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We have simulated, as a showcase, the pentapeptide Met-enkephalin (Tyr-Gly-Gly-Phe-Met) to visualize the energy landscape and to investigate the conformational coverage by the multicanonical method. We obtained a three-dimensional topographic picture of the whole energy landscape by plotting the histogram with respect to energy (temperature) and the order parameter, which gives the degree of resemblance of any created conformation with the global energy minimum.

A combination of replica exchange Monte Carlo sampling techniques and energy landscape paving approach is presented. This hybrid algorithm combines the features of the energy landscape paving (ELP) and replica exchange methods (REM). I have tested its performance in studying the low-energy conformations of the benchmark peptide Met-enkephalin.

We have performed multicanonical simulations of hydrophobic-hydrophilic heteropolymers with a simple effective, coarse-grained off-lattice model to study the structure and the topology of the energy surface. The multicanonical method samples the whole rugged energy landscape, in particular the low-energy part, and enables one to better understand the critical behaviors and visualize the folding pathways of the considered protein model.

We discuss applicability of principal component analysis (PCA) for protein tertiary structure prediction from amino acid sequence. The algorithm presented in this paper belongs to the category of protein refinement models and involves establishing a low-dimensional space where the sampling (and optimization) is carried out via particle swarm optimizer (PSO). The reduced space is found via PCA performed for a set of low-energy protein models previously found using different optimization techniques. A high frequency term is added into this expansion by projecting the best decoy into the PCA basis set and calculating the residual model. This term is aimed at providing high frequency details in the energy optimization. The goal of this research is to analyze how the dimensionality reduction affects the prediction capability of the PSO procedure. For that purpose, different proteins from the Critical Assessment of Techniques for Protein Structure Prediction experiments were modeled. In all the cases, both the energy of the best decoy and the distance to the native structure have decreased. Our analysis also shows how the predicted backbone structure of native conformation and of alternative low energy states varies with respect to the PCA dimensionality. Generally speaking, the reconstruction can be successfully achieved with 10 principal components and the high frequency term. We also provide a computational analysis of protein energy landscape for the inverse problem of reconstructing structure from the reduced number of principal components, showing that the dimensionality reduction alleviates the ill-posed character of this high-dimensional energy optimization problem. The procedure explained in this paper is very fast and allows testing different PCA expansions. Our results show that PSO improves the energy of the best decoy used in the PCA when the adequate number of PCA terms is considered.