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Functional connotation of WGD and non-WGD paralogs Next, we focused on the difference in function between local and global duplicates. Whole-genome and local duplications are different biological processes, and the analysis of WGD and non-WGD paralogs can help understanding the biological constraints laying behind the ... |
. In particular, different works proved that WGD and non-WGD duplicates are enriched for different functional classes of genes. Thus, we set out to quantify with our methods how the effects of the WGD on the genome are qualitatively different from those brought by local duplications. |
Domain-based analysis Functional assignment of domains can be used for evaluating the evolutionary destiny of duplicates. We considered two functional classifications for domains given in the SCOP database |
. We then proceeded to evaluate the trends in domain duplications, regardless from the specific protein they were duplicated with. We assigned domains to a set [MATH] if they were duplicated in at least one WGD paralog, and a set [MATH] if they appeared in at least one local duplication (see Methods). We considered par... |
[MATH] ) than expected from a hypergeometric null model (figure ). Thus, there is a dominant common set of domains that is prone to be duplicated, regardless of the local or global duplication mode. |
On the other hand, the observed distribution of the fraction of WGD versus non-WGD duplicate proteins where each domain topology is found is very uneven (supplementary figure S5 ). This trend indicates the existence of two populations of domain topologies: those that are duplicated only outside the WGD, and those that ... |
[MATH] , the domains only found in non-WGD duplicates, for functional enrichment. For the finer categories of the SCOP functional classification we found a few cases where the enrichment was biased in two opposite ways in the two sets, i.e. categories having a positive [MATH] -score for WGD domains, and a negative [MAT... |
The categories that show a bias for WGD-specific domains (belonging to [MATH] ) correspond to functions that are growth-related (ribosomes, translation), involved in regulation of gene transcription and degradation (transcription factors, proteases), primary metabolism (coenzymes) or cell adhesion. On the other hand, a... |
[MATH] was found in functional categories related to transport, post-transcriptional regulatory processes and secondary metabolism. Surprisingly, we found that the category DNA repair and replication tends to be enriched among domains duplicated locally rather than globally. Weaker signals for the same trend were found... |
Gene Ontology analysis In parallel, we performed a more standard functional characterization based on Gene Ontology analysis on the proteins, along the lines of previous studies |
. We considered the disjoint sets of WGD and non-WGD paralogs. For each set we extracted the over-represented GO terms, and we compared them looking for the terms shared between WGD and non WGD-paralogs or specifically connected to a group (over-represented in a group and not significantly present in the other). WGD an... |
In accordance with the domain-based analysis and with the previous hierarchical analysis derived from expression profiles and functional annotations |
, we find that WGD paralogs are enriched for genes involved in “fundamental” processes such as for example, ribosomes and translation, regulation of cell cycle, regulation of developmental processes, sporulation, NADP metabolic process. On the other side the non-WGD paralogs are enriched for genes involved in “peripher... |
Finally, a recent study by Guan and coworkers found that WGD duplicates are more likely to share interaction partners and biological functions than non-WGD duplicates. To confirm the latter result, we analyzed the distribution of the GO similarity normalized histograms for all the pairs of the two disjoint sets. Indeed... |
Discussion Homology among distant paralogs and orthologs proteins is a difficult task because of sequence divergence. But it is well known that the structure of a protein is more conserved than its sequence. To score distant relationships among yeast and |
K. waltii proteins we used SCOP superfamilies domain assignments. This choice has three main reasons. First, these domains contain three-dimensional structural information, and are not solely based on sequence similarity, so that they can be considered, at least to a certain extent, “independent” from sequence alignmen... |
, which give a term of comparison. The criteria and scores we used assume that two proteins derived from the same common ancestor if they have the same domain architecture, or a series of domains from the same protein families. This method allowed us to compare the more distant structural homology relationships with th... |
. A thorough analysis of the role of these parameters is presented in ref. Domain architecture and homology. Despite the sparse coverage of structural domains, it seems evident from our results that even elementary domain based homology criteria can recover most of the information obtained through sequence alignments t... |
and have a similar percentage of homologs not detected in Ensembl, while criterion , follows a different trend. This last criterion is the only one that allows for insertion of external domains after duplication, which is an event that has been observed and can be expected from our knowledge of the evolutionary dynamic... |
