Environmental effects on phosphoryl group bonding probed by vibrational spectroscopy: Implications for understanding phosphoryl transfer and enzymatic catalysis

Article abstract of DOI:10.1021/ja026481z

We have used vibrational spectroscopy to study bonding in monosubstituted dianionic phosphates, both to learn more about basic properties intrinsic to this important class of biological substrates and to assess the ability of vibrational spectroscopy to provide a "sensor" or probe of the local environment experienced by the phosphoryl group. We examined the bonding properties of the phosphoryl group via vibrational spectroscopy for a series of compounds in which the phosphoryl substituent was varied systematically and extensively. A broad linear correlation of the bridging P-O(R) bond length and the pK_a of the substituent alcohol was observed. The results indicate that the P-O(R) bond changes by only ～0.04 A with alcohol substituents that vary in pK_a by ～12 units, suggesting that phosphoryl group bonding responds in a subtle but regular manner to changes in the local environment. We also determined the effect on the phosphoryl bonding from changes in the solvent environment. Addition of dimethyl sulfoxide (DMSO) elongates the bridging bond, presumably as a result of lessened solvation to the nonbridging oxygens and conservation of bond order to phosphorus. Finally, we have addressed the relationship between groundstate bonding properties and reactivity, as changing the leaving group substituent and adding DMSO have large rate effects, and it was previously proposed that lengthening of the bond to be broken is the cause of the increased reactivity. The results herein suggest, however, that the change in the bridging bond energy is small compared to the changes in energy that accompany the observed reactivity differences. Further analysis indicates that electrostatic interactions can provide a common driving force underlying both bond lengthening and the observed rate increases. We suggest that ground-state distortions of substrates bound to enzymes can provide a readout of the electrostatic active site environment, an environment that is otherwise difficult to assess.

Full text of DOI:10.1021/ja026481z

Published on Web 08/31/2002
Environmental Effects on Phosphoryl Group Bonding Probed
by Vibrational Spectroscopy: Implications for Understanding
Phosphoryl Transfer and Enzymatic Catalysis
Hu Cheng,¶,| Ivana Nikolic-Hughes,# Jianghua H. Wang,¶, Hua Deng,¶
Patrick J. O’Brien,†,x Li Wu,‡ Zhong-Yin Zhang,‡ Daniel Herschlag,*,#,†,§ and
Robert Callender*,¶
Contribution from the Department of Biochemistry, Albert Einstein College of Medicine,
Bronx, New York 10461-1602, Department of Chemical Engineering, Stanford UniVersity,
Stanford, California 94305-5025, Department of Biochemistry, Stanford UniVersity,
Stanford, California 94305-5307, Department of Molecular Pharmacology, Albert Einstein
College of Medicine, Bronx, New York 10461-1602, and Department of Chemistry,
Stanford UniVersity, Stanford, California 94305-5080
Received April 10, 2002
Abstract: We have used vibrational spectroscopy to study bonding in monosubstituted dianionic phosphates,
both to learn more about basic properties intrinsic to this important class of biological substrates and to
assess the ability of vibrational spectroscopy to provide a “sensor” or probe of the local environment
experienced by the phosphoryl group. We examined the bonding properties of the phosphoryl group via
vibrational spectroscopy for a series of compounds in which the phosphoryl substituent was varied
systematically and extensively. A broad linear correlation of the bridging P-O(R) bond length and the pKa
of the substituent alcohol was observed. The results indicate that the P-O(R) bond changes by only ∼0.04
Å with alcohol substituents that vary in pKa by ∼12 units, suggesting that phosphoryl group bonding responds
in a subtle but regular manner to changes in the local environment. We also determined the effect on the
phosphoryl bonding from changes in the solvent environment. Addition of dimethyl sulfoxide (DMSO)
elongates the bridging bond, presumably as a result of lessened solvation to the nonbridging oxygens and
conservation of bond order to phosphorus. Finally, we have addressed the relationship between ground-
state bonding properties and reactivity, as changing the leaving group substituent and adding DMSO have
large rate effects, and it was previously proposed that lengthening of the bond to be broken is the cause
of the increased reactivity. The results herein suggest, however, that the change in the bridging bond energy
is small compared to the changes in energy that accompany the observed reactivity differences. Further
analysis indicates that electrostatic interactions can provide a common driving force underlying both bond
lengthening and the observed rate increases. We suggest that ground-state distortions of substrates bound
to enzymes can provide a readout of the electrostatic active site environment, an environment that is
otherwise difficult to assess.
bond reorganization process.1 For instance, these residues may
act to form a covalent adduct, to abstract or donate a proton, or
Introduction
Enzymatic catalysis is central to biological function, and much
effort over the past decades has focused on elucidating the basic
mechanisms of enzymatic catalysis. In recent years, approaches
of molecular biology have readily allowed assessment of the
catalytic effects of individual side chain mutations. Residues
that give large effects upon mutation are typically found within
active sites and most often appear to play direct roles in the
to hydrogen bond with a group that develops charge in the
transition state. High-resolution X-ray structures of enzymes,
especially in complex with substrates and transition-state
analogues, have helped identify these residues and the interac-
tions they make with the substrate. Thus, this structural
information has served as a powerful aid in the development
of coherent mechanistic descriptions of the reactions taking place
within enzyme active sites.2 However, enzymes are more than
a collection of “catalytic residues”. A full understanding of their
* To whom correspondence should be addressed. E-mail: call@
bioc.aecom.yu.edu and herschla@cmgm.stanford.edu.
¶ Department of Biochemistry, Albert Einstein.
# Department of Chemical Engineering, Stanford University.
† Department of Biochemistry, Stanford University.
(1) (a) Plapp, B. V. Methods Enzymol. 1995, 249, 91. (b) Gerlt, J. A. Chem.
ReV. 1987, 87, 1079.
‡ Department of Molecular Pharmacology, Albert Einstein.
§ Department of Chemistry, Stanford University.
(2) See, for example: (a) Muller, Y. A.; Schulz, G. E. Science 1993, 259,
965. (b) Anderson, A. C.; Perry, K. M.; Freymann, D. M.; Stroud, R. M.
J. Mol. Biol. 2000, 297, 645. (c) Zechel, D. L.; Withers, S. G. Acc. Chem.
Res. 2000, 33, 11. (d) Schlichting, I.; Berendzen, J.; Chu, K.; Stock, A.
M.; Maves, S. A.; Benson, D. E.; Sweet, B. M.; Ringe, D.; Petsko, G. A.;
Sligar, S. G. Science 2000, 287, 1615.
| Present Address: Department of Diagnostic Radiology, Yale University.
Present Address: Marubeni America Corporation, New York.
x Present Address: Department of Biological Chemistry and Molecular
Pharmacology, Harvard Medical School.
9
10.1021/ja026481z CCC: $22.00 © 2002 American Chemical Society
J. AM. CHEM. SOC. 2002, 124, 11295-11306
11295

A R T I C L E S
Cheng et al.
catalytic power must extend beyond the energetic view provided
by rate effects from site-directed mutagenesis and the pictorial
account of the bound reactants obtained by X-ray crystal-
lography.
behavior of monosubstituted phosphates and the electrostatic
environment of the phosphoryl group, including that within
enzyme active sites.
Materials and Methods
Polanyi, Pauling, Jencks, and others recognized that enzymes
provide an environment that is preorganized for recognition of
transition states and distinct from that in aqueous solution.3
However, the specific properties of active site environments have
been more difficult to describe and understand. For example,
there has been much discussion of the dielectric constant within
enzyme active sites, as electrostatic interactions are generally
more effective in a low dielectric environment.4 However, the
dielectric constant describes a bulk property of a substance,
whereas our interest is in describing the effects of the enzyme
environment on substrates that are bound within the active site.
Specific local and molecular interactions between the enzyme
and the substrate determine the energetic effect of a change in
charge distribution and therefore must be considered.5
The most common probe of local effects within enzymes and
their active sites has been measurements of pKa values.4c,6 These
values can be measured in favorable cases and compared to
those observed in water, the gas phase, and various organic
solvents. Nevertheless, the observed pKa is not simply a function
of the electrostatic environment prior to protonation (or depro-
tonation). Upon protonation, for example, a hydrogen bond
acceptor is converted to a hydrogen bond donor, and additional
space is required to accommodate the transferred proton; the
enzyme (or complex) therefore rearranges. Thus, the change in
pKa is a function of both the electrostatic environment preceding
protonation and the ability of the site to rearrange to accom-
modate the newly protonated functional group.
Computation offers a nonperturbing approach to assess the
electrostatic environment within an active site.5 While powerful
in principle, limitations remain in the accuracy of computation
and, as importantly, in the ability to test computation and
connect it to relevant experimental observables.
