QM/MM free energy simulations: recent progress and challenges

Abstract

Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g., replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g., hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyze two different approaches: the QM/MM-MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analyzed here, both approaches seem productive although care needs to be exercised when analyzing the perturbative corrections.

Multiscale Quantum Mechanics/Molecular Mechanics Simulations with Neural Networks

“…One possible improvement is to calculate the free energy difference in Step 5 using a linear response approximation after a short-time MD sampling at the high level. 8,10 For the long-time dynamic simulations on larger biochemical systems, the “learn-on-the-fly” simulation on the high-level potential energy surface predicted with QM/MM-NN is a good candidate to reduce the error from reweighting. 79–81 Compared with some existing correction schemes with reparametrization on SQM models, 28–30 the combination with neural network make it more attractive in two aspects.…”

“…It is partially due to the similarity on the critical structures such as transition state and local minima along the reaction path at two levels. 10 The choice of reaction coordinates is also essential. In principle the error from reweighting can be remedied with additional samplings on the exact or NN-predicted high-level potential energy surface, but it is beyond our consideration in this paper.…”

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.…”

“…[81][82][83][84][85][86] For the calculation of single-ion hydration free energies, two main strategies have been explored to date for achieving such a combination. The most common approach is the cluster-continuum approach, 53,56,[87][88][89][90][91] often referred to as a particular instance of quasi-chemical theory, [92][93][94] in which QM energy calculations are performed on small ion-water clusters (different sizes and geometries) and the bulk intrinsic hydration free energy is calculated by subsequently embedding the cluster configurations into a CE solvent environment.…”

QM/MM Analysis of Transition States and Transition State Analogues in Metalloenzymes

“…While some types of calculations are fairly specialized, others are readily accomplished with user-friendly software and can therefore be adopted and used effectively by experimental chemists themselves to obtain the desired information. We begin by providing a brief survey of the types of calculations commonly used for studying (metallo)enzymes; more details can be found in several recent review articles by us[48, 90] and others[21, 122], as well as in the other chapters in this volume. We will then use a case study of the metalloenzyme alkaline phosphatase (AP) to illustrate details of how one may use calculations for understanding enzyme chemistry and make clear connections to experimental measurements.…”