Modeling cell signaling networks

Virtual Transcriptomics: Noninvasive Phenotyping of Atherosclerosis by Decoding Plaque Biology From Computed Tomography Angiography Imaging

[Figure: see text].

Stability Analysis of a Signaling Circuit with Dual Species of GTPase Switches

GTPases are molecular switches that regulate a wide range of cellular processes, such as organelle biogenesis, position, shape, function, vesicular transport between organelles, and signal transduction. These hydrolase enzymes operate by toggling between an active ("ON") guanosine triphosphate (GTP)-bound state and an inactive ("OFF") guanosine diphosphate (GDP)-bound state; such a toggle is regulated by GEFs (guanine nucleotide exchange factors) and GAPs (GTPase activating proteins). Here we propose a model for a network motif between monomeric (m) and trimeric (t) GTPases assembled exclusively in eukaryotic cells of multicellular organisms. We develop a system of ordinary differential equations in which these two classes of GTPases are interlinked conditional to their ON/OFF states within a motif through coupling and feedback loops. We provide explicit formulae for the steady states of the system and perform classical local stability analysis to systematically investigate the role of the different connections between the GTPase switches. Interestingly, a coupling of the active mGTPase to the GEF of the tGTPase was sufficient to provide two locally stable states: one where both active/inactive forms of the mGTPase can be interpreted as having low concentrations and the other where both m- and tGTPase have high concentrations. Moreover, when a feedback loop from the GEF of the tGTPase to the GAP of the mGTPase was added to the coupled system, two other locally stable states emerged. In both states the tGTPase is inactivated and active tGTPase concentrations are low. Finally, the addition of a second feedback loop, from the active tGTPase to the GAP of the mGTPase, gives rise to a family of steady states that can be parametrized by a range of inactive tGTPase concentrations. Our findings reveal that the coupling of these two different GTPase motifs can dramatically change their steady-state behaviors and shed light on how such coupling may impact signaling mechanisms in eukaryotic cells.

Impact of explicit area scaling on kinetic models involving multiple compartments

BACKGROUND

Computational modelling of cell biological processes is a frequently used technique to analyse the underlying mechanisms and to generally understand the behaviour of these processes in the context of a pathway, network or even the whole cell. The most common technique in this context is the usage of ordinary differential equations that describe the kinetics of the relevant processes in mechanistic detail. Here, it is usually assumed that the content of the cell is well-stirred and thus homogeneous - which is of course an over-simplification, but often worked in the past. However, many processes happen at membranes and thus not in 3D, but in 2D. The scaling of the rates of these processes poses a special problem, if volumes of compartments are changed. They will typically scale with an area, but not with the volume of the involved compartment. However, commonly, this is neglected when setting up models and/or volume scaling also sometimes automatically happens when using modelling software in the field.

RESULTS

Here, we investigate generic as well as specific, realistic cases to find out, how strong the impact of the wrong scaling is for the outcome of simulations. We show that the importance of correct area scaling depends on the architecture of the reaction site and its changes upon volume alterations and it is hard to foresee, if it has a significant impact or not just by looking at the original model set-up. Moreover, scaled rates might exhibit more or less control over the behaviour of the system and therefore, accordingly, incorrect scaling will have more or less influence.

CONCLUSIONS

Working with multi-compartment reactions requires a careful consideration of the correct scaling of the rates when changing the volumes of the involved compartments. The error following incorrect scaling - often done by scaling with the volume of the respective compartments can lead to significant aberrations of model behaviour.

Mathematical Modeling of p53 Pathways

Cells have evolved balanced systems that ensure an appropriate response to stress. The systems elicit repair responses in temporary or moderate stress but eliminate irreparable cells via apoptosis in detrimental conditions of prolonged or severe stress. The tumor suppressor p53 is a central player in these stress response systems. When activated under DNA damage stress, p53 regulates hundreds of genes that are involved in DNA repair, cell cycle, and apoptosis. Recently, increasing studies have demonstrated additional regulatory roles of p53 in metabolism and mitochondrial physiology. Due to the inherent complexity of feedback loops between p53 and its target genes, the application of mathematical modeling has emerged as a novel approach to better understand the multifaceted functions and dynamics of p53. In this review, we discuss several mathematical modeling approaches in exploring the p53 pathways.

Soft Set Theory for Decision Making in Computational Biology under Incomplete Information

The study of biological systems is complex and of great importance. There exist numerous approaches to signal transduction processes, including symbolic modeling of cellular adaptation. The use of formal methods for computational systems biology eases the analysis of cellular models and the establishment of the causes and consequences of certain cellular situations associated to diseases. In this paper, we define an application of logic modeling with rewriting logic and soft set theory. Our approach to decision making with soft sets offers a novel strategy that complements standard strategies. We implement a metalevel strategy to control and guide the rewriting process of the Maude rewriting engine. In particular, we adapt mathematical methods to capture imprecision, vagueness, and uncertainty in the available data. Using this new strategy, we propose an extension in the biological symbolic models of Pathway Logic. Our ultimate aim is to automatically determine the rules that are most appropriate and adjusted to reality in dynamic systems using decision making with incomplete soft sets.

