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CHM 376 Biochemistry I
Fall 2023
Problem Set 9B: Enzyme Kinetics
1.
Define the following terms: kinetics
and chemical kinetics
. 2.
What is the meaning of the term rate enhancement? 3.
Can enzymes make unfavorable
reactions favorable
? Do enzymes change K
eq
? How can
a thermodynamically unfavorable reaction be made favorable? 4.
What is the approximate range of rate enhancements observed in enzymes?
5.
Why is the study of kinetics useful in understanding the stabilization of the transition states by enzymes?
6.
What is site directed mutagenesis and how can it be used to investigate the mechanism of transition state stabilization by enzymes?
7.
How can enzyme kinetics be used to understand the role of an enzyme within a cell? How can enzyme kinetics be used to optimize the (research, clinical, and industrial) laboratory use of enzymes?
8.
How do catalysts accelerate the rate of a reaction? Use a plot of kinetic energy (x axis) and number of molecules (y axis) to explain your answer. Then use transition state theory to answer the same question. 9.
Show that the bimolecular association rate constant (
kinetic
) has units of M
-1
s
-1
, that the unimolecular dissociation rate constant (
kinetic
) has units of s
-1
. Using the relationship between these two different rate constants, what are the units of the dissociation constant
(
thermodynamic
)?
10. Write the K
D
(or K
d
, as it means the same thing) for myoglobin in terms of association and dissociation rate constants. (
This is the same question as #5 but phrased slightly differently
). 11. What do we mean by the phrase, “the binding constant is determined by how fast things come together and how fast they fall apart”?
12. Explain the phrase, “myoglobin can do two things, but enzymes can do three things”. What are the two things that myoglobin can do and what is the one thing enzymes can do that myoglobin
cannot?
13. Write the equation for
in terms of k
a
(or k
1
, the same thing) and k
d
(or k
-1
, the same thing), and [L].
14. What is the Brown-Henri hypothesis? How does the Brown-Henri hypothesis relate enzyme function to myoglobin? What is different between an enzyme and a protein like myoglobin? Why, according to Brown and Henri, is there a point where increasing the concentration of substrate does not increase the rate at which product is formed?
15. What is the steady state assumption
? How does it differ from the equilibrium assumption? According to either assumption does the concentration of ES change during enzyme catalysis?
16. Write the mathematical rate model for the Brown-Henri hypothesis. There are three rate constants (
assuming catalysis is irreversible
). What chemical reaction does k
1
describe and what are its units? What does k
-1
describe and what are its units? What does k
2
describe and what are its units? How is an enzyme, according to Brown and Henri, like myoglobin? How is it
different?
17. Write the M-M equation. Why is an M-M plot of M-M kinetics hyperbolic?
18. Write an equation for V
max
in terms of enzyme amount (or concentration) and k
2
. Under what conditions does the observed rate equal V
max ? 19. Define V
max
. What is the turnover number
? What are the units of turnover number
? What are the two potential units for V
max
, and in what way are they similar and different? How does V
max
depend on [S]? How does V
max
depend on [E
t
]? How many more ways can I ask the exact same question?
20. Using relatively simple experiments, is it possible to determine the value of k
1
and k
-1
?
21. Write an equation in terms of rate constants that describes the fraction of enzymes bound by substrate. Show that the units of this expression (called K
M
) are concentration. Show that when
[S] = K
M
, v
o
= V
max
/2. 22. Assuming K
M
= 2mM, at what concentration of [S] would v
o
= 0.36 X V
max
?
23. Is K
M
an intrinsic property of an enzyme or does it describe a specific enzyme-substrate pair? Can an enzyme have more than one K
M
value?
24. What information can be obtained from analyzing a progress curve? How do we obtain the data to create a progress curve. Is the entire progress used to obtain this information, or is the analysis restricted to a subset of the entire data? Explain why
this is. 25. How is data obtained from a progress curve? What is the relationship between the initial slope
of the data on a progress curve and the rate of a chemical reaction. 26. What information is presented on an M-M plot? What is the general shape of the data plotted on an M-M plot? Use your knowledge of receptor-ligand interactions to speculate why this is.
27. Write the full Henri-Michaelis-Menten equation of enzyme kinetics, including the rate constants for each step. Check the Michaelis-Menten equation on your fact sheet. Notice that it does not include the full expression including all rate constants. This means that you must know how each term is expressed in terms of rate constants.
