The rate of spontaneous cleavage of the glycosidic bond of adenosine

Article abstract of DOI:10.1016/j.bioorg.2010.05.003

Previous estimates of the rate of spontaneous cleavage of the glycosidic bond of adenosine were determined by extrapolating the rates of the acid- and base-catalyzed reactions to neutral pH. Here we show that cleavage also proceeds through a pH-independent mechanism. Rate constants were determined as a function of temperature at pH 7 and a linear Arrhenius plot was constructed. Uncatalyzed cleavage occurs with a rate constant of 3.7 × 10^-12 s^-1 at 25 °C, and the rate enhancement generated by the corresponding glycoside hydrolase is ～5 × 10¹²-fold.

Full text of DOI:10.1016/j.bioorg.2010.05.003

Bioorganic Chemistry 38 (2010) 224–228
Contents lists available at ScienceDirect
Bioorganic Chemistry
journal homepage: www.elsevier.com/locate/bioorg
The rate of spontaneous cleavage of the glycosidic bond of adenosine
*
Randy B. Stockbridge, Gottfried K. Schroeder, Richard Wolfenden
Department of Biochemistry and Biophysics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 16 April 2010
Available online 4 June 2010
Previous estimates of the rate of spontaneous cleavage of the glycosidic bond of adenosine were deter-
mined by extrapolating the rates of the acid- and base-catalyzed reactions to neutral pH. Here we show
that cleavage also proceeds through a pH-independent mechanism. Rate constants were determined as a
function of temperature at pH 7 and a linear Arrhenius plot was constructed. Uncatalyzed cleavage occurs
with a rate constant of 3.7 ꢀ 10ꢁ12 sꢁ1 at 25 °C, and the rate enhancement generated by the correspond-
ing glycoside hydrolase is ꢂ5 ꢀ 1012-fold.
Keywords:
Adenosine
Nucleoside N-ribohydrolase
Ricin
Ó 2010 Elsevier Inc. All rights reserved.
Thermodynamics of activation
Rate enhancement
Glycoside cleavage
1. Introduction
purine hydrolysis indicate that the mechanisms are similar and in-
volve protonation at N7 (pKa ꢂ ꢁ1.6 [10]) followed by nucleophile
Enzymes that catalyze the hydrolysis of the N-glycoside bonds
of ribonucleosides are required for ribonucleoside salvage and
tRNA modification. The mammalian enzymes that catalyze N-gly-
cosidic bond cleavage involve covalent intermediates (tRNA trans-
glycosylases, [1]) or substrate activation by exogenous anions
(purine nucleoside phosphorylases, [2]), but some plants [3], pro-
tists [4], and bacteria [5] possess enzymes that catalyze the direct
hydrolysis of the glycoside bond. Trypanosomes, including the
parasites that cause sleeping sickness in humans and livestock in
sub-Saharan Africa, lack a de novo purine synthesis pathway and
instead scavenge purine ribonucleosides from their mammalian
hosts [6]. These parasites convert the purine ribonucleosides to
purines using nucleoside N-ribohydrolases that differ substantially
from the purine nucleoside phosphorylases of mammalian purine
salvage [2]. Plant-derived ribosome-inactivating proteins, includ-
ing ricin A-chain, also have ribohydrolytic activity. Ricin halts
translation by catalyzing the depurination of a single adenosine
residue in the ribosomal RNA [7].
Enzymes that furnish large rate enhancements are especially
sensitive to inhibition [8]. Thus, information about the rate of the
uncatalyzed hydrolysis of ribonucleosides would be useful in esti-
mating the potential binding affinities of transition state analogs
of these enzymes. For both ricin and purine nucleoside ribohydro-
lases, effective inhibitors have been designed by analogy to acid-
catalyzed glycosidic bond hydrolysis [9]. Kinetic isotope effects on
the adenosine N7 and C10 atoms for acid-catalyzed and enzymatic
attack at C10 [4,11,12].
