Cation-π Interactions of Methylated Ammonium Ions: A Quantum Mechanical Study

Abstract

Cation-π interactions of methylated ammonium ions play a key role in a broad range of biochemical systems. These include methyl-lysine binding proteins which bind to methylated sites on histone proteins, lysine demethylase enzymes which demethylate these sites, and neurotransmitter receptor complexes which bind choline derived ligands. Recognition in these systems is achieved through an ‘aromatic cage’ motif in the binding site. Here we use high level quantum mechanical calculations to address how cation-π interactions of methylated ammonium ions are modulated by a change in methylation state and interaction geometry. We survey methyl-lysine and choline derived complexes in the Protein Databank to validate our results against available structural data. A quantitative description of cation-π interactions of methylated ammonium systems is critical to structure-based efforts to target methyl-lysine binding proteins and demethylase enzymes in the treatment of unregulated transcriptional control, and neurotransmitter receptors in the treatment of neurological disease. It is our hope that our work will serve as a benchmark for the development of physical chemistry based force fields that can accurately model the contribution of cation-π interactions to binding and specificity in these systems.

Introduction

Cation-π interactions involving methylated ammonium ions play a significant role in molecular recognition and protein-protein interactions.^1-3 Early studies showed that ammonium and methyl-ammonium ions form strong complexes with benzene.⁴ Subsequent studies showed that water soluble quaternary ammonium compounds could form host guest complexes with natural and synthetic aryl receptors such as cyclophane.^5-7 Choline, and choline derived ligands such as acetylcholine and phosphocholine, bind to their receptors via interactions between a trimethyl-ammonium head group and an aromatic cage of two to four Trp, Tyr, or Phe residues.^8-10 The same aromatic cage motif is utilized by methyl-lysine binding proteins in the recognition of lysine methylated sites on the tails of histone proteins.^11-17

Lysine methylation is a post-translational modification in which one, two, or three methyl groups are added to the side chain nitrogen atom of a lysine residue. In histone proteins, this modification plays a key role in epigenetic control of transcriptional regulation which for the most part is effected indirectly through recruitment of “reader” proteins which bind to the methylated lysines.^18-19 Methyl-lysine binding proteins are specific for particular methylation states, for example the Chp1 chromodomain²⁰ and the PHD finger of the ING4 and ING2 tumor suppressors^16,21-22 have the highest affinity for trimethyl-lysine, while the Tudor domains, found in the DNA repair protein 53BP1 and its homolog Crb2, preferentially bind to dimethyl-lysine.^12,23 It has further been shown that methylation of a single site can result in different functional consequences depending on the number of methyl groups that have been added.²⁵

Over the past ten years it has become apparent that lysine methylation is a dynamic process in which methyl groups can be removed from histone proteins by the action of lysine demethylase enzymes.²⁶ Like methyl-lysine binding proteins, these enzymes are characterized by aromatic binding sites and are specific for methylation state; for example lysine-specific demethylase 1(LSD1) does not demethylate trimethyl-lysine while JMJD2A is specific to the trimethylated state.^27,28 Deregulation of either methylation or demethylation results in malfunctioning transcriptional control and is associated with cancer development. Thus, both histone methyl transferases and histone lysine demethylases are considered to be potential targets for inhibition in the treatment of cancer.^26,29

Several noncovalent binding forces come into play in determining methyl-lysine binding specificity. In lower methylation states hydrogen bonding occurs between the side chain amino proton and a nearby acidic residue,^30,31 and smaller size cavities present steric hindrance against higher methylation states. Hydrophobic desolvation, which refers to the reduction in the free energy cost of desolvating a methylated lysine in place of an unmethylated one, favors binding of higher methylation states. The effect of hydrophobic desolvation has been observed in a range of systems including host systems that prefer methylated over unmethylated guests,^32,33 beta hairpin peptides whose stability is enhanced by the interaction between one or more Trp residues and a methylated Lys residue,^34-36 and the factor Xa protein which shows higher affinities to more methylated ligands.³⁷ Cation-π interactions represent another noncovalent binding force; these interactions occur between the charged methyl-lysine residue and surrounding aromatic residues. The primarily electrostatic nature of this interaction dictates that the larger size and more dispersed positive charge of the more methylated ion results in weaker interactions for higher methylation states.¹ An understanding of methyl-lysine binding specificity depends on precise models which can quantify the competing noncovalent forces which come into play within a particular binding site, and is critical for the development of synthetic, and potentially therapeutic, receptors which bind to these sites.^38-40

