Solvent isotope effects in H2O-D2O mixtures (proton inventories) on serine-protease-catalyzed hydrolysis reactions. Influence of oxyanion hole interactions and medium effects

Article abstract of DOI:10.1021/ja9614326

Rates of hydrolysis of succinyl-Ala-Ala-Pro-Phe-p-nitroanilide catalyzed by subtilisin and its N155G mutant were measured in H₂O, D₂O, and 'HDO' (1:1 H₂O:D₂O). The solvent isotope effects (proton inventories) de

Full text of DOI:10.1021/ja9614326

8802
J. Am. Chem. Soc. 1996, 118, 8802-8807
Solvent Isotope Effects in H O-D O Mixtures (Proton
2
2
Inventories) on Serine-Protease-Catalyzed Hydrolysis Reactions.
Influence of Oxyanion Hole Interactions and Medium Effects
1
2
2
,2
2
T. K. Chang, Y. Chiang, H.-X. Guo, A. J. Kresge,* L. Mathew,
1
1
M. F. Powell, and J. A. Wells
Contribution from the Department of Chemistry, UniVersity of Toronto,
Toronto, Ontario M5S 1A1, Canada, and Genentech, Inc., 460 Point San Bruno BouleVard,
South San Francisco, California 94080
X
ReceiVed April 30, 1996
Abstract: Rates of hydrolysis of succinyl-Ala-Ala-Pro-Phe-p-nitroanilide catalyzed by subtilisin and its N155G mutant
were measured in H2O, D2O, and “HDO” (1:1 H2O:D2O). The solvent isotope effects (proton inventories) determined
by these data showed no differences between the wild-type and mutant enzymes, despite the fact that the mutation
removes a hydrogen-bonding interaction in the oxyanion hole of the enzyme worth two orders of magnitude in
reaction rate. This suggests that curvature previously observed (ref 10) in the proton inventory for a reaction catalyzed
by methyl chymotrypsin is also not due to oxyanion hole interactions, and this curvature can in fact be accounted for
by a medium effect. Proton inventory analysis of the isotope effects for subtilisin and its mutant also indicate the
presence of strong medium effects in those systems.
Solvent isotope effects on reaction rates in H2O-D2O
Scheme 1
mixtures are commonly analyzed using the formalism repre-
sented by eq 1,3 in which kx is the rate constant
,4
q
kx Π (1 - x + xφ )
i
i
)
(1)
IS
kH
Π (1- x + xφ )
j
j
The right side of eq 1 must include terms of the form (1 -
x + xφ) for all exchangeable sites in both the transition state
and the initial state. When applied to enzymatic reactions,
however, an abbreviated version of eq 1 retaining only transition
state terms is often used, under the assumption that initial state
determined in an H2O-D2O mixture of deuterium atom fraction
x, kH is the corresponding rate constant determined in H2O, and
q
IS
φ and φ are fractionation factors for hydrogenic sites in the
transition state and the initial state, respectively. Fractionation
factors are partial isotope effects expressed as D:H ratios at
particular sites relative to the D:H ratio of the solvent with which
they are equilibrated. They reflect the tightness of bonding to
the hydrogens they represent: fractionation factors are signifi-
cantly different from unity for hydrogens being transferred,
where they represent primary isotope effects, and also for
hydrogens in strong hydrogen bonds, whose overall bonding is
loose.7 Analyses using this fractionation factor formalism are
often called proton inventories, especially when applied to
enzyme catalyzed reactions.8
IS
fractionation factors will either be unity (φ ) 1.00) or will
IS
q
not change between initial state and transition state (φ ) φ )
and will therefore drop out of the full expression. In this
circumstance, eq 1 will reduce to a linear function in x if only
one transition state fractionation factor is significantly different
q
from unity; to a quadratic function if two φ differ from unity;
q
to a cubic function if three φ differ from unity; etc. In practice,
while it is usually possible to determine whether an experimen-
tally derived relationship is linear or curved, because departures
from linearity are ordinarily quite small, it is generally difficult
to tell whether the curvature is quadratic, cubic, or of some
higher order.
A number of proton inventories for serine protease catlayzed
hydrolyses of ester and amide subtrates have been determined,
and some have been found to be linear and some curved.9 This
difference has been interpreted in terms of a reaction mechanism
involving the catalytic triad found in the active site of all serine
proteases, consisting of Ser-195, His-57, and Asp-102 (chy-
motrypsin numbering), shown in Scheme 1. As the carbonyl
carbon atom of the hydrolysis substrate is attacked by the
hydroxyl group of Ser-195, the nucleophilicity of this hydroxyl
group is increased by transfer of its proton to the imidazole
X
Abstract published in AdVance ACS Abstracts, September 1, 1996.
(
(
(
(
1) Genentech, Inc.
2) University of Toronto.
