Stimulus currents and neuronal responses

As I understand it, if a subthreshold current of unlimited duration is injected in a neuron, a passive response is observed, like an RC circuit. The membrane potential is depolarized by some arbitrary amount, before gradually stabilizing due to more and more current flowing through the resistive branch of the circuit.

So yesterday, I was looking at some HH simulators when I noticed that increasing the duration of a normally subthreshold current pulse would allow it to depolarize the membrane to threshold. How is that? Can someone please point out the error in my logic here?

Also to clarify: I am not familiar with the dynamics of the HH model, so please take it as such.

If you inject a current into a model cell with no active components (no voltage-gated channels), you'll see a capacitive response, because that's basically all you have: the membrane acts like a capacitor in parallel with a resistor. Adding a current charges the capacitor and you have an "exponential decay"-shaped change towards a new equilibrium potential.

When you stop injecting current, you'll again have an "exponential decay"-style return to the baseline.

However, the HH model includes active conductances: voltage-gated channels that change state according to voltage. "Action potential" is the name given to a positive-feedback opening of sodium channels: voltages more positive than rest open some channels, which open additional channels, etc. "Threshold" refers to a voltage that triggers a full positive-feedback activation of these channels. Sometimes it's stated to be a particular voltage, but that's not really true; threshold depends on the whole state of the system: voltage and state of all the gates of different channel types.

However, any depolarization will open some voltage-gated channels beyond those open at rest, it's just that up until threshold there aren't enough open to trigger the positive feedback. The reason is that voltage-gated sodium channels don't just open and close, they also inactivate. In the HH model, this is represented by the "h" gate.

If you inject a brief positive current, you'll open some channels and get a little "bump" in the voltage afterwards that then returns to baseline as those channels close/inactivate. If you inject a longer current, you'll open a few more channels and also the "bump" from the open channels will sum with your injected current. If you're right around threshold, that could cause you to exceed the threshold for positive feedback and therefore an action potential.

Though the question is different, a lot of this same reasoning is found in my answer to another question here: Hodgkin huxley neuron not spiking consistently for currents greater than threshold?

• Thank you for your prompt answer! I think I get it now. Can you just allow me one more question? It’s been bothering me a bit! Apr 14, 2022 at 20:59
• It goes like this: a stimulus current, at the beginning of an AP, depolarizes the membrane towards threshold right? For some reason textbooks always pretend like they don’t exist once the membrane reaches threshold and an action potential fires. So let’s assume that the stimulus current is on, for the whole duration of the action potential. My question is: would that change any of the AP’s characters? For example, increase its amplitude or duration? The one with amplitude specially resonates with me, as I imagine that the current would depolarize the membrane all the time while it’s flowing. Apr 14, 2022 at 21:15
• @CalyxOfHelp Happy to answer if you post as a separate question. Would be ideal if you quoted from your textbook or another citable source, and take some steps to think about what the answer might be and describe your thinking (sort of "show your work"). That'll help me write an answer that specifically addresses the gaps you have. Apr 14, 2022 at 21:18
• Ok, I'll try to write it soon, thank you! Apr 14, 2022 at 21:40