However, the rate of adenosine hydrolysis at pH 7 – and thus the
rate enhancements provided by ricin and purine nucleoside N-ribo-
hydrolases, which act on their natural substrates at neutral pH –
does not appear to have been established. Adenosine hydrolysis is
catalyzed by both acid and base [13–15], and the rate of hydrolysis
at pH 7 has been estimated by adding the extrapolated rate con-
stants of the H+ and OHꢁ– catalyzed reactions [14]. But those data
were obtained over a relatively narrow pH range, and rate constants
have not been measured at pH 7 (Fig. 1). Thus, it is not known
whether the rate equation includes a term for the uncatalyzed
hydrolysis of adenosine, or, alternatively, whether the observed
rate at pH 7 is a composite of the rate terms for acid- and base-cat-
alyzed glycosidic bond cleavage in roughly equal proportions. To
the extent that the base-catalyzed reaction contributes to the ob-
served rate constant at pH 7, it would not be a good model for the
enzymatic reaction because it proceeds through an indirect mech-
anism that involves formation of an N6-ribosyl adenine intermedi-
ate and opening of the imidazole moiety of the adenine ring [15].
In the present work, we conducted experiments at elevated
temperatures to establish whether uncatalyzed glycosidic bond
cleavage occurs. We show that a pH-independent term exists in
the rate equation for adenosine hydrolysis, and that the rate
enhancement generated by adenine nucleoside hydrolases is
ꢂ5 ꢀ 1012-fold.
2. Materials and methods
* Corresponding author. Address: 120 Mason Farm Rd., Genetic Medicine Suite
3010, Chapel Hill, NC 27599, United States. Fax: +1 919 966 2852.
E-mail address: water@med.unc.edu (R. Wolfenden).
Reagents were obtained from Sigma–Aldrich Co. In a typical
experiment, adenosine (0.015 M) and an anionic buffer (0.1 M) were
0045-2068/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved.
doi:10.1016/j.bioorg.2010.05.003

R.B. Stockbridge et al. / Bioorganic Chemistry 38 (2010) 224–228
225
Fig. 1. Representation of the pH profile used by Garrett and Mehta [14] to estimate
the rate of adenosine cleavage at pH 7. Data were collected at 80 °C over the pH
range indicated by the gray bars. The solid line represents the extrapolation of those
data.
sealed in quartz tubes under vacuum and incubated in convection
ovens (Barnsted/Thermolyne Corp., model 47900) at temperatures
between 110 and 190 °C for varying lengths of time. Buffers used
were sodium arsenate (pH 2.3–3.4, pH 7.0–7.2, and pH 10.5–10.7),
potassium formate (pH 3.4–4.7), potassium acetate (pH 4.6–5.3),
potassium phosphate (pH 6.2–7.0), ethyl phosphonate (pH 7.3–
8.4), and sodium carbonate (pH 9.6–10.4). After reaction, samples
were mixed with D2O containing 0.1 M phosphate buffer (pH 6.8)
and pyrazine (4H, d = 8.6, 1 ꢀ 10ꢁ3 M) as an internal integration
standard. 1H NMR spectra were obtained immediately after admix-
ture with D2O. Separate experiments monitoring the exchange of
adenine protons with D2O showed that after 1 h ꢂ1% of the adenine
protons had exchanged. Data were acquired using a Varian 500 MHz
spectrometer with a cold probe for a minimum of four transients
using a standard water suppression pulse sequence. Spectra were
analyzed offline using Spinworks [16]. The integrated intensities
of the peaks arising from the anomeric (C10) proton of adenosine
and the C2 and C8 protons of adenine were used to determine the
extent of reaction. Reaction mixtures (diluted 1000-fold) were also
analyzed spectrophotometrically in the UV range using a Hewlett–
Packard 8452A diode array spectrophotometer.
Fig. 2. The logarithm of the rate (sꢁ1) of adenine formation from adenosine versus
pH at 130 °C (pH values determined at 25 °C). (A) Points used to determine the acid-
and base-catalyzed rates are shown in yellow (pH values 1.0–4.6) and red (pH
values 9.2–11.0), respectively. The linear regressions fit to those points are shown
as dashed lines. The mean value for rate determined at pH 7 (kuncat) is indicated by
the solid horizontal line at x = ꢁ5.94. The standard error for the measurement of
kuncat is indicated by the shaded area. The sum of the extrapolated acid- and base-
catalyzed rates at pH 7 is indicated by the open point at pH 7. The standard error for
the extrapolation is indicated by the error bars. (B) Data points with a solid line that
represents the theoretical expression for kobs, comprised of calculated rate
Prior to 1H NMR identification, adenine b-ribofuranoside (the
constants for kacid, kbase, and kuncat (see Section 3.1, Eq. (1)) (For interpretation of
the references to color in this figure legend, the reader is referred to the web version
of this article.).
starting material), adenine, adenine
a-ribofuranoside, adenine
a-ribopyranoside, and adenine b-ribopyranoside were isolated by
HPLC on a reverse phase C18 column (Whatman Partisil ODS3).
