Electronic Effects Governing Peptide Distortions Figure 2. Pep model in vacuo: Dv9 variation as a function of y9. Results from calculations at the PBE0/6-31G(d) (N) level and MP2/6-31G(d) (&) level for the conformer Q9i+1 = 60u (see Fig. S1). On the right side, schematic drawings of conformers of a peptide model characterized by different y values are shown. The projections are drawn by looking along the Ca-C bond (see also Fig. S2). The S substituent stands for the CH3-CO-NH- and the CH3- group in Ala1 and Pep model, respectively. doi:10.1371/journal.pone.0024533.g002 Geometry optimizations performed with more extended basis sets (PBE0/6-31+G(d,p), PBE0/6-311+G(2d,2p), MP2/6-31+G(d,p) confirm the PBE0/6-31G(d) and MP2/6-31G(d) results (Fig. S4). To further investigate the y9/v9 dependence, we studied in more details the y9 = 150u conformer, where a methyl group is perpendicular to the peptide plane and the largest negative value of Dv9 is predicted (Fig. 2). In particular, we performed a series of Single Point energy calculations for different Dv9 values in the range +20u/220u (Fig. 3). In order to evaluate and isolate the effect of v9 variations, we kept all the other geometrical degrees of freedom frozen to the values optimized for y9 = 120u. This latter conformer, due the symmetrical placement of the methyl groups with respect to the peptide plane (Fig. S2), exhibits a Cs symmetry and a predicted Dv9 = 0u. Furthermore, to definitively check the reliability of PBE0 functional (see also Supporting Information, Text S1) we repeated these calculations by using different Quantum Mechanical methods (PBE0, MP2, QCISD and CCSD(T)). Independently of the computational approach em- ployed, the energy plot presents a minimum for negative values of Dv9 (22u,25u) (Fig. 3). In addition, the curve is significantly asymmetric. For instance, a distortion of Dv9 = +20u from the planarity causes an energy destabilization by ,0.7 kcal/mol larger than a v9 distortion of the same entity but in the opposite direction (Dv9 = 220u). It is encouraging that, despite their very limited Figure 3. Pep model in vacuo: Minimized energy for the y9 = 1506 conformer at different Dv9 values. Comparison of results from different QM methods. doi:10.1371/journal.pone.0024533.g003 computational cost, PBE0/6-31G(d) calculations provide a picture close to that of CCSD(T)/6-311+G(2d,2p), also from a quantita- tive point of view: the energy values predicted by two methods are always within 0.3 kcal/mol (see also Text S1). The results obtained by the different QM methods employed are very similar, as suggesting that the dependence of Dv9 on y9 traces back to a very basic mechanism, likely involving the interaction between the electronic orbitals of the peptide group and those of the Ca substituents. Summarizing the results reported in this section, the study of the simple Pep model shows that noticeable deviations from peptide bond planarity are possible, exhibiting a clear sinusoidal dependence on the position of the Ca-X substituent with respect to the peptide plane (in line with the trend observed in protein structures (ref. 23 and below). From the methodological point of view, simple PBE0/6-31G(d) calculations can provide a reliable estimate of the above phenomena, being in good agreement with the prediction of the other QM methods examined (including DFT calculations with M05-2X functional, Fig. S5), although showing a slightly larger tendency to keep the peptide group planar. As a consequence, we can expect that our subsequent PBE0/6-31G(d) analysis provides a lower bound to the Dv9 values. Carbonyl carbon pyramidalization hC. The distortion from planarity of the peptide linkage, measured by the v angle, may be also associated to other geometrical parameters. Therefore, we started to analyze peptide parameters directly related to the planarity of the amide moiety such as the carbonyl carbon pyramidalization, which also represents a deviation from peptide planarity. It can be measured by the hC angle, defined as (v2v3+p) mod2p where v3 is the dihedral angle defined by the a atoms OCNi+1C i+1 (Fig. 1B) [14]. Previous statistical analysis of ultra-high resolution structures revealed a clear dependence of hC on the y dihedral angle, i.e. the direction of carbonyl carbon atom pyramidalization (above or below the peptide plane) change every 60u of rotation around y [4,21,23]. Calculations on Pep, carried out at PBE0/6-31G(d) level, confirm the experimental trends (Fig. 4). Fig. 4 also shows that hC dihedral angle presents the same y dependence of Dv. Indeed, a strong positive correlation (R = 0.93) between Dv and hC is PLoS ONE | www.plosone.org 3 September 2011 | Volume 6 | Issue 9 | e24533