834 J. Am. Chem. Soc., Vol. 120, No. 4, 1998
Communications to the Editor
than expected on the basis of a Brønsted plot based on the
behavior of several activated phosphodiesters examined earlier
by Kirby and Varvoglis.8 Extrapolation to room temperature
(Figure 2) yields a first-order rate constant of 4.6((2.0) × 10-14
s-1 at 25 °C. Comparison of this value with the kinetic constants
reported for Escherichia coli alkaline phosphatase acting on
methyl phosphate9 indicates that this enzyme enhances the rate
of reaction by a factor of at least 1015-fold and that, in the
transition state, the formal dissociation constant of the enzyme-
substrate complex is less than 3 × 10-20 M. When the rate of an
enzyme reaction is governed by a physical process such as
substrate binding or product release, which has no counterpart in
the uncatalyzed reaction, comparison of enzymatic and nonen-
zymatic reaction rates gives only a minimal impression of the
enzyme’s ability to stabilize the transition state for substrate
transformation according to the mechanism by which the reaction
proceeds at the active site.2 The rate of the alkaline phosphatase
reaction has been shown to be limited by a physical step, rather
than by the making and breaking of chemical bonds in
substrates.10-12 Accordingly, this dissociation constant may
represent an upper limit.
(CH3O)2PO2- is hydrolyzed >99.5% by cleavage between carbon
and oxygen, as indicated by GC-MS analysis of the methanol
produced; this reaction was found to be catalyzed by nucleophilic
anions. Extrapolation to room temperature yields a first-order
rate constant of 1.6((0.8) × 10-13 s-1 at 25 °C for the uncatalyzed
carbon-oxygen cleavage of (CH3O)2PO2- by water.16 This rate
constant, as low as it is, is inappropriate for comparison with
reactions catalyzed by phosphomonoesterases, which proceed with
P-O cleavage. Instead, this value, combined with the finding
that less that 0.5% of the nonenzymatic reaction occurs by
phosphorus-oxygen cleavage, places an upper limit of 10-15 s-1
on the first-order rate constant for the phosphorus-oxygen
-
cleavage of (CH3O)2PO2 at 25 °C, substantially lower than
suggested in a preliminary report in which the site of bond
cleavage had not been established.1 Comparison with kinetic
constants reported for staphylococcal nuclease17 indicate that this
enzyme enhances the rate of phosphorus-oxygen cleavage by a
factor of at least 1017-fold and that the formal dissociation constant
of this enzyme’s complex with the activated substrate is less than
10-22 M in the transition state.
The present rate comparisons suggest that the transition state
affinities of phosphoric ester hydrolases approach the extremely
low value (5 × 10-24 M) recorded earlier for orotidine 5′-
phosphate decarboxylase1 and identify these hydrolases as
proficient catalysts that should furnish sensitive targets for
inhibitor design. It is also evident that phosphodiesters, with a
half-life of 130 000 years at 25 °C, are well-suited to the storage
of genetic information. Even at this rate, a human DNA molecule,
with ∼3 × 109 base pairs, would be expected to experience one
bond cleavage in 24 min in the absence of repair, if the
phosphodiester bonds of DNA are assumed to be equivalent to
dimethyl phosphate in their rates of hydrolysis.
Similar experiments, conducted on dimethyl phosphate at 140-
230 °C, show that this compound undergoes hydrolysis with rate
constants that do not vary significantly between pH 5 and 13,
after extrapolation to zero buffer concentration at any single
-
temperature, consistent with decomposition of (CH3O)2PO2
(Figure 1b).14 An Arrhenius plot indicates (Figure 2) that the
-
heat of activation for hydrolysis of (CH3O)2PO2 is 25.9 kcal/
mol, and the entropy of activation is -34 cal deg-1 mol-1
.
(8) Kirby, A. J.; Varvoglis, A. G. J. Am. Chem. Soc. 1967, 89, 415-423.
(9) Williams, A.; Naylor, R. A. J. Chem. Soc. B 1971, 1973-1979. The
reaction catalyzed by alkaline phosphatase is not ideal for this comparison,
as it proceeds through a covalent intermediate. Qualitatively, this comparison
seems justified to the extent that an active site serine side chain may resemble
a bound water molecule in its inherent chemical reactivity.
(10) Labow, B. I.; Herschlag, D.; Jencks, W. P. Biochemistry 1993, 32,
8737-8741.
Acknowledgment. A. J. Kirby provided helpful advice at several
stages during this work, and we are also grateful to N. H. Williams and
D. Herschlag for useful discussions. We thank Asoka Ranasinghe for
performing methanol analyses by GC-MS. This research was supported
by NIH Grant GM-18325.
(11) Hengge, A. C.; Edens, W. A.; Elsing, H. J. Am. Chem. Soc. 1994,
116, 5045-5049.
(12) Simopoulos, T. T.; Jencks, W. P. Biochemistry 1994, 33, 3, 10375-
JA9733604
10380.
(13) Bunton, C. A.; Mhala, M. M.; Oldham, K. G.; Vernon, C. A. J. Chem.
Soc. 1960, 3293-3301.
(15) Haake, P. C.; Westheimer, F. H. J. Am. Chem. Soc. 1961, 83, 1102-
1109.
(14) Dimethyl phosphate cleavage is subject to catalysis by KOH (refs 7
and 15), and preliminary experiments indicate that, in strong alkali, the heat
of activation is substantially less positive than the heat of activation for water
attack on the dimethyl phosphate anion. Under those conditions (>0.3 M
KOH), methyl phosphate accumulates in measurable quantities during the
hydrolysis of dimethyl phosphate.
(16) Because of major differences in energy of activation, dimethyl
phosphate anion is more rapidly hydrolyzed than methyl phosphate dianion
at temperatures below 50 °C. These rates of reaction are too low to be of
practical value in the preparation of monoesters, but see footnote 14 above.
(17) Serpersu, E. H.; Shortle, D.; Mildvan, A. S. Biochemistry 1986, 25,
5, 68-77.