Electronic Effects Governing Peptide Distortions Figure 4. Pep model in vacuo: Dv9 (&) and hC (N) as a function of y9. doi:10.1371/journal.pone.0024533.g004 observed with a slope of approximately 1 (y = 0.01+0.93x). This means that the dihedral angle v3 (Fig. 1B) tends to be zero, i.e. the a N-CH3 (i.e. Ni+1C i+1-like) bond tends to eclipse the C-O bond. However, the correlation between Dv and hC is significantly larger than that observed in proteins, in line with a general tendency found in the comparison of the experimental data with those derived from calculations on Pep. Despite the similarity of the trends, correlations are enhanced in the simplified system. This suggests that the complexity of protein structures and the interactions with the environment attenuate the entity of these correlations. Ala1 in aqueous solution v dihedral angle. After having assessed the reliability of our computational approach, we tackled the study of a peptide system by checking the dependence of Dv on the peptide conformation. To this aim, we fully optimized the geometry of Ala1 in water solution at the PCM/PBE0/6-31G(d) level, on a grid of (15u615u) in the populated (Q,y) regions of the Ramachandran plot (Fig. 5A), for which a comparison with the available experimental data is possible. We repeated the surveys of Dv variations in proteins to corroborate our previous analysis [23] by using a much larger structure database (1749 non-redundant protein chains refined at resolution equal or better than 1.6 A˚) extracted from the Protein Data Bank [37] (Fig. 5B). To exclude regions with increased local flexibility, that are less accurate or completely undefined from the structural point of view even in high resolution structures, we omitted residues with higher than average main-chain B-factors (see Materials and Methods for details). A comparative inspection of Figs. 5A–B clearly shows that QM calculations on Ala1 and experimental data provide very similar trends. Both approaches demonstrate that peptide conformations with significant deviations from the planarity (Dv?0u) are predominant. Indeed, planar peptides are detected only for specific y values (,180u, 120u, 60u, and 0u). Dv exhibits a clear-cut sinusoidal dependence on y: positive and negative values of Dv alternate every 60u of y. Although some dependency on the Q angle is also detectable, the trend is less evident. It is worth noting that in the region with y,60u, the values of Dv displayed by conformation with positive and negative Q angles are very similar. In order to better discriminate between intrinsic and environ- mental effects, we performed our analysis on Ala1 in vacuo. As detailed in the Supporting Information (Text S1, Fig. S6), although a sinusoidal dependence of Dv on y is found, significant discrepancies between computed and experimental values in protein are observed in the region Q,0u, y,0u as well as in the regions with Q.0u (Fig. S6). The largest discrepancies are found in regions with y angles close to 0u. For these conformations the close approach of the NH groups of the two adjacent peptide units (Figs. S2 and S7) allows for the formation of a pseudo hydrogen-bond interaction between the amide moieties. Gas phase calculations likely overestimate the influence of those hydrogen bonds on Ala1 conformation. These interactions are instead reliably described by simple but accurate, continuum solvent models like PCM. Carbonyl carbon pyramidalization hC. Present statistical surveys carried out on high resolution protein structures show, in agreement with previous analyses [21,23], a clear dependence of hC on the y dihedral angle (Fig. 5D). As shown in Figs. 5C–D our calculations on Ala1 in aqueous solution provide a picture in good agreement with the experi- mental one: hC angle exhibits the same dependence of Dv on y, with maximum (and minimum) values appearing every 120u. A positive correlation between Dv and hC is observed. The linear regression analysis gives a correlation coefficient R = 0.63 (y = 20.0013+0.59x) very close to that provided by the statistics of experimental protein structures [23]. The computational trends obtained for Ala1 in the gas phase are also similar to the experimental ones, also in regions where Dv variations are not in line with the experimental trends (Fig. S8). Explaining the experimental and computational trends In the above paragraphs we have shown that calculations on small model systems and the survey of high resolution protein crystallographic structures provide very similar indications on the dependence of several geometrical parameters on y. As discussed in detail in the Supporting Information (Text S1), a survey of small molecule structures from the CSD database [38] (Figs. S9 and S10) provides trends fully consistent with those found in proteins, since Dv and hC exhibit a clear-cut dependence on y. In order to unveil the basic chemical-physical effects underlying this phenomenon, we have resorted to Natural Bond Orbital PLoS ONE | www.plosone.org 4 September 2011 | Volume 6 | Issue 9 | e24533