Maiorov V N, Crippen G M
College of Pharmacy, University of Michigan, Ann Arbor 48109, USA.
Proteins. 1995 Jul;22(3):273-83. doi: 10.1002/prot.340220308.
Protein structures are routinely compared by their root-mean-square deviation (RMSD) in atomic coordinates after optimal rigid body superposition. What is not so clear is the significance of different RMSD values, particularly above the customary arbitrary cutoff for obvious similarity of 2-3 A. Our earlier work argued for an intrinsic cutoff for protein similarity that varied with the number of residues in the 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 of molecules. When rho is less than 0.4-0.5, protein structures are visually recognized to be obviously similar, but the mathematically pleasing intrinsic cutoff of rho < 1.0 corresponds to overall similarity in folding motif at a level not usually recognized until smoothing of the polypeptide chain path makes it striking. When the structures are scaled to unit radius of gyration and equal principle moments of inertia, the comparisons are even more universal, since they are no longer obscured 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 comparisons rises only slowly with the number of residues. This level is close to an intrinsic cutoff between similar and dissimilar comparisons, namely the maximal scaled rho possible for the two structures to be more 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 being compared. For proteins having fewer than 100 residues, the 1% rho falls below the intrinsic cutoff, so that for very small proteins, geometrically significant similarity can often occur by chance. We believe these ideas will be helpful in judging success in NMR structure determination and protein folding modeling.
蛋白质结构通常通过在最佳刚体叠加后原子坐标的均方根偏差（RMSD）进行比较。然而，不同RMSD值的意义并不那么明确，特别是高于习惯上设定的2 - 3埃明显相似性的任意截止值时。我们早期的工作提出了蛋白质相似性的内在截止值，该值随所比较的多肽链中的残基数而变化。在此，我们基于RMSD引入一种新的结构相似性度量rho，它与所涉及分子的大小或分子的任何其他特殊性质无关。当rho小于0.4 - 0.5时，蛋白质结构在视觉上被认为明显相似，但数学上令人满意的rho < 1.0的内在截止值对应于折叠基序的整体相似性，这种相似性在多肽链路径平滑使其显著之前通常未被识别。当结构按单位回转半径和相等的主惯性矩进行缩放时，比较更加通用，因为它们不再被整体大小和椭圆率的差异所掩盖。随着链长增加，随机结构对的rho分布向更高值倾斜，但最佳1%比较的rho值仅随残基数缓慢上升。这个水平接近相似和不相似比较之间的内在截止值，即两个结构彼此比与对方镜像更相似时可能的最大缩放rho值。内在截止值与所比较的残基或点数无关。对于残基少于100个的蛋白质，1%的rho低于内在截止值，因此对于非常小的蛋白质，几何上显著的相似性常常可能偶然出现。我们相信这些想法将有助于判断核磁共振结构测定和蛋白质折叠建模的成功与否。
