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n→π* Interactions in Proteins

Hydrogen bonds between backbone amides are common in folded proteins. Here, we show that an intimate interaction between backbone amides likewise arises from the delocalization of a lone pair of electrons (n) from an oxygen atom to the antibonding orbital (π*) of the subsequent carbonyl group. Natural bond orbital analysis predicted significant n→π* interactions in certain regions of the Ramachandran plot. These predictions were validated by a statistical analysis of a large, non-redundant subset of protein structures determined to high resolution. The correlation between these two independent studies is striking. Moreover, the n→π* interactions are abundant, and especially prevalent in common secondary structures such as α-, 310-, and polyproline II helices, and twisted β-sheets. In addition to their evident effects on protein structure and stability, n→π* interactions could play important roles in protein folding and function, and merit inclusion in computational force fields.

The extent of overlap between donor and acceptor orbitals is governed by their relative spatial orientation. Contrary to the expectations of valence shell electron pair repulsion (VSEPR) theory, the two lone pairs of divalent oxygen do not occupy equivalent orbitals 6 that resemble "rabbit ears" 7 , 8 . For example, the lone pairs of a carbonyl oxygen are not in sp 2 hybrid orbitals, but reside in non-degenerate s-rich and p-rich orbitals. The s-rich lone pair (n s ) has ~60% s-and 40% p-character; whereas the p-rich lone pair (n p ) has ~100% pcharacter. In an amide oxygen, n s is aligned with the σ bond of the carbonyl group (Fig. 1a), and n p is orthogonal to the π bond of that group (Fig. 1b).
We postulate that an α-helix avails both of these lone pairs. In particular, n s delocalizes over the antibonding orbital (σ*) of an N-H bond to form a hydrogen bond between residues i and i+4 in a polypeptide chain (Fig. 1c), 1 -4 , 9 . Likewise, n p is poised to delocalize over the antibonding orbital (π*) of the i+1 carbonyl group (Fig. 1d). Model studies investigating peptides, peptoids, and related small molecules have revealed that the ensuing n→π* interaction can alter conformational preferences 10 -20 .
Here, we perform a thorough survey of protein conformational space for significant n→π* interactions. First, we employ calculations to anticipate the main-chain dihedral angles that give rise to significant n→π* interactions. We then perform a statistical analysis of a large, non-redundant subset of high-resolution protein crystal structures in the Protein Data Bank (PDB 21 ) to search for such interactions. The results of these calculations and structural analyses indicate that n→π* interactions are abundant and widespread in proteins.

Prevalence of n→π* interactions
We sought to identify regions of protein conformational space that could contain significant n→π* interactions (Fig. 2). We did so by creating and analyzing a computational library of allowed conformations. This library was generated with a tetramer of alanine residues capped at its N-terminus with an acetyl group and at its C terminus with a methylamino group (AcAla 4 NHMe). The conformations calculated by natural bond orbital (NBO) methods to have favorable n→π* interaction energies (E n→π* ; Table S1) are depicted in a Ramachandran-type plot in Fig. 2b. Briefly, two broken elliptical regions are favored, one in each half of the ψ range. The uppermost region stretches from the allowed, through partially allowed β-region, and into the α L conformations; the other spans the allowed through partially allowed α-region and disallowed regions in the lower-right quadrant of the plot.
The NBO analyses predict what protein conformations could give rise to n→π* interactions. Do actual proteins avail those conformations and thus employ n→π* interactions? To answer this question, we generated a subset of high-resolution (≤1.6 Å), and non-redundant (≤30% pairwise sequence identity) X-ray crystal structures from the PDB. Within this set, n→π* interactions between backbone carbonyl groups of consecutive residues (residue pairs) were identified using the operational definition given in Fig. 2a. At distances ≤3.2 Å, the van der Waals' surfaces of the two carbonyl groups interpenetrate, putting these contacts in the realm of quantum mechanics rather than classical electrostatics 16 , 20 ; the allowed angles are reminiscent of the Bürgi-Dunitz trajectory for nucleophilic attack on a carbonyl carbon (~109°). Residue pairs that tested positive for n→π* interactions are depicted in red on a Ramachandran plot, Fig. 2c. For comparison, the φ,ψ angles for all other residue pairs from the whole subset are depicted in black. As might be expected, the observed n→π* interactions occur in allowed regions of Ramachandran space, Fig. 2c. What is remarkable, however, is that the favored regions for n→π* interactions anticipated by the computational analyses correspond to those identified in the PDB search. The correlation is not exact because the hot spots identified by our computational analyses report on n→π* interactions only, without any steric considerations, and therefore cover regions of conformational space that are disallowed in protein structures.
Thus, both the computational and the crystallographic analyses suggest widespread and abundant n→π* interactions in the allowed regions of the Ramachandran plot. Importantly, we found n→π* interactions in all 1731 of the selected protein crystal structures, with proportions in the range 5-97% (mean: 34%). A breakdown of these data by secondary structure is detailed in Table 1. n→π* interactions were especially prevalent in right-and left-handed α-helices, but were less common in β-strands. One quarter of the residues in lefthanded polyproline II (P II ) helices participate in n→π* interactions. A similar fraction was found in residues not in regular secondary structures, on the right-hand side of the Ramachandran plot (Table 1 and Fig. 2).

