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Berg JM, Tymoczko JL, Stryer L. Biochemistry. 5th edition. New York: W H Freeman; 2002.

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Biochemistry. 5th edition.

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Problems

1. Shape and dimension. (a) Tropomyosin, a 70-kd muscle protein, is a two-stranded α-helical coiled coil. Estimate the length of the molecule. (b) Suppose that a 40-residue segment of a protein folds into a two-stranded antiparallel β structure with a 4-residue hairpin turn. What is the longest dimension of this motif?

(a) Each strand is 35 kd and hence has about 318 residues (the mean residue mass is 110 daltons). Because the rise per residue in an α helix is 1.5 Å, the length is 477 Å. More precisely, for an α-helical coiled coil the rise per residue is 1.46 Å so that the length will be 464 Å.

(b) Eighteen residues in each strand (40 minus 4 divided by 2) are in a β-sheet conformation. Because the rise per residue is 3.5 Å, the length is 63 Å.

2. Contrasting isomers. Poly-l-leucine in an organic solvent such as dioxane is α helical, whereas poly-l-isoleucine is not. Why do these amino acids with the same number and kinds of atoms have different helix-forming tendencies?

The methyl group attached to the β-carbon atom of isoleucine sterically interferes with α-helix formation. In leucine, this methyl group is attached to the γ-carbon atom, which is farther from the main chain and hence does not interfere.

3. Active again. A mutation that changes an alanine residue in the interior of a protein to valine is found to lead to a loss of activity. However, activity is regained when a second mutation at a different position changes an isoleucine residue to glycine. How might this second mutation lead to a restoration of activity?

The first mutation destroys activity because valine occupies more space than alanine does, and so the protein must take a different shape, assuming that this residue lies in the closely packed interior. The second mutation restores activity because of a compensatory reduction of volume; glycine is smaller than isoleucine.

4. Shuffle test. An enzyme that catalyzes disulfide-sulfhydryl exchange reactions, called protein disulfide isomerase (PDI), has been isolated. PDI rapidly converts inactive scrambled ribonuclease into enzymatically active ribonuclease. In contrast, insulin is rapidly inactivated by PDI. What does this important observation imply about the relation between the amino acid sequence of insulin and its three-dimensional structure?

The native conformation of insulin is not the thermodynamically most stable form since it contains two separate chains linked by disulfide bonds. Insulin is formed from proinsulin, a single-chain precursor, that is cleaved to form insulin with 33 residues once the disulfide bonds have formed.

5. Stretching a target. A protease is an enzyme that catalyzes the hydrolysis of the peptide bonds of target proteins. How might a protease bind a target protein so that its main chain becomes fully extended in the vicinity of the vulnerable peptide bond?

A segment of the main chain of the protease could hydrogen bond to the main chain of the substrate to form an extended parallel or antiparallel pair of β strands.

6. Often irreplaceable. Glycine is a highly conserved amino acid residue in the evolution of proteins. Why?

Glycine has the smallest side chain of any amino acid. Its size often is critical in allowing polypeptide chains to make tight turns or to approach one another closely.

7. Potential partners. Identify the groups in a protein that can form hydrogen bonds or electrostatic bonds with an arginine side chain at pH 7.

Glutamate, aspartate, and the terminal carboxylate can form salt bridges with the guanidinium group of arginine. In addition, this group can be a hydrogen-bond donor to the side chains of glutamine, asparagine, serine, threonine, aspartate, and glutamate, and to the main-chain carbonyl group.

8. Permanent waves. The shape of hair is determined in part by the pattern of disulfide bonds in keratin, its major protein. How can curls be induced?

Disulfide bonds in hair are broken by adding a thiol and applying gentle heat. The hair is curled, and an oxidizing agent is added to re-form disulfide bonds to stabilize the desired shape.

9. Location is everything. Proteins that span biological membranes often contain α helices. Given that the insides of membranes are highly hydrophobic (Section 12.2.1), predict what type of amino acids would be in such a helix. Why is an α helix particularly suited to exist in the hydrophobic environment of the interior of a membrane?

