Solvent deuterium isotope effect on the binding of β-D-galactopyranosyl derivatives to β-galactosidase (Escherichia coli, lac Z)

Article abstract of DOI:10.1006/bioo.1999.1157

A value of 1.8 has been determined for (K₁)(HOH)/(K₁)(DOD), the ratio of the values of K₁ for competitive inhibition of β-galactosidase by isopropyl β-D-thiogalactopyranoside in H₂O and D₂O. This is s

Full text of DOI:10.1006/bioo.1999.1157

Bioorganic Chemistry 8, 49–56 (2000)
doi:10.1006/bioo.1999.1157, available online at http://www.idealibrary.com on
Solvent Deuterium Isotope Effect on the Binding of
β-D-Galactopyranosyl Derivatives to β-Galactosidase
(
Escherichia coli, lac Z )1
2
John P. Richard and Deborah A. McCall
Department of Chemistry, University at Buffalo, SUNY, Buffalo, New York 14260-3000
Received June 3, 1999
A value of 1.8 has been determined for (K
competitive inhibition of β-galactosidase by isopropyl β-D-thiogalactopyranoside in H
and D O. This is similar to the value of 1.7 for (K DOD, the ratio of the Michaelis
constants determined for the β-galactosidase-catalyzed hydrolysis of 4-nitrophenyl β-D-
galactopyranoside (Gal-OPNP) in H O and D O. The similarity of these solvent deuterium
isotope effects suggests that the observed isotope effect on K corresponds, mainly, to the
isotope effect on the dissociation constant K for Gal-OPNP. The implications of these
results for the interpretation of the solvent deuterium isotope effects on kcat and kcat /K for
I
)
HOH/(K
I I
)DOD, the ratio of the values of K for
2
O
2
m
)
HOH/(K
m
)
2
2
m
d
m
β-galactosidase-catalyzed hydrolysis of Gal-OPNP is discussed.
© 2000 Academic Press
INTRODUCTION
We would like to understand the mechanistic implications of the following kinetic
isotope effects that have been reported in the literature for the β-galactosidase-catalyzed
hydrolysis of 4-nitrophenyl β-D-galactopyranoside (Table 1) (1–3).
(1) The small and essentially identical α-deuterium kinetic isotope effects on
k /K and k (Table 1) (1,2), which require that the changes in hybridization at the
cat
m
cat
α-carbon of the substrate on proceeding to the rate-limiting transition states for k /Km
cat
and k be essentially the same.
cat
1
8
(
2) The O-leaving group isotope effects on k /K and k . Significant isotope
cat
m
cat
effects are observed on each of these kinetic parameters, consistent with significant
changes in bonding at oxygen on proceeding to the respective rate-determining tran-
sition states (3), but the difference in these isotope effects is consistent with somewhat
greater changes in bonding at the rate-determining transition state for kcat compared
with that for k /K .
cat
m
1
2
This work was supported by a grant from the National Institutes of Health (GM 39754).
To whom correspondence and reprint requests should be addressed. Fax: (716) 645-6963. E-mail:
jrichard@chem.buffalo.edu.
4
9
0
045-2068/00 $35.00
Copyright © 2000 by Academic Press
All rights of reproduction in any form reserved.

