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J. Phys. Chem. B 2007, 111, 8242-8249

A Preference for Edgewise Interactions between Aromatic Rings and Carboxylate Anions: The Biological Relevance of Anion-Quadrupole Interactions Michael R. Jackson,† Robert Beahm,† Suman Duvvuru,‡ Chandrasegara Narasimhan,‡ Jun Wu,‡ Hsin-Neng Wang,‡ Vivek M. Philip,‡ Robert J. Hinde,§ and Elizabeth E. Howell*,†,‡ Department of Biochemistry, Cellular, and Molecular Biology, UniVersity of Tennessee, KnoxVille, Tennessee 37996-0840, Genome Science and Technology Program, UniVersity of Tennessees Oak Ridge National Laboratory, 1060 Commerce Park, Oak Ridge, Tennessee 37830-8026, and Department of Chemistry, UniVersity of Tennessee, KnoxVille, Tennessee 37996-1600 ReceiVed: September 21, 2006; In Final Form: May 1, 2007

Noncovalent interactions are quite important in biological structure-function relationships. To study the pairwise interaction of aromatic amino acids (phenylalanine, tyrosine, tryptophan) with anionic amino acids (aspartic and glutamic acids), small molecule mimics (benzene, phenol or indole interacting with formate) were used at the MP2 level of theory. The overall energy associated with an anion-quadrupole interaction is substantial (-9.5 kcal/mol for a benzene-formate planar dimer at van der Waals contact distance), indicating the electropositive ring edge of an aromatic group can interact with an anion. Deconvolution of the longrange coplanar interaction energy into fractional contributions from charge-quadrupole interactions, higherorder electrostatic interactions, and polarization terms was achieved. The charge-quadrupole term contributes between 30 to 45% of the total MP2 benzene-formate interaction; most of the rest of the interaction arises from polarization contributions. Additional studies of the Protein Data Bank (PDB Select) show that nearly planar aromatic-anionic amino acid pairs occur more often than expected from a random angular distribution, while axial aromatic-anionic pairs occur less often than expected; this demonstrates the biological relevance of the anion-quadrupole interaction. While water may mitigate the strength of these interactions, they may be numerous in a typical protein structure, so their cumulative effect could be substantial.

1. Introduction Noncovalent interactions, such as ionic interactions, hydrogen bonds, hydrophobic interactions, and dispersion forces play a central role in biological structure-function relationships. Both intra- and intermolecular interactions can have noncovalent components. Protein folding is an example of an intramolecular interaction, while ligand binding and protein association are examples of intermolecular interactions. Recent studies suggest that other types of noncovalent interactions may also play a role in folding and binding. For example, Dougherty1,2 has proposed that a cation-π interaction occurs between the negative face of aromatic groups (i.e., π clouds) and the positively charged amino acids lysine and arginine; molecular mechanics studies using the OPLS force field suggest that the electrostatic component of this cation-π interaction may contribute 2-3 kcal/mol of stabilization energy (in solution) to these close contacts.3 Ligand binding also can involve cation-π interactions.4 Two other types of weak interactions that may be important in folding and binding involve CH-π and CH-O contacts.5-7 In these interactions, a -CH group forms a weak hydrogen bond with the face of an aromatic ring or a backbone oxygen, respectively. Recent calculations also predict stacked amino acids, particularly involving phenylalanine, could be * Corresponding author. Tel: 865-974-4507. Fax: 865-974-6306. E-mail: [email protected]. † Department of Biochemistry, Cellular, & Molecular Biology, University of Tennessee. ‡ Genome Science and Technology Program, University of Tennessees Oak Ridge National Laboratory. § Department of Chemistry, University of Tennessee.

