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

Formation of BCR oligomers provides a mechanism for B cell affinity discrimination

B cells encounter antigen over a wide affinity range, from K(A)=10(5) M(-1) to K(A)=10(10) M(-1). The strength of B cell antigen receptor (BCR) signaling in response to antigen increases with affinity, a process known as "affinity discrimination". In this work, we use a computational simulation of B cell surface dynamics and membrane-proximal signaling to show that affinity discrimination can arise from the formation of BCR oligomers. It is known that BCRs form oligomers upon encountering antigen, and that the size and rate of formation of these oligomers both increase with affinity. In our simulation, we have introduced a requirement that only BCR-antigen complexes that are part of an oligomer can engage cytoplasmic signaling molecules such as Src-family kinases. Our simulation shows that as affinity increases, BCR signaling activity increases in addition to the number of collected antigen. Our results are also consistent with the existence of an experimentally-observed threshold affinity of activation at K(A)=10(5)-10(6) M(-1) (no signaling activity below this affinity value) and affinity discrimination ceiling of K(A)=10(10) M(-1) (no affinity discrimination above this affinity value). Comparison with experiments shows that the time scale of BCR oligomer formation predicted by our model (less than 10 s) is well within the time scale of experimentally observed association of BCR with Src-family kinases (10-20 s).

A computational model for early events in B cell antigen receptor signaling: analysis of the roles of Lyn and Fyn

BCR signaling regulates the activities and fates of B cells. BCR signaling encompasses two feedback loops emanating from Lyn and Fyn, which are Src family protein tyrosine kinases (SFKs). Positive feedback arises from SFK-mediated trans phosphorylation of BCR and receptor-bound Lyn and Fyn, which increases the kinase activities of Lyn and Fyn. Negative feedback arises from SFK-mediated cis phosphorylation of the transmembrane adapter protein PAG1, which recruits the cytosolic protein tyrosine kinase Csk to the plasma membrane, where it acts to decrease the kinase activities of Lyn and Fyn. To study the effects of the positive and negative feedback loops on the dynamical stability of BCR signaling and the relative contributions of Lyn and Fyn to BCR signaling, we consider in this study a rule-based model for early events in BCR signaling that encompasses membrane-proximal interactions of six proteins, as follows: BCR, Lyn, Fyn, Csk, PAG1, and Syk, a cytosolic protein tyrosine kinase that is activated as a result of SFK-mediated phosphorylation of BCR. The model is consistent with known effects of Lyn and Fyn deletions. We find that BCR signaling can generate a single pulse or oscillations of Syk activation depending on the strength of Ag signal and the relative levels of Lyn and Fyn. We also show that bistability can arise in Lyn- or Csk-deficient cells.

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.

RuleBender: integrated modeling, simulation and visualization for rule-based intracellular biochemistry

BACKGROUND

Rule-based modeling (RBM) is a powerful and increasingly popular approach to modeling cell signaling networks. However, novel visual tools are needed in order to make RBM accessible to a broad range of users, to make specification of models less error prone, and to improve workflows.

RESULTS

We introduce RuleBender, a novel visualization system for the integrated visualization, modeling and simulation of rule-based intracellular biochemistry. We present the user requirements, visual paradigms, algorithms and design decisions behind RuleBender, with emphasis on visual global/local model exploration and integrated execution of simulations. The support of RBM creation, debugging, and interactive visualization expedites the RBM learning process and reduces model construction time; while built-in model simulation and results with multiple linked views streamline the execution and analysis of newly created models and generated networks.

CONCLUSION

RuleBender has been adopted as both an educational and a research tool and is available as a free open source tool at http://www.rulebender.org. A development cycle that includes close interaction with expert users allows RuleBender to better serve the needs of the systems biology community.

Quantitative nanoscale analysis of IgE-FcεRI clustering and coupling to early signaling proteins

Antigen-mediated cross-linking of IgE bound to its receptor, FcεRI, initiates a transmembrane signaling cascade that results in mast cell activation in the allergic response. Using immunogold labeling of intact RBL mast cells and scanning electron microscopy (SEM), we visualize molecular reorganization of IgE-FcεRI and early signaling proteins on both leaflets of the plasma membrane, without the need for ripped off membrane sheets. As quantified by pair correlation analysis, we observe dramatic changes in the nanoscale distribution of IgE-FcεRI after binding of multivalent antigen to stimulate transmembrane signaling, and this is accompanied by similar clustering of Lyn and Syk tyrosine kinases, and adaptor protein LAT. We find that Lyn co-redistributes with IgE-FcεRI into clusters that cross-correlate throughout 20 min of stimulation. Inhibition of tyrosine kinase activity reduces the numbers of both IgE-FcεRI and Lyn in stimulated clusters. Coupling of these proteins is also decreased when membrane cholesterol is reduced either before or after antigen addition. These results provide evidence for involvement of FcεRI phosphorylation and cholesterol-dependent membrane structure in the interactions that accompany IgE-mediated activation of RBL mast cells. More generally, this SEM view of intact cell surfaces provides new insights into the nanoscale organization of receptor-mediated signaling complexes in the plasma membrane.

