QM/MM Free-Energy Perturbation Compared to Thermodynamic Integration and Umbrella Sampling:  Application to an Enzymatic Reaction

Abstract

We used the free-energy perturbation (FEP) method in quantum mechanics/molecular mechanics (QM/MM) calculations to compute the free-energy profile of the hydroxylation reaction in the enzyme p-hydroxybenzoate hydroxylase (PHBH). k statistics were employed to analyze the FEP sampling including estimation of the sampling error. Various approximations of the free-energy perturbation method were tested. We find that it is adequate not only to freeze the density of the QM part during the dynamics at frozen QM geometry but also to approximate this density by electrostatic-potential-fitted point charges. It is advisable to include all atoms of a QM/MM link in the perturbation. The results of QM/MM-FEP for PHBH are in good agreement with those of thermodynamic integration and umbrella sampling.

Reorganization Energy for Internal Electron Transfer in Multicopper Oxidases

“…Test calculations at the semiempirical level have shown that this is does not affect the final free energies significantly. 70 The QTCP calculations were performed as previously described, 68,69,71,72 with simple extensions to the QM/MM-2QM case: First, each redox state was optimised by QM/MM-2QM, using a solvated spherical system with a radius of 38 Å. 37 Second, the total system was moved into a periodic octahedral box and was further solvated with water molecules extending at least 9 Å from the original system, giving a total of 12270 water molecules (a set of QTCP calculations in which the solvent shell was increased to 15 Å or 19803 water molecules was also performed).…”

“…73,74 FEP free energies and their uncertainties were estimated by cumulant expressions. 73 The perturbations were divided into several steps: We performed nine simulations with the geometry of the reactant state, but with charges of the QM system that were linearly transformed from the reactant state to the product state by a coupling parameter, λ, assuming the values of 0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, and 1. This was accomplished by simply changing the charges in the parameter file, whereas the coordinates of the QM system were kept to those of the reactant state.…”

Catalytic Cycle of Multicopper Oxidases Studied by Combined Quantum- and Molecular-Mechanical Free-Energy Perturbation Methods

“…FEP free energies and their uncertainties were estimated by cumulant expressions. 65,67 Several methods were used to estimate long-range electrostatic effects outside the simulated system. The results presented in the text and the tables were obtained with periodic systems and Ewald summation (as in the MD simulations).…”

Computational Studies of the Mechanism of Catalysis and Inhibition of Cysteine Proteases

“…Thus, the problem lies in the inability to explore all the configurations leaving the system to evolve freely, the simulation would not be able to access to the structures with a higher potential energy as for example the structures of TS. There are several methods for overcoming the sampling problem like thermodynamic integration, 302 or umbrella sampling. 303 The umbrella sampling method proposed by J. P. Valleau and G. M Torrie, was the one used in this Doctoral Thesis and it will be analyzed in the section 6.3.2.…”