Learning time-varying information flow from single-cell epithelial to mesenchymal transition data

Cellular regulatory networks are not static, but continuously reconfigure in response to stimuli via alterations in protein abundance and confirmation. However, typical computational approaches treat them as static interaction networks derived from a single time point. Here, we provide methods for learning the dynamic modulation of relationships between proteins from static single-cell data. We demonstrate our approach using TGFß induced epithelial-to-mesenchymal transition (EMT) in murine breast cancer cell line, profiled with mass cytometry. We take advantage of the asynchronous rate of transition to EMT in the data and derive a pseudotime EMT trajectory. We propose methods for visualizing and quantifying time-varying edge behavior over the trajectory, and a metric of edge dynamism to predict the effect of drug perturbations on EMT.

Tamoxifen-Induced Apoptosis of MCF-7 Cells via GPR30/PI3K/MAPKs Interactions: Verification by ODE Modeling and RNA Sequencing

Tamoxifen (Nolvadex) is one of the most widely used and effective therapeutic agent for breast cancer. It benefits nearly 75% of patients with estrogen receptor (ER)-positive breast cancer that receive this drug. Its effectiveness is mainly attributed to its capacity to function as an ER antagonist, blocking estrogen binding sites on the receptor, and inhibiting the proliferative action of the receptor-hormone complex. Although, tamoxifen can induce apoptosis in breast cancer cells via upregulation of pro-apoptotic factors, it can also promote uterine hyperplasia in some women. Thus, tamoxifen as a multi-functional drug could have different effects on cells based on the utilization of effective concentrations or availability of specific co-factors. Evidence that tamoxifen functions as a GPR30 (G-Protein Coupled Receptor 30) agonist activating adenylyl cyclase and EGFR (Epidermal Growth Factor Receptor) intracellular signaling networks, provides yet another means of explaining the multi-functionality of tamoxifen. Here ordinary differential equation (ODE) modeling, RNA sequencing and real time qPCR analysis were utilized to establish the necessary data for gene network mapping of tamoxifen-stimulated MCF-7 cells, which express the endogenous ER and GPR30. The gene set enrichment analysis and pathway analysis approaches were used to categorize transcriptionally upregulated genes in biological processes. Of the 2,713 genes that were significantly upregulated following a 48 h incubation with 250 μM tamoxifen, most were categorized as either growth-related or pro-apoptotic intermediates that fit into the Tp53 and/or MAPK signaling pathways. Collectively, our results display that the effects of tamoxifen on the breast cancer MCF-7 cell line are mediated by the activation of important signaling pathways including Tp53 and MAPKs to induce apoptosis.

Complexity: the organizing principle at the interface of biological (dis)order

The term complexity means several things to biologists.When qualifying morphological phenotype, on the one hand, it is used to signify the sheer complicatedness of living systems, especially as a result of the multicomponent aspect of biological form. On the other hand, it has been used to represent the intricate nature of the connections between constituents that make up form: a more process-based explanation. In the context of evolutionary arguments, complexity has been defined, in a quantifiable fashion, as the amount of information, an informatic template such as a sequence of nucleotides or amino acids stores about its environment. In this perspective, we begin with a brief review of the history of complexity theory. We then introduce a developmental and an evolutionary understanding of what it means for biological systems to be complex.We propose that the complexity of living systems can be understood through two interdependent structural properties: multiscalarity of interconstituent mechanisms and excitability of the biological materials. The answer to whether a system becomes more or less complex over time depends on the potential for its constituents to interact in novel ways and combinations to give rise to new structures and functions, as well as on the evolution of excitable properties that would facilitate the exploration of interconstituent organization in the context of their microenvironments and macroenvironments.

Modulation of gap junction-associated Cx43 in neural stem/progenitor cells following traumatic brain injury

Restoration of learning and memory deficits following traumatic brain injury (TBI) is attributed, in part, to enhanced neural stem/progenitor cell (NSPCs) function. Recent findings suggest gap junction (GJ)-associated connexin 43 (Cx43) plays a key role in the cell cycle regulation and function of NSPCs and is modulated following TBI. Here, we demonstrate that Cx43 is up-regulated in the dentate gyrus following TBI and is expressed on vimentin-positive cells in the subgranular zone. To test the role of Cx43 on NSPCs, we exposed primary cultures to the α-connexin Carboxyl Terminal (αCT1) peptide which selectively modulates GJ-associated Cx43. Treatment with αCT1 substantially reduced proliferation and increased caspase 3/7 expression on NSPCs in a dose-dependent manner. αCT1 exposure also reduced overall expression of Cx43 and phospho (p)-Serine368. These findings demonstrate that Cx43 positively regulates adult NPSCs; the modulation of which may influence changes in the dentate gyrus following TBI.

