Efficient solvation free energy simulations: impact of soft-core potential and a new adaptive λ-spacing method

Prediction of toluene/water partition coefficients of SAMPL9 compounds: comparison of the molecular dynamics force fields GAFF/RESP and GAFF/IPolQ-Mod + LJ-fit

The SAMPL9 blind challenge aims to predict the toluene/water partition coefficient of 16 active pharmaceutical ingredients. In this work, the transfer free energy between the solvation in water and toluene is predicted by molecular dynamics simulations using the MBAR method [M. R. Shirts and J. D. Chodera, J. Chem. Phys., 2008, 129, 123105] with replica exchange molecular dynamics [Y. Sugita, A. Kitao and Y. Okamoto, J. Chem. Phys., 2000, 113, 6042-6051]. Thereby, simulation results using the force field GAFF/IPolQ-Mod + LJ-fit [A. Mecklenfeld and G. Raabe, ADMET and DMPK, 2020, 8, 274-296] are compared to simulations with the standard GAFF/RESP model [J. Wang, R. M. Wolf, J. W. Caldwell, P. A. Kollman and D. A. Case, J. Comput. Chem., 2004, 25, 1157-1174]. By statistical evaluation of RMSD and R2, we compare the results with other participants of the blind challenge. Furthermore, we provide a detailed analysis of solvation structures using the combined distribution function for simulations in water and the plane projection analysis for simulations in toluene, and we work out differences and similarities of the two force fields. These studies allow to gain important insights to increase the understanding of the mechanism of interactions between the drugs and the solvent.

Molecular dynamics studies of the solubility behavior of carbon dioxide (CO2 ), difluoromethane (R-32), 1-chloro-3,3,3-trifluoropropene (R-1233zd(E)) and 2,3,3,3-tetrafluoro-1-propene (R-1234yf) in pentaerythritol tetra(2-ethylhexanoate) (PEB8), pentaerythritol tetrabutyrate (PEC4) and pentaerythritol tetraoctanoate (PEC8)

To reduce the climate impact of thermal engines such as heat pumps or refrigeration machines, refrigerants with a low global warming potential need to be paired with fitting lubricants. As the contamination of those liquid components influences the efficiency and lifetime of these machines, knowledge about their solubility behavior is of great interest. Molecular simulations offer mighty tools to investigate these solubilities while giving structural insight into the systems. Here the solubility behavior of CO2 , R-32, R-1233zd(E), and R-1234yf in PEB8, PEC4, and PEC8 is compared through the solvation free energy ∆GSolv obtained by molecular dynamics simulations. To derive ∆GSolv at low computational cost, an iterative method is used to find an optimal number and distribution of intermediate states. The resulting distributions are investigated with regard to different parameters of the employed softcore-potential. ∆GSolv values for the different refrigerant-lubricant pairings at different temperatures are provided, followed by a structural analysis.

On the Path to Optimal Alchemistry

Alchemical free energy calculations have become a standard and widely used tool, in particular for calculating and comparing binding affinities of drugs. Although methods to compute such free energies have improved significantly over the last decades, the choice of path between the end states of interest is usually still the same as two decades ago. We will show that there is a fundamentally arbitrary, implicit choice of parametrization of this path. To address this, the notion of the length of a path or a metric is required. A metric recently introduced in the context of the accelerated weight histogram method also proves to be very useful here. We demonstrate that this metric can not only improve the efficiency of sampling along a given path, but that it can also be used to improve the actual choice of path. For a set of relevant use cases, the combination of these improvements can increase the efficiency of alchemical free energy calculations by up to a factor 16.

Alchemical Free Energy and Hamiltonian Replica Exchange Molecular Dynamics to Compute Hydrofluorocarbon Isotherms in Imidazolium-Based Ionic Liquids

Ionic liquids (ILs) have shown promise for applications that leverage differential gas solubility in an IL solvent, e.g., gas separations. Although most available literature provides Henry's law constants, the ability to efficiently estimate full isotherms is important for engineering design calculations. Molecular simulation can be used as a tool to predict full isotherms of gas in ILs. However, particle insertions or deletions in a charge-dense IL medium and the sluggish conformational dynamics of ILs present two sampling challenges for these systems. We therefore devised a method that uses Hamiltonian replica exchange (HREX) molecular dynamics (MD) combined with alchemical free energy calculations to compute full solubility isotherms of two different hydrofluorocarbons (HFCs) in imidazolium-based IL binary mixtures. This workflow is significantly faster than the Gibbs ensemble Monte Carlo (GEMC) simulations which fail to deal with the slow conformational relaxation caused by the sluggish dynamics of ILs. Multiple free energy estimators, including thermodynamic integration, free energy perturbation, and multistate Bennett acceptance ratio method, provided consistent results. Overall, the simulated Henry's law constant, isotherm curvature, and solubility trends match experimental results reasonably well. We close by calculating the full solubility isotherms of two HFCs in IL mixtures that have not been reported in the literature, demonstrating the potential of this method to be used for solubility prediction and setting the stage for future computational screening studies that search for the "best" IL to separate azeotropic HFC mixtures.

