Please use this identifier to cite or link to this item: doi:10.22028/D291-31048
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Title: Stochastic hybrid models of gene regulatory networks - A PDE approach
Author(s): Kurasov, Pavel
Lück, Alexander
Mugnolo, Delio
Wolf, Verena
Language: English
Title: Mathematical biosciences
Volume: 305
Startpage: 170
Endpage: 177
Publisher/Platform: Elsevier
Year of Publication: 2018
Publikation type: Journal Article
Abstract: A widely used approach to describe the dynamics of gene regulatory networks is based on the chemical master equation, which considers probability distributions over all possible combinations of molecular counts. The analysis of such models is extremely challenging due to their large discrete state space. We therefore propose a hybrid approximation approach based on a system of partial differential equations, where we assume a continuous-deterministic evolution for the protein counts. We discuss efficient analysis methods for both modeling approaches and compare their performance. We show that the hybrid approach yields accurate results for sufficiently large molecule counts, while reducing the computational effort from one ordinary differential equation for each state to one partial differential equation for each mode of the system. Furthermore, we give an analytical steady-state solution of the hybrid model for the case of a self-regulatory gene.
DOI of the first publication: 10.1016/j.mbs.2018.09.009
URL of the first publication: https://www.sciencedirect.com/science/article/pii/S0025556418302098
Link to this record: hdl:20.500.11880/29197
http://dx.doi.org/10.22028/D291-31048
ISSN: 0025-5564
1879-3134
Date of registration: 28-May-2020
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Informatik
Professorship: MI - Prof. Dr. Verena Wolf
Collections:UniBib – Die Universitätsbibliographie

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