Convergence of QM/MM free-energy perturbations based on molecular-mechanics or semiempirical simulations

Abstract

Lately, there has been great interest in performing free-energy perturbation (FEP) at the combined quantum mechanics and molecular mechanics (QM/MM) level, e.g. for enzyme reactions. Such calculations require extensive sampling of phase space, which typically is prohibitive with density-functional theory or ab initio methods. Therefore, such calculations have mostly been performed with semiempirical QM (SQM) methods, or by using a thermodynamic cycle involving sampling at the MM level and perturbations between the MM and QM/MM levels of theory. However, the latter perturbations typically have convergence problems, unless the QM system is kept fixed during the simulations, because the MM and QM/MM descriptions of the internal degrees of freedom inside the QM system are too dissimilar. We have studied whether the convergence of the MM -QM/MM perturbation can be improved by using a thoroughly parameterised force field or by using SQM/MM methods. As a test case we use the first half-reaction of haloalkane dehalogenase and the QM calculations are performed with the PBE, B3LYP, and TPSSH density-functional methods. We show that the convergence can be improved with a tailored force field, but only locally around the parameterised state. Simulations based on SQM/MM methods using the MNDO, AM1, PM3, RM1, PDDG-MNDO, and PDDG-PM3 Hamiltonians have slightly better convergence properties, but very long simulations are still needed (B10 ns) and convergence is obtained only if electrostatic interactions between the QM system and the surroundings are ignored. This casts some doubts on the common practice to base QM/MM FEPs on semiempirical simulations without any reweighting of the trajectories.

Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid host–guest binding energies

“…Similar corrections have been used in similar contexts before [68][69][70][71][72][73][74]. Unfortunately, such an approach becomes unstable if the differences between the MM and QM potentials are too large, leading to corrections that depend only in a few of the DFT calculations [90]. In the present case, this gives a correction of 35-92 kJ/mol for the host simulations but -51 to -149 kJ/mol in water (Table 3).…”

“…The reason for this is most likely the poor precision of the corrections (5-13 kJ/mol), caused by the large difference between the MM and QM potentials [90]. Of course, this could be improved by running more DFT calculations, but the results indicate that 25-169 times more calculations are needed to bring the uncertainty down to 1 kJ/mol.…”

Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration

“…It has attracted renewed interest in recent years, 84,86 in the form of sampling approaches involving either the reweighting or perturbation of MM trajectories to the QM/MM level [185][186][187][188][189][190][191][192][193][194] (including the so-called paradynamics [195][196][197][198] or the continuous switching between MM and QM/MM interactions. 199 The advantage of adjusting the parameters of the MM model to improve the convergence has also been noted in this context.…”

Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4

“…Recent applications of such approaches involve the calculation of solvation free energies of ligands [3, 9] or the computation of free energy barriers in enzymatic reactions. [42, 41, 16] More applications have been made possible by the development of QM/MM alchemical free energy calculations[32, 50] and improved sampling methods[28]. A novel alternative to the approaches mentioned above is the use of re-weighting in the form of Non-Boltzmann Bennett (NBB).…”