3) Kresge, A. J. Pure Appl. Chem. 1964, 8, 243-258.
4) This relationship is often called the Gross-Butler equation, after
5
6
pioneering work done by Gross and Butler on phenomena in H2O-D2O
mixtures. Gross and Butler, however, derived only a special case of eq 1,
that pertaining to the ionization of a monobasic acid, and the completely
general relationship of eq 1 was not available until it first appeared in ref
3
.
(
5) Gross, P.; Steiner, H.; Krauss, F. Trans. Faraday Soc. 1936, 32, 877-
8
79. Gross, P.; Wischin, A. Trans. Faraday Soc. 1936, 32, 879-883. Gross,
P.; Steiner, H.; Suess, H. Trans. Faraday Soc. 1936, 32, 883-899. Gross,
P.; Steiner, H.; Krauss, F. Trans. Faraday Soc. 1938, 34, 351-356.
(6) Hornell, J. C.; Butler, J. A. V. J. Chem. Soc. 1936, 1361-1366. Orr,
W. J. C.; Butler, J. A. V. J. Chem. Soc. 1937, 330-335. Nelson, W. E.;
Butler, J. A. V. J. Chem. Soc. 1938, 957-962.
(8) For a recent review, see: Quinn, D. M.; Sutton, L. D. In Enzyme
Mechanisms from Isotope Effects; Cook, P. F., Ed.; CRC Press: Boca Raton,
FL, 1991; pp 73-126.
(9) For a review, see: Venkatasubban, K. S.; Schowen, R. L. CRC Crit.
ReV. Biochem. 1984, 17, 1-44.
(7) Kreevoy, M. M.; Liang, T. M. J. Am. Chem. Soc. 1980, 102, 3315-
3
322. Cleland, W. W. Biochemistry 1992, 31, 317-319. Cleland, W. W.;
Kreevoy, M. M. Science, 1994, 264, 1887-1890. Frey, P. A.; Whitt, S.
A.; Tobin, J. B. Science 1994, 264, 1927-1930.
S0002-7863(96)01432-1 CCC: $12.00 © 1996 American Chemical Society

SolVent Isotope Effects in H2O-D2O Mixtures
J. Am. Chem. Soc., Vol. 118, No. 37, 1996 8803
side chain of His-57, and this may or may not be accompanied
by a second proton transfer from the back side of the forming
imidazolium ion to the carboxylate group of Asp-102. Linear
proton inventories have been taken as evidence that only the
first proton transfer, that from serine to histidine, is taking place,
whereas curved proton inventories have been taken to mean
that the second proton transfer, that from histidine to aspartate,
is occurring as well.
a much simpler system which nevertheless still retains many
of the features of enzyme-substrate association: complex
formation between R-cyclodextrin and p-nitrophenoxide ion.
It is the degree of curvature that carries the mechanistic
information in a proton inventory, and curvature is maximized
at the midpoint near x ) 0.5. Following Albery,15 we have
consequently concentrated our measurements in this region,
dubbed “HDO”, in addition to x ) 0 and x ) 1.
Several years ago, a critical experiment was performed whose
A portion of the present work has been published in
10
outcome cast doubt upon this interpretation. It was found that
a hydrolysis reaction catalyzed by a chymotrypsin derivative
whose His-57 imidazole hydrogen had been replaced by a
methyl group, and a second proton transfer to Asp-102 was
consequently impossible, still gave a curved proton inventory.
This unexpected result was rationalized by proposing that the
curvature in this case was caused by strengthened hydrogen
bonding interactions between the substrate and groups situated
in the oxyanion hole of the enzyme. This experiment, however,
nevertheless showed that curved proton inventories do not
necessarily signify occurrence of a second proton transfer.
In order to determine whether oxyanion hole interactions can
in fact influence proton inventories, we have examined a
hydrolysis reaction catalyzed by an enzyme in which this
interaction has been impaired by site-directed mutagenesis. Such
an experiment cannot be performed with chymotrypsin, for the
hydrogen bonding interactions in the oxyanion hole of this
enzyme are provided by main-chain amide groups, and removing
them would destroy the enzyme. In subtilisin, however, only
one of the oxyanion hole interactions is provided by a main
chain amidestwo others are furnished by the side chains of
Asn-155 and Thr-220. Site-directed mutagenesis has shown that
16
preliminary form.
Experimental Section
Materials. Wild-type subtilisin BPN′ and its N155G mutant were
1
7
prepared and purified as has already been described.
materials were best available commercial grades.
All other
Enzyme Kinetics. Rates of the enzyme-catalyzed hydrolysis of
succinyl-Ala-Ala-Pro-Phe-p-nitroanilide were determined by monitoring
the appearance of p-nitroaniline through its absorbance at λ ) 410 nm.
