Hybrid simulation of biochemical systems using hybrid adaptive Petri nets

Due to the heterogeneity of many real biochemical systems, stochastic simulation methods do not scale well as systems become more complex and larger, whereas approximations provided by continuous models fail to capture the stochastic behavior of molecular species at very low numbers. A hybrid simulation method is a natural idea to resolve this dilemma. In this paper, we propose a novel notion of Petri net called hybrid adaptive Petri net (HAPN), which is a unified framework to conveniently incorporate ordinary differential equations (ODEs), stochastic models, static hybrid and adaptive hybrid models. By exploring the mutual dependence of transitions, we make an improvement on the hybrid simulation algorithm and achieve a substantial saving on computational cost. We implement an HAPN simulator on MATLAB and employ the improved algorithm in the simulator. Two numerical examples are used to evaluate the accuracy and efficiency of our improved algorithm.