Signaling pathways are responsible for the regulation of cell processes, such as monitoring the external environment, transmitting information across membranes, and making cell fate decisions. Given the increasing amount of biological data available and the recent discoveries showing that many diseases are related to the disruption of cellular signal transduction cascades, in silico discovery of signaling pathways in cell biology has become an active research topic in past years. However, reconstruction of signaling pathways remains a challenge mainly because of the need for systematic approaches for predicting causal relationships, like edge direction and activation/inhibition among interacting proteins in the signal flow. We propose an approach for predicting signaling pathways that integrates protein interactions, gene expression, phenotypes, and protein complex information. Our method first finds candidate pathways using a directed-edge-based algorithm and then defines a graph model to include causal activation relationships among proteins, in candidate pathways using cell cycle gene expression and phenotypes to infer consistent pathways in yeast. Then, we incorporate protein complex coverage information for deciding on the final predicted signaling pathways. We show that our approach improves the predictive results of the state of the art using different ranking metrics.
Predictive understanding of the myriads of signal transduction pathways in a cell is an outstanding challenge of systems biology. Such pathways are primarily mediated by specific but transient protein-protein interactions, which are difficult to study experimentally. In this study, we dissect the specificity of protein-protein interactions governing two-component signaling (TCS) systems ubiquitously used in bacteria. Exploiting the large number of sequenced bacterial genomes and an operon structure which packages many pairs of interacting TCS proteins together, we developed a computational app…
Eukaryotic cells transmit information by signaling through complex networks of interacting proteins. Here we develop a theoretical and computational framework that relates the biophysics of protein-protein interactions (PPIs) within a signaling network to its information processing properties. To do so, we generalize statistical physics-inspired models for protein binding to account for interactions that depend on post-translational state (e.g. phosphorylation). By combining these models with information-theoretic methods, we find that PPIs are a key determinant of information transmission wit…
Eukaryotic cells transmit extracellular signal information to cellular interiors through the formation of a ternary complex made up of a ligand (or agonist), G-protein, and G-protein coupled receptor (GPCR). Previously formalized theories of ternary complex formation have mainly assumed that observable states of receptors can only take the form of monomers. Here, we propose a multiary complex model of GPCR signaling activations via the vector representation of various unobserved aggregated receptor states. Our results from model simulations imply that receptor aggregation processes can govern …
We investigate the influences of the excluded volume of molecules on biochemical reaction processes on 2-dimensional surfaces using a model of signal transduction processes on biomembranes. We perform simulations of the 2-dimensional cell-based model, which describes the reactions and diffusion of the receptors, signaling proteins, target proteins, and crowders on the cell membrane. The signaling proteins are activated by receptors, and these activated signaling proteins activate target proteins that bind autonomously from the cytoplasm to the membrane, and unbind from the membrane if activate…
One of the key characteristics of cancer cells is an increased phenotypic plasticity, driven by underlying genetic and epigenetic perturbations. However, at a systems-level it is unclear how these perturbations give rise to the observed increased plasticity. Elucidating such systems-level principles is key for an improved understanding of cancer. Recently, it has been shown that signaling entropy, an overall measure of signaling pathway promiscuity, and computable from integrating a sample's gene expression profile with a protein interaction network, correlates with phenotypic plasticity and i…
The network paradigm is increasingly used to describe the dynamics of complex systems. Here we review the current results and propose future development areas in the assessment of perturbation waves, i.e. propagating structural changes in amino acid networks building individual protein molecules and in protein-protein interaction networks (interactomes). We assess the possibilities and critically review the initial attempts for the application of game theory to the often rather complicated process, when two protein molecules approach each other, mutually adjust their conformations via multiple…
Biological information processing as implemented by regulatory and signaling networks in living cells requires sufficient specificity of molecular interaction to distinguish signals from one another, but much of regulation and signaling involves somewhat fuzzy and promiscuous recognition of molecular sequences and structures, which can leave systems vulnerable to crosstalk. This paper examines a simple computational model of protein-protein interactions which reveals both a sharp onset of crosstalk and a fragmentation of the neutral network of viable solutions as more proteins compete for regi…
