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Descriptive performance Intuitively, a decent explanatory grammar generates parse trees consistent with spatial structure of the protein. Perhaps the most straightforward approach to assess descriptive performance is to use the UST of the maximum likelihood parse tree as a predictor of spatial contacts between position... |
Implementation The PCFG-CM parser and the Protein Grammar Evolution framework were implemented in C++ using GAlib (Wall, 2005 and Eigen (Guennebaud et al., 2010 . Performance measures were implemented in Python 2 (van Rossum and de Boer, 1991 using Biopython (Cock et al., 2009 , igraph (Csardi and Nepusz, 2006 , NumPy ... |
Results 3.1 Materials Probabilistic grammars were estimated for three samples of protein fragments based on functionally relevant gapless motifs (Sigrist et al., 2002 ; Bailey and Elkan, 1994 . Within each sample, all sequences shared the same length, which avoided sequence length effects on grammar scores (which could... |
CaMn : a Calcium and Manganese binding site from the legume lectins (Sharon and Lis, 1990 collected according to the PROSITE PS00307 pattern (Sigrist et al., 2013 true positive and false negative hits. Boundaries of the motif were extended to cover the entire binding site, similarly to (Dyrka and Nebel, 2009 . The moti... |
NAP : the Nicotinamide Adenine dinucleotide Phosphate binding site fragment from an aldo/keto reductase family (Bohren et al., 1989 collected according to the PS00063 pattern true positive and false negative hits (four least consistent sequences were excluded). The motif is only a part of the binding site of the relati... |
HET-s : the HET-s-related motifs r1 and r2 involved in the prion-like signal transduction in fungi identified in a recent study (Daskalov et al., 2015 . The largest subset of motifs with length of 21 amino acids was used to avoid length effects on grammar scores. When interacting with a related motif r0 from a cooperat... |
Diversity of sequences ranged from the most homogenous CaMn to the most diverse HET-s, which consisted of 5 subfamilies (Daskalov et al., 2015 |
Negative samples were designed to roughly approximate the entire space of protein sequences. They were based on the negative set from (Dyrka and Nebel, 2009 , which consisted of 829 single chain sequences of 300-500 residues retrieved from the Protein Data Bank (Berman et al., 2000 at identity of 30% (accessed on 12th ... |
All samples were made non-redundant at level of sequence similarity around 70%. Contact pairings were assigned manually and collectively to all sequences in the set based on a selected available spatial structure of a representative positive sequence in the PDB database (Fig. ). |
3.2 Performance Probabilistic grammars with the contact rules [MATH] were learned through estimation of probabilities of rules [MATH] for non-probabilistic CFG [MATH] using input samples made of sequences coupled with the contact map [MATH] , or using sequences alone [MATH] . Probabilistic grammars without the contact ... |
3.2.1 Discriminative power For evaluation of discriminative power of the PCFG-CM approach, rule probabilities were estimated using the maximum-likelihood estimator (denoted ML) and the contrastive estimator with regard to the contact map (denoted CE(m)). Discriminative performance of the resulting probabilistic grammar... |
The baseline here is the average precision of grammars estimated without contact constraints, [MATH] and [MATH] , tested on sequences alone [MATH] , which ranged from 0.43-0.46 for HET-s to 0.94-0.96 for CaMn. The scores show negative correlation with diversity of the samples and limited effect of adding contact rules ... |
[MATH] performed much worse when tested on the samples with the contact map [MATH] , which indicates that preference for parses consistent with [MATH] is at best limited when training without constraints. |
For all three samples, the highest AP (0.91-0.98) achieved grammars obtained using the contrastive estimation with regard to the contact map [MATH] tested on the samples with the map [MATH] . The improvement relative to the baseline was most pronounced for HET-s, yet still statistically significant ( [MATH] ) for NAP. ... |
The maximum-likelihood grammars estimated with the contact information [MATH] tested on [MATH] performed worse than the contrastively estimated grammars but comparably or significantly better (HET-s) than the baseline. The average precision of [MATH] was consistently lower when tested without the map on sequences alone... |
