440 – kinetics review questions
1. For the following reaction, at equilibrium [S] = 5 mM, [P] = 0.5 mM, and kf = 10 s-1.
kf
S
P
kr
a) Calculate Keq (the equilibrium constant) and kr.
b) A catalyst increases kf by a factor of 106. Calculate Keq and kr for these conditions.
c) Draw a reaction coordinate diagram that includes both the uncatalyzed and catalyzed reactions.
2. Shown below is the Michealis-Menton plot for the reaction of 0.1 nM enzyme with its substrate.
Use this plot to determine numerical values (with units) for kcat and KM .
kcat =
3. Schistosomiasis is second only to malaria in a ranking of the most socio-economically devastating
parasistic diseases. You are studying the parasite that causes schistosomiasis. In particular you are
studying an enzyme within this parasite with the long term goal of designing inhibitors against it.
a) Describe the series of experiments you will perform to determine the values for the MichaelisMenton parameters for this enzyme.
b) You have determined that the value for an observed rate constant increases with decreasing pH.
What hypothesis could you formulate based on this result? Explain.
440 – kinetics review questions
4. We have discussed a number of strategies enzymes may use to catalyze reactions. The following
questions refer to these different strategies.
(a) In the chemical formation of anhydrides, (shown in equations 1 & 2, below), the rate constant for
the second reaction (eq. 2) is 3 x 107 –fold faster than that for the first reaction (eq. 1). Describe in
detail how enzymes might use a similar effect or strategy to catalyze reactions.
reaction
relative rate
Eq. 1
1
3 x 107
Eq. 2
b) As shown below, chymotrypsin catalyzes the hydrolysis of specific substrates (eq. 3) significantly
faster than nonspecific substrates (eq. 4). This increase is not seen as tighter binding of the specific
substrates. Explain in detail.
reaction
relative rate
uncat.
cat.
Eq.
3
1
1012
Eq.
4
1
105
440 – kinetics review questions
5. Consider the following mechanism:
E+S
k1
k2
 ES 
k-1
EP
k3

E+P
where all steps are accurately depicted as reversible or irreversible. Imagine that substrate (S) is
colorless and product (P) is yellow whether or not it is bound to the enzyme. You properly set up an
experiment in which you can monitor the formation of P over time under multiple turnover conditions
by quantitatively measuring the increase in yellow color. Some of your data are shown below.
a) Explain why this result is unlikely to be due to product inhibition.
b) Provide and defend an alternate explanation for the two phases that you observe in the time course
for the formation of P.
% of
total PA
0.5
time
6. The ribozyme from the hepatitis delta virus (HDV) is a self-cleaving RNA molecule. Due to the
nature of this ribozyme, you can physically only perform single turnover reactions. Why is this true?
7. Sometimes my kids and I do "science" experiments in the kitchen. Our longtime favorite is the
addition of vinegar (acetic acid) to baking soda (sodium biocarbonate). The solution gets very fizzy as
the acid reacts with the bicarbonate to produce carbon dioxide and water. If my kids would only put
their minds to it, I'm sure they could figure out how to measure the rate for the conversion of the
bicarbonate to CO2 and H2O in solution. We could then compare this rate to the rate for the same
chemical conversion as catalyzed by the enzyme carbonic anhydrase in muscle tissues throughout our
bodies.
Based on the theory that describes an increase in "effective concentration" in an enzyme active site,
would you predict the enzymatic rate to be equal to, faster than, or slower than the corresponding rate
of reaction in solution.
440 – kinetics review questions
8. Cellular tRNA molecules are initially transcribed as longer, precursor molecules that contain extra
nucleotides at their 5' end. The enzyme RNase P catalyzes the production of mature tRNA molecules
from these precursor-tRNA molecules through the hydrolysis of a specific phosphodiester bond, as
shown in the following sketch.
+ E
tRNA
+
+ E
tRNA
(pre-tRNA)
(mature(leader
tRNA)
sequence)
The biological substrate for RNase P (pre-tRNA) has many (>30) nucleotides in the leader sequence.
However, artificial substrates with as few as 1 nucleotide in the leader (1-tRNA) are cleaved by RNase
P in vitro. You are able to do binding experiments in which you watch substrate binding to RNase P in
the absence of product formation. So, just observing E + S  ES, you obtain the following data.
substrate name
leader length
KD, nM
pre-tRNA
33
0.4
2-tRNA
2
19
1-tRNA
1
3000
tRNA (product)
0
200
Discuss these data in terms of general theories of enzyme catalysis. For example, consider any
suggestions you can make about the catalytic strategies used by RNase P. Keep in mind that all
nucleotides present in 1-tRNA are also present in substrates with longer leader sequences.
