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PROTEINS: Structure, Function, and Genetics 24495-501 (1996)
Ion Pair Formation of Phosphorylated Amino Acids
and Lysine and Arginine Side Chains:
A Theoretical Study
Janez Mavri' and Hans J. Vogel'
IBIOSON Research Institute, Department of Biophysical Chemistry, University of Groningen, 9747 AG Groningen,
the Netherlands; 2Department of Biological Sciences, University of Calgary, Calgary T2N 1N4, Canada
Protein phosphorylation is
one of the major signal transduction mechanisms for controlling and regulating intracellular processes. Phosphorylation of specific hydroxylated amino acid side chains (Ser, Thr,
Tyr) by protein kinases can activate numerous
enzymes; this effect can be reversed by the action of protein phosphatases. Here we report a b
initio (HF/6-31G*and Becke3LYP/6-31G*)and
semiempirical (PM3) molecular orbital calculations pertinent to the ion pair formation of the
phosphorylated amino acids with the basic side
chains of Lys and Arg. Methyl-, ethyl-, and phenylphosphate, as well as methylamine and methylguanidinium were used as model compounds
for the phosphorylated and basic amino acids,
respectively. Phosphorylated amino acids were
calculated as mono- and divalent anions. Our
results indicate that the PSerlPThr ion pair interaction energies are stronger than those with
PTyr. Moreover, the interaction energies with
the amino group of Lys are generally more favorable than with the guanidinium group of
Arg. The Lys amino groups form stable bifurcated hydrogen bonded structures; while the
Arg guanidinium group can form a bidentate
hydrogen bonded structure. Reasonable values
for the interaction free energies in aqueous solution were obtained for some complexes by the
inclusion of a solvent reaction field in the computation (PM3-SM3). o 1996 Wiley-Liss, Inc.
Key words: ab initio calculations, density functional theory, semiempirical calculations, solvent reaction field,
phosphoserine, phosphothreonine,
phosphotyrosine, hydrogen bonding
to a protein could control the activity of glycogendegrading enzyme^.^.^ It is now known that phosphorylation of hydroxyl groups of specific amino acid
sidechains by protein kinases can give rise to controlled activation of a multitude of important enzymes and proteins. The subsequent inactivation of
these systems requires the removal of the phosphate
group, a reaction catalyzedby protein phosphatases.
The activity of the protein kinases and phosphatases
is controlled by hormones, secondary messenger
pathways, e t ~Protein
. ~
kinases can be divided in a
range of classes, which all have their unique group
of target enzymes; they recognize short specific
amino acid sequences adjacent to the site of phosph~rylation.~,~
Recently the three-dimensional
structures of protein kinases7,' and protein phosp h a t a s e ~involved
~ ~ ~ ~ in signal transduction have
been elucidated by X-ray crystallography. As a result, significant progress has been made in our understanding of the mode of substrate recognition,
and the regulation of protein phosphorylation
events. However, since only few structural studies
for proteins in their phospho- and dephospho-forms
have been reported to date, our knowledge regarding the activating or inhibitory effects on the overall
enzyme structure is limited.',12 This is particularly
the case for Ser/Thr-phosphorylatedenzymes,which
make up a class of proteins that is distinct from the
Tyr-phosphorylatedproteins. The former are mainly
present in the intracellular milieu, while the latter
are primarily-but
not exclusively-transmembrane proteins.l3,I4Phosphorylation of Ser/Thr sites
Abbreviations: EP1, monoanionic ethyl phosphate; EP2, dianionic ethyl phosphate; MEPUB, methyl phosphate; PEPUP,
phenylphosphate; MA, methylamine; MG, methylguanidium;
BSSE, basis set superposition error; pmf, potential of mean
force; PSer, phosphoserine; PThr, phosphothreonine; PTyr,
phosphotyrosine; HF, Hartree Fock; DFT, density functional
theory; MO, molecular orbital.
Post- or cotranslational modification of proteins
provides for an important extension of the genetic
code.' Of the many different modifications that have
been found to date, protein phosphorylation is perhaps the most widespread. It was realized almost 50
years ago that the covalent attachment of phosphate
Received July 7, 1995; revision accepted October 26, 1995.