important.8,9 While these interactions are weak, they may be numerous in a typical protein structure, so their overall effect may be substantial. An additional noncovalent interaction that may be relevant for biochemical systems is that between negatively charged amino acid sidechains and the positively charged ring edge of aromatic groups. The positive charge on the ring edge of these groups is associated with the quadrupole moment of the aromatic ring, so this interaction can be termed an anion-quadrupole interaction. The notion of such an interaction may seem provocative, because at first glance it involves an interaction between an electron-donating anion and an aromatic π cloud. However the quadrupolar charge distribution of the aromatic group gives points near the ring edge a positive electrostatic potential and points above and below the ring a negative electrostatic potential.1 Anions might thus interact favorably with the ring edge. Previous studies of anion-quadrupole interactions have typically focused on electron-deficient π rings by incorporating strong electron-withdrawing substituents and include theoretical predictions of binding energies in fluorobenzene derivatives, fluoro-s-triazine, and tetrafluoroethene as well as other molecules possessing a π system.10-22 Experimental evidence for “anion-π” interactions includes spectroscopic, NMR and crystallographic data of anion binding sites in electron deficient aromatics and host-guest molecular complexes, as well as other compounds found by screening the Cambridge Structural Database.23-27 Examples of anion-quadrupole interactions in biology are less clear. However Thomas et al. found a preference for oxygen atoms (predominately carbonyl oxygens) to occur at the ring

10.1021/jp0661995 CCC: $37.00 © 2007 American Chemical Society Published on Web 06/20/2007

Anion-Quadrupole Interactions in Proteins? edge of phenylalanines.28 Burley and Petsko found possible examples of oxygen and sulfur interactions with aromatic ring edges, both within proteins and between proteins and ligands.29 Biological cysteine-arene interactions show three geometrical preferences, one of which is an edgewise binding configuration.30,31 Also, a statistical preference for an edgewise interaction between aromatic rings and Asp or Glu residues has already been noted in the Atlas of Protein Side chain Interactions,32 although no interpretation has been presented (see also http:// www.biochem.ucl.ac.uk/bsm/sidechains/). Studies by Kallenbach et al.33-35 using short R-helical peptides with glutamatephenylalanine pairs positioned at i and i + 4 spacing indicate this pair provides additional stability (roughly 0.5 kcal/mol) to the helix. Recently, Jouglin et al. found that tryptophan and tyrosine (as well as histidine and arginine) residues show the most enrichment at phosphoresidue binding sites.36 These various observations, as well as our own docking results between R67 dihydrofolate reductase and reduced nicotinamide mononucleotide37 led us to investigate the notion of anion-quadrupole interactions in proteins. Possible manifestations of these interactions include close contacts between the carboxylate side chains of glutamate or aspartate residues and the ring edges of phenylalanine, tyrosine, or tryptophan. Anion-quadrupole interactions may also play a role in ligandprotein binding; possible examples of this include aromatic protein groups interacting with phosphate groups (in NADPH, NADH, ATP, ADP, cyclic AMP, RNA, and DNA, for example) as well as interactions between amino acids with negatively charged side chains (Asp and Glu) and aromatic ligand groups such as the bases of DNA, the oxidized nicotinamide ring, and the fully oxidized pteridine ring of folate, among others. In this research, we have used quantum chemical calculations to compute the interaction energy associated with close contacts between benzene and the formate anion; these two species serve as small molecule mimics of the aromatic amino acid phenylalanine and the anionic residues aspartate and glutamate. The interaction energies were computed for several different pair geometries at both the Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels of theory using the aug-cc-pVDZ atom-centered basis set. Strategies were devised for extracting those contributions to the interaction energy that can be attributed to electrostatic and polarization contributions. Finally, analysis of high-resolution, non-redundant crystal structures from the PDB Select38,39 showed a preference for the phenylalanine ring edge to interact with the carboxylate group of Asp or Glu. Our calculations suggest that this preference is driven in part by favorable anion-quadrupole interactions and polarization interactions associated with this binding motif. 2. Materials and Methods Unless otherwise stated, the quantum chemical calculations reported here were performed using Gaussian 98 or Gaussian 0340 at the Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels of theory. The aug-cc-pVDZ atom-centered basis set was employed in all calculations;41,42 spherical Gaussians were used except where otherwise indicated. In the MP2 calculations, the 1s orbitals of carbon and oxygen atoms were frozen. Interaction energy calculations were performed with the benzene center of mass held at the origin of the spherical coordinate system and the benzene molecule stationed in the (x,y) plane, with CH bonds oriented along the positive and negative y axes. The counterpoise method43 was used to correct for basis set superposition error in all benzene-formate calculations. Ab initio energies were recorded to a precision of 10-10

