Rules for modeling signal-transduction systems

Systems biology and inflammation

Inflammation is a complex, multiscale biological response to threats - both internal and external - to the body, which is also required for proper healing of injured tissue. In turn, damaged or dysfunctional tissue stimulates further inflammation. Despite continued advances in characterizing the cellular and molecular processes involved in the interactions between inflammation and tissue damage, there exists a significant gap between the knowledge of mechanistic pathophysiology and the development of effective therapies for various inflammatory conditions. We have suggested the concept of translational systems biology, defined as a focused application of computational modeling and engineering principles to pathophysiology primarily in order to revise clinical practice. This chapter reviews the existing, translational applications of computational simulations and related approaches as applied to inflammation.

Molecular machines or pleiomorphic ensembles: signaling complexes revisited

Signaling complexes typically consist of highly dynamic molecular ensembles that are challenging to study and to describe accurately. Conventional mechanical descriptions misrepresent this reality and can be actively counterproductive by misdirecting us away from investigating critical issues.

Efficient stochastic simulation of reaction-diffusion processes via direct compilation

We present the Stochastic Simulator Compiler (SSC), a tool for exact stochastic simulations of well-mixed and spatially heterogeneous systems. SSC is the first tool to allow a readable high-level description with spatially heterogeneous simulation algorithms and complex geometries; this permits large systems to be expressed concisely. Meanwhile, direct native-code compilation allows SSC to generate very fast simulations.

The complexity of cell signaling and the need for a new mechanics

Cell signaling systems respond to multiple inputs, such as ligands of cell-surface receptors; and produce multiple outputs, such as changes in gene expression and cellular activities, including motility, proliferation, and death. This "macroscopic" input-output behavior is generated by a web of molecular interactions that can be viewed as taking place at a lower, "microscopic" level. These interactions prominently involve posttranslational modification of proteins and the nucleation of protein complexes. Behaviors at both the micro- and macroscopic levels are complex and must be probed systematically and characterized quantitatively as a prelude to the development of a predictive understanding of a cell signaling system. We must also have a theoretical framework or a mechanics within which we can determine how macroscopic behaviors emerge from known microscopic behaviors or change with manipulations of microscopic behaviors. To connect behaviors at both levels, we suggest that a new mechanics is now required. Newly available data support the idea that this mechanics should enable one to track the site-specific details of molecular interactions in a model, such as the phosphorylation status of individual amino acid residues within a protein.

Science Signaling Podcast: 30 June 2009

Mathematical modeling of signaling pathways can be used to identify candidate targets for cancer therapies.

Adiabatic coarse-graining and simulations of stochastic biochemical networks

We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical networks, which rests on elimination of fast chemical species without a loss of information about mesoscopic, non-Poissonian fluctuations of the slow ones. Our approach is similar to the Born-Oppenheimer approximation in quantum mechanics and follows from the stochastic path integral representation of the cumulant generating function of reaction events. In applications with a small number of chemical reactions, it produces analytical expressions for cumulants of chemical fluxes between the slow variables. This allows for a low-dimensional, interpretable representation and can be used for high-accuracy, low-complexity coarse-grained numerical simulations. As an example, we derive the coarse-grained description for a chain of biochemical reactions and show that the coarse-grained and the microscopic simulations agree, but the former is 3 orders of magnitude faster.

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.

Quantifying stochastic effects in biochemical reaction networks using partitioned leaping

"Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address this issue using the "partitioned leaping algorithm" (PLA) [L. A. Harris and P. Clancy, J. Chem. Phys. 125, 144107 (2006)], a recently introduced multiscale leaping approach. We use the PLA to investigate stochastic effects in two model biochemical reaction networks. The networks that we consider are simple enough so as to be accessible to our intuition but sufficiently complex so as to be generally representative of real biological systems. We demonstrate how the PLA allows us to quantify subtle effects of stochasticity in these systems that would be difficult to ascertain otherwise as well as not-so-subtle behaviors that would strain commonly used "exact" stochastic methods. We also illustrate bottlenecks that can hinder the approach and exemplify and discuss possible strategies for overcoming them. Overall, our aim is to aid and motivate future applications of leaping by providing stark illustrations of the benefits of the method while at the same time elucidating obstacles that are often encountered in practice.

