Biology · Simulator 036
Inject current into a neuron and watch its membrane voltage. Weak pulses fade away; strong ones trigger an all-or-nothing action potential. Hold the current on to see repetitive firing, and find how firing rate depends on stimulus strength.
This simulator uses the FitzHugh–Nagumo model, a two-variable simplification of the Hodgkin–Huxley equations:
dv/dt = v − v³/3 − w + I
τ dw/dt = v + a − b w
v is the (scaled) membrane voltage, w a slow recovery variable (standing in for sodium inactivation and potassium activation), and I the injected current. The fast cubic term gives the explosive rise of the spike; the slow w brings the voltage back down and makes the cell temporarily refractory.
Key behaviours: a threshold (small inputs decay, larger ones fire), all-or-nothing spikes of similar size, a refractory period when a second pulse fails, and repetitive firing above a critical sustained current, at a rate that increases with I. For display, voltage is mapped to millivolts (rest ≈ −65 mV, peak ≈ +30 mV) and time to milliseconds.
Qualitative model with standard parameters (a = 0.7, b = 0.8, τ = 12.5); real neurons have many more channel types. Units are rescaled for readability.
Why is a neuron's signal strength usually encoded by how often it fires rather than by the size of each spike?
Spikes are all-or-nothing, so their height is fixed by the membrane dynamics, not by the input. What changes with stimulus strength is the time to recover and re-fire, so firing rate carries the information. Raise the sustained current from 0.35 to 0.8 and watch the rate climb (about 11 → 14 Hz in this model) while spike height stays the same. Real neurons have a much wider rate range.