Modeling the early signaling events mediated by FcepsilonRI

bnglViz: online visualization of rule-based models

MOTIVATION

Rule-based modeling is a powerful method to describe and simulate interactions among multi-site molecules and multi-molecular species, accounting for the internal connectivity of molecules in chemical species. This modeling technique is implemented in BioNetGen software that is used by various tools and software frameworks, such as BioNetGen stand-alone software, NFSim simulation engine, Virtual Cell simulation and modeling framework, SmolDyn and PySB software tools. These tools exchange models using BioNetGen scripting language (BNGL). Until now, there was no online visualization of such rule-based models. Modelers and researchers reading the manuscripts describing rule-based models had to learn BNGL scripting or master one of these tools to understand the models.

RESULTS

Here, we introduce bnglViz, an online platform for visualizing BNGL files as graphical cartoons, empowering researchers to grasp the nuances of rule-based models swiftly and efficiently, and making the exploration of complex biological systems more accessible than ever before. The produced visualizations can be used as supplemental figures in publications or as a way to annotate BNGL models on web repositories.

AVAILABILITY AND IMPLEMENTATION

Available at https://bnglviz.github.io/.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

MCell-R: A Particle-Resolution Network-Free Spatial Modeling Framework

Spatial heterogeneity can have dramatic effects on the biochemical networks that drive cell regulation and decision-making. For this reason, a number of methods have been developed to model spatial heterogeneity and incorporated into widely used modeling platforms. Unfortunately, the standard approaches for specifying and simulating chemical reaction networks become untenable when dealing with multistate, multicomponent systems that are characterized by combinatorial complexity. To address this issue, we developed MCell-R, a framework that extends the particle-based spatial Monte Carlo simulator, MCell, with the rule-based model specification and simulation capabilities provided by BioNetGen and NFsim. The BioNetGen syntax enables the specification of biomolecules as structured objects whose components can have different internal states that represent such features as covalent modification and conformation and which can bind components of other molecules to form molecular complexes. The network-free simulation algorithm used by NFsim enables efficient simulation of rule-based models even when the size of the network implied by the biochemical rules is too large to enumerate explicitly, which frequently occurs in detailed models of biochemical signaling. The result is a framework that can efficiently simulate systems characterized by combinatorial complexity at the level of spatially resolved individual molecules over biologically relevant time and length scales.

The role of basophils as innate immune regulatory cells in allergy and immunotherapy

Basophils are circulating cells that are associated quite exclusively with allergy response and hypersensitivity reactions but their role in the immune network might be much more intriguing and complex than previously expected. The feasibility of testing their biology in vitro for allergy research and diagnosis, due fundamentally to their quite easy availability in the peripheral blood, made them the major source for assessing allergy in the laboratory assay, when yet many further cells such as mast cells and eosinophils are much more involved as effector cells in allergy than circulating basophils. Interestingly, basophil numbers change rarely in peripheral blood during an atopic response, while we might yet observe an increase in eosinophils and modification in the biology of mast cells in the tissue during an hypersensitivity response. Furthermore, the fact that basophils are very scanty in numbers suggests that they should mainly serve as regulatory cells in immunity, rather than effector leukocytes, as still believed by the majority of physicians. In this review we will try to describe and elucidate the possible role of these cells, known as "innate IL4-producing cells" in the immune regulation of allergy and their function in allergen immunotherapy.

Disease associated cellular machinery in anaphylaxis - And the de novo paradigm shift

Anaphylaxis is a sudden immune reaction against an allergen that can potentially lead to Anaphylactic Shock (AS). This immune reaction is characterized by an increase in Immunoglobulin-E (IgE) type of antibodies that bind with FcεRI receptors on mast cells to release inflammatory mediators. Various intracellular signaling molecules downstream of IgE/ FcεRI axis play a potential role in cytokine, chemokine and eicosanoid secretion as well as degranulation of immune cells causing vasodilation, vascular permeability, and reduction of intravascular volume leading to cardiovascular collapse. Here, we discuss the cellular machinery of anaphylaxis and the de novo paradigm shift in the cellular aspects of AS.