J. Phys. Chem. B, Vol. 111, No. 28, 2007 8243 TABLE 1: Properties of Benzene and Formate Monomers property benzene MP2 energy HF energy Rxx Rzz Θ CC bond length CH bond length formate MP2 energy HF energy CH bond length CO bond length OCO angle CX distance

units Hartrees Hartrees Å3 Å3 Coulombs Å2 Å Å Hartrees Hartrees Å Å deg Å

MP2 optimized HF optimized geometry geometry -231.540214 -230.725322 12.31 6.82 -2.79E-19 1.409036 1.094209 -188.773483 -188.227224 1.136416 1.269633 130.14 0.632469

-230.728364 11.63 6.69 -3.05E-19 1.389626 1.080555 -188.230755 1.124945 1.235233 130.27 0.681574

hartrees. All fits of ab initio energies described below are leastsquares fits, and were computed using either Maple 944 or Gnuplot 3.7.45 Previous studies indicate that the aug-cc-pVDZ basis set provides a reasonably accurate description of molecular interactions in π-bearing systems.16,46-50 Tsuzuki et al. compared the interaction energies computed for benzene dimers at the MP2 level of theory and at the coupled cluster CCSD(T) level of theory; for the large intermolecular distances considered here (>21 Å), the MP2 and CCSD(T) interaction energies obtained by Tsuzuki et al. nearly coincide, indicating that at these distances, dispersion interactions involving benzene are well described by the MP2 level of theory.48 A second quantum chemical calculation for evaluating the benzene-formate interaction energy used a Kitaura-Morokuma (KM) energy decomposition analysis.51-54 Details are given in Supporting Information. A C++ program named STAAR (STatistical Analysis of Aromatic Rings) was written to analyze a subset of the Hobohm and Sander subset38,39 of the PDB, which includes nonredundant, high-resolution structures. In our calculations, only crystal structures with a resolution of e2 Å were analyzed; this corresponded to 946 entries in the PDB (October 2004 release). STAAR locates aromatic rings and determines their centers of mass (using only C, N and O atoms in the ring framework). For each aromatic ring, STAAR then calculates the distance r between the ring’s center of mass and the nearest oxygen atom in a Glu or Asp carboxylate group, and the angle θ between the plane of the ring and the vector connecting the ring center of mass with this oxygen atom. Only pairs with r e 7 Å were retained for further analysis. STAAR handles alternate locations for atoms, as high-resolution X-ray structures sometimes report two or more conformers. STAAR identifies and then uses the conformers that are closest to each other. The output from STAAR was analyzed using the statistical package R, version 1.5.0,55 to generate histograms representing the distributions of r and θ. CHARMM56 version 33a was used for molecular mechanics calculations. Force field parameters were from MacKerell et al.57 and Pavelites et al.58 3. Results A. Monomer Properties. Table 1 lists various geometric parameters and electrical properties computed for the benzene and formate monomers at their HF and MP2 equilibrium geometries. In this table, X denotes the formate center of charge; the three components of the formate dipole moment are zero in a coordinate system whose origin is at this point.

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Figure 1. Benzene-formate pairs. Four coplanar dimers of benzene and formate (at right) were constructed and labeled BF1-4. The dihedral angle θ between the planes containing the benzene and formate monomers was varied in the BF1 pair from 0° to 90° by 30° increments (at left). The center-of-mass for benzene is shown in purple while the center-of-charge for formate is yellow. The atoms are colored as follows: carbon (green), oxygen (red), and hydrogen (blue).

