Binding Free Energies of Host–Guest Systems by Nonequilibrium Alchemical Simulations with Constrained Dynamics: Illustrative Calculations and Numerical Validation

Screening Power of End-Point Free-Energy Calculations in Cucurbituril Host-Guest Systems

End-point free-energy methods as an indispensable component in virtual screening are commonly recognized as a tool with a certain level of screening power in pharmaceutical research. While a huge number of records could be found for end-point applications in protein-ligand, protein-protein, and protein-DNA complexes from academic and industrial reports, up to now, there is no large-scale benchmark in host-guest complexes supporting the screening power of end-point free-energy techniques. A good benchmark requires a data set of sufficient coverage of pharmaceutically relevant chemical space, a long-time sampling length supporting the trajectory approximation of the ensemble average, and a sufficient sample size of receptor-acceptor pairs to stabilize the performance statistics. In this work, selecting a popular family of macrocyclic hosts named cucurbiturils, we construct a large data set containing 154 host-guest pairs, perform extensive end-point sampling of several hundred nanosecond lengths for each system, and extract the free-energy estimates with a variety of end-point free-energy techniques, including the advanced three-trajectory dielectric-constant-variable regime proposed in our recent work. The best-performing end-point protocol employs GAFF2 for solute descriptions, the three-trajectory end-point sampling regime, and the MM/GBSA Hamiltonian in free-energy extraction, achieving a high ranking metrics of Kendall τ > 0.6, a Pearlman predictive index of ∼0.8, and a high scoring power of Pearson r > 0.8. The current project as the first large-scale systematic benchmark of end-point methods in host-guest complexes in academic publications provides solid evidence of the applicability of end-point techniques and direct guidance of computational setups in practical host-guest systems.

Local Resampling Trick for Focused Molecular Dynamics

We describe a method that focuses sampling effort on a user-defined selection of a large system, which can lead to substantial decreases in computational effort by speeding up the calculation of nonbonded interactions. A naive approach can lead to incorrect sampling if the selection depends on the configuration in a way that is not accounted for. We avoid this pitfall by introducing appropriate auxiliary variables. This results in an implementation that is closely related to "configurational freezing" and "elastic barrier dynamical freezing." We implement the method and validate that it can be used to supplement conventional molecular dynamics in free energy calculations (absolute hydration and relative binding).

Molecular Modelling of Ionic Liquids: Situations When Charge Scaling Seems Insufficient

Charge scaling as an effective solution to the experiment-computation disagreement in molecular modelling of ionic liquids (ILs) could bring the computational results close to the experimental reference for various thermodynamic properties. According to the large-scale benchmark calculations of mass density, solvation, and water-ILs transfer-free energies in our series of papers, the charge-scaling factor of 0.8 serves as a near-optimal option generally applicable to most ILs, although a system-dependent parameter adjustment could be attempted for further improved performance. However, there are situations in which such a charge-scaling treatment would fail. Namely, charge scaling cannot really affect the simulation outcome, or minimally perturbs the results that are still far from the experimental value. In such situations, the vdW radius as an additional adjustable parameter is commonly tuned to minimize the experiment-calculation deviation. In the current work, considering two ILs from the quinuclidinium family, we investigate the impacts of this vdW-scaling treatment on the mass density and the solvation/partition thermodynamics in a fashion similar to our previous charge-scaling works, i.e., scanning the vdW-scaling factor and computing physical properties under these parameter sets. It is observed that the mass density exhibits a linear response to the vdW-scaling factor with slopes close to -1.8 g/mL. By further investigating a set of physiochemically relevant temperatures between 288 K and 348 K, we confirm the robustness of the vdW-scaling treatment in the estimation of bulk properties. The best vdW-scaling parameter for mass density would worsen the computation of solvation/partition thermodynamics, and a marginal decrease in the vdW-scaling factor is considered as an intermediate option balancing the reproductions of bulk properties and solvation thermodynamics. These observations could be understood in a way similar to the charge-scaling situation. i.e., overfitting some properties (e.g., mass density) would degrade the accuracy of the other properties (e.g., solvation free energies). Following this principle, the general guideline for applying this vdW-tuning protocol is by using values between the density-derived choice and the solvation/partition-derived solution. The charge and current vdW scaling treatments cover commonly encountered ILs, completing the protocol for accurate modelling of ILs with fixed-charge force fields.

