Dynamical study of $$\mathbf{Na }_}$$ Na v channel excitability under mechanical stress

Abstract

Alteration of \(\hbox {Na}_v\) channel functions (channelopathies) has been encountered in various hereditary muscle diseases. \(\hbox {Na}_v\) channel mutations lead to aberrant excitability in skeletal muscle myotonia and paralysis. In general, these mutations disable inactivation of the \(\hbox {Na}_v\) channel, producing either repetitive action potential firing (myotonia) or electrical dormancy (flaccid paralysis) in skeletal muscles. These "sick-excitable" cell conditions were shown to correlate with a mechanical stretch-driven left shift of the conductance factors of the two gating mechanisms of a fraction of \(\hbox {Na}_v\) channels, which make them firing at inappropriate hyperpolarised (left-shifted) voltages. Here we elaborate on a variant of the Hodgkin–Huxley model that includes a stretch elasticity energy component in the activation and inactivation gate kinetic rates. We show that this model reproduces fairly well sick-excitable cell behaviour and can be used to predict the parameter domains where aberrant excitability or paralysis may occur. By allowing us to separate the incidences of activation and inactivation gate impairments in \(\hbox {Na}_v\) channel excitability, this model could be a strong asset for diagnosing the origin of excitable cell disorders.

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