Gale Rhodes
Department of Chemistry
University of Southern Maine
Portland, Maine 04104-9300
Saturation equations provide the basis for understanding a vast array of ligand-protein interactions.
Here is some additional practice with saturation equations.
USM Students: AFTER completing your work on these problems, ask your instructor for solutions.
Use the following data:
1. Calculate the fractional saturation Y for myoglobin when pO2 is 2.43 torr and when pO2 is 5.5 torr.
2. Calculate the fractional saturation Y for hemoglobin when pO2 is 15.0 torr and when pO2 is 87.5 torr.
3. The difference in fractional saturation between two locations A and B is defined as DY = |YA - YB|. (|x| means the absolute value of x.) DY is a measure of how much oxygen a transporter can deliver between two locations having different pO2 .
a. In the lungs, pO2 is about 100 torr. In active muscle, pO2 is about 20 torr. Calculate the difference in fractional saturation between lungs and muscle tissue (DY = |Ylungs - Ytissues|) for hemoglobin.
b. In the light of your answer to a, approximately how many molecules of O2 will be transported from lungs to tissues (in one trip) by 100 molecules of hemoglobin? How many millimoles of O2 will be transported from lungs to tissues (in one trip) by 1.00 millimole of hemoglobin?
4. a) Calculate DY = |Ylungs - Ytissues| for a mutant hemoglobin that is noncooperative. Assume that the mutant has a normal P50.
b) On what part of the hemglobin molecule would you expect to find the abnormal amino acid in this mutant: at the oxygen-binding site, at the heme-binding site, at subunit interfaces, on exposed surface, or at the 2,3-BPG binding site? Explain.
5. a) Calculate DY = |Ylungs - Ytissues| for a mutant hemoglobin that shows normal cooperativity, but has a P50 of 10.0 torr.
b) On what part of the hemglobin molecule would you expect to find the abnormal amino acid in this mutant: at the oxygen-binding site, at the heme-binding site, at subunit interfaces, on exposed surface, or at the 2,3-BPG binding site? Explain.
6. This one is for calculus lovers... anyone out there?. (Adapted from Biochemistry, L. Stryer, Feeeman, 1995, problem 10, p.180.)
a) Calculate the optimal P50 for an oxygen-transporting protein that moves oxygen between two compartments A (pO2 = a torr) and B (pO2 = b torr). Hint: You are seeking the value of P50 for which the function DY = |YA - YB| has a maximum value. To find maxima and minima of mathematical functions, you differentiate the function with respect to the desired variable (in this case, P50 ), set the derivative equal to zero (because the derivative is zero when the function is at a max or min), and solve the resulting equation for P50. It turns out (take my word for it) that you get the same result whether the protein is cooperative or not. so make it easy on yourself and assume that n = 1.
b) Use the result in a) to calculate the optimum P50 for hemoglobin in transporting oxygen from lungs to tissues. This is the value of P50 that maximizes DY = |Ylungs - Ytissues|.
c) Are you surprised that P50 for wild-type hemoglobin differs from this optimal value? Can you think of possible reasons?