Bigger, better, faster: principles and models of AKAP anchoring protein signaling

A kinase anchoring proteins (AKAPs) bind multiple signaling proteins and have subcellular targeting domains that allow them to greatly impact cellular signaling. AKAPs localize, specify, amplify, and accelerate signal transduction within the cell by bringing signaling proteins together in space and time. AKAPs also organize higher-order network motifs such as feed forward and feedback loops that may create complex network responses, including adaptation, oscillation, and ultrasensitivity. Computational models have begun to provide an insight into how AKAPs regulate signaling dynamics and cardiovascular pathophysiology. Models of mitogen-activated protein kinase and epidermal growth factor receptor scaffolds have revealed additional design principles and new methods for representing signaling scaffolds mathematically. Coupling computational modeling with quantitative experimental approaches will be increasingly necessary for dissecting the diverse information processing functions performed by AKAP signaling complexes.

Sepsis: from pattern to mechanism and back

Sepsis is a clinical entity in which complex inflammatory and physiological processes are mobilized, not only across a range of cellular and molecular interactions, but also in clinically relevant physiological signals accessible at the bedside. There is a need for a mechanistic understanding that links the clinical phenomenon of physiologic variability with the underlying patterns of the biology of inflammation, and we assert that this can be facilitated through the use of dynamic mathematical and computational modeling. An iterative approach of laboratory experimentation and mathematical/computational modeling has the potential to integrate cellular biology, physiology, control theory, and systems engineering across biological scales, yielding insights into the control structures that govern mechanisms by which phenomena, detected as biological patterns, are produced. This approach can represent hypotheses in the formal language of mathematics and computation, and link behaviors that cross scales and domains, thereby offering the opportunity to better explain, diagnose, and intervene in the care of the septic patient.

Discrimination of membrane antigen affinity by B cells requires dominance of kinetic proofreading over serial engagement

B-cell receptor signaling in response to membrane-bound antigen increases with antigen affinity, a process known as affinity discrimination. We use computational modeling to show that B-cell affinity discrimination requires that kinetic proofreading predominate over serial engagement. We find that if B-cell receptors become signaling-capable immediately upon antigen binding, which results in decreasing serial engagement as affinity increases, then increasing affinity can lead to weaker signaling. Rather, antigen must stay bound to B-cell receptors for a threshold time of several seconds before becoming signaling-capable, a process similar to kinetic proofreading. This process overcomes the loss in serial engagement due to increasing antigen affinity, and replicates the monotonic increase in B-cell signaling with increasing affinity that has been observed in B-cell activation experiments. This finding matches well with the experimentally observed time (∼20 s) required for the B-cell receptor signaling domains to undergo antigen and lipid raft-mediated conformational changes that lead to Src-family kinase recruitment. We hypothesize that the physical basis for a threshold time of antigen binding might lie in the formation timescale of B-cell receptor dimers. The time required for dimer formation decreases with increasing antigen affinity, thereby resulting in shorter threshold antigen binding times as affinity increases. Such an affinity-dependent kinetic proofreading requirement results in affinity discrimination very similar to that observed in biological experiments. B-cell affinity discrimination is critical to the process of affinity maturation and the production of high-affinity antibodies, and thus our results have important implications in applications such as vaccine design.

B cell activation triggered by the formation of the small receptor cluster: a computational study

We proposed a spatially extended model of early events of B cell receptors (BCR) activation, which is based on mutual kinase-receptor interactions that are characteristic for the immune receptors and the Src family kinases. These interactions lead to the positive feedback which, together with two nonlinearities resulting from the double phosphorylation of receptors and Michaelis-Menten dephosphorylation kinetics, are responsible for the system bistability. We demonstrated that B cell can be activated by a formation of a tiny cluster of receptors or displacement of the nucleus. The receptors and Src kinases are activated, first locally, in the locus of the receptor cluster or the region where the cytoplasm is the thinnest. Then the traveling wave of activation propagates until activity spreads over the whole cell membrane. In the models in which we assume that the kinases are free to diffuse in the cytoplasm, we found that the fraction of aggregated receptors, capable to initiate B cell activation decreases with the decreasing thickness of cytoplasm and decreasing kinase diffusion. When kinases are restricted to the cell membrane - which is the case for most of the Src family kinases - even a cluster consisting of a tiny fraction of total receptors becomes activatory. Interestingly, the system remains insensitive to the modest changes of total receptor level. The model provides a plausible mechanism of B cells activation due to the formation of small receptors clusters collocalized by binding of polyvalent antigens or arising during the immune synapse formation.

