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 ABSTRACT 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 INTRODUCTION 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. 0 1996 WILEY-LISS, INC. 496 J. MAVRI AND H.J. VOGEL 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 chains. 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 497 PHOSPHOAMINO ACID ION PAIR FORMATION TABLE I. Ab Initio Calculated Energies and Distances for Divalent Anions Complex MEP2..MA EP2..MA PHEP2..MA MEP2..MG EP2..MG PHEP2..MG HFi6-3lG* AE (kcaVmol) -215.79 -213.09 -200.37 -196.75 - 194.22 -181.29 HF/6-31G* AE (BSSE) (kcal/mol) -211.38 -208.96 -196.49 -191.24 -188.80 -176.56 found. Semiempirical MO calculations were performed on a Silicon Graphics R4400 workstation. RESULTS 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*) -228.75 -225.09 -209.53 -209.27 -205.89 -191.12 HF/6-31G* Closest N-0 (A) 2.53,2.53 2.53,2.53 2.63,2.70 2.57,2.59 2.58,2.60 2.61,2.63 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 kcal/m01.~~ Moreover, -~~ 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 498 J. MAVRI AND H.J. VOGEL TABLE 11. Semiempirical Calculated Distances, Energies, and Free Energies for Divalent Anions PM3 AE (kcal/mol) -2 11.43 -210.27 - 190.2 -194.79 -193.69 - 176.4 Complex MEP2..MA EP2..MA PHEP2..MA MEP2..MG EP2..MG PHEP2..MG PM3 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. DISCUSSION 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 In 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 + (A) PM3-SM3 AG (assoc) (kcaVmol) -2.09 -3.87 -28.45 -0.36 -1.42 -28.01 PM3-SM3 Closest N-O (A) 2.65, 2.68 2.65, 2.69 2.66,2.69 2.78,2.78 2.78,2.78 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 499 PHOSPHOAMINO ACID ION PAIR FORMATION TABLE 111. Semiempirical Calculated Distances, Energies, and Free Energies for Monovalent Anions PM3 AE (kcal/mol) Linear MEPl..MA EPl..MA PHEPl..MA Bifurcated MEPl..MA EPl..MA PHEPl..MA Bidentate MEPl..MG EPl..MG PHEPl..MG - 104.33 PM3 Closest N-0 (A) PM3-SM3 AG (assoc.) (kcal/mol) PM3-SM3 Closest N-0 (A) -103.34 -98.42 2.65,3.07 2.65,3.04 2.66, 3.16 -4.84 -3.54 -0.40 2.77,3.22 2.77,3.19 2.76,3.26 102.39 -102.22 -92.68 2.63,2.63 2.63,2.64 2.65, 2.65 +6.05 i-5.73 + 8.71 2.73,2.74 2.72,2.72 2.76, 2.77 -96.22 -96.12 -88.02 2.70,2.71 2.70,2.71 2.72, 2.73 +3.55 + 3.72 + 5.93 2.80, 2.81 2.80, 2.80 2.83, 2.82 - n 0 A 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. 500 J. MAVRI AND H.J. VOGEL a 0, V A n B Fig. 2. Ab initio HFi6-31G’ calculated structures of (A) methyl-phosphate and methyl guanidinium; (B) phenyl-phosphate and methyl guanidinium. ACKNOWLEDGMENTS 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. REFERENCES 1. Graves, D., Wang, J., Martin, B. “Post- and Co-Translational Modification of Proteins.” Oxford: Oxford University Press, 1994. 2. Krebs, E.G. Protein phosphorylation and cellular regulation I (Nobel Lecture). Angew. Chem. Int. Ed. Engl. 32: 1122-1129,1993. 3. Fischer, E.H. Protein phosphorylation and cellular regulation I1 (Nobel Lecture). Aneew. Chem. Int. Ed. E n-d . 32:1130-1137, 1993. 4. Cohen, P. Signal integration a t the level of protein kinases, protein phosphatases and their substrates. Tr. Biochem. Sci. 17408-413, 1992. 5. Kemp, B.E., Pearson, R.B. Protein kinase recognition sequence motifs. Tr. Biochem. Sc. 15:342-346, 1990. 