Temperature effects on the catalytic activity of the D38E mutant of 3-Oxo-Δ5-steroid isomerase: Favorable enthalpies and entropies of activation relative to the nonenzymatic reaction catalyzed by acetate ion

Article abstract of DOI:10.1021/ja046819k

3-Oxo-Δ⁵-steroid isomerase (ketosteroid isomerase, KSI) catalyzes the isomerization of 5-androstene-3,17-dione (1) to 4-androstene-3,17-dione (3) via a dienolate intermediate (2^-). KSI catalyzes this conversion about 13 orders of magnitude faster than the corresponding reaction catalyzed by acetate ion, a difference in activation energy (ΔG^?) of ～18 kcal/mol. To evaluate whether the decrease in ΔG^? by KSI is due to enthalpic or entropic effects, the activation parameters for the isomerization of 1 catalyzed by the D38E mutant of KSI were determined. A linear Arrhenius plot of k _cat/K_M versus 1/T gives the activation enthalpy (ΔH^? = 5.9 kcal/mol) and activation entropy (TΔS^? = -2.6 kcal/mol). Relative to catalysis by acetate, D38E reduces ΔH^? by ～10 kcal/mol and increases TΔS^? by ～5 kcal/mol. The activation parameters for the microscopic rate constants for D38E catalysis were also determined and compared to those for the acetate ion-catalyzed reaction. Enthalpic stabilization of 2^- and favorable entropic effects in both chemical transition states by D38E result in an overall energetically more favorable enzymatic reaction relative to that catalyzed by acetate ion.

Full text of DOI:10.1021/ja046819k

Published on Web 12/01/2004
Temperature Effects on the Catalytic Activity of the D38E
5
Mutant of 3-Oxo-∆ -Steroid Isomerase: Favorable Enthalpies
and Entropies of Activation Relative to the Nonenzymatic
Reaction Catalyzed by Acetate Ion
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 28, 2004; E-mail: pollack@umbc.edu
5
Abstract: 3-Oxo-∆ -steroid isomerase (ketosteroid isomerase, KSI) catalyzes the isomerization of 5-
-
androstene-3,17-dione (1) to 4-androstene-3,17-dione (3) via a dienolate intermediate (2 ). KSI catalyzes
this conversion about 13 orders of magnitude faster than the corresponding reaction catalyzed by acetate
q
q
ion, a difference in activation energy (∆G ) of ∼18 kcal/mol. To evaluate whether the decrease in ∆G by
KSI is due to enthalpic or entropic effects, the activation parameters for the isomerization of 1 catalyzed by
the D38E mutant of KSI were determined. A linear Arrhenius plot of kcat/K
M
versus 1/T gives the activation
q
q
enthalpy (∆H ) 5.9 kcal/mol) and activation entropy (T∆S ) -2.6 kcal/mol). Relative to catalysis by
q
q
acetate, D38E reduces ∆H by ∼10 kcal/mol and increases T∆S by ∼5 kcal/mol. The activation parameters
for the microscopic rate constants for D38E catalysis were also determined and compared to those for the
acetate ion-catalyzed reaction. Enthalpic stabilization of 2 and favorable entropic effects in both chemical
-
transition states by D38E result in an overall energetically more favorable enzymatic reaction relative to
that catalyzed by acetate ion.
Introduction
to the corresponding nonenzymatic reaction enables a unique
assessment of the specific forces driving enzyme catalysis. It
Enzymes are able to enhance the rate of chemical reactions
by as much as 23 orders of magnitude. The dramatic effects
of enzymes on reaction rates have been postulated to arise from
1
has generally been found that enzymes function by their ability
q
to drastically reduce the enthalpy of activation (∆H ) while only
q
15-20
2
-4
minimally affecting the entropy of activation (T∆S ).
a variety of factors, such as orbital steering, stereopopulation
5
6
7
There are several enzymes for which the activation enthalpies
and entropies have been determined. A comparison of the
control, near attack conformations (NACs), chelation effects,
8
9-13
strain-distortion, transition-state stabilization,
substrate
7
14
enzymatic rate constant, k , to the rate constant for the
destabilization, and preorganization of the active site. Alter-
natively, one may wish to assess the enthalpic and entropic
contributions to catalysis inherent in enzyme reactions relative
to those in solution reactions. Generally, enthalpic contributions
arise predominantly from ionic and polar interactions, whereas
entropic contributions arise from solvation changes to an enzyme
cat
corresponding nonenzymatic reaction, knon, shows moderate to
drastic reductions in the activation enthalpy with chorismate
q
20
q
mutase (∆∆H ) 9 kcal/mol), mandelate racemase (∆∆H )
1
9
q
1
5.5 kcal/mol), and yeast OMP decarboxylase (∆∆H ) 33.4
1
5
15
kcal/mol). Since these and other enzymes effect little to no
changes in the activation entropy, the reduction in enthalpy is
the driving force in such enzymatic reactions. Notably though,
there are a few instances in which an enzyme increases the
entropy of activation, contributing several orders of magnitude
to the enzymatic rate acceleration. For example, deamination
of 5,6-dihydrocytidine by cytidine deaminase is ∼8 kcal/mol
entropically more favorable than the corresponding non-
enzymatic deamination, with no change in the activation
7
and/or substrate and reorganization of the active site. Com-
parison of the activation parameters of the enzymatic reaction
(
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16416
9
J. AM. CHEM. SOC. 2004, 126, 16416-16425
10.1021/ja046819k CCC: $27.50 © 2004 American Chemical Society

D38E Mutant of 3-Oxo-∆5-Steroid Isomerase
A R T I C L E S
Scheme 1
Scheme 2
To better understand enthalpic and entropic contributions to
enzyme catalysis, it is instructive to compare an enzymatic
reaction to the same reaction catalyzed by a model compound,
thereby enabling the determination of the function of “the rest
of the enzyme” in catalysis. This approach requires that the
mechanisms for the enzymatic reaction and the nonenzymatic
model reaction be similar and that both be known in sufficient
detail so that the individual steps of catalysis can be compared.
In complicated mechanisms, particularly one in which there is
more than one rate-determining step, it is difficult to attribute
overall changes in entropy and enthalpy (knon, kcat, or kcat/KM)
to specific mechanistic details. However, a comparison of the
entropic and enthalpic activation parameters for the individual
steps of enzymatic and nonenzymatic reactions could lead to
an analysis of catalysis in terms of specific changes in chemical
structure, electrostatic interactions, and solvation. This report
describes the determination of the activation parameters for the
microscopic rate constants of the isomerization of 5-androstene-
it and both Tyr14 and Asp99.24,29 Subsequent reprotonation at
C-6 by Asp38 results in the conjugated product. The isomer-
ization of 1 is also catalyzed by acetate through a similar
mechanism, although at a much slower rate.
rate constants for both KSI- and acetate-catalyzed isomerization
(Scheme 2) have been determined, and free energy profiles for
2
1,27
Microscopic
2
6,27
the complete reactions have been characterized.
A comparison of the free energy profiles of KSI-catalyzed
and acetate-catalyzed isomerization shows important differences
between the two reactions (Figure 1). In the nonenzymatic
reaction, the intermediate partitions back to reactant ∼50-fold
3
3
,17-dione (1) to 4-androstene-3,17-dione (3) catalyzed by
-oxo-∆ -steroid isomerase (ketosteroid isomerase, KSI) and a
5
comparison of these parameters to the activation parameters for
2
1
q
the nonenzymatic reaction catalyzed by an acetate ion.
