Geometric Filtering of Pairwise Atomic Interactions Applied to the Design of Efficient Statistical Potentials Afra Zomorodian a , Leonidas Guibas a , Patrice Koehl b,∗ a Department of Computer Science Stanford University Stanford, CA 94305, USA b Department of Computer Science and Genome Center University of California, Davis Davis, CA 95616, USA Abstract Distance-dependent, pairwise, statistical potentials are based on the concept that the packing observed in known protein structures can be used as a reference for comparing different 3D models for a protein. Here, packing refers to the set of all pairs of atoms in the molecule. Among all methods developed to assess three- dimensional models, statistical potentials are subject both to praise for their power of discrimination, and to criticism for the weaknesses of their theoretical founda- tions. Classical derivations of pairwise potentials assume statistical independence of all pairs of atoms. This assumption, however, is not valid in general. We show that we can filter the list of all interactions in a protein to generate a much smaller subset of pairs that retains most of the structural information contained in proteins. The filter is based on a geometric method called alpha shapes that captures the packing in a conformation. Statistical scoring functions derived from such subsets perform as well as scoring functions derived from the set of all pairwise interactions. Key words: Protein structure, Delaunay, Alpha Shape, Geometric Filtering, Statistical Potentials ∗ Corresponding author. Email addresses: afra@cs.stanford.edu (Afra Zomorodian), guibas@cs.stanford.edu (Leonidas Guibas), koehl@cs.ucdavis.edu (Patrice Koehl). Preprint submitted to Elsevier Science 7 March 2006