Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems

  • Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

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Author:Stefanie Winkelmann, Christof Schütte
Document Type:Article
Parent Title (English):The Journal of Chemical Physics
Volume:147
Issue:11
First Page:114115-1
Last Page:114115-18
Fulltext Url:http://scitation.aip.org/content/aip/journal/jcp/147/11/10.1063/1.4986560
Year of first publication:2017
Preprint:urn:nbn:de:0297-zib-64264
DOI:http://dx.doi.org/10.1063/1.4986560

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