title: Dynamic partitioning for hybrid simulation of the bistable HIV-1 transactivation network.
abstract: BACKGROUND
  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.
  
  
  BACKGROUND
  Software and benchmark models used for this publication can be made available upon request from the authors.
authors.affiliation: Coordinated Science Laboratory, University of Illinois at Urbana-Champaign 1308 W. Main Street, Urbana, IL 61801, USA.
authors.forename: Mark
authors.initials: M
authors.lastname: Griffith
authors.forename: Tod
authors.initials: T
authors.lastname: Courtney
authors.forename: Jean
authors.initials: J
authors.lastname: Peccoud
authors.forename: William H
authors.initials: WH
authors.lastname: Sanders
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D015696:Gene Products, tat / Q000737:chemistry*; D007700:Kinetics; D015233:Models, Statistical; D009010:Monte Carlo Method; D040901:Proteomics / Q000379:methods*; D012984:Software; D013269:Stochastic Processes; D013997:Time Factors; D015533:Transcriptional Activation
chemical_list: D015696:Gene Products, tat