In this work, we use nonenzymatic systems to show that
vibrational spectroscopy can provide a sensitive probe of the
environment of the phosphoryl group, a group commonly
transferred in enzymatic catalysis. The bond order and length
of the bridging P-O bond, the bond that is broken during the
transfer reaction, appears to be accurately determined by
vibrational spectroscopy. We have used Raman and infrared
(IR) spectroscopy to determine the vibrational properties of the
phosphoryl group for a series of monosubstituted phosphate
dianions. We have also determined these properties for two
phosphate esters as a function of solvent composition. The
results provide a foundation for understanding both the bonding
Chemicals. Disodium salts of para-nitrophenyl phosphate (pNPP)7
and phenyl phosphate (PP) were purchased from Aldrich and used
without further purification. The disodium salt of methyl phosphate
was obtained via hydrolysis of the methyl phosphorodichloridate with
sodium hydroxide in access. Dicyclohexylammonium salts of isopropyl
phosphate, butyl phosphate, allyl phosphate, 2-methoxyethyl phosphate,
2-cyanoethyl phosphate, propargyl phosphate, 2,2,2-trifluoroethyl phos-
phate, 2,2,2-trichloroethyl phosphate, and 2,2,3,3,3-pentafluoropropyl
phosphate were synthesized as previously described.8 Disodium salts
of the above series of alkyl phosphates were obtained via anion
exchange chromatography. Cyclohexylammonium salts of 4-cyanophe-
nyl, 3-nitrophenyl, 4-bromophenyl, 4-fluorophenyl, and 4-methylphenyl
phosphates were synthesized and characterized as previously described.9
2-Aminoethyl, acetyl, 1-naphthyl, 2-naphthyl, glucose-1-, uridine-5-,
guanosine-5-, glycerol-2-, glucose-6-, and inorganic phosphate, phos-
phorylcholine, and phosphoenolpyruvate were purchased from Sigma.
Dimethyl sulfoxide (DMSO) and tetramethylammonium hydroxide
(TMAH) were also purchased from Sigma. Sodium hydroxide (NaOH)
and sodium chloride were purchased from Fisher.
Raman Spectroscopy. The Raman spectrometer used in these studies
has been described in detail.10 Light at 568.2 nm at about 100 mW
from a Coherent INNOVA 400-K3-krypton ion laser was used to excite
Raman scattering from the sample. Scattered light was analyzed by a
Triplemate spectrometer (Spex Industries, Metuchen, NJ) and detected
by an optical multichannel analyzer (Model LN/CCD-1152UV detector
with a ST-133 controller; Princeton Instrument, Princeton, NJ). Data
were acquired, stored, and analyzed on a Macintosh IIfx computer
(Apple, Cupertino, CA). All spectra were calibrated against the known
Raman frequencies of toluene. Sample concentrations were 50 mM
and spectra were taken at room temperature, unless noted otherwise.
FTIR Spectroscopy. IR absorbance spectra were measured with a
Magna 760 Fourier transform spectrometer (Nicolet Instruments Corp.,
WI), using a MCT detector. A dual cell shuttle accessory was used to
keep the sample and reference in identical environments to obtain
difference spectra of the highest possible quality (discussed in detail
in ref 11); this permits a sequential and repeated measurement of the
sample and reference spectra. Spectra were collected in the range of
740-4000 cm-1 with BaF2 cells and 25-µm spacers, although data
below 900 cm-1 is obscured by the water and cell background. The
resolution was set at 2 cm-1 and a Happ-Genzel apodization was
applied. Temperature of the sample cell was controlled by a model
RTE-111 (Neslab Instruments Inc.) bath circulator. Sample concentra-
tions were 5 mM and spectra were taken at 25 °C, unless noted
otherwise. For both Raman and FTIR measurements in aqueous
solution, the pH was at least 1.5 pH units above the pKa2 for the
compound, to ensure that the spectra of the dianion was monitored.
No buffer was used in the sample. To ensure that the spectra of the
dianion was monitored for mixed water/DMSO solutions, all the
measurements were performed in 7-20 mM sodium or tetramethyl-
(3) (a) Pauling, L. Chem. Eng. News 1946, 24, 1375. (b) Warshel, A. J. Biol.
Chem. 1998, 273, 27035. (c) Jencks, W. P. Catalysis in Chemistry and
Enzymology; McGraw-Hill: New York, 1969. (d) Fersht, A. Enzyme
structure and mechanism; W. H. Freeman & Co.: New York, 1977. (e)
Bruice, T. C.; Benkovic, S. J. Biochemistry 2000, 39, 6267. (f) Polanyi,
M. Z. Elektrochem. 1921, 27, 142.
(4) See, for example: (a) Rees, D. C. J. Mol. Biol. 1980, 141, 323. (b) Li, Y.
K.; Kuliopulos, A.; Mildvan, A. S.; Talalay, P. Biochemistry 1993, 32,
1816. (c) Sternberg, M. J. E.; Hayes, F. R. F.; Russell, A. J.; Thomas, P.
G.; Fersht, A. R. Nature 1987, 330, 86.
(5) (a) Gilson, M. K.; Honig, B. H. Nature 1987, 330, 84. (b) Warshel, A.;
Russell, S. T. Q. ReV. Biophys. 1984, 17, 283. (c) Lee, L. P.; Tidor, B.
Nat. Struct. Biol. 2001, 8, 73. (d) Schaefer, M.; Karplus, M. J. Phys. Chem.
1996, 100, 1578.
(6) See, for example: (a) Thornburg, L. D.; Henot, F.; Bash, D. P.; Hawkinson,
D. C.; Bartel, S. D.; Pollack, R. M. Biochemistry 1998, 37, 10499. (b)
Czerwinski, R. M.; Harris, T. K.; Massiah, M. A.; Mildvan, A. S.; Whitman,
C. P. Biochemistry 2001, 40, 1984.
(7) Abbreviations: DMSO, dimethyl sulfoxide; FTIR, Fourier Transform
Infrared; MCT, Mercury-Cadmium-Telluride; NaOH, sodium hydroxide;
pNPP, para-nitrophenyl phosphate; P-O, phosphorus-oxygen bond;
P‚‚O, the phosphorus-oxygen nonbridging bond (there are three such
bonds in monosubstituted phosphates); P-O(R), the phosphorus-oxygen
bond bridging the phosphate moiety with the leaving group for monosub-
stituted phosphates; PP, phenyl phosphate; TMAH, tetramethylammonium
hydroxide; TS, transition state; vu, valence unit; υ, fundamental frequency;
υa, antisymmetric stretch frequency; υs, symmetric stretch frequency.
(8) Kirby, A. J. Chem. Ind. 1963, 1877.
(9) (a) Hall, A. D.; Williams, A. Biochemistry 1986, 25, 4784. (b) Zhang, Z.-
Y.; Etten, R. L. V. J. Biol. Chem. 1991, 266, 1516.
(10) Callender, R.; Deng, H. Annu. ReV. Biophys. Biomol. Struct. 1994, 23, 215.
(11) Cheng, H.; Sukal, S.; Deng, H.; Leyh, T. S.; Callender, R. Biochemistry
2001, 40, 4035.
9
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Phosphoryl Bonding Probed by Vibrational Spectroscopy
A R T I C L E S
out reactions in glass vials, as reaction mixtures in Eppendorf tubes
gave side products at elevated temperatures used to follow PP
hydrolysis. For both pNPP and PP, reactions were first order in
substrate, and rate constants were obtained by a nonlinear fit to a single
exponential (Kaleidagraph, Synergy Software). End points of inorganic
phosphate for PP reactions were routinely 50-80% of the total amount
of starting phosphate ester (determined following total enzymatic
hydrolysis with E. coli alkaline phosphatase), suggesting the occurrence
of side reactions. This introduces uncertainty in the measured rate
constants of on the order of ∼2-fold. For both pNPP and PP, varying
the hydroxide ion concentration over a 20-fold range gave effects of
<2-fold on the observed rate constants, suggesting that hydrolysis of
the dianion was being followed. The rate constants with tetramethyl-
ammonium hydroxide and sodium hydroxide were the same, within
experimental error, suggesting that there were no ion specific effects.
Control reactions with PP in which sodium chloride was used to
maintain constant ionic strength gave the same rate constants, within
error.
Figure 1. The symmetric and antisymmetric stretches of the P‚‚O
nonbridging bonds.
ammonium hydroxide (see Hydrolysis of pNPP and PP in DMSO).
The IR measurements of each sample were completed within 20 min
of sample preparation, to ensure that significant hydrolysis does not
occur. The Raman measurements were performed in ∼80 min.
Data Processing. Omnic 4.0a (Nicolet Instruments, Corp.) and Igor
pro 3.1 (Wavemetrics Inc.) software were used to analyze and process
the data. Spectra subtraction, second derivative, and Fourier self-
deconvolution (FSD) were performed with the Omnic 4.0a software.
As the conditions for the sample and reference measurements were
the same, a direct subtraction of reference from sample usually resulted
in a good difference spectrum. In particular, because water has no peak
around the phosphate bands, a direct subtraction for spectra obtained
in aqueous solution is reliable.11 The spectrum of DMSO contains
substantial absorbance at 1316 cm-1 and 1400-1450 cm-1. Thus, small
differences between the sample and reference can give spurious bands
at these wavelengths. To remove spectral contributions from the DMSO
peaks at 1316 cm-1 and 1400-1450 cm-1 for experiments in water/
DMSO mixtures, the reference spectrum was multiplied by a factor
slightly varying from one.
The antisymmetric stretching band of inorganic phosphate in the IR
spectra is distinct from other bands, so that the frequency can be read
directly from the spectrum. For monosubstituted phosphates on the other
hand, the observed antisymmetric stretching band (Figure 1) exhibits
small features on top of the otherwise smooth absorption band. In these
cases, the C3V symmetry of the -PO32- moiety has been lifted and the
observed band is the superposition of two broad “antisymmetric-like”
bands at slightly different frequencies. Two approaches were taken to
obtain the frequency of the antisymmetric stretch, υa, in these cases.