KSI has been studied extensively by us and by others,
more often than it proceeds to product (corresponding to a ∆∆G
2
2-36
21,27
of ∼2 kcal/mol).
In the enzymatic reaction, however, the
and significant mechanistic detail is known. KSI catalyzes the
isomerization of 1 to its conjugated isomer 3 through a dienolate
2
6
intermediate at a rate near the diffusion-controlled limit.
37
Although there was some initial disagreement, the mechanism
of Scheme 1 is now generally agreed upon.1
9,33,35
This mech-
anism involves an initial proton abstraction from C-4 of 1 by
the active site base, Asp38, to give a negatively charged
-
oxyanion (2 ), which is stabilized by hydrogen bonds between
(
(
(
21) Houck, W. J.; Pollack, R. M. J. Am. Chem. Soc. 2003, 125, 10206.
22) Talalay, P.; Wang, V. S. Biochim. Biophys. Acta 1955, 18, 300.
23) Benisek, W. F.; Ogez, J. R.; Smith, S. B. Ann. N. Y. Acad. Sci. 1980, 346,
1
15.
24) Kuliopolis, A.; Mildvan, A. S.; Shortle, D.; Talalay, P. Biochemistry 1989,
8, 149.
25) Eames, T. C. M.; Pollack, R. M.; Steiner, R. F. Biochemistry 1989, 28,
269.
26) Hawkinson, D. C.; Eames, T. C. M.; Pollack, R. M. Biochemistry 1991,
0, 10849.
(
(
(
2
6
3
(
27) Zeng, B.; Pollack, R. M. J. Am. Chem. Soc. 1991, 113, 3838.
28) 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.
(
(
(
(
29) Thornburg, L. D.; H e´ not, F.; Bash, D. P.; Hawkinson, D. C.; Bartel, S. D.;
Pollack, R. M. Biochemistry 1998, 37, 10499.
30) Cho, H.-S.; Ha, N.-C.; Choi, G.; Kim, H.-J.; Lee, D.; Oh, K. S.; Kim, K.
S.; Lee, W.; Choi, K. Y.; Oh, B.-H. J. Biol. Chem. 1999, 274, 32863.
31) Pollack, R. M.; Thornburg, L. D.; Wu, Z. R.; Summers, M. F. Arch.
Biochem. Biophys. 1999, 370, 9.
Figure 1. Free energy diagram for isomerization of 1 to 3 catalyzed by
WT (-) and by acetate ion (‚ ‚ ‚), based on previously determined rate
constants at 25.0 °C.2
6,27
Enzymatic conversions are first order (s ), and
-1
-
1
-1
32) Thornburg, L. D.; Goldfeder, Y. R.; Wilde, T. C.; Pollack, R. M. J. Am.
Chem. Soc. 2001, 123, 9912.
acetate ion-catalyzed conversions are second order (M
corresponds to the reaction coordinate for KSI-catalyzed isomerization. The
s ). The x-axis
(33) Feierberg, I.; Åqvist, J. Biochemistry 2002, 41, 15728.
(34) Park, H.; Merz, K. M., Jr. J. Am. Chem. Soc. 2003, 125, 901.
(35) Mazumder, D.; Kahn, K.; Bruice, T. C. J. Am. Chem. Soc. 2003, 125, 7553.
(36) Yun, Y. S.; Lee, T. H.; Nam, G. H.; Jang, do S.; Shin, S.; Oh, B. H.; Choi,
K. Y. J. Biol. Chem. 2003, 278, 28229.
-
Ac
corresponding acetate ion-catalyzed mechanism is AcO + 1 h TS1
h
-
Ac
-
AcOH + 2 h TS2 h AcO + 3. Barriers due to E + 1 association/
dissociation and barriers due to acetate-catalyzed rate constants assume a
standard state of 1 M.
J. AM. CHEM. SOC.
9
VOL. 126, NO. 50, 2004 16417

A R T I C L E S
Scheme 3
Houck and Pollack
Cloning, Expression, and Purification of D38E. Preparation of
the D38E mutant of KSI is based on a combination of published
procedures2
9,40
and is summarized below. The pKSItac vector, which
contains the KSI gene,41 and two primers designed to introduce the
D38E mutation, 5′-GCCACGGTGGAAGAACCCTGTGGTTCCG-3′
and 5′-CGGTGCCACCTTCTTGGGCACCCAAGGC-3′, were used to
prepare the mutant D38E-KSI. PCR reactions were carried out in a
PTC-100 Programmable Thermocycler (MJ Research) according to the
following protocol: step 1, 0.5 min at 95 °C; step 2, 1.0 min at 55 °C;
step 3, 6.0 min at 70 °C for 16 cycles, preceded by an initial melting
period of 1 min at 95 °C, according to guidelines in Stratagene’s
QuickChange Site-Directed Mutagenesis Kit. Recombinant vectors were
transformed into XL2-Blue Ultracompetent Escherichia coli cells
(Stratagene) and selected by ampicillin resistance. Plasmid DNA was
rate constants for partitioning of the intermediate (k-1KSI and
purified using a QIAprep Spin Miniprep Kit (Qiagen) and was
sequenced by the Biopolymer Laboratory at the University of Maryland,
Baltimore.
KSI
KSI
k2 ) are almost identical, leading to a partitioning ratio (k-1
/
KSI
q
26
k2 ) of about three (∆∆G ∼ 0.6 kcal/mol). Thus, the relative
energies of the two chemical transition states for interconversion
of E1 h E2 and E2 h E3 (TS1 and TS2, respectively) are
about the same for KSI catalysis but quite different for acetate
Cells were grown in 100 mL of LB medium (100 µg/mL of
ampicillin) for 16 h at 37 °C with shaking (200 rpm) and then were
transferred to 2 L of LB medium (0.5 µM IPTG and 100 µg/mL of
ampicillin) and grown for an additional 20 h at the same conditions.
Harvested cells were pelleted by centrifugation and disrupted by
BugBuster Protein Extraction Reagent (Novagen). The resultant mixture
was centrifuged again to remove debris, and soluble protein was
precipitated by dropwise addition of a solution of 95% ethanol and
ion catalysis. The ability of KSI to isomerize 1 ∼13 orders of
magnitude faster than does acetate2
6,27
can be attributed to (1)
the stabilization of the enzyme-bound intermediate and flanking
transition states by >10 orders of magnitude26 and (2) the ability
of KSI to discriminate between the two chemical transition
states.32 It is unclear how KSI is able to discriminate between
2 2
MgCl (final concentrations were 80% ethanol, 5mM MgCl ). This
mixture was stirred for an additional hour after precipitation and was
left at 4 °C overnight. The precipitate was recovered by centrifugation
and resuspended in 10 mM Tris phosphate buffer (pH 7.0). After another
centrifugation, insoluble protein was removed, and the supernatant was
loaded onto a prepared DEAE-Sephacel anion exchange column (10
mM Tris phosphate, pH 7.0). D38E-KSI was eluted with 500 mL of
a linear gradient buffer (10-200 mM Tris phosphate, pH 7.0). Fractions
were analyzed by UV and SDS-PAGE, and those that contained
D38E-KSI were pooled. D38E-KSI was precipitated with solid
ammonium sulfate to give ∼52% saturation. After the mixture was
slowly stirred at 4 °C overnight, the pellet was centrifuged, resuspended
in 10 mM potassium phosphate, and dialyzed against several liters of
these two seemingly similar chemical transition states (Scheme
3), and the specific factors governing both substrate and
intermediate binding are unknown.
