Diffusive propagation of nervous signals and their quantum control

Abstract

The governing theory of electric signal transfer through nerve fibre, as established by Hodgkin and Huxley in the 1950s, uses for the description of action potential a clever combination of various concepts of electrochemistry and circuit theory; however, this theory neglects some fundamental features of charge transport through any conductor, e.g., the existence of a temporary charged layer on its boundary accompanied by an external electric field. The consequences of this fact are, among others, the introduction of a non-adequate concept of “conduction velocity” and the obscure idea of saltatory propagation of action potential in myelinaed nerve fibres. Our approach, based on standard transport theory and, particularly, on the submarine cable model, describes the movement of the front of the action potential as a diffusion process characterized by the diffusion constant DE. This process is physically realized by the redistribution of ions in the nervous fluid (axoplasm), which is controlled by another diffusion constant DΩ ≪ DE. Since the action bound with the movement of Na+ and K+ cations prevailing in the axoplasm is comparable with the Planck constant ℏ (i.e. DΩ → ℏ∕2M, where M is ion mass), signal transfer is actually a quantum process. This fact accounts for the astonishing universality of the transfer of action potential, which is proper to quite different species of animals. As is further shown, the observed diversity in the behaviour of nerve tissues is controlled by the scaling factor $$\sqrt{(D_{\Omega} / D_E)}$$ , where DΩ is of a quantum nature and DE of an essentially geometric one.