Universal scaling and ferroelectric hysteresis regimes in the giant squid axon propagating action potential: a Phase Space Approach

The experimental data for the giant squid axon propagated action potential is examined in phase space. Plots of capacitive and ionic currents vs. potential exhibit linear portions providing temperature dependent time rates and maximum conductance constants for sodium and potassium channels. First order phase transitions of ionic channels are identified. Incorporation of time rates into Avrami equations for fractions of open channels yields for each channel a temperature independent dimensionless constant that is remarkably close in value to the fine structure constant. It also yields temperature independent scaling exponents θx. Evidence is presented that the action potential traverses a ferroelectric hysteresis loop starting with a linear outgoing current followed by incoming sodium current that is accompanied with a channels lattice morphing in the negative resistance region. This results in a second order phase transition polarization flip at the peak of the action potential, followed by closing of sodium and opening of potassium channels, and finally closing the loop by reversing the polarization flip as the resting potential is reached. The existence of this hysteresis loop for the giant squid action potential suggests the possibility of neurons with two stable states, the basis for memory storage and retrieval.