Reconstructing the action potential

Hodgkin and Huxley felt that they could not be sure that they understood the ionic basis of the action potential until they could reproduce its shape with their equations. Cole told John Moore that Hodgkin and/or Huxley had expressed to him their reservations about whether or not they would ever achieve this goal. After having chosen the form of the equations to be used, they consolidated all of their data to find the appropriate voltage-sensitive rate constants.

Then, as Hodgkin relates in his memoirs:


Numerical integration by hand-crank calculator

Huxley began the slow work of using a Brunsviga 20 manually cranked calculator with numbers entered by a set of adjusting levers (projecting from the wheels that were rotated by the hand crank). The output was a line of digits on the wheels to be read and transcribed to paper. First, he found that the time and voltage sensitivities of the ionic conductances could be reproduced. Then the long process of numerical integration of the action potential began. Tabular records of the rate and state variables were entered into the the levers and transcribed from the dials for small increments of time. Huxley used a tedious iterative, error-correcting, numerical integration method to estimate and correct for numerical integration errors. The fact that the whole process for calculation of a 4-5 ms interval, showing the initiation of and recovery following an action potential, could be accomplished in 8 hours is astonishing. The calculated action potentials were -- with the exception of a small "gratuitous bump" late in the falling phase -- excellent reproductions of the experimental observations under a variety of conditions.


Numerical integration today - -

Of course, both the speed and power of today's desktop computers far surpass those of the 1950s, but it is interesting to compare by how much. The first numerical integration of the Hodgkin and Huxley equations on an early automatic computer in the United States took 30 minutes to accomplish what Huxley did in 8 hours (causing Kacy Cole to quip that this machine had "16 Huxley power"). With CPU clock speeds now (January 2000) in excess of 800 MHz, one's desktop computer can match the speed of an axon in calculating an action potential! But plotting takes a bit longer.