Calculating Power for Active Na+ Pumping During Nerve Conduction

[Jodi]

Hi; Could somebody please help me with the following question: During the action potential, Na+ ions move into the cell at a rate of 3.03E-7 mol/m^2*s. How much power must be produced by the "active Na+ pumping" system to produce this flow agaisnt a +33.9 mV potential difference? Assume that the axon is 12.0 cm long and 20.4 um in diameter. I do not understand how to go about this question, and how do I incorporate the rate into it as well? Could somebody please help me. Thanks a lot.

 

[quasar987]

There's one thing I don't get. The ions are moving insides a cell. At first I though this axon thing is a sort of tube through which the ions move. But the axon's 12 cm long, so that can't be it.

What's the axon?

 

[Jodi]

The axon...

Hi; The axon is sort of like a tube, because impulses travel through the cell by coming in from small tube like appendages called dendrites, into the cell body, and than travel out via the axon...which is like a long tail. Signals are received by the dendrites and are propagated along the axon. I hope that clarifies some things up. Thanks.

 

[quasar987]

Not really. So do you know if this problem does or does not juste reduces to finding the power needed to pump the ions along the axon?

 

[Jodi]

Um I'm thinking that I will have to use this equation: R= resitivity*L/A, and therefore I need that 12 cm to use as my length and the diameter to use as my area. I'm guessing I can use this equation to solve for R, but than how do I use the rate? That is what confuses me. Thanks.

 

[quasar987]

Ah I see. I had not seen the problem from this angle. But what is the resistivity of the liquid in the axon? If we don't have that, we're kinda stuck.

 

[Jodi]

I'm not sure about the resitivity, but would this help: That the concentration of Na+ inside axon is 15 mol/m^3 and the concentration of Na+ ouside axon is 140 mol/m^3.
And the area of a cylinder (like the axon) is 2(pi)(r)(L).

 

[quasar987]

Personally, I think the answer would be independent of the length of the axon.

The work needed to transport a charge q through a potential different V is W=qV. So the power is P = dW/dt = dq/dt V = I*V (where I is the current).

At 1e (the elementary charge) Coulomb per ion, calculate the total charge passing through a "slice" of the axon every second. (This is easy, given the rate 3.03E-7 mol/m^2*s). That's the current. Multiply that by V and that's your power.