Cation-π interactions are not easily modeled by traditional molecular mechanics force fields due to effects such as induction, polarization, and quadropole moment interactions, which may all contribute to the strength of the interaction.^{1, 41} Quantum mechanical studies on model systems are the benchmark for the parameterization and formulation of force fields that can be used to quantify the energetics of chemical and biochemical systems.^42-44 Recent works that have utilized quantum mechanical calculations on cation-π systems to parameterize polarizable molecular mechanics force fields include Orabi and Lamoureux⁴⁵ and Ansorg et al.⁴⁶ Here we conduct high level quantum mechanical calculations to address how cation-π interactions in methylated ammonium systems are affected by changes in methylation state and interaction geometry. We use ammonium ions that are methylated to different degrees as models for methyl-lysine and quaternary ammonium compounds; and benzene as a model for the aromatic amino acids Trp, Tyr, and Phe. While the most preferred geometry for a simple cation interacting with benzene places the cation directly over the center of the benzene ring (axial position),¹ it has been shown that almost half of the cation-π interactions between residues in the Protein Databank (PDB)⁴⁷ are off-axis.⁴⁸ Since studies that have shown that even interactions placing the cation in the plane of the benzene ring can be attractive,⁴⁹ our model systems consist of methylated ammonium ions at angles of 0-90° from the axial position. Finally, we compare our theoretical results with experimental complexes of methyl-lysine binding proteins and receptors of choline derived ligands in the PDB to get a sense of how predicted favored geometries of interaction are reflected in actual protein complexes. It is hoped that our work will contribute to the development of improved models to describe specificity, recognition, and binding energies in methylated ammonium systems.

Methods

Quantum Mechanical Calculations

Initial coordinates for all geometries were set up in Maestro⁵⁰ using the default geometries for the ammonium ion and benzene. Following the work of others^44,49 geometries for the benzene-ammonium complexes are described based on three parameters as shown in Figure 1: R, the distance between the ammonium nitrogen atom and the center of the benzene ring; theta (θ), the angle between the axial to the ring and the direction of R (such that θ=0° places the cation directly above the center of the ring); and psi (ϕ) for off- axis geometries, referring to whether the cation is aligned on a vertical place with a benzene hydrogen atom (ϕ=0°) or is positioned in between two hydrogen atoms (ϕ=30°). Geometries are labeled θ_ϕ (for example 30_0) in the context of this work. For consistency, interaction geometries for the mono-, di-, tri- and tetra-methylated ammonium ions were generated directly from the benzene-ammonium geometries by adding the appropriate number of methyl groups to the ammonium ion. Methyl groups were added to the position that would place the group farthest from the benzene ring. While this choice is arbitrary, subsequent optimization steps allow for the relaxation of the configuration of the methylated ion.

Figure 1.

Geometries for Cation-π Systems.⁴⁹

All calculations were carried out with the Jaguar software package.⁵¹ Potential energy surfaces (PES) were generated for each geometry by adjusting the distance R from two to seven Angstroms at one Angstrom intervals, and then at intervals of 0.05 Angstroms around the region of the minimum. The benzene molecule and ammonium cations were held rigid and single point energies were calculated using the M06−2X⁵² functional with the 6−31++G** basis set. Default grids and SCF convergence criteria as implemented in Jaguar were used. Interaction energies were obtained by subtracting the energies of the monomers from the energy of the complex.

The calculation of the PES surface was followed by a more rigorous quantum mechanical calculation for each complex at its minimum energy distance based on the PES. Counterpoise calculations⁵³ were implemented in Jaguar using the M06−2X⁵² functional with the aug-cc-pVTZ without f functions basis set. The counterpoise calculation involves geometry optimization of the complex, geometry optimization of each of the monomers in its own basis set, single-point calculations of each of the monomers in its own basis set in the geometries adopted in the complex, and single-point counterpoise calculations on each of the monomers in the geometries adopted in the complex using the basis set of the complex. For the geometry optimization of the complex, constraints were implemented to fix the value of theta at 0°, 30°, 60°, or 90° as it was set in the initial geometry. This was done by positioning a dummy atom in the axial position directly above the center of the ring and constraining the angle between the dummy atom, the centroid of the benzene ring, and the nitrogen atom of the cation. The position of the centroid was also constrained with respect to the ring. For two cases in which the SCF calculation did not converge, the value of R was increased by 0.1 Angstroms above its value from the minimum of the PES, and the calculation was repeated. Interaction energies and basis set superposition errors (BSSE)⁵³ were calculated for each system.