B. MP2 Interaction Energies of Benzene-Formate Pairs. We computed the MP2 interaction energies for several representative planar benzene-formate (BF) pairs, shown in Figure 1. In Figure 2a, we show how the MP2 interaction energy for these four planar dimers varies with the distance r between the benzene center of mass and the formate center of charge. All four planar dimers show minima in the one-dimensional potential energy curves V(r); the BF1 pair has the deepest minimum, with the potential energy, V, equal to -9.5 kcal/mol at r ) 4.5 Å. At the same geometry, the RHF/aug-cc-pVDZ potential energy is V ) -8.0 kcal/mol, and the B3LYP/augcc-pVDZ potential energy is V ) -8.0 kcal/mol. The MP2/ aug-cc-pVTZ energy for this geometry is -9.8 kcal/mol, only 3% more attractive than the MP2/aug-cc-pVDZ energy. This suggests that our MP2/aug-cc-pVDZ energies are already fairly close to the MP2 basis set limit. A full optimization of the dimer starting from this geometry leads to a planar, C2V-symmetry, BF1-like local minimum (with 42 real, positive vibrational frequencies) at the RHF/aug-cc-pVDZ, MP2/aug-cc-pVDZ, and B3LYP/aug-cc-pVDZ levels of theory. These optimizations were performed using NWChem 5.0.59 We also investigated the basis set dependence of the MP2 potential energy by calculating the energies of the BF1-BF4 dimers, each at the bottom of their respective one-dimensional potential energy curves, at the MP2 level of theory with an atomcentered basis set consisting of aug-cc-pVTZ on C and O and cc-pVTZ on H. These potential energies were less than 3% different from the energies given in Figure 2a using GAMESS60 for the calculations. The formate monomer was rotated above the plane of the benzene ring, as shown in Figure 1, to investigate whether formate binds preferentially to the ring edge. Figure 2b shows how the benzene-formate MP2 interaction energy depends on r at four values of θ, the elevation angle of the formate monomer. This angle is the dihedral angle between the planes defined by the benzene and formate monomers; the formate monomer is positioned such that its C2V rotational symmetry axis is in the (x, z) plane and is collinear with the benzene center of mass. Note that for an axial approach of formate (θ ) 90°), the benzene-formate interaction energy is positive for all values of r; this is in accord with the electrostatic potential associated

Figure 2. MP2 potential energy for the benzene-formate pairs as a function of distance and angle. Panel A shows the distance relationships for the four coplanar pairs depicted in Figure 1. Data for the BF1 pair are shown by the red circle points and solid line, the BF2 pair by black diamond points and dashed line, the BF3 pair by purple square points and dotted line and the BF4 pair by orange triangle points and dotdash line. Panel B shows the angle dependence of the potential energy plots for the BF1 pair. The coplanar interaction is given by red circle points (solid line), the interaction at θ ) 30° is given by blue triangle points (dashed line), the interaction at θ ) 60° by green square points (dotted line), and the interaction at θ ) 90° by purple triangle points (dash-dot line). The red circle points are identical for panels A and B.

with the benzene ring, which is negative above and below the face of the ring. The interaction energy curves shown in Figure 2b are thus consistent with an attractive anion-quadrupole interaction that stabilizes coplanar benzene-formate dimers. To quantify the energetic contribution made by this interaction, we must isolate it from other contributions to the benzene-formate interaction energy; to do so, we examine the interaction between benzene and a positive or negative point charge. C. Interaction between Benzene and a Point Charge. We consider the interaction between benzene and a point charge of strength q*qe located at (r,ψ,φ), where qe ()1.602 × 10-19 C) is the magnitude of the charge on the electron, r is the distance between the point charge and the benzene center of mass and ψ and φ are respectively the spherical polar and azimuthal angles

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Figure 3. Interaction between benzene and a point charge of strength q located at distance r ) 15.9 Å and angles (ψ,φ) ) (90°,0). The points are from MP2/aug-cc-pVDZ computations; the curve is a fit to these points using the first two terms of eq 1.

of the charge in the benzene-fixed coordinate system described earlier. The angle θ ) |ψ - 90°| describes the elevation of the point charge above the plane defined by the benzene ring. The potential energy V for benzene interacting with a distant point charge can be written as a power series in charge, q:61

V ) Ves(r,ψ,φ)q + Vpol(r,ψ,φ)q2 + Vhyp(r,ψ,φ)q3 + ...