Elution was performed isocratically with 0.05 M potassium phos-
phate (pH 5.4) and 5% methanol at a flow rate of 1 mL/min. Ade-
the best fit lines in the acid range (pH 1.2–4.7) and the basic ranges
(pH 9.6–10.7) are ꢁ0.93 and +0.96 respectively, very close to the val-
ues ꢁ1.0 and +1.0 expected for acid- and base-catalyzed reactions.
When these lines are extrapolated to pH 7, the logarithm of the
rate of the acid-catalyzed reaction is ꢁ7.66 with a standard error
of 0.482 logarithmic units. The logarithm of the base-catalyzed
reaction at pH 7 is ꢁ7.57 with a standard error of 0.381 logarithmic
units. The sum of the extrapolated rate constants of the acid- and
base-catalyzed reactions is 4.9 ꢀ 10ꢁ8 sꢁ1 (log k = ꢁ7.31 with a
combined standard error of 0.43 logarithmic units). That value is
smaller than the rate of glycosidic bond cleavage that was deter-
mined at pH 7 from six independent measurements, 1.1 ꢀ 10ꢁ6 sꢁ1
(log k = ꢁ5.94 with a standard deviation of 0.08 logarithm units).
Using the hypothesis test for the difference between two means,
the difference between the measured rate of glycosidic bond cleav-
age and the rate expected for the sums of acid- and base-catalyzed
glycoside bond cleavage at pH 7 is significant with p < 0.005. These
findings indicate the presence of an uncatalyzed reaction at neutral
pH that proceeds with a rate constant of 1.1 ( 0.3) ꢀ 10ꢁ6 sꢁ1
at 130 °C.
nine, adenine
eluted after 15 min, and adenine b-ribofuranoside and adenine
-ribopyranoside eluted after 25 min.
a-ribofuranoside, and adenine b-ribopyranoside
a
3. Results
3.1. pH profile
Adenosine decomposition was monitored at 130 °C in anionic
buffers (0.1 M) ranging between pH 1.2 and pH 10.7 (pH measured
at 25 °C). Separate experiments showed that the effect of ionic
strength on the rate of glycosidic bond cleavage is modest. The rate
increased by ꢂ2-fold as the concentration of potassium chloride in-
creased from 0–1.0 M. The rate of glycosidic bond cleavage was
determined based on the appearance of adenine using 1H NMR. Sep-
arate experiments showed adenine to be stable at 130 °C for the
lengths of time at the pH values over which data were gathered. In
a plot of the logarithm of the rate versus pH (Fig. 2A), the slopes of

226
R.B. Stockbridge et al. / Bioorganic Chemistry 38 (2010) 224–228
Fig. 4. Arrhenius plot for cleavage of the adenosine glycosidic bond. Data were
obtained between 110 and 190 °C.
isosbestic points (Fig. 3) indicating that glycosidic bond cleavage
proceeds without the accumulation of an intermediate in which
the adenine ring has opened. In contrast, isosbestic points were
not observed for the decomposition of adenosine in alkaline solu-
tion, and the mechanism for base-catalyzed hydrolysis was pro-
posed partly on that basis [14,15]. This qualitative observation
provides additional evidence that the reaction at neutral pH does
not include a significant contribution from the base-catalyzed
reaction, and therefore that the neutral reaction is distinct from
the sum of the acid- and base-catalyzed reactions.
Fig. 3. Time course for adenosine decomposition at 150 °C and pH 7.0. (A) Adenine
(kmax = 261) and adenosine (kmax = 260) monitored with UV spectroscopy. The UV
spectra have isosbestic points at 220, 245, and 280 nm. (B) The relative concen-
trations of adenine b-ribofuranoside (starting material, black), adenine (red),
adenine
a-ribofuranoside (green), adenine a-ribopyranoside (blue), adenine b-
ribopyranoside (pink), and assorted breakdown products (dashed line) (For
interpretation of the references to color in this figure legend, the reader is referred
to the web version of this article.).