Methylated Lysine Residues in the Protein Databank

We searched the Protein Databank (PDB)⁴⁷ for all entries containing a methyl-lysine residue using the three letter codes MLZ, MLY, and M3L to search for mono-, di- and tri-methyl lysine respectively. In all, we identified four, nine, and 25 entries containing mono-, di- and tri- methyl lysine respectively. Choline and choline derived ligands such as phosphocholine and acetylcholine are also characterized by the ‘aromatic cage’ recognition mode; as such, our study includes twenty PDB entries containing choline and choline derived ligands. These structures were drawn from a table compiled by Cheng et al. of all choline ligand containing entries as of August 2012;⁵⁴ our set includes the structure with the highest resolution from each bolded entry (indicating the presence of cation-π interactions) on that list. For each methyl-lysine residue or choline ligand, we identified all interactions with aromatic residues using the literature reference included in the PDB entry; in all, 11, 30, 74, and 46 interactions were identified for mono-, di-, tri-methyl lysine residues, and choline ligands, respectively. NMR entries, or entries that did not have an associated literature reference, were excluded from our study. For each interaction, we calculated R, the distance between the ammonium nitrogen atom and the center of the aromatic ring of the interacting Trp, Tyr, or Phe residue; and theta (θ), the angle between the axial to the ring and the direction of R.

Results

Quantum Mechanical Calculations

The Potential energy surfaces (PES) and the counterpoise calculations show that for all methylation states, the most favored geometry places the cation directly above the center of the benzene ring (Table I and Figs. 2 and 3). Methylation results in less favorable interaction energies and a slight shift to the right in the minimum energy distance (R) which becomes more notable in the transition from partial (mono, di, tri) to full methylation (tetra) (Fig. 2 and Table II). All off-axis geometries, i.e. θ=30°, 60° and 90°, show attractive interaction energies.

Table I.

Counterpoise energies and basis set superposition errors for methylammonium ions interacting with benzene, after constrained optimization using the aug-cc-pVTZ without f functions basis set and M06−2X functional.

Initial Geometry	Counterpoise Energies (kcal/mol)
	NH4+	CH3NH3+	(CH3)2NH2+	(CH3)3NH+	(CH3)4N+
0_0	−19.0±0.1	−18.1±0.6	−17.0±0.7	−16.7±1.1	−8.8±0.7
30_0	−14.6±0.2	−14.0±0.1	−12.9±0.5	−12.7±0.7	−8.2±0.7
30_30	−15.1±0.0	−13.0±0.2	−12.9±0.6	−12.8±0.6	−8.1±0.7
60_0	−9.0±0.1	−8.5±0.2	−7.8±0.6	−7.5±0.7	−3.9±0.7
60_30	−9.0±0.1	−8.7±0.2	−7.9±0.6	−7.6±0.7	−3.9±0.7
90_0	−4.7±0.1	−4.1±0.2	−4.0±0.6	−3.9±0.6	0.5±0.1
90_30	−4.7±0.1	−4.3±0.2	−4.3±0.6	−3.8±0.5	−0.5±0.2

Figure 2.

Potential energy surfaces for ammonium, mono-, di-, tri-, and tetra-methyl ammonium ions interacting with benzene, generated with 631**++ basis set and M06−2X functional.

Figure 3.

Counterpoise energies for ammonium and methylammonium ions interacting with benzene, after constrained optimization using the aug-cc-pVTZ without f functions basis set and M06−2X functional. Axes indicate theta and psi angles of starting geometries, and energies of the optimized systems.

Table II.

Interaction geometries for methylammonium ions interacting with benzene, after constrained optimization using the aug-cc-pVTZ without f functions basis set and M06−2X functional. R refers to the distance between the ammonium nitrogen and the center of the benzene ring, θ refers to the angle between the ammonium nitrogen and the axial to the ring, and ϕ refers to where the cation is positioned with respect to the benzene hydrogen atoms.

