Activation enthalpies and entropies for the microscopic rate constants of acetate-catalyzed isomerization of 5-androstene-3,17-dione

Article abstract of DOI:10.1021/ja035957r

Both acetic acid and acetate catalyze the isomerization of 5-androstene-3,17-dione (1) to its conjugated isomer, 4-androstene-3,17-dione (3), through a dienol(ate) intermediate. The temperature dependence of the overall isomerization rate constants and of the microscopic rate constants for this isomerization was determined, and the Arrhenius plots give the activation enthalpy and entropy for each step. The source of the activation energy for the overall isomerization and for each of the individual steps is predominantly enthalpic, with a moderate to low entropic penalty. Additionally, the entropy and enthalpy for the keto - enol equilibrium of 1 and dienol were determined; this equilibrium is entirely controlled by enthalpy with no entropic contribution. The relevance of these results to the mechanism of the isomerization of 1 catalyzed by the enzyme 3-oxo-Δ⁵-steroid isomerase is discussed.

Full text of DOI:10.1021/ja035957r

Published on Web 07/30/2003
Activation Enthalpies and Entropies for the Microscopic Rate
Constants of Acetate-Catalyzed Isomerization of
5-Androstene-3,17-dione
Wendy J. Houck and Ralph M. Pollack*
Contribution from the Department of Chemistry and Biochemistry, UniVersity of Maryland,
Baltimore County, 1000 Hilltop Circle, Baltimore, Maryland 21250
Received May 5, 2003; E-mail: pollack@umbc.edu
Abstract: Both acetic acid and acetate catalyze the isomerization of 5-androstene-3,17-dione (1) to its
conjugated isomer, 4-androstene-3,17-dione (3), through a dienol(ate) intermediate. The temperature
dependence of the overall isomerization rate constants and of the microscopic rate constants for this
isomerization was determined, and the Arrhenius plots give the activation enthalpy and entropy for each
step. The source of the activation energy for the overall isomerization and for each of the individual steps
is predominantly enthalpic, with a moderate to low entropic penalty. Additionally, the entropy and enthalpy
for the keto-enol equilibrium of 1 and dienol were determined; this equilibrium is entirely controlled by
enthalpy with no entropic contribution. The relevance of these results to the mechanism of the isomerization
5
of 1 catalyzed by the enzyme 3-oxo-∆ -steroid isomerase is discussed.
Introduction
Isomerizations involving enol(ate) intermediates have been
proton abstraction from the R-carbon of the ketone to form an
intermediate dienol(ate), followed by subsequent reprotonation
17,18
at the γ-carbon.
An important example of this type of
extensively studied because of their simple chemistry and the
occurrence of this type of reaction in the action of many
important enzymes. Much effort has gone into the elucidation
of the mechanisms of enzymes that catalyze this reaction, such
reaction is the isomerization of 5-androstene-3,17-dione (1), a
substrate for KSI, to its conjugated isomer, 4-androstene-3,17-
dione (3), shown in Scheme 1. Isomerization of 1 is catalyzed
by acid, hydroxide, and acetate, as well as KSI.8
19
20
11
1
-4
5-7
as triosephosphate isomerase, 4-oxalocrotonate isomerase,
5
8-14
and 3-oxo-∆ -steroid isomerase (ketosteroid isomerase, KSI).
Scheme 1
The chemistry that occurs is of particular interest because these
enzymes are able to accelerate the rate of reaction up to 15
orders of magnitude.15,16
The general mechanism for the nonenzymatic isomerization
of â,γ-unsaturated ketones involves acid- or base-catalyzed
(
1) Knowles, J. R. Philos. Trans. Biol. Sci. 1991, 322, 115.
2) Raines, R. T.; Sutton, E. L.; Straus, D. R.; Gilbert, W.; Knowles, J. R.
Biochemistry 1986, 25, 7145.
Our interest in the acetate-catalyzed isomerization of 1 is
related to its use as a model for the corresponding isomerization
by KSI. Acetate is a particularly good model for KSI because
(
(
3) Hermes, J. D.; Blacklow, S. C.; Knowles, J. R. Cold Spring Harbor Symp.
Quant. Biol. 1987, 52, 597.
(1) the reaction mechanisms are quite similar, (2) KSI uses the
(4) Amyes, T. L.; O’Donoghue, A. C.; Richard, J. P. J. Am. Chem. Soc. 2001,
1
23, 11325.
same functional group as the active site base, Asp38, and (3)
(
5) Whitman, C. P. Arch. Biochem. Biophys. 2002, 402, 1.
6) Czerwinski, R. M.; Harris, T. K.; Massiah, M. A.; Mildvan, A. S.; Whitman,
C. P. Biochemistry 2001, 40, 1984.
2
1,22
(
acetate and Asp38 of KSI have similar pKa’s.
Both mech-
anisms involve proton abstraction from C-4 by a carboxylate
followed by reprotonation at C-6. Because of these similarities,
acetate has served as a useful model to study the kinetics and
(
(
(
7) Taylor, A. B.; Czerwinski, R. M.; Johnson, W. H., Jr.; Whitman, C. P.;
Hackert, M. L. Biochemistry 1998, 37, 14692.
8) Pollack, R. M.; Thornburg, L. D.; Wu, Z. R.; Summers, M. F. Arch.
Biochem. Biophys. 1999, 370, 9.
9-11
9) Thornburg, L. D.; Goldfeder, Y. R.; Wilde, T. C.; Pollack, R. M. J. Am.
Chem. Soc. 2001, 123, 9912.
mechanism of KSI.
We have previously determined the free-
energy profile for both the KSI-catalyzed isomerization of 1
(
10) Hawkinson, D. C.; Eames, T. C.; Pollack, R. M. Biochemistry 1991, 30,
1
0849.
(
(
11) Zeng, B.; Pollack, R. M. J. Am. Chem. Soc. 1991, 113, 3838.
