Rules for modeling signal-transduction systems

Specification, annotation, visualization and simulation of a large rule-based model for ERBB receptor signaling

BACKGROUND

Mathematical/computational models are needed to understand cell signaling networks, which are complex. Signaling proteins contain multiple functional components and multiple sites of post-translational modification. The multiplicity of components and sites of modification ensures that interactions among signaling proteins have the potential to generate myriad protein complexes and post-translational modification states. As a result, the number of chemical species that can be populated in a cell signaling network, and hence the number of equations in an ordinary differential equation model required to capture the dynamics of these species, is prohibitively large. To overcome this problem, the rule-based modeling approach has been developed for representing interactions within signaling networks efficiently and compactly through coarse-graining of the chemical kinetics of molecular interactions.

RESULTS

Here, we provide a demonstration that the rule-based modeling approach can be used to specify and simulate a large model for ERBB receptor signaling that accounts for site-specific details of protein-protein interactions. The model is considered large because it corresponds to a reaction network containing more reactions than can be practically enumerated. The model encompasses activation of ERK and Akt, and it can be simulated using a network-free simulator, such as NFsim, to generate time courses of phosphorylation for 55 individual serine, threonine, and tyrosine residues. The model is annotated and visualized in the form of an extended contact map.

CONCLUSIONS

With the development of software that implements novel computational methods for calculating the dynamics of large-scale rule-based representations of cellular signaling networks, it is now possible to build and analyze models that include a significant fraction of the protein interactions that comprise a signaling network, with incorporation of the site-specific details of the interactions. Modeling at this level of detail is important for understanding cellular signaling.

State-time spectrum of signal transduction logic models

Despite the current wealth of high-throughput data, our understanding of signal transduction is still incomplete. Mathematical modeling can be a tool to gain an insight into such processes. Detailed biochemical modeling provides deep understanding, but does not scale well above relatively a few proteins. In contrast, logic modeling can be used where the biochemical knowledge of the system is sparse and, because it is parameter free (or, at most, uses relatively a few parameters), it scales well to large networks that can be derived by manual curation or retrieved from public databases. Here, we present an overview of logic modeling formalisms in the context of training logic models to data, and specifically the different approaches to modeling qualitative to quantitative data (state) and dynamics (time) of signal transduction. We use a toy model of signal transduction to illustrate how different logic formalisms (Boolean, fuzzy logic and differential equations) treat state and time. Different formalisms allow for different features of the data to be captured, at the cost of extra requirements in terms of computational power and data quality and quantity. Through this demonstration, the assumptions behind each formalism are discussed, as well as their advantages and disadvantages and possible future developments.

Competing G protein-coupled receptor kinases balance G protein and β-arrestin signaling

The molecular mechanisms and hidden dynamics governing ERK activation by the angiotensin II type 1A receptor are studied and deciphered, revealing a signal balancing mechanism that is found to be relevant to a range of other seven transmembrane receptors.

An ODE-based dynamical model of ERK activation by the prototypical angiotensin II type-1A seven transmembrane receptor has been built and validated.

In order to deal with a limited number of experimental read-outs, unknown parameters have been inferred by simultaneously fitting control and perturbed conditions.

In addition to its well-established function in G-protein uncoupling, G protein-coupled receptor kinase 2 has been shown to exert a strong negative effect on β-arrestin-dependent signaling and by doing so, to balance G-protein and β-arrestin signaling.

This novel function of G protein-coupled receptor kinase 2 has also been evidenced in primary vascular smooth muscle cells naturally expressing the AT_1AR and in HEK293 cells expressing other 7TMRs.

Seven-transmembrane receptors (7TMRs) are involved in nearly all aspects of chemical communications and represent major drug targets. 7TMRs transmit their signals not only via heterotrimeric G proteins but also through β-arrestins, whose recruitment to the activated receptor is regulated by G protein-coupled receptor kinases (GRKs). In this paper, we combined experimental approaches with computational modeling to decipher the molecular mechanisms as well as the hidden dynamics governing extracellular signal-regulated kinase (ERK) activation by the angiotensin II type 1A receptor (AT_1AR) in human embryonic kidney (HEK)293 cells. We built an abstracted ordinary differential equations (ODE)-based model that captured the available knowledge and experimental data. We inferred the unknown parameters by simultaneously fitting experimental data generated in both control and perturbed conditions. We demonstrate that, in addition to its well-established function in the desensitization of G-protein activation, GRK2 exerts a strong negative effect on β-arrestin-dependent signaling through its competition with GRK5 and 6 for receptor phosphorylation. Importantly, we experimentally confirmed the validity of this novel GRK2-dependent mechanism in both primary vascular smooth muscle cells naturally expressing the AT_1AR, and HEK293 cells expressing other 7TMRs.

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.

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.