The amino acids would be hydrophobic in nature. An α helix is especially suited to cross a membrane because all of the amide hydrogen atoms and carbonyl oxygen atoms of the peptide backbone take part in intrachain hydrogen bonds, thus stabilizing these polar atoms in a hydrophobic environment.

10. Issues of stability. Proteins are quite stable. The lifetime of a peptide bond in aqueous solution is nearly 1000 years. However, the ΔG°′ of hydrolysis of proteins is negative and quite large. How can you account for the stability of the peptide bond in light of the fact that hydrolysis releases much energy?

The energy barrier that must be crossed to go from the polymerized state to the hydrolyzed state is large even though the reaction is thermodynamically favorable.

11. Minor species. For an amino acid such as alanine, the major species in solution at pH 7 is the zwitterionic form. Assume a pKa value of 8 for the amino group and a pKa value of 3 for the carboxylic acid and estimate the ratio of the concentration of neutral amino acid species (with the carboxylic acid protonated and the amino group neutral) to that of the zwitterionic species at pH 7.

Using the Henderson-Hasselbach equation, we find the ratio of alanine-COOH to alanine-COO- at pH 7 to be 10-4. The ratio of alanine-NH2 to alanine-NH3+, determined in the same fashion, is 10-1. Thus, the ratio of neutral alanine to zwitterionic species is 10-4 × 10-1 = 10-5.

12. A matter of convention. All l amino acids have an S absolute configuration except l-cysteine, which has the R configuration. Explain why l-cysteine is designated as the R absolute configuration.

The assignment of absolute configuration requires the assignment of priorities to the four groups connected to a tetrahedral carbon. For all amino acids except cysteine, the priorities are: (1) amino group; (2) carbonyl group; (3) side chain; (4) hydrogen. For cysteine, because of the sulfur atom in its side chain, the side chain has a greater priority than does the carbonyl group, leading to the assignment of an R rather than S configuration.

13. Hidden message. Translate the following amino acid sequence into one-letter code: Leu-Glu-Ala-Arg-Asn-Ile-Asn-Gly-Ser-Cys-Ile-Glu-Asn-Cys-Glu-Ile-Ser-Gly-Arg-Glu-Ala-Thr.

LEARNINGSCIENCEISGREAT.

14. Who goes first? Would you expect Pro-X peptide bonds to tend to have cis conformations like those of X-Pro bonds? Why or why not?

No, Pro-X would have the characteristics of any other peptide bond. The steric hindrance in X-Pro arises because the R group of Pro is bonded to the amino group. Hence, in X-Pro, the proline R group is near the R group of X. This would not be the case in Pro-X.

15. Matching. For each of the amino acid derivatives shown below (A-E), find the matching set of φ and ψ values (a-e).

Image ch3fb14.jpg

A, c; B, e; C, d; D, a; E, b.

16. Concentrate on the concentration. A solution of a protein whose sequence includes three tryptophan residues, no tyrosine residues, and no phenylalanine residues has an absorbance of 0.1 at 280 nm in a cell with a path length of 1 cm. Estimate the concentration of the protein in units of molarity. If the protein has a molecular mass of 100 kd, estimate the concentration in units of milligrams of protein per milliliter of solution.

With the use of Beer's law and the value of ϵ obtained from Section 3.1 (ϵ = 3400 M-1 cm-1), the concentration of tryptophan is found to be ≈30 μM. Because there are three molecules of tryptophan per molecule of protein, the concentration of protein is ≈10 μM. There is 1 mg of protein per milliliter of solution.

Media Problem

Image mouse.jpg You can use the Structural Insights and Conceptual Insights as visual aids to help you answer Media Problems. Go to the Website: www.whfreeman.com/biochem5, and select the applicable module.

17. Inside-out, back-to-front. In the Media Problem section of the Structural Insights module on protein structure, you can examine molecular models of four putative protein structures. One of the four structures has been determined by x-ray crystallography. The other three have been made-up, and in fact are very unlikely to occur. Which are the structures that are unlikely to occur and why?

By agreement with the publisher, this book is accessible by the search feature, but cannot be browsed.

Copyright © 2002, W. H. Freeman and Company.
Bookshelf ID: NBK22487

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