To explore the effect of myelination on the leakiness of an axon, let\'s compare
ID: 53308 • Letter: T
Question
To explore the effect of myelination on the leakiness of an axon, let's compare the rate of diffusion of potassium in an isolated axon with and without myelination. The axon is cylindrical in shape, with a membrane thickness of 20 nm, a length of 150pm and a diameter of 30 pm. Because this is an isolated axon, the ends of the axon are covered with glass and will not allow diffusion. Therefore when calculating surface area you will ignore the "top" and "bottom" of the cylinder; area is given by A =2 pi rh. The concentration of potassium inside of the cell is 3.0 Times 10-5 M and the concentration outside of the cell is 1.7 Times 10-5 M. The diffusion coefficient for K+ is D = 1.9 Times 10-9 m2/s. When the axon has myelin, 70% of the surface is covered with Schwann cells. Compare the diffusion rate (mol/s) of potassium with and without myelin in our axon. (HINT: Be careful of your units! These might be useful: 1 L = 1 Times 10-3 m3; 1 mu m = 10-6m; 1 nm = 10-9 m.) With all other values being equal, what would be the diameter (mu m) of an un-myelinated axon that has the same diffusion rate for potassium as our myelinated axon? Using the same concentrations for potassium given above, what is the membrane potential (mV) due to potassium in our axon? The system is at 30 degree C; R/F = 8.528 Times 10-4 V/KExplanation / Answer
A.
The following are the values given:
Thickness of membrane = 20nm
Length of the membrane = 150 m, diameter of the membrane = 30m
Concentration of K+ inside of the cell = 3.0 × 10-5
Concentration of K+ outside of the cell = 1.7 × 10-5
Diffusion coefficient D = 1.9 × 10-9
Diffusion rate (jx) =
=
The rate of diffusion of K+ ions when the membrane surface is 70% covered, is
0.5 × 10-12 m/sec.
Diffusion rate without myelin sheath is calculated as given below:
Thickness of the myelin sheath is 20 nm. Without myelin sheath, the diameter of the axon is 29.98 m, whereas the radius is 14.99 m
Diffusion across the membrane is calculated as given below:
Surface area of myelin sheath =
Without myelin sheath, the permeability of membrane for K+ ions is 1.7 ×10-12 m/sec
C.
Membrane potential is calculated from Nernst equation