Chapter 33 — Exercises

Sixty problems on amino acids, peptides, and proteins. Drawing required wherever a structure or mechanism is asked for. ∗ marks problems with full worked solutions in Appendix Answers to Selected Exercises.

Section A — Amino acid structure

33.1∗ (routine) Draw the structure of each amino acid in zwitterion form (at physiological pH 7.4): (a) glycine, alanine, valine (b) lysine, arginine, histidine (c) aspartate, glutamate (d) serine, threonine, cysteine

33.2 (routine) Identify the side-chain chemistry class for each amino acid in 33.1.

33.3∗ (routine) Draw glycine, alanine, and valine in 3D. Identify the L-configuration. Why is glycine the only achiral natural amino acid?

33.4 (routine) Why are L-amino acids the dominant configuration in biology? What are the consequences for protein synthesis machinery?

33.5 (moderate) Some bacteria use D-amino acids in their cell walls (e.g., D-alanine in peptidoglycan). Why is this evolutionarily significant? Connect to antibiotic mechanism.

33.6 (challenge) A drug like vancomycin recognizes the D-Ala-D-Ala dipeptide of bacterial cell walls. Why is the recognition specific? What happens if the bacteria mutates to D-Ala-D-Lac? (Answer: vancomycin resistance.)

Section B — Zwitterions and pI

33.7∗ (routine) Calculate pI for: (a) glycine (pKa values 2.34, 9.60) (b) aspartate (pKa values 1.99, 3.86, 9.82) (c) lysine (pKa values 2.18, 8.95, 10.53) (d) histidine (pKa values 1.82, 6.04, 9.17)

33.8 (routine) A solution at pH 4 contains glycine, aspartate, and lysine. Predict the dominant ionic form of each.

33.9 (moderate) Use isoelectric focusing (IEF): if a peptide of pI 7.4 is placed in an IEF gel with a pH gradient from 3 to 11, where does it stop migrating? Why?

33.10 (moderate) A peptide has 3 acidic residues, 1 basic residue, and an N-terminal amine + C-terminal carboxyl. Predict the pI without solving exactly.

33.11 (moderate) A protein has a pI of 8.5. At pH 7, what is its net charge? At pH 10? At pH 5?

33.12 (challenge) Histidine's pKa of 6.0 is unusual. Where does it come in protein function? Hint: think about acid/base catalysis at physiological pH.

Section C — Peptide bond

33.13∗ (routine) Draw the structure of the tripeptide Gly-Ala-Ser (in N-to-C order). Identify each peptide bond.

33.14 (routine) Why does the peptide bond have partial double-bond character? Sketch the resonance structures.

33.15 (routine) A peptide bond's cis-trans equilibrium: 99% trans for non-Pro peptide bonds; ~5-10% cis when followed by proline. Why is proline special?

33.16 (moderate) Calculate the half-life of a peptide bond in water at 25 °C, given that the rate constant is 3 × 10⁻¹¹ s⁻¹ (Wolfenden 2011). Result should be ~600 years.

33.17 (challenge) A protease can hydrolyze a peptide bond in 10 ms. Calculate the rate enhancement vs. uncatalyzed (use 33.16). Verify it's ~10¹² × — characteristic of high-quality enzymes.

Section D — SPPS (Solid-Phase Peptide Synthesis)

33.18∗ (routine) Outline the SPPS synthesis of the dipeptide Gly-Ala using Fmoc strategy. Show all steps.

33.19 (routine) What is the role of: (a) the resin in SPPS (b) Fmoc protection on each amino acid (c) HBTU coupling reagent (d) piperidine

33.20 (routine) Why is Fmoc protection preferred over Boc in modern SPPS?

33.21 (moderate) Design an SPPS synthesis of a 5-mer peptide: Met-Phe-Ser-Lys-Glu. Identify the coupling steps and the side-chain protecting groups needed.

33.22 (moderate) Why must side chains of Lys and Glu be protected during SPPS? What protecting groups are typically used?

33.23 (challenge) A student's SPPS of a 30-mer peptide fails at step 25 (low coupling yield for one specific amino acid). Suggest possible causes and remedies.

33.24 (challenge) Insulin (51 amino acids) was synthesized chemically in 1963 (Du Vigneaud & Bauer). Why is this an extraordinarily difficult synthesis? Why was it eventually replaced by recombinant DNA technology?

Section E — Protein structure

33.25∗ (routine) Identify each as primary, secondary, tertiary, or quaternary structure: (a) the amino acid sequence of insulin (b) the α-helix of myoglobin (c) the 3D fold of myoglobin (d) the four subunits of hemoglobin

33.26 (routine) Sketch the geometry of an α-helix: ~3.6 amino acids per turn, ~5.4 Å pitch. What hydrogen bond stabilizes it (residue i to residue i+4)?

33.27 (routine) Sketch the geometry of a β-sheet (parallel and antiparallel). What hydrogen bonds connect adjacent strands?

33.28 (moderate) Why does proline disrupt α-helices and β-sheets? Hint: the cyclic side chain has restricted backbone angles.

33.29 (moderate) Why are α-helices and β-sheets preferred over random coil? Use thermodynamic arguments.

33.30 (challenge) The Ramachandran plot shows allowed φ and ψ angles. Why are some regions allowed (α-helix at φ ≈ -60°, ψ ≈ -45°) and others forbidden? Hint: van der Waals clashes between the substituents.

Section F — Protein folding

33.31∗ (routine) Anfinsen's experiment: a denatured protein refolds to the native state. What does this prove about protein structure determinants?