In a previous paper we introduced a method called augmented sparse reconstruction (ASR) that identifies links among nodes of ordinary differential equation networks, given a small set of observed trajectories with various initial conditions. The main purpose of that technique was to reconstruct intracellular protein signaling networks. In this paper we show that a recursive augmented sparse reconstruction generates artificial networks that are homologous to a large, reference network, in the sense that kinase inhibition of several reactions in the network alters the trajectories of a sizable n…
Signaling events in eukaryotic cells are often guided by a scaffolding protein. Scaffold proteins assemble multiple proteins in a spatially localized signaling complex and exert numerous physical effects on signaling pathways. To study these effects, we consider a minimal, three-state kinetic model of scaffold mediated kinase activation. We first introduce and apply a path summation technique to obtain approximate solutions to a single molecule master equation that governs protein kinase activation. We then consider exact numerical solutions. We comment on when this approximation is appropriat…
Spatial heterogeneity is a hallmark of living systems, even at the molecular scale in individual cells. A key example is the partitioning of membrane-bound proteins via lipid domain formation or cytoskeleton-induced corralling. Yet the impact of this spatial heterogeneity on biochemical signaling processes is poorly understood. Here we demonstrate that partitioning improves the reliability of biochemical signaling. We exactly solve a stochastic model describing a ubiquitous motif in membrane signaling. The solution reveals that partitioning improves signaling reliability via two effects: it mo…
Robustness and sensitivity of responses generated by cell signaling networks has been associated with survival and evolvability of organisms. However, existing methods analyzing robustness and sensitivity of signaling networks ignore the experimentally observed cell-to-cell variations of protein abundances and cell functions or contain ad hoc assumptions. We propose and apply a data driven Maximum Entropy (MaxEnt) based method to quantify robustness and sensitivity of Escherichia coli (E. coli) chemotaxis signaling network. Our analysis correctly rank orders different models of E. coli chemota…
The problem of reconstructing and identifying intracellular protein signaling and biochemical networks is of critical importance in biology today. We sought to develop a mathematical approach to this problem using, as a test case, one of the most well-studied and clinically important signaling networks in biology today, the epidermal growth factor receptor (EGFR) driven signaling cascade. More specifically, we suggest a method, augmented sparse reconstruction, for the identification of links among nodes of ordinary differential equation (ODE) networks from a small set of trajectories with diff…
Scaffolding proteins that direct the assembly of multiple kinases into a spatially localized signaling complex are often essential for the maintenance of an appropriate biological response. Although scaffolds are widely believed to have dramatic effects on the dynamics of signal propagation, the mechanisms that underlie these consequences are not well understood. Here, Monte Carlo simulations of a model kinase cascade are used to investigate how the temporal characteristics of signaling cascades can be influenced by the presence of scaffold proteins. Specifically, we examine the effects of spa…
LBBE, CNRS UMR 5558, Université Lyon 1（里昂第一大学CNRS UMR 5558计算与进化生物学实验室）；Microsoft Research New England（微软新英格兰研究院）；Human Genetics Foundation（人类遗传学基金会）；Politecnico di Torino（都灵理工大学）；Université of Toulouse（图卢兹大学）；UMR CNRS-INSA 5504（法国国家科学研究中心-图卢兹国立应用科学学院UMR 5504联合研究单位）；INRA 792（法国国家农业研究院792研究单位）
External information propagates in the cell mainly through signaling cascades and transcriptional activation, allowing it to react to a wide spectrum of environmental changes. High throughput experiments identify numerous molecular components of such cascades that may, however, interact through unknown partners. Some of them may be detected using data coming from the integration of a protein-protein interaction network and mRNA expression profiles. This inference problem can be mapped onto the problem of finding appropriate optimal connected subgraphs of a network defined by these datasets. Th…
Proteins with multiple binding sites play important roles in cell signaling systems by nucleating protein complexes in which, for example, enzymes and substrates are co-localized. Proteins that specialize in this function are called by a variety names, including adapter, linker and scaffold. Scaffold-mediated nucleation of protein complexes can be either constitutive or induced. Induced nucleation is commonly mediated by a docking site on a scaffold that is activated by phosphorylation. Here, by considering minimalist mathematical models, which recapitulate scaffold effects seen in more mechan…
Living cell signaling systems include multistep biochemical signaling reaction cascades (BSCs) comprising modifications of molecular signaling proteins. Substantial data on BSCs have been accumulated in the field of molecular biology and the analysis of signaling systems requires qualitative evaluation. However, quantification of the information and channel capacity of BSCs has not been focused on from the perspective of information theory. In the current study, we aimed to derive basic equations for describing the channel capacity and information density of BSCs using the fluctuation theorem.…