12) Zhao, Q.; Abeygunawardana, C.; Gittis, A. G.; Mildvan, A. S. Biochemistry
(17) Noyce, D. S.; Evett, M. J. Org. Chem. 1972, 37, 394.
(18) Whalen, D. L.; Weimaster, J. F.; Ross, A. M.; Radhe, R. J. Am. Chem.
Soc. 1976, 98, 7319.
(19) Malhotra, S. K.; Ringold, H. J. J. Am. Chem. Soc. 1965, 87, 3228.
(20) Pollack, R. M.; Mack, J. P. G.; Eldin, S. J. Am. Chem. Soc. 1987, 109,
5048.
(21) Dean, J. A., Ed. Lange’s Handbook of Chemistry, 13th ed.; McGraw-Hill:
New York, 1985; pp 5-62.
(22) Pollack, R. M.; Bantia, S.; Bounds, P. L.; Koffman, B. M. Biochemistry
1986, 25, 1905.
1
997, 36, 14616.
(
(
(
(
13) Massiah, M. A.; Abeygunawardana, C.; Gittis, A. G.; Mildvan, A. S.
Biochemistry 1998, 37, 14701.
14) Ha, N. C.; Choi, G.; Choi, K. Y.; Oh, B. H. Curr. Opin. Struct. Biol. 2001,
1
1, 674.
15) Whitman, C. P.; Aird, B. A.; Gillespie, W. R.; Stolowich, N. J. J. Am.
Chem. Soc. 1991, 113, 3154.
16) Radzicka, A.; Wolfenden, R. Science 1995, 267, 90.
10206
9
J. AM. CHEM. SOC. 2003, 125, 10206-10212
10.1021/ja035957r CCC: $25.00 © 2003 American Chemical Society

Enthalpy and Entropy of 5-Androstene-3,17-dione
A R T I C L E S
Table 1. Rate Constants for the Overall Isomerization of 1 to 3
a
Catalyzed by Acetic Acid and Acetate Ion
5
HOAc
5
OAc
temperature
°C)b
10 kisom
10 kisom
(
(M-1 s-1
)
(M-1 s-1
)
1
1
2
2
2
3
3
0.3
5.2
0.0
5.0
9.9
4.7
9.8
0.55 ( 0.05
1.0 ( 0.2
1.8 ( 0.4
2.2 ( 0.4
3.6 ( 0.8
5.0 ( 1.0
5.7 ( 1.6
1.06 ( 0.05
1.4 ( 0.2
2.5 ( 0.4
3.3 ( 0.4
5.4 ( 0.8
8.4 ( 1.0
14.9 ( 1.6
a
.3% MeOH, µ ) 1.0 M with NaCl. b Reported temperatures are (0.1
3
°
C.
and the corresponding acetate-catalyzed reaction at 25°.10,11 In
each case, all of the microscopic rate constants of Scheme 1
were determined. The present work extends those experiments
with acetate to cover a range of temperatures. The activation
enthalpies and entropies for the enolization and ketonization
steps, as well as the equilibrium constants for various species
of the isomerization reaction, are analyzed and discussed.
Figure 1. Plot of the temperature dependence of isomerization of 1
catalyzed by acetic acid ([) and acetate ion (0). Error bars represent one
standard deviation.
Table 2. Rate Constants for the Conversion of 1 to 2 Catalyzed by
Acetate Iona
Results
3
OAc(4R)
3
OAc(4â)
1
temperature
°C)b
10 k
(M-1 s-1
1
10 k
(M-1 s-1
)
Thermodynamic activation parameters for reactions can be
determined through an examination of temperature-dependent
kinetics according to the Arrhenius law: ln(k) ) ln(A) - Ea/
RT, where k is the rate constant, Ea is the activation energy
(
)
1
1
2
2.8
9.2
5.5
0.73 ( 0.08
1.33 ( 0.13
1.7 ( 0.5
0.63 ( 0.11
0.91 ( 0.18
1.8 ( 0.2
q
related to the enthalpy of activation (∆H ), R is the ideal gas
32.9
4.8 ( 0.9
4.4 ( 0.7
constant, T is the temperature in degrees Kelvin, and A is a
preexponential term related to the entropy of activation (∆S )
as shown in eq 1:
a
3.3% MeOH, µ ) 1.0 M with NaCl. b Reported temperatures are (0.2
q
°
C.
C-4 of 1 in D2O was monitored by NMR in acetic acid/acetate
ion buffers (pD ) 4.5-5.5, ca. 13-33 °C). Peaks due to the
two C-4 protons, R and â, have chemical shifts of 2.82 and
∆
S/R
A ) (k T/h)e
(1)
B
1
1
Over small temperature ranges, a plot of ln(k) vs 1/T is gen-
erally linear, yielding a slope that corresponds to the enthalpy of
activation. From the intercept of this line, the entropy of activa-
tion can be determined. In a similar manner, by measuring equil-
ibrium constants (K) over a range of temperatures, the enthalpies
and entropies associated with these equilibria can be determined
using the van’t Hoff equation, ln(K) ) -∆H/RT + ∆S/R.
Temperature Dependence of the Rate Constant for
Overall Isomerization of 1 to 3 (kisom). Acetate-catalyzed iso-
merization of 1 was monitored spectrally by observing the in-
crease in absorbance at 248 nm due to conversion of 1 to 3
3.45 ppm, respectively. These peaks were integrated relative
to the C-19 methyl peak (1.2 ppm) as a function of time using
FELIX 2.3 software (Biosym Technologies, San Diego, CA).
The 1.2 ppm peak was normalized to 1.000 at t ) 0 s and did
not change with respect to time; thus, it serves as an internal
standard. Relative integration areas for both C-4R and C-4â
protons vs time were fit to a pseudo-first-order exponential decay
to yield values of the rate constants for exchange of H-4R and
H-4â, kobsR and kobs , respectively. Plots of kobs and kobsâ vs
the concentration of acetate are linear, with no contribution from
HOAc catalysis and yield the second-order rate constants for
â
R
OAc
OAc
(
4
pH ) 3.7-5.3, ca. 10-40 °C). The reaction was followed for
-5 half-lives, and progress curves were fit to a first-order ex-
ponential increase to give the observed rate constants. These rate
constants were then plotted vs total acetate concentration
the conversion of 1 to 2, k1 (4R) and k1 (4â), respectively
(Table 2).
