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.

在几乎所有活生物体中都观察到昼夜节律振荡，这是显着的生物节奏。在这项研究中，我们研究了果蝇的昼夜节律模型中产生的各种分叉现象。在果蝇中，众所周知，每种蛋白质水平的昼夜节律振荡是由per-TIM复合物对Per和Tim基因表达的负反馈产生的，该反馈是为两种蛋白质编码的。为了研究果蝇中蛋白质的昼夜节律振荡，已经提出了一种数学模型。该模型不仅可以考虑到诸如恒定黑暗之类的环境条件下的常规昼夜振荡，而且还会导致更复杂的振荡现象，包括混乱和生育不良。通过使用Kawakami方法计算分叉，我们获得了与稳定且不稳定的不变集有关的详细分叉图，并确定模型产生复杂振荡以及常规的昼夜节律振荡的参数区域。此外，我们研究了在模型中观察到的分叉，该模型结合了对光黑暗（LD）周期的影响，并表明光引起的参数周期性变化的波形具有显着影响，这显着影响由LD Cycles cycadian振荡器的强迫项对全球分叉行为的类型或动态行为的类型。

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

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

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