This is a real model of a nerve cell, the 1952 Hodgkin–Huxley equations, running live in your browser about 96,000 steps a second. Turn the sound on: every click is one action potential, because the sound is the membrane voltage.
Firing rate0 Hz
Membrane now−65 mV
Last spike lasted–
How hard the cell is pushed (noisy, like real synapses).
Blocks voltage-gated Na⁺ channels.
Blocks voltage-gated K⁺ channels.
Sound needs a tap first (your browser's rule). It clicks: keep headphones low.
Inside one spike
The last action potential, slowed down about 1,000 times. Red is the Na⁺ conductance (m³h), grey the K⁺ conductance (n⁴). The dashed line is a normal spike, for comparison.
Push harder and the spikes come faster; they do not get bigger. The nervous system codes "how strong" with rate, not size.
Try: slide Input from 3 to 12.
Na⁺ in, then K⁺ out
Na⁺ channels open first and the voltage shoots up (depolarization). K⁺ channels open a little later and bring it back down (repolarization), overshooting into a brief undershoot.
Watch red, then grey, above.
Refractory periods
Right after a spike, Na⁺ channels sit inactivated (the h gate). For about 1–2 ms nothing can fire it again (absolute); for a few ms more only a stronger zap can (relative).
Try: zap twice at 1 ms, then 8 ms.
Two drugs, two jobs
Lidocaine blocks Na⁺ channels: no spike starts, so no pain signal leaves. TEA blocks K⁺ channels: spikes still start, but each one takes longer to end, and with too little K⁺ current the cell cannot hold its rest: it starts firing on its own.
In a neuron at 37 °C, [K+] is 140 mM inside and 4 mM outside, so its K+ equilibrium potential is E_K = 61.5 mV × log10(4/140) ≈ −95 mV. If extracellular [K+] rises to 8 mM while intracellular [K+] stays at 140 mM, E_K becomes about:
Pick one. The red pen does the rest.
The deciding lineThe Nernst equation for K+ at 37 °C is E_K = 61.5 mV × log10([K+]out/[K+]in); E_K depends on the logarithm of the concentration ratio, so doubling [K+]out shifts it by 61.5 × log10 2 ≈ 18.5 mV toward zero.
Why C: 61.5 × log10(8/140) = 61.5 × (−1.243) = −76 mV. Equivalently, doubling [K+]out adds 61.5 × log10 2 = 18.5 mV to −95 mV: the smaller K+ gradient makes E_K less negative.
Why each choice fails
AScale slip: doubling [K+]out does not double E_K. The potential tracks the logarithm of the ratio, and a smaller K+ gradient makes it less negative: −95 + 18.5 ≈ −76 mV, not 2 × (−95) = −190 mV.
BDirection reversed: the step size, 18.5 mV, is right, but raising [K+]out shrinks the K+ gradient, so E_K moves toward zero (−76 mV), not away from it (−113 mV).
CHolds: 61.5 × log10(8/140) = −76 mV, 18.5 mV less negative than −95 mV.
DScale slip: the K+ gradient does halve (140/4 = 35 to 140/8 = 17.5), but E_K depends on the logarithm of that ratio, not the ratio itself, so it shifts by only 61.5 × log10 2 = 18.5 mV, to −76 mV, not to −95/2 ≈ −47 mV.