(1)

Here Ves(r,ψ,φ)q describes the electrostatic components of the benzene-point charge interaction, Vpol(r,ψ,φ)q2 describes the (linear) polarization of the benzene molecule by the point charge, and Vhyp(r,ψ,φ)q3 and higher powers of q omitted from eq 1 represent deviations from a linear polarization response which arise from the hyperpolarizabilities of benzene. For a given location (r,ψ,φ) of the point charge, we can isolate the terms in eq 1 by computing V for six values of q (q ) (1, (2, and (3). We then fit these six values of V to the three terms shown explicitly in eq 1. We do this for distances r ranging from 15.9 to 47.6 Å for point charges approaching the edge of the benzene ring along the direction (ψ,φ) ) (90°,0) and for point charges approaching the face of the ring along (ψ,φ) ) (0,0). We find that Ves changes by less than 0.5% when Vhyp is either included in or excluded from the fitting function; this indicates that at these r values, terms beyond q2 make negligible contributions to V. We therefore included only Ves and Vpol in the fit. Figure 3 shows how the combination of these two terms fits the calculated values of V at r ) 15.9 Å and (ψ,φ) ) (90°,0). The electrostatic contribution to V can be written as an inverse power series in r:61

Ves(r,ψ,φ) ) (qe) (4πo)-1 [Θ P2(cos ψ)/r3 + Φ P4(cos ψ)/r5 + ...] (2) where P2(x) and P4(x) are Legendre polynomials, normalized so that Pn(1) ) 1, o is the permittivity of a vacuum, and Θ and Φ are, respectively, the quadrupole and hexadecapole moments of benzene. The first term omitted from eq 2 is proportional to 1/r7. To determine Θ and Φ from our energy calculations, we fit r3 Ves for each of the two directions of approach of the point charge to the equation:

r3Ves ) a + b/r2

(3)

Figure 4. Electrostatic interaction between benzene and a point charge of strength q ) 1 at distance r and angles (ψ, φ) ) (90°, 0). The points are obtained from MP2/aug-cc-pVDZ computations and the corresponding curve is a fit to these points using eq 3.

TABLE 2: Coefficients Describing the Benzene-Single Point Charge Interaction at the MP2 Level of Theorya coefficient

units

edge

face

a b c d

kcal mol-1 Å3 kcal mol-1 Å5 kcal mol-1 Å4 kcal mol-1 Å6

-290 -1554 -2044 -20110

579 -4527 -1132 3699

a The a and b terms describe the electrostatic effects (from the anionquadrupole and anion-hexadecapole terms), while the c and d terms describe polarization effects (from the dipole-dipole polarizability tensor R for benzene and benzene’s quadrupole-quadrupole and dipole-octopole polarizability tensors C and E).

treating 1/r as the independent variable in the fitting procedure and using energies for r g 21.2 Å only. Figure 4 depicts the data and the fit for edge-on approach of the point charge. The a and b values obtained for the two approach directions are listed in Table 2. From the angular dependence of the Legendre polynomials in eq 2, we see that the ratios a(ψ ) 0, φ ) 0)/a(ψ ) 90°, φ ) 0) and b(ψ ) 0, φ ) 0)/b(ψ ) 90°, φ ) 0) should have the values -2 and 8/3 ) 2.66, respectively; the corresponding ratios obtained from the fits to the energy calculations are -2.00 and 2.91, suggesting that the two terms shown explicitly in eq 2 describe the benzene-point charge electrostatic interaction fairly well for r g 21.2 Å. In addition, we note that a(ψ ) 0, φ ) 0) ) qeΘ/4πo; the value a(ψ ) 0, φ ) 0) obtained from the fit is in excellent agreement with the MP2/aug-cc-pVDZ quadrupole moment (Θ) listed in Table 1. The polarization contribution to V can also be written as an inverse power series in r:

Vpol(r,ψ,φ) ) A(ψ,φ)/r4 + B(ψ,φ)/r6 +...