Address reprint requests to Hans J . Vogel, Department of
Biological Sciences, University of Calgary, 2500 University
Drive N.W., Calgary T2N 1N4, Canada.
Janez Mavri's permanent address is National Institute of
Chemistry, P.O. Box 30, Hajdrihova 19, 61115, Ljubljana, Slovenia.
generally constitutes an on-off switch for enzyme activity.",14 In contrast, most of the phospho Tyr residues function as recognition sites for the binding of
so-called SH2 domains (src-homology)of various enz y m e ~ , ' ~ -thus
' ~ resulting in a localization of these
proteins to membrane sites. In spite of the functional differences of PSerIPThr and PTyr it is clear
that the dianionic phosphomonoester groups often
interact with the side chains of the basic amino acids Arg and Lys. This has prompted us to embark
on detailed studies concerning the interaction between basic and phosphorylated amino acid side
In this contribution we have used theoretical calculations to study the interactions of the phosphomonoester groups of the negatively charged
phosphorylated amino acid side chains, with the positively charged amino or guanidium groups of the
basic amino acids. We have shown earlier that this
computational approach can provide valuable information regarding the salt linkage formation of posttranslationally modified amino acid sidechains.lg
Moreover, similar calculations are also used t o explore amino acid side chain cation interactions.20-22
Our calculations were performed on the model compounds methyl-, ethyl- and phenylphosphate, to approximate PSerIPThr and PTyr residues, respectively. We have focused primarily on the dianions,
as this form would be predominantly present in
vivo.12 However, because the second pKa of the
phosphomonoester group is close to the physiologically relevant pH-range," we have also performed
some calculations for the monovalent anions. As
monovalent cations that are representative for the
basic amino acids, we have used methylamine and
methylguanidinum; these two cations have been
used extensively in previous theoretical studies of
ion pair formation with formate and acetate (Glu
and Asp side chains) and dimethyl phosphate (DNA
backbone and membrane phospholipids).'9~20~23-27
Reasonable starting structures for our calculations
were taken from the latter studies. Ab initio calculations were performed on the Hartree Fock (HF)
level using the 6-31G* basis set.28Ab initio computations of (multiple) anions can in principle be improved by addition of diffuse basis functions, however recent calculations have shown that such
larger basis sets do not significantly improve the
outcome of calculations for orthophosphates.20~2g~30
In addition, we performed single point calculations
using the nonlocal density functional theory approach on the Becke 3LYP
Furthermore, parallel semiempirical calculations were performed on the PM3
Since the interaction
energies between the various mono- and divalent
ions considered here would be very sensitive to the
surrounding solvent,34we have also performed calculations with a solvent reaction field using PM3SM3.35-37
Computational Methods
Molecular orbital (MO) calculations were performed using the approach of supermolecules, i.e.,
the interaction energy is calculated as the total energy of the complex minus the energy of both individual ions. Ions were geometry optimized in vacuo.
Because of the high computational demands for a full
geometry optimization of the complex, rigid monomers were used during the optimization. In order to
prevent migration of protons in the complexes, N-H
distances were constrained a t their monomer values,
during the in vacuo optimizations; this ion-pair resembles the situation in polar media. In this fashion
the interaction energy component originating from
the distortion of the geometry is lost. Since the main
objective of this work is to study the trends in the
interaction energy for a series of related ions, we
assume that this component is transferable and does
not effect the overall trend. Ab initio calculations
were performed using the Gaussian-92" suite of programs implemented on a Convex 3860 computer. The
6-31G* basis set was used a t the Hartree-Fock level
of theory. This double-zetabasis set, augmented with
polarization functions on heavy atoms, is relatively
flexible and offers a compromise between the reliability of the results and the length of the computations. Basis set superposition errors were calculated
by the counterpoise method.38 Since the size of the
systems precludes the application of configurational
interaction or even Moller-Plesset perturbational approaches, we performed instead density functional
theory (DFT) Becke3LYP/6-31G* calculations32233
using the HF/6-31G*geometries. For a review of DFT
methods, see Ziegler.39In this fashion at least part of
the dispersion energy is taken into account. Recent
c a l c ~ l a t i o nhave
s ~ ~ shown that the inclusion of nonlocal corrections into DFT calculations is essential
for the evaluation of the energetics of intermolecular
and intramolecular processes.
