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

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

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.

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.

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.

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.

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.

Signal transduction at point-blank range: analysis of a spatial coupling mechanism for pathway crosstalk.

The plasma membrane provides a physical platform for the orchestration of molecular interactions and biochemical conversions involved in the early stages of receptor-mediated signal transduction in living cells. In that context, we introduce here the concept of spatial coupling, wherein simultaneous recruitment of different enzymes to the same receptor scaffold facilitates crosstalk between different signaling pathways through the local release and capture of activated signaling molecules. To study the spatiotemporal dynamics of this mechanism, we have developed a Brownian dynamics modeling approach and applied it to the receptor-mediated activation of Ras and the cooperative recruitment of phosphoinositide 3-kinase (PI3K) by activated receptors and Ras. Various analyses of the model simulations show that cooperative assembly of multimolecular complexes nucleated by activated receptors is facilitated by the local release and capture of membrane-anchored signaling molecules (such as active Ras) from/by receptor-bound signaling proteins. In the case of Ras/PI3K crosstalk, the model predicts that PI3K is more likely to be recruited by activated receptors bound or recently visited by the enzyme that activates Ras. By this mechanism, receptor-bound PI3K is stabilized through short-range, diffusion-controlled capture of active Ras and Ras/PI3K complexes released from the receptor complex. We contend that this mechanism is a means by which signaling pathways are propagated and spatially coordinated for efficient crosstalk between them.

Cell population-based model of dermal wound invasion with heterogeneous intracellular signaling properties.

A deterministic model of dermal wound invasion, which accounts for the platelet-derived growth factor (PDGF) gradient sensing mechanism in fibroblasts mediated by cell surface receptors and the phosphoinositide 3-kinase (PI3K) signal transduction pathway, was previously described (Biophys J 2006; 90:2297-308). Here, we extend that work and implement a hybrid modeling strategy that treats fibroblasts as discrete entities endowed with heterogeneous properties, namely receptor, PI3K and 3' phosphoinositide phosphatase expression levels. Analysis of the model suggests that the wound environment fosters the advancement of cells within the population that are better fit to migrate and/or proliferate in response to PDGF stimulation. Thus, cell-to-cell variability results in a significantly higher rate of wound invasion as compared with the deterministic model, in a manner that depends on the way in which individual cell properties are sampled or inherited upon cell division.

Reactions on cell membranes: comparison of continuum theory and Brownian dynamics simulations.

Biochemical transduction of signals received by living cells typically involves molecular interactions and enzyme-mediated reactions at the cell membrane, a problem that is analogous to reacting species on a catalyst surface or interface. We have developed an efficient Brownian dynamics algorithm that is especially suited for such systems and have compared the simulation results with various continuum theories through prediction of effective enzymatic rate constant values. We specifically consider reaction versus diffusion limitation, the effect of increasing enzyme density, and the spontaneous membrane association/dissociation of enzyme molecules. In all cases, we find the theory and simulations to be in quantitative agreement. This algorithm may be readily adapted for the stochastic simulation of more complex cell signaling systems.

Ligand accumulation in autocrine cell cultures.

Cell-culture assays are routinely used to analyze autocrine signaling systems, but quantitative experiments are rarely possible. To enable the quantitative design and analysis of experiments with autocrine cells, we develop a biophysical theory of ligand accumulation in cell-culture assays. Our theory predicts the ligand concentration as a function of time and measurable parameters of autocrine cells and cell-culture experiments. The key step of our analysis is the derivation of the survival probability of a single ligand released from the surface of an autocrine cell. An expression for this probability is derived using the boundary homogenization approach and tested by stochastic simulations. We use this expression in the integral balance equations, from which we find the Laplace transform of the ligand concentration. We demonstrate how the theory works by analyzing the autocrine epidermal growth factor receptor system and discuss the extension of our methods to other experiments with cultured autocrine cells.

Boundary homogenization for trapping by patchy surfaces.

We analyze trapping of diffusing particles by nonoverlapping partially absorbing disks randomly located on a reflecting surface, the problem that arises in many branches of chemical and biological physics. We approach the problem by replacing the heterogeneous boundary condition on the patchy surface by the homogenized partially absorbing boundary condition, which is uniform over the surface. The latter can be used to analyze any problem (internal and external, steady state, and time dependent) in which diffusing particles are trapped by the surface. Our main result is an expression for the effective trapping rate of the homogenized boundary as a function of the fraction of the surface covered by the disks, the disk radius and trapping efficiency, and the particle diffusion constant. We demonstrate excellent accuracy of this expression by testing it against the results of Brownian dynamics simulations. (c) 2004 American Institute of Physics.