Quantitative Adverse Outcome Pathways and Their Application to Predictive Toxicology

A quantitative adverse outcome pathway (qAOP) consists of one or more biologically based, computational models describing key event relationships linking a molecular initiating event (MIE) to an adverse outcome. A qAOP provides quantitative, dose-response, and time-course predictions that can support regulatory decision-making. Herein we describe several facets of qAOPs, including (a) motivation for development, (b) technical considerations, (c) evaluation of confidence, and (d) potential applications. The qAOP used as an illustrative example for these points describes the linkage between inhibition of cytochrome P450 19A aromatase (the MIE) and population-level decreases in the fathead minnow (FHM; Pimephales promelas). The qAOP consists of three linked computational models for the following: (a) the hypothalamic-pitutitary-gonadal axis in female FHMs, where aromatase inhibition decreases the conversion of testosterone to 17β-estradiol (E2), thereby reducing E2-dependent vitellogenin (VTG; egg yolk protein precursor) synthesis, (b) VTG-dependent egg development and spawning (fecundity), and (c) fecundity-dependent population trajectory. While development of the example qAOP was based on experiments with FHMs exposed to the aromatase inhibitor fadrozole, we also show how a toxic equivalence (TEQ) calculation allows use of the qAOP to predict effects of another, untested aromatase inhibitor, iprodione. While qAOP development can be resource-intensive, the quantitative predictions obtained, and TEQ-based application to multiple chemicals, may be sufficient to justify the cost for some applications in regulatory decision-making.

Systems pharmacology and enhanced pharmacodynamic models for understanding antibody-based drug action and toxicity

Pharmacokinetic (PK) and pharmacodynamic (PD) models seek to describe the temporal pattern of drug exposures and their associated pharmacological effects produced at micro- and macro-scales of organization. Antibody-based drugs have been developed for a large variety of diseases, with effects exhibited through a comprehensive range of mechanisms of action. Mechanism-based PK/PD and systems pharmacology models can play a major role in elucidating and integrating complex antibody pharmacological properties, such as nonlinear disposition and dynamical intracellular signaling pathways triggered by ligation to their cognate targets. Such complexities can be addressed through the use of robust computational modeling techniques that have proven powerful tools for pragmatic characterization of experimental data and for theoretical exploration of antibody efficacy and adverse effects. The primary objectives of such multi-scale mathematical models are to generate and test competing hypotheses and to predict clinical outcomes. In this review, relevant systems pharmacology and enhanced PD (ePD) models that are used as predictive tools for antibody-based drug action are reported. Their common conceptual features are highlighted, along with approaches used for modeling preclinical and clinically available data. Key examples illustrate how systems pharmacology and ePD models codify the interplay among complex biology, drug concentrations, and pharmacological effects. New hybrid modeling concepts that bridge cutting-edge systems pharmacology models with established PK/ePD models will be needed to anticipate antibody effects on disease in subpopulations and individual patients.

Inflammation Following Traumatic Brain Injury in Humans: Insights from Data-Driven and Mechanistic Models into Survival and Death

Inflammation induced by traumatic brain injury (TBI) is a complex mediator of morbidity and mortality. We have previously demonstrated the utility of both data-driven and mechanistic models in settings of traumatic injury. We hypothesized that differential dynamic inflammation programs characterize TBI survivors vs. non-survivors, and sought to leverage computational modeling to derive novel insights into this life/death bifurcation. Thirteen inflammatory cytokines and chemokines were determined using Luminex™ in serial cerebrospinal fluid (CSF) samples from 31 TBI patients over 5 days. In this cohort, 5 were non-survivors (Glasgow Outcome Scale [GOS] score = 1) and 26 were survivors (GOS > 1). A Pearson correlation analysis of initial injury (Glasgow Coma Scale [GCS]) vs. GOS suggested that survivors and non-survivors had distinct clinical response trajectories to injury. Statistically significant differences in interleukin (IL)-4, IL-5, IL-6, IL-8, IL-13, and tumor necrosis factor-α (TNF-α) were observed between TBI survivors vs. non-survivors over 5 days. Principal Component Analysis and Dynamic Bayesian Network inference suggested differential roles of chemokines, TNF-α, IL-6, and IL-10, based upon which an ordinary differential equation model of TBI was generated. This model was calibrated separately to the time course data of TBI survivors vs. non-survivors as a function of initial GCS. Analysis of parameter values in ensembles of simulations from these models suggested differences in microglial and damage responses in TBI survivors vs. non-survivors. These studies suggest the utility of combined data-driven and mechanistic models in the context of human TBI.

Comparison of human cell signaling pathway databases--evolution, drawbacks and challenges

Elucidating the complexities of cell signaling pathways is of immense importance to gain understanding about various biological phenomenon, such as dynamics of gene/protein expression regulation, cell fate determination, embryogenesis and disease progression. The successful completion of human genome project has also helped experimental and theoretical biologists to analyze various important pathways. To advance this study, during the past two decades, systematic collections of pathway data from experimental studies have been compiled and distributed freely by several databases, which also integrate various computational tools for further analysis. Despite significant advancements, there exist several drawbacks and challenges, such as pathway data heterogeneity, annotation, regular update and automated image reconstructions, which motivated us to perform a thorough review on popular and actively functioning 24 cell signaling databases. Based on two major characteristics, pathway information and technical details, freely accessible data from commercial and academic databases are examined to understand their evolution and enrichment. This review not only helps to identify some novel and useful features, which are not yet included in any of the databases but also highlights their current limitations and subsequently propose the reasonable solutions for future database development, which could be useful to the whole scientific community.

