Hodgkin-Huxley spiking neuron model in Python

The Hodgkin-Huxley model (published on 1952 in The Journal of Physiology [1]) is the most famous spiking neuron model (also if there are simpler alternatives like the “Integrate-and-fire” model which performs quite well). It’s made up of a system of four ordinary differential equations that can be easily integrated using several different tools. The main idea is based on an electrical representation of the neuron, considering only Potassium (K) and Sodium (Na) voltage-gated ion channels (even if it can be extended to include more channels). A schematic representation is shown in the following figure: The elements are: Cm: a capacitance per unit area representing the membrane lipid-bilayer (adopted value: 1 µF/cm²) gNa: voltage-controlled conductance per unit area associated with the Sodium (Na) ion-channel (adopted value: 120 µS/cm²) gK: voltage-controlled conductance per unit area associated with the Potassium (K) ion-channel (adopted value: 36 µS/cm²) gl: conductance per unit area associated with the leak channels (adopted […]