The Arrhenius plots of ln k1OAc(4R) and ln k1OAc(4â) are linear
q
(Figure 2), with slopes corresponding to ∆H ) 15 ( 2 kcal/
-
(
[AcO ] + [AcOH]) to yield kisom. y-Intercepts of plots of kisom
mol and 16.4 ( 1.9 kcal/mol, respectively, and y-intercepts cor-
OAc
OAc
OAc
q
vs the mole fraction of acetate (mf ) at mf
) 0 and mf
responding to T∆S ) -6 ( 2 and -5.0 ( 1.8 kcal/mol,
)
1 yield the second-order rate constants for acetic acid-catalyzed
respectively.
HOAc
isomerization of 1 (kisom
) and acetate ion-catalyzed isomer-
Temperature Dependence of the Rate Constant for
Conversion of 2 to 1 (k-1). Conversion of 2 to 1 was monitored
by using sequential-mixing stopped flow, as previously de-
OAc
ization of 1 (kisom ), respectively (Table 1). As was previously
observed in our laboratory,11 isomerization of 1 to 3 is catalyzed
by both acetic acid and acetate ion. Agreement with previously
determined values at 25.0 °C is excellent ((<5%).
11
-
scribed. Dienolate (2 ) is formed by rapidly mixing a solution
2
0
of 1 with 0.1 M NaOH for ca. 0.5 s. When this solution is
quenched with acetate buffer, 2 is rapidly protonated to give
OAc
HOAc
-
Arrhenius plots of ln kisom
and ln kisom
are shown in
q
Figure 1, with slopes corresponding to ∆H ) 15.2 ( 0.8 and
2, which is then converted more slowly, almost exclusively, to
1, resulting in a decrease in absorbance. The decay traces at
243 nm were fit to a first-order exponential decay to give the
rate constants for acetate ion-catalyzed conversion of 2 to 1 at
pH 3.9-5.1, ca. 7-41 °C. Since the rate of isomerization of 1
13.5 ( 0.8 kcal/mol, respectively, and y-intercepts corresponding
q
to T∆S ) -8.3 ( 0.8 and -10.3 ( 1.0 kcal/mol, respectively.
Temperature Dependence of the Rate Constant for
Conversion of 1 to 2 (k1). Proton exchange with deuterium at
J. AM. CHEM. SOC.
9
VOL. 125, NO. 34, 2003 10207

A R T I C L E S
Houck and Pollack
Table 4. Rate Constants for Hydroxide-Catalyzed Interconversion
-a
of 1 and 2
temperature
°C)b
OH
H O
-1
(s-1
)
k
1
k
2
(
(M-1 s-1
)
15.9
20.3
25.6
30.7
35.5
40.3
27.3 ( 0.1
35.0 ( 0.2
49.2 ( 0.7
65.5 ( 1.3
81.7 ( 0.6
113 ( 3
1.17 ( 0.01
1.89 ( 0.03
2.90 ( 0.09
4.51 ( 0.17
7.40 ( 0.09
10.6 ( 0.4
a
.3% MeOH, µ ) 1.0 M with NaCl. b Reported temperatures are (0.1
3
°
C.
buffer results almost exclusively in formation of 1 rather than
3
)
(e.g., k-1 . k2), k2 can be calculated from the equation kisom
k1k2/k-1. Calculations using the rate constants from the
previous three sections show that conversion of 2 to 3 is
Figure 2. Plot of the temperature dependence of acetate ion-catalyzed
proton abstraction of H-4R (O) and H-4â (f) from 1. Error bars represent
one standard deviation.
OAc
HOAc
catalyzed by both acetate ion (k2 ) and acetic acid (k2
)
(
Supporting Information, Table S1). The activation parameters
OAc
q
q
for k2
1
are ∆H ) 12.0 ( 1.8 kcal/mol and T∆S ) -8.4 (
HOAc
q
.8 kcal/mol, and for k2
they are ∆H ) 10.3 ( 1.7 kcal/
q
mol and T∆S ) -10 ( 2 kcal/mol.
Temperature Dependence of the Rate Constant for
-
Hydroxide-Catalyzed Interconversion of 1 and 2 . When 1
is mixed with relatively high concentrations of NaOH, the
-
absorbance increases rapidly because of formation of 2 and
-
20
then more slowly as 2 is converted into 3. To make formation
of 3 invisible, the absorbance was monitored at or near 255
-
nm, the isosbestic point for 2 and 3. These traces were fit to
a single exponential increase to give the observed pseudo-first-
order rate constants for hydroxide-catalyzed deprotonation of
1
. Observed rate constants (an average of 6-10 runs) were
-
plotted vs [HO ] at each temperature (ca. 16-40 °C). The slopes
of these lines are equal to the second-order rate constants for
hydroxide-catalyzed proton abstraction from C-4 of 1 to form
-
OH
2
(k1 ), and the y-intercepts are equal to the rate constants
Figure 3. Plot of the temperature dependence of acetate ion-catalyzed
protonation at C-4 of 2. Error bars represent one standard deviation.
-
H O
for water-catalyzed protonation of 2 at C-4 to give 1 (k-1 2 )
q
q
OH
(Table 4). Values of ∆H and T∆S for k1 are 9.5 ( 0.2 and
Table 3. Rate Constants for the Conversion of 2 to 1 Catalyzed
H O
-
5.7 ( 0.2 kcal/mol, respectively, and for k-1
2
the values
by Acetate Iona
are 16.3 ( 0.4 and -0.6 ( 0.4 kcal/mol, respectively.
