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

A Hill-based reformulation of selected Hodgkin-Huxley gating relationships preserves HH-like spike waveforms and frequency-current behavior while enabling explicit parameter mapping from activation descriptors under kinetic assumptions.

• Why it matters: Mutation reports often provide steady-state voltage shifts without enough kinetic data to uniquely determine a conductance-based model, limiting reproducible links from gating changes to excitability.
• What they did: The authors reformulate HH gating with Hill relations, then use an A863P kinetic-sensitivity analysis and retrospective benchmarks on Nav1.7 mutations A863P, F1449V, and A1632G.
• The result: The Hill model reproduces the qualitative excitability increase for these Nav1.7 mutations but overestimates threshold reduction magnitude, and it does not show superior quantitative prediction versus classical HH under specified kinetic assumptions.

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