One was to take υa as the frequency at the center of the absorption
band. The other was to determine the two-component antisymmetric-
like stretch frequencies by calculation from the second derivative or
by Fourier spectral deconvolution. The two approaches yielded the same
value for bond lengths, using the formulas below, to within (0.001 Å.
Hence, the simpler method was adopted and the average antisymmetric
stretch frequency is reported below. The only exception is pNPP, for
which the positions of the antisymmetric bands were difficult to
determine because the two antisymmetric modes overlap with a mode
arising from the phenyl moiety. It was found useful in this case to
employ Gaussian curve fitting of the FTIR spectra, using the peak
positions found by second derivative and spectra deconvolution as initial
peak placement. The corresponding Raman spectrum of pNPP was taken
also to help identify the observed phenyl band in the phosphoryl
antisymmetric stretch mode region, as this band was simultaneously
Raman and IR active (unlike the antisymmetric stretch mode).
Hydrolysis of pNPP and PP in DMSO. Reactions were carried
out with 50-200 µM pNPP (25 °C) or 200-500 µM PP (95 °C) and
1-20 mM sodium hydroxide or tetramethylammonium hydroxide in a
series of water/DMSO mixtures. For pNPP, aliquots were removed and
production of p-nitrophenolate was followed at 410 nm (ꢀ ) 1.82 ×
104 M-1 cm-1 at pH 10). For PP, inorganic phosphate formation was
monitored using a modified molybdate assay.12 It was necessary to carry
Results
The vibrational frequencies of the -PO32- moiety were used
to determine the bond length and bond order of the bridging
bond for a wide series of monosubstituted phosphates,
RO-PO32-, in aqueous solution and for two of these compounds
in mixed water/DMSO solutions. In general, a highly accurate
determination of bond lengths of small molecules in solution
from vibrational frequencies is feasible (see below). This
approach, however, has not seen wide use in recent years. For
this reason, we provide an overview of how vibrational
frequencies are related to bond lengths and bond orders.
Vibrational Data Analysis: General Principles. Gordy,13
on the basis of earlier work of Badger,14 established empirical
correlations relating the frequencies of vibrational modes to bond
length and bond order, through the force constant of the mode.
These correlations hold up well for simple molecules or
molecular fragments whose vibrational coordinates can be
approximated as a diatomic oscillator; i.e., the measured fre-
quency is proportional to the square root of the bond’s force
constant divided by a suitable reduced mass. The accuracy of
calculating a bond length from vibrational frequencies in these
cases was as good as the accuracy of bond length measurements
via crystallography, about 1% at the time of Gordy’s work.
In general, bond length versus frequency correlations are less
accurate for polyatomic molecules. This is because interactions
between nonbonded atoms show up as mode-mode coupling
between internal coordinates of the molecule. Hence, the normal
mode for a polyatomic molecule is typically not a simple
diatomic oscillator but rather involves contributions from several
internal coordinates. For phosphates of varying ionization states,
including dianionic phosphate monoesters, the subject of this
report, the normal modes of the stretch motions of nonbridging
P‚‚O bonds are not simple diatomic oscillators. For example,
the individual frequencies of the dianionic phosphate symmetric,
υs, and antisymmetric, υa, stretch modes (Figure 1) depend on
the force constant and reduced mass of the relevant P‚‚O bond
and also on the molecule’s geometry and, to a lesser extent,
other factors, such as off-diagonal coupling terms.15
Normal-mode analysis guided by ab initio calculations
suggested an approach to isolate the properties of the P‚‚O
(13) Gordy, W. J. Chem. Phys. 1946, 14, 305.
(14) Badger, R. M.; Bauer, S. H. J. Chem. Phys. 1937, 5, 839.
(15) Deng, H.; Wang, J.; Callender, R.; Ray, W. J. J. Phys. Chem. B 1998, 102,
3617.
(12) Taussky, H. H.; Shorr, E.; Kurzmann, G. J. Biol. Chem. 1953, 202, 675.
9
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A R T I C L E S
Cheng et al.
bonds: in the geometric average frequency of the phosphate
symmetric and antisymmetric stretch frequencies, geometrical
contributions cancel one another. Thus, the geometrical mean
is referred to as the “fundamental frequency”.15 The fundamental
frequency, denoted as υ here, is then approximated as propor-
tional to the square root of the P‚‚O force constant divided by
the reduced mass. Previous results with inorganic phosphate
ions suggest that bond lengths can be determined to a high
degree of accuracy via this approach.15 Below we describe how
the fundamental frequency is obtained for monosubstituted
phosphate dianions.
There are three independent nonbonded P‚‚O stretch modes
of the -PO32- moiety. For dianionic phosphate monoesters that
2-
preserve the C3V symmetry of the -PO3 moiety, the normal
modes are characterized by two doubly degenerate antisym-
metric stretches, υa, located near 1110 cm-1, and one symmetric
stretch, υs, located near 970 cm-1 (Figure 1). The symmetric
mode is allowed in Raman spectroscopy and weakly observed
in the IR while the antisymmetric mode is allowed in IR and
only weakly observed in Raman, allowing the above assign-
ments. It is sometimes necessary to perform both Raman and
IR spectroscopies to measure the symmetric and antisymmetric
modes.
Figure 2. Vibrational spectra of allyl phosphate in an aqueous solution.
(a) IR spectrum of allyl dianionic phosphate and (b) the corresponding
second derivative spectrum. The spectrum is of 10 mM allyl phosphate in
20 mM NaOH at a resolution of 2 cm-1
.
The fundamental frequency is given by
O‚‚P‚‚O angle adopts a range of angles by thermal motion, and
this results in a range of bond force constant values. These
changes are additive for the antisymmetric mode frequency but
cancel out for the symmetric mode.
The three frequencies for allyl phosphate, 980, 1084, and 1109
cm-1, yield a fundamental frequency of υ ) 1059 cm-1 using
Equation 2. Using the average frequency of the antisymmetric
stretches υa) 1096 cm-1, rather than the two peak frequencies
revealed by the second derivative analysis, and υs ) 980 cm-1
in Equation 1 yields the same value for υ.
υ ) [(υs2 + 2υa2)/(3)]1/2
(1)
For monosubstituted phosphates, the bond lengths of the three
nonbridging P‚‚O bonds are equal. When the C3V symmetry is
not retained, the degeneracy of the antisymmetric stretch modes
is lifted, and three different frequencies are measured for the
2-
stretch modes of the -PO3 fragment. The fundamental
frequency is then defined by
υ ) [(υs2 + υa12 + υa22)/(3)]1/2
(2)
Prior work comparing vibrational spectra and bond lengths
derived from X-ray structures for crystals of inorganic phosphate
and phosphate esters yielded the following empirical relationship
between the fundamental frequency and length of the nonbridg-
Typically, one of the bands is “symmetric-like” and the other
two are “antisymmetric-like” in their polarization attributes as
well as their relative band intensities in the Raman and IR
spectra.
2-
ing bond (or average bond length in a nonsymmetrical -PO3
fragment):15
Vibrational Spectra, Fundamental Frequency, and Bond
Orders and Lengths: Allyl Phosphate as an Example. Figure
2a shows the IR spectrum of allyl phosphate dianion. The
relatively weak band near 980 cm-1 is assigned to the symmetric
RP‚‚O ) 0.2835 Å‚ln(224500 cm-1/υ)
(3)
The bond length of the nonbridging P‚‚O bonds of allyl
phosphate dianion is then calculated to be RP‚‚O ) 1.518 Å,
using the fundamental frequency υ ) 1059 cm-1 derived above.
Determination of Bond Order and Bond Length for the
P-O(R) Bridging Bond: The Allyl Phosphate Example
Continued. The intensity of the stretching mode of the P-O(R)
bridging bond is typically substantially weaker than the non-
bridging P‚‚O vibrations. It is therefore difficult to measure,
especially for compounds bound to proteins. In addition, while
the bond lengths determined using an equation analogous to
Equation 3 and the nonbridging P-O stretch frequencies have
been empirically quite close to bond lengths determined from
X-ray crystallography,15 the exact equation parameters have not
been determined for calculating the bridging bond length using
Equation 3. Nevertheless, this bond is often of primary interest,
as it is the bond that is broken in many nonenzymatic and
enzymatic reactions. We therefore outline an indirect approach,
developed previously15 and used by us in several studies (e.g.,
2-
mode stretch of the nonbridging P‚‚O bonds of the -PO3
fragment while the relatively stronger band near 1100 cm-1
represents the antisymmetric stretches. The 980 cm-1 band was
observed in separate Raman measurements (data not shown),
but the two antisymmetric modes were too weak to be observed
in the Raman spectrum. The two antisymmetric-like modes in
this spectrum are not at the same frequency, as two overlapping
bands are evident near 1100 cm-1. Second derivative analysis
of the IR spectrum (Figure 2b) yields peak frequencies for the
two antisymmetric modes of 1084 and 1109 cm-1. The
antisymmetric modes are not only more intense than the
symmetric stretch, as expected in the IR spectrum, but also
substantially broader. We have attributed this difference in
bandwidth to the dependence of the symmetric and antisym-
metric stretch frequencies on the O‚‚P‚‚O angle.15,16 The
(16) Wang, J.; Xiao, D.; Deng, H.; Webb, M. R.; Callender, R. Biochemistry
1998, 37, 11106.