On the other hand, the different behavior of criterion could suggest a lower reliability compared to the other ones. It is important to stress that the architecture comparison methods implemented in this paper can show false-positive matches. In other words, the less restrictive the criterion is, the higher is the poss... |
Overall, while some instances could represent false positives, we believe it is natural to expect that some others represent distant relationships that are not detected as paralogs by sequence alignment methods, but are recognized by domain-based methods. Our tools do not allow to quantify these false positives directl... |
Thus, the above evidence goes in favor of using structural domains as a simple and computationally effective tool to discover gene duplications. At the same time, it points to some limitations of these methods. The most important of these is that currently no tool is available to quantify the failure rate of domain-bas... |
, or that the partial coverage of domain databases does not enable to resolve distinct architectures. However, an exact quantification of these processes is lacking. |
Domain structure and function of duplicate proteins. A second and more biological question is to use domain architectures to understand gene duplication, and in particular the differences between local duplications and the WGD. To approach this question, we compared the results of our domain similarity scores with a fu... |
Following duplications, proteins show divergence in their domain architectures. Our scoring criteria quantify the rate of divergence of architectures. For all duplications, the already mentioned fact that domain scores remain constant and close to one as a function of duplication age indicates a strong trend of conserv... |
on the same sets of duplicates showing a marked trend for divergence in function with increasing duplication age. An explanation of this phenomenon may be the fact that proteins evolve with point mutations affecting one nucleotide at a time. Domain topology can withstand these mutations without changing significantly, ... |
Obviously, this functional divergence cannot exceed the physical possibilities of a domain topology: a kinase domain will never bind to DNA. This is compatible with our observation that GO similarities do not drop to zero, and even very ancient duplicates always retain some degree of functional overlap. Along the same ... |
observe that the functional fates of duplicates rarely diverge with respect to biochemical function, but typically diverge with respect to regulatory control. The typical case when this is known to happen is that of transcription factors |
, where the migration of sequences within the same DNA-binding fold can lead to major changes in the affinity for a given set of sequences, and thus to large variation on the set of regulated targets. More simply, GO term divergence could come to a change of cellular compartment or biological process while performing s... |
Biological Process and Cellular Component We extracted from our set some paralogs that maintain exactly the same domain architecture after duplication, while changing their molecular function, their cellular compartment and/or the biological process in which they are involved (GO term similarity [MATH] ). It is the cas... |
Naturally, the coverage of domains on genomes is only partial, which leaves the question open of whether the observed trends of functional annotations with duplication age are due to modifications in the space of domains that are not visible to our methods. While of course this may happen, it seems unlikely that this c... |
, supplementary figure S4 ) do not change. Specificity of the Whole-Genome Duplication. We now revert to the specific features of the whole-genome duplication. Double-sided domain architecture comparison of |
S. cerevisiae WGD paralogs with their K. waltii ortholog allows to evaluate asymmetric evolution at the domain level. Comparing with a suitable null model, we found no systematic trend for asymmetry (table ). This is not unexpected, as domains are much more stable than sequences in evolution, so that, even in presence ... |
From the functional viewpoint, we observe that the WGD does not follow a different trend in GO-term similarity between paralogs than expected from its age. Thus, we have to conclude that a “functional burst” correlated to accelerated evolution |
does not differentiate the global duplication from local ones, or that this trend is not visible from the data available to us. Partitioning the universe of all S. cerevisiae domains in locally and globally duplicated ones yields two sets of WGD and non-WGD domains, that can have an intersection, as the same domain can... |
However, the domains of WGD duplicates laying outside common set of duplicable domains remain significant, as they give rise to evident peaks in the frequency of observing a domain in the sets of WGD and non-WGD duplicates. Moreover, they are also significant functionally. Indeed, the disjoint sets of WGD-specific and ... |
In agreement with these results, we find that fundamental functions, such as ribosomes and translation are enriched in the WGD while peripheral functions, such as secondary metabolism are enriched for local duplications. The rationale for this result might be that functions related to core biological processes, or in g... |
. On the other hand, global moves such as the WGD could release these constraints and allow “recycling” and disentanglement of more elaborate cell machinery. |
