Stochastic simulation has been an important tool to study the inherent stochasticity in the dynamics of cellular biochemical systems. Multiple time scales in cellular chemically reacting systems present a challenge for the efficiency of stochastic simulation. Numerous model reductions have been proposed to accelerate the simulation of chemically reacting systems by exploiting time scale separation. However, these are often identified and deployed manually, requiring expert knowledge. This is time-consuming, prone to error, and opportunities for model reduction may be missed, particularly for large models.

To meet this challenge, we studied and examined the validity criteria and efficiency gains of different model reduction techniques for different simulation algorithms. Specifically, we compared the validity conditions and efficiency gains of Michaelis-Menten model reduction applied to both SSA and tau-leaping algorithms. Results show that although the condition for validity of the reduction is the same for both algorithms, the reduction results in a substantial speed-up under a different range of conditions for SSA than for tau-leaping.

Based on those results, we proposed an automatic model reduction framework for stochastic simulation. It consists of two parts: a model reduction detection algorithm and a model reduction application algorithm. The model reduction detection algorithm uses an adaptively weighted Petri net to dynamically identify opportunities for model reductions for both the SSA and tau-leaping simulation, with no requirement of expert knowledge input. The model reduction application algorithm automatically applies model reductions that are both valid and beneficial. Results are presented to demonstrate the utility and effectiveness of both algorithms in the context of tau-leaping.