a binary BNM that recapitulates in a simple manner the response to ICLs mediated by the FA/BRCA pathway [78]. Given that the different components of the network might remain unchanged, up-regulated or down-regulated instead of binary, an additional representation of the FA/BRCA network as a discrete ternary logical net- work might be also feasible [79], however a binary BNM resulted optimal given that our system presents gene expression showing a pattern of binary states (over-expressed, Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 16 of 22 Table 3 Correlation between experimental validations and nodes in the FA/BRCA BNM Process Nodes in the Experimental markers Validated role References FA/BRCA BNM used in this study in the BNM DNA damage ICL MMC FA cells are [21, 25, 26] induction hypersensitive to ICL inducing agents Upstream FAcore Non-evaluated ICL recognition [14, 16, 17] FA/BRCA FANCD2I proteins pathway NUC1 NUC2 DNA repair ADD γ H2AX, ICLs are unhooked [13, 21] intermediaries DSB CA in metaphase by FA core-recruited spreads DNA-endonucleases that generate a DSB and an ADD Downstream TLS Non-evaluated The ADD and DSB [14, 15, 18, 54] FA/BRCA FAHRR are repaired by TLS pathway and FA-dependent downstream homologous recombination repair, respectively. FA cells accumulate DSBs Alternative HRR2 Non-evaluated FA cells use [49, 56] DNA repair NHEJ alternative DNA pathways repair pathways, mainly NHEJ HRR2 is a criptic repair choice Checkpoint ATR Cell cycle arrest Upon DNA damage [27, 28, 31] ATM in G2, pCHK1-S341, normal and FA p53 p21 gene expression, cells activate MYT1, WEE1, p21 the G2/M checkpoint proteins Checkpoint CHKREC MPM2 mitotic index, The checkpoint [83, 84] and this work recovery cytokinesis block assay, is inactivated by G2/M transcriptional CHKREC after program, WIP1, PLK1, DNA repair CDC25, Aurora A FA cells seem to have proteins a lower threshold for CHKREC activation compared to normal cells under-expressed) or protein concentrations that can reach a saturation regime (full acti- vation) or remain in small concentrations (inactive). In addition the change to a ternary system would increase the possible states of the system from 32,768 to 14,348,907 states, thus augmenting the computational work. Our modeling of the FA/BRCA regulatory network has led to the observation that CHKREC is a mechanism conferring stability to this system in wild type and FA cells ([38] and this work). CHKREC is fully activated once the G2/M checkpoint has been satisfied Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 17 of 22 leading to the division of the cell [42]. CHKREC is mainly composed of phosphatases, such as WIP1, that inactivate the G2 checkpoint and protein-kinases that release the cell cycle blockage, such as Aurora A and PLK1 [41, 80]. Notably, the negative circuits mediated by CHKREC seem to be a central part of the control system of the FA/BRCA network: they are activated when the system induces the expression of its own inhibitors, and are necessary to attenuate the stimulatory signals arising from DNA damage (Fig. 1 and Fig. 2). When simulating mutants, we noticed that CHKREC function inactivates the check- point in FA core mutants despite unrepaired DNA damage, thus resolving the G2/M checkpoint arrest and allowing cell division. Therefore we should notice ele- vated/unchanged levels in the expression, quantity or activity of CHKREC components in FA cells with damaged DNA compared to undamaged normal cells, indicating that FA cells conserve checkpoint resolution capacity and are poised for cell divi- sion when the DNA damage checkpoint response ceases. To test the function of the CHKREC node, we experimentally evaluated the cell division capacity as well as check- point/CHKREC activation in FA-A lymphoblasts after induction of DNA damage with MMC. We evaluated the G2 blockage and found accumulation of FA-A cells into the G2 phase compartment after induction of DNA damage (Fig. 3a left panel) and a reduced num- ber of FA-A mitotic cells in comparison to normal cells after MMC exposition (Fig. 3a right panel). We also detected high CHK1 phosphorylation levels (Fig. 3b) as well as high p21 gene expression (Fig. 3c) in FA-A cells. CHK1 is a key protein kinase that transduces the DNA damage signaling, and p21 is a direct p53 transcription target, therefore an increase in p21 activation is the result of p53-increased activity, thus demonstrating that FA cells achieve a correct activation of the checkpoint that blocks the G2/M transition [27, 28]. p21 is a negative regulator of Cyclin B/CDK1 complex and is necessary to avoid the G2/M transition in presence of DNA damage [81]. Thus, CHK1 phosphorylation and p21 expression augment when a cell is exposed to DNA damaging agents and would be expected to drop-off once a cell has repaired the DNA damage [82]. When we evaluated the cell division capacity in a CB block assay, we did not observe differences in the frequency of binucleated cells between normal and FA-A cells (Fig. 4 middle panel), although MMC limited tetranucleated cells production in both cell types (Fig. 4c bottom panel). These results show that, under these experimental conditions, both FA-A and normal cells divide to a similar extent after induction of DNA damage by MMC. The capability of FA cells to divide with unrepaired DNA damage was evaluated by quantifying the frequency of DNA damage induced by MMC in cells committed to divide by scoring CAs in metaphase spreads, as well as in cells that have already performed cell division by quantifying the micronuclei observed in binucleated and tetranucleated cells. Our results showed, in both assays, that FA-A cells exposed to MMC carry significant DNA damage during mitosis and, nonetheless divide (Fig. 4b). Our BNM allowed us to propose that CHKREC function in FA cells might ignore in a certain level the presence of unrepaired DNA damage and could be responsible for their division, therefore we expected that normal and FA-A cells would have simi- lar activation levels of the CHKREC components. To test this possibility, we measured the expression of the G2 transcriptional program genes that promote CDK activity and Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 18 of 22 progression into mitosis, namely WIP1, Cyclin A2, Cyclin B1, PLK1, CDC25 and FOXM1 [43] (Fig. 5a–e) and evaluated the activation of some of the proteins involved in check- point and CHKREC (Fig. 6). In the first assay we observed that the expression of the genes that enable CHKREC and cell division are similar in normal/undamaged cells and dam- aged FA cells, even when FA cells carry a higher number of CAs. In addition, we observed co-expression of checkpoint and CHKREC proteins in FA cells treated with MMC (Fig. 6 and 7), indicating that damaged FA cells are poised for an eventual cell division despite DNA damage (Fig. 8). Checkpoint activation, cell cycle arrest and DNA repair require a great number of protein posttranslational modifications for their establishment. Dedicated enzymes that remove these modifications or degrade modified proteins allow checkpoint silencing and recovery [84]. WIP1 phosphatase and PLK1 kinase emerge as the coordinators of check- point silencing and recovery, respectively, however if there exist a certain order in their activation remains elusive. In general terms for cell division, Cyclin B levels must gradu- ally increase, while CDC25 phosphatase should remove any inhibitory phosphorylation of CDK1, thus promoting Cyclin B/CDK1 complex formation and mitotic entry. However, after induction of DNA damage, the G2 checkpoint inhibits CDK1 activity through p21, whilst WEE1 and MYT1 kinases degrade CDC25, avoiding mitotic entry [42, 70, 80]. WIP1 phosphatase dephosphorylates ATM, p53, CHK1, CHK2, γ H2AX and the p(S/T)Q motif originally modified by ATM and ATR [85, 86]. During CHKREC, Aurora- A kinase activates PLK1, which in turn targets WEE1 for proteasomal degradation and releases CDK1 from blockage [42, 87–89], in addition PLK1 interferes with CHK1, CHK2 and p53 stability, thus it also has an active role turning-off the DNA damage checkpoint [40]. Fig. 8 CHKREC components activation in normal and FA cells. After DNA damage induction, the cell activates the DNA damage integrity checkpoints, the G2/M checkpoint specifically avoids the transition of the cell from G2 to M phase with unrepaired DNA damage. Once the DNA has been repaired, the G2/M checkpoint is satisfied and the cell activates the CHKREC, a process that inactivates checkpoint proteins and promotes cell division. Upper panel. Normal cells activate CHKREC with repaired chromosomes. Bottom panel. FA cells activate CHKREC despite unrepaired chromosomes. The specific mechanism triggering this inappropriate CHKREC activation in FA cells remains unknown Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 19 of 22 In Fig. 6b we observe that the concentration of WIP1 is increased in normal cells and reduced in FA cells; on the contrary PLK1 is reduced in normal cell and increased in FA cells. Interestingly, PLK1 activity is redundant in unperturbed mitotic entry whereas it becomes essential in CHKREC after DNA damage [88, 89], consistently it is activated in our experiments in damaged FA-A cells. As FA cells carry spontaneous unrepaired DNA damage, this implies that their transition through G2 is always perturbed to a certain extent, thus PLK1 should become essential for FA cells survival. Given this, PLK1 over-activation must be involved in the adaptation of FA cells to DNA dam- age. Recent evidence shows that PLK1 activity is gradually increased during an ongoing DNA damage-induced cell cycle arrest and if the activity of the kinase exceeds beyond a certain level, the cell progresses to mitosis despite DNA damage persistance [83]. G2 checkpoint recovery might thus represent a checkpoint adaptation, where DNA dam- age triggers an arrest whose duration is not necessarily conditioned by DNA repair [84]. Regarding this, PLK1 might have a more critical role than WIP1 in the delivery of FA cells with unrepaired DNA damage from the G2 arrest, or WIP1 is acting before than the time-point that we are evaluating in this assays, hence we are not able to detect WIP1 protein (Fig. 6b). The distinction between both possible scenarios deserves further research. A final aspect to be considered are the findings of Ceccaldi and coworkers [31], who described an attenuated G2/M checkpoint activity in adult FA individuals that, con- comitantly to low CHK1 and p53 protein levels, allowed the escape of unrepaired DNA damage. Although they demonstrate that downregulation of the ATR-CHK1 axis is responsible for this phenotype, it remains elusive if this reduced checkpoint activity might be due to CHKREC over-activation or ectopic activity. In this study we set the basis to explore this possibility in FA individuals with an attenuated G2/M checkpoint and the general mechanism allowing G2/M resolution in non-attenuated FA individuals. Further, modeling the full interaction between the G2/M checkpoint and CHKREC, as well as a systematic inhibition of CHKREC components in FA cells, will shed light into the intricate interactions between these two processes. Our results show that highly damaged FA-A cells preserve the capacity to divide after a cell cycle arrest induced by DNA damage, a result that is consistent with our BNM FA core null mutant simulations. Nonetheless, the definition of the specific trigger for cell division remains unknown. To our judgment, the CHKREC hypothesis became the most rele- vant hypothesis emerging from our BNM given that CHKREC promotion might enable cell survival and amelioration of blood cell counts in pancytopenic FA patients, however CHKREC overexpression might also lead to exhaustion of the hematopoietic stem cell compartment as well as selection of malignant clones. Therefore, the thorough study of this process becomes relevant for the understanding of hematopoiesis and carcinogenesis in a FA background. Conclusion In this study we propose through network modeling that CHKREC, a program neces- sary for cell division after DNA damage, becomes activated in FA core mutant cells with unrepaired DNA damage. We experimentally show that highly damaged FA-A cells have CHKREC expression levels similar to those observed in normal undamaged cells, thus FA-A cells might ignore the presence of broken chromosomes through this process. We Rodríguez et al. Theoretical Biology and Medical Modelling (2015) 12:19 Page 20 of 22 observed that despite a prominent G2 arrest after MMC exposure, FA cells were able to activate the mechanisms that allow cell division (Fig. 8). FA cells are prone to apoptosis due to their DNA repair defects, however a great quan- tity of them divide in spite of unrepaired DNA damage, thus allowing the survival of FA individuals. The study of the mechanisms that allow FA cells to survive may help to develop novel therapies designed to promote hematopoiesis, as well as to avoid the division of malignant clones in FA patients. Competing interests The authors declare that they have no competing interests. Authors’ contributions AR, LM and SF conceived the project; AR, DS and EA developed the BNM; AR, LT, UJ, DS, BGT, EC and AMS performed experiments; RO and POW provided essential reagents; LM coordinated computational work; SF coordinated laboratory work. All authors read and approved the final manuscript. Acknowledgements Authors thank our colleagues at Dr. Frías’ laboratory for insightful discussions and Anet Rivera Osorio for invaluable assistance with experiments. This work was supported in part by grants from Universidad Nacional Autónoma de México PAPIIT IN200514 and IA201713, and Instituto Nacional de Pediatría-SSA, Fondos Federales 043-12. AR received the 346717 scholarship from Consejo Nacional de Ciencia y Tecnología (CONACyT). We thank S Becerra and J Yañez from IBT UNAM for primer synthesis. Author details 1Laboratorio de Citogenética, Departamento de Investigación en Genética Humana, Instituto Nacional de Pediatría, D.F., México. 2Programa de Doctorado en Ciencias Biomédicas, Universidad Nacional Autónoma de México, D.F., México. 3Instituto de Ecología, Universidad Nacional Autónoma de México, D.F., México. 4C3, Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, D.F., México. 5Current address: INRIA, Virtual Plants Project Team, UMR AGAP, Montpellier, France. 6Departamento de Ciencias de la Salud, Universidad Autónoma Metropolitana-Iztapalapa, D.F., México. 7Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, D.F., México. Received: 26 May 2015 Accepted: 12 August 2015 References 1. Surralles J, Jackson SP, Jasin M, Kastan MB, West SC, Joenje H. Molecular cross-talk among chromosome fragility syndromes. Genes Dev. 2004;18(12):1359–70. 2. Aurias A, Antoine JL, Assathiany R, Odievre M, Dutrillaux B. 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Mol Cell. 2004;15(5):799–811.	26385365	ATR = ( ( ATM ) AND NOT ( CHKREC ) ) OR ( ( ICL ) AND NOT ( CHKREC ) ) FAHRR = ( ( FANCD2I AND ( ( ( DSB ) ) ) ) AND NOT ( NHEJ AND ( ( ( CHKREC ) ) ) ) ) ICL = ( ( ICL ) AND NOT ( DSB ) ) p53 = ( ( ATM ) AND NOT ( CHKREC ) ) OR ( ( NHEJ ) AND NOT ( CHKREC ) ) OR ( ( ATR ) AND NOT ( CHKREC ) ) ATM = ( ( ( DSB ) AND NOT ( CHKREC ) ) AND NOT ( FAcore ) ) OR ( ( ( ATR ) AND NOT ( CHKREC ) ) AND NOT ( FAcore ) ) HRR2 = ( ( ( ( TLS AND ( ( ( NUC2 AND DSB ) ) ) ) AND NOT ( FAHRR ) ) AND NOT ( CHKREC ) ) AND NOT ( NHEJ ) ) OR ( ( ( NUC2 AND ( ( ( DSB AND ICL AND NHEJ ) ) ) ) AND NOT ( FAHRR ) ) AND NOT ( CHKREC ) ) NUC1 = ( FANCD2I AND ( ( ( ICL ) ) ) ) ADD = ( ( ( NUC1 ) AND NOT ( TLS ) ) AND NOT ( TLS ) ) OR ( ( NUC2 ) AND NOT ( TLS ) ) CHKREC = ( ( ( FAHRR ) AND NOT ( DSB ) ) OR ( ( TLS ) AND NOT ( DSB ) ) OR ( ( HRR2 ) AND NOT ( DSB ) ) OR ( ( NHEJ ) AND NOT ( DSB ) ) ) OR NOT ( TLS OR FAHRR OR DSB OR ADD OR HRR2 OR ICL OR CHKREC OR NHEJ ) DSB = ( ( ( ( NUC2 ) AND NOT ( FAHRR ) ) AND NOT ( HRR2 ) ) AND NOT ( NHEJ ) ) OR ( ( ( ( NUC1 ) AND NOT ( FAHRR ) ) AND NOT ( HRR2 ) ) AND NOT ( NHEJ ) ) TLS = ( ( FAcore AND ( ( ( ADD ) ) ) ) AND NOT ( CHKREC ) ) OR ( ( ADD ) AND NOT ( CHKREC ) ) FANCD2I = ( ( FAcore AND ( ( ( DSB ) AND ( ( ( ATR OR ATM ) ) ) ) OR ( ( ATR OR ATM ) ) ) ) AND NOT ( CHKREC ) ) FAcore = ( ( ICL AND ( ( ( ATR OR ATM ) ) ) ) AND NOT ( CHKREC ) ) NUC2 = ( ( ICL AND ( ( ( ATR OR ATM ) ) ) ) AND NOT ( FAcore AND ( ( ( FANCD2I ) ) ) ) ) OR ( ( NUC1 AND ( ( ( ICL AND p53 ) ) ) ) AND NOT ( FAcore AND ( ( ( FANCD2I ) ) ) ) ) NHEJ = ( ( ( ( NUC2 AND ( ( ( DSB ) ) ) ) AND NOT ( HRR2 ) ) AND NOT ( CHKREC ) ) AND NOT ( FAHRR ) )
1 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 www.nature.com/scientificreports Network modelling reveals the mechanism underlying colitis- associated colon cancer and identifies novel combinatorial anti-cancer targets Junyan Lu1,, Hanlin Zeng1,, Zhongjie Liang2,, Limin Chen1, Liyi Zhang1, Hao Zhang1, Hong Liu1, Hualiang Jiang1, Bairong Shen2, Ming Huang1, Meiyu Geng1, Sarah Spiegel3 & Cheng Luo1,2 The connection between inflammation and tumourigenesis has been well established. However, the detailed molecular mechanism underlying inflammation-associated tumourigenesis remains unknown because this process involves a complex interplay between immune microenvironments and epithelial cells. To obtain a more systematic understanding of inflammation-associated tumourigenesis as well as to identify novel therapeutic approaches, we constructed a knowledge-based network describing the development of colitis-associated colon cancer (CAC) by integrating the extracellular microenvironment and intracellular signalling pathways. Dynamic simulations of the CAC network revealed a core network module, including P53, MDM2, and AKT, that may govern the malignant transformation of colon epithelial cells in a pro-tumor inflammatory microenvironment. Furthermore, in silico mutation studies and experimental validations led to a novel finding that concurrently targeting ceramide and PI3K/AKT pathway by chemical probes or marketed drugs achieves synergistic anti-cancer effects. Overall, our network model can guide further mechanistic studies on CAC and provide new insights into the design of combinatorial cancer therapies in a rational manner. Inflammation and cancer are closely correlated1. The link between inflammation and cancer development is especially strong in patients with colorectal cancer (CRC), which is one of the most common malig- nancies and a leading cause of cancer mortality worldwide2. An increased risk of CRC development has been observed in patients with inflammatory bowel disease (IBD)3, and nonsteroidal anti-inflammatory drugs are effective in preventing colon neoplasia4. Dysregulations of the immune microenvironment and several inflammation-related signalling pathways, such as TNF-α /NF-κ B, IL-6/STAT3, COX-2/PGE2 and TGF-β /SMADs, have been shown to contribute to the development of inflammation-associated cancers5–9. In addition, emerging evidence suggests a possible link between the inflammatory microenvironment and cancer therapy resistance10. Nevertheless, most of these studies have focused on a single molecule or pathway. Information on how the immune microenvironment affects cancer development and how the inflammatory signalling pathways crosstalk with classical tumourigenesis pathways is still lacking. Therefore, to gain a holistic view on the mechanism of the development of inflammation-associated 1State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China. 2Soochow University, Center for Systems Biology, Jiangsu, China. 3Department of Biochemistry and Molecular Biology, Virginia Commonwealth University School of Medicine, Richmond, VA 23298, USA. These authors contributed equally to this work. Correspondence and requests for materials should be addressed to M.H. (email: mhuang@simm.ac.cn) or M.G. (email: mygeng@simm.ac.cn) or C.L. (email: cluo@simm.ac.cn) received: 15 January 2015 accepted: 07 September 2015 Published: 08 October 2015 OPEN www.nature.com/scientificreports/ 2 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 cancers, as well as to identify effective therapeutic targets, the extracellular microenvironment and intra- cellular signalling should be considered as a complex system and studied in a more systematic manner. To date, network modelling has been successfully used in the study of complex biological systems11–13. Existing knowledge of individual pathways can be incorporated into an integrated biological network, which could be further converted into a dynamic and predictive model using various mathematical modelling techniques. Boolean network models are the simplest discrete mathematical models and assume only two states (ON or OFF) for each node in the biological networks. Dynamic Boolean net- work models have been successfully applied in studies of complex diseases and biological processes, such as survival signalling of T-cell large granular lymphocyte (T-LGL) leukaemia13, hepatocyte growth factor (HGF)-induced keratinocyte migration12, immune cell differentiation14, and cell cycle regulation11. Boolean network models have also been used to integrate microenvironment components and signaling pathways to study cancer biology and predict therapy outcomes15,16. Boolean network models are espe- cially useful when the biochemical kinetic parameters of a certain biological process are unknown or the networks contain different species of biological entities, such as proteins, small molecules, mRNAs, and even cells. In the present work, we constructed a Boolean network model describing the growth and survival of preneoplastic epithelial cells in an inflammatory microenvironment, aiming to systematically study the molecular mechanisms underlying the development of colitis-associated colon cancer (CAC). The ability of the network model to recapture experimental observations validated its rationality. The detailed dynamic properties of the CAC network model under normal or dysregulated inflammatory microen- vironments were characterised. Our simulation results suggest the constant activation of the node rep- resenting dendritic cells (DC) creates a pro-tumor inflammatory microenvironment. Attractor analysis identified a key regulatory module involving P53, MDM2, GSK3-β and AKT signalling that may govern the malignant transformation of epithelial cells in this pro-tumour inflammatory microenvironment. Furthermore, in silico perturbation studies and experimental validations led us to identify several novel drug combinations that could significantly inhibit proliferation and induce apoptosis of tumour cells under an inflammatory stimulus. Taken together, our study integrates the extracellular microenviron- ment and intracellular signalling to provide a holistic view of inflammation-associated cancer. Our dry lab model and experimental findings can accelerate mechanistic studies and the development of novel combinatorial therapies for CAC and other inflammation-associated cancers. Results The CAC network representing intestinal epithelial cells in an immune microenvironment. By performing extensive literature and database searches, we constructed a knowledge-based network link- ing inflammatory signalling and cell proliferation and survival pathways of premalignant intestinal epi- thelial cells (IECs) (Fig. 1). We designated this network model as the CAC network. The entire CAC network incorporates 70 nodes and 153 edges. It can be divided into two parts: the IEC part, which contains nodes representing intracellular signalling components, and the immune microenvironment part, which contains the nodes representing immune cells, cytokines and chemokines. We also mod- elled ‘Proliferation’ and ‘Apoptosis’ as two output nodes to summarise the final biological effects of the inflammatory signalling. The nomenclature of all the nodes in the network is provided in Supplementary Table S1, and the biological description of the CAC network is presented in Supplementary Methods. The topology properties of the CAC network are summarised in Supplementary Table S2. The properties of the CAC network resemble those of general biological networks, which are characterised by higher clustering coefficient than random networks (Supplementary Table S2) and approximate power-law dis- tributions of node degrees (Supplementary Fig. S1). However, as the size of the CAC network is relatively small and its topology has been simplified, the quantitative characterisation of the network topology is not very informative and therefore we are focusing more on the dynamic properties of the CAC network. To further characterise the dynamic cell signaling events, we translated the CAC network into a Boolean network model, in which the network node was described by one of two possible states: ON or OFF. The ON state can be biologically interpreted as the activation of a gene/protein, or the production of a small molecule whereas the OFF state means the inhibition of a gene/protein or the absence of a small molecule. The regulatory relationships between upstream nodes (regulators) and downstream nodes (targets) are expressed by the logical operators AND, OR and NOT. The Boolean logical rules that govern the states of all these nodes are listed in Supplementary Table S3 and a thorough justification of these rules is provided in Supplementary Methods. Preliminary robustness tests suggested the CAC network model was robust to small amounts of noise (Supplementary Fig. S2), which is in accord with the general feature of biological networks. Dynamics of the CAC network model in a normal immune microenvironment. We first exam- ined whether our CAC network model could reproduce the experimental observations of the IECs in a normal immune microenvironment, including a non-inflammatory microenvironment and a normal inflammatory response. To simulate a non-inflammatory microenvironment, we fixed the states of all the nodes in the immune microenvironment (cyan nodes in Fig. 1) to OFF to represent the absence of inflammatory factors. We also fixed the state of the APC node to ON to represent premalignant IECs, in which the adenomatous polyposis coli (APC) protein is constantly expressed and activated to suppress www.nature.com/scientificreports/ 3 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 β -catenin signalling17. Subsequently, we iterated the model using the general asynchronous (GA) updat- ing method from a large number (5,000) of randomly selected initial states. When simulating a dynamic Boolean model using asynchronous updating methods, the frequency of a node being in the ON state (activation frequency) can give qualitative indications of the probability that a certain signaling compo- nent or a biological process being activated in a real cell. The activation frequencies of the two output nodes – Proliferation and Apoptosis at each simulation step were recorded to evaluate the impact of the microenvironment on cell survival states (Fig. 2a). In order to facilitate the comparison between our simulation results and previous experimental observations, we also recorded the activation frequen- cies of three nodes representing STAT3, NF-κ B and β -catenin transcription factors (STAT3, NFKB and BCATENIN), whose activations have been considered as hallmarks of CAC17–20. After 1000 steps of iteration, the Proliferation node rested in the OFF state, suggesting the IECs were unable to proliferate under non-inflammatory microenvironment. STAT3, NFKB and BCATENIN also stabilised in the OFF state within 1500 steps (Fig. 2a). By contrast, the steady activation frequency of the Apoptosis node was approximately 30%, indicating that a fraction of the epithelial cells could undergo apoptosis under non-inflammatory conditions. We then performed network reduction of the CAC network under the non-inflammatory microenvironment and identified its attractors (Supplementary Table S4). Attractors present the long-term behaviours of a Boolean model and can be regarded as potential stable states of a cell under certain conditions21. In consistence with the numerical simulation results from random initial states, two attractors, which represents the resting and apoptosis states of epithelial cells can be identified under this condition. These simulation results can be biologically interpreted as the tendency of IECs to remain in a resting state without inflammatory signals, but they also possess the capability Figure 1. Topology of the CAC network. Five colours were used to represent the nodes with different biological functions. The nodes in cyan belong to the extracellular immune microenvironment; the nodes in orange primarily participate in inflammatory signalling; the nodes in green primarily mediate cell proliferation; and the nodes in red regulate cell survival. The two purple nodes represent the output effects (proliferation and apoptosis) of the network model. An arrowhead represents positive regulation (activation or upregulation), whereas a diamond indicates negative regulation (inhibition or downregulation). www.nature.com/scientificreports/ 4 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 to undergo spontaneous apoptosis. Above simulation results are supported by previous findings that spontaneous apoptosis of the colon epithelium is a crucial mechanism for maintaining the homeostasis of gastrointestinal tissues22. Dendritic cells (DCs) are known as the most potent dedicated antigen-presenting cells specialised to initiate and maintain immunity and tolerance23. Therefore, we next simulated the normal initiation of an inflammatory response by setting the initial state of DC to the ON state to simulate the transient activa- tion of dendritic cells. Compared with the simulation results in the non-inflammatory microenvironment (Fig. 2a), the transient activation of DC moderately increased the activation frequency of Proliferation (Fig. 2b), whereas the activation frequency of Apoptosis was unchanged. In accordance, the CAC net- work under this condition possessed attractors that represent proliferation phenotypes in addition to apoptosis and resting phenotypes (Supplementary Table S4).The transient activation of DC also activated STAT3, NFKB and BCATENIN, as well as other immune cells with different activation frequencies; how- ever, none of them exceeded 0.5 (Fig. 2c and Supplementary Fig. S3). The activation frequencies of the immune suppressive nodes, such as IL10, was generally higher than that of the pro-inflammatory nodes, such as TNFA and IL6 (Fig. 2c). Therefore, our model suggests that the transient activation of DCs may initiate a controlled inflammatory reaction and eventually lead to an immune suppressive microenviron- ment, which does not support the uncontrolled growth of epithelial cells. These results are in agreement with observations that the normal microenvironment of colon mucosa is in an immune suppressive state, even if the colon contains a large amount of microbiota and antigens24. Effect of different immune microenvironments on IECs. Because the inflammatory microen- vironment is a mixture of different types of infiltrated immune cells, we evaluated the effect of differ- ent immune microenvironments on IECs by iteratively fixing one or a group of immune cell nodes at the ON state to mimic their constant presence in the microenvironment. The activation frequencies of Proliferation, Apoptosis, and different cytokine nodes in the corresponding immune microenvironment are shown in Table 1. Because there were 63 different combinations, only the combined activations of immune cell nodes that have additive effects to single activations are shown. We observed that in con- trast to the transient activation of DC, maintaining DC in the ON state permanently, which could be biologically interpreted as the constant activation of dendritic cells, created the most pro-proliferation microenvironment, in which the activation of Proliferation significantly increased and the activation of Apoptosis was blocked (line 1). This observation is supported by experimental findings that although the Figure 2. Dynamics of the CAC network model in the non-inflammatory microenvironment. (a,b) Activation frequencies for five nodes, including Proliferation, Apoptosis, STAT3, NFKB and BCATENIN, were observed in the non-inflammatory microenvironment (a) and during transient activation of the DC node (b,c) The stabilised activation frequencies for all the microenvironment nodes when the initial state of DC was set to ON and other microenvironment nodes were initially set to OFF. www.nature.com/scientificreports/ 5 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 transient activation of DCs initiates a controlled inflammatory reaction24, the sustained activation of DCs leads to chronic inflammation in IBDs25, which enhances the growth and survival of IECs7,26. In addition to DC, the constant activation of MAC, CTL or TH1 in the microenvironment could also increase the activation of Proliferation while decreasing the activation of Apoptosis (lines 2, 4 and 5). However, constant activation of TREG or TH2 slightly induced the activation of Proliferation but significantly increased the activation of Apoptosis (lines 3 and 6). Upon TREG activation, we observed increased activation of IL10 and TGFB and decreased activation of TNFA and IL6 (line 3 compared with lines 1 and 2). This observation is consistent with previous findings in which regulatory T cells were shown to reduce tumour growth in CAC cases by producing immune suppressive cytokines (e.g., IL-10 and TGF-β ) and reducing pro-inflammatory cytokines (e.g., TNF-α and IL-6)27. Interestingly, although the activation of CTL alone induced the activation of Proliferation but not Apoptosis (line 4), the com- bined activation of CTL and TREG significantly reduced Proliferation and increased Apoptosis, forming the most anti-tumourigenic microenvironment (line 11). This result reiterates the clinical phenomenon that CTL contributes to intestinal inflammation and promotes tumour growth in CAC cases28, despite of previous observations that infiltration of CTL is commonly correlated with favourable prognosis in sporadic colon cancers29. The effect of combined activation of CTL and TREG on the states of Apoptosis indicates that the additional activation of Treg cells can restore the cytotoxic function of CTL and there- fore enhance immune surveillance. We also identified several novel immune cell combinations that exhibited various effects on the states of Proliferation, Apoptosis and the cytokine nodes (lines 7–10 and lines 12–14), revealing the complex influence of the immune microenvironment on the survival and proliferation of IECs. These predictions can be useful for rationally designing immune therapies to restore normal microenvironments or for building anti-tumour microenvironments by modulating immune cells. Dynamics of the CAC network model in a pro-tumour inflammatory microenvironment. Notably, Proliferation did not reach full activation, even under the strongest tumour-promoting microen- vironment (fixing DC at ON). This result could be biologically interpreted as a controlled growth of the premalignant IECs in an inflammatory microenvironment. We then characterised the dynamic prop- erties of the CAC network model under this tumour-promoting microenvironment to understand the regulatory mechanisms of cellular proliferation and to identify the factors responsible for the malignant transformation of the IECs. After a transient activation, Apoptosis was eventually stabilised in the OFF state in all simulations, whereas the activation frequency of Proliferation was approximately 0.6 (Fig. 3a). The activation frequencies of STAT3 and NFKB were significantly increased compared with those in the non-inflammatory condition and the normal inflammatory response (Fig. 3a compared with Fig. 2a,b), which is consistent with experimental observations that these two transcription factors were highly active DC MAC TREG CTL TH1 TH2 Proliferation Apoptosis TNFA IL6 TGFB IFNG IL10 IL12 IL4 1 • 0.66 0 0.06 1 0 0.06 0.94 1 1 2 • 0.5 0 1 1 0 0.58 0.42 1 1 3 • 0.21 0.55 0 0.21 1 0 1 0 0 4 • 0.5 0 1 1 0 1 0 1 1 5 • 0.5 0 1 1 0 1 0 1 1 6 • 0.22 0.54 0 0.22 0.78 0 1 0 1 7 • • 0.59 0 0 1 1 0 1 1 1 8 • • 0.5 0 1 1 0 1 0 1 1 9 • • • 0.43 0.57 0 1 1 1 1 1 1 10 • • • • 0.5 0 1 1 1 1 1 1 1 11 • • 0.17 0.83 0 0.17 1 1 1 0 0 12 • • • 0.58 0.42 0 1 0 1 1 1 1 13 • • • • 0.49 0 1 1 0 1 1 1 1 14 • • 0.17 0.83 0 0.17 0.83 1 1 0 1 Table 1. Activation frequencies of Proliferation, Apoptosis and inflammatory cytokines for different combinatorial activations of immune cells. • indicates that the immune cell node in the header of the corresponding column was fixed in the ON state. www.nature.com/scientificreports/ 6 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 under inflammatory stimulus7,30. BCATENIN was partially activated, although we maintained APC in the ON state. Fixing APC in the OFF state to simulate the inactivation mutation of APC protein led to the full activation of BCATENIN. However, the activation frequency of Proliferation was not further increased (Supplementary Fig. S4). Clinical observations have shown that although APC mutations are one of the earliest events in sporadic colorectal cancers and are considered essential for the transition of preneoplastic cells to aberrant crypt foci and adenoma17,31, these mutations occur much later in CAC cases32,33. To further study the dynamic properties of the CAC network in the pro-tumor inflammatory microen- vironment, we performed network reduction and analysed the attractor structure of the CAC network under this pro-tumour microenvironment (fixing DC in the ON state). The first step of network reduc- tion identified 33 nodes that were stabilised either in the ON or OFF state. In particular, the nodes cor- relating with cell proliferation, such as RAS, RAF, MEK, ERK, and FOS, were stabilised in the ON state. Previous studies have shown that ERK/MAPK (extracellular signal-regulated kinase/mitogen-activated protein kinase) signaling can be activated by pro-inflammatory cytokines in IBD cases34 and that they are over-activated in both sporadic colon cancer and CAC35,36. In addition, Apoptosis and other nodes correlating with apoptotic cell death, such as BAX, TBID, CERAMIDE, CYTC, CASP3, CASP8, CASP9, MOMP and PP2A, were all stabilised in the OFF state, indicating the entire apoptosis pathway was blocked by the pro-tumor inflammatory microenvironment. After removing stabilised nodes, simple intermediate nodes, and nodes with zero out-degrees, the final reduced network comprised 21 nodes and 39 interac- tions (Fig. 3b). The Boolean rules governing the reduced network are provided in Supplementary Table S5. We identified three attractors of the reduced CAC network model: a complex attractor (Attractor 1) that contained 48 states, and two cyclic attractors (Attractors 2 and 3) that contained six states each (Table 2). By analysing the system’s states within these attractors, we found three activation patterns for each node in the sub-network. One pattern was full activation, in which the node was stabilised at ON in all states within an attractor; another pattern was partial activation, in which the node states oscillated between ON and OFF and half were ON; and the last pattern was inactivation, in which the node was stabilised at OFF in all states. Nodes STAT3, JAK and SOCS formed a negative feedback loop, and they oscillated in all the attractors; however, their activation patterns were the same. Therefore, these three nodes were excluded from further activation pattern analysis. Figure 3c shows the different Figure 3. Dynamics of the CAC network model in the pro-tumour inflammatory microenvironment. (a) The activation frequencies of Proliferation, Apoptosis, STAT3, NFKB and BCATENIN were observed in the pro-tumour inflammatory microenvironment. (b) The final reduced CAC network topology in the pro-tumour microenvironment. A green line with an arrowhead represents positive regulation, whereas a red line with a diamond indicates negative regulation. (c) The node activation patterns in the 21-node sub- network. Only the nodes that possess different activation patterns in the three attractors are shown. White, grey and black boxes represent inactivation, partial activation and full activation, respectively. (d) The core regulatory network that governed the behaviour of the CAC network in the pro-tumour inflammatory microenvironment. www.nature.com/scientificreports/ 7 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 activation patterns of the nodes within the three attractors. The pro-proliferate nodes AKT, BCATENIN, CYCLIND1, IKK, JUN and NFKB were all fully activated in Attractor 1, indicating a tendency for the IECs to undergo proliferation. However, P53 and P21 were partially activated in Attractor 1. Thus, the activation frequency of Proliferation was then restricted by the partial activation of P21 according to the Boolean function (Proliferation* = CYCLIND1 and not P21) of the reduced CAC network. Therefore, Attractor 1 represented a limited proliferation state. In Attractor 2, AKT, BCATENIN and CYCLIND1 were fully activated, and P21 was inactivated; thus, this attractor represented a proliferation state. Both CYCLIND1 and P21 were inactivated in Attractor 3; therefore, this attractor represented a resting state. When using synchronous updating methods, we found the reduced network had 28 attractors, which could also be grouped into three phenotypic classes: resting, limited proliferation and proliferation (Supplementary Table S6). By iteratively fixing one node in the sub-network to either an ON or OFF state, we identified a core regulatory network that governed the behaviour of the CAC network in the pro-tumour environment (Fig. 3d). Fixing AKT or CYCLIND1 in the OFF state could cause all state trajectories to fall into the resting attractor. Fixing GSK3B, P21, P53 or PTEN in the ON state had the same effect on the attractor landscape. Currently, alteration of the PTEN/PI3K/AKT signalling axis is a well-accepted driving force in carcinogenesis, and AKT has been shown to be dysregulated in most colon cancers37,38. Notably, our model herein emphasised that AKT activation was essential for accessing the attractor representing pro- liferation under an inflammatory stimulus. In addition, our model suggested that GSK3-β might play a tumour suppressor role in CAC by inhibiting CYCLIND1 and MDM2 in the pro-tumor inflammatory microenvironment (Fig. 3d). Most importantly, we observed that only the permanent inactivation of P53 or the activation of an endogenous P53 inhibitor, MDM2, could lead all the simulation trajectories to fall into the proliferation attractor. This effect can be biologically interpreted as a mutation or the constant suppression of P53, endowing IECs with the capability of uncontrolled growth and thereby initiating malignant transformation. Therefore, the simulation results suggest P53 pathway may act as the last guard before malignant transition in a strong pro-tumour inflammatory microenvironment, which is supported by the observation that P53 mutation (but not APC mutation) is a common event in the initiation phase of CAC progress39. The changes of the output effects under various conditions showed similar trends when different updating methods were used (Supplementary Table S7), indicating the overall dynamic properties of our Boolean network are not sensitive to the updating methods. Key nodes regulating malignant transformation revealed by systematic node perturbations. We subsequently performed a systematic node perturbation analysis on the entire CAC network to iden- tify other nodes that may mediate malignant transformation in an inflammatory microenvironment. We maintained DC in the ON state to mimic the premalignant IECs in a tumour-promoting microen- vironment and perturbed the states of other nodes in the CAC network. For the nodes that became stabilised in either an ON or OFF state, we fixed each node in the opposite of its stabilised state and continued updating other nodes. For the oscillated nodes, we perturbed each node twice by fixing the node to either ON or OFF. These perturbations mimic the manipulation of biological systems through genetic or chemical approaches, such as gene knockdown or treating cells with active compounds. We then observed the stabilised activation frequencies of the output nodes, Proliferation and Apoptosis, to evaluate the perturbation effect. Through this method, we identified 36 of 109 perturbations that could affect the activation of Proliferation or Apoptosis. We manually categorised these perturbations into pro-proliferative, anti-proliferative, and pro-apoptosis groups according to their effects on the states of Proliferation and Apoptosis. As shown in Fig. 4, the pro-proliferative group contains the perturbations that lead to a high activa- tion frequency (> 90%) of Proliferation. The perturbed nodes in this group come from four pathways: the P53 pathway (P53, MDM2), the PI3K/AKT pathway (PI3K, AKT, PTEN, and GSK3B), the NF-κ B pathway (NFKB, IKK, IKB) and the COX2/PGE2 pathway (PGE2, EP2 and COX2). The P53 node and PI3K/AKT pathway nodes also exists in the anti-proliferative group when set in the opposite states (Fig. 4). The critical roles of P53, MDM2 and AKT in CAC progress have been revealed by the above attractor analysis. The aberrant activation of NF-κ B and COX2/PGE2 signalling has also been detected in most CAC cases7,9. The pro-apoptotic perturbations include the inhibition of ERK MAPKs pathway ID Type Length Basin size Exclusive basin size Phenotype 1 Complex attractor 48 75% 12.5% Limited proliferation 2 Limited cycle 6 75% 2.05% Proliferation 3 Limited cycle 6 70% 0.03% Resting Table 2. Attractors of the reduced CAC network shown in Fig. 3b. The attractors can have shared basins since the general asynchronous updating method was used. Therefore, both the total basin size and the exclusive basin size were calculated for each attractor. www.nature.com/scientificreports/ 8 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 nodes (RAS, RAF, MEK and ERK) and the inhibition of IL6 signalling nodes (IL6 and GP130). Previous findings indicate that ERK MAPKs are the major regulators of proliferation during colon carcinogene- sis35, and the suppression of the ERK MAPK pathway inhibits proliferation and induce apoptosis of IECs in an inflammatory microenvironment40. Blocking IL-6 signalling with an anti-interleukin-6 receptor antibody or inhibiting IL-6 trans-signalling with TGF-β has also been shown to suppress tumour pro- gression in colon cancer41. Notably, the perturbations of the nodes that participate in sphingolipid metab- olism (CERAMIDE, SPHK1) are part of the pro-apoptotic group. A recent finding has demonstrated that SPHK1/S1P signalling plays a crucial role in linking chronic inflammation and CAC and that inhibiting SPHK1 could effectively reduce CAC development42. In all, 29 of 36 predictions made by in silico perturbations can be supported by previous experi- mental observations, which validates the rationality of our model (Supplementary Table S8). The per- turbation analysis also led to the novel prediction that activation of GSK3B, SMAD, ROS, PP2A, ATM, or CERAMIDE could inhibit proliferation or induce apoptosis of preneoplastic IECs in the pro-tumor inflammatory microenvironment, indicating that these molecules can be potential therapeutic targets for preventing CAC development. In silico double perturbation study and experimental validations identify novel drug com- binations. As both our model and previous experimental studies indicate that P53 is crucial for the malignant transformation of IECs in an inflammatory microenvironment, we maintained DC in the ON state and P53 in the OFF state simultaneously to mimic the state of a neoplastically transformed epithelial cell in a pro-proliferative microenvironment. We subsequently performed perturbation anal- ysis on the CAC network model under this condition to identify potential therapeutic targets for treat- ment of CAC. In this situation, only 18 of 89 perturbations could lower the activation frequency of Proliferation by over 50% (Supplementary Fig. S5), indicating that the CAC network in the neoplasti- cally transformed state was more robust than that in the pre-transformed state. Only two perturbations could induce the activation of Apoptosis: activation of MOMP and activation of CASP3 (Supplementary Fig. S5). However, MOMP or Caspase3 activation represent the terminal events in apoptotic cell death, and therefore, manipulating these processes therapeutically is impractical. The robustness of the CAC network model in the P53-inactive state suggested that the single target therapy may be less effective in killing tumour cells that had previously developed in CAC cases. We further performed double per- turbations by altering the state of two nodes simultaneously to seek possible combinatorial therapeutic approaches. We found several combined perturbations that could inhibit proliferation while increasing apoptosis (Table 3). However, not all of these perturbations are therapeutically accessible because of the lack of modulators, such as small molecule inhibitors. Among the double perturbations, we found some promising combinations that involve the activation of the CERAMIDE pathway while inhibiting the PI3K/AKT pathway. The above dynamic analysis indicated that AKT may play an important role in forming the attractor for the proliferation state, and several inhibitors of the PI3K/AKT pathway are under clinical evaluation43. Ceramide has also been previously shown to induce apoptosis and to sensitise tumour cells to radiotherapy44,45. Therefore, these combinations may be more clinically applicable than other predicted combinations. We then proceeded to validate the utility of these combinatorial perturbations in HT29 colon cancer cells, which have a P53 R273H inactivation mutation46. The impact of the inflammatory microenviron- ment was integrated by constantly exposing cells to the treatment with IL6 plus TNF-α , which resulted in the activation of STAT3 and NF-κ B signalling (Supplementary Fig. S6a). As predicted, short chain, cell permeable C2-ceramide, which has been shown to increase endogenous long chain ceramides47, Figure 4. Node perturbation results of the CAC network model in the pre-transformed state. The activation frequencies of node Proliferation and Apoptosis corresponding to each perturbation are shown. (+ ) indicates that the node was fixed in the ON state, and (− ) indicates that the node was fixed in the OFF state. www.nature.com/scientificreports/ 9 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 exerted synergistic effect with the AKT pan-inhibitor MK2206 (Fig. 5a) or PI3Kα /δ inhibitor GDC0941 (Fig. 5b) on cell viability under several concentrations, indicated by a combination index (CI) less than 1. To further understand the mechanism of the combinational effect of AKT inhibitors and ceramide, we extracted the sub-network related to ceramide, the PI3K/AKT pathway and inflammatory activation from the global CAC network. According to the sub-network shown in Fig. 5c, PI3K/AKT and ceramide signalling converged on the mitochondrial apoptotic pathway. Ceramide treatment could induce mito- chondrial apoptosis by directly activating MOMP (mitochondria outer membrane permeabilisation) and PP2A. MOMP could then disrupt the outer mitochondrial membrane (OMM) and mediate the subse- quent release of death-promoting proteins, such as cytochrome C, whereas PP2A could dephosphorylate and inactivate the anti-apoptotic protein BCL-2 and partially mediate Akt dephosphorylation. However, when the CERAMIDE node was activated alone, the mitochondrial apoptotic pathway was inhibited by activated AKT. AKT activated anti-apoptotic BCL-2 family proteins, such as BCL-2 and BCL-xL, by phosphorylating and inhibiting pro-apoptotic BCL-2 family proteins, such as BAD, BIM and BAX. Through the activation of mTOR, AKT can also inhibit PP2A and prevent the dephosphorylation and inactivation of BCL-248. Accordingly, a combination of BCL2 inhibitor ABT263 and C2-ceramide also had synergistic effect on cell viability (Fig. 5d). However, individual inhibition of the AKT node failed to activate mitochondrial apoptosis due to the absence of pro-apoptotic stress, such as the activation of CERAMIDE node. We found MOMP could only be fully activated when the CERAMIDE node was fixed in the ON state while the AKT node remained OFF, leading to the activation of downstream CYTC, CASP9 and CASP3, and consequently, cell apoptosis. To further validate this mechanism, we detected apoptosis using AnnexinV-propidium iodide dual staining. In accordance with our model, combined treatment of MK2206 and C2-ceramide showed strong synergistic apoptotic effects on HT29 cells (Fig. 5e). C2-ceramide or MK2206 alone induced approximately 20% cell apoptosis, whereas their combination significantly increased the apoptosis level to 40–60% (Fig. 5e). These results agree with those obtained by the combination of siRNA against AKT1, 2 and 3 and C2-ceramide (Fig. 5f and Supplementary Fig. S6b). We consistently observed the cleavage of caspase 3, 8 and 9 and PARP follow- ing combined treatment with MK2206 and C2-ceramide (Fig. 5g). The occurrence of apoptosis stemmed from a key mitochondrial event, namely cytochrome C release, which was not induced by individual treatments compared with the control group but was significantly increased after the combination of MK2206 and C2-ceramide (Fig. 5h). To further explore the clinical potential of our combination strategy, we tested combinations of mar- keted chemotherapeutic drugs. Epidermal growth factor receptor (EGFR) is one of the upstream tyrosine kinases of the PI3K/AKT pathway. Dosing HT-29 cells with C2-ceramide together with lapatinib or gefitinib, two clinically used EGFR inhibitors, exerted synergistic effects on cell viability (Supplementary Fig. S6c and S6d). In addition, PI3K/AKT inhibitors and FTY720 (fingolimod), which has previously been shown to inhibit and degrade SPHK149, and conversely increase ceramide levels50, also had com- binatory effects, although to a lesser extent than C2-ceramide (Supplementary Fig. S6e and S6f). In agreement with our previous findings that FTY720 stimulates endogenous ceramide accumulation by modulating sphingolipid metabolism50, FTY720 treatment elevated ceramide levels in HT-29 cells (Supplementary Fig. S6g). Taken together, experimental validations of the effective drug combinations and related mechanisms in colon cancer cells further supported the rationality of our model. Most importantly, the combination Nodes BAX(+) TBID(+) FAS(+) CYTC(+) CASP8(+) CASP9(+) CERAMIDE(+) AKT(− ) 0.06/0.4 0.06/0.41 0.06/0.68 0.05/0.34 0.06/0.69 0.06/0.47 0/1 PI3K(− ) 0.06/0.4 0.06/0.41 0.07/0.67 0.06/0.34 0.07/0.68 0.06/0.47 0/1 PTEN(+ ) 0.06/0.4 0.06/0.41 0.06/0.68 0.05/0.35 0.07/0.68 0.06/0.47 0/1 PP2A(+ ) 0/1 0/1 0.06/0.94 0.06/0.34 0/1 006/0.47 0/1 BCL2(− ) 0/1 0/1 NA NA 0/1 NA 0/1 RAS(− ) 0/0.41 0/0.41 0/0.84 0/0.35 0/0.69 0/0.48 0.06/0.94 IL6(− ) 0/1 0/1 0/1 0/1 0/1 0/1 0/1 GP130(− ) 0.06/0.94 0.06/0.91 0.06/0.94 0.05/0.95 0.05/0.95 0.06/0.94 0.06/0.94 IKK(− ) 0.37/0.45 0.33/0.46 0.12/0.72 0.4/0.38 0.12/0.72 0.25/0.51 0/1 IKB(+ ) 0.33/0.46 0.33/0.46 0.1/0.73 0.38/0.38 0.1/0.73 0.22/0.52 0/1 NFKB(− ) 0.33/0.46 0.33/0.46 0.1/0.73 0.37/0.39 0.1/0.73 0.22/0.51 0/1 IAP(− ) NA NA NA 0/1 0/1 0/1 NA Table 3. Double perturbations that may sensitise IECs to pro-apoptotic signals. (+ ) indicates fixing the node in the ON state (activation), (− ) indicates fixing the node in the OFF state (inhibition). The results are shown as the activation frequency of Proliferation/the activation frequency of Apoptosis, and NA indicates no additional effect on Apoptosis and Proliferation compared with single perturbation. www.nature.com/scientificreports/ 10 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 strategy provides a mechanism-based rational therapeutic approach for CAC, as well as for other inflammation-associated cancers. Discussion In this article, we presented a reconstruction of the CAC network and its implementation as a discrete dynamic Boolean model. The rationality of the CAC network model was justified by comparing the simulation results with existing observations, as well as novel experimental validations. Comprehensive analysis of the dynamic properties of the CAC network was also performed to unravel the missing link between chronic inflammation and cancer development and to identify potential therapeutic targets. Figure 5. Experimental validations of drug combination predictions that targeting AKT plus exogenous C2-ceramide reduced cell viability and increased cell apoptosis. (a) The combination effects of C2- ceramide and MK2206 on the viability of HT29 cells were determined by calculating the CI values for each data point. CI < 1 indicates a synergistic effect. (b) The combination effects of C2-ceramide and GDC0941 on the viability of HT29 cells. (c) The sub-network related to PI3K/AKT and ceramide signalling extracted from the entire CAC network. A green line with an arrowhead indicates positive regulation (activation or upregulation), whereas a red line with a diamond indicates negative regulation (inhibition or downregulation). (d) The combination effects of C2-ceramide and ABT263 on the viability of HT29 cells. (e) Synergistic apoptotic effects of C2-ceramide and MK2206 on HT29 cells. (f) Mean percentage of apoptotic cells treated with siAKT1/2/3 and/or 15 μ M C2-ceramide. ‘NC’ group stands for the scrambled negative siRNA pools, which was used as a negative control; ‘#1’ and ‘#2’ groups stand for AKT siRNA pools that contain different siRNA sequences listed in Supplementary Methods. (g) Immunoblots of lysates from cells treated with 15 μ M C2-ceramide and 10 μ M or 15 μ M MK2206 for 24 h. (h) Flow cytometry detection of mitochondrial cytochrome C levels in HT29 cells treated with DMSO (red line), 15 μ M C2-ceramide (blue line), 10 μ M MK2206 (orange line) and 15 μ M C2-ceramide+ 10 μ M MK2206 (green line) for 24 h. The bar graphs (right) show the relative fluorescence intensities representing mitochondrial cytochrome C levels. Data are representative of three independent experiments (mean ± s.e.m.). P < 0.01 and *P < 0.001 (Student’s t-test). ns, not significant. www.nature.com/scientificreports/ 11 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 Through manipulation of the nodes in the microenvironment component of the CAC network model, we suggests that dendritic cells play critical roles in forming the pro-proliferative inflammatory microen- vironment. The transient activation of DCs initiates a controlled inflammatory reaction and eventually leads to an immune suppressive microenvironment, whereas the sustained activation of DCs leads to a dysregulated inflammatory microenvironment, which strongly supports the proliferation and survival of IECs. In addition, we thoroughly characterized the dynamic properties of CAC network under the pro-tumor inflammatory microenvironment and identified a core regulatory network that governed the cell outcome. According to the core regulatory network, P53 inactivation was found to be critical for malignant transformation of epithelial cells under the pro-tumor inflammatory microenvironment. The result was supported by current findings of a dysregulated P53 pathway during CAC development and partly explained that in the ‘two-hit’ model, a somatic mutation is necessary for tumour initiation in a pro-tumour inflammatory microenvironment39. Subsequent systematic perturbation analysis indicated that various dysregulations could facilitate the malignant transformation of preneoplastic IECs in an inflammatory microenvironment, including the hyperactivation of the NF-κ B, PI3K/AKT or the COX2 pathways. Many perturbations were also predicted to suppress cell survival and proliferation of IECs in an inflammatory microenvironment, such as the inhibition of the ERK/MAPK pathway or the SPHK1/S1P pathway. These perturbations can be used as an early intervention method to prevent CAC development. However, the CAC network in a P53 inactive state, which mimicked malignant transformed IECs, was more resistant to perturba- tions. Double perturbation studies on the P53-inactivated CAC network suggested that combinatorial intervention methods through multi-targeted drugs or drug combinations could be more effective at treating later-stage CAC patients. Most importantly, we discovered and validated some novel combina- torial therapeutic approaches. We found that simultaneously inhibiting PI3K/AKT signalling and add- ing C2-ceramide, a pro-apoptotic sphingolipid signalling molecule, had a synergistic cytotoxic effect on colon cancer cells under an inflammatory stimulus. We explored the underlying mechanism of this synergistic effect by combining biochemical experiments and network simulations. We demonstrated that this effect was primarily attributed to regulation of the mitochondrial apoptotic pathway. As a pro-apoptotic signalling molecule, ceramide can directly or indirectly target mitochondria and lead to the release of apoptotic proteins, such as cytochrome C, and initiate the apoptosis machinery51,52. However, in many tumour cells, the PI3K/AKT pathway is highly active, which could in turn adversely affect the integrity of the mitochondria outer membrane by indirectly activating anti-apoptotic BCL-2 family proteins, such as BCL-2 or BCL-xL53. Our simulation results and previous experimental findings also suggest that inflammatory signalling can activate the AKT pathway to enhance survival of tumour cells. Therefore, only when PI3K/AKT signalling is blocked can the apoptosis machinery effectively be activated by a pro-apoptotic stimulus, such as ceramide (Fig. 6). Our results may also explain previous findings in which D, L-threo-1-phenyl-2-decanoylamino-3-morpholino-1-propanol (PDMP), a modula- tor of ceramide metabolism that elevates endogenous ceramide levels, could sensitise leukemic cells to the treatment of ABT263, an inhibitor of anti-apoptotic BCL2-like proteins54. Figure 6. Proposed model for the synergistic effect between ceramide and PI3K/AKT pathway inhibitors in inducing apoptotic cell death of cancer cells. Ceramide directly or indirectly targets mitochondria, leading to the release of apoptotic proteins, such as cytochrome C, and activates caspases. However, if the PI3K/AKT pathway is activated by an inflammatory stimulus or other growth factors, it can preserve the integrity of the mitochondrial outer membrane by activating the anti-apoptotic BCL-2 family of proteins, such as BCL-2 or BCL-xL, by inhibiting PP2A or BAD. Therefore, ceramide and PI3K/AKT pathway inhibitors exert a synergistic cytotoxic effect on cancer cells. Note: the arrows in this simplified scheme are not intended to indicate direct physiological interactions. www.nature.com/scientificreports/ 12 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 We are aware that this model is unable to capture the full complexity of CAC development. Some unknown factors may be present in CAC development, and merely incorporating outcomes, such as proliferation and apoptosis, is insufficient to assess tumour development. However, the basic property of tumour cells is uncontrolled proliferation, and inducing growth arrest or apoptosis is the most effective method to prevent cancer development. Therefore, our theoretical model can provide valuable informa- tion to guide further experimental studies, and this model can be easily refined and expanded with the availability of additional information. In conclusion, the dynamic modelling of the CAC development process can lead to a better mechanis- tic understanding of CAC and other inflammation-associated cancers because CAC serves as a paradigm for inflammation-associated cancer development. Our model and experimental findings will also be helpful in identifying novel therapeutic targets and the design of combinatorial therapeutic approaches to achieve early prevention and treatment of CAC. Materials and Methods Construction of the CAC network. A hierarchical method was used to construct the CAC network. First, signalling components that are critical participants in IBD and colorectal cancer, as indicated by a literature search, were collected. These components were used as seed nodes to build the initial network model. Then, the initial network was expanded using the GeneGo database (http://www.genego.com/). The regulatory relationships were then verified manually, and the interactions that were not specifically mentioned to be relevant to colitis or colon cancer were removed. Further, a similar approach, such as the one Zhang et al.13,55 used in constructing T-LGL network model, was adopted to remove the redundant and indirect interactions between nodes. Boolean dynamic modelling. In the Boolean model, each node has only two discrete states: ON and OFF (1 and 0). The regulatory relationships between upstream nodes (regulators) and downstream nodes (targets) are expressed by the logical operators AND, OR and NOT56. The future state of each node can be determined by the current states of the nodes and the Boolean transfer function , → , { } f : {0 1} 0 1 i ki , where ki is the number of regulators of node i. In Boolean models, the time variable is discrete and usually designated as steps. To propagate the discrete states of a Boolean model, different node-updating strategies have been proposed, such as synchronous and asynchronous update methods21. In this study, we mainly used a general asynchronous (GA) method57, in which a randomly selected node is updated at each time step. To evaluate the general behaviour trends for all nodes in the network model, multiple replicate simulations were performed from the same initial conditions but with random update orders. These trends can be reflected by the activation frequency for each node, which was calculated by dividing the number of simulations where the node is ON by the total replicate number. The GA method has been widely used in modelling signal transduction networks and has been suggested to be the most informa- tive and computationally efficient method among asynchronous updating strategies21,56. We also com- pared the simulation results using synchronous method, GA method and another asynchronous updating method—random order asynchronous (ROA) method58. Network reduction. Considering that the size of the state space of a Boolean model is exponentially dependent on the node number (a Boolean network with n nodes has 2n states) and attractor identifica- tion is a strong NP-complete problem, tracking all of the attractors within a relatively small network is computationally demanding. Therefore, we used a network reduction method proposed by Saadatpour et al.21 to reduce the node number while maintaining the long-term behaviour of the dynamic model. First, the nodes that stabilise in an attracting state (ON or OFF) during the entire simulation are elimi- nated. The attracting states of these nodes are only determined by the states of the input nodes and can be readily identified by inspecting the Boolean functions. Second, the simple mediator nodes, with both in-degrees and out-degrees equal to one, are iteratively removed, and their input and output nodes are connected directly. The dangling nodes (nodes with zero out-degrees) are also removed. This method can effectively reduce the network size and maintain the fixed point, as well as the complex attractor of Boolean models, using either synchronous or GA methods. Attractor identification. When updating a Boolean model, the state of the whole system at a certain time step is defined by the collection of the states of all the nodes at that step. As the Boolean model evolves over time, all the possible states of the system constitute the state space, which can be represented by a state transition graph whose nodes are the states of the system and the edges are allowed transitions among states. Attractors are special states in the state transition graph that the system will eventually settle down to and will not transit to other states. An attractor can either be a fixed point, in which the state of the system does not change, or a complex attractor, in which the states traverse regularly or irregularly over a series of states56. To identify the attractors of the reduced CAC network model, we firstly constructed the state transi- tion graph by updating the model starting from all possible initial states. Subsequently, the strongly con- nected components (SCCs) of the state transition graph were identified. SCCs are subgraphs of a directed graph in which every node is reachable from every other node. Complex attractors of a Boolean model www.nature.com/scientificreports/ 13 Scientific Reports \| 5:14739 \| DOI: 10.1038/srep14739 are the SCCs with empty out-component of the state transition graph59. Fixed point attractors can also be identified by this approach because a fixed point can be regarded as an SCC that contains only one state and is strongly connected to itself. The states in the state transition graph that can reach a certain attractor were marked as the basin states of that attractor. Coding. We implemented the functions used in this study into an open source Python software package named SimpleBool, which can be downloaded at https://github.com/SimpleBool/SimpleBool. SimpleBool directly reads model and parameter input files to perform dynamic simulations, attractor identification and in silico perturbation studies. SimpleBool can run in a stand-alone mode, and there- fore, coding experience is not required. Readers can refer to the website for further guidance on how to use the software. Antibody and compounds. Antibodies against STAT3, p-STAT3 (Y705), P65, p-P65 (S536), AKT, p-AKT (S473), PARP, cleaved-caspase 3, cleaved-caspase 8 and cleaved-caspase 9 were obtained from Cell Signalling Technology. Anti-GAPDH antibody was from Epitomics. MK2206, GDC0941 and ABT263 were purchased from Selleckchem. Cell line, cell culture and in vitro experiments. HT29 cells were obtained from the American Type Culture Collection (Rockville, USA). Cell line identity is routinely monitored by short tandem repeat (STR) analysis. Cell lines were grown at 37 °C in a 5% CO2 incubator. The cell medium was McCoy’s 5a (Gibco) supplemented with 10% FBS; 50 U/ml penicillin, 50 U/ml streptomycin.50 ng/ml IL6 (PeproTech) and 10 ng/ml TNF-α (PeproTech) were added to the medium to model an inflammatory microenvironment. Cell viability was measured using the Cell Proliferation Reagent sulforhodamine B (SRB, sigma). For siRNA transfection, cells were plated at 3 × 105 cells/ml in OPTI-MEM serum-free medium and transfected with a specific siRNA duplex using Lipofectamine® RNAiMAX Reagent Agent (Life Technologies) according to the manufacturer’s instructions. Synergy between combination treat- ments was determined by the combination index using CompuSyn software, available online. Flow cytometry. Cells were plated and treated the following day with the indicated agents. Cells were detached using trypsin-EDTA, resuspended in growth medium and counted. To detect cell apoptosis using Annexin V/propidium iodide staining, 1 × 106 cells were washed with cold PBS, resuspended in 100 μ l of binding buffer, and then, propidium iodide and FITC-labelled antibody against annexin V were added according to the manufacturer’s protocol (Vazyme Biotech). FlowCellect Cytochrome c Reagents (Millipore) were obtained for analysis of cytochrome C release from mitochondria. Briefly, 1 × 105 cells were washed with PBS, and then, a permeabilsation buffer working solution and a fixation buffer work- ing solution were added sequentially to achieve selective permeabilisation of mitochondria while leaving the mitochondrial membrane intact. Finally, 10 μ l of either the anti-IgG1-FITC isotype control or the anti-cytochrome c-FITC antibody was added to each sample according to the manufacturer’s protocol. 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Acknowledgements We are extremely grateful to Dr. Sarah Spiegel for the great discussion and suggestion which significantly improve the quality of our manuscript. We gratefully acknowledge financial support from the Hi- Tech Research and Development Program of China (2012AA020302 to CL), the Ministry of Science and Technology of China (2015CB910304 to HL), the National Natural Science Foundation of China (91029704 to CL, 91229204 to HL, 81302700 to ZL, 21472208 to CL, 81230076 and 21210003 to HJ). Author Contributions C.L., M.H. and M.G. conceived the project. J.L., Z.L., H.L.Z.(Hanlin Zeng), M.H., M.G. and C.L. designed the experiments. J.L. and Z.L. completed the coding part. L.C., L.Z. and H.Z. (Hao Zhang) collected data from literature and database. J.L., H.J., Z.L. and C.L. designed and performed computational studies and analysed the data. H.L.Z. and M.H. performed all cell-based assays. J.L., Z.L., H.L.Z., M.H., H.L., B.S. and C.L. analysed the data and wrote the manuscript. S.S. provided suggestions and helped with manuscript editing. All authors read and approved the final manuscript. Additional Information Supplementary information accompanies this paper at http://www.nature.com/srep Competing financial interests: The authors declare no competing financial interests. How to cite this article: Lu, J. et al. Network modelling reveals the mechanism underlying colitis- associated colon cancer and identifies novel combinatorial anti-cancer targets. Sci. Rep. 5, 14739; doi: 10.1038/srep14739 (2015). This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Com- mons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/	26446703	ROS = ( ( TNFR ) AND NOT ( SOD ) ) MEK = ( RAF ) OR ( ROS ) Proliferation = ( ( ( CYCLIND1 AND ( ( ( FOS ) ) ) ) AND NOT ( P21 ) ) AND NOT ( CASP3 ) ) SMAD7 = ( NFKB ) OR ( SMAD ) SMAD = ( ( TGFR ) AND NOT ( JUN ) ) CFLIP = ( NFKB ) PP2A = ( ( CERAMIDE ) AND NOT ( AKT ) ) TH1 = ( ( ( ( IFNG ) AND NOT ( IL4 ) ) AND NOT ( IL10 ) ) AND NOT ( TGFB ) ) OR ( ( ( ( IL12 ) AND NOT ( IL4 ) ) AND NOT ( IL10 ) ) AND NOT ( TGFB ) ) JNK = ( MEKK1 ) OR ( ASK1 ) BCATENIN = NOT ( ( APC AND ( ( ( GSK3B ) ) ) ) ) TNFR = ( TNFA ) IL10 = ( TH2 ) OR ( TREG ) TGFB = ( TREG ) IFNG = ( CTL ) OR ( TH1 ) STAT3 = ( JAK ) RAS = ( EP2 ) OR ( GP130 ) MOMP = ( ( CERAMIDE ) AND NOT ( BCL2 ) ) OR ( ( BAX ) AND NOT ( BCL2 ) ) OR ( ( TBID ) AND NOT ( BCL2 ) ) DC = ( ( TNFA ) AND NOT ( IL10 ) ) OR ( ( CCL2 ) AND NOT ( IL10 ) ) CERAMIDE = ( ( SMASE ) AND NOT ( SPHK1 ) ) IL6 = ( MAC ) OR ( DC ) OR ( NFKB ) CASP9 = ( ( ( CYTC ) AND NOT ( P21 ) ) AND NOT ( IAP ) ) Apoptosis = ( CASP3 ) ATM = ( ROS ) CYTC = ( MOMP ) P53 = ( ( PTEN ) AND NOT ( MDM2 ) ) OR ( ( ATM ) AND NOT ( MDM2 ) ) OR ( ( JNK ) AND NOT ( MDM2 ) ) SMAC = ( MOMP ) CTL = ( ( IFNG ) AND NOT ( TGFB ) ) COX2 = ( TNFR AND ( ( ( S1P ) ) ) ) CASP3 = ( ( CASP9 ) AND NOT ( IAP ) ) OR ( ( CASP8 ) AND NOT ( IAP ) ) ERK = ( MEK ) GSK3B = NOT ( ( AKT ) OR ( EP2 ) ) FOS = ( ERK ) TREG = ( ( IL10 ) AND NOT ( IL6 ) ) OR ( ( DC ) AND NOT ( IL6 ) ) MEKK1 = ( TGFR ) OR ( CERAMIDE ) OR ( TNFR ) NFKB = NOT ( ( IKB ) ) FADD = ( FAS ) OR ( TNFR ) TNFA = ( MAC ) BCL2 = ( ( ( STAT3 ) AND NOT ( P53 ) ) AND NOT ( PP2A ) ) OR ( ( ( NFKB ) AND NOT ( P53 ) ) AND NOT ( PP2A ) ) CYCLIND1 = ( ( BCATENIN ) AND NOT ( GSK3B ) ) OR ( ( JUN ) AND NOT ( GSK3B ) ) OR ( ( STAT3 ) AND NOT ( GSK3B ) ) JAK = ( ( GP130 ) AND NOT ( SOCS ) ) PTEN = ( ( ( P53 ) AND NOT ( JUN ) ) AND NOT ( NFKB ) ) SMASE = ( FADD ) OR ( P53 ) IL4 = ( DC ) OR ( TH2 ) MDM2 = ( ( ( P53 AND ( ( ( AKT ) ) ) ) AND NOT ( ATM ) ) AND NOT ( GSK3B ) ) TBID = ( ( CASP8 ) AND NOT ( BCL2 ) ) JUN = ( ( BCATENIN AND ( ( ( JNK ) ) ) ) AND NOT ( GSK3B ) ) OR ( ( ERK AND ( ( ( JNK ) ) ) ) AND NOT ( GSK3B ) ) S1P = ( SPHK1 ) SPHK1 = ( TNFR ) OR ( ERK ) MAC = ( ( IFNG ) AND NOT ( IL10 ) ) OR ( ( CCL2 ) AND NOT ( IL10 ) ) TGFR = ( ( TGFB ) AND NOT ( SMAD7 ) ) PGE2 = ( COX2 ) RAF = ( CERAMIDE ) OR ( RAS ) SOCS = ( STAT3 ) P21 = ( ( ( P53 ) AND NOT ( CASP3 ) ) AND NOT ( GSK3B ) ) OR ( ( ( SMAD ) AND NOT ( CASP3 ) ) AND NOT ( GSK3B ) ) BAX = ( ( TBID AND ( ( ( PP2A ) ) ) ) AND NOT ( AKT ) ) OR ( ( P53 AND ( ( ( PP2A ) ) ) ) AND NOT ( AKT ) ) IKK = ( AKT ) OR ( TNFR AND ( ( ( S1P ) ) ) ) FAS = ( CTL ) CCL2 = ( NFKB ) EP2 = ( PGE2 ) SOD = ( STAT3 ) OR ( NFKB ) PI3K = ( ( EP2 ) AND NOT ( PTEN ) ) OR ( ( RAS ) AND NOT ( PTEN ) ) AKT = ( ( ( PI3K ) AND NOT ( CASP3 ) ) AND NOT ( PP2A ) ) IL12 = ( MAC ) OR ( DC ) CASP8 = ( ( ( FADD ) AND NOT ( P21 ) ) AND NOT ( CFLIP ) ) ASK1 = ( ( ROS ) AND NOT ( P21 ) ) IKB = NOT ( ( IKK ) ) GP130 = ( IL6 ) TH2 = ( ( ( IL4 ) AND NOT ( IFNG ) ) AND NOT ( TGFB ) ) IAP = ( ( NFKB ) AND NOT ( SMAC ) ) OR ( ( STAT3 ) AND NOT ( SMAC ) )
