Use of Theoretical Descriptors toCharacterize Cation–π Binding Sitesin (Macro)molecules

JOHAN WOUTERSFacultés Universitaires Notre Dame de la Paix, 61 Rue de Bruxelles, B-5000 Namur, Belgium

Received 12 November 1999; accepted 22 February 2000

ABSTRACT: A metal cation–π (Na+-tryptophane) interaction was detected inthe crystallographic structure of a thermophilic Bacillus stearothermophilustriosephosphate isomerase mutant (bTIMmut). The geometry of this particularinteraction between a cation and an aromatic ring was analyzed, and theoreticaldescriptors were derived. In particular, the program GRID emerges as a rapiddiagnostic tool to detect cation–π binding sites in (macro)molecules when anappropriate probe is used. This procedure offers an attractive alternative toab initio calculated molecular electrostatic potential maps. The influence ofdifferent force fields (amber, cvff, cff91) and of a series of parameters [partialcharge (q), dielectric constant (ε), polarizability (via the Aij term of the nonbondLennard–Jones potential)] was also tested in optimization procedures. Thegeometries of the complexes were compared to ab initio (molecularorbital—HF/6-31G∗∗, and density functional theory—DFT[B3LYP]/6-31G∗∗)calculations and experimental geometries of cation–π interactions observed insmall molecules crystal structures. This work leads to an optimum methodologythat was applied with success to the simulation of the cation–π interactionobserved in bTIMmut. c© 2000 John Wiley & Sons, Inc. J Comput Chem 21:847–855, 2000

Keywords: cation–π ; GRID; DFT[B3LYP]/6-31G∗∗; force field; polarizationeffects

Correspondence to: J. Wouters; e-mail: wouters@scf.fundp.ac.beContract/grant sponsor: FNRS

Journal of Computational Chemistry, Vol. 21, No. 10, 847–855 (2000)c© 2000 John Wiley & Sons, Inc.

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Introduction

T he cation–π interaction discovered by Dough-erty and coworkers has received much at-

tention as a new type of binding force importantin biological molecular recognition and enzymecatalysis.1, 2 The cation–π interaction is a generalnoncovalent binding force, in which the face ofaromatic rings provides a region of negative elec-trostatic potential that can bind various cations (al-kali, alkaline–earth metal, and even organic cations)with considerable strength. On this basis, molecu-lar systems with circular arrangements of aromaticunits have been designed as ionophores and modelsfor biological receptors.1, 3 Some of those moleculescould be used for effective separation of radioac-tive isotopes like 137Cs and 90Sr, which are majorconstituents of nuclear wastes. A large numberof studies of synthetic receptors have documentedthe importance of cation–π interaction in aqueousmedia.1 Those studies showed that the binding cav-ities of synthetic receptors (e.g., cyclophane hosts)can compete with aqueous solvation of a cation (inwater, the cation is very well solvated) and bind ittightly.

In a biological context, it is the aromatic sidechains of phenylalanine, tyrosine, and tryptophane(Trp) that can be expected to be involved in cation–πinteractions, and an increasing number of evidenceindicate a prominent role for such cation–π inter-actions in structural biology in general.1, 4 – 6 The-oretical studies and survey of protein structuresclearly indicate that, of the natural amino acids, Trppresents the most potent cation–π binding site, thesix-ring of the indole side chain being favored.1, 3, 6

This was recently confirmed in a 2 Å crystallo-graphic structure of hen white-egg lysozyme pre-senting a metal cation–π interaction between a Na+sodium cation and Trp 123.6 Cation–π interactionis also thought to be responsible for the binding ofthe quaternary ammonium group of acetylcholine(ACh) to a tryptophane residue (Trp 149 of the αsubunit) in the agonist binding site of the nicotinicreceptor.4 Cation–π interactions have been consid-ered in diverse other systems such as voltage-gatedion (K+) channels, the cyclase enzymes of steroidbiosynthesis, and enzymes that catalyze methyla-tion reactions involving S-adenosylmethionine.1, 3

