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.
Keywords: Neighborhood solution; Off-lattice model; Protein structure; Thermodynamic behavior.