Temperature Dependence of the Equilibrium Constants
OAc
temperature
k
-1
(
°C)b
(M-1 s-1
)
1
2
for Ionization of 1(Ka ) and 2(Ka ). The ionization constant for
6
.5
0.18 ( 0.02
0.276 ( 0.009
0.473 ( 0.010
0.668 ( 0.008
0.913 ( 0.013
1.52 ( 0.09
1
1
(Ka ) can be calculated from the experimentally determined rates
for enolization (k1 ) and for reketonization (k-1 2 ), along with
the value for the ion activity product constant of water (KW).
1
2
2
3
3
4
2.8
0.9
5.5
0.0
4.9
0.7
OH
H O
OH
H O
The natural logarithms of both k1 and k-1
2
are linear with
respect to inverse temperature (Figure 4) and can be used with
2.3 ( 0.3
23
the known temperature dependence of KW to calculate the tem-
a
.3% MeOH, µ ) 1.0 M with NaCl. b Reported temperatures are (0.1
1
3
perature dependence of Ka (Supporting Information, Table S2).
°
C.
1
The value obtained for Ka at 25.0 °C is (1.73 ( 0.10) ×
-
13
1
1
0
M (pKa ) 12.76), which is in excellent agreement with
to 3 is much slower than the conversion of 2 to 1, there is neg-
ligible interfering absorbance change due to conversion of 1 to
2
0,24
previously determined values.
In a similar manner, the
2
ionization constant for 2 (Ka ) can be calculated from the
3. Plots of the observed rate constants vs total acetate concentra-
2
1
OAc
OAc
relationship Ka ) Ka k-1 /k1
Table S2). The value obtained for Ka at 25.0 °C is (3.0 ( 0.5)
10 M (pKa ) 10.5), which is in good agreement with the
(Supporting Information,
tion are linear with no contribution from catalysis by HOAc.
Table 3 lists these second-order rate constants (k-1 ) at each
2
OAc
-
11
2
×
temperature. Agreement with previously reported values at 25.0
1
1
1
2
previously determined value. Van’t Hoff plots of Ka and Ka
1
1
°
C
is excellent ((<5%). The Arrhenius plot of the natural
vs temperature yield the following enthalpies and entropies for
OAc
q
logarithm of k-1
12.4 ( 0.5 kcal/mol and T∆S ) -5.2 ( 0.5 kcal/mol.
Temperature Dependence of the Rate Constant for the
Conversion of 2 to 3 (k2). Since partitioning of 2 in acetate
is linear (Figure 3), giving values of ∆H
q
)
(23) Dean, J. A., Ed. Lange’s Handbook of Chemistry, 13th ed.; McGraw-Hill:
New York, 1985; pp 5-7.
(
24) Pollack, R. M.; Zeng, B.; Mack, J. P. G.; Eldin, S. J. Am. Chem. Soc.
1989, 111, 6419.
10208 J. AM. CHEM. SOC.
9
VOL. 125, NO. 34, 2003

Enthalpy and Entropy of 5-Androstene-3,17-dione
A R T I C L E S
Table 5. Thermodynamic Activation Parameters for
-
Interconversion of 1, 2, 2 , and 3
rate
∆G‡a
∆H‡
T∆S‡a
reaction
constant
(kcal/mol)
(kcal/mol)
(kcal/mol)
1
1
1
+ -OAc f 3
kisomOAc
HOAc
23.5 ( 0.1 15.2 ( 0.8
-8.3 ( 0.8
+ HOAc f 3
kisom
23.7 ( 0.1 13.5 ( 0.8 -10.3 ( 1.0
-
OAc
+
OAc f 2
k1 (4R)
21.1 ( 0.1
15 ( 2
-6 ( 2
OAc
k1 (4â)
21.4 ( 0.1 16.4 ( 1.9
17.6 ( 0.1 12.4 ( 0.5
20.4 ( 0.1 12.0 ( 1.8
20.7 ( 0.1 10.3 ( 1.7
-5.0 ( 1.8
-5.2 ( 0.5
-8.4 ( 1.8
-10 ( 2
-
-
OAc
2
2
2
1
2
2
2
+
+
OAc f 1
OAc f 3
k-1
k2
k2
k1
OAc
HOAc
+ HOAc f 3
-
-
OH
+
OH f 2
15.1 ( 0.1
9.5 ( 0.2
-5.7 ( 0.2
-0.6 ( 0.4
-4.2 ( 0.7
-2.1 ( 1.2
-0.7 ( 0.3
-
-
-
H O
+ H2O f 1
k-1
2
16.8 ( 0.1 16.3 ( 0.4
HOAc
+ HOAc f 3 k2′
12.5 ( 0.1
(4R) 10.1 ( 0.1
(4â) 10.3 ( 0.1
8.4 ( 0.6
8.0 ( 1.7
9.6 ( 1.8
HOAc
HOAc
+ HOAc f 1 k-1′
k-1′
a
Values given at 298 K.
example is the study by Vlas a´ k and Mindl, who determined
the enthalpies and entropies of activation for the alkaline hy-
drolysis of aryl carbazates. Although values of ∆G for hy-
Figure 4. Plots of the temperature dependence of hydroxide-catalyzed
OH
proton abstraction from 1 (k1 , b) and water-catalyzed protonation at C-4
-
H O
31
q
of 2 (k-1 2 , f). Error bars represent one standard deviation. Absence of
error bars indicate that the error is less than the size of the symbol.
droxide-catalyzed hydrolysis of both phenylcarbazate and phen-
q
yl-2-methyl carbazate are similar (∆G ) 20.7 and 22.1 kcal/
these ionizations: ∆H°Ka1 ) 7.8 ( 0.4 kcal/mol and T∆S°Ka
1
)
mol, respectively), the difference in their entropies of activation
2
2
-
)
9.6 ( 0.5 kcal/mol; ∆H°Ka ) 4.6 ( 0.3 kcal/mol and T∆SK°a
-9.7 ( 0.5 kcal/mol (Table 6).
q
is quite large (T∆S ) -0.6 and -10.8 kcal/mol, respectively).
