polyelectrolyte block copolymer and oppositely charged surfactant

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Molecular modelling of cation–π interactions a

Guillaume Lamoureux & Esam A. Orabi

a

a

Department of Chemistry and Biochemistry, Centre for Research in Molecular Modeling, Concordia University, 7141 Sherbrooke Street West, Montréal, Québec, H4B 1R6, Canada Version of record first published: 04 Jul 2012.

To cite this article: Guillaume Lamoureux & Esam A. Orabi (2012): Molecular modelling of cation–π interactions, Molecular Simulation, 38:8-9, 704-722 To link to this article: http://dx.doi.org/10.1080/08927022.2012.696640

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Molecular Simulation Vol. 38, Nos. 8 – 9, July– August 2012, 704–722

Molecular modelling of cation– p interactions Guillaume Lamoureux* and Esam A. Orabi Department of Chemistry and Biochemistry, Centre for Research in Molecular Modeling, Concordia University, 7141 Sherbrooke Street West, Montre´al, Que´bec H4B 1R6, Canada (Received 6 March 2012; final version received 23 April 2012)

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Cation – p interactions have long been considered a challenge for molecular modelling and a shortcoming of most of the commonly used biomolecular force fields. In this article, we provide an overview of current research on molecular modelling of cation – p interactions, with an emphasis on applications to proteins and on our recent polarisable models based on the classical Drude oscillator. We describe the main approaches used to model cation – p interactions in solution and illustrate their relevance to a few case studies: the stability of the villin headpiece subdomain, the blockade of potassium channels by quaternary ammonium ions, and the permeation of ammonium across transporters of the Amt/MEP family. Keywords: molecular modelling; cation –p interactions; cation – aromatic interactions; proteins

Guillaume Lamoureux was born in Que´bec City, Canada, in 1973. He received his B.Sc. in Physics from Universite´ Laval in 1995 and his M.Sc. degree from Universite´ de Sherbrooke in 1997. He received his Ph.D. in Physics from Universite´ de Montre´al in 2005, for his work on polarisable force fields for biomolecular systems (under the supervision of Benoıˆt Roux). From 2000 to 2004, he was a visiting graduate assistant at the Weill Cornell Medical College of Cornell University. After postdoctoral studies in the laboratory of Michael L. Klein at University of Pennsylvania, he joined the faculty of the Department of Chemistry and Biochemistry of Concordia University in 2007.

Esam A. Orabi was born in Assiut, Egypt, in 1983 and received his B.Sc. degree in Chemistry from Assiut University in 2004. He received his M.Sc. degree from Concordia University in 2011 and is currently pursuing his Ph.D. degree at the same university, working on molecular modeling of ions in biological systems.

1.

Introduction

Cation – p interactions, more properly called ‘cation – aromatic interactions’, refer to the non-covalent association of a positively charged moiety with the face of an aromatic ring [1]. In the context of proteins, the term is used to describe the affinity of the ammonium group of lysine (Lys) or the guanidinium group of arginine (Arg) – or the occasional protonated histidine (His) – for the aromatic side chains of tryptophan (Trp), phenylalanine

*Corresponding author. Email: [email protected] ISSN 0892-7022 print/ISSN 1029-0435 online q 2012 Taylor & Francis http://dx.doi.org/10.1080/08927022.2012.696640 http://www.tandfonline.com

(Phe) and tyrosine (Tyr) [2,3]. Proteins also participate in cation – p interactions with small molecules, providing either the ‘aromatic’ part of the pair (to small ions such as Kþ and NHþ 4 or to cationic moieties of larger ligands) or the ‘cation’ part (to aromatic moieties of drug molecules, for instance). Cation– p interactions in condensed phase present an unusual challenge for molecular modelling: they bring together compounds that, from the conventional

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Molecular Simulation 705 perspective of force field development, are presumed to never ‘mix’: a hydrophobic aromatic group and a hydrophilic cation. Since most molecular models for condensed-phase simulations rely on the assumption that a hydrophobic molecule will be found in non-polar environments, cation – p interactions raise significant transferability issues. In this article, we provide an overview of the molecular modelling approaches to cation – p interactions, with an emphasis on the models used in simulations of biomolecules. We also review our recent work on the molecular modelling of cation –p interactions using polarisable force fields. (For a general presentation of cation –p interactions in biological context, we refer the reader to Refs [4 – 6].) The article is divided as follows: in Section 2, we present an overview of the literature on ab initio and density functional theory (DFT) calculations on small cation – p clusters, using benzene as prototype p system. In Section 3, we describe the main modelling approaches to investigate cation – p complexes in solution and discuss their performance and their limitations. In Section 4, after reviewing results from the literature regarding the general occurrence of cation –p pairs in proteins, we discuss instances of protein simulations in which cation – p interactions have been shown to play a critical role. Section 5 is a short recapitulation of the salient points. 2.

Modelling gas-phase clusters

2.1 Ab initio and DFT calculations Small cation – p clusters are amenable to high-level ab initio quantum chemistry calculations and to DFT calculations, and there is a large body of literature related to cation – p interactions relevant to areas such as physical organic chemistry, supramolecular chemistry, biochemistry, and drug design. Reviews on the physical/computational aspects of the topic have been published by Kim et al. [7] and Frontera et al. [8]. Since our focus is on cation – p interactions in condensed phase (in proteins, particularly), we restrict our overview to systems that are either highly prototypical or immediately relevant to protein structure and protein– ligand binding. By far the most commonly examined system is the ion – benzene dimer (see Figure 1(a)), which has been investigated for the alkali metal ion series (Liþ, Naþ, Kþ, Rbþ and Csþ; see Ref. [9] for instance), as well as for biologically relevant cations such as ammonium [10 –13], methylammonium (MAþ) [14], and tetramethylammonium (TMAþ) [11,12,14– 18] (see Table 1 for a summary of results). Benzene is generally viewed as a minimal model for Phe and Tyr side chains and for the six-membered ring of Trp and as a comparison point for substituted [19 –24] and polycyclic [25,26] aromatics. Significant gains in accuracy have been realised since the original HF/STO-3G calculations on the benzene – Naþ

(a)

(b)

+

(c)

+

+

Figure 1. (a) Cation – p interaction between a monovalent cation and a benzene molecule. Cation –(benzene)2 complexes in (b) sandwiched and (c) stacked arrangements. The dipoles induced by the cation in the aromatic molecules create a repulsive force for the sandwiched configuration (Ecoop . 0) and an attractive force for the stacked configuration (Ecoop , 0).

complex by Sunner et al. [27] (DE ¼ 2 25.6 kcal/mol) and the benzene –Kþ complex by Huzinaga (DE ¼ 2 12.4 kcal/mol, as reported in Ref. [27]). State-of-the-art, CCSD(T)/CBS estimates of the interaction energies have been reported for the alkali metal ion complexes [9] in good agreement with experimental data (see Table 1). More recently, energy surfaces of Liþ, Naþ, Kþ and NHþ 4 complexes have been investigated at the CCSD(T)/6311þ þ G(2d,2p) level [13] and at the CCSD(T)/CBS level for the Naþ complex [28], which provide valuable benchmark data for the parameterisation of empirical interaction models. One of the essential conclusions coming from these computational studies – of relevance to biomolecular simulations – is that Naþ, Kþ and NHþ 4 ions (as well as ZNHþ 3 groups) interact almost as strongly with benzene as with water. The complexation energies with water are 2 24.0 kcal/mol for sodium [29], 2 17.9 kcal/mol for potassium [29] (both at the MP2/CBS level) and 2 20.3 kcal/mol for ammonium [30] (at the MP2(FC)/ 6-311þ þ G(d,p) level). By comparison, the complexation energies with benzene are 2 25.4, 2 20.6 and 2 16.4 kcal/mol, respectively (see Table 1). High-level calculations on clusters containing multiple benzene molecules were also reported, with a focus on understanding either the binding of large ions in the socalled ‘aromatic cages’ (TMAþ in various ‘p – cation – p’ sandwiched conformations [31] and TMAþ surrounded by 1– 4 benzene molecules [32]; see Figure 1(b)) or the binding enhancement resulting from stacking additional aromatic groups under a cation –p pair [33 – 35] (see Figure 1(c)). The magnitude of this enhancement, not unexpectedly, depends on the size of the ion: small ions