28. What is a progress curve
? What are on the x- and y- axes of a progress curve
? Why is the progress curve approximately hyperbolic
? How do we properly obtain the rate of a chemical reaction from a progress curve? Why do we only use the initial portion of the Progress Curve to obtain data for out M-M plot?
29. Explain the following statement: the observed rate of an enzyme catalyzed reaction is equal to the rate of the chemical step times the fraction of the enzymes bound to substrate
. 30. Using the full M-M equation, show that at high substrate concentration [S] >>> (k
-1
+ k
2
) / k
1
)),
that the rate of the enzyme catalyzed reaction = k
2
[E
t
] where k
2
is the rate of the chemical
reaction step (product formation) and [E
t
] is the concentration of enzyme. Explain why we call
this value V
max
?
31. Use the M-M equation to show that the units of the rate are the same as the units used to calculate V
max
, not the units used to calculate K
M
. 32. What is the distinction between the rate law for enzyme catalysis of a substrate at low substrate concentrations and high substrate concentrations? (
The answer to this question is not
explicitly in the PowerPoint. You need to think this one through
.)
33. How does the Brown-Henri model (hypothesis) account for the shape of the M-M plot of the enzyme invertase
?
34. Draw a set of ideal progress curves showing three different concentrations of substrate [S
1
] > [S
2
] > [S
3
]. Explain, in no more than 3 sentences how useful information is extracted from this graph. Next, construct an M-M plot for an enzyme following ideal M-M kinetics, showing how the data extracted from the progress curves is used to construct the M-M plot. Label the position of K
m
and V
max on your plot. As you work on this problem recall the distinction between an M-M plot and an enzyme following M-M kinetics. Also remember that the similarity in the appearance of the Progress Curve and the M-M plot showing M-M kinetics is entirely superficial. Do not confuse a Progress Curve with an M-M plot. 35. Why does the M-M plot of an enzyme that follows M-M kinetics show zero order kinetics at high substrate concentration? 36. What is K
m
? Write K
m
in terms of the rate constants from the H-M-M model of enzyme- catalyzed reactions? What is K
m
a measure of? How can we use K
m
to determine the fraction of
enzymes that are actively processing substrate into product? (
Note: you will no
t be given this equation on an exam. This is something you must know
). Given an M-M plot, how can we find K
m
? What is the major challenge associated with the approach you just suggested?
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37. Consider the following data obtained from an enzyme catalyzed reaction:
V
o
(
mol/min)
substrate added (
mol/L)
217 0.8
325 2
433 4
488 6
647 1000
648
1500
What is the approximate
K
m
for the enzyme? Explain your answer. Do not perform a calculation for this problem. Use a reasonable approximation
.
38. Two different enzymes are able to catalyze the same reaction A
B. They both have the same V
max
but differ their K
m
for substrate A. For enzyme 1, the K
m
is 1.0 mM. For enzyme 2, the K
m
is 10 mM. When enzyme 1 was incubated with 0.1 mM A, it was observed that B was produced at a rate of 0.0020 mmols/minute. (a) What is the value of V
max
of the enzymes? (b) What will be the rate of production of B when enzyme 2 is incubated with 0.1 mM A? (c) What will be the rate of production of B when enzyme 1 is incubated with 1 M A. Can you explain your result for (c) and why it did not require you to actually do any additional math
?
39. What is V
max
? Provide both a mathematical and written description of V
max
? How can V
max
be experimentally altered? How can we use V
max
to determine the turnover number (k
cat
) of an enzyme-catalyzed reaction? What is the major challenge of determining V
max
from an M-M plot?
(
I have asked this question several times on this Problem Set in a variety of ways. Make sure you can recognize the different ways we can use/interpret V
max
. In particular, make sure you can make a high-quality estimate of V
max
from looking at kinetics data, and use this V
max
as the basis for more complex calculations
). 40. Why is it challenging to obtain the parameters V
max
and K
m
from a M-M plot? Explain the Lineweaver-Burk approach to determining the parameters V
max
and K
m
of an enzyme-catalyzed
reaction.
41. An enzyme, known to follow M-M kinetics, was studied and the following data was obtained:
[S] mM
Rate Product Formed (
mol/min)
1.5
0.21
2.0
0.24
3.0
0.28
4.0
0.33
8.0
0.40
16.0
0.45
Use L-B analysis to determine K
m
and V
max
of this enzyme acting on substrate. (
You will need computer-graphing software, such as EXCEL, to complete this problem. On an exam, a graph may
be provided for you, but you might still need to label each axis and interpret the parameters from the graph.
