Methodology article

A Dominated Coupling From The Past algorithm for the stochastic simulation of networks of biochemical reactions

Martin Hemberg and Mauricio Barahona

BMC Systems Biology 2008, 2:42doi:10.1186/1752-0509-2-42

Published:	8 May 2008

Abstract (provisional)

Background

In recent years, stochastic descriptions of biochemical reactions based on the Master Equation (ME) have become widespread. These are especially relevant for models involving gene regulation. Gillespie's Stochastic Simulation Algorithm (SSA) is the most widely used method for the numerical evaluation of these models. The SSA produces exact samples from the distribution of the ME for finite times. However, if the stationary distribution is of interest, the SSA provides no information about convergence or how long the algorithm needs to be run to sample from the stationary distribution with given accuracy.

Results

We present a Perfect Sampling algorithm for the Master Equation (ME) of networks of biochemical reactions prevalent in gene regulation and enzymatic catalysis. Our algorithm provides an extension to Gillespie's SSA by combining it with Dominated Coupling From The Past (DCFTP) techniques. The algorithm is applicable to networks of reactions with uni-molecular stoichiometries and sub-linear, (anti-)monotone propensity functions.

Conclusions

The resulting DCFTP-SSA guarantees sampling from the stationary distribution of the ME and can be used to study steady-state properties of a broad class of stochastic biochemical networks.