706 G. Lamoureux and E.A. Orabi Table 1.

Experiment (DH o298 )

Ab initio

Ab initio targeta

CHARMM22/27b

Drudec

Drude (cation –p)d

–

239.46

2 35.14

2 21.08 (224.00)

217.68

225.59

2 21.04

2 17.14 (219.58)

212.85

216.22

2 17.01

2 16.78 (217.96)

–

214.03

2 16.86

Csþ

2 15.5 ^ 1.2e

2 16.21 (218.00)

–

211.39

2 16.26

NHþ 4 TMAþ

2 17.1 ^ 1.0l 2 9.4 ^ 1.0m

238.0g 2 35.8h 225.4g 2 22.2h 220.6g 2 16.5h 217.1g 2 16.8k 213.1g 2 16.3k 216.4h 28.39n 2 8.16o

2 34.89 (238.84)

Rbþ

2 39.3 ^ 3.3e 2 37.9f 2 22.5 ^ 1.5e 2 28.0i 2 17.7 ^ 1.0e 2 18.3j 2 16.4 ^ 1.0e

2 17.58 (219.78) –

– –

– –

2 17.56 –

Cation Liþ Naþ Kþ

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Interaction energies of ion– benzene dimers (in kcal/mol).

a Basis set superposition error (BSSE)-corrected MP2(FC)/6-311þþ G(d,p) calculations from Orabi and Lamoureux [30]. Rbþ and Csþ complexes calculated according to Ref. [208], using Gaussian 09 [209] (non-BSSE-corrected values in brackets). b Calculated using the CHARMM22/27 force field for benzene [30] and the Beglov and Roux parameters [210] for Naþ and Kþ ions. c Calculated from the original ion [90] and benzene [91] Drude oscillator models, using Lorentz–Berthelot combination rules for the Lennard-Jones parameters. d Polarisable force field of Orabi and Lamoureux [30]. Force field ˚, for the Rbþ and Csþ complexes parameterised according to the protocol of Ref. [30]. For Rbþ: Emin ¼ 0.2730669 kcal/mol, Rmin/2 ¼ 1.7855083 A ˚ . For Csþ: Emin ¼ 0.2766036 kcal/mol, Rmin/2 ¼ 2.0238218 A ˚ , Emin,CsC ¼ 0.7180642 kcal/mol, Emin,RbC ¼ 0.6010380 kcal/mol, Rmin,RbC ¼ 3.62408630 A ˚ . e Collision-induced dissociation data from Amicangelo and Armentrout [203]. f Mass spectrometry data from Woodin and Rmin,CsC ¼ 3.7249085 A Beauchamp [204]. g CSSD(T)/CBS calculations from Feller et al. [9]. h CSSD(T)/6-311þþ G(2d,2p) with counterpoise corrections from Marshall et al. [13]. i Mass spectrometry data from Guo et al. [205]. j Mass spectrometry data from Sunner et al. [27]. k MP2/aug-cc-pVTZ calculations from Coletti and Re [208]. l Mass spectrometry data from Deakyne and Meot-Ner [206], corrected according to Ref. [16]. m Mass spectrometry data from Meot-Ner and Deakyne [207]. n MP2/aug-cc-pVDZ calculation from Kim et al. [11]. o MP2/6-311þþ G(d,p) calculation from Reddy and Sastry [12].

such as Liþ or Naþ, which generate large electric fields at close range, display significant binding non-additivity [33 – 35] – mostly due to additional interactions between the dipoles induced in the benzene molecules [30] – but large alkylated ions such as TMAþ do not [31,32]. Electronic structure calculations of cation –p systems involving benzene and water-coordinated Mg2þ and Ca2þ ions have been reported as well [36,37], showing that, although these divalent metals may not directly coordinate a benzene molecule in aqueous solution, they may bind as supramolecular ions [Mg(H2O)6]2þ and [Ca(H2O)6]2þ. The cation –p interaction energies for these ‘dressed’ ions are in fact comparable to those of the Naþ, Kþ and NHþ 4 complexes: 2 21.55 kcal/mol for the hexaaqua magnesium complex and 2 18.53 kcal/mol for the hexaaqua calcium complex [36]. Similarly, ammonia-coordinated trivalent cobalt, in the form of [Co(NH3)6]3þ, was shown to interact strongly with benzene (DE ¼ 2 31.34 kcal/mol) [38] and with ethylene (DE ¼ 2 17.02 kcal/mol) [39]. These binding motifs are relevant to the understanding of interactions between metals and second-shell aromatic residues in metalloenzymes [40].

3.

Modelling small cation – p complexes in solution

The presence of a solvent weakens the affinity of cation – p complexes because it creates competing ‘cation – solvent’ and ‘p –solvent’ interactions. For instance, the stability of a cation – benzene pair in water is determined by the free energy of hydration of the dimer, DGhydr(Mþ – benz),

relative to the sum of the free energies of hydration of the monomers, DGhydr(Mþ) þ DGhydr(benz). Since benzene is weakly soluble in water (DGhydr(benz) ¼ 2 0.8 kcal/mol, [41]), the stability of the complex can be rationalised in terms of the free energy reward for bringing the benzene molecule in the first solvation shell of the ion and reducing benzene’s exposure to water versus the free energy penalty for displacing water molecules from the first solvation shell of the ion and disrupting its overall hydration structure. A strong cation – benzene interaction in gas phase may translate into low affinity in solution if jDGhydr(Mþ)j @ jDGhydr(Mþ – benz)j.

3.1 Continuum approaches Gallivan and Dougherty [42] have performed a revealing series of electronic structure calculations of MAþ in complex with benzene (forming a cation –p interaction) and with acetate (forming a salt bridge). The complex was described at the HF/6-31þG* level of theory and embedded in a reaction field representing the dielectric response of the solvent and including energetic contributions due to surface tension induced by the solute [43]. These calculations have shown that, while the acetate complex is much more stable than the benzene complex in gas phase, the affinity of the cation – anion pair decreases dramatically in solution, while that of the cation – p pair is only mildly reduced [42]. In water, the cation – p interaction energy was in fact predicted to be stronger than that of the salt bridge: 2 5.5 kcal/mol for the

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Molecular Simulation 707 MAþ – benzene pair but only 2 2.2 kcal/mol for the MAþ – acetate pair [42]. Similar calculations had been performed by Mavri and Hadzˇi [44] for various methylated ammonium ions paired with benzene, indole, and phenol – with the purpose of estimating the free energy of cation –p complexation in the low-dielectric environment of a receptor protein. In contradiction with Gallivan and Dougherty, these calculations suggest that cation –p complexes are less stable in a low-dielectric environment (1 ¼ 20) than in water (1 ¼ 78.3) – except for TMAþ ions, which display a greater affinity for benzene, indole, and phenol at 1 ¼ 20 than at 1 ¼ 78.3. The choice of the continuum solvent model therefore appears to be critical (see Ref. [45]). A large number of implicit solvation methods have been developed over the years – and coupled to electronic structure calculation codes – and provide estimates that agree well with experimental free energies of solvation. For a review of the various methods and their application, see Refs [46,47]. For the purpose of modelling cation – p interactions, the most useful method would take into account the possible non-zero ionic strength of the solvent (such as the IEF-PCM method of Cossi et al. [48]) and would correctly describe the highly concave geometries typical of ‘host – guest’ systems [49]. 3.2

Pairwise-additive force fields

A molecular model in which the solvent is explicitly represented requires all physical quantities (DGhydr, notably) to be averaged over a large number of solvent configurations, sampled from molecular dynamics or Monte Carlo simulations. While this represents an initial burden compared to implicit solvent approaches, it ultimately allows for a more realistic description of the cation – p pair itself, which is usually not locked into a single conformation. Pairwise-additive force fields, such as the OPLS [50,51], traPPE-EH [52,53], AMBER [54] and CHARMM [55] force fields, are the most convenient interaction models whenever large numbers of atoms are simulated. The pairwise-additive character of these force fields derives from the fact that, apart from the few terms describing the energy of covalent bonds stretching, valence angles bending and torsion angles twisting (all grouped under the term ‘Ubond’), all contributions to the potential energy U of the system are described as a sum over pairs of atoms: U ¼ U bond þ