We used various analytical and numerical techniques to elucidate signal propagation in a small enzymatic cascade which is subjected to external and internal noise. The nonlinear character of catalytic reactions, which underlie protein signal transduction cascades, renders stochastic signaling dynamics in cytosol biochemical networks distinct from the usual description of stochastic dynamics in gene regulatory networks. For a simple 2-step enzymatic cascade which underlies many important protein signaling pathways, we demonstrated that the commonly used techniques such as the linear noise appro…
We apply the methods of optimal experimental design to a differential equation model for epidermal growth factor receptor (EGFR) signaling, trafficking, and down-regulation. The model incorporates the role of a recently discovered protein complex made up of the E3 ubiquitin ligase, Cbl, the guanine exchange factor (GEF), Cool-1 (Beta-Pix), and the Rho family G protein Cdc42. The complex has been suggested to be important in disrupting receptor down-regulation. We demonstrate that the model interactions can accurately reproduce the experimental observations, that they can be used to make predic…
In systems biology new ways are required to analyze the large amount of existing data on regulation of cellular processes. Recent work can be roughly classified into either dynamical models of well-described subsystems, or coarse-grained descriptions of the topology of the molecular networks at the scale of the whole organism. In order to bridge these two disparate approaches one needs to develop simplified descriptions of dynamics and topological measures which address the propagation of signals in molecular networks. Here, we consider the directed network of protein regulation in E. coli, ch…
Tumors bearing Ras mutations are notoriously difficult to treat. Drug combinations targeting the Ras protein or its pathway have also not met with success. Pathway drug cocktails, which are combinations aiming at parallel pathways, appear more promising; however, to be usefully exploited, a repertoire of classified pathway combinations is desirable. This challenge would be facilitated by the availability of the structural network of signaling pathways. When integrated with functional and systems-level clinical data they can be powerful in advancing novel therapeutic platforms. Based on structu…
Biological signaling pathways based upon proteins binding to one another to relay a signal for genetic expression, such as the Bone Morphogenetic Protein (BMP) signaling pathway, can be modeled by mass action kinetics and conservation laws that result in non-closed form polynomial equations. Accurately determining parameters of biological pathways that represent physically relevant features, such as binding affinity of proteins and their associated uncertainty, presents a challenge for biological models lacking an explicit likelihood function. Additionally, parameterizing non-closed form biolo…
Angiotensin II (AngII) type 1 receptor (AT1R) is a G protein-coupled receptor known for its role in numerous physiological processes and its implication in many vascular diseases. Its functions are mediated through G protein dependent and independent signaling pathways. AT1R has several endogenous peptidic agonists, all derived from angiotensinogen, as well as several synthetic ligands known to elicit biased signaling responses. Here, surface plasmon resonance (SPR) was used as a cell- based and label-free technique to quantify, in real time, the response of HEK293 cells stably expressing the …
Naively, one expects the information communicated by an enzyme downstream within a signaling network, in which the enzyme is embedded, to grow monotonically with the enzyme's rate of product formation. However, here we observe that this does not necessarily hold true for allosterically regulated enzymes, often observed in signaling networks. In particular, we find that the mutual information between the catalytic sites of an allosterically regulated enzyme and a receiver protein downstream in the signaling pathway depends on the transition kinetics between the different allosterically regulate…
Molecular processes of neuronal learning have been well-described. However, learning mechanisms of non-neuronal cells have not been fully understood at the molecular level. Here, we discuss molecular mechanisms of cellular learning, including conformational memory of intrinsically disordered proteins and prions, signaling cascades, protein translocation, RNAs (microRNA and lncRNA), and chromatin memory. We hypothesize that these processes constitute the learning of signaling networks and correspond to a generalized Hebbian learning process of single, non-neuronal cells, and discuss how cellula…
G-protein coupled receptors (GPCRs), a major gatekeeper of extracellular signals on plasma membrane, are unarguably one of the most important therapeutic targets. Given the recent discoveries of allosteric modulations, an allosteric wiring diagram of intramolecular signal transductions would be of great use to glean the mechanism of receptor regulation. Here, by evaluating betweenness centrality ($C_B$) of each residue, we calculate maps of information flow in GPCRs and identify key residues for signal transductions and their pathways. Compared with preexisting approaches, the allosteric hotsp…
To illustrate the power of the biophysical approach in solving important problems in life science, I present here one of our current research projects as an example. We have developed special biophotonic techniques to study the dynamic properties of signaling proteins in a single living cell. Such a study allowed us to gain new insight into the signaling mechanism that regulates programmed cell death.