Initial Geometry θ_ϕ	NH4+		CH3NH3+		(CH3)2NH2+		(CH3)3NH+		(CH3)4N+
	R(Å)	ϕ	R(Å)	ϕ	R(Å)	ϕ	R(Å)	ϕ	R(Å)	ϕ
0_0	2.9	-	3.0	-	3.0	-	3.0	-	4.2	-
30_0	3.4	5-10	3.5	20-25	3.5	25-30	3.5	25-30	4.3	0-5
30_30	3.5	10-15	3.4	5-10	3.5	5-10	3.6	25-30	4.4	0-5
60_0	4.1	25-30	4.2	25-30	4.1	25-30	4.2	25-30	5.1	25-30
60_30	4.1	25-30	4.2	25-30	4.2	25-30	4.2	25-30	5.2	25-30
90_0	4.4	25-30	4.4	25-30	4.6	25-30	4.6	25-30	8.0	15-20
90_30	4.4	25-30	4.4	25-30	4.6	25-30	4.6	25-30	6.4	25-30

Figure 4 shows the optimized geometries produced by the counterpoise calculations for the 0_0, 30_0, 60_0, 90_0 geometries; these were generated by superimposing the benzene molecules of each of the optimized systems. Results show that the cations adopt a similar configuration in the off-axis θ=0° and θ=30° geometries, which changes as the cation moves further away from the axial position to θ=60° and θ=90°.

Figure 4.

Optimized geometries of methylammonium ions interacting with benzene, after constrained optimization using the aug-cc-pVTZ without f functions basis set and M06−2X functional.

For the off axis-geometries (θ=30°, 60°, 90°) the PES show a preference, in the form of more favorable interaction energies, for the cation being positioned in between two hydrogen atoms (ϕ=30°) instead of directly above a hydrogen atom (ϕ=0°) (Fig. 2). Figure 5 shows the optimized 60_0 geometry of tetramethyl-ammonium as an example. This preference is particularly notable in the counterpoise calculations (Table II). Independent of the starting geometry (i.e. for both ϕ=0° and ϕ=30°), the optimized systems show the cation at or near the ϕ=30° position. The angle ϕ was measured by positioning the benzene ring in the plane of the Maestro visualization window, drawing a bond between the nitrogen atom of the cation and the ring centroid, and inspecting the position of the bond with respect to the two closest carbon atoms.

Figure 5.

Two views of optimized geometry for tetramethyl-ammonium interacting with benzene highlighting θ=60° (left) and ϕ=30° (right).

Cation-π Interactions in Methylated Protein Structures

In all, 161 cation-π interactions between methyl-lysine or choline groups, and aromatic residues, were identified among experimental structures in the PDB. These include 11 mono-, 30 di-, 74 tri-methyllysine, and 46 choline ligands; interacting with 73 Trp, 60 Tyr, and 28 Phe residues. Notably, only one of the 46 choline interactions is with a Phe residue. Figure 6 shows interaction geometries for these cation-π interactions. Geometries are characterized by R, the distance between the ammonium nitrogen atom and the center of the aromatic ring of the interacting Trp, Tyr, or Phe residue; and theta (θ), the angle between the axial to the ring and the direction of R.

Figure 6.

Geometries of interaction for methyl-lysine residues and choline ligands interacting with aromatic residues in 58 protein complexes in the Protein Databank. R refers to the distance between the ammonium nitrogen and the center of the aromatic ring, and θ refers to the angle between the axial to the center of the ring and the direction of R.

For all systems, ammonium-aromatic interactions show a clustering at R=4.0-4.5 Å and θ=0-30°. For the combined set of trimethyl-lysine and choline structures, average values are R=4.8±0.6 Å and θ=22.1±11.9°. These averages are consistent across residue types, for Tyr, Trp, and Phe residues in this set, average R values are 4.8±0.6 Å, 4.7±0.5 Å, and 5.2±0.8 Å, and average theta values are 20.0±11.5°, 23.0 ±10.5°, and 25.8±15.0° respectively. For interactions between partially methylated lysine residues and Tyr, there is potential for hydrogen bonding between the amide hydrogen and the hydroxyl of Tyr. To address whether hydrogen bonding, rather than cation-π interactions, accounts for these interactions, we measured the N-O distance between the nitrogen of the mono- or di-methyllysine amide and the oxygen of the Tyr hydroxyl group. For these seventeen cases, the N-O distance ranges between 4.5 and 7.5 Å (hydrogen bond cutoffs are typically ~4 Å) and as such hydrogen bonding is not likely to play a role.

