Reduction methods for multiple-time-scale biochemical reaction networks
by
Chang Hyeong Lee
Worcester Polytechnic Institute

In this talk, we consider deterministic and stochastic descriptions of reaction networks in which different reactions occur on at least two distinct time scales. In the deterministic description, based on perturbation analysis and complex reaction network theory, we derive a necessary and sufficient condition under which there is a complete separation of slow and fast variables, and we discuss network topological properties which guarantee that the condition is satisfied. Given this condition, we obtain an explicit expression for the reduced equation on the slow time scale and we clarify the geometric meaning of the reduction. In the stochastic description, by applying a state space decomposition method, we rigorously obtain the reduced master equation from the full master equation of the system, which enables us to implement an efficient simulation algorithm. Lastly, we illustrate the numerical accuracy and efficiency of the reduction method by simulating several multiple-time-scale deterministic and stochastic models including a stochastic reaction-diffusion model of gene expression.

Date received: May 15, 2008