Free Energy Analyses for the ATP Hydrolysis in Aqueous Solution by Large-Scale QM/MM Simulations Combined with a Theory of Solutions

Abstract

We conducted a set of molecular simulations referred to as QM/MM-ER, which combines a hybrid QM/MM with a theory of solutions, to elucidate the microscopic mechanism for the free energy release $\varDelta G_\mathrm{{hyd}}$ associated with hydrolyses of ATP (adenosine triphosphate) or PPi (pyrophosphoric acid) in aqueous solutions. A particular interest is placed on an experimental fact that $\varDelta G_\mathrm{{hyd}}$ stays almost constant irrespective of the number of excess charges on these solute molecules. In the QM/MM-ER simulations the free energy $\varDelta G_\mathrm{{hyd}}$ was decomposed into the contributions $\varDelta G_\mathrm{{ele}}$ and $\varDelta G_\mathrm{{sol}}$ which are, respectively, the free energies due to the electronic states and the solvations of the solutes. It was revealed that $\varDelta G_\mathrm{{ele}}$ is largely negative on the hydrolyses; that is, the products (ADP and Pi) are much stable in the electronic free energies than the reactants. This is attributed mostly to the reduction of the Coulomb repulsion among the excess electrons on ATP or PPi associated with the fragmentation. On the contrary, $\varDelta G_\mathrm{{sol}}$ was found to be highly positive indicating the reactant states are much favorable for hydrations than the products, which can be qualitatively understood in terms of the Born’s solvation model. Thus, a drastic compensation takes place between the two free energy contributions $\varDelta G_\mathrm{{ele}}$ and $\varDelta G_\mathrm{{sol}}$ resulting in a modest free energy release $\varDelta G_\mathrm{{hyd}}$ on hydrolyses. A set of classical molecular dynamics simulations for hydrolyses in ethanol was also performed to examine the effect of the dielectric constant of the solvent on the energetics. It was shown that the superb balance between $\varDelta G_\mathrm{{ele}}$ and $\varDelta G_\mathrm{{sol}}$ established in water is seriously degraded in the ethanol solution.