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Phosphoryl Bonding Probed by Vibrational Spectroscopy
A R T I C L E S
2-
Table 1. Vibrational Frequencies of the -PO3 Moiety and the
Derived P-O(R) Bond Length for a Series of Alkyl Phosphate
Monoesters
ref 11 and 16), to estimate the bond order and bond length for
the bridging P-O bond from the vibrational frequencies of the
nonbridging bonds. Results described in a later section (Direct
Measurement of the P-O(R) Bond Length of pNPP Using the
P-O(R) Stretch) offer support for the accuracy of this approach.
The first step in determining the bridging bond order and
length from the nonbridging P‚‚O stretch frequencies rests on
the network theory developed by Brown and co-workers as a
refinement method for small molecule crystallography.17a-c In
this approach, the sum of the bond orders of all the bonds of a
specific atom is fixed to the atomic valence; for phosphates this
is 5.0. Although conservation of valence lacks theoretical basis,
this bond valence paradigm has been shown to yield accurate
bond length refinements in small molecule crystallographic
studies and appears to have reasonable predictive value for
modest changes.17a-c In addition, analysis of crystal structures
of a wide series of -PO4 derivatives indicates that the sum of
all the P-O bond lengths to a single phosphorus atom is nearly
constant (6.177 ( 0.030 Å), providing specific support for the
validity of conservation of valence for phosphorus.17d
alcohol substituent
pK a
νsb (cm-1
)
νac (cm-1
)
ν.d (cm-1
)
Rbridginge (Å)
a
pentafluoro-2-propanol 10.1f
983
976
981
985
981
980
986
982
978
981
980
983
973
971
1110
1112
1106
1112
1105
1104
1103
1100
1098
1194
1196
1195
1092
1089
1069
1069
1066
1071
1065
1064
1065
1062
1060
1058
1059
1059
1053
1050
1.616
1.615
1.612
1.619
1.612
1.611
1.612
1.608
1.605
1.603
1.605
1.605
1.599
1.596
phosphoenolpyruvate
trichloroethanol
trifluorethanol
2-aminoethanol
2-propynol
11.1g
12.2
12.4
12.65h
13.6
13.9
14.0i
14.4
14.8
15.5
15.5
16.1j
17.1j
choline
2-cyanoethanol
2-glycerol
2-methoxyethanol
2-propenol
methanol
butanol
2-propanol
a The pKa of the alcohol substituent is from ref 37, unless otherwise
noted. b Symmetric mode frequency. c Doubly degenerate antisymmetric
mode frequency. The average frequency is reported for cases in which the
degeneracy of the two antisymmetric modes has been lifted. d Fundamental
frequency (Equation 1). e Bond length of the bridging P-O(R) bond,
calculated as described in the Results. f The pKa of pentafluoroisopropyl
alcohol is approximated on the basis of the pKa values for the tri- and hexa-
fluoro-2-propanol (from ref 37). Each additional fluorine atom is expected
to lower the pKa of the 2-propanol by ∼0.8 pKa units. g The pKa of “the
enol of pyruvate” is assumed to be equal to that of hydroxyethylene.42 h From
The second step of the analysis rests on relating bond order,
bond length, and vibrational frequencies. The equation that
defines the relationship between bond order and bond length
for phosphates is15
j
ref 38. i From ref 39. From ref 40.
SP-O (vu) ) (RP-O/1.620 Å)-4.29
(4)
the three P‚‚O bonds, and subtracting the total from five yields
1.040 vu for the bridging P-O(R) bond. Use of SP-O ) 1.040
vu in Equation 4 gives a bridging bond length of 1.605 Å.
The accuracy in the absolute value of the bond lengths
obtained from this method has been estimated to be (0.004 Å
on the basis of comparisons of spectroscopically determined
bond lengths for methyl phosphate and triphenylphosphine oxide
crystals to bond lengths from small molecule diffraction studies
of these compounds.15 A large part of this error arises from
mode-mode couplings between P‚‚O stretches and other
modes, which affect the character of the stretch mode. These
couplings vary among the different phosphate compounds to
some extent. An accuracy of (0.004 Å corresponds to an error
of (13 cm-1, using Equation 3 to relate frequency to bond
length. The precision of the measurement of vibrational
frequencies is much higher than this, about (2 cm-1, and the
issue of mode-mode coupling is not as important for compari-
sons of the same molecule in different environments since the
coupling parameters remain essentially constant. Hence, calcu-
lating bond length changes when a specific molecule undergoes
a change in environment is expected to be more accurately
determined. It is unclear what the accuracy is in that case as
there are no experimental benchmarks, but an accuracy of better
than (0.001 Å is possible using the ultimate accuracy provided
by the precision in the measurement of frequency. Finally, the
conclusions drawn herein rely on the interpretation of the
vibrational frequencies and would be unaffected by limitations
in our ability to convert frequencies to accurate bond lengths.
Vibrational Spectra and Bridging P-O Bond Length for
a Series of Monosubstituted Phosphates. Tables 1 and 2
tabulate the vibrational frequencies of the nonbridging P‚‚O
stretches, the calculated bridging P-O bond length, and the pKa
Furthermore, appropriate substitution of bond length derived
in Equation 3 into Equation 4 yields the following relationship
between the bond order of the P-O nonbridging bonds and the
fundamental frequency:
SP‚‚O (vu) ) [0.175‚ln(224500 cm-1/υ)]-4.29
(5)
SP-O is the bond order of the P-O bond (either bridging or
nonbridging), RP-O is the length of the P-O bond (either
bridging or nonbridging), and υ is the fundamental frequency
for the nonbridging P‚‚O bonds as defined above (Equations 2
and 3; in units of cm-1). Equation 4 holds for either bridging
or nonbridging bonds while Equation 5 holds only for the
nonbridging bonds. When used to calculate bond order of the
P-O(R) bridging bond, Equation 5 underestimates the bond
order by about 5%, according to network theory.18 The total
2-
bond order of the nonbridging bonds in the -PO3 fragment
is therefore determined from empirical relationship in Equation
5, and the bond order of the bridging bond is then inferred by
subtracting this number from 5. The bond length of the bridging
P-O(R) bond is subsequently calculated through the use of
Equation 4.
The value of υ ) 1059 cm-1 for allyl phosphate dianion (see
previous section) yields an average bond order of SP‚‚O
)
1.320 valence units (vu) for each of the three nonbridging
P‚‚O bonds using Equation 5. Multiplying 1.320 by three, for
(17) (a) Brown, I. D.; Shannon, R. D. Acta Crystallogr. 1973, A29, 3617. (b)
Brown, I. D.; Wu, K. K. Acta Crystallogr. 1976, B32, 1957. (c) Brown, I.
D. Acta Crystallogr. 1992, B48, 553. (d) Calleri, M.; Speakman, J. C. Acta
Crystallogr. 1964, 17, 1097.
(18) Inherent to this error analysis is the assumption that the total bond order to
phosphorus is equal to five (see refs 15 and 17a-c). The bond order of the
bridging P-O(R) bond is underestimated by about 5% via the use of
Equation 5, compared to the bond order calculated for the P-O(R) bridging
bond by subtracting from five the total bond order for the P‚‚O nonbridg-
ing bonds (calculated via the use of Equation 5).15
2-
of the ROH substituent for several RO-PO3 compounds, in
aqueous solution. The vibrational data analysis employed was
the same as that described above by way of example for the
allyl phosphate dianion.
9
J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002 11299

A R T I C L E S
Cheng et al.
2-
2-
Table 2. Vibrational Frequencies of the -PO3 Moiety and the
Derived P-O(R) Bond Length for a Series of Aromatic (A) and
Other (B) Monosubstituted Phosphates
Table 3. Vibrational Frequencies of the -PO3 Moiety and the
Derived Bridging P-O(R) Bond Length of pNPP in Varying
Amounts of DMSO Cosolvent
a
compound
pK a
νsb (cm-1
)
νac (cm-1
)
ν.d (cm-1
)
Rbridginge (Å)
% DMSO log(khyd
)
νsb (cm-1
)
νa1c (cm-1
)
νa2c (cm-1
)
νd(cm-1
)
Rbridginge (Å)
a
(A) aromatic phosphates
0
25
50
60
70
80
90
-7.0
981
980
978
978
977
977
976
1111
1110
1110
1112
1113
1119
1125
1133
1136
1137
1139
1141
1146
1156
1077
1077
1077
1078
1079
1082
1088
1.625
1.625
1.625
1.627
1.628
1.632
1.638
2-
4-nitrophenyl-PO3
7.1
7.95
8.4
983
983
985
982
980
986
982
983
983
1120
1118
1118
1108
1110
1112
1108
1109
1108
1076
1075
1076
1068
1068
1072
1068
1069
1068
1.625
1.622
1.622
1.614
1.615
1.619
1.614
1.616
1.615
-6.6
-6.0
-5.7
-5.0
-4.2
-2.5
2-
4-cyanophenyl-PO3
2-
3-nitrophenyl-PO3
2-
4-Br-phenyl-PO3
9.3
2-
1-naphthyl-PO3
2-naphthyl-PO3
phenyl-PO3
9.3f
9.6f
9.95
9.95
2-
2-
2-
a The hydrolysis rate constant (khyd) in min-1 was measured as described
in the Materials and Methods. b Symmetric mode frequency. c Two anti-
symmetric mode frequencies. d Fundamental frequency (Equation 2). e Bond
length of the bridging P-O(R) bond, calculated as described in the Results.
