Research Article: Hybrid stochastic simulations of intracellular reaction-diffusion systems
Computational Biology and Chemistry
Discrete Semantics for Hybrid Automata
Discrete Event Dynamic Systems
Hybrid simulation of biochemical systems using hybrid adaptive Petri nets
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
Stochastic Petri net models of Ca2+ signaling complexes and their analysis
Natural Computing: an international journal
Simulation techniques for the calculus of wrapped compartments
Theoretical Computer Science
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Motivation: The stochastic kinetics of a well-mixed chemical system, governed by the chemical Master equation, can be simulated using the exact methods of Gillespie. However, these methods do not scale well as systems become more complex and larger models are built to include reactions with widely varying rates, since the computational burden of simulation increases with the number of reaction events. Continuous models may provide an approximate solution and are computationally less costly, but they fail to capture the stochastic behavior of small populations of macromolecules. Results: In this article we present a hybrid simulation algorithm that dynamically partitions the system into subsets of continuous and discrete reactions, approximates the continuous reactions deterministically as a system of ordinary differential equations (ODE) and uses a Monte Carlo method for generating discrete reaction events according to a time-dependent propensity. Our approach to partitioning is improved such that we dynamically partition the system of reactions, based on a threshold relative to the distribution of propensities in the discrete subset. We have implemented the hybrid algorithm in an extensible framework, utilizing two rigorous ODE solvers to approximate the continuous reactions, and use an example model to illustrate the accuracy and potential speedup of the algorithm when compared with exact stochastic simulation. Availability: Software and benchmark models used for this publication can be made available upon request from the authors. Contact: tod@crhc.uiuc.edu Supplementary information: Complete lists of reactions and parameters of the HIV-1 Tat transactivation model, as well as additional results for other benchmark models, are available at http://www.mobius.uiuc.edu/bioinfo06/