Hill-Based Reformulation of the Hodgkin-Huxley Model for Mapping Gating Changes to Neuronal Excitability

Conductance-based models link ion-channel gating to neuronal excitability, but mutation reports often provide steady-state voltage shifts without sufficient kinetic measurements to specify a unique model. We introduce a Hill-based reformulation of selected Hodgkin-Huxley (HH) gating relationships and evaluate its usefulness under this low-information constraint. The hybrid formulation retains canonical HH-like spike waveforms and frequency-current behavior after a modest remapping of applied current, while providing an explicit mapping from reported activation descriptors to model parameters under specified assumptions. An A863P kinetic-sensitivity analysis shows how steady-state constraints and kinetic assumptions jointly shape excitability predictions in both classical HH and Hill-based implementations. The Hill formulation makes this mapping reproducible through explicit parameter relations, whereas refitting classical HH rates requires additional fitting choices; both approaches still require kinetic assumptions. Retrospective benchmarks using the Nav1.7 mutations A863P, F1449V, and A1632G show that the Hill-based model captures the qualitative increase in excitability but overestimates the magnitude of threshold reduction. Classical HH comparisons for A863P demonstrate that similar qualitative predictions can also be obtained under specified kinetic assumptions. These findings support the Hill formulation as a reproducible framework for mapping reported gating changes onto HH-like excitability, without establishing superior quantitative prediction of mutation effects. Quantitative transfer to mutation-specific neuronal behavior requires additional kinetic and cellular constraints.