## The Temporal Behavior of Sodium and Potassium Conductance

The gating parameters m, n, and h specify the change in sodium and potassium conductance following a depolarizing voltage-clamp step. The sodium and potassium conductance is given by

The potassium conductance is given by

where gNa and gK are the maximal sodium and potassium conductances, and m, n, and h are given by Equations (7-6), (7-8), and (7-9), respectively. Thus, following a depolarization, the sodium conductance rises in proportion to the third power of the activation parameter m and falls in direct proportion to the decline in the inactivation parameter, h. Figure 7-16a summarizes the responses of each gating parameter separately and also shows the product m3h, which governs the time-course of the sodium conductance after depolarization. The potassium conductance rises as the fourth power of its activation parameter, n, and does not inactivate, as shown in Figure 7-16b. The names

Figure 7-16 The time-courses of sodium conductance and potassium conductance following a step depolarization.

(a) Sodium conductance reflects the time-course of both inactivation (h) and activation (m). In the case of activation, channel opening is proportional to the third power of m. The rise and fall of sodium conductance is proportional to m3h.

(b) The rise of potassium conductance is proportional to the fourth power of the activation parameter, n.

Maximum -

Na+ channel gating parameters

Minimum

Maximum -

Na+ channel gating parameters

Minimum

Time

Depolarization

Time

Depolarization

Maximum

K+ channel gating parameter

Minimum

Time

n used in Chapter 6 for the various voltage-sensitive gates of the potassium and sodium channels derive from the variables chosen by Hodgkin and Huxley to represent these activation and inactivation parameters. The sodium activation gate is called the m gate, the sodium inactivation gate the h gate, and the potassium gate the n gate to reflect the roles of those parameters in Equations (7-10) and (7-11).

The surest test of a theory like the Hodgkin and Huxley theory of the action potential is to see if it can quantitatively describe the event it is supposed to explain. Hodgkin and Huxley tested their theory in this way by determining if they could quantitatively reconstruct the action potential of a squid giant axon using the system of equations they derived from their analysis of voltage-clamp data. Because the action potential does not occur under voltage-clamp conditions, this required knowing both the voltage dependence and the time dependence of a large number of parameters. This included knowing how the rate constants for all three gating particles and how the maximum values of h, m, and n depend on the membrane voltage. All of these parameters could be determined experimentally from a complete set of voltage-clamp experiments, allowing Hodgkin and Huxley to calculate the action potential that would occur if their axon were not voltage clamped. They then compared their calculated action potential with the action potential recorded from the same axon when the voltage-clamp apparatus was switched off. They found that the calculated action potential reproduced all the features of the real one in exquisite detail, confirming that they had covered all the relevant features of the nerve membrane involved in the generation of the action potential.

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