). 42. How do we define the catalytic efficiency
of an enzyme? Which parameter is the best measure of the catalytic efficiency, and why? Calculate the catalytic efficiency for the enzyme from Problem #41. 43. Show, using the M-M equation, that when [S] >>> K
m
, v
o
= V
max
. Show, using the M-M equation that when [S] <<<K
m
, v
o
=[S][E
t
]k
cat
/K
m
. Explain the significance of the M-M under both high and
low substrate conditions.
44. What is catalytic perfection
? What physical phenomenon defines the upper limit on how fast an enzyme can convert a product into substrate? How does this phenomena drive the evolution of enzymes that participate in channeling? Use the M-M equation to show that the limit on efficiency is the rate of binding the substrate to the enzyme. 45. Write the equation for the random TCM and the ordered TCM models, including all rate constants. What is the major distinction between the random TCM and the ordered TCM?
46. Write the equation for the Ping-Pong (PiPo) model of enzyme kinetics. What is the major distinction between the random/ordered type kinetics and Ping-Pong kinetics?
47. A true story. An enzyme can catalyze a reaction with either of 2 substrates, S
1
or S
2
. The K
m
for S
1
was found to be 2.0 mM and the K
m
for S
2
was found to be 20 mM. A student determined that the V
max
was the same for the two substrates. Unfortunately
, she lost the page of her notebook and needs to know the value for V
max
. She carried out two reactions, one with 0.1 mM S
1
and the other with 0.1 mM S
2
. Unfortunately
, she forgot to label which reaction tube contained which substrate. Determine the value of V
max
from the results she obtained. Tube Number
Rate of Formation of Product
1
0.5
2
4.8
48. An enzyme catalyzes a reaction at a velocity of 20
mol/min when the concentration of substrate (S) is 0.01 M. The K
m
for this substrate is 1 X 10
– 5
M. Assuming that Michaelis-Menten kinetics are followed, what will the reaction velocity be when the concentration of S is (a) 1 X 10
– 5
M and (b) 1 X 10
– 6
M?
49. When 10
g of an enzyme of Mass (M
r
) 50,000 g / mol is added to a solution containing its substrate at a concentration one hundred timed K
m
, it catalyzes the conversion of 75
mol of substrate into product in 3 minutes. What is the k
cat (k
2
) of the enzyme? Recall that k
cat
and k
2
are, for our purposes, equivalent. 50. The muscle enzyme lactate dehydrogenase
catalyzes the reaction: pyruvate +NADH + H
+
lactate + NAD
+
. Solutions of NADH, but not NAD
+
, absorb light at
= 340 nm. Explain how this phenomenon could be used to design an enzyme activity assay for lactate dehydrogenase
. Note that the answer to this question is not in the PowerPoint. You need to use your prior knowledge of biochemistry concepts to work through this problem, as it involves concepts that span multiple topics.
Discuss your approach with your recitation group before speaking with your instructor.
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Related Questions
84°F
Partly sunny
Only the substrate molecule for a particular enzyme will fit into the active site. This is known as the lock-and-key mechanism. What does that
say about the relationship between the enzyme and the substrate?
O
The enzyme will catalyze two chemical reactions with one substrate.
The enzyme will catalyze all chemicals with one substrate.
O
The enzyme will not catalyze any chemicals with any substrates.
O
The enzyme will catalyze only one chemical with only one substrate.
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10:28
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arrow_forward
21. Michaelis-Menten kinetics is sometimes referred to as “saturation” kinetics. Why? 22. Give the Michaelis-Menten equation and define each term in it. Does this equation apply to all enzymes? If not, to which kind does it not apply? 23. Methanol (wood alcohol) is highly toxic because it is converted to formaldehyde in a reaction catalyzed by the enzyme alcohol dehydrogenase:NAD+ + methanol → NADH + H+ + formaldehydePart of the medical treatment for methanol poisoning is to administer ethanol (ethyl alcohol) in amounts large enough to cause intoxication under normal circumstances. Explain this in terms of what you know about examples of enzymatic reactions.
arrow_forward
4. What is the difference between catalysts and
intermediates?
Catalysts may appear in rate law expressions.