We have previously determined the activation parameters for
the acetate-catalyzed isomerization of 1 to 3 and found that,
generally, the microscopic rate constants are both enthalpically
and entropically costly.21 The present work resolves the
microscopic rate constants for the D38E mutant of KSI into
their enthalpic and entropic contributions to the overall free
energy. We use the D38E mutant of KSI because the activity
of the wild-type enzyme is partly diffusion controlled, making
a detailed evaluation of the temperature-dependent reaction
kinetics difficult. However, only chemical steps contribute to
the reaction rate for D38E, although this mutant still has
significant catalytic activity (kcat/KM and kcat are only ∼300-
1
0 mM potassium phosphate. Purity was assayed by SDS-PAGE to
be ∼95% or greater. A slight band below D38E-KSI was observed
only after overloading the gel ∼10 times. Concentration was determined
by using the published value for specific activity.38
Overall Isomerization of 1 to 3 Catalyzed by an Acetate Ion and
Acetic Acid. Acetate-catalyzed isomerization of 1 to 3 was monitored
on a Varian Cary 100 biospectrophotometer at 248 nm, at 10-40 °C
38
and 200-fold less than that of the wild type, respectively). The
carboxylate functionality is retained upon mutation of Asp to
Glu, and the free energy profile of D38E has also been
characterized, allowing a determination of the microscopic rate
constants.38 As with WT, there is no single rate-determining
(λmax for 3 ) 248 nm and does not vary significantly over the
temperature range studied), and at various concentrations of EDTA
-
(conditions in cuvette: [1] ≈ 60 µM, [AcO ]/[AcOH] ) 0.2-5.7,
-
[AcO + AcOH] ) 0.230-3.00 M, [EDTA] ) 0.01, 0.1, 1, 10, or
-
100 mM, µ ) 1.0 M with NaCl, 3.3% MeOH). Progress curves were
monitored for ca. 7-10 half-lives. After completion, steroids were
extracted three times with chloroform in a 1:1 ratio; the organic layers
were pooled, and solvent was removed under vacuum. Product identity
was verified on an Agilent 1100 Series, Bruker Esquire 3000 Plus LC/
MS, equipped with an APCI source (positive ion mode) using a
step for D38E, and the partitioning ratio of 2 by D38E is near
unity.
Materials and Methods
Materials. 5-Androstene-3,17-dione was prepared by G. Blotny of
this laboratory according to a previously published procedure.39 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 units of the values given throughout the
text. For all of the kinetic experiments, solutions were thermostated
for at least 15 min so that constant temperature was maintained prior
to commencing a run.
2
Beckman Ultrasphere C-18 column with a 45:55 H O/MeOH mobile
phase. Compound 3 and an unidentified side product eluted with
retention times of ∼7.7 min (m/z ) 287), and 3.2 min (m/z ) 301),
respectively. The identity of 3 was verified by running a known sample
in a separate experiment under conditions as described above.
For kinetic experiments, the overall isomerization of 1 by AcOH/
AcO- (kisom) was monitored at 13.1-40 °C. Before data collection
(
37) Zhao, Q.; Abeygunawardana, C.; Gittis, A. G.; Mildvan, A. S. Biochemistry
1
997, 36, 14616.
(40) Hawkinson, D. C.; Pollack, R. M.; Ambulos, N. P. Biochemistry 1994, 33,
(
38) Zawrotny, M. E.; Pollack, R. M. Biochemistry 1994, 33, 13896.
12172.
(
39) Pollack, R. M.; Zeng, B.; Mack, J. P. G.; Eldin, S. J. Am. Chem. Soc.
(41) Brooks, B.; Benisek, W. F. Biochem. Biophys. Res. Commun. 1992, 184,
1
989, 111, 6419.
1386.
16418 J. AM. CHEM. SOC.
9
VOL. 126, NO. 50, 2004

D38E Mutant of 3-Oxo-∆5-Steroid Isomerase
A R T I C L E S
began, acetate buffers were thermostated at each temperature for at
least 15 min and an additional 2 min after addition of 1, at which point
constant temperature was maintained. At each temperature, initial rates
were determined from the first 3-4% of the reaction at several substrate
concentrations and at least three different total acetate concentrations
Table 1. Rate Constants for the Overall Isomerization of 1 to 3
Catalyzed by Acetic Acid and Acetate Iona
105
k
HOAc
×
105
k
OAc
×
isom
isom
T (°
C)b
(M- s-1)
1
(M- s-1)
1
1
18.0
25.0
3.1
0.83 ( 0.05
1.44 ( 0.09
2.83 ( 0.02
5.45 ( 0.13
12.4 ( 0.2
1.10 ( 0.08
1.34 ( 0.06
3.09 ( 0.07
5.25 ( 0.12
12.2 ( 0.2
-
at three or four pHs (conditions in cuvette: [1] ≈ 8-98 µM, [AcO ]/
-
[
AcOH] ) 0.20-5.0, [AcO + AcOH] ) 0.0290-2.91 M, [EDTA]
3
4
0.0
0.0
)
10.0 mM, µ ) 1.0 M with NaCl, 3.3% MeOH).
Overall Isomerization of 1 to 3 Catalyzed by D38E. Kinetic
parameters for the overall isomerization of 1 to 3 by D38E were
determined on a Varian Cary 100 biospectrophotometer at 248 nm and
a
With 10 mM EDTA, 3.3% MeOH, µ ) 1.0 M with NaCl. b Reported
temperatures are (0.2 °C.
∼
5-30 °C, in ∼5° increments. For a typical experiment, 100 mM
potassium phosphate (3.3% MeOH, pH 7.0) was incubated in a
thermostated cell for at least 15 min, until the desired temperature was
reached, and for an additional 2 min after addition of 1 (final [1] ≈
acetic acid/acetate buffer, significant side reactions occur
probably oxidation), thereby giving an observed rate constant
that is actually an upper limit of the overall isomerization rate
constant. Therefore, we re-evaluated our previous kinetic
results by performing the isomerization reactions in the
presence of 10 mM EDTA, which substantially reduces or
eliminates side product formation. At [EDTA] g 10.0 mM,
side product formation is reduced to e2% over the temperature
range studied. Control experiments with EDTA in water, without
acetate buffer, show that EDTA does not significantly catalyze
isomerization.
Isomerization of 1 in acetic acid/acetate buffer was monitored
by observing the increase in absorbance at 248 nm due to
conversion of 1 to 3 (pH ) 3.9-5.3, ∼13-40 °C). Initial rates
were determined from the first 3-4% of the reaction for at least
five substrate concentrations. The slope of the initial rate versus
substrate concentration plot gives the observed pseudo-first-
44
(
10-110 µM). Buffer-catalyzed isomerization was monitored for 2 min.
D38E-catalyzed isomerization was then initiated by the rapid addition
of enzyme (final concentration: [D38E] ) 0.50-3.0 µM). The D38E-
catalyzed rate of formation of 3 was determined from the first 8-12%
of the reaction and was corrected by subtracting the rate of the buffer-
catalyzed isomerization. Experiments were performed in triplicate.