Discussion

Energies calculated in the counterpoise calculations compare well with reported experimental results for ammonium ions interacting with benzene; these values from the literature are −19.3, −18.8, −15.9 and −9.4 kcal/mol for ammonium, mono-, tri- and tetramethylammonium respectively.^2,55 Thus our results demonstrate that a counterpoise calculation using the aug-cc-pVTZ without f functions basis set and M06−2X functional is an effective approach to calculating the absolute and relative binding energies of simple cation-π systems. Our findings that off-axis geometries, including orthogonal (θ=90°) interactions, may be attractive, and the preference for the ϕ=30° position in between benzene hydrogen atoms, are consistent with the results of Marshall et al.⁴⁹ for complexes of Li⁺, Na⁺, K⁺ and NH₄⁺, with benzene. Our results show that methylation of the ammonium ions results in less favorable interaction energies, with the most significant increase in energy occurring in the transition from partial to full methylation. This is to be expected, as the positive charge is increasingly dispersed over the larger methyl groups in place of the smaller hydrogen atoms.

For the unmethylated ammonium ion we compare our results with those of Marshall et al.⁴⁹ which were performed using the CCSD(T) method, often considered the gold standard for quantum mechanical calculations.^43,56 For all systems, our calculations show more favorable interaction energies. This difference results in part from the geometry optimization step of our protocol in which only the value of theta is fixed, while the PES curves presented by Marshall et al. were performed with rigid monomers at fixed values of both theta and psi. For the optimized θ=0° and θ=30° geometries, our reported energies are lower than the corresponding CCSD(T) energies by 1.6-2.6 kcal/mol. For the optimized θ=60° and θ=90° geometries, which are all characterized by ϕ≈30°, our reported energies are within 1.1-1.5 kcal of the corresponding 60_30 and 90_30 CCSD(T) energies. The changes in interaction energy as the cation is incrementally moved from the axial (θ=0°) to orthogonal (θ=90°) position are comparable in both sets of calculations, and both show that in the orthogonal position, the attractive energy retains a significant part of its value at θ=0° (25% for our calculations, 21% for the CCSD(T) calculations). The R values of our optimized geometries are within 0.2 Å of the minimum energy distances of the corresponding CCSD(T) curves which were calculated for a dense set of grid points.⁴⁹

Our survey of methyl-lysine and choline cation-π interactions in the PDB shows that geometries are clustered at 4.0≤R≤4.5 Å and 0°≤θ≤30° with average values of R=4.8±0.6 Å and θ=22.1±11.9°. The clustering around the axial position can be understood in light of the more favorable interaction energies for the θ=0° and θ=30° geometries as compared to those further away from the axial position. The average R value for all interactions characterized by 0°≤θ≤30° (81% of interactions) is 4.6±0.6 Å, which is consistent with the R values of the optimized tetramethyl-ammonium systems generated by our quantum mechanical calculations. An earlier survey⁴⁸ of 910 Arg and Lys cation-π interactions in 96 PDB entries showed that 51% of all geometries were characterized by 0°≤θ≤30°, with an average R value for these interactions of 4.1±0.2 Å . The higher average R value for the structures in our study is consistent with results of our quantum mechanical calculations which show that the most favorable distance for ammonium-aromatic interactions increases with increasing methylation of the ammonium ion.

Methyl-lysine residues and choline molecule head groups are typically surrounded by an aromatic cage of two to four aromatic residues. It is unknown whether the effect of several aromatic donors is additive; future studies, along the lines of a recent study of a cation-π sandwich model,⁵⁷ will address the effect of multiple aromatic groups on the interactions described here. Also to be addressed is the effect of the identity of the donor aromatic residue on the strength of the cation-π interaction; among the interactions in our dataset, most are with Trp or Tyr (37% and 45% respectively) and a smaller percentage are with Phe (17%).

Conclusions

This work presents state-of-the-art quantum mechanical calculations focused on cation-π interactions of ammonium ions, and the effect of methylation state and geometry on the energetics of these interactions. Understanding the contribution of cation-π interactions to binding and specificity in histone binding proteins and lysine demethylase enzymes is critical to elucidating the mechanisms of transcriptional regulation, and structure-based therapeutic efforts to target these proteins. Our study also has relevance to receptors of choline and choline derived ligands which are recognized by a trimethyl-ammonium headgroup. Acetylcholine, and many acetylcholine esterase inhibitors currently used or being developed for the treatment of Alzheimer’s disease, utilize cation-π interactions between an ammonium cation and aromatic residues in the enzyme binding site.⁵⁸ Recent studies have further shown that cation-π interactions of phosphotidylcholine are involved in the recognition of target lipids by peripheral membrane proteins.^54,59 It is hoped that our work will contribute to the development of physical chemistry based models that can quantify the contribution of cation-π interactions to binding and specificity across a broad range of biochemical systems.