An Interaction Library for the FcεRI Signaling Network

Antigen receptors play a central role in adaptive immune responses. Although the molecular networks associated with these receptors have been extensively studied, we currently lack a systems-level understanding of how combinations of non-covalent interactions and post-translational modifications are regulated during signaling to impact cellular decision-making. To fill this knowledge gap, it will be necessary to formalize and piece together information about individual molecular mechanisms to form large-scale computational models of signaling networks. To this end, we have developed an interaction library for signaling by the high-affinity IgE receptor, FcεRI. The library consists of executable rules for protein–protein and protein–lipid interactions. This library extends earlier models for FcεRI signaling and introduces new interactions that have not previously been considered in a model. Thus, this interaction library is a toolkit with which existing models can be expanded and from which new models can be built. As an example, we present models of branching pathways from the adaptor protein Lat, which influence production of the phospholipid PIP₃ at the plasma membrane and the soluble second messenger IP₃. We find that inclusion of a positive feedback loop gives rise to a bistable switch, which may ensure robust responses to stimulation above a threshold level. In addition, the library is visualized to facilitate understanding of network circuitry and identification of network motifs.

Exact hybrid particle/population simulation of rule-based models of biochemical systems

Detailed modeling and simulation of biochemical systems is complicated by the problem of combinatorial complexity, an explosion in the number of species and reactions due to myriad protein-protein interactions and post-translational modifications. Rule-based modeling overcomes this problem by representing molecules as structured objects and encoding their interactions as pattern-based rules. This greatly simplifies the process of model specification, avoiding the tedious and error prone task of manually enumerating all species and reactions that can potentially exist in a system. From a simulation perspective, rule-based models can be expanded algorithmically into fully-enumerated reaction networks and simulated using a variety of network-based simulation methods, such as ordinary differential equations or Gillespie's algorithm, provided that the network is not exceedingly large. Alternatively, rule-based models can be simulated directly using particle-based kinetic Monte Carlo methods. This “network-free” approach produces exact stochastic trajectories with a computational cost that is independent of network size. However, memory and run time costs increase with the number of particles, limiting the size of system that can be feasibly simulated. Here, we present a hybrid particle/population simulation method that combines the best attributes of both the network-based and network-free approaches. The method takes as input a rule-based model and a user-specified subset of species to treat as population variables rather than as particles. The model is then transformed by a process of “partial network expansion” into a dynamically equivalent form that can be simulated using a population-adapted network-free simulator. The transformation method has been implemented within the open-source rule-based modeling platform BioNetGen, and resulting hybrid models can be simulated using the particle-based simulator NFsim. Performance tests show that significant memory savings can be achieved using the new approach and a monetary cost analysis provides a practical measure of its utility.

Rule-based modeling is a modeling paradigm that addresses the problem of combinatorial complexity in biochemical systems. The key idea is to specify only those components of a biological macromolecule that are directly involved in a biochemical transformation. Until recently, this “pattern-based” approach greatly simplified the process of model building but did nothing to improve the performance of model simulation. This changed with the introduction of “network-free” simulation methods, which operate directly on the compressed rule set of a rule-based model rather than on a fully-enumerated set of reactions and species. However, these methods represent every molecule in a system as a particle, limiting their use to systems containing less than a few million molecules. Here, we describe an extension to the network-free approach that treats rare, complex species as particles and plentiful, simple species as population variables, while retaining the exact dynamics of the model system. By making more efficient use of computational resources for species that do not require the level of detail of a particle representation, this hybrid particle/population approach can simulate systems much larger than is possible using network-free methods and is an important step towards realizing the practical simulation of detailed, mechanistic models of whole cells.

Computational modeling of the main signaling pathways involved in mast cell activation

A global and rigorous understanding of the signaling pathways and cross-regulatory processes involved in mast cell activation requires the integration of published information with novel functional datasets into a comprehensive computational model. Based on an exhaustive curation of the existing literature and using the software CellDesigner, we have built and annotated a comprehensive molecular map for the FcεRI signaling network. This map can be used to visualize and interpret high-throughput expression data. Furthermore, leaning on this map and using the logical modeling software GINsim, we have derived a qualitative dynamical model, which recapitulates the most salient features of mast cell activation. The resulting logical model can be used to explore the dynamical properties of the system and its responses to different stimuli, in normal or mutant conditions.

