---
title: "Hodgkin–Huxley Model: How a Squid Axon Fires an Action Potential Interactive Lab | Sandbox Physics"
description: "What turns a small shock into an all-or-none spike, and what do the clamp currents reveal? Positive feedback through sodium channels."
canonical_url: "https://sandboxphysics.com/labs/hodgkin-huxley-clamp/"
language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/hodgkin-huxley-clamp/"
last_modified: "2026-10-31"
---

FR42 · Neural statistical physics

# Hodgkin–Huxley Model: How a Squid Axon Fires an Action Potential

**What turns a small shock into an all-or-none spike, and what do the clamp currents reveal?** Positive feedback through sodium channels. A shock that depolarizes the membrane past about 6.5 millivolts opens sodium gates faster than potassium gates, so sodium rushes in and the voltage climbs to about 105 millivolts. Slower sodium inactivation and potassium opening then bring it back. Below that threshold the membrane just rings and settles.

Shock, step or voltage-clamp the 1952 Hodgkin–Huxley membrane. Watch the gates open, find the threshold and compare the ion movement with their Table 5.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

The membrane follows the equations of Hodgkin and Huxley (1952) for a space-clamped squid axon, with their rate constants and conductances. The voltage u is the depolarization from rest in mV, positive inside, so it has the opposite sign to the 1952 paper. Currents are per square centimetre and outward positive. The bright trace is the model. The grey trace is a synthetic recording: the model plus amplifier noise drawn from a seeded generator, not measured squid data. The sodium and potassium movement uses the definition of their Table 5, net movement minus the resting flux over the same window.

Synthetic recording over the model truth

Sodium and potassium currents in the model

The same protocol over a range of settings

More numbers and how they are computed

- **Extreme of the synthetic recording**: $0$
- **Extreme of the model trace**: $0$
- **Amplifier noise added to the recording**: $0$
- **Shock threshold at this temperature**: $0$
- **Rate factor from temperature**: $0$
- **Spikes in the sweep**: $0$
- **Maximum rate of rise**: $0$
- **Window for the ion movement**: $0$

Every readout is measured on the model trace. The synthetic recording only shows what an amplifier with this noise would add. The summary curve reruns the model once per point. The exported file holds both traces, the seed and the settings.

Physics tutorial

## A spike is a race between sodium and potassium gates

**Background** The membrane of a squid giant axon is a thin insulator with sodium and potassium channels in it. In 1952 Hodgkin and Huxley held its voltage fixed, measured the currents that flowed, and wrote four equations that reproduce the action potential they had not fitted.

**Why it matters** The same equations answer several questions at once: why there is a threshold, why a second shock soon after the first does nothing, why a steady current gives a train of spikes, and why releasing a hyperpolarized membrane can fire it.

Start with the essentials

- **Focus question**: What turns a small shock into an all-or-none spike, and what do the clamp currents reveal?
- **One-sentence intuition**: Depolarization opens the fast sodium activation gates $m$, sodium flows in and depolarizes the membrane further. The slower inactivation $h$ and potassium activation $n$ then end the spike. In this model the feedback wins only above a shock of about $6.5\ \mathrm{nC\,cm^{-2}}$ at 6.3 °C.

### Core mathematical model

#### Current balance of the membrane

$$
C_M\frac{du}{dt}=-\bar g_{\mathrm{Na}}m^3h\,(u-u_{\mathrm{Na}})-\bar g_{\mathrm K}n^4(u-u_{\mathrm K})-\bar g_l(u-u_l)+I
$$

Here $u$ is the depolarization from rest and outward current is positive. Each ionic current is a conductance times the distance from its reversal potential, $u_{\mathrm{Na}}=115\ \mathrm{mV}$ and $u_{\mathrm K}=-12\ \mathrm{mV}$.

#### First-order gates

$$
\frac{dx}{dt}=\phi\,[\alpha_x(u)(1-x)-\beta_x(u)\,x]=\frac{x_\infty(u)-x}{\tau_x(u)},\qquad x\in\{m,h,n\}
$$

Each gate relaxes toward its steady value with a voltage-dependent time constant. Near rest, $\tau_m$ is more than twenty times shorter than $\tau_h$ and $\tau_n$, which is why sodium wins at first.

#### A brief shock sets the starting voltage

$$
\Delta u=\frac{q}{C_M},\qquad C_M=1\ \mu\mathrm{F\,cm^{-2}}\ \Rightarrow\ 1\ \mathrm{nC\,cm^{-2}}\mapsto1\ \mathrm{mV}
$$

A shock much shorter than any gate time only charges the capacitor, so its charge per area is the initial depolarization.

### Common difficulties

#### The peak is not the sodium potential

**Typical misconception** At the top of the spike the membrane reaches the sodium reversal potential.

**Better mental model** The model peaks near $105\ \mathrm{mV}$, about $10\ \mathrm{mV}$ below $u_{\mathrm{Na}}$, because potassium and leak conductances are already pulling the other way.

#### Threshold is not a fixed voltage

**Typical misconception** A spike fires whenever the voltage crosses one fixed value.

**Better mental model** The threshold depends on the state of the gates. Shortly after a spike a larger shock fails, and a release from hyperpolarization fires with no depolarizing shock at all.

### Run the experiment

1. 01

   #### Fire one spike

   Leave the one-spike preset running and watch the gates beside the axon.

   **What to observe:** The shock starts the membrane at $15\ \mathrm{mV}$. Sodium gates open first, the voltage peaks near $105\ \mathrm{mV}$ about 1.2 ms later, and potassium brings it back below rest.

2. 02

   #### Step below threshold

   Choose Just below threshold.

   **What to observe:** A shock of $6\ \mathrm{nC\,cm^{-2}}$ only rings and decays. The model threshold is $6.50\ \mathrm{nC\,cm^{-2}}$, consistent with the 1952 report that 7 mV fires and 6 mV does not.

3. 03

   #### Clamp the voltage

   Choose Voltage clamp separates the currents.

   **What to observe:** At a command of $60\ \mathrm{mV}$ the current is first inward, about $-1.27\ \mathrm{mA\,cm^{-2}}$, carried by sodium, then outward, about $1.64\ \mathrm{mA\,cm^{-2}}$, carried by potassium.

Physical conclusion

An action potential is what a capacitor does when a fast positive feedback and a slower negative feedback share it. The voltage clamp separates the two in time, which is how Hodgkin and Huxley measured them.

## Related experiments and articles

Statistical physics of neurons · Reading path

### From a charged membrane to avalanches in a network of neurons

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **The membrane stores charge like a capacitor**](https://sandboxphysics.com/stories/neural-statistical-physics/the-membrane-as-a-capacitor/)
2. [Article **Voltage clamp separates the sodium and potassium currents**](https://sandboxphysics.com/stories/neural-statistical-physics/voltage-clamp-and-gates/)
3. [Article **The action potential from one equation, all or none**](https://sandboxphysics.com/stories/neural-statistical-physics/the-action-potential/)
4. [Article **Reading Hodgkin and Huxley 1952 with questions in hand**](https://sandboxphysics.com/stories/neural-statistical-physics/reading-hodgkin-and-huxley-1952/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)