title: Delay-independent stability of genetic regulatory networks.
abstract: Genetic regulatory networks can be described by nonlinear differential equations with time delays. In this paper, we study both locally and globally delay-independent stability of genetic regulatory networks, taking messenger ribonucleic acid alternative splicing into consideration. Based on nonnegative matrix theory, we first develop necessary and sufficient conditions for locally delay-independent stability of genetic regulatory networks with multiple time delays. Compared to the previous results, these conditions are easy to verify. Then we develop sufficient conditions for global delay-independent stability for genetic regulatory networks. Compared to the previous results, this sufficient condition is less conservative. To illustrate theorems developed in this paper, we analyze delay-independent stability of two genetic regulatory networks: a real-life repressilatory network with three genes and three proteins, and a synthetic gene regulatory network with five genes and seven proteins. The simulation results show that the theorems developed in this paper can effectively determine the delay-independent stability of genetic regulatory networks.
authors: Department of Mechanical Engineering and Divisionof Biomedical Engineering, University of Saskatchewan, Saskatoon, SK S7N5A9, Canada. faw341@mail.usask.ca
authors: Fang-Xiang
authors: FX
authors: Wu
mesh_terms: D000465:Algorithms; D017398:Alternative Splicing / Q000235:genetics; D001185:Artificial Intelligence; D003198:Computer Simulation; D005786:Gene Expression Regulation; D005823:Genetics; D008957:Models, Genetic; D016571:Neural Networks, Computer; D012333:RNA, Messenger / Q000235:genetics; D013816:Thermodynamics
chemical_list: D012333:RNA, Messenger