Electrostatic interactions play a prominent andsometimes dominant role in the binding of cationto π systems, involving the interaction of the cationwith the large permanent quadrupole moment ofthe aromatic.7, 8 For this reason, ab initio quantum

mechanical calculations on small model systemscan predict cation–π binding abilities of aromaticsystems. The stability of cation–π complexes canbe adequately approached by studying simple sys-tems using ab initio theory (single determinants or,better, introducing electronic correlation) and ex-tended basis sets.1, 7 – 10 For example, a compellingcorrelation was shown between ab initio quantummechanical predictions of cation–π binding abili-ties and the affinity values (EC50) of ACh for aseries of engineered receptors.4 Good correlationsbetween the electrostatic component of an OPLS(optimized potentials for liquid simulations) forcefield and ab initio HF/6-31G∗∗ binding energies werealso reported for Lys-Phe and Arg-Phe cation–πpairs retrieved from the protein crystal structures.10

Force field calculations are also able to predictcation–π interactions. The combination of van derWaals and Coulomb forces, as prescribed in theCHARMm parameters, are sufficient to model theinteraction between K+ and aromatic amino acidswithin 5 kcal/mol when empirical corrections areincluded to describe backbone atoms.11

Ab initio calculated MEP are useful qualitativetools to detect cation–π binding sites.8, 9 In the caseof macromolecules, computation of the ab initio MEPmaps on a grid covering the entire molecule requiresconsiderable computational effort. As an alterna-tive to MEP maps, the program GRID12, 13 was usedon a series of model systems and was able to de-tect cation binding sites. This procedure is bettersuited to investigate large structures and allowsthe identification of putative cation–π binding sitesin (macro)molecules, as illustrated in the case ofthe structure of a thermophilic Bacillus stearother-mophilus triosephosphate isomerase mutant (bTIM-mut).

In devising a method to develop large-scale com-putational strategies for ion–protein interactions,various approaches are possible. Because ab initio(molecular orbital, density functional theory) meth-ods does usually not address problems of this mag-nitude, empirical (force field) methods must be pur-sued. In this contribution, an existing force field wasmodified and adapted by modulating the polariz-ability contribution in the Lennard–Jones function.An optimization methodology has been establishedby assessing the influence of a series of parameters(partial charge, dielectric constant, and polarizabil-ity) on the geometries of cation–π complexes inproteins. The resulting procedure was applied withsuccess to the simulation of the cation–π interactionobserved in bTIMmut.

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This work points to the important role that bothelectrostatic and polarization terms play in the de-scription of the cation–π interaction.

Material and Methods

DETECTION OF CATION-BINDING SITES USINGTHE PROGRAM GRID

The suite of programs GRID12, 13 installed on anOctane SGI Workstation running Irix6 was usedto identify cation–π binding sites, first on modelcation–aromatics (cation: Na+ or NH+4 , aromatic:benzene or indole), and then on the entire structure(2 Å) of a thermophilic Bacillus stearothermophilustriosephosphate isomerase mutant14 (bTIMmut,PDB code: 1B9B). The program GRIN was first runonce on the different systems to define a grid overthe molecule and the interactions of a series of smallchemical groups (probes) with the structures (tar-gets) was evaluated using GRID. The probes used inthis study include the sp3 amine NH3 cation (N3+),sp3 amine NH2 cation (N2+), sp3 amine NH cation(N1+), sp2 amine NH2 cation (N2=), sp2 amine NHcation (N1=), trimethylamine cation (NM3), sodium(NA+), potassium (K+), and lithium (LI+) parame-ters.

Basically, GRID is a computational procedure fordetecting energetically favorable binding sites on(macro)molecules. At each node of a defined grid,the nonbonded interaction energies (Exyz) are calcu-lated as the electrostatic (Eel), hydrogen bond (Ehb),and Lennard–Jones (Elj) interactions of chemicallyselective probes with the chosen targets [eq. (1)].

