TY - JOUR
T1 - Analytical approximations for spatial stochastic gene expression in single cells and tissues
AU - Smith, Stephen
AU - Cianci, Claudia
AU - Grima, Ramon
PY - 2016/5/4
Y1 - 2016/5/4
N2 - Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared to 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.
AB - Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared to 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.
U2 - 10.1098/rsif.2015.1051
DO - 10.1098/rsif.2015.1051
M3 - Article
VL - 13
JO - Journal of the Royal Society Interface
T2 - Journal of the Royal Society Interface
JF - Journal of the Royal Society Interface
SN - 1742-5689
IS - 118
ER -