Statistical validation of the root-mean-square-distance, a measure of protein structural proximity

Despite its well-documented limitations, the root-mean-square-distance (rmsd) between pairs of equivalent atoms is routinely used to monitor the degree of similarity between two optimally superposed protein three-dimensional structures. A robust method for assessing the statistical significance of the difference between two rmsd values is presented here. It is based on the comparison of two protein structures through the correlation coefficient between equivalent inter-atomic distances and the subsequent application of the Fisher transformation that allows one to estimate the probability of identity between two correlation coefficient values. The relationship between the rmsd and Fisher correlation coefficient allows then to estimate the statistical significance of the difference between two rmsd values. Such a procedure is exemplified with the analysis of the possible classifications of the immunoglobulin-like domains of filamin and is compared to related estimations of structural similarity. The possibility to estimate the probability of the difference between two rmsd values can be used to optimize the protein structural classifications and comparisons, independent of the procedure used to derive the rmsds.