Chetan Pahlajani
University of Delaware
Title: Averaging for some stochastic chemical kinetics models
I will describe recent results on averaging for some models from stochastic chemical kinetics. These results were motivated by some problems in gene expression. The process of gene expression is the sequence of chemical reactions through which genes (segments of DNA) synthesize protein. I will start with a simple gene network (consisting of a single gene, its mRNA and protein) with two distinct time scales where the network displays a negative feedback mechanism - the protein is an inhibitor for its own production. The study is carried out in the framework of the 'linear noise approximation' - one has here a multiscale ODE (the reaction rate ODE of deterministic chemical kinetics) driving a multiscale SDE (a linear SDE describing Gaussian fluctuations about the ODE). Using singular perturbation theory of ODE and SDE, reduced models obtained by averaging are identified. I will also discuss extensions to more general (multiscale) chemical kinetics systems. (joint work with Paul Atzberger, Mustafa Khammash)
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Last Modified: February 26, 2009