B cells are activated in response to binding of appropriate ligands, which induces the aggregation of B cell receptors. The formation of even small clusters containing less than 1% of all the receptors is sufficient for activation. This observation led us to a model in which the receptor cluster serves only as a switch that turns on the activation process involving also the remaining receptors. The idea of the model exploits the fact the Src kinase - BCR system is bistable, and thus its local activation may start the propagation of a traveling wave, which spreads activation over the entire membrane. We found that the minimal size of the activatory cluster decreases with the thickness of the cytoplasm and kinase diffusion coefficient. It is particularly small when kinases are restricted to the membrane. These findings are consistent with the properties of B cells, which prior to activation have extremely thin cytoplasmic layer and in which Src family kinases (interacting with the receptors) are tethered to the membrane.

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.

Structural basis for Fc gammaRIIa recognition of human IgG and formation of inflammatory signaling complexes

The interaction of Abs with their specific FcRs is of primary importance in host immune effector systems involved in infection and inflammation, and are the target for immune evasion by pathogens. FcγRIIa is a unique and the most widespread activating FcR in humans that through avid binding of immune complexes potently triggers inflammation. Polymorphisms of FcγRIIa (high responder/low responder [HR/LR]) are linked to susceptibility to infections, autoimmune diseases, and the efficacy of therapeutic Abs. In this article, we define the three-dimensional structure of the complex between the HR (arginine, R134) allele of FcγRIIa (FcγRIIa-HR) and the Fc region of a humanized IgG1 Ab, hu3S193. The structure suggests how the HR/LR polymorphism may influence FcγRIIa interactions with different IgG subclasses and glycoforms. In addition, mutagenesis defined the basis of the epitopes detected by FcR blocking mAbs specific for FcγRIIa (IV.3), FcγRIIb (X63-21), and a pan FcγRII Ab (8.7). The epitopes detected by these Abs are distinct, but all overlap with residues defined by crystallography to contact IgG. Finally, crystal structures of LR (histidine, H134) allele of FcγRIIa and FcγRIIa-HR reveal two distinct receptor dimers that may represent quaternary states on the cell surface. A model is presented whereby a dimer of FcγRIIa-HR binds Ag-Ab complexes in an arrangement that possibly occurs on the cell membrane as part of a larger signaling assembly.

Rule-based modelling of iron homeostasis in tuberculosis

To establish itself within the host system, Mycobacterium tuberculosis (Mtb) has formulated various means of attacking the host system. One such crucial strategy is the exploitation of the iron resources of the host system. Obtaining and maintaining the required concentration of iron becomes a matter of contest between the host and the pathogen, both trying to achieve this through complex molecular networks. The extent of complexity makes it important to obtain a systems perspective of the interplay between the host and the pathogen with respect to iron homeostasis. We have reconstructed a systems model comprising 92 components and 85 protein-protein or protein-metabolite interactions, which have been captured as a set of 194 rules. Apart from the interactions, these rules also account for protein synthesis and decay, RBC circulation and bacterial production and death rates. We have used a rule-based modelling approach, Kappa, to simulate the system separately under infection and non-infection conditions. Various perturbations including knock-outs and dual perturbation were also carried out to monitor the behavioral change of important proteins and metabolites. From this, key components as well as the required controlling factors in the model that are critical for maintaining iron homeostasis were identified. The model is able to re-establish the importance of iron-dependent regulator (ideR) in Mtb and transferrin (Tf) in the host. Perturbations, where iron storage is increased, appear to enhance nutritional immunity and the analysis indicates how they can be harmful for the host. Instead, decreasing the rate of iron uptake by Tf may prove to be helpful. Simulation and perturbation studies help in identifying Tf as a possible drug target. Regulating the mycobactin (myB) concentration was also identified as a possible strategy to control bacterial growth. The simulations thus provide significant insight into iron homeostasis and also for identifying possible drug targets for tuberculosis.

Exact solutions to a spatially extended model of kinase-receptor interaction

B and Mast cells are activated by the aggregation of the immune receptors. Motivated by this phenomena we consider a simple spatially extended model of mutual interaction of kinases and membrane receptors. It is assumed that kinase activates membrane receptors and in turn the kinase molecules bound to the active receptors are activated by transphosphorylation. Such a type of interaction implies positive feedback and may lead to bistability. In this study we apply the Steklov eigenproblem theory to analyze the linearized model and find exact solutions in the case of non-uniformly distributed membrane receptors. This approach allows us to determine the critical value of receptor dephosphorylation rate at which cell activation (by arbitrary small perturbation of the inactive state) is possible. We found that cell sensitivity grows with decreasing kinase diffusion and increasing anisotropy of the receptor distribution. Moreover, these two effects are cooperating. We showed that the cell activity can be abruptly triggered by the formation of the receptor aggregate. Since the considered activation mechanism is not based on receptor crosslinking by polyvalent antigens, the proposed model can also explain B cell activation due to receptor aggregation following binding of monovalent antigens presented on the antigen presenting cell.