The physics of protein-DNA interaction networks in the control of gene expression

Protein-DNA interaction networks play a central role in many fundamental cellular processes. In gene regulation, physical interactions and reactions among the molecular components together with the physical properties of DNA control how genes are turned on and off. A key player in all these processes is the inherent flexibility of DNA, which provides an avenue for long-range interactions between distal DNA elements through DNA looping. Such versatility enables multiple interactions and results in additional complexity that is remarkably difficult to address with traditional approaches. This topical review considers recent advances in statistical physics methods to study the assembly of protein-DNA complexes with loops, their effects in the control of gene expression, and their explicit application to the prototypical lac operon genetic system of the E. coli bacterium. In the last decade, it has been shown that the underlying physical properties of DNA looping can actively control transcriptional noise, cell-to-cell variability, and other properties of gene regulation, including the balance between robustness and sensitivity of the induction process. These physical properties are largely dependent on the free energy of DNA looping, which accounts for DNA bending and twisting effects. These new physical methods have also been used in reverse to uncover the actual in vivo free energy of looping double-stranded DNA in living cells, which was not possible with existing experimental techniques. The results obtained for DNA looping by the lac repressor inside the E. coli bacterium showed a more malleable DNA than expected as a result of the interplay of the simultaneous presence of two distinct conformations of looped DNA.

Computational approaches for analyzing information flow in biological networks

The advancements in "omics" (proteomics, genomics, lipidomics, and metabolomics) technologies have yielded large inventories of genes, transcripts, proteins, and metabolites. The challenge is to find out how these entities work together to regulate the processes by which cells respond to external and internal signals. Mathematical and computational modeling of signaling networks has a key role in this task, and network analysis provides insights into biological systems and has applications for medicine. Here, we review experimental and theoretical progress and future challenges toward this goal. We focus on how networks are reconstructed from data, how these networks are structured to control the flow of biological information, and how the design features of the networks specify biological decisions.

Proteus: a web-based, context-specific modelling tool for molecular networks

SUMMARY

Molecular networks are often studied in diverse cellular or experimental contexts, with highly context-specific details. Modelling introduces further choices as to levels of mathematical description. The resulting possibilities are difficult to explore rapidly, hampering the integration of modelling and experiment. We have developed Proteus, a web-based, context-specific tool for building compartmentalized, ordinary differential equation (ODE) models. It is inspired by the idea of a molecular 'toolkit' for Ca(2+) signalling. Toolkits in Proteus are context-independent representations of biological systems as sets of components, which may correspond to mechanisms of differing levels of complexity. Users pick and choose components from a toolkit and, for each component, pick and choose from different mechanisms, each of which describes a different instantiation of the component's mechanism. Proteus combines these choices into a system of ODEs, which may then be downloaded in SBML (Systems Biology Markup Language), Matlab or Fortran format and independently analyzed. Toolkits, components and mechanisms are user-constructible, either de novo or by cannibalizing existing models, including all those in the Biomodels database. A wide variety of context-specific models may thereby be rapidly built, modified and explored.

AVAILABILITY AND IMPLEMENTATION

Proteus, implemented in C#, and a prototype toolkit for modelling calcium signalling are freely and universally available at www.modularmodeling.com

CONTACT

gnad.florian@gene.com; jeremy@hms.harvard.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Combinatorial complexity and compositional drift in protein interaction networks

The assembly of molecular machines and transient signaling complexes does not typically occur under circumstances in which the appropriate proteins are isolated from all others present in the cell. Rather, assembly must proceed in the context of large-scale protein-protein interaction (PPI) networks that are characterized both by conflict and combinatorial complexity. Conflict refers to the fact that protein interfaces can often bind many different partners in a mutually exclusive way, while combinatorial complexity refers to the explosion in the number of distinct complexes that can be formed by a network of binding possibilities. Using computational models, we explore the consequences of these characteristics for the global dynamics of a PPI network based on highly curated yeast two-hybrid data. The limited molecular context represented in this data-type translates formally into an assumption of independent binding sites for each protein. The challenge of avoiding the explicit enumeration of the astronomically many possibilities for complex formation is met by a rule-based approach to kinetic modeling. Despite imposing global biophysical constraints, we find that initially identical simulations rapidly diverge in the space of molecular possibilities, eventually sampling disjoint sets of large complexes. We refer to this phenomenon as "compositional drift". Since interaction data in PPI networks lack detailed information about geometric and biological constraints, our study does not represent a quantitative description of cellular dynamics. Rather, our work brings to light a fundamental problem (the control of compositional drift) that must be solved by mechanisms of assembly in the context of large networks. In cases where drift is not (or cannot be) completely controlled by the cell, this phenomenon could constitute a novel source of phenotypic heterogeneity in cell populations.