Partitioning of 2 by D38E. D38E-catalyzed partitioning was
2
1
4
4
3
8
determined as described previously, using a Hi-Tech SF-61 DX2
double-mixing stopped-flow spectrophotometer at or near 243 nm (the
-
isosbestic point for 2 and 3 varies somewhat with temperature) and
at 15.3-39.8 °C in ∼5° increments. All of the solutions were
thermostated for at least 15 min prior to mixing until the desired
temperature was reached. A solution of 1 in 20% MeOH was mixed
with 0.5 M NaOH in a 1:1 ratio and was allowed to react for ∼0.5 s,
-
thereby generating 2 . The resultant solution was quenched in a 1:5
ratio with a buffered solution of D38E to produce 2 (final conditions
in the observation cell: [2] ≈ 30 µM, 100 mM phosphate, pH 7.0,
obs
order rate constant, kisom , at each concentration of buffer
(Table S1 in the Supporting Information). For each mole fraction
of acetate, mf , plots of kisom versus total buffer concentra-
tion ([AcO ] + [AcOH]) are linear and give slopes that equal
3
.3% MeOH, [D38E] ) 0.281-1.05 µM). The change in absorbance
was monitored until 2 had been completely converted into either 1 or
OAc
obs
3
.
-
pH
the second-order rate constant, kisom . Y-intercepts of plots of
Results
Thermodynamic activation parameters for reactions can be
determined through an examination of temperature-dependent
kinetics, according to the equation
kisom versus the mole fraction of acetate ion, mfOAc, at mf
pH
OAc
0 and mfOAc ) 1, yield the second-order rate constants for
)
HOAc
acetic acid-catalyzed isomerization of 1, kisom
ion-catalyzed isomerization of 1, kisom , respectively (Table
). Arrhenius plots of ln kisom
are linear and give ∆H ) 16.1 ( 1.0 and 17.5 ( 0.6 kcal/mol,
respectively, and T∆S ) -7.5 ( 0.8 and -6.1 ( 0.6 kcal/
mol, respectively.
The rate constants for acetate ion-catalyzed isomerization,
kisom , in the presence of EDTA agree well with those of our
previous work, which was done in the absence of EDTA.21
However, the rate constants for acetic acid-catalyzed isomer-
ization, kisom
, and acetate
OAc
OAc
and ln kisomHOAc versus 1/T
1
q
q
q
ln(k) ) ∆S /R + ln(k T/h) - ∆H /RT
(1)
B
q
q
where k is the rate constant, ∆S is the entropy of activation; R
is the ideal gas constant, kB is the Boltzmann constant; T is the
q
OAc
temperature in degrees Kelvin; h is Planck’s constant, and ∆H
is the enthalpy of activation. Over small temperature ranges, a
plot of ln(k) versus 1/T is generally linear, yielding a slope that
corresponds to the enthalpy of activation. From the intercept
HOAc
, while independent of EDTA at temperatures
q 42
of this line, the entropy of activation (T∆S ) can be determined.
<25.0 °C, are ∼2-fold faster in the presence of EDTA than
In a similar manner, by measuring equilibrium constants (K)
over a range of temperatures, we determined the enthalpies and
entropies associated with these equilibria using the van’t Hoff
equation, ln(K) ) -∆H°/RT + ∆S°/R.43
Temperature Dependence of the Rate Constant for
Overall Isomerization of 1 to 3 by Acetate (kisom). In the
course of this work, we found that under some conditions in
those without it at temperatures >25.0 °C. This results in
q
q
significantly different values for ∆H and T∆S for the acetic
acid-catalyzed isomerization, kisom
kcal/mol, respectively, but with no change in the acetate ion-
catalyzed parameters.
Temperature Dependence of the Kinetic Parameters for
D38E (kcat/KM, kcat, and KM). D38E-catalyzed isomerization
of 1 was monitored by observing the increase in absorbance at
HOAc
, by about +4 and -4
(
42) 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, which are also reported in kcal/mol. Since
T∆S is temperature dependent, convention dictates that the activation and
equilibrium parameters discussed here be given at 298 K. Thus, a negative
value for T∆S is considered an entropy loss (unfavorable), while a positive
value for T∆S is considered an entropy gain (favorable).
2
48 nm due to conversion of 1 to 3 (at ∼5-30 °C). Double
reciprocal plots yield the catalytic constants kcat/KM, kcat, and
KM at each temperature (Table 2). On the basis of the value for
(44) de la Mare, P. B. D.; Wilson, R. D. J. Chem. Soc., Perkin Trans. 2 1977,
(43) The van’t Hoff equation used here assumes a standard state of 1 M.
157.
J. AM. CHEM. SOC.
9
VOL. 126, NO. 50, 2004 16419

A R T I C L E S
Houck and Pollack
Table 2. Kinetic Constants for D38E-Catalyzed Isomerization of
1
Scheme 5
a
×
10-
6
k
cat/K
M
k
cat
K
M
1
-1
T (°
C)b
(M- s-1)
(s )
(µM)
5
.4
1.6 ( 0.1
1.9 ( 0.1
2.5 ( 0.1
3.6 ( 0.3
3.3 ( 0.2
4.0 ( 0.2
53 ( 1
71 ( 3
101 ( 5
145 ( 8
180 ( 9
250 ( 20
33 ( 2
37 ( 3
40 ( 3
40 ( 4
55 ( 3
63 ( 5
1
1
2
2
2
0.3
5.3
0.1
5.0
9.9
a
With 100 mM potassium phosphate buffer, pH 7.0, 3.3% MeOH.
Reported temperatures are (0.2 °C.
a
- b
b
Table 4. Rate Constants for D38E-Catalyzed Partitioning of 2
T (°
C)c
k
2
off (s-1)d
k
-1
D38E
(s-1)e
k
2
D38E
(s-1)e
Table 3. Thermodynamic Parameters for D38E-catalyzed
Isomerization of 1 to 3
15.3
800
1100
1800
2900
4000
5000
210
290
480
780
1060
1390
230
340
570
910
1410
1930
2
2
0.2
5.4
qa
qa
qa
kinetic constant
∆G
∆H
T∆S
kcat/KM
kcat
8.5 ( 0.1
14.3 ( 0.1
5.8 ( 0.1
23.5 ( 0.1
5.9 ( 0.8
10.1 ( 0.3
4.3 ( 0.6
16.1 ( 1.0
-2.6 ( 1.0
-4.2 ( 0.3
-1.5 ( 0.7
-7.5 ( 0.8
30.4
35.2
39.8
KM
OAc
kisom
a
Values are an average of at least six individual trials. b With 100 mM
a
c
Values given in kcal/mol at 298 K. Values for KM are ∆G°, ∆H°, and
potassium phosphate buffer, pH 7.0, 3.3% MeOH. Reported temperatures
are (0.2 °C. d Error is ∼100%. Error is ∼20%.
e
T∆S°.
