Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network

• Published in: Bioinformatics 2006-11, Vol.22 (22), p.2782-2789
• Main Authors: Griffith, Mark, Courtney, Tod, Peccoud, Jean, Sanders, William H.
• Format: Article
• Language: English
• Subjects: Algorithms; Biological and medical sciences; Computational Biology - methods; Fundamental and applied biological sciences. Psychology; Gene Products, tat - chemistry; General aspects; Human immunodeficiency virus 1; Kinetics; Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects); Models, Statistical; Monte Carlo Method; Proteomics - methods; Software; Stochastic Processes; Time Factors; Transcriptional Activation
• ISSN: 1367-4803; 1460-2059; 1367-4811
• DOI: 10.1093/bioinformatics/btl465

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:[e-mail] 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