Parametric resonance and amplification in excitable membranes. The Hodgkin-Huxley model

It has previously been shown by different investigators that the excitable membrane shows a resonant sensitivity to periodic external perturbations, but its Q -factor is, as a rule, low. The present paper analyses the possible ways of increasing the membrane Q , using a model of the Hodgkin-Huxley type. It is found, in particular, that it can be increased considerably by modulating periodically the membrane capacitance or the activation and inactivation rate constants of ionic channels, with a frequency of about 2 f 0 ( f 0 being the fundamental frequency of damped oscillations in the membrane), the extent of modulation not exceeding the critical value 2/ Q . In this case, a significant parametric amplification of the membrane current takes place. If the modulation coefficient is above 2/ Q , the membrane can display a parametric resonance that causes stable self-oscillations in the potential with a frequency ∼ f 0 . The conditions for the realization of parametric amplification and resonance in biological membranes are discussed.