A bipolar clamp mechanism for activation of Jak-family protein tyrosine kinases

Most cell surface receptors for growth factors and cytokines dimerize in order to mediate signal transduction. For many such receptors, the Janus kinase (Jak) family of non-receptor protein tyrosine kinases are recruited in pairs and juxtaposed by dimerized receptor complexes in order to activate one another by trans-phosphorylation. An alternative mechanism for Jak trans-phosphorylation has been proposed in which the phosphorylated kinase interacts with the Src homology 2 (SH2) domain of SH2-B, a unique adaptor protein with the capacity to homo-dimerize. Building on a rule-based kinetic modeling approach that considers the concerted nature and combinatorial complexity of modular protein domain interactions, we examine these mechanisms in detail, focusing on the growth hormone (GH) receptor/Jak2/SH2-Bβ system. The modeling results suggest that, whereas Jak2-(SH2-Bβ)₂-Jak2 heterotetramers are scarcely expected to affect Jak2 phosphorylation, SH2-Bβ and dimerized receptors synergistically promote Jak2 trans-activation in the context of intracellular signaling. Analysis of the results revealed a unique mechanism whereby SH2-B and receptor dimers constitute a bipolar ‘clamp’ that stabilizes the active configuration of two Jak2 molecules in the same macro-complex.

Janus kinases (Jaks) interact with and activate receptors on the cell surface that mediate changes in gene expression. How these interactions are promoted and regulated is of central interest in fields such as cellular endocrinology and immunology. Here, detailed computational models of Jak activation are offered at the level of protein modification states and interaction domains, wherein the specification of only a handful of binding/reaction rules can produce networks comprised of thousands of differential equations. Specifically, we investigated the role of an adaptor protein, SH2-B, revealing a novel mechanism whereby it cooperates with receptors to form a stable complex that juxtaposes two Jak molecules for efficient activation. We refer to this mode of molecular assembly as the bipolar clamp mechanism.

Programming with models: modularity and abstraction provide powerful capabilities for systems biology

Mathematical models are increasingly used to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations presents a fundamental barrier to progress. Overcoming this requires modularity, enabling sub-systems to be specified independently and combined incrementally, and abstraction, enabling generic properties of biological processes to be specified independently of specific instances. These, in turn, require models to be represented as programs rather than as datatypes. Programmable modularity and abstraction enables libraries of modules to be created, which can be instantiated and reused repeatedly in different contexts with different components. We have developed a computational infrastructure that accomplishes this. We show here why such capabilities are needed, what is required to implement them and what can be accomplished with them that could not be done previously.

Systems-level interactions between insulin-EGF networks amplify mitogenic signaling

Crosstalk mechanisms have not been studied as thoroughly as individual signaling pathways. We exploit experimental and computational approaches to reveal how a concordant interplay between the insulin and epidermal growth factor (EGF) signaling networks can potentiate mitogenic signaling. In HEK293 cells, insulin is a poor activator of the Ras/ERK (extracellular signal-regulated kinase) cascade, yet it enhances ERK activation by low EGF doses. We find that major crosstalk mechanisms that amplify ERK signaling are localized upstream of Ras and at the Ras/Raf level. Computational modeling unveils how critical network nodes, the adaptor proteins GAB1 and insulin receptor substrate (IRS), Src kinase, and phosphatase SHP2, convert insulin-induced increase in the phosphatidylinositol-3,4,5-triphosphate (PIP₃) concentration into enhanced Ras/ERK activity. The model predicts and experiments confirm that insulin-induced amplification of mitogenic signaling is abolished by disrupting PIP₃-mediated positive feedback via GAB1 and IRS. We demonstrate that GAB1 behaves as a non-linear amplifier of mitogenic responses and insulin endows EGF signaling with robustness to GAB1 suppression. Our results show the feasibility of using computational models to identify key target combinations and predict complex cellular responses to a mixture of external cues.

Internal coarse-graining of molecular systems

Modelers of molecular signaling networks must cope with the combinatorial explosion of protein states generated by posttranslational modifications and complex formation. Rule-based models provide a powerful alternative to approaches that require explicit enumeration of all possible molecular species of a system. Such models consist of formal rules stipulating the (partial) contexts wherein specific protein-protein interactions occur. These contexts specify molecular patterns that are usually less detailed than molecular species. Yet, the execution of rule-based dynamics requires stochastic simulation, which can be very costly. It thus appears desirable to convert a rule-based model into a reduced system of differential equations by exploiting the granularity at which rules specify interactions. We present a formal (and automated) method for constructing a coarse-grained and self-consistent dynamical system aimed at molecular patterns that are distinguishable by the dynamics of the original system as posited by the rules. The method is formally sound and never requires the execution of the rule-based model. The coarse-grained variables do not depend on the values of the rate constants appearing in the rules, and typically form a system of greatly reduced dimension that can be amenable to numerical integration and further model reduction techniques.

