```Please help to solve the 3 problems
2. Burst-phase kinetics
Using p-nitrophenyl acetate as a substrate for chymotrypsin, a rapid release (or /burst") of
p-nitrophenyl is initially observed, followed by a slower steady-state release. The amount
of product released in the initial burst phase is stoichiometric with the amount of enzyme
present in the reaction. Explain.
4. Uncompetitive inhibition
The reaction below represents the mechanism of action of an uncompetitive inhibitor.

(a) Draw a standard Michaelis-Menten curve in the absence and presence of increasing
amounts of inhibitor. Repeat for a double reciprocal (Lineweaver-Burk) plot.
(b) Explain the results obtained in part (a).
5. Transition state theory
(a) After running a reaction at several different temperatures, you determine the value of
the pre-factor A from an Arrhenius plot. You re-run the experiment with a catalyst
and find that A increases by 50%, so that Acat = 1:5Auncat. In lecture, we used
transition state theory to connect A to microscopic and thermodynamic factors. In
terms of these factors, offer an explanation for how the catalyst increases A.
(b) How much does the catalyst change the activation energy of the reaction if kcat =
2kuncat?

Chemistry C130/MCB C100A Problem Set 10
due April 30, 2014 (15 pts)
Please turn in your homework at the beginning of class on Wednesday.
1. Michaelis-Menten kinetics (5 pts)
(a) From the data below, calculate KM and Vmax using a Lineweaver-Burk or similar
plot. If 1.65 µg of enzyme was used in each assay and the molecular weight of the
enzyme is 36 kDa, calculate kcat and kcat /KM . Show your work.
[S] (mM)
1.8
0.9
0.4
0.2
0.1

d[P ]/dt (nmol/min)
assay 1
assay 2
4.75
4.44
3.55
3.20
2.15
2.19
1.28
1.32
0.74
0.76

(b) Why does the observed rate begin to plateau, even though the concentration of
(c) Why is it important that [enzyme]

[substrate]?

(d) A homologous enzyme isolated from a di?erent species is reported to have a KM of
0.1 mM. What does this tell you about the relative binding a?nities of these two
enzymes for this substrate?
2. Burst-phase kinetics (2 pts)
Using p-nitrophenyl acetate as a substrate for chymotrypsin, a rapid release (or “burst”) of
p-nitrophenyl is initially observed, followed by a slower steady-state release. The amount
of product released in the initial burst phase is stoichiometric with the amount of enzyme
present in the reaction. Explain.
3. Inhibition (3 pts)
[S] (µM)
3
5
10
30
90

Velocity (µmol/min)
No inhibitor Inhibitor
10.4
2.1
14.5
2.9
22.5
4.5
33.8
6.8
40.5
8.1

The kinetics of an enzyme are measured as a function of substrate concentration in the
presence and absence of 2 mM inhibitor (I).
1

(a) What are the values of KM and Vmax in the absence of inhibitor? In its presence?
(b) What type of inhibition is this?
(c) What is the binding constant of this inhibitor?
(d) If [S] = 10 µM and [I] = 2 mM, what fraction of the enzyme molecules have a bound
substrate? A bound inhibitor?
(e) If [S] = 30 µM, what fraction of the enzyme molecules have a bound substrate in
the presence and absence of 2 mM inhibitor? Compare this ratio with the ratio of
the reaction velocities under the same conditions.
4. Uncompetitive inhibition (3 pts)
The reaction below represents the mechanism of action of an uncompetitive inhibitor.

(a) Draw a standard Michaelis-Menten curve in the absence and presence of increasing
amounts of inhibitor. Repeat for a double reciprocal (Lineweaver-Burk) plot.
(b) Explain the results obtained in part (a).
5. Transition state theory (2 pts)
(a) After running a reaction at several di?erent temperatures, you determine the value of
the pre-factor A from an Arrhenius plot. You re-run the experiment with a catalyst
and ?nd that A increases by 50%, so that Acat = 1.5Auncat . In lecture, we used
transition state theory to connect A to microscopic and thermodynamic factors. In
terms of these factors, o?er an explanation for how the catalyst increases A.
(b) How much does the catalyst change the activation energy of the reaction if kcat =
2kuncat ?
6. Di?usion (3 pts extra credit)
(a) The protein cyclophilin is a monomer with a di?usion constant of 1.2 × 10?8 cm2 /sec
in water at 25? C. Cyclophilin binds HIV capsid and the resulting complex has a
di?usion constant of 7 × 10?9 cm2 /sec. What is the di?erence in the typical (rms)
distance that cyclophilin alone will travel versus the cyclophilin-capsid complex in
10 seconds?
2
(b) There are approximately 250 million hemoglobin molecules per red blood cell. How
many collisions will an oxygen molecule of radius 0.21 nm have with hemoglobin of
radius 3 nm in a blood cell of volume 10?16 m3 in 1 sec at 25? C? Assume both
molecules are well approximated by spheres, and that the viscosity is that of pure
water.
(c) What is the typical (rms) distance traveled by a spherical HIV virus of radius 120
nm in 1 hour through the bloodstream (viscosity = 3 cP) at 37? C?
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