BSCI 426/BIOL 622                  Fall '14                         Problem Set 6

assigned: 10/09/14

due: 10/16/14

1. Ion flow through membranes:

a. Estimate the unidirectional flux per unit area of K⁺ through a phospholipid membrane given the following:
radius of K⁺ = 0.16 nm
diffusion constant of K⁺ = 1.9 x 10^-5 cm² sec^-1
dielectric constant of the membrane = 4
the concentration of K⁺ in the aqueous medium is 0.1 M

b. How long would it take for this unidirectional flux to change the concentration in a cell by 10% (ignore the flux from inside the cell to outside) given a cell that is 10 micrometers in diameter and contains 0.01 M K⁺?

c. How would the results in (a) and (b) change if the dielectric constant were 15?

2. Consider proteolipid vesicles that contain only one protein: a symport for transport of a substrate and a proton.

i) Write down an equation that expresses the equilibrium relationship between the gradient of the substrate and the gradient of protons across the membrane.

ii) If the pH in the vesicle is 8 and that outside is 7 and the transmembrane potential of the vesicle is -180 mV, what are the concentration ratios for the substrates in each of the following situations (i.e. at equilibrium)?

Charge on substrate	Stoichiometry (# protons transported per substrate)
0	1
0	2
+1	1
+1	2
-1	1
-1	2
-2	1
-2	2