A Reaction-Diffusion Master Equation-Based Method for the Modeling and Simulation of Biochemical Pathways

Several methodologies exist for the modeling and simulation of biochemical pathways. The different methodologies have different assumptions and address the system at varying abstraction levels. Methods differ in their type (deterministic or stochastic) and in their representation of time and space. One such class of methods are the reaction-diffusion master equation (RDME)-based algorithms which describe the stochastic evolution of a spatially-inhomogeneous biochemical system over time and space. The Next Subvolume Method (NSM) and the Gillespie-Multi-Particle (GMP) method are two widely-used RDME-based simulation methods.

The first part of this talk presents a survey of the methodologies used for the modeling and simulation of biochemical networks, their underlying assumptions, advantages, and disadvantages. Also, an extensive review of the relevant biochemical models is provided for each method.

The second part of this talk describes an RDME-based method that incorporates the NSM into the GMP method in an attempt to speed up the processing of reaction events in the latter. The combined GMP-NSM algorithm has been tested on a number of toy models, as well as models of real-world biochemical systems. The results indicate that the combined GMP-NSM method outperforms the GMP method on models where the average rate of reaction events over the whole system is higher than the average rate of diffusion events.