RCH 3 ̈ ̈ ̈ O Interactions in Biological Systems : Are They Trifurcated H-Bonds or Noncovalent Carbon Bonds ?

In this manuscript, we combine high-level ab initio calculations on some model systems (XCH3 σ-hole/H-bond donors) and a Protein Data Bank (PDB) survey to distinguish between trifurcated H-bonds and noncovalent carbon bonds in XCH3 ̈  ̈  ̈O complexes (X = any atom or group). Recently, it has been demonstrated both experimentally and theoretically the importance of noncovalent carbon bonds in the solid state. When an electron-rich atom interacts with a methyl group, the role of the methyl group is commonly viewed as a weak H-bond donor. However, if the electron-rich atom is located equidistant from the three H atoms, the directionality of each individual H-bond in the trifurcated binding mode is poor. Therefore, the XCH3 ̈  ̈  ̈O interaction could be also defined as a tetrel bond (C ̈  ̈  ̈O interaction). In this manuscript, we shed light into this matter and demonstrate the importance of XCH3 ̈  ̈  ̈O noncovalent carbon bonding interactions in two relevant protein-substrate complexes retrieved from the PDB.


Introduction
Supramolecular chemistry is a multidisciplinary field of research that develops very fast and has a deep impact [1,2] in the scientific community.Undoubtedly, the comprehension of the great deal of noncovalent forces, which are the basis of highly specific recognition, is crucial for the chemists working in this discipline.For instance, interactions between hosts and guests govern the creation of assemblies with high affinities even in highly competitive media [3][4][5][6].For this reason, the correct description and understanding of noncovalent interactions between molecules is essential for being successful in this field of research.In general, strong and highly directional interactions, such as hydrogen bonding and σ-hole bonding [7][8][9][10][11][12][13][14][15][16][17], and less directional forces like ion pairing are used for this purpose.
The allocation of a hydrogen atom between a donor (D) and acceptor (A) moiety, D-H¨¨¨A hydrogen bonding [18] is a particularly well studied and established supramolecular interaction ranging in strength from very weak (~1 kcal/mol) [19] to very strong (~40 kcal/mol) [20].The weakest H-bonding interactions are established between weakly polarized D-H bonds (e.g., aliphatic CH) and mildly electron-rich H-acceptor moieties (e.g., alkene π-electrons) [21][22][23].While a single interaction is energetically insignificant, when several weak H-bonds coexist they can stabilize protein structures [24][25][26] and contribute to the binding of proteins to carbohydrates [27][28][29][30][31]. Apart from this weak bonding interaction, recent theoretical explorations have suggested that pnicogen and tetrel atoms in their sp 3 hybridized form can act as electron poor entities suitable to accommodate an electron-rich guest [16,[32][33][34][35][36][37].Surprisingly few studies have been dedicated to studying the most abundant of these atoms, namely, the carbon atom.As a matter of fact, it has recently been reported that strong complexes are formed between electron-rich entities and 1,1,2,2-tetracyanocyclopropane [38][39][40].Moreover, the ability of the carbon atom in a methyl group or in an aliphatic chain (sp 3 hybridized) to participate in σ-hole interactions (as a σ-hole donor, i.e. electron acceptor) has been explored by Mani and Arunan [41].They demonstrated that the carbon atom in fact could act as an electrophilic center which can non-covalently bond with electron-rich entities leading to noncovalent carbon bonding, following a nomenclature analogous to other σ-hole interactions [7][8][9][10][11][12][13][14][15][16][17].The theoretical predictions were confirmed experimentally by Guru Row's group [42], thus validating the existence of this type of bonding by means of X-ray charge density analysis.Electron density topologies in two prototypical crystal structures with potential carbon bonding motifs (R 3 N + -CH 3 ¨¨¨O/Cl) were reported and revealed two distinct features of bond paths.That is, for the X-ray structure with the R 3 N + -CH 3 ¨¨¨Cl motif, the bond path revealed a C-H¨¨¨Cl hydrogen bond and for the other motif the bond path connected the electron-rich oxygen atom with the -CH 3 carbon atom; remarkably, no other bond paths connected the oxygen atom to the C-H hydrogen atoms.More recently, cooperativity effects involving carbon bonding interactions, and other noncovalent interactions have been analyzed in several theoretical studies [43][44][45].
The presence of methyl groups is abundant in many biologically relevant ligands and electron-rich O atoms are ubiquitous in proteins.Therefore, we wondered if perhaps weak non-covalent bonding with sp 3 hybridized carbon could have some relevance in ligand-protein complexes.Our approach was to conduct a rigorous statistical survey of the PDB together with quantum mechanical computations on the RI-MP2/aug-cc-pVTZ level of theory on some model systems.For the present theoretical study, we considered the sp 3 C-atom in several exemplifying molecules (1-3, see Figure 1) and computed their complexes with the electron-rich O atom of two molecules (formaldehyde and HO ´).In addition, using Bader's theory of "atoms in molecules" [46], we analyzed the bond path connecting the O atom with the CH 3 group in several complexes with the purpose of differentiating the H-bonding from the carbon bonding.From the PDB search, we analyzed the impact of the X-CH 3 ¨¨¨O interactions in biologically relevant protein-ligand complexes.these atoms, namely, the carbon atom.As a matter of fact, it has recently been reported that strong complexes are formed between electron-rich entities and 1,1,2,2-tetracyanocyclopropane [38][39][40].Moreover, the ability of the carbon atom in a methyl group or in an aliphatic chain (sp 3 hybridized) to participate in σ-hole interactions (as a σ-hole donor, i.e. electron acceptor) has been explored by Mani and Arunan [41].They demonstrated that the carbon atom in fact could act as an electrophilic center which can non-covalently bond with electron-rich entities leading to noncovalent carbon bonding, following a nomenclature analogous to other σ-hole interactions [7][8][9][10][11][12][13][14][15][16][17].The theoretical predictions were confirmed experimentally by Guru Row's group [42], thus validating the existence of this type of bonding by means of X-ray charge density analysis.Electron density topologies in two prototypical crystal structures with potential carbon bonding motifs (R3N + -CH3  [43][44][45]. The presence of methyl groups is abundant in many biologically relevant ligands and electronrich O atoms are ubiquitous in proteins.Therefore, we wondered if perhaps weak non-covalent bonding with sp 3 hybridized carbon could have some relevance in ligand-protein complexes.Our approach was to conduct a rigorous statistical survey of the PDB together with quantum mechanical computations on the RI-MP2/aug-cc-pVTZ level of theory on some model systems.For the present theoretical study, we considered the sp 3 C-atom in several exemplifying molecules (1-3, see Figure 1) and computed their complexes with the electron-rich O atom of two molecules (formaldehyde and HO − ).In addition, using Bader's theory of "atoms in molecules" [46], we analyzed the bond path connecting the O atom with the CH3 group in several complexes with the purpose of differentiating the H-bonding from the carbon bonding.From the PDB search, we analyzed the impact of the X-CH3•••O interactions in biologically relevant protein-ligand complexes.

