Quantifying the roles of space and stochasticity in computer simulations for cell biology and cellular biochemistry.

Most of the fascinating phenomena studied in cell biology emerge from interactions among highly organized multimolecular structures embedded into complex and frequently dynamic cellular morphologies. For the exploration of such systems, computer simulation has proved to be an invaluable tool, and many researchers in this field have developed sophisticated computational models for application to specific cell biological questions. However, it is often difficult to reconcile conflicting computational results that use different approaches to describe the same phenomenon. To address this issue systematically, we have defined a series of computational test cases ranging from very simple to moderately complex, varying key features of dimensionality, reaction type, reaction speed, crowding, and cell size. We then quantified how explicit spatial and/or stochastic implementations alter outcomes, even when all methods use the same reaction network, rates, and concentrations. For simple cases, we generally find minor differences in solutions of the same problem. However, we observe increasing discordance as the effects of localization, dimensionality reduction, and irreversible enzymatic reactions are combined. We discuss the strengths and limitations of commonly used computational approaches for exploring cell biological questions and provide a framework for decision making by researchers developing new models. As computational power and speed continue to increase at a remarkable rate, the dream of a fully comprehensive computational model of a living cell may be drawing closer to reality, but our analysis demonstrates that it will be crucial to evaluate the accuracy of such models critically and systematically.

Domain-oriented reduction of rule-based network models.

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

Combinatorial complexity and dynamical restriction of network flows in signal transduction.

The activities and interactions of proteins that govern the cellular response to a signal generate a multitude of protein phosphorylation states and heterogeneous protein complexes. Here, using a computational model that accounts for 307 molecular species implied by specified interactions of four proteins involved in signalling by the immunoreceptor FcepsilonRI, we determine the relative importance of molecular species that can be generated during signalling, chemical transitions among these species, and reaction paths that lead to activation of the protein tyrosine kinase (PTK) Syk. By all of these measures and over two- and ten-fold ranges of model parameters--rate constants and initial concentrations--only a small portion of the biochemical network is active. The spectrum of active complexes, however, can be shifted dramatically, even by a change in the concentration of a single protein, which suggests that the network can produce qualitatively different responses under different cellular conditions and in response to different inputs. Reduced models that reproduce predictions of the full model for a particular set of parameters lose their predictive capacity when parameters are varied over two-fold ranges.