Abstract
Nerve conduction in unmyelinated fibers has long been described based on the equivalent circuit model and cable theory. However, without the change in ionic concentration gradient across the membrane, there would be no generation or propagation of the action potential. Based on this concept, we employ a new conductive model focusing on the distribution of voltage-gated sodium ion channels and Coulomb force between electrolytes. Based on this new model, the propagation of the nerve conduction was suggested to take place far before the generation of action potential at each channel. We theoretically showed that propagation of action potential, which is enabled by the increasing Coulomb force produced by inflowing sodium ions, from one sodium ion channel to the next sodium channel would be inversely proportionate to the density of sodium channels on the axon membrane. Because the longitudinal number of sodium ion channel would be proportionate to the square root of channel density, the conduction velocity of unmyelinated nerves is theoretically shown to be proportionate to the square root of channel density. Also, from a viewpoint of equilibrium state of channel importation and degeneration, channel density was suggested to be proportionate to axonal diameter. Based on these simple basis, conduction velocity in unmyelinated nerves was theoretically shown to be proportionate to the square root of axonal diameter. This new model would also enable us to acquire more accurate and understandable vision on the phenomena in unmyelinated nerves in addition to the conventional electric circuit model and cable theory.
Highlights
The generation and conduction of an action potential on the surface of an axonal membrane has been described as a physiological electric circuit, known as an “equivalent circuit model” (Figure 1; Hartline and Colman, 2007)
The conventional concept of equivalent circuit model and cable theory were absolutely wonderful models, both of which well reproduced the electric phenomenon happening along the axonal membrane (Hodgkin and Huxley, 1952)
The previous model did not fully accommodate the principles that the axoplasm is consisted of randomly migrating ion particles and water molecules, without closed circuit of metal leads to transmit electrical potential, and that action potential cannot be generated without preceding change of ionic concentration gradient across the axon membrane
Summary
The generation and conduction of an action potential on the surface of an axonal membrane has been described as a physiological electric circuit, known as an “equivalent circuit model” (Figure 1; Hartline and Colman, 2007). On the basis of this equivalent circuit model, the conduction of the nerve is often described by using a theory in which the conduction is regarded as an electric current on imaginary electric longitudinal leads running inside and outside the axon membrane, known as a cable theory (Koch, 1984). In this theory, based on Ohm’s law and Kirchhoff ’s law, the membrane potential at a specific position and time (VM(x, t)) can be described by the equation shown below, known as a cable equation.
Published Version (Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have