X

uij ðr ij Þ:

ð1Þ

ij

Each pairwise contribution u depends only on the types of atoms i and j and on the distance rij between them. It is usually defined as the sum of an electrostatic contribution (described by a ‘1/r’ Coulomb term) and a van der Waals

contribution w (often described by a ‘12 –6’ Lennard-Jones term): uij ðr ij Þ ¼

qi qj þ wij ðr ij Þ: r ij

ð2Þ

Used within the context for which they are designed, pairwise-additive force fields can be highly accurate in terms of both structure and thermodynamics. Unfortunately, few of them have been a priori adjusted to reproduce cation – p interactions and to ‘balance’ with competing cation – solvent interactions [56]. One exception is the model for benzene and alkali metal cations of Albertı´ et al. [57], which was specifically calibrated for cation –benzene pairs micro-solvated by a small number of argon atoms. The model, which describes cation – Ar and benzene – Ar interactions as well [58], was used to study low-temperature processes in small clusters of relevance to mass spectrometry [58 –61]. It was also applied to ‘sandwiched’ benzene – Kþ –benzene complexes [62] – which, as is discussed later, display an anti-cooperative behaviour that cannot be described by an additive force field. In their investigation of the association of alkali metal ions with benzene in water, Kumpf and Dougherty [63] have used the OPLS force field for water and benzene [64] along ˚ qvist [65] for with the OPLS-compatible parameters of A þ þ þ þ Li , Na , K and Rb . They did not, however, use the OPLS parameters to calculate the benzene–ion interaction energy because, ‘out of the box’, these parameters are severely underestimating the cation–p energies – likely because they underestimate the permanent quadrupole of benzene and neglect the induction of a dipole in the electric field of the ion [66]. Kumpf and Dougherty [63] instead calculated the free energy of solvation of the complexes using cation–p interaction energies derived from electronic structure calculations. The motivation of Kumpf and Dougherty’s investigation was to understand the selectivity of potassium channels against other ions of the alkali metal series. Although the original relevance of that study was lost with the discovery of the first potassium channel structure [67] (showing no aromatic groups in the so-called ‘selectivity filter’), the concern remains: an accurate model for cations in solvent combined with an accurate model for aromatic molecules in solvent does not necessarily make for an accurate model for cation–p pairs in solvent. For the calculation of the ammonium – toluene potential of mean force (PMF) in water, Chipot et al. [68] have used an empirical correction to the AMBER force field in the form of a ‘12 – 10’ potential energy term between the nitrogen atom of the ion and carbon atoms of the toluene ring. With this correction, they find a free energy minimum of 2 5.47 kcal/mol, for an ammonium ˚ ion located on the C6 symmetry axis of the ring, 3.05 A away from the centre of the aromatic plane [68] – surprisingly close to the 2 5.5 kcal/mol continuum solvent

708 G. Lamoureux and E.A. Orabi

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estimate of Gallivan and Dougherty [42] for the MAþ – benzene pair. By contrast, the same PMF without the ‘12 – 10’ correction displays a shallow free energy minimum of only 2 0.76 kcal/mol [68]. The issue of transferability is probably less of a concern for larger ions, which polarise the aromatic group to a lesser extent. Duffy et al. [69] have used the OPLS force field to calculate the TMAþ – benzene and guanidinium – benzene PMFs in water. They find a free energy minimum of 2 3.31 kcal/mol for the TMAþ – benzene complex (at a ˚ ) and of 2 3.20 kcal/mol centre-to-centre distance of 4.75 A for the guanidinium –benzene complex (at a centre-to˚ ) [69]. centre distance of 3.50 A

3.3 Polarisable force fields 3.3.1 Importance of polarisability The case for using polarisable force fields for cation – p systems was made early by Caldwell and Kollman [66], and further rationalised by Orozco and co-workers [70,71] and Ponomarev et al. [72]. Using the OPLS force field as an example, Caldwell and Kollman have shown that additive models underestimate the interaction energies of the Kþ and NHþ 4 – benzene dimers by about 9 –10 kcal/mol – something that had already been noticed by Kumpf and Dougherty [63] – but that these models could be rescued by the inclusion of atomic polarisability. The inclusion of explicit polarisation also allows the permanent quadrupole moment of the benzene molecule to be brought closer to its gas-phase value [66]. A more subtle, yet essential advantage of polarisable force fields over additive force fields is also manifested in cation – (benzene)2 clusters [30]. Ab initio calculations of Kþ in complex with two benzene molecules show that the total stabilisation energy of the cluster (Etot) is nonadditive [30,34,35] and it cannot be written as the sum of interactions between pairs of fragments in the position they are found in the cluster. An additional contribution coming from the cooperativity (or anti-cooperativity) of the individual interaction can be defined as Ecoop ¼ Etot 2 ðEM2benz1 þ EM2benz2 þ Ebenz12benz2 Þ: ð3Þ

Since Etot is a negative number for any stable complex, a positive Ecoop indicates that the interactions are competitive: any two molecules considered are destabilised by the presence of the third one. Conversely, a negative Ecoop indicates that the interactions are cooperative. In the case of potassium, Ecoop is about þ 2.5 kcal/mol when the ion is sandwiched between the benzene molecules (forming a ‘competitive’ p –cation –p arrangement; see Figure 1(b)) and about 2 1.0 kcal/mol when the two benzene molecules are stacked on the same side of the ion (forming a ‘cooperative’ cation – p – p arrangement; see Figure 1(c))

[30]. This 3.5 kcal/mol difference, which becomes even larger if Kþ is replaced by Naþ (5.0 kcal/mol) or Liþ (12.2 kcal/mol) [30], can be represented only by a polarisable force field that describes the induction of a dipole perpendicular to the aromatic plane – and creates a dipole – dipole repulsion in sandwiched complexes and a dipole – dipole attraction in stacked complexes. Pairwise corrections can compensate for energy discrepancies in isolated cation – p pairs, but cannot adequately describe the various configurations of cation – (p)2, cation – (p)3 and cation – (p)4 clusters. For this reason, modelling approaches such as Chipot et al.’s [68] short-range ‘12 – 10’ correction for the ammonium –benzene complex and Minoux and Chipot’s [73] ‘12 –4’ correction for ammonium – aromatic complexes are likely not transferable to systems of cations coordinated by multiple aromatic groups. Chipot and co-workers were fully aware of the issue at the time and have since then developed a polarisable force field that describes both cation – water and cation – benzene interactions [74,75]. Polarisable force fields are being developed through multiple concurrent efforts, and we refer the reader to Refs [76,77] for a review. For large-scale protein simulations, polarisable force fields of note are AMBER ff02 (using inducible point dipoles) [78,79], OPLS/PFF (using inducible point dipoles) [80 – 82], CHARMM fluctuating charges [83 –85], CHARMM Drude oscillators [76,86], PIPF-CHARMM (using inducible point dipoles) [87] and AMOEBA (using static multipoles and inducible dipoles) [88]. Another promising (although more complex) approach, developed using the ammonium – benzene dimer as a test case, relies on dipolar and ‘charge-flow’ polarisabilities derived from high-level ab initio calculations [74,75]. This combined ‘charge-flow þ dipole induction’ representation is in principle more accurate to describe electronic induction in aromatic moieties such as benzene [89]. 3.3.2

Drude oscillator model for cation – p interactions

We have recently parameterised a polarisable force field for cation – p interactions based on classical Drude oscillators [30] (see Table 1). The force field is built upon the polarisable SWM4-NDP water model [86], which was calibrated to reproduce the main properties of liquid water, including self-diffusion coefficient and dielectric constant. The SWM4-NDP model was used to develop a polarisable force field for various biologically relevant ions [90] and is currently being used as the foundation for a polarisable force field for proteins, lipids, and nucleic acids [76]. Compatible polarisable force fields were developed for benzene/toluene [91] and indole/3-methylindole [92], which are model compounds for the Phe and Trp side chains. The Drude oscillator model for benzene reproduces

