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|Title:||Stochastic hybrid models of gene regulatory networks - A PDE approach|
|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|
|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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