Changes in Sodium and Potassium Conductances

An equivalent circuit for an excitable membrane is shown in Figure 1. In the resting membrane of a neuron there is a small leak conductance \({(g}_{L})\) that is predominantly a K⁺ ion conductance, which sets the membrane potential close to but not quite at the equilibrium potential for K⁺ ions. There are two other conductances, which correspond to the voltage gated sodium and potassium channels, \(g_{\mathit{Na}}\) and \(g_{K}\) respectively. These are variable conductances, meaning that their value can change over time. At rest the voltage gated Na⁺ and K⁺ channels are normally closed and \(g_{\mathit{Na}}\) and \(g_{K}\) are close to zero.

Figure 1 (Left panel) Equivalent circuit for an electrically excitable cell. The leak conductance (g_L) maintains the cell at the resting membrane potential. The two variable conductances (g_Na and g_K) are closed at rest but rapidly increase during an action potential. (right panel) Changes in Na⁺ ion and K⁺ ion conductance during the course of an action potential.

An action potential is initiated when sodium channels begin to open and the conductance to Na⁺ ions begins to rise. During the upstroke of an action potential the Na⁺ ion conductance increases rapidly. The sodium channels begin to inactivate quite rapidly after opening so that \(g_{\mathit{Na}}\) begins to decline soon after reaching a peak. Following a brief delay, the potassium channels also begin to open and \(g_{K}\) increases, although more slowly and to a lesser extent than \(g_{\mathit{Na}}\).

The entire duration of the action potential is about 1 millisecond, although this is quite variable for different types of neurons. The rapid termination of the action potential is due to two factors:

1. Inactivation of the sodium conductance

2. Activation of the delayed potassium conductance

Immediately following the action potential, during the after-hyperpolarization phase, \(g_{K}\) is still elevated as the potassium channels slowly begin to deactivate. As a consequence, the membrane conductance for K⁺ ions is elevated relative to rest during this period, and this pushes the membrane potential very close to \(E_{K}\), the equilibrium potential for K⁺ ions. The membrane potential returns to the resting value as the potassium channels continue to deactivate.

It is important to understand that the Na⁺ and K⁺ channels have very different kinetics, the rates at which they open, close and inactivate. The Na⁺ channels activate quickly and then inactivate quickly. The K⁺ channels activate more slowly than the Na⁺ channels and this delay allows the Na channels to initiate the upstroke of the action potential. The K⁺ channels have relatively slow deactivation kinetics and even slower inactivation kinetics. Inactivation is so slow that it is normally ignored when thinking about the action potential.

Changes in the Kinetic State of the Sodium and Potassium Channels During the Action Potential

As described in the previous chapter the sodium and potassium channels can cycle between three different states; closed, open and inactivated. These states predominate at different stages of the action potential (Figure 2).

1. At rest the activation gates of both channels are closed, and the channels are not inactivated.

2. During the upstroke of the action potential, depolarization causes the activation gates of the Na⁺ channel to open. This produces a large increase in the permeability to Na⁺ ions. The K⁺ channels also begin to open but much more slowly so that most are still closed during the upstroke.

3. During the repolarizing phase, the Na⁺ channel inactivation gate closes and the activation gates of the K⁺ channels are now fully open. This point corresponds to the absolute refractory period because the Na⁺ channels are inactivated and are not ready to re-open and initiate another action potential.

4. During the afterhyperpolarization phase, the K⁺ channels are still open and the Na⁺ channels are beginning to recover from inactivation. This point corresponds to the relative refractory period.

Figure 2 Cartoon showing the changing states of the Na⁺ and K⁺ channels during the course of an action potential.

You can think of the potassium channel activation gate as being on a stiffer hinge than the sodium channel gate. It responds to voltage but not as quickly as the sodium channel activation gate. This simple model is not too far removed from reality. The K⁺ channel is more resistant to the conformational change that produces channel opening than is the Na⁺ channel in response to the same change in membrane potential.

Refractory Period

An excitable membrane is said to be refractory when it either cannot support an action potential or when it can only do so if given a larger stimulus than normal. These two types of refractoriness are known as the absolute refractory period and the relative refractory period. The absolute refractory period corresponds to a period when most of the sodium channels are inactivated and there are insufficient closed channels ready to re-open to generate an action potential. During the relative refractory period there are enough sodium channels in the closed state available to produce an action potential but because there are still potassium channels open during the afterhyperpolarization phase a larger injected current is required in order to trigger an action potential.

Positive Feedback Cycle during the Upstroke of the Action Potential

The upshoot of the action potential is created by a positive feedback cycle (Figure 3). The opening of sodium channels produces an inward current that further depolarizes the membrane potential, which allows more sodium channels to open. This cycle repeats until most of the channels have opened.

This positive feedback cycle is the basis of the all-or-none behavior of the action potential. Once the membrane potential reaches threshold and the sodium channels begin to open, the cycle tends to run to completion, driving the membrane potential up towards the Na⁺ ion equilibrium potential. The threshold potential is roughly equivalent to the potential at which the sodium channels begin to open.

Figure 3 Positive feedback cycle during action potential upstroke.