Exyz =∑

Eel +∑

Ehb +∑

Elj (1)

The electrostatic contribution contains a dielectricterm combining the dielectric ξ (=4) of the homo-geneous protein phase and the solution dielectricε (=80) and incorporates the electrostatic chargeson the probe group and the pairwise protein atom.A direction-dependent 6-4 function is used for hy-drogen bonds. A 12-6 Lennard–Jones potential isadded to complete the estimation of the nonbondedinteraction energies.

Energy minima correspond to preferred nonbondarrangements of atoms in molecular assemblies.

Contour surfaces at appropriate energy levelsare computed and displayed by computer graph-ics together with the target structure. A detaileddescription of the GRID program, the force fieldsparameters, and calculations can be found in theoriginal article.11

GEOMETRY OF THE CATION–π INTERACTIONS

Experimental Structures

Experimental cation–aromatic geometries wereobtained from small molecule crystal structuresdeposited at the Cambridge Structure Database(CSD).15 Structures corresponding to metal cation–πcomplexes involving either Na+ or K+ were re-trieved from Version 5.14 (containing over 175,000entries) of CSD using the Quest3D program andanalyzed with the Vista interface. Only structurespresenting at least three CAr-X distance (where X =Na+ or K+ and CAr is an aromatic carbon in asix-membered ring) between 1.0 and 4.5 Å were re-tained and further analyzed. This search criterionrejected all fragments for which the cation is not fac-ing the aromatic ring. The search was performed ofprecise organic structures (R1 < 7%).

Geometry Optimizations

Molecular mechanics optimizations of a series ofcation–aromatic systems were performed with theDiscover program (MSI, San Diego, 1998). In the in-put geometries, the cation (Na+ sodium cation) isplaced about 3 Å, facing an aromatic (benzene orindole) ring. Preliminary calculations show that, inpractice, the final geometry is not influenced by theinitial position of the cation with benzene or indole,suggesting the presence of a single energy mini-mum. For other heterocycles (as, e.g., in imidazoleof histidines or ring systems of nucleic acids) newtypes of interactions can occur and complicate theanalysis by introducing new energy minima.

A series of force fields (amber, cvff, cff91) andforce fields parameters [partial charge (q), dielectricconstant (ε), polarizability (via the Aij term of thenonbond Lennard–Jones potential)] have been usedto optimize model systems: (a) the influence of thepartial charge (q) on the cation has been investigatedby modifying this parameter in the geometry file:q = 0 or 1; (b) electrostatic effects were also stud-ied by performing the computations with differentdielectric constants: distance-dependent dielectricε = Nr (N = 1, 2, 4) or constant dielectric ε = E(E = 1, 20, 77); (c) the influence of the polarizabil-ity was approached by modifying the first term of a(6-12) Lennard–Jones potential [eq. (2)]. The Aij pa-rameter is a function of the polarizability (αi) of thenonbond, interacting atoms.

Eij = Aij/r12ij − Bij/r6

ij (2)

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with Aij = (AiiAjj)1/2 = 2eijr∗ij12 where eij is the poten-

tial well depth (kcal mol−1) and r∗ij is the interatomicdistance (Å) at which the minimum occurs.

Different expression of the nonbond interactionpotential were obtained by substituting the Aii para-meter associated to a sodiun cation (fixed to 14,000kcal mol−1 in the cvff force field) by ANa

ii = MAii

(M = 0.1, 1, 10, 100, 1000).The final geometries have been compared to ex-

perimental (CSD) structures and to ab initio [mole-cular orbital (HF/6-31G∗, HF/AM1), density func-tional theory (DFT[B3LYP]/6-31G∗∗)] optimizedstructures obtained with the program Gaussian-9416

running on an IBM parallel SP2 processor. An opti-mization procedure was derived from the study ofthe benzene–Na+ system and applied to the struc-ture of bTIMmut. In this procedure, the partialcharge on the sodium was q = +1, a distance-dependent dielectric ε = 4r was used, and the Aii

value for Na+ was fixed to 100 times the originalvalue of the cvff force field. All residues within 8 Åof Trp9 were allowed to move during the minimiza-tion (final max derivative requested on the energy=0.05 kcal mol−1).