Notably high AP for CaMn with [MATH] tested on [MATH] and with [MATH] tested on [MATH] can be contributed to relatively strong signal from the long stem-like part of the motif particularly suitable for modeling with the contact rules. |
3.2.2 Descriptive power For evaluation of descriptive power of the PCFG-CM approach, rule probabilities were estimated using the maximum-likelihood estimator (denoted ML) and the contrastive estimator with regard to sequences (denoted CE(X)). Descriptive value of the most probable parse trees generated using the result... |
The baseline here are the results for grammars with the contact rules estimated without contact constraints [MATH] . The most likely parse trees generated using these grammars conveyed practically no information about contacts for NAP and HET-s (recall w.r.t [MATH] close to zero) and limited information about contacts ... |
Importantly, consistency of the most likely parse trees with the protein structure measured by the precision followed a similar pattern and increased from 0.13 for HET-s, 0.14 for NAP, and 0.69 for CaMn when learning on [MATH] , to respectively 0.52-0.57, 0.64, and 0.84-0.87, when learning on [MATH] . Accordingly, eval... |
Discussion and conclusions 4.1 Analysis of computational results Computational validation of discriminatory power showed that additional knowledge present in the partial contact map can be effectively incorporated into the probabilistic grammatical framework through the concept of syntactic tree consistent with the con... |
Computational validation of descriptive power showed that the most likely parse trees, derived for inputs defined only by sequences, reproduced vast majority of contacts (recall of at least 0.79 at [MATH] ) enforced by the contact-map constrained training input. Moreover, precision of contact prediction at [MATH] and s... |
Reasonable performance of grammars estimated with contact constraints [MATH] on sequences alone (AP from 0.60 to 0.95) is encouraging as it gives a hint of performance of the PCFG-CM approach in its potential most general application to model very diverse data sets where each training sequence is associated with a diff... |
4.2 Limitations and perspectives The computational experiments mainly served assessing intuitions, which led to development of the PCFG-CM approach. Full scale practical application to bioinformatic problems such as sequence search would certainly require several enhancements. For example, accurate accounting for vario... |
Though tested in the learning setting consisting in optimizing only rule probabilities, the estimators defined in the present PCFG-CM framework can be used in more general learning schemes inferring also the grammar structure. Indeed, such schemes may even more benefit from constraining the larger search space. It is a... |
Contributions The PCFG-CM framework was proposed by WD and elaborated by WD, FC and JT. Implementation of the special instance, computational experiments and analysis of results were carried out by WD. The paper was written by WD, FC and JT. |
Acknowledgements This research has been partially funded by National Science Centre, Poland [grant no 2015/17/D/ST6/04054] and was supported by the E-SCIENCE.PL Infrastructure. Computational experiments have been partially carried out using resources provided by Wroclaw Centre for Networking and Supercomputing () [gran... |
# Source: arxiv 1805.08777 # Title: Early Cancer Detection in Blood Vessels Using Mobile Nanosensors # Sections: all # Downloaded: 2026-03-03T05:17:59.887481+00:00 |
Early Cancer Detection in Blood Vessels Using Mobile Nanosensors Abstract In this paper, we propose using mobile nanosensors (MNSs) for early stage anomaly detection. For concreteness, we focus on the detection of cancer cells located in a particular region of a blood vessel. These cancer cells produce and emit special... |
Introduction Molecular communication (MC) is an emerging technology enabling communication among nanomachines. Inspired by biological systems, synthetic diffusion-based MC systems have been proposed as a potential solution for communication in nanonetworks where molecules play the role of information carriers |
. Nanonetworks are envisioned to facilitate revolutionary applications in areas such as biological engineering, healthcare, and environmental monitoring |
One of the key challenges in health monitoring and disease diagnosis applications is the problem of anomaly detection , e.g., early cancer detection , which has received significant attention in medicine and other related fields |
