What is the probability of a chance prediction of a protein structure with an rmsd of 6 Å?

Background: The root mean square deviation (rmsd) between corresponding atoms of two protein chains is a commonly used measure of similarity between two protein structures, The smaller the rmsd is between two structures, the more similar are these two structures. In protein structure prediction, one needs the rmsd between predicted and experimental structures for which a prediction can be considered to be successful. Success is obvious only when the rmsd is as small as that for closely homologous proteins (< 3 Angstrom). To estimate the quality of the prediction in the more general case, one has to compare the native structure not only with the predicted one but also with randomly chosen protein-like folds, One can ask: how many such structures must be considered to find a structure with a given rmsd from the native structure? Results: We calculated the rmsd values between native structures of 142 proteins and all compact structures obtained in the threading of these protein chains over 364 non-homologous structures, The rmsd distributions have a Gaussian form, with the average rmsd approximately proportional to the radius of gyration. Conclusions: We estimated the number of protein-like structures required to obtain a structure within an rmsd of 6 Angstrom to be 10(4)-10(5) for chains of 60-80 residues and 10(11)-10(12) structures for chains of 160-200 residues. The probability of obtaining a 6 Angstrom rmsd by chance is so remote that when such structures are obtained from a prediction algorithm, it should be considered quite successful.