title: On multistability of delayed genetic regulatory networks with multivariable regulation functions.
abstract: Many genetic regulatory networks (GRNs) have the capacity to reach different stable states. This capacity is defined as multistability which is an important regulation mechanism. Multiple time delays and multivariable regulation functions are usually inevitable in such GRNs. In this paper, multistability of GRNs is analyzed by applying the control theory and mathematical tools. This study is to provide a theoretical tool to facilitate the design of synthetic gene circuit with multistability in the perspective of control theory. By transforming such GRNs into a new and uniform mathematical formulation, we put forward a general sector-like regulation function that is capable of quantifying the regulation effects in a more precise way. By resorting to up-to-date techniques, a novel Lyapunov-Krasovskii functional (LKF) is introduced for achieving delay dependence to ensure less conservatism. New conditions are then proposed to ensure the multistability of a GRN in the form of linear matrix inequalities (LMIs) that are dependent on the delays. Our multistability conditions are applicable to several frequently used regulation functions especially the multivariable ones. Two examples are employed to illustrate the applicability and usefulness of the developed theoretical results.
authors.affiliation: Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Pan
authors.forename: Zidong
authors.initials: Z
authors.lastname: Wang
authors.forename: Huijun
authors.initials: H
authors.lastname: Gao
authors.forename: Yurong
authors.initials: Y
authors.lastname: Li
authors.forename: Min
authors.initials: M
authors.lastname: Du
mesh_terms: D000465:Algorithms; D016203:CDC2 Protein Kinase / Q000235:genetics / Q000378:metabolism; D018797:Cell Cycle Proteins / Q000235:genetics / Q000378:metabolism; D003198:Computer Simulation; D019926:Cyclin B / Q000235:genetics / Q000378:metabolism; D005786:Gene Expression Regulation / Q000502:physiology; D053263:Gene Regulatory Networks / Q000502:physiology*; D007763:Lac Operon / Q000502:physiology; D008957:Models, Genetic; D058615:Synthetic Biology / Q000379:methods
chemical_list: D018797:Cell Cycle Proteins; D019926:Cyclin B; D016203:CDC2 Protein Kinase