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Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks

Altintan, Derya and Koeppl, Heinz (2021):
Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks. (Postprint)
In: BIT Numerical Mathematics, 60 (2), pp. 261-294. Springer, ISSN 0006-3835, e-ISSN 1572-9125,
DOI: 10.26083/tuprints-00017586,
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Item Type: Article
Origin: Secondary publication service
Status: Postprint
Title: Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks
Language: English
Abstract:

Cellular reactions have a multi-scale nature in the sense that the abundance of molecular species and the magnitude of reaction rates can vary across orders of magnitude. This diversity naturally leads to hybrid models that combine continuous and discrete modeling regimes. In order to capture this multi-scale nature, we proposed jump-diffusion approximations in a previous study. The key idea was to partition reactions into fast and slow groups, and then to combine a Markov jump updating scheme for the slow group with a diffusion (Langevin) updating scheme for the fast group. In this study we show that the joint probability density function of the jump-diffusion approximation over the reaction counting process satisfies a hybrid master equation that combines terms from the chemical master equation and from the Fokker–Planck equation. Inspired by the method of conditional moments, we propose a efficient method to solve this master equation using the moments of reaction counters of the fast reactions given the reaction counters of the slow reactions. For each time point of interest, we then solve a set of maximum entropy problems in order to recover the conditional probability density from its moments. This finally allows us to reconstruct the complete joint probability density over all reaction counters and hence obtain an approximate solution of the hybrid master equation. Finally, we show the accuracy of the method applied to a simple multi-scale conversion process.

Journal or Publication Title: BIT Numerical Mathematics
Journal volume: 60
Number: 2
Publisher: Springer
Classification DDC: 500 Naturwissenschaften und Mathematik > 500 Naturwissenschaften
500 Naturwissenschaften und Mathematik > 530 Physik
500 Naturwissenschaften und Mathematik > 570 Biowissenschaften, Biologie
Divisions: 18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
Date Deposited: 16 Feb 2021 09:30
Last Modified: 16 Feb 2021 09:30
DOI: 10.26083/tuprints-00017586
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-175866
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/17586
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