title: Bifurcations in a mathematical model for circadian oscillations of clock genes.
abstract: Circadian oscillations with a period of about 24h are observed in nearly all living organisms as conspicuous biological rhythms. In this paper, we investigate various kinds of bifurcation phenomena produced in a circadian oscillator model of Drosophila. In Drosophila, it is known that circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes that code for the two proteins. For studying circadian oscillations of proteins in Drosophila, a mathematical model has been proposed. The model cannot only account for regular circadian oscillations in environmental conditions such as constant darkness, but also give rise to more complex oscillatory phenomena including chaos and birhythmicity. By calculating bifurcations using Kawakami's method, we obtain detailed bifurcation diagrams related to stable and unstable invariant sets, and identify parameter regions in which the model generates complex oscillations as well as regular circadian oscillations. Moreover, we study bifurcations observed in the model incorporating the effect on a light-dark (LD) cycle and show that the waveform of the periodic variation in the light-induced parameter has a marked influence on the global bifurcation structure or the type of dynamic behavior resulting from the forcing term of the circadian oscillator by the LD cycles.
authors.affiliation: Aihara Complexity Modelling Project, ERATO, Japan Science and Technology Agency (JST), 3-23-5 August House 2F Uehara, Shibuya-ku, Tokyo 151-0064, Japan. tsumoto@aihara.jst.go.jp
authors.forename: Kunichika
authors.initials: K
authors.lastname: Tsumoto
authors.forename: Tetsuya
authors.initials: T
authors.lastname: Yoshinaga
authors.forename: Hitoshi
authors.initials: H
authors.lastname: Iida
authors.forename: Hiroshi
authors.initials: H
authors.lastname: Kawakami
authors.forename: Kazuyuki
authors.initials: K
authors.lastname: Aihara
mesh_terms: D000818:Animals; D001683:Biological Clocks / Q000235:genetics / Q000502:physiology*; D002940:Circadian Rhythm / Q000235:genetics*; D004330:Drosophila / Q000235:genetics / Q000502:physiology*; D005786:Gene Expression Regulation / Q000502:physiology; D017344:Genes, Insect; D008957:Models, Genetic