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Molecular Simulation 709 the essential properties of the neat liquid at room temperature and pressure – including the dielectric constant, which is fundamentally impossible to capture without explicit polarisability – while improving the quadrupole moment of the monomer [91]. The Drude oscillator model introduces explicit polarisation by replacing each atomic partial charge qi at position ri by a charge qi – qD,i and by allowing the remaining charge qD,i (the ‘Drude particle’) to move in the direction of the electrostatic field by a distance proportional to the magnitude of that field. In a static field, this displacement vector di corresponds to the minimum-energy position of a charge qD,i coupled to a fixed point ri by a harmonic spring constant kD. The charges on individual Drude particles are set to qD,i ¼ 2 (aikD)1/2, where ai is the isotropic polarisability of atom i and kD has a uniform value for all atoms. Anisotropic polarisabilities, if required, are described using a tensorial form of the spring constant [93]. Once this replacement is performed on all (non-hydrogen) atoms, the induced dipoles can be calculated in a selfconsistent manner by finding the displacements that minimise the sum of the Coulomb energy and the energy of the harmonic springs. The Drude oscillator force field and simulation algorithm were implemented in the CHARMM software (see Ref. [94] for details) and have recently been adapted to NAMD [95]. In the CHARMM additive force field, two covalently bonded atoms labelled ‘1’ and ‘2’ interact only through the Ubond term (see Equation (1)): the non-bonded term u12(r12) is excluded from the total potential energy U under the assumption that it does not accurately describe the interaction between the two bonded atoms. The term u13(r13) between two atoms ‘1’ and ‘3’ covalently bonded to a common atom ‘2’ is excluded as well. For the CHARMM Drude oscillator force field, this prescription is slightly modified: the ‘1 – 2’ and ‘1 –3’ atoms interact only through their induced dipoles, represented by the 2 qD charge at position r and the þ qD charge at position r þ d. To prevent over-polarisation, the pairs of charges interact through a screened Coulomb term of the form ‘S(r)/r’ instead of the usual ‘1/r’ term [91,93,96]. This short-range dipole –dipole interaction allows the Drude oscillator model to reproduce the polarisability anisotropy of benzene, toluene, indole, and 3-methylindole using isotropic polarisabilities on all atoms [91,92]. A singular feature of the Drude oscillator model for cation – p interactions is the presence of a massless, non-atomic site at the centre of the six-membered rings of benzene, toluene, indole, and 3-methylindole [30,97]. This site, labelled as ‘X’ and constructed using the LONEPAIR facility of CHARMM, has no electric charge and interacts only with cations strictly through a Lennard-Jones term. It is used to describe more accurately the energy surfaces of þ þ Naþ/NHþ 4 – benzene dimers [30], and of Na /NH4 – þ þ toluene, NH4 – indole, and NH4 – 3-methylindole dimers

[97]. It was found unnecessary for the Liþ/Kþ –benzene, Li þ/K þ – toluene, Na þ /K þ – indole, and Na þ/K þ – 3methylindole dimers [30,97]. In the gas phase, the Drude oscillator cation – p model captures the competitivity and cooperativity (Ecoop) of the various arrangements of cation –(benzene)2 clusters [30]. For small ions such as Liþ, Naþ, Kþ and NHþ 4 , the difference in cooperativity between a ‘sandwiched’ and a ‘stacked’ conformation (see Figure 1) is 11.03 kcal/mol for Liþ, 4.36 kcal/mol for Naþ, 2.80 kcal/mol for Kþ and 3.59 kcal/mol for NHþ 4 (compared to 12.21, 5.03, 3.53 and 3.98 kcal/mol, respectively, calculated at the MP2(FC)/6-311þ þ G(d,p) level) [30]. A non-polarisable model, however accurate at reproducing the energetics of a cation – p pair, yields Ecoop ¼ 0 by definition. The Drude oscillator model was used to investigate the thermodynamics of association of cation – benzene pairs and cation – (benzene)2 triples in water [30]. Liþ – and Naþ – benzene complexes were found to be unstable due to the high thermodynamic cost of displacing a water molecule from the first solvation shell of the ions. Kþ – and NHþ 4 – benzene complexes are stable, even though water molecules are displaced from the first solvation shell of the ions upon formation of the complex [30] (two water molecules for Kþ and one for NHþ 4 ). The model predicts that the Kþ – (benzene)2 and NHþ – 4 (benzene)2 complexes adopt a ‘triangle’ geometry that forms two cation – p interactions at almost right angles and allows the hydrophobic association of the benzene molecules while minimising cation dehydration [30]. Figure 2 presents an additional application of the model, in which the radial PMFs of Kþ – benzene and NHþ 4 –benzene pairs in aqueous solution presented in Figure 5 of Ref. [30] are broken down into 2D PMFs, showing separately the effect of the distance and of the deviation from the C6 symmetry axis of the benzene molecule. The directionality of the interaction in solution is apparent: the ion is significantly more stable along the u ¼ 0 line (facing the benzene ring) than along the u ¼ 908 line (in the plane of the benzene ring). Also of interest is that NHþ 4 appears to be weakly binding the benzene molecule at any orientation – even from the edge – while Kþ does not. The strong directional interaction displayed in Figure 2 would be observed only if the cation –p pair was preoriented (as in a protein-binding site). In solution, it is significantly weakened by the orientational fluctuations of the aromatic molecule – which is why the effective PMF of association is only 1.2-kcal/mol deep for Kþ and 1.4kcal/mol deep for NHþ 4 [30]. 3.4

Ab initio and QM/MM molecular dynamics

Molecular dynamics simulations using atomic forces derived from an electronic structure calculation are computationally expensive and are typically used to

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710 G. Lamoureux and E.A. Orabi

Figure 2. (Colour online) 2D PMFs of (b) Kþ – benzene and (c) NHþ 4 – benzene pairs solvated in water. The PMF corresponds to the function 2 kBT ln[r(r,u)/2pr sin u ], where r is the distance to the benzene centre and u is the angle relative to the C6 symmetry axis of benzene (a). Each distribution r(r,u) is calculated from a 125-ns long molecular dynamics trajectory obtained using the force field and simulation protocol of Ref. [30]. To prevent unproductive sampling, a restraint force is applied to ˚. the solute pair for r . 7 A

study reactions in solution [98,99]. Nevertheless, there are numerous instances in the literature where such methods were used to study non-covalent association such as ion hydration (see, e.g., Ref. [100]) and ion – aromatic interactions in water. At the same time as Duffy et al. [69] (who were using the OPLS force field), Gao et al. [101] have investigated the association of TMAþ with benzene in aqueous solution using a hybrid quantum mechanics/molecular mechanics (QM/MM) approach relying on the AM1 semi-empirical QM model [102] for the solute molecules and on the TIP3P additive force field [103] for the solvent molecules.