Computational approaches for translational clinical research in disease progression

Today, there is an ever-increasing amount of biological and clinical data available that could be used to enhance a systems-based understanding of disease progression through innovative computational analysis. In this article, we review a selection of published research regarding computational methods, primarily from systems biology, which support translational research from the molecular level to the bedside, with a focus on applications in trauma and critical care. Trauma is the leading cause of mortality in Americans younger than 45 years, and its rapid progression offers both opportunities and challenges for computational analysis of trends in molecular patterns associated with outcomes and therapeutic interventions.This review presents methods and domain-specific examples that may inspire the development of new algorithms and computational methods that use both molecular and clinical data for diagnosis, prognosis, and therapy in disease progression.

Modeling and simulation of aggregation of membrane protein LAT with molecular variability in the number of binding sites for cytosolic Grb2-SOS1-Grb2

The linker for activation of T cells (LAT), the linker for activation of B cells (LAB), and the linker for activation of X cells (LAX) form a family of transmembrane adaptor proteins widely expressed in lymphocytes. These scaffolding proteins have multiple binding motifs that, when phosphorylated, bind the SH2 domain of the cytosolic adaptor Grb2. Thus, the valence of LAT, LAB and LAX for Grb2 is variable, depending on the strength of receptor activation that initiates phosphorylation. During signaling, the LAT population will exhibit a time-varying distribution of Grb2 valences from zero to three. In the cytosol, Grb2 forms 1∶1 and 2∶1 complexes with the guanine nucleotide exchange factor SOS1. The 2∶1 complex can bridge two LAT molecules when each Grb2, through their SH2 domains, binds to a phosphorylated site on a separate LAT. In T cells and mast cells, after receptor engagement, receptor phosphoyrlation is rapidly followed by LAT phosphorylation and aggregation. In mast cells, aggregates containing more than one hundred LAT molecules have been detected. Previously we considered a homogeneous population of trivalent LAT molecules and showed that for a range of Grb2, SOS1 and LAT concentrations, an equilibrium theory for LAT aggregation predicts the formation of a gel-like phase comprising a very large aggregate (superaggregate). We now extend this theory to investigate the effects of a distribution of Grb2 valence in the LAT population on the formation of LAT aggregates and superaggregate and use stochastic simulations to calculate the fraction of the total LAT population in the superaggregate.

Computational modeling of cellular signaling processes embedded into dynamic spatial contexts

Cellular signaling processes depend on specific spatiotemporal distributions of their molecular components. Multi-color high-resolution microscopy now permits detailed assessment of such distributions, providing the input for fine-grained computational models that explore the mechanisms governing dynamic assembly of multi-molecular complexes and their role in shaping cellular behavior. However, incorporating into such models both complex molecular reaction cascades and the spatial localization of signaling components within dynamic cellular morphologies presents substantial challenges. Here we introduce an approach that addresses these challenges by automatically generating computational representations of complex reaction networks based on simple bi-molecular interaction rules embedded into detailed, adaptive models of cellular morphology. Using examples of receptor-mediated cellular adhesion and signal-induced localized MAPK activation in yeast, we illustrate the capacity of this simulation technique to provide insights into cell biological processes. The modeling algorithms, implemented in a version of the Simmune tool set, are accessible through intuitive graphical interfaces as well as programming libraries.

Computational modeling of signal transduction networks: a pedagogical exposition

We give a pedagogical introduction to computational modeling of signal transduction networks, starting from explaining the representations of chemical reactions by differential equations via the law of mass action. We discuss elementary biochemical reactions such as Michaelis-Menten enzyme kinetics and cooperative binding, and show how these allow the representation of large networks as systems of differential equations. We discuss the importance of looking for simpler or reduced models, such as network motifs or dynamical motifs within the larger network, and describe methods to obtain qualitative behavior by bifurcation analysis, using freely available continuation software. We then discuss stochastic kinetics and show how to implement easy-to-use methods of rule-based modeling for stochastic simulations. We finally suggest some methods for comprehensive parameter sensitivity analysis, and discuss the insights that it could yield. Examples, including code to try out, are provided based on a paper that modeled Ras kinetics in thymocytes.

Rule-based multi-level modeling of cell biological systems

BACKGROUND

Proteins, individual cells, and cell populations denote different levels of an organizational hierarchy, each of which with its own dynamics. Multi-level modeling is concerned with describing a system at these different levels and relating their dynamics. Rule-based modeling has increasingly attracted attention due to enabling a concise and compact description of biochemical systems. In addition, it allows different methods for model analysis, since more than one semantics can be defined for the same syntax.

RESULTS

Multi-level modeling implies the hierarchical nesting of model entities and explicit support for downward and upward causation between different levels. Concepts to support multi-level modeling in a rule-based language are identified. To those belong rule schemata, hierarchical nesting of species, assigning attributes and solutions to species at each level and preserving content of nested species while applying rules. Further necessities are the ability to apply rules and flexibly define reaction rate kinetics and constraints on nested species as well as species that are nested within others. An example model is presented that analyses the interplay of an intracellular control circuit with states at cell level, its relation to cell division, and connections to intercellular communication within a population of cells. The example is described in ML-Rules - a rule-based multi-level approach that has been realized within the plug-in-based modeling and simulation framework JAMES II.

