Calculate and compare the value of the gate h in the Hodgkin

Calculate and compare the value of the gate h in the Hodgkin-Huxley model
for a) rest, and b) for a long pulse holding the membrane 25 mV below rest
(hyperpolarization, negative relative to rest using modern sign convention).

Solution

The Hodgkin-Huxley model is based on mathematical calculations to elucidate the generation of nerve action potential. In cell membranes, the channels responsible for the generation of action potential are also known as voltage -gated channels. Among these membrane channels, one set is permeable to Na⁺ ions whereas the other set of channels are permeable to K⁺ ions.

It is the Na⁺ ion voltage gated channels, that consist of m-gates (activation) and h-gates (inactivation). For successful transport of ions through channel, all the gates must be open.

(a) At rest: The h-gate is open during resting potential, that is the h-variable is high during rest. During depolarization, the h-gate closes, but slowly as compared to the opening of the m-gates. It has a value of 0.5 pico Siemens.

(b) At 25mV below rest, i.e. -90mV: The h-gate again opens during this period and does not allow another action potential to start. This period is known hyperpolarization and h-variable value is high during this time.