(4)

where the first term omitted is proportional to 1/r8. Here A(ψ, φ) is related to the dipole-dipole polarizability tensor R for benzene and B(ψ, φ) is related to benzene’s quadrupolequadrupole and dipole-octopole polarizability tensors C and E. For an edge-on approach of the point charge, A(ψ ) 90°, φ ) 0) ) qe2 (4π0)-1 Rxx/2, while for a point charge approaching the face of the benzene ring, A(ψ ) 0, φ ) 0) ) qe2(4π0)-1Rzz/2. To obtain values for A(ψ, φ) and B(ψ, φ),

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we fit r4 Vpol for each of the two directions of approach to the equation

r4Vpol ) c + d/r2

(5)

again treating 1/r as the independent variable and using energies for r g 21.2 Å only. Table 2 lists the resulting c and d values for the two approach directions. The values obtained for c are in good agreement with the polarizability-dependent expressions for A(ψ ) 0, φ ) 0) and A(ψ ) 90°, φ ) 0) given above. D. Additional Calculations. A second quantum chemical calculation for evaluating the benzene-formate interaction energy used a Kitaura-Morokuma (KM) energy decomposition analysis.51-54 While the KM calculations are much faster, they do not always appear to reflect accurately the energetic contributions, particularly at θ ) 90°. Thus the results from these calculations are provided as Supporting Information. E. MP2 Interaction Energies of Phenol-Formate and Indole-Formate Pairs. Our benzene-formate interaction energy calculations are intended to mimic interactions between the aromatic amino acid phenylalanine and the anionic amino acids aspartate and glutamate. Tyrosine and tryptophan are also aromatic amino acids, and may additionally exhibit a preference for planar interactions with anionic species. We used phenol and indole as mimics for tyrosine and tryptophan, and investigated the stability of coplanar dimers of these molecules with formate by performing MP2 interaction energy calculations of the dimers. The dimers and their corresponding interaction energies are shown in Figures 5 and 6. The greatest binding energy is obtained for structures in which formate is positioned near the OH moiety of phenol or the NH moiety of indole. These structures display a favorable dipolecharge interaction and also permit the monomers to form hydrogen bonds, thus the binding energy is substantially larger than that in the benzene-formate pair. Although this makes it difficult to quantify the role that anion-quadrupole interactions play in the stabilization of these structures, we note that when formate binds to the edge of phenol or indole opposite the OH or NH bond (structures PF3, PF4, and IF3), the binding energy is still reasonably large, and is comparable to that for the BF1 structure. F. Statistical Analysis of Structures from the Protein Data Bank. Insight into the biological relevance of directional binding between anionic and aromatic amino acids comes from our analysis of structures in the Protein Data Bank (PDB). We investigated the frequency of aromatic-anionic pair formation in the Hobohm and Sander subset of the PDF (October 2004 release), which includes nonredundant, high-resolution structures. In the 946 structures analyzed, we found 6652 pairs between Phe and either Asp or Glu, 8458 pairs between Tyr and either Asp or Glu, and 3272 pairs between Trp and either Asp or Glu. Figure 7 shows the angular distribution of these pairs, and compares the observed distribution with a random one. Nearly planar aromatic-anionic amino acid pairs are more likely than expected from a random angular distribution, while axial aromatic-anionic pairs are less likely than expected; this is in accord with our observation that formate binds preferentially at the ring edge of benzene. Figure 8 shows the distribution of distances for near-coplanar Phe-Asp and Phe-Glu pairs, and indicates that these pairs predominantly occur when the residues are separated by a distance of 4.5 Å or larger; as we note below, these distances are precisely those where the charge-quadrupole interaction described by the leading term

Figure 5. Phenol-formate (PF) planar dimers. All dimer pairs are superimposed, each pair is labeled near the formate position and its interaction energy given in kcal/mol at the HF and MP2 levels. Each molecule was optimized at the MP2 level of theory; molecules were manually aligned in-plane and within van der Waals contact using Sybyl7.0. The atoms are colored as follows: carbon (green), oxygen (red), and hydrogen (white).