The promise of discovering a functional blueprint of a cellular system from large-scale and high-throughput sequence and experimental data is predicated on the belief that the same top-down investigative approach that proved successful in other biological problems (e.g. DNA sequencing) will be as effective when it comes to inferring more complex intracellular processes. The results in this paper address this fundamental issue in the specific context of transcription regulatory networks. Although simple recurring regulatory motifs have been identified in the past, due to the size and complexity…
Flagellated bacteria, such as Escherichia coli, perform directed motion in gradients of concentration of attractants and repellents in a process called chemotaxis. The E. coli chemotaxis signaling pathway is a model for signal transduction, but it has unique features. We demonstrate that the need for fast signaling necessitates high abundances of the proteins involved in this pathway. We show that further constraints on the abundances of chemotaxis proteins arise from the requirements of self-assembly, both of flagellar motors and of chemoreceptor arrays. All these constraints are specific to …
The novel coronavirus SARS-CoV-2 has resulted in a global pandemic with worldwide 6-digital infection rates and thousands death tolls daily. Enormeous effords are undertaken to achieve high coverage of immunization in order to reach herd immunity to stop spreading of SARS-CoV-2 infection. Several SARS-CoV-2 vaccines, based either on mRNA, viral vectors, or inactivated SARS-CoV-2 virus have been approved and are being applied worldwide. However, recently increased numbers of normally very rare types of thromboses associated with thrombocytopenia have been reported in particular in the context o…
Integrin signaling regulates cell migration and plays a pivotal role in developmental processes and cancer metastasis. Integrin signaling has been studied extensively and much data is available on pathway components and interactions. Yet the data is fragmented and an integrated model is missing. We use a rule-based modeling approach to integrate available data and test biological hypotheses regarding the role of talin, Dok1 and PIPKI in integrin activation. The detailed biochemical characterization of integrin signaling provides us with measured values for most of the kinetics parameters. Howe…
We propose a model of parameter learning for signal transduction, where the objective function is defined by signal transmission efficiency. We apply this to learn kinetic rates as a form of evolutionary learning, and look for parameters which satisfy the objective. This is a novel approach compared to the usual technique of adjusting parameters only on the basis of experimental data. The resulting model is self-organizing, i.e. perturbations in protein concentrations or changes in extracellular signaling will automatically lead to adaptation. We systematically perturb protein concentrations a…
There are many mathematical models of biochemical cell signaling pathways that contain a large number of elements (species and reactions). This is sometimes a big issue for identifying critical model elements and describing the model dynamics. Thus, techniques of model reduction can be used as a mathematical tool in order to minimize the number of variables and parameters. In this thesis, we review some well-known methods of model reduction for cell signaling pathways. We have also developed some approaches that provide us a great step forward in model reduction. The techniques are quasi stead…
Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs fo…
It is now well established that the cell is a highly crowded environment. Yet, the effects of crowding on the dynamics of signaling pathways, gene regulation networks and metabolic networks are still largely unknown. Crowding can alter both molecular diffusion and the equilibria of biomolecular reactions. In this review, we first discuss how diffusion can affect biochemical networks. Diffusion of transcription factors can increase noise in gene expression, while diffusion of proteins between intracellular compartments or between cells can reduce concentration fluctuations. In push-pull network…
Conformational barcodes tag functional sites of proteins, and are decoded by interacting molecules transmitting the incoming signal. Conformational barcodes are modified by all co-occurring allosteric events induced by post-translational modifications, pathogen, drug binding, etc. We argue that fuzziness (plasticity) of conformational barcodes may be increased by disordered protein structures, by integrative plasticity of multi-phosphorylation events, by increased intracellular water content (decreased molecular crowding) and by increased action of molecular chaperones. This leads to increased…
The human neurotensin 1 receptor (hNTS1) is a G protein-coupled receptor involved in many physiological functions, including analgesia, hypothermia, and hypotension. To gain a better understanding of which signaling pathways or combination of pathways are linked to NTS1 activation and function, we investigated the ability of activated hNTS1, which was stably expressed by CHO-K1 cells, to directly engage G proteins, activate second messenger cascades and recruit \b{eta}-arrestins. Using BRET-based biosensors, we found that neurotensin (NT), NT(8-13) and neuromedin N (NN) activated the Gαq-, Gαi…
We present a new experimental-computational technology of inferring network models that predict the response of cells to perturbations and that may be useful in the design of combinatorial therapy against cancer. The experiments are systematic series of perturbations of cancer cell lines by targeted drugs, singly or in combination. The response to perturbation is measured in terms of levels of proteins and phospho-proteins and of cellular phenotype such as viability. Computational network models are derived de novo, i.e., without prior knowledge of signaling pathways, and are based on simple n…