Sepsis: Something old, something new, and a systems view

Sepsis is a clinical syndrome characterized by a multisystem response to a microbial pathogenic insult consisting of a mosaic of interconnected biochemical, cellular, and organ-organ interaction networks. A central thread that connects these responses is inflammation that, while attempting to defend the body and prevent further harm, causes further damage through the feed-forward, proinflammatory effects of damage-associated molecular pattern molecules. In this review, we address the epidemiology and current definitions of sepsis and focus specifically on the biologic cascades that comprise the inflammatory response to sepsis. We suggest that attempts to improve clinical outcomes by targeting specific components of this network have been unsuccessful due to the lack of an integrative, predictive, and individualized systems-based approach to define the time-varying, multidimensional state of the patient. We highlight the translational impact of computational modeling and other complex systems approaches as applied to sepsis, including in silico clinical trials, patient-specific models, and complexity-based assessments of physiology.

Using hierarchical clustering and dendrograms to quantify the clustering of membrane proteins

Cell biologists have developed methods to label membrane proteins with gold nanoparticles and then extract spatial point patterns of the gold particles from transmission electron microscopy images using image processing software. Previously, the resulting patterns were analyzed using the Hopkins statistic, which distinguishes nonclustered from modestly and highly clustered distributions, but is not designed to quantify the number or sizes of the clusters. Clusters were defined by the partitional clustering approach which required the choice of a distance. Two points from a pattern were put in the same cluster if they were closer than this distance. In this study, we present a new methodology based on hierarchical clustering to quantify clustering. An intrinsic distance is computed, which is the distance that produces the maximum number of clusters in the biological data, eliminating the need to choose a distance. To quantify the extent of clustering, we compare the clustering distance between the experimental data being analyzed with that from simulated random data. Results are then expressed as a dimensionless number, the clustering ratio that facilitates the comparison of clustering between experiments. Replacing the chosen cluster distance by the intrinsic clustering distance emphasizes densely packed clusters that are likely more important to downstream signaling events.We test our new clustering analysis approach against electron microscopy images from an experiment in which mast cells were exposed for 1 or 2 minutes to increasing concentrations of antigen that crosslink IgE bound to its high affinity receptor, FcϵRI, then fixed and the FcϵRI β subunit labeled with 5 nm gold particles. The clustering ratio analysis confirms the increase in clustering with increasing antigen dose predicted from visual analysis and from the Hopkins statistic. Access to a robust and sensitive tool to both observe and quantify clustering is a key step toward understanding the detailed fine scale structure of the membrane, and ultimately to determining the role of spatial organization in the regulation of transmembrane signaling.

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.

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.

Shaping the response: the role of FcεRI and Syk expression levels in mast cell signaling

Many receptor systems initiate cell signaling through ligand-induced receptor aggregation. For bivalent ligands binding to mono- or bivalent receptors, a plot of the equilibrium concentration of receptors in aggregates against the log of the free ligand concentration, the cross-linking curve, is symmetric and bell shaped. However, steady state cellular responses initiated through receptor cross-linking may have a different dependence on ligand concentration than the aggregated receptors that initiate and maintain these responses. The authors illustrate by considering the activation of the protein kinase Syk that rapidly occurs after high affinity receptors for IgE, FcεRI, are aggregated on the surface of mast cells and basophils. Using a mathematical model of Syk activation the authors investigate two effects, one straightforward and one less so, that result in Syk activation not qualitatively following the cross-linking curve. Model predictions show that if the mechanism by which Syk is fully activated involves the transphosphorylation of Syk by Syk, then Syk activation curves can be either bell shaped or double humped, depending on the cellular concentrations of Syk and FcεRI. The model also predicts that the Syk activation curve can be non-symmetric with respect to the ligand concentration. The cell can exhibit differential Syk activation at two different ligand concentrations that produce identical distributions of receptor aggregates that form and dissociate at the same rates. The authors discuss how, even though it is only receptor aggregates that trigger responses, differences in total ligand concentration can lead to subtle kinetic effects that yield qualitative differences in the levels of Syk activation.

Efficient modeling, simulation and coarse-graining of biological complexity with NFsim

Managing the overwhelming numbers of molecular states and interactions is a fundamental obstacle to building predictive models of biological systems. Here we introduce the Network-Free Stochastic Simulator (NFsim), a general-purpose modeling platform that overcomes the combinatorial nature of molecular interactions. Unlike standard simulators that represent molecular species as variables in equations, NFsim uses a biologically intuitive representation: objects with binding and modification sites acted on by reaction rules. During simulations, rules operate directly on molecular objects to produce exact stochastic results with performance that scales independently of the reaction network size. Reaction rates can be defined as arbitrary functions of molecular states to provide powerful coarse-graining capabilities, for example to merge Boolean and kinetic representations of biological networks. NFsim enables researchers to simulate many biological systems that were previously inaccessible to general-purpose software, as we illustrate with models of immune system signaling, microbial signaling, cytoskeletal assembly and oscillating gene expression.

