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Potassium channels help to repolarize the cell after depolarization. But if the potassium channels are blocked, potassium ions cannot flow out of the cell to increase the membrane potential. Thus, one would expect that, at least for some period of time, the cell would be "stuck" in a depolarized state.

How long can this state last? Can a neuron go on indefinitely in a depolarized state if potassium ion channels are blocked? Will it find some other way to depolarize the cell? Will the cell die?

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The voltage-gated potassium channels are there only to swiftly repolarize the membrane potential. Ultimately it is the Na,K-ATPase that has to pump the various ions back where they belong (Na out, K in), also when potassium channels are active. So when the potassium channels are blocked, the Na,K-ATPase will restore the membrane potential, albeit in the order of seconds instead of milliseconds.

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    $\begingroup$ That was my intuition, but I couldn't find anyone who would confirm that the pumps have enough power to actually do that sufficiently to return the membrane potential to its resting voltage. excellent! $\endgroup$
    – Stan Shunpike
    Jul 22, 2015 at 17:24

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