title: Gene expression dynamics with stochastic bursts: Construction and exact results for a coarse-grained model.
abstract: We present a theoretical framework to analyze the dynamics of gene expression with stochastic bursts. Beginning with an individual-based model which fully accounts for the messenger RNA (mRNA) and protein populations, we propose an expansion of the master equation for the joint process. The resulting coarse-grained model reduces the dimensionality of the system, describing only the protein population while fully accounting for the effects of discrete and fluctuating mRNA population. Closed form expressions for the stationary distribution of the protein population and mean first-passage times of the coarse-grained model are derived and large-scale Monte Carlo simulations show that the analysis accurately describes the individual-based process accounting for mRNA population, in contrast to the failure of commonly proposed diffusion-type models.
authors.affiliation: Theoretical Physics Division, School of Physics and Astronomy, The University of Manchester, United Kingdom and Max Planck Institute for the Physics of Complex Systems, Dresden, Germany.
authors.forename: Yen Ting
authors.initials: YT
authors.lastname: Lin
authors.affiliation: Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109-1107 USA; Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043 USA; and Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040 USA.
authors.forename: Charles R
authors.initials: CR
authors.lastname: Doering
mesh_terms: D004058:Diffusion; D005786:Gene Expression Regulation; D008957:Models, Genetic; D009010:Monte Carlo Method; D012333:RNA, Messenger / Q000235:genetics / Q000378:metabolism; D013269:Stochastic Processes
chemical_list: D012333:RNA, Messenger