Overview of the Hodgkin–Huxley Squid
Giant Axon Model
Background
In the early 1950s, Alan Hodgkin and Andrew Huxley studied the squid giant axon (SGA) to
understand the fundamental electrical properties of neurons. Because of its large diameter
(∼500–1000 µm), the squid axon made it possible to insert electrodes and record ionic
currents. Their work led to the Hodgkin–Huxley (HH) model, which mathematically
describes how neurons generate and propagate action potentials (APs) by modeling the
dynamics of ion channels in the cell membrane.
The HH model remains a cornerstone of computational neuroscience and bioelectricity.
It provides a framework for understanding how excitable cells work, from neurons to muscle
fibers and cardiac cells.
The Core Model
The HH model treats the axonal membrane as an electrical circuit:
• Membrane capacitance (Cm ) stores charge.
• Ion channels are represented as voltage-dependent conductances with reversal (equilibrium) potentials.
• Ionic currents flow according to Ohm’s law:
Iion = g(V − E).
The membrane voltage dynamics are governed by:
Cm
dV
= Iext − (IN a + IK + IL )
dt
where V is the membrane potential, Iext is externally applied current, and IN a , IK , IL are
the sodium, potassium, and leak currents.
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Cm
IN aIKIL g
L
gN
a
gK
Vm
Simplified equivalent circuit of the HH membrane model.
Ionic Currents
Sodium (Na+ ) current:
max 3
IN a = gN
a m h(V − EN a )
Responsible for the rapid depolarization of the action potential.
Potassium (K+ ) current:
max 4
IK = gK
n (V − EK )
Responsible for repolarization.
Leak current:
IL = gL (V − EL )
Represents background passive ionic flow.
Gating Variables
Ion channel “gates” are voltage-dependent probabilities:
• m = Na+ activation
• h = Na+ inactivation
• n = K+ activation
Each evolves according to:
dx
= αx (V )(1 − x) − βx (V )x,
dt
x ∈ {m, h, n}
where αx (V ) and βx (V ) are voltage-dependent rate constants.
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Why This Matters
The HH model bridges biology, physics, and mathematics. It provides:
• A mechanistic understanding of how ion channels shape action potentials.
• A framework for linking physiology to differential equations.
• Foundational knowledge for neuroscience, electrophysiology, and biomedical engineering.
This model remains a powerful example of how quantitative analysis can explain complex
biological functions.
Membrane Potential (mV)
AP waveform
Time (ms)
Stylized action potential produced by the HH model.
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