The authors attribute this to a difference in the mechanism of
hydrolysis for the two seemingly similar carbazates. Thus,
phenylcarbazate undergoes an E1cB mechanism because of the
loss of the ionizable proton on the nitrogen adjacent to the car-
bonyl group, whereas phenyl-2-methyl carbazate, which does not
have an ionizable proton at that position, undergoes a BAc2
mechanism.
Discussion
Several factors determine the overall entropy change for
second-order reactions between two molecules, A and B: (1)
reorganization of the solvent molecules surrounding the reactants
q
when A and B are brought together results in a positive ∆S ,
(
2) restriction of translational and rotational motion when A
Very little research has focused on activation enthalpies and
entropies for enolizations. Chiang et al. have examined the
temperature dependence of perchloric acid-catalyzed enolization
of acetone and ketonization of its enol in both water and
q
and B are brought together results in a negative ∆S , and (3)
other properties specific to A and B and the nature of the ensuing
transition state may result in either a positive or negative ∆S .
For example, when neutral reactants form charged transition
states, the entropy of activation is usually negative because of
restriction of solvent molecules, whereas when charged reactants
form uncharged (or less charged) transition states, the entropy
of activation is usually positive because of the freeing up of
solvent molecules.25 Additionally, the formation of low-
frequency vibrational levels often results in a positive change
q
3
2
acetonitrile. They found the entropies of activation for
enolization of acetone to be similar in both water and acetonitrile
q
32
(T∆S ) -3.6 and -1.7 kcal/mol, respectively). Additionally,
the enthalpies of activation for this enolization are similar in
q
both solvents (∆H ) 20.0 and 20.2 kcal/mol, respectively).
They compared the thermodynamic parameters for the keto-
enol equilibrium in solution with those in the gas phase and
found the values to be similar also. While these studies and
26-28
in entropy.
Bimolecular reactions generally result in a neg-
2
9,31,33,34
others
have interpreted the thermodynamic activation
ative entropy of activation, which is predominantly due to the
loss of translational and overall rotational motion.26 Moore and
parameters for relatively simple bimolecular processes, there
have been no comprehensive studies of the temperature depen-
dence of the microscopic rate constants for acid and base-
catalyzed enolization/ketonization or isomerization.
Jencks compared an intermolecular nucleophilic attack of acetate
on p-nitrophenylthioacetate to form acetic anhydride to the intra-
molecular reaction of p-nitrophenyl thiosuccinate to form suc-
cinic anhydride. The intramolecular reaction has a more favor-
able entropy of activation by ca. 5 kcal/mol.30 The authors attri-
bute this entropy difference to the two reactants having already
been brought together in the unimolecular reaction, thereby
overcoming the negative entropy associated with that step.
29
Overall Isomerization of 1 to 3. Isomerization of 1 to 3 is
q
catalyzed by both acetic acid and acetate ion. While ∆G for
q
both processes is similar (∆G HOAc ) 23.5 ( 0.1 kcal/mol and
q
∆
G OAc ) 23.7 ( 0.1 kcal/mol), the enthalpies and entropies
of activation differ slightly (Table 5). That is, while the enthalpy
The magnitude of activation entropies can vary because of
the relative importance of the above factors. One notable
(
30) Entropy (∆S), as determined from eq 1, has units of cal/mol K. We report
and discuss the entropic contribution to free energy (T∆S) in kcal/mol for
comparison to ∆H and ∆G. Thus, a negative value for T∆S is considered
an entropy loss (entropic disadvantage), while a positive value for T∆S is
considered an entropy gain (entropic advantage).
(
25) Carey, F. A.; Sundberg, R. J. AdVanced Organic Chemistry, Part A:
Structure and Mechanisms, 3rd ed.; Plenum: New York, 1990; p 196.
26) Page, M. I.; Jencks, W. P. Proc. Natl. Acad. Sci. U.S.A. 1971, 68, 1678.
27) Tidor, B.; Karplus, M. J. Mol. Biol. 1994, 238, 405.
(31) Vlas a´ k, P.; Mindl, J. J. Chem. Soc., Perkin Trans. 2 1997, 1401.
(32) Chiang, Y.; Kresge, A. J.; Schepp, N. P. J. Am. Chem. Soc. 1989, 111,
3977.
(33) Casale, J. F.; Lewin, A. H.; Bowen, J. P.; Carroll, F. I. J. Org. Chem.
1992, 57, 4906.
(34) Bowden, K.; Byrne, J. M. J. Chem. Soc., Perkin Trans. 2 1997, 123.
(
(
(
28) Vill a´ , J.; Sˇ trajbl, M.; Glennon, T. M.; Sham, Y. Y.; Chu, Z. T.; Warshel,
A. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 11899.
(29) Moore, S. A.; Jencks, W. P. J. Biol. Chem. 1982, 257, 10882.
J. AM. CHEM. SOC.
9
VOL. 125, NO. 34, 2003 10209

A R T I C L E S
Houck and Pollack
Table 6. Thermodynamic Equilibrium Parameters for
Scheme 2
-
Interconversion of 1, 2, and 2
equilibrium
constant
∆G°a
(kcal/mol)
∆H°
(kcal/mol)
T∆S°a
(kcal/mol)
reaction
-
+
Ka1
Ka
1
2
2
1
h 2 + H
17.4 ( 0.1 7.8 ( 0.4 -9.6 ( 0.5
14.5 ( 0.1 4.6 ( 0.3 -9.7 ( 0.5
7.9 ( 0.1 3.6 ( 0.2 -4.2 ( 0.7
-
+
2
h 2 + H
-
+ -OAc h 2 + HOAc Keq
h 2
Kext
2.9 ( 0.1 3.2 ( 0.4
0.1 ( 0.5
a
Values given at 298 K.
Scheme 3
of activation is more favorable for the acid-catalyzed process,
the entropy of activation is more favorable for the base-catalyzed
process by ca. 2 kcal/mol. Since isomerization of 1 to 3 by
acetate ion/acetic acid involves several steps and is pH depend-
ent, it is necessary to determine the activation parameters for
each of these steps, k1, k-1, and k2, to make useful interpretations
of the thermodynamic data.
