An improved stochastic fractal search algorithm for 3D protein structure prediction

Stochastic Fractal Search Algorithm Improved with Opposition-Based Learning for Solving the Substitution Box Design Problem

The main component of a cryptographic system that allows us to ensure its strength against attacks, is the substitution box. The strength of this component can be validated by various metrics, one of them being the nonlinearity. To this end, it is essential to develop a design for substitution boxes that allows us to guarantee compliance with this metric. In this work, we implemented a hybrid between the stochastic fractal search algorithm in conjunction with opposition-based learning. This design is supported by sequential model algorithm configuration for the proper parameters configuration. We obtained substitution boxes of high nonlinearity in comparison with other works based on metaheuristics and chaotic schemes. The proposed substitution box is evaluated using bijectivity, the strict avalanche criterion, nonlinearity, linear probability, differential probability and bit-independence criterion, which demonstrate the excellent performance of the proposed approach.

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.

PathMolD-AB: Spatiotemporal pathways of protein folding using parallel molecular dynamics with a coarse-grained model

Solving the protein folding problem (PFP) is one of the grand challenges still open in computational biophysics. Globular proteins are believed to evolve from initial configurations through folding pathways connecting several thermodynamically accessible states in a free energy landscape until reaching its minimum, inhabited by the stable native structures. Despite its huge computational burden, molecular dynamics (MD) is the leading approach in the PFP studies by preserving the Newtonian temporal evolution in the canonical ensemble. Non-trivial improvements are provided by highly parallel implementations of MD in cost-effective GPUs, concomitant to multiscale descriptions of proteins by coarse-grained minimalist models. In this vein, we present the PathMolD-AB framework, a comprehensive software package for massively parallel MD simulations using the canonical ensemble, structural analysis, and visualization of the folding pathways using the minimalist AB-model. It has, also, a tool to compare the results with proteins re-scaled from the PDB. We simulate and analyze, as case studies, the folding of four proteins: 13FIBO, 2GB1, 1PLC and 5ANZ, with 13, 55, 99 and 223 amino acids, respectively. The datasets generated from simulations correspond to the MD evolution of 3500 folding pathways, encompassing 35×106 states, which contains the spatial amino acid positions, the protein free energies and radii of gyration at each time step. Results indicate that the speedup of our approach grows logarithmically with the protein length and, therefore, it is suited for most of the proteins in the PDB. The predicted structures simulated by PathMolD-AB were similar to the re-scaled biological structures, indicating that it is promising for the study of the PFP study.

Protein structure optimization using improved simulated annealing algorithm on a three-dimensional AB off-lattice model

This paper proposed an improved simulated annealing (ISA) algorithm for protein structure optimization based on a three-dimensional AB off-lattice model. In the algorithm, we provided a general formula used for producing initial solution, and designed a multivariable disturbance term, relating to the parameters of simulated annealing and a tuned constant, to generate neighborhood solution. To avoid missing optimal solution, storage operation was performed in searching process. We applied the algorithm to test artificial protein sequences from literature and constructed a benchmark dataset consisting of 10 real protein sequences from the Protein Data Bank (PDB). Otherwise, we generated C_α space-filling model to represent protein folding conformation. The results indicate our algorithm outperforms the five methods before in searching lower energies of artificial protein sequences. In the testing on real proteins, our method can achieve the energy conformations with C_α-RMSD less than 3.0 Å from the PDB structures. Moreover, C_α space-filling model may simulate dynamic change of protein folding conformation at atomic level.