scholarly journals Multiresolution stochastic simulations of reaction–diffusion processes

2008 ◽  
Vol 10 (39) ◽  
pp. 5963 ◽  
Author(s):  
Basil Bayati ◽  
Philippe Chatelain ◽  
Petros Koumoutsakos
Keyword(s):  
Diffusion Processes ◽  
Reaction Diffusion ◽  
Stochastic Simulations

scholarly journals Analytical approximations for spatial stochastic gene expression in single cells and tissues

2016 ◽  
Vol 13 (118) ◽  
pp. 20151051 ◽  
Author(s):  
Stephen Smith ◽  
Claudia Cianci ◽  
Ramon Grima
Keyword(s):  
Gene Expression ◽  
Diffusion Coefficients ◽  
Brownian Dynamics ◽  
Diffusion Processes ◽  
Single Cells ◽  
Reaction Diffusion ◽  
Intrinsic Noise ◽  
Stochastic Simulations ◽  
Analytical Approximations ◽  
Diffusive Effects

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.

Nonlinear Reaction-Diffusion Processes for Nanocomposites

2021 ◽  
Author(s):  
Jesús Ildefonso Díaz ◽  
David Gómez-Castro ◽  
Tatiana A. Shaposhnikova
Keyword(s):  
Diffusion Processes ◽  
Reaction Diffusion ◽  
Nonlinear Reaction
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