Significance of Xaa-Pro dipeptides
The mean φ angle for the residues on the left-hand side of the Ramachandran plot-i.e., that occupied by right-handed α-helices and β-strands-involved in n→π* interactions is −63.3° ± 5.6° (Fig. 2c), which is close to the distribution of φ angles for proline residues (−65.0° ± 10.6°). This correlation, as well as prior results with a peptidic model system 11 , 16 , suggested that proline could be particularly suited for engaging in an n→π* interaction when found at the acceptor (i+1) position and led us to examine Xaa-Pro dipeptides (where Xaa is any amino acid), using Xaa-Ala and Xaa-Gly as control pairs. We found that Xaa-Pro pairs contributed significantly to the prevalence of n→π* interactions in both α-helices and βstrands (Table 1). For α-helices, the amino-acid preference for n→π* interaction decreased in the order: Pro > Ala > Gly > all other amino acids, with almost all the proline residues participating in n→π* interactions. For β-strands in which n→π* interactions were found, the amino-acid preference decreased in the order: Pro ≫ Gly > all, with a ten-fold preference for proline over glycine. In P II helices, the distribution was less and differently skewed, all = Ala > Pro ≫ Gly; we return to this important point below. In regions without regular secondary structure, a similar distribution was observed, with proline engaging in proportionally fewer n→π* interactions than alanine and all other residues, but more than glycine. Fig. 2a) for Xaa-Pro, Xaa-Gly, and Xaa-Ala dipeptides in protein structures. For α-helices, β-strands, P II helices, and runs of residues with no secondary structure, we found that the mean O i-1 ···C i distance in Xaa-Pro was shorter by ~0.1 Å than the same distance in Xaa-Gly and Xaa-Ala (Fig. 3). In α-helices, the mean O i-1 ···C i =O i angle was 107.2° ± 6.5° for Xaa-Pro motifs, compared with 103.0° ± 7.6° for Xaa-Gly and 102.9° ± 4.6° for Xaa-Ala. This wider angle is close to the Bürgi-Dunitz trajectory. In β-strands, the mean O i-1 ···C i =O i angle was 103.8° ± 13.5° for Xaa-Pro, compared with 118.1° ± 9.3° for Xaa-Ala and 112.7° ± 11.3° for Xaa-Gly. Insufficient data were available for Xaa-Gly pairs in P II helices due to the requisite nonredundancy of the dataset. Many collagen structures, which consist of three intertwined glycine-and proline-rich P II helices 15 , were removed because of similarity through their Pro-Hyp-Gly repeats. To address this issue explicitly, we examined 15 high-resolution (≤1.6 Å) structures of collagen-like peptides. We found the mean value of d in Xaa-Pro dipeptides to be shorter than in Xaa-Gly, by ~0.1 Å, similar to the difference found in αhelices and β-strands. The mean O i-1 ···C i =O i angles were, however, shallower (80.9° ± 2.2° for Xaa-Gly; 89.4° ± 2.4° for Xaa-Pro) than that for an optimal n→π* interaction, which precluded their designation as n→π* interactions in the original search ( Table 1).

Continuity of n→π* interactions
To identify only definitive cases of n→π* interactions, we employed a conservative operational definition in our PDB search (Fig. 2a). The value of E n→π* is, however, a continuum that depends on the values of d and θ. The NBO analyses indicate significant conformational stabilization offered by the n→π* interaction, even at angles outside the range 99° ≤ θ ≤ 119° (Fig. 4a). In other words, significant n→π* interactions are likely to be more abundant than implied by the constrained PDB data depicted in Fig. 2c and 3. For example, the mean O i-1 ···C i =O i angle in P II helices was only slightly shallower than 99° for Xaa-Ala (97.7° ± 9.5°) and Xaa-Pro (95.6° ± 8.7°) dipeptides.

Predetermination of n→π* interactions?
Do n→π* interactions stabilize protein structures, or are their signature O i-1 ···C i distances and O i-1 ···C i =O i angles merely an artifact of protein topology? To address this question, we analyzed the relationship between d and θ for all residue pairs in the 1731 high-resolution structures used to generate Fig. 2c and 3. We found that α-helices, the most prevalent secondary structure in the dataset, are dominated by values of d ≤ 3.2 Å and θ near 100° (Fig. 4b), as expected from Fig. 3. The tendency of θ to be near 100° when d ≤ 3.2 Å is also evident in residues pairs that are not in an α-helix (i.e., largely unconstrained by secondary structure; Fig. 4c). The value of θ varies widely, however, when d > 3.2 Å, an unexpected result if the distances and angles are topological artifacts. In other work, some of us have discovered that in the absence of an n→π* interaction, the donor group neither makes a short contact with the acceptor (d > 3.2 Å) nor resides along the Bürgi-Dunitz trajectory (θ ≈ 125°) 20 . These results suggest that n→π* interactions are not an artifact of protein topology.