5
0
RICHARD AND McCALL
TABLE 1
Kinetic Isotope Effects on the Hydrolysis of 4-Nitrophenyl β-D-Galactopyranoside Catalyzed
by β-Galactosidase
Kinetic parameter
Isotope effecta
k
cat/K
k
cat
b
1.07 ± 0.03c
1.014 ± 0.003
1
1.04 ± 0.02d
1.022 ± 0.002
1.7
α-Deuterium isotope effect
18
e
O-Leaving group isotope effect
Solvent deuterium isotope effect
f
a
The ratio of the kinetic parameters for reactions with the substrate Gal-OPNP, or the reaction medium,
labeled with the light and heavy isotopes.
b
At pH 7.0 for reactions of Gal-OPNP labeled with hydrogen and deuterium at the anomeric carbon.
Data from Ref. 1.
c
d
Data from Ref. 2.
e
f
At pH 7.0 for reactions of Gal-OPNP labeled with 16O and 18O at the leaving-group oxygen (3).
2 2
For reactions of unlabeled Gal-OPNP in H O and D O (2). The values of the kinetic parameters used
to calculate these isotope effects were determined at the pL maximum for the respective reactions.
(3) The contrasting large difference between the values of 1.0 and 1.7, respectively,
for the solvent deuterium isotope effects on k /K and k (2). This, nominally, is con-
cat
m
cat
sistent with very different degrees of cleavage of the bond to a solvent-derived hydron
at the transition state for k (significant bond cleavage) and k /K (little bond cleav-
cat
cat
m
age). However, it is not easily reconciled with the much smaller differences observed
18
for the α-deuterium isotope effects and the O-leaving group isotope effects on k /K
cat
m
and k (Table 1).
cat
What has not been considered when interpreting the solvent deuterium isotope
effects is the possibility that the rate-limiting transition states for kcat and k /K are
cat
m
similar with respect to extent of transfer of a solvent-derived hydron to the oxygen
leaving group, but that the difference in these isotope effects reflects a solvent isotope
effect on the dissociation constant for the substrate Gal-OPNP. We report here that the
solvent deuterium isotope effect on the inhibition constant K for the competitive
I
inhibitor isopropyl β-D-thiogalactopyranoside (Gal-SIP) is similar to the solvent deu-
terium isotope effect on K for Gal-OPNP. This result provides a precedent for a sol-
m
vent deuterium isotope effect on the affinity of sugar derivatives for β-galactosidase,
and it suggests that the difference in the solvent isotope effects on kcat and k /Km
cat
reported in Table 1 is due largely to a solvent isotope effect on substrate binding.
Therefore, the difference in the extent of cleavage of the bond to a solvent-derived
hydron on proceeding to the respective rate-determining transition states for kcat and

ISOTOPE EFFECTS ON β-GALACTOSIDASE
51
k /K is much smaller than that suggested by the difference in the observed solvent
cat
m
deuterium isotope effects.
MATERIALS AND METHODS
Materials. Reagent grade organic and inorganic chemicals were obtained from com-
mercial sources and were used without further purification. Water was distilled and passed
through a Milli-Q water purification system. 4-Nitrophenyl β-D-galactopyranoside (Gal-
OPNP), isopropyl β-D-thiogalactopyranoside (Gal-SIP), and β-galactosidase (Grade VIII
from Escherichia coli.) were purchased from Sigma. Deuterium oxide (99.9%) was pur-
chased from Cambridge Isotope Laboratories. Solution pH was determined using an Orion
Model 601A pH meter equipped with a Radiometer GK2321C combination electrode that
was standardized at pH 7.00 and 10.00. Values of pD were obtained by adding 0.40 to the
observed pH meter reading (4).
The concentration of isopropyl β-D-thiogalactopyranoside (Gal-SIP) in stock solu-
tions in H O or D O was determined as the concentration of D-galactose that is formed
2
2
upon quantitative hydrolysis of the sugar derivative. Gal-SIP was hydrolyzed for six
hours at 100°C in a sealed vial that contained concentrated HCl or DCl. The solution
was then neutralized with NaOH or NaOD and a measured aliquot added to a cuvette
+
that contained 0.90 mM NAD in sodium pyrophosphate buffer at pH 8.6. The con-
centration of D-galactose was determined from the change in absorbance at 340 nm
−1
−1
observed upon addition of galactose dehydrogenase (∆ε = 6200 M cm ). There was
good agreement (±5%) between the concentrations of Gal-SIP determined by this
method and those calculated from the weighed mass of Gal-SIP in the stock solutions.
Enzyme assays. Enzyme assays were carried out at 25°C in 33 mM sodium phosphate
at pH 7.0 containing 1 mM MgCl
pD 7.4 containing 1 mM MgCl and 130 mM NaCl. The enzyme-catalyzed hydrolysis of
-nitrophenyl β-D-galactopyranoside at pH 7.0 and at pD 7.4 was monitored by following
the increase in absorbance at 405 nm. The initial velocities for the enzyme-catalyzed reac-
2
and 130 mM NaCl; or in 33 mM sodium phosphate at
2
4
−1
−1
tion were calculated using values of 8900 and 7200 M cm for the difference in extinc-
tion coefficients (∆ε405) of Gal-OPNP and 4-nitrophenol in H O and D O, respectively, that
2
2
was determined for the complete hydrolysis of a known concentration of this substrate in
the respective buffers (5).
Vmax
Km )app
[ ]
S
+ S
[ ]
ν =
[1]
(
Values of (K ) and Vmax for the β-galactosidase-catalyzed hydrolysis of Gal-OPNP
m app
in the presence of increasing fixed concentrations of the competitive inhibitor Gal-SIP
were determined from the nonlinear least squares fit to Eq. [1] of the initial velocities
determined for 10–12 different concentrations of Gal-OPNP using SigmaPlot from
Jandel Scientific. The standard deviation for the kinetic parameters obtained from this
fitting procedure is better than ±5%.
RESULTS
−
1
Values of k = 160 s and K = 30 µM were determined in H O at pH 7.0 and values
cat
1
m
2
−
of k = 89 s and K = 18 µM were determined in D O at pD 7.4 for β-galactosidase-
cat
m
2