The AM1 model is computationally efficient enough that Gao et al. could estimate the PMF of association. The free energy minimum they find, 21.8 kcal/mol at a ˚ distance, corresponds to a solvent-separated pair. 7.5 A By contrast, the OPLS force field yields a 23.31 kcal/mol ˚ ) and no free energy minimum at contact distance (4.75 A free energy minimum at solvent-separated distances [69]. Given that the AM1 model underestimates the electrostatic potential surface of benzene and the gas-phase interaction energy with substituted ammonium ions [20], it is likely that the QM(AM1)/MM simulations will underestimate the stability of the complex. More recently, Sa et al. [104] have performed a fully quantum mechanical simulation of an NHþ 4 – benzene pair in water with Car – Parrinello molecular dynamics (CPMD) [105]. Using constrained dynamics, the authors have calculated two different PMFs of association: ‘en face’, moving the NHþ 4 ion along the C6 symmetry axis of the benzene molecule, and ‘edge-on’, keeping the ion in the plane of the benzene molecule. The ‘en face’ PMF displays a deep free energy minimum of 2 5.75 ˚ from the ring centre. kcal/mol, at a distance of 3.25 A By contrast, the ‘edge-on’ PMF displays a shallow free energy minimum of 2 0.33 kcal/mol. The results of Sa et al. can be directly compared to those of Figure 2(c), obtained using the Drude oscillator model. The cut through the u ¼ 0 axis of the 2D PMF of Figure 2(c) corresponds to the ‘en face’ PMF of Sa et al. While the equilibrium distances are in good agreement ˚ for the Drude oscillator model versus 3.25 A ˚ for the (3.3 A Sa et al. simulation), the free energy minima are markedly different: 2 2.8 kcal/mol for the Drude oscillator model versus 2 5.75 kcal/mol for the Sa et al. simulation. On the other hand, the cut through the u ¼ 908 axis of Figure 2(c) is significantly deeper than the ‘edge-on’ PMF of Sa et al.: 2 0.6 kcal/mol versus 2 0.33 kcal/mol. As mentioned previously, a similarly deep ‘en face’ PMF was obtained by Chipot et al. [68] for the NHþ 4 – toluene pair using a corrected additive force field ˚ separation). The NHþ – toluene (2 5.47 kcal/mol at 3.05 A 4 PMF is less deep once averaged over the orientational ˚ separfluctuations of toluene: 2 2.99 kcal/mol at 3.16 A ation [68], which is comparable to the 2 3.31 kcal/mol free energy minimum of the TMAþ – benzene pair modelled with the OPLS force field [69]. Given that the solubility of benzene in aqueous ammonium salt solutions increases with the size of the ion þ þ [NHþ 4 , TMA , tetraethylammonium (TEA )] [106], we expect the depth of the benzene – ion PMF to increase with the size of the ion as well. The orientationally averaged free energy minima are with respect to the trend in this regard. For the NHþ 4 – benzene pair, the Drude oscillator force field predicts 2 1.4 kcal/mol and the CPMD simulation predicts about 2 1.6 kcal/mol (a number we estimate based on the minima of the ‘en

Molecular Simulation 711

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face’ and ‘edge-on’ PMFs) [104]; for the NHþ 4 –toluene pair, the corrected AMBER force field predicts 2 2.99 kcal/mol [68]; for the TMAþ –benzene pair, the OPLS force field predicts 2 3.31 kcal/mol [69]. The QM(AM1)/MM simulation predicts 2 1.8 kcal/mol [101], but this is likely an underestimation. In contrast to cation –p interactions in water, p – p interactions are less sensitive to issues of transferability. Our recent estimate of the benzene – benzene affinity in water using a polarisable force field (2 1.1 kcal/mol) [30] is closer to the experimental value (2 1.00 ^ 0.05 kcal/mol [107]) but not markedly different from earlier estimates using additive force fields from Jorgensen and Severance (2 1.5 kcal/mol) [64], Linse (2 0.50 kcal/mol) [108], and Chipot et al. (2 0.36 kcal/mol) [109].

4. Modelling cation –p interactions in proteins Many computational studies of small cation –p systems are motivated by their relevance to protein structure and ligand binding, yet few have attempted to bring these improved models to all-atom protein simulations. A notable exception is the recent simulations of Hagiwara et al. [110], which use a numerical, grid-based force field to describe a structurally important Naþ – Phe interaction in thermoalkalophilic T1 lipase. Hagiwara et al. show that the stability of the catalytic site requires a correct description of the cation –p interaction. In this section, we first describe where cation – p interactions are statistically expected to be found in proteins, then we discuss the importance of molecular models for cation – p interactions in three different contexts: protein structure, proteins in lipid membranes and protein– ligand complexes.

4.1 Surveys of protein structures Surveys of high-resolution protein structures from the Protein Data Bank (PDB) looking for cation – p pairs between Arg/Lys and Phe/Trp/Tyr side chains (or ‘amino– aromatic’ pairs, when Asn/Gln/His side chains are considered instead of Arg/Lys) [3,73,111– 113], have shown that these interactions are more common than expected from chance alone. Using an energetic criterion to define a properly formed cation –p interaction, Gallivan and Dougherty [3] have found that 26% of all Trp in (non-redundant) protein structures are involved in cation – p interactions. This proportion is lower for other amino acids (18% for Arg, 7% for Lys, 10% for Phe and 14% for Tyr [3]), but remains sizeable. In terms of their exposure to solvent, cation – p pairs inherit the characters of both amino acids: like aromatic residues, few are found highly solvent-exposed but, like cationic residues, few are found completely buried in the

hydrophobic core of the protein [42]. While half of all Arg/Lys side chains (in non-redundant protein structures) have more than 34% of their surface exposed to the solvent, half of all Phe/Trp/Tyr side chains have less than 3% of their surface exposed [42]. In other words, the ‘median’ solvent exposure is 34% for cationic side chains but only 3% for aromatic side chains. Cation –p pairs, as a whole, have a median solvent exposure of 20% [42]. A statistical survey of amino acid pairs at protein– protein interfaces shows that the most over-represented ‘charged-hydrophobic’ pair is Arg – Trp [114] – the same as for monomeric proteins [3]. Although the typical mode of interaction for these pairs was reported not to be proper ‘cation – p’ but ‘aliphatic – aromatic’ [114], a more recent survey [115] using an energy-based definition of cation – p pairs (from Gallivan and Dougherty [3]) has uncovered a significant number of proper interfacial cation – p interactions. While this second survey shows Arg– Trp to be the most over-represented cation – p pair as well, given the occurrences of the individual amino acids at protein– protein interfaces [115], it shows that Arg –Tyr is the most frequent pair. This is partially due to the fact that protein– protein interfaces are naturally rich in Arg and Tyr residues [115]. A survey of amino acid pairs involved in the packing of transmembrane helices has revealed that Arg – Trp and Lys –Tyr pairs – potentially forming cation – p interactions – are found in transmembrane helices more often than in globular protein helices [116]. These residues (Arg, Lys, Trp and Tyr) happen to be enriched in transmembrane helices at the level of the lipid head groups [117,118] – consistent with the fact that Trp and Tyr are both aromatic and polar and that cation –p pairs are rarely completely solvent-exposed or completely buried. By contrast, no such enrichment is observed for Phe, which is distributed more evenly throughout the thickness of the membrane [118]. More recently, Reddy et al. [119] have screened the Cambridge Structural Database and the PDB for ‘cation– p –p’ motifs involving Liþ, Naþ, Kþ, Mg2þ and Ca2þ, on the assumption that these interactions were cooperative and therefore should be over-represented. While ‘cation– p –p’ motifs can indeed be found in the PDB, it is not clear whether they are significantly enriched [120,121]. 4.2 Protein stability and folding Cation –p interactions have been directly implicated in the stability of small a-helices [122 –124]. In these helical systems, a pair of Arg/Lys and Phe/Trp/Tyr placed at positions i and i þ 4 contributes to the free energy of folding by about 0.1 – 0.4 kcal/mol (as measured by circular dichroism [122 – 124]). Cation –p interactions have also been shown to stabilise b-hairpin peptides by 0.2 kcal/mol for Phe –Lys interactions and 0.5 kcal/mol for Trp – Arg interactions [125], and by as much as 1.0 kcal/mol for

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712 G. Lamoureux and E.A. Orabi individual cation – p interactions forming a Trp – Lys– Trp pocket [126]. Because simulations of protein folding performed with all-atom molecular dynamics remain a major computational challenge, all-atom force fields have been compared in terms of their folding performance for only a handful of systems (e.g. see Ref. [127]). Extensive simulations using various additive force fields have been performed on the fast-folding villin headpiece subdomain HP36 [128 – 133] which, experiments suggest, contains a Phe47 –Arg55 pair forming a cation –p interaction in the folded state [130]. Some of these simulations were reported to yield a stable Phe47 – Phe58 hydrophobic contact [131,132] or a stable Asp44 –Arg55 salt bridge [132] but, whether due to force field artefacts or insufficient sampling, few were reported to form a stable Phe47 –Arg55 cation – p pair [130]. The time scale for the folding of the villin headpiece, of the order of the microsecond, has now been many times broken by simulations based on additive force fields [133]. It is to be expected that a new wave of simulations – for which the sampling issue is settled – will bring systematic improvements to the force fields. The villin headpiece has recently been simulated for a few tens of nanoseconds using the polarisable AMOEBA force field [88], but no observations were reported concerning the stability of the Phe47 – Arg55 pair. While polarisable force fields will probably not be mature enough for de novo protein-folding simulations for a few more years, they will likely have some earlier uses for the refinement of existing protein structures [134 – 136]. For instance, structural data on the villin headpiece are unclear on how Phe47 contributes to the stability of the protein [130]. The X-ray structure shows the residue Phe47 ˚ ) and at at cation – p binding distance of Arg55 (4.5 A ˚ ), but the NMR hydrogen-bonding distance of Asp44 (2.7 A ˚ away from Arg55 and 7.9 A ˚ structures show Phe47 6.3 A away from Asp44 [130]. A better-balanced description of cation – p interactions would likely provide a more Table 2.

