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Analysis of Myotonia Paradox on the Hodgkin-Huxley Equations for Muscle Fibers

肌纤维Hodgkin-Huxley方程的肌强直悖论分析

基本信息

批准号：
10650064
负责人：
TERADA Kazuko
金额：
$ 2.11万
依托单位：
Toho University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

项目摘要

There are diseases named myotonia and periodic paralysis. Some of those get worse in coldness and some are not affected by temperature. This phenomena is cold myotonia paradox and why it occurs is not known. The purpose of our study is two research on the mechanism it occurs by using the Hodgkin-Huxley Equations for muscle fibers (denoted HHM below).Experimentary derived HHM exist only for frogs. In our investigation, it is not adapt for a model of human diseases. So we construct HHM for mammalian from data of mammalian muscle on literature.Bifurcation phenomena of HHM for mammalian are investigated by the theory of nonlinear dynamical systems and numerical calculations. Bifurcation parameters are the chloride conductance and some parameters of sodium channel which are known to change in the diseases.As results, both in changes in chloride conductance and the sodium parameters, no temperature dependency are not observed in HHM.On the bifurcation diagram on two-parameter plane of HHM around an inclination-flip bifurcation point, the parameter plane is separated into three regions : normal firing, repetitive firing (myotonia) and depolarization of the resting potential (periodic paralysis). The normal region and the two other regions are separated by homoclinic bifurcations, and the myotonia region and the paralysis region are separated by double cycle bifurcations.Some diseases of sodium channel defect are known to get worse in low temperature, but our results in HHM are not. It might be because the sodium channel defects we took in HHM are wrong or because the temperature dependence we took in HHM are not fit with real muscle.

有一些疾病称为肌强直和周期性麻痹。其中一些在寒冷时会变得更严重，而另一些则不受温度影响。这种现象是冷性肌强直悖论，其发生原因尚不清楚。我们研究的目的是通过使用肌肉纤维的霍奇金-赫胥黎方程（下面表示为 HHM）对其发生机制进行两项研究。实验衍生的 HHM 仅适用于青蛙。在我们的研究中，它不适合人类疾病模型。因此我们根据文献中哺乳动物肌肉的数据构建了哺乳动物的HHM。利用非线性动力系统理论和数值计算研究了哺乳动物HHM的分岔现象。分叉参数是氯电导和钠通道的一些参数，已知这些参数会在疾病中发生变化。因此，在 HHM 中，氯电导和钠参数的变化均未观察到温度依赖性。在围绕倾斜翻转分叉点的 HHM 两参数平面上的分叉图上，参数平面分为三个区域：正常放电、重复放电（肌强直）和静息电位去极化（周期性麻痹）。正常区域和其他两个区域由同宿分叉分开，肌强直区域和麻痹区域由双循环分叉分开。已知一些钠通道缺陷疾病在低温下会恶化，但我们在 HHM 中的结果并非如此。这可能是因为我们在 HHM 中获取的钠通道缺陷是错误的，或者是因为我们在 HHM 中获取的温度依赖性与真实肌肉不相符。