Time-dependent membrane ionic currents

The appropriate depolarizing stimulus activates the capacitive currents (IC, Equation S2.2). Accumulating charges on the membrane capacitor (armatures with kinetics that depend on the biophysical characteristics of the membrane itself) effect an initial depolarization up to -50/-55 mV (between 0.5 and 0.8 ms in Figure 5.9).

Capacitive depolarization increases both sodium and potassium currents. If the increase were synchronous, i.e., if the currents were only voltage-dependent, the membrane potential would behave as described in Paragraph 5.3. What enables a change towards positive potential values is the difference between the kinetics of the membrane currents, defined as the time dependence of the ionic conductances.

Figure 5.9. The stimulus (S) applied to the cell causes the membrane capacitance to charge. The membrane depolarizes, and activating the sodium and potassium currents (I_Na and I_K, top), reaches the peak of the action potential (bottom). I_m currents are expressed in arbitrary units (a.u.)

In the description of membrane currents using Ohm's law (Equations 5.2 and 5.3), time is not taken into account. Both currents flow immediately following a stimulus, but only when voltage- and time-dependent currents are involved is it possible to have an effective transient excitation wave.

The sodium current is activated at a potential of -50/-55 mV with fast kinetics. The potassium current also activates at the same potential, but its kinetics are much slower (Figure 5.9). In this way, the membrane potential reaches positive values very quickly.

The sodium current increases with a positive feedback mechanism, generally called the Hodgkin cycle (Figure 5.10), according to which the same sodium current, by depolarizing the membrane, exponentially increases its permeability.

If time dependence were only a characteristic of the activation of membrane currents, after an initial peak of the potential up to positive values, the membrane potential would stabilize at an intermediate value between E_K and E_Na. In order for the potassium current to re-establish the negative membrane potential, the sodium current must be impaired. Because depolarization activates the sodium current, it is not possible that the same process promotes its deactivation.

Rather, the mechanism is based on a time-dependent process. Immediately following activation, the sodium current declines using a separate process from that responsible for activation. The presence of time-dependent inactivation of the fast sodium current is an essential condition to allow the potential to repolarize (Figure 5.11).

Figure 5.11. Inactivation of the sodium current (I_Na) and prevalence of the potassium current (I_K) allow repolarization of the membrane potential. I_m currents are expressed in arbitrary units (a.u.)

As the sodium current decreases, the outward potassium current takes over, driving the membrane potential back towards EK. To repolarize the membrane, the potassium current decreases, but not in a time-dependent manner, as in the case of the sodium current, but by a decrease in the driving force for the potassium ions. This decrease is called deactivation (Figure 5.12).

Figure 5.12. During repolarization, the potassium current (I_K) decreases but with a delay relative to the potential, which becomes more negative than the resting potential. I_m currents are expressed in arbitrary units (a.u.)

When the sodium current inactivates and potassium remains the sole current present, the membrane potential temporarily hyperpolarizes due to the persistency of sodium current inactivation. Inactivation is removed in a voltage-dependent manner by hyperpolarization. This concludes the action potential cycle by re-establishing the original cell resting potential.