PROBLEMS

Question 7.1

Screening the biosphere. The first protein structure to have its structure determined was myoglobin from sperm whale. Propose an explanation for the observation that sperm whale muscle is a rich source of this protein.

Question 7.2

Hemoglobin content. The average volume of a red blood cell is 87 μm3. The mean concentration of hemoglobin in red cells is 0.34 g ml−1.

213

  1. What is the weight of the hemoglobin contained in an average red cell?

  2. How many hemoglobin molecules are there in an average red cell? Assume that the molecular weight of the human hemoglobin tetramer is 65 kDa.

  3. Could the hemoglobin concentration in red cells be much higher than the observed value? (Hint: Suppose that a red cell contained a crystalline array of hemoglobin molecules in a cubic lattice with 65 Å sides.)

Question 7.3

Iron content. How much iron is there in the hemoglobin of a 70-kg adult? Assume that the blood volume is 70 ml kg−1 of body weight and that the hemoglobin content of blood is 0.16 g ml−1.

Question 7.4

Oxygenating myoglobin. The myoglobin content of some human muscles is about 8 g kg−1. In sperm whale, the myoglobin content of muscle is about 80 g kg−1.

  1. How much O2 is bound to myoglobin in human muscle and in sperm whale muscle? Assume that the myoglobin is saturated with O2, and that the molecular weights of human and sperm whale myoglobin are the same.

  2. The amount of oxygen dissolved in tissue water (in equilibrium with venous blood) at 37°C is about 3.5 × 10−5 M. What is the ratio of oxygen bound to myoglobin to that directly dissolved in the water of sperm whale muscle?

Question 7.5

Tuning proton affinity. The pKa of an acid depends partly on its environment. Predict the effect of each of the following environmental changes on the pKa of a glutamic acid side chain.

  1. A lysine side chain is brought into proximity.

  2. The terminal carboxyl group of the protein is brought into proximity.

  3. The glutamic acid side chain is shifted from the outside of the protein to a nonpolar site inside.

Question 7.6

Saving grace. Hemoglobin A inhibits the formation of the long fibers of hemoglobin S and the subsequent sickling of the red cell on deoxygenation. Why does hemoglobin A have this effect?

Question 7.7

Carrying a load. Suppose that you are climbing a high mountain and the oxygen partial pressure in the air is reduced to 75 torr. Estimate the percentage of the oxygen-carrying capacity that will be utilized, assuming that the pH of both tissues and lungs is 7.4 and that the oxygen concentration in the tissues is 20 torr.

Question 7.8

Bohr for me, not for thee. Does myoglobin exhibit a Bohr effect? Why or why not?

Question 7.9

High-altitude adaptation. After spending a day or more at high altitude (with an oxygen partial pressure of 75 torr), the concentration of 2,3-bisphosphoglycerate (2,3-BPG) in red blood cells increases. What effect would an increased concentration of 2,3-BPG have on the oxygen-binding curve for hemoglobin? Why would this adaptation be beneficial for functioning well at high altitude?

Question 7.10

Blood doping. Endurance athletes sometimes try an illegal method of blood doping called autologous transfusion. Some blood from the athlete is removed well before competition, and then transfused back into the athlete just before competition.

  1. Why might blood transfusion benefit the athlete?

  2. With time, stored red blood cells become depleted in 2,3-BPG. What might be the consequences of using such blood for a blood transfusion?

Question 7.11

I’ll take the lobster. Arthropods such as lobsters have oxygen carriers quite different from hemoglobin. The oxygen-binding sites do not contain heme but, instead, are based on two copper(I) ions. The structural changes that accompany oxygen binding are shown below. How might these changes be used to facilitate cooperative oxygen binding?

Question 7.12

A disconnect. With the use of site-directed mutagenesis, hemoglobin has been prepared in which the proximal histidine residues in both the α and the β subunits have been replaced by glycine. The imidazole ring from the histidine residue can be replaced by adding free imidazole in solution. Would you expect this modified hemoglobin to show cooperativity in oxygen binding? Why or why not?

214

Question 7.13

Successful substitution. Blood cells from some birds do not contain 2,3-bisphosphoglycerate but, instead, contain one of the compounds in parts a through d, which plays an analogous functional role. Which compound do you think is most likely to play this role? Explain briefly.

Question 7.14

Theoretical curves. (a) Using the Hill equation, plot an oxygen-binding curve for a hypothetical two-subunit hemoglobin with n = 1.8 and P50 = 10 torr. (b) Repeat, using the concerted model with n = 2, L = 1000, c = 0.01, and KR = 1 torr.

Question 7.15

Parasitic effect. When P. falciparum lives inside red blood cells, the metabolism of the parasite tends to release acid. What effect is the presence of acid likely to have on the oxygen-carrying capacity of the red blood cells? On the likelihood that these cells sickle?

Data Interpretation Problems

Question 7.16

Primitive oxygen binding. Lampreys are primitive organisms whose ancestors diverged from the ancestors of fish and mammals approximately 400 million years ago. Lamprey blood contains a hemoglobin related to mammalian hemoglobin. However, lamprey hemoglobin is monomeric in the oxygenated state. Oxygen-binding data for lamprey hemoglobin are as follows:

pO2

Y

pO2

Y

pO2

Y

0.1

.0060

  2.0

.112

 50.0

.889

0.2

.0124

  3.0

.170

 60.0

.905

0.3

.0190

  4.0

.227

 70.0

.917

0.4

.0245

  5.0

.283

 80.0

.927

0.5

.0307

  7.5

.420

 90.0

.935

0.6

.0380

10.0

.500

100

.941

0.7

.0430

15.0

.640

150

.960

0.8

.0481

20.0

.721

200

.970

0.9

.0530

30.0

.812

 

 

1.0

.0591

40.0

.865

 

 

  1. Plot these data to produce an oxygen-binding curve. At what oxygen partial pressure is this hemoglobin half-saturated? On the basis of the appearance of this curve, does oxygen binding seem to be cooperative?

  2. Construct a Hill plot using these data. Does the Hill plot show any evidence for cooperativity? What is the Hill coefficient?

  3. Further studies revealed that lamprey hemoglobin forms oligomers, primarily dimers, in the deoxygenated state. Propose a model to explain any observed cooperativity in oxygen binding by lamprey hemoglobin.

Question 7.17

Leaning to the left or to the right. The illustration below shows several oxygen-dissociation curves. Assume that curve 3 corresponds to hemoglobin with physiological concentrations of CO2 and 2,3-BPG at pH 7. Which curves represent each of the following perturbations?

  1. Decrease in CO2

  2. Increase in 2,3-BPG

  3. Increase in pH

  4. Loss of quaternary structure

Chapter Integration Problems

Question 7.18

Location is everything. 2,3-Bisphosphoglycerate lies in a central cavity within the hemoglobin tetramer, stabilizing the T state. What would be the effect of mutations that placed the BPG-binding site on the surface of hemoglobin?

Question 7.19

A therapeutic option. Hydroxyurea has been shown to increase the expression of fetal hemoglobin in adult red blood cells, by a mechanism that remains unclear. Explain why hydroxyurea can be a useful therapy for patients with sickle-cell anemia.

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