Local energy landscape flattening: parallel hyperbolic Monte Carlo sampling of protein folding

Among the major difficulties in protein structure prediction is the roughness of the energy landscape that must be searched for the global energy minimum. To address this issue, we have developed a novel Monte Carlo algorithm called parallel hyperbolic sampling (PHS) that logarithmically flattens local high-energy barriers and, therefore, allows the simulation to tunnel more efficiently through energetically inaccessible regions to low-energy valleys. Here, we show the utility of this approach by applying it to the SICHO (SIde-CHain-Only) protein model. For the same CPU time, the parallel hyperbolic sampling method can identify much lower energy states and explore a larger region phase space than the commonly used replica sampling (RS) Monte Carlo method. By clustering the simulated structures obtained in the PHS implementation of the SICHO model, we can successfully predict, among a representative benchmark 65 proteins set, 50 cases in which one of the top 5 clusters have a root-mean-square deviation (RMSD) from the native structure below 6.5 A. Compared with our previous calculations that used RS as the conformational search procedure, the number of successful predictions increased by four and the CPU cost is reduced. By comparing the structure clusters produced by both PHS and RS, we find a strong correlation between the quality of predicted structures and the minimum relative RMSD (mrRMSD) of structures clusters identified by using different search engines. This mrRMSD correlation may be useful in blind prediction as an indicator of the likelihood of successful folds.