Understanding the sub-cellular dynamics of silicon transportation and synthesis in diatoms using population-level data and computational optimization

Controlled synthesis of silicon is a major challenge in nanotechnology and material science. Diatoms, the unicellular algae, are an inspiring example of silica biosynthesis, producing complex and delicate nano-structures. This happens in several cell compartments, including cytoplasm and silica deposition vesicle (SDV). Considering the low concentration of silicic acid in oceans, cells have developed silicon transporter proteins (SIT). Moreover, cells change the level of active SITs during one cell cycle, likely as a response to the level of external nutrients and internal deposition rates. Despite this topic being of fundamental interest, the intracellular dynamics of nutrients and cell regulation strategies remain poorly understood. One reason is the difficulties in measurements and manipulation of these mechanisms at such small scales, and even when possible, data often contain large errors. Therefore, using computational techniques seems inevitable. We have constructed a mathematical model for silicon dynamics in the diatom Thalassiosira pseudonana in four compartments: external environment, cytoplasm, SDV and deposited silica. The model builds on mass conservation and Michaelis-Menten kinetics as mass transport equations. In order to find the free parameters of the model from sparse, noisy experimental data, an optimization technique (global and local search), together with enzyme related penalty terms, has been applied. We have connected population-level data to individual-cell-level quantities including the effect of early division of non-synchronized cells. Our model is robust, proven by sensitivity and perturbation analysis, and predicts dynamics of intracellular nutrients and enzymes in different compartments. The model produces different uptake regimes, previously recognized as surge, externally-controlled and internally-controlled uptakes. Finally, we imposed a flux of SITs to the model and compared it with previous classical kinetics. The model introduced can be generalized in order to analyze different biomineralizing organisms and to test different chemical pathways only by switching the system of mass transport equations.

RegPhos 2.0: an updated resource to explore protein kinase-substrate phosphorylation networks in mammals

Protein phosphorylation catalyzed by kinases plays crucial roles in regulating a variety of intracellular processes. Owing to an increasing number of in vivo phosphorylation sites that have been identified by mass spectrometry (MS)-based proteomics, the RegPhos, available online at http://csb.cse.yzu.edu.tw/RegPhos2/, was developed to explore protein phosphorylation networks in human. In this update, we not only enhance the data content in human but also investigate kinase-substrate phosphorylation networks in mouse and rat. The experimentally validated phosphorylation sites as well as their catalytic kinases were extracted from public resources, and MS/MS phosphopeptides were manually curated from research articles. RegPhos 2.0 aims to provide a more comprehensive view of intracellular signaling networks by integrating the information of metabolic pathways and protein-protein interactions. A case study shows that analyzing the phosphoproteome profile of time-dependent cell activation obtained from Liquid chromatography-mass spectrometry (LC-MS/MS) analysis, the RegPhos deciphered not only the consistent scheme in B cell receptor (BCR) signaling pathway but also novel regulatory molecules that may involve in it. With an attempt to help users efficiently identify the candidate biomarkers in cancers, 30 microarray experiments, including 39 cancerous versus normal cells, were analyzed for detecting cancer-specific expressed genes coding for kinases and their substrates. Furthermore, this update features an improved web interface to facilitate convenient access to the exploration of phosphorylation networks for a group of genes/proteins. Database URL: http://csb.cse.yzu.edu.tw/RegPhos2/

In silico modeling of Itk activation kinetics in thymocytes suggests competing positive and negative IP4 mediated feedbacks increase robustness

The inositol-phosphate messenger inositol(1,3,4,5)tetrakisphosphate (IP₄) is essential for thymocyte positive selection by regulating plasma-membrane association of the protein tyrosine kinase Itk downstream of the T cell receptor (TCR). IP₄ can act as a soluble analog of the phosphoinositide 3-kinase (PI3K) membrane lipid product phosphatidylinositol(3,4,5)trisphosphate (PIP₃). PIP₃ recruits signaling proteins such as Itk to cellular membranes by binding to PH and other domains. In thymocytes, low-dose IP₄ binding to the Itk PH domain surprisingly promoted and high-dose IP₄ inhibited PIP₃ binding of Itk PH domains. However, the mechanisms that underlie the regulation of membrane recruitment of Itk by IP₄ and PIP₃ remain unclear. The distinct Itk PH domain ability to oligomerize is consistent with a cooperative-allosteric mode of IP₄ action. However, other possibilities cannot be ruled out due to difficulties in quantitatively measuring the interactions between Itk, IP₄ and PIP₃, and in generating non-oligomerizing Itk PH domain mutants. This has hindered a full mechanistic understanding of how IP₄ controls Itk function. By combining experimentally measured kinetics of PLCγ1 phosphorylation by Itk with in silico modeling of multiple Itk signaling circuits and a maximum entropy (MaxEnt) based computational approach, we show that those in silico models which are most robust against variations of protein and lipid expression levels and kinetic rates at the single cell level share a cooperative-allosteric mode of Itk regulation by IP₄ involving oligomeric Itk PH domains at the plasma membrane. This identifies MaxEnt as an excellent tool for quantifying robustness for complex TCR signaling circuits and provides testable predictions to further elucidate a controversial mechanism of PIP₃ signaling.