Finally, we can speculate on the consequences of the fact that the functional dichotomy is also found at the domain level. If it is true that function migrates abundantly, the functional dichotomy of local and global duplicates may emerge from migration of function maintaining similar domain structures. However, this c... |
Methods Data Sets. We used the SUPERFAMILY database version 1.69 for the SCOP superfamily domains assignment, and the functional annotation of domains. We implemented a C code to reconstruct the protein domain architectures, as ordered lists of domains and “gaps” (a protein subsequence of 100 AA or more not scored for ... |
(release 50) . For K. waltii-S. cerevisiae WGD duplicates we referred to refs. and to ref. ; the latter study was also used for the datation of duplicates. |
Homology criteria. Three different homology criteria were used to compare the domain architecture of proteins Criterion considers exactly matching architectures. The underlying biological hypothesis is that divergence after duplication does not change the domain architecture of the proteins, implying that divergence be... |
Domain architecture comparison scores. We defined two different methods to compare proteins in their structural properties. The first “domain score” quantifies the variation in the domains of the two architectures, and is defined as the number of common domains domains between the two architectures, divided by the tota... |
Domain-based functional analysis. Duplicate proteins with nonempty domain architecture were divided into two disjoint sets of WGD and non-WGD duplicates. The first set, from ref. |
, is composed by 692 S. cerevisiae proteins, estimated to be 62% of the total WGD paralogs. The second set (1863 proteins) was defined by those proteins coded by a gene with at least one known homolog, from which we removed the other set. Structural domains extracted from the two sets were divided accordingly into thre... |
[MATH] belonging either to WGD paralogs or to non-WGD paralogs, using as universe the set of all distinct domains found in S. cerevisiae |
Gene Ontology analysis We downloaded the Gene Ontology (GO) annotation DAGs from the GO website ( ) and the gene product annotations from the Ensembl database, version 46. We considered a gene annotated to a GO term if it was directly annotated to it or to any of its descendants in the GO tree. We used the SYNERGY algo... |
for defining paralogy classes. Orthologs and paralogs were considered different groups. As a reference, 100 pairs of sets were considered, each consisting of 1000 randomly assorted genes with the only constraint that each gene was chosen only once in each pair. For each group we implemented an exact Fisher’s test to as... |
. Fisher’s test gives the probability [MATH] of obtaining an equal or greater number of genes annotated to the term in a set made of the same number of genes, but randomly selected. Subsequently, the terms shared by both groups and the exclusive terms (terms present in only one group) were extracted. Finally, we filter... |
. For each duplication date group we calculated the mean and the standard deviation of the mean of the GO term similarity. Acknowledgement |
We would like to thank Hervé Isambert for useful discussions, and Paolo Provero for critical reading of this manuscript. Supporting Information |
# Source: arxiv 0812.2408 # Title: Outer-totalistic cellular automata on graphs # Sections: all # Downloaded: 2026-03-02T08:58:11.106083+00:00 |
Outer-totalistic cellular automata on graphs Abstract We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically sensitive elementary cellul... |
Introduction —Cellular automata (CA) on graphs in principle provide the possibility to monitor systematic changes of dynamics under variation of network topology. In practice, however, unambiguously studying the relation between topology and dynamics with CA is conceptually difficult, since changes in topology inevitab... |
The formalism —Within the CA framework, the discrete (binary) state [MATH] of a node [MATH] at time [MATH] solely depends on its own state and the states of its [MATH] neighboring nodes at time [MATH] . All cells are updated synchronously by the same, time-independent rule [MATH] . To implement CA on a directed or undi... |
[MATH] . Our strategy instead is to impose constraints on the rule space, motivated by simple physical requirements, in order to obtain a set of discrete rules, implementable on arbitrary topologies: |
Homogeneity [MATH] , i.e. the same rule applies to all nodes in the graph. Isotropy [MATH] , i.e. rules may not depend on the order of neighboring states and are thus functions of the density of neighboring states, [MATH] . Here, [MATH] is represented by the adjacency matrix |
[MATH] : If a link connects node [MATH] to node [MATH] [MATH] , and we call [MATH] an input node of [MATH] . The number of all input nodes is called the in-degree of node [MATH] [MATH] |
Functional simplicity, i.e. the rule [MATH] is a piecewise constant function of the density [MATH] Elementary Cellular Automata —The simplest CA, termed elementary CA (ECA) Wolfram ( 1983 , are defined on a one-dimensional grid with minimal neighborhood size, [MATH] , and a binary state space, |
[MATH] . The [MATH] different neighborhood configurations [MATH] result in [MATH] possible rules. In this set, [MATH] rules fulfill the conditions mentioned above and depend only on the state [MATH] [MATH] or [MATH] ) and on the density [MATH] of neighboring states (0, 1/2, or 1). These 64 rules are called outer-totali... |
