title: Time-Delayed Models of Gene Regulatory Networks.
abstract: We discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.
authors.affiliation: Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK.
authors.forename: K
authors.initials: K
authors.lastname: Parmar
authors.affiliation: Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK.
authors.forename: K B
authors.initials: KB
authors.lastname: Blyuss
authors.affiliation: Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9QH, UK.
authors.forename: Y N
authors.initials: YN
authors.lastname: Kyrychko
authors.affiliation: Department of Engineering Mathematics, University of Bristol, Bristol BS8 1TR, UK.
authors.forename: S J
authors.initials: SJ
authors.lastname: Hogan
mesh_terms: D019295:Computational Biology; D017143:Fuzzy Logic; D053263:Gene Regulatory Networks; D006801:Humans; D055641:Mathematical Concepts; D008957:Models, Genetic; D009369:Neoplasms / Q000235:genetics*; D017711:Nonlinear Dynamics; D012333:RNA, Messenger / Q000235:genetics; D012334:RNA, Neoplasm / Q000235:genetics; D013269:Stochastic Processes; D013997:Time Factors
chemical_list: D012333:RNA, Messenger; D012334:RNA, Neoplasm