# The Alpha and Beta Components of the Hodgkin-Huxley Model

The Alpha and Beta Components of the Hodgkin-Huxley Model

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

C=(V-)+(V-)+I(t)

dV

dt

g

K

V

K

g

Na

V

Na

g

K

g

K,max

4

n

g

Na

g

Na,max

3

m

dn

dt

α

n

β

n

dm

dt

α

m

β

m

dh

dt

α

h

β

h

V

K

V

Na

V

C

I

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 .

g

Na

g

K

R

m

n

h

m

h

+

Na

+

K

n