Fuzzy logic analysis of kinase pathway crosstalk in TNF/EGF/insulin-induced signaling

When modeling cell signaling networks, a balance must be struck between mechanistic detail and ease of interpretation. In this paper we apply a fuzzy logic framework to the analysis of a large, systematic dataset describing the dynamics of cell signaling downstream of TNF, EGF, and insulin receptors in human colon carcinoma cells. Simulations based on fuzzy logic recapitulate most features of the data and generate several predictions involving pathway crosstalk and regulation. We uncover a relationship between MK2 and ERK pathways that might account for the previously identified pro-survival influence of MK2. We also find unexpected inhibition of IKK following EGF treatment, possibly due to down-regulation of autocrine signaling. More generally, fuzzy logic models are flexible, able to incorporate qualitative and noisy data, and powerful enough to produce quantitative predictions and new biological insights about the operation of signaling networks.

Cells use networks of interacting proteins to interpret intra-cellular state and extra-cellular cues and to execute cell-fate decisions. Even when individual proteins are well understood at a molecular level, the dynamics and behavior of networks as a whole are harder to understand. However, deciphering the operation of such networks is key to understanding disease processes and therapeutic opportunities. As a means to study signaling networks, we have modified and applied a fuzzy logic approach originally developed for industrial control. We use fuzzy logic to model the responses of colon cancer cells in culture to combinations of pro-survival and pro-death cytokines, making it possible to interpret quantitative data in the context of abstract information drawn from the literature. Our work establishes that fuzzy logic can be used to understand complex signaling pathways with respect to multi-factorial activity-based protein data and prior knowledge.

Simulation of large-scale rule-based models

MOTIVATION

Interactions of molecules, such as signaling proteins, with multiple binding sites and/or multiple sites of post-translational covalent modification can be modeled using reaction rules. Rules comprehensively, but implicitly, define the individual chemical species and reactions that molecular interactions can potentially generate. Although rules can be automatically processed to define a biochemical reaction network, the network implied by a set of rules is often too large to generate completely or to simulate using conventional procedures. To address this problem, we present DYNSTOC, a general-purpose tool for simulating rule-based models.

RESULTS

DYNSTOC implements a null-event algorithm for simulating chemical reactions in a homogenous reaction compartment. The simulation method does not require that a reaction network be specified explicitly in advance, but rather takes advantage of the availability of the reaction rules in a rule-based specification of a network to determine if a randomly selected set of molecular components participates in a reaction during a time step. DYNSTOC reads reaction rules written in the BioNetGen language which is useful for modeling protein-protein interactions involved in signal transduction. The method of DYNSTOC is closely related to that of StochSim. DYNSTOC differs from StochSim by allowing for model specification in terms of BNGL, which extends the range of protein complexes that can be considered in a model. DYNSTOC enables the simulation of rule-based models that cannot be simulated by conventional methods. We demonstrate the ability of DYNSTOC to simulate models accounting for multisite phosphorylation and multivalent binding processes that are characterized by large numbers of reactions.

AVAILABILITY

DYNSTOC is free for non-commercial use. The C source code, supporting documentation and example input files are available at http://public.tgen.org/dynstoc/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Integrated analysis of breast cancer cell lines reveals unique signaling pathways

Mapping of sub-networks in the EGFR-MAPK pathway in different breast cancer cell lines reveals that PAK1 may be a marker for sensitivity to MEK inhibitors.

Background

Cancer is a heterogeneous disease resulting from the accumulation of genetic defects that negatively impact control of cell division, motility, adhesion and apoptosis. Deregulation in signaling along the EgfR-MAPK pathway is common in breast cancer, though the manner in which deregulation occurs varies between both individuals and cancer subtypes.

