title: Periodic, Quasi-periodic and Chaotic Dynamics in Simple Gene Elements with Time Delays.
abstract: Regulatory gene circuit motifs play crucial roles in performing and maintaining vital cellular functions. Frequently, theoretical studies of gene circuits focus on steady-state behaviors and do not include time delays. In this study, the inclusion of time delays is shown to entirely change the time-dependent dynamics for even the simplest possible circuits with one and two gene elements with self and cross regulations. These elements can give rise to rich behaviors including periodic, quasi-periodic, weak chaotic, strong chaotic and intermittent dynamics. We introduce a special power-spectrum-based method to characterize and discriminate these dynamical modes quantitatively. Our simulation results suggest that, while a single negative feedback loop of either one- or two-gene element can only have periodic dynamics, the elements with two positive/negative feedback loops are the minimalist elements to have chaotic dynamics. These elements typically have one negative feedback loop that generates oscillations, and another unit that allows frequent switches among multiple steady states or between oscillatory and non-oscillatory dynamics. Possible dynamical features of several simple one- and two-gene elements are presented in details. Discussion is presented for possible roles of the chaotic behavior in the robustness of cellular functions and diseases, for example, in the context of cancer.
authors.affiliation: Department of Physics, School of Science and Engineering, Meisei University, 2-1-1 Hodokubo, Hino-shi, Tokyo 191-8506, Japan.|Center for Theoretical Biological Physics, Rice University, Houston, TX 77005-1827, USA.
authors.forename: Yoko
authors.initials: Y
authors.lastname: Suzuki
authors.affiliation: Center for Theoretical Biological Physics, Rice University, Houston, TX 77005-1827, USA.
authors.forename: Mingyang
authors.initials: M
authors.lastname: Lu
authors.affiliation: Center for Theoretical Biological Physics, Rice University, Houston, TX 77005-1827, USA.|School of Physics and Astronomy and The Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv 69978, Israel.
authors.forename: Eshel
authors.initials: E
authors.lastname: Ben-Jacob
authors.affiliation: Center for Theoretical Biological Physics, Rice University, Houston, TX 77005-1827, USA.|Department of Physics and Astronomy, Rice University, Houston, TX 77005-1827, USA.|Department of Chemistry, Rice University, Houston, TX 77005-1827, USA.|Department of Biochemistry and Cell Biology, Rice University, Houston, TX 77005-1827, USA.
authors.forename: José N
authors.initials: JN
authors.lastname: Onuchic
mesh_terms: D003198:Computer Simulation; D053263:Gene Regulatory Networks; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D012045:Regulatory Sequences, Nucleic Acid / Q000235:genetics*