A higher-order numerical framework for stochastic simulation of chemical reaction systems

Tamás Székely, Kevin Burrage, Radek Erban, Konstantinos C Zygalakis

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we present a framework for improving the accuracy of fixed-step methods for Monte Carlo simulation of discrete stochastic chemical kinetics. Stochasticity is ubiquitous in many areas of cell biology, for example in gene regulation, biochemical cascades and cell-cell interaction. However most discrete stochastic simulation techniques are slow. We apply Richardson extrapolation to the moments of three fixed-step methods, the Euler, midpoint and θ-trapezoidal τ-leap methods, to demonstrate the power of stochastic extrapolation. The extrapolation framework can increase the order of convergence of any fixed-step discrete stochastic solver and is very easy to implement; the only condition for its use is knowledge of the appropriate terms of the global error expansion of the solver in terms of its stepsize. In practical terms, a higher-order method with a larger stepsize can achieve the same level of accuracy as a lower-order method with a smaller one, potentially reducing the computational time of the system.
Original languageEnglish
Article number85
JournalBMC Systems Biology
Volume6
Issue number1
DOIs
Publication statusPublished - 15 Jul 2012

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