Dynamics of growth factor production in monolayers of cancer cells and evolution of resistance to anticancer therapies

Tumor heterogeneity is well documented for many characters, including the production of growth factors, which improve tumor proliferation and promote resistance against apoptosis and against immune reaction. What maintains heterogeneity remains an open question that has implications for diagnosis and treatment. While it has been suggested that therapies targeting growth factors are robust against evolved resistance, current therapies against growth factors, like antiangiogenic drugs, are not effective in the long term, as resistant mutants can evolve and lead to relapse. We use evolutionary game theory to study the dynamics of the production of growth factors by monolayers of cancer cells and to understand the effect of therapies that target growth factors. The dynamics depend on the production cost of the growth factor, on its diffusion range and on the type of benefit it confers to the cells. Stable heterogeneity is a typical outcome of the dynamics, while a pure equilibrium of nonproducer cells is possible under certain conditions. Such pure equilibrium can be the goal of new anticancer therapies. We show that current therapies, instead, can be effective only if growth factors are almost completely eliminated and if the reduction is almost immediate.

Evolutionary game theory of growth factor production: implications for tumour heterogeneity and resistance to therapies

Background:

Tumour heterogeneity is documented for many characters, including the production of growth factors, one of the hallmarks of cancer. What maintains heterogeneity remains an open question that has implications for diagnosis and treatment, as drugs that target growth factors are susceptible to the evolution of resistance.

Methods:

I use evolutionary game theory to model collective interactions between cancer cells, to analyse the dynamics of the production of growth factors and the effect of therapies that reduce their amount.

Results:

Five types of dynamics are possible, including the coexistence of producer and non-producer cells, depending on the production cost of the growth factor, on its diffusion range and on the degree of synergy of the benefit it confers to the cells. Perturbations of the equilibrium mimicking therapies that target growth factors are effective in reducing the amount of growth factor in the long term only if the reduction is extremely efficient and immediate.

Conclusion:

Collective interactions within the tumour can maintain heterogeneity for the production of growth factors and explain why therapies like anti-angiogenic drugs and RNA interference that reduce the amount of available growth factors are effective in the short term but often lead to relapse. Alternative strategies for evolutionarily stable treatments are discussed.

Comparison of models for IP3 receptor kinetics using stochastic simulations

Inositol 1,4,5-trisphosphate receptor (IP₃R) is a ubiquitous intracellular calcium (Ca²⁺) channel which has a major role in controlling Ca²⁺ levels in neurons. A variety of computational models have been developed to describe the kinetic function of IP₃R under different conditions. In the field of computational neuroscience, it is of great interest to apply the existing models of IP₃R when modeling local Ca²⁺ transients in dendrites or overall Ca²⁺ dynamics in large neuronal models. The goal of this study was to evaluate existing IP₃R models, based on electrophysiological data. This was done in order to be able to suggest suitable models for neuronal modeling. Altogether four models (Othmer and Tang, 1993; Dawson etal., 2003; Fraiman and Dawson, 2004; Doi etal., 2005) were selected for a more detailed comparison. The selection was based on the computational efficiency of the models and the type of experimental data that was used in developing the model. The kinetics of all four models were simulated by stochastic means, using the simulation software STEPS, which implements the Gillespie stochastic simulation algorithm. The results show major differences in the statistical properties of model functionality. Of the four compared models, the one by Fraiman and Dawson (2004) proved most satisfactory in producing the specific features of experimental findings reported in literature. To our knowledge, the present study is the first detailed evaluation of IP₃R models using stochastic simulation methods, thus providing an important setting for constructing a new, realistic model of IP₃R channel kinetics for compartmental modeling of neuronal functions. We conclude that the kinetics of IP₃R with different concentrations of Ca²⁺ and IP₃ should be more carefully addressed when new models for IP₃R are developed.

Signaling network prediction by the Ontology Fingerprint enhanced Bayesian network

BACKGROUND

Despite large amounts of available genomic and proteomic data, predicting the structure and response of signaling networks is still a significant challenge. While statistical method such as Bayesian network has been explored to meet this challenge, employing existing biological knowledge for network prediction is difficult. The objective of this study is to develop a novel approach that integrates prior biological knowledge in the form of the Ontology Fingerprint to infer cell-type-specific signaling networks via data-driven Bayesian network learning; and to further use the trained model to predict cellular responses.

RESULTS

We applied our novel approach to address the Predictive Signaling Network Modeling challenge of the fourth (2009) Dialog for Reverse Engineering Assessment's and Methods (DREAM4) competition. The challenge results showed that our method accurately captured signal transduction of a network of protein kinases and phosphoproteins in that the predicted protein phosphorylation levels under all experimental conditions were highly correlated (R2 = 0.93) with the observed results. Based on the evaluation of the DREAM4 organizer, our team was ranked as one of the top five best performers in predicting network structure and protein phosphorylation activity under test conditions.

CONCLUSIONS

Bayesian network can be used to simulate the propagation of signals in cellular systems. Incorporating the Ontology Fingerprint as prior biological knowledge allows us to efficiently infer concise signaling network structure and to accurately predict cellular responses.

Bio-logic builder: a non-technical tool for building dynamical, qualitative models

Computational modeling of biological processes is a promising tool in biomedical research. While a large part of its potential lies in the ability to integrate it with laboratory research, modeling currently generally requires a high degree of training in mathematics and/or computer science. To help address this issue, we have developed a web-based tool, Bio-Logic Builder, that enables laboratory scientists to define mathematical representations (based on a discrete formalism) of biological regulatory mechanisms in a modular and non-technical fashion. As part of the user interface, generalized “bio-logic” modules have been defined to provide users with the building blocks for many biological processes. To build/modify computational models, experimentalists provide purely qualitative information about a particular regulatory mechanisms as is generally found in the laboratory. The Bio-Logic Builder subsequently converts the provided information into a mathematical representation described with Boolean expressions/rules. We used this tool to build a number of dynamical models, including a 130-protein large-scale model of signal transduction with over 800 interactions, influenza A replication cycle with 127 species and 200+ interactions, and mammalian and budding yeast cell cycles. We also show that any and all qualitative regulatory mechanisms can be built using this tool.

