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We present a highly efficient and accurate hybrid stochastic simulationalgorithm (HSSA) for the purpose of simulating a subset of biochemicalreactions of large gene regulatory networks (GRN). The algorithm relies on theseparability of a GRN into two groups of reactions, A and B, such that thereactions in A can be simulated via a stochastic simulation algorithm (SSA),while those in group B can yield to a deterministic description via ordinarydifferential equations. First, we derive exact expressions needed to sample thenext reaction time and reaction type, and then give two examples of how a GRNcan be partitioned. Although the methods presented here can be applied to avariety of different stochastic systems within GRN, we focus on simulatingmRNAs in particular. To demonstrate the accuracy and efficiency of thisalgorithm, we apply it to a three-gene oscillator, first in one cell, and thenin an array of cells (up to 64 cells) interacting via molecular diffusion, andcompare its performance to the Gillespie algorithm (GA). Depending on theparticular numerical values of the system parameters, and the partitioningitself, we show that our algorithm is between 11 and 445 times faster than theGA.

Exact derivation and practical application of a hybrid stochastic simulation algorithm for large gene regulatory networks