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.

A detailed mathematical model predicts that serial engagement of IgE-Fc epsilon RI complexes can enhance Syk activation in mast cells

The term serial engagement was introduced to describe the ability of a single peptide, bound to a MHC molecule, to sequentially interact with TCRs within the contact region between a T cell and an APC. In addition to ligands on surfaces, soluble multivalent ligands can serially engage cell surface receptors with sites on the ligand, binding and dissociating from receptors many times before all ligand sites become free and the ligand leaves the surface. To evaluate the role of serial engagement in Syk activation, we use a detailed mathematical model of the initial signaling cascade that is triggered when FcepsilonRI is aggregated on mast cells by multivalent Ags. Although serial engagement is not required for mast cell signaling, it can influence the recruitment of Syk to the receptor and subsequent Syk phosphorylation. Simulating the response of mast cells to ligands that serially engage receptors at different rates shows that increasing the rate of serial engagement by increasing the rate of dissociation of the ligand-receptor bond decreases Syk phosphorylation. Increasing serial engagement by increasing the rate at which receptors are cross-linked (for example by increasing the forward rate constant for cross-linking or increasing the valence of the ligand) increases Syk phosphorylation. When serial engagement enhances Syk phosphorylation, it does so by partially reversing the effects of kinetic proofreading. Serial engagement rapidly returns receptors that have dissociated from aggregates to new aggregates before the receptors have fully returned to their basal state.

Translational systems biology of inflammation: potential applications to personalized medicine

A central goal of industrialized nations is to provide personalized, preemptive and predictive medicine, while maintaining healthcare costs at a minimum. To do so, we must confront and gain an understanding of inflammation, a complex, nonlinear process central to many diseases that affect both industrialized and developing nations. Herein, we describe the work aimed at creating a rational, engineering-oriented and evidence-based synthesis of inflammation geared towards rapid clinical application. This comprehensive approach, which we call 'Translational Systems Biology', to date has been utilized for in silico studies of sepsis, trauma/hemorrhage/traumatic brain injury, acute liver failure and wound healing. This framework has now allowed us to suggest how to modulate acute inflammation in a rational and individually optimized fashion using engineering principles applied to a biohybrid device. We suggest that we are on the cusp of fulfilling the promise of in silico modeling for personalized medicine for inflammatory disease.

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.

Perspectives for computer modeling in the study of T cell activation

The T cell receptor (TCR) is responsible for discriminating between self- and foreign-derived peptides, translating minute differences in amino-acid sequence into large differences in response. Because of the great variability in the TCR and its ligands, activation of T cells by foreign peptides is a quantitative process, dependent on a mix of upstream signals and downstream integration. Accordingly, quantitative data and computational models have shed light on many important aspects of this process: molecular noise in ligand recognition, spatial dynamics in T cell-APC (antigen presenting cell) interactions, graded versus all-or-none decision making by the TCR apparatus, mechanisms of peptide antagonism and synergism, and the tunability and robustness of activation thresholds. Though diverse in their formalism, these studies together paint a picture of how modeling has shaped and will continue to shape understanding of T cell immunobiology.

Modeling multivalent ligand-receptor interactions with steric constraints on configurations of cell-surface receptor aggregates

We use flow cytometry to characterize equilibrium binding of a fluorophore-labeled trivalent model antigen to bivalent IgE-FcepsilonRI complexes on RBL cells. We find that flow cytometric measurements are consistent with an equilibrium model for ligand-receptor binding in which binding sites are assumed to be equivalent and ligand-induced receptor aggregates are assumed to be acyclic. However, this model predicts extensive receptor aggregation at antigen concentrations that yield strong cellular secretory responses, which is inconsistent with the expectation that large receptor aggregates should inhibit such responses. To investigate possible explanations for this discrepancy, we evaluate four rule-based models for interaction of a trivalent ligand with a bivalent cell-surface receptor that relax simplifying assumptions of the equilibrium model. These models are simulated using a rule-based kinetic Monte Carlo approach to investigate the kinetics of ligand-induced receptor aggregation and to study how the kinetics and equilibria of ligand-receptor interaction are affected by steric constraints on receptor aggregate configurations and by the formation of cyclic receptor aggregates. The results suggest that formation of linear chains of cyclic receptor dimers may be important for generating secretory signals. Steric effects that limit receptor aggregation and transient formation of small receptor aggregates may also be important.

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.