The Cell Collective: toward an open and collaborative approach to systems biology

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.

Swimming upstream: identifying proteomic signals that drive transcriptional changes using the interactome and multiple "-omics" datasets

Signaling and transcription are tightly integrated processes that underlie many cellular responses to the environment. A network of signaling events, often mediated by post-translational modification on proteins, can lead to long-term changes in cellular behavior by altering the activity of specific transcriptional regulators and consequently the expression level of their downstream targets. As many high-throughput, "-omics" methods are now available that can simultaneously measure changes in hundreds of proteins and thousands of transcripts, it should be possible to systematically reconstruct cellular responses to perturbations in order to discover previously unrecognized signaling pathways. This chapter describes a computational method for discovering such pathways that aims to compensate for the varying levels of noise present in these diverse data sources. Based on the concept of constraint optimization on networks, the method seeks to achieve two conflicting aims: (1) to link together many of the signaling proteins and differentially expressed transcripts identified in the experiments "constraints" using previously reported protein-protein and protein-DNA interactions, while (2) keeping the resulting network small and ensuring it is composed of the highest confidence interactions "optimization". A further distinctive feature of this approach is the use of transcriptional data as evidence of upstream signaling events that drive changes in gene expression, rather than as proxies for downstream changes in the levels of the encoded proteins. We recently demonstrated that by applying this method to phosphoproteomic and transcriptional data from the pheromone response in yeast, we were able to recover functionally coherent pathways and to reveal many components of the cellular response that are not readily apparent in the original data. Here, we provide a more detailed description of the method, explore the robustness of the solution to the noise level of input data and discuss the effect of parameter values.

Models at the single cell level

Many cellular behaviors cannot be completely captured or appropriately described at the cell population level. Noise induced by stochastic chemical reactions, spatially polarized signaling networks, and heterogeneous cell-cell communication are among the many phenomena that require fine-grained analysis. Accordingly, the mathematical models used to describe such systems must be capable of single cell or subcellular resolution. Here, we review techniques for modeling single cells, including models of stochastic chemical kinetics, spatially heterogeneous intracellular signaling, and spatial stochastic systems. We also briefly discuss applications of each type of model.

RegPhos: a system to explore the protein kinase-substrate phosphorylation network in humans

Protein phosphorylation catalyzed by kinases plays crucial regulatory roles in intracellular signal transduction. With the increasing number of experimental phosphorylation sites that has been identified by mass spectrometry-based proteomics, the desire to explore the networks of protein kinases and substrates is motivated. Manning et al. have identified 518 human kinase genes, which provide a starting point for comprehensive analysis of protein phosphorylation networks. In this study, a knowledgebase is developed to integrate experimentally verified protein phosphorylation data and protein-protein interaction data for constructing the protein kinase-substrate phosphorylation networks in human. A total of 21,110 experimental verified phosphorylation sites within 5092 human proteins are collected. However, only 4138 phosphorylation sites (∼20%) have the annotation of catalytic kinases from public domain. In order to fully investigate how protein kinases regulate the intracellular processes, a published kinase-specific phosphorylation site prediction tool, named KinasePhos is incorporated for assigning the potential kinase. The web-based system, RegPhos, can let users input a group of human proteins; consequently, the phosphorylation network associated with the protein subcellular localization can be explored. Additionally, time-coursed microarray expression data is subsequently used to represent the degree of similarity in the expression profiles of network members. A case study demonstrates that the proposed scheme not only identify the correct network of insulin signaling but also detect a novel signaling pathway that may cross-talk with insulin signaling network. This effective system is now freely available at http://RegPhos.mbc.nctu.edu.tw.

The mEPN scheme: an intuitive and flexible graphical system for rendering biological pathways

BACKGROUND

There is general agreement amongst biologists about the need for good pathway diagrams and a need to formalize the way biological pathways are depicted. However, implementing and agreeing how best to do this is currently the subject of some debate.

RESULTS

The modified Edinburgh Pathway Notation (mEPN) scheme is founded on a notation system originally devised a number of years ago and through use has now been refined extensively. This process has been primarily driven by the author's attempts to produce process diagrams for a diverse range of biological pathways, particularly with respect to immune signaling in mammals. Here we provide a specification of the mEPN notation, its symbols, rules for its use and a comparison to the proposed Systems Biology Graphical Notation (SBGN) scheme.

CONCLUSIONS

We hope this work will contribute to the on-going community effort to develop a standard for depicting pathways and will provide a coherent guide to those planning to construct pathway diagrams of their biological systems of interest.

Construction of a large scale integrated map of macrophage pathogen recognition and effector systems

BACKGROUND

In an effort to better understand the molecular networks that underpin macrophage activation we have been assembling a map of relevant pathways. Manual curation of the published literature was carried out in order to define the components of these pathways and the interactions between them. This information has been assembled into a large integrated directional network and represented graphically using the modified Edinburgh Pathway Notation (mEPN) scheme.

