How do four differential equations reproduce a spike? · Lobeworks/17

One equation charges the membrane as a capacitor, Cm dV/dtC_m,dV/dtCm​dV/dt, with the sodium, potassium and leak currents, and three describe gates that relax towards voltage-dependent targets: mmm opens sodium, hhh closes it, nnn opens potassium.

How do four differential equations reproduce a spike?

One equation charges the membrane as a capacitor, Cm dV/dtC_m,dV/dtCm​dV/dt, with the sodium, potassium and leak currents, and three describe gates that relax towards voltage-dependent targets: mmm opens sodium, hhh closes it, nnn opens potassium. The spike falls out of their different speeds. The fast mmm feeds back on the voltage and drives it up, then the slower hhh and nnn catch up and bring it down, and the time hhh takes to recover is the refractory period. Hodgkin and Huxley fitted the rates to the squid giant axon in 1952 and the equations reproduced the shape, threshold and speed of the real impulse.