Gaussian-weighted RMSD superposition of proteins: a structural comparison for flexible proteins and predicted protein structures

Many proteins contain flexible structures such as loops and hinged domains. A simple root mean square deviation (RMSD) alignment of two different conformations of the same protein can be skewed by the difference between the mobile regions. To overcome this problem, we have developed a novel method to overlay two protein conformations by their atomic coordinates using a Gaussian-weighted RMSD (wRMSD) fit. The algorithm is based on the Kabsch least-squares method and determines an optimal transformation between two molecules by calculating the minimal weighted deviation between the two coordinate sets. Unlike other techniques that choose subsets of residues to overlay, all atoms are included in the wRMSD overlay. Atoms that barely move between the two conformations will have a greater weighting than those that have a large displacement. Our superposition tool has produced successful alignments when applied to proteins for which two conformations are known. The transformation calculation is heavily weighted by the coordinates of the static region of the two conformations, highlighting the range of flexibility in the overlaid structures. Lastly, we show how wRMSD fits can be used to evaluate predicted protein structures. Comparing a predicted fold to its experimentally determined target structure is another case of comparing two protein conformations of the same sequence, and the degree of alignment directly reflects the quality of the prediction.