Error bound and simulation algorithm for piecewise deterministic approximations of stochastic reaction systems

In cellular reaction systems, events often happen at different time and abundance scales. It is possible to simulate such multi-scale processes with exact stochastic simulation algorithms, but the computational cost of these algorithms is prohibitive due to the presence of high propensity reactions. This observation motivates the development of hybrid models and simulation algorithms that combine deterministic and stochastic representation of biochemical systems. Based on the random time change model we propose a hybrid model that partitions the reaction system into fast and slow reactions and represents fast reactions through ordinary differential equations (ODEs) while the Markov jump representation is retained for slow ones. Importantly, the partitioning is based on an error analysis which is the main contribution of the paper. The proposed error bound is then used to construct a dynamic partitioning algorithm. Simulation results are provided for two elementary reaction systems.