Measurements were performed using Cary 118 and 2200 spectrometers
whose cell compartments were thermostatted at 25.0 ( 0.05 °C.
Zero-order initial rates of reaction, V, for fitting of the Michaelis-
Menten expression, eq 3, were determined at different substrate
concentrations, [s], by adding
Vm [s]
V )
(3)
KM + [s]
successive amounts of substrate to the same reaction mixture. Enyzme
plus buffer solution, made by adding 30 µL of enzyme stock solution
(H
O, HDO, or D O solvent) to 1.00 mL buffer contained in a low-
2 2
volume cuvette, was first allowed to come to temperature equilibrium
with the spectrometer cell compartment. Two µL of substrate stock
solution (DMSO solvent) was then added, and the change in absorbance
was recorded for 2-4 min. A second 2-µL portion of substrate stock
solution was then added, and the change in absorbance was recorded
again. This process was usually repeated for six substrate additions,
after which another set of six determinations was performed using
substrate stock solution of a different concentration. Four to six such
sets of six measurements were usually made, and in this way a number
of reaction velocities, V, at different substrate concentrations distributed
11
the interaction with Asn-155 is by far the stronger of these two,
and an X-ray structure determination indicates that the third
interaction, that with the main chain amide group, must operate
12
over a longer distance and is consequently weak. We have
therefore performed our study using the N155G mutant of
subtilisin in which Asn-155 is replaced by glycine, a residue
with no side-chain capable of providing a hydrogen bonding
interaction.
The substrate we have used is succinyl-Ala-Ala-Pro-Phe-
about K
M M
, [s] ) (0.05-15) K , were supplied. The extent of reaction
13
nitroanilide, and the reaction we have studied is consequently
the amide hydrolysis shown in eq 2. We
during the 2-4 min over which the zero-order rate measurements were
made varied from just under 10% to less than 1%. The absorbance
versus time records were accurately linear; their slopes were determined
by eye, and these were then converted to rates of change of substrate
concentration using the extinction coefficient for p-nitroaniline ꢀ )
-
1
-1 13
8
480 M cm
.
Substrate concentrations used for fitting of eq 3
were average values for the period over which absorbances were
recorded; these were calculated from knowledge of the substrate stock
solution concentrations, the rate of reaction, and the times over which
absorbance was measured plus the intervals between successive
additions. A representative Michaelis-Menten plot is shown in Figure
1; it may be seen that the data conform to this rate law well.
constructed proton inventories using both Vm (maximum veloc-
ity) and Vm/KM (first-order) rate constants, and by taking the
ratios (Vm/KM):Vm, we also obtained proton inventories based
upon 1/KM values. For anilide substrates such as the one we
used, acyl-enzyme formation is believed to be rate-determin-
ing, and 1/KM then takes on the form of an enzyme-substrate
association constant. Because we found there to be an ap-
preciable solvent isotope effect on 1/KM, we also investigated
First-order rates of reaction were determined at initial substrate
concentrations much less than K
3 reduces to the first-order expression V ) (V
M
, [s]
o
) (0.004-0.02) K
M
, where eq
/K ) [s]. These reactions
m
M
were allowed to run essentially to completion (5 half-lives or longer).
The data obeyed the first-order rate law well, and rate constants were
calculated by nonlinear least squares fitting of an exponential expres-
sion.
1
4
2 2
In all cases, groups of measurements in H O, HDO, and D O
(10) Scholten, J. D.; Hogg, J. L.; Raushel, F. M. J. Am. Chem. Soc. 1988,
solutions were made on the same day using the same enzyme stock
1
10, 8246-8247.
(
11) Braxton, S.; Wells, J. A. J. Biol. Chem. 1991, 266, 11797-11800.
12) McPhalen, C. A.; James, M. N. G. Biochemistry 1988, 27, 6582-
(15) (a) Albery, W. J.; Davies, M. H. J. Chem. Soc., Faraday Trans. II
1972, 68, 167-181. (b) Albery, W. J. In Proton Transfer Reactions, Caldin,
E. F., Gold, V., Ed.; Chapman and Hall: London, 1975, Chapter 9.
(16) Chiang, Y.; Kresge, A. J.; Chang, T. K.; Powell, M. F.; Wells, J.
A. J. Chem. Soc., Chem. Comm. 1995, 1587-1588.
(17) Carter, P.; Wells, J. A. Proteins: Struct. , Funct., Genet. 1990, 7,
335-342.
(
6
598.
(
13) Del Mar, E. G.; Largman, C.; Brodrick, J. W.; Geokas, M. C. Anal.
Biochem. 1979, 99, 316-320.
14) Wells, J. A.; Cunnngham, B. C.; Graycar, T. P.; Estell, D. A. Phil.
Trans. Roy. Soc. London A 1986, 317, 415-423.
