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

Abstract

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 Calpha 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.

A Constrained K-shortest Path Algorithm to Rank the Topologies of the Protein Secondary Structure Elements Detected in CryoEM Volume Maps

“…Although there are different topologies, the ones that satisfy the density requirement and the -sheet constraints can be quite limited. The results in this paper further demonstrated our previous finding about the amazing properties of SSE topologies that is the native topology is near the top of the entire topological space [31]. Figure 5 shows an example of the correct and incorrect topology.…”

Tracing Beta Strands Using StrandTwister from Cryo-EM Density Maps at Medium Resolutions

“…Given the positions of a helices and b strands in a density map, one can match them with secondary structure sequence segments that can be predicted from the amino acid sequence to derive the overall topology of a protein chain (Al Nasr et al, 2011;Baker et al, 2011;Biswas et al, 2012;Lindert et al, 2012;Lu et al, 2008). Once the topology is determined, backbone and side chains can be constructed and evaluated using energy functions (Al Nasr et al, 2010;Lindert et al, 2012;Sun and He, 2009). Pathwalking derives a Ca trace directly from pseudoatoms extracted from the density map (Baker et al, 2012b).…”

Orientations of beta-strand traces and near maximum twist

“…We demonstrated that DP-TOSS, a constrained K-shortest path method, is effective finding the topology from large proteins such as those with 33 helices [14]. Once limited possible matches are predicted, atomic models can be built and selected using energy functions [15][16][17][18]. Although it is possible to detect the location of major β-sheets, it has been a challenging problem to detect β-strands from the β-sheet density.…”