Results and Discussion

In the course of our study of the effect ofside-direct mutagenesis on the thermostability oftriosephosphate isomerases, the crystal structureof a thermophilic Bacillus stearothermophilus TIMmutant has been refined at 2 Å resolution.14 Theprotein crystallizes as a dimer in the asymmetricunit. In both monomers, a residual density peak ap-pears in the difference Fourier, close to Trp9. Severalarguments6 suggest that this peak corresponds to asodium cation facing the six-ring of the indole lat-eral chain of the tryptophane with distances around4.3 Å from the aromatic carbons (Fig. 1).

Interestingly, the cation–π binding site in bTIM-mut is near the surface of the protein, a fact alsonoticed for the lysozyme sodium–Trp complex.6

This could be related to the great desolvation en-ergy of the cation, the lateral chain of the tryptophancompeting with aqueous solvation. The presence ofPhe 21 and Glu 17 close to Trp9 in the cation bind-ing site, could indicate an additional role for thoseresidues in the stability of the sodium–indole inter-action.

FIGURE 1. Two perpendicular views of theenvironment of Trp9 in the crystal structure of thethermophilic Bacillus stearothermophilus TIM(H12N/K13G) double mutant. The geometry of thecation–π interaction is very similar in both monomers sothat only one site (monomer A) is discussed.

DETECTION OF CATION-BINDING SITES USINGTHE PROGRAM GRID

Electrostatic interactions play a prominent rolein the binding of cations to π systems. Therefore,ab initio calculated molecular electrostatic poten-tial (MEP) surfaces provide useful guidelines forpredicting cation–π binding sites on small prototyp-ical (hetero)cycles.7, 8 The position of the maximumof the negative MEP over the center of the aro-matic corresponds to the position of the ion in thecation–π interaction, and the more negative theelectrostatic potential, the stronger the interaction.Anticipating that one may wish to apply this theo-retical approach to more complicated systems, it hasbeen established that MEP surfaces derived fromlower levels of theory (e.g., semiempirical AM1),more readily applied to larger systems, could stillbe useful.8 However, in the case of macromolecules,computation of the MEP surfaces on a grid cover-ing the entire molecule, even using the AM1 levelof theory, still requires considerable computationaleffort.

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The program GRID offers an attractive alterna-tive to MEP surfaces, and could be used to detectcation–π binding sites, even in protein structures.A series of probes were run over a benzene or anindole ring to test this approach. Among the probes,the trimethylamine cation (NM3) probe generatesattractive (negative) contours above the faces of thearomatic, revealing a potential cation binding site(Fig. 2a). Other probes proved less useful in detect-ing those sites. The same results are obtained withan indole replacing the benzene ring. Probes defin-ing cations [sodium (NA+), potassium (K+), andlithium (LI+)] were unable to locate the cation–πbinding sites. One must be cautious about interpret-ing the physical significance of force field calcula-tions. The fact the NM3 is the best probe in this

FIGURE 2. Attractive (negative) contours generatedabove the faces of the aromatic with the trimethylaminecation (NM3) probe, revealing a potential cation bindingsite for small model rings (benzene and indole, a) and inthe crystallographic structure of the Bacillusstearothermophilus TIM mutant (b).

TABLE I.Parameters Defining the Probes in the GRID Program.