Modeling and experimental analyses reveals signaling plasticity in a bi-modular assembly of CD40 receptor activated kinases

Depending on the strength of signal dose, CD40 receptor (CD40) controls ERK-1/2 and p38MAPK activation. At low signal dose, ERK-1/2 is maximally phosphorylated but p38MAPK is minimally phosphorylated; as the signal dose increases, ERK-1/2 phosphorylation is reduced whereas p38MAPK phosphorylation is reciprocally enhanced. The mechanism of reciprocal activation of these two MAPKs remains un-elucidated. Here, our computational model, coupled to experimental perturbations, shows that the observed reciprocity is a system-level behavior of an assembly of kinases arranged in two modules. Experimental perturbations with kinase inhibitors suggest that a minimum of two trans-modular negative feedback loops are required to reproduce the experimentally observed reciprocity. The bi-modular architecture of the signaling pathways endows the system with an inherent plasticity which is further expressed in the skewing of the CD40-induced productions of IL-10 and IL-12, the respective anti-inflammatory and pro-inflammatory cytokines. Targeting the plasticity of CD40 signaling significantly reduces Leishmania major infection in a susceptible mouse strain. Thus, for the first time, using CD40 signaling as a model, we show how a bi-modular assembly of kinases imposes reciprocity to a receptor signaling. The findings unravel that the signalling plasticity is inherent to a reciprocal system and that the principle can be used for designing a therapy.

Network-of-queues approach to B-cell-receptor affinity discrimination

The immune system is one of the most complex signal processing machineries in biology. The adaptive immune system, consisting of B and T lymphocytes, is activated in response to a large spectrum of pathogen antigens. B cells recognize and bind the antigen through B-cell receptors (BCRs) and this is fundamental for B-cell activation. However, the system response is dependent on BCR-antigen affinity values that span several orders of magnitude. Moreover, the ability of the BCR to discriminate between affinities at the high end (e.g., 10^{9}M^{-1}-10^{10}M^{-1}) challenges the formulation of a mathematical model able to robustly separate these affinity-dependent responses. Queuing theory enables the analysis of many related processes, such as those resulting from the stochasticity of protein binding and unbinding events. Here we define a network of queues, consisting of BCR early signaling states and transition rates related to the propensity of molecular aggregates to form or disassemble. By considering the family of marginal distributions of BCRs in a given signaling state, we report a significant separation (measured as Jensen-Shannon divergence) that arises from a broad spectrum of antigen affinities.

Deciphering the structure and function of FcεRI/mast cell axis in the regulation of allergy and anaphylaxis: a functional genomics paradigm

Allergy and anaphylaxis are inflammatory disorders caused by immune reactions mainly induced by immunoglobulin-E that signal through the high-affinity FcεRI receptor to release the inflammatory mediators from innate immune cells. The FcεRI/mast cell axis is potently involved in triggering various intracellular signaling molecules to induce calcium release from the internal stores, induction of transcription factors such as NF-kB, secretion of various cytokines as well as lipid mediators, and degranulation, resulting in the induction of allergy and anaphylaxis. In this review, we discuss various cellular and molecular mechanisms triggered through FcεRI/mast cell axis in allergy and anaphylaxis with a special emphasis on the functional genomics paradigm.

Guidelines for visualizing and annotating rule-based models

Rule-based modeling provides a means to represent cell signaling systems in a way that captures site-specific details of molecular interactions. For rule-based models to be more widely understood and (re)used, conventions for model visualization and annotation are needed. We have developed the concepts of an extended contact map and a model guide for illustrating and annotating rule-based models. An extended contact map represents the scope of a model by providing an illustration of each molecule, molecular component, direct physical interaction, post-translational modification, and enzyme-substrate relationship considered in a model. A map can also illustrate allosteric effects, structural relationships among molecular components, and compartmental locations of molecules. A model guide associates elements of a contact map with annotation and elements of an underlying model, which may be fully or partially specified. A guide can also serve to document the biological knowledge upon which a model is based. We provide examples of a map and guide for a published rule-based model that characterizes early events in IgE receptor (FcεRI) signaling. We also provide examples of how to visualize a variety of processes that are common in cell signaling systems but not considered in the example model, such as ubiquitination. An extended contact map and an associated guide can document knowledge of a cell signaling system in a form that is visual as well as executable. As a tool for model annotation, a map and guide can communicate the content of a model clearly and with precision, even for large models.