Preliminary MEP Analysis
We firstly computed the molecular electrostatic potential (MEP) mapped onto the van der Waals surface in very simple compounds (XCH3) to explore the existence/absence of a σ-hole in the carbon atom (along the extension of the X-C bond) and to compare its electrostatic potential to that measured along the C-H bonds of the methyl group.In particular we computed the MEP surfaces of fluoromethane, dimethylether, dimethylthioether, dimethylformamide (DMF), acetonitrile, and methylamine, and the results are shown in Figure 2. In fluoromethane and dimethylether, an evident σ-hole is observed (see Figure 2a,b) in the C atom with a MEP value that is comparable to that observed in the H atoms. Therefore, either the carbon or the hydrogen bonding interactions should

Preliminary MEP Analysis
We firstly computed the molecular electrostatic potential (MEP) mapped onto the van der Waals surface in very simple compounds (XCH 3 ) to explore the existence/absence of a σ-hole in the carbon atom (along the extension of the X-C bond) and to compare its electrostatic potential to that measured along the C-H bonds of the methyl group.In particular we computed the MEP surfaces of fluoromethane, dimethylether, dimethylthioether, dimethylformamide (DMF), acetonitrile, and methylamine, and the results are shown in Figure 2. In fluoromethane and dimethylether, an evident Crystals 2016, 6, 26 3 of 13 σ-hole is observed (see Figure 2a,b) in the C atom with a MEP value that is comparable to that observed in the H atoms. Therefore, either the carbon or the hydrogen bonding interactions should be equally favored, at least electrostatically, in both molecules.For the DMF and acetonitrile molecules, a perfectly defined σ-hole is not observed; however, both molecules present a significantly positive value of MEP at the C atom.Finally, the methylamine and dimethylthioether molecules (see Figure 2d,e) do not present a σ-hole at the C atom, although the electrostatic potential is slightly positive.Consequently, both molecules are better H-bond donors than carbon bond donors in terms of electrostatic effects.
Crystals 2016, 6, 26 3 of 13 be equally favored, at least electrostatically, in both molecules.For the DMF and acetonitrile molecules, a perfectly defined σ-hole is not observed; however, both molecules present a significantly positive value of MEP at the C atom.Finally, the methylamine and dimethylthioether molecules (see Figures 2d,e) do not present a σ-hole at the C atom, although the electrostatic potential is slightly positive.Consequently, both molecules are better H-bond donors than carbon bond donors in terms of electrostatic effects.

