  The generation of action potential brings into play specific mechanosensory
stimuli manifest in the variation of membrane capacitance, resulting from the
selective membrane permeability to ions exchanges and testifying to the central
role of electromechanical processes in the buildup mechanism of nerve impulse.
As well established [See e.g. D. Gross et al, Cellular and Molecular
Neurobiology vol. 3, p. 89 (1983)], in these electromechanical processes the
net instantaneous charge stored in the membrane is regulated by the rate of
change of the net fluid density through the membrane, orresponding to the
difference in densities of extacellular and intracellular fluids. An
electromechanical model is proposed for which mechanical forces are assumed to
result from the flow of ionic liquids through the nerve membrane, generating
pressure waves stimulating the membrane and hence controlling the net charge
stored in the membrane capacitor. The model features coupled nonlinear partial
differential equations: the familiar Hodgkin-Huxley's cable equation for the
transmembrane voltage in which the membrane capacitor is now a capacitive
diode, and the Heimburg-Jackson's nonlinear hydrodynamic equation for the
pressure wave controlling the total charge in the membrane capacitor. In the
stationary regime, the Hodgkin-Huxley cable equation with variable capacitance
reduces to a linear operator problem with zero eigenvalue, the bound states of
which can be obtained exactly for specific values of characteristic parameters
of the model. In the dynamical regime, numerical simulations of the modified
Hodgkin-Huxley equation lead to a variety of typical figures for the
transmembrane voltage, reminiscent of action potentials observed in real
physiological contexts.