RESEARCH ARTICLE Mathematical Modelling of Molecular Pathways Enabling Tumour Cell Invasion and Migration David P. A. Cohen1,2,3, Loredana Martignetti1,2,3, Sylvie Robine1,4, Emmanuel Barillot1,2,3, Andrei Zinovyev1,2,3‡, Laurence Calzone1,2,3‡* 1 Institut Curie, Paris, France, 2 INSERM, U900, Paris, France, 3 Mines ParisTech, Fontainebleau, Paris, France, 4 CNRS UMR144, Paris, France ‡ These authors are joint senior authors on this work. * laurence.calzone@curie.fr Abstract Understanding the etiology of metastasis is very important in clinical perspective, since it is estimated that metastasis accounts for 90% of cancer patient mortality. Metastasis results from a sequence of multiple steps including invasion and migration. The early stages of metastasis are tightly controlled in normal cells and can be drastically affected by malignant mutations; therefore, they might constitute the principal determinants of the overall meta- static rate even if the later stages take long to occur. To elucidate the role of individual muta- tions or their combinations affecting the metastatic development, a logical model has been constructed that recapitulates published experimental results of known gene perturbations on local invasion and migration processes, and predict the effect of not yet experimentally assessed mutations. The model has been validated using experimental data on transcrip- tome dynamics following TGF-β-dependent induction of Epithelial to Mesenchymal Transi- tion in lung cancer cell lines. A method to associate gene expression profiles with different stable state solutions of the logical model has been developed for that purpose. In addition, we have systematically predicted alleviating (masking) and synergistic pairwise genetic interactions between the genes composing the model with respect to the probability of acquiring the metastatic phenotype. We focused on several unexpected synergistic genetic interactions leading to theoretically very high metastasis probability. Among them, the syn- ergistic combination of Notch overexpression and p53 deletion shows one of the strongest effects, which is in agreement with a recent published experiment in a mouse model of gut cancer. The mathematical model can recapitulate experimental mutations in both cell line and mouse models. Furthermore, the model predicts new gene perturbations that affect the early steps of metastasis underlying potential intervention points for innovative therapeutic strategies in oncology. PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 1 / 29 a11111 OPEN ACCESS Citation: Cohen DPA, Martignetti L, Robine S, Barillot E, Zinovyev A, Calzone L (2015) Mathematical Modelling of Molecular Pathways Enabling Tumour Cell Invasion and Migration. PLoS Comput Biol 11(11): e1004571. doi:10.1371/journal. pcbi.1004571 Editor: Edwin Wang, National Research Council of Canada, CANADA Received: December 19, 2014 Accepted: September 29, 2015 Published: November 3, 2015 Copyright: © 2015 Cohen et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: This work was funded by INVADE grant from ITMO Cancer (Call Systems Biology 2012) to DPAC LM AZ EB LC; and “Projet Incitatif et Collaboratif Computational Systems Biology Approach for Cancer” from Institut Curie; http://curie. fr/recherche/programmes-incitatifs-cooperatifs-l% E2%80%99institut-curie to DPAC LM AZ EB LC. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Author Summary We provide here a logical model that proposes gene/pathway candidates that could abro- gate metastasis. The model explores the mechanisms and interplays between pathways that are involved in the process, identifies the main players in these mechanisms and gives some insight on how the pathways could be altered. The model reproduces phenotypes of published experimental results such as the double mutant Notch+/+/p53-/-. We have also developed two methods: (1) to predict genetic interactions and (2) to match transcrip- tomics data to the attractors of a logical model and validate the model on cell line experiments. Introduction Understanding the etiology of metastasis is very important in clinical perspective. Despite the progress with treatment of the primary tumours, the chances of survival for a patient decrease tremendously once metastases have developed [1]. It is estimated that metastasis accounts for 90% of cancer patient mortality [2]. It is now understood that the metastatic process follows a sequence of multiple steps, each being characterised by a small probability of success: 1) infil- tration of tumour cells into the adjacent tissue, 2) migration of tumour cells towards vessels, 3) intravasation of tumour cells by breaching through the endothelial monolayer, 4) travelling in the circulatory or in the lymphoid system, 5) extravasation when circulating tumour cells re- enter a distant tissue, and 6) colonisation and proliferation in distant organs [3]. The early stages of invasion and migration are tightly controlled in normal cells and can be drastically affected by malignant mutations. It has been shown indeed that primary and secondary tumours have a common gene signature [4] that mediates the initial stages of metastasis while extravasation and colony formation by a (tumour) cell does not require malignant gene alter- ations [5], supporting the idea that the later stages of metastasis are affected by the anatomical architecture of the vascular system [6]. Here, we focus on the ability of cancer cells to infiltrate and migrate into the surrounding tissue. The first step towards the formation of secondary tumours is acquiring the ability to migrate. In order to gain motile capacity, epithelial cells need to change their morphology through Epithelial to Mesenchymal Transition (EMT), a process which occurs during develop- ment (EMT type 1), wound healing (EMT type 2) and under pathological conditions such as cancer (EMT type 3) [7,8]. EMT type 3 is characterised by both loss of E-cadherin (cdh1) and invasive properties at the invasive front of the tumour [9]. Gene expression of E-cadherin is inhibited by the transcription factors Snai1/2, Zeb1/2 and Twist1, while gene expression of N- cadherin (cdh2) is induced by the same transcription factors [8,10,11]. These transcription factors activate other genes that initiate EMT [11–13] and are induced by several signalling pathways including TGF-β, NF-κB, Wnt and Notch pathways [8,14,15]. On the contrary, the transcription factor p53 has been shown to inhibit EMT via degradation of Snai2 [16]; how- ever, a p53 loss of function (LoF) alone is not sufficient to induce EMT [17]. After the switch of E-cadherin to N-cadherin expression, the cell-cell contacts are weakened [18,19] and cancer cells can pass the basal membrane to infiltrate the surrounding tissue [20]. The process of local invasion can be active since tumour cells can secrete Matrix Metalloproteinases (MMPs) that dissolve the lamina propria [21]. MMPs are also able to digest other components of the extra- cellular matrix (ECM) and thereby to release growth factors and cytokines that are attached to the ECM [21,22] which in turn activate the tumour cell’s ability to propagate the dissolvement of the lamina propria. Finally, after dissolving the lamina propria and invading the (local) Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 2 / 29 Competing Interests: The authors have declared that no competing interests exist. stroma, cancer cells can migrate to distant sites by intravasation and extravasation of the vascu- lar system [2]. To gain insight in the regulation of the metastatic process, several groups have developed mathematical models of various aspects of it [23–29] (S1 Text). Our aim is to understand the role of gene alterations in the development of metastasis. In many (experimental or in silico) models, EMT is described as a very important step in acquir- ing metastasis and even considered to be synonymous to appearance of metastasis [30–32]. Due to EMT role in metastasis, much research has been performed to elucidate its regulation. The regulation of EMT is known to be complex and simple intuition is not sufficient to com- prehend how genetic alterations (mutations and copy number variations) affect it. Logical modelling can give qualitative insight on how they could affect EMT and subsequently metastasis. Previously, we have constructed a detailed map of molecular interactions involved in EMT regulation which is freely available at [33], and based on its structural analysis, we hypothesized a simple qualitative mechanism of EMT induction through upregulation of Notch and simulta- neously deletion of p53. This prediction has been experimentally validated in a mouse model of colon carcinoma [31]. In the present study, we significantly extend the biological context and provide a mathemat- ical framework for the description of the necessary conditions for having metastasis, going beyond the regulation of EMT only. We take into consideration the gained motility and ability to invade as determinants of the metastatic process. For this purpose we largely extended and re-designed the signalling network including more molecular players and phenotypes, and translated the network into a formal mathematical model, allowing prediction of the metastasis probability and the systematic analysis of mutant properties. Therefore, this work represents a significant progress with respect to the previous results, allowing reconsideration of the qualita- tive hypothesis suggested before using a formal mathematical modelling approach. First, we introduce a logical model that recapitulates the molecular biology of the early steps in metastasis. The construction of the influence network and the choice of the logical rules are both based on knowledge derived from scientific articles. The final readouts of the model are the phenotype variables CellCycleArrest, Apoptosis and the aggregated phenotype Metastasis that combines the phenotypes EMT, Invasion and Migration. We have chosen those final read-outs, as we believe that a metastatic phenotype depends on the occurrence of EMT, invasion and migration. In addition, apoptosis is of importance to the system as during healthy conditions, the cells undergo apoptosis when the cells detach from the basal membrane [34]. Suppressing apoptosis during migration is a required key feature. Our interest in cell cycle arrest is due to results of the mouse model [31] that show decreased proliferation. We try to model this feature in our logical model by looking at the regulation of cell cycle arrest. We did not focus on other phenotypes (or cancer hallmarks) such as prolifera- tion explicitly, senescence, or angiogenesis. These are often considered in cancer studies but they were out of the scope of this work, which focused on depicting early invasion modes and not specifically on how tumour growth is regulated. The model inputs have been selected to represent external signals necessary for the metastasis initiation pathways. The Boolean model that we show here describes a possible regulation of the metastatic potential of a single tumour cell and not of multiple cells or a tissue. We provide a simplified version of the model where some genes are grouped into modules (or pathways) allowing an analysis based on pathways rather than individual genes. Both ver- sions of the models are validated by reproducing the phenotypic read-outs of published experi- mental mouse and cell line models. We then analyse the two models and formulate several types of predictions: at the level of individual genes, e.g. exploring the individual role of each EMT inducer in metastasis; and at Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 3 / 29 the level of pathways, e.g. investigating the functional role of each pathway in triggering metas- tasis. The logical models can suggest a systematic mechanistic explanation for the majority of experimentally validated mutations on the local invasion and migration processes. Moreover, we were able to establish a link between the solutions of the mathematical model and the gene expression data from cell lines in which EMT was transiently induced. In addition, we have applied this method to the analysis of transcriptomes of tumour biopsies. Lastly, we investigate how genetic interactions between different gene mutations can affect the probability of reaching a metastatic outcome. Our analysis predicts the effect of single mutations and the genetic interactions between two single mutations with respect to several cellular phenotypes. Our model proves an exceptionally efficient synergetic effect of increased activity of Notch in combination with a decreased activity of p53 on metastasis in accordance with our previous work [31]. Materials and Methods The influence network The construction of the influence network is based on scientific articles that describe the inter- actions between nodes of the model. We first selected the main genes or proteins that may con- tribute to activating EMT, regulating early invasion and triggering metastasis. We then searched for experimentally proven physical interactions that would link all these players, and simplified the detailed mechanisms into an influence network. For example, it has been shown experimentally that AKT protein phosphorylates and stabilises MDM2, which in turn inhibits p53 by forming a complex, leading to protein degradation of p53. We simplified the biochemi- cal reactions by a negative influence from AKT to p53. The influence network is then translated into a mathematical model using Boolean formalism (see below for details). We verified the coherence of the network by comparing the outcome of the perturbed model to the observed phenotypes of mutants found in the literature. The final model is the result of several iterations that led to the accurate description of most of the published mutants related to the genes included in our model. Once the model was able to reproduce most of the published mutant experiments, we simulated mutants and conditions not yet assessed experimentally and pre- dicted the outcome. The Boolean formalism From the influence network recapitulating known facts about the processes, we develop a math- ematical model based on the Boolean formalism. To do so, we associate to a node of the influ- ence network a corresponding Boolean variable. The variables can take two values: 0 for absent or inactive (OFF), and 1 for present or active (ON). The variables change their value according to a logical rule assigned to them. The state of a variable will thus depend on its logical rule, which is based on logical statements, i.e., on a function of the node regulators linked with logi- cal connectors AND (also denoted as &), OR (\|) and NOT (!). A state of the model corresponds to a vector of all variable states. All possible model states are connected into a transition graph where the nodes are model states and the edges correspond to possible transitions from one model state to another. The transition graph is based on asynchronous update, i.e., each vari- able in the model state is updated one at a time as opposed to all together in the synchronous update strategy. Attractors of the model refer to long-term asymptotic behaviours of the sys- tem. Two types of attractors are identified: stable states, when the system has reached a model state whose successor in the transition graph is itself; and cyclic attractors, when trajectories in the transition graph lead to a group of model states that are cycling. In this model, no cyclic attractors were found for the wild type case. However, we do not guarantee the non-existence Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 4 / 29 of cyclic attractors in some of the perturbed cases, as perturbations of the model may create new dynamics. The logical rules A logical rule is written for each variable of the model, corresponding to a node in the influence network, in order to define how its status evolves (ON or OFF). In this rule, the variables of the input nodes are linked by logical connectors according to what is known about their combined activities. There are several cases to consider: (1) The simplest logical rule that can be assigned is when a variable depends on the activity of a single input: for instance, the transcription factor Twist induces the transcription of the cdh2 gene (see Table 1); (2) In the case of an input that has a negative effect on the activity of its target, the Boolean operator “NOT” or “!” is used: EMT is, for example, activated by CDH2 but inactivated by CDH1, thus for EMT to be activate, CDH1 should be OFF and CDH2 should be ON. The complete logical rule for the activation of EMT will be EMT = 1 (ON) if CDH2 &! CDH1 (see Table 1); (3) In some cases, a gene can be activated by two independent genes reflecting two different conditions and thus inputs are Table 1. Logical rules describing the activity of a node. Node Rule AKT1 CTNNB1 & (NICD \| TGFbeta \| GF \| CDH2) & ! p53 & ! miR34 & ! CDH1 AKT2 TWIST1 & (TGFbeta \| GF \| CDH2) & !(miR203 \| miR34 \| p53) CDH1 !TWIST1 & ! SNAI2 & ! ZEB1 & ! ZEB2 & ! SNAI1 & ! AKT2 CDH2 TWIST1 CTNNB1 !DKK1 & ! p53 & ! AKT1 & ! miR34 & ! miR200 & ! CDH1 & ! CDH2 & ! p63 DKK1 CTNNB1 \| NICD ERK (SMAD \| CDH2 \| GF \| NICD) & ! AKT1 GF !CDH1 & (GF \| CDH2) miR200 (p63 \| p53 \| p73) & !(AKT2 \| SNAI1 \| SNAI2 \| ZEB1 \| ZEB2) miR203 p53 & !(SNAI1 \| ZEB1 \| ZEB2) miR34 !(SNAI1 \| ZEB1 \| ZEB2) & (p53 \| p73) & AKT2 & ! p63 & ! AKT1 NICD !p53 & ! p63 & ! p73 & ! miR200 & ! miR34 & ECM p21 ((SMAD & NICD) \| p63 \| p53 \| p73 \| AKT2) & !(AKT1 \| ERK) p53 (DNAdamage \| CTNNB1 \| NICD \| miR34) & ! SNAI2 & ! p73 & ! AKT1 & ! AKT2 p63 DNAdamage & ! NICD & ! AKT1 & ! AKT2 & ! p53 & ! miR203 p73 DNAdamage & ! p53 & ! ZEB1 & ! AKT1 & ! AKT2 SMAD TGFbeta & ! miR200 & ! miR203 SNAI1 (NICD \| TWIST1) & ! miR203 & ! miR34 & ! p53 & ! CTNNB1 SNAI2 (TWIST1 \| CTNNB1 \| NICD) & ! miR200 & ! p53 & ! miR203 TGFbeta (ECM \| NICD) & ! CTNNB1 TWIST1 CTNNB1 \| NICD \| SNAI1 VIM CTNNB1 \| ZEB2 ZEB1 ((TWIST1 & SNAI1) \| CTNNB1 \| SNAI2 \| NICD) & ! miR200 ZEB2 (SNAI1 \| (SNAI2 & TWIST1) \| NICD) & ! miR200 & ! miR203 CellCycleArrest (miR203 \| miR200 \| miR34 \| ZEB2 \| p21) & ! AKT1 Apoptosis (p53 \| p63 \| p73 \| miR200 \| miR34) & ! ZEB2 & ! AKT1 & ! ERK EMT CDH2 & ! CDH1 Invasion (SMAD & CDH2) \| CTNNB1 Migration VIM & AKT2 & ERK & ! miR200 & ! AKT1 & EMT & Invasion & ! p63 Metastasis Migration doi:10.1371/journal.pcbi.1004571.t001 Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 5 / 29 linked by an OR, e.g., DKK can be activated either by CTNNB1 or by NICD, independently of each other; (4) In some other cases, two activators are linked by an AND connector, e.g., ZEB2 whose activity depends on several inputs including TWIST1 & SNAI2 which are needed simul- taneously: it has been observed experimentally that both transcription factors Twist1 and Snai2 are required to induce gene expression of zeb2. All models are available in GINsim format in S1 File. Computing phenotype probabilities using MaBoSS MaBoSS is a C++ software for simulating continuous/discrete time Markov processes, defined on the state transition graph describing the dynamics of a Boolean network. The rates up (change from OFF to ON) and down (from ON to OFF) for each node are explicitly provided in the MaBoSS configuration file together with logical functions, which allows working with physical time explicitly. All rates are set to be 1 in this model since it is difficult to estimate them from available experimental facts. Probabilities to reach a phenotype are computed as the probability for the phenotype variable to have the value ON, by simulating random walks on the probabilistic state transition graph. The probabilities for the selected outputs are reported for each mutant based on predefined initial conditions (which can be all random). Since a state in the state transition graph can combine the activation of several phenotype variables, not all phenotype probabilities appear to be mutually exclusive. For example, Apoptosis phenotype variable activation is always accompanied by activation of CellCycleArrest phenotype variable (because p53 is a transcription factor of p21, responsible for cell cycle arrest, and the miRNAs, activated by the p53 and its family members, lead to a cell cycle arrest), and activation of the Metastasis phenotype variable is only possible when all three EMT, Invasion and Migration phenotype variables are activated. With MaBoSS, we can predict an increase or decrease of a phenotype probability when the model variables are altered, which may correspond to the effect of particular mutants or drug treatments. If mutation A increases the Apoptosis probability when compared to the Apoptosis probability in wild type, we conclude that mutant A is advantageous for apoptosis. All models are available in MaBoSS format in S1 File. Module activity The pathway activity (synonymously, module activity) score in a tumour sample is defined as the contribution of this sample into the first principal component computed for all samples on the set of the module target genes, as it was done in [35]. This way, we test target gene sets selected from MSigDB [36] and KEGG [37] databases together with few tens of gene sets assembled by us from external sources. The gene lists for each module is provided in S5 Table. Differential activity score of each module was estimated by t-test between metastatic and non- metastatic groups and significantly active/inactive modules were selected according to p-value <0.05 condition. Transcriptomics data for tumour samples We conducted our study on the publicly available data of human colon cancer from TCGA described in [38]. By excluding rectal cancers from the original dataset, the remaining 105 tumour samples were included in our analysis, classified into two groups (‘metastatic’ M1 = 17 tumours and ‘non-metastatic’ M0 = 88 tumours) according to clinical information about metastasis appearance during cancer progression. Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 6 / 29 Transcriptomics data for cell lines We used gene expression data generated from A549 lung adenocarcinoma cell line that was treated with TGF-β1 ligand at eight different time points [39]. In short, gene expression was measured for three replicates at each time point using Affymetrix Human Genome U133 Plus 2.0 Array. For more information about treatment and growth protocols see [40]. Matching transcriptomics data to logical steady states on EMT-induced cancer cell lines We followed the following six steps to link transcriptome data to the stable states of the model (described in detail in S2 Text): (1) We first matched the genes of the model with their HUGO names. For phenotypes such as Apoptosis, Migration or Invasion, the genes coding for CASP9, CDC42, and MMP2 were used as biomarkers, respectively. These readouts were selected as the most representative of the process; they were chosen based on the changes of the expression of a list of candidate genes we explored throughout the experiments. (2) We averaged the genes over the 3 replicates for time point T0 (initiation of experiment with no TGF-β), for T8 (identi- fied as the beginning of EMT), for T24 (EMT in process) and for T72 (last point). (3) Using several methods (binarization algorithms available in [41]), we identified a threshold of expres- sion and binarized the data accordingly. Among our list of genes, only 11 of them have signifi- cant expression dynamics along the experiment: cdh1, cdh2, ctnnb1, egfr, mapk1, mmp2, smad3, snai2, tgfb1, vim and zeb1. The other genes were either always ON or always OFF throughout the 72 hours of experiments because the expression is either above or below the threshold we set. (4) We associated a label (phenotype) to the 9 stable states of the logical model based on the activity status of the phenotype variable. (5) The similarity matrix was computed according to the following rule: for each stable state and for each time point, if a gene is ON (= 1) or OFF (= 0) in both the vector of discretized expression data and the vector of the stable state, we set the entry in the similarity matrix to 1, otherwise, it is set to 0. (6) For each time point and each stable state, we then summed up the corresponding similarity matrix row, and set an expression-based phenotypic (EBP) score for each stable state. The highest EBP score for each time point corresponds to the phenotype that is the closest to the studied sample and is representative of the status of the cells. Non-linear principal component analysis by elastic maps method The non-linear principal manifold was constructed for the distribution of all single and double mutants of the model in the space of computed model phenotype probabilities, using elastic maps method and ViDaExpert software [42–44]. We preferred using a non-linear version of principal component analysis (PCA) for data visualisation in this case, because it is known to better preserve the local neighbourhood distance relations and allows more informative visual estimation of clusters compared to the linear PCA of the same dimension [42]. For data analy- sis, only those “mixed” phenotypes were selected whose probability expectation over the whole set of single and double mutants was more than 1%. It resulted in a set of 1059 single and dou- ble mutants embedded into 6-dimensional space of phenotype probabilities for which the prin- cipal manifold was computed. Synthetic interactions with respect to metastatic phenotype The results of double mutants were used to quantify the level of epistasis between two model gene defects (resulting either from gain-of-function mutation of a gene or from its knock-out or loss-of-function mutation) with respect to metastatic phenotype. The level of epistasis was Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 7 / 29 quantified using the simplest multiplicative null model applied for the event of not having metastasis: ε = (1-p12)-(1-p1)(1-p2), where p1 and p2 are the probabilities of having metastasis in single mutants, and p12 was the probability of having metastasis in the double mutant. Therefore, negative values of the epistasis score E correspond to synergistic interactions when two gene defects amplify each other’s effect stronger than expected in the multiplicative model. On the contrary, positive values correspond to alleviating effect, when the effect of one gene defect could be masked (sometimes, even reduced to zero) by the second mutation. For genetic network visualisation, we kept the most significant interactions with ε<-0.2 or ε>0.3 values. These thresholds were chosen because at these levels we observed gaps in the distribution of ε values. The complete list of interactions together with p1, p2, p12 and ε values can be found as a Cytoscape 3 session (S2 File). Results Construction of an influence network regulating EMT, invasion and cell migration Mesenchymal cells are characterised by their increased motility, loss of cdh1 (coding for E-cad- herin) expression, increased expression of cdh2 (coding for N-cadherin), and presence of vimentin (Vim) [7,10,45]. The EMT program can be initiated by the transcription factors snai1, snai2, zeb1, zeb2 and twist1. They are considered to be the core regulators of EMT as each has been shown to down-regulate cdh1 [46–50]. In turn, the genes coding for these core EMT-regulators are subjected to regulation by other signalling pathways. The TGF-β pathway has been reported to be able to induce EMT [7,51], but other pathways are also involved in EMT including Wnt, Notch and PI3K-AKT pathways [52–56]. Furthermore, microRNAs regulate the Snai and Zeb family members. For example, miR200 targets snai2, zeb1 and zeb2 mRNA [57–59] whereas miR203 targets snai1 and zeb2 mRNA [59], and miR34 targets snai1 mRNA [60]. The transcription of these microRNAs is under the control of p53 [61–64]. The miR200 expression can also be induced by p63 and p73 proteins, while miR34 is only induced by p73 but is down-regulated by p63 [65–67]. The microRNAs can be down-regulated by the EMT-inducers Snai1/2, and Zeb1/2 [59,60,68]. Note that the proteins p63 and p73 have been identified as members of the p53 protein family since their amino acid sequences share high similarity with that of p53 [69]. They are able to bind to the promoters of the majority of the p53-target genes and therefore have overlapping functions in cell cycle arrest and apoptosis [70,71]. The p53-family members are involved in cross-talks with Notch and AKT pathways: p63 protein is inhibited by the Notch pathway, p53 by AKT1 and AKT2 [69,72–76] while p73 is down-regulated by p53 (itself negatively regulated by p73), AKT1, AKT2, and Zeb1 [69,72,77]. The PI3K-AKT pathway has been considered to be important in evading apoptosis and cell cycle arrest by modulating the TRAIL pathway, down-regulating pro-apoptotic genes and phosphorylating p21 [78–80]. More recently, AKT has been assigned additional but important roles in the development of metastasis. AKT1 suppresses apoptosis upon cell detachment (anoikis) of the ECM [34]. The different isoforms of AKT seem to have opposing roles in the regulation of microRNAs: AKT1 inhibits miR34 and activates miR200 while AKT2 inhibits miR200 and activates miR34 [81]. Another opposing role for both AKT isoforms has been found in migration. AKT1 inhibits migration by phosphorylating the protein Palladin; phos- phorylated Palladin forms actin bundles that inhibit migration. AKT2 increases the protein Palladin stability and upregulates β1-integrins stimulating migration [82,83] or by inhibiting TSC2 that, in turn, activates RHO [84]. Furthermore, AKT1 inhibits cell cycle arrest while AKT2 activates it [85,86] (all these effects are shown implicitly in Fig 1A). Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 8 / 29 Fig 1. Regulatory networks of mechanisms leading to EMT, invasion, migration and metastasis. A. Detailed network of the pathways involved in metastasis. B. Modular network derived from network in A. doi:10.1371/journal.pcbi.1004571.g001 Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 9 / 29 Extracellular stimuli are also included in the logical model. Growth factors (GF) are soluble ligands that can be excreted locally or from longer distances and are able to activate the PI3K-AKT, and MAPK pathways [87,88]. Another extracellular stimulus might be the extracel- lular microenvironment (ECMicroenv) with components that are not soluble including the extracellular matrix. The ligands for the TGF-β pathway can be imbedded in the extracellular matrix [89–91] and the ligands for the Notch pathway are transmembrane proteins from adja- cent neighbouring cells [92,93]. These mechanisms are depicted in an influence network (Fig 1A). The network is composed of nodes and edges, where some nodes represent biochemical species (proteins, miRNAs, pro- cesses, etc.) and others represent phenotypes, and edges represent activating (green) or inhibi- tory (red) influences of one node onto other node. Each edge is annotated and supported by experimental papers (see S1 Table). Throughout the article, we will use the general term “phe- notypes” to refer to “phenotype variables”, which correspond to the four outputs: CellCycleArr- est, Apoptosis, Metastasis (depending on EMT, Migration and Invasion), and Homeostatic State (HS) as presented below. Mathematical modelling of the influence network Construction of a logical model and its stable states. The network of Fig 1A is translated into a logical model using GINsim software [94]: a logical rule is assigned to each node of the network (Table 1, and Materials and Methods). Once the logical rules are set for each node of the network, the Boolean model can simulate solutions or outcomes that correspond to attrac- tors in the state transition graph (see Materials and Methods for details). The model, for the wild type condition (i.e. no mutations or gene alterations), counts nine stable states for all com- binations of inputs (Table 2). To each stable state, a phenotype is assigned based on the genes that are activated (variable is ON, thus equal to 1). The phenotypes identified are: CellCycleArr- est together with Apoptosis; CellCycleArrest together with EMT; Metastasis (depending on three other processes: EMT, Migration and Invasion); and a stable state with only Cdh1 ON. This state corresponds to a state where metastasis is inhibited by Cdh1 activity. We refer to it as the homeostatic state (HS). It is a particular state of an epithelial cell that is not explicitly repre- sented as a phenotype variable in this mathematical model. Four out of the nine stable states lead to Apoptosis, in the presence of DNA damage and absence of growth factors (GF). Two sta- ble states show an EMT phenotype alone (without inducing Metastasis). In these stable states, Invasion and Migration are not activated because TGF-β pathway is not initially ON. The last two stable states lead to Metastasis in the presence of growth factors. GF activates the ERK path- way that switches off the p53-family targets and permits the triggering of events leading to metastases. Indeed, several studies have shown the importance of ERK in migration [95–97]. Testing robustness of the model with respect to small changes in the logical rules. We systematically checked the effect of changing the logical operators of the model from “OR” to “AND”, and vice versa, onto the resulting model phenotype probabilities. More specifically, we generated model variants with one change of a logical operator in one logical rule, two changes in the same logical rule, or one single change in two different logical rules, leaving the rest of logical operators the same as in the wild type model. Therefore, we considered all model vari- ants different from the wild type model by at most two different logical operators. The analysis resulted in 8001 model variants. We first show that the distributions of phenotype probabilities after these changes are con- centrated around the wild type probability values (S6 Fig). Metastasis appeared to be the least robust model phenotype, which confirms the fact that there are some necessary conditions that need to be met to lead to metastasis (illustrated by Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 10 / 29 AND operators in the logical rules). If approximately 49% of changes in the logical rules have minor or no effect onto the Metastasis phenotype probability, some modifications in some rules changed the Metastasis phenotype to zero (implicating p63, p73, AKT1 variables of the model and, to a lesser extent, CTNNB1, miR34, p53). Most of the rules that concern these vari- ables are indeed more stringent. A change from an AND gate to an OR gate for the case of p63 or AKT1 has an important impact on the metastasis process. For instance, if p63 is more pres- ent, because it is inactivated with fewer constraints, it can block more easily migration and thus, metastasis. These logical rules should be considered more carefully than the others because a mistake in defining these rules can have more drastic effects on the model properties than any other modifications. We also performed a reproducibility analysis of individual logical stable states in the models differing from the wild type model by one or two changes in the same logical rule or one change in two logical rules as presented above. The wild type model is characterized by nine Table 2. The nine stable states of the mathematical model. The label of the columns corresponds to the phenotypic outputs. HS Apop1 Apop2 Apop3 Apop4 EMT1 EMT2 M1 M2 Metastasis 0 0 0 0 0 0 0 1 1 Migration 0 0 0 0 0 0 0 1 1 Invasion 0 0 0 0 0 0 0 1 1 EMT 0 0 0 0 0 1 1 1 1 Apoptosis 0 1 1 1 1 0 0 0 0 CellCycleArrest 0 1 1 1 1 1 1 1 1 ECMicroenv 0 0 0 1 1 0 0 1 1 DNAdamage 0 1 1 1 1 1 0 1 0 GF 0 0 0 0 0 1 1 1 1 TGFbeta 0 0 0 1 1 0 0 1 1 p21 0 1 1 1 1 0 0 0 0 CDH1 1 1 1 1 1 0 0 0 0 CDH2 0 0 0 0 0 1 1 1 1 VIM 0 0 0 0 0 1 1 1 1 TWIST1 0 0 0 0 0 1 1 1 1 SNAI1 0 0 0 0 0 1 1 1 1 SNAI2 0 0 0 0 0 1 1 1 1 ZEB1 0 0 0 0 0 1 1 1 1 ZEB2 0 0 0 0 0 1 1 1 1 AKT1 0 0 0 0 0 0 0 0 0 DKK1 0 0 0 0 0 0 0 1 1 CTNNB1 0 0 0 0 0 0 0 0 0 NICD 0 0 0 0 0 0 0 1 1 p63 0 0 1 0 1 0 0 0 0 p53 0 1 0 1 0 0 0 0 0 p73 0 0 1 0 1 0 0 0 0 miR200 0 1 1 1 1 0 0 0 0 miR203 0 1 0 1 0 0 0 0 0 miR34 0 0 0 0 0 0 0 0 0 AKT2 0 0 0 0 0 1 1 1 1 ERK 0 0 0 0 0 1 1 1 1 SMAD 0 0 0 0 0 0 0 1 1 doi:10.1371/journal.pcbi.1004571.t002 Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 11 / 29 stable states, including the homeostatic state (HS) (see Table 2). 8001 model variants men- tioned above are characterized by 68726 stable states counted in total. Hence, in average, each model variant is characterized by 8 or 9 stable states, which might be different from the wild type model. In total, we have counted 1176 distinct stable states in all the 8001 model variants, observed with different frequencies (S6 Table). The nine stable states of the wild type model are robustly reproducible, being the most frequently observed stable states, and accounting for 59% of all observed stable states in different model variants. Another 13% of observed stable states differ from one of the wild type stable states by only one change in the Boolean variable values (DIST_TO_WT = 1). Some modifications of logical rules for CTNNB1 or NICD lead to very rarely observed atypical but very different from the wild type stable states (DIS- T_TO_WT = 12). Based on all these analyses, we conclude that the nine wild type model stable states are robust and “typical” with respect to moderate random modifications of the logical rules and fragile to few targeted modifications. Model reduction into a modular network. To make our modelling more insightful, we reduced the complexity by lumping variables into modules corresponding to signalling path- ways: the TGF-β pathway (TGFb_pthw consisting of TGFbeta, SMAD), Notch pathway (Notch_pthw, includes activated Notch intracellular domain (NICD), the WNT pathway (WNT_pthw consisting of DKK1, CTNNB1), the p53 pathway (p53, consisting of p53), the p63-p73 proteins (p63_73 consisting of p63 and p73), the miRNA (miR34, miR200, miR203), the EMT regulators (EMT_reg including Twist1, Zeb1, Zeb2, Snai1, Snai2, Cdh2, Vim), E- cadherin (Ecadh with Cdh1), growth factors (GF), the ERK pathway (ERK_pthw: ERK), p21 is included in the CellCycleArrest phenotype, AKT1 module and AKT2 module. In the reduced model (Fig 1B), the inputs (ECMicroenv and DNAdamage) and (final and intermediate) out- puts (Migration, Invasion, Metastasis, and Apoptosis) are conserved. The reduced model pro- duces the same stable states (for the wild type conditions) as those of the initial model (Fig 1A, see S4 Text). Validation of the Boolean model. We simulated the genetic perturbations that corre- spond to published experimental settings and verified that the stable states of the mathematical model correspond to the experimental observations. An overexpression or gain of function (GoF) of a gene is simulated by forcing the value of the node to ON and a deletion or loss of function (LoF) by forcing the value of the node to OFF. We first simulated not only previously described mutants but also mutants that have not yet been experimentally validated (see S4 Table). The mathematical model is able to reproduce the experimental results of almost all described mutants. In few cases, there is a discrepancy between the mathematical and the bio- logical model due to three reasons described below: 1) Metastasis in our logical model is defined as colonisation of tumour cells into distant organs through migration in the systemic and/or lymphatic vessels. A limitation of the cell line model is that a metastatic output cannot be measured. 2) Dosage-dependent effects cannot be modelled using the logical formalism. For example, our model predicts metastasis in a kras GoF while the mouse model does not develop distant metastatic tumours. A possibility for the difference is that in the mouse model the wild type kras allele is still present (a heterozygous mutation) while in our model KRAS mutant is homozygous. It has been reported that the remaining wild type kras gene has still tumour sup- pressive properties: it can reduce tumourigenesis in lung [98,99] and in colon cancer cell line by inhibiting proliferation [100]. Other studies in cancer cell lines that are heterozygous for kras mutation showed that the wild type kras gene in those cell lines decreased the migration and colonisation capacity [101,102] suggesting a dose-dependent effect [103]. This might indi- cate that mouse mutants homozygous for kras mutation may develop distant metastasis as pre- dicted by our mathematical model. 3) Simulating mutations of genes that are not explicitly represented as a node in the model has its limitations because the network does not describe Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 12 / 29 exactly the function of such node. For example, even though PTEN is not a variable of our model, we simulated a pten mutation to understand the controversial results of such deletion on metastasis in experimental models. The pten LoF mutations have been associated with many different types of cancers [104–106] and recently it has been demonstrated that pten mutations cause genomic instability [107,108]. In our model, in order to simulate a PTEN LoF, its two targets, AKT1 and AKT2, are forced to be ON: PTEN inhibits activation of AKT iso- forms [109–111]. The model predicts that a PTEN LoF alone or in combination with gene mutations will reach the stable states without having metastasis while metastasis is observed in the mouse model. In our model, due to activation of AKT1 by the PTEN LoF, metastasis is pre- vented, because AKT1 inhibits migration as mentioned before. A recent study indicates that in PTEN-deficient tumours, AKT2 is the active isoform [112] but not AKT1. The model confirms this study: when we simulate the single AKT2 activation as a result of PTEN LoF, the model predicts a stable state in which metastasis can be reached (All references and model results are available in S4 Table). Role of different pathways/modules in triggering metastasis To assess the importance of each pathway on metastasis, apoptosis and cell cycle arrest, we simulated a gain of function or a loss of function, in the reduced model, for each module and for all combinations of inputs. These simulations mean that when an important entity in a pathway is altered, it affects the whole pathway activity. The model shows that mutations lead- ing to either GoF or LoF of each pathway have opposing results in the occurrence of migration and for the occurrence of metastasis (S2 Table). The Notch_pthw is an exception in this: both a GoF and LoF of the Notch pathway can lead to a stable state solution with metastasis ON. This might indicate that Notch (pathway) activity must be in a certain range in order to have a non- pathological effect or that Notch is important for the functioning of some dynamic feedback controls preventing metastasis (so fixing it at a particular value would destroy these feedbacks). In addition, GoF of the Notch_pthw, TGFb_pthw, ERK_pthw, EMT_reg or AKT2 shows their inhibitory role in the apoptotic process as it has been demonstrated before [113–117]. For the p53, TGF-β, EMT_reg and miRNA pathways, mutations leading to activation or inhibition have opposing results in regulating invasion when either the pathway is activated or inhibited. This effect on invasion is a direct result of having an activating or inhibiting role on EMT except for the TGF-β pathway. The role of TGF-β pathway has been investigated. The activation of TGF-β pathway might be dependent on the micro-environment as its ligands can be found in the extracellular matrix [89–91]. The triple mutant: Notch_pthw GoF, p53 LoF and TGFb_pthw LoF leads to one stable state in which the EMT_reg is ON but no metastasis, migration, invasion or apoptosis are reachable (S2 Table) indicating that activation of TGF-β pathway (e.g., by the peripheral tumour cells more exposed to the micro-environment) is required to have metastasis in the double mutant by activating invasion [118,119]. Comparing the Boolean model with dynamical transcriptomic data on EMT induction and tumoral transcriptomes. In this section, the aim is to investigate if the model can predict temporal trends in the dynamics of high-throughput data in cancer cell lines or to retrospec- tively predict a possible appearance of metastasis using the model. Is it possible to correlate experimental or clinical data to the stable states of the model? We first analysed the publicly available colon gene expression dataset generated by The Cancer Genome Atlas (TCGA) project [38]. Student t-test between metastatic and non- metastatic tumours was performed for genes included in the influence network to identify sig- nificant changes in their expression between the two groups (S1 Fig). Few significant Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 13 / 29 differences were observed in the expression of the influence network genes in these two groups. Moreover, there was no significant differential expression of the EMT regulators observed between the two groups: expression of the EMT regulators seems to be OFF in these tumours. Since single gene-based analysis of colon cancer did not show significant differential changes in the expression of the influence network genes, we investigated the expression of the down- stream targets for the transcription factors in the modular network (Notch_pthw, p53, p63_p73, EMT regulators, etc.) and recapitulated their expression into a pathway activity score (see Methods). The assumption was that the differential activity of a given transcription factor can be better reflected by a score based on the expression of its target genes rather than from its own individual expression. For the nodes that are not transcription factors (AKT1, AKT2, etc.) we considered all genes involved in the same network module. We observed that the targets of Notch pathway, Wnt pathway, p63_p73, and AKT1 and AKT2 downstream genes showed sig- nificantly higher activity score in metastatic compared to non-metastatic samples whereas p53 and microRNAs targets were less active in metastatic samples. However, the EMT regulator module showed almost no difference in module activity even if all regulators were combined in one module (See S2 and S3 Figs). Indeed, in the recent colorectal tumour-specific EMT signa- ture established by Tan et al. [120] none of the genes of our EMT module were included. This means that at least in the colorectal cancer, the transcriptional dynamics of the EMT genes has relatively small amplitude, when measured on the bulk of the tumour. Based on our analysis, we hypothesize that only a small portion of the tumour cells in a tumour sample are undergoing EMT and as a result, the EMT signal is strongly diluted when looking at the whole cell population in a sample taken from the tumour bulk. This low signal to noise ratio is not favourable to study the dynamics of the EMT process, and subsequently, the metastatic process. We thus analysed publicly available transcriptomics data from cancer cell lines in which EMT has been induced. In a study conducted by Sartor and colleagues [39], lung carcinoma cell lines were administered with increasing amount of TGF-β and genome-wide transcriptome was measured at eight different time points, following the induction of EMT. The induction of EMT was accompanied by increasing expression for some of the EMT regulators (S4 Fig). The expression of these regulators follows a sigmoid curve in response to TGF-β induction. For a given time-point, we checked if the expression level of the components of our model could be associated to a particular steady state of the model. We expect our model to reflect the behaviour of EMT expression level at early or late time points. We then determined the consistency of the EMT induction experiment with the logical model following the steps presented in Materials and Methods section (and in S2 Text for details of each step). The resulting EBP (expression-based phenotypic) score of the method represents how similar an experimental condition is to a stable state. Thus, the higher the EBP score for a stable state is, the more similar the data are to that stable state, and as an extension, to the phenotype variable associated to that stable state. The computed EBP scores at each time point illustrate the evolution of the data in terms of the stable states. At T0, the highest EBP score is associated with apoptosis. At T8, both metastasis and apoptosis stable states have the highest EBP score illustrating the balance of phenotypes observed in the gradual entry into EMT. At T24 and at T72, the metastatic phenotype has the highest EBP score suggesting that EMT has occurred. Based on the above-mentioned results, the logical model is in accordance with the time course experiments in EMT-induced cell lines. With this similarity EBP score, we have developed a method to characterise tumours in terms of a particular biological process (how the metastatic process follows EMT, migration and invasion here) with respect to the solutions of a logical model. Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 14 / 29 Role of individual EMT regulators in triggering metastasis To identify for each EMT regulator (Snai1, Snai2, Zeb1, Zeb2, Twist1) their specific role in the different cell fates considered in our model, we simulated LoF and GoF mutants and observed that all GoF, except for that of Snai2, led to the loss of apoptosis (S3 Table). Metastasis can be reached for all GoF mutants but other phenotypes can still be reached depending on the combi- nations of inputs. The single deletions of each EMT regulator show that Zeb2 and Twist1 are required for metastasis. Zeb2 controls migration mainly through VIM but has no direct impact on invasion. Twist1 LoF, on the contrary, modulates negatively the possibility to reach not only the metastatic phenotype but also EMT, migration and invasion. Twist1 controls EMT through Cdh2 that controls migration and EMT. Other factors, such as CTNNB1 (β-catenin) or TGF-β, play a role in triggering the metastatic process by modulating invasion or migration, but our model suggests that the main EMT regulators are Zeb2, Twist1 or Snai2, either as loss of func- tion for Zeb2 and Twist1, or gain of function for Snai2. Note that by definition, Cdh2 is abso- lutely required for metastasis to occur because of its direct role in controlling EMT and migration. In our model, Cdh1 inhibits EMT (directly) and migration (through CTNNB1 and VIM) but not invasion. Since all three phenotypes are required for metastasis, the process is thus impaired when Cdh1 is over-expressed [121,122]. Modelling synthetic interactions between genes composing the model The probability of achieving the metastatic phenotype for all possible single and double mutants was systematically computed using MaBoSS [123]. Each single and double mutant is characterised by the distribution of phenotype probabilities. A non-linear PCA analysis was performed as described in Methods, which allowed to group together single and double mutants having similar effect on the model phenotypes (Fig 2A). In this plot, one can Fig 2. A. Genetic interactions between two mutants leading to the masking or the antagonism of a phenotype (metastasis). Application of non-linear dimension reduction for visualising the distribution of phenotype probabilities, computed with MaBoSS for all single and double mutants of the model. The grading in the background shows the density of points (mutants) projections. Six clusters are distinguished based on this grading. Wild-type model, all single over-expression and knockout mutants and the NICD GoF / p53 LoF mutant are labelled. Note that each gene pair in this plot is represented by four different double mutants (small red points) corresponding to LoF/LoF, LoF/GoF, GoF/LoF, GoF/GoF combinations. B. Genetic interaction network showing the most significant synergistic (shown in green) and alleviating (masking, showing in red) interactions between GoF and LoF mutants with respect to the probability of having metastasis. The size of the node reflects the metastasis probability for individual mutation. The thickness of the edge reflects the absolute value of epistasis measure (see Methods). doi:10.1371/journal.pcbi.1004571.g002 Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 15 / 29 distinguish six major clusters (a to f) which can be tentatively annotated as “almost wild-type” (no significant changes in the phenotype probabilities compared to the wild-type model), “risk of metastasis” (elevated probability of having metastasis though not equal to 1), “apoptotic” (for these mutants Apopotosis and CellCycleArrest phenotypes are activated), “EMT without migration” (for these mutants, presented as two clusters, the formation of metastases cannot be accomplished because the cells did not acquire ability to migrate), “cell cycle arrest only” (these mutants are found arrested without starting EMT or invasion or apoptotic programs). The direction of increased metastasis probability is shown by dashed line in Fig 2A, which ends at NICD GoF/p53LoF double mutant for which the probability of having metastasis equals to 1, according to the model (whereas single p53 LoF mutation belongs to “almost wild type” and single NICD GoF mutation belongs to “risk of metastasis” clusters respectively). Synthetic interactions with respect to metastatic phenotype. The most significant genetic interactions with respect to probability of having metastasis (see Methods) are shown in Fig 2B. The following observations can be made: (1) Hubs in this genetic interaction network are the genes for which a single mutation (GoF) leads to a significant increase in having the metastatic phenotype. These genes are akt2, twist1, snai1, and snai2; (2) There are a number of genes whose LoF or GoF lead to a significantly masking effect on the phenotype caused by the hub-gene mutations (red edges in Fig 2B). For example, overexpression of p53 gene or knock- out of erk gene drastically decreases the probability of metastatic phenotype in SNAI1 LoF mutant; (3) There are relatively few synergistic effects observed between single mutants (green edges in Fig 2B). Some of them have been experimentally performed while other synergistic interactions are rather unexpected such as GoF for both AKT2 and NICD, and can be a subject of further experimental work. There are four synergistic interactions, which result in augmenting the probability of having metastasis to 100%. First, two of them are combinations of NICD GoF and p53 LoF (NICD+/ p53-), or simultaneous NICD GoF and p73 GoF (NICD+/p73+). These two interactions can be considered as being dependent, since overexpression of p73 leads to downregulation of p53 function [124,125]. The other two interactions (SNAI2 GoF and NICD GoF, AKT2 GoF and NICD GoF) are potential amplifier mechanisms for appearance of metastasis in NICD GoF mutant alone. In addition, we classified all gene pairs into five large clusters according to four different combinations of in silico mutation types (LoF/LoF, LoF/GoF, GoF/LoF, GoF/GoF). Inside each cluster, the gene pairs can be ranked according to the strength of the activating effect of one of the mutation combinations on the Metastasis phenotype (S5 Fig). Moreover, all gene pairs can be ranked according to the amplitude, i.e. the difference between the maximal and minimal metastatic phenotype probabilities among four values (LoF/LoF, LoF/GoF, GoF/LoF, GoF/ GoF). The most distinguished gene pair in this analysis is p53/NICD, which is a unique and extreme case of the gene pair cluster when any combination of mutation types besides LoF/ GoF makes the metastatic phenotype non-reachable (zero or close to zero probability) while the synthetic-dosage interaction LoF/GoF makes the metastatic phenotype unavoidable (prob- ability one) (cluster 3 in S5 Fig). Synthetic dosage interaction between Notch and p53 genes. Using MaBoSS, we have been able to quantify the changes of probabilities for reaching each phenotype relative to the wild type model. We are thus interested in results such as: “more or less apoptosis than in wild type”. We simulated three mutants with MaBoSS: p53 LoF (Fig 3B), NICD GoF (Fig 3C) and the double mutant NICD+/p53- (Fig 3D). These simulations are of particular interest since they show an example of genetic interaction predicted to have the probability of metastasis pheno- type equals to 1, as presented above. Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 16 / 29 The probabilities of the four phenotypes for wild type conditions are shown in Fig 3A. They show all possible phenotypes for all input configurations. Note that Metastasis can be only reached in the wild type for a particular set of initial conditions (ECMicroenv, GF and TGFbeta all ON), which might correspond to extreme situations. The mutant p53 LoF is very similar to the wild type in terms of possible phenotypes (Fig 2A). The NICD GoF mutation, compared to the wild type, showed an increased probability for EMT as previously reported [126]. Metasta- sis could be reached as well in this single mutant with a higher probability than in the wild type; Apoptosis is no longer reachable, confirming that Notch pathway is a pro-survival path- way (Figs 2A and 3C). In addition, in this mutant, Metastasis was clearly blocked by p53 since a loss of function of p53 in a NICD GoF mutant completely suppressed both the EMT and Fig 3. MaBoSS simulation of wild type, of individual mutations of p53 and NICD and of the double mutant. The probabilities associated with each phenotype represent the number of stochastic simulations leading to each phenotype from pre-defined initial conditions. A. Wild type, see text. B. p53 LoF, same phenotypes found in (A) are reachable but with different probabilities than wild type conditions. C. NICD GoF, apoptosis is no longer reachable. D. p53 LoF and NICD GoF, only metastasis is observed. Note that HS stands for “Homeostatic State” and CCA for “CellCycleArrest.” doi:10.1371/journal.pcbi.1004571.g003 Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 17 / 29 Invasion phenotypes present in the single mutant, and only Metastasis could be reached (Fig 3D). The deletion of both p63 and p73 in a NICD GOF mutant maintained the EMT pheno- type (not shown) proving the importance of p53 in protecting the cells from metastasis. In this context, we further investigated the role of TGF-β pathway in metastasis. Although the NICD GoF/p53 LoF double mutation has been predicted to be the best mutation to acquire metastasis, an important role for the TGF-β pathway is suggested by the model. The triple mutant NICD GoF, p53 LoF and TGF-β LoF (S4 Table) seems to suppress the metastatic pro- cess in the model: cells are able to go through EMT but cannot invade the tissue. Suppressing the TGF-β pathway might be an interesting therapeutic option to control metastasis in patients; however more studies are required to test this hypothesis. Discussion In this study, we propose a logical model focusing on the specific conditions that could allow the occurrence of metastasis. Our model of the metastatic process represents its early steps: EMT, invasion and migration. A cell acquires the capability to migrate when both EMT and invasion abilities have been acquired. These steps are regulated by several signalling pathways, where genetic aberrations could influence the efficiency of metastatic process. Both the influ- ence network and the assignment of logical rules for each node of this network have been derived from what has been published from experimental works as of today. With this model, we were able to explore known conditions (and predict new ones) required for the occurrence of metastasis. Our influence network describes the regulation of EMT, invasion, migration, cell cycle arrest and apoptosis known from the literature. In this regulatory network, cell cycle arrest and apoptosis are mechanisms or phenotypes that maintain homeostasis of organs [127] or ways to evade metastasis. Cell migration depends on pathways involving AKT, ERK, Vimen- tin, miR200 and p63 but also on the acquisition of EMT and invasive abilities such as produc- ing MMPs to dissolve the laminae propria enabling migration to distant sites. Cells that have only invasive properties are not able to move as they are still well attached to their surrounding neighbouring cells resulting in absence of cell migration. Only when those two requirements are met and the other pathways allow migration, can metastasis occur. The role of each EMT regulator, for acquiring invasive properties, has been investigated and the model shows that each individual EMT regulator is sufficient to induce EMT when over- expressed and with the appropriate initial conditions. The model also predicts that a LoF muta- tion of the EMT regulators does not affect metastasis except for ZEB2 and TWIST1: ZEB2 inhi- bition leads to abrogation of migration, while a TWIST1 LoF leads to inhibition of EMT, since TWIST1 is the only transcription factor that can induce transcription of cdh2 gene which is required to have EMT. These regulators are interesting targets for therapy since both are more downstream in the metastasis’ cascade knowing that most activating mutations occur relatively more upstream e.g. KRAS and EGFR mutations. The model has been validated using experimental data by matching the transcriptomic data with stable state solutions of the logical model. The direct comparison between stable states and gene expression of tumour samples shows no conclusive results. This may be due to that only at the front of tumours, cells undergo EMT and this signal is obscured by the bulk of the tumour [30,128]. On the other hand, the model matches well the transcriptomic data from a time course experiment of lung carcinoma cell lines in which EMT was induced by increasing concentration of TGF-β. Qualitative simulations of the model using MaBoSS confirmed that single mutations are not sufficient to enable metastasis. Therefore, we systematically computed the level of epistasis of each two-gene mutation with respect to reaching the metastatic phenotype. We determined Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 18 / 29 which double mutations are the most efficient for inducing metastasis with NICD GoF/p53 LoF mutations being the most efficient combination of gene knock-out and over-dosage, as this double mutant leads in silico to 100% probability of having metastasis. In our previous work, this specific double mutation NICD GoF/p53 LoF has been carried out experimentally in a mouse model, by crossing the villin-CreERT2 mice [129] (in this study referred as p53 LoF) and RosaN1ic mice [130] (in this study referred as NICD GoF) with the isogenic C57BL/6 animals to generate the NICD GoF/p53 LoF compound mice. These com- pound mice develop intestinal tumours with metastatic tumours to distal organs [31]. Our logi- cal model successfully reproduces experimental observations of the compound mouse and proposes mechanisms explaining the metastatic phenotype with high penetrance in mice. In addition, we have investigated the role of TGF-β pathway in metastasis and showed its crucial role in the metastatic phenotype in the double mutant. Suppressing the TGF-β pathway might be an interesting target therapy to control metastasis, however future studies are required. We also explored the activity of the Wnt pathway in the double mutant. Increased activity of the Wnt pathway due to mutations in the apc and ctnnb1 genes leads to tumourigenesis of many cancers [131–133] and subsequently to metastasis [134,135]. Our mathematical model predicts phenotypes that correspond to adenocarcinomas as a result of linear progression of acquired mutations during sporadic colorectal cancer (CRC) suggested by the “Vogelstein sequence” [136] but no metastasis is reached with the model. Indeed, when we simulate APC LoF, KRAS GoF and p53 LoF (the Vogelstein sequence), the model predicts stable states of cells that are not arrested in the cell cycle, can undergo EMT and can invade (see S4 Table). Thus our logical model supports the hypothesis that the Wnt pathway contributes to tumour initiation [137]. However, there is still a debate if the Wnt pathway is actively involved in metastasis. For example, a negative correlation has been demonstrated between the presence of β-catenin and metastasis in breast cancer [138], in lung cancer [139–141], and in CRC [142– 144]. It has been also demonstrated that the canonical Wnt pathway (β-catenin-dependent pathway) is suppressed at the leading edge of the tumour [145] and this might happen without affecting the β-catenin protein levels [146,147]. In the mouse model with Notch GoF /p53 LoF double mutation, in some tumours samples, mutations in apc and ctnnb1 have been found but also tumours without those mutations have been shown to acquire metastasis. Both truncated APC and mutations in β-catenin correspond in our mathematical model to full activation of CTNNB1 and this will induce activation of AKT1. In our model, activation of AKT1 will inhibit migration and therefore inhibit metastasis. Appearance of metastasis in the mouse model with activated Wnt pathway might be putatively explained if one looks at the length of the truncated APC isoform for tumours with apc mutation. The APC mutation found in the Notch GoF /p53 LoF mouse model results in a relatively large truncated APC isoform that might still have inhibitory effect on β-catenin [148]. More details about the APC isoforms and its effect on β-catenin can be found in S3 Text. Another explanation for having metastasis in tumours with active Wnt pathway might be the involvement of another mutation that affects the akt1 or the akt2 gene. According to our model, the Wnt pathway inhibits metastasis by up-regulation of AKT1. There are tumours in CRC patients (TCGA data from http://cbioportal.org, [31]) that can have an akt2 gene amplifi- cation or a homozygous deletion or missense mutation of akt1. AKT2 induces migration while AKT1 inhibits migration thus the ratio AKT1 to AKT2 might be an important determinant for acquiring metastasis in the colon. Indeed studies have shown that AKT2 is predominant in sporadic colon cancer [149] and have a critical role in metastasis in CRC [150]. A Boolean model of EMT induction has been recently published, where the theoretical pre- diction that the Wnt pathway can be activated upon TGF-β administration was validated experimentally by measuring increased gene expression of the Wnt target gene axin2 in Huh7 Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 19 / 29 and PLC/PRF/5 cell lines [151]. Those cell lines are derived from hepatocellular carcinomas [152,153] and both can harbour known mutations [154] and unconfirmed mutations (http:// tinyurl.com/l6mjd8y) that affect the signalling pathways: the Wnt pathway has constitutive activity in the Huh7 cell line [137,155]. An alternative explanation could be that our model is more specific for epithelial cancers as the model depicts many reactions observed in epithelial cells; it has been shown that different types of cancer have different protein (or isoforms) abun- dance [112,149]. Therefore, our model might be less adequate in predicting the activity for cer- tain nodes for hepatocellular carcinoma and lung adenocarcinoma. EMT is considered to be the first step and is very often modelled as an equivalent of having metastasis once it is activated. We provide here a logical model that proposes the involvement of three independent processes in order to have metastasis: EMT, invasion and migration. These phenotypes are controlled by an intricate network and only when EMT, invasion and migration do occur, can metastasis happen. The logical model explores the mechanisms and interplays between pathways that are involved in the processes, identifies the main players in these mechanisms and gives insight on how these pathways could be altered in a therapeutic perspective. Note that other mechanisms involving other alterations in the pathways that we model, or in other pathways might also take place, and we do not claim that our approach cover all possibilities of inducing metastasis. Still, our approach provides candidate interven- tion points for designing innovative anti-metastatic strategies. Supporting Information S1 Text. Review on published articles of mathematical models of EMT. (DOCX) S2 Text. Link between model solutions and transcriptomics data. (DOCX) S3 Text. Description of Wnt pathway. (PDF) S4 Text. From the master model to the reduced model. (DOCX) S1 Fig. Colon transcriptomics data. Mean value expression for each gene is mapped on the network. The figure is the same for both metastatic and non-metastatic samples. (PNG) S2 Fig. Modular network of the metastasis model. (PDF) S3 Fig. Colon transcriptomics data mapped onto the modular network. The score for the modules are calculated based on the expression of target genes for metastatic and non- metastatic samples. (PDF) S4 Fig. Mean gene expression value of the three replicates for the genes of the network at 4 different time points: At t = 0, at t = 8h, at t = 24h and at t = 72h. Green nodes correspond to low expression and red nodes to high expression. The minimum and maximum expression val- ues are set over the whole dataset and are the same for the four graphs. (PDF) S5 Fig. Distribution of pairs of genes of the mathematical model in the four-dimensional space of Metastasis probabilities, corresponding to four possible mutation type Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 20 / 29 combinations LoF/LoF, LoF/GoF, GoF/LoF, GoF/GoF (here LoF is Loss-of-Function and GoF is Gain-of-Function). The image shows a two-dimensional projection onto a non-linear principal manifold from the space defined by four metastatic phenotype probabilities [p(LoF/ LoF);p(GoF/GoF); p(LoF/GoF)+p(GoF/LoF);\|p(LoF/GoF)-p(GoF/LoF)\|]. Projection density is shown in the background by grey shading. The size of the node corresponds to the amplitude of the node pair (maximum difference in phenotype probability between the four mutants: LoF/LoF, GoF/GoF, GoF/LoF, LoF/GoF), such that the most sensitive (allowing control of phe- notype to maximal degree) gene pairs correspond to bigger node sizes. Five clusters are identi- fied: they correspond to five patterns which existence can be guessed from the symmetry considerations and which are shown on the right panels. 1a) Any GoF cancels the phenotype while double LoF can amplify it (14% of gene pairs); 1b) Any LoF cancels the phenotype while double GoF can amplify it (13%); 2a) Double GoF cancels the phenotype, double LoF or syn- thetic-dosage interaction can amplify it (23%); 2b) Double LoF cancels the phenotype, double GoF or synthetic-dosage interaction (LoF/GoF or GoF/LoF) can amplify it (16%); 3) Double LoF and double GoF cancel the phenotype, while synthetic-dosage interaction can amplify it (30%). TP53-NICD (top-left corner) mutant is an extreme example of group 3. NICD-AKT2 (bottom-left corner) is an extreme example of group 2b. (PNG) S6 Fig. Results of robustness tests for the logical model with respect to small changes in the logical rules of the model. In the wild type logical model, for each logical rule, several "variant" models were created by changing one or two "OR" or "AND" operators to "AND" or "OR" oper- ators respectively. The resulting distributions of phenotype probabilities over all such model modifications are shown. (PDF) S1 Table. Annotations of the logical model. (DOCX) S2 Table. Phenotypes that can be reached by setting the activity of a single module or path- way to always ON (GoF: gain of function) or always OFF (LoF: loss of function). (XLSX) S3 Table. Phenotypes that can be reached by setting the activity of a single EMT regulator to always ON (GoF: gain of function) or always OFF (LoF: loss of function). EMT regula- tors: Snai1, Snai2, Zeb1, Zeb2, and Twist1. (XLSX) S4 Table. Table of mutants. For each condition or mutation, all possible inputs are considered. Thus, all possible outputs corresponding to stable states are shown in this table (values for internal variables are not shown). The existence of a stable state in accordance with what has been published is enough to conclude that the mutant is validated: there exists a condition for which the model explains the experiments. The fact that other stable states exist shows that for some particular conditions, the stable state could be reachable. For instance, for NICD GoF, we see that a stable state with metastasis exits which has not been observed in experi- ments. However, for this stable state, all p53 family members are OFF, thus, it is a particular sit- uation. (DOCX) S5 Table. Signatures of module activity. (XLS) Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 21 / 29 S6 Table. Robustness analysis; table of mutants for the logical stable states of the perturbed models. (XLSX) S1 File. Detailed and modular models in GINsim and MaBoSS formats. The zip file includes: Detailed model in GINsim format (SuppMat_Model_Master_Model.zginml), Modu- lar model in GINsim format (SuppMat_Model_ModNet.zginml), SuppMat_MaBoSS_Master- Model.bnd (To simulate the model, MaBoSS needs to be downloaded from maboss.curie.fr and launched with the following command line:./MaBoSS -c SuppMat_MaBoSS_MasterModel.cfg -o SuppMat_MaBoSS_MasterModel SuppMat_MaBoSS_MasterModel.bnd), SuppMat_Ma- BoSS_MasterModel.cfg, SuppMat_MaBoSS_ModNet.bnd (To simulate the model, MaBoSS needs to be downloaded from maboss.curie.fr and launched with the following command line:./MaBoSS -c SuppMat_MaBoSS_ModNet.cfg -o SuppMat_MaBoSS_ModNet SuppMat_ MaBoSS_ModNet.bnd), SuppMat_MaBoSS_ModNet.cfg. (ZIP) S2 File. SuppMat_metastasis_mutants.cys. (ZIP) Acknowledgments We are thankful to Prof Dr Daniel Louvard for critical reading and advising on the manuscript. Author Contributions Conceived and designed the experiments: DPAC LM SR EB AZ LC. 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Mol Cancer 7: 21. doi: 10.1186/1476-4598-7-21 PMID: 18282277 Modelling of Metastasis Process PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004571 November 3, 2015 29 / 29	26528548	EMT = ( ( CDH2 ) AND NOT ( CDH1 ) ) p21 = ( ( ( SMAD AND ( ( ( NICD ) ) ) ) AND NOT ( ERK ) ) AND NOT ( AKT1 ) ) OR ( ( ( p63 ) AND NOT ( ERK ) ) AND NOT ( AKT1 ) ) OR ( ( ( p73 ) AND NOT ( ERK ) ) AND NOT ( AKT1 ) ) OR ( ( ( AKT2 ) AND NOT ( ERK ) ) AND NOT ( AKT1 ) ) OR ( ( ( p53 ) AND NOT ( ERK ) ) AND NOT ( AKT1 ) ) p53 = ( ( ( ( ( NICD ) AND NOT ( p73 ) ) AND NOT ( AKT2 ) ) AND NOT ( SNAI2 ) ) AND NOT ( AKT1 ) ) OR ( ( ( ( ( CTNNB1 ) AND NOT ( p73 ) ) AND NOT ( AKT2 ) ) AND NOT ( SNAI2 ) ) AND NOT ( AKT1 ) ) OR ( ( ( ( ( DNAdamage ) AND NOT ( p73 ) ) AND NOT ( AKT2 ) ) AND NOT ( SNAI2 ) ) AND NOT ( AKT1 ) ) OR ( ( ( ( ( miR34 ) AND NOT ( p73 ) ) AND NOT ( AKT2 ) ) AND NOT ( SNAI2 ) ) AND NOT ( AKT1 ) ) p63 = ( ( ( ( ( ( DNAdamage ) AND NOT ( AKT2 ) ) AND NOT ( NICD ) ) AND NOT ( AKT1 ) ) AND NOT ( p53 ) ) AND NOT ( miR203 ) ) NICD = ( ( ( ( ( ( ECM ) AND NOT ( p73 ) ) AND NOT ( miR200 ) ) AND NOT ( miR34 ) ) AND NOT ( p53 ) ) AND NOT ( p63 ) ) Invasion = ( SMAD AND ( ( ( CDH2 ) ) ) ) OR ( CTNNB1 ) AKT2 = ( TWIST1 AND ( ( ( TGFbeta OR CDH2 OR GF ) AND ( ( ( NOT miR34 AND NOT miR203 AND NOT p53 ) ) ) ) ) ) AKT1 = ( ( ( ( CTNNB1 AND ( ( ( TGFbeta ) ) OR ( ( CDH2 ) ) OR ( ( NICD ) ) OR ( ( GF ) ) ) ) AND NOT ( CDH1 ) ) AND NOT ( p53 ) ) AND NOT ( miR34 ) ) miR200 = ( ( ( ( ( ( p63 ) AND NOT ( SNAI2 ) ) AND NOT ( AKT2 ) ) AND NOT ( SNAI1 ) ) AND NOT ( ZEB2 ) ) AND NOT ( ZEB1 ) ) OR ( ( ( ( ( ( p73 ) AND NOT ( SNAI2 ) ) AND NOT ( AKT2 ) ) AND NOT ( SNAI1 ) ) AND NOT ( ZEB2 ) ) AND NOT ( ZEB1 ) ) OR ( ( ( ( ( ( p53 ) AND NOT ( SNAI2 ) ) AND NOT ( AKT2 ) ) AND NOT ( SNAI1 ) ) AND NOT ( ZEB2 ) ) AND NOT ( ZEB1 ) ) miR34 = ( ( ( AKT2 AND ( ( ( NOT ZEB2 AND NOT SNAI1 AND NOT ZEB1 ) AND ( ( ( p73 OR p53 ) ) ) ) ) ) AND NOT ( p63 ) ) AND NOT ( AKT1 ) ) Metastasis = ( Migration ) SNAI1 = ( ( ( ( ( NICD ) AND NOT ( miR203 ) ) AND NOT ( CTNNB1 ) ) AND NOT ( miR34 ) ) AND NOT ( p53 ) ) OR ( ( ( ( ( TWIST1 ) AND NOT ( miR203 ) ) AND NOT ( CTNNB1 ) ) AND NOT ( miR34 ) ) AND NOT ( p53 ) ) VIM = ( ZEB2 ) OR ( CTNNB1 ) ZEB2 = ( ( ( NICD ) AND NOT ( miR203 ) ) AND NOT ( miR200 ) ) OR ( ( ( SNAI1 ) AND NOT ( miR203 ) ) AND NOT ( miR200 ) ) OR ( ( ( SNAI2 AND ( ( ( TWIST1 ) ) ) ) AND NOT ( miR203 ) ) AND NOT ( miR200 ) ) ZEB1 = ( ( NICD ) AND NOT ( miR200 ) ) OR ( ( SNAI2 ) AND NOT ( miR200 ) ) OR ( ( TWIST1 AND ( ( ( SNAI1 ) ) ) ) AND NOT ( miR200 ) ) OR ( ( CTNNB1 ) AND NOT ( miR200 ) ) TGFbeta = ( ( ECM ) AND NOT ( CTNNB1 ) ) OR ( ( NICD ) AND NOT ( CTNNB1 ) ) CDH2 = ( TWIST1 ) DKK1 = ( NICD ) OR ( CTNNB1 ) TWIST1 = ( SNAI1 ) OR ( NICD ) OR ( CTNNB1 ) ERK = ( ( NICD ) AND NOT ( AKT1 ) ) OR ( ( CDH2 ) AND NOT ( AKT1 ) ) OR ( ( GF ) AND NOT ( AKT1 ) ) OR ( ( SMAD ) AND NOT ( AKT1 ) ) SMAD = ( ( ( TGFbeta ) AND NOT ( miR203 ) ) AND NOT ( miR200 ) ) CellCycleArrest = ( ( miR200 ) AND NOT ( AKT1 ) ) OR ( ( miR203 ) AND NOT ( AKT1 ) ) OR ( ( ZEB2 ) AND NOT ( AKT1 ) ) OR ( ( p21 ) AND NOT ( AKT1 ) ) OR ( ( miR34 ) AND NOT ( AKT1 ) ) miR203 = ( ( ( ( p53 ) AND NOT ( ZEB1 ) ) AND NOT ( SNAI1 ) ) AND NOT ( ZEB2 ) ) Apoptosis = ( ( ( ( miR200 ) AND NOT ( ZEB2 ) ) AND NOT ( ERK ) ) AND NOT ( AKT1 ) ) OR ( ( ( ( p63 ) AND NOT ( ZEB2 ) ) AND NOT ( ERK ) ) AND NOT ( AKT1 ) ) OR ( ( ( ( p73 ) AND NOT ( ZEB2 ) ) AND NOT ( ERK ) ) AND NOT ( AKT1 ) ) OR ( ( ( ( miR34 ) AND NOT ( ZEB2 ) ) AND NOT ( ERK ) ) AND NOT ( AKT1 ) ) OR ( ( ( ( p53 ) AND NOT ( ZEB2 ) ) AND NOT ( ERK ) ) AND NOT ( AKT1 ) ) SNAI2 = ( ( ( ( NICD ) AND NOT ( miR200 ) ) AND NOT ( miR203 ) ) AND NOT ( p53 ) ) OR ( ( ( ( CTNNB1 ) AND NOT ( miR200 ) ) AND NOT ( miR203 ) ) AND NOT ( p53 ) ) OR ( ( ( ( TWIST1 ) AND NOT ( miR200 ) ) AND NOT ( miR203 ) ) AND NOT ( p53 ) ) GF = ( ( CDH2 ) AND NOT ( CDH1 ) ) OR ( ( GF ) AND NOT ( CDH1 ) ) CDH1 = NOT ( ( SNAI1 ) OR ( SNAI2 ) OR ( TWIST1 ) OR ( ZEB2 ) OR ( ZEB1 ) OR ( AKT2 ) ) Migration = ( ( ( ( VIM AND ( ( ( ERK AND AKT2 AND Invasion AND EMT ) ) ) ) AND NOT ( miR200 ) ) AND NOT ( AKT1 ) ) AND NOT ( p63 ) ) p73 = ( ( ( ( ( DNAdamage ) AND NOT ( p53 ) ) AND NOT ( AKT2 ) ) AND NOT ( AKT1 ) ) AND NOT ( ZEB1 ) ) CTNNB1 = NOT ( ( AKT1 ) OR ( miR200 ) OR ( p63 ) OR ( CDH2 ) OR ( CDH1 ) OR ( DKK1 ) OR ( p53 ) OR ( miR34 ) )
Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 DOI 10.1186/s12976-015-0023-0 RESEARCH Open Access A Boolean network model of human gonadal sex determination Osiris Ríos1,2, Sara Frias1,3, Alfredo Rodríguez1,4, Susana Kofman5, Horacio Merchant3, Leda Torres1* and Luis Mendoza3,6* *Correspondence: ledactorres@gmail.com; lmendoza@biomedicas.unam.mx 1Instituto Nacional de Pediatría, Laboratorio de Citogenética, Av. Insurgentes Sur 3700 C, 04530 México City, México 3Instituto de Investigaciones Biomédicas, UNAM, 04510 Mexico City, México Full list of author information is available at the end of the article Abstract Background: Gonadal sex determination (GSD) in humans is a complex biological process that takes place in early stages of embryonic development when the bipotential gonadal primordium (BGP) differentiates towards testes or ovaries. This decision is directed by one of two distinct pathways embedded in a GSD network activated in a population of coelomic epithelial cells, the Sertoli progenitor cells (SPC) and the granulosa progenitor cells (GPC). In males, the pathway is activated when the Sex-Determining Region Y (SRY) gene starts to be expressed, whereas in females the WNT4/β-catenin pathway promotes the differentiation of the GPCs towards ovaries. The interactions and dynamics of the elements that constitute the GSD network are poorly understood, thus our group is interested in inferring the general architecture of this network as well as modeling the dynamic behavior of a set of genes associated to this process under wild-type and mutant conditions. Methods: We reconstructed the regulatory network of GSD with a set of genes directly associated with the process of differentiation from SPC and GPC towards Sertoli and granulosa cells, respectively. These genes are experimentally well-characterized and the effects of their deficiency have been clinically reported. We modeled this GSD network as a synchronous Boolean network model (BNM) and characterized its attractors under wild-type and mutant conditions. Results: Three attractors with a clear biological meaning were found; one of them corresponding to the currently known gene expression pattern of Sertoli cells, the second correlating to the granulosa cells and, the third resembling a disgenetic gonad. Conclusions: The BNM of GSD that we present summarizes the experimental data on the pathways for Sertoli and granulosa establishment and sheds light on the overall behavior of a population of cells that differentiate within the developing gonad. With this model we propose a set of regulatory interactions needed to activate either the SRY or the WNT4/β-catenin pathway as well as their downstream targets, which are critical for further sex differentiation. In addition, we observed a pattern of altered regulatory interactions and their dynamics that lead to some disorders of sex development (DSD). Keywords: Sex determination, Gonadal sex determination, Boolean model, Gene regulatory network © 2015 Ríos et al. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons. org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 2 of 18 Background Sex development is a complex biological process that occurs during the embryonic and fetal stages of an individual. For a better understanding sex development is divided into three consecutive steps: 1) chromosomal sex determination (CSD); 2) gonadal sex determination (GSD); and 3) phenotypic sex differentiation (PSD). CSD is estab- lished at conception when the complement of sex chromosomes, XX or XY, is received. GSD, which is the process that we analyze in this study, refers to the set of genes and their regulatory interactions that trigger the development toward testes or ovaries, underlined by a gene regulatory network [1–4]. Finally, PSD involves the development of the female and male internal and external genitalia in response to the hormones secreted by the ovaries and testes. Both male and female PSD occur in two tempo- ral phases, the first occurs within the fetus after GSD and the second occurs during puberty [5, 6]. GSD occurs within a heterogeneously composed structure called bipotential gonadal primordium (BGP). This structure, located on the ventromedial surface of the mesonephros [5–7], is critical for sex development since it can differentiate either as testes or ovaries [8]. The BGP originates the actual gonad that is composed by a) the germinal cells (GCs), b) the steroidogenic somatic cells, such as the theca cells in ovary and the Leydig cells in testis that produce stradiol and testosterone, respectively; and c) the support somatic cells, including granulosa cells in ovary and Sertoli cells in testis. Sertoli and granulosa cells originate from a common population of coelomic epithelial cells corresponding to the Sertoli progenitor cells (SPC) or granulosa progenitor cells (GPC) that migrate towards the BGP [9, 10]. In males, the SPCs start to differentiate toward Sertoli cells after 44 days of development (Carnegie-Stage 18). The mechanism involves activation of the expression of the Sex-determining Region Y gene (SRY) that codifies the SRY transcription factor [9, 11]. SRY associates with other transcription fac- tors (i.e., CBX2, SF1) to regulate expression of the SOX9 gene that positively regulates the expression of genes associated to Sertoli cells (i.e., SOX9, FGF9, PGD2, DHH, AMH) [2]. In females, where SRY is absent, GSD initiates after 49 days of development (Carnegie- Stage 20). In this case, the GPCs of coelomic origin differentiate towards granulosa cells by the action of a distinct gene regulatory pathway. Most likely, an increased amount of the transcription factor β-catenin up-regulates a set of downstream genes associated to granulosa, such as FOXL2 and RSPO1 [2, 12, 13]. Thus, the mechanism underlying GSD involves a common population of undifferentiated cells with the potential to diverge into two cell fates. The male pathway leads towards Sertoli cell fate determination and dif- ferentiation, whereas the female pathway leads to granulosa cell fate determination and differentiation. Once differentiated, the Sertoli cells act as organizing centers, enclosing GCs to form testicular cords and secreting factors such as DHH and PDGF, which are essential for development of the fetal population of Leydig cells [14]. Granulosa cells are the female equivalent of the Sertoli cells, as they enclose GCs and secrete factors necessary for oocyte growth and maturation. The regulatory network controlling GSD and differentia- tion toward Sertoli or granulosa cell consists, in a broad sense, of multiple target genes, different types of RNAs, transcription factors, nuclear receptors and signaling molecules. These elements are present in undifferentiated cells and interact in a concerted way either Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 3 of 18 activating or repressing target genes at the time of GSD to balance the fate toward Sertoli or granulosa cells [15–17]. The total number of genes implicated in the regulatory network of GSD of humans and mammals remains elusive, as well as their complete regulatory interactions and their effects on the process of Sertoli or granulosa cells differentiation. However, it is well known that mutations in their components underlay the so-called disorders of sex devel- opment (DSD), a series of genetic conditions characterized by anomalies in gonads as well as in internal and external genitalia. The incidence of DSDs, as estimated by the The Lawson Wilkins Pediatric Endocrine Society (LWPES) and the European Society for Pediatric Endocrinology (ESPE), is 1 in 4,500 births [18] and can be attributed to muta- tions in various genes of the GSD network. For example, mutations in CBX2, GATA4 and WT1 genes result in a wide range of phenotypic alterations characterized by ambiguous or female external genitalia with the presence or absence of Mullerian structures in 46,XY DSDs patients [19]. In contrast, 46,XX DSDs cause masculinization of the female fetus (normal males with no ovarian tissue) [20]. In other cases 46,XX DSD patients have a female phenotype but fail to develop ovaries, presenting instead a “streak gonad”? (streaks of connective fibrous tissue) [21]. Boolean network models (BNM) are formal tools for analyzing the structure and dynamic behavior of genetic regulatory networks. BNM are best suited for describing poorly-characterized systems with no or few kinetic details, such as the GSD network. These models represent molecular entities (genes, transcription factors and RNAs) as nodes interacting among them within a network. Each node can have only two qualitative states: 0 (OFF) and 1 (ON). The OFF state is equivalent to a below-threshold concen- tration or activity, which is insufficient to initiate the intended process or regulation, while the ON state is equivalent to an above-threshold concentration or activity [22]. The ON/OFF state of a node within the network is determined by a Boolean function that encompasses the known regulatory elements of the target node (transcription factors, nuclear receptors, signaling molecules). The state of these regulatory elements is updated over consecutive time steps of a simulation until the system converges to either a steady state or a cycle. BNMs describe the dynamic state of the nodes in a network by updating the state of the nodes according with the set of regulatory functions [23]. BNMs have been implemented for the analysis of developmental programs such as flower morphogenesis in A. thaliana [24], early cardiac development in mice [25], and expression pattern of the segment polarity genes in Drosophila [26] to name a few. Despite the relatively high incidence of DSDs, their molecular basis at the level of the regulatory network remain poorly understood. Thus, we are interested in constructing a BNM of the process of gonadal sex determination with an emphasis on the regulatory elements that are present at early stages of development and control the differentiation of SCP and GCP towards Sertoli and granulosa cells, respectively, allowing us to analyze the origin of some DSDs. For in-depth reviews about the genes involved in GSD and DSDs see: [18, 19, 27, 28], as well as the list of genes and interactions in the Additional file 1 of the supplementary information. In this study we present a BNM that describes the dynamics of the GSD regulatory network starting from the UGR until Sertoli/granulosa cells differentiation. The pro- posed regulatory network incorporates a large amount of published information related to functional interactions among the genes involved in this process, while the BNM of Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 4 of 18 GSD describes the dynamics of the elements contained within the network under wild- type and mutant conditions. With the current model we explore a formal description of the functional relationships among the genes and gene products associated to GSD, and generate some predictions about the expected regulatory behavior under wild-type or altered conditions within elements of the UGR and elements of the bipotential gonadal primordium such as CBX2, GATA4, and WT1. Additional predictions are indicated in the female pathway where the transcription factor β-catenin seems to play an impor- tant role in the activation of female-specific genes (for example, WNT4, RSPO1, and FOXL2). Methods The network of gonadal sex determination To construct the network we selected a set of genes with well-known clinical and experimental data demonstrating their association to GSD under wild-type and mutant conditions. The genes, depicted in a regulatory diagram (Fig. 1), include: CBX2, NR5A1, GATA4, WT1pKTS, WT1mKTS, NR0B1, SRY, SOX9, FGF9, PGD2, DHH, AMH, DKK1, DMRT1, CTNNB1, WNT4, FOXL2, RSPO1, and a special node called UGR. The inter- actions among these nodes are denoted by edges. We distinguish positive interactions (activation) by connecting two nodes with an arrow-head line. Negative interactions (inhibition) are denoted by connecting two nodes with a bar-head line. The regulatory interactions among nodes were inferred, with emphasis in humans, from: (1) clinical studies of patients with DSDs, which carried mutations on sex deter- mining genes; (2) genetic expression patterns associated to GSD (between 5th and 8th weeks of embryonic development); and (3) molecular evidence of interactions at the level of transcriptional regulation of target genes (i.e., up or down regulation of a tar- get gene by means of protein-DNA interactions under wild type, mutated or transgenic constructs). Experimental evidence on mice was integrated into the network when neces- sary, especially in the female pathway where human information is lacking. References to clinical and experimental data can be found in the Additional file 1 of the Supplementary Information. The network includes the special UGR node, representing the urogenital ridge, an embryonic structure precursor of the nephrogenic cord and gonads. The UGR node encompasses the following genes: LHX1, LHX9, EMX2, PAX2 and, PAX8. Although expression of these genes is essential for growth and maintenance of the UGR, little evidence was found in human, as well as in mouse, about their specific regulatory inter- actions, thus these genes were grouped within the UGR node, since mutations in any of these genes impair subsequent gonadal development [29–31]. The pathway towards pre-Sertoli or pre-granulosa cells is shown in Fig. 1. The blue nodes correspond to Sertoli cell fate determination pathway and include: SRY, SOX9, FGF9, PGD2, DHH, AMH, DKK1 and DMRT1 nodes, whereas the pink nodes correspond to granulosa cell fate determination pathway including: CTNNB1, WNT4, FOXL2 and RSPO1. Notice that the granulosa cell fate determination was complemented with mice information. For example, we considered the canonical Wnt4/β-catenin pathway as a key regulatory element of female nodes within the network since relative expression of Fst, Gng13, Foxl2, Irx3 and, Sp5 has been shown to be down-regulated when β-catenin is lost in female mice in early stages of ovarian development [32]. Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 5 of 18 Fig. 1 Network of Gonadal Sex Determination leading to Sertoli or granulosa cell fate commitment and differentiation. The network was inferred from reviewed experimental evidence of genes associated within the process and structured according to developmental stages in: urogenital ridge (UGR node), bipotential gonadal primordium (yellow nodes), male pathway of sex determination (blue nodes), female pathway of sex determination (pink nodes). Nodes represent genes; arrow lines denote activation; bar head lines indicate inhibition; black, blue and, pink solid lines represent validated interactions in human; green solid lines represent interactions validated in mouse; punctuated lines in orange represent model predictions Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 6 of 18 The network as a Boolean model The process of GSD is poorly characterized at the quantitative level, i.e., kinetic informa- tion regarding the interactions of the elements of this regulatory network is still lacking, therefore the implementation of the GSD network as a continuous model is, at this moment, out of reach. Given this, we decided to model the network as a discrete dynami- cal system so as to describe the qualitative observations that are experimentally reported. Specifically, we used a Boolean approach where every node might have one of two pos- sible states; 1 (ON) or 0 (OFF), indicating that a given node within the network model is active or inactive, respectively. To determine the activation state of each node in the GSD model we translated the experimental regulatory interactions into a set of Boolean functions with the use of the logical operators AND, OR and NOT (Table 1). The logical operator AND is used if two nodes named A and B are required to activate a third node named C. The logical operator OR is used if two nodes named A or B can activate, by its own, node C. The logical oper- ator NOT is used if node A is an inhibitor of node B. Thus, the state of a given node over time is determined by the activation state of its regulators. We integrated to the model additional regulatory interactions not reported by observational or experimental studies (Table 2). These interactions were inferred from analysis of the dynamics of the Boolean model and might be considered as model predictions that deserve further experimen- tation to be validated. Interactions of model predictions are shown in Fig. 1 as orange dashed lines. We performed an initial exhaustive evaluation of the dynamic behavior of the wild type model, simulating all possible initial activation states. Three fixed-point attractors were obtained, and we performed a search focused in finding the state transitions cor- responding to both male and female pathways. To recover the wild type “male pathway”, we initiated the simulations with the UGR node in ON. In contrast, to created a wild type “female pathway”, without the SRY node, we set the UGR and WNT4 nodes as active Table 1 Set of functions for the Boolean model of gonadal sex determination UGR, UGR & ! (NR5A1 \| WNT4) CBX2, UGR & ! (NR0B1 & WNT4 & CTNNB1) GATA4, (UGR \| WNT4 \| NR5A1 \| SRY) WT1mKTS, (UGR \| GATA4) WT1pKTS, (UGR \| GATA4) & ! (WNT4 & CTNNB1) NR5A1, (UGR \| CBX2 \| WT1mKTS \| GATA4) & ! (NR0B1 & WNT4) NR0B1, (WT1mKTS \| (WNT4 & CTNNB1)) & ! (NR5A1 & SOX9) SRY, ((NR5A1 & WT1mKTS & CBX2) \| (GATA4 & WT1pKTS & CBX2 & NR5A1) \| (SOX9 \| SRY)) & ! (CTNNB1) SOX9, ((SOX9 & FGF9) \| (SRY \| PGD2) \| (SRY & CBX2) \| (GATA4 & NR5A1 & SRY)) & ! (WNT4 \| CTNNB1 \| FOXL2) FGF9, SOX9 & ! WNT4 PGD2, SOX9 DMRT1, (SRY \| SOX9) & ! (FOXL2) DHH, SOX9 DKK1, (SRY \| SOX9) AMH, ((SOX9 & GATA4 & NR5A1) \| (SOX9 & NR5A1 & GATA4 & WT1mKTS)) & ! (NR0B1 & CTNNB1) WNT4, (GATA4 \| (CTNNB1 \| RSPO1 \| NR0B1)) & ! (FGF9 \| DKK1) RSPO1, (WNT4 \| CTNNB1) & ! (DKK1) FOXL2, (WNT4 & CTNNB1) & ! (DMRT1 \| SOX9) CTNNB1, (WNT4 \| RSPO1) & ! (SRY \| (SOX9 & AMH)) Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 7 of 18 Table 2 Set of regulatory interactions inferred from analysis of the dynamics of the Boolean model, colored in orange, that deserve further experimentation to be validated UGR, UGR & ! (NR5A1 \| WNT4) CBX2, UGR & ! (NR0B1 & WNT4 & CTNNB1) GATA4, (UGR \| WNT4 \| NR5A1 \| SRY) WT1mKTS, (UGR \| GATA4) WT1pKTS, (UGR \| GATA4) & ! (WNT4 & CTNNB1) NR5A1, (UGR \| CBX2 \| WT1mKTS \| GATA4) & ! (NR0B1 & WNT4) NR0B1, (WT1mKTS \| (WNT4 & CTNNB1)) & ! (NR5A1 & SOX9) SRY, ((NR5A1 & WT1mKTS & CBX2) \| (GATA4 & WT1pKTS & CBX2 & NR5A1) \| (SOX9 \| SRY)) & ! (CTNNB1) SOX9, ((SOX9 & FGF9) \| (SRY \| PGD2) \| (SRY & CBX2) \| (GATA4 & NR5A1 & SRY)) & ! (WNT4 \| CTNNB1 \| FOXL2) FGF9, SOX9 & ! WNT4 PGD2, SOX9 DMRT1, (SRY \| SOX9) & ! (FOXL2) DHH, SOX9 DKK1, (SRY \| SOX9) AMH, ((SOX9 & GATA4 & NR5A1) \| (SOX9 & NR5A1 & GATA4 & WT1mKTS)) & ! (NR0B1 & CTNNB1) WNT4, (GATA4 \| (CTNNB1 \| RSPO1 \| NR0B1)) & ! (FGF9 \| DKK1) RSPO1, (WNT4 \| CTNNB1) & ! (DKK1) FOXL2, (WNT4 & CTNNB1) & ! (DMRT1 \| SOX9) CTNNB1, (WNT4 \| RSPO1) & ! (SRY \| (SOX9 & AMH)) at the beginning of simulations. Besides the wild type model, we simulated all possible loss and gain of function of single mutants, so as to describe alterations in activation states that might be interpreted as alterations in gene expression. Loss and gain of func- tion single mutants were simulated by fixing the relevant node to 0 or 1, respectively. All simulations were carried out under the synchronous updating scheme with the use of BoolNet [33]. Testing properties of the Boolean model: random networks and robustness of attractors We performed tests by creating random networks in order to analyze the frequency of appearance of point attractors identical to those of the wild type model (Fig. 2). The tests consisted in the construction of 1000 random networks with 19 nodes each one. The number of inputs for each node in the random networks was the same as in the original model. We kept this configuration in order to be consistent with the network architecture of the model. The wild type attractors shown in (Fig. 2) were compared by performing three independent tests of 1000 random networks each one. Additionally, we tested the Fig. 2 Fixed point attractors of the Boolean model of gonadal sex determination. The attractors were obtained by simulating all possible (219) initial activation states. The attractor with the largest basin of attraction (50.95 %) can be interpreted as the gene expression profile observed in the somatic pre-Granulosa cells. The attractor with the second-largest basin (48.91 %) can be interpreted as the gene expression profile observed in the somatic pre-Sertoli cells. The model also presents a third attractor with a small basin covering only 0.14 % of the state space interpreted as a null attractor due to a UGR node set to zero Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 8 of 18 robustness of the attractors of the BNM with a set of 1000 perturbed copies of the network by using the testNetworkProperties function of BoolNet [33]. This test gives the percent- age of the original attractors shown in Fig. 2 recovered after 1000 copies of the Boolean model functions randomly perturbed. Results The network of gonadal sex determination The network was constructed with 19 nodes and 78 regulatory interactions: 42 of these interactions have been reported in humans; 12 in mice and 24 were predicted from analysis of transition states of the simulated Boolean model. The network is directed towards the male pathway if the SRY node is active. SRY leads to activation of SOX9, which in turn activates FGF9, PGD2, DMRT1, DHH, DKK1, and AMH nodes. At the same time, the female pathway is repressed by inactivating CTNNB1 and FOXL2 nodes (Fig. 1). On the contrary, the network is directed towards the female pathway in absence of SRY and when the WNT4, CTNNB1, RSPO1 and, FOXL2 nodes are active. In this case, the male pathway is repressed by CTNNB1 and FOXL2 mediated inactivation of SOX9, DMRT1 and AMH (Fig. 1). Predictions of the Boolean model The current model contains 24 interactions inferred from dynamic modeling, these are predominantly related to the UGR node and the genes expressed in the bipotential gonad. Model predictions were drawn as orange dashed lines within the following nodes: UGR, CBX2, GATA, WT1mKTS, WT1pKTS, NR0B1, SRY, DMRT1, DKK1, WNT4 and CTNNB1 (Fig. 1). The model predicts that the activity of UGR depends of an activation self-loop and functions as an input to activate CBX2, GATA4, Wt1mKTS, WT1pKTS, and NR5A1 (Table 2). The scarcity of information regarding UGR function and mainte- nance clearly indicates that more experimental studies are necessary to understand the mechanisms of gene expression control in the BGP especially for CBX2, GATA4 and WT1. Dynamic behavior of the gonadal sex determination Boolean network model The dynamic behavior of the GSD BNM was exhaustively analyzed by starting the dynamical simulations of the system from all possible 219 = 524288 initial states. After simulations, three fixed-point attractors where obtained (Fig. 2). The first of these attrac- tors can be interpreted as the gene expression profile observed in Sertoli cells, the second can be interpreted as the gene expression profile observed in granulosa cells, and the third attractor, with a very small basin of attraction, might represent a disgenetic gonad without Sertoli or granulosa activity. After the initial exhaustive search of the GSD attractors, we performed a search focused in finding the state transitions of both male and female pathways. In the case of 46,XY simulations, the UGR node was set to ON in the initial condition (Time step 0) to transit toward the BPG and then turning ON the SRY node leading toward the Sertoli cell attrac- tor. Since 46,XX wild type females do not have SRY gene, we searched from all possible initial states the activation patterns that had UGR and female nodes as initial condition. From this search we found that UGR + WNT4 were the initial conditions (Time-step 0) to transit from the BPG toward the granulosa attractor. Thus in male and female simula- tions we started with an active UGR node as the initial condition, followed by activation of Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 9 of 18 the nodes representing the BPG (CBX2, GATA4, WT1mKTS, WT1pKTS, and NR5A1). The NR0B1, WNT4 and RSPO1 nodes were subsequently activated, in agreement with the reported gene expression patterns, showing that these genes are co-expressed in both male and female embryos during the stage of BPG and previous to GSD (Fig. 3a and b) [7, 34]. If the simulation transited toward the Sertoli attractor, then the NR0B1, WNT4 and RSPO1 nodes were inactivated by NR5A1, SRY, SOX9 and DKK1 nodes. In male the expression of NROB1 is dosage sensitive, since duplication of this gene in 46,XY patients produces a male-to-female sex reversal with streak gonads [35]. It is important to notice that NR0B1 might play an important role in male after the time of GSD because NR0B1 knockout mice showed disorganized Sertoli, Leydig and germ cells due to defects in testis cord formation [36]. Thus, it has been suggested that NR0B1 has a time frame of expression [37] with reduced levels of the DAX1 protein during GSD. Since the BNM con- siders active or inactive states, the NR0B1 node was inactive at the sixth time step, which corresponds to the Sertoli attractor (Fig. 3a) When the UGR + WNT4 nodes were set to ON, two fixed point attractors were obtained: (1) the granulosa attractor and the (2) dysgenetic gonad attractor. Thus the transition towards the granulosa attractor is characterized by the initial activation of the UGR + WNT4 and BPG nodes, followed by activation of the NR0B1, RSPO1, FOXL2 and CTNNB1. As we previously stated, β-catenin, plays a key role in up-regulation of pre- granulosa genes in female mouse [32], this factor actively antagonizes SOX9 and AMH expression, inactivating the pathway toward Sertoli cells (Fig. 3b) [38, 39]. The attrac- tor with no activity reflects the importance of the UGR node within the network model a b Fig. 3 State transitions leading to a fixed point attractor corresponding to pre-Sertoli or to pre-granulosa cells. The state of the nodes over time was simulated starting from an activated UGR node (1). White and black cells represent inactive or active nodes respectively. The fixed point attractor toward pre-Sertoli is given by activation of SRY node (a). The point attractor is in agreement with experimental observations after six time steps, whereas the fixed point attractor toward granulosa is given by absence of SRY and activated UGR+WNT4 nodes (b). The point attractor is in agreement with experimental observations after three time steps Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 10 of 18 given that loss of function mutants of UGR components have an impaired subsequent gonadal development, as observed in mouse. Therefore, the dysgenetic gonad attractor (i.e., streaks of fibrous tissue instead of a gonad) might be interpreted as a condition expected in some individuals when gonadal development fails, especially in the case of LHX1, LHX9, EMX2, PAX2 and PAX8 mutants. In summary, state transitions in Fig. 3a and b qualitatively coincide with gene expres- sion patterns observed during GSD [7, 34]. However, notice that the state transitions and steady state attractors must be considered as snapshots of the gene expression pat- tern between 41–52 days of development and do not represent the complete process of gonadal development. Modeling disorders of sex development 46,XX sex reversal We simulated the DSD known as 46,XX sex reversal or testicular DSD, characterized by an apparently normal development of male structures, including testes and male internal/external genitalia [20, 40]. To simulate such a condition either the SRY node or the SOX9 node were left permanently active (ON = 1) during the entire simulation (Fig. 4a, b). The SRY node activates SOX9 in coordination with CBX2, GATA4, WT1 and NR5A1, SOX9 in turn inhibits the female pathway through CTNNB1 inactivation. CTNNB1 is the node of the transcription factor β-catenin, a key regulatory element of the female pathway. Our BNM generates in both simulations a Sertoli-like attractor that presents activation of the FGF9, PGD2, DMRT1, DHH, DKK1 and AMH nodes. The sim- ulation observed in Fig. 4a might be interpreted as the process underlying a 46,XX sex a b Fig. 4 Modeling 46,XX sex reversal. The SRY node was kept as active (1) so as to simulate traslocation in a 46,XX background. SRY activates SOX9 in combination with CBX2, GATA4, WT1 and NR5A1. Then, SOX9 activates nodes associated with the male pathway (i.e., FGF9, PGD2, DHH, AMH). The fixed point attractor can be interpreted as a 46,XX sex reversal after three time steps (a). The SOX9 node was set as active in order to simulate a duplication in a 46,XX background (b). The resulted activation states were similar to the observed in the male pathway. Thus, the fixed point attractor can be interpreted as a 46,XX sex reversal in absence of SRY, as reported in clinical cases Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 11 of 18 reversal when the SRY gene is translocated to one autosomic chromosome or to the X chromosome, whereas the simulation in Fig. 4b might represent a 46,XX sex reversal due SOX9 gene duplication. 46,XY (SRY-) sex reversal SRY is considered the trigger of the male pathway and testis development [9]. This tran- scription factor possesses a highly conserved domain called HMG box that binds to the GAACAAAG DNA motif and bends the DNA molecule about 80 degrees. The loss of its chromatin-remodeling activity [41] is considered to impair the three dimensional archi- tecture of chromatin and compromises the proper interaction of SRY with its target genes. Mutation of the DNA binding region of SRY in 46,XY subjects has been associated with female external genitalia, normal Mullerian ducts and streak gonads [42]. When we sim- ulated the SRY loss of function, the female pathway was activated by the CTNNB1 node and the male pathway blocked through a CTNNB1 and FOXL2- mediated SOX9 inhi- bition. SRY is considered the trigger of testis development by expressing in the somatic pre-Sertoli cells [9]. The mechanism suggested for normal function of this transcrip- tion factor is a highly conserved domain within the protein, called High Mobility Group (HMG box). Concerning the model simulation in Fig. 5c, loss-of-function of SRY leads to inacti- vation of the male and activation of the female pathway. To this respect, Hawkings and colleagues [42] described five subjects with 46,XY karyotype associated with completely female external genitalia, normal Mullerian ducts, and streak gonads. All the patients showed mutations in the DNA binding region of the SRY protein [42]. Since model sim- ulations agree with clinical observations of loss-of-function mutations in the HMG box of SRY, we interpret this simulation as the possible gene expression dynamics in a 46,XY (SRY-) individual during the time of GSD. In these subjects the female pathway would become active by increasing amounts of β-catenin within the cell nucleus and active repression of the male pathway by a B-catenin and FOXL2-mediated inhibition of SOX9. Given this results we interpret that our simulations (Fig. 5c) resemble the early gene expression dynamics in a 46,XY (SRY-) individuals. Modeling other DSDs Other relevant elements that have a common function in both male and female pathways at the BPG and thorough the differentiation of testis and ovaries are the transcription factors GATA4 and WT1. In the case of GATA4, it has been observed in mice that GATA4 is expressed at E10.5 during formation of the UGR and its deficiency impairs subsequent gonadal differentiation [43]. In the male pathway, GATA4 associates with the -KTS isoform of WT1 protein for an optimal activation of the SRY gene [44]. Other example of the GATA4 protein activity in the male pathway is its role in the activa- tion of the AMH gene in association with SF1 and WT1-KTS transcription factors [45, 46]. Simulation of GATA4 loss of function in the male pathway is given in Fig. 6 (notice the altered dynamics of activation patterns compared with the wild-type simula- tion shown in Fig. 3a). WT1mKTS, WT1pKTS, NR5A1 and AMH nodes were inactive in the attractor because the GATA4 node is their positive regulator. The SRY node remained active due to an activation self-loop and additional interactions with NR5A1, WT1mKTS, CBX2 and a possible feedback loop with SOX9, thus the altered activation Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 12 of 18 Fig. 5 Modeling 46,XY sex reversal. The CBX2 node was inactivated in order to simulate a loss of function mutation in a 46,XY background which resulted in a steady state attractor that showed activation of female nodes (a). The NR0B1 node was set as active in order to simulate a duplication in a 46,XY background. The activation states were altered and resulted in an steady state attractor with activated female nodes (b). The SRY node was inactivated in order to simulate a loss of function mutation which resulted in a steady state attractor that showed activation of female nodes (c) Fig. 6 State transitions when the GATA4 node was inactive (0) in a 46,XY context. The GATA4 node was inactivated in order to simulate a loss of function mutation in a 46,XY background which resulted in inactivated AMH node although an attractor with activated male nodes was recovered Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 13 of 18 state shown in Fig. 6 might be interpreted as the source of a DSD. To this respect, the clinical spectrum of developmental anomalies due to GATA4 mutations in male patients is variable. Patients might show bilateral dysgenetic testes containing Sertoli cells and no visible Leydig cells and show male internal genitalia to normal-ambiguous external genitalia [46]. On the other hand, WT1 has a key role in the development of kidney and gonads, its expression is observed at the UGR and continues through the differentiation of testis and ovaries interacting in both pathways of cell differentiation. Homozygous mutations in mice are embryonic lethal and result in renal agenesis, as well as cardiac and gen- ital tract abnormalities [29]. Since WT1 is an important element in early stages of gonadal development we simulated the loss of function of WT1 in a 46,XY context (Fig. 7), notice that the attractor has an activation pattern similar to the female path- way. Importantly, mutations in this gene impair the development of male in a certain degree; mutations in the intron 9 splice site of the WT1 gene affects the balance of the +KTS/-KTS isoforms impairing the development of testis resulting in streak gonads and ambiguous external genitalia [47]. In females the role of WT1 is less defined, how- ever there is experimental evidence about its role in the positive regulation of the NR0B1 gene by binding to two potential sites located at the 5 flanking region of the gene [48]. We analyzed in addition the effect of loss-of-function mutations in the NR5A1 node. Since the dynamics of the simulations of WT1 and NR5A1 were identical we show only the attractor in Fig. 7. Testing properties of the Boolean model: random networks and robustness of the attractors On average, the three independent tests of 1000 random networks generated 103,000 attractors each one. We found that none of the random networks recovered the set of three point attractors of the wild type model shown in Fig. 2. This results indicate that the attractors of our BNM could not be expected in a network made with random interac- tions. Thus, the attractors in Fig. 2 can be considered as biologically meaningful and not a statistical artifact. Concerning the test of attractor robustness we observed that 95 % of the perturbed networks recovered less than 30 % of the original attractors of our model. This means that the model is relatively sensitive to perturbations in the functions of the model. The reduced robustness can be due to the scarce redundancy in the model, given that we opted by including a small number of regulatory molecules, so as to be close to a minimal model. We expect that the introduction of more nodes and regulatory feedback circuits would result in an increased robustness. Fig. 7 Fixed point attractors when setting NR5A1 or WT1 inactive (0) in a 46,XY context Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 14 of 18 Discussion The classical observations of Alfred Jost (1947) that early castration in utero of rabbit fetuses resulted in female internal and external genitalia (independent of their chro- mosomal sex complement) lead to the hypothesis of a testis-determining factor (TDF). According to this hypothesis the ovary was considered the default developmental state, while testis represented an induced and active state that repressed female development. Experimental evidence accumulated in the last 20 years have enriched our view of sex determination where developmental programs toward testis or ovaries represent two independent antagonistic regulatory pathways of high complexity intertwined in a regulatory network: the GSD network. The BNM used in this study, although discrete in its approach, can be considered as a simplified version of a very dynamic and complex biological network that incorporates the major regulatory elements of the GSD network. The GSD BNM summarizes in a formal language the set of experimentally-confirmed interactions associated with the pro- cess of GSD. Although the attractors obtained in our model cannot be interpreted as as anatomical structures of high developmental complexity, they can be reliably seen as the gene expression profiles expected during the process of determination and differentiation of SPC and GPC towards Sertoli and granulosa cells respectively. The network of gonadal sex determination We inferred the regulatory network of human GSD and modeled it as a BNM. With such a model we were able to describe the molecular dynamics of the first stage in gonadal mor- phogenesis, which is the cell fate determination and further differentiation of Sertoli and granulosa cells. The network contains 19 nodes as well as their regulatory interactions, as evidenced by published experimental and clinical data. Recent studies regarding early gonadal differentiation suggest a highly complex biolog- ical process regulated by many, probably hundreds, of genes. However, our BNM shows that only a handful of them are sufficient to activate the male or female pathway, allowing us to propose that the gonadal fate commitment and differentiation is a direct conse- quence of activation and repression of a transcriptional program encoded as a regulatory network. Although part of the information used to infer this regulatory network was taken from experiments in mice, we consider that the model might be considered as a good approximation to the corresponding regulatory network in humans. The Boolean model of gonadal sex determination The BNM describes the dynamics of 19 nodes associated with GSD between 41–52 days of embryonic development. The results cannot be considered as final activation states of the biological process, instead they should be considered as a snapshot in the pro- cess of Sertoli and granulosa cell differentiation. At the quantitative level, GSD is poorly understood given the lack of information about kinetic details of each regulatory ele- ment, therefore it is difficult to establish a continuous model with differential equations with the current available data. Despite the large amount of gene expression data, little is known about the regulatory mechanisms leading to GSD under normal conditions, as well as their downstream effects under mutant conditions. To shed light about the regula- tory mechanisms we used a discrete modeling approach because most of the information relies on qualitative descriptions. Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 15 of 18 Model predictions and the role of the UGR and bipotential gonad genes in early gonadal development The UGR is a very important structure within the developing embryo since it is the com- mon structure that leads to testis and ovaries. Notice that just a few regulatory elements of the UGR have been studied. For example, Lhx1 expression has been reported in mice and has a key role in the development of kidney, female reproductive tract and anterior head [30]. Conditional knockout mice lack uterus, cervix and upper vagina [49]. Lhx9 has a role in the activation of Nr5a1 gene, in synergy with Wt1 in mice. Other example is given by PAX2 and PAX8 genes. In humans, these genes have a role in the activation of the WT1 gene [29, 50] thus, we underline the need for additional studies regarding the regulatory interactions that led to the establishment of the UGR and BPG primordium. As we mentioned previously, the human female pathway is less characterized, and its current cumulative knowledge is mainly based on mice findings. In this case, the GATA4- FOG2 complex has an important function by activating the Fst, Wnt4, Sprr2d, Foxl2, Gng13 genes [32]. It has been observed in female mice that loss of function of Gata4 impairs the expression of these genes and leads to the development of a male-specific coelomic vessel [32]; therefore GATA4 can be considered as a key regulatory element in the early stages of gonadal development toward ovaries. The role of WNT4/β-catenin in the female pathway Concerning the female pathway most of the inferred interactions derive from mice. To this respect we notice the role of the WNT4 and βcatenin nodes in the regulation of WNT4, RSPO1, and FOXL2. In the biological process we predict a key role of β-catenin regulating the female pathway. The general mechanism of the canonical Wnt4/β-catenin signaling pathway can be explained as follows: the pathway is initiated by expression of the wingless-type MMTV integration site family, member 4 (WNT4). The product of this gene is a ligand that binds to Frizzled (Fz) and LRP5/6 co-receptors at the plasma mem- brane, disengaging β-catenin from the proteins of the “destruction complex”? (Axin and APC). Then β-catenin translocate into the nucleus where associates with TCF7/LEF, this protein contains an HMG box with capacity to recognize specific DNA sequences. The β-catenin-TCF7/LEF complex activates target genes, whereas in absence of β-catenin TCF7/LEF alone represses gene transcription [51, 52]. From the set of interactions inferred from mice, that fitted perfectly in our model, we would expect that β-catenin might have an important role regulating the expression of the FST, FOXL2 and IRX3 genes in humans. The BNM of GSD summarizes in a formal language the set of experimentally-confirmed interactions associated with the process of GSD. The attractors of our model can be interpreted as the gene expression profiles expected during the process of GSD and dif- ferentiation of Sertoli or granulosa cell lineages. According to our simulations, the loss of function of GATA4 results in inactivation of the AMH node in the attractor. This result is particularly interesting given the existence of the persistent Müllerian duct syndrome (PMDS), a relatively rare inherited defect in the sexual differentiation, characterized by failure in the regression of the Müllerian ducts in males. Affected individuals present per- sistent uterus and tubes due to a defect in the synthesis of the AMH hormone, which is normally produced by the Sertoli cells. Mutations in the AMH gene have been reported in these patients [20, 53], however the majority of PMDS remain without molecular Ríos et al. Theoretical Biology and Medical Modelling (2015) 12:26 Page 16 of 18 diagnosis, therefore GATA4 mutations emerge, according to our model predictions, as a potential PMSD causing gene. Conclusions We propose the present model as a starting point for future mathematical modeling and integration of experimental research regarding sex development. The model can be upgraded in several aspects for example, incorporating additional nodes and interactions, as well as modeling more cell lineages of the gonad such as the Leydig or theca cells. Finally the current BNM describes the dynamics of the GSD network under perturba- tions. Importantly the analysis of these states can have potential implications in the study of DSDs. Additional file Additional file 1: Supplementary information. (PDF 47 kb) Competing interests The authors declare that they have no competing interests. Authors’ contributions LT and SF conceived the project; OR, LM and AR developed the BNM and performed the simulations; LT and LM coordinated computational work; OR, LT, LM, AR and SF, analyzed the data.; SK and HM provided important contribution for including nodes and interactions and for discussion; OR, SF, and LT, wrote the manuscript. All authors read and approved the final manuscript. Acknowledgements OR thanks the support from the program Doctorado en Ciencias Biológicas, UNAM, and the scholarship 173000 from Consejo Nacional de Ciencia y Tecnología (CONACyT). This work was supported by grants from CONACYT 166012 to HM, Universidad Nacional Autónoma de México PAPIIT IN200514 to LM, and Recursos Fiscales para la Investigación del Instituto Nacional de Pediatría, proyecto 057/2014 to LT. Adhemar Liquitaya from CompBioLab IIB, UNAM, aid with the test of random networks. Author details 1Instituto Nacional de Pediatría, Laboratorio de Citogenética, Av. Insurgentes Sur 3700 C, 04530 México City, México. 2Programa de Doctorado en Ciencias Biológicas, UNAM, Mexico City, México. 3Instituto de Investigaciones Biomédicas, UNAM, 04510 Mexico City, México. 4Programa de Doctorado en Ciencias Biomédicas, UNAM, Mexico City, México. 5Facultad de Medicina/Hospital General de Mexico, Mexico City, México. 6C3, Centro de Ciencias de la Complejidad, UNAM, 04510 Mexico City, México. 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Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color ﬁgure charges • Immediate publication on acceptance • Inclusion in PubMed, CAS, Scopus and Google Scholar • Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit	26573569	WT1mKTS = ( GATA4 ) OR ( UGR ) CTNNB1 = ( ( ( RSPO1 ) AND NOT ( SRY ) ) AND NOT ( SOX9 AND ( ( ( AMH ) ) ) ) ) OR ( ( ( WNT4 ) AND NOT ( SRY ) ) AND NOT ( SOX9 AND ( ( ( AMH ) ) ) ) ) AMH = ( ( SOX9 AND ( ( ( GATA4 AND NR5A1 ) ) OR ( ( WT1mKTS AND GATA4 AND NR5A1 ) ) ) ) AND NOT ( NR0B1 AND ( ( ( CTNNB1 ) ) ) ) ) UGR = ( ( ( UGR ) AND NOT ( WNT4 ) ) AND NOT ( NR5A1 ) ) NR5A1 = ( ( UGR ) AND NOT ( NR0B1 AND ( ( ( WNT4 ) ) ) ) ) OR ( ( GATA4 ) AND NOT ( NR0B1 AND ( ( ( WNT4 ) ) ) ) ) OR ( ( CBX2 ) AND NOT ( NR0B1 AND ( ( ( WNT4 ) ) ) ) ) OR ( ( WT1mKTS ) AND NOT ( NR0B1 AND ( ( ( WNT4 ) ) ) ) ) DHH = ( SOX9 ) FGF9 = ( ( SOX9 ) AND NOT ( WNT4 ) ) SOX9 = ( ( ( ( PGD2 ) AND NOT ( CTNNB1 ) ) AND NOT ( FOXL2 ) ) AND NOT ( WNT4 ) ) OR ( ( ( ( GATA4 AND ( ( ( SRY AND NR5A1 ) ) ) ) AND NOT ( CTNNB1 ) ) AND NOT ( FOXL2 ) ) AND NOT ( WNT4 ) ) OR ( ( ( ( SRY ) AND NOT ( CTNNB1 ) ) AND NOT ( FOXL2 ) ) AND NOT ( WNT4 ) ) OR ( ( ( ( FGF9 AND ( ( ( SOX9 ) ) ) ) AND NOT ( CTNNB1 ) ) AND NOT ( FOXL2 ) ) AND NOT ( WNT4 ) ) OR ( ( ( ( CBX2 AND ( ( ( SRY ) ) ) ) AND NOT ( CTNNB1 ) ) AND NOT ( FOXL2 ) ) AND NOT ( WNT4 ) ) WT1pKTS = ( ( GATA4 ) AND NOT ( WNT4 AND ( ( ( CTNNB1 ) ) ) ) ) OR ( ( UGR ) AND NOT ( WNT4 AND ( ( ( CTNNB1 ) ) ) ) ) WNT4 = ( ( ( CTNNB1 ) AND NOT ( FGF9 ) ) AND NOT ( DKK1 ) ) OR ( ( ( NR0B1 ) AND NOT ( FGF9 ) ) AND NOT ( DKK1 ) ) OR ( ( ( GATA4 ) AND NOT ( FGF9 ) ) AND NOT ( DKK1 ) ) OR ( ( ( RSPO1 ) AND NOT ( FGF9 ) ) AND NOT ( DKK1 ) ) FOXL2 = ( ( ( WNT4 AND ( ( ( CTNNB1 ) ) ) ) AND NOT ( SOX9 ) ) AND NOT ( DMRT1 ) ) PGD2 = ( SOX9 ) DMRT1 = ( ( SOX9 ) AND NOT ( FOXL2 ) ) OR ( ( SRY ) AND NOT ( FOXL2 ) ) GATA4 = ( NR5A1 ) OR ( UGR ) OR ( WNT4 ) OR ( SRY ) DKK1 = ( SRY ) OR ( SOX9 ) NR0B1 = ( ( WNT4 AND ( ( ( CTNNB1 ) ) ) ) AND NOT ( NR5A1 AND ( ( ( SOX9 ) ) ) ) ) OR ( ( WT1mKTS ) AND NOT ( NR5A1 AND ( ( ( SOX9 ) ) ) ) ) SRY = ( ( CBX2 AND ( ( ( WT1mKTS AND NR5A1 ) ) ) ) AND NOT ( CTNNB1 ) ) OR ( ( GATA4 AND ( ( ( CBX2 AND WT1pKTS AND NR5A1 ) ) ) ) AND NOT ( CTNNB1 ) ) OR ( ( SOX9 ) AND NOT ( CTNNB1 ) ) OR ( ( SRY ) AND NOT ( CTNNB1 ) ) CBX2 = ( ( UGR ) AND NOT ( NR0B1 AND ( ( ( WNT4 AND CTNNB1 ) ) ) ) ) RSPO1 = ( ( WNT4 ) AND NOT ( DKK1 ) ) OR ( ( CTNNB1 ) AND NOT ( DKK1 ) )
RESEARCH ARTICLE A Network Model to Describe the Terminal Differentiation of B Cells Akram Méndez1,2, Luis Mendoza2,3* 1 Programa de Doctorado en Ciencias Bioquímicas, Universidad Nacional Autónoma de México, Ciudad de México, México, 2 Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de México, Ciudad de México, México, 3 C3, Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Ciudad de México, México * lmendoza@biomedicas.unam.mx Abstract Terminal differentiation of B cells is an essential process for the humoral immune response in vertebrates and is achieved by the concerted action of several transcription factors in response to antigen recognition and extracellular signals provided by T-helper cells. While there is a wealth of experimental data regarding the molecular and cellular signals involved in this process, there is no general consensus regarding the structure and dynamical prop- erties of the underlying regulatory network controlling this process. We developed a dynam- ical model of the regulatory network controlling terminal differentiation of B cells. The structure of the network was inferred from experimental data available in the literature, and its dynamical behavior was analyzed by modeling the network both as a discrete and a con- tinuous dynamical systems. The steady states of these models are consistent with the pat- terns of activation reported for the Naive, GC, Mem, and PC cell types. Moreover, the models are able to describe the patterns of differentiation from the precursor Naive to any of the GC, Mem, or PC cell types in response to a specific set of extracellular signals. We sim- ulated all possible single loss- and gain-of-function mutants, corroborating the importance of Pax5, Bcl6, Bach2, Irf4, and Blimp1 as key regulators of B cell differentiation process. The model is able to represent the directional nature of terminal B cell differentiation and qualitatively describes key differentiation events from a precursor cell to terminally differenti- ated B cells. Author Summary Generation of antibody-producing cells through terminal B cell differentiation represents a good model to study the formation of multiple effector cells from a progenitor cell type. This process is controlled by the action of several molecules that maintain cell type specific programs in response to cytokines, antigen recognition and the direct contact with T helper cells, forming a complex regulatory network. While there is a large body of experi- mental data regarding some of the key molecules involved in this process and there have been several efforts to reconstruct the underlying regulatory network, a general consensus PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 1 / 26 a11111 OPEN ACCESS Citation: Méndez A, Mendoza L (2016) A Network Model to Describe the Terminal Differentiation of B Cells. PLoS Comput Biol 12(1): e1004696. doi:10.1371/journal.pcbi.1004696 Editor: Thomas Höfer, German Cancer Research Center, GERMANY Received: June 17, 2015 Accepted: December 7, 2015 Published: January 11, 2016 Copyright: © 2016 Méndez, Mendoza. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: This work was funded by Programa de Apoyo a Proyectos de Investigación e Inovación Tecnológica, grant IN200514 to LM, Dirección General de Asuntos del Personal Académico de la Universidad Nacional Autónoma de México (http:// dgapa.unam.mx); and Scholarship 384318 to AM, Consejo Nacional de Ciencia y Tecnología (http:// www.conacyt.mx). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. about the structure and dynamical behavior of this network is lacking. Moreover, it is not well understood how this network controls the establishment of specific B cell expression patterns and how it responds to specific external signals. We present a model of the regula- tory network controlling terminal B cell differentiation and analyze its dynamical behavior under normal and mutant conditions. The model recovers the patterns of differentiation of B cells and describes a large set of gain- and loss-of-function mutants. This model pro- vides an unified framework to generate qualitative descriptions to interpret the role of intra- and extracellular regulators of B cell differentiation. Introduction Adaptive immunity in vertebrates depends on the rapid maturation and differentiation of T and B cells. While T cells originate cell-mediated immune responses, B cells are responsible for the humoral response of the organism by means of the production of high-affinity antibodies. B cells develop in the bone marrow from hematopoietic progenitors, and migrate as mature B cells (Naive) to the germinal centers (GCs), which are highly specialized environments of the secondary lymphoid organs [1]. There, B cells are activated by antigens (Ag) and undergo diversification of the B cell receptor (BCR) genes by somatic hypermutation (SHM), as well as the subsequent expression of distinct isotypes by class switch recombination (CSR) [2]. After the activation due to Ag recognition, Naive and GC B cells differentiate into antibody-produc- ing plasma cells (PC), as well as memory cells (Mem) [3]. Cytokines secreted by T-helper cells, such as IL-2, IL-4 and IL-21 as well as the direct contact with these cells, mediated by the union CD40 receptor on B cells with its ligand CD40L, play a key role in the determination of B cell fate [4], since these external signals act as instructive cues that promote the differentiation from a cell progenitor to multiple cell types (Fig 1). Terminal differentiation of B cells is controlled by the concerted action of multiple tran- scription factors that integrate physiologic signals in response to BCR cross-linking, extracellu- lar cytokines, and the direct interaction with T cells, thus creating a complex regulatory network. These factors appear to regulate mutually antagonistic programs and can be divided into those that promote and maintain B cell identity, such as Pax5, Bcl6 and Bach2, and those that control differentiation into memory cells or plasma cells, i.e., Irf4, Blimp1 and XBP1, as has been shown by multiple functional, biochemical and gene expression analysis [5–7]. A type is characterized by the expression of a specific set of master transcriptional regula- tors. Naive B cells express Pax5 and Bach2, which are induced at the onset of B cell develop- ment, and are maintained through all developmental stages upon plasma cell differentiation [8, 9]. Furthermore, Pax5 is essential for the maintenance of B cell identity, since Pax5 deficiency results in the acquisition of multilineage potential [10]. Both Pax5 and Bach2 are required to inhibit PC differentiation [11, 12]. In addition to Pax5 and Bach2, GC cells express Bcl6, a tran- scription factor necessary for germinal center formation that allows the SHM and CSR pro- cesses to occur [13–15]. Development of B cells toward Mem cells requires Bcl6 downregulation and the induction of Irf4 [16, 17]. Conversely, PCs are characterized by the expression of Blimp1 and XBP1 that along with Irf4, inhibit the B cell identity program [5, 18]. Although a number of molecules that play a key role in the process of the terminal differen- tiation of B cells are known, it is not completely clear how such molecules regulate each other to ensure the proper appearance of GC, Mem, and PC from progenitor Naive B cells. There exist models describing several aspects of the differentiation of B cells such as the decisions pro- moting the developmental processes of CSR and SHM [19, 20], the response to environmental Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 2 / 26 Competing Interests: The authors have declared that no competing interests exist. contaminants that disrupt B cell differentiation [21, 22], the B cell exit from the GC phase for the differentiation into plasma or memory cells [23], as well as the dynamics of B cell differenti- ation inside the complex microenvironment of germinal centers [24, 25]. Nonetheless, a gen- eral consensus about the regulatory network controlling cell fate decisions of B lymphocytes is lacking. The modeling of regulatory networks has been shown to be a valuable approach to under- stand the way cells integrate several signals that control the differentiation process [26, 27]. In particular, the logical modeling approach has been useful to qualitatively describe biological processes for which detailed kinetic information is lacking [28]. This type of modeling usually focus on the nature and number of steady states reached by the network, which are often inter- preted as stable patterns of gene expression that characterize multiple cell fates [29]. In this par- adigm, the transit from one steady state to another occurs when cells receive a specific external stimuli, such as hormones, cytokines, changes in osmolarity, etc. These external stimuli are sensed and integrated to create an intracellular response that may trigger a global response such as cell growth, division, differentiation, etc. External signals are usually continuous in nature, i.e., they are present as concentration gradients of external molecules that may attain different values of strength and duration. Therefore it becomes desirable to develop models Fig 1. Terminal B cell differentiation. Precursor Naive B cells can differentiate into three possible cell types depending on proper molecular stimuli. Cytokines secreted by T-helper cells play a central role in the determination of B cell fate. IL-2 and IL-4 are required for the transition of Naive to GC cells. Direct contact of B cells with T cells by means of the CD40L receptor promote the differentiation of Naive or GC cells toward the Mem cell type. Antigen (Ag) activation drives terminal differentiation toward the PC cells, a process that is favored by the presence of IL-21. doi:10.1371/journal.pcbi.1004696.g001 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 3 / 26 that incorporate the possibility of following the response of the network to continuous signals while at the same time, describe qualitatively the directional and branched nature of cell differ- entiation processes. In this work we infer the regulatory network that controls the terminal differentiation of B cells. We then construct two dynamical systems, one discrete and one continuous, to analyze the dynamical properties of the regulatory network. Specifically, we find the stationary states of the models, and compare them against the known stationary molecular patterns observed in Naive, GC, Mem, and PC cells, under wild type and mutant backgrounds. Finally, we show that the dynamical models are able to describe the cellular differentiation pattern under a vari- ety of external signals. Importantly, the models predict the existence of several interactions nec- essary for the network to ensure the proper pattern of terminal differentiation of B cells. Furthermore, the continuous model predicts the existence of intermediary states that could be reached by the network, but that have not been reported experimentally. Results We inferred the regulatory network that controls the terminal differentiation of B cells from experimental data available in the literature referring to the key molecules involved in the con- trol of terminal B cell differentiation from the precursor B cell (Naive) to GC, Mem or PC cell types (Fig 2). The network contains 22 nodes representing functional molecules or molecular complexes, namely AID, Ag, Bach2, Bcl6, BCR, Blimp1, CD40, CD40L, ERK, IL-2, IL-2R, IL-4, IL-4R, IL-21, IL-21R, Irf4, NF-κB, Pax5, STAT3, STAT5, STAT6 and XBP1. These nodes have 39 regulatory interactions among them, being either positive or negative. S1 Table contains the set of key references used to infer the regulatory network depicted in Fig 2. Fig 2. The regulatory network of B cells. Nodes represent molecules or molecular complexes. Positive and negative regulatory interactions among molecules are represented as green continuous arrows and red blunt arrows respectively. doi:10.1371/journal.pcbi.1004696.g002 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 4 / 26 The regulatory network consists of two sets of nodes, i.e., those pertaining to a core module integrated by the master transcriptional regulators of terminal B cell differentiation (Bach2, Bcl6, Blimp1, Irf4, Pax5 and XBP1) and a set of nodes representing several signal transduction cas- cades (Ag/BCR/ERK, CD40L/CD40NF-κB, IL-2/IL-2R/STAT5, IL-4/IL-4R/STAT6 and IL-21/ IL21R/STAT3) representing key external signals required for the control of the differentiation process. The nodes corresponding to these signaling pathways are active if a external stimuli is present, i.e., if a extracellular molecule is available, it is recognized by a specific receptor that transduce the signal by a messenger molecule, which in turn regulates the expression of the tran- scription factors in the core regulatory network. Most interactions among the nodes in Fig 2 were inferred from the literature. However, we found necessary to incorporate to the network the interactions Pax5 ! Bcl6, Irf4 a Pax5 and the self-regulatory interactions Bcl6 ! Bcl6, and Pax5 ! Pax5 so as to obtain attractors with biological significance. Therefore, these four regulatory interactions constitute predictions of our model. The following paragraphs resume the reasons to incorporate such unreported interactions into our regulatory network model. B cells develop in the bone marrow from hematopoietic progenitors that progressively lose its multipotent potential as they commit with the B cell lineage. This process strictly depends on the expression of Pax5, which induces chromatin changes of B cell specific genes and restricts the developmental potential of lymphoid progenitors by repressing genes associated with other cell type programs [30, 31]. Pax5 is upregulated at the onset of B cell development until differentiation to plasma cells [7]. During early stages of B cell development, Pax5 expres- sion is positively controlled by the transcription factor Ebf1 [32], which in turn is activated by Pax5 [33], thus conforming a mutually activatory regulatory circuit that controls B cell identity. However, the signals that maintain Pax5 expression throughout late stages of B cell differentia- tion are not well understood. Therefore, a positive autoregulatory interaction for Pax5 was included in order to account for the direct mechanisms, possibly via the positive regulatory cir- cuit between Ebf1 and Pax5, or indirect mechanisms, via other signals, that might sustain high Pax5 expression during late B cell differentiation. Once B cells have completed their development in the bone marrow, they migrate to the bloodstream into the secondary lymphoid organs where they complete maturation throughout the germinal center reaction. The transcription factor Bcl6 is essential for germinal center for- mation, since Bcl6 deficiency results in the absence of germinal centers in mice [9, 15]. Given that Pax5 is required from the beginning of B cell development [10], it was necessary to include a positive regulatory signal from Pax5 to Bcl6 to keep Bcl6 in an active state when the Pax5 node is active. A high expression of Bcl6 is required during the GC phase where it controls the expression of genes necessary for the germinal center program, such as DNA damage response and apo- ptosis, thus promoting the processes of SHM and CSR and cell proliferation [6]. It has been shown that mutations that disrupt a negative autoregulatory circuit deregulate Bcl6 expression and contribute to extensive proliferation in dense large B cell lymphoma (DLBCL) [34]. More- over, it has been reported that in normal conditions there exist epigenetic mechanisms associ- ated with positive regulation of Bcl6 expression during the GC phase that overcome its negative autoregulation [35, 36]. However, the precise mechanisms and signals that maintain high levels of Bcl6 in GCs are not fully understood. Therefore, we found necessary to include a positive autoregulatory interaction for Bcl6 in order to account for the possible role of these mechanisms in GC cell differentiation. Direct contact of B cells with T cells mediated by the union of the CD40 receptor with its ligand CD40L induce the expression of Irf4 [16]. It has been shown that low levels of Irf4 pro- mote the early B cell program, while high Irf4 levels inhibit GC program and promote differen- tiation toward the Mem or PCs in later stages of B cell differentiation [18, 37]. Given that Pax5 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 5 / 26 is an essential regulator of the B cell identity program [10], a negative interaction between Pax5 and Irf4 was incorporated to simulate a constant activation of the Pax5 circuit when the Irf4 node is low and to inhibit Pax5 activation when Irf4 present at high levels. Attractors of the wild type network We studied the dynamical behavior of the discrete and the continuous systems so as to obtain their attractors. The discrete version of the B cell regulatory network was studied by exhaus- tively testing the behavior of the network from all possible initial conditions. The system reaches exactly four fixed point attractors, shown in Table 1. Notably, there is a one-to-one relation of these four attractors with the expression patterns of the cell types shown in Fig 1. We labeled the attractors as Naive, GC, Mem, and PC. It is important to remember that each attractor represents a different configuration pattern of the network at the steady state. Specifically, the first attractor, where the nodes Pax5 and Bach2 are active, can be interpreted as the activation pattern of Naive cells. The second attractor, with high levels of Bcl6, Pax5, and Bach2, corresponds to the GC cell type. The third attractor, with high levels of Irf4, Pax5, and Bach2, along with the absence of Bcl6 can be interpreted as the Mem cell fate. Finally, the fourth attractor, with high Blimp1, Irf4, and XBP1, corresponds to the pattern of the cell type PC (Fig 3). In the discrete version of the model, the set of initial states draining to the attractors, i.e the basins of attraction, do not partition the state space evenly. The percentage of initial states lead- ing to each of the attractors were as follows: Naive = 56.25%, GC = 6.25%, Mem = 6.25%, PC = 31.25%. The size of the basins reflects how an attractor can be attained from different ini- tial configurations, and may indicate the relative stability of such steady state [38]. It has been suggested that different basins represent stable or semistable cellular differentiation states [29]. Moreover, in order to transit form one steady state to another, a specific external signal would need to trigger a response in order to overcome the basin of attraction such that a different attractor could be reached by the system. Configurations with larger basins can be easily reached from many initial states, therefore, different perturbations could be buffered and cana- lized by the network towards a particular steady state [39]. Since the Naive and PC states have larger basins than that for GC or Mem attractors, it is possible to suggest that the former are relatively more stable than the later. Importantly, the proportion of basin sizes of the Naive, GC and Mem attractors agree with in vivo measures of B Table 1. Attractors of the discrete and continuous models of the B cell regulatory network. Naive GC Mem PC Node Disc. Cont. Disc. Cont. Disc. Cont. Disc. Cont. Bach2 1 1.0E + 0 1 1.0E + 0 1 1.0E + 0 0 1.1E −22 Bcl6 0 1.8E −22 1 1.0E + 0 0 1.4E −22 0 1.0E −22 Blimp1 0 2.3E −22 0 1.3E −22 0 1.3E −22 1 1.0E + 0 Irf4 0 1.7E −22 0 9.7E −23 1 1.0E + 0 1 1.0E + 0 Pax5 1 1.0E + 0 1 1.0E + 0 1 1.0E + 0 0 1.0E −22 XBP1 0 2.3E −22 0 1.2E −22 0 9.9E −23 1 1.0E + 0 For the continuous system we present averages from a total of 500,000 runs from random initial states. The standard deviation are smaller than 1E−22 in all cases. For simplicity, only the nodes conforming the network core are shown. The rest of nodes belong to the signal transduction cascades, and all of them are in the inactive state, i.e. 0. doi:10.1371/journal.pcbi.1004696.t001 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 6 / 26 cells where the Naive progenitor is more abundant in proportion than the other three cell types [40, 41]. However in spite of the low abundance of PC cells in vivo as a result of a selection pro- cess of B lymphocytes during the germinal center reaction, the largest basins corresponding to the progenitor Naive and terminally differentiated PC cells suggest that the regulatory network assures the formation of these cell types in a robust manner. Contrary to discrete systems, continuous dynamical systems have an infinite number of possible initial states so that the search for attractors by sampling a large number of random initial states can lead to the possibility to miss attractors with small basins of attraction. Indeed, the sampling of initial states resulted in the finding of only four attractors for the continuous model, which resulted identical to the attractors of the discrete model, see Table 1. Therefore, to find possible missing attractors we made an exhaustive perturbation study by temporarily modifying the activation state of each node in the four attractors found by random sampling [42]. With this approach we found three more fixed point attractors in the continuous model. These extra attractors are characterized by intermediate values of activation of the nodes con- forming the network core and do not have a counterpart in the discrete model, since the dis- crete model can attain only 0 or 1 activation values (Table 2). These attractors with intermediate values may represent possible unstable activation states that can be reached by the system but have not been yet experimentally observed or may corre- spond to transient differentiation states. Indeed, one of the attractors (“New3” attractor) found in Table 2 shows intermediate levels of Bcl6 and Irf4, in spite of the antagonistic role of these two factors, suggesting that low levels of Irf4 controls the establishment of stationary states prior to Bcl6 downregulation. This attractor may correspond to the known activation pattern of centrocytes, which are Irf4int, Bcl6hi B cells exiting the GC reaction that represent an inter- mediate cellular state between GC and PC cells [43]. This result supports the role of Irf4 as a regulator of the differentiation process prior the terminal differentiation to PCs since it has been observed that intermediate levels of Irf4 promote the GC program, whereas high levels of Irf4 promote Bcl6 downregulation and further PC differentiation as B cells exit the germinal center [44]. Fig 3. Attractors and cell types The stationary states of the regulatory network correspond to multiple activation patterns that characterize different cell types. doi:10.1371/journal.pcbi.1004696.g003 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 7 / 26 The differentiation process The B cell regulatory network is able to describe the differentiation process outlined in Fig 1, from the Naive precursor to any of the GC, Mem, or PC cell types by means of sequential pulses of extracellular signals known to direct terminal B cell differentiation (Fig 4). The system is initialized starting from the Naive attractor, and the system is perturbed at a time t 25 with a single high pulse of IL-2 or IL-4 for 2 or more time units. Computationally, this is achieved by fixing the variable IL −4 = 1 and the equation dIL4 dt ¼ 0 for the indicated period of time. This signal was intended to mimic the effect of subjecting the Naive cell to a saturating extra- cellular concentration of IL-2 or IL-4 for a brief incubation time. After the pulse, the entire sys- tem was left to evolve until it converged. This perturbation is sufﬁcient to move the dynamical system to the GC attractor which is in agreement with the observations that IL-2 and IL-4 pro- mote B cell proliferation and germinal center formation, and are also necessary signals for the transition of Naive B cells to GC B cells [45–47]. Differentiation of either Naive or GC cells to Mem cells is mediated by the activation of the CD40 receptor by its ligand CD40L [48], which leads to Irf4 induction and to the repression of Bcl6 [16]. Our model recovers these differentiation routes with a saturating activation of CD40L for 2 or more abitrary time units, which leads to the activation of Irf4 node when the Table 2. Fixed point attractors of the continuous system not found in the random search. Attractor Node New1 New2 New3 AID 0 0 0 Ag 0 0 0 Bach2 1 1 1 Bcl6 0.5 0 0.5 BCR 0 0 0 Blimp1 0 0 0 CD40 0 0 0 CD40L 0 0 0 ERK 0 0 0 IL-2 0 0 0 IL-2R 0 0 0 IL-4 0 0 0 IL-4R 0 0 0 IL-21 0 0 0 IL-21R 0 0 0 Irf4 0 0.5 0.5 NF-κB 0 0 0 Pax5 1 1 1 STAT3 0 0 0 STAT5 0 0 0 STAT6 0 0 0 XBP1 0 0 0 Three ﬁxed point attractors were found with the perturbation analysis that has not been found in the random search. These attractors are characterized by intermediate values of the nodes. doi:10.1371/journal.pcbi.1004696.t002 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 8 / 26 Pax5 node is active and Blimp1 is not present. Activation of Irf4 downregulates Bcl6 and directs the transition from the GC to the Mem attractor of the dynamical system, see Fig 4. Similarly, starting from any of the Naive, GC, or Mem attractors, the system is able to move to the PC attractor by applying a saturating signal of either IL-21 or Ag. This is consistent with the experimental reports where BCR activation by Ag induce Blimp1 upregulation, as well as Pax5 and Bcl6 downregulation thus promoting plasma cell differentiation from either Naive, GC, or Mem cell types [49–51]. This process is facilitated by the presence of IL-21 which is transduced by STAT3 [52, 53]. For both the discrete and continuous models we obtained the same biological relevant tran- sition paths that describe the wild type differentiation pattern outlined in Fig 1. However, given that the continuous model has 7 fixed-point attractors, its complete fate map is larger than that for the discrete model (S1 Fig). Nonetheless, the continuous model also presents the known biologically relevant transitions. It has been suggested that progression toward a terminal differentiated state involves several epigenetic changes that reduce the options of a cell to differentiate to other cell types, possibly by several mechanisms that constraint the function of the components of a regulatory network thus reducing the dimensionality of the state space and controlling the compartmentalization of this space into basins of attraction with different sizes [29]. Therefore, the presence of exter- nal signals could affect the way the nodes of the network activate in response to these signals which in turn regulate the activation of multiple parts of the network to control the establish- ment of stationary states of the system and the transitions between these states. Interestingly, Fig 4. Differentiation from Naive to the PC cell type. The changes in the activation of all nodes of the network are shown as a heatmap which scales from blue to red as the activation level goes from 0 to 1, respectively. Extracellular signals are simulated as a burst for two or more units of time (arrows). Starting from the Naive (Bach2+, Pax5+) stationary state (t = 0 to t 25), the system moves to the GC attractor (Bach2+, Bcl6+, Pax5+) due to the presence of a simulated pulse of IL-4 (t 25) which in turn transit to the Mem attractor (Bach2+, Irf4+, Pax5+) due to the action of CD40L (t 55) and finally, Mem attractor moves to the PC state (Blimp1+, Irf4+) by the presence of Ag signal (t 75). doi:10.1371/journal.pcbi.1004696.g004 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 9 / 26 no transitions from the PC state to other attractors were obtained in any of the two models, suggesting that the network controls B cell differentiation towards an effector cell fate in an irreversible manner while allowing the transition between precursor cell fates (Fig 5). Simulation of mutants To gain further insight of the dynamical behavior of the B cell regulatory network we systemat- ically simulated all possible single loss- and gain-of-function mutants and evaluated the sever- ity of each mutation by comparing the resulting attractors with those of the wild type model. Loss-of-function mutations were simulated by fixing at 0 the value of a node, whereas gain-of- function was simulated by fixing at 1 the same activation state of a node. For each mutant, its attractors were found, exhaustively in the case of the discrete model, and for the continuous Fig 5. Complete fate map. Nodes represent the fixed point attractors, and the edges correspond to all the possible single-node perturbations able to move the system from one attractor to another. For the continuous model, perturbations are simulated by temporarily change the value of a single node to 0, 1 or 0.5, represented by the symbols “−”, “+” and “int”, respectively. For example, IL-2+ means that a temporal activation of IL-2 is able to cause the system to move from the Naive attractor to the GC attractor. Biologically relevant differentiation routes are represented as blue arrows. doi:10.1371/journal.pcbi.1004696.g005 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 10 / 26 version, by running the dynamical system from 5000 random initial states and solving the equations numerically until the system converged. Tables 3, 4 and 5 shows that the mutants can be grouped according to whether its effect results in the loss of one or more attractors with respect to the wild type model or if it results in the appearance of atypical attractors not found in the wild type model. Importantly, both the discrete and continuous versions of the model were able to describe most of the reported mutants for the six master regulators that conform the core of the net- work. For instance, the simulated loss-of-function of the Blimp1 node results in the disappear- ance of the PC attractor, which is in accordance with the experimentally acknowledged role of Blimp1 as an essential regulator for PC differentiation [54]. Although absence of Blimp1 in B cells impedes PC differentiation, it does not affect the establishment of Naive, GC or Mem cell types [54–56], which is in turn reflected by the model since the network reaches all the Naive, GC and Mem attractors in spite of the loss-of-function of the Blimp1 node (Table 3). Additionally, for Blimp1 null mutant a distinct attractor was found showing low Pax5 and high Irf4 levels. It has been reported that Pax5 inactivation along with Irf4 induction precedes Blimp1 expression and while Irf4 activation is not sufficient to rescue PC differentiation in the absence of Blimp1, the coordinate expression of both factors is necessary for complete terminal Table 3. Simulated null mutant attractors. Mutant model Obtained pattern Effect References Bach2 [0, 0, 0, 0, 1, 0] Naive-like Only similar attractors to the wild type fates were found. [9, 12, 19] [0, 1, 0, 0, 1, 0] GC-like [0, 0, 0, 1, 1, 0] Mem-like [0, 0, 1, 1, 0, 1] PC Bcl6 [1, 0, 0, 0, 1, 0] Naive Loss of GC attractor. [13–15, 57, 58] [1, 0, 0, 1, 1, 0] Mem [0, 0, 1, 1, 0, 1] PC Blimp1 [1, 0, 0, 0, 1, 0] Naive Loss of PC attractor. A distinct attractor with high Irf4 levels found. [54, 56, 59] [1, 1, 0, 0, 1, 0] GC [1, 0, 0, 1, 1, 0] Mem [0, 0, 0, 1, 0, 0] Other Irf4 [1, 0, 0, 0, 1, 0] Naive Only Naive and GC attractors are reached by the network. Loss of Mem and PC attractors. [18, 37, 60, 61] [1, 1, 0, 0, 1, 0] GC Pax5 [0, 0, 1, 1, 0, 1] PC Inactivation of Pax5 drives the system to the PC state. An attractor not reported in literature was found. [8, 30, 62, 63] [0, 0, 0, 0, 0, 0] Other XBP1 [1, 0, 0, 0, 1, 0] Naive Mild effect over the PC attractor. Naive, GC and Mem attractors are not affected [64, 65] [1, 1, 0, 0, 1, 0] GC [1, 0, 0, 1, 1, 0] Mem [0, 0, 1, 1, 0, 0] PC-like Null mutant attractors. The attractors found for each null mutant model and the literature supporting its effect are summarized, for simplicity, only the patterns of activation for the nodes that conform the core of the network, namely Bach2, Bcl6, Blimp1, Irf4, Pax5 and XBP1 are shown. The steady state pattern for each mutant is shown in the following order: [Bach2, Bcl6, Blimp1, Irf4, Pax5, XBP1]. doi:10.1371/journal.pcbi.1004696.t003 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 11 / 26 B cell differentiation [56]. Therefore, this attractor may represent a cellular state prior to the PC state. Similarly to the Blimp1 null mutation, the simulated gain-of-function mutants for the Pax5, Bcl6 or Bach2 nodes also result in the loss of the PC attractor but the other three wild type acti- vation patterns are still reached by the network (Table 4), the constitutive activation of any of these nodes maintains the system in attractors corresponding to precursor B cell fates, in accor- dance with the observations showing that forced expression of Pax5 or Bach2 in mature B cells inhibit terminal differentiation to PCs and are required to maintain the B cell identity program [12, 66, 67]. Moreover, for the Bach2 gain-of-function model an additional attractor was found. This attractor is characterized by high levels of Bach2 and Irf4 and low Pax5 in a pattern similar to the Mem attractor, this attractor may correspond to a state previous to PC differenti- ation where Bach2 avoids Blimp1 activation when Pax5 is inactive [56, 68]. The simulated Irf4 loss-of-function results in the loss of PC and Mem cell attractors (See Table 3). Since Irf4 deficient B cells are unable to differentiate into Mem and PCs, the attractors Table 4. Simulated constitutive mutant attractors. Mutant model Obtained pattern Effect References Bach2 [1, 0, 0, 0, 1, 0] Naive Loss of PC attractor. An attractor with active Bach2 and Irf4 was found. [12] [1, 1, 0, 0, 1, 0] GC [1, 0, 0, 1, 1, 0] Mem [1, 0, 0, 1, 0, 0] Other Bcl6 [1, 1, 0, 0, 1, 0] GC Only GC and similar attractor are reached. [34, 66, 69– 71] [1, 1, 0, 1, 1, 0] Other [0, 1, 0, 1, 0, 0] Other Blimp1 [0, 0, 1, 1, 0, 1] PC The system stays in the PC state. Loss of Naive, GC and Mem attractors. [5, 72–76] Irf4 [1, 0, 0, 1, 1, 0] Mem The system reaches only the Mem and PC attractors. [18, 44, 70] [0, 0, 1, 1, 0, 1] PC Pax5 [1, 0, 0, 0, 1, 0] Naive Loss of PC attractor, the other three wild type activation patterns are reached by the network. [63, 67, 77, 78] [1, 1, 0, 0, 1, 0] GC [1, 0, 0, 1, 1, 0] Mem XBP1 [1, 0, 0, 0, 1, 1] Naive-like Activation of XBP1 node does not affects the establishment of any of the Naive, GC, Mem or PC attractors. Only similar attractors to the wild type patterns were found. [54] [1, 1, 0, 0, 1, 1] GC-like [1, 0, 0, 1, 1, 1] Mem-like [0, 0, 1, 1, 0, 1] PC Constitutive mutant attractors. The attractors found for each mutant model and the literature supporting its effect are summarized, for simplicity, only the patterns of activation for the nodes that conform the core of the network, namely Bach2, Bcl6, Blimp1, Irf4, Pax5 and XBP1 are shown. The steady state pattern for each mutant is shown in the following order: [Bach2, Bcl6, Blimp1, Irf4, Pax5, XBP1]. doi:10.1371/journal.pcbi.1004696.t004 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 12 / 26 found for this mutant support the role of Irf4 in the formation of PC and Mem cell types [18, 37, 60, 61]. Induction of Irf4 promotes the formation of Mem cells and PC differentiation [18, 44, 70], which is also described by the model as simulated gain-of-function of the Irf4 recovers only two attractors corresponding to the Mem and PC states. Therefore, constitutive activation of the Irf4 node drives the system to the Mem and PC cell fate states. Conversely, constitutive activation of the Bcl6 node results into three attractors, one of them corresponds to the GC cell pattern, the other two attractors correspond to patterns where Bcl6 is active along with Irf4. These activation patterns coincide with the expression patterns observed for centrocytes, which are Bcl6+ Irf4+ B cells exiting from the GC reaction [79]. This result suggest that sustained activation of the Bcl6 node drives the system to a GC or GC-like state, in accordance with the reported observations where Bcl6 enforced expression in B cells blocks terminal differentiation and regulates GC formation [34, 66, 71, 80]. Bach2 null mutation does not affects the formation of any of the Naive, GC, Mem or PC cell types, thus confirming its role as a dispensable regulator of B cell terminal differentiation, but a necessary negative regulator for Blimp1 expression and PC formation. Only similar attractors to the wild type fates were found [9, 12, 19]. Bcl6 null mutant mice does not form GC cells but differentiation to Naive, Mem or PC cell types is not affected. Also, Bcl6-deficient B cells can differentiate into Mem cells or PC inde- pendently of germinal center reactions. Accordingly the GC attractor is lost in the simulated Bcl6 loss-of-function mutant [13–15, 57, 58]. Deletion of Pax5 in mice results in the loss of B cells from early pro-B stage. Inactivation of Pax5 in mature B cells results in the repression of genes necessary for B cell identity. Pax5 defi- cient B cells differentiate towards the PC cell fate and show Blimp1 up-regulation. Conditional inactivation of Pax5 in mice mature B cells promotes differentiation toward PCs, in line with Table 5. Summary of the simulated mutants and external signals. Mutant models and simulated signals Resulting attractors with respect to the wild type model Bach2+, Bcl6+, Blimp1−, Irf4−, Pax5+ Loss of PC attractor Bcl6+, IL-2+, IL-2R+, STAT5+, IL-4+, IL-4R+, STAT6+, Irf4+, CD40L+, CD40+, NF-κB+, Blimp1+, Ag+, BCR+, ERK+, IL-21+, IL- 21R+, STAT3+ Loss of Naive attractor Bach2+, Bach2−, XBP1+ Replaced Naive, Mem and GC attractor by similar ones Bcl6−, IL-21+, IL-21R+, STAT3+, Ag+, BCR+, ERK+, CD40L+, CD40+, NF-κB+ Loss of GC attractor Bcl6+, IL-4+, IL-4R+, STAT6+ Only the GC and GC-like attractors are found Blimp1−, Pax5− Atypical attractor found Blimp1+, Ag+, BCR+, ERK+, IL-21+, IL-21R+, STAT3+ Only PC attractor is found Irf4+, CD40L+, CD40+, NF-κB+ Only Mem and PC attractors are found Irf4− Loss of Mem and PC attractors Irf4−, Ag+, BCR+, ERK+ Loss of Mem attractor XBP1+ Replaced PC attractor by a similar one Effect of all possible single gain- and loss-of-function mutants of the B cell model with respect to wild type, as reﬂected by their type of attractors. Symbols “+” and “−” after a node name denote gain-of-function and loss-of-function mutations, respectively. The effect of the continued activation of the nodes pertaining to signaling pathways is also indicated with the symbol “+” and summarized in the table. doi:10.1371/journal.pcbi.1004696.t005 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 13 / 26 the PC attractor found for this mutant. An attractor not reported in literature was found which may correspond to the total loss of expression of the B cell lineage factors [8, 30, 62, 63]. XBP1 is not strictly required for initiation of PC cell differentiation or for previous differen- tiation stages of terminal B cell differentiation. The network reaches all the wild type attractors [64, 65]. Forced expression of Blimp1 promotes terminal differentiation to PC cells. Only the PC attractor was found for this simulated mutant [5, 72–76]. Loss-of-function of XBP1 affects subsequent PC development but it does not impairs B cell differentiation or the establishment of any of the Naive, GC, Mem and PC cell types [54]. Accordingly, similar attractors to the wild type patterns were found. It is important to note that not all single loss- or gain-of-function mutants have a severe effect on the dynamics of our B cell differentiation model, since simulated Bach2 and XBP1 constitutive and null mutations result in attractors similar to the wild type, suggesting that these nodes have only a mild effect on the global behavior of the network. However, the Bach2 node is not dispensable since the constitutive activation of this node avoided the network for reach the PC attractor, in accordance with its biological role as an inhibitor of PC differentia- tion [12]. These results show the contribution of each node to the dynamics of network and therefore indicate the importance of these factors as regulators of the differentiation process. Given that the expression patterns defining each cell type are controlled by the core module of the regulatory network, the attractors found for the wild-type models as well as for the single loss- and gain-of-function mutants persist even in the absence of external signals. However, as mentioned in the above paragraphs, external stimuli can drive the system from one steady state to another, thus affecting the way the network controls the establishment of different expres- sion patterns. Therefore, we simulated the continuous presence of external signals by fixing the activation value of the nodes representing signaling pathways, namely Ag, BCR, CD40, CD40L, ERK, IL-2, IL-2R, IL-4, IL-4R, IL-21, IL-21R, NF-κB, STAT3, STAT5, and STAT6, in order to analyze how its continued activation influences the behavior of the core regulatory network affecting the appearance and maintenance of multiple cell fates. For clarity, the effect of the continued stimulation by external signals and the effect of the simulated mutants on the sta- tionary patterns reached by the network is summarized in Table 5. Discussion The hematopoietic system is well characterized at the cellular level, and there exist several efforts to reconstruct and analyze parts of its underlying molecular regulatory network to understand the differentiation process of multiple cell types. Network modeling has become an appropriate tool for the systematic study of the dynamical properties of specific regulatory net- works and signaling pathways. The dynamic behavior of even relatively simple networks is nei- ther trivial nor intuitive. Moreover, experimental information about the kinetic parameters of the molecules conforming such networks is generally lacking. However, the use of qualitative methods shows that it is possible to predict the existence of expression patterns or pointing at missing regulatory interactions. The model presented in this work describes the activation states observed experimentally for Naive, GC, Mem and PC cell types. This model is also able to describe the differentiation pattern from Naive B cells to GC, Mem and PC subsets in response to specific external signals. Despite the lack of qualitative information it was possible to reconstruct the regulatory network of B cells and propose a basic regulatory architecture. This model propose the existence of some missing regulatory interactions and activation states not documented in the literature that might play an important role in the context of terminal B cell differentiation. Importantly, Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 14 / 26 these interactions constitute specific predictions that can be tested experimentally. It is also rel- evant to stress that the proposed regulatory interactions might be attained by way of intermedi- ary molecules not included in the regulatory network. This is so because the whole network modeling approach is based upon the net effect of one node over another, focusing on whether the flow of information is known, rather than relying on the direct physical contact between molecules. Furthermore, the results suggest that the dynamical behavior of the B cell regulatory network is to a large extent determined by the structure of the network rather than the detail of the kinetic parameters, in accordance to analyses of related models [42, 81, 82]. While Boolean networks constitute a valuable modeling approach of choice whenever there is only qualitative data available, for this biological system we wanted to incorporate qualitative continue variables that in addition to the identification of the stationary states as in the discrete model, allows for the analysis of the effect of gradients of external signals. The dynamical behav- ior of the model resembles the qualitative behavior of the differentiation process by recovering the transition of the system from a Naive state to the terminally differentiated PC state under the presence of external signals. This result recapitulates the directional and branched nature of B cell differentiation events and supports the key role of extracellular signals in the maintenance and instruction of the differentiation process. Importantly, the model allows the exploration of system transitions that describe the differentiation form one cell type to another, it is interesting to note that no transitions from the PC state to other attractors were obtained, suggesting that the B cell regulatory network assures the differentiation towards an effector cell fate in an irre- versible manner whereas allowing plasticity of the precursor cell fates. There are several ways in which our model could be improved in future versions. One gen- eral change may be the implementation of the model as a stochastic dynamical system. Although both the stochastic and deterministic models retain the same steady states, the imple- mentation as a stochastic system could be useful to generate information about the probability of the cells to transit from one state to another. Another possible route of refinement of the models would be the inclusion of a specific time scale. Both the discrete and continuous models presented here use qualitative modeling frame- works, with results having arbitrary time units. In order to incorporate phenomena with spe- cific timescales, it will be necessary either to calibrate the continuous dynamical system by scanning for appropriate values for the parameters, or alternatively make use of a quantitative modeling framework. Also, it possible to add other layers of regulation to the model, for exam- ple by incorporating the effect of chromatin remodeling on the availability of some genes. However, given that we were able to recover with a small qualitative network the basic patterns of activation, it is possible that the role played by the levels of regulation not included in the present model may significantly reduce the number of possible transitory trajectories of the system, instead of determining nature and number of the stationary states themselves. Finally, despite the qualitative nature of the model presented here, we believe it might be used as seed to analyze important biological and clinical phenomena, given that deregulation of the master regulators included in the network are known to be involved in oncogenic events occurring in multiple lymphomas. For instance, aberrant expression of Bcl6 may lead to consti- tutive repression of genes necessary for exit of the GC program and normal differentiation, therefore contributing to lymphomagenesis [83]. In addition, activation of Irf4 leads to exten- sive cell proliferation and survival [84]. The present model could serve as a starting framework to test different hypothesis regarding the possible routes by which the expression of the afore- mentioned factors and other components of the network could be regulated in order to find therapeutic intervention strategies or to test how deregulation of the known mechanisms could lead to pathological conditions, thus contributing to our knowledge on the development of lymphomas. Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 15 / 26 Materials and Methods Molecular basis of the B cell regulatory network We inferred the regulatory network controlling terminal B cell differentiation from experimen- tal data available in literature. The evidence used to recover the nodes and interactions of the B cell regulatory network (Fig 2) is summarized in the following paragraphs. The transition from Naive B cells to GC, Mem, and antibody-secreting PCs is regulated by the coordinated activity of transcription factors that act as key regulators of the differentiation process. These factors appear to regulate mutually antagonistic genetic programs and can be divided into those that promote and maintain the B cell program, such as Pax5, Bcl6, and Bach2, and those that con- trol terminal differentiation into memory cells or plasma cells, such as Irf4 and Blimp1 and XBP1 [7]. Pax5 functions as the master regulator of B cell identity, it is expressed at the onset of B cell differentiation and is maintained in all developmental stages of B cells upon commitment to plasma cells. Pax5-deficiency results in the loss of B cell identity and the acquisition of multili- neage potential [10]. Pax5 directly inhibits Blimp1 transcription by binding to the promoter of Prdm1 the gene encoding Blimp1 [11]. In turn, Blimp1 represses Pax5 [78], thus conforming a mutually exclusive regulatory circuit. Along with Pax5, Bach2 avoids PC differentiation and promotes class switch recombination by repressing Blimp1 through binding to a regulatory ele- ment on the Prdm1 gene [12]. Bach2 is positively regulated by Pax5 [31], while being repressed by Blimp1 in PCs, thus creating a mutual inhibition feedback loop [19]. Bcl6 expression is induced upon arrival of Naive B cells into the germinal centers. Bcl6 is a transcription factor essential for germinal center formation, since deficiency of Bcl6 results in the absence of germinal centers in mice [14, 15]. The signals that promote high Bcl6 expression in GC cells are not fully understood. However, it has been shown that mutations that disrupt a negative autoregulatory circuit of Bcl6 deregulate its expression and promote the proliferation of GC cells in dense large B cell lymphomas (DLBCL) [34]. Moreover, it has been reported that there exists a positive regulatory mechanism controlling high Bcl6 expression during the GC phase that overcome its negative autoregulation [35, 36]. In accordance with these data, we found necessary to include in our model a positive autoregulatory interaction for Bcl6 (Bcl6 ! Bcl6) in order to account for the required signals that maintain high Bcl6 activation levels in GC cells. Additionally, the presence of IL-2 and IL-4 produced by follicular T helper cells play an important role in the transition from Naive to GC cells, as these signals are required for the maintenance and proliferation of GC cells. IL-2/IL-2R and IL-4/IL-4R signals are transduced by STAT5 and STAT6, respectively, thus positively regulating the expression of Bcl6 [46]. Bcl6 binds directly to the Prdm1 promoter and down-regulates the expression of Blimp1 in GC cells, thus preventing the terminal differentiation to PCs [85]. Conversely, Bcl6 is a direct target of Blimp1. This creates a mutual inhibition circuit among Bcl6 and Blimp1 [86]. Maturation of GC cells towards the Mem or PC cell fates requires the downregulation of Bcl6 [17]. This pro- cess also depends on the activation of BCR by Ag recognition, as well as on the direct contact of B cells with T helper cells which leads to BCR activation and the proteosomal degradation of Bcl6, mediated by ERK [49]. The direct contact between B and T cells is mediated by the union of CD40 with its ligand CD40L, which in turn activates NF-κB, a positive regulator of Irf4 [16]. Irf4 is a key regulator required for the development of Mem cells from Naive and GC cells, and is involved in the con- trol of CSR and PC differentiation [18, 37]. It has been shown that low levels of Irf4 promote CSR while high Irf4 levels promote PC differentiation. Irf4 inhibits Bcl6 by binding to a regula- tory site in the Bcl6 gene promoter in response to the direct contact of B and T cells [16]. Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 16 / 26 Conversely, Bcl6 is a direct negative regulator of Irf4 in GC cells [87, 88], thus generating a mutual inhibition circuit between Bcl6 and Irf4. Moreover, high Irf4 expression is maintained through direct binding of Irf4 to its own promoter creating a positive autoregulatory circuit [61]. Irf4 also plays an important role in early stages of B cell development where it regulates Pax5 expression through the formation of molecular complexes in the Pax5 enhancer region [89]. Similarly, Pax5 activation during B cell development is maintained by the transcription factor Ebf1 [33] which in turn is activated by Pax5 [32], therefore conforming a mutually posi- tive regulatory circuit. However, the role of the regulatory circuits between Pax5, Irf4 and Ebf1 during terminal B cell differentiation is not clearly understood. Nevertheless, we found neces- sary to include these interactions in our model (Pax5 ! Pax5 and Irf4 a Pax5) in order to account for the known activation patterns for these two regulators. Therefore, these interac- tions constitute predictions of the model that may support an important role of these regula- tory interactions during the late stages of B cell differentiation. The processes of CSR and SHM are controlled by the action of AID [90] which is regulated by the direct binding of Pax5, NF-κB and STAT6 to its regulatory regions in response to IL-4 and CD40 signals [91–93]. AID expression is inhibited in PCs by Blimp1 [5]. Finally, PC differentiation program is regulated by the coordinated activity of Blimp1, Irf4 and XBP1. Blimp1 is specifically expressed in PCs and its activation is sufficient to drive mature B cell differentiation towards the PC fate [56]. Blimp1 is induced by the direct binding of Irf4 to an intronic region of the Prdm1 gene [18, 61]. Also Blimp1 is involved in Irf4 activation con- forming a double positive regulatory circuit. Deficient B cells do not express Irf4 and fail to dif- ferentiate into PCs [94, 95]. In turn, Blimp1 activates XBP1 [64] which is normally repressed by Pax5 in mature B cells [65]. The regulatory network as a discrete dynamical system Boolean networks constitute the simplest approach to modeling the dynamics of regulatory networks. A Boolean network consists of a set of nodes, each of which may attain only one of two states: 0 if the node is OFF, or 1 if the node is ON [96, 97]. The level of activation for the i- th node is represented by a discrete variable xi, which is updated at discrete time steps accord- ing to a Boolean function Fi such that xi(t+1) = Fi[x1(t), x2(t), . . ., xn(t)], where [x1(t), x2(t), . . ., xn(t)] is the activation state of the regulators of the node xi at time t. The Boolean function Fi is expressed using the logic operators ^ (AND), _ (OR), and ¬ (NOT). In our model, all Fis are updated simultaneously, which is known as the synchronous approach. The resulting set of Fis is shown in Table 6. We obtained all the attractors of the Boolean model by testing all possible initial states under a synchronous updating scheme using the R package BoolNet [99]. Moreover, we simu- lated all possible single loss- and gain-of-function mutants by fixing the value of each node to 0 or 1, respectively. The complete discrete model is available for testing in The Cell Collective (http://www. thecellcollective.org/) model B cell differentiation [98]. Furthermore, the model is available as the accompanying file S1 File (Bcells_model.xml) in SBMLqual format. The regulatory network as a continuous dynamical system The B cell regulatory network was converted into a continuous dynamical system by using the standardized qualitative dynamical systems method (SQUAD) [104, 105] with the modifica- tion by Sánchez-Corrales and colaborators [42] to include into the equations a version of the regulatory logic rule for each node. This methodology offers two main advantages, first, it allows to construct a qualitative model in spite of the lack of kinetic information, making use Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 17 / 26 only of the regulatory interactions of the network, and second, since the external signals are continuous in nature, this methodology permit to study the response of the network to such signals while at the same time allowing a direct comparison with the Boolean model. Moreover, due to its formulation as a set of ordinary differential equations, it may find additional unstable steady states, cyclic behavior, or attraction basins with respect to Boolean approaches [105]. The SQUAD method approximate a Boolean system with the use of a set of ordinary differ- ential equations, where the activation level of a node is represented by a variable xi which is normalized in the range [0, 1]. This is a dimensionless variable since it represents the functional activation level of a node, but it may be used to represent the normalized concentration of the active form of a molecule or a macromolecular complex. The change of the xi node over time is Table 6. Logical rules. The set of Boolean rules defining the regulatory network of the terminal differentiation of B cells. Logic rule Description References AID (STAT6 _ (NF-κB ^ Pax5)) ^¬ Blimp1 AID node is positively regulated by the presence of Pax5 in response to CD40 and IL-4 signals, transduced by NF-κB and STAT6 respectively. AID is active only if its inhibitor Blimp1 is absent. [91–93] Bach2 Pax5 ^¬ Blimp1 Bach2 node is activated if its positive regulator Pax5 is active and the suppressor Blimp1 is absent. [19, 31] Bcl6 (STAT5 _ STAT6 _ (Pax5 ^Bcl6)) ^¬ (Blimp1 _ Irf4 _ ERK) The node Bcl6 is induced in response to IL-2 and IL-4, transduced by STAT5 and STAT6 respectively. Its activation depends on the presence of Pax5 (proposed as a positive interaction), and on the mechanisms maintaining its own expression (proposed as a positive autoregulation). Bcl6 node is repressed if either the nodes Blimp1, Irf4 or ERK are active. [35, 36, 46] BCR Ag BCR node is activated by the input node Ag, simulating the presence of extracellular antigen. [100] Blimp1 (ERK _ STAT3) _ (Irf4 ^¬ (Pax5 _ Bcl6 _ Bach2)) Blimp1 is activated by Irf4 if all its inhibitors, Pax5, Bcl6 and Bach2 are inactive. Blimp1 is induced by Ag and IL-21 which are transduced by ERK and STAT3, respectively. [49, 50, 52– 54] CD40 CD40L The CD40 node is activated by the input node CD40L simulating the direct contact of B with T cells mediated by the union of the CD40 receptor with its ligand. [16] ERK BCR BCR cross-linking promotes ERK activation after Ag stimulation [49, 51, 76] IL-2R IL-2 The IL-2R node is induced by the input node IL-2, simulating the activation of the IL-2R receptor by IL-2 stimulation, a signal involved in GC differentiation [4] IL-4R IL-4 The IL-4 input node induces the IL-4R node simulating the activation of the IL-4R receptor activation by the cytokine IL-4 required for GC differentiation. [4] IL-21R IL-21 The IL-21R receptor is induced by IL-21, a signal required for differentiation toward PCs [101–103] Irf4 (NF-κB _ Irf4) _ (Blimp1 ^¬ Bcl6) Irf4 is induced in response to CD40L signals, transduced by the node NF-κB. Irf4 regulates its own activation and is positively regulated by Blimp1 if its inhibitor Bcl6 is off. [16, 18, 61, 89] NF-κB CD40 Activation of the CD40 receptor promotes the activation of the transcription factor NF-κB in response to CD40L stimulation [16] Pax5 (Pax5 _ ¬ Irf4) ^¬(Blimp1 _ ERK) Pax5 is maintained active by low levels of Irf4, proposed as a negative interaction, and possibly by a positive regulatory circuit with Ebf1 that plays a key role during early B cell differentiation, included as a positive autoregulatory interaction. Pax5 is inhibited if Blimp1 or ERK are present. [11, 51, 78] STAT3 IL-21R IL-21 signals are transduced by STAT3, represented in the model as a positive interaction of the IL-21R receptor with STAT3. [101–103] STAT5 IL-2R Activation of the IL-2R receptor by IL-2 induces STAT5 activation [46] STAT6 IL-4R Activation of the IL-4R receptor induces STAT6 in response to IL-4 stimulation [91] XBP1 Blimp1 ^¬ Pax5 XBP1 is activated by Blimp1 if the suppressor Pax5 is absent [65] The rules determining the state of activation of each node as a function of its regulatory inputs are expressed by the use of the logic operators ^ (AND), _ (OR), and ¬ (NOT). doi:10.1371/journal.pcbi.1004696.t006 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 18 / 26 controlled by an activation term and a decay term as described by: dxi dt ¼ e0:5hi þ ehiðoi0:5Þ ð1 e0:5hiÞð1 þ ehiðoi0:5ÞÞ gixi ð1Þ In Eq (1) parameters hi and γi are the gain of the input of the node and the decaying rate, respectively. The term ωi is the continuous form of the logical rule describing the response of the node xi to its regulatory inputs, as defined for the discrete dynamical system in the previous section. The logical statements defined for the discrete model are converted into their continu- ous equivalent by changing A ^ B, A _ B, and ¬A in an expression of classic logic into min(A, B), max(A, B), and 1−A, respectively, thus creating a fuzzy-logic expression. Note that the term ωi cannot be applied to all nodes of Fig 2, because there are five of them that do not have any regulatory inputs, therefore equations representing these nodes contain only the term for the decaying rate. The activation term for Eq (1) has the form of a sigmoid as a function of the total input to a node ωi, and was constructed so as to pass through the points (0,0), (0.5,0.5), (1,1) for any posi- tive value of h. We found that for values of h 50, the curve is very close to a step function; for intermediate values of h the function is similar to a logistic curve and as h approaches 0 the function is almost a straight line (Fig 6). This characteristic allows the study of different quali- tative response curves on the overall behavior of the regulatory network, while at the same time conserving the direct comparison against a Boolean model due to the three fixed points men- tioned above. Since there is a lack of published quantitative data that could be used to estimate the values of either of the hi and γi parameters to solve the system of equations, we decided to Fig 6. The activation part of Eq (1) is a sigmoid function of the total input of the node (ωi) Regardless of the value of h, the sigmoid touches the points (0,0), (0.5,0.5) and (1,1). For values of h 50 the curve resembles a step function. doi:10.1371/journal.pcbi.1004696.g006 Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 19 / 26 use a set of default values. Therefore, all h’s were set to 50 and γ = 1 so as to obtain steep response curves, thus making an easy comparison of the discrete model against the current continuous model and/or forthcoming models. We found that values h 6¼ {4,8} and γ = 1 recover the experimentally observed patterns of expression S2 Fig. In contrast to the relative insensitivity of changes in the strength of interac- tions h, the attractors are highly sensitive to changes in values of the decay rate γ. Eq (1) is con- structed in such a way that γ has to have a value equal to 1 in order for xi’s to lie in the closed interval [0, 1]. Now, values of γ different than 1 make all attractors to disappear S3 Fig. The attractors of the B cell regulatory network model, therefore, are highly dependent on the value used in the parameter specifying the decaying rate. The resulting dynamical system in shown as S2 Table in the Supporting Information, and available as the supplementary S1 File. Due to the high non-linearity of the continuous system of equations, we located the steady states of this model by numerically solving the system of equations from 500,000 random initial states and letting it converge, with the use of the R pack- age deSolve [106], the detailed attractors found for both the wild type and the mutant models are shown in S2 File. Supporting Information S1 Table. Table of interactions. Key references supporting network interactions. (PDF) S2 Table. The B cell network as a continuous dynamical system. The set of ordinary differen- tial equations conforming the continuous version of the B cell regulatory network model. (PDF) S1 Fig. Complete fate map for the discrete model. (TIFF) S2 Fig. Location of the fixed-point attractors as a function of the parameter h. (TIFF) S3 Fig. Location of the fixed-point attractors as a function of the parameter γ. (TIFF) S1 File. SBMLqual format version of the B cell model. Complete model for testing in the The Cell Collective platform (http://www.thecellcollective.org/), model B cell differentiation and file Bcell_model.xml. (XML) S2 File. Detailed attractors of wild type and simulated mutants. (XLSX) Acknowledgments We want to thank Carlos Ramírez and Nathan Weinstein for their valuable comments during the preparation of this manuscript. Author Contributions Conceived and designed the experiments: LM. Performed the experiments: AM. Analyzed the data: AM LM. Contributed reagents/materials/analysis tools: AM. Wrote the paper: AM LM. 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Network Model of B Cells PLOS Computational Biology \| DOI:10.1371/journal.pcbi.1004696 January 11, 2016 26 / 26	26751566	XBP1 = ( Blimp1 AND ( ( ( NOT Pax5 ) ) ) ) Blimp1 = ( ( ( ( Irf4 AND ( ( ( NOT Bcl6 OR NOT Bach2 OR NOT Pax5 ) ) ) ) AND NOT ( Bach2 ) ) AND NOT ( Pax5 ) ) AND NOT ( Bcl6 ) ) OR ( ( ( ( ERK ) AND NOT ( Bach2 ) ) AND NOT ( Pax5 ) ) AND NOT ( Bcl6 ) ) OR ( ( ( ( STAT3 ) AND NOT ( Bach2 ) ) AND NOT ( Pax5 ) ) AND NOT ( Bcl6 ) ) Bach2 = ( ( Pax5 ) AND NOT ( Blimp1 ) ) IL-21R = ( IL-21 ) STAT3 = ( IL-21R ) CD40 = ( CD40L ) Bcl6 = ( ( ( ( Bcl6 AND ( ( ( Pax5 ) ) ) ) AND NOT ( Blimp1 ) ) AND NOT ( ERK ) ) AND NOT ( Irf4 ) ) OR ( ( ( ( STAT5 ) AND NOT ( Blimp1 ) ) AND NOT ( ERK ) ) AND NOT ( Irf4 ) ) OR ( ( ( ( STAT6 ) AND NOT ( Blimp1 ) ) AND NOT ( ERK ) ) AND NOT ( Irf4 ) ) STAT5 = ( IL-2R ) Irf4 = ( ( Blimp1 ) AND NOT ( Bcl6 ) ) OR ( ( Irf4 ) AND NOT ( Bcl6 ) ) OR ( NF-kB ) AID = ( STAT6 AND ( ( ( NOT Blimp1 ) ) ) ) OR ( NF-kB AND ( ( ( Pax5 ) ) AND ( ( NOT Blimp1 ) ) ) ) IL-2R = ( IL-2 ) IL-4R = ( IL-4 ) Pax5 = ( ( ( ( Pax5 AND ( ( ( NOT Irf4 ) ) OR ( ( Pax5 ) ) ) ) AND NOT ( ERK ) ) AND NOT ( Blimp1 ) ) ) OR NOT ( Irf4 OR Pax5 OR ERK OR Blimp1 ) NF-kB = ( CD40 ) STAT6 = ( IL-4R ) ERK = ( BCR ) BCR = ( Ag )
ORIGINAL RESEARCH published: 14 April 2016 doi: 10.3389/fgene.2016.00044 Frontiers in Genetics \| www.frontiersin.org 1 April 2016 \| Volume 7 \| Article 44 Edited by: Ekaterina Shelest, Hans-Knöll-Institute, Germany Reviewed by: Julio Vera González, University Hospital Erlangen, Germany Nils Blüthgen, Charité-Universitätsmedizin Berlin, Germany Correspondence: Hauke Busch h.busch@dkfz.de; Melanie Boerries m.boerries@dkfz.de †Present Address: Steffen Knauer, Cold Spring Harbor Laboratory, Cold Spring Harbor, NY, USA ‡These authors are co-ﬁrst authors. §These authors are co-last authors. Specialty section: This article was submitted to Bioinformatics and Computational Biology, a section of the journal Frontiers in Genetics Received: 20 November 2015 Accepted: 14 March 2016 Published: 14 April 2016 Citation: Offermann B, Knauer S, Singh A, Fernández-Cachón ML, Klose M, Kowar S, Busch H and Boerries M (2016) Boolean Modeling Reveals the Necessity of Transcriptional Regulation for Bistability in PC12 Cell Differentiation. Front. Genet. 7:44. doi: 10.3389/fgene.2016.00044 Boolean Modeling Reveals the Necessity of Transcriptional Regulation for Bistability in PC12 Cell Differentiation Barbara Offermann 1‡, Steffen Knauer 1 †‡, Amit Singh ‡, María L. Fernández-Cachón 1, Martin Klose 1, Silke Kowar 1, Hauke Busch 1, 2, 3§ and Melanie Boerries 1, 2, 3§ 1 Systems Biology of the Cellular Microenvironment Group, Institute of Molecular Medicine and Cell Research, Albert-Ludwigs-University Freiburg, Freiburg, Germany, 2 German Cancer Consortium, Freiburg, Germany, 3 German Cancer Research Center, Heidelberg, Germany The nerve growth factor NGF has been shown to cause cell fate decisions toward either differentiation or proliferation depending on the relative activity of downstream pERK, pAKT, or pJNK signaling. However, how these protein signals are translated into and fed back from transcriptional activity to complete cellular differentiation over a time span of hours to days is still an open question. Comparing the time-resolved transcriptome response of NGF- or EGF-stimulated PC12 cells over 24 h in combination with protein and phenotype data we inferred a dynamic Boolean model capturing the temporal sequence of protein signaling, transcriptional response and subsequent autocrine feedback. Network topology was optimized by ﬁtting the model to time-resolved transcriptome data under MEK, PI3K, or JNK inhibition. The integrated model conﬁrmed the parallel use of MAPK/ERK, PI3K/AKT, and JNK/JUN for PC12 cell differentiation. Redundancy of cell signaling is demonstrated from the inhibition of the different MAPK pathways. As suggested in silico and conﬁrmed in vitro, differentiation was substantially suppressed under JNK inhibition, yet delayed only under MEK/ERK inhibition. Most importantly, we found that positive transcriptional feedback induces bistability in the cell fate switch. De novo gene expression was necessary to activate autocrine feedback that caused Urokinase-Type Plasminogen Activator (uPA) Receptor signaling to perpetuate the MAPK activity, ﬁnally resulting in the expression of late, differentiation related genes. Thus, the cellular decision toward differentiation depends on the establishment of a transcriptome-induced positive feedback between protein signaling and gene expression thereby constituting a robust control between proliferation and differentiation. Keywords: PC12 cells, Boolean modeling, NGF signaling, EGF signaling, bistability 1. INTRODUCTION The rat pheochromocytoma cells PC12 are a long established in vitro model to study neuronal diﬀerentiation, proliferation and survival (Greene and Tischler, 1976; Burstein et al., 1982; Cowley et al., 1994). After stimulation with the nerve growth factor (NGF), a small, secreted protein from the neurotrophin family, PC12 cells diﬀerentiate into sympathetic neuron-like cells, which is Offermann et al. Boolean Model of PC12 Cell Differentiation morphologically marked by neurite outgrowth over a time course of up to 6 days (Levi-Montalcini, 1987; Chao, 1992; Fiore et al., 2009; Weber et al., 2013). NGF binds with high aﬃnity to the TrkA receptor (tyrosine kinase receptor A), thereby activating several downstream protein signaling pathways including primarily the protein kinase C/phospholipase C (PKC/PLC), the phosphoinositide 3-kinase/protein kinase B (PI3K/AKT) and the mitogen-activated protein kinase/extracellular signal- regulated kinase (MAPK/ERK) pathways (Kaplan et al., 1991; Jing et al., 1992; Vaudry et al., 2002). Beyond these immediate downstream pathways, further studies showed the involvement of Interleukin 6 (IL6), Urokinase plasminogen activator (uPA) and Tumor Necrosis Factor Receptor Superfamily Member 12A (TNFRSF12A) in PC12 cell diﬀerentiation (Marshall, 1995; Wu and Bradshaw, 1996; Leppä et al., 1998; Xing et al., 1998; Farias- Eisner et al., 2000, 2001; Vaudry et al., 2002; Tanabe et al., 2003). Sustained ERK activation is seen as necessary and suﬃcient for the successful PC12 cell diﬀerentiation under NGF stimulation (Avraham and Yarden, 2011; Chen et al., 2012), whereas transient ERK activation upon epidermal growth factor (EGF) stimulation results in proliferation (Gotoh et al., 1990; Qui and Green, 1992; Marshall, 1995; Vaudry et al., 2002). In fact, selective pathway inhibition or other external stimuli that modulate the duration of ERK activation likewise determine the cellular decision between proliferation and diﬀerentiation (Dikic et al., 1994; Vaudry et al., 2002; Santos et al., 2007). Consequently, the MAPK signaling network, as the key pathway in the cellular response, has been studied thoroughly in vitro and in silico (Sasagawa et al., 2005; von Kriegsheim et al., 2009; Saito et al., 2013). Interestingly, both EGF and NGF provoke a similar transcriptional program within the ﬁrst hour. Therefore, diﬀerences in cellular signaling must be due (i) to diﬀerential regulation of multiple downstream pathways and (ii) late gene response programs (>1 h) that feed back into the protein signaling cascade. As an example for pathway crosstalk, both, the MAPK/ERK and c-Jun N-terminal kinase (JNK) pathways regulate c-Jun activity and are necessary for PC12 cell diﬀerentiation (Leppä et al., 1998; Waetzig and Herdegen, 2003; Marek et al., 2004), while uPA receptor (uPAR) signaling, as a result of transcriptional AP1 (Activator Protein-1) regulation, is necessary for diﬀerentiation of unprimed PC12 cells (Farias-Eisner et al., 2000; Mullenbrock et al., 2011). In the present study, we combined time-resolved transcriptome analysis of EGF and NGF stimulated PC12 cells up to 24 h with inhibition of MAPK/ERK, JNK/JUN, and PI3K/AKT signaling, to develop a Boolean Model of PC12 cell diﬀerentiation that combines protein signaling, gene regulation and autocrine feedback. The Boolean approach allows to derive important predictions without detailed quantitative kinetic data and parameters over diﬀerent time scales (Singh et al., 2012). Protein signaling comprised MAPK/ERK, JNK/JUN, and PI3K/AKT pathways. Based on the upstream transcription factor analysis and transcriptional regulation of Mmp10 (Matrix Metallopeptidase 10), Serpine1 (Serpin Peptidase Inhibitor, Clade E, Member) and Itga1 (Integrin, Alpha 1), we further included an autocrine feedback via uPAR signaling. The model topology was trained on the transcriptional response after pathway inhibition. Inhibition of JNK completely blocked PC12 cell diﬀerentiation and long-term expression of target transcription factors (TFs), such as various Kruppel-like factors (Klf2, 4, 6 and 10), Maﬀ(V-Maf Avian Musculoaponeurotic Fibrosarcoma Oncogene Homolog F) and AP1. Interestingly, inhibition of MEK (mitogen-activated protein kinase kinase), blocking the phosphorylation of ERK, slowed down, but not completely abolished cell diﬀerentiation. Neurite quantiﬁcation over 6 days conﬁrmed a late and reduced, but signiﬁcant PC12 diﬀerentiation, which hinted at alternative pathway usage through JNK. Inhibition of the PI3K/AKT pathway, which is involved in cell proliferation (Chen et al., 2012), even increased the neuronal morphology and neurite outgrowth. In conclusion, our Boolean modeling approach shows the complex interplay of protein signaling, transcription factor activity and gene regulatory feedback in the decision and perpetuation of PC12 cell diﬀerentiation after NGF stimulation. 2. MATERIALS AND METHODS 2.1. Cell Culture and Stimulation PC12 cells were obtained from ATCC (American Type Culture Collection, UK) and were cultured at 37◦C at 5% CO2 in RPMI 1640 medium, supplemented with 10% Horse Serum, 5% Fetal Bovine Serum, 1% penicillin/streptomycin (PAN Biotech, Germany) and 1% glutamine (PAN Biotech, Germany). For cell stimulation, 500,000 cells/well were seeded on collagen coated 6 well plates (Corning, NY, USA). The following day, cells were stimulated with 50 ng/ml rat nerve growth factor (NGF; Promega, Madison, WI, USA) or 75 ng/ml epidermal growth factor (EGF; R&D Systems; Wiesbaden, Germany) for the corresponding times. For the pathway inhibition experiments, the following inhibitors were used and added 60 min before NGF was added, mitogen-activated protein inhibitor at a concentration of 20 µM (MEKi; U0126 from Promega, Madison, WI, USA), phosphoinositide 3-kinase inhibitor at a concentration of 40 µM (PI3Ki; LY-294002 from Enzo Life Sciences, New York, USA) and c-Jun N-terminal kinase inhibitor at a concentration of 20 µM (JNKi; SP600125 from Sigma- Aldrich, St. Louis, USA). The inhibitors were dissolved in DMSO and were further diluted in cell culture medium at their working concentration. Control cells were treated with DMSO at the same concentration that was present in the cells with inhibitor treatment. 2.2. RNA Isolation and Quantitative Real Time PCR (qRT-PCR) Total RNA was isolated from 500,000 cells per timepoint according to the manufacturer’s protocol (Universal RNA Puriﬁcation Kit, Roboklon, Germany). RNA integrity was measured using an Agilent Bioanalyzer-2000 (Agilent Technologies GmbH, Waldbronn, Germany), and its content quantiﬁed by NanoDrop ND-1000 (Thermo Fisher Scientiﬁc, Wilmington, USA). For RT-qPCR, double strand cDNA was synthesized from 1 µg of total RNA using the iScriptTM cDNA Synthesis kit (Quanta Biosciences, Gaithersburg, USA) according to the manufacturer instructions. RT-qPCR was performed in a CFX96 instrument (BioRad, Hercules, CA, USA) using a Frontiers in Genetics \| www.frontiersin.org 2 April 2016 \| Volume 7 \| Article 44 Offermann et al. Boolean Model of PC12 Cell Differentiation SYBR Green master mix. Relative gene expression levels were calculated with the 2-11Ct method, using HPRT1 and 18S ribosomal RNA as reference genes. Post-run analyses were performed using Bio-Rad CFX Manager version 2.0 and the threshold cycles (Cts) were calculated from a baseline subtracted curve ﬁt. See Supplementary Table 1 for primer pair sequences. 2.3. Microscopy and Quantiﬁcation Live phase contrast images from PC12 cells under the diﬀerent conditions were acquired using a Nikon Eclipse Ti Inverted Microscope (Nikon; Düsseldorf, Germany) equipped with a Perfect Focus System (PFS) and a Digital cooled Sight Camera (DS-QiMc; Nikon, Germany) as described in (Weber et al., 2013). Brieﬂy, PC12 cells were cultured in collagen coated 6-well plates (500,000 cells/well) and treated as described in “Cell culture and stimulation” and 150 images per well, every second day were recorded with the same spatial pattern. Cell diﬀerentiation is calculated by the ratio of the two described imaging features (Weber et al., 2013) convex hull (CH) to cell area (CA) for 150 images per well over 6 days (Weber et al., unpublished data). 2.4. Western Blot For each timepoint and condition 3 × 106 PC12 cells (for inhibition experiments) or 5 × 106 PC12 cells (for EGF vs. NGF comparison) were seeded in 10cm collagen coated Cell BIND dishes (Corning; Germany). Cells were collected after 5, 10, 30 min, 1, 2, 4, 6, 8, 12, 24, and 48 h in 200 µl RIPA buﬀer (containing 0.5% SDS), supplemented with proteinase inhibitor (complete mini EDTA free tablets, Roche, Basel, Switzerland) and Benzonase (Merck), and lysed for 20 min under agitation. A total of 30 µg protein was loaded per lane and run in 10% SDS- polyacrylamide gels, transferred to polyvinylidene diﬂuoride membranes. Membranes were cut horizontally into fragments according to the expected sizes of the protein of interest and immunoblotted with antibodies against total p44/42 (ERK1/2, 1:2000, #9102S, Cell Signaling Technology [CST]), phospho p44/42 (pERK1/2, 1:2000, #9101S, CST), total JNK (JNK1/2, 1:1000, #9258S, CST), phospho JNK (Thr183/Tyr185, 1:1000, #4668S, CST), total AKT (1:1000, #4691S, CST), phospho AKT (1:1000, Ser473, #9271S, CST) or GAPDH (1:2000,# MAB374, Millipore) overnight at 4◦C. Proteins were visualized with chemiluminescence on SuperSignal West Pico Chemiluminiscent Substrate imager (Thermo-Fischer, Massachusetts, USA) after 1h of incubation with appropriate horseradish peroxidase-linked secondary antibody (Sigma- Aldrich). Immunoblots were quantiﬁed using ImageJ (image analyzer camera LAS4000, Fujiﬁlm, Tokyo, Japan). Blots were normalized to total GAPDH and an internal standard (IS) was used for normalization between membranes. 2.5. Microarray Analysis and Data Pre-processing Time-resolved gene expression data of stimulated PC12 were recorded at t = [1, 2, 3, 4, 5, 6, 8, 12, 24] h and t = [1, 2, 3, 4, 6, 8, 12, 24] h for NGF and EGF stimulation, respectively. Control timepoints were measured at 0, 2, 4, 6, 8, 12, 24 h. Total RNA was isolated, labeled and hybridized to an Illumina RatRef-12 BeadChip (Illumina, San Diego, CA, USA) according to the manufacturers protocol. Raw microarray data were processed and quantile normalized using the Bioconductor R package beadarray (Ritchie et al., 2011). Illumina Probes were mapped to reannotated Entrez IDs using the Illumina Ratv1 annotation data (v. 1.26) from Bioconductor. If several probes mapped to the same Entrez ID, the one having the largest interquartile range was retained. This resulted in 15,348 annotated genes, whose expression was further batch corrected according to their chip identity (Johnson et al., 2007). Finally, gene expression time series were smoothed by a 5th order polynomial to take advantage of the high sampling rate and replicates at 0, 12, and 24 h. Microarray data have been deposited at Gene Expression Omnibus (GEO) under the accession number GSE74327. 2.6. Multi-Dimensional Scaling To determine signiﬁcantly regulated genes over time we performed a multi-dimensional scaling (MDS) using the HiT- MDS algorithm (Strickert et al., 2005). The algorithm projects the 15348 × 15348 distance matrix D of the pairwise Euclidean distances between all genes onto a two dimensional space, while preserving distances in D as best as possible. Genes varying strongly and uniquely over time will appear as outliers in the MDS point distribution. The uniqueness of a gene expression proﬁle was quantiﬁed by ﬁtting a two-dimensional skewed Gaussian distribution (Azzalini, 2015) to the MDS point density function. 2.7. Clustering Gene Expression Patterns To cluster the gene timeseries, we applied the Cluster Aﬃnity Search Technique (CAST), which considers the genes and their similarity over times as nodes and weighted edges of graph, respectively (Ben-Dor et al., 1999). All clusters are considered as unrelated entities and there is no pre-deﬁned number of clusters. Instead a threshold parameter, here t = 0.8, determines the aﬃnity between genes and this the ﬁnal number of gene clusters. Inverse or anti-correlative behavior of genes after NGF or EGF stimulation was determined by ﬁtting a linear model to the smoothed gene expression. Genes having a signiﬁcant slope with opposite sign and an r2 > 0.7 were taken as anti-correlated. 2.8. Enrichment Analysis of Transcription Factor Target Gene Sets Upstream analysis for putative transcription factors regulating the EGF and NGF transcriptome responses over time were assessed by a Gene Set Enrichment analysis (Luo et al., 2009) using paired control to treatment samples for each timepoint with an overall cutoﬀq-value < 0.01. As gene sets we used the transcription factor target lists from the Molecular Signatures Database (MSigDB, version 5.0) (Subramanian et al., 2005), for which we mapped the human genes to the rat orthologs using BiomaRt (Huang et al., 2014). Frontiers in Genetics \| www.frontiersin.org 3 April 2016 \| Volume 7 \| Article 44 Offermann et al. Boolean Model of PC12 Cell Differentiation 2.9. Boolean Model We used a Boolean model framework for dynamic analysis of PC12 cell diﬀerentiation. Based on our microarray data and literature knowledge we constructed a highly connected prior knowledge network (PKN) consisting of 63 nodes and 109 edges (cf. Supplementary Table 2). The R/Bioconductor package CellNetOptimizer (CNO) (Saez-Rodriguez et al., 2009) was used to optimize the PKN by reducing redundant nodes, unobservable states and edges. For this we rescaled the qRT-PCR fold change values between 0 and 1 and then transformed with a Hill function f (x) = xn xn + kn as suggested in Saez-Rodriguez et al. (2009), where n = 2 and k = 0.5 denote the Hill coeﬃcient and the threshold, above which a node is considered “on,” respectively. Changing the Hill coeﬃcient between 1 ≤n ≤6 did not change the results qualitatively. Model topology optimization was performed via the CellNORdt, which allows ﬁtting with time course data. (See Supplementary Table 3 for stimulus, inhibition and time course data). We set the maximal CPU run time for the underlying genetic algorithm (GA) to 100 s and the relative tolerance to 0.01, using default parameters from the CNO otherwise. A representative evolution of the average and best residual error in a GA run is depicted in Supplementary Image 1A. The solutions quickly converge to a quasi steady state within the time window of simulation of 100 s. The following edges were ﬁxed to prior to optimization based on literature knowledge: NGF →PI3K, NGF →RAS, NGF →PLC, AP1 →NPY, MEK/ERK & JNK →Jund, MEK/ERK & JNK →Junb, Fosl1 & Jund →AP1, Mmp10 → RAS, RAS →MEK, PLC →MEK. Model optimization was performed 100 times and edges were retained, if they appeared in 70% of the runs. This cutoﬀwas chosen to generate a sparse network with robust edges. Performing more runs did not change the results qualitatively (cf. Supplementary Image 1B). Model simulations were performed using the R/Bioconductor package BoolNet (Müssel et al., 2010). The reference publications from which the interactions have been inferred as well as their Boolean transition functions are listed in Supplementary Table 4. 3. RESULTS 3.1. Gene Response of PC12 Cells Diverges for NGF and EGF on Long Time Scales To elucidate the dynamic gene response of NGF and EGF, we measured the transcriptome dynamics using Illumina RatRef- 12 Expression BeadChips. PC12 cells were either stimulated with NGF or EGF, and collected at the following timepoints: 1, 2, 3, 4, 5, 6, 8, 12, and 24 h. The unstimulated control samples (ctrl) were collected in parallel. Gene expression time series were smoothed by a 5th order polynomial to take advantage of the high sampling rate. Finally, we mapped array probes to their respective Entrez IDs, resulting in 15,348 annotated genes. A bi plot of the principal component analysis (PCA) for the 1000 most varying genes depicted a clear separation of the control, NGF and EGF samples. The PCA scores, representing the NGF and EGF treated samples, showed a qualitatively similar behavior up to 4 h after stimulation, yet diﬀered markedly beyond that time (Figure 1A, left). The absolute length and direction of the PCA loadings (Figure 1A, right) indicate the contribution of individual genes to the position of the scores. Correspondingly, several immediate early genes, such as Junb (Jun B Proto- Oncogene), Fos (FBJ Murine Osteosarcoma Viral Oncogene Homolog), Ier2 (Immediate Early Response 2), and Egr1 (Early Growth Response 1) contributed to the early gene response under both EGF and NGF stimulation, while members of the uPAR/Integrin signaling complex, such as Mmp13/10/3 (Matrix Metallopeptidase 13/10/3), Plat (Plasminogen Activator, Tissue) and Serpine1 (Serpin Peptidase Inhibitor, Clade E, Member 1) determined, among others, the separation of the NGF from the EGF trajectory. Loadings that point toward the control and late EGF response samples, like Cdca7 (Cell Division Cycle Associated 7) and G0s2 (G0/G1 Switch 2), are clearly related to cell cycle progression and additionally highlight the diﬀerence in proliferation vs. diﬀerentiation. In conclusion, the NGF gene response, and thus PC12 cell diﬀerentiation, must be determined by late transcriptional feedback events, that trigger and sustain MAPK/ERK signaling. Next, we sought to functionally analyze the transcriptional diﬀerences in early and late gene regulation after EGF and NGF stimulation. For this we selected genes that are (i) strongly regulated (log2 fold change of < −1.7 or > 1.7 in two consecutive timepoints) and (ii) have a unique temporal expression proﬁle according to a multi-dimensional scaling (MDS) analysis (p-value < 0.01) (cf. Supplementary Image 2). We found 152 and 402 genes, meeting both criteria, in the EGF and NGF data, respectively, among which 126 genes are shared by both conditions. Figure 1B depicts a clustering of these diﬀerentially i.e., top-regulated genes. A cluster aﬃnity search technique (Ben-Dor et al., 1999) identiﬁed ﬁve EGF (E1-E3b) and seven NGF (N1-N4B) gene response clusters (cf. Supplementary Table 5 and Supplementary Image 3). Interestingly, the EGF stimulus induced a short pulse-like response with rapid return to original gene expression levels, while the NGF stimulus induced a combination of short-impulse like (N1 - N2b) and long sustained gene expression patterns with several clusters (N3a- N4b) sustaining their expression over time (cf. circled insets in Figure 1B). Figure 1C depicts a network representation of the enrichment analysis using a hypergeometric test on Gene Ontologies (GO). Enriched upregulated biological functions were identiﬁed in gene lists E1, E2a, N1, N2a, N3a, N4a and in both groups of inversely regulated genes (cf. Supplementary Table 6). Nodes correspond to GO terms, with numbers indicating the joint enrichment scores. Nodes sharing at least 20 percent of their genes are connected by solid or dotted edges, if the connected nodes lie within a stimulus or across NGF and EGF treatment. Early transcription factor activity is common to both, NGF and EGF signaling, (clusters E1 and N1) as well as MAPK signaling genes (clusters E2a and N3a). The latter, however, is more prominent and enriched at later points in time after NGF stimulation (N3a) compared to the EGF induced response (E2a). Here, a less and earlier enrichment of MAPK signaling genes was seen. Moreover, a second network of transcription factor activity could be identiﬁed after NGF stimulation (cluster N2a) that does not have any equivalent after EGF stimulation. It seems, that the initial response (ﬁrst hour) is Frontiers in Genetics \| www.frontiersin.org 4 April 2016 \| Volume 7 \| Article 44 Offermann et al. Boolean Model of PC12 Cell Differentiation FIGURE 1 \| Gene response dynamics after NGF or EGF stimulation. (A) Principal component analysis (PCA) of the PC12 cell transcriptomes after NGF (red), EGF (blue) and control treatment (gray). The PCA scores (left panel) and loadings (right panel) correspond to the samples and genes, respectively. Samples in the left panel have been connected to guide the eye. Clearly, EGF and NGF samples remain close in the ﬁrst 3 h and separate at later timepoints, indicating a different cellular phenotype. Right panel: 50 largest loading vectors indicating the impact and time of action of individual genes. Immediate early genes, like Fos or Ier2 point toward early timepoints, while loadings pointing toward the right, like Vgf or Npy, correspond to late timepoints and are most likely involved in differentiation. (B) Expression clusters of top regulated genes. The left and right panels depict the response of individual genes to EGF and NGF stimulation, respectively (gray lines). Cluster centroids are marked by lines with the cluster size encoded by line thickness. The circular inserts depict the cluster centroid envelopes for EGF and NGF, respectively. (C) Network representation of functional enrichment of NGF and EGF response genes. The network is comprised of GO-term clusters having a signiﬁcant enrichment (−log10(p-value) > 1.3) as shown in bold black numbers. Red, gray and green nodes contain in this order top-regulated genes, inversely-regulated genes between EGF and NGF or both. The vertical node location corresponds to the peak regulation of their genes, while node size is proportional to the number of genes in a functional category. Edges indicate a gene overlap of > 20% between nodes, being drawn as dashed lines, if they are shared between EGF and NGF. controlled by a shared set of top-regulated genes (cf. Figure 1C, dashed lines). The cell-fate speciﬁc processes, however, seem to be orchestrated by diﬀerent set of genes (cf. Figure 1C, separate networks). Many of the genes executing proliferation or diﬀerentiation speciﬁc processes fall into the category of inversely regulated genes and are not amongst the set of top- regulated genes identiﬁed earlier (cf. Figure 1C, green and gray nodes, cf. Material and Methods, cf. Supplementary Table 7). The genes involved in the procession of extracellular matrix and cytoplasmic vesicles, however, constitute an exception: these genes are both top and inverse-regulated (cf. Figure 1C, green nodes). In summary, functional analysis of the gene clusters revealed an initiation of the diﬀerentiation and proliferation process by a shared set of diﬀerentially regulated genes. Speciﬁc functions, such as transmission of nerve impulse or DNA replication, however, seemed to be executed by two distinct gene groups that are when comparing the EGF to the NGF stimulus inversely regulated over time. Additionally, a second network of genes involved in transcription factor activity was identiﬁed in the NGF data set, which lacked a corresponding network in the EGF data set. 3.2. Simulation of a Boolean Network Based on the above gene response analyses we sought to identify the mechanisms that sustain MAPK signaling activity after NGF stimulation. Our transcriptome timeseries analysis revealed that the decision process between proliferation and diﬀerentiation was spread out over several hours during which transcriptional feedback through an additional set of transcription factors was present after NGF stimulation, only (cf. Figure 1C). To further elucidate the transcription factors upstream of the gene Frontiers in Genetics \| www.frontiersin.org 5 April 2016 \| Volume 7 \| Article 44 Offermann et al. Boolean Model of PC12 Cell Differentiation response after EGF or NGF stimulation we performed a gene set enrichment analysis (GSEA) (Luo et al., 2009) on the paired NGF to control and EGF to control transcriptome timeseries. As gene sets we used the motif gene sets from the Molecular Signatures Database (MSigDB v5.0) (Subramanian et al., 2005) and mapped the human genes onto the rat orthologs using BiomaRt (Huang et al., 2014). Figure 2A compares the temporal signiﬁcance of transcription factors for EGF and NGF stimulation. EGF elicited an early, yet transient signiﬁcance of all transcription factors, while the time-resolved transcription factor signiﬁcances for NGF showed early, transient and late activity. Figure 2B depicts the diﬀerences in TF signiﬁcance between NGF and EGF. The most down-regulated TFs relative to EGF are E2F1, EBF1, SOX9 and SP1, all of which are linked to cell proliferation (Bastide et al., 2007; Hallstrom et al., 2008; Györy et al., 2012; Zhang et al., 2014). Mullenbrock et al. (2011) showed late NGF-induced genes up to 4 h were preferentially regulated by AP1 and CREB (cAMP response element-binding protein). While AP1 was among the most persistently up-regulated transcription factors, we found a transient signiﬁcance for CREB1, only, peaking at 3 and 6 h, under EGF or NGF stimulation, respectively, which indicated the importance of further TFs beyond that time window. In fact, we found the highest positive diﬀerences in the transcription factors BACH2, AP1, as well as ELF2 and ETV4. The latter two belong to the ETS transcription factor family. In particular ETV4, a member of the PEA3 subfamily of ETS, has been shown to promote neurite outgrowth (Fontanet et al., 2013; Kandemir et al., 2014). BACH2, member of the BTB-basic region leucine zipper transcription factor family, is known to down- regulate proliferation and is involved in neuronal diﬀerentiation of neoblastoma cells via p21 expression (Shim et al., 2006) and it interacts with the transcription factor MAFF (V-Maf Avian Musculoaponeurotic Fibrosarcoma Oncogene Homolog F) (Kannan et al., 2012) that is necessary for diﬀerentiation. To analyze the early cellular response upon treatment, we additionally compared the phosphorylation levels of pERK, pAKT and pJNK under NGF and EGF stimulation over time (Figure 2C). As expected, pERK increased after NGF and EGF stimulation, showing a persistent up-regulation for 8 h or pulse-like response, respectively. pJNK was continuously up- regulated under NGF relative to EGF stimulation, whereas pAKT responded similar to both stimuli, yet showed a consistently higher phosphorylation under EGF beyond 2 h. Taken together, this corroborates the roles of both pERK and pJNK as well as pAKT in PC12 cell diﬀerentiation and proliferation, respectively (Waetzig and Herdegen, 2003; Chen et al., 2012). Based on the combined transcriptome, upstream transcription factor and protein analyses we next developed a comprehensive prior knowledge interaction network (PKN) for NGF induced PC12 cell diﬀerentiation. The PKN comprises key players of known pathways involved in PC12 cell diﬀerentiation, such as ERK/PLC/PI3K/JNK/P38/uPAR/NPY and integrin signaling, as well as “linker nodes” to obtain a minimal, yet fully connected network, consisting of 63 nodes and 109 reactions (cf. Supplementary Table 4 for reference publications). The network is depicted in Supplementary Image 4 with diﬀerentially regulated genes obtained from our timeseries marked in red and points of inhibition indicated by orange. A Cytoscape readable network format is provided in Supplementary Table 2. Albeit the included PKN pathways are much more complex, our focus was on simulating a biologically plausible signaling ﬂow, including protein signaling, gene response and autocrine signaling as follows: stimulated TrkA receptor activates the downstream pathways PLC/PKC, MAPK/ERK, PI3K/AKT, and JNK/P38. Phosphorylated ERK, PI3K and P38/JNK together activate diﬀerent transcription factors such as Fosl1, Fos, Junb, Btg2, Klf2/5/6/10, Cited2, Maﬀ, and Egr1, which are important for PC12 cell diﬀerentiation according to our analysis and literature (Cao et al., 1990; Ito et al., 1990; Levkovitz and Baraban, 2002; Gil et al., 2004; Eriksson et al., 2007). Junb and Fos initiate the AP1 system, which in turn induces uPA/uPAR signaling, triggering the formation of plasmin (Avraham and Yarden, 2011). The latter is a major factor for the induction of Mmp3/Mmp10, linking degradation of the extracellular matrix (ECM) with integrin signaling. The integrins transmit extracellular signaling back via the focal adhesion kinase (FAK) (Singh et al., 2012). FAK activates again the SHC protein, which closes the autocrine signaling. Previous studies reported that uPAR expression is necessary for NGF-induced PC12 cell diﬀerentiation (Farias-Eisner et al., 2000; Mullenbrock et al., 2011). A second autocrine signaling loop in the initial PKN putatively acts via the AP1 system, which in turn activates the Neuropeptide Y (NPY/NPYY1 pathway). NPY is a sympathetic co-transmitter that acts via G protein-coupled receptors through interactions with its NPYY1 receptors (Selbie and Hill, 1998; Pons et al., 2008). NPYY1 receptor further activates Ca2+ dependent PKC /PLCgamma and subsequently convergences to ERK signaling. To optimize the highly connected PKN we used CellNetOptimizer (CNO) (Saez-Rodriguez et al., 2009). The CNO ﬁrst compresses the network, i.e., it deletes unobservable nodes and then optimizes the network topology using a genetic algorithm. We trained the PKN using gene expression of selected diﬀerentially regulated genes under NGF stimulus and inhibition of either MEK, JNK, or PI3K (Figure 3A, MEKi, JNKi and PI3Ki). The overall gene response showed a gradual decline in fold change from NGF via MEK to JNK inhibition, while inhibition of PI3K only moderately impacted the gene expression (Figure 3A). The most aﬀected genes under MEK and JNK inhibition were members of the uPAR signaling pathway, Mmp10, Mmp3, and Plaur as well as the transcription factors Fosl1 and Egr1, Plaur, Dusp6 (Dual Speciﬁcity Phosphatase 6) and lastly Npy. Topology optimization using the above perturbations led to a greatly reduced network. Optimization lumped linear pathways into one node, such as the autocrine feedback via uPA/PLAT to Itga1 and FAK or MEK to ERK transition. The reduced network revealed both MAPK/ERK and JNK as the central network hubs, distributing the upstream signals to downstream genes. It includes two positive feedback via AP1 and uPAR signaling back to FAK and MAPK as well as AP1 to Npy and PKC/PLC back to MAPK. To comply with prior knowledge, we re-expanded linear Frontiers in Genetics \| www.frontiersin.org 6 April 2016 \| Volume 7 \| Article 44 Offermann et al. Boolean Model of PC12 Cell Differentiation FIGURE 2 \| Upstream analysis of gene expression timeseries. (A) Upstream Gene Set Enrichment Analysis for transcription factors. The heatmaps depict the signiﬁcance of transcription factors putatively controlling the gene response after EGF (left) or NGF stimulation (right). All TFs are signiﬁcantly regulated (FDR corrected p-value < 0.01) after NGF treatment. TFs have been clustered by their Euclidean distance across all conditions using a complete linkage method. (B) Difference in TF p-value signiﬁcance (NGF-EGF). Rows were ordered from the most positive to the most negative difference at t = 12 and 24 h. (C) Time-resolved quantiﬁcation of pERK, pAKT and pJNK after EGF and NGF treatment. Original western blots from PC12 cells treated with 75 ng/ml EGF and 50 ng/ml NGF over time. GAPDH is shown as loading control, IS: Internal Standard. Statistical analysis of the pERK/ERK, pAKT/AKT and pJNK/JNK levels are shown on the right panel. An increased and signiﬁcant higher pERK/ERK level is shown in NGF stimulated (shown as black bars) cells compared to EGF (shown as white bars). A similar trend is visible for pJNK/JNK. A denotes a p-value < 0.05, data points obtained in duplicates and triplicates. Frontiers in Genetics \| www.frontiersin.org 7 April 2016 \| Volume 7 \| Article 44 Offermann et al. Boolean Model of PC12 Cell Differentiation FIGURE 3 \| Selective inhibition of NGF-induced PC12 differentiation. (A) Fold change values of selected response genes in PC12 cells after NGF stimulation under additional inhibition of MEK (NGF+MEKi), JNK (NGF+JNKi), or PI3K (NGF+PI3Ki). Fold change values have been calculated from biological triplicates relative to the unstimulated control per timepoint. To retain the contrast of less variable genes the maximal fold change has been restrained to +6. Genes have been clustered by their Euclidean distance across all conditions using a complete linkage method. (B) Optimized Boolean Network based on the training data in (A). Nodes in red have been measured on the transcript level. Orange nodes indicate inhibited proteins. pathways and added known down-stream target genes, such that the ﬁnal network, shown in Figure 3B, comprised 32 nodes and 52 edges. We assumed that PC12 diﬀerentiation occurs, if the majority of these genes is activated together with uPAR signaling. Due to the inherent diﬃculty of Boolean networks to incorporate negative feedback loops, we revised the network topology of the reduced network to include transient gene activity of several moderately responding genes. Klf4 and Btg2 have been previously been indicated as immediate early genes in PC12 cell diﬀerentiation (Dijkmans et al., 2009) and are involved in growth arrest (Tirone, 2001; Yoon et al., 2003), which is a necessary prerequisite for diﬀerentiation and degradation of Frontiers in Genetics \| www.frontiersin.org 8 April 2016 \| Volume 7 \| Article 44 Offermann et al. Boolean Model of PC12 Cell Differentiation mRNA, respectively. While the explicit mechanism of how Klf4 and Btg2 are regulated remains unclear, we assumed an auto- inhibition once they mediated their growth arrest eﬀect. Zfp36 belongs to the TTP (Tristetraprolin) family of proteins and has been shown to degrade AU-rich mRNAs, particularly of early response genes (Amit et al., 2007). It negatively regulates its own expression (Tiedje et al., 2012) and therefore in the model eﬀectively delays the activity of AP1 before switching itself oﬀ. Of note, another member of the TTP protein family, Zfp36l2 (zinc ﬁnger protein 36, C3H type-like 2) is constitutively expressed at long times after NGF stimulation (data not shown) and might act as another long-term negative feedback regulator and causing downregulation of Egr1, Fos, and Junb. Indeed, our experimental data revealed a reduction on gene expression of Egr1, Fos and Junb over time (Figure 3A). We simulated the optimized and re-expanded Boolean network (cf. Supplementary Table 8) using the BoolNet R/Bioconductor package (Müssel et al., 2010), performing two types of simulations. First, we tested the robustness and alternative attractors by setting NGF to “on” and randomly initializing all other network nodes. The nodes were then synchronously updated until a steady state was reached. Within n = 107 diﬀerent simulations, the same ﬁnal network state with “cell diﬀerentiation” set to “on” was always reached. Although this was not an exhaustive search given the number of possible initial network states, it still demonstrated the robustness of the network output. Next, to show the information ﬂow from the NGF receptor to the downstream nodes under diﬀerent inhibitory conditions, we initialized all nodes except NGF to “oﬀ” and performed synchronous updates until a steady state was reached (Figure 4A). Without inhibition, NGF sequentially switches on MAPK, AKT and JNK pathways as well as uPAR signaling. Klf4, Btg2, and Zfp36 become transiently active, with the latter delaying AP1 activity. Blocking MEK (NGF+MEKi) inhibited ERK and thus several downstream targets, including the uPAR feedback. As the latter is assumed indispensable for PC12 cell diﬀerentiation, (Farias-Eisner et al., 2000, 2001), the model predicted inhibition of PC12 cell diﬀerentiation. The same phenotype is found, when blocking JNK (NGF+JNKi). In comparison to NGF+MEKi it even abrogated the activity of downstream targets altogether. Inhibition of PI3K (NGF+PI3Ki) solely aﬀected PI3K and its downstream target protein AKT and target genes Maﬀand Klf10, yet cell diﬀerentiation persisted. Taken together, we developed a core network from the downstream interactome of PC12 cell pathways involved in diﬀerentiation. The model captured the dynamic pathway activation after NGF stimulation and various inhibitions. It assigned central and synergistic roles for ERK and JNK in PC12 diﬀerentiation with JNK having the largest impact on the network activity. 3.3. Model Analysis and Experimental Conﬁrmation Network simulations were conﬁrmed by live phase-contrast imaging (Figure 4B) and western blot analyses (Figure 5). We measured the convex hull (CH) to cell area (CA) ratio of PC12 cells on days 2, 4, and 6. A large convex hull due to extended neurite (marked as red arrow heads in Figure 4B) and small overall cell area is indicative of diﬀerentiation (Figure 4B, right panel). Clearly, the continuous CH/CA ratio at day 2 was largest for NGF stimulation and NGF stimulation with additional PI3K inhibition, which corresponded well with the cell diﬀerentiation set to “on” in the network simulations under these condition. One can speculate whether inhibition of the pro-proliferative PI3K pathway ampliﬁes cell diﬀerentiation, possibly relieving a negative feedback. Indeed, a Western blot of the pERK/ERK ratio depicted a trend to higher ERK phosphorylation relative to NGF stimulation under PI3K inhibition (Figure 5) and phase- contrast images of PC12 cells show more and longer neurites in comparison to cells treated only with NGF or in combination to MEKi and JNKi (Figure 4B, NGF+PI3Ki). Interestingly, image analysis suggested not a stop, but rather a delay of cell diﬀerentiation under MEK inhibition. In detail, PC12 cells show no neurites under MEKi after 2 days of combined NGF treatment compared to NGF alone or NGF-PI3Ki. After 4 and 6 days of NGF+MEKi treatment, less cells have neurites in comparison to cells that were only treated with NGF (Figure 4B, NGF+MEKi). In line with literature, pERK levels were reduced, yet pJNK levels were likewise increased, indicating a redirection of protein activity under MEK inhibition (Figure 5, right panel). Likewise, the gene expression showed a reduced, but not completely abolished fold change for Mmp10 (Figure 3A) and also an up- regulation of Dusp6. Although the discrete Boolean model could not simulate gradual responses, MEK inhibition still resulted in the activation of several downstream target genes necessary for PC12 cell diﬀerentiation, while none of these were active under JNK inhibition. In summary, modeling and simulation suggested that PC12 diﬀerentiation involved the activity of both JNK/JUN, MAPK/ERK and PI3K/AKT signaling pathways. The establishment of a positive, autocrine feedback loop was indispensable to active late and persistent gene expression. 4. DISCUSSION PC12 cells are a well established model to study the cellular decisions toward proliferation or diﬀerentiation. Nevertheless, there is still a lack of understanding on how protein signaling and gene regulation interact on diﬀerent time scales to decide on a long-term, sustained phenotype. Given the fact that PC12 cell cycle and diﬀerentiation last up to 4 and 6 days, respectively (Greene and Tischler, 1976; Luo et al., 1999; Adamski et al., 2007), late events occurring beyond the ﬁrst hours are most likely to be important for sustaining the cellular decision. However, few studies that have compared the long-term eﬀect of EGF and NGF in PC12 cells. They focused either on NGF alone (Dijkmans et al., 2008, 2009), on individual (Angelastro et al., 2000; Marek et al., 2004; Lee et al., 2005; Chung et al., 2010), or early time-points (Mullenbrock et al., 2011). Previous studies have identiﬁed expression of immediate early genes (IEG), such as Egr1, Junb, and Fos together with delayed early genes (DEG), like Dusp6, Mmp3/10, Fosl1, and Atf3 as necessary for PC12 cell diﬀerentiation (Vician et al., Frontiers in Genetics \| www.frontiersin.org 9 April 2016 \| Volume 7 \| Article 44 Offermann et al. Boolean Model of PC12 Cell Differentiation FIGURE 4 \| Network simulation of time sequential pathway activation and experimental validation. (A) The heatmaps depict the path to attractor upon NGF stimulation. Columns correspond to synchronous update steps of the Boolean network. Time progresses from left to right until a steady state is reached. Initially all nodes, except NGF, are set to zero. Colored boxes correspond to activated nodes with the color denoting individual pathways/node categories. Cells are predicted to differentiate, if the node “Cell differentiation” is active, as in the case for NGF, or NGF+PI3Ki treatment. (B) Left: phase contrast images for days 2, 4, and 6 are shown for the 4 different conditions: NGF (control), NGF+MEKi, NGF+PI3Ki and NGF+JNKi. Red arrows depict sites of neurite outgrowth in differentiating PC12 cells. Bar: 100 µm. Right: statistical analysis of PC12 cell differentiation from phase contrast imaging for the different conditions are shown as convex hull (CH) to cell area (CA) ratio. Bars show Mean ± SEM, n = 2, (t-test p-value < 0.05). 1997; Levkovitz et al., 2001; Dijkmans et al., 2008; Mullenbrock et al., 2011). However, we found all these genes strongly regulated by both EGF and NGF stimulation (Supplementary Table 5), however, showing diﬀerences in their expression kinetics (Figure 1). Akin to diﬀerences in the pERK dynamics, these results suggest that cellular decisions toward diﬀerentiation or proliferation are driven by the diﬀerences in the gene expression kinetics. It has been suggested before that distinct cellular stimuli activate similar sets of response genes, whose expression dynamics, rather than their composition, determine cellular decisions (Murphy and Blenis, 2006; Amit et al., 2007; Yosef and Regev, 2011). Single expression bursts are likely to stimulate proliferation, while complex, wave-like expression patterns induce diﬀerentiation (Bar-Joseph et al., 2012). Accordingly, EGF elicited a pulse-like gene response, while NGF induced a complex, wave-like gene response (Figure 1B). After EGF stimulation the expression of IEGs, Egr1, Fos, and Junb was quickly attenuated through the rapid up-regulation of their negative regulators, namely Fosl1, Atf3, Maﬀ, Klf2, and Zfp36l2 and contributing to Frontiers in Genetics \| www.frontiersin.org 10 April 2016 \| Volume 7 \| Article 44 Offermann et al. Boolean Model of PC12 Cell Differentiation FIGURE 5 \| Quantiﬁcation of pERK, pAKT and pJNK levels under NGF and individual inhibitor treatments. Determination of pERK/ERK, pAKT/AKT and pJNK/JNK under NGF, NGF+MEKi, NGF+JNKi and NGF+PI3Ki treatment. Left panel: pERK/ERK levels decrease over time under NGF plus MEK and JNK inhibition. In contrast, PI3K inhibition shows a similar increase and sustained pERK/ERK levels over time compared to NGF treated PC12 cells alone. Interestingly, pAKT/AKT is increased under NGF+MEKi treatment, which is particularly signiﬁcant in the early timepoints (30 min and 1 h) compared to NGF alone or the other two inhibitors. The latter two show decreased pAKT/AKT levels over time (middle panel). A denotes a p-value < 0.05, data points obtained in duplicates and triplicates. a pulse-like gene expression. Furthermore, Fosl1 counteracts Fos and AP1 (Hoﬀmann et al., 2005) and Atf3 has been shown to modulate Egr1 activity (Giraldo et al., 2012), while Maﬀand Klf2 negatively regulate serum response and STAT-responsive promoter elements (Amit et al., 2007). The same genes respond after NGF stimulation, however with a delayed response and might be one of the reasons for the stronger and longer gene and pERK response under NGF stimulation (Murphy et al., 2002, 2004; Murphy and Blenis, 2006; Saito et al., 2013). A recent study by Mullenbrock et al. (2011) compared the transcriptome response of PC12 cells to EGF and NGF stimulation up to 4 h. Using chromatin immunoprecipitation they found a preferential regulation of late genes through AP1 and CREB TFs after NGF stimulation, which is in line with our ﬁndings (Figure 2A). However, we predicted a constitutive signiﬁcance for AP1 up to 24 h, while CREB1 displayed a transient importance, being most abundant at 6 h after stimulation. Furthermore, we found a switch in the composition of transcriptional master regulators between 4 and 12 h. During this time, late TFs, such as BACH2, ETS1 and ELF2 become active. Supplementary Image 5 depicts a Volcano plot of their target genes. Beyond the early gene targets, such as Fosl1 or Junb, the late TFs additionally target related to cytoskeleton, morphogenesis and apoptosis, such as Tumor Necrosis Factor Receptor Superfamily, Member 12A (Tnfrsf12a), Doublecortin- Like Kinase 1 (Dclk1), Nerve Growth Factor Inducible Vgf, Coronin, Actin Binding Protein, 1A (Coro1a, Growth Arrest And DNA-Damage-Inducible, Alpha (Gadd45a) and Npy. Of note, we found Rasa2 among the targets, which has recently been identiﬁed as a driver for diﬀerentiation through a negative feedback between PI3K and RAS (Chen et al., 2012). A recent study by Aoki et al. (2013) investigated the down- stream gene response upon light-induced intermittent and continuous ERK activation in normal rat kidney epithelial cells. Similar to the TF activity after EGF and NGF stimulation in PC12 cells, intermittent pERK activity caused up-regulation of Fos, Egfr, Ier2, and Fgf21, which were putatively controlled through serum response factor (SRF) and CREB binding sites, while sustained pERK activity caused gene regulation controlled by AP1 and BACH1. One can speculate that it is more the temporal dynamics of pERK and less the upstream ligands, such as EGF or NGF, that eventually encode the transcriptional program deciding on the cell fate. To elucidate the various pathways and downstream target genes under NGF stimulation we constructed a Boolean model based on our transcriptome and additional literature data. A prior knowledge network revealed a highly interconnected pathway map transmitting NGF-induced signals. Training the network via inhibition of MEK, JNK or PI3K reduced the number of edges and nodes by about 80% and revealed the MAPK/JNK pathway as second signaling hub next to MAPK/ERK. Moreover, blocking the JNK pathway had a more drastic eﬀect on cell diﬀerentiation than blocking MAPK/ERK via inhibition of MEK through UO126. Indeed, studies on the eﬀect of MEK inhibition for PC12 cell diﬀerentiation are inconclusive. Early studies report how MEK inhibition completely averted PC12 cell diﬀerentiation (Pang et al., 1995; Klesse et al., 1999), while recent experiments suggest a decrease, rather than full inhibition of diﬀerentiation (Levkovitz et al., 2001; Chung et al., 2014). Our results were in line with the latter. Despite a signiﬁcant reduction in pERK (Figure 5), our cell morphology measurements detected merely a decrease in the formation of neurites, rather than full inhibition of diﬀerentiation. The reason for this discrepancy could lie in the time scale of observation. MEK inhibition delayed diﬀerentiation and it took 6 days to eventually overcome this delay (Figure 4B). This conﬁrmed the modeling results, which established JNK as key regulator that is closely interlinked with MAPK/ERK signaling. In concert with pERK, also pJNK becomes constitutively active upon NGF stimulation (Figure 2C). Moreover, blocking pERK through MEK even increased pJNK (and pAKT) levels, while pERK decreased after JNK inhibition, verifying a crosstalk between JNK and ERK pathways. Previous reports suggested such a crosstalk due to dual-phosphatase interaction (Fey et al., 2012), while other studies proposed that JNK phosphorylates RAF (Adler et al., 2005; Chen et al., 2012) and thereby contributing to MAPK/ERK activity. However, the mechanistic details governing Frontiers in Genetics \| www.frontiersin.org 11 April 2016 \| Volume 7 \| Article 44 Offermann et al. Boolean Model of PC12 Cell Differentiation the crosstalk remain unclear so far. In conclusion, while previous studies assigned parallel, non-redundant roles to MAPK/ERK and MAPK/JNK (Waetzig and Herdegen, 2003), our results show that JNK signaling might be even the main driver for PC12 cell diﬀerentiation. Next to the negative feedback loops through Klf4, Zfp36, and Btg2, arresting cell cycle and attenuating mRNA abundance, we included also two positive feedback loops via uPAR and integrin signaling as well as through Neuropeptide Y and PKC/PLC signaling. Positive feedback loops are a common regulatory pattern in molecular biology to induce bistability switch-like behavior, particularly in cell fate decisions and diﬀerentiation (Xiong and Ferrell, 2003; Mitrophanov and Groisman, 2008; Kueh et al., 2013). In fact, multiple feedbacks deciding between PC12 cell diﬀerentiation and proliferation, have been studied on the level of MAPK signaling (Santos et al., 2007; von Kriegsheim et al., 2009). Recently, Ryu et al. (2015) used a FRET construct to quantify pERK dynamics on a single cell level after growth factor stimulation. While the cell population average still resembled the hitherto described transient and sustained pERK activity after respective EGF and NGF stimulation, the authors found a highly heterogenous response on the single cell level. Pulsed stimulation, however, not only synchronized MAPK activity between cells, but also triggered PC12 diﬀerentiation upon EGF stimulation, if the integrated pERK signal was large enough. The authors concluded that thus not only MAPK signaling, but also further pathways are responsible for the cell fate decision. Sparta et al. (2015) used a similar experimental approach to single cell response of human MCF10A-5e cells to show that EGFR activity induced a frequency modulation response, while TrkA activity caused amplitude modulation of pERK levels. The authors explained these ﬁnding by additional receptor- dependent signaling networks beyond the core Ras-Raf-MEK- ERK pathway. Extending on this idea, our data and model suggest autocrine signaling as further feedbacks that sustain the expression of diﬀerentiation inducing TFs. Indeed, uPAR and also Npy activity were strongly correlated with diﬀerentiation (Figure 3A) and neither Npy nor uPAR signaling were activated upon EGF stimulation (data not shown). In line with this ﬁnding previous studies reported that uPAR expression is necessary for NGF-induced PC12 cell diﬀerentiation (Farias-Eisner et al., 2000; Mullenbrock et al., 2011). SERPINE1 regulating the plasminogen activator-plasmin proteolysis was shown to promote neurite outgrowth and phosphorylation of the TrkA receptor and ERK (Soeda et al., 2006, 2008). In our model we included the necessity of uPAR signaling though the activation of late genes, such as Klf5, yet the causal relationship between uPAR signaling and late gene expression remains unclear. However, uPAR signaling could constitute the additional positive feedbacks beyond MAPK signaling that were predicted by Ryu et al. (2015), which would be interesting to test on the single cell level. Reporters for uPAR and/or JNK activity should likewise show a heterogenous activity and correlate with the per-cell diﬀerentiation status, which could potentially be modeled within a stochastic diﬀerential equation framework. In conclusion, our approach has identiﬁed the short and long-term transcriptional activity in PC12 cells after NGF and EGF stimulation. Modeling the pathway orchestration using a Boolean model we identiﬁed feedback regulations beyond MAPK signaling that attenuate and sustain the cellular decision toward diﬀerentiation. Extending on previous studies we established JNK as a key player in PC12 cell diﬀerentiation that might have equal, if not even more importance than ERK during this process. Over time AP1 was accompanied by a variety of transcription factors serving signal attenuation, signal maintenance and morphological change of the cell, which demonstrates that the decision toward diﬀerentiation is a time sequential process over at least 12 h. AUTHOR CONTRIBUTIONS MF, SKn, MK, SK, and BO performed the experiments. MF, SKn, AS, and BO performed the data analysis. HB And MB conceived the project, performed the data analysis and wrote the manuscript with BO. All authors approved the ﬁnal manuscript. ACKNOWLEDGMENTS This work was was supported by the Deutsche Forschungsgemeinschaft grant InKoMBio: SPP 1395. The authors greatly acknowledge the Genomics and Proteomics Core Facility, German Cancer Research Center/DKFZ, Heidelberg, Germany for their microarray service. SUPPLEMENTARY MATERIAL The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fgene. 2016.00044 REFERENCES Adamski, D., Mayol, J.-F., Platet, N., Berger, F., Hérodin, F., and Wion, D. (2007). Eﬀects of Hoechst 33342 on C2c12 and PC12 cell diﬀerentiation. FEBS Lett. 581, 3076–3080. doi: 10.1016/j.febslet.2007. 05.073 Adler, V., Qu, Y., Smith, S. J., Izotova, L., Pestka, S., Kung, H. F., et al. (2005). Functional interactions of Raf and MEK with Jun-N-terminal kinase (JNK) result in a positive feedback loop on the oncogenic Ras signaling pathway. 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The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Frontiers in Genetics \| www.frontiersin.org 15 April 2016 \| Volume 7 \| Article 44	27148350	ERK = ( MEK ) Dusp6 = ( ETS1 ) ECM = ( Mmp3/10 ) BTG2 = ( AKT ) OR ( JNK ) Fosl1 = ( JNK ) OR ( AKT ) OR ( ERK ) MKK7 = ( MEKK1 ) Mmp3/10 = ( Plasmin ) Plasmin = ( uPA/PLAT ) PI3K = ( TrkA ) Npy = ( AP1 ) RAS = ( SOS ) MSK1/2 = ( P38 ) OR ( ERK ) KLF2 = ( AKT ) OR ( JNK ) OR ( ERK ) AKT = ( PI3K ) uPA/PLAT = ( uPAR ) FOS = ( AKT ) OR ( JNK ) OR ( ERK ) JNK = ( MKK7 ) OR ( MEKK4 ) GRB2 = ( SHC ) SHC = ( TrkA ) OR ( FAK ) MKK6 = ( MEKK4 ) DAG = ( PLC ) FRS2 = ( TrkA ) JUNB = ( JNK ) OR ( AKT ) OR ( ERK ) ETS1 = ( JNK ) OR ( ERK ) Egr1 = ( JNK ) OR ( AKT ) OR ( ERK ) RAC1 = ( RAS ) ATF2 = ( P38 ) OR ( JNK ) OR ( ERK ) ZFP36 = ( JNK ) OR ( ERK ) PKC = ( Ca2+ ) OR ( DAG ) P53 = ( AKT ) OR ( JNK ) OR ( ERK ) MEKK4 = ( RAC1 ) KLF6 = ( JNK ) OR ( P53 ) RAF = ( PKC ) OR ( RAS ) KLF4 = ( JNK ) OR ( AKT ) OR ( ERK ) Itga1 = ( ECM ) Mapk3k = ( MEKK4 ) G_i_o = ( NPYY1 ) ARC = ( CREB ) OR ( Egr1 ) SOS = ( GRB2 ) CITED2 = ( CREB ) OR ( ERK ) OR ( P53 ) AP1 = ( JUNB ) OR ( Fosl1 ) OR ( FOS ) OR ( JUND ) KLF10 = ( AKT ) OR ( JNK ) OR ( ERK ) MEKK1 = ( RAC1 ) PLC = ( G_i_o ) OR ( TrkA ) MYC = ( AKT ) OR ( JNK ) OR ( ERK ) SRF = ( RSK ) JUND = ( JNK ) OR ( ERK ) NPYY1 = ( Npy ) P38 = ( Mapk3k ) OR ( MKK6 ) FAK = ( Itga1 ) OR ( RAP1 ) KLF5 = ( AKT ) OR ( ERK ) OR ( P53 ) uPAR = ( AP1 ) Stat3 = ( JNK ) OR ( ERK ) Maff = ( ATF2 ) OR ( JNK ) OR ( ERK ) Ca2+ = ( PLC ) TrkA = ( NGF ) CREB = ( AKT ) OR ( MSK1/2 ) OR ( RSK ) RAP1 = ( C3G ) C3G = ( FRS2 ) MEK = ( RAF ) OR ( MEKK1 ) RSK = ( ERK )