RESULTS

The diagram includes detailed views of the toll-like receptor (TLR) pathways, other pathogen recognition systems, NF-kappa-B, apoptosis, interferon signalling, MAP-kinase cascades, MHC antigen presentation and proteasome assembly, as well as selected views of the transcriptional networks they regulate. The integrated pathway includes a total of 496 unique proteins, the complexes formed between them and the processes in which they are involved. This produces a network of 2,170 nodes connected by 2,553 edges.

CONCLUSIONS

The pathway diagram is a navigable visual aid for displaying a consensus view of the pathway information available for these systems. It is also a valuable resource for computational modelling and aid in the interpretation of functional genomics data. We envisage that this work will be of value to those interested in macrophage biology and also contribute to the ongoing Systems Biology community effort to develop a standard notation scheme for the graphical representation of biological pathways.

Rapidly exploring structural and dynamic properties of signaling networks using PathwayOracle

BACKGROUND

In systems biology the experimentalist is presented with a selection of software for analyzing dynamic properties of signaling networks. These tools either assume that the network is in steady-state or require highly parameterized models of the network of interest. For biologists interested in assessing how signal propagates through a network under specific conditions, the first class of methods does not provide sufficiently detailed results and the second class requires models which may not be easily and accurately constructed. A tool that is able to characterize the dynamics of a signaling network using an unparameterized model of the network would allow biologists to quickly obtain insights into a signaling network's behavior.

RESULTS

We introduce PathwayOracle, an integrated suite of software tools for computationally inferring and analyzing structural and dynamic properties of a signaling network. The feature which differentiates PathwayOracle from other tools is a method that can predict the response of a signaling network to various experimental conditions and stimuli using only the connectivity of the signaling network. Thus signaling models are relatively easy to build. The method allows for tracking signal flow in a network and comparison of signal flows under different experimental conditions. In addition, PathwayOracle includes tools for the enumeration and visualization of coherent and incoherent signaling paths between proteins, and for experimental analysis - loading and superimposing experimental data, such as microarray intensities, on the network model.

CONCLUSION

PathwayOracle provides an integrated environment in which both structural and dynamic analysis of a signaling network can be quickly conducted and visualized along side experimental results. By using the signaling network connectivity, analyses and predictions can be performed quickly using relatively easily constructed signaling network models. The application has been developed in Python and is designed to be easily extensible by groups interested in adding new or extending existing features. PathwayOracle is freely available for download and use.

Reaction-diffusion modeling ERK- and STAT-interaction dynamics

The modeling of the dynamics of interaction between ERK and STAT signaling pathways in the cell needs to establish the biochemical diagram of the corresponding proteins interactions as well as the corresponding reaction-diffusion scheme. Starting from the verbal description available in the literature of the cross talk between the two pathways, a simple diagram of interaction between ERK and STAT5a proteins is chosen to write corresponding kinetic equations. The dynamics of interaction is modeled in a form of two-dimensional nonlinear dynamical system for ERK-and STAT5a -protein concentrations. Then the spatial modeling of the interaction is accomplished by introducing an appropriate diffusion-reaction scheme. The obtained system of partial differential equations is analyzed and it is argued that the possibility of Turing bifurcation is presented by loss of stability of the homogeneous steady state and forms dissipative structures in the ERK and STAT interaction process. In these terms, a possible scaffolding effect in the protein interaction is related to the process of stabilization and destabilization of the dissipative structures (pattern formation) inherent to the model of ERK and STAT cross talk.

The signaling petri net-based simulator: a non-parametric strategy for characterizing the dynamics of cell-specific signaling networks

Reconstructing cellular signaling networks and understanding how they work are major endeavors in cell biology. The scale and complexity of these networks, however, render their analysis using experimental biology approaches alone very challenging. As a result, computational methods have been developed and combined with experimental biology approaches, producing powerful tools for the analysis of these networks. These computational methods mostly fall on either end of a spectrum of model parameterization. On one end is a class of structural network analysis methods; these typically use the network connectivity alone to generate hypotheses about global properties. On the other end is a class of dynamic network analysis methods; these use, in addition to the connectivity, kinetic parameters of the biochemical reactions to predict the network's dynamic behavior. These predictions provide detailed insights into the properties that determine aspects of the network's structure and behavior. However, the difficulty of obtaining numerical values of kinetic parameters is widely recognized to limit the applicability of this latter class of methods. Several researchers have observed that the connectivity of a network alone can provide significant insights into its dynamics. Motivated by this fundamental observation, we present the signaling Petri net, a non-parametric model of cellular signaling networks, and the signaling Petri net-based simulator, a Petri net execution strategy for characterizing the dynamics of signal flow through a signaling network using token distribution and sampling. The result is a very fast method, which can analyze large-scale networks, and provide insights into the trends of molecules' activity-levels in response to an external stimulus, based solely on the network's connectivity. We have implemented the signaling Petri net-based simulator in the PathwayOracle toolkit, which is publicly available at http://bioinfo.cs.rice.edu/pathwayoracle. Using this method, we studied a MAPK1,2 and AKT signaling network downstream from EGFR in two breast tumor cell lines. We analyzed, both experimentally and computationally, the activity level of several molecules in response to a targeted manipulation of TSC2 and mTOR-Raptor. The results from our method agreed with experimental results in greater than 90% of the cases considered, and in those where they did not agree, our approach provided valuable insights into discrepancies between known network connectivities and experimental observations.

