Computation of the free energy change associated with one-electron reduction of coenzyme immersed in water: A novel approach within the framework of the quantum mechanical/molecular mechanical method combined with the theory of energy representation

The isoalloxazine ring (flavin ring) is a part of the coenzyme flavin adenine dinucleotide and acts as an active site in the oxidation of a substrate. We have computed the free energy change Delta mu(red) associated with one-electron reduction of the flavin ring immersed in water by utilizing the quantum mechanical/molecular mechanical method combined with the theory of energy representation (QM/MM-ER method) recently developed. As a novel treatment in implementing the QM/MM-ER method, we have identified the excess charge to be attached on the flavin ring as a solute while the remaining molecules, i.e., flavin ring and surrounding water molecules, are treated as solvent species. Then, the reduction free energy can be decomposed into the contribution Delta mu(red)(QM) due to the oxidant described quantum chemically and the free energy Delta mu(red)(MM) due to the water molecules represented by a classical model. By the sum of these contributions, the total reduction free energy Delta mu(red) has been given as -80.1 kcal/mol. To examine the accuracy and efficiency of this approach, we have also conducted the Delta mu(red) calculation using the conventional scheme that Delta mu(red) is constructed from the solvation free energies of the flavin rings at the oxidized and reduced states. The conventional scheme has been implemented with the QM/MM-ER method and the calculated Delta mu(red) has been estimated as -81.0 kcal/mol, showing excellent agreement with the value given by the new approach. The present approach is efficient, in particular, to compute free energy change for the reaction occurring in a protein since it enables ones to circumvent the numerical problem brought about by subtracting the huge solvation free energies of the proteins in two states before and after the reduction.