Problem 1
Properties of the Peptide Bond In x-ray studies of crystalline peptides, Linus Pauling and Robert Corey found that the \(\mathrm{C}-\mathrm{N}\) bond in the peptide link is intermediate in length (1.32 Å) between a typical \(\mathrm{C}-\mathrm{N}\) single bond \(\left(1.49 \AA^{\circ}\right)\) and \(\mathrm{a} \mathrm{C}=\mathrm{N}\) double bond \((1.27\) A). 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 \(a\)-carbon atoms attached to the \(\mathrm{C}-\mathrm{N}\) are always trans to each other (on opposite sides of the peptide bond). a. What does the length of the \(\mathrm{C}-\mathrm{N}\) bond in the peptide linkage indicate about its strength and its bond order (i.e., whether it is single, double, or triple)? b. What do Pauling and Corey's observations tell us about the ease of rotation about the \(\mathrm{C}-\mathrm{N}\) peptide bond?
Problem 5
Some natural proteins are rich in disulfide bonds, and their mechanical properties, such as tensile strength, viscosity, and hardness, correlate with the degree of disulfide bonding. a. Glutenin, a wheat protein rich in disulfide bonds, imparts the cohesive and elastic character of dough made from wheat flour. Similarly, the hard, tough nature of tortoise shell results from the extensive disulfide bonding in its \(a\) keratin. What is the molecular basis for the correlation between disulfide-bond content and mechanical properties of the protein? b. Most globular proteins denature and lose their activity when they are briefly heated to \(65^{\circ} \mathrm{C}\). However, the denaturation of globular proteins that contain multiple disulfide bonds often requires longer heat exposure at higher temperatures. One such protein is bovine pancreatic trypsin inhibitor (BPTI), which has 58 amino acid residues in a single peptide chain and contains three disulfide bonds. After a solution of denatured BPTI is cooled, the protein regains its activity. What is the molecular basis for this property of BPTI?
Problem 9
Under the proper environmental conditions, the salt-loving archaeon Halobacterium halobium synthesizes a membrane protein \(\left(M_{\mathrm{r}} 26,000\right)\), known as bacteriorhodopsin, which is purple because it contains retinal (see Fig, 10-20). 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 \(a\)-helical segments, each of which traverses the bacterial cell membrane (thickness \(45 \AA\) ). Calculate the minimum number of amino acid residues necessary for one segment of \(a\) helix to traverse the membrane completely. Estimate the fraction of the bacteriorhodopsin protein that is involved in membrane-spanning helices. (Use an average amino acid residue weight of 110 .)
Problem 10
Margaret Oakley Dayhoff originated the idea of protein superfamilies after noticing that proteins with diverse amino acid sequences can have similar tertiary structures. Why can protein structure be more highly conserved than individual amino acid sequences?
Problem 14
Protein-Folding Therapies The Food and Drug Administration recently approved the drug lumacaftor for the treatment of cystic fibrosis in patients with the F508 \(\Delta\) CFTR mutation. This mutation is a genetically encoded deletion of amino acid F508 from the protein. About \(2 / 3\) of cystic fibrosis patients have this mutation, and lumacaftor is one of the first drugs that functions as a pharmacological chaperone to correct a defect in the protein-folding process. However, lumacaftor is not always effective in treating patients who have other CFTR mutations that result in misfolding. Why is lumacaftor able to correct the misfolding of some mutant CFTR proteins and not others?
Problem 15
Which structural biology method (CD, x-ray crystallography, NMR, or cryo-EM) is best suited to each task? a. Obtaining an ultra-high resolution \((<1.5 \AA)\) structure of a drug bound to its protein target b. Obtaining a low-to-medium resolution (5-10 \AA) reconstruction of the \(11 \mathrm{MDa}(11,000,000 \mathrm{Da})\) bacterial flagellar motor c. Identifying the protonation state and \(\mathrm{p} K_{\mathrm{a}}\). of a His side chain in an enzyme active site d. Determining whether a protein is intrinsically disordered or contains secondary structure elements
Problem 18
Mirror-Image Proteins As noted in \(\underline{\text { Chapter } 3}\), "The amino acid residues in protein molecules are almost all L stereoisomers." It is not clear whether this selectivity is necessary for proper protein function or is an accident of evolution. To explore this question, Milton and colleagues (1992) published a study of an enzyme made entirely of \(\mathrm{D}\) stereoisomers. The enzyme they chose was HIV protease, a proteolytic enzyme made by HIV that converts inactive viral preproteins to their active forms. Previously, Wlodawer and coworkers (1989) had reported the complete chemical synthesis of HIV protease from L-amino acids (the L-enzyme), using the process shown in Eigure 3-30. Normal HIV protease contains two Cys residues, at positions 67 and \(95 .\) Because chemical synthesis of proteins containing Cys is technically difficult, Wlodawer and colleagues substituted the synthetic amino acid L- \(a\)-amino- \(n\)-butyric acid (Aba) for the two Cys residues in the protein. In the authors' words, this was done to "reduce synthetic difficulties associated with Cys deprotection and ease product handling." a. The structure of Aba is shown below. Why was this a suitable substitution for a Cys residue? Under what circumstances would it not be suitable?
