Electronic Effects Governing Peptide Distortions Figure 5. Dependence of Dv and hC on peptide conformation. Dv vs. peptide conformation (A) Ala1 model in solvent (B) high resolution protein structures (resolution better than 1.6 A˚ ; Gly and Pro residues excluded from the database); hC vs. peptide conformation (C) Ala1 model in solvent (D) high resolution protein structures (resolution better than 1.6 A˚ ; Gly and Pro residues excluded from the database). Each experimental point is the average of at least 100 independent values. doi:10.1371/journal.pone.0024533.g005 (NBO) analysis. NBO theory expresses the first order density matrix in terms of ‘localized’ one-center (core electrons, lone pairs) and two-centers (filled/bonding or empty/antibonding) orbitals, giving a compact and accurate description of the total n-electron density according to simple Lewis-like scheme. Besides being an useful tool for discussing our results in terms of simple ‘Pauling’ resonance structures (see Fig. 1A), the NBO analysis allows also to evaluate how the orientation of the Ca substituents affects the properties of the bonding and antibonding orbitals of the amide moiety. A simple inspection of the three highest energy occupied p molecular orbitals (one of them mainly corresponding to the nitrogen lone pair) and the lowest energy unoccupied one, depicted for the y9 = 150u conformer in Fig. 6, reveals that the Atomic orbitals of the Ca substituents noticeably participate to the amide p system. NBO analysis indicates indeed that the Natural Hybrid Orbitals of the Ca substituents (either s bonding or s* anti-bonding) interact with the amide p system. Indeed, to get a deeper insight we monitored how the interactions between the Natural Bond Orbitals change as a function of y9 in the simplest Pep model, for which all the trends are more easily recognizable. Before analyzing the different degrees of freedom, it is noteworthy that the interaction between the C a - moiety (Ca-X s and s* NBOs) and the CO p system (p and p* NBOs) is not negligible with respect to the interaction of the nitrogen lone pair (n NBO) and the CO p system. Indeed, the former interaction is about ,8– 10 kcal/mol (Fig. S11), i.e. the 15% of the nitrogen nRp* amide interaction (,60–70 kcal/mol, see later in the text). The survey of the experimental protein structures and QM calculations on Ala1 show that noticeable deviations from the peptide bond planarity are found for well-defined values of y. NBO analysis indicates indeed that, depending on y, the maximum of stability of the amide p system is not reached for a planar arrangement and, on the contrary, small deviations from Dv planarity can be energetically favored. We analyzed the orbital interaction energies for two representative y9 conformers of Pep, namely y9 = 120u and y9 = 150u. Calculations and statistical surveys indicate a preferred Dv = 0u for the former and a maximum (negative) distortion of Dv for the latter. Since our PBE0/6-31G(d)NBO analysis shows that the CO pRCaCb s* PLoS ONE | www.plosone.org 5 September 2011 | Volume 6 | Issue 9 | e24533