4-F-phenyl-PO3
2-
4-methylphenyl-PO3
10.2
(B) sugar phosphates and other phosphates
2-
glucose-1-PO3
5′-GMP
12.4g
14h
14h
14.7g
968
978
980
980
983
984
1106
1098
1100
1095
1130
1084
1062
1060
1062
1058
1083
1052
1.608
1.605
1.608
1.604
1.632
1.597
2-
Table 4. Vibrational Frequencies of the -PO3 Moiety and the
5′-UMP
glucose-6-PO3
Derived Bridging P-O(R) Bond Length of PP in Varying Amounts
2-
of DMSO Cosolvent
2-
acetyl-PO3
4.8
2-
a
νsb (cm-1
)
νac (cm-1
)
ν.d (cm-1
)
Rbridginge (Å)
HPO4
16.4i
% DMSO
T (°C)
log(khyd
)
0
0
90
95
25
95
95
95
-9.4f
-5.3f
-2.8
-1.7
981
980
975
973
1110
1111
1125
1131
1968
1069
1077
1081
1.615
1.616
1.625
1.630
a The pKa of the alcohol substituent is from ref 37, unless otherwise
noted. b Symmetric mode frequency. c Doubly degenerate antisymmetric
mode frequency. The average frequency is reported for the cases in which
the degeneracy of the two antisymmetric modes has been lifted. d Funda-
mental frequency (Equation 1). e Bond length of the bridging P-O(R) bond,
calculated as described in the Results. f From ref 41. g From ref 38. h In
the absence of experimental data, we approximate the pKa of the 5′-hydroxyl
of guanosine and uridine to be ∼14. This is because the pKa for
2-methoxyethanol is 14.8, and the presence of 3′- and 2′-hydroxyls in the
sugar moiety is expected to lower the pKa for the 5′-hydroxyl, relative to
the pKa for the 2-methoxyethanol. i From ref 43.
a The hydrolysis rate constant (khyd) in min-1 was measured as described
in the Materials and Methods, unless noted otherwise. b Symmetric mode
frequency. c Doubly degenerate antisymmetric mode frequency (the average
frequency is reported for the cases in which the degeneracy of the two
antisymmetric modes has been lifted). d Fundamental frequency (Equation
1). e Bond length of the bridging P-O(R) bond, calculated as described in
the Results. f The hydrolysis rate constant for the aqueous reaction has been
extrapolated on the basis of a series of measurements at higher temperatures
(O’Brien, P. J.; Wolfenden, R.; Herschlag, D. unpublished results).
spectrum of phenyl phosphate. The two strong bands at 1111
and 1137 cm-1 are assigned to the two antisymmetric-like
vibrations of the nonbridging P‚‚O bonds. Substituting 978,
1111, and 1137 cm-1 into Equation 2 for υs, υa1, and υa2 yields
a fundamental frequency of υ ) 1077 cm-1. The P-O(R) bond
lengths can then be determined as described above (Determi-
nation of Bond Order and Bond Length for the P-O(R)
Bridging Bond: The Allyl Phosphate Example Continued).
Table 3 lists the measured hydrolysis rate constants for pNPP
in various water/DMSO mixtures at 25 °C. The rate constant is
highly sensitive to the DMSO content, increasing dramatically
for DMSO concentrations greater than 70-80%, as previously
noted.19 Also given in Table 3 are the nonbridging phosphate
stretch modes (see Figure 3 for the 50/50% spectrum), the
calculated fundamental frequency, and the calculated bridging
bond length (see above). Table 4 provides the hydrolysis rate
constants for phenyl phosphate (see Materials and Methods).
The measured frequencies are quite insensitive to temperature
while the hydrolysis rate constants are quite sensitive. This is
expected if temperature has little effect on the structure of the
ground state but simply raises the percentage of molecules with
sufficient energy to cross the transition-state barrier.
Figure 3. Vibrational spectra of pNPP in 50% DMSO/water solution. The
spectrum between 1000 cm-1 and 1070 cm-1 is not shown because of the
large absorbance of DMSO in this region. The spectrum is that of 5 mM
pNPP and 7 mM TMAH, at room temperature, and the resolution is 2 cm-1
.
The left band at 978 cm-1 corresponds to the symmetric P‚‚O stretch of
phosphate. The peak on the right, corresponding to the antisymmetric stretch,
is composed of several bands. A Gaussian decomposition fit using three
Gaussian functions is shown.
Direct Measurement of the P-O(R) Bond Length of pNPP
Using the P-O(R) Stretch. The bond length of the bridging
P-O(R) bond can be estimated directly from Equation 3, using
the same parameters derived for the nonbridging bonds. The
frequency of the bridging bond stretch is then substituted for
the fundamental frequency, υ. We estimate that the bond length
Bridging P-O Bond Length of pNPP and PP in Water/
DMSO Mixtures. Figure 3 shows the IR spectra of pNPP in a
50% water/DMSO mixture. The symmetric stretch is located
at 978 cm-1. The spectrum in the antisymmetric mode frequency
range is complicated. Gaussian curve fitting of the spectrum in
this region revealed three overlapping peaks at 1111, 1113, and
1137 cm-1 (Figure 3). The small peak at 1113 cm-1 is assigned
to a mode on the phenyl ring as a similar band shows up in the
(19) (a) Abell, K. W. Y.; Kirby, A. J. Tetrahedron Lett. 1986, 27, 1085. (b)
Grzyska, P. K.; Czyryca, P. G.; Golightly, J.; Small, K.; Larsen, P.; Hoff,
R. H.; Hengge, A. C. J. Org. Chem. 2002, 67, 1214.
9
11300 J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002

Phosphoryl Bonding Probed by Vibrational Spectroscopy
A R T I C L E S
comparison shows that consistent values of the bridging bond
length are obtained from the two methods.
Discussion
Phosphoryl transfer is likely the most common class of
reactions in biology. Decades of study of phosphoryl transfer
by structure-reactivity approaches have provided much insight
into these reactions and their transition states.20,21 To further
our understanding of how phosphoryl compounds react, we have
focused on determination of basic properties of these com-
pounds, and to further our understanding of how phosphoryl
transfer reactions are catalyzed, we have focused on understand-
ing the environment at the site of catalysis.
Vibrational spectroscopy offers a unique and direct probe of
the actual bonding and bond properties of phosphoryl com-
pounds. Previous work and the results described herein suggest
that properties of the nonbridging bonds of the phosphoryl group
can be ascertained to high precision ((0.004 Å), despite the
occurrence of complex vibrational modes; this is accomplished
by appropriate combination of the observed phosphoryl vibra-
tional modes. Assuming only a conservation of the valence bond
order for the phosphorus atom, this analysis can be extended to
yield the bonding properties of the P-O(R) bridging bonds
the bond that is broken during phosphoryl transfer (see ref 15
and Results herein). The ability to obtain P-O(R) bridging bond
lengths via this analysis, which are in agreement with those
obtained by direct consideration of the stretching vibrational
mode of the P-O(R) bridging bond within experimental error,
provides further support for this approach.
In the sections that follow, we address what has been revealed
about the fundamental properties of the P-O(R) bridging bond
and the applicability of vibrational spectroscopy as a sensitive
probe for the electrostatic environment of the phosphoryl group.
First, we describe bonding properties derived from vibrational
spectroscopy for a series of monosubstituted phosphoryl com-
pounds, in which the phosphoryl substituent has been varied
systematically and extensively. Next, we describe phosphoryl
bonding changes due to variation of the solvent environment,
also derived from vibrational spectroscopy. We then discuss
the relationship between the ground-state bonding properties
and reactivity. Finally, we discuss implications of this work for
enzymatic catalysis.
Figure 4. The Raman spectra of the P-O(R) stretch of pNPP in DMSO/
water mixtures, (a) to (f): 0, 20, 50, 60, 70, and 80% DMSO. 6-Deuterated
DMSO was used to avoid the high Raman signal from protonated DMSO
in this region. The spectra are of 10 mM pNPP in 20 mM NaOH at a
resolution of 6 cm-1
.
