Predicting protein tertiary structure and its uncertainty analysis via particle swarm sampling.

We discuss the relationship between the problem of protein tertiary structure prediction from the amino acid sequence and the uncertainty analysis. The algorithm presented in this paper belongs to the category of decoy-based modeling, where different known protein models are used to establish a low dimensional space via principal component analysis. The low dimensional space is utilized to perform an energy optimization via a family of very explorative particle swarm optimizers to find the global minimum. The aim of this procedure is to get a representative sample of the nonlinear equivalent region, that is, protein models that have their energy lower than a certain energy bound. The posterior analysis of this family provides very valuable information about the backbone structure of the native conformation and its possible alternate states. This methodology has the advantage of being simple and fast and can help refine the tertiary protein structure. We comprehensively illustrate the performance of our algorithm on one protein from the CASP-9 protein structure prediction experiment. We also provide a theoretical analysis of the energy landscape found in the tertiary structure protein inverse problem, explaining why model reduction techniques (principal component analysis in this case) serve to alleviate the ill-posed character of this high dimensional optimization problem. In addition, we expand the computational benchmark with a summary of other CASP-9 proteins in the Appendix.