# Nerve conduction question

• Jodi

#### 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.

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?

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.

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?

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.

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.

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).

Personally, I think the answer would be independant 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.