Intermediates may appear in rate law expres-
sions.
A catalyst gets made by an early step in a mech-
anism, but used up again in a later step.
An intermediate gets made by an early step in a
mechanism, but used up again in a later step.
arrow_forward
What is the function of the enzyme lactase?
arrow_forward
Consider this organic mechanism:
1
wwww.
H
c+
C
C
H-CI:
~
Does this mechanism describe an acid/base
reaction?
O
Note for advanced students: we mean only acid-
base reactions in the Brønsted-Lowry sense.
Which reactants, if any, are acting as Brønsted-
Lowry acids?
Which reactants, if any, are acting as Brønsted-
Lowry bases?
If you said this mechanism does describe an acid-
base reaction, draw the products of the reaction
on the right-hand side above.
X $
2
C
Yes!
Certainly not.
Who knows? We need more information
to decide.
2
Click and drag to
start drawing a
structure.
S
?
0
3
olo
Ar
3:
arrow_forward
When the energy of activation is low, many molecules have enough energy to cross the energy barrier and the reaction is
fast.
A) True
False
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->
esc
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$4
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7
1
2
3
4
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tab
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く
arrow_forward
A student proposes the following mechanism for the reaction, A→B:
A+X→AX
AX→B+X
Which of the following conclusions is most likely to be true?
A.
If correct, then X appears to be a catalyst.
B.
This doesn't make sense since this there is only one reactant and one product.
C.
This mechanism isn't right since a reactant appears that is not in the reaction.
D.
This mechanism is consistent with a second order reaction.
arrow_forward
What does "shape-selective catalysis" mean to you? Zeolites make effective shape-selective catalysts; why?
arrow_forward
(Q80) Using the information provided (and your work from Q79), what is the numerical value of the
rate constant for the rate law determined in Q79?
CHCI3 (g) + Cl2 (g) --> CCI4 (g) + HCI (g)
[CHCI3] (M)
[C2] (M)
Initial Rate (M/s)
0.010
0.010
0.0035
0.020
0.010
0.0069
0.020
0.020
0.0098
0.040
0.040
0.027
arrow_forward
Consider this organic mechanism:
X
olo
H-C1:
G
Click and drag to start
drawing a structure.
Ar
1
2
Does this mechanism describe an acid/base
reaction?
Note for advanced students: we mean only acid-
base reactions in the Brønsted-Lowry sense.
Yes!
O Certainly not.
OWho knows? We need more
information to decide.
Which reactants, if any, are acting as Brønsted-
Lowry acids?
01
02
Which reactants, if any, are acting as Brønsted-
Lowry bases?
01
02
If you said this mechanism does describe an
acid-base reaction, draw the products of the
reaction on the right-hand side above.
arrow_forward
Please explain it. ASAP
arrow_forward
1) Discuss the transition state(s) in reaction coordinate diagram in the context of ΔG.
2) If an enzyme deceases the activation energy, ΔG‡, by the quantity X, we learned that the forward rate constant is increased by multiplication with the factor eX/RT. Why does this simple fact demonstrate that small changes in activation energy give big changes in catalyzed rates?
7)Two people study the same enzyme. They get different Vmax in each experiment, but the same kcat. Why?
arrow_forward
Consider this organic mechanism:
A
H
H
: OH
1
2
Does this mechanism describe an acid/base
reaction?
Note for advanced students: we mean only acid-
base reactions in the Brønsted-Lowry sense.
Yes!
O Certainly not.
OWho knows? We need more
information to decide.
Which reactants, if any, are acting as Brønsted-
Lowry acids?
01
02
Which reactants, if any, are acting as Brønsted-
Lowry bases?
01
02
If you said this mechanism does describe an
acid-base reaction, draw the products of the
reaction on the right-hand side above.
Explanation
Check
X
X
Click and drag to stało
drawing a structure.
G
洄
18
P
arrow_forward
What is the activation of the forward reaction if the reactants have a ∆G = –10 kJ, the transition state has a ∆G = +15 kJ and the products have a ∆G = –50 kJ?
arrow_forward
ch 4 pdf
Diagrams, below.
a. Label the X and Y axes as either Increasing Energy or Reaction Coordinate, as in
Loudon.
b. Label the Reactants (R), Products (P) and Transition State (TS)
c. Indicate the standard free energy of activation (activation barrier, AGo) for each
step of each diagram, using the labels and arrows as Loudon does. Assume the
scales are the same in each diagram.
d. Indicate the standard free energy of reaction (AGo) in each.
e. How many steps are there for this reaction?
faster and slower step in each diagram.
