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One could read "Local anesthetics produce a very slight, virtually insignificant, decrease in potassium (K+) conductance through the nerve membrane." At Handbook of Local Anesthesia 7th edition by Stanley Malamed.

If potassium ion diffusion is not blocked, that means that there is still an ionic current which means electricity production and most important, the production of a magnetic field, which I assume is what depolarizes adjacent parts of the membrane, why this potassium ion current is not enough to start an action potential? Do the voltage generated by sodium and potassium ions must be add up in order to trigger an action potential?

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In general, action potentials are initiated by an inflow of Na+ that depolarizes the neuron. Only after that, K+ channels open up that re-polarize the membrane potential to get the neuron back in business for a next action potential. In a way, the K+ channels open only at the tail end of the action potential, Na+ leads the potential change (Fig. 1). Here is a link to a credible chapter on the action potential that describes it all in more detail.

Note that K+ channels mediating action potentials are mainly voltage gated, meaning they start opening only when the membrane potential depolarizes. The same goes for the Na+ channels; they need an initial depolarization of the cell membrane due to neurotransmitter release to start opening. It has nothing to do with electromagnetic fields.

Anesthetics work in a variety of ways, so to answer any question on the relation between anesthetics and K+ channel kinetics, more information is necessary, but I think the matter is already cleared up by this answer.

AP
Fig. 1. Channel dynamics during action potential generation. source: Idaho University

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    $\begingroup$ Thank you very much! I really appreciate it! $\endgroup$
    – Quique
    Dec 27, 2021 at 16:23
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    $\begingroup$ @Quique - no worries. If this is the answer you are looking for, please accept to let others know you found your answer $\endgroup$
    – AliceD
    Dec 27, 2021 at 16:45
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I don't know much about the effects of anesthetics, but I have taught basic nerve function at university level, so I hope I can help a little with that part. Potassium flow does not start an action potential - on the contrary, increased potassium flow makes it harder to depolarize the membrane and initiate an action potential.

A brief explanation on membrane potentials and action potentials: During rest the flow of potassium is much higher than the flow of sodium (and also chloride) and hence the membrane potential is driven towards the Nernst potential for potassium. The resting potential is often somewhere between - 40 to - 80 mV depending on cell type. To initiate an action potential the membrane potential needs to depolarize enough to exceed the threshold for opening voltage-gated sodium channels. The ion flow across the membrane will then be dominated by sodium and the membrane potential then moves towards the Nernst potential for sodium (which is positive, maybe 40-50 mV). These voltage-gated sodium channels will then close shortly after and then stay closed for some refractory period where they can't open, which brings the membrane potential back to the resting potential, because the flow will then again become dominated by potassium flow. There are also voltage-gated potassium channels in the membrane that open with a slight delay compared to the voltage-gated sodium channels. The opening of these potassium channels result in a faster return to the resting potential after the peak of each action potential.

Regarding your question on a small (but insignificant) decrease in potassium conductance: Decreased potassium flow will bring the membrane potential further away from the Nernst potential for potassium and closer to the Nernst potential for sodium, i.e. causes a slight depolarization, which makes it slightly easier for the membrane potential to exceed the threshold for opening voltage-gated sodium channels and initiate an action potential. If the flow of potassium is completely blocked, the membrane potential would be determined by the relative permeability of chloride and sodium.

The Goldman equation is the key to understanding membrane potentials, and relative permeability changes between the potassium, chloride and sodium ions (and in some cases calcium ions) is what drives an action potential.

Neuroscience by Purves et al is a good resource on all of this.

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