Protein Decoy Generation Using Branch and Bound with Efficient Bounding

Abstract

We propose a new discrete protein structure model (using a modified face-centered cubic lattice). A novel branch and bound algorithm for finding global minimum structures in this model is suggested. The objective energy function is very simple as it depends on the predicted half-sphere exposure numbers of C _α -atoms. Bounding and branching also exploit predicted secondary structures and expected radius of gyration. The algorithm is fast and is able to generate the decoy set in less than 48 hours on all proteins tested.

Despite the simplicity of the model and the energy function, many of the lowest energy structures, using exact measures, are near the native structures (in terms of RMSD). As expected, when using predicted measures, the fraction of good decoys decreases, but in all cases tested, we obtained structures within 6 Å RMSD in a set of low-energy decoys. To the best of our knowledge, this is the first de novo branch and bound algorithm for protein decoy generation that only depends on such one-dimensional predictable measures. Another important advantage of the branch and bound approach is that the algorithm searches through the entire conformational space. Contrary to search heuristics, like Monte Carlo simulation or tabu search, the problem of escaping local minima is indirectly solved by the branch and bound algorithm when good lower bounds can be obtained.