Multistability of genetic regulatory networks

Abstract

Multistability is found to be an important recurring theme in synthesis biology. In this article, the multistability analysis problem is investigated by applying control theory and mathematical tools. Both the modelling and analysis issues are discussed. Specifically, the genetic regulatory networks (GRNs) with multistability are modelled as switched systems with interval time-varying delays and parameter uncertainties, where the piecewise-affine models are used to approximate the inherent non-linearities existing in the GRNs. Then, by using a novel Lyapunov functional approach and linear matrix inequality (LMI) techniques, a few delay-dependent criteria for the multistability of such genetic regulatory networks are established in the form of LMIs, which can be readily verified by using standard numerical software. A three-component network and a genetic toggle switch with bistability are employed to illustrate the applicability and usefulness of the developed theoretical results.

Keywords:

• multistability
• genetic regulatory networks
• linear matrix inequality
• switched system
• robust stability
• interval time-varying delay

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 60504008, 60774073 and 60804028, and the Program for New Century Excellent Talents in Universities of China.