Figure 6. Schematic representation of Pep model molecular orbitals. The three highest energy occupied p orbitals (A, B mainly corresponding to CO p bonding orbitals, C mainly to the Nitrogen Lone Pair) and the lowest energy unoccupied one (D, mainly corresponding to CO p* antibonding orbital) are schematically depicted for the y9 = 150u conformer with fixed Dv9 = 0u. doi:10.1371/journal.pone.0024533.g006 interactions provide limited stabilizing effects, we report the most stabilizing interactions involving the CO p system, i.e. the N a b sRCO p* interactions (Text S1, Fig. 7). nRCO p* and the C C For y9 = 120u the maximum interaction energy between the nitrogen lone pair n and the CO p* NBO is obtained when the amide moiety is perfectly planar. On the contrary, negative distortions of Dv lead to a significant increase of the N nRCO p* interaction for y9 = 150u (Fig. 7). Analogously, CaCb sRCO p* is also favored by negative values of Dv, when y9 is 150u. Although most of our interpretation is based on the Pep model, we have repeated the NBO analysis for two representative structures of Ala1 (Q = 2135u, y = 150u and for Q = 260u, y = 245u) in order to examine the effect of the substitution of a sp3 carbon atom (Pep) with a sp2 nitrogen atom (Ala1). We Electronic Effects Governing Peptide Distortions examined two Ala1 conformers which exhibit the largest negative and positive values of Dv. The results indicate that in Ala1 the sRp* interactions are not significantly weakened (Fig. 7 and Fig. S12). Although the relative weight of the two sRp* and pRs* interactions can be different for a specific Ca-X s bond contribution as well as for specific values of the Q angles, the dominance of the sRp* interactions holds for the whole -CaX3 moiety. The trends of the orbital interaction energy vs. Dv obtained for Pep are fully reproduced for Ala1 (Fig. S12), thus confirming that the N nRCO p* interaction is the most significant effect modulating the distortion from the planarity also in this more realistic peptide system. Collectively, our results indicate that the driving force for the planarity distortion is the maximization of N nRCO p*, and, to a lesser extent, of Ca-X sRCO p* interaction energy. The influence of y on the strength of the ‘amide resonance interaction’ can be qualitatively explained by considering the electronic repulsion between the Ca substituents and the electrons of the lone pair of the nitrogen atom. This repulsion disturbs the delocalization of the N lone pair in the p system and is expected to be minimal when two Ca substituents are in ‘trans’ position with respect to the CN bond and the other one lies in the amide plane without interfering with the p system (y = 0u,2120u,120u). In fact, as shown in Fig. S13, the populations of N n and CO p* NBOs exhibit minima and maxima, respectively, for y9 = 0u,2120u,120u. On the other hand, the maximum of the repulsion should be observed when two Ca substituents are located on the same semi- space containing the CN bond (y = 180u,260u,60u). In these latter conditions, the repulsion may decrease the interaction of the N n orbital with the p system, thus leading to a maximum of the N n and a minimum of the CO p* NBO populations (Fig. S13). Discussion The findings described in previous sections highlight the intricate relationships between different geometrical parameters within the peptide bonds. We have integrated the results of quantum mechanical calculations of simple peptide model compounds with those of statistical analyses of high-resolution protein crystal structures. Figure 7. NBO analysis for different Dv9 values. Pep model: Orbital interaction energy for the y9 = 120u conformer (squared symbols) and the y9 = 150u conformer (diamond symbols) vs. Dv9. (& y9 = 120u, Ca-Cb sRCO p*; ¤ y9 = 150u, Ca-Cb sRCO p*; % y9 = 120u, N nRCO p*; e y9 = 150u, N nRCO p*); Ala1-Solv model: Orbital interaction energy for the (Q = 2135u, y = 150u) conformer vs. Dv9. (N Ca-Cb sRCO p*; # N nRCO p*). doi:10.1371/journal.pone.0024533.g007 PLoS ONE | www.plosone.org 6 September 2011 | Volume 6 | Issue 9 | e24533