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As I understand it, ions flow down their electrochemical potentials through ion channels during a neuron's action potential. Otherwise, ion pumps work to restore and maintain the resting membrane potential. What is the energy cost of a neuron's action potential? That is, how much work must the ion pumps perform to restore the resting membrane potential after an action potential occurs?

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    $\begingroup$ There is a misconception in your question that comes up a lot, most recently here: biology.stackexchange.com/questions/62752/… The Na/K pump is not necessary for restoring membrane potential after an action potential, it is necessary for maintaining the concentration gradient of sodium and potassium ions over the long term. $\endgroup$ – Bryan Krause Jul 19 '17 at 18:23
  • $\begingroup$ Thanks for the clarification. Is it then correct to say that running the Na/K pumps to maintain the concentration gradient are the primary energetic costs of neuron action potential signaling? $\endgroup$ – fragapanagos Jul 19 '17 at 19:04
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    $\begingroup$ Yes, that's correct. The pumps will also have to operate even if there are no action potentials, though action potentials do increase the demand on the pumps. However, so does subthreshold activity: both EPSCs and IPSCs result in ion flow down concentration gradients as well. $\endgroup$ – Bryan Krause Jul 19 '17 at 19:12
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There's a few [1, 2, 3] sources that claim it's on the order of $10^8$ ATPs per action potential. The first paper (which is a review that cites the second paper) also has some equations for converting from ATPs to free energy, although that's going to be very context dependent.

If you can't access the third paper, someone has helpfully entered the relevant figures into the bionumbers site.

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