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The spatiotemporal master equation: approximation of reaction-diffusion dynamics via Markov state modeling

Please always quote using this URN: urn:nbn:de:0297-zib-60999
  • 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.
Author:Stefanie WinkelmannORCiD, Christof Schütte
Document Type:ZIB-Report
Tag:chemical master equation; reaction-diffusion; stochastic chemical kinetics
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J27 Continuous-time Markov processes on discrete state spaces
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C22 Interacting particle systems [See also 60K35]
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]
CCS-Classification:G. Mathematics of Computing / G.3 PROBABILITY AND STATISTICS / Stochastic processes (NEW)
Date of first Publication:2016/11/18
Series (Serial Number):ZIB-Report (16-60)
Published in:AIP - Journal of Chemical Physics 145 (2016)
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