Many remarkable molecular functions of proteins use their characteristic global and slow conformational dynamics through coupling of local chemical states in reaction centers with global conformational changes of proteins. To theoretically examine the functional processes of proteins in atomic detail, a methodology of quantum mechanical/molecular mechanical (QM/MM) free-energy geometry optimization is introduced. In the methodology, a geometry optimization of a local reaction center is performed with a quantum mechanical calculation on a free-energy surface constructed with conformational samples of the surrounding protein environment obtained by a molecular dynamics simulation with a molecular mechanics force field. Geometry optimizations on extensive free-energy surfaces by a QM/MM reweighting free-energy self-consistent field method designed to be variationally consistent and computationally efficient have enabled examinations of the multiscale molecular coupling of local chemical states with global protein conformational changes in functional processes and analysis and design of protein mutants with novel functional properties.

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