Complexation energies (kcal/mol) of MAþ and MeGdmþ with aromatic ligands.

Cation

Ligand

MAþ

Benzene Toluene Indole 3-Methylindole Phenol p-Methylphenol Benzene Toluene Indole 3-Methylindole Phenol p-Methylphenol

MeGdmþ

consistent picture of the various interactions at the core of the villin headpiece (p – p stacking, cation –p interactions and salt bridges). It would also likely help in understanding the stability of the Arg– Trp – Arg ‘cation – p – cation’ structure observed in folding intermediates for simulations of lysozyme [137,138]. Table 2 reports the ab initio interaction energies of MAþ and methylguanidinium (MeGdmþ) ions with benzene, toluene, indole, 3-methylindole, phenol and p-methylphenol. These molecules serve as prototype compounds for the parameterisation of the CHARMM22/27 force field for Arg, Lys, Phe, Trp and Tyr side chains. The lowest-energy structure of each complex is presented in Figure 3 along with other low-energy structures. The ab initio energies are systematically underestimated by the CHARMM22/27 force field (see Table 2), as well as by the AMBER force field [73]. The deviation relative to ab initio data is larger for the MAþ complexes due to the smaller size of the ion and the stronger electric field it generates (see Figure 3). Pairwise corrections, in the form of additional ‘1/r n’ terms, have been proposed to alleviate these problems for both the CHARMM and AMBER force fields [73,139]. Despite their simplicity, they have been seldom used for protein simulations. For protein structure prediction, statistical potentials such as Rosetta [140] or OPUS-PSP [141] may actually provide a more convenient alternative to all-atom force fields. For instance, the statistical potential for cation – p amino acid pairs of Gilis et al. [142] correlates very well (0.96) with the Hartree-Fock (HF) and MøllerPlesset (MP2) ab initio interaction energies of the equivalent fragments in gas phase – better than the CHARMM27 energies of the same fragments. Statistical potentials are constructed to reproduce the most probable arrangement of residues and are therefore likely to capture the affinities of amino acids in a protein environment. They are, however, ultimately limited by their pairwise additivity and their coarse-grained representation of the amino acids.

MP2(full)/6-311þ þG(d,p)a 216.26 217.93 222.86 223.99 217.62 219.22 212.99 214.28 219.95 220.75 216.59 217.90

(2 19.68) (2 21.51) (2 27.11) (2 28.29) (2 21.21) (2 22.80) (2 17.31) (2 18.88) (2 25.53) (2 26.87) (2 21.59) (2 23.06)

CHARMM22/27b

Differencec

2 13.09 2 13.21 2 20.01 2 19.92 2 18.41 2 18.09 2 11.90 2 12.66 2 19.54 2 19.40 2 17.96 2 17.86

3.17 4.72 2.85 4.07 20.79 1.13 1.09 1.62 0.41 1.35 21.37 0.04

a BSSE-corrected energies calculated using Gaussian 09 [209] (non-BSSE-corrected values in brackets). b Calculated using the CHARMM22/27 force field for the model compounds [30], in the conformations corresponding to the MP2 calculations. c Relative to the BSSE-corrected energies.

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Molecular Simulation 713

Figure 3. (Colour online) Optimised structures of MAþ and MeGdmþ ions in complex with model compounds of Phe, Trp and Tyr, calculated at the MP2(full)/6-311þ þG(d,p) level of theory. For each complex, the most stable conformation of the ion is represented as opaque ‘sticks’. (These structures are labelled with BSSE-corrected complexation energies, reproduced from Table 2.) Stable sub-optimal conformations are displayed as transparent ‘sticks’. None of the sub-optimal conformations have energies more than 1.2 kcal/mol above the global minimum.

Drude oscillator polarisable models for MAþ and MeGdmþ are currently being developed by Lopes and MacKerell. Our own tests using a preliminary version of the models (Lopes and MacKerell, private communication) with the existing models for aromatic compounds [91,92] confirm that they significantly improve the description of cation –p interactions. 4.3

Protein – lipid interactions

Trp is known to anchor membrane proteins in the lipid bilayer [143] and is involved in the action of antimicrobial peptides (known to disrupt bacterial membranes) [144].

A Trp residue is driven to the interface of the lipid membrane likely by the competition between the hydrophobicity of the aromatic group and its potential to form hydrogen bonds and cation – p interactions [139,145] (depending on the composition of the membrane). Cation– p interactions between the Trp residues of transmembrane protein gramicidin A and the charged head groups of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE) and 1-palmitoyl-2-oleoyl-sn-glycero-3phosphocholine (POPC) lipid bilayers (ammonium, þ ZNHþ 3 , for POPE and trimethylammonium, ZNðCH3 Þ3 , for POPC) were investigated by Petersen et al. [146]. The system was simulated using the CHARMM27 force field and the four Trp residues of gramicidin A were systematically analysed for possible cation –p interactions with the lipids. Except for the more buried Trp4, all surface Trp residues (Trp9, Trp11, and Trp13) were observed to form cation – p interactions in the POPE membrane [146]. However, only the outermost Trp13 was found to form cation – p interactions in POPC [146], consistent with the fact that TMAþ interacts with 3-methylindole less strongly than NHþ 4 – at least in a hydrophobic, low-dielectric environment. Many factors are at play in determining the energetics of Trp anchoring [146,147], including the bilayer thickness and the physiological salt concentration but, since the POPE and POPC lipid head groups of the CHARMM27 force field were developed from the model compounds MAþ and TMAþ, it may be expected that the underestimated MA þ – 3-methylindole interaction energy reported in Table 2 would translate into weak interactions between Trp and POPE lipid head groups. As noted by Petersen et al. [146], inclusion of molecular polarisability may help in striking a more realistic balance among these different factors. This balance is likely essential to accurately simulate lipid – protein interactions in mixed membranes or the effect of local and general anaesthetics. In particular, the potency of aromatic anaesthetic molecules correlates surprisingly well with their affinity at forming cation – p interactions [148]. 4.4

Protein –ligand binding

A recent survey of protein–ligand contacts in the PDB [149] shows numerous instances of cation–p interactions. While a number of reviews have been devoted to some of the most biologically important cases [4–6,150], only a large-scale analysis (using a tool such as Relibase [151,152]) could do justice to the variety of ligand-binding modes involving at least one cation–p interaction. For instance, Biot et al. [45,153] have extracted from the PDB a series of fragment pairs representative of protein–adenine (Ade) interactions. They have found that their relative occurrences follow the trend Arg–Ade . Asn/Gln–Ade . Lys–Ade [45] and correlate with interaction energies calculated at the MP2 level in an IEF-PCM continuum solvent.

714 G. Lamoureux and E.A. Orabi After a short description of the widespread motif of an ammonium/trimethylammonium group bound to an ‘aromatic cage’, we discuss two cases that illustrate two very different ligand-binding modes: TEAþ binding to the extracellular surface of potassium channels and NHþ 4 binding to the extracellular site of Amt/MEP ammonium transporters.

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4.4.1

Aromatic cages

Early efforts on modelling cation – p interactions were motivated by protein structures such as (ligand-bound) immunoglobulin Fab McPC603 [154,155] and acetylcholinesterase [156,157]. The immunoglobulin structure shows a pocket formed by residues Trp107H, Tyr33H and Tyr100L, which binds the trimethylammonium (ZNðCH3 Þþ 3 ) end of the phosphocholine ligand (see Figure 4(a)). The acetylcholinesterase structure, on the other hand, shows a pocket formed by residues Trp84 and Phe330 and the negatively charged Glu199 (see Figure 4(b)).

