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 Δ μ_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 Δ μ_red (QM) due to the oxidant described quantum chemically and the free energy Δ μ_red (MM) due to the water molecules represented by a classical model. By the sum of these contributions, the total reduction free energy Δ μ_red has been given as -80.1 kcal/mol. To examine the accuracy and efficiency of this approach, we have also conducted the Δ μ_red calculation using the conventional scheme that Δ μ_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 Δ μ_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.