Minimizing the Hodgkin-Huxley Model

Memristor (memory resistor) is a passive electrical circuit element whose instantaneous resistance depends not only on the voltage, but the history of the current applied to it. The first memristor was fabricated in 2008 by the HP labs in a semiconductor titanium-dioxide thin film. Apart from its potential for high-density memory storage, the electrical properties of a memristor share similarities with those of ion channels in biological membranes including axons. The electrical response of an axon is traditionally modeled using Hodgkin-Huxley equations. The purpose of this research is to investigate the characteristics that are required to mimic the spiking response of a neuron. We introduce a minimal Hodgkin-Huxley model for steady state stimulus in which the leakage channel, membrane capacitance, and potassium and leakage equilibrium voltages are absent. Our results show that the potassium and sodium ion channels, individually, are essential for action potential; they also show that the generation of action potential requires more than one type of ion channels. Thus, our research sheds light on the feasibility of creating artificial axons (and neural networks) with thin-film memristors.