The Hybrid Idea of Optimization Methods Applied to the Energy Minimization of (Prion) Protein Structures Focusing on the beta2-alpha2 Loop

In molecular mechanics, current generation potential energy functions provide a reasonably good compromise between accuracy and effectiveness. This paper firstly reviewed several most commonly used classical potential energy functions and their optimization methods used for energy minimization. To minimize a potential energy function, about 95\% efforts are spent on the Lennard-Jones potential of van der Waals interactions; we also give a detailed review on some effective computational optimization methods in the Cambridge Cluster Database to solve the problem of Lennard-Jones clusters. From the reviews, we found the hybrid idea of optimization methods is effective, necessary and efficient for solving the potential energy minimization problem and the Lennard-Jones clusters problem. An application to prion protein structures is then done by the hybrid idea. We focus on the $\beta$2-$\alpha$2 loop of prion protein structures, and we found (i) the species that has the clearly and highly ordered $\beta$2-$\alpha$2 loop usually owns a 3$_{10}$-helix in this loop, (ii) a "$\pi$-circle" Y128--F175--Y218--Y163--F175--Y169--R164--Y128(--Y162) is around the $\beta$2-$\alpha$2 loop.