NM3 N3+ N2+ N1+ NA+

VDWR 2.550 1.750 1.700 1.650 0.950NEFF 33 9 8 7 8ALPH 7.600 2.130 1.700 1.400 0.240Q 0.840 0.660 0.660 0.660 1.000EMIN 0.000 −2.500 −3.000 −3.000 0.000RMIN 0.000 1.600 1.600 1.600 0.000JD 0 3 2 1 0JA 0 0 0 0 0JTYPE 0 3 22 0 111

VDWR, van der Waals radius (Angstrom). NEFF, effec-tive number of electrons. ALPH, polarizability (alph) (Angs-trom∗∗3). Q, electrostatic charge. EMIN, optimal H-bond en-ergy (kcal/M). RMIN, hydrogen bonding radius (Angstrom).JD, number of hydrogen bonds donated. JA, number of hy-drogen bonds accepted. JTYPE, hydrogen-bonding type.

study is more related to the parametrization of theforce field than the cation of the cation–π interac-tion. Comparison of the parameters defining differ-ent probes (Table I) suggests that the polarizabilityof the chemical group (α) could be a discriminatingproperty in locating cation–π sites. The polarizabil-ity term is particularly important in the case of atrimethylamine cation probe (α = 7.6 Å3). The in-fluence of polarizability has been incorporated inthe next part where optimization procedures weredesigned to predict the geometry of cation–π com-plexes for (macro)molecular systems.

The trimethylamine cation (NM3) probe has beenfurther used to scan the crystallographic structure ofthe Bacillus stearothermophilus TIM mutant. The re-sulting grid, contoured for negative values, clearlyindicates an attractive region facing Trp9 (Fig. 2b).It corresponds to the position of the cation in thecrystal structure. In large (macromolecular) systemsfor which ab initio calculations may not be feasi-ble, it thus appears that running the GRID progamwith the trimethylamine cation (NM3) probe canbe used as predictive descriptor to locate cation–πbinding sites. Studies on other proteins with knowncation–π sites are currently under way.

GEOMETRY OF THE CATION–π INTERACTIONMODELED BY MOLECULAR MECHANICS

Ab initio quantum mechanical and molecular me-chanical calculations on small model systems canbe used to predict cation–π binding abilities ofaromatics.1 – 5 However, the geometry of the com-plexes is more difficult to approach by theoretical

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methods.6 Benzene is the prototype of aromatic sys-tem and a good starting point for understandingthe side chains of Phe, Tyr, and Trp. For example,different levels of theory agree that the preferredgeometry for a simple ion (Li+, Na+) interactingwith benzene place the metal cation over the cen-ter of the ring, along the sixfold axis. But in the finaloptimized structures, the distance between the cen-troid of the ring and the cation varies significantlyfrom one method to another.

From studies of small molecule crystal structures,a cation–aromatic plane (Na+-centroid of the ben-zene) distance around 3.36 Å is expected.6 This dis-tance can be compared to the experimental geome-tries observed in proteins between the indole ringof Trp and the cation: 4.07 in HEW lysozyme (1lpi6)and 4.14 and 4.32 Å in bTIMmut, for the two mole-cules in the asymmetric unit, respectively.

In the ab initio (HF/6-31G∗∗ or DFT[B3LYP]/6-31G∗∗) optimized geometry (Table II), the Na+-centroid distance is shorter by about 30%. Intro-duction of electronic correlation effects (densityfunctional theory) only slightly increases the ion-

aromatic distance, and still underestimates experi-mental values. This is not surprising, as the geome-tries obtained by calculations are better compared togas phase geometries rather than to X-ray structuresthat are influenced by packing effects. Moreover, theunitary charge on the metal cation–π complex is justa model.

The aim of this work was to devise a methodto develop large-scale computational strategies forcation–π interactions in proteins. Ab initio (molec-ular orbital or density functional theory) methodsdo not usually address problems of this magni-tude and so empirical (force field) methods must bepursued. A systematic comparison of optimizationprocedures based on molecular mechanics has beenapplied first to model sodium–benzene complexes.The influence of force fields (amber, cvff, cff91) andparameters [partial charge (q), dielectric constant(ε), polarizability (via the Aij term of the nonbondLennard–Jones potential)] was studied (Table II). Inall final geometries, the cation occupies a positionover the center of the benzene ring, along its sixfoldaxis.

