Adaptive time-stepping in the numerical solution of the reaction-diffusion master equation

Stochastic modeling and simulation are essential tools for studying cellular processes. The dynamics of spatially heterogeneous biochemical systems with species in low amounts is governed by a discrete, stochastic model, the Reaction-Diffusion Master Equation (RDME). The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is an exact numerical method for the RDME, but is prohibitively slow as it simulates every chemical reaction and diffusion event. To overcome this difficulty, an approximate strategy, the tau-leaping scheme, was developed that steps over multiple reactions and diffusion events. Mathematical models of biochemical systems are often prone to stiffness, thus computationally challenging. In this thesis, we propose an adaptive time-stepping scheme for the tau-leaping method for the RDME. This strategy is compared to the ISSA, for several models of interest. The numerical results show that the proposed adaptive technique significantly speeds-up the simulation, while maintaining excellent accuracy of the numerical solution.