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Models for Rhythmic Phenomena for Living Bodies and Their Applications

生物体节律现象模型及其应用

基本信息

批准号：
08640285
负责人：
WATANABE Masaji
金额：
$ 1.41万
依托单位：
Okayama University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1998
项目状态：
已结题

项目摘要

Sleep-wake rhythm and periodic body temperature change persist with period close to 24-hour even in isolation from 24-hour environmental change, which shows that these periodic changes are generated by some endogenous mechanism. These periodic changes observed in living things are called circadian rhythms. In order to help finding the mechanism of circadian rhythms, we set up mathematical models, analyze them, and verify analytical results with numerical analysis. Besides circadian rhythms, oscillations of some glycolytic intermediates are other periodic phenomena observed in living things. The period of biochemical oscillations ranges a few minutes to 10 minutes, and the period of circadian rhythms are more than 100 times as long. In spite of the significant difference, one can not deny some sort of relation between circadian rhythms and biochemical reactions, because circadian rhythms are observed in variety of living things, and because biochemical reactions are essential for living things to obtain energy. In this study, we suppose that a part of a living thing is surrounded by another part. In case there is no transport of substances between them, the change of concentrations of substances in the inner part is governed by a nonlinear oscillator. Then we assume that there is transport of the substances between the parts. The assumption leads to a system in which a system governing the concentrations in the inner part and a system governing the concentrations in the outer part are coupled. Assuming that a non oscillator has some characteristics, we show that periodic solutions of the coupled system can exist. Moreover, we analyze the system to find conditions under which oscillations of long period can be generated from oscillations of relatively short period. We analyze a model for a electrical circuit anda model for a biochemical reactions, numerically, and verify the results of analysis.

睡眠-觉醒节律和周期性体温变化即使与24小时的环境变化隔离，也以接近24小时的周期持续存在，这表明这些周期性变化是由某些内源性机制产生的。在生物体中观察到的这些周期性变化被称为昼夜节律。为了更好地揭示昼夜节律的机制，我们建立了数学模型，并进行了分析，并用数值分析验证了分析结果。除了昼夜节律，一些糖酵解中间产物的振荡是在生物中观察到的其他周期性现象。生物化学振荡的周期在几分钟到10分钟之间，而昼夜节律的周期则长达100倍以上。尽管存在显著差异，但我们不能否认昼夜节律和生化反应之间存在某种联系，因为昼夜节律在各种生物中都可以观察到，而且生化反应是生物获得能量所必需的。在这项研究中，我们假设生物的一部分被另一部分包围。在它们之间没有物质传输的情况下，内部物质浓度的变化由非线性振荡器控制。然后，我们假设在部件之间存在物质的传输。这个假设导致了一个系统，其中控制内部浓度的系统和控制外部浓度的系统是耦合的。假设非振子具有某些特征，我们证明了耦合系统的周期解的存在性。此外，我们分析了系统的条件下，长周期的振荡可以产生相对较短的周期的振荡。我们分析了一个电路模型和一个生化反应模型，数值计算，并验证了分析结果。