Semiempirical MO calculations were performed
on the PM3
In order to be consistent with
the ab initio calculations, the same procedure for
geometry optimizations was applied. In addition,
calculations of complexes involving single charged
anions with methylammonium and methylguanidinium, respectively, were performed. A solvent reaction field was included in the calculations a t the
semiempirical MO level using the PM3-SM3 method
of Cramer and T r ~ h l a r . Through
3 ~ ~ ~ ~the inclusion
of the solvent reaction field, the energy surface acquires the meaning of the free energy hypersurface.
The program AMSOL 3.433 was used throughout.
Complete geometry optimizations with the solvent
reaction field is very time consuming owing to the
fact that analytical gradients are not available.
Therefore, we retained the inter-ion orientations
from the in vacuo calculations and varied the interionic distance until a free energy minimum was
TABLE I. Ab Initio Calculated Energies and Distances for Divalent Anions
AE (kcaVmol)
- 194.22
AE (BSSE) (kcal/mol)
found. Semiempirical MO calculations were performed on a Silicon Graphics R4400 workstation.
Complexes With Double Charged Phosphates
The interaction energies calculated ab initio for
the basic side chain analogs and the phosphorylated
compounds are collected in Table I. The HF/6-31G*
as well as the Becke3LYP/6-3lg* calculations predict the MEP2-MA complex to be the most stable,
while the PHEPB-MA complex appears to be the
least stable. The BSSE corrected values clearly show
the same trend. The BSSE correction reduces the
interaction energies by about 5 kcaymol; this relatively small BSSE error indicates that the applied
basis set is flexible enough to describe the interaction energy properly. Relative to the Hartree-Fock
values, the DFT calculations predict interaction energies that are more favorable. This additional stabilization can be interpreted as (part of the) dispersion energy which is taken into account in the DFT
calculation. However, it should be noted that Ruiz et
al.41 have shown that DFT calculations can overestimate interaction energies, in situations where
charge transfer can take place. Also, other corrections may have to be considered for such hydrogenbonded system^.^'
The semiempirical PM3 calculations of complexes
involving MA show the same trend as the ab initio
values (see Table 11).The only exception is that the
difference in the interaction energies between the
MEP2-MA and EP2-MA complexes is significantly
decreased relative to their ab initio values. Again,
the predicted interaction energy is the most favorable for the complex involving MEPB and least favorable for the PHEP2 complex. Stabilization energies of the complexes involving MG are less
favorable relative to their MA analogs. This is found
in the ab initio as well as the PM3 calculations. A
simple explanation for the weaker MG complexes
relative to the MA complexes is that in MG the
charge is more dispersed, while the minimal distance between the ions is about the same.
Our calculations indicate that the complexes involving double charged negative phosphate ions
form stable structures with bifurcated hydrogen
bonds with MA, and give a bidentate hydrogen
Becke 3LYP/6-31G*
HF/6-31GAE (kcal/mol*)
Closest N-0 (A)
bonding pattern with MG (see Figs. 1 and 2). The
strength of the complexation for both series is reflected in the length of the hydrogen bonds. From
Table I it is evident that a t all levels of theory, with
increasing strength of the interaction, the hydrogen
bonds are also shortening.
In order to take into account the effect of the polarizable aqueous environment, calculations were
also performed on the PM3-SM3 level. The results
are collected in Table 11. In contrast to the in vacuo
calculations, the interaction free energy is the most
favorable for both complexes involving the PHEP2
ions, while least favorable for the MEPB ions. The
values obtained for the PHEPB ions seems unrealistic, however.
It is worthwhile to emphasize that the free energy
associated with the EPP-MA formation approaches
experimental, by determined values of -3 to -5
the potential of mean force
was determined for the association of EP2 and MA,
by calculating the interaction free energies along a
fixed line. It clearly indicates a contact ion pair minimum and a solvent separated ion pair minimum.