RESEARCH ARTICLE Open Access Analysis of a dynamic model of guard cell signaling reveals the stability of signal propagation Xiao Gan and Réka Albert* Abstract Background: Analyzing the long-term behaviors (attractors) of dynamic models of biological systems can provide valuable insight into biological phenotypes and their stability. In this paper we identify the allowed long-term behaviors of a multi-level, 70-node dynamic model of the stomatal opening process in plants. Results: We start by reducing the model’s huge state space. We first reduce unregulated nodes and simple mediator nodes, then simplify the regulatory functions of selected nodes while keeping the model consistent with experimental observations. We perform attractor analysis on the resulting 32-node reduced model by two methods: 1. converting it into a Boolean model, then applying two attractor-finding algorithms; 2. theoretical analysis of the regulatory functions. We further demonstrate the robustness of signal propagation by showing that a large percentage of single-node knockouts does not affect the stomatal opening level. Conclusions: Combining both methods with analysis of perturbation scenarios, we conclude that all nodes except two in the reduced model have a single attractor; and only two nodes can admit oscillations. The multistability or oscillations of these four nodes do not affect the stomatal opening level in any situation. This conclusion applies to the original model as well in all the biologically meaningful cases. In addition, the stomatal opening level is resilient against single- node knockouts. Thus, we conclude that the complex structure of this signal transduction network provides multiple information propagation pathways while not allowing extensive multistability or oscillations, resulting in robust signal propagation. Our innovative combination of methods offers a promising way to analyze multi-level models. Keywords: Network model, Discrete dynamic model, Biological network, Signal transduction, Plant signaling, Attractor, Stomatal opening, Network reduction, Boolean conversion, Stable motif Background Modeling offers a comprehensive way to understand bio- logical processes by integrating the components involved in them and the interactions between components. Models can recapitulate and explain the emergent out- come(s) of the process [1, 2]. Representing cellular pro- cesses that involve many proteins and small molecules by a signal transduction network can reveal indirect rela- tionships between components and provide new insight [3–5]. Such network usually consists of nodes represent- ing biological entities, and edges representing interac- tions. Once a network has been constructed, dynamic modeling, where each node in the network is associated with a variable representing its abundance or activity, can further describe the behavior of the network. Dy- namic models can have continuous variables whose change is described by differential equations [6], discrete variables described by discrete (logical) regulatory func- tions [7, 8], or a combination of continuous and discrete variables [9]. The major advantage of discrete dynamic and continuous-discrete hybrid models is that they use many fewer parameters than continuous models and thus need less parameter estimation [10–12]. Modeling allows one to analyze the biological system represented by the network in silico, when performing the relevant experiment is infeasible. It also helps identify general principles of biological systems [13, 14]. * Correspondence: rza1@psu.edu Department of Physics, The Pennsylvania State University, University Park, PA, USA © 2016 The Author(s). Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Gan and Albert BMC Systems Biology (2016) 10:78 DOI 10.1186/s12918-016-0327-7 The biological process of stomatal opening in plants is a good example of a complex system wherein modeling leads to significant gain in understanding [15, 16]. Sto- mata are pores on leaf surfaces that allow the plant to exchange carbon dioxide (CO2) and oxygen with the at- mosphere. Stomata are formed by two guard cells that can change shape: swelling of guard cells leads to stoma- tal opening; their shrinking leads to stomatal closure. The shape of each guard cell is directly controlled by water flow through the membrane, which is in turn con- trolled by ion flow. Different signals can affect the guard cell, changing its ion concentration in direct and indirect ways, resulting in stomatal opening or closure [17–19]. These signals include light of different wavelengths, CO2 concentration in the air, and plant hormones like absci- sic acid (ABA). The regulation of stomatal opening is es- sential to plants, as it controls vital activities like the uptake of CO2 for photosynthesis, and the unavoidable water loss through evaporation [20]. Through extensive experimentation over several decades, more than 70 proteins and small molecules have been identified to participate in this process. Sun et al. [15] recently constructed a signal transduc- tion network based on conclusions from more than 85 articles in the literature, describing how more than 70 nodes (proteins, small molecules, ions) interact with each other in the stomatal opening process. The net- work, reproduced as Fig. 1 [15], includes four source nodes that correspond to the signals red light, blue light, CO2, and ABA. The more than 150 edges are directed and signed, with arrowheads indicating activation and terminal black circles indicating inhibition. Translating this network into a dynamic model, Sun et al. characterized each node with a discrete variable de- scribing its activity and with a discrete (logical) regula- tory function describing its regulation. Twenty-one out of the 70 nodes in the model are multi-level, the rest are Boolean (binary). The levels reflect relative and qualita- tive information: a level of 2 is a higher level than 1, but should not be interpreted as twice as high. A few Fig. 1 The signal transduction network responsible for stomatal opening, as reconstructed by Sun et al. [15]. The color of a node marks which signal regulates this node. Red nodes are regulated solely by red light. Blue nodes are regulated solely by blue light. Yellow nodes are regulated solely by ABA. Grey nodes are regulated by CO2. Purple nodes are regulated by both blue and red light. Green nodes are regulated by blue (and potentially, red) light and ABA. White nodes are source nodes not regulated by any of the four signals. To improve visualization, certain pairs of edges with the same starting or end nodes overlap. Nodes with multiple levels in the dynamic model are represented by red shadows; the others are Boolean. The full names of the network components denoted by abbreviated node names are given in Table 1. This figure and part of its caption is reproduced from Sun Z, Jin X, Albert R, Assmann SM (2014) Multi-level Modeling of Light-Induced Stomatal Opening Offers New Insights into Its Regulation by Drought. PLoS Comput Biol 10(11): e1003930. doi:10.1371/journal.pcbi.1003930 Gan and Albert BMC Systems Biology (2016) 10:78 Page 2 of 14 discrete values are not integers; e.g. stomatal opening is a weighted sum with non-integer weights. The dynamic model has ~1031 states. The logical regulatory functions, describing each node’s future state based on the states of the node’s regulators, use a combination of Boolean logic operators (And, Or, Not), algebraic operations, and input-output tables. For example, the regulatory function of PRSL1 is: PRSL1 ¼ phot1complexOr phot2: Here for simplicity the node states are denoted by the node names; the asterisk in “PRSL1” indicates that this will be the next state of the PRSL1. The “Or” Boolean operator expresses that either of the blue light receptors, i.e. the phot1 complex or phot2, can independently acti- vate PRSL1. The Sun et al. model starts from an initial condition representative of closed stomata. Then a combination of the four input signals is applied. Red light, blue light, and ABA are represented as binary variables, and exter- nal CO2 is represented with three states: 0 (CO2 free air), 1 (ambient CO2) and 2 (high CO2). The system’s re- sponse is simulated through repetitive re-evaluation of each node’s state until a stable value of stomatal opening is observed. The model successfully captures stomatal opening in response to combinations of the signals. It also successfully reproduces stomatal opening under most of the experimentally studied perturbation scenar- ios (i.e. genetic knockouts or external supply of compo- nents). In total, the model is consistent with 63 out of 66 experimental observations collected by Sun et al. [15]. The model predicts the outcome of a large number of scenarios that have not been explored experimentally so far. It also revealed a gap of knowledge regarding the cross-talk of red light and ABA signaling, and filled it with a newly predicted interaction. Although the Sun et al. model recapitulates existing knowledge and offers new predictions, the model’s full dynamic repertoire could not be characterized due to its large state space. Instead, Sun et al. focused on tracking the output node, stomatal opening, and a few selected internal nodes, in time. In this paper we apply multiple methods to analyze the model and aim to fully map all its potential long-term behaviors, or in other words, attractors. Methods Attractors of a dynamical system An attractor is a set of states from which only states in the same set can be reached. Attractors that consist of a single state are called stable steady states or fixed points; attractors that contain multiple states are called complex attractors or oscillations [10]. In biological networks, attractors often have significant biological meaning. In a cell signaling network, attractors correspond to cell types, cell fates or behaviors [21]. For example, one at- tractor can represent a healthy differentiated cell, while another attractor can represent an abnormally motile cancer cell [22]. Update scheme of a discrete time model In the Sun et al. model, as in most discrete dynamic models, time is an implicit variable. As there is very little information about the kinetics of the nodes in the sto- matal opening network, the model incorporates an elem- ent of stochasticity in timing. The timing does not affect a system’s fixed point attractors, but it can change the complex attractors and the possibility of reaching a given attractor from a given initial state [10]. In the Sun et al. model, a random–order asynchronous update is used. Specifically, at each time step, a random order of nodes (excluding the four input nodes and the output node stomatal opening) is generated, and each node’s state is reevaluated in this order; stomatal opening is al- ways updated last. In the next time step a different order is generated randomly. In this paper, we use a different type of stochastic update, called general asynchronous update, wherein a randomly selected node is updated at each time step. This is required by the network reduc- tion method we use. Although this theoretically could cause a difference in complex attractors, we will show that in this specific model the two update methods yield the same attractors. Network reduction To reduce the Sun et al. model’s state space, we apply a network reduction method developed by Saadatpour et al. [23] that is proven to preserve the attractors of a Boolean model. Two types of nodes can be reduced (eliminated or merged): source nodes with no incoming edges, and simple mediator nodes that have one incom- ing and/or one outgoing edge. In the reduction, the source node’s state is directly plugged into the regulatory function of all of its direct successor nodes; then the source node is eliminated. For a simple mediator node with one predecessor (regulator) and one successor (tar- get), its regulator is connected to its target and the me- diator node is merged into the regulator. If there is one regulator and several targets of the mediator node, but no direct edges between the regulator and any of the tar- gets, the mediator node is merged into the regulator. Conversely, if there are several regulators and one target of the mediator node, but no direct edges among any of the regulators and the target, the mediator node is merged into its target. Although this method is not proven in the multi-level case, we conjecture that attrac- tors are also conserved for a multi-level model, and will Gan and Albert BMC Systems Biology (2016) 10:78 Page 3 of 14 show from the results that in the Sun et al. model this reduction method preserved all attractors. Elimination of redundant edges During the process of creating a discrete dynamic model from biological data, when an influence is weaker than other influences, the modeler may choose to omit this influence or, alternatively, include it a redundant way. The latter choice was made by Sun et al. in four cases, leading to four regulatory functions that contain an in- put that does not affect the outcome of the regulatory function. One of these is ROS ¼ NADPH And AtrbohD=F Or NADPH And AtrbohD=F And CDPK Or Not Atnoa1 The italicized words “And”, “Or” and “Not” are Bool- ean logic operators; the non-italicized words represent node names. In this regulatory function every node is Boolean (binary). The first clause “NADPH And Atr- bohD/F” and the second “NADPH And AtrbohD/F And CDPK” are connected with an “Or” rule, with the result that the node “CDPK” does not have any influence on the outcome. Therefore, we can prune the edge from CDPK to ROS without changing the model’s dynamics. We similarly prune three additional redundant edges. Converting a multi-level model to Boolean There are several possibilities to convert a multi-level model to Boolean [24]. The standard method used in the case of logical models of regulatory networks is the Van Ham mapping [25, 26]. It preserves the dynamics of the original model if the variables in the original model can be represented by integers and if the original model only allows state transitions in which one node changes its state by one level [26]. The Sun et al. model does not satisfy these criteria. However there still is a conclusion that we can use: All types of conversions maintain the fixed points and the reachability of states (i.e. if there is a sequence of state transitions from state A to state B before conversion, there must be a sequence of state transitions from the corresponding state A’ to state B’ after the conversion) [26]. So the worst distortion of attractors due to the conversion is the merging of two complex attractors into one. In this light we choose to use an economic mapping of each multi-level node into as many Boolean nodes as necessary for the binary rep- resentation of the corresponding integer. We will show that in this specific model, the conversion did not change the attractors. Abbreviations Table 1 summarizes the full names of the network com- ponents denoted by abbreviated node names in Fig. 1. The same abbreviations are used in the original Sun et al. model and the reduced model developed in this paper. Results Network reduction The Sun et al. model has a huge state space of ~1031 states, making its analysis difficult. To obtain a smaller state space, we reduce the size of the network by applying a network reduction technique developed by Saadatpour et al. [23] that is proven to preserve the attractors of Bool- ean models (see Methods). All source nodes other than the four signals (blue light, red light, CO2, and abscisic acid) and all simple mediator nodes are identified and re- duced. This process is done iteratively until it cannot be done any more. A total of 7 source nodes (14-3-3 protein- phot1, PIP2C, AtNOA1, Nitrate, PP1cn, mitochondria, and CHL1), and 19 simple mediator nodes (phot1, phot2, NIA1, H+-ATPase, LPL, ATP, acid. of apoplast, [NO3 −]v, [Cl−]v, NADPH, [malate2−]v, PA, ABA receptors, OST1, PRSL1, PIP2PM, AtrbohD/F, Nitrite, and phot1complex) are eliminated. Several of the simple mediator nodes form lin- ear paths (e.g. phot1, OST1) thus their iterative reduction shortens the linear paths in the network. In addition, 16 of the 19 reduced mediators have a regulatory function of the form “B = A”. It is intuitive that reduction of this node type preserves the attractors. We do not eliminate the four signal nodes because we want to simultaneously explore all the combinations of input signals. We also choose to not reduce the five nodes (Kin, Kout, Kc, Ca2+-ATPase, mesophyll cell photo- synthesis) whose merging with their sole regulator would result in a self-loop (self-regulation), because such self- loops may be difficult to interpret. Two additional nodes with significant biological meaning to the network (sucrose, stomatal opening), are not reduced either. Another form of network reduction is the elimination of redundant edges (see Methods). After removal of re- dundant edges, the node CDPK becomes a sink node, thus it can also be eliminated. The reduction of the above-described nodes and redundant edges simplifies the network from 70 nodes to 42 nodes, with an esti- mated state space of ~1022 states. Simplification of regulatory functions In order to further reduce the state space from ~1022 to a manageable size, we grouped state values so that nodes are represented with fewer states. This grouping was guided by the 66 experimental observations summarized in Sun et al.; we aimed to maintain the reduced model’s results consistent with these experimental observations. For example, in the Sun et al. model [15] the regula- tory function of Stomatal Opening is a weighted sum of different ions and sucrose: Gan and Albert BMC Systems Biology (2016) 10:78 Page 4 of 14 Stomatal opening ¼ ½Cl−vcontribution þ ½NO3 −vcontribution þ ½Kþv þ ½malate2−vcontribution þ sucrose−RIC7=6 The weights of the anion contributions to the osmotic potential were chosen based on the literature. Also, the anion contributions must not exceed a pro- portion of [K+]v due to charge balance. The anion contributions are [malate2−]v contribution ≤0.425 × [K+]v; [NO3 −]v contribution ≤0.10 × [K+]v; [Cl−]v contribution ≤ 0.05 × [K+]v. The primary contributions come from [K+]v and sucrose. We grouped the stomatal opening values into 6 groups with different [K+]v and sucrose values (see Table 2 and Additional file 1). The first two columns indicate the [K+]v and su- crose levels. The third column is the possible values of stomatal opening in the Sun et al. model for the given [K+]v and sucrose levels. Note that here we only show [K+]v, sucrose and stomatal opening value com- binations observed in the simulations of the 66 Table 1 Full names of the network components denoted by abbreviated node names in Fig. 1 Abbreviation Full name Abbreviation Full name 14-3-3 proteinH- ATPase 14-3-3 protein that binds to the H+-ATPase 14-3-3 proteinphot1 14-3-3 protein that binds to phototropin 1 ABA abscisic acid ABI1 2C-type protein phosphatase acid. of apoplast the acidification of the apoplast AnionCh anion efflux channels at the plasma membrane AtABCB14 ABC transporter gene AtABCB14 Atnoa1 protein nitric oxide-associated 1 AtrbohD/F NADPH oxidase D/F AtSTP1 H-monosaccharide symporter gene AtSTP1 Ca2+-ATPase Ca2+-ATPases and Ca2+/H+ antiporters responsible for Ca2+ efflux from the cytosol CaIC inward Ca2+ permeable channels CaR Ca2+ release from intracellular stores carbon fixation light-independent reactions of photosynthesis CDPK Ca2+-dependent protein kinases CHL1 dual-affinity nitrate transporter gene AtNRT1.1 Ci intercellular CO2 concentration FFA free fatty acids H+-ATPase the phosphorylated H+-ATPase at the plasma membrane prior to the binding of the H+-ATPase 14-3-3 protein H +-ATPasecomplex 14-3-3 protein bound H+-ATPase KEV K+ efflux from the vacuole to the cytosol Kin K+ inward channels at the plasma membrane Kout K+ outward channels at plasma membrane LPL lysophospholipids NADPH reduced form of nicotinamide adenine dinucleotide phosphate NIA1 nitrate reductase NO nitric oxide OST1 protein kinase open stomata 1 PA phosphatidic acid PEPC phosphoenolpyruvate carboxylase phot1 phototropin 1 phot1complex 14-3-3 protein bound phototropin 1 phot2 phototropin 2 Photophos- phorylation light-dependent reactions of photosynthesis PIP2C phosphatidylinositol 4,5-bisphosphate located in the cytosol PIP2PM phosphatidylinositol 4,5-bisphosphate located at the plasma membrane PLA2β phospholipase A2β PLC phospholipase C PLD phospholipase D PMV electric potential difference across the plasma membrane PP1cn the catalytic subunit of type 1 phosphatase located in the nucleus PP1cc the catalytic subunit of type 1 phosphatase located in the cytosol protein kinase a serine/threonine protein kinase that directly phosphorylates the plasma membrane H-ATPase PRSL1 type 1 protein phosphatase regulatory subunit 2-like protein1 RIC7 ROP-interactive CRIB motif-containing protein 7 ROP2 small GTPase ROP2 ROS reactive oxygen species [Ca2+]c cytosolic Ca2+ concentration [Cl−]c/v cytosolic/vacuolar Cl−concentration [K+]c/v cytosolic/vacuolar K+ concentration [malate2−]a/c/v apoplastic/ cytosolic/vacuolar malate2−concentration [NO3 −]a/c/v apoplastic/cytosolic/vacuolar nitrate concentration Gan and Albert BMC Systems Biology (2016) 10:78 Page 5 of 14 experimentally studied scenarios reported by Sun et al. [15]. More stomatal opening values are possible when considering node perturbations. The 4th col- umn shows the simplified stomatal opening level after grouping. The update function for the simplified sto- matal opening level covers all possible values of [K+]v and sucrose (see Additional file 1). Similarly to the original model, the simplified states represent qualitative, relative categories. For example, a stomatal opening level of 2 is not twice as high as level 1. We choose the simplified stomatal opening values so that there is no state “4”, to better reflect an experimen- tally observed synergistic effect between blue and red light [18, 19, 27]. Simulation results with the simplified regulatory function are that under monochromatic red light stomatal opening =1; under monochromatic blue light stomatal opening =3; under dual beam the stomatal opening =5, which is larger than the sum “1 + 3”. This qualitatively reproduces the experimental observation that under dual beam illumination stomata open to a size much larger than the sum of opening under mono- chromatic blue or red light. We find by simulation of the reduced model, using the same initial condition as the Sun et al. model, that the simplification of the stomatal opening regula- tory function results in only 3 additional cases of in- consistency with experimental observations out of a total of 66 experimentally studied scenarios. Add- itional file 2 lists all experimental observations and com- pares them to the relevant simulation results. Ignoring the contribution of malate2−, NO3 −, and RIC7 to stomatal open- ing each causes one additional discrepancy; ignoring Cl− does not cause any additional discrepancy. Ignoring these nodes trades a decrease in accuracy for a significant in- crease in simplicity. The simplification of the stomatal opening regulatory function eliminates the effect of vacuolar anions and of RIC7 on stomatal opening. As a result we can further simplify the Sun et al. model by eliminating 10 nodes in total, [malate2−]a, [malate2−]c, starch, [Cl−]c, [NO3 −]c, [NO3 −]a, ROP2, RIC7, ABC, and PEPC. The only edge from these nodes to other nodes is [malate2−]a → AnionCh. In section 3 of Additional file 3 we show that eliminating this edge does not change the system’s long- term behavior, i.e. attractors. Also, the regulatory func- tion describing the cytosolic K+ concentration, [K+]c, can be simplified without loss, as described in section 3 of Additional file 3. After this simplification we have a net- work of 32 nodes, 81 edges, indicated on Fig. 2. We will refer to this model as the “reduced model”. A list of nodes and their regulatory functions is provided in Additional file 1. Identifying strongly connected components (SCCs) is important for attractor analysis, as complex dy- namic behavior such as oscillations or multi-stability requires feedback loops [7]. There are three SCCs in the network of the reduced model, as marked in Fig. 2. The NO cycle contains three nodes and three positive edges. The Ci SCC contains three nodes, which form two negative feedback loops. The Ion SCC is the most complex, containing 13 nodes and 26 edges, 7 of which are negative. Next we perform attractor analysis using two methods: 1. by converting the reduced model to Boolean and applying two analysis tools; 2. by analyzing the regula- tory functions theoretically. The former method finds all stable steady states and candidate oscillations; the latter confirms the results of the first method and gives insight about perturbation scenarios. Conversion of nodes from multi-level to Boolean states and attractor analysis We perform the conversion to Boolean to enable at- tractor analysis by existing software tools. Zañudo et al. [28] proposed an algorithm to find the attractors of a Boolean network based on the concept of “stable motif”, a strongly-connected group of nodes that can stabilize regardless of their inputs. The algorithm finds all stable motifs, which determine the part of the network that stabilizes in an attractor. After a stable motif is found, one can plug in its stabilized state into the network, and obtain a smaller remaining network. After repeating this, eventually the remaining part is either nothing (indicat- ing a fixed point/stable steady state) or a candidate oscil- lating sub-network. Compared with other software tools [29, 30], the major advantage of this algorithm is that it finds all the attractors of Boolean networks with hun- dreds of nodes [28]. Application of this powerful method requires a Boolean model, so we convert the multi-level model into Boolean first (see Methods). An example of conversion is given in Table 3. Table 2 Grouping of the stomatal opening values by the level of [K+]v and sucrose [K+]v Sucrose Stomatal opening value in the Sun et al. model Simplified stomatal opening value 0 0 0 0 0 1 or 2 1 or 2 1 1 0 1.58 1 1.8 1 3.84 2 1.5 2 4.36 2 2 0 or 1 3.15 or 4.15 3 4.5 0 or 2 5.18 or 8.92 3 6 0 9.28 or 9.45 5 6 2 11.28 or 11.45 5 9 0 or 2 14.01 or 16.01 6 Gan and Albert BMC Systems Biology (2016) 10:78 Page 6 of 14 More detailed examples of the conversion of the states and regulatory function of specific nodes are given in the Additional file 4. We will refer to the reduced model after conversion to Boolean variables as the “Boolean- converted reduced model”. The regulatory functions of the Boolean-converted reduced model are available in Additional file 5. When simulating the Boolean- converted reduced model, all the Boolean nodes that Fig. 2 The stomatal opening network after model reduction, with 32 nodes and 81 edges. Nodes with shadows have multiple states; other nodes are binary. The three strongly-connected components (SCCs) of the network are indicated by rectangles with dashed contours Gan and Albert BMC Systems Biology (2016) 10:78 Page 7 of 14 represent the same entity (the same multi-level node) are updated simultaneously. In this way the state transi- tions of the reduced model will be kept the same in the Boolean-converted reduced model, and therefore the Boolean conversion will not cause additional discrepan- cies from experimental observations. We apply the stable motif algorithm’s implementation, downloaded from http://github.com/jgtz/StableMotifs/ [28], to the Boolean-converted reduced model. The algo- rithm uses the Boolean regulatory functions of the con- verted model (given in Additional files 5 and 6) as input. We consider every combination of sustained states of the five signal nodes (blue light, red light, ABA, CO2, CO2_high). We find two possible stable motifs, corre- sponding to the self-regulatory node PMV_pos (one of the two Boolean nodes associated with the multi-level node PMV, see Additional files 4 and 5), in conditions where the H+-ATPasecomplex is inactive. These two stable motifs indicate the bistability of PMV. Under its influ- ence, another node, Kout, will also be bistable. The algo- rithm also indicates that for any signal combination, every node, except [Ca2+]c and Ca2+-ATPase, will stabilize in a fixed state. [Ca2+]c has three states, and in the Boolean-converted model it is represented by two nodes, Cac and Cac_high. Cac_high, which represents the higher level of [Ca2+]c, stabilizes at zero in all situa- tions. Cac and Ca2+-ATPase may oscillate in conditions where blue light is present and ABA is absent (a total of six cases, two of which allow PMV bistability). Table 4 summarizes key features of the attractors found by the stable motif algorithm for all 24 input combinations. Attractors where Ca2+ oscillation is not possible are fixed points (stable steady states). We verified the obtained attractors with GINsim [12], a software suite capable of model construction, simula- tion, and analysis. GINsim can compute all stable steady states (called stable states in GINsim), or determine complex attractors by mapping the state transitions. The stable steady states found by GINsim are identical to those found by the stable motif algorithm. To verify and further explore the complex attractors, we use the simu- lation function of GINsim, starting from a state in the complex attractor. The result that the system oscillates between four states, where only the state of Cac and Ca2 +-ATPase changes, agrees with the findings of the stable motif algorithm. We summarize the GINsim computa- tion/simulation results in Additional file 7. Additional file 8 indicates the Boolean-converted reduced model in SBML-qual format [29], a general format for biological model to be analyzed using various tools including GINsim. We can also connect the stable motif analysis results to network reduction. We have previously decided to not reduce the four nodes that correspond to input sig- nals. If we do consider a specific input combination when using network reduction, e.g. blue light and red light with normal CO2 without ABA, we can reduce much more of the network: two of the three SCCs, namely the NO cycle and the Ci SCC, will stabilize and can be eliminated. Only the Ion SCC and its sole output stomatal opening remain, indicating that this SCC is not driven solely by the external signals and has the capacity for oscillations or multi-stability. This is consistent with the results found by stable motif analysis, according to which the NO cycle and the Ci SCC attain a steady state and the Ion SCC admits a [Ca2+]c - Ca2+-ATPase oscilla- tion and PMV bistability. This consistency supports the appropriateness of the network reduction method and of the Boolean conversion. Theoretical analysis of the reduced model To gain additional insight into the attractors of the re- duced model and their potential changes due to node perturbations, we analyze the reduced model theoretic- ally. Specifically, we aim to answer the question: Can there be other types of oscillation, or can there be add- itional multi-stability, if a node is knocked out (fixed in the OFF state) or is constitutive active (fixed in the high- est state)? We first test whether the network and regulatory rules allow multi-stability or oscillations. This analysis is based on R. Thomas’s conjectures [7]: The presence of a positive (negative) feedback loop - a cycle with an even (odd) num- ber of inhibitory edges - in the network is a necessary but not sufficient condition for the occurrence of multiple steady states (oscillations). The conjectures have been proven in the case of discrete dynamic systems [31–34]. Since only feedback loops are candidates for potential multi-stability or oscillations, we analyze the regulatory functions of each strongly connected component of the network. For each feedback loop, we identify a sufficient condition for the nodes to stabilize in a specific state. The violation of this condition becomes a further necessary condition of multi-stability or oscillation. Here we de- scribe the main steps and results of the analysis; the de- tailed analysis is in Additional file 3. Table 3 Example of Boolean conversion Level of the original node State of Boolean node_2 State of Boolean node_1 0 0 0 1 0 1 2 1 0 3 1 1 The multi-level node shown in the 1st column is mapped into two Boolean nodes, shown in the 2nd and 3rd columns, using the binary representation of the corresponding integer. Gan and Albert BMC Systems Biology (2016) 10:78 Page 8 of 14 The NO cycle is composed of the nodes PLD, ROS, NO, and the three positive edges between them. It does not have any negative edges, so it cannot oscillate. A fixed ABA value is sufficient to stabilize each node of the cycle in a specific state, thus the cycle does not admit multi-stability under any perturbation. The Ci SCC has three nodes, Ci, mesophyll cell photo- synthesis (MCPS), carbon fixation, and four edges that form two negative feedback loops, one between carbon fixation and Ci, and the other between Ci and MCPS. Despite the existence of negative feedback, this cycle will stabilize if given a fixed CO2 value. From this we know that this cycle cannot oscillate or admit multi-stability under any perturbation. The Ion SCC has 13 nodes. To reduce its complexity we show that the key node [Ca2+]c, which has states 0,1, and 2, cannot enter state 2 in the long term under any perturbation. Since most nodes respond to [Ca2+]c only if [Ca2+]c =2, we can eliminate all edges that depend only on “[Ca2+]c =2”, and obtain a simplified Ion SCC, as shown in Fig. 3. The Ca2+ SCC ([Ca2+]c, Ca2+ ATPase, PLC, CaR) now becomes a sink SCC. The only negative edge in this sub-network is from Ca2+-ATPase to [Ca2+]c. These two nodes are known to oscillate. The positive feed- back loop formed by [Ca2+]c, PLC, and CaR will stabilize if given fixed inputs. So there cannot be multi-stability. For the nodes outside of the Ca2+ feedback loops, we show that the edges from KEV and [K+]v are redundant in the long term, so there are no feedback loops except the PMV self- loop. PMV is not capable of having oscillations, but can have bistability (as also indicated by the stable motif analysis). The bistability can affect at most one other node, Kout, under any perturbation. This means that the bistability has very limited effect on the attractor of the reduced model. Now we can summarize our conclusions and return to the question we sought to answer: there is no oscillation except in the calcium nodes; there is no multi-stability except in the nodes PMV and Kout. These statements are true under any perturbation. Moreover, for the calcium oscillation, [Ca2+]c cannot enter the state 2, so the sub- network between [Ca2+]c and Ca2+-ATPase is a negative feedback loop between two Boolean nodes, with the regulatory functions Ca2+ ATPase* = [Ca2+]c; [Ca2+]c* = not Ca2+ ATPase. It results in the simplest type of oscil- lation, as also found by GINsim simulation. For the PMV bistability, even if the bistability exists, most nodes, especially the output node stomatal opening, still have a unique value. Thus the theoretical analysis, in agreement with the computational analysis, leads to very strong conclusions about the reduced model’s dynamic repertoire. We can also show that the reduction or Boolean con- version did not change the attractors of the Sun et al. model. Although the reduction we used is only proven in the Boolean case, Naldi et al. showed that for multi- valued models, removal of non-autoregulated nodes, like in our reduction, preserves crucial dynamical properties [35], including fixed point attractors and the two-node simple oscillation we found. So our reduction is valid in this specific model. To confirm that the Boolean conver- sion preserved attractors, we note that in the Boolean- Table 4 Summary of the attractors found using the stable motif algorithm BL RL CO2 CO2_high ABA SO (Bool) SO Ca2+ Oscillation Possible? PMV_pos bistability 0 0 Any Any Any 000 0 No Yes 0 1 0 0 1 000 0 No No 0 1 1 Any 1 000 0 No Yes 1 Any 1 0 1 000 0 No No 1 Any 1 1 1 000 0 No Yes 0 1 1 Any 0 010 1 No Yes 1 Any 1 1 0 010 1 Yes Yes 0 1 0 0 0 101 3 No No 1 0 1 0 0 101 3 Yes No 1 Any 0 0 1 101 3 No No 1 0 0 0 0 110 5 Yes No 1 1 1 0 0 110 5 Yes No 1 1 0 0 0 111 6 Yes No The first five columns indicate the input signal combination. The setting CO2_high = 1 and CO2 = 0 is not included because it is not biologically meaningful. The “SO (Bool)” column indicates the state of the Boolean node combination representing stomatal opening. The “SO” column is the state of stomatal opening when converted back to an integer. Note that the stomatal opening level of four is not defined, and no attractors have a stomatal opening level of two. The next column indicates whether Ca2+ oscillation can possibly happen under the given signal combination. The last column indicates whether bistability of PMV_pos can be observed under this setting. In those cases, two stable steady states with (PMV_pos = 0, Kout = 0) and (PMV_pos = 1, Kout = 1) can be observed. The rest of the nodes are unaffected by this two-node bistability Gan and Albert BMC Systems Biology (2016) 10:78 Page 9 of 14 converted reduced model we found fixed point attractors and a complex attractor in which only two nodes oscil- late. Because the only potential change to attractors as a consequence of the conversion is merging of complex attractors [26], it is straightforward that the attractors have been conserved during the conversion, as the two- node oscillation found is the simplest type of complex attractor and cannot be a result of attractor merging. In addition, using general asynchronous update instead of random order asynchronous update does not cause any changes to the attractor, because the update schemes do not affect fixed points or the two-node simple oscillation we found. Stability of guard cell signal transduction Our previous results indicate the stability of the system in the sense that all the initial conditions lead to the same attractor except for up to four nodes. We also examine another facet of the system’s stability: the ro- bustness of the stomatal opening in response to node perturbations that render them non-functional. We per- form a systematic analysis of single-node knockouts of every non-signal node in the reduced model, under all combinations of light, CO2 and ABA conditions. For each signal combination, we set the perturbed node’s ini- tial state and regulatory function to 0, initialize the rest of the nodes in the condition representative of closed stomata, and then simulate the reduced model until it reaches its attractor. In the absence of ABA under each light and CO2 condition, 60–90 % perturbation scenarios produce the same stomatal opening value as the unper- turbed system (Table 5). These results are similar to those reported by Sun et al. for the original model [15] (see Additional file 9). In the presence of ABA 50–90 % perturbation scenarios produce the same stomatal open- ing value as the unperturbed system, and 4–16 % knock- outs lead to a higher stomatal opening value. Perturbations in the ABA = 1 case were not studied by Sun et al., but our simulations of the original model give the same qualitative results as the reduced model. These results indicate the closeness of the perturbed attractor (at least in terms of the stomatal opening value) to the unperturbed attractor in more than 50 % of single node perturbations. They also suggest the resilience of the sto- matal opening process against internal failures and perturbations. Extending the conclusions to the original model We found that in the reduced model there is no oscilla- tion except in the calcium nodes; there is no multi- stability except in the nodes PMV and Kout. Because the reduction we used has been shown to conserve Fig. 3 The Ion SCC after reducing all edges that depend on calcium. All regulators of this sub-network have been omitted. On the left, [Ca2+]c related nodes form a sink sub-network Gan and Albert BMC Systems Biology (2016) 10:78 Page 10 of 14 attractors [23, 35], we know that our attractor conclu- sions can be immediately extended to all nodes in the original model except the reduced nodes and stomatal opening. Next we extend the attractor analysis to include the reduced nodes as well. First we consider the nodes reduced during the first step of network reduction, i.e. non-signal source nodes and simple mediator nodes. These nodes are trivially in- capable of having multi-stability and oscillations them- selves, so we need only to consider their perturbations. Perturbation of a simple mediator node can always be replaced by a corresponding (set of) perturbation(s) in the mediator node’s direct successor(s), so these pertur- bations have already been considered. Perturbing a non- signal source node may theoretically cause a difference, however the nodes in this category in the Sun et al. model represent molecules that are abundant in the cell or cell environment, thus their perturbation is not bio- logically relevant or practical. Next we consider the anion nodes reduced due to the simplified stomatal opening rule. Recall that these nodes do not affect other nodes except stomatal opening in the long term. There cannot be multi-stability in anion nodes unless the assumptions of sufficient initial [NO3 −]a and starch concentration, and sufficient initial mito- chondrial TCA cycle activity are violated (details are provided in Additional file 3, section 5 and 6). Since there is no support for interventions that would lead to the violation of these assumptions, it is reasonable to conclude that no multi-stability can be found in the re- duced nodes under biologically relevant situations. We also found that there can be an additional oscillation in the RIC7 path (involving the nodes ROP2, RIC7 and SO) when a special set of perturbations is applied. Under that case, the nodes RIC7 and SO will oscillate. Since the ef- fect of this behavior is small (within 5 % of the unper- turbed SO value in the Sun et al. model [15]), it has little biological significance. There are no more possible oscillations as there are no more negative feedback loops. To conclude, the original Sun et al. model has os- cillations only in cytosolic Ca2+ ([Ca2+]c) and Ca2+ ATPase, and has multi-stability only in PMV and Kout, under situations that are biologically meaningful. Discussion The conclusions we obtained can tell us how to control this network model. Generally in engineering applica- tions, control means to drive a system into an arbitrary state [36, 37]. However in biological systems, it is more meaningful to drive the system into one of its natural attractors rather than into an arbitrary state, as the attractors correspond to stable phenotypes [38]. To con- trol the attractor of a Boolean system, one needs to con- trol only its input nodes and a subset of nodes in each Table 5 Summary of systematic perturbation results Light, CO2 and ABA condition Unperturbed SO level Simplified SO level Percentage of cases with unchanged SO value 0 1 2 3 5 6 Percentage of single knockouts that lead to each SO level Dual Beam Mod. CO2 ABA OFF 5 4 % 31 % 65 % 65 % Low CO2 6 31 % 4 % 65 % 65 % High CO2 1 4 % 96 % 96 % Blue Light Mod. CO2 3 35 % 65 % 65 % Low CO2 5 31 % 4 % 65 % 65 % High CO2 1 4 % 96 % 96 % Red Light Mod. CO2 1 4 % 96 % 96 % Low CO2 3 35 % 65 % 65 % High CO2 1 4 % 96 % 96 % Dual Beam Mod. CO2 ABA ON 0 85 % 4 % 8 % 4 % 85 % Low CO2 3 46 % 50 % 4 % 50 % Blue Light Mod. CO2 0 85 % 4 % 8 % 4 % 85 % Low CO2 3 46 % 50 % 4 % 50 % Red Light Low CO2 0 96 % 4 % 96 % The first set of columns, with the header ‘Light, CO2 and ABA condition’, indicate the input signal combinations. The abbreviation “Mod.” means moderate CO2 concentration. Note that we do not list the four input combinations (high CO2 with ABA and with any type of light, or moderate CO2 with ABA and red light) wherein all simulated stomatal opening values are zero. The 2nd column is the simulated stomatal opening (SO) level in the unperturbed system. The 3rd column set shows the percentage of single-node knockouts that yield the corresponding SO level. There is no stomatal opening level 4 in the reduced model. No entry means zero percentage. The last column is the percentage of settings where the stomatal opening remains at the same level as the unperturbed case. A complete table of perturbation results is provided in Additional file 9 Gan and Albert BMC Systems Biology (2016) 10:78 Page 11 of 14 stable motif [39]. Our integrated analysis, involving Boolean conversion, indicates that to control the at- tractor that the stomatal opening network evolves into, one only needs to control the input signals and PMV, even in case of perturbations. In particular, to control the stomatal opening value, one only needs to control the input signals, under any perturbation. The reduced model provides new biological insights. Normally, when ABA is present, stomata will close. However in some knockout mutants stomata can open to a certain extent in the presence of ABA, al- though the opening level is not as much as in the case without ABA [15]. Such partial reversals of the effect of ABA are important for understanding the mechanism of stomatal opening. For example, Sun et al. reported that OST1 knockout (OST1 is kept 0) and inhibition of the NADPH oxidase (AtrbohD/F is kept 0) yielded partially restored SO level in simula- tions, in agreement with experimental observations (see Additional file 2 for the comparison of the equivalent simulations in the reduced model with experiments). Simplification of the Sun et al. model allows easier simulation of more perturbation scenar- ios, e.g. the systematic identification of possible par- tial reversals. Table 6 indicates all the partial reversals due to single node knockouts in the reduced model. Our results reproduce the observation that knockout of nodes in the ABA pathway (PLD, NO, ROS) can cause partial reversals of ABA’s effect. We find that AnionCh knockout can partially restore stomatal opening inhib- ited by ABA, a result not reported by Sun et al., but which is supported by experimental evidence [40]. In addition, Table 6 offers a new biological prediction: low CO2 concentration can partially restore stomatal open- ing when ABA is present. This is consistent with the knowledge that CO2-free air promotes stomatal opening in the absence of ABA [41]. This CO2 effect suggests a mechanism of cross-talk between CO2 and ABA. Im- portantly, apart from the five nodes listed in Table 6, no other node’s knockout can reverse ABA’s inhibition of stomatal opening. The perturbation results of Table 5 offer many more new predictions. Our combination of techniques offers a powerful frame- work for determining the dynamic repertoire of a multi- level dynamic model. Multi-level models are more accur- ate than Boolean models in describing the quantitative characteristics of dynamic systems, but there are few gen- eral methods to analyze multi-level models [10, 12]. By combining different existing methods, we were able to overcome the limitations of each method. Our successful combination of existing methods offers a promising way to analyze multi-level models, and might point towards a general strategy to analyze the attractors of multi-level models, biological or non-biological. A notable future direction for this work is to develop an alternative way to determine the attractors of multi- level models by extending the concept of stable motifs. Compared with conversion to a Boolean model, then ap- plying Boolean stable motif algorithm, extending the stable motif algorithm to multi-level models can avoid potential attractor change issues. Development of such a technique will allow easy and powerful attractor analysis for multi-level models. Conclusions We obtained a very strong conclusion about the attrac- tors of the Sun et al. stomatal opening model: under any combination of sustained signals, all nodes in the model converge into steady states, with the potential exception of the cytosolic Ca2+ ([Ca2+]c) and Ca2+ ATPase. Varia- tions in the initial condition of non-source nodes or in process timing (node update sequence) can drive at most two nodes, PMV and Kout, into a different attractor. This high degree of attractor similarity is somewhat unex- pected, as the network has a large strongly connected component and several feedback loops. Thus, despite the decidedly non-linear structure of the network, most parts of the system behave in the consistent manner of a linear pathway. This is a distinct feature of the stomatal opening model: many dynamic models of biological systems have multiple, diverse attractors [22, 42]. The models of these systems will evolve into drastically different attractors when starting from different initial conditions, sometimes even when starting from the same initial condition, dem- onstrating different biological trajectories. In the stomatal opening model, however, the uniqueness of the steady state stomatal opening level suggests that the final extent of the stomatal opening response is robust and resilient Table 6 Nodes whose knockouts diminish ABA’s inhibition of stomatal opening Light, CO2 and ABA condition Unperturbed SO level Nodes whose knockout results in a partially restored SO, and the corresponding SO value CO2 NO PLD ROS AnionCh Dual Beam Moderate CO2, ABA is present 0 3 3 5 3 2 Blue Light 0 3 2 3 2 1 Red Light 0 3 1 The first set of columns, with the header ‘Light, CO2 and ABA condition’, indicate the input signal combinations. The 2nd column is the stomatal opening without perturbations. The 3rd column set indicates the nodes whose knockout would yield a stomatal opening level that is higher than the unperturbed value of 0. CO2 knockout means CO2 being set to zero (CO2 free air). No entry means the setting does not cause partial reversal Gan and Albert BMC Systems Biology (2016) 10:78 Page 12 of 14 against changes in initial conditions or in timing. Note that although a change in the initial condition will not change the steady-state opening level, it may change the steady state of PMV and Kout, and may change how fast the system converges to an attractor. We also showed that the reduced stomatal opening model does not admit additional, emergent oscillations or multi-stability under any biologically relevant node per- turbation (knockout or constitutive activity). We further demonstrate the robustness of the system by examining the stomatal opening level under single node knockouts: in most cases the signals are still likely to propagate and lead to a similar degree of stomatal opening as in the absence of perturbation. This robustness is unlike a single linear path- way, which would be very sensitive to node disruption. We suggest that the role of the strongly connected components in the network could be to provide multiple paths for the signal to propagate, but at the same time not allowing ex- tensive multistability or oscillations. Our innovative com- bination of existing methods offers a promising way to analyze multi-level models. Additional files Additional file 1: Regulatory functions of the reduced stomatal opening model. (DOCX 38 kb) Additional file 2: Compilation of comparisons between published experimental observations and the reduced model’s results for simulations of the identical conditions. (DOCX 163 kb) Additional file 3: Analysis of stomatal opening model. Detailed derivation of attractor analysis and other statements made in the main article. (DOCX 98 kb) Additional file 4: Examples of converting a multi-level update function to Boolean. (DOCX 38 kb) Additional file 5: Regulatory functions of the Boolean-converted reduced stomatal opening model. (DOCX 25 kb) Additional file 6: Text file of the Boolean-converted reduced stomatal opening model to be used in the stable motif algorithm. The stable motif algorithm and instructions about how to use it can be found from this link: https://github.com/jgtz/StableMotifs. (TXT 4 kb) Additional file 7: GINsim attractor analysis of the Boolean-converted reduced stomatal opening model. (DOCX 42 kb) Additional file 8: Boolean-converted reduced stomatal opening model in SBML format. This file format can be used in various tools, including GINsim. (SBML 199 kb) Additional file 9: Stomatal opening levels for simulated single node knockouts in the simplified model under all input signal combinations. (XLSX 15 kb) Acknowledgements The authors thank Zhongyao Sun, Jorge G. T. Zañudo and Prof. Sarah Assmann for helpful discussions. Funding This project was supported by National Science Foundation (NSF) grants IIS 1160995, PHY 1205840 and MCB 1244303. The NSF had no role in the design of the study, analysis and interpretation of data or in writing the manuscript. Availability of data and materials The datasets supporting the conclusions of this article are included within the article and its additional files. Authors’ contributions XG developed the reduced model and performed the analysis under the advice and supervision of RA. Both authors wrote the manuscript. Both authors have read and approved the final version of the manuscript. Competing interests The authors declare that they have no competing interests. Consent for publication Not applicable. The article does not contain any individual person’s data. Ethics approval and consent to participate Not applicable. The article does not involve human participants, human data or human tissue. Received: 10 June 2016 Accepted: 11 August 2016 References 1. Stigler B, Chamberlin HM. 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J Theor Biol. 2003;223(1):1–18. • We accept pre-submission inquiries • Our selector tool helps you to ﬁnd the most relevant journal • We provide round the clock customer support • Convenient online submission • Thorough peer review • Inclusion in PubMed and all major indexing services • Maximum visibility for your research Submit your manuscript at www.biomedcentral.com/submit Submit your next manuscript to BioMed Central and we will help you at every step: Gan and Albert BMC Systems Biology (2016) 10:78 Page 14 of 14	27542373	PP1cc_2 = ( ( ( PLD AND ( ( ( NOT phot1_complex AND NOT BL ) ) ) ) AND NOT ( PLD_high ) ) OR ( ( phot1_complex AND ( ( ( NOT PLD ) ) ) ) AND NOT ( PLD_high ) ) OR ( ( BL AND ( ( ( NOT PLD ) ) ) ) AND NOT ( PLD_high ) ) ) OR NOT ( PLD OR phot1_complex OR BL OR PLD_high ) Kv = ( Kc ) carbfix_high = ( Ci AND ( ( ( phph_high ) ) ) ) OR ( CO2 AND ( ( ( phph_high ) ) ) ) sucrose = ( ( PLD ) AND NOT ( ABA ) ) Kin = ( FFA AND ( ( ( NOT Ci_sup OR NOT Ci ) AND ( ( ( PMV_neg ) ) ) ) ) ) OR ( ABA AND ( ( ( NOT Ci_sup OR NOT Ci ) AND ( ( ( PMV_neg ) ) ) ) ) ) OR ( PMV_neg AND ( ( ( NOT Cac_high AND NOT ABA AND NOT Ci_sup AND NOT FFA ) ) ) ) PLD = ( ABA ) OR ( NO ) PLA2 = ( BL ) OR ( RL ) OR ( phot1_complex ) Kout = ( PMV_pos AND ( ( ( Ci ) AND ( ( ( Ci_sup ) ) ) ) OR ( ( NOT ROS ) ) OR ( ( NOT NO ) ) OR ( ( ABA ) ) OR ( ( NOT FFA ) ) ) ) Cac = ( ABA ) OR ( ( CaR ) AND NOT ( CaATPase ) ) OR ( ( CaIc ) AND NOT ( CaATPase ) ) PK_2 = ( ( ( Ci_sup AND ( ( ( PP1cc_1 ) AND ( ( ( NOT PP1cc_3 AND NOT PP1cc_2 ) ) ) ) OR ( ( PP1cc_3 AND PP1cc_2 ) AND ( ( ( NOT PP1cc_1 ) ) ) ) OR ( ( PP1cc_1 AND PP1cc_2 ) AND ( ( ( NOT PP1cc_3 ) ) ) ) ) ) AND NOT ( Ci ) ) OR ( PP1cc_1 AND ( ( ( Ci ) AND ( ( ( NOT Ci_sup AND NOT PP1cc_2 ) ) ) ) ) ) OR ( ( ( PP1cc_3 AND ( ( ( NOT PP1cc_1 AND NOT PP1cc_2 ) ) ) ) AND NOT ( Ci_sup ) ) AND NOT ( Ci ) ) OR ( ( ( PP1cc_2 AND ( ( ( NOT PP1cc_3 AND NOT PP1cc_1 ) ) OR ( ( PP1cc_3 AND PP1cc_1 ) ) OR ( ( PP1cc_1 ) AND ( ( ( NOT PP1cc_3 ) ) ) ) ) ) AND NOT ( Ci_sup ) ) AND NOT ( Ci ) ) ) OR NOT ( PP1cc_3 OR PP1cc_1 OR Ci_sup OR PP1cc_2 OR Ci ) FFA = ( PLA2 ) HATPase_3 = ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( FFA AND ( ( ( phph_high AND PK_2 AND PK_3 ) AND ( ( ( NOT PK_1 AND NOT PLA2 ) ) ) ) ) ) AND NOT ( phph AND ( ( ( NOT phph_high ) ) ) ) ) AND NOT ( phph AND ( ( ( NOT phph_high ) ) ) ) ) AND NOT ( phph AND ( ( ( NOT phph_high ) ) ) ) ) AND NOT ( phph AND ( ( ( NOT phph_high ) ) ) ) ) AND NOT ( phph AND ( ( ( NOT phph_high ) ) ) ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( phph_high ) ) AND NOT ( phph_high ) ) AND NOT ( phph_high ) ) OR ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( PLA2 AND ( ( ( PK_1 AND PK_3 ) AND ( ( ( NOT PK_2 AND NOT FFA ) ) ) ) ) ) AND NOT ( phph AND ( ( ( NOT phph_high ) ) ) ) ) AND NOT ( phph AND ( ( ( NOT phph_high ) ) ) ) ) AND NOT ( phph AND ( ( ( NOT phph_high ) ) ) ) ) AND NOT ( phph AND ( ( ( NOT phph_high ) ) ) ) ) AND NOT ( phph AND ( ( ( NOT phph_high ) ) ) ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( phph_high ) ) AND NOT ( phph_high ) ) AND NOT ( phph_high ) ) AND NOT ( phph_high ) ) AND NOT ( phph_high ) ) KEV = ( Cac_high AND ( ( ( Kv ) ) ) ) Kc = ( ( ( ( ( ( HATPase_3 AND ( ( ( HATPase_2 AND Kv AND KEV AND AnionCh ) ) OR ( ( HATPase_2 AND Kin AND AnionCh ) ) ) ) AND NOT ( Kout ) ) AND NOT ( Kout ) ) AND NOT ( AnionCh ) ) AND NOT ( AnionCh_high ) ) AND NOT ( AnionCh_high ) ) OR ( ( ( ( HATPase_2 AND ( ( ( Kin ) ) OR ( ( Kv AND KEV ) ) ) ) AND NOT ( Kout ) ) AND NOT ( AnionCh ) ) AND NOT ( AnionCh_high ) ) OR ( ( HATPase_1 AND ( ( ( Kin ) ) OR ( ( Kv ) AND ( ( ( KEV ) ) ) ) ) ) AND NOT ( Kout ) ) SO_2 = ( HATPase_2 AND ( ( ( Kv ) ) ) ) OR ( sucrose AND ( ( ( NOT Kv ) ) ) ) NO = ( phph AND ( ( ( ROS ) ) ) ) CaR = ( PLC ) OR ( NO ) PLD_high = ( ABA AND ( ( ( NO ) ) ) ) HATPase_2 = ( ( ( ( ( ( FFA AND ( ( ( phph_high AND PK_2 AND PK_1 ) AND ( ( ( NOT PK_3 ) ) ) ) ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) OR ( ( ( ( ( PLA2 AND ( ( ( PK_2 AND phph ) AND ( ( ( NOT PK_1 AND NOT FFA AND NOT PK_3 ) ) ) ) ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) AND NOT ( Cac_high ) ) ROS = ( phph AND ( ( ( PLD ) AND ( ( ( NOT ABI1 ) ) ) ) ) ) SO_3 = ( HATPase_3 AND ( ( ( Kv ) ) ) ) PMV_neg = ( ( ( HATPase_3 AND ( ( ( NOT PMV_pos ) ) OR ( ( AnionCh AND PMV_neg ) ) ) ) AND NOT ( Cac_high ) ) AND NOT ( KEV ) ) OR ( ( PMV_neg AND ( ( ( Cac_high ) AND ( ( ( HATPase_2 OR HATPase_3 OR HATPase_1 ) ) ) ) OR ( ( PMV_pos ) AND ( ( ( NOT Cac_high AND NOT HATPase_2 AND NOT KEV AND NOT HATPase_3 AND NOT AnionCh AND NOT HATPase_1 ) ) ) ) OR ( ( NOT Cac_high AND NOT HATPase_2 AND NOT KEV AND NOT PMV_pos AND NOT HATPase_3 AND NOT AnionCh AND NOT HATPase_1 ) ) OR ( ( NOT Cac_high ) AND ( ( ( HATPase_2 OR HATPase_3 OR HATPase_1 ) ) ) ) ) ) AND NOT ( AnionCh ) ) OR ( ( ( HATPase_2 AND ( ( ( NOT PMV_pos ) ) OR ( ( AnionCh AND PMV_neg ) ) ) ) AND NOT ( Cac_high ) ) AND NOT ( KEV ) ) OR ( ( ( HATPase_1 AND ( ( ( NOT PMV_pos ) ) OR ( ( AnionCh AND PMV_neg ) ) ) ) AND NOT ( Cac_high ) ) AND NOT ( KEV ) ) MCPS = ( Ci AND ( ( ( RL OR BL ) ) ) ) OR ( Ci_sup AND ( ( ( RL OR BL ) ) ) ) AnionCh_high = ( ( ABA ) AND NOT ( ABI1 ) ) OR ( Ci AND ( ( ( Ci_sup ) ) ) ) OR ( ( Cac_high ) AND NOT ( ABI1 ) ) SO_1 = ( HATPase_1 AND ( ( ( Kv ) ) ) ) phph = ( BL ) OR ( RL ) AnionCh = ( ( ( ( ABA AND ( ( ( ABI1 ) AND ( ( ( NOT phot1_complex AND NOT BL ) ) ) ) OR ( ( NOT Cac_high AND NOT ABI1 AND NOT Ci_sup AND NOT Ci ) ) OR ( ( NOT ABI1 ) AND ( ( ( Ci_sup ) ) OR ( ( Ci ) ) ) ) ) ) AND NOT ( ABI1 ) ) AND NOT ( ABI1 ) ) OR ( ( Cac_high ) AND NOT ( ABI1 ) ) OR ( Ci_sup AND ( ( ( NOT Cac_high AND NOT ABA AND NOT ABI1 AND NOT phot1_complex AND NOT BL ) ) ) ) OR ( Ci AND ( ( ( Ci_sup ) ) ) ) OR ( ABI1 AND ( ( ( NOT ABA AND NOT phot1_complex AND NOT BL ) ) ) ) ) OR NOT ( Cac_high OR ABA OR ABI1 OR phot1_complex OR Ci_sup OR Ci OR BL ) PLC = ( BL ) OR ( ABA AND ( ( ( Cac ) ) ) ) ABI1 = NOT ( ( ABA ) ) PP1cc_1 = ( BL ) OR ( phot1_complex ) Cac_high = ( ( CaR AND ( ( ( ABA ) ) ) ) AND NOT ( CaATPase ) ) OR ( ( CaIc AND ( ( ( ABA ) ) ) ) AND NOT ( CaATPase ) ) Ci = ( CO2 AND ( ( ( NOT MCPS_high AND NOT CO2_high AND NOT carbfix_high ) ) OR ( ( CO2_high ) ) ) ) phot1_complex = ( BL ) PK_1 = ( ( ( PP1cc_1 AND ( ( ( NOT PP1cc_2 ) ) OR ( ( PP1cc_2 ) AND ( ( ( NOT PP1cc_3 ) ) ) ) ) ) AND NOT ( Ci ) ) AND NOT ( Ci_sup ) ) OR ( ( Ci_sup AND ( ( ( PP1cc_1 AND PP1cc_2 ) AND ( ( ( NOT PP1cc_3 ) ) ) ) OR ( ( PP1cc_3 AND PP1cc_1 ) AND ( ( ( NOT PP1cc_2 ) ) ) ) ) ) AND NOT ( Ci ) ) OR ( ( Ci AND ( ( ( PP1cc_1 AND PP1cc_2 ) ) AND ( ( NOT PP1cc_3 ) ) ) ) AND NOT ( Ci_sup ) ) OR ( ( ( PP1cc_2 AND ( ( ( PP1cc_3 ) AND ( ( ( NOT PP1cc_1 ) ) ) ) ) ) AND NOT ( Ci ) ) AND NOT ( Ci_sup ) ) HATPase_1 = ( ( PLA2 AND ( ( ( PK_2 AND PK_1 AND PK_3 AND phph ) AND ( ( ( NOT FFA ) ) ) ) OR ( ( PK_2 AND PK_3 AND phph ) AND ( ( ( NOT PK_1 AND NOT FFA ) ) ) ) OR ( ( PK_1 AND phph ) AND ( ( ( NOT PK_2 AND NOT FFA AND NOT PK_3 ) ) ) ) OR ( ( PK_1 AND PK_3 ) AND ( ( ( NOT PK_2 AND NOT FFA ) ) ) ) OR ( ( PK_2 AND PK_1 ) AND ( ( ( NOT FFA ) ) ) ) ) ) AND NOT ( Cac_high ) ) OR ( ( FFA AND ( ( ( PK_2 AND PK_3 AND phph ) AND ( ( ( NOT PK_1 ) ) ) ) OR ( ( PK_1 AND phph ) AND ( ( ( NOT PK_2 ) ) ) ) OR ( ( PK_2 AND PK_1 ) AND ( ( ( NOT PK_3 ) ) ) ) OR ( ( PK_1 AND PK_3 ) AND ( ( ( NOT PK_2 ) ) ) ) OR ( ( PK_2 AND PK_1 AND PK_3 ) ) ) ) AND NOT ( Cac_high ) ) PP1cc_3 = ( ( PLD_high AND ( ( ( NOT phot1_complex AND NOT BL ) ) ) ) OR ( BL AND ( ( ( PLD ) AND ( ( ( NOT PLD_high ) ) ) ) ) ) OR ( phot1_complex AND ( ( ( PLD ) AND ( ( ( NOT PLD_high ) ) ) ) ) ) ) OR NOT ( PLD OR phot1_complex OR BL OR PLD_high ) PK_3 = ( PP1cc_1 AND ( ( ( PP1cc_2 ) AND ( ( ( NOT PP1cc_3 AND NOT Ci_sup AND NOT Ci ) ) ) ) OR ( ( PP1cc_3 AND Ci_sup ) AND ( ( ( NOT Ci AND NOT PP1cc_2 ) ) ) ) OR ( ( PP1cc_3 AND Ci ) AND ( ( ( NOT Ci_sup AND NOT PP1cc_2 ) ) ) ) ) ) MCPS_high = ( Ci AND ( ( ( RL AND BL ) ) ) ) OR ( Ci_sup AND ( ( ( RL AND BL ) ) ) ) CaIc = ( PMV_neg ) OR ( ROS ) phph_high = ( RL AND ( ( ( BL ) ) ) ) carbfix = ( Ci AND ( ( ( phph ) ) ) ) OR ( CO2 AND ( ( ( phph ) ) ) ) Ci_sup = ( CO2 AND ( ( ( MCPS_high OR CO2_high OR carbfix_high ) ) ) ) CaATPase = ( Cac ) PMV_pos = ( ( ( Cac_high AND ( ( ( NOT HATPase_2 AND NOT HATPase_3 AND NOT HATPase_1 ) ) ) ) AND NOT ( AnionCh ) ) AND NOT ( PMV_neg ) ) OR ( AnionCh AND ( ( ( NOT HATPase_2 AND NOT HATPase_3 AND NOT HATPase_1 ) AND ( ( ( Cac_high ) ) ) ) OR ( ( PMV_pos ) AND ( ( ( NOT Cac_high AND NOT HATPase_2 AND NOT HATPase_3 AND NOT HATPase_1 AND NOT PMV_neg ) ) ) ) OR ( ( KEV ) AND ( ( ( NOT Cac_high AND NOT HATPase_2 AND NOT HATPase_3 AND NOT HATPase_1 ) ) ) ) ) ) OR ( ( ( KEV AND ( ( ( NOT HATPase_2 AND NOT HATPase_3 AND NOT HATPase_1 ) ) ) ) AND NOT ( AnionCh ) ) AND NOT ( PMV_neg ) ) OR ( ( ( ( PMV_pos AND ( ( ( KEV AND AnionCh ) AND ( ( ( HATPase_2 OR HATPase_3 OR HATPase_1 ) ) ) ) OR ( ( Cac_high AND AnionCh ) AND ( ( ( HATPase_2 OR HATPase_3 OR HATPase_1 ) ) ) ) ) ) AND NOT ( AnionCh ) ) AND NOT ( PMV_neg ) ) AND NOT ( PMV_neg ) )
ORIGINAL RESEARCH published: 19 August 2016 doi: 10.3389/fphys.2016.00349 Frontiers in Physiology \| www.frontiersin.org 1 August 2016 \| Volume 7 \| Article 349 Edited by: Christian Diener, National Institute of Genomic Medicine, Mexico Reviewed by: Oksana Sorokina, University of Edinburgh, UK Marcio Luis Acencio, Norwegian University of Science and Technology, Norway Correspondence: Luis Mendoza lmendoza@biomedicas.unam.mx Rosana Pelayo rosanapelayo@gmail.com Specialty section: This article was submitted to Systems Biology, a section of the journal Frontiers in Physiology Received: 22 March 2016 Accepted: 02 August 2016 Published: 19 August 2016 Citation: Enciso J, Mayani H, Mendoza L and Pelayo R (2016) Modeling the Pro-inﬂammatory Tumor Microenvironment in Acute Lymphoblastic Leukemia Predicts a Breakdown of Hematopoietic-Mesenchymal Communication Networks. Front. Physiol. 7:349. doi: 10.3389/fphys.2016.00349 Modeling the Pro-inﬂammatory Tumor Microenvironment in Acute Lymphoblastic Leukemia Predicts a Breakdown of Hematopoietic-Mesenchymal Communication Networks Jennifer Enciso 1, 2, Hector Mayani 1, Luis Mendoza 3 and Rosana Pelayo 1* 1 Oncology Research Unit, Mexican Institute for Social Security, Mexico City, Mexico, 2 Biochemistry Sciences Program, Universidad Nacional Autónoma de Mexico, Mexico City, Mexico, 3 Departamento de Biología Molecular y Biotecnología, Instituto de Investigaciones Biomédicas, Universidad Nacional Autónoma de Mexico, Mexico City, Mexico Lineage fate decisions of hematopoietic cells depend on intrinsic factors and extrinsic signals provided by the bone marrow microenvironment, where they reside. Abnormalities in composition and function of hematopoietic niches have been proposed as key contributors of acute lymphoblastic leukemia (ALL) progression. Our previous experimental ﬁndings strongly suggest that pro-inﬂammatory cues contribute to mesenchymal niche abnormalities that result in maintenance of ALL precursor cells at the expense of normal hematopoiesis. Here, we propose a molecular regulatory network interconnecting the major communication pathways between hematopoietic stem and progenitor cells (HSPCs) and mesenchymal stromal cells (MSCs) within the BM. Dynamical analysis of the network as a Boolean model reveals two stationary states that can be interpreted as the intercellular contact status. Furthermore, simulations describe the molecular patterns observed during experimental proliferation and activation. Importantly, our model predicts instability in the CXCR4/CXCL12 and VLA4/VCAM1 interactions following microenvironmental perturbation due by temporal signaling from Toll like receptors (TLRs) ligation. Therefore, aberrant expression of NF-κB induced by intrinsic or extrinsic factors may contribute to create a tumor microenvironment where a negative feedback loop inhibiting CXCR4/CXCL12 and VLA4/VCAM1 cellular communication axes allows for the maintenance of malignant cells. Keywords: cancer systems biology, acute lymphoblastic leukemia, tumor microenvironment, CXCL12, pro-inﬂammatory bone marrow, early hematopoiesis, network modeling, dynamical systems INTRODUCTION Cancer is currently considered as a global child health priority (Gupta et al., 2014). The application of eﬀective treatments to decrease overall childhood cancer mortality requires a comprehensive understanding of its origins and pathobiology, along with accurate diagnosis and early identiﬁcation of high-risk groups (reviewed in Vilchis-Ordoñez et al., 2016). Strikingly, the Enciso et al. Modeling CXCR4/CXCL12 Disruption in Acute Leukemia clinical, molecular and biological heterogeneity of malignant diseases indicating an unsuspected multiclonal diversity has highlighted their complexity and the uncertainty of their cell population dynamics. Novel theoretical and experimental integrative strategies have changed our perspective of cancer, from a hierarchical, deterministic and unidirectional process to a multi-factorial network where genetics interacts with micro and macro environmental cues that contribute to the etiology and maintenance of tumor cells (Notta et al., 2011; Davila-Velderrain et al., 2015; Tomasetti and Vogelstein, 2015). Furthermore, stochastic eﬀects associated with the number of stem cell divisions have been proposed as major contributors, often even more signiﬁcant than hereditary or external factors (Tomasetti and Vogelstein, 2015). B-cell acute lymphoblastic leukemia (B-ALL) is largely the result of a growing number of cooperating genetic and epigenetic aberrations that corrupt hematopoietic developmental pathways and ultimate lead to uncontrolled production of malignant B lymphoid precursor cells within the bone marrow (BM) (Pelayo et al., 2012; Purizaca et al., 2012). Leukemic cell inﬁltration and treatment failure worsen the outcome of the disease and remain the foremost cause of relapse. Recent advances suggest the ability of leukemia initiating cells to create abnormal BM microenvironments, promoting high proliferation and early diﬀerentiation arrest at the expense of normal cell fate decisions (Colmone et al., 2008; Raaijmakers, 2011; Vilchis- Ordoñez et al., 2015). Intrinsic damage and/or remodeling of cell compartments that shape the distinct BM niches may account to microenvironmental regulation of quiescence, proliferation, diﬀerentiation and blastic cell migration. Leukemic cells compete for niche resources with their normal hematopoietic counterparts (Wu et al., 2009), culminating in the displacement of the latter, as observed in xenotransplantation mice models (Colmone et al., 2008). Moreover, the marrow microenvironment provides leukemic precursors with dynamic interactions and regulatory signals that are essential for their maintenance, proliferation and survival. Although, the underlying molecular mechanisms are poorly deﬁned, these niches protect tumor cells from chemotherapy-induced apoptosis, showing a new perspective on the evolution of chemoresistance (Ayala et al., 2009: Shain et al., 2015; Tabe and Konopleva, 2015), and emphasizing the need for new models that theoretically or experimentally replicate the interplay between tumor and stromal cells under normal and pathological settings. As suggested by our previous ﬁndings, ALL lymphoid precursors have the ability of responding to pathogen- or damage- associated molecular patterns via Toll-like receptor signaling by secreting soluble factors and altering their diﬀerentiation potentials (Dorantes-Acosta et al., 2013). The resulting pro-inﬂammatory microenvironment may expose them to prolonged proliferation, contributing tumor maintenance in a self-sustaining way while prompting the NF-κB-associated proliferation of normal progenitor cells (Vilchis-Ordoñez et al., 2015, 2016). Some hematopoietic growth factors and pro-inﬂammatory cytokines, including granulocyte-colony stimulating factor (G-CSF), IFNα, IL-1α, IL-1β, IL-7, and TNFα were highly produced by ALL cells from a conspicuous group of patients co-expressing myeloid markers (Vilchis-Ordoñez et al., 2015). Of note, mesenchymal stromal cells (MSCs) from ALL BM have shown atypical production of pro-inﬂammatory factors whereas disruption of the major cell communication pathway is apparent by detriment of CXCL12 expression and biological function (Geay et al., 2005; Colmone et al., 2008; van den Berk et al., 2014). Considering that the CXCL12/CXCR4 axis constitutes the most critical component of the perivascular and reticular BM niches supporting the hematopoietic stem and progenitor cells (HSPCs) diﬀerentiation and maintenance within the BM, as well as the early steps of B cell development (Ma et al., 1998; Tokoyoda et al., 2004; Sugiyama et al., 2006; Greenbaum et al., 2013), an obstruction of the HSPC-MSC interaction may have substantial implications in the overall stability of these processes. Whether the inﬂammation-derived signals provide a mechanism for leukemic cells to survive, to induce changes in lineage cell fate decisions, or to prompt niche remodeling in leukemia settings, are currently topical questions. Mathematical model strategies have become powerful approaches to complex biological systems and may contribute to unravel the hematopoietic-microenvironment interplay that facilitates tumor cells prevalence (Altrock et al., 2015; Enciso et al., 2015). Through continuous dynamic modeling with diﬀerential equations we have learned seminal aspects of multi-compartment and multi-clonal behavior of leukemic cell populations (Stiehl and Marciniak-Czochra, 2012; Enciso et al., 2015), leading to novel proposals on disease development driven by unbalanced competition between normal and pre- leukemic cells (Swaminathan et al., 2015). Both stochastic and deterministic models have been useful to simulate cell fate decisions and predict clonal evolution (reviewed in Enciso et al., 2015). Certainly, incorporating tumor microenvironment in cancer modeling is expected to change our vision of biochemical interactions in niche remodeling-dependent hematopoietic growth, as recently demonstrated for myeloma disease (Coelho et al., 2016). By developing and simulating a dynamic Boolean system, we now investigate the biological consequences of microenvironmental perturbation due by temporal TLR signaling on crucial communication networks between stem/progenitor cells (HSPCs) and MSCs in ALL. We propose that NF-κB dependent tumor-associated inﬂammation co- participate in malignant progression concomitant to normal hematopoietic failure through disruption of CXCL12/CXCR4 and VLA4/VCAM-1 communication axes. MATERIALS AND METHODS Manual Curation Strategy Based on the crucial and unique role of the CXCL12/CXCR4 axis in the regulation of maintenance, biological activity, and niche communication-derived cell fate decisions of seminal cells, including pluripotent embryonic stem cells and multipotent hematopoietic stem cells, construction and updating of molecular interactions of relevance involved careful manual curation of primary hematopoietic cell research. Moreover, of special Frontiers in Physiology \| www.frontiersin.org 2 August 2016 \| Volume 7 \| Article 349 Enciso et al. Modeling CXCR4/CXCL12 Disruption in Acute Leukemia interest was the attention to the hematopoietic malignancies, which in contrast to solid tumors, display a distinct CXCL12- mediated microenvironmental behavior. Thus, although the modeled signaling pathways could be considered generic to all tissues, the organ, stage of cell diﬀerentiation and surrounding microenvironment may inﬂuence the net result of interactions. Taking into account this considerations, most published work that has been used for the reconstruction of our proposed model, include data from molecular interactions in HSPCs. Some of the interactions have been reported in a number of diﬀerent tissues and predicted to be conserved in the hematopoietic system. Finally, as there is not enough data to model hematopoietic-microenvironment restricted to Homo sapiens and some interactions might be crucial for the molecular connectivity of the model, we have used information from diﬀerent species when needed. A detailed referencing of all reports used for the model reconstruction is provided as Supplemental Material (Tables S1, S2, and reference list). Molecular Basis for the Network Reconstruction The connectivity among key molecules involved in the communication between HSPCs and MSCs within the BM was inferred through the curated experimental literature. Speciﬁcally, we were interested in recovering the network components, their interactions, and the nature of the interactions (activation/positive or inactivation/negative). The resulting general network incorporates transcriptional factors, kinases, membrane receptors, interleukines, integrins, growth factors, and chemokines from Homo sapiens and Mus musculus species. Importantly, to simplify the modeling process, some groups of molecules were considered as single functional modules, thus encompassing a series of sequential steps that lead to the activation or inactivation of a certain node (e.g., PI3K/Akt). The following paragraphs summarize the principle evidence used to reconstruct the HSPC-MSC network and infer the logical rules for computational simulation of the system as a discrete dynamical model. A detailed referencing is provided as Supplemental Material (Tables S1, S2, and reference list). The CXCR4/CXCL12 chemokine pathway was considered as the central axis for the network construction considering its essential role in homeostasis maintenance (Sugiyama et al., 2006; Tzeng et al., 2011) and B lineage support (Ma et al., 1998; Tokoyoda et al., 2004). Furthermore, recent observations suggest that this axis is disrupted by up-stream molecular deregulations both in MSC and leukemic blasts harvested from ALL patients, aﬀecting the maintenance of hematopoietic cells within their regulatory niches (Geay et al., 2005; Colmone et al., 2008; van den Berk et al., 2014). Besides the well-studied CXCR4/CXCL12 chemotactic interaction, CXCR4 activation increases the aﬃnity between vascular cellular adhesion molecule-1 (VCAM-1) expressed on the surface of MSC and its receptor VLA-4 on HSPC. Both pathways, CXCR4/CXCL12 and VLA-4/VCAM-1, are known to play coordinately a central role in HSPC migration, engraftment and retention within the BM (Peled et al., 2000; Ramirez et al., 2009), converge in triggering the PI3K/Akt and ERK signals, and share common up-stream regulators involving molecular factors guiding inﬂammatory responses. As mentioned in the Introduction, recent evidence indicates the secretion of high levels of pro-inﬂammatory cytokines by a conspicuous group of ALL patients (Vilchis-Ordoñez et al., 2015), thereby presumably contributing to remodeling of the normal hematopoietic microenvironment (Colmone et al., 2008). Of note, interleukin-1α (IL-1α) and IL-1β, which