Exam 2, BICH 410 (TuTh 12:45-2), Tuesday, Oct. 22, 1996

Write your name on each page. Write concise answers to demonstrate effectively your mastery of the subject material. Show your work in order to receive partial credit where applicable.

1. (8 pts) 15 micrograms of an enzyme of molecular weight 30,000 working at Vmax catalyzes the conversion of 60 micromole of substrate into product in 3 min. What is the enzyme's turnover number (in sec-1)? You must show your work.
Vmax = kcat[ET]
turnover number, kcat = Vmax / [ET]
Vmax = (60 micromole / 3 min)(1 min / 60 sec) = 0.333 micromole/sec
ET = 15 microgram / 30,000 microgram/micromole = 0.0005 micromole
Hence, kcat = (0.333 micromole/sec) / 0.0005 micromole = 667 / sec

2. (13 pts) (a) Draw the catalytic triad of chymotrypsin at the stage in the mechanism where there is a covalent acyl intermediate. Structures of the amino acid side chains are necessary.
(b) Describe in words what happens next in the deacylation phase of the reaction.
Part (a): See Fig. 8-19 (between (c) and (d)) in book; or transparency handout from lecture
Part (b): Water performs a nucleophilic attack on the carbonyl carbon. It is made a stronger nucleophile because the histidine side chain acts as a general base, eventually removing a proton from the water. A tetrahedral oxyanion transition state forms. The transition state breaks down upon release of the carboxyl group of the half-product, and reformation of the serine -OH group. The histidine acts as a general acid, donating a proton to the serine oxygen (the proton first removed from the water). The product is released, and the enzyme active site is back to the starting state.

3. (30 pts) Fill in the blanks with the best answer.
(a) Use the following list of amino acids: glycine, arginine, glutamic acid, isoleucine, serine (each amino acid can be used more than once, or not at all in the questions for part (a) below)
most likely amino acid to occur in a beta turn _________________
Answer: glycine
most likely amino acids to participate in a salt bridge (ionic interaction) ____________________, ___________________
Answer: arginine, glutamic acid
most likely amino acid to be located in the interior of a folded, globular protein ____________
Answer: isoleucine
most likely amino acid to be reversibly phosphorylated in a regulatory enzyme ____________
Answer: serine
(b) Write the Michaelis-Menten equation:
Answer: V0 = (Vmax[S]) / (Km + [S])
(c) Chymotrypsinogen and trypsinogen are examples of a __________________.
Answer: zymogen
(d) A heterotropic positive modulator of aspartate transcarbamoylase is ______________. The K0.5 of this enzyme in the presence of the positive modulator is _____________ than the situation without the modulator.
Answer: ATP, less
(e) A first order rate constant has units of _____________.
Answer: time-1 or sec-1 or min-1
(f) A conservative amino acid substitution for aspartic acid is _________________.
Answer: glutamic acid
(g) Name an ionizable amino acid residue that, when located near the amino terminus of an alpha helix, will tend to destabilize the structure (at pH 7) __________________.
Answer: arginine or lysine
(h) Type of protein chromatography that separates based on size and shape of the macromolecule _________________________
Answer: gel filtration (molecular exclusion, size exclusion)
(i) Reagent that breaks peptide bonds to the C-terminal side of methionines _______________
Answer: cyanogen bromide (CNBr)
(j) Predominant type of secondary structure found in myoglobin _________________
Answer: alpha helix

4. (6 pts) For the binding of a ligand, L, to a protein, P, (P + L <-> PL) write expressions for:
(a) theta (fraction of binding sites on the protein that are occupied by the ligand)
(b) Ka, the association constant
(c) Kd, the dissociation constant
(a) theta = [PL] / ([P] + [PL])
(b) Ka = [PL] / ([P][L])
(c) Kd = ([P][L]) / [PL]

5. (6 pts) Write the pathway of equilibria involved in the enzyme-catalyzed bisubstrate reaction, S1 + S2 <-> P1 + P2, in which there is an ordered reaction proceeding through a ternary complex. Circle the ternary complex.
E + S1 <-> ES1
ES1 + S2 <-> ES1S2 -> E + P1 + P2
The ternary complex is ES1S2

6. (6 pts) What effect would you expect each of the following to have on the P50 of hemoglobin? (remember that P50 is the oxygen partial pressure for half-saturation). Your answer should be either "increase," "decrease," or "no effect."
(a) increase in pH from 7.2 to 7.4
Answer: decrease
(b) increase in partial pressure of CO2 from 20 to 40 mm Hg
Answer: increase
(c) dissociation into monomer polypeptide chains
Answer: decrease (becomes like myoglobin, with hyperbolic saturation curve; shifts to the left and has a lower P50

7. (10 pts) Draw the polypeptide backbones of 2 antiparallel beta strands, each of which contain four amino acid residues. Indicate with dotted lines all hydrogen bonds that join these two strands. With arrows indicate one bond that is described by a phi angle and one bond that is described by a psi angle.
Answer: see Fig. 7-9 (a) in textbook
phi angle describes bond between N and Calpha
psi angle describes bond between Calpha and C

8. (10 pts) The steady state kinetics of an enzyme are studied in the absence and presence of an inhibitor (inhibitor A). The initial rate is given as a function of substrate concentration in the following table:
V0 in units of (mmol/L)/min; [S] in units of mmol/L
[S] V0, no inhibitor V0, with inhibitor A
1.25 1.75 0.98
1.67 2.11 1.18
2.50 2.63 1.47
5.00 3.51 1.96
10.00 4.21 2.35
100.00 5.13 2.87

Using the graph paper on the next page, draw double-reciprocal plots to analyze this data. Determine: (a) the Km and Vmax in the absence and presence of inhibitor; (b) What type of inhibitor is A?
Expand the data table by calculating 1 /[S] and 1 / V0
[S] V0, no inhibitor V0, with inhibitor A1 /[S]1 / V0, no inhib.1 / V0, + inhib.
1.25 1.75 0.980.80.571.02
1.67 2.11
2.50 2.63 1.470.40.380.68
5.00 3.51 1.960.20.280.51
10.00 4.21 2.350.10.240.43
100.00 5.13 2.870.010.190.35

Then plot on graph paper: 1 / V0 on y-axis and 1 / [S] on x-axis. Draw two lines, one without inhibitor and one with inhibitor. Lines intersect on x-axis - implies same Km
Part (a): From graph
no inhibitor: 1 / Vmax = 0.19 min/mM; therefore Vmax = 5.26 mM/min
-1 / Km = -0.4 mM-1; therefore Km = 2.5 mM
plus inhibitor: 1 / Vmax = 0.34 min/mM; therefore Vmax = 2.94 mM/min
-1 / Km = -0.4 mM-1; therefore Km = 2.5 mM
Part (b): noncompetitive inhibitor, because Vmax is less, but Km is the same.

9. (11 pts) (a) Draw and label a reaction coordinate diagram for an uncatalyzed reaction, S <-> P, and the same reaction catalyzed by an enzyme, E, that proceeds through an ES complex. On your diagram, point out the overall free energy change for each reaction, the transition states, and the activation energies for both the uncatalyzed and catalyzed reactions.
(b) Write a mathematical expression that relates the rate constant and activation energies for a chemical reaction.
Part (a): see Figs. 8-4 and 8-3 in textbook
Part (b): k = (constant) e(-G(act)) / RT
(k is proportional to e-G(act) is sufficient)