Protein structures with many or few n→π* interactions
Some of the 1731 structures that we examined had an inordinately high or low fraction of residues in n→π* interactions, according to the criteria in Fig. 2a. These structures are listed and depicted in Table S5. In 8 structures, >80% of the residues participate in n→π* interactions. These are small α-helical proteins; five comprise single α-helices, three have helix-turn-helix structures. Interestingly, almost all of them are coiled-coil proteins, and the extensive n→π* interactions could enhance the rigidity of those coiled coils. At the other end, 39 structures have <10% of the residues in n→π* interactions. In these structures, almost all the secondary structure is β-sheet, and only four structures have any residues in αhelices. For these structures, the proportion of residues not in regular secondary structures is slightly greater than in the entire data set (37% versus 34%). Proteins in this group include streptavidin, tumor necrosis factor-α, and a variety of carbohydrate-binding proteins.
We searched the PDB for runs of four or more n→π* interactions not contained within common secondary structural elements in proteins. This search returned only eight hits from a possible 7833 sets of four residues. Detailed examination showed that these hits were located between α-helices or β-strands, except for one that formed part of an iron-binding site (residues 246-251 inclusive in cytosine deaminase, PDB code 1ra0 22 , of which His246 is a ligand to the iron ion). Most notably, however, in a wider search of the PDB, we found a run of four n→π* interactions in the selectivity filter of the potassium ion channel from Streptomyces lividans (KcsA; Fig. 5) 23 , while n→π* interactions were nearly absent in the structure of the filter region determined at high K + concentration.

n→π* interactions in quadrants of the Ramachandran plot
Our computational and structural analyses reveal abundant and widespread n→π* interactions in three quadrants of the Ramachandran plot. This finding has implications for common secondary structures, as follows.
The existence of an n→π* interaction in α-helices is supported by much evidence. Two diagnostic signatures of the quantum mechanics that underlie the n→π* interaction 16 have been observed in α-helices: pyramidalization of the acceptor carbonyl group 24 and polarization of its π-electron cloud 25 . The origin of these perturbations was unknown.
In addition to stabilizing the α-helix, we hypothesize that the n→π* interaction could have an important role in α-helix formation. The nucleation of an α-helix is energetically unfavorable: forming the characteristic i→i+4 hydrogen bond necessitates the restriction of at least six main-chain dihedral angles, and a consequent loss in conformational entropy; and the enthalpy of a helix-coil transition has been estimated to be ~0.9 kcal/mol/residue 26 . Additionally, considerable enthalpic cost is incurred because the amidic dipoles of adjacent residues repel each other in an α-helical conformation 27 . The n→π* interaction, which operates between the i and i+1 residues, could mitigate these energetic penalties. Consistent with this proposal, we note that proline is a strong helix initiator 28 -31 , and has a high propensity for engaging in the n→π* interaction (Table 1) 10 -13 , 16 . Moreover, the purported intermediacy of the 3 10 -helix 32 -35 and its prevalence at α-helix termini suggest that the strong n→π* interaction within a 3 10 helix (1.3 kcal/mol) could have an important role in αhelix formation. The short O i-1 ···C i distance induced by an n→π* interaction (Fig. 1d) causes lateral compaction of the α-helix that could align the hydrogen bond donor and acceptor groups for a stronger i→i+4 hydrogen bond (Fig. 1c).
Neither parallel nor anti-parallel β-strands of the φ = 0 to −180°, ψ = 0 to 180° quadrant exhibit significant n→π* interactions. In these extended structures, adjacent carbonyl groups are too distal for an intimate interaction (d > 3.2 Å). Nonetheless, a significant proportion of β-sheets have a twist with d < 3.2 Å. It is plausible that the n→π* interaction provides a consequential conformational stabilization to these twisted β-strands, which then form twisted β-sheets. Occasionally, β-strands have an amplified right-handed twist resulting in local disruption of the β-sheet structure. Such β-bulges are involved in the dimerization of immunoglobulin domains and can assist in enclosing the active sites of proteins 36 -39 . Two common types of β-bulges, the G1 and wide types, adopt φ and ψ dihedral angles indicative of considerable n→π* interactions. In particular, of all sets of three residues comprising G1 bulges in our dataset identified using Promotif 40 , the 25% that partake in n→π* interactions have constrained mean (φ, ψ) angles (Residue X: −68.0° ± 5.5°,130.4° ± 6.6°; Residue 1: 58.4° ± 17.6°, 36.4° ± 11.0°; Residue 2: −68.7° ± 6.8°, 136.9° ± 6.5°) which place them in energetic 'hotspots' on the Ramachandran plot. The contribution of n→π* interactions within P II helical strands to the conformational stability of the collagen triple helix has been described previously 15 .
β-Turns have been implicated in protein folding 41 , 42 . Our computational analyses indicate that n→π* interactions confer conformational stability to the i+1 residues in common type I and type II β-turns (Fig. 2b). As in an α-helix (Fig. 1c,d), the donor oxygen participates in a hydrogen bond (here, i→i+3) along with the n→π* interaction. We note that the i+1 residues of β-turns, like all of the residues in a P II helix, adopt their conformation without the aid of local or intra-secondary structure hydrogen bonds. Accordingly, the n→π* interaction could have a special role to play in the stability of these structures.
Although they occur less frequently than their right-handed counterparts in proteins, lefthanded helices of the φ = 0 to 180°, ψ = 0 to 180° quadrant play distinctive structural and functional roles in substrate specificity, cofactor binding, and protein-protein interactions 43 . For example, the left-handed α-helical conformation of MPK-3 is critical for the binding and subsequent negative regulation of mitogen-activated protein kinase (MAPK) 44 . The n→π* interaction could play an important role in the stability and folding of the left-handed α-helices and 3 10 helices.

