The Dependence of the Maximum Rate of Rise of the Action Potential Upstroke on Membrane Properties

The maximum rate of rise of the action potential (Vmax) is often used to study the maximum sodium conductance (GNa) of excitable membranes, by assuming that Vmax is proportional to GNa. However, the real relation between Vmax and GNa is uncertain. We use simple analytical descriptions of the membrane currents to investigate this relation. If (1) the sodium conductance is greater than the non-sodium conductance of the membrane, (2) the sodium current is activated extremely quickly, and (3) the sodium current is inactivated extremely slowly, then Vmax will indeed be proportional to GNa. However, if conditions (1) or (3) are not satisfied, the Vmax-GNa relation will be non-proportional, such that a certain fractional change of GNa produces a larger fractional change of Vmax. If condition (2) is not satisfied the Vmax-GNa relation is distorted in the opposite direction, such that a certain fractional change of GNa produces a smaller fractional change of Vmax. Measurements of Vmax are usually performed in preparations where voltage clamping cannot be used to study GNa directly. However, voltage clamping is necessary to verify that conditions (1)-(3) are satisfied. The results of studies using Vmax alone as a measure of GNa should be assessed with caution.