Neuronal excitability and parameter variability in the Hodgkin-Huxley model

by Alon Korngreen

Biophysically detailed neuron models are often built as a one-way pipeline in which voltage-clamp data are reduced to a single set of best-fit channel parameters, which are then combined into a deterministic spiking model. This practice discards experimentally observed scatter and fitting uncertainty, obscuring the mechanisms by which robustness and degeneracy arise in excitable systems. Here, I reintroduce fitted-parameter uncertainty into the Hodgkin-Huxley model and embed uncertainty and global sensitivity analysis into model construction. I digitized sodium and potassium rate-constant data from the original Hodgkin and Huxley figures and used bootstrap resampling to estimate uncertainty in the fitted voltage-dependent kinetic parameters. I then propagated these uncertainty estimates through a spatially extended squid axon cable model using large-scale Monte Carlo simulations, in which each sample defined a complete set of kinetic, conductance, passive, and structural parameters. At the channel level, first-order Sobol sensitivity indices revealed that all kinetic parameters contribute to output variance in a strongly time-dependent manner, with distinct parameters controlling transient and steady-state behavior for potassium and sodium conductances. At the level of neuronal excitability, the simulations produced a heterogeneous population of firing behaviors, including non-firing, phasic, regular, and spontaneous activity. Across stimulus amplitudes, the dominant firing mode was a single spike at stimulus onset, consistent with the physiological role of the squid giant axon in rapid escape behavior. The canonical 1952 Hodgkin-Huxley parameter set fell within the regularly firing minority subpopulation, rather than representing a unique or dominant solution. In the phasic subpopulation, action potential propagation and conduction velocity varied widely yet remained within experimental ranges. Finally, global sensitivity analysis during spiking showed uniformly small first-order Sobol indices but large total-order indices, indicating that excitability is governed primarily by strong interactions among all parameters rather than by any subset. Together, these results support reframing the Hodgkin-Huxley model as an experimentally constrained ensemble of behaviors rather than a single privileged parameter set, with physiologically relevant firing patterns emerging from structured regions of the parameter space.