Winkelmann, S. and Schütte, Ch. (2017) Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems. Journal of Chemical Physics, 147 (11). pp. 118.

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Official URL: http://dx.doi.org/10.1063/1.4986560
Abstract
Wellmixed 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 wellknown 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 wellmixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative selfregulation 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.
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:  2120 
Deposited By:  Silvia Hoemke 
Deposited On:  20 Oct 2017 12:06 
Last Modified:  20 Oct 2017 12:06 
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