Ethanol electro-oxidation reaction on the Pd(111) surface in alkaline media: insights from quantum and molecular mechanics

The ethanol electro-oxidation catalyzed by Pd in an alkaline environment involves several intermediate reaction steps promoted by the hydroxyl radical, OH. In this work, we report on the dynamical paths of the first step of this oxidation reaction, namely the hydrogen atom abstraction CH₃CH₂OH + OH → CH₃CHOH + H₂O, occurring at the Pd(111) surface and address the thermodynamic stability of the adsorbed reactants by means of quantum and molecular mechanics calculations, with special focus on the effect of the solvent. We have found that the impact of the solvent is significant for both ethanol and OH, contributing to a decrease in their adsorption free energies by a few dozen kcal mol^-1 with respect to the adsorption energy under vacuum. Furthermore, we observe that hydrogen atom abstraction is enhanced for those simulation paths featuring large surface-reactant distances, namely, when the reactants weakly interact with the catalyst. The picture emerging from our study is therefore that of a catalyst whose coverage in an aqueous environment is largely dominated by OH with respect to ethanol. Nevertheless, only a small amount of them, specifically those weakly bound to the catalyst, is really active in the ethanol electro-oxidation reaction. These results open the idea of a rational design of co-catalysts based on the tuning of surface chemical properties to eventually enhance exchange current density.

Modeling Kinetics and Thermodynamics of Guest Encapsulation into the [M4L6]12- Supramolecular Organometallic Cage

The encapsulation of molecular guests into supramolecular hosts is a complex molecular recognition process in which the guest displaces the solvent from the host cavity, while the host deforms to let the guest in. An atomistic description of the association would provide valuable insights on the physicochemical properties that guide it. This understanding may be used to design novel host assemblies with improved properties (i.e., affinities) toward a given class of guests. Molecular simulations may be conveniently used to model the association processes. It is thus of interest to establish efficient protocols to trace the encapsulation process and to predict the associated magnitudes ΔG_bind and ΔG_bind^⧧. Here, we report the calculation of the Gibbs energy barrier and Gibbs binding energy by means of explicit solvent molecular simulations for the [Ga₄L₆]^12– metallocage encapsulating a series of cationic molecules. The ΔG_bind^⧧ for encapsulation was estimated by means of umbrella sampling simulations. The steps involved were identified, including ion-pair formation and naphthalene rotation (from L ligands of the metallocage) during the guest’s entrance. The ΔG_bind values were computed using the attach–pull–release method. The results reveal the sensitivity of the estimates on the force field parameters, in particular on atomic charges, showing that higher accuracy is obtained when charges are derived from implicit solvent quantum chemical calculations. Correlation analysis identified some indicators for the binding affinity trends. All computed magnitudes are in very good agreement with experimental observations. This work provides, on one side, a benchmarked way to computationally model a highly charged metallocage encapsulation process. This includes a nonstandard parameterization and charge derivation procedure. On the other hand, it gives specific mechanistic information on the binding processes of [Ga₄L₆]^12– at the molecular level where key motions are depicted. Taken together, the study provides an interesting option for the future design of metal–organic cages.

Role of Displacing Confined Solvent in the Conformational Equilibrium of β-Cyclodextrin

This study investigates the role of hydration and its relationship to the conformational equilibrium of the host molecule β-cyclodextrin. Molecular dynamics simulations indicate that the unbound β-cyclodextrin exhibits two state behavior in explicit solvent due to the opening and closing of its cavity. In implicit solvent, these transitions are not observed, and there is one dominant conformation of β-cyclodextrin with an open cavity. Based on these observations, we investigate the hypothesis that the expulsion of thermodynamically unfavorable water molecules into the bulk plays an important role in controlling the accessibility of the closed macrostate at room temperature. We compare the results of the molecular mechanics analytical generalized Born plus nonpolar solvation approach to those obtained through grid inhomogeneous solvation theory analysis with explicit solvation to elucidate the thermodynamic forces at play. The work illustrates the use of continuum solvent models to tease out solvation effects related to the inhomogeneity and the molecular nature of water and demonstrates the key role of the thermodynamics of enclosed hydration in driving the conformational equilibrium of molecules in solution.

Use of Interaction Energies in QM/MM Free Energy Simulations

The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the "indirect" approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig's equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig's equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig's equation. One particularly popular notion is that the convergence of Zwanzig's equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig's equation) are indeed reduced, our results and analysis demonstrate that this "interaction energy approximation" (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.

Consistent Prediction of Mutation Effect on Drug Binding in HIV-1 Protease Using Alchemical Calculations

Despite a large number of antiretroviral drugs targeting HIV-1 protease for inhibition, mutations in this protein during the course of patient treatment can render them inefficient. This emerging resistance inspired numerous computational studies of the HIV-1 protease aimed at predicting the effect of mutations on drug binding in terms of free binding energy Δ G, as well as in mechanistic terms. In this study, we analyze ten different protease-inhibitor complexes carrying major resistance-associated mutations (RAMs) G48V, I50V, and L90M using molecular dynamics simulations. We demonstrate that alchemical free energy calculations can consistently predict the effect of mutations on drug binding. By explicitly probing different protonation states of the catalytic aspartic dyad, we reveal the importance of the correct choice of protonation state for the accuracy of the result. We also provide insight into how different mutations affect drug binding in their specific ways, with the unifying theme of how all of them affect the crucial drug binding regions of the protease.