[EQUATION] We distinguish the following cases for the rule parameters [MATH] : The state [MATH] may be [MATH] or [MATH] independently of the state [MATH] itself, or it may remain unchanged [MATH] ) or be flipped ( [MATH] ), [MATH] . The frequently used majority rule |
Crutchfield and Mitchell ( 1995 ); Moreira et al. ( 2004 ); Amaral et al. ( 2004 ); Nochomovitz and Li ( 2006 for example, where a node [MATH] is mapped onto [MATH] if the density |
[MATH] is below [MATH] above [MATH] , and stays in its state otherwise, is described in our formalism by [MATH] For [MATH] , the corresponding CA rules are called totalistic Wolfram ( 1983 , since [MATH] depends exclusively on the density [MATH] of the input states. Only these rules have strict RBN rule equivalents (se... |
Aside from the initial system state [MATH] at [MATH] , the patterns of rule [MATH] and rule [MATH] are perfectly symmetric under the action of the operator [MATH] . The operator [MATH] |
exchanges all 0s and 1s in an array of elements, which can be both a pattern consisting of 0’s and 1’s or a set of rule parameters. Note that the elements [MATH] remain unaffected under the action of |
[MATH] . Generally, the symmetric rule to [MATH] is rule [MATH] The patterns emerging from the action of a rule onto an initial state, written as [MATH] , are identical to the inverted patterns emerging from the inverted initial state |
[MATH] due to [MATH] [MATH] . Explicitly, the symmetric rule to [MATH] , corresponding to the ECA with rule number 218 Wolfram ( 1983 , is [MATH] with ECA rule number 164 (see Table |
for more examples). Some rules, like the majority rule [MATH] , are self-symmetric. After elimination of all symmetric counterparts, 34 different ECA rules remain. |
Which of these 34 rules are topologically sensitive? That is, which lead to patterns of considerably different complexity when implemented on the regular ECA grid and the RBN architecture? Wolfram classified CA heuristically according to the complexity of the emerging patterns into the four Wolfram classes Wolfram ( 19... |
Marr and Hütt ( 2006 2005 ); Marr et al. ( 2007 . The Shannon entropy [MATH] serves as a measure for the homogeneity of the spatio-temporal pattern, by averaging over all nodes: [MATH] . The probabilities [MATH] and [MATH] denote the ratios of 0’s and 1’s in the time series of node [MATH] . The word entropy [MATH] serv... |
We compare [MATH] random initial conditions on the regular architecture with [MATH] samples of a randomized graph, where the number of incoming and outgoing links of every node is preserved and kept to [MATH] , but the link architecture has been randomized |
Trusina et al. ( 2004 . Notably, for a considerably large number of randomization steps, we generate random regular graphs Wormald ( 1999 rather than Poisson-distributed random graphs |
Erdős and Rényi ( 1959 We classify rules as topologically sensitive, if the difference of the mean entropies for regular and randomized architectures is beyond the standard deviation of the difference. Out of the 34 rules, 14 rules fulfill that condition for at least one observable, [MATH] or [MATH] . These can be divi... |
(a). Moreover, these four rules react specifically to topological changes. Figure (b) shows the Shannon entropy against the number of randomization steps performed. While the patterns of rules [MATH] and [MATH] change already when a small number of shortcuts are introduced into the system, [MATH] stays constant in this... |
Regular graphs —How much complexity is possible on regular graphs? With growing neighborhood size [MATH] , the number of possible densities [MATH] and therefore the number of possible rules increases. For the sake of simplicity, we restrict our investigation to a binary state space and to rules with a single threshold:... |
[EQUATION] For networks with [MATH] , 11 different threshold parameters [MATH] lead to 336 different rules, where symmetric rules are considered only once. To estimate the number of rules with complex (that is in our context: non-trivial) patterns, we calculate [MATH] for time evolutions. The word entropy is a feasible... |
[MATH] . However, the exact values of these thresholds do not alter our results qualitatively. As shown in Figure , the number of possible rules (dashed line) increases linearly with [MATH] , while a maximum of complex patterns (full lines) occurs for [MATH] . The striking overall reduction of complexity for neighborho... |
Complex networks —The formalism of Eq. ( ) can be transferred to networks of arbitrary topology. Compared to regular graphs with global neighborhood size [MATH] , the case where [MATH] will rarely occur in graphs with heterogeneous connectivity. We thus simplify the set of possible rules with single threshold: By setti... |
[MATH] and the threshold parameter [MATH] As a first exemplary application, we consider scale-free graphs, Barabási and Albert ( 1999 with a power law degree distribution, a property often found in real-life networks Albert and Barabási ( 2002 ); Newman ( 2003 . Due to their pivotal topological property, the existence ... |
Maslov and Sneppen ( 2002 ); Trusina et al. ( 2004 ); Weber et al. ( 2008 . Here we want to study how degree correlations in a scale-free graph affect its ability to generate complex patterns. We implement all resulting rules on randomized, hierarchized and anti-hierarchized variants of scale-free graphs with 200 nodes... |
