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

Altıntan, Derya ; Koeppl, Heinz (2024)
Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks.
In: BIT Numerical Mathematics, 2020, 60 (2)
doi: 10.26083/tuprints-00027079
Article, Secondary publication, Publisher's Version

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Item Type: Article
Type of entry: Secondary publication
Title: Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks
Language: English
Date: 13 May 2024
Place of Publication: Darmstadt
Year of primary publication: 2020
Place of primary publication: Dordrecht [u.a.]
Publisher: Springer Nature
Journal or Publication Title: BIT Numerical Mathematics
Volume of the journal: 60
Issue Number: 2
Collation: 34 Seiten
DOI: 10.26083/tuprints-00027079
Corresponding Links:
Origin: Secondary publication service

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.

Uncontrolled Keywords: Jump-diffusion approximation, Chemical master equation, Fokker–Planck equation, Maximum entropy approach
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-270799
Classification DDC: 500 Science and mathematics > 510 Mathematics
500 Science and mathematics > 570 Life sciences, biology
Divisions: 18 Department of Electrical Engineering and Information Technology > Self-Organizing Systems Lab
Date Deposited: 13 May 2024 09:55
Last Modified: 13 May 2024 09:55
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/27079
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