Plants depend on the signaling of the phytohormone auxin for their development and for responding to environmental perturbations. The associated biomolecular signaling network involves a negative feedback at the level of the Aux/IAA proteins which mediate the influence of auxin (the signal) on the ARF transcription factors (the drivers of the response). To probe the role of this feedback, we consider alternative in silico signaling networks implementing different operating principles. By a comparative analysis, we find that the presence of a negative regulatory feedback loop allows the system …
The mating pathway in \emph{Saccharomyces cerevisiae} is one of the best understood signal transduction pathways in eukaryotes. It transmits the mating signal from plasma membrane into the nucleus through the G-protein coupled receptor and the mitogen-activated protein kinase (MAPK) cascade. According to the current understandings of the mating pathway, we construct a system of ordinary differential equations to describe the process. Our model is consistent with a wide range of experiments, indicating that it captures some main characteristics of the signal transduction along the pathway. Inve…
Integrins are allosteric cell adhesion receptors that control many important processes, including cell migration, proliferation, and apoptosis. Ligand binding activates integrins by stabilizing an integrin conformation with separated cytoplasmic tails, thus enabling the binding of proteins that mediate cytoplasmic signaling. Experiments demonstrate a high sensitivity of integrin signaling to ligand density and this has been accounted mainly to avidity effects. Based on experimental data we have developed a quantitative Monte Carlo model for integrin signal initiation. We show that within the p…
Motivation: Signaling pathways control a large variety of cellular processes. However, currently, even within the same database signaling pathways are often curated at different levels of detail. This makes comparative and cross-talk analyses difficult. Results: We present SignaLink, a database containing 8 major signaling pathways from Caenorhabditis elegans, Drosophila melanogaster, and humans. Based on 170 review and approx. 800 research articles, we have compiled pathways with semi-automatic searches and uniform, well-documented curation rules. We found that in humans any two of the 8 path…
The asymmetric Hopfield model is used to simulate signaling dynamics in gene/transcription factor networks. The model allows for a direct mapping of a gene expression pattern into attractor states. We analyze different control strategies aiming at disrupting attractor patterns using selective local fields representing therapeutic interventions. The control strategies are based on the identification of signaling $bottlenecks$, which are single nodes or strongly connected clusters of nodes that have a large impact on the signaling. We provide a theorem with bounds on the minimum number of nodes …
Biochemical reaction networks in living cells usually involve reversible covalent modification of signaling molecules, such as protein phosphorylation. Under conditions of small molecule numbers, as is frequently the case in living cells, mass action theory fails to describe the dynamics of such systems. Instead, the biochemical reactions must be treated as stochastic processes that intrinsically generate concentration fluctuations of the chemicals. We investigate the stochastic reaction kinetics of covalent modification cycles (CMCs) by analytical modeling and numerically exact Monte-Carlo si…
The recognition of essential proteins not only can help to understand the mechanism of cell operation, but also help to study the mechanism of biological evolution. At present, many scholars have been discovering essential proteins according to the topological structure of protein network and complexes. While some proteins still can not be recognized. In this paper, we proposed two new methods complex degree centrality (CDC) and complex in-degree and betweenness definition (CIBD) which integrate the local character of protein complexes and topological properties to determine the essentiality o…
Multistationarity in biological systems is a mechanism of cellular decision making. In particular, signaling pathways regulated by protein phosphorylation display features that facilitate a variety of responses to different biological inputs. The features that lead to multistationarity are of particular interest to determine as well as the stability properties of the steady states. In this paper we determine conditions for the emergence of multistationarity in small motifs without feedback that repeatedly occur in signaling pathways. We derive an explicit mathematical relationship between the …
Cancer cells are widely known to be protected from apoptosis, which is a major hurdle to successful anti-cancer therapy. Over-expression of several anti-apoptotic proteins, or mutations in pro-apoptotic factors, has been recognized to confer such resistance. Development of new experimental strategies, such as in silico modeling of biological pathways, can increase our understanding of how abnormal regulation of apoptotic pathway in cancer cells can lead to tumour chemoresistance. Monte Carlo simulations are in particular well suited to study inherent variability, such as spatial heterogeneity …
In this paper we show that living cells can multiplex biochemical signals, i.e. transmit multiple signals through the same signaling pathway simultaneously, and yet respond to them very specifically. We demonstrate how two binary input signals can be encoded in the concentration of a common signaling protein, which is then decoded such that each of the two output signals provides reliable information about one corresponding input. Under biologically relevant conditions the network can reach the maximum amount of information that can be transmitted, which is 2 bits.
