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We discuss the use of the Singular Value Decomposition as a model reduction technique in Protein Tertiary Structure prediction, alongside to the uncertainty analysis associated to the tertiary protein predictions via Particle Swarm Optimization (PSO). The algorithm presented in this paper corresponds to the category of the decoy-based modelling, since it first finds a good protein model located in the low energy region of the protein energy landscape, that is used to establish a three-dimensional space where the free-energy optimization and search is performed via an exploratory version of PSO. The ultimate goal of this algorithm is to get a representative sample of the protein backbone structure and the alternate states in an energy region equivalent or lower than the one corresponding to the protein model that is used to establish the expansion (model reduction), obtaining as result other protein structures that are closer to the native structure and a measure of the uncertainty in the protein tertiary protein reconstruction. The strength of this methodology is that it is simple and fast, and serves to alleviate the ill-posed character of the protein structure prediction problem, which is very highly dimensional, improving the results when it is performed in a good protein model of the low energy region. To prove this fact numerically we present the results of the application of the SVD-PSO algorithm to a set of proteins of the CASP competition whose native’s structures are known. 

We discuss applicability of Principal Component Analysis and Particle Swarm Optimization in protein tertiary structure prediction. The proposed algorithm is based on establishing a low-dimensional space where the sampling (and optimization) is carried out via Particle Swarm Optimizer (PSO). The reduced space is found via Principal Component Analysis (PCA) performed for a set of previously found low- energy protein models. A high frequency term is added into this expansion by projecting the best decoy into the PCA basis set and calculating the residual model. Our results show that PSO improves the energy of the best decoy used in the PCA considering an adequate number of PCA terms.