Mélykúti, B. and Burrage, K. and Zygalakis, K. C. (2010) *Fast stochastic simulation of biochemical reaction systems by alternative formulations of the Chemical Langevin Equation.* Not specified . (Submitted)

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## Abstract

The Chemical Langevin Equation (CLE), which is a stochastic differential equation (SDE) driven by a multidimensional Wiener process, acts as a bridge between the discrete Stochastic Simulation Algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. The CLE model is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. The contribution of this work is that we observe and explore that the CLE is not a single equation, but a parametric family of equations, all of which give the same finite-dimensional distribution of the variables. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation. On the practical side, we show that in the case where there are m1 pairs of reversible reactions and m2 irreversible reactions only m1+m2 Wiener processes are required in the formulation of the CLE, whereas the standard approach uses 2m1 + m2. We illustrate our findings by considering alternative formulations of the CLE for a

HERG ion channel model and the Goldbeter–Koshland switch. We show that there are considerable computational savings when using our insights.

Item Type: | Article |
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Subjects: | D - G > General |

Research Groups: | Oxford Centre for Collaborative Applied Mathematics |

ID Code: | 896 |

Deposited By: | Kate Lewin |

Deposited On: | 11 Feb 2010 08:04 |

Last Modified: | 11 Feb 2010 08:04 |

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