Results

We were interested in identifying subnetworks within the EgfR-MAPK pathway that are similarly deregulated across subsets of breast cancers. To that end, we mapped genomic, transcriptional and proteomic profiles for 30 breast cancer cell lines onto a curated Pathway Logic symbolic systems model of EgfR-MAPK signaling. This model was composed of 539 molecular states and 396 rules governing signaling between active states. We analyzed these models and identified several subtype-specific subnetworks, including one that suggested Pak1 is particularly important in regulating the MAPK cascade when it is over-expressed. We hypothesized that Pak1 over-expressing cell lines would have increased sensitivity to Mek inhibitors. We tested this experimentally by measuring quantitative responses of 20 breast cancer cell lines to three Mek inhibitors. We found that Pak1 over-expressing luminal breast cancer cell lines are significantly more sensitive to Mek inhibition compared to those that express Pak1 at low levels. This indicates that Pak1 over-expression may be a useful clinical marker to identify patient populations that may be sensitive to Mek inhibitors.

Conclusions

All together, our results support the utility of symbolic system biology models for identification of therapeutic approaches that will be effective against breast cancer subsets.

GetBonNie for building, analyzing and sharing rule-based models

SUMMARY

GetBonNie is a web-based application for building, analyzing and sharing rule-based models encoded in the BioNetGen language (BNGL). Tools accessible within the GetBonNie environment include (i) an applet for drawing graphs that correspond to BNGL code; (ii) a network-generation engine for translating a set of rules into a chemical reaction network; (iii) simulation engines that implement generate-first, on-the-fly and network-free methods for simulating rule-based models; and (iv) a database for sharing models, parameter values, annotations, simulation tasks and results.

AVAILABILITY

GetBonNie is free at (http://getbonnie.org).

Computational systems biology of the cell cycle

One of the early success stories of computational systems biology was the work done on cell-cycle regulation. The earliest mathematical descriptions of cell-cycle control evolved into very complex, detailed computational models that describe the regulation of cell division in many different cell types. On the way these models predicted several dynamical properties and unknown components of the system that were later experimentally verified/identified. Still, research on this field is far from over. We need to understand how the core cell-cycle machinery is controlled by internal and external signals, also in yeast cells and in the more complex regulatory networks of higher eukaryotes. Furthermore, there are many computational challenges what we face as new types of data appear thanks to continuing advances in experimental techniques. We have to deal with cell-to-cell variations, revealed by single cell measurements, as well as the tremendous amount of data flowing from high throughput machines. We need new computational concepts and tools to handle these data and develop more detailed, more precise models of cell-cycle regulation in various organisms. Here we review past and present of computational modeling of cell-cycle regulation, and discuss possible future directions of the field.

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.

Virtual Cell modelling and simulation software environment

The Virtual Cell (VCell; http://vcell.org/) is a problem solving environment, built on a central database, for analysis, modelling and simulation of cell biological processes. VCell integrates a growing range of molecular mechanisms, including reaction kinetics, diffusion, flow, membrane transport, lateral membrane diffusion and electrophysiology, and can associate these with geometries derived from experimental microscope images. It has been developed and deployed as a web-based, distributed, client-server system, with more than a thousand world-wide users. VCell provides a separation of layers (core technologies and abstractions) representing biological models, physical mechanisms, geometry, mathematical models and numerical methods. This separation clarifies the impact of modelling decisions, assumptions and approximations. The result is a physically consistent, mathematically rigorous, spatial modelling and simulation framework. Users create biological models and VCell will automatically (i) generate the appropriate mathematical encoding for running a simulation and (ii) generate and compile the appropriate computer code. Both deterministic and stochastic algorithms are supported for describing and running non-spatial simulations; a full partial differential equation solver using the finite volume numerical algorithm is available for reaction-diffusion-advection simulations in complex cell geometries including 3D geometries derived from microscope images. Using the VCell database, models and model components can be reused and updated, as well as privately shared among collaborating groups, or published. Exchange of models with other tools is possible via import/export of SBML, CellML and MatLab formats. Furthermore, curation of models is facilitated by external database binding mechanisms for unique identification of components and by standardised annotations compliant with the MIRIAM standard. VCell is now open source, with its native model encoding language (VCML) being a public specification, which stands as the basis for a new generation of more customised, experiment-centric modelling tools using a new plug-in based platform.

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.

ALC: automated reduction of rule-based models

Background

Combinatorial complexity is a challenging problem for the modeling of cellular signal transduction since the association of a few proteins can give rise to an enormous amount of feasible protein complexes. The layer-based approach is an approximative, but accurate method for the mathematical modeling of signaling systems with inherent combinatorial complexity. The number of variables in the simulation equations is highly reduced and the resulting dynamic models show a pronounced modularity. Layer-based modeling allows for the modeling of systems not accessible previously.