. Since early cancer detection can significantly decrease cancer mortality, great efforts have been devoted to the investigation of new technologies for detecting the symptoms of cancer at an early stage |
. These symptoms are characteristics that can indicate the presence of anomaly, and include cancer biomarkers Cancer biomarkers cover a broad range of biochemical entities such as nucleic acids, proteins, sugars, small metabolites, and cytogenetic and cytokinetic parameters as well as entire cancer cells found in body ... |
Among these biomarkers, proteins are of particular interest since they are primarily found in blood and urine where they can be measured with current medical technologies, such as clinical blood tests |
It has been shown in that abnormal behavior/expressions of protein biomarkers can be associated with particular cancers. For example, [MATH] -fetoprotein, carcinoma antigen [MATH] , carcinoembryonic antigen, and prostate-specific antigen are common biomarkers for liver, ovarian, colorectal, and prostate cancers, respec... |
Conventional blood tests may not be able to detect biomarkers secreted by cancer cells in the early stages of a cancer due to the very low concentration of the biomarkers inside the cardiovascular system (CS) |
. However, close to the cancer cells, the concentration of the cancer biomarkers is high such that reliable detection is possible if a corresponding sensor passes in the vicinity of the cancer cells. In this paper, we propose the use of engineered nanosensors for this purpose. Such nanosensors play a key role in nanome... |
The ability of engineered nanosensors to fast and intelligently release, move, observe, and read inside the CS motivates the investigation of the use of mobile nanosensors (MNSs) for anomaly detection |
. In particular, MNSs can be released from an injection site, move through the CS, become activated at sites of high biomarker concentration, and eventually be captured at a fusion center (FC) which then decides on the presence of an anomaly. The time interval between release and capture of the MNSs at the FC is called... |
Anomaly detection has been extensively studied in different fields, including computer science, segmentation of biomedical signals, and fraud detection for credit cards, see e.g. |
and . However, in the context of MC, the amount of related prior work is limited. In , anomaly detection in molecular nanonetworks is studied and a suboptimal decision rule is employed to combine the observations at the FC. More recently, in |
, both optimal and near-optimal decision rules are developed for networks where nanosensors employ either one or multiple types of molecules to relay their gathered information to the FC. However, both |
and assume that the nanosensors are fixed , i.e., they do not move inside the CS. In , an MC system for tumor detection in blood vessels is proposed. In this work, the authors assume that specific nanorobots are injected into the CS which are attracted by the tumor cells. After detection of a tumor, these nanorobots re... |
, a graph-based model for mobile MC systems with several bio-nanomachines is proposed, and the concentration of the bio-nanomachines is numerically evaluated. It is shown that similar to |
, the concentration of the considered bio-nanomachines is high in the vicinity of tumor cells. We note that the cardiovascular network is highly complex and the propagation of the molecules within this network is therefore very complicated. Hence, most prior works relied on extensive simulations to analyze sensing syst... |
. On the contrary, in this paper, by developing a simplified yet meaningful model for the CS, we establish an analytical framework for analyzing the proposed detection system which provides useful insights for system design. In particular, we consider collaborative anomaly detection where multiple MNSs are released at ... |
and references therein. The MNSs may ultimately reach an FC which decides on the presence of an anomaly based on the activation levels of the observed MNSs. Relying on multiple MNSs is motivated by the fact that, in general, healthy cells also release a small amount of the same type of biomarkers into the CS as the can... |
[MATH] Although in general the CS has a highly complex structure, we propose a simplified yet meaningful model for the blood vessels of the CS facilitating first-order insights about the propagation of biomarkers and MNSs through the CS. In particular, we model blood vessels as two-dimensional (2-D) rectangles and simp... |