Scheme 4
Table 5. Summary of the Rate and Equilibrium Constants for
Isomerization of 1 to 3 Catalyzed by D38E and Acetate Ion
a
b
∆
G c,d
(kcal/mol)
∆
H c
(kcal/mol)
T
∆
S c,d
(kcal/mol)
reaction
constant
E1 h E + 1
KS
k1
5.8 ( 0.1 4.3 ( 0.6 -1.5 ( 0.7
13.9 ( 0.1 7.6 ( 0.1 -6.3 ( 0.1
13.8 ( 0.1 13.9 ( 0.5 0.0 ( 0.5
13.7 ( 0.1 15.5 ( 0.3 1.8 ( 0.3
0.0 ( 0.1 -6.3 ( 0.5 -6.3 ( 0.5
D38E
E1 f TS1
E2 f TS1
E2 f TS2
E1 h E2
D38E
k-1
D38E
k2
Kint
D38E
E + 1 f TS1
k1
k1
/KS 8.1 ( 0.1 3.3 ( 0.7 -4.8 ( 0.8
21.4 ( 0.1 16.4 ( 1.9 -5 ( 2
-
Ac
OAc
OAc
AcO + 1 f TS1
-
Ac
Ac
AcOH + 2 f TS1
k-1′
10.3 ( 0.1 9.6 ( 1.8 -0.7 ( 0.3
12.5 ( 0.1 8.4 ( 0.6 -4.2 ( 0.7
-
HOAc
AcOH + 2 f TS2
k2′
-
-
1
AcO + 1 h AcOH + 2 Keq
11.1 ( 0.1
7 ( 2
-4 ( 2
KM (55 µM at 25.0 °C), the observed activity at 25.0 °C is
entirely due to D38E and not to any contaminating wild type.
If a small amount of wild-type KSI were present, the KM
determined by these experiments would be identical to that for
a
From the present work. b From previous work (ref 21). Reported
c
q
values of ∆G, ∆H, and T∆S are activation ( ) parameters for rate constants.
For the equilibrium constants, values for ∆G, ∆H, and T∆S correspond to
that for a standard state (degree) of 1 M. d Values are given at 298 K.
2
6
WT (∼300 µM). Plots of the natural logarithm of the rate
q
q
constants versus 1/T are linear and yield ∆H and T∆S for
D38E catalysis, along with the thermodynamic parameters from
the van’t Hoff plot for KM (Table 3).
to Scheme 5 did give values for kcat/KM that are within ∼20%
of the actual values determined from initial rate experiments.
49
D38E
D38E
The rate constants koff, k-1
are given in Table 4. Both k-1
increasing temperature, and linear Arrhenius plots give values
for the enthalpy and entropy of activation for both protonation
steps (Table 5). Additionally, the thermodynamic activation
parameters for D38E-catalyzed proton abstraction from C-4
, and k2
at each temperature
and k2D38E increase with
D38E
Temperature Dependence of D38E-Catalyzed Partitioning
of 2. Partitioning of the intermediate (2) by D38E was monitored
by the sequential-mixing stopped-flow method, as previously
3
8
-
described. Dienolate (2 ) was formed by rapidly mixing a
solution of 1 with 0.5 M NaOH for ∼0.5 s. When this solution
-
q
q
D38E
is quenched with a buffered solution of D38E, 2 is protonated
(∆H and T∆S for k1
) can be calculated from these rate
to give 2, which then partitions to 1 and 3 (Scheme 4). The
constants, based on analysis of Scheme 2, by the net rate
5
0
D38E
variation in UV absorbance was monitored at the isosbestic point
constant approximation and the assumption that k2
is
), using the following equa-
) kcat(k2D38E + k-1D38E)/(k2D38E - kcat). These values
3
9
D38E
D38E
for 2 and 3 and follows the general trend of previous data.
An initial rapid decrease, which is the result of the partitioning
irreversible (i.e., k-2
tion: k1
, k2
D38E
D38E
D38E
of 2 to 1 (k-1
) and 2 to 3 (k2
) by D38E, is followed by
are also given in Table 5.
a subsequent slower increase in absorbance, resulting from
conversion of 1 to 3 (kcat/KM).
Discussion
These kinetic traces were fit to the reaction mechanism
The often dramatic reduction in free energy for an enzymatic
reaction is typically discussed in terms of the enzyme’s ability
to stabilize the bound transition state(s) relative to that of the
transition state(s) in solution. However, an analysis of
enzymatic thermodynamic activation parameters can enable a
more detailed discussion of the mechanism(s) of stabilization
of the transition state(s) than a consideration of free energies
45
(
Scheme 5) using the KINSIM/FITSIM program. The diffusion
2
46
rate constant, kon , was calculated for each temperature and
was not allowed to vary throughout fitting. The calculated rate
constants for the overall isomerization (kcat/KM) are not reported
in Table 4 because the time scale required to monitor partitioning
is too short to observe significant isomerization. However, fits
1
0
16420 J. AM. CHEM. SOC.
9
VOL. 126, NO. 50, 2004

D38E Mutant of 3-Oxo-∆5-Steroid Isomerase
A R T I C L E S
q
q
alone. Enthalpic stabilization generally results from favorable
polar and electrostatic interactions between enzyme and the
transition state, whereas entropic stabilization can be attributed
to changes in conformation or to changes in solvation. Jencks
has argued that enzymes catalyze reactions primarily by making
entropic changes from an enzyme-substrate complex to prod-
In many cases, both T∆S and ∆H for the enzymatic reaction
16-19
are more favorable than those for the nonenzymatic reaction,
1
5
although there are exceptions to this trend. It is generally
thought that the majority of entropy loss for a nonenzymatic
reaction results from bringing two or more molecules together,
and the entropy changes from the bond making/bond breaking
7
7
ucts more favorable than in solution. Jencks reasoned that, in
steps of catalysis are minimal. The typically large enthalpic
a bimolecular reaction between A and B in solution, decreases
in entropy result from losses of both translational and rotational
freedom. He maintained that enzymes overcome unfavorable
costs due to bond making/bond breaking can be overcome by
an enzyme’s ability to provide favorable ionic and hydrogen
bonding interactions that are not available in solution.
7
14
entropy by bringing A and B together in the active site so that
once bound, the entropy change from ground state to transition
state is minimal or even positive. Thus, the conversion of the
enzyme-substrate complex to products (kcat) often shows a
more-favorable entropy than that of the corresponding non-
enzymatic reaction in aqueous solution. For example, kcat for
cytidine deaminase-catalyzed deamination of 5,6-dihydro-
cytidine is ∼8 kcal/mol entropically more favorable than the
spontaneous first-order reaction.18 The favorable entropy is
attributed to changes in the active-site hydration and conforma-
tion of a glutamate residue.18 Warshel, however, has argued
that the Jencks’ rationale overestimates the contribution of
entropy to catalysis.
Complicating the interpretation of differences in activation
parameters between enzymatic and nonenzymatic reactions is
the fact the there are often several steps that contribute to the
overall enzymatic rate constant, including binding, product
release, and chemical steps. Similarly, observed nonenzymatic
rate constants are generally a combination of individual steps,
each with a distinct transition state. Although the activation
parameters for the overall rate constants of both enzymatic and
nonenzymatic reactions have been determined in many cases,
we are unaware of any previous studies that have examined
these parameters for the microscopic rate constants of both
enzymatic and nonenzymatic reactions. Additionally, enzymatic
reactions are often compared to nonenzymatic reactions in
moderately dilute buffer, which may not provide the best model
for the enzymatic mechanism. While these comparisons are
useful, the ability to determine differences in the detailed
transition-state interactions requires a comparison of an enzy-
matic reaction to a specific nonenzymatic reaction catalyzed
by an appropriate model compound. KSI provides an excellent
system to do just that by a comparison of the activation
parameters of the microscopic rate constants for D38E to the
activation parameters of the acetate ion-catalyzed isomeriza-
13
In a recent review by Wolfenden,51 the catalytic power (kcat/
KM) of single substrate enzymes is attributed to their ability to
q
q
lower ∆H , while effecting minimal changes in ∆S , relative to
an uncatalyzed reaction in aqueous solution. He concluded that
the affinity of a transition state for an enzyme is due to
predominantly electrostatic interactions, including hydrogen
bonds, that act in concert with one another. Indeed, these
interactions are necessary in a variety of enzymatic reactions,
1
7
such as deamination of cytidine by cytidine deaminase,
1
9
racemization of mandelate by mandelate racemase, and
21
tion.
