Figure 1. Diagram of model systems. (A) Classical representation of the major resonance forms of the peptide bond studied; (B) N-acetyl N- methylalaninamide (Ala1); (C) Simplified model (Pep). Definitions of backbone conformation angles are shown. doi:10.1371/journal.pone.0024533.g001 evident ones. More subtle deformations involve pyramidalizations at either the carbonyl carbon (hC) or the nitrogen (hN) atom of the peptide bond. All aspects of peptide deformation have been extensively analyzed but a comprehensive picture of the process is far to be achieved. Even analyses of peptide bond distortions as function of the local conformation carried out by surveying peptide and protein structure databases have led to different interpretations [16,21– 23]. Indeed, MacArthur and Thornton found a correlation between the direction of nonplanar deformation (positive or negative v values) and the handedness of the protein main-chain twist [16]. On the other hand, taking advantage of the dramatic increase in the number of high- and ultrahigh-resolution protein structures solved in the last decade [24–26], we recently observed a correlation between the peptide bond planarity deviation and the dihedral y angle [21,23]. We have also shown that the peptide bond distortions (measured by v dihedral angle) and carbonyl carbon pyramidalization atom (hC) are related processes that exhibit the same dependency on the y angle [23]. Due to the inherent X-ray inability to accurately detect hydrogen atom positions, pyramidalization at the peptide nitrogen atom (hN) cannot be analyzed in protein crystal structures, and remains a rather controversial issue [10,11,14,16,18,20,27]. The electronic and conformational properties of amide bond have been extensively investigated by using computational approaches, often with contrasting results [28,29]. In fact, studies Electronic Effects Governing Peptide Distortions of the rotational barrier along the C-N bond have either confirmed or challenged the simple resonance model [12,30–32]. Contradictory pictures of charge distributions on the amide group atoms in the planar and twisted forms have also been obtained [12,31,33,34]. Finally, theoretical studies aimed to connect peptide bond deviations with the local conformation have failed in detecting systematic trends [19,35]. It is thus clear that, notwithstanding all the experimental and computational efforts, a comprehensive picture of the electronic effects modulating the conformational properties of the peptide bond is still lacking and the factors underlying the deviation from a planar geometry are far from being assessed. Due to the general relevance of the above topics, we have carried out a thorough quantum-mechanical study of different peptide model systems, specifically tailored to allow an easier decomposition of all the chemical-physical effects into play, including solvent effects by means of the Polarizable Continuum Model (PCM) [36]. Different QM methods (DFT, MP2, CCSD(T)) provide a convergent and consistent description of the most relevant stereo-electronic local effects governing the peptide bond planarity and its dependence on other peptide degrees of freedom. In order to dissect the role of local and non- local effects on the geometrical parameters of the peptide bond, we have integrated the theoretical studies with thorough survey of high-resolution protein and peptide structural databases. Both approaches show that small planarity deviations cannot be considered an exception but, on the contrary, occur for most of the states of the Ramachandran space. Results The model system used to study backbone correlations by quantum-mechanics was the peptide-like system denoted as Ala1 (Fig. 1B). Despite being a minimal peptide model, as we shall discuss in the next sections, Ala1 exhibits a significant degree of complexity, since the presence of hydrogen bonding donor (NH) and acceptor (CO) groups favors the formation of intra-residue hydrogen bonds. This may, in turn, affect the geometry of the amide moieties and makes the interpretation of the computational results rather difficult. Therefore, we started analyzing the Pep model, where a methyl group replaced the acetyl moiety at the C- terminus of Ala1 (Fig. 1C). Pep: A simple model v dihedral angle. We have carried out geometry optimi- zations of Pep for different values of the C9CaCN dihedral angle. Since this dihedral angle corresponds to y in Ala1 parent model, we labeled it as y9. In particular, we analyzed the v9 variation as a function of y9. We have repeated this analysis for different values of the CNC0H dihedral angle, labeled as Q9i+1 since this dihedral angle would correspond to Qi+1 if Pep were inserted in a polypeptide chain. As discussed in detail in the Supporting Information (Text S1), although Q9i+1 can affect v9, the qualitative picture does not depend on the orientation of the terminal methyl group and we shall thus discuss here only the results obtained for Q9i+1 = 60u (Fig. S1). As shown in Fig. 2, according to both PBE0/ 6-31G(d) and MP2/6-31G(d) calculations v9 has noticeable deviations from planarity (Dv9 up to 3.5u) and exhibits a - clear sinusoidal dependence on y9, with minima and maxima spaced by 60u. The largest Dv9 deviations are found for y9 values providing one Ca-X substituent perpendicular to the peptide plane, whereas structures with one substituent eclipsed to the peptide plane exhibit smaller Dv9 values (Fig. 2 and Fig. S2). Similar trends are displayed by the conformers with Q9i+1 = 0u or 30u (Fig. S3). PLoS ONE | www.plosone.org 2 September 2011 | Volume 6 | Issue 9 | e24533