(

8804 J. Am. Chem. Soc., Vol. 118, No. 37, 1996
Chang et al.
solution. Replicate measurements made at the beginning and end of
the day showed that the enzyme solutions were stable for this period
of time.
Cyclodextrin Complex Formation. Equilibrium constants for
complex formation between R-cyclodextrin and p-nitrophenoxide ion
were determined using the shift to longer wavelengths that the
absorption band of this ion at λmax ) 400 nm undergoes upon inclusion
into the cyclodextrin. The change in absorbance accompanying
complex formation is greatest at λ ) 370 nm, and measurements were
consequently made at this wavelength, using a Cary 2200 spectrometer
with cell compartment thermostatted at 25.0 ( 0.05 °C. Absorption
measurements were made on a series of solutions of fixed p-
-4
nitrophenoxide concentration (ca. 10 M) but increasing R-cyclodextrin
concentration. This was accomplished by making successive additions
of a solution containing R-cyclodextrin and p-nitrophenol to a buffer
-
2-
3
solution (0.1 M HCO
3
/CO
, pH ) 10.0) containing p-nitrophenol
at exactly the same concentration as the cyclodextrin solution. The
data were analyzed by nonlinear least squares fitting of eq 4, in which
A is
2
Figure 1. Michaelis-Menten plot for the hydrolysis in D O solution
of succinyl-Ala-Ala-Pro-Phe-p-nitroanilide catalyzed by wild-type
subtilisin.
(a + b + 1/K) -
x
(a + b + 1/K) - 4ab
2
A ) ꢀ b + (ꢀ - ꢀ )
{
}
p
c
p
(
4)
absorbance, ꢀ
p
c
and ꢀ are extinction coefficients of free and complexed
p-nitrophenoxide ion respectively, a and b are stoichiometric concentra-
tions of R-cyclodextrin and p-nitrophenoxide ion, respectively, and K
is the complex association constant. The value of b for each series of
p c
solutions was supplied whereas ꢀ , ꢀ , and K were parameters
determined by the fitting procedure. Figure 2 shows a representative
set of data and the line produced by the fit; it may be seen that the
relationship of eq 4 is obeyed quite well.
Results
Enzyme Kinetics. Zero-order initial rates of hydrolysis of
succinyl-Ala-Ala-Pro-Phe-p-nitroanilide catalyzed by wild-type
subtilisin and its N115G mutant were determined in H2O, HDO,
and D2O solution at substrate concentrations in the vicinity of
KM ([s]o ) (0.5-15) KM). The data so obtained were analyzed
by fitting of the Northrop version of the Michaelis-Menten
equation,1 which gives maximum velocities, Vm, and first-order
rate constants, Vm/KM, directly. The measurements were made
in sets using the same enzyme stock solution for all three
solvents; this ensured that enzyme concentrations were exactly
the same in all three solvents and that the isotope effects were
consequently being evaluated at the same enzyme concentration.
Each Michaelis-Menten plot was based on 20-40 initial rate
values, and 10 such plots were constructed with the wild-type
enzyme and 14 with the mutant. The parameters obtained from
these analyses were formulated into HDO/H2O and D2O/H2O
isotope effects on Vm and Vm/KM by taking appropriate ratios.
The results are summarized in Table S119 and are displayed in
Figure 3.
Figure 2. Relationship between absorbance and R-cyclodextrin
concentration produced by complex formation with p-nitrophenoxide
ion in H O solution.
2
8
Rates of enyzmatic hydrolysis were also determined at low
substrate concentrations ([s]o ) 0.004-0.02 KM) where the
enzyme-catalyzed reactions become a first-order process with
rate constant equal to Vm/KM. Measurements in H2O, HDO,
and D2O were again made in sets using the same enzyme stock
solution, and replicate determinations (3-8) were made for each
solvent within a given set. Nine such sets of measurements
were made with the wild-type enzyme and three with the mutant.
The isotope effects obtained are listed in Table S21 and are
also displayed in Figure 3.
Figure 3. Solvent isotope effects for the hydrolysis of succinyl-Ala-
Ala-Pro-Phe-p-nitroanilide by subtilisin (O, solid line) and its N155G
mutant (4, broken line).
Both kinds of rate measurements (zero- and first-order) were
done in TRIS or carbonate buffers at pHs ranging from 8.2 to
9
1
0.0; this variation in pH was found to have no systematic
(18) Northrop, D. B. In Isotope Effects on Enzyme-Catalyzed Reactions;
influence on the isotope effects. The enzyme stock solutions
were made using either H2O, HDO, or D2O as the solvent, and
this difference was also found to have no influence on the
isotope effects.
Cleland, W. W., O’Leary, M. H., Northrop, D. B., Eds.; University Park
Press: Baltimore, MD, 1977; pp 122-152.
(19) Supporting information; see paragraph at the end of this paper
regarding availability.