33.32 (routine) What is the dominant force in protein folding? Identify the hydrophobic effect and explain why nonpolar side chains cluster in the interior.

33.33 (moderate) A protein is denatured by 8 M urea at room temperature. What is the role of urea? How does removing it allow refolding?

33.34 (moderate) Disulfide bonds (Cys-Cys) form during oxidative folding. What is the role of cysteine in stabilizing tertiary structure?

33.35 (challenge) Levinthal's paradox: a 100-residue protein has 10⁶⁰ possible conformations; could not search them all in the age of the universe. How do proteins fold in seconds? Identify the funnel-shaped energy landscape and partial folding pathways.

33.36 (challenge) Some proteins fail to fold (intrinsically disordered proteins, IDPs). What is their function? How can they "function" without folding?

Section G — Protein folding in disease

33.37∗ (routine) Misfolding diseases include Alzheimer's, Parkinson's, prion diseases, cystic fibrosis. Identify the common chemistry: misfolded proteins aggregate (form non-functional structures).

33.38 (routine) The amyloid-β peptide of Alzheimer's disease forms β-sheet aggregates ("plaques"). Sketch a generic amyloid β-sheet stack. Why are these aggregates so stable?

33.39 (moderate) Prion diseases (mad cow, CJD): the misfolded prion protein recruits normal protein to misfold. How is this different from amyloid disease?

33.40 (moderate) Cystic fibrosis is caused by misfolding of the CFTR protein (a chloride channel). Why does the misfolded form not reach the cell surface? Connect to quality control in the cell.

33.41 (challenge) Some drugs (e.g., tafamidis for transthyretin amyloidosis) bind misfolded proteins to stabilize them. Identify the chemistry: the drug locks the protein in a non-aggregating conformation.

Section H — AlphaFold and computational biology

33.42∗ (routine) AlphaFold (2020) predicts protein structure from sequence. What is the algorithm's input? What is its output?

33.43 (routine) Why is AlphaFold's accuracy near experimental? What kinds of information does it use (multiple sequence alignment, coevolutionary signal, etc.)?

33.44 (moderate) A new protein has a sequence with no homologs. Predict whether AlphaFold can model it accurately. What are the limitations?

33.45 (challenge) How does AlphaFold handle protein-protein complexes? Why is this harder than single-protein folding?

33.46 (challenge) AlphaFold-Multimer extends AlphaFold to predict multi-protein complexes. Some predictions are excellent; others fail. What features make a complex predictable vs. not?

Section I — Enzyme catalysis

33.47∗ (routine) Sketch the serine protease catalytic triad: Ser, His, Asp. Identify each residue's role.

33.48 (routine) Mechanism of serine protease (chymotrypsin) catalysis: 6 elementary steps. Sketch them. Identify the acyl-enzyme intermediate.

33.49 (moderate) Why is His important in serine protease? It acts as both general acid and general base. Explain.

33.50 (moderate) Other enzyme mechanisms: cysteine proteases (use Cys-SH instead of Ser-OH), aspartic proteases (use Asp side chains for general acid catalysis), metalloproteases (use Zn²⁺). Compare each.

33.51 (challenge) HIV protease is an aspartic protease. Drugs against it (saquinavir, ritonavir) are designed as transition state analogs. Sketch a generic HIV protease inhibitor with the central -OH (a transition state mimic).

33.52 (challenge) Carbonic anhydrase (a Zn²⁺ enzyme) catalyzes CO₂ + H₂O ↔ HCO₃⁻ + H⁺. What is the role of zinc?

Section J — Spectroscopy and analytics

33.53∗ (routine) UV absorbance of a protein: peak at 280 nm. Which residues contribute? (Trp, Tyr, Phe.) Why is this useful for protein concentration measurement?

33.54 (routine) A circular dichroism (CD) spectrum shows distinct signatures for α-helix, β-sheet, and random coil. Which feature in the CD allows distinguishing α from β?

33.55 (moderate) A peptide is digested by trypsin (cleaves after Lys or Arg) and the peptides are analyzed by mass spectrometry. Predict the cleavage products of: H₂N-Arg-Ala-Lys-Gly-Phe-Lys-Met-Ser-OH.

33.56 (challenge) A protein is sequenced by Edman degradation (N-terminal amino acid removal one at a time). After 5 cycles, the sequence is Met-Phe-Ser-Lys-Gly. Identify the mechanism of Edman degradation (formation of phenylthiohydantoin from N-terminal residue).

Section K — Multistep synthesis and integrative

33.57∗ (routine) Design a synthesis of N-acetyl-Gly-Ala using SPPS-style chemistry.

33.58 (moderate) Design a synthesis of a peptide with a non-natural amino acid (e.g., D-alanine). What modifications to standard SPPS are needed?

33.59 (challenge) Outline the synthesis of a cyclic peptide (e.g., cyclosporin-like). What strategy joins the N- and C-termini?

33.60 (challenge) Outline the chemistry of an antibody-drug conjugate (ADC), where a cytotoxic drug is attached to an antibody via a lysine or cysteine. What is the linker chemistry?

Notes for instructors: Common stumbling blocks for Chapter 33: (1) Memorizing the 20 amino acids — practice with flash cards or peer quizzing. (2) Calculating pI for tripeptides with multiple ionizable groups. (3) Recognizing the role of Fmoc vs. Boc in SPPS. (4) Connecting protein folding thermodynamics to misfolding diseases. Computational exercises: use AlphaFold to predict the structure of a small known protein; compare to the experimental structure.