Table 5. Comparison of the P-O(R) Bridging Bond Lengths
Determined from the Analysis of the Nonbridging Bond Vibrational
Modes and from Direct Analysis of the P-O(R) Bond Vibrational
Mode
% DMSO
nbridginga (cm-1
)
Rbridgingb (Å)
Rbridgingc (Å)
Rbridging Rbridging (Å)
0
25
50
60
70
80
733
730
726
722
720
715
1.623
1.624
1.626
1.627
1.628
1.630
1.625
1.625
1.625
1.627
1.628
1.632
-0.002
-0.001
0.001
0.000
0.000
-0.002
a Stretching frequency of the bridging P-O(R) bond of pNPP in various
water/DMSO solutions (data presented in Figure 4). b Bond length of the
bridging P-O(R) bond, calculated directly from Equation 3 and the
stretching frequency of the bridging P-O(R) bond. c Bond length of the
bridging P-O(R) bond, calculated from the nonbridging bond stretch
frequencies using Equations 4 and 5, as discussed in the Results. Values
are from Table 3.
of the P-O(R) bond derived from the direct use of Equation 3
will yield results that underestimate the P-O(R) bond length
by ∼0.2%, on the basis of comparisons with crystallographic
data for model compounds.15 Figure 4 shows the Raman spectra
of pNPP in various water/DMSO mixtures in the region of the
P-O(R) bridging bond stretch (Raman spectroscopy is used
since this mode is highly obscured by solvent and cell
background in the IR). Table 5 gives the values of the bridging
P-O(R) stretch frequency for pNPP in water/DMSO mixtures
and the P-O(R) bond length, R′P-O(R), calculated using the
bridging P-O(R) stretch frequency directly as υ in Equation
3. Also tabulated is the bond length, RP-O(R), derived from
Equations 4 and 5, using the frequencies associated with the
nonbridging bonds and the network theory, as described above.
The bond lengths derived from the two procedures are in close
agreement.
Substituent Effects on Phosphoryl Group Bonding: Cor-
relation of the Bridging P-O(R) Bond Length with Sub-
stituent pKa. Kirby and co-workers carried out a systematic
small molecule crystallography study, probing bonding for a
series of substituted aryl acetals. The results suggested that
substituents that lowered the pKa of the aryl group stabilized a
longer C-O(R) bond,22,23 presumably because of electron-
withdrawing effects that lessen the electron density on the
oxygen atom and thereby weaken the bond or through-space
substituent effects that electrostatically stabilize greater electron
(20) (a) Cleland, W. W.; Hengge, A. C. FASEB J. 1995, 9, 1585. (b) Benkovic,
S. J.; Schray, K. J. In Transition States of Biochemical Processes; Gandour,
R. D., Schowen, R. L., Eds.; Plenum: New York, 1978; p 493. (c) Williams,
A. J. Am. Chem. Soc. 1985, 107, 6335. (d) Thatcher, G. R. J.; Kluger, R.
AdV. Phys. Org. Chem. 1989, 25, 99.
(21) Hengge, A. C. In ComprehensiVe Biological Catalysis; Sinnott, M. L., Ed.;
Academic Press: London, 1998; p 517.
These results validate two important points. First, the bond
order of the bridging P-O(R) bond does indeed weaken as the
amount of DMSO is increased. The P-O(R) stretch frequency
is directly correlated to the electron density in the bond so that
a lower frequency means a smaller bond order. In addition, the
(22) (a) Allen, F. H.; Kirby, A. J. J. Am. Chem. Soc. 1984, 106, 6197. (b) Briggs,
A. J.; Glenn, R.; Jones, P. G.; Kirby, A. J.; Ramaswamy, P. J. Am. Chem.
Soc. 1984, 106, 6200.
(23) Jones, P. G.; Kirby, A. J. J. Am. Chem. Soc. 1984, 106, 6207.
9
J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002 11301

A R T I C L E S
Cheng et al.
Scheme 1
Figure 5. The bond length of the bridging P-O(R) bond for alkyl
phosphate monoesters, RO-PO32-, plotted as a function of the pKa of the
alcohol (ROH) substituent. The data are taken from Table 1 for a series of
alkyl phosphates, the point for trifluroethyl phosphate is depicted by the
open symbol. The line is a least-squares fit to the data; excluding the
trifluoroethyl phosphate data point44 (open square) gives R (Å) ) 1.647 -
0.00284‚pKa, with the correlation coefficient R2 ) 0.87. Inclusion of
trifluoroethyl phosphate gave R (Å) ) 1.650 - 0.00304 × pKa, with the
correlation coefficient R2 ) 0.82.
density on the oxygen atom and thereby preferentially stabilize
a longer C-O(R) bond. An analogous correlation was suggested
for phosphoryl compounds,23 but acquiring data for an extensive
series of phosphoryl compounds is hampered by the difficulty
in crystallizing these compounds in homologous crystal environ-
ments. For this reason and because vibrational studies can be
carried out in and compared between solution, protein, and
crystal environments, we have turned to Raman and IR
spectroscopy of a series of phosphoryl compounds to probe the
bonding properties of the phosphoryl group in aqueous solution.
In the simplified model of Scheme 1, the alkyl substituents
of dianionic alkyl phosphate monoesters are schematically and
approximately represented as dipoles.24 The greater the positive
charge potential from this dipole, the lower the pKa of the
alcohol, as the dipole provides greater stabilization of the
negative charge present in the alkoxide but not the alcohol.
Analogously, as the P-O(R) bond lengthens, negative charge
accumulates on the bridging oxygen, all other factors being
equal. (This can be thought of as a greater contribution from
an alkoxide ion resonance form.) Thus, there is a simple
prediction that the P-O(R) bond will lengthen as the pKa of
the alcohol substituent decreases. Nevertheless, the extent of
bond lengthening from this effect could not be predicted, nor
was it apparent if the effect would be large enough to detect or
if other factors idiosyncratic to the individual alkyl phosphate
dianions would obscure the predicted trend.
series of simple alkyl phosphate dianions. There is a linear
increase in the bond length as the substituent pKa decreases,
suggesting that phosphoryl group bonding responds in a regular
manner.
Given this trend, we next determined whether an extended
correlation could be obtained for a wider variety of monosub-
stituted phosphoryl compounds. Figure 6 presents data for the
alkyl phosphates as well as several aryl phosphates, more
complex alkyl phosphates, and inorganic phosphate, as a
function of the pKa of the phosphoryl substituent. A single line
gives a good fit to all of the data, spanning a range of substituent
pKa values of >12 units (see Figure 6 legend). The slope of
this line is ∼0.003 Å/(pKa unit). Nevertheless, there may be
small differences in the dependencies for the alkyl and aryl
phosphates and the deviations may arise because of different
mechanisms underlying the pKa effects (such as inductive versus
resonance).
The slope of the correlation in Figure 6 is of the same order
of magnitude as the slope of ∼0.006 Å/(pKa unit) estimated
from the previous limited X-ray data,23 although a direct
comparison is difficult because of the following: the lower
dielectric and different local environment in the crystal compared
to aqueous solution, the effects of different counterions and
crystal forms on the bond lengths for the four compounds used
in the X-ray correlation, and the relatively large uncertainty in
the bond lengths determined crystallographically (standard
deviations of (0.005 to (0.02 Å).23 The possibility of
systematic errors in determination of bond lengths from
vibrational data has also not been rigorously eliminated.
The phosphoryl substituents span of 12.3 pKa units corre-
sponds to a ∆∆G of 16.8 kcal/mol for the deprotonation
equilibrium to form the oxyanion.26 Thus, a group that stabilizes
the oxyanion by ∼17 kcal/mol lengthens the P-O-(R) bond
by only ∼0.04 Å. As described in the following sections, the
relationship of these parameters to changes in reactivity and to
Figure 5 shows the bond length for the bridging P-O(R)
bond, derived from vibrational spectra (Table 1 and Results),
plotted as a function of the pKa of the alcohol substituent for a
(24) We use a simplified model to understand stabilization of the leaving group
alkoxide ion substituent. Several studies have suggested that substituents
in nonconjugated systems exert their effects predominantly through space
rather than through the bonded chain (see, for example, ref 25 and references
therein), so that consideration of substituents as attached dipoles, as in
Scheme 1, may provide a reasonable representation. This approximation
is useful conceptually for the treatment presented in the text, but it is not
required for the conclusions that are drawn. For instance, for conjugated
systems, resonance effects are likely important.
9
11302 J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002

Phosphoryl Bonding Probed by Vibrational Spectroscopy
A R T I C L E S
Scheme 2
Figure 6. The bond length of the bridging P-O(R) bond for various
monosubstituted phosphates, RO-PO32-, plotted as a function of the pKa
of the ROH substituent. The data are taken from Table 1 and Table 2B for
alkyl phosphates (9), Table 2A for aromatic phosphates (b), and Table 2B
for acetyl phosphate (2) and inorganic phosphate (1). The solid line is a
least-squares fit to all the data: R (Å) ) 1.642 - 0.00257‚pKa, with the
correlation coefficient R2 ) 0.92. The dotted line is a least-squares fit to
the aromatic phosphates data: R (Å) ) 1.650 - 0.00356‚pKa, with the
correlation coefficient R2 ) 0.80. The dashed line is a least-squares fit to
the alkyl phosphate data from Tables 1 and 2B, excluding trifluoroethyl
phosphate.44 R (Å) ) 1.645 - 0.00275 × pKa, with the correlation
coefficient R2 ) 0.83.
(Scheme 2), DMSO is poor at solvating anions, such as the
nonbridging phosphoryl oxygen atoms (see, for example ref 27).
This limitation presumably arises because the positive end of
the DMSO dipole is sequestered behind the two methyl groups
(Scheme 2A). This limits both the close approach of the dipole
and the number of DMSO molecules that can align around the
phosphoryl group. The lessened favorable electrostatic inter-
actions with the nonbridging phosphoryl oxygen atoms upon
addition of DMSO will favor states with less charge accumula-
tion on these atoms; this provides an energetic “incentive” to
shorten these bonds (Scheme 2B). Analysis of the “fundamental
frequency” described in the Results indicates that as the fraction
of DMSO in the solvent increases, the nonbridging P-O bonds
are indeed shortened by a small but readily measurable amount.