, we assume a quasi-steady state behavior for the number of biomarkers in the blood vessels during the comparatively short observation window. |
[MATH] We calculate the time-dependent probability density function (PDF) of the location of one biomarker released by a cancer cell inside a cancerous blood vessel. Subsequently, we derive the steady-state spatial concentration of the biomarkers inside the cancerous blood vessel, due to a continuous release of biomark... |
[MATH] Based on the results obtained for one cancerous blood vessel, we extend our model to networks comprising several blood vessels, which are part of the entire CS. To this end, we decompose the networks into three main building blocks, namely straight edges junction nodes , and bifurcation nodes , and analytically ... |
[MATH] We also derive the statistics of the activation levels of the MNSs traveling through the blood vessels of a given network. Furthermore, based on the proposed system model, we formulate a hypothesis testing framework to decide at the FC whether cancer cells are present in the CS or not. To this end, we derive the... |
for a given number of MNSs observed and read out at the FC by assuming that the FC knows the structure of the entire network. We then derive a simple and practical detector, which we refer to as sum detector , that adds up the activation levels of the MNSs observed at the FC. Next, we evaluate the performance of the pr... |
The remainder of this paper is organized as follows. In Section II, we provide the system model. In Section III, we develop a model for cancerous blood vessels and derive the steady-state distribution of the biomarkers inside the blood vessels of a sample network of the CS. In Section IV, we derive the statistics of th... |
II System Model In this section, we introduce the system model considered in this paper. We consider a part of the CS comprising several blood vessels. The blood vessels may be interpreted as the edges of a network. The edges may merge, thus forming nodes, cf. Fig. We assume that in one specific point of the network, p... |
In the following, we develop a simplified model for the CS suitable for formulating a decision problem. Then, we provide a model for biomarker detection at the MNSs. |
II-A A Simplified Model for the Cardiovascular System In general, the CS is highly complex. Therefore, in order to keep our analysis tractable, we are interested in developing a simplified model, which retains the relevant characteristics of the CS. To this end, we consider a similar model as the one proposed in 24 , C... |
. The biomarkers secreted by healthy cells can be interpreted as environmental noise. In addition, instead of considering a complex 3-D model for the CS, to facilitate first-order insights about the propagation of biomarkers and MNSs through the CS, we consider a simplified 2-D model for the network, as depicted in Fig... |
, but also facilitates the derivation of closed-form expressions for the biomarker concentration and the activation levels of the MNSs for the proposed MNS-based approach for the anomaly detection problem. |
II-B Cancerous Blood Vessel We adopt a simple model for the cancerous blood vessel. In particular, for the blood vessels, we assume a 2-D rectangular shape with length [MATH] and height [MATH] and reflective boundaries. The cancer biomarkers are released into one of the blood vessels at position [MATH] , as depicted in... |
, which imposes a non-uniform flow velocity along the [MATH] -axis. However, for tractability of the analysis, and similar to , and |
, we assume a uniform flow with constant velocity [MATH] Furthermore, we assume that the cancer resides in one specific capillary while the released biomarkers spread into all neighboring edges and nodes. We also assume that the biomarkers degrade at a rate of [MATH] [s -1 ] and are released at a constant rate of [MATH... |
. The release rate depends on the stage of the cancer, i.e., in the early stages, it is very low, and in the final stages, it can be very high. For the flow velocity change at the interconnections of the vessels, i.e., the nodes of the network, we also assume uniform flow, where the velocity of the incoming and outgoin... |
, due to the conservation of mass. The mathematical model of the biomarker release rate and the biomarker distribution inside the CS will be presented in Section III |
II-C Mobile Nanosensors MNSs are employed to decide on the presence of cancer cells in a network of interconnected blood vessels. We assume that the MNSs are injected at one specific site of the network and that each MNS has a small area, [MATH] , and can measure the number of biomarkers within this area |