Energetic and Geometric Results
Table 1 reports the interaction energies and equilibrium distances of the optimized complexes 4-12 (see Figures 1 and 3) computed at the RI-MP2/aug-cc-pVTZ level of theory.In complexes 7 and 10, where the OH − anion interacts with charged carbon bond donors, the noncovalent complex was not found; instead, a nucleophilic SN2 reaction occurs in the optimization.In formaldehyde complexes, we studied the influence of the orientation of the lone pairs of the O atom on the interaction energy and equilibrium distance.At this point, it should be noted that we used two charged carbon bond donors for the following reasons.First, the utilization of trimethylsulfonium was chosen to mimic the SAM cofactor (important in methyl transfer enzymatic processes).Second, we used methanaminium because, at physiological conditions, the amine groups are likely protonated.
From the inspection of the results summarized in Table 1 and Figure 3, several points are worth discussing.First, in the fluoromethane complexes, the interaction energy with the charged OH − guest is large and negative (−12.9 kcal/mol), modest for the complex with the neutral formaldehyde guest (−1.9 kcal/mol).Interestingly, the carbon bonding complexes (or trifurcated H-bonded) were found to be minima on the potential hypersurface.Moreover, the orientation of the oxygen lone pairs in the formaldehyde in its complexes with fluoromethane does not influence either the interaction energy or the equilibrium distance (complexes 5 and 6).Second, the trimethylsulfonium and methanaminium complexes with neutral formaldehyde present large interaction energies, being

Energetic and Geometric Results
Table 1 reports the interaction energies and equilibrium distances of the optimized complexes 4-12 (see Figures 1 and 3) computed at the RI-MP2/aug-cc-pVTZ level of theory.In complexes 7 and 10, where the OH ´anion interacts with charged carbon bond donors, the noncovalent complex was not found; instead, a nucleophilic S N 2 reaction occurs in the optimization.In formaldehyde complexes, we studied the influence of the orientation of the lone pairs of the O atom on the interaction energy and equilibrium distance.At this point, it should be noted that we used two charged carbon bond donors for the following reasons.First, the utilization of trimethylsulfonium was chosen to mimic the SAM cofactor (important in methyl transfer enzymatic processes).Second, we used methanaminium because, at physiological conditions, the amine groups are likely protonated.
From the inspection of the results summarized in Table 1 and Figure 3, several points are worth discussing.First, in the fluoromethane complexes, the interaction energy with the charged OH ´guest is large and negative (´12.9 kcal/mol), modest for the complex with the neutral formaldehyde guest (´1.9 kcal/mol).Interestingly, the carbon bonding complexes (or trifurcated H-bonded) were found to be minima on the potential hypersurface.Moreover, the orientation of the oxygen lone pairs in the formaldehyde in its complexes with fluoromethane does not influence either the interaction energy or the equilibrium distance (complexes 5 and 6).Second, the trimethylsulfonium and methanaminium complexes with neutral formaldehyde present large interaction energies, being more favorable with the protonated amine.Third, the interaction energies are identical for both orientations of formaldehyde; however, in the case of trimethylsulfonium, the C¨¨¨O equilibrium distance is longer in complex 8 than in 9 and the S-C¨¨¨O angle is smaller (172.0 ˝in 8 and 178.6 ˝in 9, see Figure 3b).This behavior is not observed in methanaminium complexes 11 and 12, and both present almost identical geometric and energetic features.3b).This behavior is not observed in methanaminium complexes 11 and 12, and both present almost identical geometric and energetic features.

AIM Analysis
We used Bader's theory of "atoms in molecules" (AIM) to characterize the noncovalent bonds in complexes 4-12 and to differentiate the type of interaction (carbon or hydrogen bonding).A bond critical point (CP) and a bond path connecting two atoms is unambiguous evidence of interaction.The AIM distribution of critical points and bond paths computed for the complexes is shown in Figure 4.In all CH3F complexes (Figure 4a), the interaction is characterized by the presence of a bond CP that connects the O atom with the carbon atom, thus confirming the carbon bonding nature of this interaction.The value of ρ at the bond CP that emerges upon complexation is larger in complex 4 than in either complex 5 or 6, in agreement with the interaction energies and equilibrium distances.In trimethylsulfonium complex 9, where the S-C•••O angle is close to 180°, the AIM analysis shows a bond CP and bond path unambiguously connecting the C and O atoms.In complex 8, where the S-