were substantially elevated, play an ampliﬁcation role on inﬂammation increasing the expression of other cytokines, like G-CSF (Majumdar et al., 2000; Allakhverdi et al., 2013), and setting a positive feedback loop with the PI3K co-activation of NF- κB (Reddy et al., 1997; Sizemore et al., 1999; Carrero et al., 2012; Bektas et al., 2014). IL-1 and G-CSF, inhibit directly and indirectly the CXCR4/CXCL12 axis. G-CSF negatively regulates CXCL12 transcription and increases the secretion of matrix metalloproteinase-9, showing the ability to degrade both CXCL12 (Lévesque et al., 2003; Semerad et al., 2005; Christopher et al., 2009; Day et al., 2015) and CXCR4 (Lévesque et al., 2003). Moreover, G-CSF promotes up-regulation of Gﬁ1 that at the time inhibits the transcription of CXCR4 (Zhuang et al., 2006; De La Luz Sierra et al., 2007; de la Luz Sierra et al., 2010). Thus, by considering this information from experimental data, we have included IL-1 and G-CSF as key elements of the BM microenvironment in the HSPC-MSC communication network. In concordance, we incorporated as a “positive control condition” an input node representing the Toll-like receptor ligand (lTLR) lipopolysaccharide (LPS), that binds TLR4 and triggers the conventional and well-known NF-κB- dependent pro-inﬂammatory response, promoting, among other transcriptional targets, the transcription of pro-IL-1β (Jones et al., 2001; Tak and Firestein, 2001; Wang et al., 2002; Khandanpour et al., 2010; Higashikuni et al., 2013). Downstream NF-κB, the expression of CXCR7 has been shown to be upregulated (Tarnowski et al., 2010), which in turn, down-regulates CXCR4 by heterodimerization, promoting its internalization and further degradation. In parallel, activated CXCR7 presents a higher aﬃnity for CXCL12 and β-arrestin, reducing CXCR4 signaling in CXCR7 and CXCR4 expressing cells (Uto-Konomi et al., 2013; Coggins et al., 2014). However, CXCR7 is unable to couple with G-protein, transducing through recruitment of β-arrestin and leading to MAP kinases Akt and ERK activation (Tarnowski et al., 2010; Uto-Konomi et al., 2013; Torossian et al., 2014). As with CXCR4, CXCR7, and VLA-4 activation in HSPC, PI3K/Akt pathway is activated on HSPC and MSC, via G-CSF receptor signaling (Liu et al., 2007; Vagima et al., 2009; Ponte et al., 2012; Furmento et al., 2014), and after LPS stimulation (Guha and Mackman, 2002; Wang et al., 2009; McGuire et al., 2013). Apparently, PI3K/Akt acts at overlapping levels on the modulation of inﬂammation. On the one hand, it increases the production of IL-1 antagonist molecules (Williams et al., 2004; Molnarﬁet al., 2005; Li and Smith, 2014) and inhibits secretion of mature IL-1β (Tapia- Abellán et al., 2014). On the other hand, it promotes nuclear translocation of the transcriptional factor Foxo3a (Brunet et al., 1999; Miyamoto et al., 2008; Park et al., 2008), down-regulating indirectly the transcription of antioxidant enzymes and enabling Frontiers in Physiology \| www.frontiersin.org 3 August 2016 \| Volume 7 \| Article 349 Enciso et al. Modeling CXCR4/CXCL12 Disruption in Acute Leukemia reactive oxygen species (ROS) accumulation, which in turn promotes maturation of pro-IL-1β and IL-1β secretion (Hsu and Wen, 2002; Yang et al., 2007; Gabelloni et al., 2013). At the mesenchymal counterpart, in addition to a number of molecules participating in the MSC-subsystem sensitivity to microenvironmental cues, we incorporated an input node representing Gap-junction conformed by connexin-43 (Cx43) that mediates direct intercellular communication between mesenchymal cells. Strikingly, its integral activity as calcium channel conductor has been shown to be a potent positive regulator of CXCL12 transcription and secretion (Schajnovitz et al., 2011). Furthermore, Cx43 expression appears to be critically disregulated in the BM stromal cells from acute leukemia patients, suggesting an important role in the hypothetic disregulation of the hematopoietic- stromal intercellular communication (Liu et al., 2010; Zhang et al., 2012). The inclusion of GSK3β and β-catenin in both subsystems was relevant due to their roles as intermediates of signaling transduction and regulation of the main intracellular communication elements proposed for our network reconstruction. The model is available in XML format (GINML) on GINsim Model Repository page (http://ginsim.org/models_ repository) (Chaouiya et al., 2012), under the title “HSPCs- MSCs. Communication pathways between Hematopoietic Stem Progenitor Cells (HSPCs) and MSCs.” Dynamical Modeling of the HSPC-MSC Network For the computational modeling of the HSPC-MSC complex system, we followed the standard steps to convert it into a discrete dynamical system, as described by Albert and Wang (2009) and Assman and Albert (2009). The Boolean approach is useful when quantitative and detailed kinetic information is lacking. In such a case, each node of the network is represented as a binary element, allowed only to have an “active” (ON) or “inactive” (OFF) state, numerically represented by 1 and 0, respectively. The activation state of each node is dependent on the activation state of its regulators, as described by Boolean functions, also called logical rules. The classical Boolean operators employed in Boolean functions are AND (&), OR (\|) and NOT (!). The AND operator is used to represent the requirement of the conjunction of two or more nodes participating in the regulation of a certain node (e.g., VLA-4 = CXCR4 & VCAM- 1 representing that VLA-4 optimal activation requires its ligand VCAM-1 and the signaling due to CXCR4 activation). When there is more than one node able to regulate another, but only one of them is suﬃcient to exert the eﬀect, the OR operator is applied (e.g., PI3K/Akt = GCSF \| ROS \| TLR representing that the activation of the G-CSF receptor, the increase of intracelular ROS concentration or the binding of a TLR ligand may activate PI3K/Akt signaling). Finally, the NOT operator represents repression of a node over another (e.g., IL-1 = (NF-κB & ROS) & !PI3K/Akt meaning that IL-1 requires the transcriptional activation of pro-IL-1 promoted by NF-κB and the post-transcriptional maturation mediated by ROS, but its signaling is inhibited by the presence of PI3K/Akt). Detailed compiling of reviewed references for the network reconstruction and the development of the logical rules can be found in Tables S1, S2. Given that each node in the network has an activation state, then the general state of a network at a given time t can be represented by a vector of n elements, where n is the number of nodes in the network. For example, the vector (00000010000000000100001000), represents a network state where only the 7th, 18th, and 23rd elements are active. In our model, this particular state represents the pattern of activation where only GSK3B_H, GSK3B_M, and VCAM1_M are active. Now, since we are implementing a dynamical system, it is necessary to specify how the network may evolve from a time t to t+1. There are two possible implementations to model the transition from one state of the network to another. On one side, the synchronous scheme update the activation state of all the nodes each time-step, assuming that all the biological processes involved in the model occur at similar time scales. And on the other side, asynchronous scheme update only one of the logical rules per time step, considering a more complex behavior of biological processes where molecular signaling is likely to change at diﬀerent time points depending on the nature of the interaction (Albert and Wang, 2009). Either one or another update scheme, take an initial combination of the nodes (initial state) and update the logical rules successively through an established number of time steps or until an steady state or attractor is reached. Attractors may be of a single state (ﬁxed point attractors) or a set of states (cyclic or complex attractors depending if they have one or more possible transition paths among their constituent states). The analysis of the nodes activation pattern in the attractors give the biological signiﬁcance of the computational simulations of the models (Albert and Wang, 2009; Assman and Albert, 2009). The dynamical behavior of the network was analyzed implementing the logical rules into BoolNet (R open-source package), and obtaining its attractors (stationary states) by applying asynchronous update strategies (Müssel et al., 2010). Under the asynchronous updating scheme, the simulation was performed using 50,000 random initial states, updating the network until either a ﬁxed point attractor or a complex attractor was reached. Conﬁdence of the model was tested through the simulation of all possible mutants (constitutive and null activation of every node) and the comparison of the resultant attractors with experimental reports about the biological eﬀects in vivo or in vitro after the use of antagonists or the generation of knock-in and knock-out models. Dynamical Multicellular Approach Assuming that every simulation beginning at a certain initial state of the network represents the dynamical proﬁle of a single cell, Wu and collaborators proposed a “population-like” analysis for a discrete model (Wu et al., 2009). Similarly, we asynchronously ran the simulations of the network from 50,000 random initial states, and then updated for 2000 time-steps, followed by calculation of the average activation value from 50,000 simulations for each node in each time-step. Such data was Frontiers in Physiology \| www.frontiersin.org 4 August 2016 \| Volume 7 \| Article 349 Enciso et al. Modeling CXCR4/CXCL12 Disruption in Acute Leukemia plotted as multi-cellular average activation graphs. Furthermore, we evaluated the eﬀect of a short (1 time-step) and a sustained (699 time-steps) temporary induction of lTLR in time-step 700 and 1400, and analyzed the dynamical eﬀects in the wild type network and in some relevant mutant networks. RESULTS Network Reconstruction The inferred HSPC-MSC network (Figure 1) constitutes the ﬁrst attempt to model relevant interaction axes between undiﬀerentiated hematopoietic cells and the BM microenvironment, that may approach us to a deeper understanding of the numerous molecular signals inﬂuencing the hematopoietic system regulation during normal and malignant processes. Our current ALL network has 26 nodes and 80 interactions. Among them, twelve nodes correspond to molecules that are expressed in HSPC and involved in intracellular signaling (PI3K/Akt, Gﬁ1, NF-κB, GSK3β, FoxO3a, ERK, β-catenin, and ROS) or cell-membrane receptors for communication with the microenvironment (CXCR4, CXCR7, VLA-4, and TLR). Eleven nodes conform the MSC subsystem, integrated by intracellular signaling molecules (PI3K/Akt, NF-κB, GSK3β, FoxO3a, ERK, β-catenin, and ROS), a gap- junction protein regulating communication among MSC (Cx43), communication ligands with HSPC (VCAM-1 and CXCL12) and TLR. Common internal nodes in both HSPC and MSC systems are representative molecules from the most studied pathways inﬂuencing proliferation, migration, survival, and -some of them- diﬀerentiation. Finally, the microenvironmental compartment is represented by G-CSF secreted by myeloid and stromal cells (Majumdar et al., 2000; Allakhverdi et al., 2013; Tesio et al., 2013; Boettcher et al., 2014), its inductor IL-1 which is secreted by MSC and HSPC, and lTLR so as FIGURE 1 \| Regulatory HSPC-MSC network. The network is constituted by three compartments represented with different geometric shapes: HSPC, MSC, and microenvironmental soluble factors. HSPC and MSC have intracellular nodes regulating the response and expression of elements mediating the communication between them. CXCR4-CXCL12 and VLA-4/VCAM-1 axes are suggested to be the most crucial communicating elements. HSPC and MSC are both susceptible of TLR stimulation with lTLR input. HSPC, hematopoietic stem and progenitor cell; MSC, mesenchymal stromal cell. Frontiers in Physiology \| www.frontiersin.org 5 August 2016 \| Volume 7 \| Article 349 Enciso et al. Modeling CXCR4/CXCL12 Disruption in Acute Leukemia TABLE 1 \| Logical rules used for HSPC-MSC modeling as a Boolean system on BoolNet. Node Logical rule Bcatenin_H !GSK3B_H CXCR4_H CXCL12_M & !(CXCR7_H \| GCSF \| Gﬁ1_H) CXCR7_H CXCL12_M & NfkB_H ERK_H ((CXCR4_H & PI3KAkt_H) \| CXCR7_H \| GCSF \| Gﬁ1_H \| ROS_H \| VLA4_H ) & !(FoxO3a_H \| GSK3B_H) FoxO3a_H (Bcatenin_H \| ROS_H) & !(ERK_H \| PI3KAkt_H) Gﬁ1_H (GCSF \| TLR_H) & !Gﬁ1_H GSK3B_H !PI3KAkt_H NfkB_H (TLR_H \| ROS_H \| (IL1 & PI3KAkt_H)) & !(FoxO3a_H) PI3KAkt_H ((CXCR4_H & CXCR7_H) \| GCSF \| ROS_H \| TLR_H \| VLA4_H) & !FoxO3a_H ROS_H IL1 & TLR_H & (!FoxO3a_H) TLR_H lTLR VLA4_H VCAM1_M & CXCR4_H Cx43_M Cx43_M Bcatenin_M !(FoxO3a_M \| GSK3B_M \| NfkB_M) CXCL12_M Cx43_M & !(Bcatenin_M \| GCSF \| NfkB_M) ERK_M GCSF \| ROS_M \| TLR_M FoxO3a_M (Bcatenin_M \| ROS_M) & !(ERK_M \| PI3KAkt_M) GSK3B_M !PI3KAkt_M NfkB_M (IL1 & PI3KAkt_M) \| (ROS_M & ERK_M) \| TLR_M ROS_M IL1 & TLR_M & (!FoxO3a_M) PI3KAkt_M GCSF \| ROS_M \| TLR_M TLR_M lTLR VCAM1_M !Bcatenin_M \| NfkB_M \| PI3KAkt_M lTLR lTLR IL1 ((ROS_M \| NfkB_M) & !PI3KAkt_M) \| ((ROS_H \| NfkB_H) & !PI3KAkt_H) GCSF IL1 Nodes representing molecules in HSPC are denoted with “_H” at the end of the node name, while nodes representing molecules in MSC are denoted with “_M.” Logical rules were constructed using the logical operators AND ( & ), OR ( \| ) and NOT ( ! ). The corresponding common names and genes ID are found in Table S3. to model a homeostasis disruption that is known to drive a pro-inﬂammatory signaling. Model inputs are Cx43 and lTLR, while the activation value of the other 24 nodes is dependent on the network topology and the initial state of the input nodes. All logical rules used for the computational simulation with BoolNet are shown in Table 1. Note that the logical rules for the input nodes include self-regulations, but these are for computational purposes to represent their sustained activation, rather than a biological reality. Attractors of the Wild-Type Network: Searching for the Relevance of TLR in the Biology of CXCL12 The asynchronous simulation of the Boolean model returned 4 attractors: 2 ﬁxed points and 2 complex attractors (Figure 2). The ﬁrst two attractors, ﬁxed point attractor 1 and 2, were identiﬁed with the physiological detached and attached state of the HSPC with its MSC counterpart, respectively. Both ﬁxed point attractors will depend on the initial states of both, TLR and Cx43. Thus, in the absence of lTLR, the ﬁnal fates will depend on the initial activation state of Cx43. However, once TLR is activated, ﬁnal fates are not contributed anymore from the activation state of Cx43. Loss of HSPC-MSC communication corresponding to a detachment state, is due to the absence of Cx43 and the consequent inactivation of CXCL12. In the activation pattern of this attractor, only VCAM-1 accompanied by GSK3β in both sub systems remained active (Tabe et al., 2007). On the contrary, when Cx43 is active (as in ﬁxed point attractor 2), CXL12 is expressed by the MSC, which in turn positively regulates the CXCR4 receptor required for the activation of the VLA- 4/VCAM-1 axis. The pattern in HSPC, correspond to ERK and PI3K/Akt activation, well-described elements downstream CXCR4 and VLA-4 (Tabe et al., 2007). β-catenin, a subject of debate about its function on stem cell maintenance, is turned on as a consequence of the GSK3β inhibition by PI3K/Akt (Dao et al., 2007). Complex attractors 1 and 2 share the same activation values in all nodes, except for the initial state of Cx43 which is an input and therefore may be consistently either active or inactive through simulation. Importantly, these two attractors have the node for ITLR active, so that under induced pro-inﬂammatory conditions the resultant perturbation of CXCR4/CXCL12 and VLA-4/VCAM-1 is exclusively dependent on CXCL12 down regulation in MSC by NF-κB. The network attractors are concordant with experimental observations (Ueda et al., 2004; Wang et al., 2012; Yi et al., 2012) with the exception of IL1 and GCSF inactivation although lTLR-induced NF-κB signaling in hematopoietic and mesenchymal compartments. In order to explain this discrepancy we may remark that an attractor is a stable network state or set of states, reached after the network went through a sequence of transient states where, in most biological systems, there is cross-pathway communication for modulating cellular response (Williams et al., 2004; Tapia- Abellán et al., 2014), so IL1 and GCSF could be activated in some transient states but down-regulated by other pathways responding to lTLR activation. Due to the existence of regulatory circuits among pathways, in the presence of ITLR there is an oscillatory behavior of ERK and Gﬁ1. Therefore, we applied the dynamic multicellular approach described by Wu et al. (2009) in order to have a deeper understanding of the HSPC- MSC model upon perturbations. The average activation value of 50,000 simulations for all nodes within the HSPC-MSC network was plotted and presented in Figure 3. The plots represent a qualitative approach for the analysis of the cell population trend under speciﬁc conditions. Considering that the initial activation values are randomly chosen, with exception of lTLR, TLR_M, and TLR_H which activation value was set to 0, the average initial activation value for the rest of the nodes correspond to 0.5. From time-step 0 to time-step 499 correspond to the stabilization of the dynamics. Of note, the plateau obtained around time- steps 500-699 corresponds to the average of the two ﬁxed point attractors. Frontiers in Physiology \| www.frontiersin.org 6 August 2016 \| Volume 7 \| Article 349 Enciso et al. Modeling CXCR4/CXCL12 Disruption in Acute Leukemia FIGURE 2 \| Asynchronous attractors from the wild type network. Dark color denotes an activation value of 1, while light color represents an activation value = 0. The blue, orange, and yellow colors distinguish the nodes in the three compartments in the HSPC-MSC network corresponding to HSPC, MSC, and microenvironmental factors, respectively. The last two attractors obtained when the initial states for the asynchronous simulation had lTLR value = 1, have two nodes (ERK_H and Gﬁ1_H) whose activation values oscillate and are responsible of the complex attractor. Oscillatory values are represented by intermediate blue color. Nodes representing molecules in HSPC are denoted with “_H” at the end of the node name, while nodes representing molecules in MSC are denoted with “_M.” Analysis of Transitory States Applied to a Multicellular Approach: from Pro-inﬂammatory Signals to CXCL12 Downregulation The short lTLR stimulation at time-step 700 and 1400 (Figures 3A–C) induces up-regulation of Gﬁ1 in HSPC (Figure 3A), and of NF-κB and PI3K/Akt in both HSPC and MSC compartments (Figures 3A,B). These nodes maintain a sustained activation as long as the lTLR is present (Figures 3D–F). In contrast, ERK, ROS and FoxO3a showed an increase but are regulated by other nodes, providing a feedback to basal values. Accompanying the cross-regulation of intracellular pathways, a decrease on CXCR4, CXCL12, VLA-4, and VCAM-1 activation is observed. As expected, there is positive signaling of the pro- inﬂammatory cytokines with a parallel co-increase of CXCR7, signals damped by PI3K/Akt and CXCL12 down-regulation, respectively. Model Validation by Mutant Analysis Listed in Table 2 are the observations from comparisons between the resultant attractors of simulations with null (“loss of function”) and constitutive expression mutants (“gain of function”), against the wild-type model. We focused on the activation value changes in the two axes of interest – CXCR4/CXCL12 and VCAM-1/VLA-4. Even though the nodes included in the reconstruction of the present model are well-studied elements of cell fate related-pathways, there is a lack of experiments correlating their perturbation with microenvironment modiﬁcations that impact HSPC behavior (Table 2, Table S4). Due to this missing data, and in order to validate the model, we now used available information of general alterations in hematopoiesis in the presence of lTLR. MSC ERK, FoxO3a, and PI3K/Akt nodes participating in CXCR4/CXCL12 and VCAM-1 VLA-4 axes regulation were not found in the revised literature. β-catenin in MSC has a role on osteoblastogenesis and its constitutive induced expression in osteoblasts in a mice model results in acute myeloid leukemia (AML) induction (Kode et al., 2014). The constitutive expression of β-catenin showed an outcome where, under non-induced inﬂammation, the CXCR4/CXCL12 axis is disrupted. This gives support to our hypothesis that CXCR4/CXCL12 is probably involved in the maintenance of leukemic cells. Furthermore, the dynamic multicellular approach in the gain of function of β- catenin in MSC, reproduced the recovery of VCAM-1 expression upon stimulation of lTLR as reported by Kincade in OP9 cells (Figure S1; Malhotra and Kincade, 2009). GSK3β inhibition in MSC has been known to function in the regulation of osteoblast and adipocyte diﬀerentiation. Besides, experimental eﬀect of a GSK3β-inhibitor on osteoblastogenesis has shown that the decrease of this kinase induces down- regulation of CXCL12 expression (Satija et al., 2013). The model is consistent with the unsteadiness of CXCL12 activation in the simulation of the mutant (Figures S2A,B). According to our hypothesis, a pro-inﬂammatory-induced CXCR4/CXCL12 disruption results in leukemic progression support. In the proposed model, overexpression of NF-κB disrupts the HSPC-MSC communication (Figure S2C). This is in agreement with the reported leukocytosis associated to up- regulation of NF-κB within BM MSCs from a mice model of high-fat diet (Cortez et al., 2013). Finally, modeling of a gain of function mutation in ROS resulted in the blocking of CXCL12 activation (Figure S2D). This is also in accordance of the recent report of oxidative damage induced by iron in MSC, resulting in down-regulation of CXCL12 expression and reduction of their hematopoietic supporting function (Zhang et al., 2015). Moreover, the iron-induced hematopoietic alterations previously observed by other groups, are attenuated by the treatment with ROS inhibitors (Lu et al., 2013). Nodes in HSPC which have been experimentally reported as dispensable for hematopoiesis, which did not show any alterations in the CXCR4/CXCL12 and VLA-4/VCAM-1 axes on the mutant simulations, are β-catenin (Figures S3A–D; Cobas et al., 2004; Jeannet et al., 2008) and CXCR7 (Figures S3E,F). Frontiers in Physiology \| www.frontiersin.org 7 August 2016 \| Volume 7 \| Article 349 Enciso et al. Modeling CXCR4/CXCL12 Disruption in Acute Leukemia FIGURE 3 \| Average activation value for intracellular HSPC nodes (A,D), intracellular MSC nodes (B,E) and communication axes among HSPC, MSC, and microenvironment (C,F). (A–C) Correspond to simulations with a short (1 time-step) stimulation of lTLR at time-steps 700 and 1400. (D–F) Correspond to simulations with lTLR stimulation at time-step 700 with a length of 699 time-steps. Nodes representing molecules in HSPC are denoted with “_H” at the end of the node name, and nodes representing molecules in MSC are denoted with “_M.” Gray area covers the stabilization time steps until attractors are reached. However, even though in vivo β-catenin null mutant HSPC does not lose long-term reconstitution capacity or multipotentiallity, its overexpression produces lose of stemness and diﬀerentiation blockage to erythroid and lymphoid lineages (Kirstetter et al., 2006; Scheller et al., 2006). Simulations of the gain of function of β-catenin resulted in the appearance of additional attractors where FoxO3a and GSK3β are increased (Figures S4A,B, S5B), suggesting a reduction in proliferation and/or apoptosis induction (Maurer et al., 2006; Yamazaki et al., 2006). In turn, the simulation of overexpression of FoxO3a showed a down- regulation of ERK and PI3K (Figures S4C, S5C). Also reported as proliferative repressors in HSPC (Hock et al., 2004; Zeng et al., 2004; Holmes et al., 2008), Gﬁ1 and GSK3β overexpression mutants inhibited ERK activation, and additionally Gﬁ1 induce the downregulation of PI3K/Akt node, CXCR4/CXCL12 and VLA-4/VCAM-1 axes (Figures S4 and S5). Disagreeing with experimental data (Holmes et al., 2008), GSK3β null mutant outcome result in an additional attractor where PI3K/Akt and ERK are inactive, notwithstanding CXCR4 and VLA4 activation (Figure S6). Of interest, NF-κB (Figure 4) and ROS (Figures S4F, S5F) constitutive expression in HSPC induce additional attractors with activation of IL-1 and G-CSF, and inhibition of axes regulating HSPC-MSC contact. A number of investigations on cancer cells report a correlation of NF- κB increased levels and CXCR4 (Richmond, 2002; Ayala et al., 2009; Shin et al., 2014). Nonetheless, a recent study in human leukemic cell lines has shown that LPS treatment increases MMP-9 activity, a metalloproteinase known to eﬃciently degrade CXCR4 and CXCL12 (Hajighasemi and Gheini, 2015). NF-κB Gain of Function Mutant as ALL Simpliﬁed Model How common alterations in ALL cells may induce BM microenvironment remodeling, regardless of the underlying Frontiers in Physiology \| www.frontiersin.org 8 August 2016 \| Volume 7 \| Article 349 Enciso et al. Modeling CXCR4/CXCL12 Disruption in Acute Leukemia TABLE 2 \| Results from the model outcome for single node mutations. Loss of function Node Model outcome Experimental evidence Bcatenin_H, CXCR7_H, ERK_H, FoxO3a_H, NfkB_H, ROS_H, Bcatenin_M, ERK_M, FoxO3a_M, NfkB_M, ROS_M, IL1, GCSF No changes in the CXCR4/CXCL12 and VLA-4/VCAM-1 axes with respect to the attractors from the wild-type model. Cobas et al., 2004; Jeannet et al., 2008; Sierro et al., 2007 CXCL12_M, CXCR4_H Loss of CXCR4/CXCL12 and VLA-4/VCAM-1 in the ﬁxed point attractor with active Cx43_M. Greenbaum et al., 2013; Sugiyama et al., 2006; Tzeng et al., 2011 Gﬁ1_H No changes in the CXCR4/CXCL12 and VLA-4/VCAM-1 axes. Stabilization of lTLR-dependent complex attractors with no activation of ERK_H . Hock et al., 2004; Zeng et al., 2004 GSK3B_H Additional ﬁxed point attractor when Cx43 is active, where FoxO3a_H is up-regulated and repressing PI3K_H and ERK_H. Also, are additional complex attractor in the presence of lTLR where FoxO3a_H inhibits PI3KAkt_H, ERK_H and NfkB_H activation. Holmes et al., 2008 PI3KAkt_H, PI3KAkt_M No changes in CXCR4/CXCL12 and VLA-4/VCAM-1 axes with respect to the attractors from the wild-type model. Under lTLR stimulation, pro-inﬂammatory cytokines turned on and in consequence ROS_H. In PI3KAkt_H null mutant, ERK_H is inhibited in every condition and FoxO3a_H is intermittently activated under lTLR stimulation. Williams et al., 2004; Champelovier et al., 2008; Xu et al., 2012 VLA-4, VCAM1_M PI3KAkt_H and ERK_H are turned off even if CXCR4/CXCL12 axis is active. Wang et al., 1998; Scott et al., 2003 GSK3B_M Fixed point attractors are lost and became complex attractors. Activation of Cx43, leads to two complex attractors of which one activates CXCR4/CXCL12 and VLA-4/VCAM-1 axes intermittently. In the absence of Cx43, two complex attractors are generated, and one of them unsteadily activate IL1 and GCSF. Satija et al., 2013 Gain of function Node Model outcome GSK3B_M, ERK_M, VCAM1_M, FoxO3a_M No changes in the CXCR4/CXCL12 and VLA-4/VCAM-1 axes with respect to the attractors from the wild-type model. NE (Not experimental evidence found) CXCR7_H, NfkB_H, Bcatenin_M, NfkB_M, PI3KAkt_M, GCSF, IL1 Loss of CXCR4/CXCL12 and VLA-4/VCAM-1 in the ﬁxed point attractor with active Cx43_M. Cortez et al., 2013; Kode et al., 2014 Bcatenin_H Under the activation of Cx43_M, an alternative steady state is reached where PI3KAkt_H and ERK_H are not expressed and instead, FoxO3a_H and GSK3B_H are active despite the activation of CXCR4_H and VLA4_H. Kirstetter et al., 2006; Champelovier et al., 2008 CXCL12_M Under lTLR stimulation, the complex attractors show a sustained activation of CXCR7_H. NE FoxO3a_H Bcatenin_H, ERK_H and PI3KAkt_H inactivation under any condition. Yamazaki et al., 2006 Gﬁ1_H Loss of CXCR4/CXCL12 and VLA-4/VCAM-1 in the ﬁxed point attractor with active Cx43_M. Stabilization of lTLR-dependent complex attractors. Hock et al., 2004; Khandanpour et al., 2013 GSK3B_H Inhibition of ERK_H and Bcatenin_H when CXCR4_H or lTLR are active. NE PI3KAkt_H Bcatenin_H remains active in the absence of Cx43 and lTLR. Wang et al., 2013 ROS_H, ROS_M Loss of CXCR4/CXCL12 and VLA-4/VCAM-1 in the ﬁxed point attractor with active Cx43_M. ROS_M overexpression mutant, activates PI3K_M, which in consequence inhibits FoxO3a_M. Lu et al., 2013; Zhang et al., 2015 VLA-4 Constitutive activation of PI3KAkt_H, ERK_H and Bcatenin_H. Schoﬁeld et al., 1998; Shalapour et al., 2011 genetic aberration, was investigated by running a dynamic multicellular simulation using the mutant network for NF- κB gain of function within the HSPC sub-system. The results shown in Figure 4 conﬁrm that NF-κB mutation in HSPC may perturb HSPC-MSC communication in parallel with the induction of other alterations previously reported in Frontiers in Physiology \| www.frontiersin.org 9 August 2016 \| Volume 7 \| Article 349 Enciso et al. Modeling CXCR4/CXCL12 Disruption in Acute Leukemia FIGURE 4 \| Dynamic multicellular simulation for a ALL simpliﬁed model addressed by NF-κB gain of function in HSPC. Average activation for intracellular HSPC nodes (A), intracellular MSC nodes (B) and communication axes among HSPC, MSC, and microenvironment (C). Nodes representing molecules in HSPC are denoted with “_H” at the end of the node name, while nodes representing molecules in MSC are denoted with “_M.” Gray area covers the stabilization time steps until attractors are reached. ALL cells, such as the increase of Gﬁ1 expression (Purizaca et al., 2013) and a pro-inﬂammatory milieu (Vilchis-Ordoñez et al., 2015). IL1 and G-CSF activation by HSPC up- regulate ERK, NF-κB and PI3K/Akt in MSC. As consequence of PI3K/Akt increase in MSC, β-catenin is up-regulated through the inhibition of GSK3β. Strikingly, the sustained activation of CXCR7 resulted as a consequence of NF- κB constitutive expression in HSPC and CXCL12 residual expression from MSC. CXCR7/CXCL12 axis was recently reported to be increased in ALL cells and a possible participation in abnormal cell migration was suggested (Melo et al., 2014). DISCUSSION According to the classical model of hematopoiesis, normal blood cells are replenished throughout life by stem and early progenitor populations undergoing stepwise diﬀerentiation processes in the context of intersinusoidal specialized niches (Purizaca et al., 2012; Vadillo et al., 2013). Cell cycle status, self-renewing capability and the central cell fate decisions depend, in great part, on the microanatomic organization and signals from the BM environment. Endosteal, perivascular and reticular niches provide support by cell-cell interactions and growth/diﬀerentiation factors that control the expression of lineage-speciﬁc transcription factors, among other elements. Within the reticular niche, mainly composed by CXCL12- abundant reticular cells (CARs), a special category of MSCs, the chemokine CXCL12 and its receptor CXCR4 play a pivotal role in the regulation of lymphopoiesis from the earliest stages of the pathway (Tokoyoda et al., 2004; Nagasawa, 2015). The transcription factor Foxc1 governs CXCL12 and stem cell factor expression, allowing the CAR niche formation for maintenance of HSC, common lymphoid progenitors, B cells, NK and plasmacytoid dendritic cells (Omatsu et al., 2014). The net balance of its disruption is instability of adaptive and innate immune cell production. Recent ﬁndings suggest that elevation of cytokines and growth factors, including G-CSF and TNFα, due to infectious stress, substantially reduce the expression of CXCL12, SCF and VCAM-1, further impairing primitive cell maintenance and prompting their proliferation and migration (Kobayashi et al., 2015, 2016). Much remains to be unraveled about CXCL12-related mechanisms of intercommunication damage that may favor growth of cancer cells at the expense of healthy hematopoiesis during biological contingencies such as hematological malignancies and biological stress. Although, genetic heterogeneity may be co-responsible for diﬀerences in ALL overall survival, response to treatment, diﬀerentiation-stage arrest or even predisposition to metastasis, a common need might be the development of biological features that provide pre-malignant cells decisive advantage over normal cells to compete for the same ecological niche. Given the importance of CXCR4/CXCL12 axis for homeostatic hematopoiesis and of its presumptive disruption in ALL BM, we now propose a Boolean model reconstructed with some of the most studied elements upstream and downstream this key communication axis. Our model shows its capacity to simulate several phenotypes relevant to ALL. According to previous experimental research, the major assumption made from this model is that the integrity of CXCR4/CXCL12 signaling, promoting the required activation of the VLA-4/VCAM-1 integrins interaction, is absolutely necessary for HSPC retention in the mesenchymal niche and in consequence, indispensable Frontiers in Physiology \| www.frontiersin.org 10 August 2016 \| Volume 7 \| Article 349 Enciso et al. Modeling CXCR4/CXCL12 Disruption in Acute Leukemia for optimal hematopoiesis regulation (Lévesque et al., 2003; Lua et al., 2012; Greenbaum et al., 2013; Park et al., 2013). The HSPC-MSC model asynchronous simulation in the absence of lTLR returned two attractors corresponding to HSPC attachment and detachment to MSC. The ‘attachment’ status, represented by the induction of CXCR4/CXCL12 and/or VLA-4/VCAM-1 axes, also exhibited PI3K/Akt and β-catenin activation within the HSPC compartment. Although there is some controversy about the β-catenin role in HSC regulation (Kirstetter et al., 2006; Duinhouwer et al., 2015), the co-activation of PI3K/Akt and β-catenin is known to promote self-renewal and HSC expansion (Perry et al., 2011). Two core pathways downstream CXCR4/CXCL12 binding are PI3K/Akt and ERK, both promoters of cell survival and regulators of proliferation. Considering that the mesenchymal stromal niche has being identiﬁed as the interface between the quiescence promoting osteoblastic niche and the vascular niche regulating ﬁnal lineage commitment and cell migration, the signals provided by mesenchymal cells should tightly regulate proliferation/expansion in order to further allow diﬀerentiation. According to this statement, the attractor representing the detached state conducts to pro-apoptosis signaling in the absence of aberrant expression of NF-κB, that relies on cytochrome C release- associated normal functions of GSK3β in HSPC (Maurer et al., 2006). By using elegant mice disease models and controlled culture systems, a wealth body of studies has recently highlighted the co- participation of inﬂammation and infectious stress in the HSPC exit from quiescence status, as well as in cancer etiology and progression (Baldridge et al., 2011; Vilchis-Ordoñez et al., 2015). Chronic inﬂammation and carcinogenesis have been closely connected via either a oncogenes-derived intrinsic pathway or through an extrinsic pathway from external factors that promote latent inﬂammatory responses involving signaling pathways such as MyD88, NF-κB, and STAT3 (Mantovani et al., 2008; Krawczyk et al., 2014). Interestingly, pattern recognition receptors (PRRs), including Toll-like receptors (TLRs) are functionally expressed from the most primitive stages of hematopoiesis and contribute to emergent cell replenishment in response to life-threatening infections or disease-associated cell damage (Nagai et al., 2006; Welner et al., 2008; Dorantes-Acosta et al., 2013; Vadillo et al., 2014). This phenomenon is called emergency hematopoiesis and is regulated at the most primitive cell level (Kobayashi et al., 2015, 2016). The potential relevance of this mechanism in leukemogenesis was the focus of this investigation, and our model allowed for the analysis of most behaviors observed under experimental settings. The discrete simulation of NF-κB constitutive expression mutant on HSPC, gave further support to our hypothesis on the perturbation of CXCR4/CXCL12 communication axis induced by pro-inﬂammatory microenvironment. The single mutation of NF-κB was suﬃcient to remodel the dynamical behavior of the three sub-systems represented, which was an unexpected behavior of the model. The dynamic analysis of the ALL- like network, also suggested the activation of an alternative communication pathway mediated by CXCR7 binding CXCL12. Inhibition of CXCL12 within the mesenchymal niche, may be fundamental for cell migration to adjacent BM structures unable to sustain proper diﬀerentiation or even to extramedullar tissues, accounting for a predictable role of this axis in metastasis. CONCLUDING REMARKS The proposed HSPC-MSC model is the ﬁrst systemic approximation to understand the intercommunication pathways underlying primitive cell retention/proliferation in the mesenchymal niche as a determinant factor for progression of hematological hyperproliferative diseases. We applied conventional discrete dynamical modeling and non-conventional population-like approaches as an average behavior of the network model. Future improvement of discrete dynamical modeling for ALL system will provide a powerful tool for investigation of unbalanced competitions between leukemic and normal hematopoietic cells within the BM. Overall, systems biology will advance our comprehensive view of the mechanisms involved in the pathogenesis of leukemic niches that may illuminate therapeutic strategies based on cell-to-cell crosstalk manipulation. AUTHOR CONTRIBUTIONS JE designed the work; generated, analyzed and interpreted data; wrote the paper. HM interpreted data; revised the work for intellectual content; wrote the paper. LM designed the work; interpreted data; revised the work for intellectual content; wrote the paper. RP designed the work; interpreted data; revised the work for intellectual content; wrote the paper. ACKNOWLEDGMENTS This work was supported by the National Council of Science and Technology (CONACyT) (Grant CB-2010-01-152695 to RP), by the Mexican Institute for Social Security (IMSS) (Grant FIS/IMSS/PROT/G14/1289 to RP) and by the “Red Temática de Células Troncales y Medicina Regenerativa” from CONACyT. LM acknowledges the sabbatical scholarships from PASPA-DAPA UNAM and CONACyT 251420. JE is scholarship holder from CONACyT and IMSS, and was awarded by the PRODESI IMSS Program. 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Frontiers in Physiology \| www.frontiersin.org 15 August 2016 \| Volume 7 \| Article 349	27594840	PI3KAkt_H = ( ( TLR_H ) AND NOT ( FoxO3a_H ) ) OR ( ( CXCR4_H AND ( ( ( CXCR7_H ) ) ) ) AND NOT ( FoxO3a_H ) ) OR ( ( VLA4_H ) AND NOT ( FoxO3a_H ) ) OR ( ( GCSF ) AND NOT ( FoxO3a_H ) ) OR ( ( ROS_H ) AND NOT ( FoxO3a_H ) ) CXCR4_H = ( ( ( ( CXCL12_M ) AND NOT ( CXCR7_H ) ) AND NOT ( GCSF ) ) AND NOT ( Gfi1_H ) ) TLR_M = ( lTLR ) GSK3B_M = NOT ( ( PI3KAkt_M ) ) ROS_H = ( ( IL1 AND ( ( ( TLR_H ) ) ) ) AND NOT ( FoxO3a_H ) ) FoxO3a_H = ( ( ( Bcatenin_H ) AND NOT ( PI3KAkt_H ) ) AND NOT ( ERK_H ) ) OR ( ( ( ROS_H ) AND NOT ( PI3KAkt_H ) ) AND NOT ( ERK_H ) ) ROS_M = ( ( IL1 AND ( ( ( TLR_M ) ) ) ) AND NOT ( FoxO3a_M ) ) ERK_H = ( ( ( CXCR4_H AND ( ( ( PI3KAkt_H ) ) ) ) AND NOT ( FoxO3a_H ) ) AND NOT ( GSK3B_H ) ) OR ( ( ( VLA4_H ) AND NOT ( FoxO3a_H ) ) AND NOT ( GSK3B_H ) ) OR ( ( ( Gfi1_H ) AND NOT ( FoxO3a_H ) ) AND NOT ( GSK3B_H ) ) OR ( ( ( CXCR7_H ) AND NOT ( FoxO3a_H ) ) AND NOT ( GSK3B_H ) ) OR ( ( ( GCSF ) AND NOT ( FoxO3a_H ) ) AND NOT ( GSK3B_H ) ) OR ( ( ( ROS_H ) AND NOT ( FoxO3a_H ) ) AND NOT ( GSK3B_H ) ) lTLR = ( lTLR ) VCAM1_M = ( ( NfkB_M ) OR ( PI3KAkt_M ) ) OR NOT ( PI3KAkt_M OR Bcatenin_M OR NfkB_M ) NfkB_H = ( ( TLR_H ) AND NOT ( FoxO3a_H ) ) OR ( ( ROS_H ) AND NOT ( FoxO3a_H ) ) OR ( ( IL1 AND ( ( ( PI3KAkt_H ) ) ) ) AND NOT ( FoxO3a_H ) ) FoxO3a_M = ( ( ( ROS_M ) AND NOT ( PI3KAkt_M ) ) AND NOT ( ERK_M ) ) OR ( ( ( Bcatenin_M ) AND NOT ( PI3KAkt_M ) ) AND NOT ( ERK_M ) ) Cx43_M = ( Cx43_M ) VLA4_H = ( VCAM1_M AND ( ( ( CXCR4_H ) ) ) ) NfkB_M = ( ROS_M AND ( ( ( ERK_M ) ) ) ) OR ( TLR_M ) OR ( IL1 AND ( ( ( PI3KAkt_M ) ) ) ) CXCR7_H = ( CXCL12_M AND ( ( ( NfkB_H ) ) ) ) Bcatenin_H = NOT ( ( GSK3B_H ) ) GSK3B_H = NOT ( ( PI3KAkt_H ) ) Gfi1_H = ( ( GCSF ) AND NOT ( Gfi1_H ) ) OR ( ( TLR_H ) AND NOT ( Gfi1_H ) ) ERK_M = ( ROS_M ) OR ( GCSF ) OR ( TLR_M ) GCSF = ( IL1 ) IL1 = ( ( NfkB_M ) AND NOT ( PI3KAkt_M ) ) OR ( ( ROS_M ) AND NOT ( PI3KAkt_M ) ) OR ( ( NfkB_H ) AND NOT ( PI3KAkt_H ) ) OR ( ( ROS_H ) AND NOT ( PI3KAkt_H ) ) TLR_H = ( lTLR ) CXCL12_M = ( ( ( ( Cx43_M ) AND NOT ( Bcatenin_M ) ) AND NOT ( NfkB_M ) ) AND NOT ( GCSF ) ) PI3KAkt_M = ( ROS_M ) OR ( GCSF ) OR ( TLR_M ) Bcatenin_M = NOT ( ( NfkB_M ) OR ( FoxO3a_M ) OR ( GSK3B_M ) )
The Author(s) BMC Bioinformatics 2017, 18(Suppl 4):134 DOI 10.1186/s12859-017-1522-2 RESEARCH Open Access Towards targeted combinatorial therapy design for the treatment of castration-resistant prostate cancer Osama Ali Arshad1,2 and Aniruddha Datta1,2* From Third International Workshop on Computational Network Biology: Modeling, Analysis, and Control (CNB-MAC 2016) Seattle, WA, USA. 02-Oct-16 Abstract Background: Prostate cancer is one of the most prevalent cancers in males in the United States and amongst the leading causes of cancer related deaths. A particularly virulent form of this disease is castration-resistant prostate cancer (CRPC), where patients no longer respond to medical or surgical castration. CRPC is a complex, multifaceted and heterogeneous malady with limited standard treatment options. Results: The growth and progression of prostate cancer is a complicated process that involves multiple pathways. The signaling network comprising the integral constituents of the signature pathways involved in the development and progression of prostate cancer is modeled as a combinatorial circuit. The failures in the gene regulatory network that lead to cancer are abstracted as faults in the equivalent circuit and the Boolean circuit model is then used to design therapies tailored to counteract the effect of each molecular abnormality and to propose potentially efficacious combinatorial therapy regimens. Furthermore, stochastic computational modeling is utilized to identify potentially vulnerable components in the network that may serve as viable candidates for drug development. Conclusion: The results presented herein can aid in the design of scientifically well-grounded targeted therapies that can be employed for the treatment of prostate cancer patients. Keywords: Prostate cancer, Gene regulatory networks, Boolean modeling, Combination therapy, Stochastic logic, Vulnerability assessment Background Prostate cancer is the most common noncutaneous male malignancy and one of the leading causes of cancer mor- tality in the western world [1]. The growth and pro- gression of prostate cancer is stimulated by androgens [2]. Androgens are male sex steroid hormones that are responsible for the development of male characteristics. Testosterone is the most important androgen in men. The effects of androgens are mediated through the androgen receptor (AR) [3]. The androgen receptor is a nuclear *Correspondence: datta@ece.tamu.edu 1Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA 2Center for Bioinformatics and Genomics Systems Engineering, Texas A&M University, College Station, TX, USA receptor, which is activated in response to the binding of androgens. Upon activation, it mediates transcription of target genes that modulate growth and differentia- tion of prostate epithelial cells. In malignant prostate cells, androgen signaling is deregulated and the homeo- static balance between the rate of cell proliferation and programmed cell death is lost. As prostate cancer relies on androgens for growth, the main line of treatment focuses on abrogating the action of androgens. Andro- gen deprivation therapy (ADT) in the form of surgical or medical castration is the cornerstone of treatment for prostate cancer [4]. Initially, androgen ablation induces significant regression of the tumor. However, the response to ADT is temporary and prostate cancer invariably stops responding to this treatment regimen, leading to a © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. The Author(s) BMC Bioinformatics 2017, 18(Suppl 4):134 Page 6 of 59 clinical condition that is known as hormone-refractory prostate cancer, androgen-independent prostate cancer or castration-resistant prostate cancer (CRPC). CRPC is a more aggressive and typically lethal phenotype where the tumor continues to grow in spite of the very low levels (<50 ng/ml) of circulating serum testosterone. Standard treatment options are limited and palliative docetaxel- based chemotherapy is generally used for patients who have become refractory to hormone treatment. How- ever, median survival time for patients following first-line chemotherapeutic treatment is just eighteen to twenty- four months [5]. There is therefore a clear rationale for advances in alternative therapeutics in order to evolve and expand the landscape of treatment options for malignant forms of prostate cancer that recur after abatement. Over recent years, there has been a significant effort towards furthering our understanding of the molecular mechanisms underpinning tumor development, growth and progression. It is now appreciated that in spite of castrate levels of androgens, the cancer cells are able to maintain persistent androgen receptor signaling through a variety of contributory mechanisms including AR gene amplification that results in overexpression of AR, gain- of-function mutations in AR which enable promiscuous activation of the receptor through other steroids or even in the absence of ligand binding, changes in AR co- activators and the expression of AR splice variants [6]. This compensatory response allows cancer cells to sur- vive in a low testosterone environment and the reactivated AR signaling axis continues to play a role after neo- plastic transformation. Additionally, certain androgen- independent cellular signaling pathways that promote proliferation and inhibit apoptosis, have been critically implicated as drivers of continued progression of prostate cancer. Hence, accumulating evidence indicates that the growth and progression of prostate cancer is a compli- cated process that involves interaction between multiple pathways. Advances in our knowledge of the biology of prostate cancer has led to the development of a number of novel therapies designed to target signaling pathways involved in disease progression. With the exception of cer- tain androgen synthesis and AR signaling antagonists that have received regulatory approval, these advanced agents are under various stages of clinical trials [7]. Castration-resistant prostate cancer is a complex mal- ady. Given the inherent complexity of the CRPC signal- ing cascade, there is no one dominant molecular driver across all tumors and hence no single drug can act as a “magic bullet” by being uniformly effective for treat- ing the malignancy [8, 9]. At best, limited benefit will be derived from targeting a single molecule. Rational com- binations of signal-modulating therapeutic agents have higher likelihood of yielding better outcomes. While there are several drugs being tested on cell lines, most of these studies focus on a single pharmaceutical agent and very few of those experiments involve trying out drug com- binations. Furthermore, prostate cancer is a markedly heterogeneous disease, with different tumors varying in their composition and makeup. In other words, different tumors will harbor different malfunctions in the signaling pathways. Thus, tailored targeted therapies based on indi- vidual tumor characteristics are required to maximize the potential benefits from treatment. Mathematical and computational modeling plays a piv- otal role in systems biology in elucidating biological insights from large-scale biomolecular signaling networks that are not amenable to straightforward intuitive inter- pretation. A diverse array of formalisms have been pro- posed in this domain as suitable representations for complex multicomponent networks such as cellular signaling pathways [10]. Amongst these frameworks, Boolean network models [11, 12] have emerged as an extremely useful parameter-free approach to cap- ture the qualitative behavior of extensive genetic net- works wherein knowledge of kinetic parameters is scarce. Boolean logic models have been successfully applied to study biological signaling networks and cellular processes [13, 14], for instance the cell cycle [15], apoptosis [16], the T cell survival network [17], hypoxia stress response pathways [18] and the gene regulatory network regulat- ing cortical area development [19]. In this paper, we use Boolean logic modeling of the key signaling pathways implicated in the development and progression of prostate cancer to simultaneously test various combinations of agents for their efficacy in attenuating cancer growth and design targeted therapies for the management of the dis- ease. In addition, we attempt to delineate components in the signaling network that can be pharmacologically manipulated to therapeutic advantage. Methods Prostate cancer signal transduction network Cellular processes such as growth and division are regu- lated by an interconnected network of molecules referred to as signaling pathways. Key cellular signal transduc- tion pathways known to play a major role in cell survival, growth, differentiation and the development of castration- resistance in prostate cancer are the Androgen Recep- tor (AR), PI3K/AKT/mTOR and Mitogen-Activated Protein Kinase (MAPK) pathways. The aberrant behavior of prostate cancer cells is characterized by dysfunction in these selective oncogenic signaling pathways promoting malignant characteristics. These pathways play a role in a diverse range of essential physiological cellular processes such as differentiation, survival, proliferation, protein synthesis and metabolism. Malfunctions in these path- ways are common in prostate cancer malignancies. For example, approximately 70% of advanced prostate cancers The Author(s) BMC Bioinformatics 2017, 18(Suppl 4):134 Page 7 of 59 have genomic alterations in the PI3K/AKT/mTOR path- way [20]. These three pathways are the most frequently over-activated pathways increasing survival of cancer cells and promoting cancer progression [21]. A schematic representation of these pathways is shown in Fig. 1 [22–24]. The pharmacologic agents depicted in red boxes in the figure are highly specific pathway inhibitors. These reagents modulate growth-factor receptors and the down- stream pathways abnormally activated in CRPC by target- ing with great specificity certain signaling nodes in the network. Boolean modeling of prostate cancer signaling In the context of methodologies that are applied to model cellular signal transduction networks, Boolean networks are probably the simplest where the state of each node in the network is either active (on) or inactive (off). In a Boolean network, the nodes are the genes and the edges represent the interaction amongst the genes. Since the molecules in a gene-regulatory-network (GRN) exhibit switch-like behavior, genes may be regarded as binary devices where a gene can be considered to be active if it is being transcribed and inactive if it is not. Moreover, the relationships amongst the genes may be represented by means of logical functions. Thus, a GRN is amenable to such a representation. The Boolean formalism is anal- ogous to a digital circuit where logic gates can be used to represent the regulatory relationships amongst the nodes and the activation level of the nodes is indicated by binary logic. The biological interactions amongst the various nodes (genes) represented in the gene regulatory net- work of Fig. 1 can therefore be translated to an equivalent Boolean circuit [25]. Let’s say either gene X or Y can acti- vate a third gene Z, then we can model this component of the signaling network with an OR gate with two inputs, namely X and Y and with output Z. Thus, the signaling network of Fig. 1 can be mapped to the combinational cir- cuit shown in Fig. 2. This digital logic circuit represents our multi-input multi-output (MIMO) systems model of the prostate cancer signaling transduction network. Cancer is a disease of abnormal cell signaling caused by a breakdown in the normal signaling pathways leading to the loss of cell cycle control and uncontrolled cell prolifer- ation. These abnormalities in the signaling network can be represented as stuck-at faults [26]. A stuck-at fault is said to occur when a line in the network is permanently set to a fixed value of one (stuck-at-one fault) or zero (stuck-at- zero fault) with the result that the state of the line is stuck at the faulty value and no longer depends on the state of the signaling network upstream that drives that line Fig. 1 Prostate cancer signal transduction network. A schematic diagram of key signaling pathways deregulated in prostate cancer. Black and red lines represent activating and inhibiting interactions respectively whereas the red boxes depict prostate cancer drugs at their corresponding points of intervention in the network The Author(s) BMC Bioinformatics 2017, 18(Suppl 4):134 Page 8 of 59 Androgens (13) NKX3.1 (7) PTEN IGF NRG1 HBEGF EGF (3) IGFR1A/B (2) EFGR (1) EGFR ERBB2 (4) ERBB2/3 (6) Ras (5) GRB2/ SOS (8) IRS1 (9) PIK3CA (10) PIP3 (11) PDPK1 (16) Raf (17) MEK1 (19) TSC1/2 (20) RHEB (12) AKT (21) mTOR (18) ERK1/2 SP1 SRF-ELK1 (15) AR-AR TMPRSS2 PSA BCL2 CDK2- Cyclin E (24) p21 (23) BAD (22) RP6SKB1 Enzalutamide AZD5363 Temsirolimus BKM120 Cixutumumab Lapatinib AZD6244 (14) AR/HSP Fig. 2 Boolean model. Combinational circuit model of prostate cancer signaling pathways. Each node is assigned a numeric label in parentheses. These labels also serve to enumerate the fault locations with stuck-at-one and stuck-at-zero faults in black and red numerals respectively. The dotted arrows indicate the intervention points for the respective drugs i.e. the faulty line has a constant (1/0) value independent of other signal values in the circuit. A stuck-at-fault can occur either at the input or output of a gate. An example of a stuck-at-fault is given in Fig. 3. Suppose the input vec- tor is <abcd>= 1100. In this case, the output is 0. However, if there is a stuck-at-one fault at the output of the NAND gate with the same input vector as before, the output of the faulty circuit is one instead of zero. This notion of stuck- at-faults has immediate biological relevance: on account of mutations or other structural abnormalities, a gene might become dysfunctional and hence stuck at a partic- ular state irrespective of the signals that it is receiving from surrounding genes [27]. These biological defects can be abstracted as stuck-at faults. For instance, as discussed earlier, a diverse array of mechanisms engender persistent AR signaling in CRPC even with castrate serum levels of androgen. This constitutive (permanent) activation of the androgen receptor where the receptor remains active i.e. continues to signal downstream even in the absence of androgens can be represented as a stuck-at-1 fault. By the same token, the inactivation in cancer of a tumor suppres- sor, which acts as a molecular brake on cell growth in a normal cell, can be represented as a stuck-at-0 fault. From our Boolean circuit model, we can explicitly enumerate the different locations where a fault can occur. These fault locations are numbered in Fig. 2 with the stuck-at-0 and 1 X a = 1 b = 1 c = 0 d = 0 0/1 Fig. 3 Circuit with stuck-at fault. An example of a stuck-at fault. In the absence of the stuck-at fault, the output is zero. If there is a stuck-at-one fault at the location marked with a cross, the output of the faulty circuit becomes one The Author(s) BMC Bioinformatics 2017, 18(Suppl 4):134 Page 9 of 59 stuck-at-1 faults in red and black numerals respectively. There is a total number of 24 possible fault locations. The objective is to counteract the effect of these faults by targeted drug intervention, so we incorporate the drugs in our model. The drug intervention points are illustrated in Fig. 2 which are the locations of the molecules that these prostate cancer drugs are known to target. Since the drugs inhibit the activity of their target i.e. the main mechanism of action of the anti-cancer drugs is to cut off downstream signaling, their action is incorporated in our model as an inverted input to an AND gate with the result that whenever the drug is applied, the gene that it targets is turned off. Simulation for fault mitigation with drug intervention We can now use our Boolean model to test different com- bination therapies in terms of their efficacy in mitigating the effects of the faults. For each fault, we would like to intervene with the best possible drug combination i.e. we want to determine which set of drugs would be most effec- tive in attempting to nullify the effect of that fault, thereby providing us with a targeted therapy based on the tumor signature. Define, the input vector as follows: INPUT = EGF, HBEGF, IGF, NRG1, PTEN, NKX3. 1, Androgens The first four components of this vector are growth fac- tors, which are external signals that stimulate a cell to grow and replicate. The next two input components, namely PTEN and NKX3.1 are tumor suppressors which act as molecular brakes on cell division. The last input vector component consists of the external hormones that stimulate the AR pathway in a normal prostate cell. The input vector is set to be [0000110]. This corresponds to all the external signals that stimulate cell growth being absent and the molecular brakes being active i.e. this input vector corresponds to a non-proliferative input which produces a non-proliferative output in the fault-free case. The output vector is defined to be: OUTPUT = SP1, SRF-ELK1, PSA, TMPRSS2, BCL2, CDK2-CyclinE The output vector consists of key markers of cell growth and proliferation in prostate cancer. In the fault-free sce- nario, a non-proliferative input to the regulatory network should produce a non-proliferative output characterized by the all-zero vector. However, faults in the network will produce a non-zero (proliferative) output even when the input is non-proliferative. The objective is to drive the faulty network’s output as close as possible to that of the fault-free circuit i.e. towards the all-zero vector through targeted drug intervention. Define, the drug vector as: DRUG VECTOR = Lapatinib, Cixutumumab, AZD6244, BKM120, AZD5363, Temsirolimus, Enzalutamide Each component of the drug vector is one if the corre- sponding drug is applied and is zero otherwise i.e. the ith bit of the drug vector is one if the drug is selected and zero if it is not. Thus, for example, the drug vec- tor [0010010] represents the combination of AZD6244 and Temsirolimus. Since, the total number of drugs is seven, the number of possible drug combinations is 128. The objective is to determine the best possible therapy for each fault. Each fault represents a different molecular abnormality and hence a tumor with a different profile. For each of the faults, the problem is to find the drug selection that can rectify the fault i.e. change the faulty output to the correct output. If that is not possible, the best drug vector will drive the output as close as pos- sible to the fault-free output. A simple metric that can be used as a distance measure to determine how far the output vector is from the fault-free vector is Hamming distance. Faults that produce an output vector with a greater Hamming distance from the correct output have more of the proliferative genes active and presumably a greater proliferative effect. Since the correct output is the all-zero vector, the Hamming distance of the output vector from the correct output is simply the Hamming weight of the output vector (for binary vectors Hamming weight is equivalent to the L1-norm). For each fault, we determine the output under every possible drug vector. The best therapy for that fault is the drug vector that produces the output with the smallest Hamming weight. In addition, since the drugs have deleterious side-effects, we would like to choose a drug combination with the fewest number of drugs. Thus, the best targeted therapy for each of the cancer-inducing faults is the one that under the presence of the fault, produces the best output with the smallest Hamming weight with the minimal number of drugs. To determine the best combination therapy across all faults, for each drug combination we determine the sum of the Hamming weights of the output vector across all possible combinations of faults and choose the drug com- bination that yields the smallest total. In order to keep the computation tractable, we restrict the number of possible faults in any fault combination to be no more than three i.e. up to three genes can be faulty simultaneously. We constrain the cardinality of the drug vector to be less than or equal to three, in essence limiting the number of drugs in the combination to three since on account of the harm- ful side-effects of the drugs, administering four or more cancer drugs simultaneously might not be prudent. Let us formalize the qualitative description above of the selection of best therapy for each fault and that of the overall optimal drug vector. For the Boolean network (BN) of Fig. 2, let N, M and P be the total number of primary inputs, primary outputs and fault locations respectively, then N=7, M=6 and P=24. Let x ∈X and z ∈Z be the input and output vectors respectively where X and Z The Author(s) BMC Bioinformatics 2017, 18(Suppl 4):134 Page 10 of 59 represent the space of all binary vectors of dimensions N and M respectively. Let x∗=[0, 0, 0, 0, 1, 1, 0] be the input vector corresponding to the non-proliferative input. Let D represent the total number of drug combinations (vectors) with no more than three drugs in any combina- tion, then D = 3 k=0 7 k . Denote each drug vector in the drug space as diwith i = 0, . . . , D −1 (d0 is the all-zero drug vector meaning no drug is applied). Let D be this space of drug vectors. Let C be the total number of fault combinations with no more than three faults in any combination, then C = 3 k=0 P k . Assign each fault combination in the fault space a label fj with j = 0, . . . , C −1 (f0 represents the fault-free case). Let F be this set of faults. Let ψ denote the mapping from a given input vector, drug combination and fault combination to an output vec- tor: x ∈X , d ∈D, f ∈F ψ−→z ∈Z i.e. ψ represents the output of the BN for a given input x when a drug combi- nation d is applied under fault scenario f . Let ψi be the ith component of this M-dimensional vector ψ. The best drug vector di, i ∈{0, 1, . . . , D −1} for each single fault fj, j ∈{1, 2, . . . , P} is the vector of smallest Hamming weight that minimizes ψ x∗, di, fj 1. The optimal drug combination across all faults is: d∗ i = arg min di C−1 j=1 ψ x∗, di, fj 1 (1) d∗ i is determined by exhaustive enumeration by explic- itly searching for the drug combination that for a non- proliferative input, minimizes the sum of Hamming weights (L1-norms) of the output vector across all possible combinations of faults. Node vulnerability assessment In electronic circuits, reliability refers to the probability of a circuit functioning as intended i.e. producing the cor- rect output. Reliability assessment is used to determine the vulnerability of a circuit to faults. A number of differ- ent techniques have been proposed for reliability analysis in digital circuits [28]. Recently, in [29] a scalable, effi- cient and accurate simulation-based framework based on stochastic computations was introduced for logic circuit reliability evaluation. In biological systems, dysfunctions in nodes in the signaling network cause deviation from normative behavior. Reliability assessment methodologies can be leveraged on Boolean network models of pathways to determine the vulnerability of the network to the dys- function of each node [30, 31]. In this section we conduct a stochastic logic based vulnerability analysis of the prostate cancer signal transduction network in order to discover the most vulnerable nodes thereby allowing us to priori- tize such segments in the network whose perturbation has the greatest potential to yield the most clinical benefit. In stochastic logic, signal probabilities are encoded in random binary bit streams (the signal probability of a node corresponds to the likelihood of that node having logic value one). For example, the binary sequence 0110010100 of length ten encodes the probability 0.4 since the propor- tion of ones in this sequence is 4 10. In practice, the length of the stochastic sequences typically used is much larger. Since the biological literature is devoid of precise lig- and binding probabilities, each primary input is assumed equally likely to be 0 or 1 i.e. all primary input signal probabilities are taken to be 0.5. Stochastic logic often makes use of Bernoulli sequences for the random binary streams where each bit in the stream is generated independently from a Bernoulli ran- dom variable with a probability of one equal to p. The use of probabilistic sequences inevitably introduces stochas- tic fluctuations which implies that the result produced is non-deterministic. These fluctuations can be signifi- cantly reduced by representing the initial input proba- bilities by non-Bernoulli sequences [32] defined as ran- dom permutations of sequences containing a fixed num- ber of ones and zeros. For a given probability p and sequence length L, a non-Bernoulli sequence contains a fixed number pL of ones, with the positions of the ones determined by a random permutation. Thus, for exam- ple, to represent the probability 0.5 by a non-Bernoulli stream of length 10, we could randomly permute the sequence 1111100000 which has five ones (instead of generating each bit from a Bernoulli random variable with p = 0.5 as would have been done to represent the same probability by a Bernoulli sequence). We use non-Bernoulli sequences of random permutations of fixed number of ones and zeros in order to encode the initial input probabilities. A logic circuit operating on stochastic bit streams (see Fig. 4 for an example), accepts as input random sequences representing the probability of each input being one and produces ones and zeros like any digital circuit [33] i.e. a stochastic logic circuit uses Boolean gates to operate on sequences of random bits. Each bit-stream represents a stochastic number interpreted as the proba- bility of seeing a one in an arbitrary position. Thus, the computations performed by such a circuit are probabilis- tic in nature. The output bit stream produced can be decoded as the probability of the output being one by counting the number of ones in the stream and dividing by its length. The vulnerability of a node is defined as the proba- bility that the system produces incorrect output if that particular node is dysfunctional (faulty) i.e. it is the proba- bility that the output of the network is different when that The Author(s) BMC Bioinformatics 2017, 18(Suppl 4):134 Page 11 of 59 0001111010 p1 = 0.5 1110000101 0111111101 p2 = 0.8 0110000101 0010100111 p3 = 0.5 0110100111 pout = 0.6 Fig. 4 A stochastic logic circuit. An example of a stochastic logic circuit node is dysfunctional and is the complement of reliability. The procedure to determine the node vulnerabilities is illustrated in Fig. 5 is as follows. We generate non- Bernoulli sequences of length L=1,000,000 in which exactly half of the bits are set to one at each of the seven initial inputs. The input stochastic sequences are propa- gated through both the original error-free circuit and the circuit in which the node of interest is dysfunctional. As discussed in the previous section, the dysfunction of a node is represented by a corresponding stuck-at fault of the requisite type at the particular location. This produces two sets of stochastic bit streams, one at each of the pri- mary outputs of the fault-free circuit and the other at the primary outputs of the unreliable circuit. The proportion of ones in the output bit stream encodes the output signal probabilities i.e. the probability of the output being one. Since the reliability of the circuit under the fault is the probability that the circuit output is same as that of the fault-free circuit, the sequence encoding the output reli- ability can be obtained from the output sequence of the faulty circuit by comparing it to the output sequence of the fault-free circuit and setting each bit to one whenever the corresponding bits in the sequences are the same and zero if they are different. The proportion of ones in this result- ing sequence will then correspond to the reliability of that output. Thus, we can obtain the stochastic sequence representing the reliability of each output by taking the XOR of each output bit stream of the faulty circuit with the complement of the corresponding output bitstreams of the fault-free circuit. For a circuit with multiple pri- mary outputs as is the case here, the stochastic sequence encoding the joint output reliability can be obtained by taking the stochastic AND of the outputs of the XOR gates as the stochastic AND operation on the output of XOR gates produces a one only if all the corresponding bits at each XOR gate are one i.e. if all the correspond- ing bits in the respective outputs of the fault-free and faulty circuit are same. We then take the complement of the bit stream at the output of this AND gate to obtain the stream that encodes vulnerability. This bit stream can then be decoded to determine the node vulnerability with the proportion of ones in this stream equivalent to the vulnerability of the node. The procedure for computing the vulnerability of a node described above and depicted in Fig. 5 is summarized as follows: Fig. 5 Computation of node vulnerability. Depicts the architecture used to compute the vulnerability of a node. x1 to x7 are the input stochastic bit streams for each of the seven primary inputs in the Boolean network model. The output bit streams for each of the six output components when these input sequences are propagated through the circuit with a dysfunctional node (whose vulnerability we want to compute) are denoted by y∗ 1 to y∗ 6 whereas those for the fault-free circuit are labeled as y1 to y6 The Author(s) BMC Bioinformatics 2017, 18(Suppl 4):134 Page 12 of 59 1. Generate non-Bernoulli streams encoding input probabilities at each of the primary inputs. 2. Propagate the input binary streams through the fault-free circuit and obtain a random bit sequence for each output. 3. Propagate the same input binary streams through the circuit with a stuck-at fault at the location of the node whose vulnerability we want to determine and again obtain a random bit sequence for each output. 4. XOR each primary output sequence from the faulty circuit obtained in step 3 with the complement of the corresponding primary output sequence from the fault-free circuit. 5. AND all the sequences obtained from each XOR gate. Take the complement of the stream so obtained. The vulnerability of the node is the fraction of ones in the resulting bit stream. Thus, in a nutshell, the node vulnerabilities are obtained by propagating the initial input stochastic bit streams encoding the input probabilities through both the faulty and fault-free circuit, comparing the respective outputs obtained from each and decoding probabilities from the resulting streams. Let x1, x2, . . . , xN represent input non-Bernoulli sequences of length L with each sequence represented as a vector of length L whose ith component is equal to the ith bit in the sequence. Define the L × N matrix X = (x⊤ 1 x⊤ 2 . . . x⊤ N). Thus, each row of this matrix con- tains the corresponding bits of each of the primary input streams. The vulnerability vj of node j ∈{1, 2, . . . , P} is given by: vj = 1 L L k=1 M i=1 ψi x = [Xk1, . . . , XkN] , d0, fj ⊕ψ′ i x = [Xk1, . . . , XkN] , d0, f0 ′ (2) where ′ is the bit-complement operator and ⊕is the binary XOR operator. Results and discussion Simulation results for drug intervention We use the Boolean network model to determine an appo- site therapy for each fault. As described in the methods section, the best targeted therapy for each of the cancer- inducing faults is the one that under the presence of the fault, produces the output with the smallest Hamming weight with the minimal number of drugs. The best ther- apy for each of the faults is shown in table 1 with the drug vector defined as before. Note that for certain faults, no drug vector can improve the output. Such faults are said to be untestable since no test (drug vector in this case) can Table 1 Best therapy for each fault Fault location Drug vector 1 1000000 2 1000000 3 0100000 4 1000000 5 0011000 6 0011000 7 0000100 8 0001000 9 0001000 10 0000100 11 0000100 12 0000100 13 0000100 14 0000001 15 0000001 16 0010000 17 0010000 18 0000000 19 0000010 20 0000010 21 0000010 22 0000000 23 0000000 24 0000000 rectify the fault. This is because there are no drugs on the fan-out of these genes. However, all these faults with the exception of fault 18 are minimally proliferative as they produce a faulty output with the least possible Hamming weight of one. Thus, there are many locations in the gene regulatory network of prostate cancer where malfunctions can occur resulting in a cancer that is different, requiring a specific targeted therapy. The table facilitates arriving at such a therapy as it maps each malfunction to an appropriate set of drugs. The look-up table can be used to devise ther- apies that have a higher likelihood of success since they are tailored specifically to the molecular abnormalities in critical pathways and thereby facilitates an individualized approach to therapy design. In order to find the best combination therapy across all possible faults, as discussed in the methods section, for each drug combination we determine the sum of the Hamming weights of the output vector across all pos- sible combinations of faults and choose the drug com- bination that yields the smallest total. This gives us the drug cocktail of AZD6244, AZD5363 and Enzalutamide The Author(s) BMC Bioinformatics 2017, 18(Suppl 4):134 Page 13 of 59 as a combination therapy for advanced prostate cancer. In a recent study, the drug combination of AZD5363 and Enzalutamide has demonstrated an impressive response in prostate cancer models [34]. Moreover, AZD6244 in partnership with an AKT pathway inhibitor (analogous to AZD5363), has been proposed as a strategy for the treatment of CRPC [35]. Thus, we propose that the aforementioned drug triad which represents a horizon- tal blockade approach, wherein combination therapy is used for the concerted pharmacologic inhibition of mul- tiple compensatory pathways, as a therapeutic modality that may attenuate prostate cancer survival and growth. Node vulnerabilities Using the framework delineated in the methods section, we quantify the vulnerability of different nodes. The vul- nerability values obtained are given in Table 2. Vulnera- bility assessment can be used to identify candidates for targeted drug development. Nodes whose vulnerabilities are higher should be presumably better targets for drugs since potentially therapeutic benefit is more likely for nodes which are more vulnerable. We observe that the Table 2 Node vulnerabilities Node Vulnerability (%) 1 6.25 2 6.25 3 6.25 4 6.25 5 6.25 6 6.25 7 24.98 8 6.25 9 6.25 10 24.98 11 24.98 12 24.98 13 24.98 14 12.47 15 12.47 16 6.25 17 6.25 18 6.25 19 1.57 20 1.57 21 1.57 22 1.57 23 1.57 24 24.98 AR-mediated signaling axis remains a valid target. Fur- thermore, we see that dysfunction in the AKT nexus and the loss of tumor-suppressors have higher vulnerability values so drugs that attempt to alleviate these aberra- tions should be efficacious in attenuating tumor growth. The design of anti-cancer therapeutics directed at the loss of tumor suppressors has been difficult [36]. Addition- ally, AKT-selective drug development is challenging due to its homology with other kinases [37]. These complica- tions notwithstanding, accelerated development of novel agents that target these aberrations is warranted. In con- trast, the vulnerabilities for certain nodes such as those in the mTOR axis are low indicating that they might not be attractive targets for drug development. Indeed, marginal clinical activity has been observed for mTOR inhibition with agents such as everolimus and temsirolimus failing to impact tumor proliferation in men with prostate cancer [4, 38]. Finally, in terms of the key pathways implicated in the disease we see that castration-resistant prostate can- cer shows most vulnerability on aggregate to dysfunction in the AKT pathway. In a study it was demonstrated that the AKT pathway dominates AR signaling in CRPC [39]. Conclusion Castration-resistant prostate cancer is a hormone refrac- tory phenotype of significant morbidity and mortality in the prostate cancer disease continuum where patients no longer respond to androgen ablation therapy. The biomolecular network representing the signaling path- ways involved in the pathogenesis of this lethal malig- nancy is translated to a digital circuit. The locations of possible malfunctions in the digital circuit are identified and computer simulation of the equivalent model is used to predict effective therapies that mitigate the effect of different faults. A prospectively attractive combinatorial therapeutic strategy for the constellation of abnormalities is to leverage an AR axis targeted agent in conjunction with reciprocal inhibitors of other dysregulated pathways that are fundamental in coordinately driving oncogene- sis. Proof of principle of clinical use for the proposed regimen remains to be demonstrated. A reliability (vulner- ability) analysis methodology of digital circuits premised on stochastic logic modeling is utilized to quantify the vul- nerability of the network to the dysfunction in discrete components in the signaling cascade thereby identifying key variables as targets for intervention that conceivably might be exploited by a new generation of novel thera- peutics. These findings can contribute to the development of new rational approaches for the possible treatment of androgen-refractory prostate cancer. There is however a paucity of companion predictive biomarkers that can be used for the stratification of patients based on molecular aberrations in order to prescribe the apposite treatment. Furthermore, the histological and clinical heterogeneity The Author(s) BMC Bioinformatics 2017, 18(Suppl 4):134 Page 14 of 59 of CRPC and the inherent redundancy along with the presence of feedback loops in pathways whose molecu- lar underpinnings in the context of the disease induction and development are not yet fully understood, tender any potential translation into objective clinical efficacy of therapeutic implications derived from computations fraught with challenges. Abbreviations ADT: Androgen deprivation therapy; AR: Androgen receptor; BCL2: B-cell lymphoma 2; BN: Boolean network; CDK2: Cyclin dependent kinase 2; CRPC: Castration resistant prostate cancer; EGF: Epidermal growth factor; GRN: Gene regulatory network; HBEGF: Heparin binding EGF-like growth factor; IGF: Insulin-like growth factor; MAPK: Mitogen activated protein kinase; MIMO: Multi-input multi-output; NRG1: Neuregulin 1; PSA: Prostate specific antigen; PTEN: Phosphatase and tensin homolog; SP1: Specificity protein 1; TMPRSS2: Transmembrane protease serine 2 Acknowledgements Not applicable. Funding Publication costs for this article have been funded by the National Science Foundation (NSF) under grant ECCS-1404314. This work was supported in part by NSF under grant ECCS-1404314 and the Texas Engineering Experiment Station (TEES) - Agrilife Center for Bioinformatics and Genomics Systems Engineering. Availability of data and materials Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study. Authors’ contributions OAA developed the computational modeling and simulations and wrote the manuscript. AD conceived the main idea. Both authors read and approved the final manuscript. Competing interests The authors declare that they have no competing interests. Consent for publication Not applicable. Ethics approval and consent to participate Not applicable. About this supplement This article has been published as part of BMC Bioinformatics Volume 18 Supplement 4, 2017: Selected original research articles from the Third International Workshop on Computational Network Biology: Modeling, Analysis, and Control (CNB-MAC 2016): bioinformatics. The full contents of the supplement are available online at https://bmcbioinformatics.biomedcentral. com/articles/supplements/volume-18-supplement-4. Published: 22 March 2017 References 1. 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Anal Cell Pathol. 2010;32:11–27. • We accept pre-submission inquiries • Our selector tool helps you to ﬁnd the most relevant journal • We provide round the clock customer support • Convenient online submission • Thorough peer review • Inclusion in PubMed and all major indexing services • Maximum visibility for your research Submit your manuscript at www.biomedcentral.com/submit Submit your next manuscript to BioMed Central and we will help you at every step:	28361666	IGFR1A/B = ( IGF ) RP6SKB1 = ( mTOR AND ( ( ( NOT Temsirolimus ) ) ) ) OR ( PDPK1 ) OR ( ERK1/2 ) p21 = NOT ( ( AKT ) ) mTOR = ( RHEB ) Ras = ( GRB2/SOS ) TMPRSS2 = ( AR/AR AND ( ( ( NOT Enzalutamide ) ) ) ) CDK2-CyclinE = NOT ( ( p21 ) ) Raf = ( PIK3CA AND ( ( ( NOT BKM120 ) ) ) ) OR ( Ras ) AR/AR = ( AKT ) OR ( AR/HSP ) EGFR/ERBB2 = ( EGF ) SRF-ELK1 = ( ERK1/2 AND ( ( ( RP6SKB1 ) ) ) ) MEK1 = ( Raf ) AR/HSP = ( Androgens ) AKT = ( ( NKX3.1 AND ( ( ( NOT PDPK1 AND NOT PTEN ) ) ) ) OR ( PTEN AND ( ( ( NOT PDPK1 AND NOT NKX3.1 ) ) ) ) OR ( PDPK1 ) ) OR NOT ( PDPK1 OR PTEN OR NKX3.1 ) PDPK1 = ( PIP3 ) GRB2/SOS = ( EFGR AND ( ( ( NOT Lapatinib ) ) ) ) OR ( EGFR/ERBB2 AND ( ( ( NOT Lapatinib ) ) ) ) OR ( ERBB2/3 AND ( ( ( NOT Lapatinib ) ) ) ) OR ( IGFR1A/B ) PIK3CA = ( Ras ) OR ( IRS1 ) OR ( ERBB2/3 ) ERK1/2 = ( MEK1 AND ( ( ( NOT AZD6244 ) ) ) ) SP1 = ( ERK1/2 ) ERBB2/3 = ( NRG1 ) PSA = ( AR/AR AND ( ( ( NOT Enzalutamide ) ) ) ) TSC1/2 = NOT ( ( AKT AND ( ( ( NOT AZD5363 ) ) ) ) ) PIP3 = ( ( PIK3CA ) AND NOT ( PTEN ) ) BCL2 = NOT ( ( BAD ) ) RHEB = NOT ( ( TSC1/2 ) ) EFGR = ( HBEGF ) OR ( EGF ) IRS1 = ( IGFR1A/B AND ( ( ( NOT Cixutumumab ) ) ) ) BAD = NOT ( ( AKT ) OR ( RP6SKB1 ) )