TABLE II.Predicted Geometries of the Cation-π Interaction (in Å) for the C6H6-Na+ Complex.

Ab initioHF/AM1 5.78HF/6-31G∗∗ 2.45B3LYP/6-31G∗∗ 2.56

Molecular Mechanics:

Influence of the force field and of the partial charge (ε = 1)Amber (q = 0) 3.41 amber (q = +1) 2.40cvff (q = 0) 2.57 cvff (q = +1) 2.32cff91 (q = 0) 3.36 cff91 (q = +1) 2.71

Influence of electrostatics (cvff)

Distance-dependent dielectric Constant dielectricε = 1r (q = 0) 2.34 ε = 1. (q = 0) 2.32ε = 2r (q = 0) 2.43 ε = 20. (q = 0) 2.55ε = 4r (q = 0) 2.49 ε = 77. (q = 0) 2.57ε = 1r (q = +1) 2.57 ε = 1. (q = +1) 2.57ε = 2r (q = +1) 2.57 ε = 20. (q = +1) 2.57ε = 4r (q = +1) 2.57 ε = 77. (q = +1) 2.57

Influence of polarizability (cvff)ANa

ii = 0.1Aii (q = 1) 1.84 ANaii = 0.1Aii (q = 0) 1.98

ANaii = Aii (q = 1) 2.34 ANa

ii = Aii (q = 0) 2.57ANa

ii = 10Aii (q = 1) 2.89 ANaii = 10Aii (q = 0) 3.25

ANaii = 100Aii (q = 1) 3.49 ANa

ii = 100Aii (q = 0) 4.10ANa

ii = 1000Aii (q = 1) 4.11 ANaii = 1000Aii (q = 0) 5.01

The distance between the sodium Na+ and the centroid of the benzene is given.

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Influence of the Partial Charge

Geometry optimizations have been performedusing the default values defined in three indepen-dent force fields (amber, cvff, cff91) for charged (q =+1) or neutral (q = 0) sodium “cations.” A constantdielectric (ε = 1) was used. The results are summa-rized in Table II.

The structures obtained by molecular mechanicsusing a charge q = +1 are similar to the HF/6-31G∗∗ ab initio optimized geometries. Switching theunit charge on the “cation” off has a direct effecton the geometry of the cation–π complex. For allthree force fields studied, the distance between thesodium and the benzene ring is systematically in-creased. The effect is particularly pronounced withthe Amber force field (distance increase of about1 Å) and less important with the cvff force field. Nostraightforward explanation was found for the dif-ferences observed between the force fields.

A temptative explanation for the influence of thecharge can, however, be proposed. Using a chargeq = 0 for the cation has the effect of decreasingthe electrostatic term in the total interaction ex-pression, and seems a good strategy to approachexperimental geometries. Reduction of the electro-static influence could be a way of compensating theabsence of explicit (de)solvation terms in the expres-sion of the nonbond energy. As no model for thesolvent is included, the calculated electrostatic in-teractions tend to be overestimated. Reducing thecharge on the cation balances this effect.

This procedure leads to optimized structures forwhich the cation–aromatic plane is still underesti-mated in comparison with experimental geometries.

Influence of Electrostatics

It has been shown that electrostatics play an im-portant role in the cation–π interaction,7, 8 and thus,electrostatic effects were studied by performing thecomputations with different dielectric constants:distance-dependent dielectric ε = Nr (N = 1, 2, 4) orconstant dielectric ε = E (E = 1, 20, 77). The partialcharge on the sodium was fixed to either 0 or +1.The results are summarized in Table II for the cvffforce field.

Generally, scaling down the electrostatics(distance-dependent dielectric ε = 4r or constantscalar dielectric ε = 77) increases the cation–aro-matic plane distance. Surprisingly, little effect isnoticed when the partial charge on the sodium isfixed to +1.

