Geometrical comparison of two protein structures using Wigner-D functions

ABSTRACT In this article, we develop a quantitative comparison method for two arbitrary protein structures. This method uses a root‐mean‐square deviation characterization and employs a series expansion of the protein's shape function in terms of the Wigner‐D functions to define a new criterion, which is called a “similarity value.” We further demonstrate that the expansion coefficients for the shape function obtained with the help of the Wigner‐D functions correspond to structure factors. Our method addresses the common problem of comparing two proteins with different numbers of atoms. We illustrate it with a worked example. Proteins 2014; 82:2756–2769. © 2014 Wiley Periodicals, Inc.