2.2 Propagation in a uniform squid axon

A major goal of Hodgkin and Huxley was to show that their equations for the ion channels was not only able to generate a realistic membrane action potential in a uniform patch but also that they would provide a reasonable propagating impulse along an axon. Huxley had developed his own methods for accurate numerical integration of an ordinary differential equation for a membrane action potential but it took him 8 hours to calculate one with the tools available at that time - manual calculators, requiring entry of data by hand and "cranking" a lever to obtain the result of a single arithmetic operation. The solution of the partial differential equation describing the membrane voltage in space as well as time for the propagation of an impulse along an axon was completely out of the question. Huxley worked around this problem by noting that, for the restricted special case of propagation of an impulse with constant form and velocity along a uniform (in diameter and channel density) axon, the "traveling wave equation", a simpler ordinary differential equation could be used. Applying this equation, he had to guess at the velocity of the propagating wave, run a calculation and see whether the solution was stable (returning to rest after a spike) or unstable (flying off to + or - infinity). After the many successive approximations required to find a value for the velocity to many significant figures, Huxley was able to calculate a reasonably shaped action potential- 18.8 M/S at a temperature of 18.5C for an axon of 476 microns in diameter. I have used this parameter set as a reference standard against which to check the accuracy of the output of our computer programs. Of course NEURON 3.0 has undergone this rigorous test. Today you need not be concerned with the problems of how to solve partial differential equations nor with numerical integration methods. You can be confident that they have been taken care of so that you can concentrate on the physiology of impulse propagation.

Run this program for a uniform squid axon to learn how the velocity of propagation is changed by: