SIZE-INDEPENDENT COMPARISON OF PROTEIN 3-DIMENSIONAL STRUCTURES

Protein structures are routinely compared by their root-mean-square de viation (RMSD) in atomic coordinates after optimal rigid body superpos ition. What is not so clear is the significance of different RMSD valu es, particularly above the customary arbitrary cutoff for obvious simi larity of 2-3 Angstrom. Our earlier work argued for an intrinsic cutof f for protein similarity that varied with the number of residues in th e polypeptide chains being compared. Here we introduce a new measure, rho, of structural similarity based on RMSD that is independent of the sizes of the molecules involved, or of any other special properties o f molecules. When rho is less than 0.4-0.5, protein structures are vis ually recognized to be obviously similar, but the mathematically pleas ing intrinsic cutoff of rho < 1.0 corresponds to overall similarity in folding motif at a level not usually recognized until smoothing of th e polypeptide chain path makes it striking. When the structures are sc aled to unit radius of gyration and equal principle moments of inertia , the comparisons are even more universal, since they are no longer ob scured by differences in overall size and ellipticity, With increasing chain length, the distribution of rho for pairs of random structures is skewed to higher values, but the value for the best 1% of the compa risons rises only slowly with the number of residues. This level is cl ose to an intrinsic cutoff between similar and dissimilar comparisons, namely the maximal scaled rho possible for the two structures to be m ore similar to each other than one is to the other's mirror image. The intrinsic cutoff is independent of the number of residues or points b eing compared. For proteins having fewer than 100 residues, the 1% rho falls below the intrinsic cutoff, so that for very small proteins, ge ometrically significant similarity can often occur by chance. We belie ve these ideas will be helpful in judging success in NMR structure det ermination and protein folding modeling. (C) 1995 Wiley-Liss, Inc.