Kinetics Problem Set 2
1.
The enzyme rhodanase catalyzes the reaction of cyanide ion with thiosulfate to form thiocyanate and
sulfite.
CN- + S-SO3-2 -> SCN- + SO3-2
The thermodynamic activation parameters of this reaction when it occurs spontaneously uncatalyzed
and when catalyzed by an inorganic metal complex and an enzyme, rhodanase, are given below. The
∆H+ and ∆S+ parameters for the enzymic reaction were derived from the temperature dependence of
Vmax. The ∆G+ for all reactions are calculated at 300 K.
Parameter
Uncatalyzed
Metal Catalyzed
Catalyzed by Rhodanase
∆G+
23.7 kcal/mole
18.3 kcal/mole
15.1 kcal/mole
∆H+
12.3 kcal/mole
9.6 kcal/mole
7.5 kcal/mole
∆S+
-38.0 e.u.
-51 e.u.
-25.2 e.u.
a.
Is the uncatalyzed reaction favorable?
reasoning.
Are the catalyzed reactions favorable?
b.
Consider the ∆G+ term for the catalyzed and uncatalyzed reactions. How do these numbers illustrate
the function of catalysts (Please be specific, equations and diagrams may help).
c.
To what can you attribute the decrease (becoming more unfavorable) in ∆S+ in the metal catalyzed
vs. uncatalyzed reaction. What special feature(s) of enzymes can explain why the enzyme catalyzed
reaction is characterized by a more favorable ∆S+ than either the uncatalyzed or metal catalyzed
reaction.
2.
Begining with enzyme and substrates, describe how you would obtain the data presented in the
enzyme catalyzed column of the table give in question 13. Be sure to include the thermodynamic
equations needed to derive the data and a brief description of how the Vmax would be determined
from velocity data. IT IS NOT NECESSARY TO DERIVE A RATE LAW.
1
Explain your
3.
Plastocyanin is an enzyme containing a single Cu++ atom. The enzyme catalyzes the single electron
oxidation of e- donating substrates. This is catalyzed by the reduction of the copper, Cu++->Cu+. This copper
reduction can be followed by monitoring the disappearence of the Cu++-associated blue color of the protein.
a. What order is displayed by the reaction:
k1
Cu++ + reduced ascorbate → Cu+ + oxidized ascorbate?
Be sure to justify your answer.
b. At a constant enzyme concentration (1 nM), the following results were obtained.
[Ascorbate], mM
Decrease in Abs/second
25
50
100
200
1.98
3.97
7.95
1.59
X 10-9
X 10-9
X 10-9
X 10-8
Calculate the rate constant for reduction of plastocyanin by ascorbate. Please detail the assumptions
you made in obtaining this value from the data.
c. Below are the temperature dependence data obtained for the reduction of plastocyanin by
ascorbate and dimethylphenylene diamine (DMPD).
Reduction by ascorbate
Temp (C)
25
30
56.2
78.2
(M-1 s-1) X 107)
k
0.795
2.37
104
1450
Reduction by DMPD
Temp (C)
10
18
25
42
60
(M-1 s-1) X 102)
k
2.34
3.25
4.5
7.5
15.2
i) Calculate the ∆H+ and ∆S+ for each set of data.
ii) For each substrate, describe whether the ∆H+ and ∆S+ parameters are favorable or unfavorable.
iii) For each substrate, consider the value of ∆S+. State whether you think the rate-limiting process
for the reduction of plastocyanin by each substrate is uni-molecular or bi-molecular. Explain your
answer. (THIS IS A HARD QUESTION, BUT NOT OUTSIDE OF YOUR EXPERTISE.)
2