Motivation: Discovering functional modules in protein-protein interaction (PPI) networks by optimization methods remains a longstanding challenge in biology. Traditional algorithms simply consider strong protein complexes that can be found in the original network by optimizing some metrics, which causes obstacles for the discovery of weak and hidden complexes shielded by stronger complexes. Also, protein complexes are not only in different density but also in a large range of scale, making it extremely difficult to be detected. Toward this objective, we propose a hierarchical hidden community …
Representation of intracellular signaling networks as directed graphs allows for the identification of regulatory motifs. Regulatory motifs are groups of nodes with the same connectivity structure, capable of processing information. The bifan motif, made of two source nodes directly cross-regulating two target nodes, is an over-represented motif in a mammalian cell signaling network and in transcriptional networks. One example of a bifan is the two MAP-kinases, p38 and JNK that phosphorylate and activate the two transcription factors ATF2 and Elk-1. We have used a system of coupled ordinary di…
In this work, we present a paradigm bridging electromagnetic (EM) and molecular communication through a stimuli-responsive intra-body model. It has been established that protein molecules, which play a key role in governing cell behavior, can be selectively stimulated using Terahertz (THz) band frequencies. By triggering protein vibrational modes using THz waves, we induce changes in protein conformation, resulting in the activation of a controlled cascade of biochemical and biomechanical events. To analyze such an interaction, we formulate a communication system composed of a nanoantenna tran…
NF-κB is a pleiotropic protein whose nucleo-cytoplasmic trafficking is tightly regulated by multiple negative feedback loops embedded in the NF-κB signaling network and contributes to diverse gene expression profiles important in immune cell differentiation, cell apoptosis, and innate immunity. The intracellular signaling processes and their control mechanisms, however, are susceptible to both extrinsic and intrinsic noise. In this article, we present numerical evidence for a universal dynamic behavior of NF-κB, namely oscillatory nucleo-cytoplasmic shuttling, due to the fundamentally stochast…
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；Morgridge Institute for Research（莫格里奇研究所）
Cells regulate themselves via dizzyingly complex biochemical processes called signaling pathways. These are usually depicted as a network, where nodes represent proteins and edges indicate their influence on each other. In order to understand diseases and therapies at the cellular level, it is crucial to have an accurate understanding of the signaling pathways at work. Since signaling pathways can be modified by disease, the ability to infer signaling pathways from condition- or patient-specific data is highly valuable. A variety of techniques exist for inferring signaling pathways. We build o…
How do single cell fate decisions induced by activation of key signaling proteins above threshold concentrations within a time interval are affected by stochastic fluctuations in biochemical reactions? We address this question using minimal models of stochastic chemical reactions commonly found in cell signaling and gene regulatory systems. Employing exact solutions and semi-analytical methods we calculate distributions of the maximum value ($N$) of activated species concentrations ($P_{max}(N)$) and the time ($t$) taken to reach the maximum value ($P_{max}(t)$) within a time window in the min…
Genomic alterations lead to cancer complexity and form a major hurdle for a comprehensive understanding of the molecular mechanisms underlying oncogenesis. In this review, we describe the recent advances in studying cancer-associated genes from a systems biological point of view. The integration of known cancer genes onto protein and signaling networks reveals the characteristics of cancer genes within networks. This approach shows that cancer genes often function as network hub proteins which are involved in many cellular processes and form focal nodes in the information exchange between many…