The simplicity of completion time distributions for common complex biochemical processes

Biochemical processes typically involve huge numbers of individual reversible steps, each with its own dynamical rate constants. For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules. In this work, we study the transient properties of such systems and fully characterize their first passage (completion) time distributions. In particular, we provide explicit expressions for the mean and the variance of the completion time for a kinetic proofreading process and computational analyses for more complicated biochemical systems. We find that, for a wide range of parameters, as the system size grows, the completion time behavior simplifies: it becomes either deterministic or exponentially distributed, with a very narrow transition between the two regimes. In both regimes, the dynamical complexity of the full system is trivial compared to its apparent structural complexity. Similar simplicity is likely to arise in the dynamics of many complex multistep biochemical processes. In particular, these findings suggest not only that one may not be able to understand individual elementary reactions from macroscopic observations, but also that such an understanding may be unnecessary.

Aggregation of membrane proteins by cytosolic cross-linkers: theory and simulation of the LAT-Grb2-SOS1 system

Ligand-induced receptor aggregation is a well-known mechanism for initiating intracellular signals but oligomerization of distal signaling molecules may also be required for signal propagation. Formation of complexes containing oligomers of the transmembrane adaptor protein, linker for the activation of T cells (LAT), has been identified as critical in mast cell and T cell activation mediated by immune response receptors. Cross-linking of LAT arises from the formation of a 2:1 complex between the adaptor Grb2 and the nucleotide exchange factor SOS1, which bridges two LAT molecules through the interaction of the Grb2 SH2 domain with a phosphotyrosine on LAT. We model this oligomerization and find that the valence of LAT for Grb2, which ranges from zero to three, is critical in determining the nature and extent of aggregation. A dramatic rise in oligomerization can occur when the valence switches from two to three. For valence three, an equilibrium theory predicts the possibility of forming a gel-like phase. This prediction is confirmed by stochastic simulations, which make additional predictions about the size of the gel and the kinetics of LAT oligomerization. We discuss the model predictions in light of recent experiments on RBL-2H3 and Jurkat E6.1 cells and suggest that the gel phase has been observed in activated mast cells.

Complexity and modularity of intracellular networks: a systematic approach for modelling and simulation

Assembly of quantitative models of large complex networks brings about several challenges. One of them is the combinatorial complexity, where relatively few signalling molecules can combine to form thousands or millions of distinct chemical species. A receptor that has several separate phosphorylation sites can exist in hundreds of different states, many of which must be accounted for individually when simulating the time course of signalling. When assembly of protein complexes is being included, the number of distinct molecular species can easily increase by a few orders of magnitude. Validation, visualisation and understanding the network can become intractable. Another challenge appears when the modeller needs to recast or grow a model. Keeping track of changes and adding new elements present a significant difficulty. An approach to solve these challenges within the virtual cell (VCell) is described. Using (i) automatic extraction from pathway databases of model components (http://vcell.org/biopax) and (ii) rules of interactions that serve as reaction network generators (http://vcell.org/bionetgen), a way is provided for semi-automatic generation of quantitative mathematical models that also facilitates the reuse of model elements. In this approach, kinetic models of large, complex networks can be assembled from separately constructed modules, either directly or via rules. To implement this approach, the strength of several related technologies is combined: the BioPAX ontology, the BioNetGen rule-based description of molecular interactions and the VCell modelling and simulation framework.

Domain-oriented reduction of rule-based network models

The coupling of membrane-bound receptors to transcriptional regulators and other effector functions is mediated by multi-domain proteins that form complex assemblies. The modularity of protein interactions lends itself to a rule-based description, in which species and reactions are generated by rules that encode the necessary context for an interaction to occur, but also can produce a combinatorial explosion in the number of chemical species that make up the signalling network. The authors have shown previously that exact network reduction can be achieved using hierarchical control relationships between sites/domains on proteins to dissect multi-domain proteins into sets of non-interacting sites, allowing the replacement of each 'full' (progenitor) protein with a set of derived auxiliary (offspring) proteins. The description of a network in terms of auxiliary proteins that have fewer sites than progenitor proteins often greatly reduces network size. The authors describe here a method for automating domain-oriented model reduction and its implementation as a module in the BioNetGen modelling package. It takes as input a standard BioNetGen model and automatically performs the following steps: 1) detecting the hierarchical control relationships between sites; 2) building up the auxiliary proteins; 3) generating a raw reduced model and 4) cleaning up the raw model to provide the correct mass balance for each chemical species in the reduced network. The authors tested the performance of this module on models representing portions of growth factor receptor and immunoreceptor-mediated signalling networks and confirmed its ability to reduce the model size and simulation cost by at least one or two orders of magnitude. Limitations of the current algorithm include the inability to reduce models based on implicit site dependencies or heterodimerisation and loss of accuracy when dynamics are computed stochastically.