Scaffold-mediated nucleation of protein signaling complexes: elementary principles

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 mechanistically detailed models, we obtain analytical and numerical results that provide insights into scaffold function. These results elucidate how recruitment of a pair of ligands to a scaffold depends on the concentrations of the ligands, on the binding constants for ligand-scaffold interactions, on binding cooperativity, and on the milieu of the scaffold, as ligand recruitment is affected by competitive ligands and decoy receptors. For the case of a bivalent scaffold, we obtain an expression for the unique scaffold concentration that maximally recruits a pair of monovalent ligands. Through simulations, we demonstrate that a bivalent scaffold can nucleate distinct sets of ligands to equivalent extents when the scaffold is present at different concentrations. Thus, the function of a scaffold can potentially change qualitatively with a change in copy number. We also demonstrate how a scaffold can change the catalytic efficiency of an enzyme and the sensitivity of the rate of reaction to substrate concentration. The results presented here should be useful for understanding scaffold function and for engineering scaffolds to have desired properties.

Reduction of calcium release site models via moment fitting of phase-type distributions

Models of calcium (Ca(2 +)) release sites derived from continuous-time Markov chain (CTMC) models of intracellular Ca(2 +) channels exhibit collective gating reminiscent of the experimentally observed phenomenon of Ca(2 +) puffs and sparks. In order to overcome the state-space explosion that occurs in compositionally defined Ca(2 +) release site models, we have implemented an automated procedure for model reduction that replaces aggregated states of the full release site model with much simpler CTMCs that have similar within-group phase-type sojourn times and inter-group transitions. Error analysis based on comparison of full and reduced models validates the method when applied to release site models composed of 20 three-state channels that are both activated and inactivated by Ca(2 +). Although inspired by existing techniques for fitting moments of phase-type distributions, the automated reduction method for compositional Ca(2 +) release site models is unique in several respects and novel in this biophysical context.

Rule-based modelling and simulation of biochemical systems with molecular finite automata

The authors propose a theoretical formalism, molecular finite automata (MFA), to describe individual proteins as rule-based computing machines. The MFA formalism provides a framework for modelling individual protein behaviours and systems-level dynamics via construction of programmable and executable machines. Models specified within this formalism explicitly represent the context-sensitive dynamics of individual proteins driven by external inputs and represent protein-protein interactions as synchronised machine reconfigurations. Both deterministic and stochastic simulations can be applied to quantitatively compute the dynamics of MFA models. They apply the MFA formalism to model and simulate a simple example of a signal-transduction system that involves an MAP kinase cascade and a scaffold protein.

In Silico Augmentation of the Drug Development Pipeline: Examples from the study of Acute Inflammation

The clinical translation of promising basic biomedical findings, whether derived from reductionist studies in academic laboratories or as the product of extensive high-throughput and -content screens in the biotechnology and pharmaceutical industries, has reached a period of stagnation in which ever higher research and development costs are yielding ever fewer new drugs. Systems biology and computational modeling have been touted as potential avenues by which to break through this logjam. However, few mechanistic computational approaches are utilized in a manner that is fully cognizant of the inherent clinical realities in which the drugs developed through this ostensibly rational process will be ultimately used. In this article, we present a Translational Systems Biology approach to inflammation. This approach is based on the use of mechanistic computational modeling centered on inherent clinical applicability, namely that a unified suite of models can be applied to generate in silico clinical trials, individualized computational models as tools for personalized medicine, and rational drug and device design based on disease mechanism.

The zipper mechanism in phagocytosis: energetic requirements and variability in phagocytic cup shape

BACKGROUND

Phagocytosis is the fundamental cellular process by which eukaryotic cells bind and engulf particles by their cell membrane. Particle engulfment involves particle recognition by cell-surface receptors, signaling and remodeling of the actin cytoskeleton to guide the membrane around the particle in a zipper-like fashion. Despite the signaling complexity, phagocytosis also depends strongly on biophysical parameters, such as particle shape, and the need for actin-driven force generation remains poorly understood.