Acetate Ion-Catalyzed Conversion of 1 to 2 (k1OAc).
Although the overall isomerization is catalyzed by both acetic
acid and acetate ion, catalysis of the initial step, proton ab-
straction from C-4, occurs only by acetate ion. Thus, the mech-
anism for formation of the dienol is most reasonably interpreted
as a simple single-step proton abstraction from either C-4R or
Scheme 4
OAc
OAc
C-4â of the steroid. Both k1 (4R) and k1 (4â) have a rela-
q
tively large enthalpic penalty (∆H ) ca. 16 kcal/mol) and a
q
moderate entropic penalty (T∆S ) ca. -5 kcal/mol) (Table 5).
These values can be compared with those for methoxide-
catalyzed proton abstraction from the R-carbon of ecgonine
q
q
33
methyl ester (∆H ) 17 kcal/mol, T∆S ) -6.6 kcal/mol)
and nucleophilic attack of hydroxide on methyl cis-3-benzoyl-
q
for protonation of acetone enol by perchloric acid (∆H ) 9.7
q
q
2
,3-diphenylacrylate (∆H ) 13.8 kcal/mol, T∆S ) -6.0 kcal/
32
HOAc
kcal/mol). The entropy of activation for k2
is quite large
34
mol). Both of these reactions result in partial bond formation
between a base or nucleophile with the reactant, and both result
in the formation of a partial negative charge at the transition state.
Similar enthalpies and entropies of activation are observed with
acetate ion-catalyzed proton abstraction from 1. As shown in
q
OAc
and negative (T∆S ) -10 kcal/mol). Similar to k1 , bringing
two reactants together is expected to result in a negative entropy.
HOAc
For k2
, however (as shown in Scheme 3), there is an
additional entropy loss during proton transfer due to the
development of two new partial charges from previously neutral
dienol. The partial positive on the enol oxygen of 2 and the
partial negative on the acetic acid oxygen are ex-
pected to restrict solvent molecules at the transition state, leading
OAc
Scheme 2, the transition state for k1 (TS1) involves (1) partial
bond formation between acetate ion and either the R or â proton
and (2) formation of an incipient carbanion at C-4 whose neg-
ative charge is delocalized onto O-3 of the carbonyl. A negative
entropy for deprotonation at either C-4R or C-4â is not
unexpected, as this step requires bringing two molecules together
HOAc
OAc
to a more negative entropy of activation for k2
Acetate Ion-Catalyzed Conversion of 2 to 3 (k2 ). The
mechanism for acetate ion-catalyzed conversion of 2 to 3 (k2
than k1
.
OAc
OAc
)
(
loss of entropy), followed by partial bond formation, which
can be broken down into two steps as shown in Scheme 4.
The first step is a rapid equilibrium between acetate ion/dienol
2
6,28
results in low-frequency vibrations (small gain of entropy).
The activation parameters of acetate-catalyzed proton abstraction
and acetic acid/dienolate (Keq), and the second step involves
OAc
(
k1 ) can also be compared to proton abstraction by hydroxide
HOAc
proton transfer from acetic acid to the dienolate at C-6 (k2′
).
OH
ion (k1 ). The activation entropies for both reactions are
The equilibrium constant for the first step is the ratio of the
experimentally indistinguishable (Table 5). The relative base
2
HOAc
ionization constants for 2 and acetic acid (Keq ) Ka /Ka
).
strengths, though, are evidenced in the lower heat of activation
Keq was calculated over a range of temperatures (Supporting
q
(
∆∆H ca. -6 kcal/mol) for the hydroxide ion reaction.
2
Information, Table S3) from the temperature dependence of Ka
HOAc
Partitioning of the Intermediate Dienol (2) (k-1 and k2).
(Table 6) and the temperature independence of Ka
over the
HOAc
HOAc
-5
23
Acetic Acid-Catalyzed Conversion of 2 to 3 (k2
). Proto-
range studied here (Ka
) 1.75 × 10 M ). The activation
OAc
nation of 2 at C-6 (k2) is catalyzed by both acetate ion (k2
)
parameters for this equilibrium are ∆HKeq ) 3.6 kcal/mol and
HOAc
HOAc
and acetic acid (k2
). The acetic acid-catalyzed conversion
) is most simply interpreted as direct protonation of 2
dienol) by acetic acid. The corresponding activation enthalpy
T∆SKeq ) -4.2 kcal/mol (Table 6). The magnitude of k2′
HOAc
HOAc
(k2
at various temperatures was calculated from the equation k2′
1
1
OAc
(
) k2 /Keq (Supporting Information, Table S3). From these
-
HOAc
for this step is 10.3 kcal/mol (Table 5), which is similar to that
results, protonation of 2 at C-6 by acetic acid (k2′
) has an
10210 J. AM. CHEM. SOC.
9
VOL. 125, NO. 34, 2003

Enthalpy and Entropy of 5-Androstene-3,17-dione
A R T I C L E S
Scheme 5
Scheme 7
As shown previously,11 protonation of 2 at C-4R is competi-
-
activation enthalpy and an activation entropy of 8.4 and -4.2
kcal/mol, respectively (Table 5).
tive with protonation at C-4â. In contrast, protonation at C-6R
is ca. 100-fold slower than at C-6â. The difference in ∆Gq
24
Comparison of the activation parameters for acetic acid-
HOAc
-
HOAc
-
catalyzed protonation of 2 (k2
) and of 2 (k2′
) indicates
between protonation of dienolate (2 ) at C-6â and C-4 (R or â)
is ca. 2 kcal/mol (Scheme 7). Although the relatively high ex-
that the enthalpies for both processes are similar within error.
q
q
However, the entropy loss for protonation of 2 is ca. 6 kcal/mol
perimental errors in the calculated values of ∆H and T∆S for
these rate constants limit the interpretation of these parameters,
it is of interest to note that the 100-fold increase in the rate of
protonation at C-4â relative to C-6â is a result of the difference
-
larger than the entropy loss for protonation of 2 . Both processes
involve diffusion and orientation of the reacting molecules,
which results in a negative activation entropy. Interestingly, the
HOAc
OAc
q
HOAc
entropy loss for k2′
is similar to that for k1 . As shown in
in the entropies of activation. T∆S for k
less favorable than for k-1′
is significantly
2
′
HOAc
q
Scheme 5 (Path A) there is little to no net change in charge in
going from the ground-state reactants to the transition state for
(4â) (T∆∆S ca. -3 kcal/mol).
