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 .

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Hodgkin and Huxley's model is based on the results of voltage clamp experiments. Approximate formulas of and :
,
,
,
,
,
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