9. One day you stumble across the following information on the CDC website:
"Dracunculiasis, more commonly known as Guinea worm disease (GWD), is a preventable
infection caused by the parasite Dracunculus medinensis…. The disease causes preventable
suffering for infected persons and is a heavy economic and social burden for affected
communities."
You immediately start considering how you can contribute to alleviating the problem of Guinea worm
disease in the world. Doing some research, you identify an enzyme that occurs in the causative
parasite that does not exist in humans. It occurs to you that this enzyme would be a good target for
inhibition.
To inhibit the enzyme, you want to develop a molecule that will bind in the active site and therefore
prevent the actual substrate from binding. Given a choice between inhibitors that resembled the
substrate, transition state, or product of this enzymatic reaction, which would you choose? In your
answer, carefully explain your reasoning as it pertains to each possible choice. (Tell me why you
chose one type of inhibitor and why you did not choose the other two types).
440 – kinetics review questions
10. Shown below is the Michealis-Menton plot for the reaction of 5 nM enzyme with substrate A.
Imagine that KM is a true KD for the reaction of this enzyme with any substrate. Add a second
Michaelis-Menton curve to this figure to represent the reaction of the same enzyme with a substrate for
which it has greater specificity (call this substrate B). Explain the choices you made.
v
[S]
11. (This question is not based on a real enzyme). Structure relevant to this question are the
following:
ATP
CTP
Enzyme Madeitup functions in vivo to transfer a phosphate group from CTP to a particular protein.
Upon substitution of CTP with ATP in vitro, ATP can act as the phosphate donor for this enzymatic
reaction.
Provide a well-reasoned hypothesis about the relative specificity of the enzyme for CTP versus ATP.
Your answer should make it clear that you understand the concept of substrate specificity as it applies
to enzymatic reactions.
440 – kinetics review questions
12. This question concerns the hydrolysis of substrate catalyzed by the enzyme chymotrypsin, as
accurately modeled below.
a) The derived steady-state equation for this enzymatic reaction is shown below. Provide the work
that leads to this equation, assuming the reaction occurs under steady-state conditions; that is, the
steady-state assumption applies to all enzyme-bound species. (Feel free to use the abbreviations S and
P in place of the molecules written above.)
k3 [ET] [S]
Rate =
k-1 + k2 k3
k1 k2
+
k3 + k2 [S]
k2
b) The substrates for this reaction are variants of N-acetyl-L-tryptophan-X, where X is further
specified in this table:
-X
kcat, s-1
- OCH2CH3
26.9
-OCH3
27.7
30.5
Use information from the steady-state rate equation to explain the fact that although the three esters
shown in the table above have vastly different chemical hydrolysis rate constants (k2), their values for
kcat are quite similar.
440 – kinetics review questions
13. a) Sketch the transition state and intermediate that occur during the hydrolysis of an amide bond,
using the starting materials shown below.
b) Provide three explanations for the observation that amide bond hydrolysis is slow at pH 7.
c) Identify two chemical mechanisms that could catalyze this reaction. Explain how catalysis would
be achieved in each mechanism.
14. You are studying the substrate specificity of enzyme E. You have done steady-state kinetics with
six substrates and classified them into two groups, class 1 and 2. Your preliminary data are shown
below.
Substrate
Class 1:
A
B
C
Class 2:
X
Y
Z
kcat (sec-1)
KM (nM)
1000
1010
998
10
11
9
55
60
50
100
100
100
a) For the following two questions:
Either answer the question and explain your answer
or explain why you cannot answer it based on the data you have collected thus far.
For which class of substrate is the enzyme more specific?
What is the origin of substrate specificity: reactivity, substrate binding affinity, or both?
b) What type of experiment will you do next and why?
440 – kinetics review questions
15. The reactions of enzyme Imaginase with two different substrates, A and B, have been studied in
steady-state experiments.
Substrate
kcat (min-1)
KM (mM)
5.0
5.0
1.0
10.0
A
B
a) In the series of steady-state (Michealis-Menton) experiments that were performed to obtain that
parameters shown above for the B substrate, what concentration of Imaginase would have been
appropriate to use: 0.1mM, 5mM, or 100mM? Circle and briefly explain your choice.
b) Using your above answer, you are set up experiments to compare the reaction of Imaginase with
500 mM A to the reaction of Imaginase with 500 mM B.
