The importance of peptide bonds in biology is not limited to their role in building protein structures. They are also reactive groups, which are substrates of a huge number of proteases. The dependence of the electronic distribution within the peptide bond on the local peptide conformation may be important for understanding the enzyme-substrate recognition process and for the elucidation of the chemical-physical bases of the catalytic process of protein/peptide degradation. Materials and Methods Systems and strategy Calculations have been performed by considering peptide models of different complexity. Most of the calculations were conducted on the so-called dipeptide analogue, N-acetyl N9- methylalaninamide (Ala1) (Fig. 1B), which contains all the relevant geometrical parameters to be analyzed. The conformational space of Ala1 has been sampled by using a grid of (Q,y) values of (15u615u). Only (Q,y) states that are significantly populated in protein/peptide experimental structures were considered. For each state, the geometry of the model has been optimized by keeping Q and y dihedral angles fixed to their starting values. The minimized structures were used to derive the dependence of the geometrical parameters (v, hC) on the main chain dihedral angles (Q,y). Calculations were also performed on the simplified system Pep (Fig. 1C) in order to get a simpler picture of the influence of the Ca substituents on the structural parameters of the amide moiety. As discussed in detail below, Pep has also been used for a preliminary assessment of the accuracy of our computational approach. Computational details The bulk of our computational analysis has been performed at the Density Functional Theory (DFT) level, by using PBE0 hybrid functional [60]. Despite the absence of adjustable parameters, PBE0 provides accurate results for a number of chemico-physical observables in several systems. In particular, PBE0 has shown a remarkable accuracy in the study of polypeptides (see Supporting Information, Text S1, for a more detailed discussion) [39]. Geometries have thus been optimized at the PBE0/6-31G(d) level in the gas phase and at the PCM/PBE0/6-31G(d) level in aqueous solution. The effect of the basis sets have been checked on Pep peptide model by performing geometry optimizations also at the PBE0/6-31+G(d,p) and PBE0/6-311+G(2d,2p) levels. In order to check the reliability of PBE0 for describing the effects that modulate peptide geometry, we have performed a thorough study of Pep, comparing the PBE0 results with those obtained by other Quantum mechanical methods. We have therefore studied the distortion from planarity of the pep- tide geometry by using MP2/6-311+G(2d,2p), QCISD/6-311+ G(2d,2p), and CCSD(T) 6-311+G(2d,2p) calculations. We also performed single-point energy calculations by using the recently developed M05-2X functional that is based on simulta- neously optimized exchange and correlation functionals, including kinetic energy density. This method has shown very good performance in the treatment of dispersion interactions in noncovalent complexes [61]. Bulk solvent effects on the ground and the excited states have been taken into account by means of the polarizable continuum model (PCM) [36]. In this model the molecule is embedded in a cavity surrounded by an infinite dielectric with the dielectric constant of the solvent (we have used standard dielectric constant 78.39 for water). Geometry optimizations in solution have been performed using UA0 radii for the solute cavity according the Electronic Effects Governing Peptide Distortions UATM model [62]. This approach has already been successfully applied to the study of the conformational properties of oligopeptides in solution. The computational results have been interpreted with the help of the Natural Bond Orbitals (NBO) analysis [63,64]. 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. All calculations have been performed by the Gaussian03 package [65]. Statistical analyses of the structural databases Statistical analyses of peptide bond geometrical parameters have been carried out by considering highly accurate structures reported in the Protein Data Bank (PDB) [37]. A preliminary dataset was generated through the PISCES server (http:// dunbrack.fccc.edu/pisces) by selecting structures refined at resolution equal or better than 1.6 A˚ with an R-factor lower than 0.20. This database was built by considering structures sharing sequence identity lower than 25%. Using these criteria, 1749 structures were selected for the 1.6 A˚ database. Since even very well refined resolution protein structures may contain regions that are locally disordered, peptide bonds were further selected based on their B-factor values. In particular, we excluded either disordered residues (containing atoms with partial occupancy) or residues with an average main-chain B-factor value higher than 1.3 the average B-factor of the main-chain of the entire protein. Only peptide planes in trans conformation were included in the analysis. As Gly and Pro residues have unique chemical structure, they were not considered. The final dataset contained 28791 residues. Surveys were also conducted on small molecule structures reported in the v5.31 release of the Cambridge Structural Database (CSD) [38]. Data were shown in the Supporting Information section (Text S1). Supporting Information Text S1 Additional details on: 1. Computations using PBE0 functional; 2. QM studies on peptide models: a survey of literature data and approaches; 3. The influence of Q9 on Dv versus y; 4. Computations on Ala1 in the gas phase; 5. Additional details on the NBO analysis; 6. Statistics on small molecule crystal structures. (DOCX) Figure S1 Schematic drawings of conformers of Pep model characterized by Q9i+1 = 06,306,606. The projections are drawn by looking along the C0-N bond. The carbonyl group and the hydrogen attached to the peptide nitrogen are shown in red and blue, respectively. It is worth noting that the Q9i+1 = 90u conformer is equivalent to the Q9i+1 = 30u conformer in terms of symmetrical arrangement of H substituents with respect to the peptide plane. (TIF) Figure S2 Schematic drawings of conformers of Ala1 model characterized by different y values. The projections are drawn by looking along the Ca-C bond. The S substituent stands for the CH3-CO-NH- group in Ala1 model. (TIF) Figure S3 Pep model in vacuo: Dv9 variation as a function of y9. (A) Calculations at the PBE0/6-31G(d) level Results for the three conformers of the terminal C0 methyl group are shown (mQ9i+1 = 0u; &Q9i+1 = 30u; NQ9i+1 = 60u) together with PLoS ONE | www.plosone.org 8 September 2011 | Volume 6 | Issue 9 | e24533