Hodgkin–Huxley model

Key takeaways

Hodgkin–Huxley model belongs to biology; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hodgkin–Huxley model to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hodgkin–Huxley model from memory before moving on to harder problems.

Reference excerpt

The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical engineering characteristics of excitable cells such as neurons and muscle cells. It is a continuous-time dynamical system. Alan Hodgkin and Andrew Huxley described the model in 1952 to explain the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon. They received the 1963 Nobel Prize in Physiology or Medicine for this work.

Basic components The typical Hodgkin–Huxley model treats each component of an excitable cell as an electrical element (as shown in the figure). The lipid bilayer is represented as a capacitance (Cm). Voltage-gated ion channels are represented by electrical conductances (gn, where n is the specific ion channel) that depend on both voltage and time. Leak channels are represented by linear conductances (gL). The electrochemical gradients driving the flow of ions are represented by voltage sources (En) whose voltages are determined by the ratio of the intra- and extracellular concentrations of the ionic species of interest. Finally, ion pumps are represented by current sources (Ip). The membrane potential is denoted by Vm. Mathematically, the current flowing into the capacitance of the lipid bilayer is written as

I c = C m d V m d t {\displaystyle I_{c}=C_{m}{\frac {{\mathrm {d} }V_{m}}{{\mathrm {d} }t}}}

and the current through a given ion channel is the product of that channel's conductance and the driving potential for the specific ion

I i = g i ( V m − V i ) {\displaystyle I_{i}={g_{i}}(V_{m}-V_{i})\;}

where V i {\displaystyle V_{i}} is the reversal potential of the specific ion channel. Thus, for a cell with sodium and potassium channels, the total current through the membrane is given by:

I = C m d V m d t + g K ( V m − V K ) + g N a ( V m − V N a ) + g l ( V m − V l ) {\displaystyle I=C_{m}{\frac {{\mathrm {d} }V_{m}}{{\mathrm {d} }t}}+g_{K}(V_{m}-V_{K})+g_{Na}(V_{m}-V_{Na})+g_{l}(V_{m}-V_{l})}

where I is the total membrane current per unit area, Cm is the membrane capacitance per unit area, gK and gNa are the potassium and sodium conductances per unit area, respectively, VK and VNa are the potassium and sodium reversal potentials, respectively, and gl and Vl are the leak conductance per unit area and leak reversal potential, respectively. The time dependent elements of this equation are Vm, gNa, and gK, where the last two conductances depend explicitly on the membrane voltage (Vm) as well.

Ionic current characterization In voltage-gated ion channels, the channel conductance is a function of both time and voltage ( g n ( t , V ) {\displaystyle g_{n}(t,V)} in the figure), while in leak channels, g l {\displaystyle g_{l}} , it is a constant ( g L {\displaystyle g_{L}} in the figure). The current generated by ion pumps is dependent on the ionic species specific to that pump. The following sections will describe these formulations in more detail.

Voltage-gated ion channels Using a series of voltage clamp experiments and by varying extracellular sodium and potassium concentrations, Hodgkin and Huxley developed a model in which the properties of an excitable cell are described by a set of four ordinary differential equations. Together with the equation for the total current mentioned above, these are:

… excerpt ends here. Continue reading the full article.

Illustrations

Hodgkin–Huxley model: The voltage v(t) (in millivolts) of the Hodgkin–Huxley model, graphed over 50 milliseconds. The injected current varies from −5 nanoamps to 12 nanoamps. The graph passes through three stages: an equilibrium stage, a single-spike stage, and a limit cycle stage. — The voltage v(t) (in millivolts) of the Hodgkin–Huxley model, graphed over 50 milliseconds. The injected current varies from −5 nanoamps to 12 nanoamps. The graph passes through three stages: an equilibrium stage, a single-spike stage, and a limit cycle stage.

Worked examples

Example 1 — a first encounter with Hodgkin–Huxley model

Start with the simplest possible case. Write down what Hodgkin–Huxley model claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In biology, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hodgkin–Huxley model before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hodgkin–Huxley model ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hodgkin–Huxley model

In research: Hodgkin–Huxley model appears in biology research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hodgkin–Huxley model in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hodgkin–Huxley model is common in secondary-school and first-year university syllabi. It links to neighbouring topics Computational neuroscience, Electrophysiology, Ion channels, so understanding it makes those chapters shorter.
In everyday life: Look for Hodgkin–Huxley model outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Hodgkin–Huxley model in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hodgkin–Huxley model means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hodgkin–Huxley model out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hodgkin–Huxley model in simple terms?

The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical engineering characteristics of excitable cells such as neurons…

Why does Hodgkin–Huxley model matter?

Because it connects several biology ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hodgkin–Huxley model?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hodgkin–Huxley model.