SolVent Isotope Effects in H2O-D2O Mixtures
J. Am. Chem. Soc., Vol. 118, No. 37, 1996 8805
gives the following relationships: (Vm/KM)x/(Vm/KM)H ) 1 -
2
(
0.054 ( 0.019)x - (0.236 ( 0.021)x for the wild-type enzyme
and (Vm/KM)x/(Vm/KM)H ) 1-(0.019(0.042)x - (0.297 (
2
0
+
(
.047)x for N115G, and (Vm)x/(Vm)H ) 1 - (0.763 ( 0.033)x
2
(0.093 ( 0.037)x for the wild-type and (Vm)x/(Vm)H ) 1 -
2
0.757 ( 0.022)x + (0.115 ( 0.024)x for N115G. Comparison
of the coefficients of these expressions shows no significant
difference between the wild-type and mutant enzymes for either
the Vm/KM or the Vm relationships. The proton inventories based
upon these rate constants are therefore the same for both
enzymes, within the precision of the present measurements.
The N115G mutation removes the major hydrogen bonding
interaction in the oxyanion hole of subtilisin. This mutation
reduces the reactivity of the enzyme by two orders of magni-
1
7,24
tude,
but the change in hydrogen bond strength to which
this rate difference corresponds is apparently not large enough
to affect the proton inventory. It is known that only hydrogens
involved in very strong hydrogen bondssthe so-called “low-
barrier hydrogen bonds” shave fractionation factors sufficiently
different from unity to affect proton inventories; evidently the
interactions present in the oxyanion hole of subtilisin are not
of this nature.
Figure 4. Solvent isotope effects for the association of p-nitro-
phenoxide ion with R-cyclodextrin.
-8
-9
Enzyme concentrations were 10 -10 M for the runs with
-6
-8
wild-type enzyme and 10 -10 M for those with the mutant.
We made no effort to fix these concentrations precisely, since
our interest was solely in rate ratios determined at the same
enzyme concentration, and this was accomplished by using the
same enzyme stock solution to measure both constituent rates
of a given ratio. Enzyme concentrations were nevertheless
known approximately, and use of these to convert the presently
evaluated rate constants into kcat and kcat/KM values gave results
consistent with the literature: for the wild-type enzyme, kcat/
7
The presently determined absence of an oxyanion-hole
influence on proton inventories suggests that the curvature found
10
in the proton inventory for methyl chymotrypsin is not due to
oxyanion hole interactions either. Only a single proton transfer
can occur in that system, and a linear proton inventory might
consequently be expected. However, as was pointed out by
-
1
14
17,20
11
5
-1 -1
s
) 32 Versus 50, 44,
or 56 and (kcat/KM)/10 M
s
25
one of us some time ago, a linear proton inventory can be
1
4
20a
)
2.0 (zero-order) or 2.5 (first-order) Versus 3.6, 2.2,
converted into a curved relationship by a sufficient number of
small changes in fractionation factors in other parts of the
system. These changes might be in fractionation factors of
exchangeable hydrogens in the enzyme and the substrate or in
fractionation factors of water molecules solvating the enzyme
and the substrate. In a system as large as an enzymatic reaction,
there are of course hundreds of hydrogens of this kind, and it
is not unlikely that the fractionation factors of some would be
altered by the conformational and other changes that occur as
the system moves from initial state to transition state.
7,20b
11
-1
17
2
.51
or 3.5 and for the mutant, kcat/s ) 0.23 Versus 0.30
3
-1 -1
and (kcat/KM)/10 M
s
) 1.3 (zero-order) or 2.6 (first -order)
Versus 1.4.17
Cyclodextrin Complex Formation. Association constants,
Kass, for complex formation between R-cyclodextrin and p-
nitrophenoxide ion were determined in H2O, HDO, and D2O.
Measurements were made in bicarbonate-carbonate buffer
solutions at pH ) 10.0, midway between the pKa of the
cyclodextrin (pKa ) 12.33)21 and p-nitrophenol (pKa ) 7.15),
in order to ensure that the cyclodextrin was essentially fully
unionized and the p-nitrophenoxide essentially fully ionized and
that the isotope effects were consequently not being influenced
by acid-base equilibration of either of these substances.
Twenty-six separate determinations of Kass were made in H2O,
eleven in HDO, and fifteen in D2O, and each determination was
based upon some 40 concentration-absorbance data pairs. The
results are summarized in Table S319 and are displayed in Figure
22
A convenient way of handling the aggregate influence of such
multiple small changes is to introduce an additional “medium
x
effect” term of the form (Φ) into the basic relationship of eq
1
5b,26
1
, as shown in eq 5.