Logical modeling of lymphoid and myeloid cell specification and transdifferentiation Samuel Collombeta,1, Chris van Oevelenb,2, Jose Luis Sardina Ortegab,2, Wassim Abou-Jaoudéa, Bruno Di Stefanob,3, Morgane Thomas-Cholliera, Thomas Grafb,c,1, and Denis Thieffrya,1 aComputational Systems Biology Team, Institut de Biologie de l’Ecole Normale Supérieure, CNRS UMR8197, INSERM U1024, Ecole Normale Supérieure, Paris Sciences et Lettres Research University, 75005 Paris, France; bHematopoietic Stem Cells, Transdifferentiation, and Reprogramming Team, Gene Regulation, Stem Cells, and Cancer Program, Center for Genomic Regulation, Barcelona Institute for Biotechnology, 08003 Barcelona, Spain; and cUniversitat Pompeu Fabra, 08002 Barcelona, Spain Edited by Ellen V. Rothenberg, California Institute of Technology, Pasadena, CA, and accepted by Editorial Board Member Neil H. Shubin November 18, 2016 (received for review September 1, 2016) Blood cells are derived from a common set of hematopoietic stem cells, which differentiate into more specific progenitors of the myeloid and lymphoid lineages, ultimately leading to differentiated cells. This developmental process is controlled by a complex regulatory network involving cytokines and their receptors, transcription factors, and chromatin remodelers. Using public data and data from our own mo- lecular genetic experiments (quantitative PCR, Western blot, EMSA) or genome-wide assays (RNA-sequencing, ChIP-sequencing), we have assembled a comprehensive regulatory network encompassing the main transcription factors and signaling components involved in my- eloid and lymphoid development. Focusing on B-cell and macrophage development, we defined a qualitative dynamical model recapitulat- ing cytokine-induced differentiation of common progenitors, the ef- fect of various reported gene knockdowns, and the reprogramming of pre-B cells into macrophages induced by the ectopic expression of specific transcription factors. The resulting network model can be used as a template for the integration of new hematopoietic differ- entiation and transdifferentiation data to foster our understanding of lymphoid/myeloid cell-fate decisions. gene network \| dynamical modeling \| hematopoiesis \| cell fate \| cell reprogramming H ematopoiesis is the process through which all blood cells are produced and renewed, starting from a common population of hematopoietic stem cells (HSCs) (1). HSCs differentiate into lineage-specific progenitors with restricted differentiation potential and expressing specific surface markers (Fig. 1A). Loss- or gain-of- function experiments targeting transcription factors (TFs) or signaling components have led to the identification of factors re- quired for specific developmental steps. Some factors are required for the development of entire lineages (e.g., Ikaros for lymphoid cells), whereas others are needed only at late stages of cell-type specification (e.g., the requirement for the paired-box factor Pax5 after the pro–B-cell stage). These factors cross-regulate each other to activate one gene-expression program and silence alternative ones. Although cell commitment to a specific lineage was long con- sidered irreversible, recent reprogramming experiments emphasized the pervasive plasticity of cellular states. Indeed, the ectopic ex- pression of various regulatory factors (mainly TFs and signaling components) can enforce the establishment of new gene-expression programs in many kinds of differentiated cells (2). Strikingly, pluri- potency can be induced in somatic cells by forcing the expression of a handful of TFs, enabling further differentiation into any cell type (3). In the hematopoietic system, TF-induced transdifferentiation between erythroid and myeloid cells and between lymphoid and myeloid cells has been described (4). In this study, we focus on B-cell and macrophage specification from multipotent progenitors (MPs) and on TF-induced trans- differentiation between these lineages. Ectopic expression of the myeloid TF C/EBPα (CCAAT/enhancer-binding protein alpha, encoded by the Cebpa gene) can induce B cells to transdifferentiate into macrophages (Fig. 1A, red arrows) (5). C/EBPα is also required for the transition from common myeloid progenitors (CMPs) to granulocyte-macrophage progenitors (GMPs), and mutation in this gene can result in acute myeloid leukemia (6). Understanding the molecular mechanisms by which such factors can induce cell- fate decisions is of primary importance and might help in the development of novel therapeutic strategies. Computational modeling of regulatory networks is increasingly recognized as a valuable approach to study cell-fate decisions. In- deed, the integration of the available information about gene regulation into a common formal framework allows us to identify gaps in our current knowledge, as successfully shown in previous studies on the differentiation of hematopoietic cells (7). Dynamic analysis can reveal nontrivial properties, including transient phe- nomena, and can be used to identify key regulatory factors or in- teractions involved in the control of cell-fate commitment (8, 9). Furthermore, genome-wide approaches such as ChIP-sequencing (ChIP-seq) can unveil novel regulations to be further incorporated in a gene-network model (10). Here, we combined a logical mul- tilevel formalism, capturing the main qualitative aspects of the dynamics of a regulatory network in the absence of quantitative kinetic data (11), with a meta-analysis of all available ChIP-seq datasets for a selection of TFs, revealing tens of previously un- known regulations. We then performed iterations of computational simulations, followed by comparisons with experimental data and adjustments of the model, to identify caveats in our model and to test the effect of putative regulations in silico before confirming them experimentally (Fig. 1B). This paper results from the Arthur M. Sackler Colloquium of the National Academy of Sciences, “Gene Regulatory Networks and Network Models in Development and Evolu- tion,” held April 12–14, 2016, at the Arnold and Mabel Beckman Center of the National Academies of Sciences and Engineering in Irvine, CA. The complete program and video recordings of most presentations are available on the NAS website at www.nasonline.org/ Gene_Regulatory_Networks. Author contributions: S.C., C.v.O., J.L.S.O., T.G., and D.T. designed research; S.C., C.v.O., J.L.S.O., and B.D.S. performed research; S.C., W.A.-J., B.D.S., M.T.-C., T.G., and D.T. analyzed data; and S.C., J.L.S.O., W.A.-J., M.T.-C., T.G., and D.T. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. E.V.R. is a guest editor invited by the Editorial Board. Data deposition: The ChIP-seq data for EBF1 and Foxo1 in pre-B cell lines and during trans- differentiation have been deposited in the Gene Expression Omnibus (GEO) database (ac- cession code GSE86420). The final model has been deposited in the BioModels database (accession no. 1610240000). 1To whom correspondence may be addressed. Email: denis.thieffry@ens.fr, samuel. collombet@ens.fr, or thomas.graf@crg.eu. 2C.v.O. and J.L.S.O. contributed equally to this study. 3Present addresses: Department of Molecular Biology, Center for Regenerative Medicine and Cancer Center, Massachusetts General Hospital, Boston, MA 02114; Department of Stem Cell and Regenerative Biology, Harvard University, Cambridge, MA 02138; Harvard Stem Cell Institute, Cambridge, MA 02138; and Harvard Medical School, Cambridge, MA 02138. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1610622114/-/DCSupplemental. 5792–5799 \| PNAS \| June 6, 2017 \| vol. 114 \| no. 23 www.pnas.org/cgi/doi/10.1073/pnas.1610622114 Results Gene Network Controlling B-Cell and Macrophage Specification. To build a model of the gene-regulatory network controlling B-cell and macrophage specification from common progenitors, we first per- formed an extensive analysis of the literature to identify the TFs and signaling pathways controlling these events. The TF PU.1 (encoded by the Spi1 gene) is required for the normal development of both lymphoid and myeloid cells (12). The development of common lymphoid progenitors (CLPs) depends on the TFs Ikaros (encoded by Ikzf1) and E2a (encoded by the transcription factor 3 gene Tcf3) (Fig. 1A) (13, 14). The B-cell lineage is further con- trolled by Mef2c, the interleukine 7 receptor (IL7r), Ets1, Foxo1, Ebf1, and Pax5 (15, 16, 17). The specification of the myeloid GMPs depends on C/EBPα (6), which is regulated by Runx1 (runt-related transcription factor 1) (18). Macrophage specification further relies on the macrophage colony-stimulating factor (M-CSF) receptor (CSF1r), on the up-regulation of PU.1, and on Cebpb and the Id proteins (including Id2) (19, 20). The TFs Egr and Gfi1 repress each other to specify macrophage versus granulocyte lineages (21); Gfi1 also is important for B-cell differentiation (22). Finally, to distinguish among the different cell types, we further consider the B-cell marker CD19, the macrophage marker Mac1 (also called “Cd11b,” encoded by the Itgam gene), and the cytokine receptor Flt3, which is expressed specifically on MPs and CLPs. We then carried out an extensive review of the literature to collect information about cross-regulations between the selected factors and grouped these regulations into four classes, depending on the available evidence: (i) functional effect, e.g., an effect inferred from gain- or loss-of-function experiments (which could be either direct or indirect); (ii) physical interaction, e.g., TF binding at a promoter or enhancer; (iii) physical and functional evidence, suggesting a direct regulation; and (iv) fully proven regulation, e.g., evidence of functional effect and physical interaction along with reported binding-site mutations affecting the functional effect or reporter assays demonstrating cis-regulatory activity. Altogether, we gathered a total of 150 items of experimental evidence (Dataset S1) supporting 79 potential regulations (Fig. S1A). Many of these regulations are sustained only by functional evidence. To assess whether they could correspond to direct regulations, we analyzed public ChIP-seq datasets targeting each of the TFs considered in our network, amounting to 43 datasets for 10 TFs in total (Dataset S2). We systematically looked for peaks in the “gene domain” (23) coding for each component involved in the network (Materials and Methods). This ChIP-seq meta-analysis confirmed 26 direct regulations (Fig. 2A, green or red cells with a star) and pointed toward 66 additional potential transcriptional regulations (gray cells with a star). For example, at the Spi1 locus, we confirmed the binding of Ikaros at known enhancers, where it was previously reported to limit the expression of Spi1 together with a putative corepressor (24). Because we also found that Pax5, Ebf1, and Foxo1 bind to the same sites (Fig. 2B), we suggest that these factors could act as corepressors. Ectopic expression of Foxo1 in macrophages induced a reduction of Spi1 expression (Fig. S1B), further confirming this negative regulation. C/EBPα Directly Represses B-Cell Genes. We have previously reported that C/EBPα can enforce B-cell TF silencing by increasing the expression of the histone demethylase Lsd1 (Kdm1a) and the his- tone deacetylase Hdac1 at the protein level and that these enzymes are required for the decommissioning of B-cell enhancers and the silencing of the B-cell program (25). Because key B-cell regulators such as Foxo1, Ebf1, and Pax5 are repressed after 3 h of C/EBPα induction (Fig. S1C), we wondered whether C/EBPα could be di- rectly responsible for this early effect. To verify this hypothesis, we reanalyzed data from ChIP-seq for C/EBPα after 3 h of induction in a reprogrammable cell line (26). As expected, we detected binding of C/EBPα at the cis-regulatory elements of Foxo1 (Fig. 2C), Ebf1, Pax5, IL7r, and Mef2c genes (Fig. S1C), supporting their direct repression by C/EBPα. Furthermore, C/EBPβ also can induce transdifferentiation of pre- B cells (5), and it has been shown that C/EBPβ can rescue the formation of granulocytes in C/EBPα-deficient mice (27). Moreover, C/EBPβ almost always binds at C/EBPα-binding sites (Fig. 2A), as exemplified by the Spi1 locus (Fig. 2B). These findings suggest a A B literature Fig. 1. (A) Schematic representation of hematopoietic cell specification. Genes in red are required for progression at the corresponding steps. C/EBPα-induced transdifferentiation is indicated by red arrows from B-lineage cells to macrophages. (B) Iterative modeling workflow. A model is first built based on the literature and is used to predict dynamical behaviors (cell phenotype, differentiation, reprogramming, and so forth). Predictions then are compared with experimental data; when the predictions and experimental data agree, further predictive simulations are performed; when they do not agree, further regulations are inferred from ChIP-seq data and are integrated into the model until simulations fully agree with data. Collombet et al. PNAS \| June 6, 2017 \| vol. 114 \| no. 23 \| 5793 SYSTEMS BIOLOGY COLLOQUIUM PAPER redundancy between these two factors in the regulation of their target genes (at least in those considered here), and we integrated this redundancy in our model. Dynamical Modeling Using Multilevel Logic. The core components and regulations collected from our analysis of the literature and ChIP-seq datasets were assembled in a regulatory graph using the GINsim software (Fig. 3). Validating all the predicted regulations (Fig. 2A, gray cells with a star) experimentally would be a daunting task. Instead, we focused on a selection of these regulations (depicted by the gray arrows in Fig. 3) and used dynamical modeling to assess their impact on cell specification. To transform our regulatory graph into a predictive dynamical model, we took advantage of a sophisticated logical (multilevel) formalism. More precisely, we associated a discrete variable with each regulatory component. These variables usually take two values (0 or 1) but can be assigned more values whenever justified. Regulations are combined into logical rules using the Boolean op- erators NOT, AND, and OR, to define the conditions enabling the activation of each model component (Materials and Methods). This formalism relies essentially on qualitative information and allows the simulation of relatively large network models (encompassing up to a few hundred components). It should be noted that the value 0 does not necessarily imply that a factor is not expressed at all but rather that its level is insufficient to affect its targets significantly. PU.1 is the only factor for which we found clear evidence supporting a distinction between two functional (non-0) levels (21). Conse- quently, we assigned a ternary variable (taking the values 0, 1, or 2) to this node and assigned Boolean variables (i.e., taking the values 0 or 1) to the other nodes. Regarding the definition of the logical rules, we first considered the regulations supported by both functional and physical evidence (depicted as green and red arrows in Fig. 3). As a default, we re- quired that all activators but no inhibitor to be present to enable target activation and further adjusted the rules based on in- formation gathered from the literature (see the rules in Materials and Methods and Dataset S3). As mentioned before, we then added selected regulations inferred from our ChIP-seq meta-analysis (depicted as gray arrows in Fig. 3) to refine our model. Modeling Different Cell-Type Phenotypes. We first assessed whether our model properly accounts for progenitor, B-cell, and macrophage gene-expression patterns. Because stable states capture the long- term behavior associated with the acquisition of gene-expression patterns during cell specification, we computed all the stable states of our model using GINsim software (28) and compared them with gene-expression data (Fig. 4A) (29). We initially found that our stable states were largely inconsistent with known patterns of gene expression (Fig. S2A), revealing important caveats in the published data on which we based our model. A first caveat concerned the regulation of Cebpa. Indeed, Cebpa is not expressed in lymphoid cells, although its well-known activa- tors PU.1 (Spi1) and Runx1 are expressed in both B cells and Foxo1 Ebf1 Bcell Pax5 Bcell Spi1 Bcell Ikzf1 Bcell Cebpa B+Cebpa Cebpa GMP Cebpa Mac Cebpb Mac H3K27ac H3K27ac Spi1 Ebf1 Bcell Pax5 Bcell Spi1 Bcell Ikzf1 Bcell Cebpa GMP Cebpa Mac Cebpb Mac Pu1 Mac Runx1 Mac Gfi1 MP Runx1 MP Foxo1 Bcell Causal + - +/- Cebpa Cebpb Regulator Target Functional Func+Phy Physical Cd19 Pax5 Ebf1 Foxo1 Tcf3 Il7r Ets1 Mef2c Flt3 Ikzf1 Gfi1 Runx1 Spi1 Csf1r Cebpa Cebpb Egr2 Id2 Itgam Cd19 Pax5 Ebf1 Foxo1 Tcf3 Il7r Ets1 Mef2c Flt3 Ikzf1 Gfi1 Runx1 Csf1r Id2 Itgam * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Spi1 Egr2 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Data from ChIP-seq A B C 10kb 100kb * Fig. 2. (A) Heatmap showing the regulations inferred from the literature and from ChIP-seq meta-analysis. (B) ChIP-seq signals and peaks (under signal) at the Spi1 locus. Black frames indicate known enhancers (24). The vertical axes represent reads per million (RPM) (maximum: 2 RPM for Ebf1 and Ikaros, 1.5 RPM for Foxo1, 1 RPM for Runx1 and Gfi1, 5 RPM for other TF). (C) ChIP-seq signals and peaks (under signal) at the Foxo1 locus. Black frames indicate B-cell enhancers in which C/EBPα binding is detected. The vertical axes represent RPM (maximum: 2 RPM for Ebf1, 5 RPM for other TFs, 3 RPM for H3K27ac). Note that Pax5 and Ikaros peaks are located downstream of the first exon and all other peaks are upstream of the TSS. Mac1 Id2 Egr1 Cebpb Cebpa Csf1r Runx1 Gﬁ1 Ikzf1 Flt3 Mef2c Ets1 Il7r E2A Foxo1 Ebf1 Pax5 Cd19 Csf1 Spi1 Il7 Csf1r activated Il7r activated Fig. 3. A regulatory graph depicting the interactions inferred from the litera- ture and ChIP-seq meta-analyses. Nodes represent genes (except for CSF1r_act and Il7r_act, which represent the activated forms of cytokine receptors), and arrows denote regulatory interactions. Orange nodes represent factors expressed in macrophages, purple nodes represent factors expressed in progenitors, and blue nodes represent factors expressed in B-lineage cells. Ellipses represent Boolean components; the rectangle emphasizes the ternary component Spi1. Green and red edges correspond to activations and inhibitions, respectively. Gray edges denote the regulations predicted by the ChIP-seq meta-analysis, which were included in the model to increase consistency with expression data. 5794 \| www.pnas.org/cgi/doi/10.1073/pnas.1610622114 Collombet et al. macrophages. Therefore, our model exhibited only Cebpa+ stable states (Fig. S2A), suggesting that an inhibitory regulation of Cebpa was missing during lymphoid specification. Foxo1, a factor control- ling the early steps of B-cell commitment (30), stands as a relevant candidate. To test this hypothesis, we performed ChIP-seq for Foxo1 in our pre–B-cell line and observed binding at the Cebpa promoter, suggesting a physical interaction and potential direct regulation of Cebpa (Fig. S2B). To test if Foxo1 has a functional effect on Cebpa expression, we ectopically expressed it in a macrophage cell line (RAW) and found a significant down-regulation of Cebpa (Fig. S2C), suggesting a direct negative regulation of Cebpa by Foxo1. We therefore refined our initial model by including this additional regulation (see the rule associated with Cebpa in Dataset S3). A second caveat revealed by our model analysis concerned the regulation of Tcf3 (encoding E2a). Indeed, E2a was expressed in all the stable states, even after Cebpa repression by Foxo1 was in- cluded (Fig. S2D), although E2a has been shown to be expressed in MPs and in lymphoid cells but not in myeloid cells. Moreover, the only factor in our model expressed in MPs and regulating E2a is PU.1, which is also known to be expressed in myeloid cells, thus suggesting a missing regulation of E2a. However, despite our ef- forts, we could not find any evidence for a myeloid repressor of E2a in either the literature or our ChIP-seq data meta-analysis. Turning to putative activators of E2a, we focused on Ikaros. In- deed, like E2a, Ikaros is required for lymphoid development, and its knockout entails a loss of lymphocytes similar to that seen with E2a knockout. Interestingly, we found that Ikaros binds the E2a promoter in B cells (Fig. S2E), suggesting a direct activation of E2a by Ikaros. Hence, we further refined our model by including this regulation (see the rule associated with E2a in Dataset S3). More surprising was the high expression of Egr2 observed in pro/ pre-B cells. We also found expression of the related factor Egr1 in two different datasets (Fig. S2 F and G). It has been reported that Egr1/2 cross-inhibits Gfi1, the first favoring macrophage specifi- cation and the second favoring B lineage (21). However, although this study shows that Egr2 has an effect on the differentiation potential of MPs, it does not demonstrate that this factor is indeed not expressed in B cells or that it can antagonize the expression of B-cell genes. To assess the expression of Egr2, Egr1, and Gfi1 at the protein level, we performed Western blots for these proteins in B cells and macrophages. We were able to detect all three proteins in B cells (Fig. S2H), confirming the gene-expression data. We therefore propose that some late B-cell factors activate both Gfi1 and Egr2, overcoming their cross-inhibitions. Because Pax5 was the only B-cell factor found in our meta-analysis to bind to Gfi1 and Egr2 loci (Fig. 2A), we consider it to be an activator of both Gfi1 and Egr2 (see corresponding rules in Dataset S3). When analyzing the resulting refined model, we found that its stable states correspond well to CLPs, GMPs, B-lineage cells, and macrophages, as defined by the known patterns of gene expression (Fig. 4B). For some genes, we obtained apparent discrepancies between expression data and stable state values; these discrep- ancies can be attributed to model discretization (see SI Materials and Methods for more details). Our analysis points to previously unrecognized regulators of E2a and Cebpa that are important at the onset of lymphoid and myeloid specification and introduces refinements of the regulations of Egr2 and Gfi1. After incorporating these regulations in our model, we used it to study the dynamics of B-cell and macrophage specification. Specification of B-Cell and Macrophage Precursors from MPs. To improve our understanding of the transcriptional regulation of hematopoietic cell specification, we performed several iterations of hypothesis- driven simulations and comparisons with experimental data, fol- lowed by model modifications to solve remaining discrepancies. First, using GINsim software, we simulated the specification of MPs, defined by the expression of Spi1, Runx1, Ikzf1, Gfi1, and Flt3. In the absence of environmental signals, we found that our model can lead to two different stable states corresponding to GMPs and CLPs (Fig. 5A). Upon stimulation with both CSF1 and IL7, the system tends to two new stable states, corresponding to macro- phages and B lineage cells, respectively. These simulations thus re- capitulate the commitment of cells to GMP- and CLP-associated states and their loss of potential for alternative lineages. Next, using stochastic simulations (see Materials and Methods and ref. 31 for more details), we analyzed the evolution of the fraction of cells expressing distinct factors associated with specific cell lineages starting with the same initial state (MPs) and environmental con- ditions (initially no stimulation, followed by stimulation with Csf1 and Il7). Our results show two waves of gene activation for both myeloid and lymphoid factors. The first wave corresponds to the progenitor (GMP or CLP) expression programs, and the second one corresponds to terminally differentiated cells (macrophages or B cells) (Fig. 5B, Top and Middle). The evolution of the different cell populations (defined by the gene-expression signatures indicated in Dataset S4) was consistent with our logical simulations, with a rapid decrease of the MP population followed by the specification toward GMPs and CLPs and then by their differentiation into macrophages and B cells, respectively (Fig. 5B, Bottom). The proportions of myeloid and lymphoid cells were ∼75 and 25%, respectively, in qualitative agreement with the higher proportion of myeloid cells present in the bone marrow (32). Tentatively, this asymmetry could be encoded in the regulatory circuitry rather than merely being the result of differences in proliferation rates. A sensitivity analysis further revealed that the proportion of lymphoid and myeloid cells was affected only by changes in the up-regulation rates of Cebpa, Foxo1, and E2a (Fig. S2I), supporting the key function of Cebpa and Foxo1 in the commitment decision (E2a being required for Foxo1 expression). To obtain more comprehensive insights into the alternative trajectories underlying myeloid and lymphoid lineage specification, we clustered the logical states (Fig. 5A) to generate a hierarchical (acyclic) graph (28) in which all the states with a similar potential (i.e., leading to the same attractors or differentiated states) are Fig. 4. (A) Gene-expression values (microarrays) in lymphoid/myeloid pro- genitors (LLPP), B cells, and macrophages (Mac) (29). These values are relative to the highest expression value. (B) Context-dependent stable states computed for the model. A yellow cell denotes the inactivation of the corresponding com- ponent, a red cell represents maximal activation (1 for Boolean components, 2 for Spi1), and an orange cell represents an intermediate level (1) for Spi1. Collombet et al. PNAS \| June 6, 2017 \| vol. 114 \| no. 23 \| 5795 SYSTEMS BIOLOGY COLLOQUIUM PAPER clustered in a single node (Fig. 5C). Interestingly, this analysis shows that the cell decision between GMPs and CLPs depends mainly on the concurrent activation of Cebpa and Foxo1, em- phasizing the importance of these factors in early hematopoietic progenitor specification. Simulation of Documented Genetic Perturbations. Next, we simulated the effects of well-documented gene loss-of-function experiments on progenitor cell specification. Our simulations faithfully recapitulated the effects of various published gene-ablation experiments (Dataset S5). For example, Cebpa knockout in MPs results in the loss of the stable states associated with GMPs and macrophages (Fig. 5D), in agreement with the reported impact in vivo (33). Pax5 knockout does not affect the formation of the progenitors but blocks the de- velopment of the B-cell lineage at the pro-B stage and prevents the acquisition of the terminal B-cell marker Cd19 (Fig. 5E), in agree- ment with published experimental data (34). However, the simulation of Spi1 knockout does not reproduce the reported viability of B cells in Spi1-knockout mice (35). This discrepancy arose because, in our model, Spi1 is required for the expression of the B-cell factors E2a, Ebf1, and Il7r. Introducing additional cross-activations between the B-cell factors and releasing the requirement of Runx1 for Ebf1 up-regulation and of Mef2c for Il7r activation could rescue the expression of the B-cell factors. When we refined the corresponding rules accordingly (Dataset S3), the resulting model showed a stable state corresponding to B-cell patterns in the Spi1-knockout condition. However, such patterns cannot be reached from a Spi1−/−MP state, because the cells end up with a complete collapse of gene expression (Fig. 5F). Dynamical Analysis of Transdifferentiation. Next, we analyzed in silico the transdifferentiation of pre-B cells into macrophages upon C/EBPα induction. We first simulated the behavior of B cells under a permanent induction of C/EBPα in the presence of CSF1 and IL7. The system converged toward a single stable state corre- sponding to macrophages, which does not further require induction of exogenous C/EBPα (Fig. S3A), in accordance with published reports (5). We then focused on the effect of transient inductions of C/EBPα. We have previously shown with our β-estradiol–inducible pre–B-cell A C D B E F environmental Fig. 5. (A) State transition graph generated by simulating the model starting from the unstable MP state in the absence of cytokine (Upper) and after the addition of CSF1 and IL7 (Lower Left and Lower Right). Nodes denote states, and arrows represent transitions between states. (B) Stochastic simulations showing the evolution over time, before and after cytokine exposition, of the fractions of cells expressing specific macrophage factors (Top), B-cell factors (Middle), and cell-type signatures (Bottom). The x and y axes represent time (in arbitrary units) and fractions of positive cells, respectively. (C) Hierarchical transition graph corresponding to the state transition graph in A. Nodes represent clusters of states, and arrows denote the possible transitions between the clusters. The labels associated with the edges highlight the crucial transitions involved in the decision between B-cell and macrophage specifications. (D–F) Schematic representations and stochastic simulations of the effects of Cebpa knockout (D), Pax5 knockout (E), or Spi1 knockout (F) on the differentiation of MPs, compared with the wild-type situation in A and B. In the cartoons, the wild-type stable states (cell types) and transitions that are lost in each mutant are displayed using light gray arrows and shading. MP, B cells, and macrophages are represented in purple, blue, and red, respectively. 5796 \| www.pnas.org/cgi/doi/10.1073/pnas.1610622114 Collombet et al. line that a 24-h induction of C/EBPα followed by washout of the inducer was sufficient to trigger irreversible reprogramming (36). Shorter inducer exposure times led to the formation of two pop- ulations: one converting into macrophages, and the other initiating transdifferentiation but returning to a B-cell state. A simulation of this process testing all possible pulse durations at once (Materials and Methods) confirms that, depending on the duration of C/EBPα induction, B cells can be reprogrammed to macrophages or can go back to a B-cell state (the state transition graph for such simulations cannot be displayed because it contains more than 30,000 states). Aiming at identifying the commitment point of reprogramming, we further analyzed the resulting hierarchical transition graph (Fig. 6A). Because endogenous Cebpa becomes activated very late during transdifferentiation (at about 48 h; see Fig. S3B), notably after the commitment point (∼24 h), we focused on the Cebpa− states (i.e., with Cebpa = 0) leading to the sole macrophage stable state (Fig. 6A, Lower). Some of these states expressed Foxo1, suggesting that the inhibition of Cebpa by Foxo1 can be overcome, in contrast with what happens during the specification of GMPs and CLPs from MPs (Fig. 5C). Interestingly, we found that these Cebpa−states show low constraints on B-cell factors, because only Pax5 must be down-regulated. Furthermore, all Cebpa−states expressed Cebpb and Spi1 at a high level, whereas Pax5 was the only B-cell factor required to be inactivated. Finally, some states were found to be Csf1r−, but only when Gfi1 is silenced (along with its activator Ikaros, at least when its repressor Egr2 is not expressed), because Gfi1 can block high Spi1 expression (21). Turning to stochastic simulations, we observed the expected loss of B-cell and gain of macrophage phenotypes for both permanent and transient C/EBPα-induced expression (Fig. S3C). However, these more quantitative simulations also revealed some inconsis- tencies. (i) Cebpa is reactivated very rapidly; this discrepancy can be circumvented by lowering the kinetic rate of Cebpa up-regulation. (ii) The timing of the repression of B-cell genes and that of the loss of CD19 marker roughly coincide; however, we observed that B-cell genes are transcriptionally repressed very rapidly (after 3 h; see Fig. S1C), whereas CD19 protein is lost only after 24 h (36). (iii) Our model also does not properly capture the fact that short C/EBPα pulses result in the loss of CD19+ cells, which are regained after Cebpa inactivation (36), suggesting that reversion of reprogram- ming is possible after short induction. The last two points suggest that B-cell TFs are rapidly down- regulated at the transcriptional level but that the corresponding proteins are retained in transdifferentiating cells for longer times, facilitating reversion of the reprogramming. To address this possi- bility, we performed a ChIP-seq for Ebf1 at several time points upon permanent induction of Cebpa. Indeed, although Ebf1 RNA de- creased by 50% after 3 h of C/EBPα induction (Fig. S1C), we ob- served that Ebf1 binding was lost only after 24 h of induction (Fig. 6B). We therefore added a delay in B-cell factor protein degrada- tion to our model (Materials and Methods), resulting in a better fit with the observed timing of events during transdifferentiation for both permanent and transient C/EBPα induction (Fig. 6C). In conclusion, our analysis suggests an important role for the Egr2-Gfi1-PU.1– and C/EBPβ-PU.1–positive loops in the irre- versible commitment during transdifferentiation and emphasizes the importance of the balance between protein degradation and transcriptional regulation kinetics in the reversibility of the reprogramming. Simulations of Combined Perturbations During Transdifferentiation. Finally, we analyzed the effects of various TF gain-/loss-of-functions on Cebpa-induced reprogramming, combining C/EBPα induction with a knockdown of Spi1 or Cebpb or with a constitutive ex- pression of E2a, Ebf1, Pax5, Foxo1, or Gfi1 (Fig. 7). As pre- viously shown (26), only the Spi1 knockdown is able to block Ebf1(protein) E2a Foxo1 Ebf1 (gene) B cell Mac Ikzf1 Pax5 Cd19 1 0.75 0.50 0.25 0 1 0.75 0.50 0.25 0 1 0.75 0.50 0.25 0 +Cebpa A 0h 3h 12h 24h 0h 18h Ebf1 H3K27ac B cell Mac B cell Mac 1 0.75 0.50 0.25 0 Fraction of positive cells Time Bcell Bcell Mac basin of attraction basin of attraction +C/EBPa 6540 states 938 states 24 states B Cebpa negative states Id2 Egr2 Cebpb Cebpa Csf1r Spi1 Runx1 Gfi1 Ikzf1 Mef2c Ets1 Il7ra Tcf3 Foxo1 Ebf1 Pax5 Variable state C 0 1 0 or 1 5kb 0h 3h 12h 24h 0h 18h Ebf1 H3K27ac 0h 3h 12h 24h 0h 18h Ebf1 H3K27ac 20kb 10kb Fig. 6. (A, Upper) Hierarchical transition graph of the simulation of B-cell transdifferentiation upon transient C/EBPα expression, taking into account all possible C/EBPα pulse durations. Nodes represent clusters of states, and arcs correspond to transitions between these clusters. (Lower) Cebpa−states (rows) of the basin of attraction of the macrophage stable state. (B) ChIP-seq signals and peaks (under signal) in B cells (in blue, time point 0 h) and after induction of C/EBPα (at 3, 12, and 24 h). The vertical axes represent RPM (maximum, 5 RPM). (C) Stochastic simulations of the fraction of cells expressing different B-cell factors (Top Panel) and cell-population signatures (Lower Three Panels) during transdifferentiation upon permanent (Upper Two Panels) or transient (Lower Two Panels) C/EBPα ectopic expression. The corresponding induction durations (in arbitrary units) are indicated by the black lines above each panel. Collombet et al. PNAS \| June 6, 2017 \| vol. 114 \| no. 23 \| 5797 SYSTEMS BIOLOGY COLLOQUIUM PAPER transdifferentiation fully under permanent induction of C/EBPα. The analysis of the HTG obtained for transient C/EBPα induction in Spi1−cells indicates that, when Ebf1 is inhibited, the expression of all genes collapses (Fig. S3D). Cebpb knockdown does not block pulse-induced transdifferentiation, but then all committed cell states become Cebpa+, suggesting that Cebpb knockdown could impair commitment if C/EBPα induction is stopped before the reactivation of endogenous Cebpa; this hypothesis remains to be tested. Interestingly, the simulation of the constitutive expression of both Foxo1 and Pax5 results in states expressing a mixture of myeloid and lymphoid genes, pointing toward ab- errant reprogramming (Fig. S3E). Discussion Models of regulatory networks are classically built from detailed reviews of the literature. Despite the massive use of high- throughput assays in the last decade, taking advantage of such data for the construction of new models or to improve preexisting ones remains challenging. Here we combined a meta-analysis of ChIP- seq data with a dynamical model analysis to uncover important regulations. Such a meta-analysis requires an extensive manual curation of the datasets. It would be tempting to explore the different logical rules in a more unsupervised way by building all possible models with all combinations of regulations and testing their accuracy in silico. Although this approach has been used previously (37), it can be applied only to a subset of possible combinations (e.g., testing the addition or removal of regulations under a general logical rule, such as requiring all activators but none of the inhibitors to enable the activation of a component) and impose certain technical constraints (e.g., limitation to Boolean variables or to synchronous updating). In this study, we first built a model based on published data and then used it to identify caveats in our current knowledge; these caveats then were addressed by exploiting relevant high- throughput datasets. Our integrative modeling approach enabled us to clarify several aspects of the regulatory network controlling lymphoid and mye- loid cell specification. First, although E2a was known to be a master regulator of lymphoid cell specification [required for both B- and T-cell specification (38)], the mechanism of its activation remained unclear, as did the mechanism of its repression in mye- loid cells. In this respect, our analysis points to Ikaros as a main activator that is itself activated by Mef2c during lymphoid differ- entiation and repressed by Cebpa during myeloid differentiation. In our model, Flt3 is considered a mere marker of multipotent/ lymphoid progenitors. Although the Flt3 pathway has been shown to be required for lymphoid development and, more particularly, for the expansion of the CLP population, its impact on cell fate (i.e., beyond proliferation and cell survival) remains unclear. Likewise, ectopic Flt3 signaling has been shown to inactivate C/EBPα through posttranslational modifications (39), but it is unclear whether this inactivation occurs in physiological conditions. The Egr2 and Gfi1 cross-inhibitory circuit has been shown to be important in the early decision between macrophage and B-cell fates (21). Our analysis suggests that this circuit becomes irrelevant after B-cell commitment, enabling high expression of Egr2 in both pre-B and mature B cells. We therefore proposed that Pax5 can act as an activator of both factors, allowing their coexpression, al- though it is possible that other factors are involved also. Concerning the regulation of Cebpa, our work emphasizes the absence of known repressors in lymphoid cells. Ebf1 has been proposed to fulfill this function (40). However, the facts that CLPs lack myeloid potential and show no Cebpa expression and that a depletion of IL7R impedes the activation of Ebf1 but still allows B-cell specification until the pre-B stage (which is devoid of mye- loid potential) suggest that another factor acting more upstream represses Cebpa. Mef2c has been shown to counteract myeloid potential (15), but we could not detect any binding at the Cebpa locus. We therefore proposed Foxo1 as a candidate repressor. Thus, according to our model, commitment during normal differ- entiation of MPs would be controlled mainly by the Cebpa–Foxo1 cross-inhibitory circuit. Hence, Foxo1−/−CLPs could show some myeloid potential. However, other factors could be involved also. In particular, the delay in Cebpa re-expression during reprogram- ming (long after Foxo1 inactivation) suggests an additional mech- anism, possibly involving epigenetic modifications. Materials and Methods ChIP-Seq Meta-Analysis. ChIP-seq data were collected from public databases (Gene Expression Omnibus), and SRR (sequenced reads run) accession numbers were gathered in Dataset S2 and were automatically downloaded using the Aspera Connect browser plug-in. SRA (Sequence Read Archive format) files were converted in FASTQ using fastq-dump and were mapped onto the mouse mm10 genome using STAR version 2.4.0f1 (41) (see parameters in SI Materials and Methods). Duplicated reads were removed using picard (broadinstitute. github.io/picard/). Bigwig tracks were made using Deeptools bamcoverage (42). Peak calling was performed using macs2 (43). Gene domains were defined as in ref. 23, and promoter regions were defined as the TF start site −5 kb/+1 kb, extended up to the next promoter regions or up to 1 Mb in the absence of other promoter regions. Peaks to gene domain associations were performed using R. Gene Network Modeling and Simulations. The logical model of hematopoietic cell specification was built using GINsim version 2.9 software (44), which is freely available from ginsim.org. All logical simulations (leading to state transition graphs and hierarchical transition graphs) and computation of stable states were performed with GINsim. Stochastic simulations of cell populations were performed using MaBoSS (31). More detailed information can be found in SI Materials and Methods. The model can be downloaded from the BioModels database under accession number 1610240000 and from the logical model repository on GINsim website (ginsim.org). Constitutive expression Pulse Knock-down Cebpa SpI1 Cebpb E2a Ebf1 Foxo1 Gfi1 Pax5 Genotype Phenotype Model Experiment Ref all 0 B cell or all 0 Mac Mac Mac Mac Mac Mac B cell or Mac B cell or Mac B cell or Mac B cell or Mac Bcell or mixed state B cell or Mac Mac Mac Mac Dead ? Mac ? ? Mac (24h pulse) Mac Mac Mac Mac (24h pulse) ? ? B-cell (24h pulse) B cell or mixed state 5 26 26 36 B cell (24h pulse) 36 26 26 26 26 26 26 26 Fig. 7. Table summarizing the impact of selected perturbations (knockin or knockout) on B-cell transdifferentiation into macrophages (Mac) upon either a permanent or a transient induction of C/EBPα. Orange boxes represent macrophages, blue boxes B cells, gray boxes all 0 stable states or cell death. Two-color boxes denote alternative outcomes (stable states). 5798 \| www.pnas.org/cgi/doi/10.1073/pnas.1610622114 Collombet et al. Cell Culture. HAFTL (pre-B) cells and the C/EBPα-ER–containing cell derivative C10 were grown in Roswell Park Memorial Institute (RPMI) medium with L-glutamine supplemented with 10% (vol/vol) FBS, 1× penicillin/streptomycin, and 50 μM β-mercaptoethanol. The RAW 264.7 (ATCC TIB-71) macrophage cell line was grown in DMEM with L-glutamine supplemented with 10% FBS and 1× penicillin/streptomycin. Western Blot. Western blots were performed using C10 cells and RAW cells as previously described (22). More information can be found in SI Materials and Methods. The following antibodies were used at dilution of 1:1,000: Gfi1 (6C5 ab21061; Abcam), Egr2 (EPR4004 ab108399; Abcam), Egr1 (s-25, sc-101033; Santa Cruz), and GAPDH (6C5 sc-32233; Santa Cruz). ChIP-Seq. ChIP-seq experiments were performed as described previously (45). DNA libraries were prepared using Illumina reagents and instructions and were sequenced on an Illumina Hi-Seq 2000 system. Data are available on the Gene Expression Omnibus (GEO) database under accession codes GSE86420 (Ebf1 and Foxo1 ChIP-seq) and GSM1290084 (previously published Cebpa ChIP- seq in Cebpa-induced B cells). Ectopic Expression of TFs and Gene-Expression Quantitative PCR. Forced ex- pression of the B-cell TF Foxo1 in RAW cells was performed using retrovirus. More information can be found in SI Materials and Methods. ACKNOWLEDGMENTS. We thank the staff of the computing platform at the Institut de Biologie de l’Ecole Normale Supérieure for support in hard- ware and software maintenance; the flow cytometry facility at the Cen- ter for Genomic Regulation (CRG)/Universitat Pompeu Fabra for help with cell sorting; the genomics facility of the CRG for sequencing; and Anna Niarakis, Ralph Stadhouders, and Tian Tian for helpful com- ments regarding earlier versions of this paper. S.C. is supported by a scholarship from the French Ministry of Superior Education and Research. J.L.S.O. was supported by a grant from the Ministry of Economy, Industry, and Competitiveness (MINECO) (IJCI-2014-21872). B.D.S. was supported by a long-term fellowship from the European Molecular Biology Organiza- tion (EMBO) (#ALTF 1143-2015). The T.G. laboratory was supported by Grant 282510 from the European Union Seventh Framework Program BLUEPRINT and Fundacio la Marato TV3. 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PNAS \| June 6, 2017 \| vol. 114 \| no. 23 \| 5799 SYSTEMS BIOLOGY COLLOQUIUM PAPER	28584084	Runx1 = ( Spi1 ) Ebf1 = ( Ebf1_gene ) E2A_gene = ( Ikzf1 AND ( ( ( Spi1 ) ) ) ) Egr1 = ( Spi1_2 ) OR ( Spi1 AND ( ( ( NOT Gfi1 ) ) ) ) OR ( Pax5_protein_active ) Cd19 = ( CD19_gene ) IL7r_activated = ( IL7 AND ( ( ( IL7r ) ) ) ) CD19_gene = ( Pax5_protein_active AND ( ( ( NOT Cebpa ) ) ) ) Spi1 = ( Spi1 AND ( ( ( Runx1 ) AND ( ( ( NOT Cebpa AND NOT Csf1r_activated ) ) OR ( ( Gfi1 ) ) OR ( ( NOT Cebpb AND NOT Csf1r_activated ) ) ) ) ) ) OR ( Foxo1 AND ( ( ( Ikzf1 AND Ebf1 ) AND ( ( ( NOT Runx1 OR NOT Spi1 ) ) ) ) ) ) Ikzf1 = ( Pax5_protein_active ) OR ( Mef2c ) Pax5_gene = ( Ebf1 AND ( ( ( NOT Cebpa OR NOT Cebpb ) ) ) ) Cebpa = ( Cebpa ) OR ( Cebpa_gene ) Foxo1_gene = ( E2A_protein_active AND ( ( ( NOT Cebpa OR NOT Cebpb ) ) ) ) Spi1_2 = ( Runx1 AND ( ( ( Csf1r_activated AND Spi1 ) AND ( ( ( Cebpa OR Cebpb ) ) ) ) ) ) Cebpb = ( Spi1_2 AND ( ( ( Cebpa OR Cebpb ) ) ) ) E2A_protein_active = ( E2A AND ( ( ( NOT Id2 ) ) ) ) Ebf1_gene = ( E2A_protein_active AND ( ( ( Ebf1 AND Ets1 AND Pax5_protein_active AND Foxo1 ) AND ( ( ( NOT Cebpa OR NOT Cebpb ) ) ) ) ) ) IL7r = ( Spi1 AND ( ( ( Mef2c ) AND ( ( ( NOT Cebpa OR NOT Cebpb ) ) ) ) ) ) OR ( Ebf1 AND ( ( ( Foxo1 ) AND ( ( ( NOT Cebpa OR NOT Cebpb ) ) ) ) ) ) Mac1_gene = ( Spi1 ) Flt3 = ( Spi1 AND ( ( ( NOT Pax5_protein_active ) AND ( ( ( Ikzf1 ) ) ) ) ) ) Cebpa_gene = ( Spi1 AND ( ( ( Runx1 ) AND ( ( ( NOT Foxo1 ) ) ) ) ) ) Gfi1 = ( Ikzf1 AND ( ( ( NOT Egr1 ) ) ) ) OR ( Cebpa AND ( ( ( NOT Egr1 ) ) ) ) OR ( Pax5_protein_active ) Pax5 = ( Pax5_gene ) Foxo1 = ( E2A ) Id2 = ( Cebpb AND ( ( ( NOT Ebf1 AND NOT Gfi1 ) AND ( ( ( Cebpa AND Spi1 ) ) ) ) ) ) E2A = ( E2A_gene ) Mef2c = ( Spi1 AND ( ( ( NOT Cebpa OR NOT Cebpb ) ) ) ) Csf1r_activated = ( Csf1r AND ( ( ( Csf1 ) ) ) ) Csf1r = ( Spi1 AND ( ( ( NOT Pax5_protein_active ) ) ) ) Mac1 = ( Mac1_gene ) Pax5_protein_active = ( Pax5 AND ( ( ( NOT Id2 ) ) ) ) Ets1 = ( E2A_protein_active )
RESEARCH ARTICLE A model of the onset of the senescence associated secretory phenotype after DNA damage induced senescence Patrick Meyer1,2☯, Pallab Maity1,2☯, Andre Burkovski3,4☯, Julian Schwab3,4, Christoph Mu¨ssel3, Karmveer Singh1,2, Filipa F. Ferreira1, Linda Krug1,2, Harald J. Maier2, Meinhard Wlaschek1,2, Thomas Wirth5, Hans A. Kestler2,3☯‡, Karin Scharffetter- Kochanek1,2☯‡ 1 Department of Dermatology and Allergic Diseases, University of Ulm, Germany, 2 Aging Research Center (ARC), University of Ulm, Germany, 3 Institute of Medical Systems Biology, University of Ulm, Germany, 4 International Graduate School in Molecular Medicine, University of Ulm, Germany, 5 Institute of Physiological Chemistry, University of Ulm, Germany ☯These authors contributed equally to this work. ‡ These authors are joint senior authors on this work. hans.kestler@uni-ulm.de Abstract Cells and tissues are exposed to stress from numerous sources. Senescence is a protective mechanism that prevents malignant tissue changes and constitutes a fundamental mecha- nism of aging. It can be accompanied by a senescence associated secretory phenotype (SASP) that causes chronic inflammation. We present a Boolean network model-based gene regulatory network of the SASP, incorporating published gene interaction data. The simulation results describe current biological knowledge. The model predicts different in-sili- co knockouts that prevent key SASP-mediators, IL-6 and IL-8, from getting activated upon DNA damage. The NF-κB Essential Modulator (NEMO) was the most promising in-silico knockout candidate and we were able to show its importance in the inhibition of IL-6 and IL-8 following DNA-damage in murine dermal fibroblasts in-vitro. We strengthen the specu- lated regulator function of the NF-κB signaling pathway in the onset and maintenance of the SASP using in-silico and in-vitro approaches. We were able to mechanistically show, that DNA damage mediated SASP triggering of IL-6 and IL-8 is mainly relayed through NF-κB, giving access to possible therapy targets for SASP-accompanied diseases. Author summary The senescence associated secretory phenotype is developed by cells undergoing perma- nent cell cycle arrest. This phenotype is characterized by the secretion of a variety of fac- tors that facilitate tissue breakdown and inflammation and is therefore theorized to, in part, be causal for aging and age-related diseases. In recent years the SASP has been impli- cated in a variety of chronic inflammatory diseases. Due to these advances, it is imperative to better understand the dynamics of this cellular phenotype and to find ways to disrupt PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 1 / 30 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Meyer P, Maity P, Burkovski A, Schwab J, Mu¨ssel C, Singh K, et al. (2017) A model of the onset of the senescence associated secretory phenotype after DNA damage induced senescence. PLoS Comput Biol 13(12): e1005741. https://doi. org/10.1371/journal.pcbi.1005741 Editor: Paola Vera-Licona, University of Connecticut Health Center, UNITED STATES Received: November 28, 2016 Accepted: August 22, 2017 Published: December 4, 2017 Copyright: © 2017 Meyer et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. This plasmid (pCAG-Cre-T2A-mRuby2) can be obtained from the authors on request and was deposited in the Addgene repository (Accession ID 102989). Funding: KS-K is supported by the German Research Foundation (DFG, SCHA411/15-2) within the Clinical Research Group KFO142 “Cellular and Molecular Mechanisms of Ageing – From Mechanisms to Clinical Perspectives”, also by the it. We have developed a Boolean network incorporating the major signaling pathways of the SASP that allows us to specifically investigate interactions of the pathways and genes involved. We validated our model by reliably reproducing published data on the SASP. We utilized our model to uncover components that directly control the detrimental effects of the senescence associated secretory phenotype that are largely caused by IL-6 and IL-8, two major factors of the SASP in establishing and spreading senescence as well as causing local inflammation. In subsequent in-vitro experiments, we were able to verify our computational results and could suggest NEMO as one potential target for therapy of SASP-related diseases. Introduction Age-related diseases can be held accountable for the major part of morbidity and mortality in an ageing population. Additionally they cause a large proportion of yearly health costs [1]. Cellular senescence is one of the most prominent events that is likely to contribute to ageing. It refers to the irreversible cell cycle arrest that is essential when cells encounter detrimental changes. Once in permanent arrest, these cells are normally cleared by the immune system before they are able to do any harm to the organism [2]. However, some of these cells persist and develop a secretory phenotype releasing a variety of factors among which pro-inflammatory cytokines, chemokines and extracellular matrix degrading proteases are included. Together these shape the senescent- associated secretory phenotype or SASP [3–5]. While the SASP can cause chronic inflammation in tissue, it can also reinforce senescence in autocrine and paracrine manner [6, 7]. This feature of the SASP not only keeps senescent cells in their growth arrested states but it promotes senescence spreading to healthy bystander cells. Therefore, the SASP contributes to the accumulation of senescent cells during ageing, but also supports the emergence of age-related chronic diseases and tissue dysfunctions by elevating inflammatory processes [6, 8]. Major soluble factors that facilitate this bystander- infection of healthy cells are IL-6 and IL-8. Both have been shown to be important in the main- tenance and spreading of oncogene- and DNA-damage-induced senescence [3]. Also, both have been shown to be highly overexpressed by senescent cells and are known to locally and systemically play important roles in the regulations of a variety of processes in the aging body [3, 4, 9]. IL-6, in fact, most likely contributes to organ dysfunction during aging thus promot- ing frailty [8]. To allow for a deeper understanding of the SASP and the dynamics of its complex interac- tions a computational model of the Regulatory Network (RN) [10] and subsequent simulations can be insightful. RNs can be described by different mathematical models such as differential equations, Bayesian networks, and Boolean networks among others [11]. The Boolean network model [12, 13], as opposed to other model approaches, can be based on qualitative knowledge only. In gene-gene interaction, for example, the expression of a gene is regulated by transcrip- tion factors binding to its regulatory regions. The activation of a gene follows a switch-like behavior depending on the concentration of its transcription factors. This behavior allows common approximation of the possible states of a gene to be active or inactive [14, 15]. Ulti- mately, this can be encoded as Boolean logical values: true (“1”) or false (“0”). The interactions between genes, e.g. whether a factor acts as an activator, repressor or both can be described by functions. These Boolean functions are the basis to simulate dynamic behavior, i.e. changes over time. As every regulatory factor has two possible states (active or inactive) in a Boolean network model, 2x possible state combinations (i.e. gene activation patterns) exist for x genes. A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 2 / 30 Graduate Training Centre GRK 1789 “Cellular and Molecular Mechanisms in Ageing (CEMMA)”, and collaborative Project FKZ0315894A SyStaR - Molecular Systems Biology of Impaired Stem Cell Function and Regeneration during Aging, and Collaborative Research Centre CRC1149 Danger Response, Disturbance Factors and Regenerative Potential after Acute Trauma and the Fo¨rderlinie Perspektivfo¨rderung “Zellula¨re Entscheidungs- und Signalwege bei der Alterung” of the Ministerium fu¨r Wissenschaft, Forschung und Kunst Baden- Wu¨rttemberg, Germany. HAK is supported by the European Community’s Seventh Framework Programme (FP7/2007–2013) under grant agreement n602783, the DFG (SFB 1074 project Z1), and the German Federal Ministry of Education and Research (BMBF, Gerontosys II, Forschungskern SyStaR, project ID 0315894A and e:Med, SYMBOL-HF, ID 01ZX1407A) Competing interests: The authors have declared that no competing interests exist. For any activation pattern, iterative updates of genes in the network through consecutive appli- cation of the Boolean rules eventually lead to sequences of gene activation patterns that are time-invariant, called attractors. These attractors can correspond to observed expression pro- files of biological phenotypes or can be used to create hypotheses to further evaluate in wet-lab experiments [16, 17]. Different update strategies for the Boolean functions exist. Using a syn- chronous update strategy means applying all Boolean functions simultaneously, also assuming that regulatory factors interact independently of one another and that their interaction has a similar time scale resolution. Relaxing these assumptions leads to the concept of asynchronous updates where each Boolean function of is updated separately one at a time in any order. This allows a more direct modelling of different time scales. The asynchronous update strategy also usually generates trajectories that are different from those of synchronous Boolean networks. The state transition graph of an asynchronous Boolean network becomes a Markov chain which requires the additional definition of transition probabilities in each node of the state graph. Interestingly, point attractors (those with one state) in asynchronous Boolean networks are the same as those in synchronous Boolean networks. However, these networks can also show loose/complex attractors [18] which are part of active research [19, 20]. Another exten- sion of Boolean networks are probabilistic Boolean networks, which may define more than one Boolean function for regulatory factors where each function has a specific probability to be chosen for update. Although this concept may closer represent a biological system, it again requires parameter estimation for the probabilities. However, estimation of the probabilities naturally demands large amounts of interaction specific data which is, for larger networks, nei- ther economically, nor experimentally viable. In our case, we decided to focus on synchronous Boolean networks, partly due to their proven usability, and their ability to reveal key dynamical patterns of the modelled system. However, to strengthen our models’ hypothesis, we addition- ally performed in-silico experiments with an asynchronous update scheme (S1 Text). Synchronous Boolean networks have been used to model the oncogenic pathways in neuro- blastoma [21], the hrp regulon of Pseudomonas syringae [22], the blood development from mesoderm to blood [23], the determination of the first or second heart field identity [24] as well as for the modeling of the Wnt pathway [25]. The qualitative knowledge base that is neces- sary to reconstruct [26] a Boolean network model consists mostly of reports on specific inter- actions that describe local regulation of genes or proteins. Boolean network models utilize this knowledge about local regulations to reconstruct a first global mechanistic model of SASP. In summary, such a model allows to generate hypotheses about regulatory influences on different local interactions. These interactions, in turn, can be tested in wet-lab in order to validate the generated hypothesis and assess the accuracy of the proposed model. Here, we present a regulatory Boolean network of the development and maintenance of senescence and the SASP incorporating published gene interaction data of SASP-associated signaling pathways like IL-1, IL-6, p53 and NF-κB. We simulated the model and retrieved steady states of pathway interactions between p53/p16INK4A steered senescence, IL-1/IL-6 driven inflammatory activity and the emergence and retention of the SASP through NF-κB and its targets. This Boolean network enables the highlighting of key players in these processes. Simulations of knock-out experiments within this model go in line with previously published data. The subsequent validation of generated in-silico results in-vitro was done in murine der- mal fibroblasts (MDF) isolated from a murine NF-κB Essential Modulator (NEMO)-knockout system in which DNA damage was introduced. The NEMO knockout inhibits IL-6 and IL-8 homologue mRNA expression and protein secretion in MDFs after DNA damage in-vitro, possibly enabling at least a lowering of the contagiousness for neighboring cells and the pro- tumorigenic potential of the SASP. The model presented in this article allows a mechanistic view on interaction between the proinflammatory and DNA-damage signaling pathways and A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 3 / 30 thereby helps to gain insights into the dynamics of the SASP. Furthermore, it enables to gener- ate extensive hypotheses about possible knockout targets that can be experimentally tested and verified in-vitro. To the best of our knowledge, this report is the first one that combined in-sil- ico simulation of the SASP with its laboratory based experimental validation. Results The network model exhibits stable states for cell cycle progression and senescence The reconstruction of a Boolean network model for SASP requires screening for many candi- date interactions in published literature and data. Although the model, after reconstruction, may be reduced in the number of components [20, 27, 28], it would potentially hide some of the interaction targets and regulatory factors with regard to the signaling cascade. The regula- tory factors defined in this model are beneficial if one wants to extend the model and include additional related signaling pathways. The subsequent model must accurately correspond to the current understanding of the process at hand, i.e., able to predict well-known phenotypes of SASP. Biological phenotypes represent a long-term behavior of a biological system based on interaction of regulatory factors. In the same sense, attractors are the long-term behavior of a Boolean network model based on the Boolean rules of modelled regulatory factors. Hence, there is a natural correspondence between biological phenotypes and attractors in the Boolean network. In the following, we use figures that depict the signaling cascade towards an attractor as well as the attractor itself. The interpretation of these attractors in the context of SASP fur- ther allows generation of hypotheses that can be tested in a biological system. The information for the reconstruction of these networks was collected from published data. An overview of the genes incorporated in this model and their interaction can be found in Fig 1. The corresponding Boolean rules are listed in Table 1. The network depicts processes following a cell cycle arrest inducing action, such as DNA damage and other cellular stresses. Here, we analyze SASP under strong DNA damage and do not distinguish between different levels of DNA damage. We first analyzed if our model can render steady states for cell cycle progression when there is no stress signal input. Our data show a normal cell cycle progression with active CDK2 and CDK4, as well as phosphorylated Rb and hence an active E2F. No other signaling pathways that are implemented in this model were activated which can be seen as normal cell cycle pro- gression (Fig 2). Upon the outside signal DNA damage, we observe first the activation of the DNA damage response with a subsequent activation of p53 and p16INK4A signaling, leading to a stop in cell cycle progression and at a later time point to permanent cell cycle arrest. Simultaneously NF-κB signaling gets activated by the DNA damage response through NEMO, giving rise to beneficial but also detrimental effects of NF-κB like the senescence associated secretory phenotype (Fig 3). After entering p53/p21 and p16INK4A mediated permanent cell cycle arrest upon DNA damage, the activation of NF-κB leads to an increase of IL-1, IL-6 as well as IL-8 expression among others [29–33]. Our model shows the direct activation of these cytokines and chemo- kines by NF-κB after its activation through the DNA damage response and NEMO (Fig 3). The Boolean network describes published knock-out and overexpression phenotypes The NF-κB pathway has been studied extensively and there are knockout mice available for all proteins of the pathway, however some of them are embryonically lethal due to the importance A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 4 / 30 of NF-κB signaling in regulating development and apoptosis. We therefore focused on pub- lished in-vitro knockout and overexpression phenotypes. IL-6 and IL-8 are extremely impor- tant in maintaining and spreading the SASP in an autocrine as well as paracrine fashion. Hence, we followed the question what knockouts and/or overexpressions the Boolean network model suggests to inhibit the expression of IL-6 and IL-8 under the assumption of existing DNA damage. These simulations are included in S1 Text. Fig 1. Boolean network for gene regulation during cell cycle progression and the onset of cell cycle arrest after DNA damage. The overview shows the network wiring of the known gene regulations during DNA damage with a focus on the DNA damage repair/cell cycle arrest signaling. Cell cycle arrested cells over time show a tendency to develop a secretory phenotype that causes them to secrete high amounts of proinflammatory factors that can negatively influence neighboring cells. Major signaling pathways of these factors are included in this overview and in the Boolean network. Arrows indicate gene activation and inhibition is depicted as bar head. However, the interaction may be more complex and the corresponding Boolean rules are given in Table 1. https://doi.org/10.1371/journal.pcbi.1005741.g001 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 5 / 30 Table 1. Boolean network for gene regulation during cell cycle progression and the onset of cell cycle arrest after DNA damage. Boolean Rules using operators “&” (logical and), “\|” (logical or) and “¬” (logical not). DNA Damage/Senescence signaling Regulatory Factor at time t+1 Boolean rule update given regulatory factor state at time t DNA Damage, Defective Telomeres, etc. DNAD DNAD This rule serves as an input signal to any kind of severe DNA damage. Oncogene induced senescence Oncogene IL8 \| IL6 Active IL-6 or IL-8 signaling characterize the activation of Oncogene. Moreover, IL-6 and IL- 8 also required for oncogene induced senescence [3]. Hypoxia Hypoxia Exogenous factor describing Hypoxia. In presence of DNA damage, a cell activates regulatory factors ATR and ATM, which subsequently activate checkpoints CHK1 and CHK2. ATM DNAD ATM is active in presence of DNA damage [57–59]. CHK2 ATM ATM subsequently activates CHK2 [60]. ATR DNAD ATR is active in presence of DNA damage [57, 59]. CHK1 ATR ATR subsequently activates CHK1 [61]. p53 (CHK2 \| CHK1 \| ATM) & (¬MDM2) p53 can be activated by any of CHK1 [62], CHK2 [62, 63] or ATM [62, 64]. However, MDM2 is a strong inhibitor of p53 [62, 65]. HIF1 Hypoxia & (¬p53) HIF1, which is active during Hypoxia [66], is inhibited by p53 [67]. p21 p53 \| HIF1 p21 is activated by p53 [68] as well as by HIF1 [69]. CDK2 E2F & (¬p21) CDK2 requires activation of E2F. p21 inhibits the CDK2 complex [68]. RB ¬(pRB \| CDK4 \| CDK2) RB, which is active in its hypophosphorylated state (RB) is hyperphosphorylated and inactivated (pRB) by CDK4 and CDK2 [70–72]. pRB (CDK4 \| CDK2) RB is phosphorylated (pRB) in presence of any cyclin dependent kinases CDK4 and CDK2 [70–72]. E2F (pRB \| E2F) & ¬RB E2F is positively autoregulated and active in presence of hyperphosphorylated RB (pRB). Active RB, however, inhibts E2F [38]. MDM2 p53 & ¬ATM p53 activates MDM2 [65, 73, 74], while ATM inhibits MDM2 [64]. p16INK4 Oncogene \| DNAD Activation of p16INK4 depends on either DNA damage or Oncogene or both [75]. CDK4 ¬(p16INK4 \| p21) CDK4 is inhibited by p16INK4 [75] and p21 [68]. NEMO DNAD NEMO is activated by DNA damage [76, 77]. IKK NEMO \| NIK \| Akt IKK can be activated by any of NEMO [78], NIK [79] or Akt [80]. IkB (NFkB \|IkB) & ¬(IKK & NEMO) IkB is activated NFkB complex or IkB itself [81]. IKK [82] and NEMO [83] together are required to inhibit IkB. NFkB IKK & ¬IkB NFkB is activated by IKK, while inhibited by IkB [82, 83]. IL-1 signaling IL1 NFkB IL1 is activated by NFkB [29, 30]. IL1R IL1 IL1 binds to and activates IL1 receptor (IL1R) [84]. MyD88 IL1R MyD88 is an adaptor molecule in IL1-IL1R pathway and bridging IL1R to the IRAK complex IL1R [84]. IRAK IL1R \| MyD88 \| IRAK IRAK is autoactivated [85, 86] and also is activated by IL1R [84, 86] and MyD88 [85, 87]. TRAF6 IRAK TRAF6 is activated by IRAK [85]. TAB (TRAF6 \| IRAK) TAB is activated by any of TRAF6 [88, 89] or IRAK [89]. TAK1 (TRAF6 \| TAB) TAK1 is activated by any of TRAF6 [88, 89] or TAB [90]. MEKK TRAF6 MEKK is activated by TRAF6 [89]. MKK (TAK1 \| MEKK) MKK is activated by any of TRAK1 [91, 92] or MEKK [93]. JNK MKK & ¬MKP1 JNK is activated by MKK [94, 95] while is inhibited by MKP1 [96]. p38 MKK & ¬MKP1 p38 is activated by MKK [97] while inhibited by MKP1 [98]. cJun (p38 \| JNK \| ERK1_2 \| CEBPbeta) & cFos cFos is required for the action of cJun and can be activated by any one of p38 [99, 100], JNK [101], ERK1_2 [102] or CEBPbeta [103]. (Continued) A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 6 / 30 RelA binds with p50 to form a transcriptionally active heterodimer (called NFkB in this model). In its inactive state, it is bound with the inhibitor of kappa B (IκB) and resides in the cytoplasm. Upon NF-κB activation, the inhibitor is phosphorylated by the inhibitor of kappa B kinases (IKK) and degraded which releases the RelA/p50 heterodimer to translocate to the nucleus and regulate the transcription of target genes. To investigate the role of RelA on the expression of IL-8, we set NFkB = 0, simulating the ablation of the transcriptionally active het- erodimer (Fig 4). The predictions of the model simulations are consistent with knock-out experiments where the absence of RelA caused a significant reduction in IL-8 production in human fibroblast (IMR-90) [7]. We also simulated the overexpression of IκB by constantly activating IκB (IkB = 1) and could show an effect comparable to the knock-out of RelA (Fig 5). In our model the overex- pression of IκB leads to the inhibition of IL-8 and IL-6 expression which is in line with a previ- ously published report, where the overexpression of a non-degradable IκBα completely abolishes IL-8 production, among other soluble factors, in human epithelial and cancer cell lines [34]. Another promising knockout described by our network is inhibitor of nuclear factor kappa-B kinase subunit gamma also known as NEMO, which is able to prevent IL-6 and IL-8 expression after DNA damage activated the DNA damage repair apparatus and cell cycle pro- gression has been stopped in-silico (Fig 6). In studies with murine NEMO knockout models it has already been shown that murine embryonic fibroblasts (MEFs) isolated from these mice show reduced NF-κB activity and IL-6 secretion upon stimulation with typical NF-κB activa- tors like IL-1 and TNF [35]. Table 1. (Continued) DNA Damage/Senescence signaling cFos p38 \| JNK \| Elk1 \| CEBPbeta \| STAT3 cFos can be activated by any one of p38 [104], JNK [104], Elk1 [103, 105, 106], CEBPbeta [103] or STAT3 [107]. AP1 cJun & cFos AP1 complex consists of both cJun and cFos [104, 108]. MPK1 AP1 AP1 activates MPK1 [96, 109, 110]. IL8 NFkB \| AP1 \| CEBPbeta IL8 is activated by anyone of NFkB [31, 111, 112], AP1 [31] or CEBPbeta [3] signals. NIK TAK1 NIK is activated by TAK1 [91, 92]. IL-6 signaling IL6 (NFkB \| ERK1_2 \| CEBPbeta) IL6 is activated by anyone of NFkB [32, 33], ERK1_2 [113, 114] or CEBPbeta [3, 115] signals. IL6R IL6 IL6 binds to and activates IL6 receptor (IL6R) [88, 116]. GP130 IL6 GP130 is activated by IL6 [117, 118]. PI3K JAK PI3K is activated by JAK [119]. JAK IL6R & ¬SOCS3 Active IL6 receptor (IL6R) activates JAK [117], while JAK is inhibited by SOCS3 [120]. Akt PI3K Akt is activated by PI3K [121, 122]. mTOR Akt mTOR is activated by Akt [123]. SOCS3 STAT3 SOCS3 is activated by STAT3 [124]. GP130, MEK1_2, and ERK1_2 together depend all on the activation of IsL6 to form a cyclic signaling cascade MEK1_2 GP130 & IL6 MEK1_2 is activated by GP130 [116, 125] as well as IL6 [116]. ERK1_2 MEK1_2 & IL6 ERK1_2 is activated by MEK1_2 [126] and IL6 [127]. Elk1 ERK1_2 Elk1 is activated by ERK1_2 [128]. CEBPbeta Elk1 CEBPbeta is activated by Elk1 [103]. STAT3 JAK \| (cFos & cJun) \| mTOR STAT3 is activated by JAK [119] or mTOR [129]. Alternatively is can be activated in presence of both cFos and cJun [130]. https://doi.org/10.1371/journal.pcbi.1005741.t001 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 7 / 30 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 8 / 30 NEMO is essential for DNA damage triggered NF-κB activation Apart from being important for the assembly of the IKK-complex, NEMO also acts as a shuttle relaying the ATM-mediated DNA damage apparatus to cellular response mechanisms. Upon DNA damage ATM can bind NEMO and trigger its translocation from the nucleus to the cyto- plasm where it activates NF-κB signaling [36]. This in turn will help cells avoid clearance through apoptosis, increasing the number of long-term senescent cells in tissues and organs of the organism and might also increase and sustain the inflammatory potential of the SASP. In order to evaluate proposed knockouts NEMO was depleted from murine dermal fibro- blasts (MDFs) using a NEMO-floxed mouse line. These MDFs were isolated from murine skin and subsequently transfected with a Cre-recombinase coding plasmid including a fluorescence reporter construct (Fig 7). To purify NEMO knockout MDFs, these cells were FACS sorted two days post-transfection (S1A Fig). Successful NEMO knockout was assessed by PCR (S1B Fig) and western blot (S1C Fig). To study the effect of DNA damage, overnight-starved MDFs were treated with 25 μM etoposide, an established DNA damage and senescence inducer, for 3 h followed by a 24 h incubation period [37]. Afterwards cell media supernatant was taken and total RNA was isolated. We first measured p21 mRNA expression as an indicator for DNA damage and cell cycle arrest. Without a significant reduction of cell viability (Fig 8A), p21 mRNA expression was upregulated more than twofold in etoposide treated compared to untreated MDFs (Fig 8B). NEMO is of high importance for DNA damage mediated nuclear translocation of the NF-κB signaling molecule p65. As shown by immunofluorescence staining of untreated NEMO wildtype MDFs compared to etoposide treated wildtype and knockout MDFs, the translocation of p65 into the nucleus upon DNA damage is significantly increased in wildtype whereas it is brought down to the level of untreated wildtype MDFs when NEMO is knocked out (Fig 8C). NEMO mediates DNA damage induced expression and secretion of IL-6 and IL-8 As we have observed the effect of a NEMO knockout on the nuclear translocation of p65 and thereby activation of NF-κB, we further explored the possible suppressive effect on IL-6 and IL-8 activation. To achieve this we isolated total RNA and analyzed the mRNA expression of IL-6 and the murine homologues of IL-8 CXCL1 (KC), CXCL2 (MIP-2) and CXCL5 (LIX). Upon DNA damage, we observed a significant reduction in IL-6 mRNA expression with a strong downregulation in untreated knockout compared to untreated wildtype. An even stron- ger downregulation in etoposide treated NEMO knockout compared to wildtype MDFs was detected. Taken together a NEMO knockout could reduce DNA-damage mediated IL-6 mRNA expression by almost tenfold (Fig 9A). Next, we measured the secretion of IL-6. While there is nearly no secretion of IL-6 in untreated wildtype as well as knockout MDFs, a strong increase in IL-6 secretion occurred in etoposide treated wildtype MDFs, whereas the NEMO knockout MDFs only shows a small increase in secretion with a more than hundredfold reduc- tion when compared with etoposide treated wildtype cells (Fig 9B). We additionally analyzed the mRNA expression of three murine IL-8 homologues to assess the impact of a NEMO knockout on DNA damage mediated IL-8 expression. We found that all three chosen Fig 2. Naturally occurring network states. Without DNA damage the resulting network state is expected to show normal cell cycle progression. As shown here this includes the activation of CDK2 (t = 5) and CDK4 (t = 2) with a subsequent phosphorylation of RB (t = 3) leading to a release of E2F (t = 4) which will release the cell into cell cycle progression. The temporal sequence is shown as t = n. Active genes are shown as green, inactive genes as dark purple. https://doi.org/10.1371/journal.pcbi.1005741.g002 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 9 / 30 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 10 / 30 homologues were significantly downregulated in NEMO knockout MDFs compared to wild- type MDFs after DNA damage. The total expression of IL-8 homologues mRNA in NEMO knockout MDFs was reduced by at least fivefold when compared to treated wildtype MDFs (Fig 9C). There is detectable secretion of IL-8 homologues in untreated wildtype and NEMO knockout MDFs, however the secretion strongly rose upon etoposide treated in wildtype cells whereas there is no detectable increase in the NEMO knockout MDFs. This effect was similarly found for the studied IL-8 homologues KC and MIP-2 (Fig 9D). However, we did not find any significant alteration in the expression of two housekeeping genes, such as beta-actin and 18s rRNA in the NEMO knockout MDFs, compared with NEMO wildtype (S2A Fig). In addition, we also did not observe any significant alteration in the expression of a wide array of genes that were predicted by Boolean network not to be changed after NEMO knockout (S2B Fig). These data show the importance of NEMO and NF-κB signaling for the activation of IL-6 and IL-8 in the case of DNA damage. In early stages DNA damaged and cell cycle arrested MDFs most likely activate secretory SASP signaling through NF-κB rather than other stress pathways. Discussion In the model of DNA damage and proinflammatory signaling presented here we collected and combined previously published knowledge on major regulators of the SASP. Using this model, we identified attractors fitting cell cycle progression and cell cycle arrest as they physiologically occur. This suggests reliability of this model in terms of reproducibility of current biological knowledge. The network model allows us to time- and cost-effectively generate hypotheses and predict gene knockouts that may influence the outcome of the SASP in-vitro. In the process of modeling, we first created individual models of DNA damage and proin- flammatory signaling. In a next step, we fused these two sub-networks to the model presented here. In S1 Text, we analyzed the impact of integrating both pathways in one Boolean network model. Our results indicate that there is not only an effect of DNA damage in the proinflam- matory signaling but also vice versa. On one hand, we deduce a stabilization of the DNA dam- age response network as the integration of both sub-networks leads to a reduction of possible attractors (87 to 19). On the other hand, the inner dynamics of each sub-network stay intact, showing biologically reproducible signaling cascades (e.g. Fig 4). In the simulation without DNA damage, only activation of cell cycle regulation genes that facilitate cell cycle progression were observed [38]. In contrast, when we entered DNA damage into the network, we detected early activation of the DNA damage response (DDR) followed by a p53/p21 mediated cell cycle arrest and at a later time point the activation of proinflamma- tory signaling through NF-κB [39, 40]. We utilized the Boolean network to simulate knockout and overexpression states that have the power to inhibit both IL-6 and IL-8 activation, such as knockouts of ATM and RelA or the overexpression of IκBα, that have previously been pub- lished to decrease IL-8 or IL-6 expression and secretion in-vitro [7, 9, 34]. One of the most prominent knockout suggestions obtained was that of NEMO, which acts as an essential mod- ulator of NF-κB signaling and is a major link between DDR and NF-κB signaling [41]. There- fore, it is a suitable target to prevent NF-κB activation, while maintaining the repair potential of the DDR. Taken together these in-silico data suggest NF-κB to be one of the major SASP Fig 3. Naturally occurring network states upon DNA damage. Upon DNA damage the first response of the cell is the activation of ATM/ATR mediated DNA damage repair (t = 2) with a subsequent activation of p53- and p16-mediated cell cycle arrest (t = 3). The DNA damage signal is relayed by the DNA damage response through NEMO (t = 3) that in turn activates NF-κB signaling (t = 4) which will ultimately lead to the activation of IL-1, IL-6 and IL-8 signaling (t = 7). The temporal sequence is shown as t = n. Active genes are shown as green, inactive genes as dark purple. https://doi.org/10.1371/journal.pcbi.1005741.g003 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 11 / 30 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 12 / 30 activators in response to DNA damage activating all three mediators of proinflammatory sig- naling depicted in this network. For the sake of manageability, the model presented here was limited to a core set of path- ways involved in senescence and the SASP. Of course, the value of the results could still be enriched by adding even more components and additional pathways, such as a more detail view on CEBP-signaling, growth factor signaling and the expansion of cell cycle related signal- ing. This would enable to simulate an even deeper level of signaling involved in the SASP. Another factor that was not viewed in this work is the influence of the intensity levels and tim- ing of expression and stimuli on the outcome of the SASP. Physiologically occurring DNA damage, for example, is not an all or nothing event but rather comes in different levels and lengths of damage that can trigger a multitude of different reactions in the cell. In future works, it would be interesting to add these into the model. Such extension would allow simula- tions of the exact amount and timing of damage needed to trigger full-blown SASP rather than senescence. Furthermore, it would possibly reveal at which point the cell decides that it is ben- eficial to trigger SASP signaling in order to warn the system of the damage and initiate clear- ance as opposed to trying to repair itself. IL-6 and IL-8 reinforce senescence in an autocrine and paracrine way, concomitantly pre- venting senescent cells from exiting cell cycle arrest and forcing neighboring cells into senes- cence themselves [3, 42]. Persistent DDR activity, that is also known to induce IL-6 and IL-8 secretion [9], could be shown in various premalignant and malignant lesions in-vivo, and is hypothesized to be one the main causes of aging [9, 43, 44]. Due to this ability to promote inva- siveness of cancer cells and the spreading of senescence to neighboring cells IL-6 and IL-8 are of special interest [3, 45]. While it is probably not detrimental to transiently activate the respec- tive signaling pathways, the long-term persistence of unrepairable DNA damage leads to a lasting activation of NF-κB through the DDR mechanisms and thereby to a prolonged stimula- tion of IL-6 and IL-8. Ultimately, this initiates and perpetuates a vicious cycle from which cells cannot escape and causes the development of the SASP. To explore and validate previously generated in-silico results in-vitro, we isolated murine dermal fibroblasts from NEMO-floxed mice and transfected these with a Cre-recombinase plasmid to deplete NEMO. Contrary to NEMO knockout MDFs we observed RelA enrichment in the nucleus in DNA damaged wildtype cells. This suggests that mainly NEMO is responsible for the forwarding of DNA damage signals from the DDR to NF-κB signaling. We were particularly interested in achieving inhibition of IL-6 and IL-8 expression and secretion in-silico and in-vitro. As we could show in our in-vitro results, DNA damaged NEMO knockout cells did not reveal any induction of IL-6 or IL-8 homologue mRNA expression, sug- gesting that DNA damage-triggered IL-6 and IL-8 expression is mainly conferred by NF-κB sig- naling. This was confirmed on protein level, showing a strong decrease in secretion of both IL-6 and IL-8 homologues in NEMO knockout MDFs. In conclusion, abolishing NEMO is sufficient to not only block the signaling from DDR to NF-κB but also to decrease expression and secre- tion of two of the most prominent and established SASP mediators IL-6 and IL-8. The question arises why damaged senescent cells have to start expressing and secreting fac- tors that are detrimental to themselves, surrounding cells and tissues. The secretion of many SASP factors can be explained firstly by the attempt to clear senescent cells from tissue by cells Fig 4. Knockouts that cause in-silico IL-6 and IL-8 inhibition for NFkB knockout. Network states present the gene activity of all genes in the model. Green boxes indicate gene activation while red boxes show gene inactivation. A knock-down or overexpression is simulated by setting a gene to 0 or 1, respectively. This simulation shows the time course of expected states after DNA damage with NF-κB switched off (NFkB = 0) which leads to an inhibition of proinflammatory signaling. https://doi.org/10.1371/journal.pcbi.1005741.g004 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 13 / 30 Fig 5. Knockouts that cause in-silico IL-6 and IL-8 inhibition for IkB overexpression. This simulation shows an overexpression of IκB (IkB = 1) showing a similar outcome as in Fig 4. https://doi.org/10.1371/journal.pcbi.1005741.g005 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 14 / 30 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 15 / 30 of the innate immune system and secondly as a warning to the microenvironment that there is a danger in the near vicinity. Senescent cells secrete different factors that attract phagocytic immune cells and induce proteolytic enzymes to facilitate their migration through the extracel- lular matrix [46]. As long as damaged cells can be cleared in early phases the SASP is probably beneficial for the organism, however once the immune system cannot keep up with the emer- gence of damaged cells, detrimental effects accumulate and tissue takes damage [2, 47]. In this phase, it would be beneficial to have the possibility to counteract the SASP and give the immune system time to catch up. In summary, we could illustrate that in-silico identification of genes with mechanistic con- tribution in the regulation of the SASP, confirmed under experimental conditions in-vitro, is a highly suitable approach and holds substantial promise to identifying therapeutic targets to delay or even prevent the detrimental SASP effects on tissue homeostasis and overall ageing. Using our Boolean model, we were able to reproduce published data in-silico and generate var- ious knockout proposals to shut down two of the most detrimental effectors of the SASP. This is of major clinical relevance in terms of tissue aging. In fact, SASP factors like IL-6 and IL-8 have been correlated with inflammaging not only driving the aging process itself, but also Fig 6. Knockouts that cause in-silico IL-6 and IL-8 inhibition for NEMO knockout. NEMO is switched off (NEMO = 0) preventing NF-κB signaling from being activated. The outcome is similar to the two previously described simulations in Figs 4 and 5. https://doi.org/10.1371/journal.pcbi.1005741.g006 Fig 7. Schematic overview of the experimental workflow. Murine dermal fibroblasts (MDFs) are isolated from NEMO-floxed mice. After short expansion in cell culture these MDFs are transfected with pCAG-Cre- T2A-mRuby2 or pCAG-mRuby2, respectively. Because of mRuby2 expression, successfully transfected cells can be sorted by FACS. Cells transfected with pCAG-Cre-T2A-mRuby2 are knocked out for NEMO while pCAG-mRuby2 transfected cells are used as wildtype controls. After transfection cells are treated with 25 μM etoposide for 3 h to induce DNA damage. 