CONCLUSIONS

Rule-based languages are a suitable starting point for developing a concise and compact language for multi-level modeling of cell biological systems. The combination of nesting species, assigning attributes, and constraining reactions according to these attributes is crucial in achieving the desired expressiveness. Rule schemata allow a concise and compact description of complex models. As a result, the presented approach facilitates developing and maintaining multi-level models that, for instance, interrelate intracellular and intercellular dynamics.

Toward a comprehensive language for biological systems

Rule-based modeling has become a powerful approach for modeling intracellular networks, which are characterized by rich molecular diversity. Truly comprehensive models of cell behavior, however, must address spatial complexity at both the intracellular level and at the level of interacting populations of cells, and will require richer modeling languages and tools. A recent paper in BMC Systems Biology represents a signifcant step toward the development of a unified modeling language and software platform for the development of multi-level, multiscale biological models.

See research article: http://www.biomedcentral.com/1752-0509/5/166

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.

Towards a quantitative model of the post-synaptic proteome

The postsynaptic compartment of the excitatory glutamatergic synapse contains hundreds of distinct polypeptides with a wide range of functions (signalling, trafficking, cell-adhesion, etc.). Structural dynamics in the post-synaptic density (PSD) are believed to underpin cognitive processes. Although functionally and morphologically diverse, PSD proteins are generally enriched with specific domains, which precisely define the mode of clustering essential for signal processing. We applied a stochastic calculus of domain binding provided by a rule-based modelling approach to formalise the highly combinatorial signalling pathway in the PSD and perform the numerical analysis of the relative distribution of protein complexes and their sizes. We specified the combinatorics of protein interactions in the PSD by rules, taking into account protein domain structure, specific domain affinity and relative protein availability. With this model we interrogated the critical conditions for the protein aggregation into large complexes and distribution of both size and composition. The presented approach extends existing qualitative protein-protein interaction maps by considering the quantitative information for stoichiometry and binding properties for the elements of the network. This results in a more realistic view of the postsynaptic proteome at the molecular level.

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.

The efficiency of reactant site sampling in network-free simulation of rule-based models for biochemical systems

Rule-based models, which are typically formulated to represent cell signaling systems, can now be simulated via various network-free simulation methods. In a network-free method, reaction rates are calculated for rules that characterize molecular interactions, and these rule rates, which each correspond to the cumulative rate of all reactions implied by a rule, are used to perform a stochastic simulation of reaction kinetics. Network-free methods, which can be viewed as generalizations of Gillespie's method, are so named because these methods do not require that a list of individual reactions implied by a set of rules be explicitly generated, which is a requirement of other methods for simulating rule-based models. This requirement is impractical for rule sets that imply large reaction networks (i.e. long lists of individual reactions), as reaction network generation is expensive. Here, we compare the network-free simulation methods implemented in RuleMonkey and NFsim, general-purpose software tools for simulating rule-based models encoded in the BioNetGen language. The method implemented in NFsim uses rejection sampling to correct overestimates of rule rates, which introduces null events (i.e. time steps that do not change the state of the system being simulated). The method implemented in RuleMonkey uses iterative updates to track rule rates exactly, which avoids null events. To ensure a fair comparison of the two methods, we developed implementations of the rejection and rejection-free methods specific to a particular class of kinetic models for multivalent ligand-receptor interactions. These implementations were written with the intention of making them as much alike as possible, minimizing the contribution of irrelevant coding differences to efficiency differences. Simulation results show that performance of the rejection method is equal to or better than that of the rejection-free method over wide parameter ranges. However, when parameter values are such that ligand-induced aggregation of receptors yields a large connected receptor cluster, the rejection-free method is more efficient.

Systems biology in immunology: a computational modeling perspective

Systems biology is an emerging discipline that combines high-content, multiplexed measurements with informatic and computational modeling methods to better understand biological function at various scales. Here we present a detailed review of the methods used to create computational models and to conduct simulations of immune function. We provide descriptions of the key data-gathering techniques employed to generate the quantitative and qualitative data required for such modeling and simulation and summarize the progress to date in applying these tools and techniques to questions of immunological interest, including infectious disease. We include comments on what insights modeling can provide that complement information obtained from the more familiar experimental discovery methods used by most investigators and the reasons why quantitative methods are needed to eventually produce a better understanding of immune system operation in health and disease.

From qualitative data to quantitative models: analysis of the phage shock protein stress response in Escherichia coli

Background

Bacteria have evolved a rich set of mechanisms for sensing and adapting to adverse conditions in their environment. These are crucial for their survival, which requires them to react to extracellular stresses such as heat shock, ethanol treatment or phage infection. Here we focus on studying the phage shock protein (Psp) stress response in Escherichia coli induced by a phage infection or other damage to the bacterial membrane. This system has not yet been theoretically modelled or analysed in silico.

