Fine-structure constant and hysteresis regimes in the giant squid propagating action potential.

Abstract

We present a phase space based phenomenological theory for the steady propagation of the action potential using the Rosenthal-Bezanilla experimental data. Time derivatives of giant squid action potential, its velocity of propagation, the radius of the axon and its capacitance, and the resistivity of axoplasm, yield the total ionic, capacitive, and membrane currents of the charge conserving cable equation. Evidence is presented that the sodium channels lattice has a polarization flip at the inception of the action potential and the corresponding flip reversal at the peak of the action potential while traversing a ferroelectric hysteresis loop. The polarization flip at the inception of the action potential is followed by capacitive polarization current known as gating current. The polarization flip at the peak of the action potential is preceded by a small sodium polarization current associated with sodium current inactivation. Ionic currents and sodium polarization ionic currentsare taken to have the familiar structure, as the product of maximum conductance, driving force, and fraction of open channels. Fractions of open channels are fitted in the lab frame by modified Avrami equations seeded with the value of the fine-structure constant α = 0.0072973... . The existence of sodium channels domains with two different symmetries, albeit only one being stable in squid axon, suggests the possibility of neurons with at least 2 stable states, the necessary condition for storage and retrieval of memories. It is expected that presented results will provide the framework for further analysis of thermodynamic phase changing behavior, the role of quantum mechanics in the flow of ions trough ionic channels and in particular the role of ferroelectric sodium channels lattice behavior in storage and retrieval of memories and nerve excitability.