BioLogic: A mathematical modeling framework for immunologists

The immune response to pathogens is a result of complex interactions among many cell types and a large number of molecular processes. As such it poses numerous challenges for modeling, simulation, and analysis. In this work we aim at addressing major issues regarding modeling of large biological systems with a special focus on the immune system. We address (1) the hierarchy in the system, from genes to organelles to cells to organs to organism, (2) the high variability due to experimentation, (3) the high variability among organisms, and (4) the need to bridge between immunologists/experimentalists and mathematicians/modelers. We provide an intuitive syntax to describe biological knowledge in terms of interactions (reactions) and objects (cells, organs, etc.) and illustrate how to use it in describing very complex systems. We describe the main elements of a simulation program that use that syntax to define models and to automatically simulate them. We restrict our discussion to modeling using logical network, although other modeling techniques, for example, differential equations and probabilistic/stochastic modeling, are also possible. Examples demonstrating the different features of the framework are given throughout the chapter.

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 proofreading model

Kinetic proofreading is an intrinsic property of the cell signaling process. It arises as a consequence of the multiple interactions that occur after a ligand triggers a receptor to initiate a ignaling cascade and it ensures that false signals do not propagate to completion. In order for an active signaling complex to form after a ligand binds to a cell surface receptor, a sequence of binding and phosphorylation events must occur that are rapidly reversed if the ligand dissociates from the receptor. This gives rise to a mechanism by which cells can discriminate among ligands that bind to the same receptor but form ligand-receptor complexes with different lifetimes. We review experiments designed to test for kinetic proofreading and models that exhibit kinetic proofreading.

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.

Exact model reduction of combinatorial reaction networks

BACKGROUND

Receptors and scaffold proteins usually possess a high number of distinct binding domains inducing the formation of large multiprotein signaling complexes. Due to combinatorial reasons the number of distinguishable species grows exponentially with the number of binding domains and can easily reach several millions. Even by including only a limited number of components and binding domains the resulting models are very large and hardly manageable. A novel model reduction technique allows the significant reduction and modularization of these models.

RESULTS

We introduce methods that extend and complete the already introduced approach. For instance, we provide techniques to handle the formation of multi-scaffold complexes as well as receptor dimerization. Furthermore, we discuss a new modeling approach that allows the direct generation of exactly reduced model structures. The developed methods are used to reduce a model of EGF and insulin receptor crosstalk comprising 5,182 ordinary differential equations (ODEs) to a model with 87 ODEs.

CONCLUSION

The methods, presented in this contribution, significantly enhance the available methods to exactly reduce models of combinatorial reaction networks.

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).

Reduced modeling of signal transduction - a modular approach

Background

Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations.

Results

We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible.

Conclusion

The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties.

Kinetic proofreading of ligand-FcepsilonRI interactions may persist beyond LAT phosphorylation

Cells may discriminate among ligands with different dwell times for receptor binding through a mechanism called kinetic proofreading in which the formation of an activated receptor complex requires a progression of events that is aborted if the ligand dissociates before completion. This mechanism explains how, at equivalent levels of receptor occupancy, a rapidly dissociating ligand can be less effective than a more slowly dissociating analog at generating distal cellular responses. Simple mathematical models predict that kinetic proofreading is limited to the initial complex; once the signal passes to second messengers, the dwell time no longer regulates the signal. This suggests that an assay for kinetic proofreading might be used to determine which activation events occur within the initial signaling complex. In signaling through the high affinity IgE receptor FcepsilonRI, the transmembrane adaptor called linker for activation of T cells (LAT) is thought to nucleate a distinct secondary complex. Experiments in which the concentrations of two ligands with different dwell times are adjusted to equalize the level of LAT phosphorylation in rat basophilic leukemia 2H3 cells show that Erk2 phosphorylation, intracellular Ca(2+), and degranulation exhibit kinetic proofreading downstream of LAT phosphorylation. These results suggest that ligand-bound FcepsilonRI and LAT form a complex that is required for effective signal transmission.

Structure-based kinetic models of modular signaling protein function: focus on Shp2

We present here a computational, rule-based model to study the function of the SH2 domain-containing protein tyrosine phosphatase, Shp2, in intracellular signal transduction. The two SH2 domains of Shp2 differentially regulate the enzymatic activity by a well-characterized mechanism, but they also affect the targeting of Shp2 to signaling receptors in cells. Our kinetic model integrates these potentially competing effects by considering the intra- and intermolecular interactions of the Shp2 SH2 domains and catalytic site as well as the effect of Shp2 phosphorylation. Even for the isolated Shp2/receptor system, which may seem simple by certain standards, we find that the network of possible binding and phosphorylation states is composed of over 1000 members. To our knowledge, this is the first kinetic model to fully consider the modular, multifunctional structure of a signaling protein, and the computational approach should be generally applicable to other complex intermolecular interactions.

