Communications to the Editor
J. Am. Chem. Soc., Vol. 121, No. 29, 1999 6967
Table 2. Mechanistic Parameters for E. coli ODCase
irreversible, and subsequent steps are not included in the
expression for V/K. A minimal mechanism is thus
parameter
lower limit
upper limit
a
c
k3/k2
k5/k4
0m
4.3m
0.1m
1.8m
1.047m
0.63m
5.0a
D Ok3
intrinsic D2O KIE
2
13k5
intrinsic 13C KIE
1.07a
a Assumed constraint based upon chemical considerations. m Math-
ematical limit within the experimental results and chemical constraints.
where substrate binding (k1, k2) is followed first by reversible
substrate protonation (k3, k4),13 and finally by irreversible decar-
boxylation (k5). The isotope effects for this mechanism are
described by the following equations:
D Ok3 + a + D OKeq/c
1 + a + 1/c
2
2
D O(V/K) )
(1)
(2)
(3)
2
13k5 + c(1 + a)
13(V/K)H O
)
)
2
1 + c(1 + a)
Figure 3. Proposed stepwise mechanism of ODCase, with protonation
at O4 followed by decarboxylation to the carbene.
13k + c D Ok4 + a/D OKeq
2
2
(
)
5
13(V/K)D O
1 + c D Ok4 + a/D OKeq
2
2
2
rate-limiting, such that the protonated intermediate preceding
decarboxylation tends to deprotonate between 62 and 91% (1.6
e 1/c e 10) of the time, are possible. Either a partially or barely
rate-limiting protonation step is compatible with these results.
These data suggest a modification of the Houk mechanism5
for ODCase as shown in Figure 3.16 In this mechanism, initial
C4 keto protonation by an essential enzymatic lysine residue
generates the C6 cation. Since protonation concomitant with
decarboxylation is excluded experimentally, we suggest that this
thermodynamically unfavorable step may instead be promoted
by a hydrogen bonding network to the C4 keto oxygen of the
orotate moiety. For this substrate, such a network has been
observed and implicated in the mechanism of the enzyme which
immediately precedes ODCase in the pyrimidine biosynthetic
pathway, orotate phosphoribosyl transferase.17 Decarboxylation
of the C6 cation then generates the carbene proposed by Lee and
Houk in the rate-limiting step.
(
)
13(V/K)H O - 1
2
D O(V/K)
2
)
(4)
13(V/K)D O - 1
K
D2O
eq
2
where D Ok3 and D Ok4 are the intrinsic D2O solvent KIEs in the
2
2
forward and reverse directions, 13k5 is the intrinsic 13C KIE, D OKeq
2
2
2
)
D Ok3/D Ok4 is the D2O solvent equilibrium isotope effect, a )
k3/k2, and c ) k5/k4.14 These equations are not independent, and
thus a unique analytical solution does not exist. However, the set
of solutions can be computed15 and represented as three-
dimensional surfaces.
Inspection of contour plots of c and D Ok3 over chemically
2
reasonable ranges for 13k5 and a (Figure 2) identified an upper
limit of 0.63 for c and a lower limit of 1.8 for D Ok3. When the
2
intrinsic solvent KIE D Ok3 is restricted to values e5.0, all solutions
2
with a g 4.3 and c e 0.10 are excluded, and 13k5 must be at least
1.047. This value compares favorably with the 13C KIE of 1.0494
( 0.0006 exhibited by the yeast enzyme at pH 4.0.4 The limits
on these mechanistic parameters are summarized in Table 2.
The multiple isotope effects measured for E. coli ODCase are
thus consistent exclusively with a stepwise mechanism. As Figure
2 illustrates, only mechanisms in which decarboxylation is highly
Acknowledgment. This work was supported by the National Institutes
of Health Grants GM33449 (J.S.B.) and GM50872 (P.F.C.)
