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Ion distribution and the relative conductances of the ions through the membrane set the membrane potential. The converse is also true: the probability of the channels' being open (and therefore the relative conductance) depends on the membrane potential. This interesting reciprocal relation makes possible nerve impulse propagation.

In the Nernst formulation, rewritten to involve both K⁺ and Na⁺, the logarithmic term consists of the sum of the two relevant ion species, each contributing in proportion to its relative permeance through the membrane. This is the Goldman-Hodgkin-Katz (GHK) equation.

Fig. 8 The GHK equation.

 
 
The Goldman-Hodgkin-Katz equation predicts the membrane potential in terms of the concentration and permeability of the diffusing ions. In the resting nerve membrane, both the diffusion gradients and the relative permeabilities favor the K⁺ system, and the GHK potential of the nerve is about –60 mV inside relative to outside. During the impulse peak, Na⁺ permeability is favored, and V_M is about +30 mV inside.

Hodgkin and Huxley (1952) elucidated the role of currents associated with the switch from resting to active state of the neuron. Their experiments and mathematical model provided the foundation for much of modern neurophysiology, including the comments in this lesson.

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