title: Bursting noise in gene expression dynamics: linking microscopic and mesoscopic models.
abstract: The dynamics of short-lived mRNA results in bursts of protein production in gene regulatory networks. We investigate the propagation of bursting noise between different levels of mathematical modelling and demonstrate that conventional approaches based on diffusion approximations can fail to capture bursting noise. An alternative coarse-grained model, the so-called piecewise deterministic Markov process (PDMP), is seen to outperform the diffusion approximation in biologically relevant parameter regimes. We provide a systematic embedding of the PDMP model into the landscape of existing approaches, and we present analytical methods to calculate its stationary distribution and switching frequencies.
authors.affiliation: Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK yenting.lin@manchester.ac.uk.
authors.forename: Yen Ting
authors.identifier: http://orcid.org/0000-0001-6893-8423
authors.initials: YT
authors.lastname: Lin
authors.affiliation: Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK.
authors.forename: Tobias
authors.identifier: http://orcid.org/0000-0003-3402-2163
authors.initials: T
authors.lastname: Galla
mesh_terms: D000818:Animals; D005786:Gene Expression Regulation / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D014176:Protein Biosynthesis / Q000502:physiology*; D012333:RNA, Messenger / Q000378:metabolism
chemical_list: D012333:RNA, Messenger
keywords: bursting noise; coarse-grained models; first passage times; piecewise deterministic Markov process; stochastic processes; weak noise limit