Supporting Information Available: Experimental data for the
determination of D O(V/K) and 13(V/K)L O; 3-Dimensional and contour plots
2
2
of c and D Ok3 vs {13k5, a}; a plot of decarboxylation commitment factors
2
vs 13k5 (PDF). This material is available free of charge via the Internet at
(10) (a) ODCase was assayed by monitoring the decrease in A280 (ꢀ ) 1350
M-1 cm-1) as OMP is converted to UMP.10b Reactions contained OMP,
enzyme, 20 mM Hepes pL 7.5, and 0.5 mM DTT at room temperature. (b)
Brody, R. S.; Westheimer, F. H. J. Biol Chem. 1979, 254, 4238-4244.
(11) (a) The method for measuring 13(V/K) by collection and isotope ratio
analysis of product CO2 is described by O’Leary.11b All reactions contained
2 mM OMP, 20 mM Hepes pL 7.5, and 0.5 mM DTT at room temperature in
sealed vacuum flasks, and were sparged overnight with N2 to remove all
contaminating CO2 prior to addition of enzyme. D2O was previously sparged
with CO2 in the presence of carbonic anhydrase to exchange excess 18O. Two
100% conversion (20 mL) and three partial conversion (60 mL) reactions
were performed in H2O and D2O. Fractional conversion of OMP to UMP
was monitored in aliquots spectrophotometrically,10 and reactions were
quenched by the addition of concentrated sulfuric acid to pH < 1. Product
CO2 was purified by three cycles of high-vacuum distillation though dry ice-
ethanol and liquid N2 traps prior to analysis by isotope ratio mass spectrometry.
(b) O’Leary, M. H. Methods Enzymol. 1980, 64, 83-104.
(12) While other schemes (e.g., solvent-sensitive conformational change
preparatory to decarboxylation) are also consistent with these data, we retain
the pre-protonation of substrate model suggested by previous studies.2-7
(13) In this derivation, the terms k3 and k4 represent “net” rate constants
that describe the entire solvent-sensitive portion of the reaction coordinate,
which may formally consist of a single or multiple microscopic steps.
(14) The forward commitment factor (partition ratio for the enzyme form
competent to undergo decarboxylation), (k5/k4)(1 + k3/k2), is divided into an
internal commitment factor (k5/k4) and an external commitment factor (k5k3/
k3k2).
JA990737S
D2O
(15) (a) According to eq 4 and the experimental results,
K ) 1.03 (
eq
0.16. This suggests that the solvent equilibrium isotope effect is, in fact, unity.
This value is not unexpected, since the fractionation factors for N-L and
O-L are unity;15b therefore, D OKeq ) 1 was used in the calculations. An array
2
of values for 13k5 and a, representing the complete range of chemically
reasonable solutions, was generated. A minimum value of 1.043 was selected
for 13k5, corresponding to the observed KIE (the observation of partially rate-
limiting D2O effects requires that 13k5 be higher than this). The upper limit
given for 13k5 was 1.07, approximating the largest known values for enzymatic
decarboxylations.15c,d The forward commitment factor a was given an initial
range of 0 to 5. Equation 2 was used to calculate c for each point in the array,
and D Ok3 was calculated with eq 1 from the resulting {13k5, a, c} array. The
2
final {13k5, a, c, D Ok3} array satisfied eqs 1, 2, and 3, and yielded values for
2
the forward commitments for decarboxylation smaller than unity, as expected.
(b) Quinn, D. M.; Sutton, L. D. In Enzyme Mechanism from Isotope Effects;
Cook, P. F., Ed.; CRC Press: Boca Raton, Florida, 1991; 73-126. (c) Karsten,
W. E.; Gavva, S. R.; Park S. H.; Cook P. F. Biochemistry 1995, 34, 3253-
60. (d) Grissom, C. B.; Cleland, W. W. Biochemistry 1988, 27, 2927-34.
(16) The Beak and Siegel mechanism2 with protonation occurring at the
C2 carbonyl is also consistent with these results. We elect to interpret the
data in the context of the Houk mechanism on the basis of its more favorable
predicted thermodynamics.
(17) Tao, W.; Grubmeyer, C.; Blanchard, J. S. Biochemistry 1996, 35, 14-
21.