These ‘aromatic cage’ structures have motivated a series of statistical analyses of contacts between aromatic molecules and quaternary ammonium (QA) moieties [151,152,158]. Recently, Campagna-Slater et al. [159,160] have used a pharmacophore screening approach to identify potential methyllysine-binding domains from the PDB. Using the binding sites of known methyllysine receptors – which are typically formed of a ‘cage’ of 2 –4 aromatic residues (Phe/Trp/Tyr) and one negatively charged residue (Asp or Glu) [159] – as basis for their pharmacophore description, they have recovered a large number of proteins in complex with QA (ZNðCH3 Þþ 3 ) ligands [160]. This confirms the specific affinity of ‘aromatic cages’ for ammonium moieties. Dougherty and co-workers have directly probed the importance of cation –p interactions for ligand binding in a variety of receptors by mutating their Phe or Trp residues to various (unnatural) fluorinated analogues [161]. Because fluorine is more electron withdrawing than hydrogen, cation – p complexes of benzene get gradually weaker as

Figure 4. (Colour online) Crystal structures of (a) phosphocholine bound to immunoglobulin Fab McPC603 (PDB ID: 2MCP), (b) decamethonium bound to acetylcholinesterase [157] (PDB ID: 1ACL), (c) triethylarsenium ion bound to the extracellular surface of KcsA [183] (PDB ID: 2BOC) and (d) ammonium ion bound to the extracellular site of AmtB (PDB ID: 1U7G). Side chains are shown as spheres and substrates as ‘sticks’ (except for the ammonium ion in (d), shown as a sphere).

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Molecular Simulation 715 more hydrogen atoms are substituted for fluorine – to the extent that hexafluorobenzene forms anion– p complexes [162]. Consequently, if a Phe or Trp residue is involved in a cation – p interaction with the ligand, it is expected that successive fluorinations of its six-membered ring will cause a systematic decrease in binding. Using this elegant experimental approach, Dougherty and co-workers have identified functionally important cation – p interactions in the following receptors: the nicotinic acetylcholine receptor (between Trp149 and the ZNðCH3 Þþ 3 group of acetylcholine) [163,164], the 5-HT3A serotonin receptor (between Trp183 and the ZNHþ 3 group of serotonin) [165,166], the GABAA [167] and GABAC receptors [168] (between a Tyr residue and the ZNHþ 3 group of GABA), the glycine receptor (between Phe159 and the N-terminus of glycine) [169] and D2 dopamine receptors (between Trp6.48 and the ZNHþ 3 group of dopamine) [170]. For a fully formed cation – p interaction, each additional fluorine atom inserted contributes to reducing the experimental binding free energy by approximately the same amount (e.g. DG). This amount DG, which correlates with the strength of the cation –p interaction itself, depends on the nature of the chemical fragments forming the cation –p pair [167 –170] but is not always consistent with the corresponding ab initio interaction energies (such as those reported in Table 2). In other words, the contribution of a cation – p interaction to the binding cannot be directly predicted from the amino acid (Phe/Trp/Tyr) and the cationic group, and a more comprehensive modelling approach is likely required. For instance, Do¨lker et al. [171] have performed ab initio calculations of MAþ and TMAþ ions and found that their affinities for benzene (mimicking Phe, Trp or Tyr) could be significantly modulated by the presence of an acetate fragment (mimicking Asp or Glu) binding the ion from the opposite side: from 2 21.6 to 2 10.8 kcal/mol for MAþ and from 2 14.8 to 2 10.6kcal/mol for TMAþ. The binding of MAþ to benzene is affected by the presence of water molecules as well [172] (although to a lesser extent).

4.4.2

Extracellular blockade of ion channels by QA ions

The activity of most potassium channels is inhibited by QA ions such as TMAþ or TEAþ [173,174]. While a concentration of QA ions on the intracellular side blocks Kþ channels fairly indiscriminately [175], the effect of QA ions on the extracellular side of the membrane is proteinspecific: some, such as the bacterial KcsA channel, are strongly inhibited by TEAþ (with KI , 1 mM) while others, such as the eukaryotic Shaker Kþ channel, are not (KI . 20 mM) [175]. This disparity in the measured KI’s suggests that QA ions have a specific mode of binding with the extracellular surface of the sensitive channels.

Heginbotham and MacKinnon [175] have proposed that the binding was driven by cation –p interactions, after observing that mutating the wild-type (non-aromatic) Thr449 residue of Shaker to either Tyr or Phe would enhance extracellular TEAþ blockade to levels comparable to that of KcsA (KI , 1 mM for both mutants, compared to KI ¼ 22 mM for the wild type [175]). They suggested that the aromatic residues at position 449 on each of the four monomers forming the channel tetramer create an aromatic cage (or ‘bracelet’) that directly coordinates the TEAþ ion [175]. This hypothesis was challenged by the first crystal structure of KcsA [67], which shows the four Tyr82 residues (equivalent to residues 449 of Shaker) approximately at the right distance to coordinate TEAþ but presenting the edges of their aromatic rings towards the centre of the pore, suggesting that the TEAþ ion would bind ‘edge-on’ (u , 908) instead of ‘en face’ (u , 0). KcsA is known to be inhibited by extracellular TEAþ [176,177] and to lose its strong TEAþ affinity (KI ¼ 3.2 mM) upon mutation of Tyr82 to threonine [176] or valine [177]. Computational studies [178 –181] of the KcsA channel (using the GROMOS87 [182], CHARMM22 [55] and AMBER [54] force fields) have essentially confirmed the ‘edge-on’ mode of TEAþ binding suggested by the KcsA crystal structure – against the original hypothesis of Heginbotham and MacKinnon. The simulations show that the TEAþ ion is stable at the extracellular entrance of the pore [178 – 180], yet that the four Tyr82 residues are too far apart to form a cation –p interaction with TEAþ, and improperly oriented. The ‘edge-on’ orientation of the Tyr residues was later observed in a crystal structure of KcsA in complex with TEAþ analogue tetraethylarsonium [183] (see Figure 4(c)). However, more recent mutagenesis experiments have provided evidence for the ‘cation – p’ nature of the TEAþ – Shaker extracellular binding [184] (see also Ref. [185] for commentary). Ahern et al. [184] have created Thr449Phe mutants using various fluorinated Phe analogues, and observed that the TEAþ affinity of the mutants decreases in proportion to the degree of fluorination of the aromatic residue inserted. Subsequently, Bisset and Chung [186] have simulated the effect of controlling the orientation and separation of the four Tyr82 residues on the binding of TEAþ to KcsA. Their simulations, which are using the same force field as Crouzy et al. [179], show that TEAþ binding affinity of the KcsA vestibule is increased – and brought closer to the experimental value – when the Tyr82 residues are constrained into a narrower ‘bracelet’ [186]. Strangely, having the Tyr82 aromatic planes facing the ion appears to be inconsequential to the binding [186]. One likely reason why all reported TEAþ blockade simulations display binding affinity in the ‘edge-on’ conformation of the channel is that the force fields on which they rely describe hydrophobic interactions better

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716 G. Lamoureux and E.A. Orabi than cation – p interactions. Presuming the weak ‘edge-on’ stabilisation already observed for NHþ 4 (see Figure 2(b)) increases as the alkyl chains of the QA ion get longer, the TEAþ –Tyr interactions may in fact be less directional and create binding affinity for any orientation of the Tyr residues. It is likely, however, that the simulations underestimate the affinity of TEAþ for ‘en face’ Tyr residues and therefore obscure any potential ‘cation– p’ contribution to the binding. A more accurate force field, which creates a significant free energy difference between the ‘edge-on’ and ‘en face’ conformations of the protein – ligand complex, would likely provide new insights on how these competing forces play out. Since this ‘cation– p’ mode of interaction was shown to affect the slow inactivation of Shaker [187] (see Ref. [188] for commentary), a more accurate force field would also likely provide information on the effect of ligand binding on the flexibility and dynamics of potassium channels. A cation –p interaction was also implicated in the blockade of the voltage-gated Nav1.4 sodium channel by tetrodotoxin (TTX), between residue Tyr401 and the guanidinium group of TTX [189]. The same Tyr residue was also related to the extracellular calcium blockade of Nav1.4, likely due to cation – p interactions with hydrated (hexaaqua) Ca2þ ions [190]. 4.4.3

