Traditional differential equation models of biochemical systems are useful when the interacting chemical species are present in high concentrations. However, many processes in biology are driven by reactions between chemicals with small copy numbers. These processes are inherently stochastic and display behavior that cannot be captured by deterministic models.

Michealis-Menten kinetics are commonly used to represent enzyme-catalyzed reactions in biochemical models. The Michaelis-Menten approximation has been thoroughly studied in the context of differential equation models. It is shown that the Michaelis-Menten approximation is applicable in discrete stochastic models and the validity conditions are the same as in the deterministic regime. We also compare the Michaelis-Menten approximation to a procedure known as the slow-scale stochastic simulation algorithm (ssSSA). Differences are examined with a strong focus on simulation efficiency, and some special cases of the stochastic formulas are confirmed using a first-passage time analysis.

Gillespie's Stochastic Simulation Algorithm (SSA) has become an invaluable tool for simulating biochemical models in a way that captures this randomness. The multiscale nature of many biological processes leads the SSA to be inefficient for many realistic problems. The ssSSA was proposed an as efficient approximate SSA method to simulate models exhibiting fast reactions in stochastic partial equilibrium. However, the ssSSA is not easy to use, as one needs to identify the fast reactions and then efficiently take them to partial equilibrium. Techniques are presented for automating the ssSSA. A strategy to automatically partition the system into fast and slow reaction subsets is proposed. A general-purpose method to estimate the equilibrium mean populations of the fast process is also provided, along with optimizations that make the performance competitive with existing model-specific approaches. Implementation details are discussed and the effectiveness of the method is demonstrated for three example models.

We present StochKit2, a software package that allows practicing scientists to perform stochastic simulations of biochemical models. StochKit2 provides highly efficient implementations of several variants of the SSA, and tau-leaping with automatic step size selection. StochKit2 features include automatic selection of the optimal SSA method, event handling, and automatic parallelism on multicore architectures. StochKit2 is freely available as open source software.