Voltage-Dependent Membrane Conductances
In the 1940's at the University of Cambridge, a pair of wacky neurobiologists, Alan Hodgkin and Andew Huxley used giant squid axons to investigate the permeability changes behind the generation of action potentials. With their various experiments they showed that the ionic permeability of neuronal membranes is voltage sensitive.  After the experiments were all said and done, they set out to describe the Na+ and K+ permeability changes of neurons mathematically.

To do so, Huxley and Hodgkin assumed ionic currents are produced by a change in membrane conductance, so the opening and closing of ion channels.
If membrane conductance follows Ohm's Law:
J=(sigma)E
or
V=IR
Voltage = Current x Resistance

Then the ionic current that flows during an increase in membrane conductance is given by:
Iion = gion (Vm - Eion)
Where Iion is the ionic current, Vm is the membrane potential, and Eion is the equilibrium potential for the ion flowing through the conductance, gion. The electrochemical driving force action on the ion is the difference between Vm and Eion.

Huxley and Hodgkin used this relationship to calculate the dependence of sodium and potassium conductances on time and membrane potential. Through their fancy experiments H and H showed ionic currents that flow within the neuronal membrane is depolarized are due to 3 different voltage-senstive processes:
1. Activation of Na+ conductance
2. Activation of K+ conductance
3. Inactivation of N+ conductance

These 3 processes relate back to the steps of an action potential, which is generated by changes in ion (Na+, K+) concentrations. To: Electrical Signaling of Nerve Cells

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