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2005 Fiscal Year Final Research Report Summary

Construction and Bifurcation Analysis in a Mathematical Model for Circadian Oscillations of Clock Genes

Research Project

Project/Area Number 16500132
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Sensitivity informatics/Soft computing
Research InstitutionThe University of Tokushima

Principal Investigator

YOSHINAGA Tetsuya  The University of Tokushima, Faculty of Medicine, Professor, 医学部, 教授 (40220694)

Project Period (FY) 2004 – 2005
KeywordsCircadian Rhythm / Clock Gene / Mathematical Model / Nonlinear Theory / Bifurcation Theory / Neuron Model
Research Abstract

Circadian oscillations with a period of about 24 h are observed in nearly all living organisms as conspicuous biological rhythms. In this research, 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.

  • Research Products

    (16 results)

All 2006 2005 2004

All Journal Article (16 results)

  • [Journal Article] Bifurcation structure of successive torus doubling2006

    • Author(s)
      Sekikawa Munehisa
    • Journal Title

      Physics Letters A 348

      Pages: 187-194

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Bifurcations in a mathematical model for circadian oscillations of clock genes2006

    • Author(s)
      Kunichika Tsumoto
    • Journal Title

      Journal of Theoretical Biology 239(1)

      Pages: 101-122

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Bifurcation structure of successive torus doubling2006

    • Author(s)
      MUNEHISA, Sekikawa
    • Journal Title

      Physics Letters A vol.348

      Pages: 187-194

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Bifurcations in a mathematical model for circadian oscillations of clock genes2006

    • Author(s)
      TSUMOTO, Kunichika
    • Journal Title

      Journal of Theoretical Biology vol.239, no.1

      Pages: 101-122

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Collapse of duck solution in a circuit driven by an extremely small periodic force2005

    • Author(s)
      Munehisa Sekikawa
    • Journal Title

      Electronics and Communications in Japan, Part 3 88(4)

      Pages: 51-59

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Bifurcation of Synchronization Phenomena Observed in a Coupled Neuron Model for Circadian Clock Rhythms2005

    • Author(s)
      Kunichika Tsumoto
    • Journal Title

      Systems and Computers in Japan 36(8)

      Pages: 1-14

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Taming Chaos現象のからくり2005

    • Author(s)
      関川宗久
    • Journal Title

      電子情報通信学会論文誌 J88-A(6)

      Pages: 788-792

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Bifurcations in Morris-Lecar Neuron Model2005

    • Author(s)
      Kunichika Tsumoto
    • Journal Title

      Neurocomputing 69(4-6)

      Pages: 293-316

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Collapse of duck solution in a circuit driven by an extremely small periodic force2005

    • Author(s)
      SEKIKAWA, Munehisa
    • Journal Title

      Electronics and Communications in Japan, Part 3 vol.88, no.4

      Pages: 51-59

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Bifurcation of Synchronization Phenomena Observed in a Coupled Neuron Model for Circadian Clock Rhythms2005

    • Author(s)
      TSUMOTO, Kunichika
    • Journal Title

      Systems and Computers in Japan vol.36, no.8

      Pages: 1-14

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On the Trick of Taming Chaos Phenomenon2005

    • Author(s)
      MUNEHISA, Sekikawa
    • Journal Title

      The Transactions of the Institute of Electronics, Information and Communication Engineers A vol.J88-A, no.6

      Pages: 788-792

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Bifurcations in Morris-Lecar Neuron Model2005

    • Author(s)
      TSUMOTO, Kunichika
    • Journal Title

      Neurocomputing vol.69, no.4-6

      Pages: 293-316

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] 時計遺伝子リズムのニューロンモデルにみられる同調現象の分岐2004

    • Author(s)
      津元国親
    • Journal Title

      電子情報通信学会論文誌 87-D-II(7)

      Pages: 1516-1528

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A method to accelerate the convergence of the PMART for computed tomography2004

    • Author(s)
      Tetsuya Yoshinaga
    • Journal Title

      WSEAS Transactions on Systems 10(3)

      Pages: 2981-2984

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Bifurcation of Synchronized Phenomena Observed in a Coupled Neuron Model for Circadian Clock Rhythms2004

    • Author(s)
      TSUMOTO, Kunichika
    • Journal Title

      The Transactions of the Institute of Electronics, Information and Communication Engineers A vol.J87-D-II, no.7

      Pages: 1516-1528

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A method to accelerate the convergence of the PMART for computed tomography2004

    • Author(s)
      YOSHINAGA, Tetsuya
    • Journal Title

      WSEAS Transactions on Systems vol.10, no.3

      Pages: 2981-2984

    • Description
      「研究成果報告書概要(欧文)」より

URL: 

Published: 2007-12-13  

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