AIM Analysis
We used Bader's theory of "atoms in molecules" (AIM) to characterize the noncovalent bonds in complexes 4-12 and to differentiate the type of interaction (carbon or hydrogen bonding).A bond critical point (CP) and a bond path connecting two atoms is unambiguous evidence of interaction.The AIM distribution of critical points and bond paths computed for the complexes is shown in Figure 4.In all CH 3 F complexes (Figure 4a), the interaction is characterized by the presence of a bond CP that connects the O atom with the carbon atom, thus confirming the carbon bonding nature of this interaction.The value of ρ at the bond CP that emerges upon complexation is larger in complex 4 than in either complex 5 or 6, in agreement with the interaction energies and equilibrium distances.In trimethylsulfonium complex 9, where the S-C¨¨¨O angle is close to 180 ˝, the AIM analysis shows a bond CP and bond path unambiguously connecting the C and O atoms.In complex 8, where the S-C¨¨¨O angle is 172 ˝, the bond path presents a different trajectory and, at first sight, seems to connect the O atom of formaldehyde to the C-H bond critical point.However, a closer look reveals that the bond path suddenly deviates when it reaches the C-H bond critical point and finally connects to the C atom.The distribution in methanaminium complexes 11 and 12 (see Figure 4c) clearly shows a bond CP and bond path connecting the C and O atoms, thus confirming the carbon bonding nature of the interaction.In all cases, the Laplacian of ρ at the bond CP that connects the O and C atoms is positive, as is common in closed shell interactions.Interestingly, for the whole series of complexes, the value of ρ strongly correlates with the interaction energies.Therefore, the value of ρ can be used as a measure of bond order in this type of noncovalent bonding.We also analyzed the effect of the X-C•••O angle on the interaction to find the value that causes a change from carbon bonding to hydrogen bonding.For this study, we progressively changed the F-C•••O angle (α) starting from 180° and moving the O atom in two opposite directions (see Figure 5a): (i) toward a single H atom (α < 180° values) and (ii) toward the middle of two H atoms (α > 180° values).In each point, we optimized the geometry and simply froze the angle to the desired value.Moreover, we analyzed the distribution of critical points in order to find the value of α where the interaction changes from carbon to hydrogen bonding.If the OH − moves to a single C-H bond (Figure 5b), the interaction rapidly changes from carbon bonding to hydrogen bonding; therefore, the critical angle is close to 170°.This result agrees with the behavior observed for complex 8 (see Figure 4) that presents an S-C•••O angle of 172°, and the bond path trajectory reveals that it is in the borderline between both interactions.When the OH − moves to the opposite direction (toward the middle of two C-H bonds), the behavior is different: For α = 190° a bond path connects the C and O atoms similarly to fully optimized complex 4. Curiously, and for α = 200° and 210°, two bond paths connect the C and O atoms, forming a bifurcated carbon bonding.As a consequence, a ring CP (yellow sphere) is also generated.Finally, at 220°, the carbon bonding changes to a bifurcated H-bonding interaction.
This analysis is useful for defining the search criteria of carbon bonding complexes in X-ray structure databases (CSD, PDB, etc.).Since the H atoms bonded to C are usually not experimentally located, there is some uncertainty regarding their real position in the CH3 group.Therefore, it is We also analyzed the effect of the X-C¨¨¨O angle on the interaction to find the value that causes a change from carbon bonding to hydrogen bonding.For this study, we progressively changed the F-C¨¨¨O angle (α) starting from 180 ˝and moving the O atom in two opposite directions (see Figure 5a): (i) toward a single H atom (α < 180 ˝values) and (ii) toward the middle of two H atoms (α > 180 values).
In each point, we optimized the geometry and simply froze the angle to the desired value.Moreover, we analyzed the distribution of critical points in order to find the value of α where the interaction changes from carbon to hydrogen bonding.If the OH ´moves to a single C-H bond (Figure 5b), the interaction rapidly changes from carbon bonding to hydrogen bonding; therefore, the critical angle is close to 170 ˝.This result agrees with the behavior observed for complex 8 (see Figure 4) that presents an S-C¨¨¨O angle of 172 ˝, and the bond path trajectory reveals that it is in the borderline between both interactions.When the OH ´moves to the opposite direction (toward the middle of two C-H bonds), the behavior is different: For α = 190 ˝a bond path connects the C and O atoms similarly to fully optimized complex 4. Curiously, and for α = 200 ˝and 210 ˝, two bond paths connect the C and O atoms, forming a bifurcated carbon bonding.As a consequence, a ring CP (yellow sphere) is also generated.Finally, at 220 ˝, the carbon bonding changes to a bifurcated H-bonding interaction.

PDB Search
We explored the PDB in order to prove the importance of carbon bonding interactions in biologically relevant molecules.The following criteria were used for the search: (i) The CH3 donor group belongs to the ligand and the O atom is part of the protein; (ii) C•••O distance (d) is shorter than 3.2 Å and the X-C•••O angle (A) >170°; (iii) only X-ray solid state structures are considered (no NMR resolved); and (iv) a resolution factor <10 Å.The search was performed using the freely available Relibase software [47].As a result, we found 459 protein-ligand complexes exhibiting this type of bonding (see ESI for the full list of hits and their geometrical features, Table S1).The histograms plots for the angle and distance are represented in Figure 6.The importance of this result should be emphasized since we found a large number of hits, taking into consideration the tight geometric criteria used and that only one electron-rich element was used in the search (O).Therefore, carbon bonding interaction in general has a bright future in this field and will likely become a prominent player for explaining some biological processes, either controlling or fine-tuning the binding of substrates to enzymes.This analysis is useful for defining the search criteria of carbon bonding complexes in X-ray structure databases (CSD, PDB, etc.).Since the H atoms bonded to C are usually not experimentally located, there is some uncertainty regarding their real position in the CH 3 group.Therefore, it is recommended that a tight criterion regarding the X-C¨¨¨O angle (i.e., α > 170 ˝) is used when searching for this type of noncovalent carbon bonding X-ray structures.

