A model analysis of the affect of slow ion channels in muscle stiffness

在某些情况下，肌强直，一种离子通道疾病，即通道病，肌肉僵硬持续相当长时间，而在其他一些情况下，它很快就会消失。正如我们之前所展示的，前一种情况可以用肌肉纤维的霍奇金-赫胥黎方程（在下面表示HHM）很好地描述。持续的肌强直与HHM的周期性解相对应。我们研究的目的是阐明短刚度，后一种情况是如何发生的。利用非线性动力系统理论和数值计算方法，研究了哺乳动物HHM的分岔现象。分析了以氯离子电导率和钠离子通道特性参数作为分岔参数的HHM分岔现象，并考察了平衡点复特征值的影响。以前对神经的Hodgkin-Huxley方程的研究表明，当将慢钠通道添加到原始的HH中时，周期解被在某些参数范围内三次或四次放电的瞬态活动所取代。虽然我们随后用慢钠通道构建了HHM，但我们不能得到与神经相同的现象。生理学研究暗示了钙依赖通道的重要性。我们在HHM中设置了依赖钙的钠离子通道。然而，我们看不到短程射击。对HHM的参数值进行进一步的研究。

In some cases of myotonia, one of the ion channel diseases, i.e. channelopathies, muscle stiffness lasts rather long, and in some other cases, it ceases quickly. The former cases are well described by the Hodgkin-Huxley equations for muscle fibers (denoted HHM below), as we have shown before. The ever-lasting myotonia corresponds to the periodic solutions in HHM.The purpose of our study is to clarify how the short stiffness, the latter cases occur.Bifurcation phenomena of HHM for mammalian are investigated by the theory of nonlinear dynamical systems and numerical calculations.The bifurcation phenomena of HHM with chloride conductance and some parameters of sodium channel characteristics as bifurcation parameters are analyzed and the affect of the complex eigenvalues of the equilibrium points are examined, first. Former studies on the Hodgkin-Huxley equations for nerve (denoted just HH below) show when the slow sodium channel are added to the original HH, the periodic solutions are replaced by transient activity of three or four firing in some parameter range. Although we constructed the HHM with slow sodium channel next, we can not derive the same phenomena as the nerve. Physiological studies imply the importance of calcium-dependent channels. So we set of calcium-dependent sodium channels in HHM. However, we could not see the short-range firings. Further study in parameter values of HHM will be done.