RESULTS

Here, we propose a novel, three-dimensional and stochastic biophysical model of phagocytosis, and study the engulfment of particles of various sizes and shapes, including spiral and rod-shaped particles reminiscent of bacteria. Highly curved shapes are not taken up, in line with recent experimental results. Furthermore, we surprisingly find that even without actin-driven force generation, engulfment proceeds in a large regime of parameter values, albeit more slowly and with highly variable phagocytic cups. We experimentally confirm these predictions using fibroblasts, transfected with immunoreceptor FcγRIIa for engulfment of immunoglobulin G-opsonized particles. Specifically, we compare the wild-type receptor with a mutant receptor, unable to signal to the actin cytoskeleton. Based on the reconstruction of phagocytic cups from imaging data, we indeed show that cells are able to engulf small particles even without support from biological actin-driven processes.

CONCLUSIONS

This suggests that biochemical pathways render the evolutionary ancient process of phagocytic highly robust, allowing cells to engulf even very large particles. The particle-shape dependence of phagocytosis makes a systematic investigation of host-pathogen interactions and an efficient design of a vehicle for drug delivery possible.

Understanding the structure and function of the immunological synapse

The immunological synapse has been an area of very active scientific interest over the last decade. Surprisingly, much about the synapse remains unknown or is controversial. Here we review some of these current issues in the field: how the synapse is defined, its potential role in T-cell function, and our current understanding about how the synapse is formed.

RuleMonkey: software for stochastic simulation of rule-based models

Background

The system-level dynamics of many molecular interactions, particularly protein-protein interactions, can be conveniently represented using reaction rules, which can be specified using model-specification languages, such as the BioNetGen language (BNGL). A set of rules implicitly defines a (bio)chemical reaction network. The reaction network implied by a set of rules is often very large, and as a result, generation of the network implied by rules tends to be computationally expensive. Moreover, the cost of many commonly used methods for simulating network dynamics is a function of network size. Together these factors have limited application of the rule-based modeling approach. Recently, several methods for simulating rule-based models have been developed that avoid the expensive step of network generation. The cost of these "network-free" simulation methods is independent of the number of reactions implied by rules. Software implementing such methods is now needed for the simulation and analysis of rule-based models of biochemical systems.

Results

Here, we present a software tool called RuleMonkey, which implements a network-free method for simulation of rule-based models that is similar to Gillespie's method. The method is suitable for rule-based models that can be encoded in BNGL, including models with rules that have global application conditions, such as rules for intramolecular association reactions. In addition, the method is rejection free, unlike other network-free methods that introduce null events, i.e., steps in the simulation procedure that do not change the state of the reaction system being simulated. We verify that RuleMonkey produces correct simulation results, and we compare its performance against DYNSTOC, another BNGL-compliant tool for network-free simulation of rule-based models. We also compare RuleMonkey against problem-specific codes implementing network-free simulation methods.

Conclusions

RuleMonkey enables the simulation of rule-based models for which the underlying reaction networks are large. It is typically faster than DYNSTOC for benchmark problems that we have examined. RuleMonkey is freely available as a stand-alone application http://public.tgen.org/rulemonkey. It is also available as a simulation engine within GetBonNie, a web-based environment for building, analyzing and sharing rule-based models.

Translational systems approaches to the biology of inflammation and healing

Inflammation is a complex, non-linear process central to many of the diseases that affect both developed and emerging nations. A systems-based understanding of inflammation, coupled to translational applications, is therefore necessary for efficient development of drugs and devices, for streamlining analyses at the level of populations, and for the implementation of personalized medicine. We have carried out an iterative and ongoing program of literature analysis, generation of prospective data, data analysis, and computational modeling in various experimental and clinical inflammatory disease settings. These simulations have been used to gain basic insights into the inflammatory response under baseline, gene-knockout, and drug-treated experimental animals for in silico studies associated with the clinical settings of sepsis, trauma, acute liver failure, and wound healing to create patient-specific simulations in polytrauma, traumatic brain injury, and vocal fold inflammation; and to gain insight into host-pathogen interactions in malaria, necrotizing enterocolitis, and sepsis. These simulations have converged with other systems biology approaches (e.g., functional genomics) to aid in the design of new drugs or devices geared towards modulating inflammation. Since they include both circulating and tissue-level inflammatory mediators, these simulations transcend typical cytokine networks by associating inflammatory processes with tissue/organ impacts via tissue damage/dysfunction. This framework has now allowed us to suggest how to modulate acute inflammation in a rational, individually optimized fashion. This plethora of computational and intertwined experimental/engineering approaches is the cornerstone of Translational Systems Biology approaches for inflammatory diseases.

