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Outward Sodium Current, Fine-structure Constant and Ferroelectric Hysteresis Regimes in the Giant Squid Axon Propagating Action Potential: a Phase Space Approach

We derive a charge-conserving phase space cable equation for the propagating action potential, expressing ionic, membrane, and capacitive currents as functions of membrane potential. Analysis of the ionic current during the recovery phase reveals an outward sodium current, unobserved in voltage-clamp experiments, arising from the axoplasmic modulated Ohmic current creating a positive charge gradient opposing the sodium concentration gradient. Using a single assumption, that the fraction of open channels follows a time-dependent modified Avrami (mAvrami) equation that incorporates the ionic time rate yielding the fine-structure constant as a dimensionless scaling factor, we fit experimental ionic currents across different ions and biological temperatures. These results accurately predict several established observations, including the delayed onset of sodium inactivation, the magnitude of gating charges, and the fact that the fraction of open sodium channels is about 1/5 when most of the gating charges have moved. These alignments with already established facts logically increase confidence that the remaining predictions/hypotheses will be confirmed by future experiments. Notably, the mAvrami kinetics predictions include a universal role for the fine-structure constant in ion traversing ionic channels, and temperature-independent ionic activation energies are suggestive of quantum tunneling. Further predictions reveal continuous phase transitions in sodium channels at both initiation and peak of the action potential, implying symmetry changes in sodium channel states and pointing to a potential mechanism for memory encoding and storage. Also, the calculated optimal sodium channel density closely matches observed values. We also show that the action potential follows a heat-releasing ferroelectric hysteresis loop.

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