Results

We develop a model of the Psp response system, and illustrate how such models can be constructed and analyzed in light of available sparse and qualitative information in order to generate novel biological hypotheses about their dynamical behaviour. We analyze this model using tools from Petri-net theory and study its dynamical range that is consistent with currently available knowledge by conditioning model parameters on the available data in an approximate Bayesian computation (ABC) framework. Within this ABC approach we analyze stochastic and deterministic dynamics. This analysis allows us to identify different types of behaviour and these mechanistic insights can in turn be used to design new, more detailed and time-resolved experiments.

Conclusions

We have developed the first mechanistic model of the Psp response in E. coli. This model allows us to predict the possible qualitative stochastic and deterministic dynamic behaviours of key molecular players in the stress response. Our inferential approach can be applied to stress response and signalling systems more generally: in the ABC framework we can condition mathematical models on qualitative data in order to delimit e.g. parameter ranges or the qualitative system dynamics in light of available end-point or qualitative information.

Reactive oxygen species production by forward and reverse electron fluxes in the mitochondrial respiratory chain

Reactive oxygen species (ROS) produced in the mitochondrial respiratory chain (RC) are primary signals that modulate cellular adaptation to environment, and are also destructive factors that damage cells under the conditions of hypoxia/reoxygenation relevant for various systemic diseases or transplantation. The important role of ROS in cell survival requires detailed investigation of mechanism and determinants of ROS production. To perform such an investigation we extended our rule-based model of complex III in order to account for electron transport in the whole RC coupled to proton translocation, transmembrane electrochemical potential generation, TCA cycle reactions, and substrate transport to mitochondria. It fits respiratory electron fluxes measured in rat brain mitochondria fueled by succinate or pyruvate and malate, and the dynamics of NAD⁺ reduction by reverse electron transport from succinate through complex I. The fitting of measured characteristics gave an insight into the mechanism of underlying processes governing the formation of free radicals that can transfer an unpaired electron to oxygen-producing superoxide and thus can initiate the generation of ROS. Our analysis revealed an association of ROS production with levels of specific radicals of individual electron transporters and their combinations in species of complexes I and III. It was found that the phenomenon of bistability, revealed previously as a property of complex III, remains valid for the whole RC. The conditions for switching to a state with a high content of free radicals in complex III were predicted based on theoretical analysis and were confirmed experimentally. These findings provide a new insight into the mechanisms of ROS production in RC.

Respiration at the level of mitochondria is considered as delivery of electrons and protons from NADH or succinate to oxygen through a set of transporters constituting the respiratory chain (RC). Mitochondrial respiration, dealing with transfer of unpaired electrons, may produce reactive oxygen species (ROS) such as O₂⁻ and subsequently H₂O₂ as side products. ROS are chemically very active and can cause oxidative damage to cellular components. The production of ROS, normally low, can increase under stress to the levels incompatible with cell survival; thus, understanding the ways of ROS production in the RC represents a vital task in research. We used mathematical modeling to analyze experiments with isolated brain mitochondria aimed to study relations between electron transport and ROS production. Elsewhere we reported that mitochondrial complex III can operate in two distinct steady states at the same microenvironmental conditions, producing either low or high levels of ROS. Here, this property of bistability was confirmed for the whole RC. The associations between measured ROS production and computed individual free radical levels in complexes I and III were established. The discovered phenomenon of bistability is important as a basis for new strategies in organ transplantation and therapy.

Measuring and modeling apoptosis in single cells

Cell death plays an essential role in the development of tissues and organisms, the etiology of disease, and the responses of cells to therapeutic drugs. Here we review progress made over the last decade in using mathematical models and quantitative, often single-cell, data to study apoptosis. We discuss the delay that follows exposure of cells to prodeath stimuli, control of mitochondrial outer membrane permeabilization, switch-like activation of effector caspases, and variability in the timing and probability of death from one cell to the next. Finally, we discuss challenges facing the fields of biochemical modeling and systems pharmacology.

Hierarchical graphs for rule-based modeling of biochemical systems

Background

In rule-based modeling, graphs are used to represent molecules: a colored vertex represents a component of a molecule, a vertex attribute represents the internal state of a component, and an edge represents a bond between components. Components of a molecule share the same color. Furthermore, graph-rewriting rules are used to represent molecular interactions. A rule that specifies addition (removal) of an edge represents a class of association (dissociation) reactions, and a rule that specifies a change of a vertex attribute represents a class of reactions that affect the internal state of a molecular component. A set of rules comprises an executable model that can be used to determine, through various means, the system-level dynamics of molecular interactions in a biochemical system.

