Effects of nonlinear membrane capacitance in the Hodgkin-Huxley model of action potential on the spike train patterns of a single neuron

Abstract

The membrane capacitance has been shown to have a nonlinear dependence on the cell membrane potential in various types of cells. But the role of the nonlinear membrane capacitance in neurons has not been studied in detail. Herein, by considering the membrane
capacitance to be a nonlinear parameter, we have explored the behavior of the cell membrane in three different types of neurons, e.g., squid giant neuron, rodent hippocampal interneuron, and rodent cortical neuron. Hodgkin-Huxley's equation of action potential was modified accordingly and simulated computationally. Our simulated results suggest that the action potential amplitude of a neuron almost remains the same for some duration when the voltage dependence parameter of the nonlinear capacitance increases up to a certain range, the initiation of the next Action Potential is delayed and the reduction in spike frequencies occurs in comparison to constant membrane capacitance. This indicates the importance of nonlinearity in membrane capacitance. Simultaneously the inter-spike interval (ISI) changes with the nonlinear membrane capacitance parameter. The gating dynamics show changes mainly in the Na+ activation current while the membrane capacitance is considered to be nonlinear. The above-mentioned computational results
are primarily predictive pending experimental verification.