Neuronal excitability and parameter variability in the Hodgkin-Huxley model

Abstract

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 variability and obscures the mechanisms by which robustness and degeneracy arise in excitable systems. Here, we reintroduce parameter variability into the Hodgkin-Huxley model and embed uncertainty and global sensitivity analysis into model construction. We digitized sodium and potassium rate constant data from the original Hodgkin and Huxley figures and used bootstrap resampling to estimate the variability of the voltage-dependent kinetic parameters. We then propagated these uncertainty estimates through a spatially extended squid axon cable model using large-scale Monte Carlo simulations. 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, sampling hundreds of thousands of parameter sets 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. At the same time, the regularly firing subpopulation exhibited a broad distribution of firing rates, with a mean that matched the classic Hodgkin-Huxley prediction. In the phasic subpopulation, action potential propagation and conduction velocity varied widely yet remained consistent with experimental ranges. Finally, global sensitivity analysis during spiking shows uniformly small first-order indices but large total-order indices, indicating that excitability is primarily governed by strong interactions among parameters rather than by any single conductance or kinetic parameter. These results support a population-based view of conductance-based modeling in which biologically relevant behavior emerges from structured regions of parameter space. Author summaryNeurons are often modelled by first fitting ion-channel data to a few parameters, then integrating them into a single-neuron model. This typical method masks the fact that actual experiments show variability and that many different parameter sets can yield similar electrical behavior. In this research, we explored what happens when we keep rather than average out that variability. We revisited Hodgkin and Huxleys classic squid giant axon studies and derived ranges for sodium and potassium channel parameters by resampling digitized points from the original Hodgkin-Huxley figures using bootstrap resampling. We then ran simulations of hundreds of thousands of squid axon models, each with a unique, experimentally grounded parameter set, and analyzed the collective results. This showed that the most common response was a single action potential rather than repetitive firing, aligning with the axons role in the rapid escape response. Additionally, we discovered that no single parameter alone controls spiking; rather, it depends on interactions among multiple parameters. Our findings advocate a practical change in biophysical modeling: instead of hunting for a single best-fit model, researchers should estimate parameter uncertainty directly from data, create large ensembles that sample this uncertainty, and perform sensitivity analyses on these ensembles before choosing any model for further study.