Vkf

012345678 Time (msec)

FIGURE 16 Simultaneous changes in Na+ (A) and K+ (B) conductance produced by voltage steps to three depolarized levels. Note the marked differences between the changes in Na+ and K+ conductance. (Modified from Hodgkin AL, Huxley AF. J Physiol 1952; 117:500.)

012345678 Time (msec)

FIGURE 16 Simultaneous changes in Na+ (A) and K+ (B) conductance produced by voltage steps to three depolarized levels. Note the marked differences between the changes in Na+ and K+ conductance. (Modified from Hodgkin AL, Huxley AF. J Physiol 1952; 117:500.)

changes of Na+ permeability, there are also voltage-dependent changes in K+ permeability. The greater the level of depolarization, the greater the increase in K+ permeability. There are two important differences between these two permeability systems. First, the changes in K+ permeability are rather slow. It takes some time for K+ permeability to begin to increase, whereas the changes in Na+ permeability begin to occur immediately after the depolarization is delivered. Second, whereas Na+ permeability exhibits inactivation, K+ permeability remains elevated as long as the membrane potential is held depolarized.

Now that it is clear that there are changes in both Na+ and K+ permeabilities, how can this information be used to better account for the entire sequence of events that underlies the action potential? The initial explanation for the rising phase of the action potential is unaltered, simply because for a period of time less than about 0.5 msec, there is no major change in K+ permeability (i.e., the change in K+ permeability is slow). In later phases of the action potential (at times greater than roughly 0.5-1 msec), we not only have to consider Na+ permeability changes but also changes in K+ permeability. What would be the consequences of not only having a fall in Na+ permeability (due to inactivation), but also a simultaneous increase in K+ permeability? Let us return to the Goldman-Hodgkin-Katz equation. At the peak of the action potential (about 0.5-1 msec from its initiation), there is very high Na+ permeability. At this time, K+ permeability begins to increase significantly. Thus, at any time after about 0.5 to 1 msec, not only will there be a certain increase in Na+ permeability, but there will also be a K+ permeability that is greater than its resting level. As a result, the value of a will be smaller than if only changes in Na+ permeability were occurring. If a is smaller, then the Na+ terms make less of a contribution to the Goldman-Hodgkin-Katz equation. Stated in a slightly different way, the K+ terms make more of a contribution, and the membrane potential will be more negative. Thus, by incorporating the finding that there is a delayed increase in K+ permeability, the membrane potential will be more negative for any given time (greater than about 0.5-1 msec) than it would have been without the changes in K+ permeability. The delayed changes in K+ permeability will tend to make the membrane potential repolarize more quickly because now there are two driving forces for repolarization. The first is Na+ inactivation, and the second is the delayed increase in K+ permeability. By incorporating the simultaneous changes in K+ permeability, we can in principle account for a shorter duration action potential.

Can the changes in K+ permeability help explain the hyperpolarizing afterpotential? The key is to understand the time course of the changes in K+ permeability. Note that the changes in K+ permeability are very slow to turn on. They are also slow to turn off. As the action potential repolarizes to the resting level, Na+ permeability returns back to its resting level. Because the K+ permeability system is slow, however, K+ permeability is still elevated. Therefore, a in the Goldman-Hodgkin-Katz equation will actually be less than its initial level of 0.01. If a is less than 0.01, the contributions of the Na+ terms become even more negligible than at rest, and the membrane potential approaches EK. Thus, because Na+ permeability decays rapidly and K+ permeability decays slowly, during the later phases of the action potential K+ permeability is elevated, and the hyperpolarizing afterpotential is produced.

Figure 17 summarizes the time course of the changes in Na+ and K+ permeability underlying the nerve action potential. Assume that by some mechanism the cell is depolarized to threshold. The depolarization initiates the voltage-dependent increase in Na+ permeability. That voltage-dependent increase in Na+ permeability produces a further depolarization, resulting in further increases in Na+ permeability. This positive-feedback cycle leads to rapid depolarization of the cell toward ENa. At the peak of the spike, which occurs about 3/4 msec from initiation of the action potential, two important processes contribute to the repolarization. First, there is the process of Na+ inactivation. As a result of the decay of Na+ permeability, the membrane potential begins to return to the resting level. As the membrane potential returns to the resting level, the Na+ permeability decreases further (i.e., deactivates), which

1 msec

FIGURE 17 Time course of changes in Na+ and K+ conductance that underlie the nerve action potential.

1 msec

FIGURE 17 Time course of changes in Na+ and K+ conductance that underlie the nerve action potential.

further speeds the repolarization process. A new feedback cycle is entered that moves the membrane potential in the reverse direction. Second, there is the delayed increase in K+ permeability. At the point in time when the action potential reaches its peak value, there is a rather dramatic change in K+ permeability. This change in K+ permeability tends to move the membrane potential toward EK. Therefore, there are two independent processes that contribute to repolarization of the action potential. One is Na+ inactivation, and the other is the delayed increase in K+ permeability. Note that when the action potential returns to its resting level of about —60 mV or so, the Na+ permeability has reached its resting level; while Na+ permeability has returned to its resting level, K+ permeability remains elevated for a period of time. Thus, the ratio of the two permeabilities will be less than it was initially, and the membrane potential will move closer to EK. Over a period of time, K+ permeability gradually decays back to its resting level, and the action potential terminates.

In summary, the initiation of the action potential can be explained by the voltage-dependent increase in Na+ permeability and the repolarization phase of the action potential by (1) the process of Na+ inactivation and (2) by the delayed increase in K+ permeability. Finally, the hyperpolarizing afterpotential can be explained by the fact that K+ permeability remains elevated for a period of time after the Na+ permeability has returned to its resting level.

Students frequently question the necessity for such an elaborate series of steps to generate short-duration action potentials. This question brings us back to a point raised at the beginning of the chapter. Recall that the nervous system codes information in terms of the number of action potentials elicited; the greater the stimulus intensity, the greater the frequency of action potentials. To encode and transmit more information per unit time, it is desirable to generate action potentials at a high frequency. With short-duration action potentials, a new action potential can be initiated soon after the first, and this requirement can be met.

The analysis of Hodgkin and Huxley, originally performed on the squid giant axon, has proved generally applicable to action potentials that are initiated in nerve axons and in skeletal muscle cells. The concept of voltage-dependent ion channels is now universal. What varies from cell to cell is the particular ion to which the channel is permeable. For example, a significant component of action potentials in smooth muscle and cardiac muscle cells is due to voltage-dependent Ca2+ channels. Many different types of voltage-dependent K+ channels have also been described.

The structure of voltage-gated Ca2+ channels is similar to that of the Na+ channel (see Fig. 14).

Voltage-activated K+ channels have similar six-membrane-spanning regions, but they differ in that the polypeptide chain does not contain multiply repeated domains. Rather, K+ channels are formed by the functional association of four separate peptides, termed a subunits, to form an ionophore. A specific region of the N-terminal domain of the a subunit appears to be essential for proper aggregation of the subunits to form the tetrameric structures of the functional channel. Variations in the structure of individual subunits as well as different combinations of the subunits contribute to the great diversity of K+ channel properties that has been observed in excitable membranes. For example, some K+ channels exhibit inactivation similar to Na+ channels. For these inactivating K+ channels, the amino terminal sequence of the polypeptide appears to act as a plug to close the channel. Another important class of K+ channels is activated by intracellular levels of Ca2+.

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