. In addition, we assume that the MNSs are passive with respect to the biomarkers, i.e., the MNSs and biomarkers move independently in the environment and do not interact with each other. In particular, an MNS can be a natural or an engineered cell which can periodically and locally measure and count the number of biom... |
The number of biomarkers inside an MNS can be determined either directly by counting the number of biomarkers bound by suitable cell-surface receptors |
, or indirectly by measuring other parameters, such as the pressure and temperature of the medium in the vicinity of an MNS’s surface |
After MNS injection, based on the direction of the flow in the blood vessel network and the topology of the network, the MNSs follow different routes where they may eventually encounter the cancer biomarkers, e.g., when passing through cancerous tissue and capillaries. The MNSs enter the cancerous vessel at positions [... |
, we assume the time interval between two consecutive measurements is large enough such that the observations are independent. Furthermore, we assume that the MNS can accumulate successive observations and the FC can read out the summation value. We will refer to this value as the activation level and denote it for the... |
II-D Fusion Center The MNSs can pass through different routes of the network and some may not arrive at the FC. Since for a given MNS the selection of the path through the network is random, a released MNS is observed at the FC with a certain probability [MATH] . Intuitively, [MATH] can be increased by choosing a favor... |
and Here, we assume that the FC can observe and read the activation levels of all MNSs that come in contact with it. After reading out the MNSs’ measurements, the FC makes a decision regarding the presence of cancer cells. Optimal and suboptimal decision rules for the FC will be provided in Section |
III Biomarker Distribution In this section, first we consider a single cancerous blood vessel and derive the distribution of the biomarkers in it as a function of time and space. Then, we extend the obtained results to a sample network of the CS and analyze the distribution of the biomarkers in the interconnected blood... |
III-A Biomarker Production Rate In the literature, several models for the production rate of cancer cells inside a blood vessel have been proposed |
. However, most of these models do not include the production rate of biomarkers secreted by cancerous and healthy cells. One recently established model for the production rates of cancerous and healthy cells as well as the biomarkers secreted by these cells is given in |
. This model can be summarized as follows. 1. The total number of cancer cells inside the cancerous tissue, denoted by [MATH] , follows a Gompertzian function |
[EQUATION] where [MATH] is the initial number of cancer cells at time zero, and [MATH] and [MATH] are the fractional growth and decay rates of the cancer cells, respectively. For [MATH] , i.e., in the early stage of a cancer, ( ) can be approximated by |
[EQUATION] 2. Unlike the cancer cells, the number of healthy cells is assumed to be constant over time, i.e., [MATH] 3. Cancerous cells and healthy cells secrete the same biomarkers into the medium with constant shedding rates [MATH] and [MATH] , respectively, where [MATH] . However, in the vasculature, on average frac... |
4. The biomarkers degrade uniformly in the blood vessel over time with constant degradation rate [MATH] Based on the above assumptions, the release rate of the biomarkers secreted by healthy cells is constant and equal to [MATH] . However, for the cancer cells, we obtain the rate of biomarker release, denoted by [MATH]... |
[EQUATION] For healthy cells, which cover the entire surface of the blood vessels, it can be shown that the total number of secreted biomarkers that are present in the environment reaches a steady-state value of [MATH] |
Moreover, at any location of the CS, we can model the number of the biomarkers within a small area [MATH] by a Poisson PMF , with a mean proportional to [MATH] . We denote this mean by [MATH] , which does not depend on [MATH] nor [MATH] On the other hand, for cancer cells, the number of secreted biomarkers does not rea... |
), using ( ) we can model the number of cancer cells during a short time interval around [MATH] (e.g. a few days), denoted by [MATH] , as constant. This implies a quasi-steady state where the secretion rate is approximately constant and equal to [MATH] during time interval [MATH] In the following subsections, we derive... |