PDB Search
We explored the PDB in order to prove the importance of carbon bonding interactions in biologically relevant molecules.The following criteria were used for the search: (i) The CH 3 donor group belongs to the ligand and the O atom is part of the protein; (ii) C¨¨¨O distance (d) is shorter than 3.2 Å and the X-C¨¨¨O angle (A) >170 ˝; (iii) only X-ray solid state structures are considered (no NMR resolved); and (iv) a resolution factor <10 Å.The search was performed using the freely available Relibase software [47].As a result, we found 459 protein-ligand complexes exhibiting this type of bonding (see ESI for the full list of hits and their geometrical features, Table S1).The histograms plots for the angle and distance are represented in Figure 6.The importance of this result should be emphasized since we found a large number of hits, taking into consideration the tight geometric criteria used and that only one electron-rich element was used in the search (O).Therefore, carbon bonding interaction in general has a bright future in this field and will likely become a prominent player for explaining some biological processes, either controlling or fine-tuning the binding of substrates to enzymes.
In the original manuscripts where the protein-ligand complexes were reported, the X-CH 3 ¨¨¨O interaction was either overlooked or considered as an H-bonding by the original authors.We selected two examples from this search to further illustrate the importance of this interaction.For the first example [48], we selected a very well resolved X-ray structure (PDB ID: 4NSY, resolution 1.1 Å. see Figure 7a) that is a covalent complex between a trypsin-type serine protease (lysyl endoproteinase, LysC) and its inhibitor N α -p-tosyl-lysyl chloromethylketone (TLCK).Chloromethyl ketones such as TLCK (Figure 7b) are well-known covalent inhibitors of cysteine and serine proteases [49].Two covalent bonds are formed with serine proteases, each one to the active-site serine and histidine.Similarly, in the LysC enzyme, the TLCK inhibitor is attacked by SER194 and by nucleophilic substitution of the Cl atom by HIS57.This covalently bonded inhibitor interacts with the other subunit by means of a noncovalent carbon bonding interaction (see Figure 7a).We constructed a model to energetically evaluate this interaction.We substituted the SER193 and HIS47 that are covalently bonded to the inhibitor by C-H bonds in order to keep the size of the system computationally approachable.The model also includes the alanine residue and part of the peptide backbone (see Figure 7c).The interaction energy is ´1.8 kcal/mol that is similar to that obtained for neutral complexes 5 and 6 (see Table 1).Remarkably, the distribution of CPs shows a bond critical point and a bond path connecting the O atom of the amide group to the carbon atom of the inhibitor, thus confirming the existence of the carbon bonding interaction in 4NSY.