Unfortunately it does not level off at large ion separation, but tends rather toward -3 kcaUmo1. A finite interaction free energy at large ion separation
is unusual, however it was also found in the system
H,O + H + + OH- (data not shown) and points to
problems in the computational methodology. We
would like t o emphasize that calculations of the potential of mean force for associatioddissociation reactions of ions is very demanding for the solvent
reaction field calculations, since the process requires
compensation of the interaction energy between the
ions with the solvation free energies. Moreover, during the separation process additional errors can be
i n t r ~ d u c e d Proper
treatment of the free energy
differences associated with the complex formation
would require treatment of the environment into
atomic details and thermal averaging using MonteCarlo or Molecular Dynamics methods.
Complexes With Single Charged Phosphates
Encouraged by the good correlation observed between the ab initio and PM3 results for the double
charged ions, a series of calculations for single
TABLE 11. Semiempirical Calculated Distances, Energies, and Free Energies for Divalent Anions
AE (kcal/mol)
-2 11.43
- 190.2
- 176.4
Closest N-0
2.54, 2.54
2.54, 2.54
2.57, 2.57
2.61, 2.62
2.61, 2.62
2.64, 2.65
charged ions were performed on the PM3 level. The
outcome of these computations is presented in Table
111. The interaction energies for the complexes with
MA and MG become less favorable by increasing the
side chain size. In contrast to double charged complexes, the single charged anion-MA complexes did
not exhibit the bifurcated hydrogen bonded complex
as a global minimum, but rather a linear one that
is somewhat more stable. For the complexes involving the PHEP1, this difference is even more pronounced.
A number of theoretical studies have shown that
monoanions such as formate and dimethyl phosphate preferentially form bifurcated hydrogen
bonded structures, when they interact with water,
NH, +, CH3-NH,
or CH,-CH,-NH,+
molec u l e ~ . ~ ~ Our
* ~ results
~ . ~ ~show
* ~that
~ - the
~ ~dianionic phospho species also have a clear minimum for
such bifurcated species, when they interact with
methylamine. Obviously the N-0 hydrogen bond
length is virtually identical for both charged oxygens of the phosphoryl groups (see Tables I and 111,
for all three phosphocompounds tested; in addition,
the results of the ab initio and semiempirical calculations were consistent in this respect. It should be
noted, however, that a t the semiempirical PM3
level, the monoanionic phosphorylated compounds
display a slight preference (-1 kcal) for a linear
structure with a single hydrogen bond, over a bifurcated structure with two hydrogen bonds. We consider this particular outcome less meaningful, since
various earlier higher level ab initio calculations
have shown that the bifurcated structure is slightly
more favorable for such an ion pair.19,20,23,25,26
fact, early lower level ab initio calculations had also
indicated a linear single hydrogen bonded struct ~ r e . ’We
~ therefore feel that this result may be explained by a not completely correct parametrization
of phosphorus in PM3. It has also been noted in earlier work that unrealistic solvation free energies associated with phosphates originate from the predicted charge distribution; however PM3 behaves
better than AM1 in this r e s p e ~ t ? ~ , Neverthe~~,*~
less, in the bimolecular complexes studied here, the
AG (assoc) (kcaVmol)
Closest N-O
2.65, 2.68
2.65, 2.69
2.78, 2.78
phosphate is more “buried than in the earlier calc u l a t i o n ~ ,and
~ ~thus
, ~ ~charge anomalies should influence our results less.
In the case of methylguanidinium and monoanions, it is well known that bidentate ion pair structures with two hydrogen bonds are preferred over
ones with a linear single hydrogen bond.20,23,27
Generally the structure involving the ENH and one of
the oNH, groups of the Arg side chain appears to be
the most stable. This orientation is also the predominant form found in crystal structures of phosphodiesters and methylguanidinium groups.24 A clear
minimum could be found for all our calculations irrespective of the level of the calculation, the phosphospecies, or its charge (see Tables 1-111). Thus, the
structures indicated in Figure 2 clearly depict the
preferred bidentate complexes, both for complexes
with the dianionic and monoanionic phospho-compounds.
