Problems | | | 1. Properties of the Peptide Bond In x-ray studies of crystalline peptides Linus Pauling and Robert Corey found that the C–N bond in the peptide link is intermediate in length (0.132 nm) between a typical C–N single bond (0.149 nm) and a C=N double bond (0.127 nm). They also found that the peptide bond is planar (all four atoms attached to the C–N group are located in the same plane) and that the two α-carbon atoms attached to the C–N are always trans to each other (on opposite sides of the peptide bond): | | | (a) What does the length of the C–N bond in the peptide linkage indicate about its strength and its bond order, i.e., whether it is single, double, or triple? | (b) In light of your answer to part (a), provide an explanation for the observation that such a C–N bond is intermediate in length between a double and single bond. | (c) What do the observations of Pauling and Corey tell us about the ease of rotation about the C–N peptide bond? | | 2. Early Observations on the Structure of Wool William Astbury discovered that the x-ray pattern of wool shows a repeating structural unit spaced about 0.54 nm along the direction of the wool fiber. When he steamed and stretched the wool, the x-ray pattern showed a new repeating structural unit at a spacing of 0.70 nm. Steaming and stretching the wool and then letting it shrink gave an x-ray pattern consistent with the original spacing of about 0.54 nm. Although these observations provided important clues to the molecular structure of wool, Astbury was unable to interpret them at the time. Given our current understanding of the structure of wool, interpret Astbury’s observations. | | 3. Rate of Synthesis of Hair α-Keratin In human dimensions, the growth of hair is a relatively slow process, occurring at a rate of 15 to 20 cm/yr. All this growth is concentrated at the base of the hair fiber, where α-keratin filaments are synthesized inside living epidermal cells and assembled into ropelike structures (see Fig. 7–13). The fundamental structural element of α-keratin is the α helix, which has 3.6 amino acid residues per turn and a rise of 0.56 nm per turn (see Fig. 7–6). Assuming that the biosynthesis of α-helical keratin chains is the rate-limiting factor in the growth of hair, calculate the rate at which peptide bonds of α-keratin chains must be synthesized (peptide bonds per second) to account for the observed yearly growth of hair. | | 4. The Effect of pH on the Conformations of Polyglutamate and Polylysine The unfolding of the α helix of a polypeptide to a randomly coiled conformation is accompanied by a large decrease in a property called its specific rotation, a measure of a solution’s capacity to rotate plane-polarized light. Polyglutamate, a polypeptide made up of only L-Glu residues, has the α-helical conformation at pH 3. However, when the pH is raised to 7, there is a large decrease in the specific rotation of the solution. Similarly, polylysine (L-Lys residues) is an α helix at pH 10, but when the pH is lowered to 7, the specific rotation also decreases, as shown by the following graph. | | | What is the explanation for the effect of the pH changes on the conformations of poly(Glu) and poly(Lys)? Why does the transition occur over such a narrow range of pH? | | 5. The Disulfide-Bond Content Determines the Mechanical Properties of Many Proteins A number of natural proteins are very rich in disulfide bonds, and their mechanical properties (tensile strength, viscosity, hardness, etc.) are correlated with the degree of disulfide bonding. For example, glutenin, a wheat protein rich in disulfide bonds, is responsible for the cohesive and elastic character of dough made from wheat flour. Similarly, the hard, tough nature of tortoise shell is due to the extensive disulfide bonding in its α-keratin. What is the molecular basis for the correlation between disulfide-bond content and mechanical properties of the protein? |
|
| | | | 6. Why Does Wool Shrink? When wool sweaters or socks are washed in hot water and/or dried in an electric dryer, they shrink. From what you know of α-keratin structure, how can you account for this? Silk, on the other hand, does not shrink under the same conditions. Explain. | | 7. Heat Stability of Proteins Containing Disulfide Bonds Most globular proteins are denatured and lose their activity when briefly heated to 65 °C. Globular proteins that contain multiple disulfide bonds often must be heated longer at higher temperatures to denature them. One such protein is bovine pancreatic trypsin inhibitor (BPTI), which has 58 amino acid residues in a single chain and contains three disulfide bonds. On cooling a solution of denatured BPTI, the activity of the protein is restored. Can you suggest a molecular basis for this property? | | 8. Bacteriorhodopsin in Purple Membrane Proteins Under the proper environmental conditions, the salt-loving bacterium Halobacterium halobium synthesizes a membrane protein (Mr 26,000) known as bacteriorhodopsin, which is purple because it contains retinal. Molecules of this protein aggregate into “purple patches” in the cell membrane. Bacteriorhodopsin acts as a light-activated proton pump that provides energy for cell functions. X-ray analysis of this protein reveals that it consists of seven parallel α-helical segments, each of which traverses the bacterial cell membrane (thickness 4.5 nm). Calculate the minimum number of amino acids necessary for one segment of α helix to traverse the membrane completely. Estimate the fraction of the bacteriorhodopsin protein that occurs in α-helical form. Justify all your assumptions. (Use an average amino acid residue weight of 110.) | | 9. Biosynthesis of Collagen Collagen, the most abundant protein in mammals, has an unusual amino acid composition. Unlike most other proteins, collagen is very rich in proline and hydroxyproline (see p. 172). Hydroxyproline is not one of the 20 standard amino acids, and its incorporation in collagen could occur by one of two routes: (1) proline is hydroxylated by enzymes before incorporation into collagen or (2) a Pro residue is hydroxylated after incorporation into collagen. To differentiate between these two possibilities, the following experiments were performed. When [14C]proline was administered to a rat and the collagen from the tail isolated, the newly synthesized tail collagen was found to be radioactive. If however, [14C]hydroxyproline was administered to a rat, no radioactivity was observed in the newly synthesized collagen. How do these experiments differentiate between the two possible mechanisms for introducing hydroxyproline into collagen? | | 10. Pathogenic Action of Bacteria That Cause Gas Gangrene The highly pathogenic anaerobic bacterium Clostridium perfringens is responsible for gas gangrene, a condition in which animal tissue structure is destroyed. This bacterium secretes an enzyme that efficiently catalyzes the hydrolysis of the peptide bond indicated in red in the sequence: | | | H2O | –X–Gly–Pro–Y– | → | –X–COO− + H3N+–Gly–Pro–Y |
| | where X and Y are any of the 20 standard amino acids. How does the secretion of this enzyme contribute to the invasiveness of this bacterium in human tissues? Why does this enzyme not affect the bacterium itself? | | 11. Formation of Bends and Intrachain Cross-Linkages in Polypeptide Chains In the following polypeptide, where might bends or turns occur? Where might intrachain disulfide cross-linkages be formed? | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | Ile– | Ala– | His– | Thr– | Tyr– | Gly– | Pro– | Phe– | Glu– | Ala– | Ala– | Met– | Cys– | Lys– | Trp– | Glu– | Ala– | Gln– | Pro– | Asp– |
| | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | Gly– | Met– | Glu– | Cys– | Ala– | Phe– | His– | Arg– |
| | 12. Location of Specific Amino Acids in Globular Proteins X-ray analysis of the tertiary structure of myoglobin and other small, single-chain globular proteins has led to some generalizations about how the polypeptide chains of soluble proteins fold. With these generalizations in mind, indicate the probable location, whether in the interior or on the external surface, of the following amino acid residues in native globular proteins: Asp, Leu, Ser, Val, Gln, Lys. Explain your reasoning. | | 13. The Number of Polypeptide Chains in an Oligomeric Protein A sample (660 mg) of an oligomeric protein of Mr 132,000 was treated with an excess of 1-fluoro-2,4-dinitrobenzene under slightly alkaline conditions until the chemical reaction was complete. The peptide bonds of the protein were then completely hydrolyzed by heating it with concentrated HCl. The hydrolysate was found to contain 5.5 mg of the following compound: | | | | However, 2,4-dinitrophenyl derivatives of the α-amino groups of other amino acids could not be found. | (a) Explain why this information can be used to determine the number of polypeptide chains in an oligomeric protein. | (b) Calculate the number of polypeptide chains in this protein. | | 14. Molecular Weight of Hemoglobin The first indication that proteins have molecular weights greatly exceeding those of the (then known) organic compounds was obtained over 100 years ago. For example, it was known at that time that hemoglobin contains 0.34% by weight of iron. | (a) From this information determine the minimum molecular weight of hemoglobin. | (b) Subsequent experiments indicated that the true molecular weight of hemoglobin is 64,500. What information did this provide about the number of iron atoms in hemoglobin? | | 15. Comparison of Fetal and Maternal Hemoglobin Studies of oxygen transport in pregnant mammals have shown that the O2-saturation curves of fetal and maternal blood are markedly different when measured under the same conditions. Fetal erythrocytes contain a structural variant of hemoglobin, hemoglobin F, consisting of two α and two γ subunits (α2γ2), whereas maternal erythrocytes contain the usual hemoglobin A (α2β2). | | | (a) Which hemoglobin has a higher affinity for oxygen under physiological conditions, hemoglobin A or hemoglobin F? Explain. | (b) What is the physiological significance of the different oxygen affinities? Explain. |
|
|