Modelling and analysis of gene regulatory network using feedback control theory

Abstract

Molecular pathways are a part of a remarkable hierarchy of regulatory networks that operate at all levels of organisation. These regulatory networks are responsible for much of the biological complexity within the cell. The dynamic character of these pathways and the prevalence of feedback regulation strategies in their operation make them amenable to systematic mathematical analysis using the same tools that have been used with success in analysing and designing engineering control systems. In this article, we aim at establishing this strong connection through various examples where the behaviour exhibited by gene networks is explained in terms of their underlying control strategies. We complement our analysis by a survey of mathematical techniques commonly used to model gene regulatory networks and analyse their dynamic behaviour.

Keywords:

• biology
• Markov processes
• feedback control
• gene regulatory networks
• stochastic gene expression
• computational modeling

Acknowledgements

The second author acknowledges research funding from the National Science Foundation through Grants ECCS-0835847 and ECCS-0802008 and funding from the Institute for Collaborative Biotechnologies through Grant DAAD19-03-D-0004 from the US Army Research Office.