Dr. Chetan Pahlajani (UCSB Math)

Title: Averaging for a multiscale stochastic model of gene expression

Abstract: The process of gene expression is the sequence of chemical reactions through which genes (segments of DNA) synthesize protein. I will discuss 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) .