Finding the consensus shape for a protein family

We define and prove properties of the consensus shape for a family of proteins, a protein-like structure that provides a compact summary of the significant structural information for a protein family. If all members of a protein family exhibit a geometric relationship between corresponding alpha carbons then that relationship is preserved in the consensus shape. In particular, distances and angles that are consistent across family members are preserved. For the consensus shape, the spacing between successive alpha carbons is variable, with small distances in regions where the members of the protein family exhibit significant variation and large distances (up to the standard spacing of about 4Å) in regions where the family members agree. Despite this non-proteinlike characteristic, the consensus shape preserves and highlights important structural information. We describe an iterative algorithm for computing the consensus shape and prove that the algorithm converges. We also present the results of experiments in which we build consensus shapes for several known protein families.