The Alpha and Beta Components of the Hodgkin-Huxley Model

The Hodgkin–Huxley (HH) neuron model is based on the following equations:

,

,

,

,

,

, where

, are the Nernst voltages for sodium and potassium [in mV];

is the membrane voltage [in mV];

is the membrane capacitance per unit area [F/cm²];

is the membrane current per unit area [mA/cm²].

The model consists of four current components: the current carried by sodium ions; the current carried by potassium ions; the current carried by other ions (designated leakage current, mainly from chloride ions); and the capacitive (displacement) current. In the standard Hodgkin–Huxley model there are only three types of channels: a sodium channel , a potassium channel , and a nonspecific leakage channel with resistance . The probability that a channel is open is described by additional variables , , and called gating variables, which evolve according to the differential equations given. The combined action of and controls the channels. The gates are controlled by .