Show your calculations for the % of product formed, with
each substrate, at a 1 minute time point here.
On this plot, show the time course data you would expect to
get for each of these reactions.
(Add numbers to the x-axis).
10.0
%
product
8.0
6.0
4.0
2.0
0.0
time
(min)
c) You are now comparing the reaction of Imaginase and 0.1 mM A to the reaction of Imaginase with
0.1 mM B. In each reaction you have the same concentration of Imaginase. If you stop the reaction
after three minutes, do you expect to see:
 more product in the A reaction (compared to the B reaction)
 less product in the A reaction (compared to the B reaction)
 the same amount of product in each reaction
Check the box corresponding to your answer and briefly explain your reasoning.
440 – kinetics review questions
16. Here are two reactions describing the chemical formation of anhydrides. (The negatively charged
oxygen attacks a carbonyl…)
reaction
Rxn. 1
Rxn. 2
In your research lab you have used in vitro evolution to develop two RNA enzymes that each function
to catalyze one of the above reactions. Enzyme 1 catalyzes Rxn 1 and Enzyme 2 catalyzes Rxn 2.
Which enzyme will cause a greater rate enhancement for its reaction? In your answer, include a
numerical estimate of the rate enhancement you expect to see in this enzyme. Explain your answer
thoroughly with valid reasoning.
17. An enzyme reacts with three different substrates (A, B, and C), under multiple turnover conditions,
with the following Michaelis-Menton parameters:
kcat (min-1)
KM (µM)
Substrate A
5
1
Substrate B
50
25
Substrate C
500
10
Answer the following questions OR briefly explain why the question is unanswerable:
a) What is the rate of the reaction of 5 nM enzyme with 200 µM substrate B?
b) For which substrate is the enzyme least specific? Explain.
c) Which substrate binds with tightest affinity to the enzyme?
d) How much product has been formed if 0.01 µM enzyme and 3 µM substrate C have reacted for 20
seconds?
440 – kinetics review questions
18. The material in this question is taken from a paper entitled "Energetic contribution of non-essential
5' sequence to catalysis in a hepatitis delta virus ribozyme" (EMBO (2001) 20, 4884). The figures
from this paper that are referred to in this question follow the entire question.
a) Based on the data in Figure 2: sketch, on ONE free energy plot, the reaction progress for a substrate
with 1 nucleotide in the 5' sequence (S1) and the reaction progress for a substrate with 2 nucleotides in
the 5' sequence (S2). Explain your choices.
Free energy diagram:
Explanation:
b) Define the concept of intrinsic binding energy.
c) In light of the data in Figure 2, what is the energetic contribution of the 5' sequence to catalysis in
this HDV ribozyme? Provide one hypothesis for the physical mechanism by which this 5' sequence
might fulfill this function.
Here are the relevant two figures:
Figure 1 (left):
The hepatitis delta virus (HDV) ribozyme nucleotides are shown
as outlined letters. Substrate nucleotides are shown as bold
letters, in the box. The ribozyme cleaves the substrate at the
position indicated by the arrow. Nucleotides below that arrow
are referred to as the 5' sequence.
440 – kinetics review questions
Figure 2 (above): Change in the cleavage rate (k2) and dissociation equilibrium constants (Kd) with increasing length of the
5' sequence. k2 and Kd were determined for wild-type substrates with length 5' to the cleavage site varying from 1 to 8 nt.
Both k2 (circles) and Kd (squares) were plotted against the number of nucleotides in their 5' sequence.
19. For the following enzymatic reaction
k1
E+S
k2
ES
k-1
k3
EP
k-2
E+P
k-3
your friend has derived the following equation to describe the steady-state rate of this reaction:
Based on this equation she claims that the release of product from the EP complex is the rate limiting
step for this reaction. Confirm or refute your friend's claim. Back up your answer with as much
specific detail as possible.
440 – kinetics review questions
%
product
formation
20. The following plots are multiple copies of the time course for the appearance of product for the
reaction of 5nM enzyme with 50 nM substrate. This enzyme substrate reaction has a KM of 10nM.
a) To this plot, add a line showing the time course for product formation for the reaction of 10 nM
enzyme and 50 nM substrate. Explain briefly.
16
12
8
4
0
0
4
8
12
16
20
24
time
(min)
%
product
formation
b) To this plot, add a line showing the time course for product formation for the reaction of 5 nM
enzyme and 100 nM substrate. Explain briefly.
16
12
8
4
0
0
4
8
12
16
20
24
time
(min)