Homework Three, Enzymes
4170
1. Consider the following (imaginary) example. An endogenous (naturally occuring) peptide called
intelligensin is shown below. Intelligensin is responsible for learning and storage of memories in
mammals. Some animals, such as Golden Retrievers, seem to express high levels of an enzyme that
degrades intelligensin. This enzyme is called intelligensinase, it is a protease enzyme that degrades
the peptide as shown below. Design an affinity-labeling agent for intelligensinase.
H2N-Ala-His-Phe-CO2H
Bond Normally
Cleaved by Enzyme
2. Design a peptidomimetic reversible inhibitor for the protease described above (intelligensinase).
3. What is the expected biological effect of the inhibitor described above? Will it make my dog
smarter or (even) less intelligent?
4. Draw the mechanism for acid-catalyzed hydrolysis of an amide bond.
5. Draw a mechanism for hydrolysis of an amide bond by a zinc-dependent protease.
6. Draw a mechanism for hydrolysis of an amide bond by a aspartyl protease.
7. Draw a mechanism for hydrolysis of an amide bond by a serine protease.
8. The molecule shown below is a mechanism-based inactivator of serine proteases. Propose a
reasonable mechanism for the enzyme inactivation. Draw a plot for enzyme activity versus time for
an experiment where the protease enzyme is treated with this agent.
O
O
O
O
9. Look back at the Pymol assignment. Design two affinity labeling agents for PTP1B.
10. When taking a reversible enzyme inhibitor, why is it necessary to take frequent doses?
11. Design a transition state analog inhibitor for isopentenyl phosphate isomerase, whose mechanism
is shown below. What are candidates for the amino acid side chains that could serve as “–BH+”?
+
B
H
O– O O– O
P –
P
O
O
O
B:
O– O O– O
P –
P
O
O
O
+
H H
+
B
H
O– O O– O
P –
P
O
O
O
12. Use a reaction coordinate diagram (plot of ΔG vs rxn coordinate) to graphically depict two
modes of enzymatic catalysis: transition state stabilization and substrate destabilization by strain
and distortion.
13. Acetylcholinesterase is the enzyme responsible for deactivating (destroying) the neurotransmitter
acetylcholine. Complete the mechanism shown below. Water is involved and acetate is a final
product.
B:
+
N
O
H
B
+
N
O
O
H
O
O–
O
(a) using principles developed in this course, design a reversible inhibitor of this enzyme
(b) design an affinity labelling agent for this enzyme (not the one I showed in class)
(c) what amino acid side chains might reasonably be expected to be involved in recognition (binding
to) the positively charged trimethylammonium group of acetylcholine?
14. The Ki of drug A for its target enzyme is 6 nM. The Ki of drug B for its target enzyme is 10 µM.
(a) based upon the data that you are given, which drug would you predict to be more potent?
(b) Let's assume that these drugs diffuse completely and randomly through all the fluid space of the
human body. Let's also assume that there are 50 liters of fluid in a human (as we have calculated
before). How much drug A will you need to administer to achieve 50% inhibition of the target
enzyme? How much drug B? Assume for this problem that an “average” drug has a MW = 250
g/mol. You may need to look at the handouts on enzyme kinetics that are posted on the course
website.
15. Based upon reactions that we have studied for the synthesis of captopril, peptides, and ibuprofen,
propose a synthesis for the peptidomimetic shown below. Start with proline and other small starting
materials that contain 4 heavy atoms or less (this atom limit does not apply to reagents, only to
fragments that end up incorporated into the final molecule).
O
S
O
N
O
H
N
Rationalize the following: This compound is an affinity labeling agent for a protease that cleaves XGly-Pro peptide sequences (where X can be any amino acid residue).
16. One way that enzymes catalyze chemical reactions is by lowering the entropy of activation. In
lecture, and in your textbook, this has been called "catalysis by proximity". A high "local
concentration" of the reaction partners is created by holding the two molecules together in close
proximity. This effect is quantiatively assessed using a term called "effective molarity". Consider
the reactions of glutathione (GSH) with the sulfonium ion shown below and calculate the effective
molarity of glutathione in the enzyme-catalyzed reaction.
GSH
H3 C
GSH
H3 C
S
S
+
+
kuncatalyzed = 0.3 M-1 s-1
OH
GSCH3
OH
Enzyme Catalyzed
k = 4 x 10-6 M-1 min-1
O
O–
+
O
O
O
OPh
CO2–
k = 0.00444 min-1
O
O
CO2Ph
O
CO2–
O
k = 0.0857 min-1
O
CO2Ph
CO2–
O
k = 1.03 min-1
O
O
CO2Ph
CO2–
O
k = 45.7 min-1
O
O
CO2Ph
OH
kcat = 1000 s -1
GSCH3
17. Calculate the effective molarities of each reaction. Explain the results.
O
S
+
O
+
S
OH
18. The enzyme histone acetyl transferase (HAT) catalyzes the transfer of the acetyl group from
acetyl coenzyme A to lysine residues on the proteins that wrap DNA in the cell nucleus. Inhibitors
of this enzyme have potential therapeutic uses (Bioorganic Medicinal Chemistry Letters 2004, 12,
3383-3390). Draw the mechanism for the normal enzymatic reaction and then design two
bisubstrate analog inhibitors against this enzyme.
Acetyl CoA
19. Look at the handout on enzyme kinetics posted on the course website. For the system:
k1
k2
E
+
S
ES
E
+
P
k-1
The reciprocal of an expanded form of the Micahelis Menten equation is often written as follows:
1 k −1 + k 3 + k1[ S ]
=
v
k1k 3 [ ET ][ S ]
where: S is the substrate, ET is the total enzyme, and v is defined as:
dP
dS
v=
=−
dt
dt
a. Define the terms Km and Vmax using the parameters that are shown above.
b. Rewrite the Micahelis-Menten equation using the terms Km and Vmax.
c. Draw a plot and annotate it so that it shows how you can obtain the values of Km and Vmax from a
series of measurements of the initial reaction velocities vo at a set of initial [So], in other words vo [So]
pairs.
20. Look at the handout regarding the kinetics of enzyme inhibition (posted on the website). Under
the following conditions, calculate the enzyme velocity (v0) in terms of Vmax.
enzyme KM = 1 x 10-3 M
[S] = 1 x 10-3 M (1 mM)
drug Ki = 1 x 10-6 M
[Drug] = 1 x 10-6 M (1 µM)
21. Enzymes (or any catalyst) accelerate reaction rates by decreasing the free energy of activation for
the reaction in question. (a) show this on a reaction-coordinate energy diagram. (b) If an enzyme is
able to decrease the energy of the transition state by, say, 5 kcal/mol how much would this increase
the reaction rate at physiological temperature? For this question, you may need to remember that
the Arrhenius equation provides a way to relate energy of activation (E) to reaction rates. In this
equation, the parameter "A" can be taken as a constant (whose value you do not need to worry
about).
Arrhenius Eqn:
k = Ae(-E/RT)
For additional problems related to enzyme-targeted drugs, work the problems at the end of the
“Enzymes” and “Enzyme Drug” chapters in Silverman’s textbook.