Results

For purposes of model annotation, we propose the use of hierarchical graphs to represent structural relationships among components and subcomponents of molecules. We illustrate how hierarchical graphs can be used to naturally document the structural organization of the functional components and subcomponents of two proteins: the protein tyrosine kinase Lck and the T cell receptor (TCR) complex. We also show that computational methods developed for regular graphs can be applied to hierarchical graphs. In particular, we describe a generalization of Nauty, a graph isomorphism and canonical labeling algorithm. The generalized version of the Nauty procedure, which we call HNauty, can be used to assign canonical labels to hierarchical graphs or more generally to graphs with multiple edge types. The difference between the Nauty and HNauty procedures is minor, but for completeness, we provide an explanation of the entire HNauty algorithm.

Conclusions

Hierarchical graphs provide more intuitive formal representations of proteins and other structured molecules with multiple functional components than do the regular graphs of current languages for specifying rule-based models, such as the BioNetGen language (BNGL). Thus, the proposed use of hierarchical graphs should promote clarity and better understanding of rule-based models.

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.

Molecular network dynamics of cell cycle control: transitions to start and finish

The cell cycle is controlled by complex regulatory network to ensure that the phases of the cell cycle happen in the right order and transitions between phases happen only if the earlier phase is properly finished. This regulatory network receives signals from the environment, monitors the state of the DNA, and decides when the cell can proceed in its cycle. The transcriptional and post-translational regulatory interactions in this network can lead to complex dynamical responses. The cell cycle dependent oscillations in protein activities are driven by these interactions as the regulatory system moves between steady states that correspond to different phases of the cell cycle. The analysis of such complex molecular network behavior can be investigated with the tools of computational systems biology. Here we review the basic physiological and molecular transitions in the cell cycle and present how the system-level emergent properties were found by the help of mathematical/computational modeling.

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.

The evolution of the phage shock protein response system: interplay between protein function, genomic organization, and system function

Sensing the environment and responding appropriately to it are key capabilities for the survival of an organism. All extant organisms must have evolved suitable sensors, signaling systems, and response mechanisms allowing them to survive under the conditions they are likely to encounter. Here, we investigate in detail the evolutionary history of one such system: The phage shock protein (Psp) stress response system is an important part of the stress response machinery in many bacteria, including Escherichia coli K12.

Here, we use a systematic analysis of the genes that make up and regulate the Psp system in E. coli in order to elucidate the evolutionary history of the system. We compare gene sharing, sequence evolution, and conservation of protein-coding as well as noncoding DNA sequences and link these to comparative analyses of genome/operon organization across 698 bacterial genomes. Finally, we evaluate experimentally the biological advantage/disadvantage of a simplified version of the Psp system under different oxygen-related environments.

Our results suggest that the Psp system evolved around a core response mechanism by gradually co-opting genes into the system to provide more nuanced sensory, signaling, and effector functionalities. We find that recruitment of new genes into the response machinery is closely linked to incorporation of these genes into a psp operon as is seen in E. coli, which contains the bulk of genes involved in the response. The organization of this operon allows for surprising levels of additional transcriptional control and flexibility. The results discussed here suggest that the components of such signaling systems will only be evolutionarily conserved if the overall functionality of the system can be maintained.

Scalable rule-based modelling of allosteric proteins and biochemical networks

Much of the complexity of biochemical networks comes from the information-processing abilities of allosteric proteins, be they receptors, ion-channels, signalling molecules or transcription factors. An allosteric protein can be uniquely regulated by each combination of input molecules that it binds. This “regulatory complexity” causes a combinatorial increase in the number of parameters required to fit experimental data as the number of protein interactions increases. It therefore challenges the creation, updating, and re-use of biochemical models. Here, we propose a rule-based modelling framework that exploits the intrinsic modularity of protein structure to address regulatory complexity. Rather than treating proteins as “black boxes”, we model their hierarchical structure and, as conformational changes, internal dynamics. By modelling the regulation of allosteric proteins through these conformational changes, we often decrease the number of parameters required to fit data, and so reduce over-fitting and improve the predictive power of a model. Our method is thermodynamically grounded, imposes detailed balance, and also includes molecular cross-talk and the background activity of enzymes. We use our Allosteric Network Compiler to examine how allostery can facilitate macromolecular assembly and how competitive ligands can change the observed cooperativity of an allosteric protein. We also develop a parsimonious model of G protein-coupled receptors that explains functional selectivity and can predict the rank order of potency of agonists acting through a receptor. Our methodology should provide a basis for scalable, modular and executable modelling of biochemical networks in systems and synthetic biology.

The complexity of biochemical networks challenges our ability to create quantitative and predictive models of cellular responses to extracellular changes. In these networks, the regulation of allosteric receptors and proteins by multiple drugs or endogenous ligands introduces “regulatory complexity” because a large number of parameters is required to describe such interactions. Protein interactions also give rise to “combinatorial complexity” by generating large numbers of protein complexes and covalent modification states. To address these twin problems, we propose a modelling framework that combines a modular description of protein structure and function with a rule-based description of protein interactions. We define the input-output function of an allosteric protein through its thermodynamic properties and structural components. We show that our “biomolecule-centric” methodology, in contrast to ad hoc approaches that emphasize the regulatory logic of interactions, can reduce the number of parameters required to model experimental observations. We also demonstrate how the application of our framework gives insights into the assembly of macromolecular complexes and increases the predictive power of a standard model of G protein-coupled receptors. These benefits are possible in many systems, given the ubiquity of allostery in biochemical networks. Our research delineates a fundamental relationship between allostery, modularity, and complexity in biochemical networks.