hydrolysis of cytidine cyclic 2′,3′-phosphate by ribonuclease
Relative to the nonenzymatic, acetate ion-catalyzed reaction
16
A. For example, deamination of cytidine by cytidine deaminase
OAc 21
(
kisom ), D38E lowers the activation enthalpy for kcat/KM by
q
is characterized by ∆H k /K ) 2 kcal/mol, whereas in solution,
cat
M
about 10 kcal/mol and raises the activation entropy by about 5
kcal/mol for the overall isomerization (Table 3). The reaction
mechanisms for both acetate- and D38E-catalyzed isomerization
have been extensively characterized, and there are several steps
that contribute to the overall isomerization rates. To make useful
comparisons, it is first necessary to consider the individual
chemical and binding steps for both reactions.
q
∆
H k ≈ 22 kcal/mol, corresponding to a reduction in activation
non
17
enthalpy of ∼20 kcal/mol. A significant portion of this
enthalpic stabilization results from the interaction between the
2
′-OH of the ribose ring of cytidine and Glu91 of cytidine
q
deaminase, as shown by an increase of ∆H kcat/KM to ∼10 kcal/
1
7
mol in the E91A mutant. This difference corresponds to a
q
∆
∆H of 8 kcal/mol, which can be attributed to the hydrogen
D38E
Substrate Binding by D38E (KM ≈ KS). Because k1
,
bonding interaction between Glu91 and 2′-OH of the ribose ring
of cytidine.
1
koff for the D38E mutant of KSI, KM may be equated to KS,
3
8
the dissociation constant for the E1 complex. The enthalpy
and entropy for dissociation of the E1 complex (KM) are given
in Table 3. Because the sign and magnitude of binding entropy
are dependent on the choice of standard state, we limit the
discussion of KS to ∆H°. The favorable enthalpy of binding
(∆H° ) -4.3 kcal/mol) may result from the difference in the
relative strength of the hydrogen bonds made in the E1 complex
and in the free species E + 1 (Scheme 6, path a). Hydrogen
bonds in the E1 complex are stronger than those in E + 1.
Both experimental and computational determinations of the
enthalpy of a hydrogen bond in water give estimates of ∼2-4
(
45) Dang, Q.; Frieden, C. Trends Biochem. Sci. 1997, 22, 317.
(
46) The rate constant for diffusion of 2 and D38E to form the E2 complex,
2
2
k
3
on , was calculated at each temperature using the equation kon ) (2RT/
2 47
0 000) × ((r
2 E 2 E
+ r ) /r r ), where R is the ideal gas constant, and T is
48
the temperature; η is the viscosity of the solvent at each temperature,
2 E 2 E
and r and r are the radii of 2 and KSI, respectively. The radii, r and r ,
were estimated by measuring the widest diameter of each molecule using
Rasmol, version 2.7.1, from the crystal structure of the KSI-equilenin
3
0
complex determined by Cho et al. (PDB ID: 1QJG).
(
(
(
47) Connors, K. A. Chemical Kinetics: The Study of Reaction Rates in Solution;
VCH Publishers: New York, 1990; p 134.
48) CRC Handbook of Chemistry and Physics, 55th ed.; Weast, R. C., Ed.;
CRC Press: Ohio, 1974; p F-49.
2
49) Values of koff are very sensitive to fixed values of kcat/K
M
, and so kcat/K
M
was allowed to vary during fitting. Because of this, the values reported in
2
2
Table 4 for koff have an error of ∼100%. Additionally, the values for koff
52,53
kcal/mol.
Increased hydrogen bond strength in even mod-
reported here are ∼1 order of magnitude greater than our previous
38
determinations, which is due to the inaccuracy of this method to determine
erately hydrophobic active sites relative to solution is not
2
D38E
D38E
2
k
off . Values of k-1
and k
2
are only slightly sensitive to koff values,
and we estimate ∼20% error in these reported rate constants.
(
(
50) Cleland, W. W. Biochemistry 1975, 14, 3220.
(52) Li, Z.; Lazaridis, T. J. Am. Chem. Soc. 2003, 125, 6636.
(53) Patil, K. J.; Pawar, R. B. Spectrochim. Acta, Part A 2003, 59, 1289.
51) Wolfenden, R. Biophys. Chem. 2003, 105, 559.
J. AM. CHEM. SOC.
9
VOL. 126, NO. 50, 2004 16421

A R T I C L E S
Scheme 6
Houck and Pollack
uncommon.54,55 Yoshida et al.56 measured the hydrogen bond
strength between phenol and various ketones in CCl4 as a model
for the interior of a protein. They found that the enthalpy of
hydrogen bond formation between phenol and 2-butanone in
CCl4 is 5.8 kcal/mol, ∼2 kcal/mol stronger than that of the
hydrogen bond in aqueous solution.56 Thus, the favorable
enthalpy for association of 1 and D38E can be attributed to the
stronger hydrogen bonding interaction in the active site relative
to that in aqueous solution.
kcal/mol per bond. The overall negative entropy (-6.3 kcal/
7
D38E
mol), associated with k1
and suggests that the active site is constricting as the hydrogen
bonds between D38E and 1 become stronger.
, is consistent with these estimates
Proton abstraction by an acetate ion from 1 has an enthalpy
of activation of 16.4 kcal/mol, which is similar to the
21
58,59
enthalpies of activation of ∼15-30 kcal/mol
typically
observed for proton abstractions from carbon atoms R to a
q
carbonyl. In the active site of KSI, ∆H is reduced by ∼9 kcal/
D38E-Catalyzed Proton Abstraction from C-4 of 1 (k1D38E).
Proton abstraction from C-4 of 1 by Glu38 results in an
6
mol, equivalent to a rate increase of ∼10 -fold. The much more
favorable enthalpy for proton transfer in the enzyme active site
q
unfavorable entropy term (T∆S ) -6.3 kcal/mol) and a
D38E
(k1
) may be due to the increased strengthening of the
q
moderate enthalpy term (∆H ) +7.6 kcal/mol). There are two
hydrogen bonds between Asp99 and Tyr14 and steroid as the
reaction progresses. The developing charge on O-3 at TS1
results in stronger hydrogen bonds at O-3 relative to the neutral
O-3 in the ground state since hydrogen bonds involving neutral
atoms are generally weaker than hydrogen bonds involving
main processes occurring at TS1: (1) proton transfer between
1
and Glu38 and (2) strengthening of the hydrogen bonds
between O-3 of 1 and both Asp99 and Try14 (Scheme 6, path
b). Partial bond formation restricts rotation of the carboxylate
of Glu38, resulting in a loss of entropy relative to the ground
60
charged atoms. In addition, the active site of KSI provides a
7,57
state, which can be estimated as 0-5 kcal/mol.
Changes in
conformation resulting from tightening of hydrogen bonds at
the transition state generally result in an entropic cost of ∼3-7
(
57) Colonna, G.; Di Masi, N. G.; Marzilli, L. G.; Natile, G. Inorg. Chem. 2003,
2, 997.
