Quantifying the Mechanism of Phosphate Monoester Hydrolysis in Aqueous Solution by Evaluating the Relevant ab initio QM/MM Free Energy Surfaces

摘要

Understanding the nature of the free energy surfaces for phosphate hydrolysis is a prerequisite for understanding the corresponding key chemical reactions in biology. Here the challenge has been to move to careful ab initio QM/MM (QM(ai)/MM) free energy calculations, where obtaining converging results is very demanding and computationally expensive. This work describes such calculations, focusing on the free energy surface for the hydrolysis of phosphate monoesters, paying a special attention to the comparison between the one water (1W) and two water (2W) paths for the proton transfer (PT) step. This issue has been explored before by energy minimization with implicit solvent models and by non-systematic QM/MM energy minimization, as well as by non-systematic free energy mapping. However, no study has provided the needed reliable 2D (3D) surfaces which are necessary for reaching concrete conclusions. Our study generated in a systematic way the 2D (3D) free energy maps for several relevant systems, comparing the results of QM(ai)/MM and QM(ai)/implicit solvent surfaces, and provides an advanced description of the relevant energetics. It is found that the 1W path for the hydrolysis of methyl diphosphate (MDP) trianion is 6–9 kcal/mol higher than the 2W path. This difference becomes slightly larger in the presence of Mg²⁺ ion, since this ion reduces the pKa of the conjugated acid form of the phosphate oxygen that accepts the proton. Interestingly, the BLYP approach (which has been used extensively in some studies) gives much smaller difference between the 1W and 2W activation barriers. At any rate, it is worth to point out that the 2W transition state for the PT is not much higher that the common plateau that serves as the starting point of both the 1W and 2W PT paths. Thus, the calculated catalytic effects of proteins based on the 2W PT mechanistic models are not expected to be different from the catalytic effects predicted using the 1W PT mechanistic models calibrated on the observed barriers in solution (as was done in all of our previous EVB studies).