Trusina et al. ( 2004 . For each graph type, we calculate the entropy signatures, given by the Shannon entropy and word entropy of the emerging patterns, for all rules. Figure shows the entropy signature difference plot, where [MATH] of the randomized graphs (R) has been subtracted from the entropy signature of the hie... |
[MATH] or [MATH] with [MATH] . Notably, rule [MATH] is a condensed form of the topology-sensitive ECA rule 108, appearing in Figure |
. For the anti-hierarchized graph with negative degree-degree correlations, a similar picture emerges (data not shown). As a second example, we consider the topology of metabolic networks, which abstracts the wiring architecture of the set of enzyme-catalyzed reactions in a specific species. Substrate graphs, where nod... |
Marr et al. ( 2007 , we recently studied the impact of the topology of metabolic networks on a specific dynamics. There we implemented and studied only a single rule, namely [MATH] as a dynamic probe and interpreted the enhanced regularizing capacity of real networks compared to randomized null models as a possible top... |
[MATH] or [MATH] while [MATH] . For all these rules, the entropy signature of real graphs is significantly smaller compared to the null model topologies. This is also true for hierarchized and anti-hierarchized null models, as well as for all other species investigated in |
Marr et al. ( 2007 . We believe that the application of dynamic probes is a particularly helpful tool for studying dynamical constraints imposed by topology. |
Discussion —Our formalism can be used to describe outer-totalistic CA and isotropic RBN rules in a common framework. It allows the comprehensive discussion of previously introduced rule sets on diverse topologies, like the selection of Boolean rules presented in Amaral et al. ( 2004 or variations of the majority rule a... |
Moreira et al. ( 2004 ); Nochomovitz and Li ( 2006 . It moreover formalizes previous attempts to generalize CA to graphs O’Sullivan ( 2001 ); Darabos et al. ( 2007 , and is easily extensible, e.g. by introducing more than just one threshold parameter or by using a larger state space. With the presented framework, the o... |
Matache and Heidel ( 2004 may be reconsidered from the more general perspective provided in this letter. As a specific example, the application of ECA rule 22 to arbitrary graphs, stated as an open question in |
Matache and Heidel ( 2004 , is straightforward with the presented formalism. Limitations arise as soon as individual node characteristics are to be taken into account. Still, the isotropic subset of canalyzing Boolean rules, as discussed in |
Paul et al. ( 2006 , can be represented with our approach. Table shows some examples of symmetric rules in our formalism, the corresponding ECA and RBN rule number and references where these rules have been previously applied. |
An analysis of topologically sensitive rules with analytical tools as developed in Drossel et al. ( 2005 or the recently introduced basin entropy Krawitz and Shmulevich ( 2007 may reveal state space changes associated with topological modifications. Such analyses can elucidate dynamic properties also relevant for regul... |
Bornholdt and Sneppen ( 2000 ); Li et al. ( 2004 ); Davidich and Bornholdt ( 2008 . From this perspective, our framework provides a means to comprehensively study the sensitivity of a system to topological perturbations and associated rule space modifications. |
# Source: arxiv 0812.4373 # Title: Differentiating information transfer and causal effect # Sections: all # Downloaded: 2026-03-02T08:58:12.382525+00:00 |
Differentiating information transfer and causal effect Abstract The concepts of information transfer and causal effect have received much recent attention, yet often the two are not appropriately distinguished and certain measures have been suggested to be suitable for both. We discuss two existing measures, transfer e... |
information theory, information transfer, causality, information flow, cellular automata, complex systems, self-organization pacs: 89.75.Fb, 89.75.Kd, 89.70.Cf, 05.65.+b |
Introduction Information transfer is currently a popular topic in complex systems science, with recent investigations spanning cellular automata Lizier et al. ( 2008a , biological signaling networks Pahle et al. ( 2008 ); Tung et al. ( 2007 , and agent-based systems Lungarella and Sporns ( 2006 In general, information ... |
Predictive transfer refers to the amount of information that a source variable adds to the next state of a destination variable; i.e. “if I know the state of the source, how much does that help to predict the state of the destination?”. This transferred information can be thought of as adding to the prediction of an ob... |
Causal effect refers to the extent to which the source variable has a direct influence or drive on the next state of a destination variable, i.e. “if I change the state of the source, to what extent does that alter the state of the destination?”. Information from causal effect can be seen to flow through the system, li... |
Unfortunately, these concepts have become somewhat tangled in discussions of information transfer. Measures for both predictive transfer Schreiber ( 2000 and causal effect Ay and Polani ( 2008 have been inferred to capture information transfer in general, and measures of predictive transfer have been used to infer caus... |
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