Potassium Conductances & Repetitive Firing

The membrane follows the standard Hodgkin & Huxley (1952) equations C dV/dt = I_inj − I_Na − I_KDR − I_A − I_leak, with the classic fast Na⁺ current (ḡNa m³h) and delayed-rectifier K⁺ current (ḡKDR n⁴) using their original squid-axon rate constants. A second, optional K⁺ current uses the fast-activating, fast-inactivating A-type kinetics of Connor & Stevens (1971) (ḡA a³b) — both K⁺ currents share the same reversal potential. Before each run, the model is first let settle for 200 ms with no injected current, at whatever K⁺ conductances are currently toggled on, so the trace always starts from that configuration's own true resting state rather than from an artificial fixed value — this is also why removing enough K⁺ conductance can leave the cell already depolarized, or already firing, before the stimulus even begins.

The delayed rectifier is what repolarizes the spike: switch it off and the membrane has nothing to pull it back down after Na⁺ channels open, so spikes broaden into a plateau and the afterhyperpolarization disappears — with it fully off here, the cell settles into a sustained depolarized "up" state instead of a resting potential. The A-type current activates quickly but also inactivates quickly at depolarized potentials; net, it acts as a brake on the first spike and on firing rate, because it turns on as the membrane approaches threshold. That's why enabling it delays the first spike and lowers firing rate for a given current — the mechanism behind "type I" excitability differences between neurons that fire fast from rheobase and ones that fire slowly and stay slow.

Spike width is measured as the time the trace spends above −20 mV around each peak; afterhyperpolarization (AHP) is how far the trough after a spike falls below that configuration's own resting potential (a negative value means the trace never gets below rest at all — e.g. when the delayed rectifier is off). The f–I curve tab repeats this at a range of current amplitudes and plots the number of action potentials fired against injected current, using the same K⁺ channel toggles as the Spike Train tab.