ICME Seminar: Eric Vanden-Eijnden

Eric Vandin-Eijnden

Courant Institute of Mathematical Sciences

Nested Stochastic Simulation Algorithms

for Chemical Kinetic Systems with Multiple Time Scales

An efficient simulation algorithm for chemical kinetic systems with

disparate rates is proposed.

This new algorithm is quite general, and it amounts to a simple and

seamless modification of the classical stochastic simulation

algorithm (SSA), also known as the Gillespie algorithm. The basic

idea is to use an outer SSA to simulate the slow processes with rates

computed from an inner SSA which simulates the fast reactions.

Averaging theorems for singularly perturbed Markov processes can be

used to identify the fast and slow variables in the system and the

effective dynamics over the slow time-scale, as well as establish

precise error estimates of the algorithm. The nested SSA will be

illustrated via several examples, including a stochastic Petri models

for virus infection and for the heat shock response of E. Coli, and

some generalization will be discussed (how to deal with system with

more than two separated time-scale, how to adaptively determine the

partition into slow and fast reactions during the simulation, etc.)