Shortening of these bonds is equivalent to an increase in double-
bond character, and, given conservation of bond order around
phosphorus, the bond order of the bridging P-O(R) bond
decreases and this bond lengthens (Tables 3 and 4). Vibrational
spectra probing the stretching mode for the bridging bond
provide direct and independent support for this conclusion (see
Table 5 and Direct Measurement of the P-O(R) Bond Length
of pNPP Using the P-O(R) Stretch in Results).
In summary, bonding of the phosphoryl group responds to
the environment. This is observed directly in the DMSO effects.
The effect of substituents on phosphoryl bonding, described in
the previous section, can also be considered as a model for
environmental effects. In this model, a series of dipoles were
introduced intramolecularly and varied regularly; in enzymes,
the active site environment includes several dipolar, charged,
and hydrophobic groups; the sum of these interactions defines
the environment of the reactive group (see Implications for
Enzymatic Catalysis below).
more general changes in environment may contribute to our
fundamental understanding of these reactions, of the enzyme
active environment, and the ability of this environment to
provide transition-state stabilization via electrostatic interactions
(see Implications for Reactivity of Phosphoryl Compounds and
Implications for Enzymatic Catalysis below). In addition,
vibrational spectra and their response to substituents and
environmental changes provide incisive physical descriptions
of monosubstituted phosphoryl compounds that may provide
critical guides and decisive tests of future computational models.
Environmental Changes and Phosphoryl Group Bond-
ing: The Effect of DMSO on the Bridging P-O(R) Bond
Length. We have used the addition of DMSO as a cosolvent
to directly probe the effect of changes in the environment
surrounding the phosphoryl group on its bonding. This general
question is of particular importance for understanding enzymatic
catalysis, as enzymes create an idiosyncratic environment within
which catalysis takes place (see Introduction and Implications
for Enzymatic Catalysis below). DMSO was chosen because it
is compatible with IR and Raman spectroscopy and because
DMSO addition was previously shown to exert a large rate effect
on the hydrolysis of a phosphate ester, pNPP.19
Upon addition of DMSO, the P-O(R) bridging bond length-
ens for both pNPP and PP (Tables 3-5). The changes are small
()0.015 Å), but there is a steady trend as the amount of DMSO
cosolvent is increased.
Scheme 2 presents a crude model that can account for this
trend. Despite the high dielectric constant of DMSO solutions
Implications for Reactivity of Phosphoryl Compounds.
The phosphoryl substituents described in Scheme 1 that lengthen
(25) (a) Cole, T. W.; Mayers, C. J.; Stock, L. M. J. Am. Chem. Soc. 1974, 96,
4555. (b) Petti, M. A.; Shepodd, T. J.; Barrans, R. E.; Dougherty, D. A. J.
Am. Chem. Soc. 1988, 110, 6825. (c) Cozzi, F.; Cinquini, M.; Annunziata,
R.; Siegel, J. S. J. Am. Chem. Soc. 1993, 115, 5330.
(27) (a) Kolthoff, I. M.; Chantooni, M. K., Jr.; Bhowmik, S. J. Am. Chem. Soc.
1967, 90, 23. (b) Matthews, W. S.; Bares, J. E.; Bartmess, J. E.; Bordwell,
F. G.; Cornforth, F. J.; Drucker, G. E.; Margolin, Z.; McCallum, R. J.;
McCollum, G. J.; Vanier, N. R. J. Am. Chem. Soc. 1975, 97, 7006. (c)
Bordwell, F. G. Acc. Chem. Res. 1988, 21, 456.
(26) (a) K1/K2 ) 10(17.1-4.8) ) 1012.3; ∆∆G ) RTln(K1/K2) ) 16.8 kcal/mol (at
298 K).
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A R T I C L E S
Cheng et al.
Scheme 3
Scheme 5
the P-O(R) bridging bond increase the rate of breaking of that
bond in phosphoryl (-PO32-) transfer reactions (Scheme 3).
DMSO, which lengthens the P-O(R) bridging bond in pNPP
and PP, also increases the rate of phosphoryl transfer (Tables 3
and 4 and ref 19). Thus, bond length correlates with reaction
rate. Kirby, and more recently Hengge, suggested that the
increase in bond lengths might be the cause of the increased
reaction rates.23,19b More generally, it is important to ascertain,
for any correlation, whether there is a cause-effect relationship,
a common underlying causative feature, or simply a coincidence.
The following analyses suggest that the magnitude of the effects
on reactivity is much larger than can be accounted for by
weakening of the bridging bond. Instead, the data and correla-
tions are readily accounted for by a common underlying
mechanism based on stabilization of negative charge on the
bridging oxygen leaving group alkoxide or phenoxide ion. Such
effects can in certain cases be described solely by electrostatic
interaction energies.
lengthening is causative of the observed rate enhancement.
Consideration of the energetics of the substituent oxygen
interactions, however, leads to a different conclusion.
2-
In the transition state for transfer of the -PO3 group, the
bond to the leaving oxygen atom is nearly broken, as judged
by linear free-energy relationships, kinetic isotope effects, and
measurements of entropy and volume of activation (Scheme
3).20,21 Thus, a nearly full negative charge is expected to reside
on this oxygen atom in the transition state. Because of the large
increase in negative charge potential at the bridging oxygen
position in the transition state, the interaction energy with the
substituent dipole is expected to be much larger in the transition
state than in the ground state. Thus, the reaction rate will
increase for the same reason underlying the bond lengthening:
the electrostatic interaction energy (Schemes 1 and 4).
Scheme 4
Analogous considerations hold for the DMSO result (Scheme
5).28 As noted above, DMSO is less effective than water at
solvating localized negative charges. Thus, the free-energy
change for transfer of a phosphoryl group from water to DMSO
is unfavorable.29 In the transition state, charge is presumably
dispersed, relative to the ground state.21,30 This charge dispersal
can occur despite the increase in charge density on the leaving
group oxygen. A decrease in charge on the three nonbridging
oxygen atoms and the ability of the aromatic ring to partially
disperse charge accumulated on the bridging oxygen atom
presumably both contribute to the charge dispersal in the
transition state. Thus, the energy penalty for transfer of the
transition state from water to DMSO is expected to be less than
that for the ground state. That is, the weaker solvation of charge
on the phosphoryl oxygens by DMSO relative to water is
expected to both lengthen the P-O(R) bridging bond, as
described above (Scheme 2), and lower the free-energy barrier
for reaction. Apparently, the solvation differences between water
and DMSO, traceable to electrostatic interaction differences,
are responsible for both the longer P-O(R) bonds and the faster
reactions in DMSO.
Scheme 4 shows a free-energy-reaction coordinate diagram
for two phosphate esters that vary in reactivity because of a
substituent on the leaving group alcohol.28 As in Scheme 1
above, the substituent interacts energetically with the bridging
oxygen. We assume a (small) partial negative charge on this
oxygen atom so that the substituent dipole that lowers the
leaving group pKa would have a small favorable interaction in
the ground state; this would lower the free energy of compound
B relative to compound A, all other factors being equal. This is
represented by the slightly lower free-energy position for
compound B in Scheme 4. As described above (Scheme 1 and
Substituent Effects on Phosphoryl Group Bonding: Correlation
of the Bridging P-O(R) Bond Length with Substituent pKa),
the substituent dipole is expected to lengthen the P-O(R) bond,
as is observed; we therefore also depict compound B’s ground
state as further advanced along the reaction coordinate than
compound A’s ground state. It is this movement along the
reaction coordinate that led to the suggestion that bond
(29) The attached alkyl group of the phosphate ester is ignored in this treatment.
This is because the phosphate ester can vary in differential solubility in
water versus DMSO depending on the alkyl group used, but this alkyl chain
is, to a reasonable approximation, unchanged in going from the ground
state to the transition state. As we are focused on reactivity, we do not
consider this portion of the phosphate ester.
(28) The free-energy reaction profile is grossly simplified, with only one
coordinate depicting the reaction progress.
(30) (a) Herschlag, D.; Jencks, W. P. J. Am. Chem. Soc. 1989, 111, 7579. (b)
Westheimer, F. H. Chem. ReV. 1981, 81, 313.
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11304 J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002

Phosphoryl Bonding Probed by Vibrational Spectroscopy
A R T I C L E S
Scheme 6
It is notable, from Schemes 4 and 5, that in one case (the
substituent effect) both the ground state and the transition state
can be stabilized from the interaction of the substituent oxygen
with the dipole, but the transition state is stabilized more,
whereas in the other case (the DMSO effect) both the ground
state and the transition state can be destabilized because of the
addition of DMSO, but the ground state is destabilized more.