Methyl-, ethyl- and phenyl-phosphate were used
here as computationally-manageable model systems
for SerP, ThrP, and TyrP, respectively. For all vacuo
calculations we found a clear trend where the interaction energy was most favorable for SerP and least
favorable for TyrP. This result was the same with
Lys or Arg as the positively charged partner in the
ion pair. Moreover, calculations at the density functional theory level, which take into account the nonlocal corrections, also showed the same trend. Our
data also show that interactions with Lys are generally stronger than with Arg. This effect is related
to the charge distribution difference for the two cations, in methylamine and Lys it more closely resembles a point charge resulting in higher electrostatic
attractions. However, given the preference for dual
hydrogen bond formation with methylguanidinium
and Arg, for example, the latter residues have a
greater capacity to orient a substrate in the active
site of a n enzyme. Both Lys and Arg residues will
therefore be important in proteinlenzyme action.
The calculations performed with a solvent reaction field can give some idea about the energetics of
ion pair interactions in an aqueous environment.
Our results indicate that reasonable values are only
obtained for the SerP and ThrP compounds. Interaction free energies of AG = - 1to -5 kcal are quite
TABLE 111. Semiempirical Calculated Distances, Energies, and Free Energies for Monovalent Anions
AE (kcal/mol)
- 104.33
Closest N-0
AG (assoc.)
Closest N-0 (A)
2.66, 3.16
2.65, 2.65
+ 8.71
2.76, 2.77
2.72, 2.73
+ 3.72
+ 5.93
2.80, 2.81
2.80, 2.80
2.83, 2.82
Fig. 1. Ab initio HF/6-31G8calculated structures of (A) ethyl-phosphateand methylamine; (B) phenyl-phosphateand methylamine.
Given the
reasonable values for such ion
complexity of such calculations, and the high demands on accuracy, it is encouraging that the PM3SM3 method gives quite a few reasonable values for
the free energy of interaction. However, the positive
AG values for some Arg complexes, and the strongly
negative values obtained for TyrP complexes are unrealistic, and show that there is room for further fine
tuning of the PM3-SM3 method.35-37,47For example, specific interactions like hydrogen bonding are
not well described by the continuum model; moreover complications arising from the parameters describing the cavity size can contribute to a n erroneous outcome.34 Be that as it may, the solvent
reaction field approach of Cramer and Truhlar has
been rather successful compared to other available
method^^^-^^ at obtaining reasonable values for the
interaction free energies and the potential of mean
force in aqueous solution.
The preferred ion pair interactions observed for
the dianionic species appear to be maintained in the
monoanionic species, This means that a reduction in
the intracellular pH, as can be found in cancer cells,
anoxic cells, or actively contracting muscle cells, is
unlikely to lead to a disruption of ion pairs involving
phosphorylated amino acids. Therefore, it is perhaps
not surprising that substitution of Asp or Glu for
SerP by molecular biology methods has been successful at mimicking the effects of stable protein
phosphorylation in many instance^.^^.^^
Finally, we would like to point out that the model
systems studied here not only provide information
about protein phosphorylation, but our results are
also directly applicable to phosphorylated glycolytic
metabolites, or binding of coenzymes such as
NADPH and coenzyme A to basic sites in the active
sites of enzymes, because dianionic phosphomonoester groups, similar to SerP, also play a major
role in the recognition and high affinity binding of
these compounds.
Fig. 2. Ab initio HFi6-31G’ calculated structures of (A) methyl-phosphate and methyl guanidinium; (B) phenyl-phosphate and methyl
This work was supported by a grant from the Alberta Heart and Stroke Foundation. H.J.V. is supported by the Alberta Heritage Foundation for Medical Research. J.M. is grateful for a long-term
fellowship from the Human Frontier Science Program and to Dr. H.J. Berendsen at the University of
Groningen for the hospitality during his stay in the
Netherlands. Support through a NATO travel grant
is gratefully acknowledged. The authors are grateful to the Supercomputer Center a t the Institute
Jozef Stefan, Ljubljana, for allocated computer time.
We are indebted to Dr. T. Ziegler (University of Calgary) for his critical reading of the manuscript. We
appreciate the help of S. Stauffer in the processing of
the manuscript.
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