A Generalized Runge-Kutta Framework for Explicit Tau-Leaping Algorithms

Gillespie’s tau-leaping algorithm has received considerable attention as a promising method for performing accelerated-stochastic simulations of multiscale chemical and biological systems.  The simplest tau-leaping algorithm has been shown to be analogous to the simple forward Euler method for numerically integrating ordinary differential equations.   A "midpoint" tau-leaping algorithm has also been proposed which is analogous to an explicit second-order Runge-Kutta integrator.  In this vein, we develop a generalized Runge-Kutta formulation of tau-leaping.  We focus exclusively on explicit methods, describing how reaction firing, postleap checking and tau-selection are accomplished within a Runge-Kutta context and contrasting with the simpler forward-Euler case.  The advantages of the approach are demonstrated via illustrative example systems simulated within the open-source modeling and simulation software package BioNetGen.