The dependence of the maximum rate of rise of the action potential upstroke on membrane properties

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