Key takeaway: In 1952, Alan Hodgkin and Andrew Huxley shoved a glass capillary electrode inside the massive axon of a squid. By utilizing a "voltage-clamp" technique, they discovered that the action potential is entirely driven by the physical flow of Sodium (Na⁺) and Potassium (K⁺) ions through microscopic channels in the cell membrane. They elegantly modeled this biological membrane as a basic electrical circuit using Ohm's law, capacitors, and resistors.
The Equivalent Electrical Circuit
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Biology as Electricity
Mapping cells to circuits.
- The Capacitor ($C_m$): The lipid bilayer of the cell membrane acts as a perfect electrical insulator between the conductive salty fluids on the inside and outside of the cell. This means it physically stores electrical charge exactly like a capacitor.
- The Resistors ($g_{Na}, g_{K}$): The ion channels embedded in the membrane act as variable resistors (or conductances, $g$). Because they open and close depending on the voltage, they are physically acting as voltage-dependent potentiometers.
- The Batteries ($E_{Na}, E_{K}$): The concentration gradients of the ions (pumped by the Na/K ATPase) act as individual batteries driving the current.
$$ I = C_m \frac{dV_m}{dt} + I_{Na} + I_K + I_L $$
$$ I = C_m \frac{dV_m}{dt} + g_{Na}m^3h(V_m - E_{Na}) + g_K n^4(V_m - E_{K}) + g_L(V_m - E_L) $$
The total current $I$ injected into the cell splits into two paths: it either charges the membrane capacitor $C_m$, or it flows outwards through the specific ion channels (Sodium, Potassium, and Leak). The variables $m, h,$ and $n$ are the "gating variables"—probabilities between 0 and 1 that dictate exactly what percentage of the ion channels are physically swung open at any given millisecond.
Hodgkin-Huxley Action Potential Simulator