Interconversion of 1 and 2: The Keto-Enol Equilibrium
HOAc
OAc
protonation of the dienolate (k2′
(
). The same is true for k1
Constant (K ). Finally, knowledge of the enthalpy and entropy
ext
Scheme 2). Conversely, for protonation of the dienol (k2HOAc
,
1
2
a a
for the acid dissociation constants for 1 (K ) and 2 (K ) (Table
Scheme 5, Path B) at the transition state, positive charge is
developing on the previously neutral ground-state dienol, and
negative charge is developing on the previously neutral ground-
state acid, restricting solvent molecules that are hydrogen bonded
to it. The result is a more negative entropy of activation for
6) allows a calculation of the enthalpy and entropy associated
with the keto-enol equilibrium (K ) and a completion of the
ext
1
a
thermodynamic cycle (Scheme 8). Ionization of both 1 (K )
2
-
1
and 2 (K ) to form 2 results in a large entropic penalty (T∆S
a
Ka
2
) -9.6 kcal/mol and T∆SKa ) -9.7 kcal/mol), which is likely
due to restriction of free solvent molecules that stabilize the
negative charge that has been formed on O-3 of the steroid. In
each case, the enthalpy of ionization is also unfavorable (∆H
) 7.8 kcal/mol and ∆HKa ) 4.6 kcal/mol). These results lead
HOAc
HOAc
k2
(Path B) than for k2′
(Path A).
Acetate Ion-Catalyzed Conversion of 2 to 1 (k-1OAc).
OAc
OAc
1
Similar to k2 , k-1
equilibrium conversion of the dienol (2) to the dienolate (2 ),
followed by protonation of 2 at C-4 by acetic acid (k-1′
can be broken down into two steps:
Ka
-
2
-
HOAc
)
to a calculated entropy for the keto-enol equilibrium between
1 and 2 (T∆SKext) of ca. 0 kcal/mol. Comparison of the structures
in Scheme 8 shows that while 2 has an additional bond with
HOAc
OAc
(Scheme 6), with k-1′
) k-1
/Keq.
OAc
2
OAc
1
HOAc
Because k-1 /Ka ) k1 /Ka , it follows that k-1′
)
k1OAcKa
HOAc
1
OAc
) k1OAc(4R) + k1 (4â), k-1′
OAc
HOAc
/Ka . Since k1
Scheme 8
HOAc
can be calculated for both the 4R and 4â protons (k-1′
and k-1′
(4R)
HOAc
(4â)) (Supporting Information, Table S3). Activation
HOAc
HOAc
enthalpies and entropies for both k-1′
(4R) and k-1′
(4â)
are given in Table 5.
Scheme 6
J. AM. CHEM. SOC.
9
VOL. 125, NO. 34, 2003 10211

A R T I C L E S
Houck and Pollack
free rotation that 1 does not (denoted x on 2 in Scheme 8) (∆S
5-40 °C with modifications as described below. For all regression
fitting, Figure P software was used.
>
0 for Kext), 2 is expected to restrict three solvent molecules,
Determination of the Rate Constant for Overall Isomerization
whereas 1 will restrict two (∆S < 0 for Kext). These entropy
terms apparently cancel out, giving ∆S ) 0 for this equilibrium.
The keto-enol enthalpy (∆HKext ) 3 kcal/mol) entirely
determines the free energy for the keto-enol equilibrium.
Relevance to the Mechanism of Action of KSI. Since
acetate serves as a good model for the active-site base in KSI
-
of 1 to 3 (kisom). Overall isomerization of 1 by AcOH/AcO (kisom
)
was monitored on a Varian Cary 100 Bio spectrophotometer at 248 nm
and 10.3-39.8 °C in ca. 5° increments (λmax for 3 is 248 nm and does
not vary significantly over the temperature range studied). Acetate
buffers were thermostated at each temperature for at least 15 min and an
additional 2 min after addition of 1, before commencing a run (cond-
(Asp38), a comparison of the activation parameters for the
itions in cuvette: [1] ∼50 µM, [AcO
-
]/[AcOH] ) 0.19-5.8, [AcO
-
enzymatic and the nonenzymatic reactions should shed light on
the catalytic strategy of KSI. A determination of the free-energy
+ AcOH] ) 0.227-3.98 M, µ ) 1.0 M with NaCl, 3.3% MeOH). At
each temperature, progress curves were monitored for 4-5 half-lives.
Determination of the Rate Constant for Conversion of 1 to 2
1
0
profiles for both the acetate- and KSI-catalyzed reactions has
shown that KSI stabilizes the intermediate dienolate relative to
solution by ca. 11 kcal/mol, leading to an internal equilibrium
(
D
°
k
1
). Proton exchange with deuterium at C-4 (k
O on a Bruker Avance 500 MHz NMR spectrometer at 12.8-32.9
C in ca. 7° increments. Deuterated acetate buffers were prepared by
adding the appropriate amount of NaOD to AcOD/D O solutions to
1
) was determined in
2
10
constant at the active site of about unity, consistent with the
expectation for an ideal or “perfect” enzyme.35 In addition, KSI
stabilizes both the enolization and ketonization transition states
2
yield the desired acetate ion/acetic acid ratio. These solutions were
thermostated in the spectrometer for at least 15 min prior to addition
of 1. Then sample tubes were ejected, and 20 µL of a stock solution of
(TS1 and TS2, respectively) by >10 kcal/mol.
