Ellipsoid-weighted protein conformation alignment

Conformation alignment is a critical step for properly interpreting protein motions and conformational changes. The most widely used approach for superposing two conformations is by minimizing their root mean square distance (RMSD). In this work, we treat the alignment problem from a novel energy-minimization perspective. To this end we associate each atom in the protein with a mean-field potential well, whose shape, ellipsoidal in general, is to be inferred from the observed or computed fluctuations of that atom around its mean position. The scales and directions of the fluctuations can be obtained experimentally from anisotropic B-factors for crystal structures or computationally. We then show that this "ellipsoid-weighted" RMSD alignment can be reformulated nicely as a point-to-plane matching problem studied in computational geometry. This new alignment method is a generalization of standard RMSD and Gaussian-weighted RMSD alignment. It is heavily weighted by immobile regions and immobile directions of the protein and hence highlights the directional motions of the flexible parts. It has an additional advantage of aligning conformations of proteins along their preferred directions of motions and could be applied to order protein conformations along its trajectory.