6. Kemp, B.E., Parker, M.W., Hu., S., Tiganis, T., House, C . Substrate and pseudosubstrate interactions with protein kinases: Determinants of specificity. Tr. Biochem. Sc. 19: 440-444, 1994. 7. Taylor, S.S., Radzio-Adzelm, E. Three protein kinase structures define a common motif. Structure 2:345-355, 1994. 8. Morgan, D.O., DeBondt, H.L. Protein kinase regulation: Insights from crystal structure analysis. Curr. Opin. Cell Biol. 6:239-246, 1994. 9. Barford, D., Flint, A.J., Tonks, N.K. Crystal structure of human protein tyrosine phosphatase 1B. Science 263: 1397-1404, 1994. I 10. Su, X.-D., Taddel, N., Stefani, M., Ramponi, G., Nordlund, P. The crystal structure of a low-molecular weight phosphotyrosine phosphatase. Nature 370575-578, 19XX. 11. Johnson, L.N., Barford, D. The effects of phosphorylation on the structure and function of proteins. Annu. Rev. Biophys. Biomol. Struct. 22:199-232, 1993. 12. Vogel, H.J. Phosphorus-31 NMR studies of phosphoproteins. Meth. Enzymol. 177:263-282, 1989. 13. Norbury, C., Nurse, P. Animal cell cycles and their control. Annu. Rev. Biochem. 61:441-470, 1993. 14. Hanks, S.K., Quinn, A.M. Protein kinase catalytic domain sequence database: Identification of conserved features of primary structure and classification of family members. Meth. Enzymol. 200:38-62, 1991. 15. Pawson, T., Gish, G.D. SH2 and SH3 domains: From structure to function. Cell 71:359-362, 1992. 16. Waksman, G., Kominos, D., Kuriyan, J. Crystal structure of the phosphotyrosine recognition domain SH2 of V-src complexed with tyrosine-phosphorylated peptides. Science 358:646-653,1992. 17. Overduin, M., Rios, C.B., Mayer, B.J., Baltimore, D., Cowburn, D. Three-dimensional solution structure of the src homology 2 domain of c-abl. Cell 70:697-704, 1992. 18. Waksman, G., Shoelson, S.E., Pant, N., Cowburn, D., Kuriyan, J. Binding of a high affinity phosphotyrosyl peptide to the src SH2 domain: Crystal structures of the complexed and peptide free forms. Cell 72:779-790, 1993. 19. Mavri, J., Vogel, H.J. Ion pair formation involving methylated lysine side chains: A theoretical study. Proteins 18: 381-389, 1994. 20. Deerfield, D.W., Nicholas, H.B., Hiskey, R.G., Pedersen, L.G. Salt or ion bridges in biological systems: A study employing quantum and molecular mechanics. Proteins 6:168-192, 1989. 21. Deerfield, D.W., Fox, D.J., Head-Gordon, M., Hiskey, R.G., Pedersen, L.G. The first solvation shell of magnesium ion in a model protein environment with formate, water, X-NH,, H,S, imidazole, formaldehyde and chloride as ligands: An a b initio study. Proteins 21:244-255, 1995. 22. Caldwell, J.W., Kollman, P.A. Cation-rn interactions: Nonadditive effects are critical in their accurate representation. J . Am. Chem. SOC.117:4177-4178, 1995. 23. Gresh, N., Pullman, B. A theoretical study of the interaction of ammonium and guanidium ions with the phosphodiester linkage. Theor. Chim. Acta (Berl). 52:67-73,1979. 24. Salunke, D.M., Vijayan, M. Specific interactions involving guanidyl group observed in crystal structures. Int. J . Pept. Protein Res. 18:348-351, 1981. 25. Alagona, G., Ghio, C., Kollman, P. Bifurcated vs. linear hydrogen bonds: Dimethyl phosphate and formate anion interactions with water. J . Am. Chem. SOC.10552265230, 1983. PHOSPHOAMINO ACID ION PAIR FORMATION 26. Prasad, C.V., Pack, G.R. Theoretical study of phosphate interaction with NH,', with Na' and with Mg2+ in the presence of water. J. Am. Chem. SOC. 1068079-8086, 1984. 