PDB Search
We explored the PDB in order to prove the importance of carbon bonding interactions in biologically relevant molecules.The following criteria were used for the search: (i) The CH3 donor group belongs to the ligand and the O atom is part of the protein; (ii) C•••O distance (d) is shorter than 3.2 Å and the X-C•••O angle (A) >170°; (iii) only X-ray solid state structures are considered (no NMR resolved); and (iv) a resolution factor <10 Å.The search was performed using the freely available Relibase software [47].As a result, we found 459 protein-ligand complexes exhibiting this type of bonding (see ESI for the full list of hits and their geometrical features, Table S1).The histograms plots for the angle and distance are represented in Figure 6.The importance of this result should be emphasized since we found a large number of hits, taking into consideration the tight geometric criteria used and that only one electron-rich element was used in the search (O).Therefore, carbon bonding interaction in general has a bright future in this field and will likely become a prominent player for explaining some biological processes, either controlling or fine-tuning the binding of substrates to enzymes.In the original manuscripts where the protein-ligand complexes were reported, the X-CH3•••O interaction was either overlooked or considered as an H-bonding by the original authors.We selected two examples from this search to further illustrate the importance of this interaction.For the first example [48], we selected a very well resolved X-ray structure (PDB ID: 4NSY, resolution 1.1 Å. see Figure 7a) that is a covalent complex between a trypsin-type serine protease (lysyl endoproteinase, LysC) and its inhibitor N α -p-tosyl-lysyl chloromethylketone (TLCK).Chloromethyl ketones such as TLCK (Figure 7b) are well-known covalent inhibitors of cysteine and serine proteases [49].Two covalent bonds are formed with serine proteases, each one to the active-site serine and histidine.Similarly, in the LysC enzyme, the TLCK inhibitor is attacked by SER194 and by nucleophilic substitution of the Cl atom by HIS57.This covalently bonded inhibitor interacts with the other subunit by means of a noncovalent carbon bonding interaction (see Figure 7a).We constructed a model to energetically evaluate this interaction.We substituted the SER193 and HIS47 that are covalently bonded to the inhibitor by C-H bonds in order to keep the size of the system computationally approachable.The model also includes the alanine residue and part of the peptide backbone (see Figure 7c).The interaction energy is −1.8 kcal/mol that is similar to that obtained for neutral complexes 5 and 6 (see Table 1).Remarkably, the distribution of CPs shows a bond critical point and a bond path connecting the O atom of the amide group to the carbon atom of the inhibitor, thus confirming the existence of the carbon bonding interaction in 4NSY.The second example we selected [50] corresponds to the structure of a M3 muscarinic acetylcholine receptor bound to tiotropium (PDB ID: 4U14, resolution 2.5 Å. see Figure 8a).Tiotropium is a muscarinic receptor antagonist (anticholinergic bronchodilator) used in the management of chronic obstructive pulmonary disease [51].The presence of a dimethylammonium group in the structure ensures their ability to form electrostatically assisted carbon (or hydrogen) bonding interactions using the R3N + -CH3 groups.As a matter of fact, an aspartate residue of the active site is very close to a carbon atom belonging to one of both methyl groups (2.935 Å) with an almost The second example we selected [50] corresponds to the structure of a M3 muscarinic acetylcholine receptor bound to tiotropium (PDB ID: 4U14, resolution 2.5 Å. see Figure 8a).Tiotropium is a Crystals 2016, 6, 26 8 of 13 muscarinic receptor antagonist (anticholinergic bronchodilator) used in the management of chronic obstructive pulmonary disease [51].The presence of a dimethylammonium group in the structure ensures their ability to form electrostatically assisted carbon (or hydrogen) bonding interactions using the R 3 N + -CH 3 groups.As a matter of fact, an aspartate residue of the active site is very close to a carbon atom belonging to one of both methyl groups (2.935 Å) with an almost linear N-C¨¨¨O angle (177.4 ˝).We used a theoretical model derived from the crystallographic coordinates that includes the antagonist and the aspartate bonded to a fragment of the peptide backbone.The AIM analysis confirms the existence of a carbon bonding interaction (see bond path in Figure 8a).The ASP147 residue is likely deprotonated in the X-ray structure, since both C-O distances are very similar (1.248 and 1.250 Å).In any case, we evaluated the interaction energy considering both possibilities.The interaction energy of the carbon bonding complex using the protonated ASP147 is -9.0 kcal/mol.Moreover, the value of the density at the bond critical point is ρ = 0.0093 a.u.These values strongly agree with those previous ones computed for methanaminium (see Table 1 and Figure 4 (complexes 11 and 12)).Considering the deprotonated ASP147, the interaction energy is very large (´73.9kcal/mol) due to the strong electrostatic contribution.Therefore, this charge-assisted carbon bonding interaction has a strong influence on the binding of tiotropium in the muscarinic acetylcholine receptor.
Crystals 2016, 6, 26 8 of 13 ρ = 0.0093 a.u.These values strongly agree with those previous ones computed for methanaminium (see Table 1 and Figure 4 (complexes 11 and 12)).Considering the deprotonated ASP147, the interaction energy is very large (−73.9kcal/mol) due to the strong electrostatic contribution.Therefore, this charge-assisted carbon bonding interaction has a strong influence on the binding of tiotropium in the muscarinic acetylcholine receptor.

NBO Analysis
To find out whether orbital effects are important to explain the carbon bonding interactions described above, we performed natural bond orbital (NBO) calculations focusing our attention on the second order perturbation analysis, due to its usefulness for studying donor-acceptor interactions [52].We carried out the NBO calculations for complex 4 and for the theoretical model used to characterize the interaction in the PDB ID 4U14 (see Figure 8c).The results of the second order perturbation analysis are summarized in Table 2.For complex 4, we found an important orbital contribution that consists in the interaction of the lone pair orbital (LP) of the donor with the C-F antibonding orbital (BD*) of the acceptor.This interaction is significant (3.5 kcal/mol) since it accounts for approximately 27% of the total interaction energy and further confirms that the interaction in complex 4 is with the σ-hole of the carbon atom.Moreover, the expected LP→BD*(C-H) orbital contribution that is typical of a hydrogen bond is less than 0.1 kcal/mol.Similarly, in the PDB 4U14, we found an interesting LP(O)→BD*(C-N) contribution that is 2.0 kcal/mol and that the LP(O)→BD*(C-H) interaction is less than 0.1 kcal/mol, in sharp agreement with the AIM analysis commented above.