24 h after treatment cell culture media is taken for ELISA measurement of secretion and cells are harvested for RNA isolation and subsequent RT-qPCR analysis. https://doi.org/10.1371/journal.pcbi.1005741.g007 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 16 / 30 promoting aging associated morbidity, frailty and mortality [48]. We additionally were able to validate and prove one of the most prominent knockout suggestions in-vitro, keeping in mind that there might always be detrimental off-target effects when altering a major signaling path- way like NF-κB. However, targeting NEMO and its interaction partners, as already shown in Fig 8. NEMO knockout murine dermal fibroblasts show a decreased nuclear translocation of p65. a. MTT assay determined optimal experimental conditions. 80% viable cells was set as threshold. After overnight serum starvation MDFs were treated with etoposide for 3 h followed by a 24 h incubation period. MTT assay was started afterwards to determine the viability of cells. Values are presented as mean ± SEM in percent. (n = 3) b. In order to evaluate DNA damage response and cell cycle arrest mRNA expression of p21 was analysed by RT-qPCR in MDFs treated with 25μM etoposide for 3 h followed by a 24 h incubation time (n = 5). Values are presented as mean ± SEM of fold change. Comparison was made with two-tailed t-test; P- value indicated the significance of difference. c. Representative immunostaining of γH2Ax (green) and p65 (red) in wildtype (NEMO WT) and NEMO knockout (NEMO k/o) MDFs treated with 25μM etoposide for 3 h with a following incubation period of 24 h. Scale bars, 50μM. The graph shows the percentage of p65 in the cytoplasm (black bars) compared to the nucleus (grey bars) as percentage of red pixels. Values are mean ± SEM in percent. Comparison was made with two-tailed t-test (n = 10); line and P-value. https://doi.org/10.1371/journal.pcbi.1005741.g008 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 17 / 30 studies of inflammatory arthritis and diffuse large B-cell lymphoma, may hold promise for the development of new therapies for age-related pathologies in which senescence and the SASP play a role [49, 50]. Fig 9. DNA damaged NEMO knockout MDFs show a decrease in IL-6 and IL-8 mRNA expression and protein secretion. a. To assess the influence of the NEMO knockout on DNA damage mediated activation of SASP signaling IL-6 mRNA expression was measured by RT-qPCR in untreated and etoposide-treated MDFs (n = 5). Cells with wildtype NEMO (black bars) or NEMO knockout (grey bars) were used. Values were presented as mean ± SEM of fold change. Comparison was made with the two-tailed t-test. b. IL-6 secretion was measured by ELISA in conditioned media of untreated and etoposide-treated MDFs (n = 5). Cells with wildtype NEMO (black bars) or NEMO knockout (grey bars) were used. Values were presented as mean ± SEM of total secretion in pg/ml, nd means non-detectable. Comparison was made with the two-tailed t-test. c. In addition to IL-6 murine IL-8 homologues KC, LIX and MIP-2 were used to further show activation of SASP signaling. mRNA of all three homologues was measured by RT-qPCR in untreated and etoposide-treated MDFs (n = 5). Cells with wildtype NEMO (black bars) or NEMO knockout (grey bars) were used. Values were presented as mean ± SEM of fold change. Comparison was made with the two-tailed t-test. d. IL-8 homologue secretion was measured by ELISA in conditioned media as previously described (n = 5). Values were presented as mean ± SEM of total secretion in pg/ ml, nd means non-detectable. Comparison was made with the two-tailed t-test. https://doi.org/10.1371/journal.pcbi.1005741.g009 A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 18 / 30 Methods Mice experiments Murine dermal fibroblasts from an inducible connective tissue-specific NEMO-deficient mouse model were used for in-vitro experiments. This mouse line (Col(I)α2-CreERT+; NEMOf/f) was generated by crossing Col(I)α2-CreERT transgenic mice [51] with NEMO floxed mice [35]. These mice were backcrossed to C57BL/6J for at least 6 generations. They were maintained in the Animal Facility of the University of Ulm with 12 h light–dark cycle and SPF conditions. The breeding of the mice and all experiments were approved by the ani- mal ethical committee (approval number, Tierversuch-Nr. 1102, Regierungspra¨sidium Tu¨bingen, Germany). For mice genotyping standard PCR techniques were used. The sequences of the primers used in this manuscript are summarized in S1 Table. Briefly, DNA was isolated from the tail tip of an individual mouse using a commercial kit (Easy DNA kit, Invitrogen). Purified DNA was later dissolved in TE and used for PCR amplification. The PCR products were run in QIAxcel Advance system (Qiagen) using the program AM320 and then documented digitally. Isolation and culture of murine dermal fibroblasts Murine dermal fibroblasts (MDFs) were isolated from ear skin of young mice and cultured as previously described [52]. Induction of DNA damage DNA damage was induced by adding etoposide to cell culture media at a concentration of 25 μM for 3 hours after overnight serum-starvation. Supernatants subsequently removed and cells were rinsed with PBS before adding fresh culture media. Cells and/or media were used 24 h later for further analysis. Cloning Recombineering technology [53] was used to constract plasmids containing CDS of both Cre recombinase and fluorescence reporter, mRuby2 or only mRuby2. pCAG-Cre vector (a gift from Connie Cepko, Addgene plasmid # 13775) was used for the recombineering. In the first construct, the aim was to insert the T2A-mRuby2 sequence before the stop codon of Cre recombinase and in the second construct, the aim was to replace the Cre ORF with mRuby2 ORF. In brief, synthetic DNA fragments were synthesized either as gBlock (IDT) or as Gen- eArt string (Thermo Scientific). Four DNA fragments were synthesized, the first one contained 5’ 50 bp homology regions to the vector (targeting 50 nucleotide upstream of Cre ORF stop codon), chloramphenicol and ccdB cassettes and 3’ terminal 50 bp homology regions to the vector (targeting 50 nucleotide downstream of last amino acid coding codon of Cre ORF, i.e., condon preceding the Cre ORF stop codon). The second synthetic fragment contained 5’ 50 bp homology regions to the vector (targeting 50 nucleotide upstream of Cre ORF start codon), chloramphenicol and ccdB cassettes and 3’ terminal 50 bp homology regions to the vector (tar- geting 50 nucleotide downsteram of Cre ORF stop codon). The third synthetic fragment con- tained 5’ 50 bp homology regions to the vector (same as fragment 1), T2A sequence-mRuby2 ORF and 3’ terminal 50 bp homology regions to the vector (same as fragment 1). The fourth synthetic fragment contained 5’ 50 bp homology regions to the vector (same as fragment 2), mRuby2 ORF and 3’ terminal 50 bp homology regions to the vector (same as fragment 2). E. coli containing pCAG-Cre was processed for electrocompetent using standard methods and these electrocompetent E coli, containing pCAG-Cre were electroporated with a dual inducible A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 19 / 30 expression plasmid pSC101-ccdA-gbaA (a gift from Prof. A. Francis Stewart) and selected for ampicillin 100μg/ml and tetracycline 3.5μg/ml at 30˚C. Next day, 4–5 colonies were expanded and the expression of recombineering proteins, λphage redα, redβ and redγ and recA (redgbaA) was induced by L-rhamnose (1.4mg/ml). After 1 h of L-rhamnose treatment, the induced E. coli were processed for electrocompetent and then electroprorated either with synthetic DNA fragments 1 or 2. After 1 h of recovery in SOC medium, the electroporated E coli, were plated in LB-agar containing ampicillin 100μg/ml, tetracycline 3.5μg/ml, chloramphenicol 25μg/ml and 1.4mg/ml L-arabinose. L-arabinose addition induced the expression of ccdA, the antidote of ccdB in that only recombined plasmid containing E. coli can survive. Thereafter colonies from fragment 1 and fragment 2 electroporated E. coli plates were picked and expanded for the verification of first recombinant product using restriction digestion analyses. The corre- sponding colony was expanded and redgbaA expression was induced by L-rhamnose for 1 h. The induced E. coli containing either recombined DNA fragment 1 or fragment 2 were made electrocompetent for the second round of recombineering. The E. coli, containing recombined DNA fragment 1 then electroporated with synthetic DNA fragment 3. The E. coli, containing recombined DNA fragment 2 were electroporated with synthetic DNA fragment 4. The recov- ered electroporated E. coli were plated in LB-agar containing ampicillin 100μg/ml and incu- bated at 37˚C overnight. Colonies from both plates were picked, expanded and verified for the second recombinant products. The correct plasmids were sequenced and verified through commercial services (Sequiserve, Germany). Plasmid preparation was performed using a com- mercially available kit (Qiagen plasmid plus kit, Qiagen). This plasmid (pCAG-Cre-T2A- mRuby2) can be obtained from the authors on request and was deposited in the Addgene repository (Accession ID 102989). Initiation of Cre activity (NEMO knockout) Early passage MDFs with a floxed NEMO allele were transfected with a Cre expressing vector using an electroporation-based transfection method (Amaxa, Lonza Group). Transfer of the plasmid was performed using a commercial kit with the AMAXA program N24 (Nucleofector Kits for Mouse or Rat Hepatocytes, Lonza). Successful NEMO knockout was assessed by PCR as explained before. FACS sorting of positive cells Two days after transfection cell populations were purified using the mRuby2-based reporter system included in the previously described Cre-expressing vectors. Gating was set for living cells and singlets, sorting was based on mRuby2 expression in the PE-channel. FACS-sorting was performed with a FACSAria III system (BD Biosciences) and analysis was done on FACS- Diva and FlowJo (Tree Star) software. Immunofluorescence staining Cells were fixed in 4% PFA in PBS for 15 min and thereafter treated with 0.1% Triton X-100 for 10 min at room temperature. Blocking was performed in 5% BSA for 1 h at room tempera- ture. Anti-p65 (#8242, 1:200, Cell Signaling) and anti-γH2A.x (ab22551, 1:200, Abcam) were used as primary antibodies overnight at 4˚C. Incubation with the secondary antibody Alexa 488 goat anti-mouse (for γH2A.x, 1:500) and Alexa 555 goat anti-rabbit (for p65, 1:500) was performed at room temperature for 1 h. A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 20 / 30 Western blotting Western blot analyses were performed as described earlier [54]. In brief, murine dermal fibroblasts were lysed in RIPA lysis buffer (25mM Tris-HCl pH 7.6, 150mM NaCl, 1% NP- 40, 1% sodium deoxycholate, 0.1% SDS) supplemented with protease and phosphatase inhibitors (Thermo Scientific). Cells in RIPA were sonicated using sonopuls HD 2070 and MS72 microtips (Bandelin). The sonicator setting was 50% power 3 cycles and 10 sec for three times. Following sonication, the lysate was centrifuged for 15 min at 14000 rpm and 4˚C. The supernatant was collected and protein concentration was measured by Bradford Assay (Biorad). 50μg of protein from each lysate was resolved in 4–20% SDS-PAGE, fol- lowed by transfer to nitrocellulose membrane and probing the membrane with anti-NEMO antibody (1:1000, Abcam). The membrane was incubated with goat anti-rabbit IgG coupled with HRP for 1 hr (Jackson ImmunoResearch). Thereafter the membrane was developed by LumiGLO chemiluminescence reagent (Cell Signaling Technologies) using Fusion FX7 Gel- doc system (Vilber Lourmat), followed by stripping with Restore Plus Western blot Strip- ping Buffer (Thermo Scientific) and re-probed with anti-β-actin antibody coupled with HRP (1:12000, Santa Cruz), finally developed the membrane using LumiGLO. Quantitative PCR Twenty-four hours after treatment, total RNA was isolated from cultured murine dermal fibroblasts using a commercial kit (RNeasy Mini Kit, Qiagen) as described by the manufac- turer. Two μg of RNA per sample were reverse transcribed using illustra Ready-To-Go RT-PCR Beads (GE Healthcare). Quantity and quality of total RNA and cDNA was assessed using Nanodrop 1000 (Thermo Scientific) and QIAxcel Advance system (Qiagen). The 7300 real time PCR system (Applied Biosystem, Life Technologies) was used to amplify cDNA using Power SYBR green mastermix (Applied Biosystems, Life Technologies). Sequences for primers used in all experiments and genotyping are provided in S1 Table. ELISA After etoposide treatment cells were supplied with fresh culture media. Culture media was taken for analysis of secreted IL-6 and murine IL-8 homologues (KC and MIP-2) 24 h after treatment. Media was stored at -80˚C until analysis. Concentrations of secreted IL-6 and murine IL-8 homologues after DNA damage were determined using commercial kits (Mouse IL-6/KC/MIP-2 Quantikine ELISA Kit, R&D) as described by the manufacturer. Statistical calculations The influence of a NEMO knockout was compared to wildtype controls based on IL-6, IL-8 homologue and p21 mRNA expression as well as IL-6 and IL-8 homologue protein secretion. The sample size for all experiments was 5 per group. The expression and secretion of the two groups was tested using unpaired two-tailed t-test. Furthermore, the influence of the NEMO knockout compared to wildtype controls on the nuclear translocation of p65 was measured by the percentage of fluorescence intensity in the cell nucleus as well as cytoplasm (sample size = 10). The fluorescence intensity was tested using unpaired two-tailed t-test. The exact p-values are depicted in the respective figures. The figures show mean values. Error bars corre- spond to the standard error of the mean. A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 21 / 30 Boolean networks In a first step, IL- and DNA-damage pathways included in the Boolean model of SASP were reconstructed individually. To generate the independent gene regulatory networks of inflam- matory and DDR signaling, we collected peer-reviewed literature that is considered relevant in the context of SASP (see Table 1). This literature reports data about the local interaction of key genes regulating each pathway. The information was collected in murine and human experi- mental in-vivo and in-vitro studies. In order to control the complexity of model we restricted the set of regulatory factors in the model to the most relevant for SASP and to those being important components of each pathway. The modeled pathways were chosen based on the requirement in the onset and maintenance of the SASP shown in studies related to senescence and the SASP. In total 80 publications were used to determine the relationships between the individual components of the model (Table 1). After the reconstruction of Boolean network models of inflammation and DNA damage response, both were combined into a larger network. The impact of combining the two net- work models instead of simulating them independently is shown by additional analysis in S1 Text. Simulations based on specific environmental (input) conditions were performed to find the corresponding attractors. Furthermore, to identify possible interaction targets, i.e., to gen- erate testable hypotheses about interventions, we fixed corresponding regulatory factors to either 0 or 1 (modelling of knockout or overexpression, similar to [55]) and reran the simula- tions (S1 Text). Given an interaction target, we looked for the attractors that positively influ- ence the DNA damage response phenotype. Network figures were drawn with Biotapestry (www.biotapestry.org). Simulations of the Boolean network were performed with the package BoolNet [12, 56] in R (www.r-project.org). This model contains two external signals (DNA damage and Activated Oncogenes). These signals do not coincide with genes within the network, but represent different stimuli from external or internal sources that are known to activate the DNA damage response and/or cell cycle arrest signaling through either p16INK4 or p53/p21. Supporting information S1 Fig. Establishment of a pure NEMO knockout murine dermal fibroblast (MDF) popula- tion. a. To purify NEMO k/o MDFs, NEMO-floxed cells were transfected with a Cre-recombi- nase vector including a mRUBY2-reporter construct. Two days post-transfection cells were purified for the NEMO k/o using flowcytometry-based sorting, gating for living cells, cell sin- glets and mRUBY2 signal (histograms; left to right). b. Successful NEMO k/o was determined using PCR analysis. DNA was isolated from FACS-sorted MDFs and later used for PCR ampli- fication. Cre-recombinase activity induced the deletion of floxed NEMO alleles resulting in a bigger sized amplification product in successful knockouts as compared to wildtype cells. c. In addition to PCR analysis a successful knockout on protein level was determined by western blotting of cell lysates equilibrated to actin expression levels. (TIF) S2 Fig. Unaltered expression of selected genes (predicted to be unaffected in NEMO knock- out) following NEMO knockout. The expression level of a set of genes that were predicted not to be changed after NEMO knockout by the Boolean network model. In a setting of 2-fold cutoff (blue dotted line), the expression of all genes remained unaltered between control and NEMO knock out MDFs. Dotted line at value ‘1’ represents level of expression in the control MDFs. (TIF) A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 22 / 30 S1 Table. Primer sequences. (DOCX) S1 Text. Simulation of SASP network with BoolNet. (PDF) Author Contributions Conceptualization: Patrick Meyer, Pallab Maity, Andre Burkovski, Christoph Mu¨ssel, Hans A. Kestler, Karin Scharffetter-Kochanek. Formal analysis: Hans A. Kestler. Funding acquisition: Hans A. Kestler, Karin Scharffetter-Kochanek. Investigation: Patrick Meyer, Pallab Maity, Julian Schwab, Hans A. Kestler, Karin Scharffet- ter-Kochanek. Methodology: Andre Burkovski, Karmveer Singh, Filipa F. Ferreira, Linda Krug, Meinhard Wlaschek, Hans A. Kestler. Project administration: Meinhard Wlaschek, Hans A. Kestler, Karin Scharffetter-Kochanek. Resources: Harald J. Maier, Thomas Wirth, Karin Scharffetter-Kochanek. Software: Andre Burkovski, Julian Schwab, Christoph Mu¨ssel, Hans A. Kestler. Supervision: Hans A. Kestler, Karin Scharffetter-Kochanek. Validation: Harald J. Maier, Thomas Wirth. Writing – original draft: Patrick Meyer, Andre Burkovski, Hans A. Kestler, Karin Scharffet- ter-Kochanek. Writing – review & editing: Pallab Maity, Julian Schwab, Christoph Mu¨ssel, Hans A. Kestler, Karin Scharffetter-Kochanek. References 1. 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A SASP model after DNA damage PLOS Computational Biology \| https://doi.org/10.1371/journal.pcbi.1005741 December 4, 2017 30 / 30	29206223	Oncogene = ( IL8 ) OR ( IL6 ) p53 = ( ( CHK1 ) AND NOT ( MDM2 ) ) OR ( ( ATM ) AND NOT ( MDM2 ) ) OR ( ( CHK2 ) AND NOT ( MDM2 ) ) ATR = ( DNAD ) CHK1 = ( ATR ) IkB = ( ( NFkB ) AND NOT ( IKK AND ( ( ( NEMO ) ) ) ) ) OR ( ( IkB ) AND NOT ( IKK AND ( ( ( NEMO ) ) ) ) ) p21 = ( p53 ) OR ( HIF1 ) TAK1 = ( TRAF6 ) OR ( TAB ) IKK = ( NEMO ) OR ( NIK ) OR ( Akt ) CHK2 = ( ATM ) MDM2 = ( ( p53 ) AND NOT ( ATM ) ) TRAF6 = ( IRAK ) ATM = ( DNAD ) p38 = ( ( MKK ) AND NOT ( MKP1 ) ) IRAK = ( IRAK ) OR ( MyD88 ) OR ( IL1R ) MyD88 = ( IL1R ) JNK = ( ( MKK ) AND NOT ( MKP1 ) ) Akt = ( PI3K ) RB = NOT ( ( pRB ) OR ( CDK4 ) OR ( CDK2 ) ) MKP1 = ( AP1 ) cJun = ( cFos AND ( ( ( JNK OR CEBPbeta OR p38 OR ERK1_2 ) ) ) ) JAK = ( ( IL6R ) AND NOT ( SOCS3 ) ) STAT3 = ( mTOR ) OR ( cFos AND ( ( ( cJun ) ) ) ) OR ( JAK ) Elk1 = ( ERK1_2 ) NEMO = ( DNAD ) GP130 = ( IL6 ) IL8 = ( CEBPbeta ) OR ( AP1 ) OR ( NFkB ) CDK4 = NOT ( ( p21 ) OR ( p16INK4 ) ) cFos = ( CEBPbeta ) OR ( p38 ) OR ( Elk1 ) OR ( JNK ) OR ( STAT3 ) MEK1_2 = ( GP130 AND ( ( ( IL6 ) ) ) ) IL1R = ( IL1 ) TAB = ( TRAF6 ) OR ( IRAK ) AP1 = ( cJun AND ( ( ( cFos ) ) ) ) p16INK4 = ( Oncogene ) OR ( DNAD ) MEKK = ( TRAF6 ) CDK2 = ( ( E2F ) AND NOT ( p21 ) ) MKK = ( MEKK ) OR ( TAK1 ) mTOR = ( Akt ) IL6 = ( CEBPbeta ) OR ( ERK1_2 ) OR ( NFkB ) IL6R = ( IL6 ) PI3K = ( JAK ) NIK = ( TAK1 ) pRB = ( CDK4 ) OR ( CDK2 ) IL1 = ( NFkB ) SOCS3 = ( STAT3 ) HIF1 = ( ( Hypoxia ) AND NOT ( p53 ) ) ERK1_2 = ( MEK1_2 AND ( ( ( IL6 ) ) ) ) NFkB = ( ( IKK ) AND NOT ( IkB ) ) CEBPbeta = ( Elk1 ) E2F = ( ( E2F ) AND NOT ( RB ) ) OR ( ( pRB ) AND NOT ( RB ) )
RESEARCH ARTICLE A systems pharmacology model for inflammatory bowel disease Violeta Balbas-Martinez1,2, Leire Ruiz-Cerda´1,2, Itziar Irurzun-Arana1,2, Ignacio Gonza´lez- Garcı´a1¤a, An Vermeulen3,4, Jose´ David Go´mez-Mantilla1¤b, Iñaki F. Troco´niz1,2* 1 Pharmacometrics & Systems Pharmacology, Department of Pharmacy and Pharmaceutical Technology, School of Pharmacy and Nutrition, University of Navarra, Pamplona, Spain, 2 IdiSNA, Navarra Institute for Health Research, Pamplona, Spain, 3 Janssen Research and Development, a division of Janssen Pharmaceutical NV, Beerse, Belgium, 4 Laboratory of Medical Biochemistry and Clinical Analysis, Faculty of Pharmaceutical Sciences, Ghent, Belgium ¤a Current address: PharmaMar, Colmenar Viejo, Madrid, Spain. ¤b Current address: Boehringer Ingelheim, Ingelheim am Rhein, Germany. * itroconiz@unav.es Abstract Motivation The literature on complex diseases is abundant but not always quantitative. This is particu- larly so for Inflammatory Bowel Disease (IBD), where many molecular pathways are qualita- tively well described but this information cannot be used in traditional quantitative mathematical models employed in drug development. We propose the elaboration and vali- dation of a logic network for IBD able to capture the information available in the literature that will facilitate the identification/validation of therapeutic targets. Results In this article, we propose a logic model for Inflammatory Bowel Disease (IBD) which con- sists of 43 nodes and 298 qualitative interactions. The model presented is able to describe the pathogenic mechanisms of the disorder and qualitatively describes the characteristic chronic inflammation. A perturbation analysis performed on the IBD network indicates that the model is robust. Also, as described in clinical trials, a simulation of anti-TNFα, anti-IL2 and Granulocyte and Monocyte Apheresis showed a decrease in the Metalloproteinases node (MMPs), which means a decrease in tissue damage. In contrast, as clinical trials have demonstrated, a simulation of anti-IL17 and anti-IFNγ or IL10 overexpression therapy did not show any major change in MMPs expression, as corresponds to a failed therapy. The model proved to be a promising in silico tool for the evaluation of potential therapeutic tar- gets, the identification of new IBD biomarkers, the integration of IBD polymorphisms to antic- ipate responders and non-responders and can be reduced and transformed in quantitative model/s. PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 1 / 19 a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Balbas-Martinez V, Ruiz-Cerda´ L, Irurzun- Arana I, Gonza´lez-Garcı´a I, Vermeulen A, Go´mez- Mantilla JD, et al. (2018) A systems pharmacology model for inflammatory bowel disease. PLoS ONE 13(3): e0192949. https://doi.org/10.1371/journal. pone.0192949 Editor: Shree Ram Singh, National Cancer Institute, UNITED STATES Received: October 17, 2017 Accepted: February 1, 2018 Published: March 7, 2018 Copyright: © 2018 Balbas-Martinez et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All relevant data are within the paper and its Supporting Information files. Funding: Development of the computational model was supported by a fellowship grant from the Navarra Government to Violeta Balba´s-Martı´nez of 61.965 Euros (http://www.navarra.es/home_es/ Actualidad/BON/Boletines/2017/18/Anuncio-5/) and Janssen Research and Development. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of Introduction Inflammatory bowel disease (IBD) is a complex gastrointestinal tract disorder characterized by a functional impairment of the gut wall affecting patients´ quality of life [1,2]. IBD includes ulcerative colitis (UC) and Crohn’s disease (CD). The natural course of IBD is highly variable [3–6] and its etiology is still unknown. The incidence of IBD has dramatically increased world- wide over the past 50 years [7], reaching levels of 24.3 per 100,000 person-years in UC and 20.2 per 100,000 person-years in CD in the developed countries [8]. There is current evidence that Interleukin 6 (IL6), Tumour necrosis factor-alpha (TNFα), Interferon Gamma (IFNƔ), Interleukin 1 beta (IL1ß), Interleukin 22 (IL22), Interleukin 17 (IL17) and Natural Killer cells (NK), among other signalling pathways, play relevant roles in the pathogenesis of IBD, which is a reflection of the complexity of that physiological system [9–12]. That complexity indicates that a universal treatment for IBD may not be feasible for the vast majority of patients [13,14]. In fact, current biological approved treatments are only palliative with a high percentage of non-responders. For example, around 50% of IBD patients treated with the current standard of care, Infliximab (an anti-TNFα) or Vedolizumab (an anti- α4β7 integrin) do not respond satisfactorily to therapy [15,16]. One characteristic of the cur- rent IBD biological treatments is that approved therapies target just one signalling pathway, which might explain the high rate of non-responders and the long-term inefficiency of most treatments [15,17]. In addition, there is evidence to suggest that optimal treatment for IBD should involve a combination of different drugs [18,19]. Therefore, there is a need, especially for complex alterations such as immune-mediated diseases, to change the paradigm of drug development, considering the main aspects (targets, cross-talking between pathways, therapy combination) from an integrative and computational perspective. Given the aforementioned biological complexity of immune-mediated diseases and the fact that current longitudinal data associated with the most relevant elements of the system are scarce, a full parameterization of IBD related systems based on a differential equation model does not yet seem feasible. However, some attempts have been made to describe quantitatively the IBD systems. For example, Wendelsdorf et al., [20] built a quantitative model based on ordinary differential equations. However, some key disease elements, such as cytokines and T cells, were incorporated non-specifically (i.e., all types of cytokine were grouped under the generic element active cytokines) in the model structure, limiting its use to explore potential therapeutic targets. More recently, Dwivendi et al., [21], based on the results of a clinical trial with the anti–IL6R antibody, Tocilizumab, have developed a multiscale systems model in Crohn’s disease, limited to the IL6–mediated immune regulation pathway. Network analysis represents a promising alternative in such data limited circumstances [22–24]. As many molecular pathways in IBD are qualitatively well described, interaction net- works may be a suitable approach for characterizing IBD. These networks are simplified repre- sentations of biological systems in which the components of the system such as genes, proteins or cells are represented by nodes and the interactions between them by edges [25]. Boolean network models, originally introduced by Kauffman [26,27], represent the simplest discrete dynamic models. These models only assume two discrete states for the nodes of a network, ON or OFF, corresponding to the logic values 1 (active) or 0 (not active, but not necessarily absent) [28]. A well-designed logic model could generate predictive outcomes given a set of initial conditions. Qualitative, logical frameworks have emerged as relevant approaches with different applications, as demonstrated by a growing number of published models [29]. Com- plementing these applications, several groups have provided various methods and tools to sup- port the definition and analysis of logical models, as it can be seen by the recent achievements of the Consortium for Logical Models and Tools (CoLoMoTo) in logical modelling [30]. A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 2 / 19 the manuscript. Janssen Research and Development provided support in the form of salaries for author AV, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific role of this author is articulated in the ‘author contributions’ section. Competing interests: We have the following interests. This study was partly funded by Janssen Research and Development, the employer of An Vermeulen. There are no patents, products in development or marketed products to declare. This does not alter our adherence to all the PLOS ONE policies on sharing data and materials, as detailed online in the guide for authors. There are already several tools for Boolean modeling of regulatory networks in which it is pos- sible to define direct activation-inhibition relationships between the components of the net- work, such as BoolNet R [31] or GINsim [32]. More recently, the R package SPIDDOR (Systems Pharmacology for effIcient Drug Development On R) among others, has imple- mented new types of regulatory interactions and perturbations within the system, such as posi- tive and negative modulators and the polymorphism-like alterations, which lead to richer dynamics between the nodes [28]. In the specific case of IBD, there have been initial attempts to develop network models. The multi-state modeling tool published by Mei et al., [33,34] can be considered a proof of concept in the application of these types of networks in mucosal immune responses. However, the number of elements that this model considers and integrates is limited for IBD characteriza- tion, since only six different cytokine types are included in the inter-cellular scale. The objective of the current manuscript is to present a Boolean based network model incor- porating the main cellular and protein components known to play a key role in IBD develop- ment and progression. The model has been built on well-established experimental knowledge, mostly of human origin, and only including animal data when no other source of information was available. Our aim has been to build a model structure facilitating key aspects in the treat- ment of immune mediated disease, such as the selection of the most promising combination therapies and the study of the impact of polymorphisms on pathway regulation, thus allowing patient stratification and personalized medicine. This study provides the scientific community with a (i) computational IBD model imple- mented in SPIDDOR R package [28], which allows translation of Boolean models (excluding models enclosing temporal operators) to a standard Markup language in Systems Biology for qualitative models (SBML qual [35]) which promotes model interoperability, and (ii) a reposi- tory with the main and updated information known of the immune system and IBD, which shows model transparency and allows model reusability. The proposed IBD model can be eas- ily expanded in size and complexity to incorporate new knowledge, or other type of informa- tion such as proteomic data. The model presented hereafter is general enough to serve as a skeleton for other relevant immune diseases such as Rheumatoid Arthritis, Psoriasis or Multi- ple Sclerosis. The manuscript is organized as follows: In the next section, Results regarding the structure of the model can be graphically visualized, and the ability of the model to recreate certain alter- ations that have been reported in IBD is demonstrated, as well as the model’s capability to reproduce the results from recent clinical trials performed in IBD patients from a high-level perspective. Applications of the model, including its advantages and limitations are then dis- cussed together with ideas for future research. Finally, the Methods section provides a detailed technical description (with the aid of supplementary material) of the network and a descrip- tion of how simulations, collection, and representation of results have been performed. Results Graphical representation, repository, and Boolean functions The graphical representation of the IBD network is shown in Fig 1. It consists of 43 nodes and 298 qualitative interactions located in three different physiological areas corresponding to (i) the lymph node, (ii) the blood and lymph circulatory system that irrigates the intestinal epithe- lial cells and (iii) the gut lumen. Definition of all nodes and the full documented regulatory interactions conforming the model structure can be found in supporting information S1 Table and S2 Table, respectively. The S2 Table is fundamental to understand the rationale for the selection and implementation A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 3 / 19 of the Boolean functions (BF). It was organized to provide a comprehensive summary of the 301 manuscripts (published over the last three decades) used to build the model, highlighting for example whether (i) a specific pathway was reported to be altered in IBD, or (ii) informa- tion was supported by human (more than the 80% of the network structure) or animal data. The Boolean operators used to define the network model of IBD were: the NOT operator which is noted as “!”, the AND operator which is noted as “&” and the OR operator which is noted as “\|”. Recent and innovative modulators and threshold operators previously described by Irurzun-Arana et al., 2017 [28] were also part of the arsenal of Boolean elements used in the model proposed (see S1 File for a detailed description of those additional Boolean elements). Regarding the input selection, as it is assumed that IBD is caused by intestinal dysbiosis, an environment of different bacteria was recreated selecting three different antigens which are components of most Bacterial Gram positive and Gram negative. Therefore, during the devel- opment of the proposed model the following assumptions were made: First, there is a chronic exposure to bacterial antigens: Peptidoglycan (PGN), Lipopolysaccharide (LPS) and Muramyl dipeptide (MDP). PGN is a component of the cell wall of all bacteria, but in particular of gram-positive bacteria, LPS is a component of the outer membrane of Gram-negative bacteria Fig 1. Graphical representation of IBD model. Nodes represent cells, proteins, bacterial antigens, receptors or ligands. Bacterial antigens trigger the IBD immune response through activation of different pattern recognition receptors (TLR2, TLR4 and NOD2) starting the innate and adaptive immune response. Reprinted from [36] under a CC BY license, with permission from the organizers of the 2016 International Conference on Systems Biology, original copyright 2016. https://doi.org/10.1371/journal.pone.0192949.g001 A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 4 / 19 [37], and MDP is a constituent of both Gram-positive and Gram-negative bacteria [38]. All three elicit strong immune responses and seem to play a critical role in the development and pathophysiology of IBD, as it has been hypothesized that the onset or relapse of IBD is trig- gered by an imbalance in self-microbiota composition than cannot be controlled by immune system [39]. Table 1 lists the initial conditions expressed by the corresponding BF, and shows that the nodes representing antigens are chronically expressed unless the natural antimicrobial peptides perforin (PERFOR), granzyme B (GRANZB) or defensins (DEF) become active. Second, there is an impairment in antigen elimination in IBD patients [1,40,41], simulated with the threshold operator Ag_elim = 6. The threshold operator means that PERFOR, GRANZB, or DEF inhibit antigen activation when any of these three nodes have been activated for at least 6 consecutive iterations (see Table 1). Third, the final readout of the network model is the average expression of the output node, Metalloproteinases (MMPs). There is solid evidence that this group of proteins is directly asso- ciated with intestinal fibrosis and tissue damage in IBD [42–46] supporting their use as a rele- vant biomarker in clinical practice as proposed by O’Sullivan et al. [47]. As it can be seen in Table 2, the nodes that directly activate MMPs are the nodes that have relevant roles in the pathogenesis of IBD [9–12,42–44,46,48]. Table 2 contains the full set of BF that modulates the signal initialized by the antigens through the activation of different pattern recognition receptors (TLR2, TLR4 and NOD2 nodes) and the impact on the output node (MMPs) as the recipient of the antigen signal inter- nal modulation. The nodes TNFα or IFNγ have the most complex pathways as can be seen in the corresponding Boolean equations (Table 2). With the aim of making the network model more accessible to the community it has been uploaded to “The Cell Collective” [49,50] platform (https://www.cellcollective.org/#cb963d7f- 75cb-4b2e-8987-0c7592a9c21d). In addition, the supporting information document S2 File provides the network model in text format ready for simulation in the R-based freely available package SPIDDOR [28] and an html tutorial as a guide to reproduce the results (S3 File). Perturbation analysis and clustering: Network robustness The results of the network perturbation analysis are presented in Fig 2. The heatmap shows the impact of a single blockage of each node in every network node. The results indicate that most node blockages did not trigger considerable changes, suggesting that the IBD network is robust [51]. Some perturbations led to a higher activation of the nodes, while down regulations were more common. The heatmap was combined with a hierarchical clustering grouping together the nodes that caused similar alterations. Knockout of the NFkß node appeared to be the most relevant alteration as it caused a reduction in expression of many of the nodes that were reported to be overexpressed in IBD patients. The knockout of the Th0 node (represent- ing activated CD4+ T cells) also elicited a reduction in MMPs. The positive effects of the NFkß and Th0 node blockades on MMPs decreased expression, resembled some of the known mech- anisms of action of glucocorticoids, inhibitors of T cell activation and proinflammatory Table 1. Boolean functions (BF) of the IBD model to simulate the initial conditions. INITIAL CONDITIONS: CHRONIC EXPOSURE PGN ¼ ! ðTAG elim¼6 i¼1 PERFORt i j TAG elim¼6 i¼1 GRANZBt i j TAG elim¼6 i¼1 DEFt iÞ MDP ¼ ! ðTAG elim¼6 i¼1 PERFORt i j TAG elim¼6 i¼1 GRANZBt i j TAG elim¼6 i¼1 DEFt iÞ LPS ¼ ! ðTAG elim¼6 i¼1 PERFORt i j TAG elim¼6 i¼1 GRANZBt i j TAG elim¼6 i¼1 DEFt iÞ https://doi.org/10.1371/journal.pone.0192949.t001 A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 5 / 19 Table 2. Boolean functions (BF) of the IBD model for the internal and the output nodes. INTERNAL NODES TLR2 = PGN TLR4 = LPS NOD2 = MDP NFkB = TLR2 \| NOD2 \| TLR4 IL6 = (MACR & PGN) \| (DC & (LPS \| PGN)) \| (Th17 & IL23) \| (NFkB &! (IL4 \| IL10)) TNFa ¼ ððNFkB&LPSÞ j ðMACR&ðIL2 j ðIFNg&LPSÞ j PGNÞÞ j ðNK&ðMDP j PGN j LPSÞ&ððIL2 j IL12Þ&ðIL2 jIL15ÞÞ j ðFIBROBLAST&IFNgÞ j ððCD4 NKG2D j CD8 NKG2D j NK NKG2DÞ&ðIEC MICA B j IEC ULPB1 6ÞÞÞ&! ðTdownregcyt¼4 i¼1 IL10t i&ðTdownregcyt¼4 i¼1 TLR2t ij Tdownregcyt¼4 i¼1 TLR4t iÞ&TNFaÞ TGFb = (Treg \| MACR) Th0 ¼ TTHR Th0¼3 i¼1 LPSt ij TTHR Th0¼3 i¼1 MDPt ij TTHR Th0¼3 i¼1 PGNt i Th0_M = (Th0 & (IL23 \| IL12)) \| Th0_M IL18 = ((MACR \| DC) & LPS) & NFkB IL1b ¼ ððMACR j DCÞ&LPS&NFkBÞ&! ðIL1b&Sdownreg cyt¼4 i¼1 IL10t iÞ IFNg ¼ ððNK&ðPGNjLPSjMDPj&ðIL23jðIL12&ðIL2jIL15 jIL18ÞÞÞÞ j ðTh0 M&ðLPS j MDP j PGNÞ &ðIL12 j IL23ÞÞ j Th1 j ððCD8 NKG2D j NK NKG2DÞ&ðIEC MICA B j IEC ULPB1 6ÞÞ j ðTh17&ðPGN j LPSj MDPÞÞ j ððMACR j Th0Þ&IL18&IL12ÞÞ&! ððIFNg&ðTdownreg cyt¼4 i¼1 TGFbt i j Tdownregcyt¼4 i¼1 IL10t i j Th2Þ IL23 = (MACR & IL1b) \| DC IL22 ¼ Th17jðNK&ððIL18&IL12Þ j IL23ÞÞjCD4 NKG2DjðððIL22&Th0&IL21Þ&!ðTupreg cyt¼3 i¼1 IL22t i& Tupreg cyt¼3 i¼1 Th0t i&Tupreg cyt¼3 i¼1 IL21t iÞÞ&! TGFbÞ IL21 = Th17 \| ((Th0 & IL6) &! (IL4 \| IFNg \| TGFb)) IL17 ¼ ðTh17 j ðTh17 M&ðLPS j MDP j PGNÞÞ j ðCD4 NKG2D&ðIEC MICA B j IEC ULPB1 6ÞÞÞ&! ððTdownreg cyt¼4 i¼1 TGFbt i j Tdownreg cyt¼4 i¼1 IL13t iÞ&IL17Þ IL10 = Treg\|(Th2 &! IL23)\|((TLR2 & NFkB) &! (MACR & IFNg)) \| ((MACR & LPS) &! IL4) \| (DC & LPS) Th17 ¼ ððTh0&ðIL1b j IL23 j IL6ÞÞ j ððTh17&IL23Þ&!ðTupreg cell¼2 i¼1 Th17t i&Tupreg cell¼2 i¼1 Il23t iÞÞÞ&! ððSdownreg cell¼2 i¼1 TGFbt ij Sdownreg cell¼2 i¼1 IL12t i j Sdownreg cell¼2 i¼1 IL4t ij Sdownreg cell¼2 i¼1 IFNgt i j Sdownreg cell¼2 i¼1 Treg t iÞ&Th17Þ Th17_M = ((Th0_M & (PGN \| MDP \| LPS)) & ((IL1b & IL6) \| IL23 \| IL2)) \| Th17_M Th1 ¼ ðTh0&ððIL12 j IFNg j IL18Þ j ðDC&IL12&IL23&LPSÞÞÞ&! ðððSdownreg cell¼2 i¼1 IL17t i& Sdownreg cell¼2 i¼1 IL12t iÞ j ðSdownreg cell¼2 i¼1 Treg t ij Sdownreg cell¼2 i¼1 Th2t ij Sdownreg cell¼2 i¼1 TGFbt i j Sdownreg cell¼2 i¼1 IL10t ij Sdownreg cell¼2 i¼1 IL4t iÞÞ&Th1Þ Th2 ¼ ðTh0&ðIL10 jððIL18&IL4Þ&!IL12ÞÞj ððTh2&IL4Þ&!ðTupreg cell¼2 i¼1 Th2t i&Tupreg cell¼2 i¼1 IL4t iÞÞÞ&! ððSdownreg cell¼2 i¼1 Tregt ij Sdownreg cell¼2 i¼1 IFNgt ij Sdownreg cell¼2 i¼1 TGFbt iÞ&Th2Þ IL4 = Th2 IL15 = (FIBROBLAST & (MDP \| LPS \| PGN)) \| (MACR & (LPS \| IFNg)) IL12 ¼ ððððMACR j DCÞ&ðLPS jPGNÞ&IFNgÞ&!ðIL12&Sdownreg cyt¼4 i¼1 TNFat iÞÞ j ðDC&IL1bÞ j ðIL12&ðIL13 j IL4ÞÞÞ&!ððSdownreg cyt¼4 i¼1 TGFbt i j Sdownreg cyt¼4 i¼1 IL10t iÞ&IL12Þ IL13 = Th2 Treg ¼ ðTTHR Th0 Treg¼3 i¼1 Th0t i&ðTGFb j TLR2ÞÞ&! ððSdownreg cell¼2 i¼1 IL6t ij Sdownreg cell¼2 i¼1 IL21t ij Sdownreg cell ¼2 i¼1 IL23t ij Sdownreg cell¼2 i¼1 Th17t ij Sdownreg cell¼2 i¼1 IL22t ij Sdownreg cell¼2 i¼1 TNFat iÞ&TregÞ NK ¼ ðIL15 jIL2 j IL12 jIL23j ðIL18&IL10ÞÞ&! ðSdownregcell¼2 i¼1 Tregt i&NKÞ DEF ¼ IL22 j IL17 j TTHR NOD2 DEF¼3 i¼1 NOD2t i IL2 = Th0 \| (Th0_M & (MDP \| LPS \| PGN)) \| DC MACR ¼ ðNFkB j ððMACR&ðIFNg jIL15ÞÞ&! ðTupreg cell¼2 i¼1 NFkBt i&ðTupreg cell¼2 i¼1 IFNgt i j Tupreg cell¼2 i¼1 IL15t iÞÞÞÞ&! ðSdownreg cell¼2 i¼1 IL10t i&MACRÞ DC ¼ NFkB&! ðSdownreg cell¼2 i¼1 IL10t i&DCÞ IEC MICA B ¼ ððLPS j MDP j PGNÞ j ðIEC MICA B&TNFaÞ&! ðTupreg rec¼2 i¼1 IEC MICA Bt i& Tupreg rec¼2 i¼1 TNFat iÞÞ&! TGFb IEC_ULPB1_6 = CD8_NKG2D & (LPS\|MDP\|PGN) CD8 NKG2D ¼ ðLPS j PGN j MDPÞ&!ððTTHR LIGANDS NKG2D¼3 i¼1 IEC MICA Bt ij TTHR LIGANDS NKG2D¼3 i¼1 IEC ULPB 1 6t i j ðSdownreg cell¼2 i¼1 IL21t i&Sdownreg cell¼2 i¼1 IL2t iÞÞ&CD8 NKG2DÞ NK NKG2D ¼ ðLPSjPGNjMDPÞ&! ðSdownreg cell¼2 i¼1 TGFbt ij TTHR LIGANDS NKG2D¼3 i¼1 IEC MICA Bt i j TTHR LIGANDS NKG2D¼3 i¼1 IEC ULPB 1 6t i jðSdownreg cell¼2 i¼1 IL21t i&Sdownreg cell¼2 i¼1 IL12t iÞÞ&NK NKG2DÞ CD4 NKG2D ¼ ðLPS j PGN j MDP j ðCD4 NKG2D&ðIL15 j TNFaÞÞ&! ðTupreg rec¼2 i¼1 CD4 NKG2Dt i &ðTupreg rec¼2 i¼1 IL15t ij Tupreg rec¼2 i¼1 TNFat iÞÞÞ&! ððSdownreg cell¼2 i¼1 IL10t i j TTHR LIGANDS NKG2D¼3 i¼1 IEC MICA Bt i j TTHR LIGANDS NKG2D¼3 i¼1 IEC ULPB 1 6t iÞ&CD4 NKG2DÞÞ FIBROBLAST ¼ ððMACR&ðIL4 j IL13 j TGFbÞÞjIL2Þ&!ððSdownreg cell¼2 i¼1 IFNgt ij Sdownreg cell¼2 i¼1 IL12t iÞ &FIBROBLASTÞ PERFOR = NK \| NK_NKG2D (Continued) A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 6 / 19 cytokines, as well as potent suppressors of the effector function of monocyte-macrophage and fibroblastic activity, interfering with the NFκB inflammatory signal [52–54]. Network accuracy and validation Experimental and clinical information. Simulations of chronic infection in IBD individ- uals show that the model reproduced satisfactorily experimental and clinical information (summarized in Table 3 and supporting information S3 Table). Fig 3 shows the results of the simulation for each network node after reaching the attractor state for virtual healthy and IBD subjects. In total, 31 upregulations in experimental studies were replicated with our simula- tions. Similarly, the 9 nodes reported as altered appeared upregulated in the simulations, and finally, the three nodes whose profiles were not known also proved to be upregulated. Clinical trials. In our simulations, three drugs that have failed to prove clinical efficacy in clinical trials (anti-IL17, anti-IFNγ and rhuIL-10) also exhibited no benefit in the simulated surrogate for the disease score (Fig 4). Simulations with anti-TNFα, a biologic therapy approved for IBD, showed a decrease in the disease score. Simulations with anti-IL12-IL23, a recently approved therapy for IBD, showed a slight decrease in MMPs and anti-IL2 therapy simulation showed a decrease similar to anti-TNFα. In addition, the new promising therapy (GMA), equivalent to an anti-MACR in our model showed a decrease in MMPs similar to that for anti-TNFα. Discussion In the current study, we present a Systems Pharmacology (SP) network model for IBD based on the main cells and proteins involved in the disease. Our analysis appears timely, as IBD has recently been attracting increasing attention [55–59]. We attempted to meet one of the major challenges in inflammatory bowel disease (IBD) which is the integration of IBD-related infor- mation to construct a predictive model. We are not the only ones following this line of research, as Lauren A Peters et al. have very recently performed a key driver analysis to identify the genes predicted to modulate network regulatory states associated with IBD [55]. Both anal- yses could be integrated in the future and inform our post-transcriptomic network with the key driver genes identified by Lauren A Peters et al. [55]. In comparison with the previous quantitative approaches for IBD [20,21,33,34], our model identified Naive CD4+ T Cells, Macrophages and Fibroblasts cells as relevant in IBD. Also, in addition to the six interleukins (TGFß, IL6, IL17, IL10, IL12 and IFNγ) considered by Mei et al. [33,34] our network involves 10 interleukins more which could represent possible IBD biomarkers [60]. The procedure to evaluate the potential role of the different components on the disease as plausible biomarkers, would be equal to the one described in section 4.5 (pertur- bation analysis and clustering), focussing on the changes in the output node. In the validation of network models, robustness and practical applicability represent critical aspects. The fact that the information gathered from the literature was obtained under very Table 2. (Continued) GRANZB = CD8_NKG2D \| NK \| NK_NKG2D \| (DC &! (LPS \| PGN)) OUTPUT NODE MMPs = (MACR & TNFa) \| (FIBROBLAST & (IL21 \| IL17 \| IL1b \| TNFa)) Bold text within Boolean equations indicates that the information belongs to animal data https://doi.org/10.1371/journal.pone.0192949.t002 A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 7 / 19 A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 8 / 19 different experimental designs/conditions/methodologies, represents a challenge with respect to validation. This led us to propose and adopt a novel strategy consisting of the comparison of the results of model-based virtual pathway simulations with those reported in the literature for IBD patients. Using this approach, we obtained a qualitative reproduction of IBD in which all the network elements that have been reported as upregulated in IBD patients appeared upre- gulated in our simulation results. The perturbation analysis of the network was performed by a single blockage in each node to analyse how that type of alteration propagates through the entire network reflecting the case of single polymorphisms, which represents the simplest case of IBD disease. Despite of the simplicity of this analysis, the results obtained from the model accuracy and validation procedures are encouraging. Results from the perturbation analysis indicate that the proposed network model is robust, as alteration in most nodes did not trigger considerable changes in the network [61]. Once validated and checked for robustness, the network was challenged to qualitatively reproduce the readouts of five different therapies reported in experimental and clinical studies. The outcome of this challenge was similar to the clinical output in IBD patients. By the simula- tion of TNFα or MACR knockout (simulating Granulocyte and Monocyte Apheresis), a decrease in MMPs node was observed, which is in line with therapy success in clinical practice by a decrease in Crohn’s Disease Activity Index (CDAI) Score [42–46],[62–68]. On other hand, IL17 or IFNγ knockout or IL10 overexpression did not show major change in MMPs expression, suggested a failed therapy as was indeed found in clinical practice [69–72]. Surprisingly, the model shows that a knockout of IL2 leads to a reduction in MMPs similar to that of a knockout of TNFα, even when previous results of clinical trials with Basiliximab or Daclizumab (monoclonal antibodies that bind to the interleukin 2 receptor CD25) in Ulcera- tive Colitis have failed to show superiority to corticosteroids alone [73,74]. The mechanism of Fig 2. IBD network perturbation analysis and clustering. The heatmap indicates the effect of single blockage of each node (columns) in every network node (rows). The colour in each cell corresponds to the Perturbation Index (PI) of the nodes. When there is no change in the expression of the node, the cells of the heatmap would be black, having a value between 0.8 and 1.25 in their PIs. Otherwise, when the perturbation causes an overexpression in a node, the cell in the heatmap would be orange coloured, with PIs values greater than 1.25. On the contrary, a value of 0.8 or smaller, blue colour, indicates that the perturbation causes a downregulation of the node. The numeric scale in the legend represents different values of the nodes PI under different perturbations. Nodes that induce similar alterations are hierarchically clustered. https://doi.org/10.1371/journal.pone.0192949.g002 Table 3. Expression of network nodes in IBD patients. NODE EXPRESSION NODE EXPRESSION NODE EXPRESSION NODE EXPRESSION PGN MDP LPS Altered IL1b Upregulated Th2 Upregulated DC Downregulated in Blood-Upregulated in mucosa TLR2 Upregulated IFNg Upregulated IL4 Altered IEC_MICA_B Upregulated TLR4 Upregulated IL23 Upregulated IL15 Upregulated IEC_ULPB1_6 Upregulated NOD2 Altered IL22 Upregulated IL12 Upregulated CD8_NKG2D Upregulated NFkB Altered IL21 Upregulated IL13 Upregulated NK_NKG2D Unknown IL6 TNFa Upregulated Upregulated IL17 Upregulated Treg Downregulated in Blood-Upregulated in mucosa CD4_NKG2D Upregulated TGFb Upregulated IL10 Upregulated NK Upregulated FIBROBLAST Upregulated Th0 Unknown Th17 Upregulated DEF Altered MMPs Upregulated Th0_M Upregulated Th17_M Upregulated IL2 Upregulated PERFOR Altered IL18 Upregulated Th1 Altered MACR Unknown GRANZB Upregulated A total of 31 nodes are reported as upregulated in IBD patients, 9 are reported to be altered (when different reports from literature are inconclusive or contradictory) and 3 nodes are unknown. https://doi.org/10.1371/journal.pone.0192949.t003 A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 9 / 19 action of corticosteroids has not been fully described, yet it is known that corticosteroids cause diminished levels of IL2 mRNA [75,76]. Together with the rest of corticosteroid inhibitory mechanisms, this would be the reason why Basiliximab or Daclizumab do not show superiority to corticosteroids alone. Among the potential applications the current network supports: (i) biomarker selection given that the cytokines TNFα, IL21, IL17 and IL1ß, which can be easily measured in periph- eral plasma with different Enzyme-linked immunosorbent assay (ELISA) kits [77,78], are the model components directly related to MMPs activation, (ii) search for optimal combination therapy to overcome the high attrition rates in phase clinical trials with single therapies which Fig 3. IBD network simulation results. Attractor state of every network node for healthy and IBD simulated individuals under chronic antigen exposure. https://doi.org/10.1371/journal.pone.0192949.g003 A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 10 / 19 are due mainly to lack of efficacy [79], and (iii) management of multiscale information such as the integration of proteomic gene expression data [55] accounting for IBD polymorphisms to anticipate responders and non-responders. With such a type of data able to correlate a genetic alteration with a decrease or an increase in protein expression, it would be possible to simulate specific genetic alteration by altering the protein expression. This would allow one of the limi- tations of the current network at the present time to be overcome with regard to the effects of Ustekinumab, a monoclonal antibody targeting free IL12 and IL23, which has been recently approved for moderately to severely active Crohn’s disease in adults who have failed to treat- ment with immunomodulators, or more than one TNFα blocker [80]. Simulation results based on the known mechanisms of Ustekinumab showed just a 4.1% decrease in tissue dam- age. On the other hand, when simulating TNFα blocker effects, tissue damage decreased by 30.6% even though a substantial percentage of patients showed poor control of the disease after treatment with anti-TNFα antibody [15,16]. We emphasize that the proposed network model is fully accessible which allows it to undergo immediate testing and further development. In that respect it should be noted that although our model intended to include information of human origin exclusively, some criti- cal pathways had to be complemented with animal derived data (although in the current case the percentage of human supported pathways is greater than in previous computational mod- els [20,81,82]), but we are aware of the wide differences in the immune system between species [83–85]. Fig 4. Comparison of MMPs expression after the simulation in IBD simulated individuals of different therapies. Simulated therapies: Anti-TNFα, GMA therapy (equivalent of knock out our MACR node), anti-IL17, human recombinant IL10 (rhulL-10), anti-IFNγ, anti-IL2 and anti-IL12-IL23. Comparing with untreated simulation, we can see a 30.7%, a 27.1%, a 31.9% and a 4.1% decrease in the MMPs expression simulating anti-TNFα, GMA therapy, anti- IL2 and anti-IL12-IL23 respectively. There is no major change in MMPs expression for the two which failed in clinical trials anti-IL17 (a 6.5% decrease) and human recombinant IL10 (a 3.2% decrease). Otherwise, anti-IFNγ therapy simulation shows an increase in MMPs expression of 16.0% compared to Untreated. https://doi.org/10.1371/journal.pone.0192949.g004 A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 11 / 19 This study addresses the goals of systems pharmacology by effectively encompassing prior knowledge to generate a mechanistic and predictive understanding at the systems level for IBD. Semi-quantitative understanding at the network level is necessary prior to the generation of detailed quantitative models for within-host disease dynamics. The current IBD model and the companion literature summary archive will drive the development of a dynamic (i.e., ordi- nary differential equation driven) model involving meaningful parameters capable of simulat- ing longitudinal data, and allowing model reduction as well the goal of parameter estimation during the clinical stages of the drug development process. In addition, our IBD network can be extended to other inflammatory diseases, as main pathways in the model are common to most inflammatory conditions [86,87], and the outputs of our nodes could also serve as inputs to broader-scale logic models; for example, incorporating structures from available logic mod- els of some of our nodes such as fibroblast [61], IL1b or IL6 [88]. In summary, we present a network model for inflammatory bowel disease which is available and ready to be used and can cope with (multi-scale) model extensions. It is supported by a comprehensive repository summarizing the results of the most relevant literature in the field. This model proved to be promising for the in silico evaluation of potential therapeutic targets, the search for pathway specific biomarkers, the integration of polymorphisms for patient strat- ification, and can be reduced and transformed in quantitative model/s. Methods Literature search and data selection The network model is based on an exhaustive bibliographic review focusing on the essential components of IBD, as previously performed by Ruiz-Cerda´ et al., in their systems pharmacol- ogy approach for lupus erythematosus [23]. Our review included around 620 papers published between October 1984 and September 2017, yet the most common reviewed articles were from 2007 or later (76%). The search of the relevant literature was made through Medical Subject Headings (MeSH) terms using different search engines such as PubMed, clinicaltrials.gov or google scholar. MeSH terms were focused on the combination of keywords and free words including: (i) relevant network components (ej.”IL6”) involved in the pathogenesis of IBD, (ii) nodes that have been reported to be altered in IBD (ej. “IL6 AND IBD”) and (iii) nodes directly affecting the expression of the nodes selected in (i) and (ii) (ej. “DC AND IL6”). The internal nodes selection was made according to the reported upregulated components in IBD patients together with the nodes (immune system cells) which are necessary to link the upregulated nodes, which were established as internal nodes. Only original papers with a clear description of experimental conditions were considered to identify the relationships between the compo- nents of the biological network. Due to the reported differences between animal and human immunology [83–85], in only few cases were animal data considered to connect nodes of criti- cal pathways when no human data were available. Annotation and system representation Annotation was crucial to organize the available literature according to its relevance. S2 Table from supplementary information shows the way the information was organized for building the network. S2 Table includes every node definition and the relationships between the nodes. Annotation included the identification of the main elements (antigens, cytokines, cells, pro- teins, membrane receptors and ligands) of IBD disease. The IBD model will be freely accessible to the public through the “The Cell Collective” repository https://cellcollective.org/#cb963d7f-75cb-4b2e-8987-0c7592a9c21d. A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 12 / 19 Boolean network building and r implementation The collection of qualitative relationships extracted from the literature was transformed into a logical model as described before by Ruiz-Cerda´ et al. [23]. Logic networks capture the dynam- ics of their components, called nodes, after selected stimuli or initial conditions [89,90]https:// paperpile.com/c/XvtklO/p0BRz+YiQ4q. In these models the relationships of activation or inhibition between nodes are described as combinations of the logic operators: AND, OR and NOT condensed in a mathematical expression called a Boolean function for each node. Posi- tive and negative modulators, and thresholds as previously described by Ruiz-Cerda´ et al.[23] and Irurzun-Arana et al. [28] were also considered to resemble better the biological system. Boolean network building and R implementation from S1 File gives a more detailed explana- tion of the modulators used in the model. Simulations The set of combined Boolean functions for the IBD model was implemented SPIDDOR [28], using RStudio Version 0.99.442. Simulations with 25 repetitions over 5000 iterations were per- formed. According to preliminary experiments, these simulation conditions were required to achieve the steady state of the network called attractor [91–93]. An attractor can be a fixed- point if it composed of one state, a simple cycle if consists of more than one state that oscillates in a cycle or a complex attractor if a set of steady-states oscillate irregularly. In each simulation, a node can show two possible values in each iteration: 0 (deactivated) or 1 (activated). The per- centage of activation of the output node (MMPs) calculated at the attractor state was used as the readout summary of the simulation exercises, as this group of proteins are directly associ- ated with intestinal fibrosis and tissue damage in IBD [42–46]. Each node was updated asynchronously [94–96] according to its Boolean function that defines the dynamics of the system. Initial conditions are explained in detail in “Simulations” from S1 File. Perturbation analysis and clustering Robustness can be defined as the system’s ability to function normally under stochastic pertur- bations [96]. The investigation of robustness in Boolean networks generally focuses on the dependence between robustness and network connectivity [97]. We performed a perturbation analysis in our IBD model to study robustness by simulating the effect of the single blockage of each node on every other node of the network [51]. This simulation was performed by using the KO_matrix.f function from SPIDDOR package with 24 repetitions over 999 iterations under asynchronous updating. Results from the simulations described above were represented as heatmaps with dendro- grams in which the number of rows and columns is equal to the number of nodes in the net- work (Fig 2). The colour in each cell of the heatmap corresponds to the Perturbation Index(PI) of the nodes, which is the probability ratio between the perturbed and the normal conditions as described by Irurzun-Arana et al. [28]. A hierarchical clustering method [98] was applied to further study which nodes cause similar alterations in the system. Network accuracy and validation Accuracy was evaluated comparing the alterations reported in the literature for IBD patients with the simulations of chronic antigen exposure for IBD or healthy individuals. A literature search of every node expression in IBD patients was performed, and the gath- ered information is condensed in S3 Table including three categories: up-, down-regulated, or A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 13 / 19 altered, whether the levels in CD, UC or both (IBD) with respect to healthy volunteers are higher, lower, or inconclusive and/or contradictory, respectively. For validation purposes, model simulations were compared against available results from clinical trials performed in IBD, CD or UC until the beginning of 2017 in https://www. clinicaltrials.gov/. All the molecules tested in clinical trials, whose mechanism of action is known and whose target were included in our network, were tested with the model. The net- work was evaluated comparing simulations and reported outcomes from clinical trials for six investigated molecules: anti-TNFα [62–65] and anti-IL12-IL23 [80], two monoclonal antibod- ies (mAb) approved for IBD disease, anti-IFNγ [69,70], anti-IL17 [72], anti-IL2 [73,74] and human recombinant IL10 (rhuIL-10) [71] which failed in clinical trials. Also a new promising therapy: Granulocyte and Monocyte Apheresis (GMA) [66–68] was tested. The reported CDAI (Crohn Disease Activity Index) was compared with the average expression of the MMPs output node in the attractor state. Supporting information S1 Table. Abbreviations. List of abbreviations. (PDF) S2 Table. IBD Network Repository. Table of nodes and interactions supported by references. (PDF) S3 Table. IBD_validation. Table of alterations in patients of IBD network nodes supported by references. (PDF) S1 File. Supporting_Information_Methods. Document with detailed description of the methodology. (DOCX) S2 File. IBD.txt. Text document with the Boolean functions written in SPIDDOR nomencla- ture for iBD simulation. (TXT) S3 File. User_Guide_SPIDDOR_IBD.html. Html tutorial about how to reproduce the results from the present manuscript with the SPIDDOR package. (HTML) Acknowledgments We would like to thank The Cell Collective team, specially to Tomas Helikar, for their help in building the model in their platform and making it more accessible to the community. Author Contributions Conceptualization: Violeta Balbas-Martinez, Jose´ David Go´mez-Mantilla, Iñaki F. Troco´niz. Data curation: Violeta Balbas-Martinez, Leire Ruiz-Cerda´, Ignacio Gonza´lez-Garcı´a. Formal analysis: Violeta Balbas-Martinez, Leire Ruiz-Cerda´, Itziar Irurzun-Arana, Jose´ David Go´mez-Mantilla. Funding acquisition: An Vermeulen, Iñaki F. Troco´niz. A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 14 / 19 Investigation: Violeta Balbas-Martinez, Leire Ruiz-Cerda´, Ignacio Gonza´lez-Garcı´a, Jose´ David Go´mez-Mantilla. Methodology: Violeta Balbas-Martinez, Itziar Irurzun-Arana, Ignacio Gonza´lez-Garcı´a, Jose´ David Go´mez-Mantilla, Iñaki F. Troco´niz. Project administration: An Vermeulen, Iñaki F. Troco´niz. Software: Violeta Balbas-Martinez, Itziar Irurzun-Arana, Ignacio Gonza´lez-Garcı´a, Jose´ David Go´mez-Mantilla. Supervision: An Vermeulen, Jose´ David Go´mez-Mantilla, Iñaki F. Troco´niz. Validation: Violeta Balbas-Martinez, Jose´ David Go´mez-Mantilla. Visualization: Violeta Balbas-Martinez. Writing – original draft: Violeta Balbas-Martinez, Iñaki F. Troco´niz. Writing – review & editing: Violeta Balbas-Martinez, Jose´ David Go´mez-Mantilla, Iñaki F. Troco´niz. References 1. Wehkamp J, Go¨tz M, Herrlinger K, Steurer W, Stange EF. Inflammatory Bowel Disease. 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A systems pharmacology model for IBD PLOS ONE \| https://doi.org/10.1371/journal.pone.0192949 March 7, 2018 19 / 19	29513758	PERFOR = ( NK_NKG2D ) OR ( NK ) Th2upregulation = ( Th2 AND ( ( ( IL4 ) ) ) ) IL15 = ( MACR AND ( ( ( LPS OR IFNg ) ) ) ) OR ( FIBROBLAST AND ( ( ( PGN OR LPS OR MDP ) ) ) ) IL23 = ( MACR AND ( ( ( IL1b ) ) ) ) OR ( DC ) CD8_NKG2D = ( ( MDP ) AND NOT ( CD8_NKG2D AND ( ( ( IL2 AND IL21 ) ) OR ( ( IEC_ULPB1_6 ) ) OR ( ( IEC_MICA_B ) ) ) ) ) OR ( ( LPS ) AND NOT ( CD8_NKG2D AND ( ( ( IL2 AND IL21 ) ) OR ( ( IEC_ULPB1_6 ) ) OR ( ( IEC_MICA_B ) ) ) ) ) OR ( ( PGN ) AND NOT ( CD8_NKG2D AND ( ( ( IL2 AND IL21 ) ) OR ( ( IEC_ULPB1_6 ) ) OR ( ( IEC_MICA_B ) ) ) ) ) Th2 = ( ( Th0 AND ( ( ( IL4 AND IL18 ) AND ( ( ( NOT IL12 ) ) ) ) OR ( ( IL10 ) ) OR ( ( Th2 AND IL4 ) AND ( ( ( NOT Th2upregulation ) ) ) ) ) ) AND NOT ( Th2 AND ( ( ( Treg OR TGFb OR IFNg ) ) ) ) ) Treg = ( ( Th0 AND ( ( ( TLR2 OR TGFb ) ) ) ) AND NOT ( Treg AND ( ( ( IL23 OR IL6 OR IL21 OR IL22 OR Th17 OR TNFa ) ) ) ) ) IL1b = ( ( MACR AND ( ( ( NFkB AND LPS ) ) ) ) AND NOT ( IL10 AND ( ( ( IL1b ) ) ) ) ) OR ( ( DC AND ( ( ( NFkB AND LPS ) ) ) ) AND NOT ( IL10 AND ( ( ( IL1b ) ) ) ) ) TLR2 = ( PGN ) Th17 = ( ( Th0 AND ( ( ( IL23 OR IL6 OR IL1b ) ) ) ) AND NOT ( Th17 AND ( ( ( IL4 OR Treg OR IL12 OR TGFb OR IFNg ) ) ) ) ) IL6 = ( MACR AND ( ( ( PGN ) ) ) ) OR ( Th17 AND ( ( ( IL23 ) ) ) ) OR ( NFkB AND ( ( ( NOT IL10 OR NOT IL4 ) ) ) ) OR ( DC AND ( ( ( PGN OR LPS ) ) ) ) IEC_ULPB1_6 = ( CD8_NKG2D AND ( ( ( PGN OR LPS OR MDP ) ) ) ) FIBROBLAST = ( ( IL2 ) AND NOT ( FIBROBLAST AND ( ( ( IL12 OR IFNg ) ) ) ) ) OR ( ( MACR AND ( ( ) OR ( ( IL4 OR IL13 OR TGFb ) ) ) ) AND NOT ( FIBROBLAST AND ( ( ( IL12 OR IFNg ) ) ) ) ) NFkB = ( TLR4 ) OR ( NOD2 ) OR ( TLR2 ) NK = ( ( IL18 AND ( ( ( IL10 ) ) ) ) AND NOT ( NK AND ( ( ( Treg ) ) ) ) ) OR ( ( IL23 ) AND NOT ( NK AND ( ( ( Treg ) ) ) ) ) OR ( ( DC AND ( ( ( IL15 ) ) ) ) AND NOT ( NK AND ( ( ( Treg ) ) ) ) ) Th0_M = ( Th0 AND ( ( ( IL23 OR IL12 ) ) ) ) OR ( Th0_M ) LPS = NOT ( ( DEF ) OR ( GRANZB ) OR ( PERFOR ) ) NK_NKG2D = ( ( MDP ) AND NOT ( NK_NKG2D AND ( ( ( IL21 ) AND ( ( ( IL12 ) ) ) ) AND ( ( IEC_ULPB1_6 ) ) AND ( ( IEC_MICA_B ) ) AND ( ( TGFb ) ) ) ) ) OR ( ( PGN ) AND NOT ( NK_NKG2D AND ( ( ( IL21 ) AND ( ( ( IL12 ) ) ) ) AND ( ( IEC_ULPB1_6 ) ) AND ( ( IEC_MICA_B ) ) AND ( ( TGFb ) ) ) ) ) OR ( ( LPS ) AND NOT ( NK_NKG2D AND ( ( ( IL21 ) AND ( ( ( IL12 ) ) ) ) AND ( ( IEC_ULPB1_6 ) ) AND ( ( IEC_MICA_B ) ) AND ( ( TGFb ) ) ) ) ) CD4_NKG2Dupregulation = ( CD4_NKG2D AND ( ( ( IL15 OR TNFa ) ) ) ) MMPs = ( MACR AND ( ( ( TNFa ) ) ) ) OR ( FIBROBLAST AND ( ( ( IL21 OR IL17 OR TNFa OR IL1b ) ) ) ) IEC_MICA_B = ( ( MDP ) AND NOT ( TGFb ) ) OR ( ( LPS ) AND NOT ( TGFb ) ) OR ( ( IEC_MICA_B AND ( ( ( TNFa ) AND ( ( ( NOT IEC_MICA_Bupregulation ) ) ) ) ) ) AND NOT ( TGFb ) ) OR ( ( PGN ) AND NOT ( TGFb ) ) DEF = ( IL22 ) OR ( NOD2 ) OR ( IL17 ) CD4_NKG2D = ( ( MDP ) AND NOT ( CD4_NKG2D AND ( ( ( IL10 ) ) OR ( ( IEC_ULPB1_6 OR IEC_MICA_B ) ) ) ) ) OR ( ( LPS ) AND NOT ( CD4_NKG2D AND ( ( ( IL10 ) ) OR ( ( IEC_ULPB1_6 OR IEC_MICA_B ) ) ) ) ) OR ( ( PGN ) AND NOT ( CD4_NKG2D AND ( ( ( IL10 ) ) OR ( ( IEC_ULPB1_6 OR IEC_MICA_B ) ) ) ) ) OR ( ( CD4_NKG2D AND ( ( ( IL15 OR TNFa ) AND ( ( ( NOT CD4_NKG2Dupregulation ) ) ) ) ) ) AND NOT ( CD4_NKG2D AND ( ( ( IL10 ) ) OR ( ( IEC_ULPB1_6 OR IEC_MICA_B ) ) ) ) ) IL12 = ( LPS AND ( ( ( IFNg ) AND ( ( ( DC ) ) OR ( ( PGN AND MACR ) ) ) ) ) ) OR ( TLR2 AND ( ( ( NFkB ) AND ( ( ( MACR OR DC ) ) ) ) ) ) IL21 = ( ( ( ( Th0 AND ( ( ( IL6 ) ) ) ) AND NOT ( IFNg ) ) AND NOT ( TGFb ) ) AND NOT ( IL4 ) ) OR ( Th17 ) IEC_MICA_Bupregulation = ( IEC_MICA_B AND ( ( ( TNFa ) ) ) ) DC = ( ( TLR4 ) AND NOT ( DC AND ( ( ( IL10 ) ) ) ) ) OR ( ( TLR2 ) AND NOT ( DC AND ( ( ( IL10 ) ) ) ) ) OR ( ( NOD2 ) AND NOT ( DC AND ( ( ( IL10 ) ) ) ) ) IFNg = ( ( ( IL18 AND ( ( ( IL12 ) AND ( ( ( Th0 OR MACR ) ) ) ) ) ) AND NOT ( IFNg AND ( ( ( IL10 OR TGFb ) ) ) ) ) AND NOT ( Th2 ) ) OR ( ( ( NK_NKG2D AND ( ( ( IEC_ULPB1_6 OR IEC_MICA_B ) ) ) ) AND NOT ( IFNg AND ( ( ( IL10 OR TGFb ) ) ) ) ) AND NOT ( Th2 ) ) OR ( ( ( CD8_NKG2D AND ( ( ( IEC_ULPB1_6 OR IEC_MICA_B ) ) ) ) AND NOT ( IFNg AND ( ( ( IL10 OR TGFb ) ) ) ) ) AND NOT ( Th2 ) ) OR ( ( ( Th1 ) AND NOT ( IFNg AND ( ( ( IL10 OR TGFb ) ) ) ) ) AND NOT ( Th2 ) ) OR ( ( ( Th17 AND ( ( ( PGN OR LPS OR MDP ) ) ) ) AND NOT ( IFNg AND ( ( ( IL10 OR TGFb ) ) ) ) ) AND NOT ( Th2 ) ) OR ( ( ( IL23 AND ( ( ( NK ) ) AND ( ( PGN OR LPS OR MDP ) ) ) ) AND NOT ( IFNg AND ( ( ( IL10 OR TGFb ) ) ) ) ) AND NOT ( Th2 ) ) TNFa = ( ( MACR AND ( ( ( LPS AND IFNg ) ) OR ( ( PGN ) ) OR ( ( IL2 ) ) ) ) AND NOT ( IL10 AND ( ( ( TNFa ) AND ( ( ( TLR4 OR TLR2 ) ) ) ) ) ) ) OR ( ( NFkB AND ( ( ( LPS ) ) ) ) AND NOT ( IL10 AND ( ( ( TNFa ) AND ( ( ( TLR4 OR TLR2 ) ) ) ) ) ) ) OR ( ( NK_NKG2D AND ( ( ( IEC_ULPB1_6 OR IEC_MICA_B ) ) ) ) AND NOT ( IL10 AND ( ( ( TNFa ) AND ( ( ( TLR4 OR TLR2 ) ) ) ) ) ) ) OR ( ( CD8_NKG2D AND ( ( ( IEC_ULPB1_6 OR IEC_MICA_B ) ) ) ) AND NOT ( IL10 AND ( ( ( TNFa ) AND ( ( ( TLR4 OR TLR2 ) ) ) ) ) ) ) OR ( ( NK AND ( ( ( PGN OR LPS OR MDP ) AND ( ( ( IL23 OR IL2 OR IL15 ) ) ) ) ) ) AND NOT ( IL10 AND ( ( ( TNFa ) AND ( ( ( TLR4 OR TLR2 ) ) ) ) ) ) ) OR ( ( FIBROBLAST AND ( ( ( IFNg ) ) ) ) AND NOT ( IL10 AND ( ( ( TNFa ) AND ( ( ( TLR4 OR TLR2 ) ) ) ) ) ) ) OR ( ( CD4_NKG2D AND ( ( ( IEC_ULPB1_6 OR IEC_MICA_B ) ) ) ) AND NOT ( IL10 AND ( ( ( TNFa ) AND ( ( ( TLR4 OR TLR2 ) ) ) ) ) ) ) IL13 = ( Th2 ) IL18 = ( LPS AND ( ( ( MACR OR DC ) ) AND ( ( NFkB ) ) ) ) TLR4 = ( LPS ) NOD2 = ( MDP ) Th1 = ( ( Th0 AND ( ( ( IL18 OR IL12 OR IFNg ) ) ) ) AND NOT ( Th1 AND ( ( ( IL10 ) ) OR ( ( Treg ) ) OR ( ( IL12 ) AND ( ( ( IL23 OR IL17 ) ) ) ) OR ( ( TGFb ) ) OR ( ( Th2 ) ) OR ( ( IL4 ) ) ) ) ) IL22upregulation = ( Th0 AND ( ( ( IL21 ) ) AND ( ( IL22 ) ) ) ) IL10 = ( MACR AND ( ( ( LPS ) AND ( ( ( NOT IL4 ) ) ) ) ) ) OR ( DC AND ( ( ( LPS ) ) ) ) OR ( TLR2 AND ( ( ( NFkB ) AND ( ( ( NOT MACR AND NOT IFNg ) ) ) ) ) ) OR ( Th2 AND ( ( ( NOT IL23 ) ) ) ) OR ( Treg ) PGN = NOT ( ( DEF ) OR ( PERFOR ) OR ( GRANZB ) ) MACR = ( ( NOD2 ) AND NOT ( MACR AND ( ( ( IL10 ) ) ) ) ) OR ( ( IFNg ) AND NOT ( MACR AND ( ( ( IL10 ) ) ) ) ) OR ( ( IL15 ) AND NOT ( MACR AND ( ( ( IL10 ) ) ) ) ) OR ( ( TLR4 ) AND NOT ( MACR AND ( ( ( IL10 ) ) ) ) ) OR ( ( TLR2 ) AND NOT ( MACR AND ( ( ( IL10 ) ) ) ) ) TGFb = ( MACR ) OR ( Treg ) GRANZB = ( CD8_NKG2D ) OR ( NK ) OR ( DC AND ( ( ( NOT PGN OR NOT LPS ) ) ) ) OR ( NK_NKG2D ) MDP = NOT ( ( DEF ) OR ( GRANZB ) OR ( PERFOR ) ) IL22 = ( NK AND ( ( ( IL18 AND IL12 ) ) ) ) OR ( Th17 ) OR ( ( Th0 AND ( ( ( IL21 ) ) AND ( ( NOT IL22upregulation ) ) AND ( ( IL22 ) ) ) ) AND NOT ( TGFb ) ) OR ( CD4_NKG2D ) Th17_M = ( Th17_M ) OR ( Th0_M AND ( ( ( PGN OR LPS OR MDP ) AND ( ( ( IL2 ) ) OR ( ( IL6 AND IL1b ) ) OR ( ( IL23 ) ) ) ) ) ) IL4 = ( Th2 ) IL17 = ( ( Th17 ) AND NOT ( IL17 AND ( ( ( IL13 OR TGFb ) ) ) ) ) OR ( ( CD4_NKG2D AND ( ( ( IEC_ULPB1_6 OR IEC_MICA_B ) ) ) ) AND NOT ( IL17 AND ( ( ( IL13 OR TGFb ) ) ) ) ) OR ( ( Th17_M AND ( ( ( PGN OR LPS OR MDP ) ) ) ) AND NOT ( IL17 AND ( ( ( IL13 OR TGFb ) ) ) ) ) IL2 = ( Th0_M AND ( ( ( PGN OR LPS OR MDP ) ) ) ) OR ( Th0 ) OR ( DC ) Th0 = ( MDP ) OR ( PGN ) OR ( LPS )

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