Conformational space annealing and an off-lattice frustrated model protein

A global optimization method, conformational space annealing (CSA), is applied to study a 46-residue protein with the sequence B9N3(LB)4N3B9N3(LB)5L, where B, L and N designate hydrophobic, hydrophilic, and neutral residues, respectively. The 46-residue BLN protein is folded into the native state of a four-stranded β-barrel. It has been a challenging problem to locate the global minimum of the 46-residue BLN protein since the system is highly frustrated and consequently its energy landscape is quite rugged. The CSA successfully located the global minimum of the 46-mer for all 100 independent runs. The CPU time for CSA is about seventy times less than that for simulated annealing (SA), and its success rate (100%) to find the global minimum is about eleven times higher. The amount of computational efforts used for CSA is also about ten times less than that of the best global optimization method yet applied to the 46-residue BLN protein, the quantum thermal annealing with renormalization. The 100 separate CSA runs produce the global minimum 100 times as well as other 5950 final conformations corresponding to a total of 2361 distinct local minima of the protein. Most of the final conformations have relatively small RMSD values from the global minimum, independent of their diverse energy values. Very close to the global minimum, there exist quasi-global-minima which are frequently obtained as one of the final answers from SA runs. We find that there exist two largest energy gaps between the quasi-global-minima and the other local minima. Once a SA run is trapped in one of these quasiglobal-minima, it cannot be folded into the global minimum before crossing over the two large energy barriers, clearly demonstrating the reason for the poor success rate of SA.