# Hodgkin huxley neuron not spiking consistently for currents greater than threshold?

Hi I am currently studying physics at the undergraduate level. As part of my final year project Ive got to implement the HH model and investigate certain types of behaviour.

My issue is the following.

I understand that for $$I_{inj}>I_{thresh}$$ we should expect action potentials that spike at a regular frequency.

Here I've got an input current that seems to generate 2 initial spikes however no further spikes are generated. Is this physical? The presence of the initial spikes must mean that the input current is greater than the threshold, but we do not see consistent spikes across the entire stimulatory current.

Increasing the current slightly gives the expected behavior:

Is this an error in the code or is this a real physical phenomena?

EDIT------------------------------ Following Bryan Krause's suggestions, here is the full picture with the gating variables.

Case 1: Stimulus current with amplitude 35 mA with period 100ms

Case 2: Stimulus current with amplitude 37 mA with period 100ms

Case 3: Stimulus current with amplitude 500 mA with period 100ms

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• @tyersome I believe I have shown my attempt at an answer by providing the second example as going by the HH model, that is what I believe should have also been observed in case 1. Nov 14 '21 at 18:26
• What are the equations this model is solving? Your case 1 looks like a strongly damped oscillator in the voltage, whereas case 2 looks like an oscillating solution. If you have a nonlinear damping constant, that could explain the difference between case 1 and 2 qualitatively. Nov 15 '21 at 17:58
• @AtmosphericPrisonEscape The HH model is quite a famous standard model in neuroscience. Nov 15 '21 at 18:21

This is happening due to sodium channel inactivation. Some relevant sources:

https://en.wikipedia.org/wiki/Ball_and_chain_inactivation

https://www.st-andrews.ac.uk/~wjh/hh_model_intro/ (I guess this link is broken for some people? works fine for me as-is; see the links before and after instead, then)

https://neuronaldynamics.epfl.ch/online/Ch2.S2.html

In the HH model, inactivation is sometimes referred to as the "h-gate" based on the parameter they use for this inactivation, assigned the variable "h".

Sodium channel inactivation changes the action potential threshold and can even prevent action potentials completely. The easy way to understand this is that inactivated channels aren't available to participate in the positive feedback loop of an action potential. Because of this, it's not quite correct to think of a constant threshold for action potentials for a given cell/model. Instead, there is a threshold for any given holding potential or recent history of the membrane potential. Most often, you'll be concerned with the threshold at the resting membrane potential, but if you apply a constant external stimulus (or if you trigger a lot of action potentials in sequence without enough time spent at hyperpolarized or resting potentials) then the number of available sodium channels is not the same as at rest.

I would suggest a couple things...first, try other steps, too! What happens if you use an even bigger stimulus? Second...plot out the HH gating parameters m, n, and h as a function of time, not just the voltage.

• Ive added a few more cases to my original question. Based on your answer I can't understand why case 3 and case 1 look identical. Nov 15 '21 at 13:48
• @Vishal Look at the h-gate! Compare h before the first stimulus to after the first action potential (or first couple, once the APs stop). Nov 15 '21 at 14:20