Model reduction using multiple time scales in stochastic gene regulatory networks

Gene network dynamics often involves processes that take place on widely differing time scales – from the order of nanoseconds to the order of several days. Multiple time scales in mathematical models often lead to serious computational difficulties, such as numerical stiffness in the case of differential equations or excessively redundant Monte Carlo simulations in the case of stochastic processes. We present a method that takes advantage of multiple time scales and dramatically reduces the computational time for a broad class of problems arising in stochastic gene regulatory networks. We illustrate the efficiency of our method in two gene network examples, which describe two substantially different biological processes – cellular heat shock response and expression of the pap gene in Escherichia coli bacteria.