At early timepoints in the reaction, five major products were
observed by 1H NMR: adenine, ribose, adenine
a-ribofuranoside
(H10 d = 6.3, d), adenine b-ribopyranoside (H10 d = 5.65, d), and a
The observed rate constant for glycosidic bond hydrolysis at
130 °C is given by:
fifth compound with a peak in the anomeric region believed to
be adenine
a-ribopyranoside. The identity of a-adenine ribofur-
kobs ¼ kacid ꢃ ½Hþꢄ þ kbase ꢃ ½OHꢁꢄ þ kuncat
ð1Þ
anoside was confirmed by addition of the authentic compound,
and the b-adenine ribopyranoside was identified by comparison
of the 1H NMR and 13C NMR spectra with published chemical shifts
[15]. The fourth product was isolated by HPLC and appears to be
where kacid (0.076 sꢁ1 Mꢁ1) and kbase (4.7 ꢀ 10ꢁ4 sꢁ1 Mꢁ1) were
determined from the values of the linear fits to data points in the
acidic and basic ranges shown in Fig. 2A at pH 0 and 11.4 (pKw at
130 °C), respectively. As noted above, kuncat is equal to 1.1 ꢀ
a
-adenine ribopyranoside on the basis of its 1H NMR chemical
shifts (Table 1). Thus, the resonance of its putative anomeric proton
(d = 5.80, s) is shifted upfield from those of the two adenine ribo-
furanosides (d = 6.34; d = 5.95), as expected for a ribopyranoside,
but downfield from the b-ribopyranoside (d = 5.68), as expected
10ꢁ6 sꢁ1. [H+] is equal to 10ꢁpH and [OHꢁ] is equal to 10pHꢁ11.4
.
Fig. 2B shows the data points from Fig. 2A along with a solid line
based on Eq. (1) for kobs
.
for an
a-ribopyranoside [17]. The chemical shifts of the anomeric
3.2. Adenosine decomposition at pH 7
protons of ribose pyranosides tend to exhibit very small coupling
constants, and are sometimes collapsed into a singlet [18]. If the ri-
bose ring were to open, then the b-furanoside starting material or
any of three additional anomers might be formed by its reclosure.
The time course of adenosine decomposition at pH 7 was mon-
itored over 24 h at 150 °C using UV spectroscopy (Fig. 3A) and 1H
NMR (Fig. 3B). UV spectra show that for the first ꢂ50% of the reac-
tion, the amount of adenosine decreases and the amount of ade-
nine increases concomitantly. The overlaid spectra show clean
We observe that the
able -ribopyranoside were all formed at similar rates and with
qualitatively similar activation parameters (Table 1). Similarly,
a-ribofuranoside, b-ribopyranoside, and prob-
a
Table 1
Activation parameters and 1H NMR chemical shifts for the formation of adenosine anomers
a-ribofuranoside, b-ribopyranoside, and a-ribopyranoside.
1H NMR
13C NMR
C10
Activation parameters
Gà
H10
H2
H8
D
D
Hà
TD
Sà
a
a
-Ribofuranosidea
-Ribopyranoside
6.34 d
5.80 s
5.68 d
8.13 s
8.21 s
8.12 s
8.32 s
8.50 s
8.23 s
83.30
–
79.05
32.8 0.4
32.9 0.2
31.9 0.2
23.9
25.6
23.4
ꢁ8.8
ꢁ7.4
ꢁ8.6
b-Ribopyranosideb
a
NMR data consistent with chemical shifts reported in [22] and data obtained with an authentic sample.
NMR data consistent with chemical shifts (obtained in DMSO-d6) reported in [15].
b

R.B. Stockbridge et al. / Bioorganic Chemistry 38 (2010) 224–228
227
Fig. 5. A possible scheme for adenosine anomerization at pH 7. The ribose ring opens, forming a carbocation on C10. In this intermediate structure, the adenine moiety, H10,
and ribose are coplanar around C10, allowing isomerization to form
- and b-pyranosides or furanosides. This scheme is not intended to depict a mechanism or transition state
structures; further kinetic analysis will be required to resolve those details.
a
thermal decomposition of the
three adenosine anomers (the b-ribofuranoside, the b-ribopyrano-
side, and the -ribopyranoside), at comparable rates.
