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Transient Stochastic Analysis of Gene Networks

Tuesday, April 22, 2008 - 10:20am - 11:00am
EE/CS 3-180
Mustafa Khammash (University of California, Santa Barbara)
Many gene regulatory networks are modeled at the mesoscopic scale, where
chemical populations change according to a discrete state (jump)
Markov process. The chemical master equation for such a process is
typically infinite dimensional and unlikely to be computationally
tractable without reduction. The recently proposed Finite State
Projection technique allows for a bulk reduction of the CME while
explicitly keeping track of its own approximation error. We show how a
projection approach can be used to directly determine the
statistical distributions for stochastic gene switch rates, escape times,
trajectory periods, and trajectory bifurcations, and to evaluate how likely
it is that a network will exhibit certain behaviors during certain intervals
of time. We illustrate these ideas through the analysis of the switching
behavior of a stochastic model of Gardner's genetic toggle switch.
MSC Code: 
76M35