QM/MM Minimum Free-Energy Path:  Methodology and Application to Triosephosphate Isomerase

Abstract

Structural and energetic changes are two important characteristic properties of a chemical reaction process. In the condensed phase, studying these two properties is very challenging because of the great computational cost associated with the quantum mechanical calculations and phase space sampling. Although the combined quantum mechanics/molecular mechanics (QM/MM) approach significantly reduces the amount of the quantum mechanical calculations and facilitates the simulation of solution phase and enzyme catalyzed reactions, the required quantum mechanical calculations remain quite expensive and extensive sampling can be achieved routinely only with semiempirical quantum mechanical methods. QM/MM simulations with ab initio QM methods, therefore, are often restricted to narrow regions of the potential energy surface such as the reactant, product and transition state, or the minimum energy path. Such ab initio QM/MM calculations have previously been performed with the QM/MM-Free Energy (QM/MM-FE) method of Zhang et al. 1 to generate the free energy profile along the reaction coordinate using free energy perturbation calculations at fixed structures of the QM subsystems. Results obtained with the QM/MM-FE method depend on the determination of the minimum energy reaction path, which is based on local conformations of the protein/solvent environment and can be difficult to obtain in practice. To overcome the difficulties associated with the QM/MM-FE method and to further enhance the sampling of the MM environment conformations, we develop here a new method to determine the QM/MM minimum free energy path (QM/MM-MFEP) for chemical reaction processes in solution and in enzymes. Within the QM/MM framework, we express the free energy of the system as a function of the QM conformation, thus leading to a simplified potential of mean force (PMF) description for the thermodynamics of the system. The free energy difference between two QM conformations is evaluated by the QM/MM free energy perturbation method. The free energy gradients with respect to the QM degrees of freedom are calculated from molecular dynamics simulations at given QM conformations. With the free energy and free energy gradients in hand, we further implement chain-of-conformation optimization algorithms in the search for the reaction path on the free energy surface without specifying a reaction coordinate. This method thus efficiently provides a unique minimum free energy path for solution and enzyme reactions, with structural and energetic properties being determined simultaneously. To further incorporate the dynamic contributions of the QM subsystem into the simulations, we develop the reaction path potential of Lu, et al. 2 for the minimum free energy path. The combination of the methods developed here presents a comprehensive and accurate treatment for the simulation of reaction processes in solution and in enzymes with ab initio QM/MM methods. The method has been demonstrated on the first step of the reaction of the enzyme triosephosphate isome...

Incorrect nucleotide insertion at the active site of a G:A mismatch catalyzed by DNA polymerase β

“…Yet, one approach to accomplish this goal is through stepwise free energy calculation with the QM/MM/molecular dynamics implementations, such as QM/ MM-FE (free energy) (13) and QM/MM-MFEP (minimum free energy path) (14). However, such calculations would be highly time-consuming.…”

Free Energies of Chemical Reactions in Solution and in Enzymes with Ab Initio Quantum Mechanics/Molecular Mechanics Methods

“…The approximate QM/MM total energy becomes (9) It has been shown that this linear-polarization QM ESP charge model yields quite accurate energetics for reaction systems, given a good initial reference state [81,61]. It is even possible to further simplify this QM ESP charge model by truncating the polarization effects of the QM ESP charges [61,62].…”

“…Beyond this distance, the MM point charges merely contribute by providing a static electrostatic potential. Therefore a simple technical scheme has been adopted in our simulations with periodic boundary condition [61,62,60] in which a cutoff of 9 ~ 14 Å was used for selecting MM charges for the QM SCF calculation. The QM calculation yielded polarized QM ESP charges that were in turn used to represent the QM subsystem during MD simulations with the long range electrostatic interactions treated by the Particle-mesh Ewald Method [63].…”

“…Quite conveniently, the reduced set of coordinates can be the same as the QM subsystems. Thus, one can construct the MFEP, a reaction path defined on the PMF of a reduced set of coordinates [61,67,68,69,70]. The contributions from the rest of the system are ensemble-averaged quantities obtained during MD simulations.…”

Density-fragment interaction approach for quantum-mechanical/molecular-mechanical calculations with application to the excited states of a Mg2+-sensitive dye

“…For this purpose, we used the QM/MM-free energy ͑QM/MM-FE͒ method 58 that has a good record in the previous studies of solution-phase and enzyme-catalyzed reactions. 59 In the first step, a gas-phase geometry optimization of KMG-20 without the bound Mg 2+ ion was performed using DFT with the B3LYP functional. Next, this structure was solvated in a 20 Å sphere of classical MM water molecules described by the TIP3P model, 60 and a QM/MM-FE optimization was carried out.…”