Protein-protein interactions play a key role in life processes. Characterization of conformational changes in proteins upon binding is important for understanding the mechanisms of protein association and for our ability to model it. Dependence of side-chain dihedral angle distribution on the conformation of the backbone has been investigated in earlier studies [1–5]. The side-chain dihedral angles are not evenly distributed, but for the most part are tightly clustered. A number of unbound rotamer libraries have been described previously [1–14] (see  for a review). Dunbrack and Cohen  used Bayesian statistics to estimate populations and dihedral angles for all amino acids rotamers at all φ and ψ values. A backbone-dependent rotamer library  was obtained by dividing φ and ψ dihedral space into 10°× 10° bins, χ angles into 120° bins, and calculating frequencies and average values of rotamers for each amino acid. A backbone-independent rotamer library was generated in a similar way. In a recent study , a new version of the backbone-dependent rotamer library was developed. It consists of rotamer frequencies, mean dihedral angles, and variances as a function of the backbone dihedral angles. In one of the latest backbone-independent rotamer libraries, the “Penultimate rotamer library”  by Lovell, Richardson and colleagues, the dihedral angle space was clustered and rotamer positions were defined as the distribution mode.
Comparison of the side-chain distribution in the core and on the surface , conducted on 19 protein structures available in 1978, revealed a small variation of the χ1 rotamers distribution. A later study  on a set of 50 non-homologous proteins showed that for all side chains, except Asp, Asn and Glu, the distributions of χ1 rotamers on the surface and in the core are not significantly different.
Comparison of the χ1 and χ2 distributions at the interface and non-interface surface was performed by Guharoy et al. . Distributions were divided into bins as in the Dunbrack’s backbone-independent rotamer library . Empirical free energies of inter-rotamer transitions were calculated and compared for the interface and non-interface areas. The rotamers free energies were different at the interface and non-interface, whereas bound and unbound free energies were essentially the same.
Conformations of surface residues in protein structures determined by crystallography are affected by the crystal packing. The area of the protein surface involved in the crystal contacts is generally smaller than in biological interfaces , and the interface packing is looser . Studies of the crystal packing effect on the surface side chains [21–23] showed that ~ 20% of the exposed side chains change conformation, and the change increases with the increase of the side-chain solvent accessibility. Large polar or charged residues Arg, Lys, Glu, Gln, as well as Ser were found to be most flexible .
The purpose of this study was to analyze and compare dihedral angle distribution functions of the side chains at the interface and non-interface areas in bound and unbound proteins. Such analysis is important for better understanding of protein interactions and development of flexible docking approaches. The dihedral-angle distribution functions (DADF) were calculated on a cubic grid dividing the dihedral space into cells for each residue type, at interface and non-interface surface, in bound and unbound structures. The correlation coefficients between bound and unbound, interface and non-interface DADFs were calculated, along with the Manhattan distance, as a measure of dissimilarity between the DADFs. All the correlation coefficients depended on the amino acid type and the grid resolution. The correlation coefficients always increased with the increase of the grid spacing, whereas the Manhattan distances decreased accordingly. Short residues with one or two dihedral angles had higher correlations and smaller Manhattan distances at small grid spacing than the longer residues. The correlation between the interface and non-interface DADFs showed a similar dependence on the grid resolution in both bound and unbound states. The differences between bound and unbound DADFs induced by biological protein-protein interactions or crystal contacts disappeared at the 70° grid spacing for interfaces and 30° for non-interface surface. The two-fold difference in the critical grid spacing indicates larger changes at the interface than on the rest of the surface. While the earlier studies [18, 24, 25] observed this trend for the side-chain rotamers, this study validates it by a more general approach based on the DADFs.