Local Propensities and Statistical Potentials of Backbone Dihedral Angles in Proteins

The following three issues concerning the backbone dihedral angles of protein structures are presented. (1) How do the dihedral angles of the 20 amino acids depend on the identity and conformation of their nearest residues? (2) To what extent are the native dihedral angles determined by local (dihedral) potentials? (3) How to build a knowledge-based potential for a residueʹs dihedral angles, considering the identity and conformation of its nearest residues? We find that the dihedral angle distribution for a residue can significantly depend on the identity and conformation of its adjacent residues. These correlations are in sharp contrast to the Flory isolated-pair hypothesis. Statistical potentials are built for all combinations of residue triplets and depend on the dihedral angles between consecutive residues. First, a low-resolution potential is obtained, which only differentiates between the main populated basins in the dihedral angle density plots. Minimization of the dihedral potential for 125 test proteins reveals that most native α-helical residues (89%) and a large fraction of native β-sheet residues (47%) adopt conformations close to their native one. For native loop residues, the percentage is 48%. It is also found that this fraction is higher for residues away from the ends of α or β secondary structure elements. In addition, a higher resolution potential is built as a function of dihedral angles by a smoothing procedure and continuous functions interpolations. Monte Carlo energy minimization with this potential results in a lower fraction for native β-sheet residues. Nevertheless, because of the higher flexibility and entropy of β structures, they could be preferred under the influence of non-local interactions. In general, most α-helices and many β-sheets are strongly determined by the local potential, while the conformations in loops and near the end of β-sheets are more influenced by non-local interactions.