Structure optimization in a three-dimensional off-lattice protein model

Sequence-based protein structure optimization using enhanced simulated annealing algorithm on a coarse-grained model

The understanding of protein structure is vital to determine biological function. We presented an enhanced simulated annealing (ESA) algorithm to investigate protein three-dimensional (3D) structure on a coarse-grained model. Inside the algorithm, we adjusted exploration equations to achieve good search intensity. To that end, our algorithm used (i) a multivariable disturbance operator for diversification of solution, (ii) a sign function to improve randomness of solution, and (iii) taking remainder operation performed on floating-point number to tackle out-of-range solution. By monitoring energy value throughout the simulation, the energy-optimal state can be found. The ESA algorithm was tested on artificial and real protein sequences with different lengths. The results show that our algorithm outperforms conventional simulated annealing algorithm and can compete with the reported algorithms before. Especially, our algorithm can obtain folding conformations with specific structural features. Further analysis shows that simulating trajectory of seeking the lowest energy can exhibit thermodynamic behavior of protein folding. Graphical Abstract.

Size-guided multi-seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size-guided multi-seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest-energy configurations of the cluster with n - 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.

Two Perturbations for Geometry Optimization of Off-lattice Bead Protein Models

Referring to the optimization algorithm previously developed for atomic clusters, the present author develops an efficient method for geometry optimization of a coarse-grained protein model expressed with two kinds of beads (hydrophilic and hydrophobic ones). In the method, two types of geometrical perturbations, center-directed bead move and one bead rotation, are used to explore new configurations and local optimizations are performed after the perturbations. The center-directed bead move is used for hydrophobic beads and the one bead rotation is performed for both hydrophobic and hydrophilic beads. The optimization method was applied to protein models consisting of 13, 20, 21, and 34 beads. The present method produced the global minima of the 13-, 21-, and 34-bead models reported in the literature and updated the lowest energies of the protein models with 20 beads. These results indicate that the present method is efficient for searching for optimal structures of proteins.