Analysis and verification of the HMGB1 signaling pathway

BACKGROUND

Recent studies have found that overexpression of the High-mobility group box-1 (HMGB1) protein, in conjunction with its receptors for advanced glycation end products (RAGEs) and toll-like receptors (TLRs), is associated with proliferation of various cancer types, including that of the breast and pancreatic.

RESULTS

We have developed a rule-based model of crosstalk between the HMGB1 signaling pathway and other key cancer signaling pathways. The model has been simulated using both ordinary differential equations (ODEs) and discrete stochastic simulation. We have applied an automated verification technique, Statistical Model Checking, to validate interesting temporal properties of our model.

CONCLUSIONS

Our simulations show that, if HMGB1 is overexpressed, then the oncoproteins CyclinD/E, which regulate cell proliferation, are overexpressed, while tumor suppressor proteins that regulate cell apoptosis (programmed cell death), such as p53, are repressed. Discrete, stochastic simulations show that p53 and MDM2 oscillations continue even after 10 hours, as observed by experiments. This property is not exhibited by the deterministic ODE simulation, for the chosen parameters. Moreover, the models also predict that mutations of RAS, ARF and P21 in the context of HMGB1 signaling can influence the cancer cell's fate - apoptosis or survival - through the crosstalk of different pathways.

The BioPAX community standard for pathway data sharing

BioPAX (Biological Pathway Exchange) is a standard language to represent biological pathways at the molecular and cellular level. Its major use is to facilitate the exchange of pathway data (http://www.biopax.org). Pathway data captures our understanding of biological processes, but its rapid growth necessitates development of databases and computational tools to aid interpretation. However, the current fragmentation of pathway information across many databases with incompatible formats presents barriers to its effective use. BioPAX solves this problem by making pathway data substantially easier to collect, index, interpret and share. BioPAX can represent metabolic and signaling pathways, molecular and genetic interactions and gene regulation networks. BioPAX was created through a community process. Through BioPAX, millions of interactions organized into thousands of pathways across many organisms, from a growing number of sources, are available. Thus, large amounts of pathway data are available in a computable form to support visualization, analysis and biological discovery.

Intrinsic information carriers in combinatorial dynamical systems

Many proteins are composed of structural and chemical features--"sites" for short--characterized by definite interaction capabilities, such as noncovalent binding or covalent modification of other proteins. This modularity allows for varying degrees of independence, as the behavior of a site might be controlled by the state of some but not all sites of the ambient protein. Independence quickly generates a startling combinatorial complexity that shapes most biological networks, such as mammalian signaling systems, and effectively prevents their study in terms of kinetic equations-unless the complexity is radically trimmed. Yet, if combinatorial complexity is key to the system's behavior, eliminating it will prevent, not facilitate, understanding. A more adequate representation of a combinatorial system is provided by a graph-based framework of rewrite rules where each rule specifies only the information that an interaction mechanism depends on. Unlike reactions, which deal with molecular species, rules deal with patterns, i.e., multisets of molecular species. Although the stochastic dynamics induced by a collection of rules on a mixture of molecules can be simulated, it appears useful to capture the system's average or deterministic behavior by means of differential equations. However, expansion of the rules into kinetic equations at the level of molecular species is not only impractical, but conceptually indefensible. If rules describe bona fide patterns of interaction, molecular species are unlikely to constitute appropriate units of dynamics. Rather, we must seek aggregate variables reflective of the causal structure laid down by the rules. We call these variables "fragments" and the process of identifying them "fragmentation." Ideally, fragments are aspects of the system's microscopic population that the set of rules can actually distinguish on average; in practice, it may only be feasible to identify an approximation to this. Most importantly, fragments are self-consistent descriptors of system dynamics in that their time-evolution is governed by a closed system of kinetic equations. Taken together, fragments are endogenous distinctions that matter for the dynamics of a system, which warrants viewing them as the carriers of information. Although fragments can be thought of as multisets of molecular species (an extensional view), their self-consistency suggests treating them as autonomous aspects cut off from their microscopic realization (an intensional view). Fragmentation is a seeded process that depends on the choice of observables whose dynamics one insists to describe. Different observables can cause distinct fragmentations, in effect altering the set of information carriers that govern the behavior of a system, even though nothing has changed in its microscopic constitution. In this contribution, we present a mathematical specification of fragments, but not an algorithmic implementation. We have described the latter elsewhere in rather technical terms that, although effective, were lacking an embedding into a more general conceptual framework, which we here provide.

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.

