Determine the biophysical mechanism of fractional Hodgkin–Huxley memory

Determine whether the memory in fractional Hodgkin–Huxley neuron models is physically located in the gating variables or in the membrane capacitance, and establish which placement better predicts neuronal recordings.

Background

The review contrasts two incompatible fractional Hodgkin–Huxley formulations. Teka, Stockton, and Santamaria place fractional dynamics on the gating variables, whereas Weinberg places them on the membrane potential through a non-ideal fractional capacitance. These choices imply different biological mechanisms and produce different dynamical behaviors.

The review states that the two formulations have never been tested against the same data. Resolving this question would determine where a physical fractional element should be incorporated in a neuromorphic implementation and whether the two models make distinguishable predictions.

References

Weinberg instead places the order on the membrane potential, entering through a non-ideal capacitance , and obtains earlier spike peaks, excitation block at large input, faster axonal propagation and self-terminating network activity. He argues the placement explicitly: the memory in the capacitance and the memory in the gates have different biophysical origins, so imposing one order on both is unjustified. His grounding for the fractional capacitance is empirical rather than derived, resting on Curie's law by way of and on measured membrane phase angles, and he states plainly that the underlying physiological mechanism is unknown.

— Fractional-order hardware for neuromorphic computing: Is the order really the problem?  (2609.10882 - Teuscher, 9 Sep 2026) in Section 3.2, “Conductance-based models: where does the memory live?”