Abstract / Description of output
Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, wellmixed systems can be modelled as Markov processes, typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA) [25]. While easy to implement and exact, the computational cost of using the Gillespie SSA to simulate such systems can become prohibitive as the frequency of reaction events increases. This has motivated numerous coarsegrained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation when all reactants are abundant, the approximation breaks down when one or more species exist only in small concentrations and the fluctuations arising from the discrete nature of the reactions become significant. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as simulating nonequilibrium systems such as cellcycle models in which a single species can cycle between abundance and scarcity. In this paper, a hybrid jumpdiffusion model for simulating wellmixed stochastic kinetics is derived. It acts as a bridge between the Gillespie SSA and the chemical Langevin equation. For low reactant reactions the underlying behaviour is purely discrete, while purely diffusive when the concentrations of all species are large, with the two different behaviours coexisting in the intermediate region. A bound on the weak error in the classical large volume scaling limit is obtained, and three different numerical discretisations of the jumpdiffusion model are described. The benefits of such a formalism are illustrated using computational examples.
Original language  English 

Pages (fromto)  398419 
Number of pages  22 
Journal  Journal of Computational Physics 
Volume  326 
Early online date  30 Aug 2016 
DOIs  
Publication status  Published  1 Dec 2016 
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Kostas Zygalakis
 School of Mathematics  Personal Chair of Mathematics of Data Science
Person: Academic: Research Active