Possible functional roles and other implications
Could n→π* interactions contribute to protein function? Their prevalence in canonical secondary structures (Table 1) implies a broad impact. We note, however, an especially intriguing situation in a non-canonical structure. The selectivity filter of the potassium channel from Streptomyces lividans (KcsA 23 ) has a run of n→π* interactions, but only in the structure determined at low K + concentration (Fig. 5). The filter is occluded in this 'closed' state, and only two dehydrated K + ions are present in the channel. At high K + concentration, n→π* interactions do not appear to play a significant role, and four dehydrated K + ions are evident within the channel. These observations suggest that mainchain oxygens in the potassium ion channel can participate in n→π* interactions or bind to K + ions, but not both.
Our results suggest several areas for future investigation. For example, we note that the formation of n→π* interactions could be cooperative, as the polarization of an acceptor C ′ i+1 =O i+1 group makes O i+1 into a better donor. We speculate that the conduit provided by n→π* interactions could facilitate the tunneling of electrons through proteins 45 . Finally, we urge the inclusion of n→π* interactions in relevant computational force fields.

Computational Analyses
Geometry optimization and frequency calculation for an AcAla 4 NHMe model peptide were performed at the B3LYP/6-31+G* level of theory with all the amide bonds locked in the trans conformation 46 . Frequency calculations of the optimized structure yielded no imaginary frequencies. The library of allowed conformations was generated by varying the φ and ψ dihedral angles systematically in increments of 5°. Natural bond orbital (NBO) analyses were performed at the B3LYP/6-311+G(2d,p) level of theory on each conformation. The NBO method transforms a calculated wavefunction into a localized form, which corresponds to the lone pair and bond elements of the Lewis structure 47 . The stabilization afforded by the n→π* interaction, E n→π* , was estimated by using second-order perturbation theory as implemented in NBO 5.0. Orbital depictions were generated with NBOView 1.1.

PDB Analyses
A subset of high-resolution (≤1.6 Å), and non-redundant (pairwise sequence identity ≤30%) protein X-ray crystal structures was collated from the PDB using PISCES 48 with data downloaded on 18 December 2007. The following operational definition was used to identify unambiguous examples of n→π* interaction in these proteins: (1) the distance between the amide oxygen (O i−1 ) and subsequent amide carbon (C′ i ) was less than the sum of their van der Waals' radii (d ≤ r O + r C = 3.2 Å; Fig. 2); and (2) the angle between O i−1 and C′ i =O i was 99° ≤ θ ≤ 119° (Fig. 2). Distributions of these short contacts were studied as a function of the main-chain dihedral angles φ and ψ. α-Helix and β-sheet assignments were made with PROMOTIF 40 , which uses modified Kabsch and Sander criteria 49 to assign secondary structure. PPII helices were assigned with the method of Stapley 50 , which assigns regions of at least four residues in length to be P II helices if their ϕ and ψ angles fall within angle constraints particular to this secondary structural class and do not fall into any structural class according to the Kabsch and Sander criteria 49 . Residue pairs were only considered to belong to a structural class if they were residues X and Y in sequence WXYZ in which all four amino acids were assigned to that structural class, with the exception of the data shown in Fig. 4b and 4c, in which only residue pairs (i.e., X and Y) were considered.

Supplementary Material
Refer to Web version on PubMed Central for supplementary material.