Physics Problem with Axon as Electrical Circuit

[Chrys]

Can someone help with this? I do not understand how the right answer is the right answer.


During an axon’s rest state, a net positive charge travels across the leakage channels and across the Na+/K+ pump:
A.

at equal rates and in the same direction.
B.

at equal rates but in opposite directions.

Correct Answer
C.

at different rates but in the same direction.
D.

at different rates and in opposite directions.
Explanation:
B. Since there is “no net transfer of charge across the membrane” in the axon’s rest state, the answer must be B. Any movement of positive charge by the battery (the Na+/K+ pump) must be cancelled by an equal, but opposite, movement of positive charge through the leakage channels.


What?! I kinda get the reasoning they are saying about balancing BUT both the Na/K pump and the K leak channels have net positive charge moving outside the cell. The Na/K puts 3+ out for every 2+ in, so net is +1 out. And K leaks let K+ out slowly to balance concentration...so how the heck does this answer make any sense? I just don't see how these would cancel each other out

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[milski]

I cannot find anything claiming that the K-leaky channels are unidirectional. It seems quite possible that at equilibrium they allow movement of K+ ions into the cell. Then again, that leaves you with the long term problem of the continuously raising concentration of K+.

 

[Chrys]

Okay that is a really good point.

 

[Shjanzey]

The most important part of the question is where they state "an axon's rest state". Right away you know equilibrium has been established so you can assume that the net charge is not changing. Look for the answer that gives you no change in net charge.

The only one that satisfies this is B. Why? Think about it as a system as a whole. Include both the "leakage" and the "pumps" into your thought processes. With both of them working together there should still be no change in resting potential. Since you know that K+ is pumped in and Na+ is pumped out, you know the charge flow is in opposite directions.

Now the only choice you can choose is one where it allows the axon to stay at rest, which means the charge going in is the same as the charge going out. Any other choice would represent an initiation of either hyperpolarization or depolarization.

I hope that clears it up for you.

 

[Gauss44]

Berkeley Review says that sodium leaks into the cell by diffusion during equilibrium because the concentration gradients are slightly stronger than the electrical gradients. (..and potassium leaks out during equilibrium. So the sodium/potassium pump off-sets that.)