Figure 6. Indole-formate (IF) planar dimers. All dimers pairs are superimposed, each pair is labeled near the formate position and its interaction energy given in kcal/mol at the HF and MP2 levels. Each molecule was optimized at the MP2 level of theory; molecules were manually aligned in-plane and within van der Waals contact using Sybyl7.0. The atoms are colored as follows: carbon (green), oxygen (red), nitrogen (blue), and hydrogen (white).

of eq 3 makes a substantial contribution to the MP2 benzeneformate interaction. 4. Discussion A. Deconvolution of the Contributions to the BF1 Pair Interaction. The overall energy associated with an anionquadrupole interaction is quite reasonable (-9.5 kcal/mol for the BF1 pair at the equilibrium distance in the gas phase). Since deconvolution of the interaction energies for the benzene-point charge pairs into their component parts yielded good agreement with the expected values, we felt confident in using the expected values to predict the behavior of the benzene-formate planar dimers. In Figure 9, we show the calculated MP2/aug-cc-pVDZ

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Figure 8. The number of interactions between Phe and Asp or Glu residues where θ ) 0-10° plotted vs distance. As the strongest anionquadrupole interaction occurs at θ ) 0°, this plot shows the number of potential pairs occurring near this value of θ ((10°) as a function of distance. The upper limit for the distance is 7 Å, as above this distance, a water molecule could fit between the pairs and disrupt the interaction. For this plot, r measures the distance between the center of mass of the aromatic ring and the nearest oxygen atom.

Figure 7. Fractional occurrence of amino acid pairs as a function of θ. Theta was varied from 0° to 10°, 10.0001° to 20°, etc., and the number of interacting pairs in the PDB Select determined using STAAR. The fraction of pairs that occurs in each 10° increment of θ was then calculated; these are the black bars in the plots. The gray bars describe the fractional number of pairs expected based on statistical considerations; these values were calculated by computing the volume of the sector (above and below the spherical bisector) divided by the total spherical volume. The top panel describes interactions of Asp or Glu with Phe, the middle panel interactions of Asp or Glu with Tyr, and the bottom panel interactions of Asp or Glu with Trp. Using a paired t-test, the probabilities that the observed aromatic-Asp or Glu distributions are different from a random distribution are at 99.2% (Phe), 99.7% (Tyr), and 99.6% (Trp) levels of confidence, respectively.

benzene-formate interaction energies V(r) for coplanar (θ ) 0°) and axial (θ ) 90°) approach of the formate, energies that were first shown in Figure 2b, along with the sum of the longrange electrostatic and polarization contributions through 1/r6, as defined by eqs 3 and 4. Although the long-range potential describes only those contributions to the benzene-formate energy arising from interactions between the formate’s overall negative charge and the benzene molecule’s quadrupole and hexadecapole moments and low-order polarizability tensors, it evidently gives a very good description of the coplanar MP2

Figure 9. MP2 potential energy for the BF1 pair as a function of distance and angle. The black circles describe the data for the edgewise interaction where θ ) 0°. The solid line shows the predicted values using the a-d coefficients from Table 2. The gray triangles describe the data for the face interaction where θ ) 90°. The dashed line shows the predicted values using the a-d coefficients from Table 2.

benzene-formate interaction for r > 4.5 Å and of the axial MP2 interaction for r > 5.5 Å. It thus appears that the energetic contributions described by eqs 2 and 4 capture the dominant features of the MP2 benzeneformate interaction, and that other contributions (such as van der Waals dispersion interactions) play a relatively minor role at these benzene-formate distances. As Figure 8 shows, these distances are precisely those for which we find frequent occurrences of nearly coplanar Phe-Asp and Phe-Glu interactions. Figure 10 decomposes the long-range coplanar interaction energy defined by eqs 2 and 4 into the contributions from charge-quadrupole interactions, higher-order electrostatic interactions, and polarization terms. Over this distance range, the charge-quadrupole term contributes between 30% and 45% of the total MP2 benzene-formate interaction; most of the rest of

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Figure 10. Deconvolution of the interaction energy for the coplanar benzene-formate (BF1) dimer (θ ) 0°). The charge-quadrupole contribution is shown by triangle points, the polarization contribution by square points and higher-order terms by circle points.

