Premium
Stochastic modelling of gene regulatory networks
Author(s) -
El Samad Hana,
Khammash Mustafa,
Petzold Linda,
Gillespie Dan
Publication year - 2005
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1018
Subject(s) - gene regulatory network , computer science , stochastic process , stochastic modelling , stochastic simulation , master equation , continuous time stochastic process , feed forward , stochastic control , stochastic differential equation , statistical physics , mathematical optimization , mathematics , optimal control , gene , engineering , physics , control engineering , biology , genetics , gene expression , statistics , quantum mechanics , quantum
Gene regulatory networks are dynamic and stochastic in nature, and exhibit exquisite feedback and feedforward control loops that regulate their biological function at different levels. Modelling of such networks poses new challenges due, in part, to the small number of molecules involved and the stochastic nature of their interactions. In this article, we motivate the stochastic modelling of genetic networks and demonstrate the approach using several examples. We discuss the mathematics of molecular noise models including the chemical master equation, the chemical Langevin equation, and the reaction rate equation. We then discuss numerical simulation approaches using the stochastic simulation algorithm (SSA) and its variants. Finally, we present some recent advances for dealing with stochastic stiffness, which is the key challenge in efficiently simulating stochastic chemical kinetics. Copyright © 2005 John Wiley & Sons, Ltd.