Results

ALC (Automated Layer Construction) is a computer program that highly simplifies the building of reduced modular models, according to the layer-based approach. The model is defined using a simple but powerful rule-based syntax that supports the concepts of modularity and macrostates. ALC performs consistency checks on the model definition and provides the model output in different formats (C MEX, MATLAB, Mathematica and SBML) as ready-to-run simulation files. ALC also provides additional documentation files that simplify the publication or presentation of the models. The tool can be used offline or via a form on the ALC website.

Conclusion

ALC allows for a simple rule-based generation of layer-based reduced models. The model files are given in different formats as ready-to-run simulation files.

Detailed qualitative dynamic knowledge representation using a BioNetGen model of TLR-4 signaling and preconditioning

INTRODUCTION

Intracellular signaling/synthetic pathways are being increasingly extensively characterized. However, while these pathways can be displayed in static diagrams, in reality they exist with a degree of dynamic complexity that is responsible for heterogeneous cellular behavior. Multiple parallel pathways exist and interact concurrently, limiting the ability to integrate the various identified mechanisms into a cohesive whole. Computational methods have been suggested as a means of concatenating this knowledge to aid in the understanding of overall system dynamics. Since the eventual goal of biomedical research is the identification and development of therapeutic modalities, computational representation must have sufficient detail to facilitate this 'engineering' process. Adding to the challenge, this type of representation must occur in a perpetual state of incomplete knowledge. We present a modeling approach to address this challenge that is both detailed and qualitative. This approach is termed 'dynamic knowledge representation,' and is intended to be an integrated component of the iterative cycle of scientific discovery.

METHODS

BioNetGen (BNG), a software platform for modeling intracellular signaling pathways, was used to model the toll-like receptor 4 (TLR-4) signal transduction cascade. The informational basis of the model was a series of reference papers on modulation of (TLR-4) signaling, and some specific primary research papers to aid in the characterization of specific mechanistic steps in the pathway. This model was detailed with respect to the components of the pathway represented, but qualitative with respect to the specific reaction coefficients utilized to execute the reactions. Responsiveness to simulated lipopolysaccharide (LPS) administration was measured by tumor necrosis factor (TNF) production. Simulation runs included evaluation of initial dose-dependent response to LPS administration at 10, 100, 1000 and 10,000, and a subsequent examination of preconditioning behavior with increasing LPS at 10, 100, 1000 and 10,000 and a secondary dose of LPS at 10,000 administered at approximately 27h of simulated time. Simulations of 'knockout' versions of the model allowed further examination of the interactions within the signaling cascade.

RESULTS

The model demonstrated a dose-dependent TNF response curve to increasing stimulus by LPS. Preconditioning simulations demonstrated a similar dose-dependency of preconditioning doses leading to attenuation of response to subsequent LPS challenge - a 'tolerance' dynamic. These responses match dynamics reported in the literature. Furthermore, the simulated 'knockout' results suggested the existence and need for dual negative feedback control mechanisms, represented by the zinc ring-finger protein A20 and inhibitor kappa B proteins (IkappaB), in order for both effective attenuation of the initial stimulus signal and subsequent preconditioned 'tolerant' behavior.

CONCLUSIONS

We present an example of detailed, qualitative dynamic knowledge representation using the TLR-4 signaling pathway, its control mechanisms and overall behavior with respect to preconditioning. The intent of this approach is to demonstrate a method of translating the extensive mechanistic knowledge being generated at the basic science level into an executable framework that can provide a means of 'conceptual model verification.' This allows for both the 'checking' of the dynamic consequences of a mechanistic hypothesis and the creation of a modular component of an overall model directed at the engineering goal of biomedical research. It is hoped that this paper will increase the use of knowledge representation and communication in this fashion, and facilitate the concatenation and integration of community-wide knowledge.

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.

Mechanistic simulations of inflammation: current state and future prospects

Inflammation is a normal, robust physiological process. It can also be viewed as a complex system that senses and attempts to resolve homeostatic perturbations initiated from within the body (for example, in autoimmune disease) or from the outside (for example, in infections). Virtually all acute and chronic diseases are either driven or modulated by inflammation. The complex interplay between beneficial and harmful arms of the inflammatory response may underlie the lack of fully effective therapies for many diseases. Mathematical modeling is emerging as a frontline tool for understanding the complexity of the inflammatory response. A series of articles in this issue highlights various modeling approaches to inflammation in the larger context of health and disease, from intracellular signaling to whole-animal physiology. Here we discuss the state of this emerging field. We note several common features of inflammation models, as well as challenges and prospects for future studies.