58) Chiang, Y.; Kresge, A. J.; Schepp, N. P. J. Am. Chem. Soc. 1989, 111,
4
(
3977.
(54) Avbelj, F.; Baldwin, R. L. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 5742.
(55) Shan, S.-O.; Herschlag, D. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 14474.
(56) Yoshida, Z.; Ishibe, N. Spectrochim. Acta, Part A 1968, 24, 893.
(59) Casale, J. F.; Lewin, A. H.; Bowen, J. P.; Carroll, F. I. J. Org. Chem.
1992, 57, 4906.
(60) Shan, S.-O.; Herschlag, D. J. Am. Chem. Soc. 1996, 118, 5515.
16422 J. AM. CHEM. SOC.
9
VOL. 126, NO. 50, 2004

D38E Mutant of 3-Oxo-∆5-Steroid Isomerase
A R T I C L E S
hydrophobic environment in which a hydrogen bond can be
strengthened substantially more than in an aqueous environ-
ment.55
mol, respectively. The negative dienolate is stabilized enthal-
pically by the formation of hydrogen bonds between O-3 of 2
-
and both Asp99 and Tyr14 (Scheme 6, path e). These hydrogen
Partitioning of 2- by D38E (k-1D38E and k2D38E). D38E
partitions the intermediate almost equally to product and
-
bonds are expected to be stronger with the oxyanion of 2 than
with the neutral carbonyl oxygen of 1, resulting in a favorable
D38E
D38E
60
35
substrate, and this ratio, defined as k2
°
/k-1
, is 1.2 at 25.0
enthalpy. Calculations by Mazumder et al. showed that for
wild-type KSI, the E2 complex is more constricted than E1,
and the negative entropy for this equilibrium is likely a result
of this more-rigid E2 complex. The equilibrium between E1
and E2 is entropically costly, but this cost is offset by the
enthalpic gain of the hydrogen bonds to the oxyanion, resulting
in Kint near unity (∆G ≈ 0 kcal/mol).
3
8
C, which is in good agreement with our previous results.
Despite the error in these measurements (∼20%), there is a
significant temperature dependence of the partitioning over the
temperature range studied here. The activation parameters for
D38E
D38E
both k-1
and k2
are largely enthalpic, with little to no
changes in entropy (Table 5). At both TS1 and TS2, partial
bond formation restricts rotational and vibrational freedom of
the active site base (Glu38) and the rotational and vibrational
freedom of the steroid (Scheme 6, paths c and d). Although the
Comparison to the Acetate-Catalyzed Isomerization. A
summary of the activation and equilibrium parameters for both
D38E- and acetate ion-catalyzed isomerization of 1 to 3 is given
q
D38E
D38E
21
∆
G values for formation of TS1 (k-1
) and TS2 (k2
)
in Table 5, and diagrams based on this and previous work are
q
D38E
are the same, ∆H for k-1
than for k2
for k-1
is ∼2 kcal/mol more favorable
shown in Figure 2. The major differences between the free
D38E
q
D38E
q
, while T∆S is more favorable for k2
than
energy (∆G ) diagrams of acetate ion and D38E catalyses are
D38E
by the same amount. Thus, the equal free energies
(1) that D38E equalizes the energies of bound substrate and
of these two transition states are due to compensating differences
in ∆H and T∆S .
bound intermediate (dienolate), whereas in solution, the inter-
q
q
-
mediate (2 ) is ∼11 kcal/mol higher in free energy and (2) that
A plausible explanation for this difference comes from a
consideration of hydration differences of the active site at the
two transition states (TS1 and TS2). Molecular dynamics
simulations of E1 indicate the presence of water, while there is
D38E lowers and equalizes the free energies of TS1 and TS2,
Ac
whereas in solution, the free energy of TS2 is greater than
Ac
that of TS1 by ∼2 kcal/mol. The overall catalytic effect of
D38E then can be attributed to a reduction of the free energy
of the intermediate and the flanking transition states and to
selective stabilization of the second chemical transition state,
relative to the first.
35
none in the simulated E2 complex. Thus, during the conversion
D38E
of E1 to E2 (k1
the reaction of E2 to E1 (k-1
into the active site. The entropy gain for release of a water
), water is released from the active site, and
D38E
) involves the re-entry of water
Determination of the activation parameters for both acetate
and D38E enables a dissection of the free energy diagrams into
their enthalpic and entropic components. Figure 2 (parts B and
C) illustrates the enthalpy (∆H) and entropy (-T∆S) changes,
respectively, that occur during the isomerization reactions. As
shown in panel A, an increase in enthalpy (∆H), which causes
a decrease in rate, is depicted as an increase in the y-axis of
Figure 2B. Similarly, in Figure 2C, an increase in -T∆S (or
decrease in entropy) is shown as an increase in the y-axis.
61,62
molecule from an active site is ∼2-3 kcal/mol,
which
suggests that water entering the active site should result in an
D38E
entropic loss of ∼2-3 kcal/mol for k-1
. Additionally,
Feierberg and Åqvist33 simulated the entire reaction coordinate
of KSI-catalyzed isomerization of 1 to 3 with and without a
water molecule present in the active site. They found that the
D38E
free energy change for the E2 to E3 conversion (k2
) is best
simulated when no water molecule is present in the active site
D38E
-
in either E2 or E3. Thus, for k-1
, there is an entropic cost
Equilibrium between 1 and 2 . One common enzymatic
due to water re-entering the active site at TS1, but there is no
strategy is to lower the free energy of highly reactive intermedi-
ates relative to reactants and products. For reversible enzymes
at equilibrium (i.e., enzymes that are not under metabolic
control), “catalytic perfection” predicts that a bound intermediate
should have about the same free energy as would the bound
substrate and bound product. Consistent with this expectation,
the bound high-energy dienolate intermediate of KSI (and D38E)
is stabilized to give an internal equilibrium constant between
E1 and E2 of about unity. For D38E, this internal equilibrium
constant results from a compensating favorable enthalpy (∆H°
D38E
such penalty in k2
(TS2), leading to a more entropically
favorable TS2 by ∼2 kcal/mol, relative to TS1.
D38E
and k2D38E are
The enthalpies of activation for both k-1
q
unfavorable (∆H ) 13.9 and 15.5 kcal/mol, respectively).
Proton transfer from Glu38 to the steroid and weakening of the
hydrogen bonds between steroid and Asp99/Tyr14 contribute
to a large, positive enthalpy of activation for both steps. The
difference in enthalpy of the two transition states (TS1 and TS2)
63
q
(
∆H ) -1.8 kcal/mol) may arise from differences in hydration.
)
-6.3 kcal/mol) and an unfavorable entropy (T∆S° ) -6.3
An additional water molecule present in TS1 could result in
kcal/mol) (Figure 2, B and C, black trace). In solution, however,
polar interactions that are not present in TS2, resulting in the
-
D38E
D38E
the relative free energy for the intermediates (2 + AcOH) is
small reduction in enthalpy for k-1
compared to k2
.
