Winkelmann, S. and Schütte, Ch. (2016) The spatiotemporal master equation: approximation of reactiondiffusion dynamics via Markov state modeling. Journal of Chemical Physics, 145 (21). p. 214107.

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Official URL: http://aip.scitation.org/doi/full/10.1063/1.497116...
Abstract
Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We present the spatiotemporal chemical master equation (STCME) as a model for stochastic reactiondiffusion systems that exhibit properties of metastability. By means of Markov state modelling, the space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as firstorder reactions, simulation of the resulting stochastic system is possible by means of Gillespie’s stochastic simulation algorithm. We first heuristically derive the STCME starting from the most detailed model of particlebased reactiondiffusion dynamics, compare it to similar approaches to reactiondiffusion master equations (RDME), and finally give a rigorous justification of the STCME by means of the Galerkin approach to discretization. The resulting form of the STCME and its algorithmic realization is then numerically tested in application to a nuclear membrane transport problem in comparison to particlebased reactiondiffusion dynamics.
Item Type:  Article 

Subjects:  Mathematical and Computer Sciences > Mathematics > Applied Mathematics 
Divisions:  Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group 
ID Code:  1944 
Deposited By:  Ulrike Eickers 
Deposited On:  02 Sep 2016 05:57 
Last Modified:  02 Nov 2017 10:02 
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