Altintan, 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
Artikel, Zweitveröffentlichung, Verlagsversion
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Kurzbeschreibung (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.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Altintan, Derya ; Koeppl, Heinz |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Hybrid master equation for jump-diffusion approximation of biomolecular reaction networks |
| Sprache: | Englisch |
| Publikationsjahr: | 13 Mai 2024 |
| Ort: | Darmstadt |
| Publikationsdatum der Erstveröffentlichung: | 2020 |
| Ort der Erstveröffentlichung: | Dordrecht [u.a.] |
| Verlag: | Springer Nature |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | BIT Numerical Mathematics |
| Jahrgang/Volume einer Zeitschrift: | 60 |
| (Heft-)Nummer: | 2 |
| Kollation: | 34 Seiten |
| DOI: | 10.26083/tuprints-00027079 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/27079 |
| Zugehörige Links: | |
| Herkunft: | Zweitveröffentlichungsservice |
| Kurzbeschreibung (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. |
| Freie Schlagworte: | Jump-diffusion approximation, Chemical master equation, Fokker–Planck equation, Maximum entropy approach |
| Status: | Verlagsversion |
| URN: | urn:nbn:de:tuda-tuprints-270799 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik 500 Naturwissenschaften und Mathematik > 570 Biowissenschaften, Biologie |
| Fachbereich(e)/-gebiet(e): | 18 Fachbereich Elektrotechnik und Informationstechnik 18 Fachbereich Elektrotechnik und Informationstechnik > Self-Organizing Systems Lab |
| Hinterlegungsdatum: | 13 Mai 2024 09:55 |
| Letzte Änderung: | 17 Mai 2024 12:19 |
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