The SCHOOL of nature: I. Transmembrane signaling

Receptor-mediated transmembrane signaling plays an important role in health and disease. Recent significant advances in our understanding of the molecular mechanisms linking ligand binding to receptor activation revealed previously unrecognized striking similarities in the basic structural principles of function of numerous cell surface receptors. In this work, I demonstrate that the Signaling Chain Homooligomerization (SCHOOL)-based mechanism represents a general biological mechanism of transmembrane signal transduction mediated by a variety of functionally unrelated single- and multichain activating receptors. within the SCHOOL platform, ligand binding-induced receptor clustering is translated across the membrane into protein oligomerization in cytoplasmic milieu. This platform resolves a long-standing puzzle in transmembrane signal transduction and reveals the major driving forces coupling recognition and activation functions at the level of protein-protein interactions-biochemical processes that can be influenced and controlled. The basic principles of transmembrane signaling learned from the SCHOOL model can be used in different fields of immunology, virology, molecular and cell biology and others to describe, explain and predict various phenomena and processes mediated by a variety of functionally diverse and unrelated receptors. Beyond providing novel perspectives for fundamental research, the platform opens new avenues for drug discovery and development.

Involvement of Fc receptors in disorders of the central nervous system

Immunoglobulins are proteins with a highly variable antigen-binding domain and a constant region (Fc domain) that binds to a cell surface receptor (FcR). Activation of FcRs in immune cells (lymphocytes, macrophages, and mast cells) triggers effector responses including cytokine production, phagocytosis, and degranulation. In addition to their roles in normal responses to infection or tissue injury, and in immune-related diseases, FcRs are increasingly recognized for their involvement in neurological disorders. One or more FcRs are expressed in microglia, astrocytes, oligodendrocytes, and neurons. Aberrant activation of FcRs in such neural cells may contribute to the pathogenesis of major neurodegenerative conditions including Alzheimer's disease, Parkinson's disease, ischemic stroke, and multiple sclerosis. On the other hand, FcRs may play beneficial roles in counteracting pathological processes; for e.g., FcRs may facilitate removal of amyloid peptides from the brain and so protect against Alzheimer's disease. Knowledge of the functions of FcRs in the nervous system in health and disease is leading to novel preventative and therapeutic strategies for stroke, Alzheimer's disease, and other neurological disorders.

Rule-based modeling of biochemical systems with BioNetGen

Rule-based modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate site-specific details about protein-protein interactions into a model for the dynamics of a signal-transduction system, but the method has other applications as well, such as following the fates of individual carbon atoms in metabolic reactions. The consequences of protein-protein interactions are difficult to specify and track with a conventional modeling approach because of the large number of protein phosphoforms and protein complexes that these interactions potentially generate. Here, we focus on how a rule-based model is specified in the BioNetGen language (BNGL) and how a model specification is analyzed using the BioNetGen software tool. We also discuss new developments in rule-based modeling that should enable the construction and analyses of comprehensive models for signal transduction pathways and similarly large-scale models for other biochemical systems.

Kinetic Monte Carlo method for rule-based modeling of biochemical networks

We present a kinetic Monte Carlo method for simulating chemical transformations specified by reaction rules, which can be viewed as generators of chemical reactions, or equivalently, definitions of reaction classes. A rule identifies the molecular components involved in a transformation, how these components change, conditions that affect whether a transformation occurs, and a rate law. The computational cost of the method, unlike conventional simulation approaches, is independent of the number of possible reactions, which need not be specified in advance or explicitly generated in a simulation. To demonstrate the method, we apply it to study the kinetics of multivalent ligand-receptor interactions. We expect the method will be useful for studying cellular signaling systems and other physical systems involving aggregation phenomena.