If more than one, label the
f. Is one reaction faster than the other?
If so, which is fastest?
_Why?
g. Is one reaction more favored than the other?
If so, which is more favored?
Why?
arrow_forward
Consider this organic mechanism:
E
H
H
1
Calculator
: OH
Click and drag to start
drawing a structure.
2
Does this mechanism describe an acid/base
reaction?
Note for advanced students: we mean only acid-
base reactions in the Brønsted-Lowry sense.
Yes!
Certainly not.
Owho knows? We need more
information to decide.
Which reactants, if any, are acting as Brønsted-
Lowry acids?
01
02
Which reactants, if any, are acting as Brønsted-
Lowry bases?
01
02
If you said this mechanism does describe an
acid-base reaction, draw the products of the
reaction on the right-hand side above.
×
olo
Ar
BE
arrow_forward
4. The reaction shown below is part of the glycolytic pathway. The standard free energy change
for this reaction is +0.4 kcal/mol.
Glucose-6-phosphate (G6P) €→ Fructose-6-phosphate (F6P)
C) Steady-state concentrations of these compounds in the cell (at 25°C) are 0.675 mM G6P and 0.0969
mM F6P. In which direction is this reaction allowed to proceed in the cell? (show calculations)
arrow_forward
Which of the following are true statements about catalysts (choose all that apply)?
O A catalyst effectively creates an extra path for the reaction to travel that is higher in energy
O A catalyst is completely consumed in a reaction
O A catalyst works by lowering the energy barrier to a reaction
O A catalyst helps keep reactants stable at higher temperatures
O An enzyme is a biological catalyst
O A catalyst is a substance that increases the rate of a chemical reaction
arrow_forward
Need help, please.
arrow_forward
elementary reaction
NO₂Cl(g) NO₂(g) + Cl(g)
2NO(g) + Br₂(g) 2NOBr(g)
F(g) + H₂(g) HF (g) + H(g)
molecularity
unimolecular
bimolecular
Cannot be determined.
unimolecular
bimolecular
Cannot be determined.
unimolecular
bimolecular
Cannot be determined.
termolecular
quadrimolecular
termolecular
quadrimolecular
termolecular
quadrimolecular
arrow_forward
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- What is the function of the enzyme lactase?arrow_forwardConsider this organic mechanism: 1 wwww. H c+ C C H-CI: ~ Does this mechanism describe an acid/base reaction? O Note for advanced students: we mean only acid- base reactions in the Brønsted-Lowry sense. Which reactants, if any, are acting as Brønsted- Lowry acids? Which reactants, if any, are acting as Brønsted- Lowry bases? If you said this mechanism does describe an acid- base reaction, draw the products of the reaction on the right-hand side above. X $ 2 C Yes! Certainly not. Who knows? We need more information to decide. 2 Click and drag to start drawing a structure. S ? 0 3 olo Ar 3:arrow_forwardWhen the energy of activation is low, many molecules have enough energy to cross the energy barrier and the reaction is fast. A) True False Gp 么 -> esc # $4 ! 7 1 2 3 4 e r t tab d f j a 00 くarrow_forward
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- Consider this organic mechanism: X olo H-C1: G Click and drag to start drawing a structure. Ar 1 2 Does this mechanism describe an acid/base reaction? Note for advanced students: we mean only acid- base reactions in the Brønsted-Lowry sense. Yes! O Certainly not. OWho knows? We need more information to decide. Which reactants, if any, are acting as Brønsted- Lowry acids? 01 02 Which reactants, if any, are acting as Brønsted- Lowry bases? 01 02 If you said this mechanism does describe an acid-base reaction, draw the products of the reaction on the right-hand side above.arrow_forwardPlease explain it. ASAParrow_forward1) Discuss the transition state(s) in reaction coordinate diagram in the context of ΔG. 2) If an enzyme deceases the activation energy, ΔG‡, by the quantity X, we learned that the forward rate constant is increased by multiplication with the factor eX/RT. Why does this simple fact demonstrate that small changes in activation energy give big changes in catalyzed rates? 7)Two people study the same enzyme. They get different Vmax in each experiment, but the same kcat. Why?arrow_forward
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