Helmholtz Energy Change between Neutral and Zwitterionic Forms of Glycine in Aqueous Solution Using Ab Initio Expanded QM/MM-MC with QM Solvent

Abstract

We present an extended methodology of the quantum mechanical/molecular mechanical framework with Metropolis Monte Carlo method (QM/MM-MC), in which close surrounding solvent molecules are included in QM subsystem to evaluate quantitatively the solvation free energy change. The neutral (N) and zwitterionic (Z) structures of glycine in aqueous solution were optimized in the combination procedure of simulated annealing with MC at MM level and QM/MM-vib geometry optimization. Helmholtz energy change between N and Z forms of glycine in aqueous solution was calculated stepwise with expanded QM/MM-MC method, and the computational result was in good agreement with the experimental value.Glycine is a molecule that can form an intramolecular hydrogen bond and may convert from a neutral (N) form to a zwitterionic (Z) form in an aqueous solution. Since the conversion between N and Z of glycine can be considered as a prototype of the tautomerization of amino acid, the process and the energy profile of the NZ conversion have been extensively studied.17 Experimentally, the free energy of Z form was estimated to be 7.27 kcal mol ¹1 lower than that of N form, 8 and the free energy barrier height from Z to N was estimated to be 14.6 kcal mol ¹1 . 9 Recently, we have shown in the quantum mechanical/molecular mechanical framework with Metropolis Monte Carlo method (QM/MM-MC method) that the free energy barrier height of a water-mediated tautomerization path is higher than that of the direct tautomerization path in aqueous environment and that it is not "proton" but "hydrogen atom" that transfers. 7In the current work, we aim at performing the quantitative calculation of the NZ free energy difference of glycine in aqueous solution. To this end, we present an extended QM/MM-MC method to calculate the Helmholtz free energy change. Solvation effect cannot be elucidated simply by taking account of only a few solvent molecules in a few selected configurations of the solvent, even if high level of theory is used. It is necessary to treat many solvent molecules and many solvent configurations explicitly. This is why several methods such as QM/MM-MC method have been adopted. If MC simulations are to be performed to sample solvent configurations satisfactorily, a lower level of theory must be used. If a lower level of theory is used throughout for free energy calculations, however, a resultant computational value may not be reliable. In this Letter, the following three points are addressed to evaluate quantitatively the free energy change in aqueous solution. The first is how to obtain a solute structure in aqueous solution, which may be largely different from that in the gas phase. The second is how to include close surrounding water molecules in QM subsystem in free energy calculations. We present a new methodology here, which we call the "expanded QM/MM-MC method." The last is how to treat the solute with higher level QM in the free energy evaluation. Thus, we present the multistage evaluation of Helmholtz energy change.At the beginning, ...