About the Hodgkin-Huxley Model
The Hodgkin-Huxley model (1952) is a mathematical model describing how action potentials in neurons are initiated and propagated. Alan Hodgkin and Andrew Huxley received the 1963 Nobel Prize in Physiology or Medicine for this work, which laid the foundation for computational neuroscience.
The model consists of four coupled ordinary differential equations: the membrane equation Cm * dV/dt = I_ext - g_Na * m^3 * h * (V - E_Na) - g_K * n^4 * (V - E_K) - g_L * (V - E_L), plus three gating variable equations for m (sodium activation), h (sodium inactivation), and n (potassium activation), each following first-order kinetics with voltage-dependent rate constants.
When the injected current exceeds a threshold (about 6.3 uA/cm^2), the neuron generates repetitive action potentials (spikes). The sodium channels (g_Na) activate rapidly causing depolarization, then inactivate while potassium channels (g_K) activate to repolarize the membrane. The interplay of these currents creates the characteristic spike waveform.
Use the injected current slider to control neuronal firing. At low currents the neuron rests silently; above threshold it fires periodically. Try the presets to explore different regimes: resting, threshold, regular spiking, fast spiking, and strong-drive spiking. The phase portrait reveals the limit cycle during spiking. In reduced mode, only the voltage trace is shown for focused observation.