TU Darmstadt / ULB / TUprints

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

Altintan, Derya ; Koeppl, Heinz (2021)
Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks.
In: BIT Numerical Mathematics, 2020, 60 (2)
doi: 10.26083/tuprints-00017586
Article, Secondary publication, Postprint

Copyright Information: CC BY 4.0 International - Creative Commons, Attribution.

Download (1MB) | Preview
Item Type: Article
Type of entry: Secondary publication
Title: Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks
Language: English
Date: 21 November 2021
Place of Publication: Darmstadt
Year of primary publication: 2020
Publisher: Springer
Journal or Publication Title: BIT Numerical Mathematics
Volume of the journal: 60
Issue Number: 2
DOI: 10.26083/tuprints-00017586
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.

Status: Postprint
URN: urn:nbn:de:tuda-tuprints-175866
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: 02 Aug 2023 08:03
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/17586
PPN: 510012450
Actions (login required)
View Item View Item