| Abstract |
Electron cryomicroscopy (Cryo-EM) is a fast developing technique aiming at the determination of the 3-dimensional structures of large protein complexes. Using this technique, protein density maps can be generated to 6 to 10 Å resolution. At such resolutions, the secondary structure elements such as helices and beta-strands can be computationally detected. However, it is not known which parts of the protein sequence correspond to the detected secondary structures. The topology in this paper refers to the linear order and the directionality of the secondary structures. For a protein with N helices and M strands, there are (N!2^N)(M!2^M) different topologies. In order to reduce such a huge topological space, we investigated if it is possible to derive a small subset of the space that contains the native topology. In particular, we investigated the question if it is possible to eliminate the majority of the topological space by measuring the contact energy directly formed by the secondary structures, whose rough location and orientation are available in the density map.
We have developed a method to calculate the contact energy for all the possible secondary structure topologies. Using a multi-well contact energy function that we developed recently, the native topology appears to have the near minimum contact energy among all the possible topologies. For all the 20 proteins we tested, contact energy formed by the secondary structures in the native topology is within the lowest 30% of the contact energies of all the possible topologies. For skeletons from 1CC5 density map, more backbone possibilities are considered and the native topology is within the lowest 1.473% of all the possible topologies.
The work in this paper demonstrated, that it is possible to directly estimate the contact energy formed by the secondary structures, instead of the entire chain, to select a small subset of the huge topological space. Given the three dimensional locations of the secondary structures, our results indicated that the number of topologies with comfortable energy increase dramatically slower than the increase of the topological space. Our results suggest that multi-well contact energy function can be used to reduce the topological space dramatically through the estimation of the contact energy formed by the secondary structure skeletons in Cryo-EM density map.
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