The differences between the enzymatic active site of KSI and
1 in MeOD was added (conditions in tube: [1] ∼100 µM, [AcO
-
]/
-
the aqueous solution in which the acetate experiments were
performed enable one to hypothesize what results might be
expected for the activation enthalpy and entropy of the corre-
sponding chemical steps on the enzyme. The hydrophobic active
site of KSI contains two hydrogen bond donors (Tyr14 and
Asp99) oriented to stabilize the negative charge on the dienolate
[AcOD] ) 0.25-2.5, [AcO ] ) 0.0221-0.400 M, µ ) 1.0 M with
NaCl, 3.3% MeOD). The reaction mixture was thermally equilibrated
for an additional 5-10 min before commencing a run. Disappearance
of both the 4R and 4â protons was monitored at 2.82 and 3.45 ppm,
respectively, for 3-4 half-lives.
Determination of the Rate Constant for Conversion of 2 to 1
(k-1). The rate constant for protonation of 2 at C-4 by acetate (k-1)
36
intermediate and the flanking transition states. Are these effects
predominantly enthalpic or entropic? In preliminary experiments,
the temperature dependence of kcat/KM for the D38E mutant of
KSI indicates that, relative to acetate-catalyzed isomerization,
the enthalpy of activation for the isomerization of 1 to 3 is
significantly lowered and the entropy of activation is signifi-
was determined using a Hi-Tech PQ/SF-53 double-mixing stopped-
flow spectrophotometer at or near 243 nm and 6.5 - 40.7 °C in ca. 5°
increments (the isosbestic point for 2 and 3 varies slightly over the
temperature range studied), similar to a method used previously in our
laboratory.11 All solutions were thermostated to reach the desired
temperature for at least 15 min prior to mixing. A solution of 1 (ca.
500 µM) in 70% MeOH was mixed with a 0.1 M solution of NaOH in
q
cantly increased, both of these effects serving to lower ∆G for
-
a 1:1 ratio and allowed to react for 0.5 s, thereby generating 2 . The
the isomerization reaction (unpublished results). These results
q
q
resulting solution was quenched with various acetate buffers in a 1:10
follow the general trend that enzymes lower ∆H and raise T∆S ,
which is seen when enzyme reactions are compared to their
nonenzymatic counterparts.37
ratio to produce 2 (conditions in the observation cell: [2] ∼50 µM,
-
-
[
AcO ]/[AcOH] ) 0.10-2.9, [AcO + AcOH] ) 0.269-1.82 M, µ
)
1.0 M with NaCl, 3.3% MeOH). The pseudo-first-order decay of 2
Previous characterization of the free-energy profile for D38E
catalysis indicates that the two chemical transition states are of
to 1 was monitored for 5-7 half-lives.
Determination of the Rate Constants for Hydroxide-Catalyzed
10
about equal energy, whereas for acetate catalysis, these
transition states differ by ca. 2 kcal/mol.11 Since the difference
between TS1and TS2 for acetate catalysis appears primarily in
the entropy term, it will be interesting to see whether D38E
equalizes the entropic penalties of both transition states to make
them equal in free energy, or whether the effect is enthalpic.
These experiments are underway in our laboratory.
-
Interconversion of 1 and 2 . The rate constants for proton abstraction
OH
-
from C-4 of 1 by hydroxide (k1 ) and reprotonation at C-4 of 2 by
H O
2 2
H O (k-1 ) were determined on a Hi-Tech SF-61 DX2 double-mixing
stopped-flow spectrophotometer at or near 255 nm and 15.9-40.3 °C
-
in ca. 5° increments (λmax for 2 varies slightly over the temperature
20
range studied), according to a previous procedure. All solutions were
thermostated for at least 15 min to reach the desired temperature prior
to commencing a run. A solution of 1 in 6.6% MeOH was rapidly
mixed with various concentrations of NaOH in a 1:1 ratio (conditions
Materials and Methods
-
Materials. 5-Androstene-3,17-dione was prepared by G. Blotny of
this laboratory according to a previously published procedure.24
Deuterated solvents and reagents were g99% atom. Acetate buffers
and hydroxide solutions were prepared with reagent-grade chemicals
or better. Buffer pH was determined on a Radiometer PHM85 Precision
pH meter and is within 0.1 unit of the values given throughout the text.
Determination of the Overall and Microscopic Rate Constants
for Acetate-Catalyzed Isomerization. The overall isomerization rate
in observation cell: [1] ∼30 µM, [HO ] ) 0.0500-0.200 M, µ ) 1.0
M with NaCl, 3.3% MeOH). The increase in absorbance due to
-
formation of 2 was monitored for 5-7 half-lives.
Acknowledgment. This research was supported by a grant
from the National Institutes of Health (GM 31885). We thank G.
Blotny of this laboratory for the gift of 5-androstene-3,17-dione.
constant, kisom, and the microscopic rate constants, k
determined as described previously over the temperature range of ca.
1
, k-1, and k
2
, were
Supporting Information Available: Tables of the calculated
1
1
HOAc
OAc
HOAc
HOAc
rate constants k2
, k2
, k-1′
(4R), and k-1′
(4â) and
1
2
of the calculated equilibrium constants Ka , Ka , and Keq (PDF).
This information is available free of charge via the Internet at
http://pubs.acs.org.
(
35) Albery, J. W.; Knowles, J. R. Biochemistry 1976, 15, 5613.
(
36) Wu, Z. R.; Ebrahimian, S.; Zawrotny, M. E.; Thornburg, L. D.; Perez-
Alvarado, G. C.; Brothers, P.; Pollack, R. M.; Summers, M. F. Science
1
997, 276, 415.
(37) Wolfenden, R.; Snider, M.; Ridgeway, C.; Miller, B. J. Am. Chem. Soc.
1
999, 121, 7419.
JA035957R
10212 J. AM. CHEM. SOC.
9
VOL. 125, NO. 34, 2003