title: Analytical approximations for spatial stochastic gene expression in single cells and tissues.
abstract: Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction-diffusion master equation (RDME) describing stochastic reaction-diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction-diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues.
authors.affiliation: School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JR, UK.
authors.forename: Stephen
authors.initials: S
authors.lastname: Smith
authors.affiliation: School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JR, UK.
authors.forename: Claudia
authors.initials: C
authors.lastname: Cianci
authors.affiliation: School of Biological Sciences, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JR, UK ramon.grima@ed.ac.uk.
authors.forename: Ramon
authors.initials: R
authors.lastname: Grima
mesh_terms: D005786:Gene Expression Regulation; D008954:Models, Biological
keywords: chemical master equation; gene expression; noise; spatial modelling; stochastic models