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November 14, 2007 A SCIENTIFIC CALCULATOR IS NEEDED FOR THIS EXAM. SHOW YOUR WORK FOR ALL CALCULATIONS, AND BE SURE TO STATE UNITS OF ANY NUMERICAL ANSWERS. If the reasoning, calculations, or answer are shown anywhere other than in the space provided, make a note in the space provided and put answer on back of SAME PAGE for same grader, since pages are separated for grading. USEFUL CONSTANTS: R (gas constant) = 8.315 J•mol–^1 •Kelvin–^1 = 8.315 x 10–^3 kJ•mol–^1 •Kelvin–^1 (25 °C) T = 298 K; human physiological temperature (37 °C) T = 310 K. Ionizable group in peptides and proteins Approximate ("generic") pKa in peptides & proteins α-amino 8. α-carboxyl 3. ε-amino 10. guanidino 12. thiol 8. imidazole 6. aromatic hydroxyl 10. side chain carboxyl 4. Potentially Useful Equations Michaelis-Menten Equation:
vo =
V max [ S ]
Km + S
Hill Equation:
log
= n log[ ligand ] – n log K 0.
Inhibition Equation:
v
KM
V max
[ I ]
KI
[ S ]
[ I ]
( KI
V max
p. 2 (19 points) p. 3 (19 points) p. 4 (13 points) p. 5 (18 points) p. 6 (16 points) p. 7 (15 points) TOTAL: (100 points)
November 14, 2007
1. Lysozyme hydrolyzes a 6-residue oligosaccharide (GlcNAc-Mur2Ac-GlcNAc-Mur2Ac-GlcNAc- Mur2Ac). Cleavage occurs between the fourth and fifth saccharide units. The first step of the chemical mechanism is shown below. The mechanism requires participation of two side chain carboxyl groups on residues Asp52 (pKa = 4.5) and Glu35 (pKa = 5.9). The graph (below, right) shows the relationship of lysozyme activity to pH. O AcN H H O OH H **CH 2 OH O O H
- O O O NAc CH 2 OH OH HO O AcN H —O O O O** First product Covalent intermediate Mur 2 Ac (^) GlcNAc O A. (6 pts) Fill in the two blank rectangles in the above mechanism with the appropriate labels (either Asp52 or Glu35) based on the information given about the pKas of these two residues. B. (8 pts) Briefly describe the catalytic roles of the two residues in the first step of the catalytic mechanism of lysozyme as specifically as you can, using appropriate terminology, such as “electrostatic catalysis”, “nucleophile”, “general acid” (or “general base”), “covalent intermediate”, “transition state”, etc., if relevant. Example: “In the first step, the carboxyl group of the ____ residue acts as a ____ to (do what to whom).” Glu^35 : Asp^52 : C. (5 pts) The Mur2Ac sugar ring that is adjacent to the lysozyme cut site does not fit its binding site without a change from the stable chair conformation to a distorted half-chair form, as shown below. Though the overall ΔG for binding the entire substrate is favorable, the distorted ring contributes unfavorably to the overall free energy of binding. How might the distortion of the substrate contribute to rate enhancement by lysozyme? O O O NHAc HO O HOH 2 C O CH 2 OH O R NHAc O CH 2 OH HO NHAc O GlcNAc Mur 2 Ac GlcNAc distorted ring in half-chair conformation lysozyme cuts here
November 14, 2007
2. (9 pts) The magnitude of the rate constant k depends on the activation energy of the reaction:
k =
! T
h
e
" # G ‡^ / RT
where κ is the Boltzmann constant and h is Planck’s constant. κT /h can be regarded as a constant at
constant temperature, so the rate constant k is proportional to e
- ΔG‡/RT , i.e., k is inversely and exponentially related to ΔG ‡ . The enzyme urease catalyzes the hydrolysis of urea to ammonia and carbon dioxide. At 21 °C (294K) , the uncatalyzed reaction has an activation energy of 125 kJ/mol, whereas in the presence of urease the activation energy is 46 kJ/mol. A. (4 pts) Calculate the difference in free energy of activation ( ΔΔ G ‡ ) between the uncatalyzed and urease-catalyzed hydrolysis of urea at 21 °C (294K). Show your work. B. (5 pts) What is the rate enhancement brought about by urease catalysis, compared to the uncatalyzed reaction? Show your work. 3. (4 pts) Briefly explain the molecular basis of one of the ways by which bacterial cells can be resistant to β-lactam antibiotics like penicillin.
November 14, 2007
4. (8 pts) In the context of a bisubstrate reaction, A. (4 pts) What is a ternary complex? B. (4 pts) A ternary complex occurs during the reaction catalyzed by an enzyme with a 1) sequential kinetic mechanism 2) ping-pong kinetic mechanism 3) both 4) neither 5. (10 pts) Ca 2+ binding proteins involved in enzyme regulation generally use one of two structural motifs for binding Ca 2+ : 1) the EF hand, or 2) multiple Gla residues. Both have been discussed in class. A. (4 pts) Name one protein as an example for each structural motif. B. (6 pts) Briefly describe how Ca 2+ binding relates to that protein’s biological function. Ca 2+ binding structure (name) A. (4 pts) name of one protein example B. (6 pts) **biological/regulatory function of that protein
- EF hand
- Gla residues**
November 14, 2007
7. (11 pts) Consider the case of a protein phosphatase that catalyzes the dephosphorylation of a specific enzyme that has a phosphoserine residue in its active form. For this protein phosphatase-catalyzed reaction, A. (4 pts) Indicate on the drawing any additional substrate(s) that would be required for the reaction to occur. B. (7 pts) Indicate using curly arrows a plausible chemical mechanism for the enzyme-catalyzed reaction, including in your mechanism specific enzyme groups that could assist in catalysis (names and states of protonation).
Enz CH 2
O P
O
O-
O-^ Enz CH 2
OH
O
P O-
O-
HO
Protein Phosphatase
8. (4 pts) Pancreatic trypsin inhibitor binds very tightly to trypsin (essentially irreversibly), but only much more weakly and reversibly to trypsinogen. What is the most likely reason for the difference in binding affinity?