XML Encoding of Features Describing Rule-Based Modeling of Reaction Networks with Multi-Component Molecular Complexes

Multi-state molecules and multi-component complexes are commonly involved in cellular signaling. Accounting for molecules that have multiple potential states, such as a protein that may be phosphorylated on multiple residues, and molecules that combine to form heterogeneous complexes located among multiple compartments, generates an effect of combinatorial complexity. Models involving relatively few signaling molecules can include thousands of distinct chemical species. Several software tools (StochSim, BioNetGen) are already available to deal with combinatorial complexity. Such tools need information standards if models are to be shared, jointly evaluated and developed. Here we discuss XML conventions that can be adopted for modeling biochemical reaction networks described by user-specified reaction rules. These could form a basis for possible future extensions of the Systems Biology Markup Language (SBML).

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.

Scaffolding protein Grb2-associated binder 1 sustains epidermal growth factor-induced mitogenic and survival signaling by multiple positive feedback loops

Grb2-associated binder 1 (GAB1) is a scaffold protein involved in numerous interactions that propagate signaling by growth factor and cytokine receptors. Here we explore in silico and validate in vivo the role of GAB1 in the control of mitogenic (Ras/MAPK) and survival (phosphatidylinositol 3-kinase (PI3K)/Akt) signaling stimulated by epidermal growth factor (EGF). We built a comprehensive mechanistic model that allows for reliable predictions of temporal patterns of cellular responses to EGF under diverse perturbations, including different EGF doses, GAB1 suppression, expression of mutant proteins, and pharmacological inhibitors. We show that the temporal dynamics of GAB1 tyrosine phosphorylation is significantly controlled by positive GAB1-PI3K feedback and negative MAPK-GAB1 feedback. Our experimental and computational results demonstrate that the essential function of GAB1 is to enhance PI3K/Akt activation and extend the duration of Ras/MAPK signaling. By amplifying positive interactions between survival and mitogenic pathways, GAB1 plays the critical role in cell proliferation and tumorigenesis.

A network model of early events in epidermal growth factor receptor signaling that accounts for combinatorial complexity

We consider a model of early events in signaling by the epidermal growth factor (EGF) receptor (EGFR). The model includes EGF, EGFR, the adapter proteins Grb2 and Shc, and the guanine nucleotide exchange factor Sos, which is activated through EGF-induced formation of EGFR-Grb2-Sos and EGFR-Shc-Grb2-Sos assemblies at the plasma membrane. The protein interactions involved in signaling can potentially generate a diversity of protein complexes and phosphoforms; however, this diversity has been largely ignored in models of EGFR signaling. Here, we develop a model that accounts more fully for potential molecular diversity by specifying rules for protein interactions and then using these rules to generate a reaction network that includes all chemical species and reactions implied by the protein interactions. We obtain a model that predicts the dynamics of 356 molecular species, which are connected through 3749 unidirectional reactions. This network model is compared with a previously developed model that includes only 18 chemical species but incorporates the same scope of protein interactions. The predictions of this model are reproduced by the network model, which also yields new predictions. For example, the network model predicts distinct temporal patterns of autophosphorylation for different tyrosine residues of EGFR. A comparison of the two models suggests experiments that could lead to mechanistic insights about competition among adapter proteins for EGFR binding sites and the role of EGFR monomers in signal transduction.

An integrated approach for inference and mechanistic modeling for advancing drug development

An important challenge facing researchers in drug development is how to translate multi-omic measurements into biological insights that will help advance drugs through the clinic. Computational biology strategies are a promising approach for systematically capturing the effect of a given drug on complex molecular networks and on human physiology. This article discusses a two-pronged strategy for inferring biological interactions from large-scale multi-omic measurements and accounting for known biology via mechanistic dynamical simulations of pathways, cells, and organ- and tissue level models. These approaches are already playing a role in driving drug development by providing a rational and systematic computational framework.

