Dizzy: Stochastic Simulation of Large-scale Genetic Regulatory Networks (supplementary Material)

In the past five years, there has been significant progress in developing high-speed algorithms for solving the stochastic kinetics of complex biochemical networks. In this section, we briefly survey some of these algorithms. Gillespie proposed a discrete-event Monte Carlo technique for generating approximate solutions to the chemical master equation for the grand probability function. During each iteration, time is advanced a random amount based on the exponential distribution, a single reaction event is selected and implemented, and all reaction probability densities are recomputed. Gillespie described two implementations of the algorithm, the Direct Method and the First Reaction Method, that differ in terms of the number of random numbers that need to be generated. Gibson and Bruck proposed an improvement to the First Reaction Method, called the Next Reaction Method. The dependencies of reaction rates on species concentrations are taken into account in such a way that reaction probability densities need only be recomputed when one of their reactants species populations has been