Modeling Neuronal Firing: A Review of The Hodgkin–Huxley Model in Computational Neuroscience

The Hodgkin–Huxley (HH) model is a set of nonlinear differential equations that describesthe initiation and propagation of action potentials through voltage-gated ion channels. Firstintroduced in 1952, the model suggests that the neuronal membrane is an electrical circuit,where the lipid bilayer functions as a capacitor and ion channels act as variable conductances.This review will discuss the theoretical background of the HH model and its mathematicaldetails, include a Python-based simulation of the HH model, and discuss the model’s widerange of applications across fields like neuroscience, cardiology, and neuromorphics. Limitations such as high computational cost, the assumption of independent gating variables, anddeterministic channel behavior are also discussed in the paper. Nevertheless, the HH modelremains a useful tool in computational neuroscience that still influences modern efforts insimulation, modeling, and engineering.