Such a medium effect does in fact
accomodate the curvature of the proton inventory for the methyl
chymotrypsin system very well: as Figure 5 shows the fit
produced by eq 5 with one transition state
4
.
q
kx
Π (1 - x + xφ )
i
i
The average of the determinations made in H2O is Kass )
x
)
(Φ)
IS
(5)
3
-1
(
2.264 ( 0.013) × 10 M , in good agreement with what
kH
Π (1 - x + xφ )
j
j
appears to be the best value available from the literature, Kass
3
-1 23
)
(2.178 ( 0.045) × 10 M .
fractionation factor, corresponding to a single proton transfer,
plus a medium effect is as good as the one originally proposed10
with three transition state fractionation factors, corresponding
to one proton transfer and two hydrogen bonding interactions.
Nonlinear least squares fitting of the medium effect model gives
φ ) 0.44 ( 0.05 and Φ ) 0.58 ( 0.05. This medium effect
is a differential quantity that compares the tightness of bonding
in the initial state of the reaction with that of the transition state.
Discussion
Oxyanion Hole Interactions. Each of the proton inventories
constructed here for hydrolysis of succinyl-Ala-Ala-Pro-Phe-
p-nitroanilide by subtilisin and its N115G mutant is well
represented by a quadratic expression, and least squares fitting
q
(20) (a) Bryan, P.; Pantoliano, M. W.; Quill, S. G.; Hsiao, H.-Y.; Poulos,
T. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 3743-3745. (b) Carter, P.; Wells,
J. A. Nature 1988, 332, 564-568.
(24) Carter, P.; Abrahamson, L.; Wells, J. A. Biochemistry 1991, 30,
6142-6148.
(21) Gelb, R. I.; Schwartz, L. M.; Bradshaw, J. J.; Laufer, D. A. Bioorg.
Chem. 1980, 9, 299-304.
22) Fernandez, L. P.; Hepler, L. G. J. Am. Chem. Soc. 1959, 81, 1783-
786.
23) Gelb, R. I.; Schwartz, L. M.; Cardelino, B.; Laufer, D. A. Anal.
Biochem. 1980, 103, 362-368.
(25) Kresge, A. J. J. Am. Chem. Soc. 1973, 95, 3065-3067.
(26) Gold, V. AdV. Phys. Org. Chem. 1969, 7, 259-331. Kresge, A. J.;
More O’Ferrall, R. A.; Powell, M. F. In Isotopes in Organic Chemistry;
Vol. 7, Buncel, E., Lee, C. C., Eds.; Elsevier: New York, 1987, pp 177-
273.
(
1
(

8806 J. Am. Chem. Soc., Vol. 118, No. 37, 1996
Chang et al.
Table 1. Models That Provide Acceptable Fits to the Combined
Proton Inventory Data for Hydrolysis of
Succinyl-Ala-Ala-Pro-Phe-p-nitroanilide by Subtilisin and Its
N155G Mutant
q
q
φIS
model
φ
1
φ
2
Φ
m
V :
1
2
3
0.42 ( 0.03 0.82 ( 0.05
0.41 ( 0.02
1.18 ( 0.04
0.41 ( 0.02
0.84 ( 0.03
1.65 ( 0.04
m M
V /K :
4
5
6
0.48 ( 0.01 1.48 ( 0.03
0.27 ( 0.02
0.43 ( 0.01
0.38 ( 0.03
that limits to two the number of independent fractionation factors
that can be determined by each proton inventory. This reduces
considerably the number of proton inventory models that should
be examined, for there are only eight variants of eq 5 with no
more than two fractionation factors.
Figure 5. Proton inventories for the hydrolysis reaction of ref 10
catalyzed by methyl chymotrypsin; lower curve: one proton transfer
plus two oxyanion hole interactions, upper curve: one proton transfer
plus medium effect.
Since wild-type subtilisin and its N155G mutant give isotope
effects that are not significantly different, data obtained with
the two enzymes were combined for fitting of eq 5. Each of
the eight possible variants of eq 5 containing no more than two
fractionation factors was examined, and three good fits were
found for the Vm isotope effects and three also for the Vm/KM
data. The fractionation factors obtained with these models are
listed in Table 1.
The requirement that transition state fractionation factors be
the same for Vm and Vm/KM proton inventories eliminates models
1
, 4, and 5, leaving a unique solution, model 6, for Vm/KM, but
still two possibilities, models 2 and 3, for Vm. A choice between
the latter two can be made, however, by using the fact that they
lead to different predictions of proton inventories on 1/KM.
Division of the expression for model 6 by that for model 2 gives
the relationship shown in eq 7 for (1/KM)x/(1/KM)H,27 whereas
division of the expression for model 6 by that for model
Figure 6. Proton inventories for the hydrolysis of succinyl-Ala-Ala-
Pro-Phe-p-nitroanilide using combined data for catalysis by subitlisin
and its N155G mutant; V
m
: model 3; V
m
/K
M
: model 6.