Here again, modulation of the dielectic constantseems a good way to reduce the influence of the

overestimated electrostatic term in the absence ofa proper model for the solvent. Modulation of thedielectric constant and/or the partial charge on thecation is, however, not sufficient to reproduce exper-imental geometries.

Influence of Polarizability

An important “nonelectrostatic” component ofthe cation–π interaction does also exist, and reflectsa combination of effects mostly related to the polar-izability of the aromatic and the cation.1, 7, 8, 17, 18 Theimportance of the polarizability term has alreadybeen revealed in the GRID procedure described ear-lier in this work.

The importance of the polarizability on finaloptimized geometries was approached by modify-ing the Aij parameter in the first term of a (6-12)Lennard–Jones potential. Different expression of thenonbond interaction potential were obtained bysubstituting the Aii parameter associated to a sodiuncation by ANa

ii = MAii (M = 0.1, 1, 10, 100, 1000). Thepartial charge on the sodium was fixed to either 0or+1. The results are summarized in Table II for thecvff force field. In this force field, the value of ANa

ii isfixed to 14,000 kcal mol−1.

Increasing the polarizability of the cation hasa deep influence on the geometry of the cation–aromatic geometry. Using a value of ANa

ii = 100Aii

brings the cation–benzene plane distance close to3.5 Å (with q = +1). A value of 100ANa

ii (100∗14,000)corresponds to the one assigned in the cvff forcefield to carbon atoms (AC

ii = 2.0 106 kcal mol−1 andAC′

ii = 3.0 106 kcal mol−1).Replacing the benzene ring by an indole ring

leads to similar conclusions. Compared to benzene,indole is clearly a stronger cation–π binder sug-gesting that Trp may be especially important incation–π binding. In electrostatic maps both thesix-membered ring and the five-membered ring ofindole generate attractive molecular electrostaticpotential, indicating that both the benzene and thepyrrole-type rings could be cation–π binding sites.However, quantitative calculations indicate that thebenzene ring of indole is the preferred cation–πbinding site. This is confirmed by our experimentalwork, where the sodium ion in the bTIMmut struc-ture lies along the sixfold axis of the benzene ring ofTrp9.

MODELING OF THE CATION–π INTERACTIONIN PROTEINS

The geometries deduced from theoretical opti-mizations are a valuable complement to the crystal

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structure geometries. An optimum protocol was de-duced from the study on small, simple systems andapplied to the bTIMmut structure. In this optimiza-tion procedure, the partial charge on the sodiumwas retained (q = +1), a distance-dependent di-electric ε = 4r was used, and the Aii value forNa+ was fixed to 100 times the original value ofthe cvff force field. All residues within 8 Å of Trp9were allowed to move during the minimization (fi-nal maximum derivative requested on the energy=0.05 kcal mol−1).

While default protocols are unable to predicta cation–π interaction with Trp9 in the structureof bTIMmut, the optimized procedure places thecation in a geometry very close to the one deducedby crystallography (Fig. 3). When no down-scalingof the electrostatic term is performed, and the polar-izability of the sodium is not magnified, electrostaticinteraction with other residues (in particular mainchain atoms: e.g., O Ser 236, O Leu 237) surround-ing the cation–π binding site are overestimated inthe calculation of the interaction energy and largedeviations from a cation–π geometry are observed.The use of a distance-dependent dielectric ε = 4 andenhanced polarizability of the cation (100 times theAii value for Na+) seems adequate to counter bal-ance this overestimation of the electrostatic term.

