Neuronal excitability and parameter variability in the Hodgkin-Huxley model

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.Author summary: Neurons are typically modeled by collapsing noisy ion-channel data into a single best-fit parameter set. I asked what happens to the classic Hodgkin-Huxley model of the squid giant axon when that uncertainty is preserved instead. Bootstrap resampling of the original 1952 rate-constant data, propagated through hundreds of thousands of cable simulations, produces a structured population of firing behaviors. Three results stand out. The dominant response is a single action potential rather than the textbook train of spikes, consistent with the axon’s role in escape behavior. The canonical 1952 parameter set represents a minority of regularly firing cases rather than the population’s typical behavior. And no single parameter controls spiking on its own; excitability emerges from interactions among many parameters. My results thus suggest that the Hodgkin-Huxley model is most informative not as a privileged parameter set but as an experimentally constrained ensemble of behaviors, and that biophysical modeling should estimate parameter uncertainty from data, build ensembles, and analyze them before drawing conclusions from any single model.