Abstract
Background In previous work [1,2], we observed that the ionic fluxes during an action potential (AP) in the squid giant axon can be divided into three functionally separate components. Of these, the component responsible for the depolarizing phase of the AP, and hence its velocity, attains a minimum as a function of the ion channel densities and the axon diameter very near the experimental values of these parameters when the AP velocity is constrained to be at a single value. Since the ion channel fluxes are proportional to the metabolic energy consumption via the ATPase Na+/K+ exchanger, this suggests that evolution, subject to an external constraint on AP velocity, has optimized ion channel densities and axon diameters for the energy associated with the velocity. The energy minimum is close to, although not identical with, a similar minimum in the total membrane capacitance. The total capacitance consists of the intrinsic membrane capacitance (about 0.88 μF/cm2) and a term proportional to the active Na+ channel density (about 1 nF/mS of Na+), the so-called sodium gating capacitance, which arises from movements of charged segments of the Na+ protein during conformal changes. In the present work, we investigate and resolve the discrepancy in the locations of the energy and membrane capacitance minima.
Highlights
In previous work [1,2], we observed that the ionic fluxes during an action potential (AP) in the squid giant axon can be divided into three functionally separate components
Since the ion channel fluxes are proportional to the metabolic energy consumption via the ATPase Na+/K+ exchanger, this suggests that evolution, subject to an external constraint on AP velocity, has optimized ion channel densities and axon diameters for the energy associated with the velocity
The amount of charge per unit axial length on the membrane capacitor at the peak of the action potential is qP = cmVmpeak, where cm is the total membrane capacitance per unit axial length. This charge is approximately equal to the total depolarizing charge crossing the membrane during the action potential, and is proportional to the metabolic energy
Summary
In previous work [1,2], we observed that the ionic fluxes during an action potential (AP) in the squid giant axon can be divided into three functionally separate components. The component responsible for the depolarizing phase of the AP, and its velocity, attains a minimum as a function of the ion channel densities and the axon diameter very near the experimental values of these parameters when the AP velocity is constrained to be at a single value. Pendent parameters, with the channel densities (consisting of voltage-gated Na+, voltage-gated K+, and nonspecific leak channels) varied by a common factor and parameterized by the maximum sodium conductance. Note that this necessitated varying the sodium gating capacitance by this factor. Constraining the velocity to be at a single value, we determined how the shape and height of the action potential varied along the resulting isovelocity curve
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