## Changes in Relative Sodium Permeability During an Action Potential

The key to understanding the origin of the action potential lies in the discussion in Chapter 5 of the factors that influence the steady-state membrane potential of a cell. Recall that the resting Em for a neuron will lie somewhere between EK and ENa. According to the Goldman equation, the exact point at which it lies will be determined by the ratio pNa/pK. As we saw in Chapter 5, pNa/pK of a resting neuron is about 0.02, and Em is near EK.

What would happen to Em if sodium permeability suddenly increased dramatically? The effect of such an increase in pNa is diagrammed in Figure 6-4. In the example, pNa undergoes an abrupt thousandfold increase, so that pNa/pK = 20 instead of0.02. According to the Goldman equation, Em would then swing from about -70 mV to about +50 mV, near ENa. When pNa/pK returns to 0.02, Em will return to its usual value near EK. Note that the swing in membrane potential in Figure 6-4 reproduces qualitatively the change in potential during an action potential. Indeed, it is a transient increase in sodium permeability, as in Figure 6-4, that is responsible for the swing in membrane polarization from near EK to near ENa and back during an action potential.

 / K = 20 PNa/PK 10 - 0 PNa/PK = 002 PNa/PK = 002 + 100 I- Em = +50 mV +50 -----------/--- ENa - +58 mV (mV) 0 I I -50 - Em - -70 mV J Em = -70 mV -100 Ek - -80 mV
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