Extending the Multi-level Method for the Simulation of Stochastic Biological Systems

• Published in: Bulletin of mathematical biology Vol. 78; no. 8; pp. 1640 - 1677
• Main Authors: Lester, Christopher, Baker, Ruth E., Giles, Michael B., Yates, Christian A.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.08.2016; Springer Nature B.V
• Subjects: Algorithms; Biochemical Phenomena; Cell Biology; Computer Simulation; Gene Regulatory Networks; Life Sciences; MAP Kinase Signaling System; Mathematical and Computational Biology; Mathematical Concepts; Mathematics; Mathematics and Statistics; Models, Biological; Models, Chemical; Models, Genetic; Monte Carlo Method; Original Article; Poisson Distribution; Stochastic Processes; Stochastic simulation; Gene regulatory networks; Multi-level; Tau-leaping; Gillespie algorithm
• ISSN: 0092-8240; 1522-9602
• DOI: 10.1007/s11538-016-0178-9

The multi-level method for discrete-state systems, first introduced by Anderson and Higham (SIAM Multiscale Model Simul 10(1):146–179, 2012 ), is a highly efficient simulation technique that can be used to elucidate statistical characteristics of biochemical reaction networks. A single point estimator is produced in a cost-effective manner by combining a number of estimators of differing accuracy in a telescoping sum, and, as such, the method has the potential to revolutionise the field of stochastic simulation. In this paper, we present several refinements of the multi-level method which render it easier to understand and implement, and also more efficient. Given the substantial and complex nature of the multi-level method, the first part of this work reviews existing literature, with the aim of providing a practical guide to the use of the multi-level method. The second part provides the means for a deft implementation of the technique and concludes with a discussion of a number of open problems.