HPC Tier Module
Hodgkin-Huxley Action Potential
Fire a Hodgkin-Huxley action potential in exact f64 RK4, anchored to rest, threshold, and refractoriness.
See it run - a worked example, 100% in this browser tab
The problem
Neurophysiology teaching and numerical verification need a Hodgkin-Huxley model that reproduces the classic resting, threshold, and refractory behavior exactly and reproducibly, not an opaque spike generator.
The local-first solution
This plugin integrates the cited 1952 HH membrane and m/h/n gating equations in exact f64 RK4 and checks the trajectory against closed-form anchors - the current-balance rest point, the all-or-none threshold, and the absolute refractory period - in your browser with no upload.
What it does
RK4 integration of the HH membrane ODE with m^3 h Na+, n^4 K+, and leak currents
Voltage-dependent alpha/beta rate functions with exact removable-singularity limits
Closed-form resting potential from the ionic current-balance root
All-or-none spike threshold with a supra-threshold overshoot above 0 mV
Absolute refractory period under a closely-spaced second pulse
GeoNum conditioning of the near-cancelling net ionic current with a Richardson fallback
Honest scope
Exact: the HH membrane and gating ODEs, the published rate functions with their removable-singularity limits, and classical RK4. It is a single isopotential, space-clamped membrane patch using the squid-axon parameter set at ~6.3 C with no temperature (Q10) rescaling; it does not model spatial propagation along the axon, other ion channels, synaptic input, channel noise, or any specific mammalian neuron. Research and education tool only - not a model of any individual's nervous system, not a medical device, and not medical advice.
Authorities cited
- Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117(4), 500-544. - the membrane equation, the m/h/n gating kinetics, and the original voltage-dependent rate-function fits to the squid giant axon. DOI 10.1113/jphysiol.1952.sp004764.
- Dayan, P., & Abbott, L. F. (2001). Theoretical Neuroscience. MIT Press, Ch. 5-6 - the modern -65 mV-convention HH rate functions (eqns 5.22-5.24) and the standard parameter set (g_Na=120, g_K=36, g_L=0.3, E_Na=50, E_K=-77, E_L=-54.387 mV).
- Gerstner, W., & Kistler, W. M. (2002). Spiking Neuron Models. Cambridge Univ. Press, Sec. 2.2 - the Hodgkin-Huxley model, threshold / all-or-none behaviour, and refractoriness.
- Izhikevich, E. M. (2007). Dynamical Systems in Neuroscience. MIT Press, Ch. 2 - the HH model as a dynamical system; rest as a stable equilibrium, the spike as a large excursion, and the refractory return.
- Koch, C. (1999). Biophysics of Computation. Oxford Univ. Press, Ch. 6 - ionic currents, conductances, and the biophysical interpretation of the HH gating variables.
- Press, W. H., et al. (2007). Numerical Recipes, 3rd ed., Sec. 17.1 - classical fourth-order Runge-Kutta (RK4), local truncation error O(h^5) / global O(h^4), used to integrate the HH system.
Fire an action potential
Compute the spike, threshold, and refractory behavior in your browser, with nothing uploaded to anyone's cloud. Save the run to Sandbox, attach it to a Worklog case, or share the parameter set through a Gate portal.