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Assume that the length of an axon membrane of about 10 cm isexcited by an action potential (length excited = nerve speedpulse duration = 50 m/s 2.0 ms = 10cm). In the resting state, the outer surface of the axon wall ischarged positively with K+ ions and the inner wall hasan equal and opposite charge of negative organic ions, as shown inFigure P18.41. Model the axon as a parallel-plate, capacitor andtake C = oA/d and Q =CV to investigate the charge as follows: Use typicalvalues for a cylindrical axon of cell thickness d =1.0 10-8 m, axon radius r = 16.0 µm, and cell-wall dielectric constant =2.9.

Figure P18.41

(a) Calculate the positive charge on theoutside of a 10 cm piece of axon when it is not conducting anelectric pulse. [Hint: calculate the charge per unit area in termsof the number of square angstroms (2)per electronic charge. An atom has a cross-section of about 12 (1 =10-10 m)].
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Your answer differs from the correct answerby orders of magnitude. C
How many K+ ions are on the outside of the axon?
K+ ions

(b) How much positive charge must flow through the cell membrane toreach the excited state of +30 mV from the resting state of -70mV?
How many sodium ions (Na+) is this?
Na+ ions

(c) If it takes 2.0 ms for the Na+ ions to enter theaxon, what is the average current in the axon wall in thisprocess?

(d) How much energy does it take to raise the potential of theinner axon wall to +30 mV, starting from the resting potential of -70 mV?

Answers (1)

  • alberttv
    Rating:5 stars

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