NBO Analysis
To find out whether orbital effects are important to explain the carbon bonding interactions described above, we performed natural bond orbital (NBO) calculations focusing our attention on the second order perturbation analysis, due to its usefulness for studying donor-acceptor interactions [52].We carried out the NBO calculations for complex 4 and for the theoretical model used to characterize the interaction in the PDB ID 4U14 (see Figure 8c).The results of the second order perturbation analysis are summarized in Table 2.For complex 4, we found an important orbital contribution that consists in the interaction of the lone pair orbital (LP) of the donor with the C-F antibonding orbital (BD*) of the acceptor.This interaction is significant (3.5 kcal/mol) since it accounts for approximately 27% of the total interaction energy and further confirms that the interaction in complex 4 is with the σ-hole of the carbon atom.Moreover, the expected LPÑBD*(C-H) orbital contribution that is typical of a hydrogen bond is less than 0.1 kcal/mol.Similarly, in the PDB 4U14, we found an interesting LP(O)ÑBD*(C-N) Crystals 2016, 6, 26 9 of 13 contribution that is 2.0 kcal/mol and that the LP(O)ÑBD*(C-H) interaction is less than 0.1 kcal/mol, in sharp agreement with the AIM analysis commented above.

SAPT Analysis
In Table 3, we summarize the DF-DFT-SAPT energy values relative to some of the carbon bonding complexes showed above in order to show the relative importance of the electrostatic contribution to the total interaction energies, especially those involving charged carbon bonding donors.The total SAPT interaction energies for these three complexes are similar to those obtained using the RI-MP2/aug-cc-pVTZ level of theory (see Table 1), attributing reliability to the partition method and the level of theory used to compute the SAPT.The energetic contributions (Table 3) indicate that the cationic complexes 9 and 12 are clearly dominated by the electrostatic term.Moreover, the contributions of induction and dispersion terms are also important.In the neutral complex 6, the electrostatic and dispersion terms equally contribute to the total interaction energy.Table 3. SAPT interaction energies (E total , kcal/mol) and their partitioning into the electrostatic, exchange, induction, dispersion, and contributions (E ee , E ex , E ind , E disp , respectively, kcal/mol) at the RI-DFT/aug-cc-pVTZ level of theory using the DF-DFT-SAPT approach.To further demonstrate the importance of electrostatic forces in the interaction energies of compounds 9 and 12, we computed the carbon bonding interaction of their equivalent neutral complexes where methylamine and dimethylthioether are used as carbon bond donors.The results are gathered in Figure 9, and it can be observed that the interaction energies are very small (-0.7 kcal/mol for 13 and ´1.1 kcal/mol for 14), in agreement with the MEP surfaces of methylamine and dimethylthioether shown in Figure 2.Moreover, the localization of the minima corresponding to the carbon bonding complexes 13 and 14 (see Figure 9) on the potential surface is worth emphasizing, since the MEP value at the H-atoms is considerably more positive than that at the C atom in both neutral molecules.

SAPT Analysis
In Table 3, we summarize the DF-DFT-SAPT energy values relative to some of the carbon bonding complexes showed above in order to show the relative importance of the electrostatic contribution to the total interaction energies, especially those involving charged carbon bonding donors.The total SAPT interaction energies for these three complexes are similar to those obtained using the RI-MP2/aug-cc-pVTZ level of theory (see Table 1), attributing reliability to the partition method and the level of theory used to compute the SAPT.The energetic contributions (Table 3) indicate that the cationic complexes 9 and 12 are clearly dominated by the electrostatic term.Moreover, the contributions of induction and dispersion terms are also important.In the neutral complex 6, the electrostatic and dispersion terms equally contribute to the total interaction energy.Table 3. SAPT interaction energies (Etotal, kcal/mol) and their partitioning into the electrostatic, exchange, induction, dispersion, and contributions (Eee, Eex, Eind, Edisp, respectively, kcal/mol) at the RI-DFT/aug-cc-pVTZ level of theory using the DF-DFT-SAPT approach.To further demonstrate the importance of electrostatic forces in the interaction energies of compounds 9 and 12, we computed the carbon bonding interaction of their equivalent neutral complexes where methylamine and dimethylthioether are used as carbon bond donors.The results are gathered in Figure 9, and it can be observed that the interaction energies are very small (-0.7 kcal/mol for 13 and −1.1 kcal/mol for 14), in agreement with the MEP surfaces of methylamine and dimethylthioether shown in Figure 2.Moreover, the localization of the minima corresponding to the carbon bonding complexes 13 and 14 (see Figure 9) on the potential surface is worth emphasizing, since the MEP value at the H-atoms is considerably more positive than that at the C atom in both neutral molecules.

Theoretical Methods
The geometries of the complexes studied herein have been fully optimized at the RI-MP2/augcc-pVTZ level of theory.Cartesian coordinates of the optimized complexes are given in the supplementary material file (Tables S2-S8).The calculations have been performed by using the program TURBOMOLE version 7.0 [53].The interaction energies were calculated with correction for

Crystals 2016, 6 , 26 5 of 13 C
•••O angle is 172°, the bond path presents a different trajectory and, at first sight, seems to connect the O atom of formaldehyde to the C-H bond critical point.However, a closer look reveals that the bond path suddenly deviates when it reaches the C-H bond critical point and finally connects to the C atom.The distribution in methanaminium complexes 11 and 12 (see Figure4c) clearly shows a bond CP and bond path connecting the C and O atoms, thus confirming the carbon bonding nature of the interaction.In all cases, the Laplacian of ρ at the bond CP that connects the O and C atoms is positive, as is common in closed shell interactions.Interestingly, for the whole series of complexes, the value of ρ strongly correlates with the interaction energies.Therefore, the value of ρ can be used as a measure of bond order in this type of noncovalent bonding.

