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

时钟基因昼夜节律振荡数学模型的构建和分岔分析

基本信息

批准号：
16500132
负责人：
YOSHINAGA Tetsuya
金额：
$ 1.02万
依托单位：
The University of Tokushima
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16500132/
关键词：
Circadian Rhythm Clock Gene Mathematical Model Nonlinear Theory Bifurcation Theory Neuron Model

项目摘要

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.

昼夜节律以约24小时的周期存在于几乎所有生物体内，是一种显著的生物节律。在这项研究中，我们研究了果蝇昼夜节律振子模型中产生的各种分叉现象。在果蝇中，已知两种蛋白质PER和TIM水平的昼夜振荡是由PER-TIM复合体对编码这两种蛋白质的PER和TIM基因表达的负反馈造成的。为了研究果蝇蛋白质的昼夜振荡，提出了一个数学模型。该模型不仅能解释恒定黑暗等环境条件下的有规律的昼夜振荡，而且还能引起包括混沌和双节律在内的更复杂的振荡现象。通过使用Kawakami方法计算分叉，我们得到了与稳定不变集和不稳定不变集相关的详细分岔图，并确定了模型产生复杂振荡和规则昼夜振荡的参数区域。此外，我们还研究了包含明暗(LD)周期影响的模型中观察到的分叉现象，结果表明，光诱导参数的周期变化的波形对整体分叉结构或由LD周期对昼夜振子的强迫项引起的动力学行为的类型有显著的影响。

项目成果

期刊论文数量（27）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Bifurcation structure of successive torus doubling

DOI：
10.1016/j.physleta.2005.08.089
发表时间：
2006-01
期刊：
Physics Letters A
影响因子：
2.6
作者：
M. Sekikawa;N. Inaba;T. Yoshinaga;T. Tsubouchi
通讯作者：
M. Sekikawa;N. Inaba;T. Yoshinaga;T. Tsubouchi

Bifurcations in Morris-Lecar neuron model

DOI：
10.1016/j.neucom.2005.03.006
发表时间：
2006-01-01
期刊：
NEUROCOMPUTING
影响因子：
6
作者：
Tsumoto, K;Kitajima, H;Kawakami, H
通讯作者：
Kawakami, H

On the Trick of Taming Chaos Phenomenon

论驯服混沌现象的窍门

DOI：
发表时间：
2005
期刊：
The Transactions of the Institute of Electronics, Information and Communication Engineers A vol.J88-A, no.6
影响因子：
0
作者：
MUNEHISA;Sekikawa
通讯作者：
Sekikawa

Bifurcation of Synchronized Phenomena Observed in a Coupled Neuron Model for Circadian Clock Rhythms

昼夜节律耦合神经元模型中观察到的同步现象的分叉

DOI：
发表时间：
2004
期刊：
The Transactions of the Institute of Electronics, Information and Communication Engineers A vol.J87-D-II, no.7
影响因子：
0
作者：
TSUMOTO;Kunichika
通讯作者：
Kunichika

Collapse of duck solution in a circuit driven by an extremely small periodic force

DOI：
10.1002/ecjc.20093
发表时间：
2005-04
期刊：
Electronics and Communications in Japan Part Iii-fundamental Electronic Science
影响因子：
0
作者：
M. Sekikawa;N. Inaba;T. Yoshinaga;H. Kawakami
通讯作者：
M. Sekikawa;N. Inaba;T. Yoshinaga;H. Kawakami