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Protein structure refinement is a crucial step for more accurate protein structure predictions. Most existing approaches treat it as an energy minimization problem to intuitively improve the quality of initial models by searching for structures with lower energy. Considering that a single energy function could not reflect the accurate energy landscape of all the proteins, our previous AIR 1.0 pipeline uses multiple energy functions to realize a multi-objectives particle swarm optimization-based model refinement. It is expected to provide a general balanced conformation search protocol guided from different energy evaluations. However, AIR 1.0 solves the multi-objective optimization problem as a whole, which could not result in good solution diversity and convergence on some targets. In this study, we report a decomposition-based method AIR 2.0, which is an updated version of AIR, for protein structure refinement. AIR 2.0 decomposes a multi-objective optimization problem into a number of subproblems and optimizes them simultaneously using particle swarm optimization algorithm. The solutions yielded by AIR 2.0 show better convergence and diversity compared to its previous version, which increases the possibilities of digging out better structure conformations. The experimental results on CASP13 refinement benchmark targets and blind tests in CASP 14 demonstrate the efficacy of AIR 2.0.

Protein Structure Refinement Using Multi-Objective Particle Swarm Optimization with Decomposition Strategy