Efficient simulation of multiscale reaction networks: A multilevel partitioning approach

Cellular reaction systems are often multiscale in nature due to wide variation in the species abundance and reaction rates. Traditional deterministic or stochastic modeling of such systems, which do not exploit this multiscale behavior, will be computationally expensive for simulation or inference purposes. This necessitates developing simplified hybrid models combining both stochastic and deterministic approaches that can substantially speed up simulation of such reaction networks. The paper proposes a layered partitioning approach which not only split the reaction set into the usual ‘fast’ and the ‘slow’ groups, but further subdivides the fast group into subgroups of super fast and moderately fast reactions. While the occurrences of reactions from the super fast and moderately fast groups are approximated by ordinary differential equations (ODEs) and Itô diffusions respectively, the discrete counting process formulation is maintained for the reactions from the slow group. The paper develops a mathematical framework for objectively identifying these three groups and performs a rigorous error analysis for the approximation proposed. One important highlight of the paper is the utilization of the error analysis in constructing an efficient dynamic algorithm that can fully automate the partitioning process and make necessary adjustments, if needed, over the course of time.