Figure 11. A comparison of BF1 energies calculated using MP2 and CHARMM. Since the fixed atomic point charges in CHARMM cannot describe polarization effects,62 our comparison uses only electrostatic energies calculated from eq 2. The dashed line (2 points) shows the calculated energy from CHARMM, while the solid line (b points) shows the energy calculated using eq 2. If polarization effects were to be included in our calculated energies, an even greater underestimation of the interaction energy would be observed.

the interaction arises from polarization contributions. One origin of this behavior comes from the large in-plane polarizability of benzene, which favors the polarization component of the interaction. Previous attempts to deconvolute energetic contributions to anion-quadrupole interactions have used the molecular interaction potential with polarization (MIPp) scheme.12,21 Garau et al. found that the electrostatic component of the anion-π interaction (six different electron deficient aromatic rings paired with Cl- at θ ) 90°) correlates with the magnitude of the quadrupole moment, Θ, while the polarization component correlates with the Rxx of the aromatic compound. Thus their approach to correlating the electrostatic interaction energy with the aromatic quadrupole was different and less quantitative, but their conclusions are similar. These previous evaluations of anion-π pairs used electron deficient rings with θ ) 90°. In contrast, our calculations focus on anion-π interactions with θ ) 0°. Here, Rxx and Rzz, the

Jackson et al. parallel and perpendicular polarizabilities have different values (see Table 1), thus they likely have different effects in these interactions. For perpendicular interactions, Rzz is involved, while for in-plane interactions, Rxx, is involved. For the anion-π case presented here, the greater polarizability associated with Rxx facilitates charge dispersion in these edgewise interactions. B. A Comparison of BF1 Calculations using MP2 and CHARMM. In most models of protein structure and dynamics that are based on classical force fields, the electrostatic interaction between amino acids is represented by pairwise interactions between partial charges located on the atoms of each amino acid. Figure 11 shows how this partial-charge approximation compares to the electrostatic interaction defined by eq 2 for benzene-formate pairs; in this figure, we have used atomic partial charges defined by the CHARMM force field for benzene and formate. Although the CHARMM force field gives the correct overall trend for the electrostatic interaction, we see that it underestimates the interaction defined by eq 2, which is calibrated against ab initio quantum chemical calculations, by about 20% over the range of distances considered here. Quantum mechanical calculations have previously been found to provide a good description of side chain to side chain H-bond geometries observed in the Protein Data Bank.49 In contrast, force field predictions based on atom centered partial charges did not agree as well with the H-bond geometries found in actual structures. This observation, coupled with our calculations as well as other computational studies,62-65 indicates that future force field development should include multipole interactions as well as polarization effects. C. Is an Anion-Quadrupole Effect Biologically Relevant? Our calculated values describe gas-phase interactions. In biological systems, water will be present and can be expected to diminish the energies involved. However, a neutral organic receptor has been found to bind an anion in solution27 and statistical analysis of the PDB Select finds a edgewise interaction preference between Asp or Glu with aromatic amino acids, supporting the likely occurrence of anion-quadrupole interactions in solution. Thus, while the individual interaction energies might be small in solution, there are numerous possibilities for these interactions to occur in proteins, thus cumulative effects could occur and enhanced binding result. A quantitative investigation of the contributions made to ligand binding and protein folding by these interactions would be the next step in identifying their biological relevance. For ion pairs or ion-receptor interactions, competition with other ions occurs and binding specificity becomes a major issue. Neutral receptors can surmount this difficulty by providing steric constraints and potentially greater ion selectivity by use of polarization (rather than nondirectional electrostatic effects) during binding.66 Both cation-π and anion-quadrupole interactions could serve to facilitate ion binding and selectivity. Abbreviations KM, Kitaura-Morokuma analysis; BF pairs, benzeneformate-pairs; IF pairs, indole-formate pairs; PF pairs, phenolformate pairs; STAAR, STatistical Analysis of Aromatic Rings program. Acknowledgment. We thank P. Archirel for helpful discussions regarding the quadrupole moment definition used in Gaussian98 and Gaussian 03, C. Ozen for early calculations, and P. Agarwal and H. Guo for reading the manuscript and providing helpful comments.

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