It is probable that each of the four adenosine anomers
undergoes hydrolysis to yield adenine. The concentrations of the
a
-furanoside yielded adenine, and
Arrhenius plot (Fig. 4) was extrapolated to yield a rate constant
of 3.7 ( 1.3) ꢀ 10ꢁ12 sꢁ1 at 25 °C, equivalent to a half-time of
ꢂ6000 years. The thermodynamics of activation were also deter-
a
mined from the Arrhenius plot: D TD
Hà = 28.0 kcal/mol, Sà =
ꢁ4.9 kcal/mol, and
D
Gà = 32.9 0.3 kcal/mol.1
a-ribofuranoside, the b-ribopyranoside, and the probable a-ribo-
pyranoside rise and fall together over the reaction time course as
intermediates. Because glycosidic bond cleavage of each anomer
should contribute to the overall rate of adenine formation, rates
were determined by measuring the rate of appearance of adenine
and the adenosine anomers in the first 10% of the reaction, when
the adenosine b-furanoside starting material was still ꢂ30 times
more prevalent than any other anomer.
4. Discussion and conclusions
4.1. Presence of an uncatalyzed reaction
Three lines of evidence indicate the existence of uncatalyzed
glycosidic bond hydrolysis at pH 7. First, at 130 °C, the observed
reaction rate at pH 7 is greater than the sum of the acid- and
base-catalyzed reactions by a factor of 23. That difference is statis-
tically significant with p < 0.005. Second, an isosbestic point is ob-
served by UV spectroscopy at pH 7, but not at alkaline pH. Thus,
Other peaks are visible in the 1H NMR spectrum, but they do not
appear until after the five initial products described earlier have
begun to accumulate (Fig. 3B). Because they are not derived from
the adenosine starting material, and adenine is thermally stable
at pH 7, these other products presumably result from the break-
down of the adenenine derivative with an open ribose ring. Impor-
tantly, N6-ribosyl adenines and triaminopyrimide present in the
1H NMR spectra of the base-catalyzed reaction are absent in the
reaction at pH 7.
1
From
D D
Gà and Hà values reported for the acid- and base-catalyzed reactions
[13,14], kuncat was expected to be the dominant term in the rate equation at pH 7 over
the range of temperatures that data were collected. At 110 °C,
D
Gà ꢂ29.4 kcal/mol for
the acid-catalyzed reaction, ꢂ28.7 kcal/mol for the base-catalyzed reaction, and
ꢂ26.6 kcal/mol for the neutral reaction. At 190 °C,
D
Gà ꢂ26.0 kcal/mol for the acid-
catalyzed reaction, ꢂ26.6 kcal/mol for the base-catalyzed reaction, and ꢂ22.7 kcal/
mol for the neutral reaction. At 25 °C, the base-catalyzed reaction might be expected
3.3. Arrhenius plots
to contribute to the observed rate constant, with
D
Gà ꢂ35.0 for the acid-catalyzed
reaction,
D
Gà ꢂ32.1 for the base-catalyzed reaction, and
D
Gà ꢂ32.9 for the neutral
The rates of glycosidic bond cleavage at pH 7 were determined
at 12 different temperatures between 110 and 190 °C. A linear
reaction. However, extrapolation of the Arrhenius plot for kuncat is expected to yield
an accurate estimate of kuncat at 25 °C.

228
R.B. Stockbridge et al. / Bioorganic Chemistry 38 (2010) 224–228
Table 2
Activation parameters and rate constants for adenosine glycosidic bond cleavage compared to the enzyme-catalyzed reaction.
D
Gà
D
Hà
TD
Sà
t1/2 (yrs)
knon
kcat
kcat/knon
Adenosine
20-Deoxy-adenosine [20]
32.9 0.3
30.9
28.0
27.1
ꢁ4.9
ꢁ3.8
6000
180
3.7 ( 1.3) ꢀ 10ꢁ12 sꢁ1
18 sꢁ1a
0.2 sꢁ1b
4.9 ꢀ 1012
1.2 ꢀ 10ꢁ10 sꢁ1
2.8 ꢀ 108c
a
b
c
kcat value for Trypanosome brucei nucleoside ribohydrolase [6].
kcat value for adenine mismatch specific glycosylase MutY from E. coli [23]. Data obtained at 37 °C.