Rules for modeling signal-transduction systems

Formalized rules for protein-protein interactions have recently been introduced to represent the binding and enzymatic activities of proteins in cellular signaling. Rules encode an understanding of how a system works in terms of the biomolecules in the system and their possible states and interactions. A set of rules can be as easy to read as a diagrammatic interaction map, but unlike most such maps, rules have precise interpretations. Rules can be processed to automatically generate a mathematical or computational model for a system, which enables explanatory and predictive insights into the system's behavior. Rules are independent units of a model specification that facilitate model revision. Instead of changing a large number of equations or lines of code, as may be required in the case of a conventional mathematical model, a protein interaction can be introduced or modified simply by adding or changing a single rule that represents the interaction of interest. Rules can be defined and visualized by using graphs, so no specialized training in mathematics or computer science is necessary to create models or to take advantage of the representational precision of rules. Rules can be encoded in a machine-readable format to enable electronic storage and exchange of models, as well as basic knowledge about protein-protein interactions. Here, we review the motivation for rule-based modeling; applications of the approach; and issues that arise in model specification, simulation, and testing. We also discuss rule visualization and exchange and the software available for rule-based modeling.

T-cell activation: A queuing theory analysis at low agonist density

We analyze a simple linear triggering model of the T-cell receptor (TCR) within the framework of queuing theory, in which TCRs enter the queue upon full activation and exit by downregulation. We fit our model to four experimentally characterized threshold activation criteria and analyze their specificity and sensitivity: the initial calcium spike, cytotoxicity, immunological synapse formation, and cytokine secretion. Specificity characteristics improve as the time window for detection increases, saturating for time periods on the timescale of downregulation; thus, the calcium spike (30 s) has low specificity but a sensitivity to single-peptide MHC ligands, while the cytokine threshold (1 h) can distinguish ligands with a 30% variation in the complex lifetime. However, a robustness analysis shows that these properties are degraded when the queue parameters are subject to variation-for example, under stochasticity in the ligand number in the cell-cell interface and population variation in the cellular threshold. A time integration of the queue over a period of hours is shown to be able to control parameter noise efficiently for realistic parameter values when integrated over sufficiently long time periods (hours), the discrimination characteristics being determined by the TCR signal cascade kinetics (a kinetic proofreading scheme). Therefore, through a combination of thresholds and signal integration, a T cell can be responsive to low ligand density and specific to agonist quality. We suggest that multiple threshold mechanisms are employed to establish the conditions for efficient signal integration, i.e., coordinate the formation of a stable contact interface.

Host-pathogen systems biology

Unlike traditional biological research that focuses on a small set of components, systems biology studies the complex interactions between a large number of genes, proteins and other elements of biological networks and systems. Host-pathogen systems biology examines the interactions between the components of two distinct organisms, either a microbial or viral pathogen and its animal host or two different microbial species in a community. With the availability of complete genomic sequences of various hosts and pathogens, together with breakthroughs in proteomics, metabolomics and other experimental areas, the investigation of host-pathogen systems on a multitude of levels of detail has come within reach.

Modeling the effects of HER/ErbB1-3 coexpression on receptor dimerization and biological response

The human epidermal growth factor receptor (HER/ErbB) system comprises the epidermal growth factor receptor (EGFR/HER1) and three other homologs, namely HERs 2-4. This receptor system plays a critical role in cell proliferation and differentiation and receptor overexpression has been associated with poor prognosis in cancers of the epithelium. Here, we examine the effect of coexpressing varying levels of HERs 1-3 on the receptor dimerization patterns using a detailed kinetic model for HER/ErbB dimerization and trafficking. Our results indicate that coexpression of EGFR with HER2 or HER3 biases signaling to the cell surface and retards signal downregulation. In addition, simultaneous coexpression of HERs 1-3 leads to an abundance of HER2-HER3 heterodimers, which are known to be potent inducers of cell growth and transformation. Our new approach to use parameter dependence analysis in experimental design reveals that measurements of HER3 phosphorylation and HER2 internalization ratio may prove to be especially useful for the estimation of critical model parameters. Further, we examine the effect of receptor dimerization patterns on biological response using a simple phenomenological model. Results indicate that coexpression of EGFR with HER2 and HER3 at low to moderate levels may enable cells to match the response of a high HER2 expresser.

Trading the micro-world of combinatorial complexity for the macro-world of protein interaction domains

Membrane receptors and proteins involved in signal transduction display numerous binding domains and operate as molecular scaffolds generating a variety of parallel reactions and protein complexes. The resulting combinatorial explosion of the number of feasible chemical species and, hence, different states of a network greatly impedes mechanistic modeling of signaling systems. Here we present novel general principles and identify kinetic requirements that allow us to replace a mechanistic picture of all possible micro-states and transitions by a macro-description of states of separate binding sites of network proteins. This domain-oriented approach dramatically reduces computational models of cellular signaling networks by dissecting mechanistic trajectories into the dynamics of macro- and meso-variables. We specify the conditions when the temporal dynamics of micro-states can be exactly or approximately expressed in terms of the product of the relative concentrations of separate domains. We prove that our macro-modeling approach equally applies to signaling systems with low population levels, analyzed by stochastic rather than deterministic equations. Thus, our results greatly facilitate quantitative analysis and computational modeling of multi-protein signaling networks.

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.