Stiffness detection and reduction in discrete stochastic simulation of biochemical systems

Typical multiscale biochemical models contain fast-scale and slow-scale reactions, where "fast" reactions fire much more frequently than "slow" ones. This feature often causes stiffness in discrete stochastic simulation methods such as Gillespie's algorithm and the Tau-Leaping method leading to inefficient simulation. This paper proposes a new strategy to automatically detect stiffness and identify species that cause stiffness for the Tau-Leaping method, as well as two stiffness reduction methods. Numerical results on a stiff decaying dimerization model and a heat shock protein regulation model demonstrate the efficiency and accuracy of the proposed methods for multiscale biochemical systems.