Measuring residue associations in protein structures. Possible implications for protein folding

We propose a number of distance measures between residues in protein structures based on average, minimum and maximum distances of all atom (backbone and side-chain) coordinates or with respect to side-chain atom coordinates only. The d1-distance (D1-distance) refers to the average distance between side-chain (backbone and side-chain) atoms of a residue pair in a given structure. The dm-distance (Dm-distance) refers to the minimum distance between side-chain atoms (non-trivial minimum distance between all atoms of a residue pair). For each distance measure, averaging and normalizing over representative protein structures, association values and closeness orderings for all amino acid types are determined. The expected associations of side-chain interactions between oppositely charged residues, among hydrophobic residues and of cysteine with cysteine are confirmed. Several surprising associations are observed relative to (1) the aromatic residues tyrosine and tryptophan, but not phenylalanine; (2) multiple histidine residues; (3) asymmetries of arginine versus lysine, aspartate versus glutamate, alanine versus glycine, and asparagine versus glutamine; (4) absence of correlations of alpha-carbon distances with side-chain distances. The all atoms D1-distance attractions are dominated by steric relationships, with glycine and alanine significantly close to all amino acids, whereas large residues are under-associated with all residue types. In contrast, for the closeness ordering corresponding to the minimum side-chain dm-distance, glycine and alanine are among the least associated. However, in the d1-distance alanine is significantly close to all hydrophobic residues with the exception of tryptophan. The dm-distance preferences display a pervasive attraction for tyrosine by almost all residue types, the prominence of tyrosine and tryptophan in cation-aromatic interactions, and the versatility of histidine in functionality. The principal findings suggest a new perspective on the early and intermediate stages of protein folding.