The optimum protocol found in this study(down-scaled electrostatics, influence of the polar-izability) may seem counterintuitive. Indeed, a clearindication that electrostatics play an important rolein the cation–π interaction, at least in the gas phase,comes from the comparison of the binding ability ofsimple alkali metals to benzene: the trend is Li+ >Na+ > K+ > Rb+.1 This is a classical electrosta-tic sequence (exactly what is seen when the ben-

FIGURE 3. Modeling of the cation (Na+)-aromaticinteraction with Trp9 of bTIMmut. The experimentalgeometry (A) is compared to the minimized geometriesobtained by standard protocols (C) or using theoptimized procedure developed in this work (B).

zene is replaced by Cl−). If polarizability, dispersionforces, or charge transfer effects were dominant, onemight have expected the larger Rb+ ion to be thestrongest binder. The large, permanent quadrupolemoment of benzene is a major part of the electrosta-tic component of the cation–π interaction.17, 18 Theagreement between the HF, DFT, and the force fieldmodeling points to the fact that the coulombic in-teraction dominates the binding. The bond energyof X-benzene (X being an alkali metal) is typically35 kcal/mol. Using a point charge instead of themetal leads to BE of about 30 kcal/mol. Thus, theelectrostatic part is responsible for the binding inthese cases. In neutral complexes this part of the in-teraction is removed and the interaction energy issmaller (and the bond length consequently longer)by almost the same amount (i.e., 30 kcal/mol).Other effects (like dispersion, charge transfer, polar-izability) start to play dominant role in the binding.The interplay of all these forces is strongly depen-dent on the (electronic) nature of X.

That said, a “nonelectrostatic” component of thecation–π interaction does exist, and reflects a combi-nation of effects mostly related to the polarizabilityof the aromatic and the cation. The importance ofthe polarizability term was underlined in the studyof the affinity of a trimethyl cation (α = 7.6 Å3)probe for the aromatics in the GRID procedure. Thisinfluence of the polarisability is also illustrated bythe importance of the Aij term of the Lennard–Jonesnonbond potential in the geometry optimization.Reduction of the electrostatics is a way to compen-sate the fact that no explicit (de)solvation effectsare taken into account. In the absence of a propermodel for the solvent, the calculated electrostatic in-teractions tend to be overestimated. This is balancedin our study by modulating the dielectric constant(distance-dependant 4∗r).

Conclusion

Evidence for the existence of metal ion–proteininteractions involving aromatic systems exist: in thecrystallographic structure of a thermophilic Bacil-lus stearothermophilus triosephosphate isomerase(H12N/K13G) mutant (bTIMmut), a sodium cationfaces the lateral chain of a tryptophan residue(Trp9).14 The distance between the ion and theindole ring (4.1–4.3 Å) is compatible with ear-lier reports,6 although longer than the mean dis-tance observed in small molecule structures (cation-centroid of the aromatic distance around 3.4 Å). Twocomplementary aspects of this metal cation–π inter-actions were addressed in the present work.

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CATION–π BINDING SITES IN (MACRO)MOLECULES

First, theoretical descriptors for detecting cation–π binding sites in (macro)molecules were found:the GRID program is a useful diagnostic procedurewhen ran with the trimethylamine cation (NM3)probe. This procedure offers an interesting alter-native to ab initio calculated molecular electrostaticpotential maps.7, 8

Second, the influence of both electrostatic andnonelectrostatic effects on the simulation of geome-tries of metal cation–π systems has been studied.An optimization methodology has been establishedby assessing the influence of a series of parameters(partial charge, dielectric constant, and polarizabil-ity) on the geometries of cation–π complexes. Be-cause ab initio (molecular orbital, density functionaltheory) methods rapidly become limted by the sizeof the system to be studied, empirical (force field)methods were pursued. Existing force fields wereadapted by modulating the polarizability contribu-tion in the Lennard–Jones function and fine tuningthe dielectric constant used during the geometryoptimization. The resulting procedure was appliedwith success to the simulation of the cation–π inter-action observed in bTIMmut.

This work points to the important role that bothelectrostatic and polarization terms play in the de-scription of the cation–π interaction.

Acknowledgments

I thank D. Maes for sending me the coordi-nates of bTIMmut before release of the crystallo-

graphic structure. I also thank the anonymous refer-ees whose comments were very much appreciated.

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