-
significantly greater than that of reactants (1 + AcO ) (∆G° )
The Keto-Enolate Equilibrium Constant (Kint). The
internal equilibrium constant between E1 and E2 (Kint) can be
1
1 kcal/mol, Figure 2A, red trace), due to both an unfavorable
enthalpy (∆H° ) +7 kcal/mol) and an unfavorable entropy
T∆S° ) -4 kcal/mol) (Figure 2, B and C, red trace). Thus,
D38E
D38E
calculated directly from the ratio k1
/k-1
. At 25.4 °C,
(
Kint ) 0.9, which is in good agreement with the previous
38
the more-favorable equilibrium at the active site of D38E is
due almost entirely to more favorable enthalpic effects for the
enzyme than that for the acetate (∆∆H° ≈ 13 kcal/mol), with
entropy differences playing only a minor role. These results are
estimate of 1.3 at 25.0 °C. The changes in enthalpy and entropy
∆H and T∆S) for this equilibrium, which were determined from
the temperature dependence of Kint, are -6.3 and -6.3 kcal/
(
(
61) Dunitz, J. D. Science 1994, 264, 670.
(
62) Suresh, S. J.; Naik, V. M. J. Chem. Phys. 2000, 113, 9727.
(63) Albery, J. W.; Knowles, J. R. Biochemistry 1976, 15, 5631.
J. AM. CHEM. SOC.
9
VOL. 126, NO. 50, 2004 16423

A R T I C L E S
Houck and Pollack
activation for this step (∆∆H k ) ∆H k1D38E/KM - ∆H k
q
q
q
OAc
)
1
1
q
1
3 kcal/mol, T∆∆S k ) 0 kcal/mol; Table 5). As discussed
1
previously, the strength of a hydrogen bond in a hydrophobic
active site is much greater than one in aqueous solution.55 Thus,
the binding of 1 to D38E (1/KS) results in enthalpically favorable
hydrogen bonding interactions relative to those in solution (∆H°
)
-4.3 kcal/mol). Additionally, the increase in hydrogen bond
strength as charge is formed on O-3 of 1 is expected to be greater
in a hydrophobic environment than in the aqueous environment
55
of acetate buffer, resulting in a reduction of enthalpy for proton
q
abstraction (∆∆H k ). Thus, the decrease in free energy for
1
q
proton abstraction by D38E relative to that of acetate (∆∆G k
1
q
D38E
q
OAc
)
∆G k
/KM - ∆G k
) -13 kcal/mol) is consistent with
1
1
favorable hydrogen bonding interactions provided by the active
site that are not present in an aqueous environment.
-
Partitioning of the Intermediate (2 ). The free energy
-
barrier for acetic acid-catalyzed protonation at C-4 of 2 is ∼2
kcal/mol lower than that for the protonation at C-6 (Figure 2A,
-
red trace). Thus, ∼98% of the time, 2 reverts back to substrate
rather than forming product. From a catalytic perspective, the
reprotonation at C-4 is a lost opportunity. Consistent with the
6
3
expectation for a “perfect” enzyme, partitioning of the
intermediate at the active site of KSI results in a roughly 1:1
mixture of products and reactants. Similarly, D38E selectively
stabilizes TS2 over TS1, leading to nearly isoenergetic transition
states (Figure 2A, black trace). We have previously postulated
a mechanistic rationale for this change in the partitioning of
the intermediate at the active site in terms of differences in
3
2
hydrogen bond strengths. We suggested that differences in
conformations of the A-ring of the steroids in the transition states
might result in stronger hydrogen bonds from Asp99 and Tyr14
to O-3 at TS2 than at TS1. In the present work, we find that
there is an entropic contribution to the partitioning. A compari-
HOAc
son of entropies of activation reveals that k-1′
is entropically
HOAc
q
favored over k2′
acetate ion-catalyzed reaction, but entropy favors k2
-k ) 1.8 ( 0.8 kcal/mol) in the enzymatic reaction (Figure
(T∆∆S k- -k ) 3.5 ( 1.0 kcal/mol) in the
1
2
D38E
q
(T∆∆S k-
1
2
2
). As discussed above, these changes in the partitioning of the
Figure 2. Reaction coordinates for D38E- (-, black) and acetate ion
intermediate at the enzyme active site may be influenced by
changes in hydration between TS1 and TS2. In the conversion
of E2 to TS1, water re-enters the active site, resulting in a loss
of entropy for this step relative to that for the conversion of E2
(-, red)-catalyzed isomerization of 1 to 3. (A) Gibbs free energy diagram,
(B) enthalpy diagram, and (C) entropy diagram. To aid in the direct
comparison of A and B, entropy units are given as -T∆S. When reading
the figure, the reader should keep in mind that an increase in -T∆S is
unfavorable and a decrease in -T∆S is favorable. Thermodynamic
parameters correspond to data at 25.0 °C, and these values are listed in
Table 5. The x-axis corresponds to the reaction coordinate for D38E-
catalyzed isomerization. The corresponding acetate ion-catalyzed mechanism
to TS2, which does not involve a hydration change, resulting
D38E
in a selective reduction of the activation barrier for k2
,
D38E
relative to k-1
.
-
Ac
-
Ac
-
is AcO + 1 h TS1 h AcOH + 2 h TS2 h AcO + 3. Barriers
due to E + 1 association/dissociation and barriers due to acetate-catalyzed
rate constants assume a standard state of 1 M.
Summary and Conclusions
Isomerization of 1 to 3 occurs 13 orders of magnitude faster
when catalyzed by KSI than when catalyzed by an acetate ion.
Determination of the activation parameters for the microscopic
rate constants for both the D38E- and the acetate ion-catalyzed
isomerization has allowed further characterization of the basis
for this catalysis. Enzymatic stabilization of the intermediate
dienolate relative to the substrate is due entirely to favorable
enthalpic interactions at the active site of KSI, which are not
available in solution, consistent with an increased hydrogen
bonding ability of the enzyme. Similarly, the more-favorable
consistent with previous work that attributes the major driving
force for stabilization of the bound intermediate to hydrogen
-
bonds from Asp99 and Tyr14 to O-3 of 2 in the hydrophobic
active site of KSI.2
8,30,32,33
Proton Abstraction from 1. The second-order rate constant
for proton abstraction catalyzed by D38E (E + 1 f TS1, k1D38E
/
KS) can be compared to the second-order rate constant for
-
Ac
OAc
acetate-catalyzed proton abstraction (AcO + 1 f TS1 , k1
)
D38E
OAc
(Table 5 and Scheme 6, path f). Proton abstraction from C-4
enthalpy of activation for k1
/KS relative to that for k1
by an acetate ion has a large enthalpic penalty and a moderate
entropic penalty (Figure 2, B and C, red trace). D38E lowers
the enthalpy of activation, but has no effect on the entropy of
for proton abstraction from C-4 of 1 indicates that the enzymatic
acceleration of this process is due to the ability of KSI to make
hydrogen bonding interactions in the active site stronger than
16424 J. AM. CHEM. SOC.
9
VOL. 126, NO. 50, 2004

D38E Mutant of 3-Oxo-∆5-Steroid Isomerase
A R T I C L E S
those available in solution. Partitioning of the intermediate,
however, has a substantial entropic component, suggesting that
equalization of the two high-energy transition states of KSI,
TS1, and TS2 may be affected by hydration changes in the
active site.
G. Blotny of this laboratory for the gift of 5-androstene-3,17-
dione.
Supporting Information Available: A table of kisomobs at
various temperatures. This information is available free of charge
via the Internet at http://pubs.acs.org.
Acknowledgment. This research was supported by a grant
from the National Institutes of Health (GM 31885). We thank
JA046819K
J. AM. CHEM. SOC.
9
VOL. 126, NO. 50, 2004 16425