5
2
RICHARD AND McCALL
SCHEME 1
catalyzed cleavage of Gal-OPNP. These kinetic parameters and the derived solvent deu-
terium isotope effects of (k ) /(k ) = 1.8 and (k /K ) /(k /K ) = 1.1 are in
cat HOH
cat DOD
cat
m HOH
cat
m DOD
good agreement with earlier literature values (1,2). Isopropyl β-D-thiogalactopyranoside
Gal-SIP) behaves as a classic competitive inhibitor of β-galactosidase (Scheme 1)
(
and causes an increase in the value of the apparent Michaelis constant (K ) for
m app
enzyme-catalyzed hydrolysis of Gal-OPNP, but no change in the value of Vmax for the
reaction catalyzed by a constant concentration of enzyme.
Figure 1 shows the effect of increasing concentrations of Gal-SIP on (K ) /(Km)o
m app
determined for β-galactosidase-catalyzed hydrolysis of Gal-OPNP in the presence of
FIG. 1. The dependence of (K
on the concentration of β-D-thiogalactopyranoside Gal-SIP in H
) and in D O at pD 7.4 (33 mM sodium phosphate, ▼ ) at 25°C.
m
)
app /(K
m
)
o
for the hydrolysis of Gal-OPNP catalyzed by β-galactosidase
2
O at pH 7.0 (33 mM sodium phosphate,
●
2

ISOTOPE EFFECTS ON β-GALACTOSIDASE
53
increasing concentrations of Gal-SIP in H O at pH 7.0 and in D O at pD 7.4 at 25°C,
2
2
where (K ) is the value of the Michaelis constant determined at a given inhibitor con-
m app
centration and (K ) is the Michaelis constant determined at [Gal-SIP] = 0 in H O or
m o
2
D O. The values of the pH and pD for these determinations are close to the pL maximum
2
for k /K determined for the β-galactosidase-catalyzed hydrolysis of Gal-OPNP. The
cat
m
data in Fig. 1 show a good fit to Eq. [2], which was derived for Scheme 1. The slope of
the correlations for reaction in H O and D O, respectively, give the inhibition constants
2
2
(KI)HOH = 56 ± 1 mM and (KI)DOD = 31 ± 2 mM for Gal-SIP. The parameter determined
in H O is in fair agreement with the literature value of K = 85 mM for Gal-SIP (6).
2
I
Combining these data for inhibition in H O and D O gives a value of (K )
/(KI)DOD =
2
2
I HOH
1
.8 for the solvent deuterium isotope effect on K for Gal-SIP. The solvent deuterium
I
isotope effect (Km)HOH /(K )
= 1.7 for Gal-OPNP is in excellent agreement with the
m DOD
value that can be calculated from the difference in the solvent deuterium isotope effects
on k and k /K (Table 1) (2).
cat
cat
m