III-B Local Cancerous Blood Vessel In this subsection, we consider a single cancerous blood vessel and evaluate the distribution of the biomarkers secreted by the cancer cells inside the blood vessel as a function of time and space. This analysis is needed to determine the PMF of the activation level of an MNS that ent... |
In small blood vessels, the blood in the [MATH] -direction can be modeled as a non-Newtonian Casson fluid, which imposes a non-uniform flow velocity profile along the [MATH] -axis |
, denoted by [MATH] . Therefore, considering that the biomarkers are released by the cancer cells at position [MATH] into the medium with a release rate of [MATH] , where [MATH] is the delta function, the following advection-diffusion equation describes the 2-D biomarker concentration |
[EQUATION] where [MATH] is the divergence operator, [MATH] is the Laplace operator, and [MATH] is the diffusion coefficient of the biomarkers. Since [MATH] is a function of [MATH] , usually numerical methods are used to solve ( |
. However, as mentioned in Section II , in this paper, to gain first-order insight, we consider a 2-D model with uniform flow, i.e., [MATH] , which allows us to analytically solve the differential equation in ( ). In particular, for uniform flow, the advection-diffusion equation for the concentration of the biomarkers ... |
[EQUATION] with boundary condition [EQUATION] To solve ( ), we first derive the spatial PDF for impulsive release of one biomarker at time [MATH] , and then use it to determine the spatial distribution of the biomarkers when they are released with constant rate [MATH] . To this end, we consider one biomarker release at... |
[EQUATION] where [MATH] is the height of the cancerous blood vessel. Then, the concentration of the biomarkers in the blood vessel at time [MATH] and location [MATH] can be obtained as follows |
[EQUATION] Given ( III-B ), in the following lemma, by evaluating ( ) we provide a closed-form expression for the steady-state concentration of the biomarkers secreted by the cancer cells. |
Lemma 1 For a single cancerous vessel with cancer cells located at [MATH] and biomarker secretion rate [MATH] , the steady-state concentration of cancer biomarkers at [MATH] is given by |
[EQUATION] where [MATH] is the sign function which is [MATH] for [MATH] [MATH] for [MATH] , and [MATH] for [MATH] Proof: [MATH] is obtained by substituting ( III-B ) into ( ) and taking the limit [MATH] , where [MATH] is given by ( ). |
Remark 1 It can be shown that for small blood vessels (such as capillaries, arterioles, and venules, where [MATH] ), the steady-state concentration of the biomarkers secreted by cancer cells [MATH] is approximately constant with respect to [MATH] for a given [MATH] . Therefore, we can approximate the concentration as |
[EQUATION] where [EQUATION] This approximation is further investigated in Section VI . We use this result to solve a 1-D advection-diffusion equation in Section III-C for a network of connected blood vessels. |
Remark 2 For typical system parameters for blood vessels and biomarkers, we have [MATH] [MATH] . Hence, ( 11 ) can be simplified as |
[EQUATION] III-C Network of Blood Vessels In this subsection, we derive closed-form expressions for the distribution of the concentration of the biomarkers inside a given network of blood vessels. The secreted biomarkers spread across multiple blood vessels which imposes further boundary conditions on the advection-dif... |
As can be observed from Fig. , a network typically comprises three fundamental blocks: I: Straight edges : The blood vessels that connect two adjacent nodes. |
II: Junction nodes : In a junction node, two or more incoming blood flows join to become one single flow. III: Bifurcation nodes : In a bifurcation node, an incoming blood flow is split into two or more outgoing flows. |
In Section III-B , we provided the steady-state concentration of the biomarkers for a local straight edge in ( 10 ). In the following, we study the effect of junction and bifurcation nodes on the concentration of the biomarkers inside the edges. |
III-C Junction Node For a junction node, we consider the case where [MATH] small edges are joined to form a bigger edge, see Fig. a). We assume that the [MATH] -th incoming edge has flow velocity [MATH] and cross-sectional area [MATH] , and the outgoing edge has flow velocity [MATH] and cross-sectional area [MATH] . Th... |
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