Another way of addressing the relationship between reactivity
and bond length is to consider the energetic perturbation of the
bridging bond over the correlation range for both the substituent
and the DMSO effect (Figure 6 and Table 3). The hydrolysis
rate is expected to change by ∼15 orders of magnitude over a
12 pKa unit range.31 This corresponds to a ∼20 kcal/mol
difference in the free energy of activation for the compounds
at the extremes of the pKa range. Ninety percent DMSO
increases the reaction rate of pNPP by 3‚104 fold (Table 3),
which corresponds to 6.2 kcal/mol of the free energy of
activation difference. The ∼0.04 Å difference in the ground-
state bond length of the P-O-(R) bond observed over the
leaving group pKa range or the ∼0.01 Å bond length change
observed for the water/DMSO study represents very small
distortions of the bridging bond in energetic terms. For example,
for a small distortion of the bridging P-O bond the change in
potential energy of the molecule is given by (1/2)‚k‚(R-Ro)2,
where k is the force constant and Ro is the bond length at
minimum energy. The force constant is calculated from the
frequency of the P-O stretch mode and the reduced mass of
this internal coordinate. Using k ) 334 N/m obtained from the
frequency of 733 cm-1 observed for pNPP in aqueous solution
(Table 5), a 0.04 and a 0.01 Å distortion (i.e., (R-Ro) yield a
potential energy change of 0.4 and 0.02 kcal/mol, respectively.
This is in general agreement with ab initio quantum mechanical
calculations which suggest that a 0.1 Å elongation of a bridging
P-O(R) bond corresponds to forces that bring to bear a stress
on the bond of only ∼1 kcal/mol.11 Thus, the energy change in
the barrier to reaction is much greater than the bond energy
difference in both correlations.
common driving force in both lengthening the P-O(R) bond
and in increasing the reaction rates.
Implications for Enzymatic Catalysis. Vibrational spectra
have been obtained for ligands of several enzymes, revealing
bonding properties within active site environments.33 The results
herein concerning bonding of phosphoryl compounds and their
solution reactivity have implications for enzymatic catalysis and
its mechanistic dissection. They underscore the potential of
vibrational spectroscopy for future investigation of enzymatic
phosphoryl transfer, as the P-O bond is highly sensitive to its
surroundings and can be well-characterized by vibrational
spectroscopy. The results herein also provide a series of
standards to gauge the behavior of phosphoryl compounds
within active sites and potentially to unravel catalytic contribu-
tions. Finally, the underlying origin of relationships between
ground-state bond distortions and reactivity described herein
has implications for understanding ground-state destabilization
in enzymatic catalysis. Each of these points is discussed briefly
below.
By definition enzymes are designed to provide preferential
stabilization of transition states relative to ground states; this is
simply the definition of catalysis according to transition-state
theory. For phosphoryl transfer, groups in and around the active
site, which create a positive potential at the position of the
leaving group oxygen atom, can stabilize the charge buildup
on this atom in the transition state (Scheme 6). The dipolar
substituents of the series of alkyl phosphates described above
provide a simplified model for this effect, showing that the
P-O(R) bond is affected by its environment (Scheme 1 and
Figure 5). Thus, the extent of perturbation of this bond may
provide a readout of the electrostatic environment within the
active site. As emphasized in the Introduction, this critical
catalytic feature is difficult to probe by traditional means.
Quantitating contributions from individual catalytic mecha-
nisms has been notoriously difficult in enzymology, in large
part because of the interdependence of active site interactions;
for example, mutating a residue that acts as a general base can
also affect the alignment of substrates in the active site. The
ability of vibrational spectroscopy to probe the electrostatic
environment of ligands within active sites without perturbing
those sites might ultimately allow quantitation of catalytic
contributions from preferential electrostatic interactions in the
transition state. Such approaches would compare vibrational
spectra of enzyme complexes to nonenzymatic standards that
relate rate effects to the local electrostatic environment deduced
via vibrational spectroscopy.
Finally, the relationship between bond length in the ground
state and reactivity can also be addressed by considering the
following thought experiment. There are cases of phosphoryl
transfer reactions with the same leaving group that involve
different amounts of bond cleavage in the transition state. This
is the case for reactions involving pyridine leaving groups, which
give Brønsted values âleaving
) -1.02 and -0.79 for
group
reactions with water and hydroxide ion, respectively.32 This
means that a fixed set of phosphoryl compounds with a fixed
set of ground-state bond lengths has different relative reaction
rates, depending on the nature of the nucleophile used in the
reaction. The ability to have different rate effects from a
common change in bond length indicates that the change in bond
length is not fully causative of the observed changes in
reactivity.
In summary, we suggest that the correlations between bond
lengths and reactivity are neither a coincidence nor indicative
of a causative relationship between bond length and reactivity.
Rather, the same electrostatic interaction energies provide a
(31) (a) On the basis of âleaving group ) -1.23 (see ref 31b). log k1/k2 ) -1.23‚
∆pKa ) -1.23‚(4.8-17.1) ) 15.1; ∆∆G ) RTln(k1/k2) ) 20.6 kcal/mol
(at 298 K). (b) Kirby, A. J.; Varvoglis, A. G. J. Am. Chem. Soc. 1967, 89,
415.
(33) For review, see: (a) Carey, P. R. J. Raman Spectrosc. 1998, 29, 7. (b)
Callender, R.; Deng, H. Annu. ReV. Biophys. Biomol. Struct. 1994, 23, 215.
(32) Herschlag, D.; Jencks, W. P. J. Am. Chem. Soc. 1989, 111, 7587.
9
J. AM. CHEM. SOC. VOL. 124, NO. 38, 2002 11305

A R T I C L E S
Cheng et al.
There has been much discussion in enzymology of substrate
destabilization and distortion and their possible roles in catalysis.
Minimally, the transition state must be preferentially stabilized
relative to the ground state, as noted above, and several
mechanisms of ground-state destabilization have been sug-
gested.34 A “mild” form of substrate destabilization may be
situations in which the enzyme picks out a minor conformer
from solution, i.e., a conformation that is not energetically
preferred, and stabilizes it at the active site because it is more
reactive. This is relatively straightforward when the conformers
are close in energy, as is often the case for bond rotations; for
example, rotations of amino acid conjugates about the pyridoxal-
amine bond results in preferential activation of different bonds.35
More severe forms of substrate destabilization have also been
discussed historically, including consideration of enzymes as
analogous to the ancient torture device, the “rack”.36 According
to this view, the enzyme would stretch the bond to be broken,
thereby activating it for reaction. Indeed, there is considerable
evidence for bond distortions of enzyme-bound species from
vibrational spectroscopy. Nevertheless, we suggest that these
distortions are not necessarily the “intent” of the enzyme in its
mission to facilitate catalysis, i.e., that these distortions are not
the cause of catalysis, just as we have suggested that the ground-
state bond distortions caused by substituents in the alkyl
phosphate series are not the cause of the observed rate effects.
Rather, we suggest that distortions may be the natural conse-
quence of placing substrates in environments designed to be
complementary to transition states. As for the model monosub-
stituted phosphates, the interactions from the surrounding
environment are the cause of both the ground-state physical
distortions and the transition-state energetic stabilization. The
extent of distortion in the ground state will reflect the stiffness
of the bonds in question and the nature of the surroundings,
properties that are of fundamental importance for understanding
reactivity and catalysis.
Acknowledgment. This work was supported by the David
and Lucille Packard Foundation Fellowship in Science and
Engineering (D.H.) and Grants from the National Institutes of
Health, GM35183 (R.C.) and GM64798 (D.H.) from the
Institute of General Medicine and CA69202 (Z-YZ) from the
Cancer Institute. IN-H is an American Heart Association
Predoctoral Fellow and gratefully acknowledges the support of
and scientific interactions with Doug Rees and members of his
laboratory. The authors thank members of the Herschlag
laboratory for comments on the manuscript.
(34) (a) Jencks, W. P. In AdVances in Enzymology and Related Areas of
Molecular Biology; Meister, A., Ed.; John Wiley & Sons: New York, 1975;
p 219. (b) Narlikar, G. J.; Gopalakrishnan, V.; McConnell, T. S.; Usman,
N.; Herschlag, D. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 3668. (c) Burke,
J. R.; Frey, P. A. Biochemistry 1993, 32, 13220.
(35) For review, see: Palcic, M. M.; Floss, H. G. In Vitamin B6 Pyridoxal
Phosphate; Dolphin, D., Poulson, R., Avramovic, O., Eds.; John Wiley &
Sons: New York, 1986; p 25.
(36) Lumry, R. AdV. Chem. Phys. 1971, 21, 567.
(37) Jencks, W. P.; Regenstein, J. Ionization Constants of Acids and Bases;
CRC: Cleveland, OH, 1976; p J187.
(38) Bourne, N.; Williams, A. J. Org. Chem. 1984, 49, 1200.
(39) Zhao, Y.; Zhang, Z.-Y. Biochemistry 1996, 35, 11797-11804.
(40) Murto, J. Acta Chem. Scand. 1964, 18, 1043-1053.
(41) Solomons, T. W. G. In Organic Chemistry; John Wiley & Sons: New
York, 1988; p 655.
(42) Guthrie, J. P.; Cullimore, P. A. Can. J. Chem. 1979, 57, 797.
(43) Sauers, C. K.; Jencks, W. P.; Broths, S. J. J. Am. Chem. Soc. 1975, 97,
5564.
JA026481Z
(44) (a) Trifluoroethyl phosphate was also an outlier in a previous linear free-
energy relationship of a series of alkyl phosphates (see ref 44b and
references therein). (b) O’Brien, P. J.; Herschlag, D. Biochemistry 2002,
41, 3207.
9
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