Is the sodium micro-channel responsible for axon properties? Hodgkin and Huxley - from empirical equations to physical modeling.
Hodgkin and Huxley solved the problem of formation and propagation of action potential in nerve axon half a century ago. They founded out that the sodium conductance increases to a maximum value within 1ms and than is inhibited within next 1ms. The sodium conductance is a very complex function of both membrane potential and time. Hodgkin and Huxley described sodium conductance by an empirical function which requires 6 functions and 20 adjustable parameters. Almost 30 years ago Sigworth and Neher showed that it is opening probability of sodium channel which is the function of time, and its amplitude is 2.5pA. Since then problem of kinetics of sodium channel seemed to be almost solved. Unfortunately, this is not the case. To explain axon properties by the 2.5pA channel found by Sigworth and Neher it’s density at axon membrane should be 1-2 per µm2 and local electric behavior of axon membrane should be erratic. Such behavior have never been shown experimentally. Moreover there are 30 to 500 fold more sodium channels in the axon membrane than measured by Sigworth and Neher.
Due to electric noise it is not possible to measure fast ion channels of amplitude lower than 0.5pA directly by the patch clamp method. Such channels do exist. It is possible to built a model low amplitude voltage gated sodium channel in which amplitude is a function of both time and potential. Such model channel stores up to a dozen of ions like in magazine of automatic rifle. When open the model channel conducts in a short time only limited number of ions in series. Its current amplitude is in order of 1fA and conductance less than 0.1pS. The Hodgkin and Huxley empirical equation can be described by a model channel in which there are only 8 constants of clear physical meaning.