Native secondary structure topology has near minimum contact energy among all possible geometrically constrained topologies

Secondary structure topology in this article refers to the order and the direction of the secondary structures, such as helices and strands, with respect to the protein sequence. Even when the locations of the secondary structure C alpha atoms are known, there are still (N!2(N)) (M!2(M)) different possible topologies for a protein with N helices and M strands. This work explored the question if the native topology is likely to be identified among a large set of all possible geometrically constrained topologies through an evaluation of the residue contact energy formed by the secondary structures, instead of the entire chain. We developed a contact pair specific and distance specific multiwell function based on the statistical characterization of the side chain distances of 413 proteins in the Protein Data Bank. The multiwell function has specific parameters to each of the 210 pairs of residue contacts. We illustrated a general mathematical method to extend a single well function to a multiwell function to represent the statistical data. We have performed a mutation analysis using 50 proteins to generate all the possible geometrically constrained topologies of the secondary structures. The result shows that the native topology is within the top 25% of the list ranked by the effective contact energies of the secondary structures for all the 50 proteins, and is within the top 5% for 34 proteins. As an application, the method was used to derive the structure of the skeletons from a low resolution density map that can be obtained through electron cryomicroscopy.