The complexity of complexes in signal transduction

Many activities of cells are controlled by cell-surface receptors, which in response to ligands, trigger intracellular signaling reactions that elicit cellular responses. A hallmark of these signaling reactions is the reversible nucleation of multicomponent complexes, which typically begin to assemble when ligand-receptor binding allows an enzyme, often a kinase, to create docking sites for signaling molecules through chemical modifications, such as tyrosine phosphorylation. One function of such docking sites is the co-localization of enzymes with their substrates, which can enhance both enzyme activity and specificity. The directed assembly of complexes can also influence the sensitivity of cellular responses to ligand-receptor binding kinetics and determine whether a cellular response is up- or downregulated in response to a ligand stimulus. The full functional implications of ligand-stimulated complex formation are difficult to discern intuitively. Complex formation is governed by conditional interactions among multivalent signaling molecules and influenced by quantitative properties of both the components in a system and the system itself. Even a simple list of the complexes that can potentially form in response to a ligand stimulus is problematic because of the number of ways signaling molecules can be modified and combined. Here, we review the role of multicomponent complexes in signal transduction and advocate the use of mathematical models that incorporate detail at the level of molecular domains to study this important aspect of cellular signaling.

Investigation of early events in Fc epsilon RI-mediated signaling using a detailed mathematical model

Aggregation of Fc epsilon RI on mast cells and basophils leads to autophosphorylation and increased activity of the cytosolic protein tyrosine kinase Syk. We investigated the roles of the Src kinase Lyn, the immunoreceptor tyrosine-based activation motifs (ITAMs) on the beta and gamma subunits of Fc epsilon RI, and Syk itself in the activation of Syk. Our approach was to build a detailed mathematical model of reactions involving Fc epsilon RI, Lyn, Syk, and a bivalent ligand that aggregates Fc(epsilon)RI. We applied the model to experiments in which covalently cross-linked IgE dimers stimulate rat basophilic leukemia cells. The model makes it possible to test the consistency of mechanistic assumptions with data that alone provide limited mechanistic insight. For example, the model helps sort out mechanisms that jointly control dephosphorylation of receptor subunits. In addition, interpreted in the context of the model, experimentally observed differences between the beta- and gamma-chains with respect to levels of phosphorylation and rates of dephosphorylation indicate that most cellular Syk, but only a small fraction of Lyn, is available to interact with receptors. We also show that although the beta ITAM acts to amplify signaling in experimental systems where its role has been investigated, there are conditions under which the beta ITAM will act as an inhibitor.

Meeting report: in silico cell signaling underground

Cell signaling is becoming a darling of systems biology. Because cell signaling is a relatively well understood, complex, but not overwhelming area of biology, it has become an attractive focal point for computational modeling and simulation efforts by engineers, computer scientists, mathematicians, and systems biologists. The flow of information within and between cells points to a possible conceptual and theoretical kinship with similar phenomena in computer networks, communication theory, information theory, and information flow in engineered systems. Although still in its infancy, the field is experiencing a growth in interest, as evidenced by the poster sessions at the recent International Conference on Systems Biology (ICSB 2002). This report focuses on some of those efforts to mathematically model and simulate cell signaling and signal transduction networks.

Quantitative aspects of signal transduction by the receptor with high affinity for IgE

Identification of the major components, how these interact with each other, and the modifications that follow in the sequence of events triggered by the receptor with high affinity for IgE, is progressing rapidly. A new challenge is to understand these interactions quantitatively. We present the fundamentals of the mechanistic model we are testing through mathematical modeling. The object is to see if the predictions of the model fit with the experimental results.

Molecular versatility of antibodies

As immunology developed into a discrete discipline, the principal experimental efforts were directed towards uncovering the molecular basis of the specificity exhibited by antibodies and the mechanism by which antigens induced their production. Less attention was given to how antibodies carry out some of their effector functions, although this subject presents an interesting protein-chemical and evolutionary problem; that is, how does a family of proteins that can bind a virtually infinite variety of ligands, many of which the species producing that protein has never encountered, reproducibly initiate an appropriate response? The experimental data persuasively suggested that aggregation of the antibody was a necessary and likely sufficient initiating event, but this only begged the question: how does aggregation induce a response? I used the IgE:mast cell system as a paradigm to investigate this subject. Data from our own group and from many others led to a molecular model that appears to explain how a cell 'senses' that antigen has reacted with the IgE. The model is directly applicable to one of the fundamental questions cited above, i.e. the mechanism by which antigens induce the production of antibodies. Although the model is conceptually simple, incorporating the actual molecular events into a quantitatively accurate scheme represents an enormous challenge.