27. Sapse, A.M., Russell, C.S. Ab initio calculations of guanidinium-carboxylate interaction. Int. J. Quant. Chem. 26: 91-99, 1984. 28. Frisch, M.J., et al. Gaussian 92/DFT, Revision G.l. Pittsburgh: Gaussian, Inc., 1993. 29. Saint Martin, H., Otega-Blake, I., Lez, A., Adamowitz, L. Ab initio calculations of the pyrophosphate hydrolysis reaction. Biochim. Biophys. Acta. 1080:205-214, 1991. 30. Colvin, M.E., Evleth, E., Akacem, Y. Quantum chemical studies of pyrophosphate hydrolysis. J. Am. Chem. SOC. 117:4357-4362, 1995. 31. Becke. A.D. Densitv-functional thermochemistrv. The role of exact exchange. 2. Chem. Phys. 98:5648-56$2, 1993. 32. Lee, C., Yang, W., Parr, R.G. Development of the ColleSalvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B. 37:785-789, 1988. 33. Cramer, C.J., Lynch, G.C., Hawkins, G.D., Truhlar, D.G. AMSOL 4.0, QCPE 606, QCPE Bull. 13:78, 1993. 34. Tomasi, J., Persico, M. Molecular interactions in solution: An overview of methods based on continuous distributions of the solvent. Chem. Rev. 94:2027-2094, 1994. 35. Cramer, C.J., Truhlar, D.G. General parametrized SCF model for free energies of solvation in aqueous solution. J. Am. Chem. SOC.113:8305-8311, 1991. 36. Cramer. C.J.. Truhlar. D.G. An SCF solvation model for the- hvdroohobic of aaue., - -r - - - - effect 'and absolute free energies ous solvation. Science 256213-217, 1992. 37. Cramer, C.J., Truhlar, D.G. AM1-SM2 and PM3-SM3 parametrized SCF solvation models for free energies in aqueous solution. J . Comp. Aid Molec. Des. 6629-666, 1992. 38. Hehre, W.J., Radom, L., Schleyer, P. von R., Pople, J.A. Ab initio molecular orbital theory. New York: Wiley, 1986. 39. Ziegler, T. Approximate density functional theory as a 40. 41. 42. 43. 44. 45. 46. 47. 48. _I 49. 501 practical tool in molecular energetics and dynamics. Chem. Rev. 91:651-667,1991. Stanton, R.V., Merz, K.M., J r . Density functional study of symmetric proton transfers. J. Chem. Phys. 101:66586665, 1994. Ruiz, E., Salahub, D.R., Vela, A. Defining the domain of density functionals: Charge transfer complexes. J . Am. 117:1141-1141, 1995. Chem. SOC. Kieninger, M., Suhai, S. Density functional studies on hydrogen-bonded complexes. Int. J . Quantum. Chem. 52: 465-478, 1994. Vogel, H.J., Bridger, W.A. Phosphorus-31 NMR pH-titration experiments of the phosphoproteins tropomyosin and glycogen phosphorylase. Can. J . Biochem. 61:363-369, 1983. Rose, G.D., Wolfenden, R. Hydrogen bonding, hydrophobicity, packing and protein folding. Annu. Rev. Biophys. Biomol. Str. 22381-415, 1993. Anderson, D.E., Becktel, W.J., Dahlquist, W.F. pH-induced denaturation of proteins: A single salt bridge contributes 3-5 kcal/mol to the free energy of folding of T, lysozyme. Biochemistry 29:2403-2408, 1990. Stewart, J.A. MOPAC: A semiempirical molecular orbital program. J . Comp. Aided Molec. Design. 4:l-104, 1990. Alkorta, I., Villar, H.O., Perez, J.J. Comparison of methods to estimate the free energy of solvation. J . Comp. Chem. 14:620-626,1993. Thorsness, P.E., Koshland, D.E., J r . Inactivation of isocitrate dehydrogenase by phosphorylation is mediated by the negative charge of the phosphate. J. Biol. Chem. 262 10422-10425,1987. Marcus, F., Rittenhouse, J., Moberly, L., Edelstein, I., Hiller, E., Rogers, D.T. Yeast fructose-1,6-bisphosphatase; properties of phospho- and dephospho-forms and two mutants in which serine l l has been changed by site-directed mutagenesis. J. Biol. Chem. 263:6058-6062, 1988.