  Classical models for predicting current flow in excitable cells such as
axons, originally proposed by Hodgkin and Huxley, rely on empirical
voltage-gating parameters that quantify ion transport across sodium and
potassium ion channels. We propose a primitive model for predicting these
currents based entirely on well-established ion diffusion coefficients. Changes
inside the excitable cell due to the opening of a central sodium channel are
confined to a growing hemisphere with a radius that is governed by the sodium
ion diffusion coefficient. The sodium channel, which is open throughout the
calculation, activates and deactivates naturally due to coupled
electrodiffusion processes. The characteristic time of current pulses, which
are in the picoampere range, increases from 10$^{-5}$ to 10$^{-1}$ s as channel
density is decreased from 10,000 to 1 channel per micrometer squared. Model
predictions are compared with data obtained from giant squid axons without
invoking any gating parameters.
