A note on the discrepancy between the predicted and observed speed of the propagated action potential in the squid giant axon

The Hodgkin–Huxley model for the ionic currents in the membrane of the squid giant axon has become the standard model for the electrophysiological behaviour of many excitable cells. A strong test of the model predicted a travelling wave speed of 18.76 m / s for the propagated action potential in an axon with a reported speed of 21.2 m / s . This discrepancy between prediction and observation was considered satisfactory when the model was proposed 50 years ago, appears not to have been re-evaluated, but is unsatisfactory for a mature and important model. The separate and combined influences of measurement error and biological variability on the discrepancy between prediction and observation are quantified, as is the effect of using of a one-dimensional model to represent a three-dimensional axon. The main tool in this investigation is the use of simulation to study the behaviour of the Hodgkin–Huxley membrane model. These studies show that measurement error in combination with biological variability cannot account for the discrepancy between prediction and observation. Also, calculation shows that the one-dimensional description of the behaviour of the axon is adequate. Further calculation shows that the travelling wave description of the propagated action potential is valid only for sufficiently long axons. In shorter axons the propagated action potential is predicted to travel faster than the travelling wave; consequently under suitable experimental conditions the discrepancy between prediction and observation may be negligible.