1 
KI 
(
Km )app
(
Km )o = 1 +
[
Gal - SIP
]
[2]
DISCUSSION
A solvent isotope effect of (KI) HOH /(KI)DOD = 1.8 (Fig. 1 and Results) has been
determined for inhibition of β-galactosidase by Gal-SIP at 25°C, where the inhibi-
tion constant K (M) is equal to the dissociation constant K for Gal-SIP (Scheme
I
d
1
). This solvent deuterium isotope effect corresponds to a 0.35 kcal/mol more
favorable binding of Gal-SIP to β-galactosidase in D O than in H O. By compari-
2
2
son, the binding of methyl α-D-mannopyranoside to the lectin concanavalin A at
5°C is 0.3 kcal/mol more favorable in D O than in H O (7). Solvent deuterium iso-
2
2
2
tope effects of this type have been treated by considering the changes in solute-
solvent interactions which occur on proceeding from the protein and free ligand to
the protein-ligand complex (7,8). There is evidence that these changes are the result
of differences in hydrogen-bond strength in H O and D O (9). However, there is no
2
2
justification for discussing our limited data within the context of changes in
solute–solvent interactions, which occur upon the binding of substrate or inhibitors
to β-galactosidase.
There are two possible explanations for the difference in the values of 1.7 and ≈
1
for the solvent deuterium isotope effects on kcat and k /K , respectively, for the
cat
m
β-galactosidase-catalyzed hydrolysis of Gal-OPNP (Table 1) (2). The isotope effect
of (Km) HOH /(Km)DOD = 1.7 is equal to the isotope effect on the dissociation constant
K for Gal-OPNP when K ≈ K for the enzyme-catalyzed reaction. Such effects on
d
d
m
K are more likely to result from isotopic substitution at the aqueous reaction medi-
d
um than from a single isotopic substitution at the substrate. Alternatively, there may
be no significant solvent deuterium isotope effect on K . In this case, the conversion
d
of the initial Michaelis complex to products must be much faster than the dissocia-
tion of substrate from this complex (k >> k , Scheme 1) so that the observed iso-
3
2
tope effect on K is equal to the isotope effect on the ratio k /k . The result is that
m
3
1
the isotope effects on kcat and K will cancel in k /K provided there is no signifi-
m
cat
m
3
cant solvent isotope effect on the substrate binding step k1.

