Analysis of the Optimal Channel Density of the Squid Giant Axon Using a Reparameterized Hodgkin–Huxley Model

Abstract

A reparameterized Hodgkin–Huxley-type model is developed that improves the 1952 model's fit to the biological action potential. In addition to altering Na⁺inactivation and K⁺activation kinetics, a voltage-dependent gating-current mechanism has been added to the model. The resulting improved model fits the experimental trace nearly exactly over the rising phase, and it has a propagation velocity that is within 3% of the experimentally measured value of 21.2 m/s (at 18.5°C). Having eliminated most inaccuracies associated with the velocity-dependent rising phase of the action potential, the model is used to test Hodgkin's maximum velocity hypothesis, which asserts that channel density has evolved to maximize conduction velocity. In fact the predicted optimal channel density is more than twice as high as the actual squid channel density. When the available capacitance is reduced to approximate more modern serial Na⁺-channel models, the optimal channel density is 4 times the actual value. We suggest that, although Hodgkin's maximum velocity hypothesis is acceptable as a first approximation, the microscopic optimization perspective of natural selection will not explain the channel density of the squid unless other constraints are taken into account, for example, the metabolic costs of velocity.