ErbB receptors in the biology and pathology of the aerodigestive tract

The most common sites of malignancies in the aerodigestive tract include the lung, head and neck and the esophagus. Esophageal adenocarcinomas (EA), esophageal squamous cell carcinomas (ESCC), and squamous cell carcinomas of the head and neck (SCCHN) are the primary focus of this review. Traditional treatment for aerodigestive tract cancers includes primary chemoradiotherapy (CRT) or surgical resection followed by radiation (or CRT). Recent developments in treatment have focused increasingly on molecular targeting strategies including cetuximab (a monoclonal antibody against epidermal growth factor receptor (EGFR)). Cetuximab was FDA approved in 2006 for treatment of SCCHN, underscoring the importance of understanding the biology of these malignancies. EGFR is a member of the ErbB family of growth factor receptor tyrosine kinases. The major pathways activated by ErbB receptors include Ras/Raf/MAPK; PI3K/AKT; PLCgamma and STATs, all of which lead to the transcription of target genes that may contribute to aerodigestive tumor progression. This review explores the expression of ErbB receptors in EA, ESCC and SCCHN and the signaling pathways of EGFR in SCCHN.

Translational systems biology: introduction of an engineering approach to the pathophysiology of the burn patient

The pathophysiology of the burn patient manifests the full spectrum of the complexity of the inflammatory response. In the acute phase, inflammation may have negative effects via capillary leak, the propagation of inhalation injury, and development of multiple organ failure. Attempts to mediate these processes remain a central subject of burn care research. Conversely, inflammation is a necessary prologue and component in the later stage processes of wound healing. Despite the volume of information concerning the cellular and molecular processes involved in inflammation, there exists a significant gap between the knowledge of mechanistic pathophysiology and the development of effective clinical therapeutic regimens. Translational systems biology (TSB) is the application of dynamic mathematical modeling and certain engineering principles to biological systems to integrate mechanism with phenomenon and, importantly, to revise clinical practice. This study will review the existing applications of TSB in the areas of inflammation and wound healing, relate them to specific areas of interest to the burn community, and present an integrated framework that links TSB with traditional burn research.

Computational models of tandem SRC homology 2 domain interactions and application to phosphoinositide 3-kinase

Intracellular signal transduction proteins typically utilize multiple interaction domains for proper targeting, and thus a broad diversity of distinct signaling complexes may be assembled. Considering the coordination of only two such domains, as in tandem Src homology 2 (SH2) domain constructs, gives rise to a kinetic scheme that is not adequately described by simple models used routinely to interpret in vitro binding measurements. To analyze the interactions between tandem SH2 domains and bisphosphorylated peptides, we formulated detailed kinetic models and applied them to the phosphoinositide 3-kinase p85 regulatory subunit/platelet-derived growth factor beta-receptor system. Data for this system from different in vitro assay platforms, including surface plasmon resonance, competition binding, and isothermal titration calorimetry, were reconciled to estimate the magnitude of the cooperativity characterizing the sequential binding of the high and low affinity SH2 domains (C-SH2 and N-SH2, respectively). Compared with values based on an effective volume approximation, the estimated cooperativity is 3 orders of magnitude lower, indicative of significant structural constraints. Homodimerization of full-length p85 was found to be an alternative mechanism for high avidity binding to phosphorylated platelet-derived growth factor receptors, which would render the N-SH2 domain dispensable for receptor binding.

Kinetic Modeling using BioPAX ontology

Thousands of biochemical interactions are available for download from curated databases such as Reactome, Pathway Interaction Database and other sources in the Biological Pathways Exchange (BioPAX) format. However, the BioPAX ontology does not encode the necessary information for kinetic modeling and simulation. The current standard for kinetic modeling is the System Biology Markup Language (SBML), but only a small number of models are available in SBML format in public repositories. Additionally, reusing and merging SBML models presents a significant challenge, because often each element has a value only in the context of the given model, and information encoding biological meaning is absent. We describe a software system that enables a variety of operations facilitating the use of BioPAX data to create kinetic models that can be visualized, edited, and simulated using the Virtual Cell (VCell), including improved conversion to SBML (for use with other simulation tools that support this format).

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).

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.

Physicochemical modelling of cell signalling pathways

Physicochemical modelling of signal transduction links fundamental chemical and physical principles, prior knowledge about regulatory pathways, and experimental data of various types to create powerful tools for formalizing and extending traditional molecular and cellular biology.