Accelerated leap methods for simulating discrete stochastic chemical kinetics

Burrage, Kevin, Mac, Shev and Tian, Tianhai (2006). Accelerated leap methods for simulating discrete stochastic chemical kinetics. In: Christian Commault and Nicholas Marchand, Lecture Notes in Control and Information Sciences: 2nd Multidisciplinary International Symposium on Positive Sys. 2nd Multidisciplinary International Symposium on Positive Sys, Grenoble, France, (359-366). 30 August -1 September, 2006.


Author Burrage, Kevin
Mac, Shev
Tian, Tianhai
Title of paper Accelerated leap methods for simulating discrete stochastic chemical kinetics
Conference Paper Type Fully Published Paper
Conference name 2nd Multidisciplinary International Symposium on Positive Sys
DOI 10.1007/11757344_46
Conference location Grenoble, France
Conference dates 30 August -1 September, 2006
Proceedings title Lecture Notes in Control and Information Sciences: 2nd Multidisciplinary International Symposium on Positive Sys   Check publisher's open access policy
Journal name Positive Systems, Proceedings   Check publisher's open access policy
Editor Christian Commault
Nicholas Marchand
Place published Berlin
Publisher Springer-Verlag Berlin
Publication date 2006
Volume number 341 (Positive Systems )
ISBN 3-540-34771-2
ISSN 0170-8643
Start page 359
End page 366
Total pages 8
Collection year 2006
Language eng
Abstract/Summary Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.
Subjects E1
239901 Biological Mathematics
230202 Stochastic Analysis and Modelling
780101 Mathematical sciences
780105 Biological sciences
060114 Systems Biology
0103 Numerical and Computational Mathematics
Q-Index Code E1

 
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