5
4
RICHARD AND McCALL
The following experimental observations provide strong support for the conclu-
sion that the solvent deuterium isotope of 1.7 on K for β-galactosidase-catalyzed
m
hydrolysis of Gal-OPNP is due mainly to a solvent isotope effect on the dissociation
constant K for this substrate.
d
(
1) There is no significant difference in the α-deuterium isotope effects on k /Km
cat
and kcat for β-galactosidase-catalyzed hydrolysis of Gal-OPNP (Table 1), and no
1
8
more than a small difference in the O-leaving group isotope effect on these kinetic
parameters (3). The observation that there is little difference in the transition states
for k /K and k with respect to rehybridization of the α-carbon and bond cleavage
cat
m
cat
to the 4-nitrophenoxy leaving group is difficult to reconcile with a large difference in
these transition states with respect to proton transfer to the leaving group.
(2) A value of 1.8 was determined for (KI)HOH /(KI)DOD for competitive inhibition of
β-galactosidase by Gal-SIP in H O and D O, where the inhibition constant K is equal
2
2
I
to the dissociation constant K for Gal-SIP. This is similar to (K )
/(K )
=
d
m
HOH
m DOD
(30 µM)/(18 µM) = 1.7 (Results) determined for enzyme-catalyzed cleavage of Gal-
OPNP at the same values of pL, which suggests that this is the solvent isotope effect
on the dissociation constant for Gal-OPNP.
(
3) A second explanation for any difference in the isotope effects on kcat and
k /K is that the former kinetic parameter is limited by the rate constant k for chem-
cat
m
3
ical bond cleavage, but that the latter parameter is limited by k for formation of the
1
3
Michaelis complex by diffusional encounter between enzyme and substrate (2). In
6
−1 −1
this case, the value of 5.6 × 10 M
s
for k /K for β-galactosidase catalyzed
cat
m
cleavage of Gal-OPNP (1) would be essentially equal to k . However, this would be
1
a rather small value for a rate constant for formation of a Michaelis complex (10).
Furthermore, if the value of k /K for β-galactosidase-catalyzed hydrolysis of Gal-
cat
m
OPNP were limited by k for formation of the Michaelis complex, then the value of
1
K = 28 µM = k /k for this substrate (1) would be larger than the dissociation con-
m
3
1
stant K = k /k (k > k for rate-determining k ); and, the value for K would be
d
2
1
3
2
1
m
expected to decrease to that for K as the rate-determining step for k /K changes
d
cat
m
from k to k for cleavage of less reactive aryl β-D-galactopyranosides. By contrast,
1
3
the values of K increase to 35 and 43 µM, respectively, for enzyme-catalyzed
m
6
−1 −1
hydrolysis of 4-cyanophenyl β-D-galactopyranoside (k /K = 1.7 × 10 M s ) and
cat
m
5
−1 −1
4
-bromophenyl β-D-galactopyranoside (k /K = 7 × 10 M s ), which are less
reactive than Gal-OPNP (k /K = 5.6 × 10 M s ) toward cleavage catalyzed by
cat
m
6
−1 −1
cat
m
β-galactosidase (1).
In conclusion, the simplest explanation for the difference in the solvent deuterium
isotope effects on k and k /K for β-galactosidase-catalyzed hydrolysis of Gal-OPNP
cat
cat
m
(Table 1) is that this reflects, mainly, the solvent deuterium isotope effect on the disso-
ciation constant for this substrate, which is similar to that determined here for the dis-
sociation of Gal-SIP.
Mechanistic implications. The results reported here provide evidence against the proposal
that there is a large difference in the degree of cleavage of the bond to a solvent-derived
3
The value of 1300 s−1 for k
for addition of solvent to the galactosyl-enzyme intermediate (E-Gal) of
s
−1
β-galactosidase catalyzed hydrolysis of Gal-OPNP is much larger than the value of 156 s for kcat for this
substrate (1). This requires that conversion of the Michaelis complex to the β-D-galactopyranosylated
3
enzyme (k , Scheme 1) be rate-determining for kcat.

ISOTOPE EFFECTS ON β-GALACTOSIDASE
55
SCHEME 2
hydron at the transition state for kcat and kcat /K
m
(2), and suggest that the rate-determining
transition states for these two processes with respect to proton transfer from solvent are
1
8
similar. The small difference in the O-leaving group effects on these kinetic parameters
Table 1) (3) may reflect the partly rate-determining nature of substrate binding on kcat /K
(
m
or a “subtle methodological artifact” resulting from the different experimental protocols
for determination of the isotope effects on these kinetic parameters (3).
Selwood and Sinnott have proposed that the β-galactosidase-catalyzed hydrolysis of Gal-
OPNP proceeds by stepwise cleavage of the bond to the 4-nitrophenoxy leaving group to
form a galactosylated-enzyme-4-nitrophenolate complex (k
tonation of the 4-nitrophenolate ion (k , Scheme 2) by Glu-461 (11), which is proposed to
be rate-limiting for kcat (2). The rate-limiting transition state for k (see 2) can account for the
following experimental observations: (a) The normal solvent deuterium isotope effect on
cat, since proton transfer to the leaving group is rate determining. (b) The small α-deuterium
isotope effect on kcat for hydrolysis of Gal-OPNP (Table 1), since the hybridization at the
3
, Scheme 2), followed by pro-
5
5
k
1
8
α-carbon of the E-Gal intermediate is similar to that at substrate. (c) The O-leaving group
effect on kcat, which would reflect the significant changes in the bonding to the leaving
4
group on proceeding from Gal-OPNP to the transition state 2. Selwood and Sinnott have
2+
5
proposed that proton transfer in the putative rate-limiting step (k , Scheme 2) is to a Mg -
4
We view a proposed concerted bimolecular displacement mechanism for β-galactosidase-catalyzed
hydrolysis of Gal-OPNP as unlikely (3). There is good evidence that the reactions of nucleophiles with the
β-D-galactopyranosylated form of the E461G mutant enzyme proceeds through a glycosyl cation interme-
diate, which is strongly stabilized by interactions with the enzyme (15). Such interactions increase the
depth of the energy well for a reaction intermediate and will strongly favor stepwise reactions, which pro-
ceed through the intermediate, relative to concerted reactions which avoid formation of the oxocarbenium
ion intermediate (16,17 ).

