A R T I C L E S
Lee et al.
for carbon atoms n and 4. KIEs were then calculated as11
Table 1. Sateady-State Kinetic Constants for Enzyme-Catalyzed 4
Hydrolyses
ln(1 - F)
ln[(1 - F) × Ri,Cn/R0,Cn
kcat/K
M
KIECn
)
(1)
cat (s-1)
(M- s-1)
1
enzyme
substrate
k
M
K (mM)
]
R-glucosidase
r-4
0.88 ( 0.05
15 ( 0.2
61 ( 9
(
recombinant, S.
cereVisiae)
â-glucosidase
where KIECn is the KIE for atom Cn, Ri,Cn and R0,Cn are isotope ratios
in 9 at times i and 0, and F is the fractional extent of reaction (F )
â-4
0.90 ( 0.15 2.0 ( 0.6 440 ( 13
[
i 0
4] /[4] ).
a
Calculated Equilibrium Isotope Effects. Equilibrium isotope effects
EIEs) were obtained from quantum mechanically optimized structures
The kinetic constants kcat and kcat/KM were calculated assuming that
the enzymes were 100% active, with the concentration of active enzyme
taken as the protein concentration.
(
of 4 and 7, and the corresponding vibrational frequencies. Optimizations
and frequency calculations were performed with Gaussian 9837 at the
RB3PW91/6-31+G** level of theory, that is, density functional theory
Quantitation based on peak heights was also attempted, but
it was accurate only in the extreme of very large peak widths
with exponential multiplication (LB > 15 Hz). With 9, such
peak widths would have given extensive peak overlap and would
therefore have been unusable (data not shown).
KIEs Measurement Method. Conditions were found for
reacting 30-40 mmol of 4 to 90% completion, and isolating
residual 4 from a 10-fold excess of contaminants (the products).
The glucose product was oxidized to gluconic acid with glucose
oxidase and removed by anion exchange chromatography.
Preliminary experiments indicated that oxidation with Br2 under
basic conditions would also be suitable (data not shown).
Quantitative peracetylation of 4 to 9 was achieved by reacting
in acetic anhydride and pyridine, then removing both, plus
acetic acid, under strong vacuum in a rotary evaporator. This
gave a 99.4% yield of r-9, with no partially acetylated peaks
visible in the C spectra. r-9 and â-9 were dissolved in an
equal mass of d6-acetone, giving 1.5 M, close to the solubility
limit. For the acid reactions, removing the 2 M HClO4 was
greatly simplified by the low solubility of KClO4 in water, 55
mM. Neutralizing with KOH gave KClO4 precipitate which was
removed by filtration.
3
8
(
DFT) with Becke’s exchange functional and Perdew and Wang’s
3
9
correlation functional. Frequency scaling was not used. Initial
optimizations were often performed at the RHF/3-21G** level of theory.
Fractionation factors (φ) at 298 and 353 K were calculated using
4
0
13
QUIVER for each optimized structure. C EIEcalc’s were calculated by
dividing the fractionation factors for 4 by 7, that is, EIEcalc ) φ /φ
All C EIEcalc’s were normalized relative to C4 so they were directly
comparable with the experimental KIEs.
To examine the effects of ring conformation, different conformers
were sought for r-4 and â-4. Starting structures with ring conformations
that were expected to be stable were optimized at a low level of theory
RHF/3-21G**) with the sugar ring dihedral angles fixed, then the
constraints were released, and a full optimization was performed before
changing to DFT.
Stable 7 ring conformations were sought, starting from different ring
conformers of r-4 and â-4, by fixing the C1-O bond at increasing
4
7
.
1
3
(
4
13
4
1
bond lengths, corresponding to Pauling bond orders
.1, and reoptimizing the rest of the structure at each fixed bond length.
After optimization at nC1-O ) 0.1, the leaving group was removed
altogether, and 7 was fully optimized. The E conformer was also found,
nC1-O ) 0.7-
0
4
which did not proceed directly from any 4 conformer.
Results
Acid-Catalyzed 4 Hydrolysis. The rate constants for acid-
-
5 -1
catalyzed hydrolysis measured here (r-4, 6.8 × 10 s ; â-4,
2.7 × 10 s ) were in reasonable agreement with previously
measured rates under the same conditions (7.3 × 10 and 1.4
10 s , respectively). A deep orange color developed in
Diels-Alder KIEs. KIEs were measured for the Diels-Alder
-
4 -1
reaction reported previously11 to determine whether accurate
-
5
KIEs could be obtained with Gaussian multiplication, as
compared with the more commonly used exponential multipli-
cation. KIEexpt’s determined in this work were within 0.001 of
the literature values with exponential multiplication, and within
.002 using Gaussian multiplication (see Supporting Informa-
tion). Gaussian multiplication was therefore used in all 9 spectra
-
4
-1
32
×
the acid-catalyzed reactions when taken to 90% completion,
presumably due to condensation reactions involving glucose.
No extra peaks appeared in the NMR spectra, implying that
the orange material was a mixture of species. Polyalcohols such
as inositol and sorbitol did not produce the orange color. NMR
quantitation of the extent of reaction based on the amount of
glucose in the reaction mixture was essentially the same as using
an internal standard; however, a succinate internal standard was
used for all KIE measurements to avoid any potential error from
glucose side reactions.
Enzyme-Catalyzed 4 Hydrolysis. Barley amylase and As-
pergillus niger amyloglucosidase could not hydrolyze r-4 and
â-4 appreciably. Yeast R-glucosidase and almond â-glucosidase
were able to hydrolyze their respective substrates to 90%
completion, although with low efficiency (Table 1). Because
of the low catalytic efficiency, the large amounts of r-4 required,
and the high cost of recombinant yeast R-glucosidase, three of
four KIE determinations were performed with partially purified
yeast R-glucosidase. KIEs with pure recombinant R-glucosidase
were indistinguishable from those with partially pure enzyme
(see Supporting Information), arguing that the same enzyme
was responsible for activity against r-4 in the partially purified
enzyme.
0
because the narrower width at the base of the peak allowed
baseline resolution of all 1 C peaks.
3
(
37) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M.
A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann,
R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin,
K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi,
R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.;
Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.;
Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz,
J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.;
Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng,
C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.;
Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon,
M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.6; Gaussian,
Inc.: Pittsburgh, PA, 1998.
(
(
(
38) Becke, A. D. Phys. ReV. A 1988, 38, 3098.
39) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244.
40) Saunders, M.; Laidig, K. E.; Wolfsberg, M. J. Am. Chem. Soc. 1989, 111,
8
989.
(
41) Pauling bond order nij between atoms i and j is defined as nij ) exp{(r
1
-
r
ij)/0.3}, where rij is the bond length between atoms i and j and r is the
1
bond length for a single bond between atoms of elements i and j (Johnston,
H. S. Gas-Phase Reaction Rate Theory; Ronald Press: New York, 1966.
Sims, L. B.; Lewis, D. E. In Bond Order Methods for Calculating Isotope
Effects in Organic Reactions; Buncel, E., Lee, C. C., Eds.; Elsevier: New
York, 1984; Vol. 6, p 161).
3772 J. AM. CHEM. SOC.
9
VOL. 126, NO. 12, 2004