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

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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.