(436c) Runge-Kutta Tau-Leaping Methods for Accelerating Stochastic Simulations of Biochemical Reaction Networks

Tau leaping [1] is a promising approach for accelerating the stochastic simulation of biochemical reaction networks. In its simplest form, the tau-leaping algorithm is analogous to the simple forward-Euler method for numerically integrating ordinary differential equations (ODEs) [1]. Since many higher-order ODE integration methods exist with properties far superior to forward Euler, it is natural to ask whether analogous tau-leaping methods are possible.

Building on prior work in this area [1-4], we have developed a general framework for implementing higher-order Runge-Kutta variants of tau leaping. The approach is novel in that it considers aspects of the tau-leaping algorithm that have not been considered previously within a higher-order context, such as the selection of time steps (tau selection) and post-leap checking. We have applied the method to the “partitioned-leaping algorithm” [5,6], a tau-leaping variant, and implemented it within the open-source modeling and simulation platform BioNetGen [7].

We present results that illustrate the advantages of higher-order tau leaping in computational systems biology. These include applications to models of gene regulation, intracellular signaling, and cell cycle progression. Specifically, we demonstrate the large gains in efficiency that can be achieved relative to exact-stochastic simulation methods [8] as well as improved accuracy relative to lower-order tau-leaping approaches.

[1] Gillespie DT (2001) Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115, 1716-1733.

[2] Burrage K, Tian T (2004) Poisson Runge-Kutta methods for chemical reaction systems. In Advances in Scientific Computing and Applications (Lu YY, Sun WW, Tang T, Ed) Science Press, Beijing/New York, pp. 82–96.

[3] Rathinam M, Petzold LR, Cao Y, Gillespie DT (2003) Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method. J. Chem. Phys. 119, 12784–12794.

[4] Cao Y, Petzold LR, Rathinam M, Gillespie DT (2004) The numerical stability of leaping methods for stochastic simulation of chemically reacting systems. J. Chem. Phys. 121, 12169–12178.

[5] Harris LA, Clancy P (2006) A “partitioned leaping” approach for multiscale modeling of chemical reaction dynamics. J. Chem. Phys. 125, 144107.

[6] Harris LA, Piccirilli AM, Majusiak ER, Clancy P (2009) Quantifying stochastic effects in biochemical reaction networks using partitioned leaping. Phys. Rev. E 79, 051906.

[7] Faeder JR, Blinov ML, Hlavacek WS (2009) Rule-based modeling of biochemical systems with BioNetGen. Methods Mol. Biol. 500, 113-167.

[8] Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434.