Rate enhancement calculated from rate constants at 37 °C.
the observed UV spectra are not consistent with a composite reac-
tion to which the base-catalyzed reaction contributes significantly.
Third, the base-catalyzed reaction yields a number of products that
can be observed in the 1H NMR spectrum including N6-ribosyl
derivatives of adenine and triaminopyrimidine. These products
were not observed for the reaction at pH 7, which also tends to
suggest that the rate constants measured at pH 7 are for a third,
uncatalyzed, reaction rather than for the combined acid- and
base-catalyzed reactions.
to be estimated. The reported rate constants are 30 sꢁ1 for ricin
A-chain [19] and 18 sꢁ1 for Trypanosome brucei nucleoside ribohy-
drolase [6]. Thus, the rate enhancement produced by both enzymes
is ꢂ5 ꢀ 1012, and these enzymes are among the more proficient
hydrolases that have been described [8].
It is also of interest to compare the rate enhancements gener-
ated by enzymes that catalyze adenosine and deoxyadenosine
hydrolysis at neutral pH. Uncatalyzed adenosine hydrolysis pro-
ceeds at a rate that is ꢂ30-fold slower than that previously re-
ported for deoxyadenosine hydrolysis [20]. (That effect of the
20 OH group on uncatalyzed glycosidic bond hydrolysis is some-
what less than the 650-fold effect that it exerts on acid-
catalyzed glycosidic bond cleavage [21].) Since many DNA glyco-
sylases exhibit rate constants below 1 sꢁ1 [20], these enzymes
are less proficient than enzymes involved in adenosine glycosidic
bond cleavage (Table 2). A quick turnover is probably less impor-
tant for enzymes involved in editing functions such as DNA exci-
sion and repair.
4.2. Mechanism of adenosine decomposition at pH 7
At pH 7, the adenine b-ribofuranoside starting material can
decompose by two principal pathways. In the first, adenosine
undergoes simple glycosidic bond hydrolysis to yield adenine and
ribose. The present results indicate that glycosidic bond cleavage
proceeds through an acid- and base-independent mechanism that
does not involve opening the adenine ring. Alternatively, the ribose
ring could open and re-close, yielding any of the other adenosine
anomers: the
Opening of the ribose ring was not observed in acid or base. To
our knowledge, this is the first time that the -furanoside and a-
a-furanoside, and the a- and b-pyranosides (Fig. 5).
Acknowledgments
a
We thank Laura Hall for performing preliminary HPLC separa-
tions of the adenosine anomers. This work was supported by NIH
grant GM-18325.
pyranoside have been obtained by the thermal degradation of ade-
nine b-ribofuranoside. Since it is likely that the open ribose ring
also re-closes to form the b-furanoside starting material, it is not
possible to determine the rate of ribose ring-opening from these
experiments. However, the sum of the rate constants of formation
of the other three anomers is similar in magnitude to the rate con-
stants of adenine formation, so it appears that ribose ring-opening
and glycosidic bond hydrolysis occur at similar rates.
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Further kinetic analysis will be required to resolve the detailed
mechanism of adenosine decomposition at pH 7. It seems probable
that both glycosidic bond hydrolysis and anomerization involve
the development of positive charge at the anomeric carbon. Such
charge development is consistent with the small increase in rate
produced by an increase in ionic strength. A carbocation at C10
and coplanar intermediate would be required to allow rotation of
H10 and the adenine moiety to form the
a-adenosine anomers
(Fig. 5). For glycosidic bond cleavage, a buildup of positive charge
on C10 has been predicted for the enzymatic glycosidic bond cleav-
ages catalyzed by trypanosomal nucleoside hydrolase [4] and ricin
A-chain (for which a carbocation intermediate bearing a full charge
was proposed, [12]) on the basis of kinetic isotope effects on C10. It
seems likely that the neutral reaction would behave similarly,
although the details of proton transfer from water to adenine are
not clear at this time.
4.3. Rate enhancements generated by nucleoside hydrolases
[22] P. Ciuffreda, S. Casati, A. Manzocchi, Magn. Reson. Chem. 45 (2007) 781–
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Comparison of rate constants observed for enzyme-catalyzed
and uncatalyzed reactions allows the rate enhancement, kcat/knon
,