Decoupling of receptor and downstream signals in the Akt pathway by its low-pass filter characteristics

In cellular signal transduction, the information in an external stimulus is encoded in temporal patterns in the activities of signaling molecules; for example, pulses of a stimulus may produce an increasing response or may produce pulsatile responses in the signaling molecules. Here, we show how the Akt pathway, which is involved in cell growth, specifically transmits temporal information contained in upstream signals to downstream effectors. We modeled the epidermal growth factor (EGF)-dependent Akt pathway in PC12 cells on the basis of experimental results. We obtained counterintuitive results indicating that the sizes of the peak amplitudes of receptor and downstream effector phosphorylation were decoupled; weak, sustained EGF receptor (EGFR) phosphorylation, rather than strong, transient phosphorylation, strongly induced phosphorylation of the ribosomal protein S6, a molecule downstream of Akt. Using frequency response analysis, we found that a three-component Akt pathway exhibited the property of a low-pass filter and that this property could explain decoupling of the peak amplitudes of receptor phosphorylation and that of downstream effectors. Furthermore, we found that lapatinib, an EGFR inhibitor used as an anticancer drug, converted strong, transient Akt phosphorylation into weak, sustained Akt phosphorylation, and, because of the low-pass filter characteristics of the Akt pathway, this led to stronger S6 phosphorylation than occurred in the absence of the inhibitor. Thus, an EGFR inhibitor can potentially act as a downstream activator of some effectors.

Modelling the response of FOXO transcription factors to multiple post-translational modifications made by ageing-related signalling pathways

FOXO transcription factors are an important, conserved family of regulators of cellular processes including metabolism, cell-cycle progression, apoptosis and stress resistance. They are required for the efficacy of several of the genetic interventions that modulate lifespan. FOXO activity is regulated by multiple post-translational modifications (PTMs) that affect its subcellular localization, half-life, DNA binding and transcriptional activity. Here, we show how a mathematical modelling approach can be used to simulate the effects, singly and in combination, of these PTMs. Our model is implemented using the Systems Biology Markup Language (SBML), generated by an ancillary program and simulated in a stochastic framework. The use of the ancillary program to generate the SBML is necessary because the possibility that many regulatory PTMs may be added, each independently of the others, means that a large number of chemically distinct forms of the FOXO molecule must be taken into account, and the program is used to generate them. Although the model does not yet include detailed representations of events upstream and downstream of FOXO, we show how it can qualitatively, and in some cases quantitatively, reproduce the known effects of certain treatments that induce various single and multiple PTMs, and allows for a complex spatiotemporal interplay of effects due to the activation of multiple PTM-inducing treatments. Thus, it provides an important framework to integrate current knowledge about the behaviour of FOXO. The approach should be generally applicable to other proteins experiencing multiple regulations.

Rule-based spatial modeling with diffusing, geometrically constrained molecules

Background

We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined.

For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided.

Results

Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa.

Conclusions

We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.

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.

Lose and gain: impacts of ERK5 and JNK cascades on each other

Kinase cascades in ERK5 (Extracellular signal-regulated kinases) and JNK (c-Jun N-terminal kinases) signaling pathways mediate the sensing and processing of stimuli. Cross-talks between signaling cascades is a likely phenomenon that can cause apparently different biological responses from a single pathway, on its activation. Feedback loops have the potential to greatly alter the properties of a pathway and its response to stimuli. Based on enzyme kinetic reactions, mathematical models have been developed to predict and analyze the impacts of cross-talks and feedback loops in ERK5 and JNK cascades. It has been observed that, there is no significant impact on neither ERK5 activation nor JNKs' activation due to cross-talks between them. But it is due to cross-talks and feedback loops in ERK5 and JNK cascade, ERK5 gets activated in a transient manner in the absence of input signals. Planning to obtain the parameter values from the experimentalist and the result should be validated by experimental verification.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11693-010-9061-4) contains supplementary material, which is available to authorized users.

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.

Hematopoiesis and its disorders: a systems biology approach

Scientists have traditionally studied complex biologic systems by reducing them to simple building blocks. Genome sequencing, high-throughput screening, and proteomics have, however, generated large datasets, revealing a high level of complexity in components and interactions. Systems biology embraces this complexity with a combination of mathematical, engineering, and computational tools for constructing and validating models of biologic phenomena. The validity of mathematical modeling in hematopoiesis was established early by the pioneering work of Till and McCulloch. In reviewing more recent papers, we highlight deterministic, stochastic, statistical, and network-based models that have been used to better understand a range of topics in hematopoiesis, including blood cell production, the periodicity of cyclical neutropenia, stem cell production in response to cytokine administration, and the emergence of imatinib resistance in chronic myeloid leukemia. Future advances require technologic improvements in computing power, imaging, and proteomics as well as greater collaboration between experimentalists and modelers. Altogether, systems biology will improve our understanding of normal and abnormal hematopoiesis, better define stem cells and their daughter cells, and potentially lead to more effective therapies.