Figure 4 .
Figure 4. Distribution of critical points (red spheres) and bond paths for complexes of fluoromethane (a); trimethylsulfonium (b); and methanaminium (c) at the RI-MP2/aug-cc-pVTZ level of theory.The value of the charge density (ρ) at the bond critical points that emerge upon complexation are indicated in a.u.

Figure 4 .
Figure 4. Distribution of critical points (red spheres) and bond paths for complexes of fluoromethane (a); trimethylsulfonium (b); and methanaminium (c) at the RI-MP2/aug-cc-pVTZ level of theory.The value of the charge density (ρ) at the bond critical points that emerge upon complexation are indicated in a.u.
tight criterion regarding the X-C•••O angle (i.e., α > 170°) is used when searching for this type of noncovalent carbon bonding X-ray structures.

Figure 5 .
Figure 5. (a) Schematic representation of the angle and both directions; (b) distribution of critical points (red spheres) and bond paths for complexes of fluoromethane with OH − using F-C•••O angles <180° at the RI-MP2/aug-cc-pVTZ level of theory; (c) same as (b) but using angles α > 180°.

Figure 6 .
Figure 6.Histograms obtained directly from the Relibase software.Distance distribution is shown on the left and the angle distribution on the right of the figure.Inset figure: definition of d and A parameters; the protein is represented in blue and the ligand in red.

Figure 5 .
Figure 5. (a) Schematic representation of the angle and both directions; (b) distribution of critical points (red spheres) and bond paths for complexes of fluoromethane with OH ´using F-C¨¨¨O angles <180 at

Figure 6 .
Figure 6.Histograms obtained directly from the Relibase software.Distance distribution is shown on the left and the angle distribution on the right of the figure.Inset figure: definition of d and A parameters; the protein is represented in blue and the ligand in red.

Figure 6 .
Figure 6.Histograms obtained directly from the Relibase software.Distance distribution is shown on the left and the angle distribution on the right of the figure.Inset figure: definition of d and A parameters; the protein is represented in blue and the ligand in red.

Figure 7 .
Figure 7. (a) X-ray structure of 4NSY with indication of the carbon bonding interaction (distance in Å); (b) chemical drawing of the TLCK; (c) AIM distribution of critical points of a model derived from the X-ray coordinates.

Figure 7 .
Figure 7. (a) X-ray structure of 4NSY with indication of the carbon bonding interaction (distance in Å); (b) chemical drawing of the TLCK; (c) AIM distribution of critical points of a model derived from the X-ray coordinates.

Figure 8 .
Figure 8.(a) X-ray structure of 4U14 with indication of the carbon bonding interaction (distance in Å); (b) chemical drawing of the tiotropium antagonist; (c) AIM distribution of critical points of a model retrieved from the X-ray coordinates.

Figure 8 .
Figure 8.(a) X-ray structure of 4U14 with indication of the carbon bonding interaction (distance in Å); (b) chemical drawing of the tiotropium antagonist; (c) AIM distribution of critical points of a model retrieved from the X-ray coordinates.
•••O/Cl) were reported and revealed two distinct features of bond paths.That is, for the X-ray structure with the R3N + -CH3••• Cl motif, the bond path revealed a C-H•••Cl hydrogen bond and for the other motif the bond path connected the electron-rich oxygen atom with the -CH3 carbon atom; remarkably, no other bond paths connected the oxygen atom to the C-H hydrogen atoms.More recently, cooperativity effects involving carbon bonding interactions, and other noncovalent interactions have been analyzed in several theoretical studies

Table 1 .
Interaction energies (BSSE corrected, ∆E BSSE , kcal/mol) and equilibrium distances (R 1 and R 2 , Å) for complexes 4-12 at the RI-MP2/aug-cc-pVTZ level of theory.favorable with the protonated amine.Third, the interaction energies are identical for both orientations of formaldehyde; however, in the case of trimethylsulfonium, the C•••O equilibrium distance is longer in complex 8 than in 9 and the S-C•••O angle is smaller (172.0° in 8 and 178.6° in 9, see Figure 1 S N 2 attack.more

Table 2 .
Donor and acceptor NBOs with indication of the second-order interaction energy E(2)and donor and acceptor orbitals for complexes 4 and PDB ID 4U14.Energy values are in kcal/mol.

Table 2 .
Donor and acceptor NBOs with indication of the second-order interaction energy E(2)and donor and acceptor orbitals for complexes 4 and PDB ID 4U14.Energy values are in kcal/mol.