Mathematical modeling as a tool for investigating cell cycle control networks

Although not a traditional experimental "method," mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems.

An optimal number of molecules for signal amplification and discrimination in a chemical cascade

Understanding the information processing ability of signal transduction pathways is of great importance because of their crucial roles in triggering various cellular responses. Despite continuing theoretical investigation, some important aspects of signal transduction such as a transient response and its connection to stochasticity originating from a small number of molecules have not yet been well understood. It is, however, through these aspects that unexpected and nontrivial properties of the information processing emerge. In this article, we analyze the transient behavior of a simple signaling cascade by taking into account the stochasticity originating from the small number of molecules. We identify several properties of the signaling cascade that emerge as a result of the interplay between the stochasticity and transient dynamics of the cascade. We specifically demonstrate that each step of the cascade has an optimal number of signaling molecules at which the average signal amplitude becomes maximal. We further investigate the connection between a finite number of molecules and the ability of the cascade to discriminate between true and error signals, which cannot be inferred from deterministic descriptions. The implications of our results are discussed from both biological and mathematical viewpoints.

Computational modelling of the receptor-tyrosine-kinase-activated MAPK pathway

The MAPK (mitogen-activated protein kinase) pathway is one of the most important and intensively studied signalling pathways. It is at the heart of a molecular-signalling network that governs the growth, proliferation, differentiation and survival of many, if not all, cell types. It is de-regulated in various diseases, ranging from cancer to immunological, inflammatory and degenerative syndromes, and thus represents an important drug target. Over recent years, the computational or mathematical modelling of biological systems has become increasingly valuable, and there is now a wide variety of mathematical models of the MAPK pathway which have led to some novel insights and predictions as to how this system functions. In the present review we give an overview of the processes involved in modelling a biological system using the popular approach of ordinary differential equations. Focusing on the MAPK pathway, we introduce the features and functions of the pathway itself before comparing the available models and describing what new biological insights they have led to.

A domain-oriented approach to the reduction of combinatorial complexity in signal transduction networks

BACKGROUND

Receptors and scaffold proteins possess a number of distinct domains and bind multiple partners. A common problem in modeling signaling systems arises from a combinatorial explosion of different states generated by feasible molecular species. The number of possible species grows exponentially with the number of different docking sites and can easily reach several millions. Models accounting for this combinatorial variety become impractical for many applications.

RESULTS

Our results show that under realistic assumptions on domain interactions, the dynamics of signaling pathways can be exactly described by reduced, hierarchically structured models. The method presented here provides a rigorous way to model a large class of signaling networks using macro-states (macroscopic quantities such as the levels of occupancy of the binding domains) instead of micro-states (concentrations of individual species). The method is described using generic multidomain proteins and is applied to the molecule LAT.

CONCLUSION

The presented method is a systematic and powerful tool to derive reduced model structures describing the dynamics of multiprotein complex formation accurately.

Algebraic dependency models of protein signal transduction networks from time-series data

Signal transduction networks are crucial for inter- and intra-cellular signaling. Signals are often transmitted via covalent modification of protein structure, with phosphorylation/dephosphorylation as the primary example. In this paper, we apply a recently described method of computational algebra to the modeling of signaling networks, based on time-course protein modification data. Computational algebraic techniques are employed to construct next-state functions. A Monte Carlo method is used to approximate the Deegan-Packel Index of Power corresponding to the respective variables. The Deegan-Packel Index of Power is used to conjecture dependencies in the cellular signaling networks. We apply this method to two examples of protein modification time-course data available in the literature. These experiments identified protein carbonylation upon exposure of cells to sub-lethal concentrations of copper. We demonstrate that this method can identify protein dependencies that might correspond to regulatory mechanisms to shut down glycolysis in a reverse, step-wise fashion in response to copper-induced oxidative stress in yeast. These examples show that the computational algebra approach can identify dependencies that may outline signaling networks involved in the response of glycolytic enzymes to the oxidative stress caused by copper.

All systems go: launching cell simulation fueled by integrated experimental biology data

Biological simulation serves to unify the basic elements of systems biology, namely, model selection, experimentation and model refinement. To select biochemical models for simulation, metabolome analysis can be performed using capillary electrophoresis or liquid chromatography coupled with mass spectrometry. In this manner, selected models can be elaborated with temporal/spatial gene and protein expression data obtained from model organisms such as Escherichia coli. The E. coli single gene deletion mutant library (KO collection) and His-tag/GFP-fusion single open reading frame clone expression library (ASKA) are powerful resources for this task. The integration of parallel experimental datasets into dynamic simulation tools forms the remaining challenge for the systematic analysis and elucidation of biological networks and holds promise for biotechnological applications.

Computational approaches for modeling regulatory cellular networks

Cellular components interact with each other to form networks that process information and evoke biological responses. A deep understanding of the behavior of these networks requires the development and analysis of mathematical models. In this article, different types of mathematical representations for modeling signaling networks are described, and the advantages and disadvantages of each type are discussed. Two experimentally well-studied signaling networks are then used as examples to illustrate the insight that could be gained through modeling. Finally, the modeling approach is expanded to describe how signaling networks might regulate cellular machines and evoke phenotypic behaviors.