6099
eng
reportzib
0
--
2016-11-18
--
The spatiotemporal master equation: approximation of reaction-diffusion dynamics via Markov state modeling
Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models (MSM) as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented.
1438-0064
urn:nbn:de:0297-zib-60999
AIP - Journal of Chemical Physics 145 (2016)
Stefanie Winkelmann
Stefanie Winkelmann
Christof Schütte
ZIB-Report
16-60
eng
uncontrolled
reaction-diffusion
eng
uncontrolled
stochastic chemical kinetics
eng
uncontrolled
chemical master equation
Stochastic processes (NEW)
Continuous-time Markov processes on discrete state spaces
Interacting particle systems [See also 60K35]
Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]
Numerical Mathematics
Schütte, Christof
SFB1114-C3
Winkelmann, Stefanie
https://opus4.kobv.de/opus4-zib/files/6099/ZIB-report_SpatiotemporalCME.pdf