Amt/MEP ammonium transporters

Our group has recently used a polarisable model of cation – p interactions to compute the NHþ 4 -binding affinity of the recruiting cavity of the AmtB transmembrane protein [97]. AmtB is a member of the Amt/MEP family of ammonium transporters, known to facilitate ammonium permeation at low concentrations. Crystal structures of AmtB [191,192] show two binding sites, S1 and S2, separated by a hydrophobic gate formed of two stacked Phe side chains (Phe107 and Phe215). Site S1, on the external side, is lined by aromatic residues Phe103, Phe107 and Trp148 and by the polar side chain of residue Ser219 – forming a compact ‘aromatic cage’ (see Figure 4(d)). Site S2, which we do not discuss here, is lined by aromatic residues Trp212 and Phe215 and by the 1-nitrogen atom of residue His168. While there is a widespread consensus that S1 binds NHþ 4 (from the crystal structures [191,192] and from functional studies [193]), computer simulations investigating the nature of NHþ 4 binding in S1 point to a disconcerting variety of interpretations (see Ref. [194] for a review). Using ab initio and QM/MM representations of site S1, Liu and Hu [195] have shown the importance of þ cation – p interactions in the binding of NHþ 4 and MA (which is also known to permeate). In a gas-phase model of the S1 site including only the first-shell residues, they find that cation –p interactions contribute to about 60% of the total interaction energy. In contrast, Nygaard et al. [196] have used a QM/MM representation of the protein to

approximate the binding free energy of NHþ 4 in S1 and found that Phe107 has a minor contribution to the binding and that Trp148 contributes to destabilising the substrate – despite presenting a more or less optimal cation – p geometry. According to Nygaard et al.’s calculations, most of the stabilisation in S1 is due to the long-range interaction of NHþ 4 with a negatively charged Asp residue ˚ away from the binding site. 6– 7 A Lin et al. [197,198] have calculated the PMF of permeation of NHþ 4 through the pore of AmtB, using the CHARMM27 force field and generic non-bonded parameters for the ammonium ion. The resulting PMF displays no significant affinity of NHþ 4 for S1. Similarly, Akgun and Khademi [199] observe no significant affinity when using the CHARMM27 force field in conjunction with their own (unreported) ammonium force field. Bostick and Brooks [200], using the OPLS force field, observe a shallow (, 1.2 kcal/mol) free energy minimum at the level of S1, but the binding mode they report does not involve any of the surrounding aromatic residues. This could be a symptom of cation – p interactions being underestimated by the OPLS force field, which may not þ stabilise the NHþ 4 –Phe107 and NH4 – Trp148 pairs enough þ compared to the NH4 –water and NHþ 4 – carbonyl pairs. Luzhkov et al. [201] have performed free energy calculations for the binding of NHþ 4 to S1 using the OPLS force field but a model for ammonium calibrated to reproduce the hydration free energy of the ion. In contrast to Bostick and Brooks, they find that NHþ 4 binds to S1 (DGbind ¼ 2 5.8 kcal/mol). While residues Phe107 and Trp148 are found to coordinate NHþ 4 in a ‘cation– p’ fashion, their contributions to the total binding energies are smaller than those of the distant Asp160 residue and the Ser219 residue. This is somewhat at variance with the picture of ammonium – benzene affinity presented in Figure 2(c). According to the crystal structure of Figure 4(d), the ion is in optimal position for cation – p binding to both ˚ away, respectively). Phe107 and Trp148 (3.5 and 3.6 A The weak ammonium binding predicted by most of these studies is likely a consequence of the force fields on which they rely, which significantly underestimate the strength of the NHþ 4 – benzene interaction compared to that of the NHþ 4 – water interaction. The interaction energy of the NHþ 4 – benzene pair is about 2 17 kcal/mol (see Table 1) and that of the NHþ 4 –water pair is about 2 20 kcal/mol [202] – only 3 kcal/mol stronger than for benzene. However, all the force fields we could reproduce (from Refs. [197,198,200,201]) yield an NHþ 4 – benzene interaction that is about 10 kcal/mol weaker than for water. Comparable underestimation is found for the CHARMM and OPLS Kþ –benzene dimers [56] (see Table 1). Since both CHARMM and OPLS force fields use the same charges and Lennard-Jones parameters for benzene and for the side chain of Phe, this likely translates into NHþ 4 – Phe interactions being underestimated as well.

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Molecular Simulation 717 To remedy the shortcomings of the CHARMM27 force field, we have simulated the binding of NHþ 4 to S1 using a hybrid polarisable mechanics/molecular mechanics (PM/ MM) representation in which NHþ 4 and all its neighbouring residues (Phe103, Phe107, Trp148, Phe215, Ser219 and two water molecules) are described using the Drude oscillator model [30,97], while the rest of the system (protein, solution and lipid membrane) is described using the additive CHARMM27 force field [55]. Free energy calculations performed using this PM/MM approach yield an NHþ 4 binding free energy DGbind ¼ 2 14.1 ^ 1.5 kcal/ mol [97]. At the free energy minimum, NHþ 4 binds Phe107 and Trp148 at optimal cation –p distances and forms a strong hydrogen bond with the hydroxyl group of Ser219, in excellent accord with the crystal structures [97,191]. While the binding mode is very similar to that found by Luzhkov et al. [201], the binding affinity is significantly higher. Amt/MEP proteins are also known to be highly selective against Naþ and Kþ [193]. Using free energy calculations, Luzhkov et al. [201] have obtained selectivities of 4.4 kcal/mol against Naþ and 2.6 kcal/mol against Kþ. Using the PM/MM representation described above, our group has found that site S1 is selective against Naþ by 9.2 kcal/mol and against Kþ by 8.2 kcal/mol [97]. We attribute this strong selectivity to the low, 4-fold to 5-fold coordination enforced by S1, which accommodates NHþ 4 but not the more highly coordinated Naþ and Kþ ions [90]. 5. Summary Cation – p interactions play an essential role in a variety of molecular assembly and molecular recognition processes. While their importance for protein stability and protein– ligand binding is widely acknowledged, they are not accurately described by the force fields commonly used for the simulation of biomolecules. Non-polarisable force fields underestimate the stability of cation – aromatic complexes for the simple reason that models for cations are usually calibrated to reproduce solubilities in water but models for aromatic molecules are calibrated to reproduce solubilities in non-polar liquids. The models do not account for the additional stabilisation due to dipole induction, since it is negligible in both these systems (because no net electric field is created on the individual molecules). In aqueous solution, this translates into insufficient binding affinity for the cation in the region above the aromatic ring. Accuracy can be partially recovered by adding cation –p specific terms to the additive force field. However, these corrections have so far not gained widespread use. They are not integrated into the standard parameter sets of force fields such as CHARMM, AMBER, OPLS or GROMOS. Induced polarisation represents a major contribution to the stability of cation–p complexes – especially for small ions such as Naþ, Kþ and NHþ 4 . Polarisable force fields have

been shown to qualitatively improve the description of cation–p interactions and are expected to provide the breakthrough development needed to simulate them realistically. The efforts required to assemble a complete polarisable force field accurate enough to simulate protein structures over extended periods of time are considerable and will likely be ongoing for a few years. However, polarisable force fields are already being used for short simulations (during which unfolding or denaturation events are unlikely to occur) or in regions of the protein that are of interest – at a ligand-binding site, for instance. As these force fields get tested and calibrated for increasingly diverse combinations of ligands, they will likely become an essential computational tool for understanding how competing molecular interactions organise in complex environments. Acknowledgements This work was supported by an FQRNT E´tablissement de nouveaux chercheurs grant, by an NSERC Discovery grant and by PROTEO and GEPROM scholarships to EAO.

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