5
4
6
RICHARD AND McCALL
-nitrophenolate chelate (2). However, this is not required by the experimental results, and
it is possible that the 4-nitrophenolate ion is stabilized by interactions with hydrogen bond
donors at the enzyme active site.
These kinetic isotope effect studies do not provide a unique description of the rate-deter-
mining transition state for β-galactosidase-catalyzed hydrolysis of Gal-OPNP, because it
m
is not clear whether the small α-deuterium isotope effects on kcat and kcat /K rigorously
exclude a mechanism in which cleavage of the C-OPNP bond is concerted with proton
transfer to the leaving group. This concerted reaction mechanism is strongly favored for
catalysis of cleavage of the physiological substrate lactose and other alkyl β-D-galactopy-
ranosides (5,12) because of the large thermodynamic driving force for proton transfer from
the acidic catalyst to the strongly basic alkoxide ion leaving group of the spontaneous reac-
tion (13,14). However, the kinetic isotope effects on the β-galactosidase-catalyzed hydrol-
ysis of these substrates have not been determined.
REFERENCES
1
2
3
4
5
6
7
. Sinnott, M. L., and Souchard, I. J. L. (1973) Biochem. J. 133, 89–98.
. Selwood, T., and Sinnott, M. L. (1990) Biochem. J. 268, 317–323.
. Rosenberg, S., and Kirsch, J. F. (1981) Biochemistry 20, 3189–3196.
. Glasoe, P. K., and Long, F. A. (1960) J. Phys. Chem. 64, 188–190.
. Richard, J. P., Westerfeld, J. G., and Lin, S. (1995) Biochemistry 34, 11703–11712.
. Deschavanne, P. J., Viratelle, O. M., and Yon, J. M. (1978) J. Biol. Chem. 253, 833–837.
. Chervenak, M. C., and Toone, E. J. (1994) J. Am. Chem. Soc. 116, 10533–10539. Isbister, B. D., Hilaire,
P. M. S., and Toone, E. J. (1995) J. Am. Chem. Soc. 117, 12877–12878.
8
9
. Connelly, P. R., Thompson, J. A., Fitzgibbon, M. J., and Bruzzese, F. J. (1993) Biochemistry 32, 5583–5590.
. Calvin, M., Hermans, J., and Scheraga, H. A. (1959) J. Am. Chem. Soc. 89, 5048–5050.
1
1
1
1
1
1
1
1
0. Hammes, G. G., and Schimmel, P. R. (1970) The Enzymes, 3rd ed., p. 67.
1. Richard, J. P., Huber, R. E., Lin, S., Heo, C., and Amyes, T. L. (1996) Biochemistry 35, 12377–12386.
2. Richard, J. P., Westerfeld, J. G., Lin, S., and Beard, J. (1995) Biochemistry 34, 11713–11724.
3. Jencks, W. P. (1972) J. Am. Chem. Soc. 94, 4731–4732.
4. Richard, J. P. (1998) Biochemistry 37, 4305–4309.
5. Richard, J. P., Huber, R. E., Heo, C., Amyes, T. L., and Lin, S. (1996) Biochemistry 35, 12387–12401.
6. Toteva, M. M., and Richard, J. P. (1997) Bioorg. Chem. 25, 239–245.
7. Jencks, W. P. (1981) Chem. Soc. Rev. 10, 345–375.