{(V /K ) /(V /K ) }
(1/K )
m
M x
m
M H
6
M x
)
)
{
(V ) /(V ) }
(1/K )
m x
m H
3
M H
The fact that it is less than unity means that the aggregate
bonding is loser in the transition state than in the initial state.
Subtilisin Proton Inventories. Hydrolysis reactions cata-
lyzed by subtilisin are believed to follow the two-state enzyme
acylation-deacylation mechanism common to serine proteases,
with acyl-enzyme, E‚S′, formation rate-determining for amide
q
x
(1 - x + xφ )(Φ )
6
)
IS
q
(1 - x + xφ )/(1 - x + xφ )
FS
x
(1 - x + xΦ )(Φ ) (7)
6
1
4
3 gives the different relationship shown as eq 8. Isotope effects
on 1/KM were obtained from the data of Table S1 by dividing
substrates, eq 6.
It follows then that KM is equal to the
1
9
dissociation constant of the
{
(V /K ) /(V /K ) }
(1/K )
kcat
H O
m
M x
m
M H
6
M x
2
)
)
E + S { } E‚S r.d.8 E‚S′
8 E + P + P
(6)
2
1
KM
fast
{(V ) /(V ) }
(1/K )
m x
m H
3
M H
q
x
x
x
x
(
1 - x + xφ )(Φ )
(Φ6)
(Φ3)
6
enzyme-substrate complex, kcat/KM is the rate constant for the
reaction starting from free enzyme and substrate as the initial
state, and kcat is the rate constant for reaction with enzyme-
substrate complex, E‚S, as the initial state. This scheme requires
that the two rate constants, kcat/KM and kcat, refer to the same
transition state, and that imposes the added restriction that proton
inventories based on the analogs of these rate constants used
here, Vm/KM and Vm, must have the same transition state
fractionation factors.
A further restriction on analysis of the present data by the
proton inventory method is imposed by the fact that, whereas
both Vm and Vm/KM isotope effects are better represented by a
quadratic than by a linear function, a cubic relationship gives
no further improvement. Fitting of forms of eq 5 with more
than two disposable parameters is therefore unwarranted, and
)
(8)
q
(1 - x + xφ )(Φ )
3
isotope effects on Vm/KM by those on Vm, and the results were
analyzed using expressions of the form of eqs 7 and 8. Model
2 requires that φ ) 1.18 ( 0.04 and Φ6 ) 1.65 ( 0.04,
whereas the fit of 1/KM isotope effects gave φ ) 1.00 ( 0.02
and Φ ) 1.82 ( 0.03, and model 3 requires that Φ6/Φ3 ) 1.97
( 0.10, whereas the fit of 1/KM isotope effects gave Φ ) 1.82
( 0.03. These comparisons show that model 3 fits the
experimental data better than model 2 and is consequently to
be preferred. This fit is illustrated in Figure 6 together with
that of model 6 for the Vm/KM isotope effects.
IS
FS
The picture that emerges from these analyses is thus one of
a reaction with a single low transition state fractionation factor

SolVent Isotope Effects in H2O-D2O Mixtures
J. Am. Chem. Soc., Vol. 118, No. 37, 1996 8807
modified by substantial medium effects. The low transition state
fractionation factor could represent a hydrogen undergoing
transfer, whose isotope effect is kH/kD ) 1/φ = 2.4, or it could
stants for such complex association can be measured without
interference from any further reaction. Cyclodextrins are also
much smaller than enzymes with far fewer exchangeable
hydrogens (only three in each of the six glucose units of
R-cyclodextrin), and they would therefore appear to be attractive,
simple models that might provide further insight into proton
inventories on enzyme-substrate complex formation. The
complex between R-cyclodextrin and p-nitrophenoxide ion is
among the strongest formed, and we consequently chose to
investigate this system.
q
refer to a hydrogen engaged in strong hydrogen bonding. Since
at least one hydrogen must be transferred in the catalytic triad
mechanism of Scheme 1, the former explanation seems the more
2
8
likely. The medium effect of Φ ) 0.84 on Vm represents a
small aggregate loosening of bonds to a number of hydrogens
as the system progresses from the enzyme substrate complex
to the transition state; these hydrogens could be in the complex
itself or in its solvation shell. The larger medium effect of Φ
The overall solvent isotope effect on this association reaction
proved to be rather weak, (Kass)D/(Kass)H ) 1.29 ( 0.01, which
puts this system into a region where the difference between
various proton inventory models is very small. The data are
consequently not very diagnostic, but they nevertheless do
conform to a simple medium effect expression well and give
the result Φ ) 1.29 ( 0.01. This medium effect is in the same
direction, Φ > 1, as that found for complex formation between
subtilisin and its hydrolysis substrate and is consequently
consistent with the explanation offered above for that effect:
as complex formation occurs and solvation is replaced by
interactions between cyclodextrin and p-nitrophenoxide ion, the
more loosely bound solvating water molecules are converted
to more tightly bound bulk water. The smaller magnitude of
the cyclodextrin medium effect is also consistent with the result
for subtilisin in that cyclodextrin and its substrate are smaller
than the subtilisin system and have fewer exchangeable hydro-
gens and solvating water molecules. Thus, although the present
solvent isotope effects on cyclodextrin-p-nitrophenoxide com-
plex formation do not provide a detailed proton inventory
analysis, they nevertheless do support the conclusion reached
above that medium effects have a decisive influence on solvent
isotope effects in the subtilisin system.
)
1.65 on Vm/KM, on the other hand, represents a larger
aggregate tightening of bonds to a number of hydrogens
anywhere in the system in the process starting with free enzyme
and substrate.
It is instructive to separate out from the medium effect on
Vm/KM that on the first step of this process, association of the
enzyme and substrate to form the enzyme-substrate complex.
This may be done by taking the ratio of medium effects on
Vm/KM and Vm, as was done above in deciding between models
2
and 3, or by fitting isotope effects on 1/KM directly, whose
result was also summarized above. The weighted average of
the two methods gives Φ ) 1.84 ( 0.03. Medium effects may
now be assigned to individual parts of the acylation stage of
the enzymatic reaction, as shown in eq 9.
Φ ) 1.84
Φ ) 0.84
E + S {
} E‚S
8 E‚S′
(9)
The considerable tightening produced by enzyme-complex
formation can thus be seen to be offset by a smaller loosening
upon progress of this complex to the transition state.
It is likely that solvating water molecules make a significant
contribution to the greater than unity character of the medium
effect on 1/KM, Φ ) 1.84. Most substances are less soluble in
Conclusions
D2O than in H2O,1
5b,29
which means that the waters solvating
We have found that removing a hydrogen-bonding interaction
in the oxyanion hole of subtilisin has no detectable influence
on solvent isotope effects for a hydrolysis reaction catalyzed
by this enzyme but that curvature in proton inventories for this
system stems from medium effects. Medium effects also can
account for the curvature of a proton inventory for a reaction
catalyzed by methyl chymotrypsin that had previously been
attributed to oxyanion hole interactions. This suggests that
oxyanion hole interactions are not strong enough to influence
proton inventories but that medium effects, which so far have
received little attention in proton inventory studies, can play
decisive roles.
them have φ < 1. If this is true of the substrate and the active
site of the enzyme in the present system, then, as the enzyme
and substrate associate to form the enzyme-substrate complex,
their solvating waters will be transformed into bulk solvent with
φ ) 1.00. The change from φ < 1 to φ ) 1.00 will then make
a greater than unity contribution to Φ on the enzyme-substrate
association step.
Cyclodextrin Proton Inventory. Cyclodextrins are cyclic
glucopyranosides with central cavitiess“active sites”sthat
mimic the catalytic action of some enzymes remarkably
closely.3 They operate, like enzymes, by first forming catalyst-
substrate complexes, and in suitable systems association con-
0
Acknowledgment. This paper is dedicated to Professor
Nelson J. Leonard on the occasion of his 80th birthday. We
are grateful to the U.S. National Institutes of Health for financial
support of this research under Grant No. GM 47539.
(
27) Because the initial state for Vm is the final state for 1/KM, the initial
IS
state fractionation factor φ in the expression for model 2 becomes the
final state fractionation factor in the expression for 1/KM.
(
φ ) 0.42 might be a composite of the fractionation factor for hydron
transfer from serine to histidine plus another for a hydron becoming engaged
in strong hydrogen bonding between histidine and aspartate. However, such
28) A referee has suggestd that the transition state fractionation factor
q
Supporting Information Available: Tables of isotope
effects (4 pages). See any current masthead page for ordering
and Internet access instructions.
q
q
a model with two transition state fractionation factors, φ1 and φ2 , produces
q
q
different values of φ1 and φ2 for Vm proton inventories than for Vm/KM
proton inventories, and it therefore does not meet the criterion that transition
state fractionation factors for the two kinds of proton inventory must be
the same.
JA9614326
(30) Bender, M. L.; Komiyama, M. Cyclodextrin Chemistry; Springer-
Verlag: Berlin, 1978. Bender, M. L. in Enzyme Mechanisms; Page, M. I.,
Williams, A., Eds.; Royal Society of Chemistry: London, 1987; pp 56-
76. Breslow, R. Acc. Chem. Res. 1995, 28, 146-153.
(
29) Arnett, E. M.; McKelvey, D. R. in Solute-SolVent Interactions;
Coetzee, J. F., Ritchie, C. D., Eds.; Marcel Dekker: New York, 1969; pp
43-398.
3