The frequency of nerve action potentials generated by applied currents

The steady frequency of nerve action potentials generated by maintained current stimuli (frequency-current curve) for the Hodgkin-Huxley equations was calculated both for a uniformly polarized membrane and a point polarized cable. The possible range of steady frequencies that can be maintained with a point polarized cable at 6.3 °C is very limited and the range is even smaller at higher temperatures. Several alterations to the Hodgkin-Huxley equations were considered, but it was concluded that further mechanisms were probably required to explain the wide range of frequencies displayed by some nerve cells. The frequency range was correlated with the time course of the afterpotentials produced by a propagated action potential. The excitability of the cable to a second current stimulus also followed the afterpotentials closely. The frequency-current curve is markedly non-linear, though, because of the non-linear current-voltage curve, the frequency is quite linearly related to the steady voltage produced if regenerative activity is blocked. The results are compared with simplified models and the experimental literature. It is likely that further mechanisms are required to explain the adaptation, variability and wide range of steady frequencies displayed by some nerve cells.