Optimal control with a strong harmonic trap

Quadratic trapping potentials are widely used to experimentally probe biopolymers and molecular machines and drive transitions in steered molecular-dynamics simulations. Approximating energy landscapes as locally quadratic, we design multidimensional trapping protocols that minimize dissipation. The designed protocols are easily solvable and applicable to a wide range of systems. The approximation does not rely on either fast or slow limits and is valid for any duration provided the trapping potential is sufficiently strong. We demonstrate the utility of the designed protocols with a simple model of a periodically driven rotary motor. Our results elucidate principles of effective single-molecule manipulation and efficient nonequilibrium free-energy estimation.

A unified approach for calculating free energies of liquid and defective crystals based on thermodynamic integration

The free energy calculation is fundamentally important in the research of physics, chemistry and materials. Thermodynamic integration is the most common way to estimate free energies. In the research, we proposed a unified approach using atomic simulations to calculate the free energies of liquid and defective crystals. The new approach is based on thermodynamic integration (TI) using two alchemical pathways. Softcore potentials are developed for three-body interatomic potentials to realize the alchemical pathways. Employing the new approach, the free energy of the liquid can be calculated without requiring another reference system. The free energy of the defective crystal can be calculated directly at high temperature. It avoids the singularity at the integration endpoint caused by the defect diffusion which is a serious problem in the widely used Einstein crystal method. In addition, the new approach can capture the whole free energy of the defective crystal including the contribution of anharmonic and configurational entropy which are particularly important at high temperature. The new method is simple yet effective and can be extended to different materials and more complex liquid and defective crystal systems.

On the Consistency of the Exfoliation Free Energy of Graphenes by Molecular Simulations

Monolayer graphene is now produced at significant yields, by liquid phase exfoliation of graphites in solvents. This has increased the interest in molecular simulation studies to give new insights in the field. We use decoupling simulations to compute the exfoliation free energy of graphenes in a liquid environment. Starting from a bilayer graphene configuration, we decouple the Van der Waals interactions of a graphene monolayer in the presence of saline water. Then, we introduce the monolayer back into water by coupling its interactions with water molecules and ions. A different approach to compute the graphene exfoliation free energy is to use umbrella sampling. We apply umbrella sampling after pulling the graphene monolayer on the shear direction up to a distance from a bilayer. We show that the decoupling and umbrella methods give highly consistent free energy results for three bilayer graphene samples with different size. This strongly suggests that the systems in both methods remain closely in equilibrium as we move between the states before and after the exfoliation. Therefore, the amount of nonequilibrium work needed to peel the two layers apart is minimized efficiently.

Binding Free Energy Calculations of Bilayer Graphenes Using Molecular Dynamics

Bilayer graphenes are dimeric assemblies of single graphene layers bound together by π-complexation interactions. Controlling these assemblies can be complicated, as the layered compounds disperse in solvents or aggregate into higher columnar configurations and clusters. One way to assess the interactions that contribute to the stability of the layered compounds is to use molecular simulation. We perform pulling molecular dynamics on bilayer graphenes with different sizes and obtain the normal and shear force profiles of dissociation. We generate pathways of dissociation along the two directions and calculate the binding free energies of the structures with umbrella sampling simulations. We show that the dissociation process is direction-dependent. Along the shear direction, we compute the same free energy for the different samples, which validates the consistency of our simulations. We notice that the dissociation is less adiabatic on the normal than the shear direction, having an entropic contribution to the Gibbs energy. This contribution is more enhanced for the larger bilayer graphenes.

Applicability of a thermodynamic cycle approach for a force field parametrization targeting non-aqueous solvation free energies

Accurate solvation free energy ΔG_solv predictions require well parametrized force fields. In order to refit Lennard-Jones (LJ) parameters for improved ΔG_solv predictions for a variety of compound classes and chemical environments, a large number of ΔG_solv calculations is required. As the calculation of ΔG_solv is computational expensive, there is need for efficient but precise calculation methods. In this work, we focus on the computation of non-aqueous solvation free energies. We compare ΔG_solv results from highly precise reference simulations for transferring a solute from the vacuum into a condensed phase and results obtained from a thermodynamic cycle implementation. As test systems, we alter LJ parameters ε and σ of widely used GAFF atom types ca, cl, n1, oh and os in various solute/solvent combinations. We examine the degree of configurational space overlap and find an impact by hydrogen bonds and the solvent accessible surface area. We conclude that the application of a thermodynamic cycle for the parametrization of force fields targeting ΔG_solv is useful if the adaptation of LJ parameters is limited to atom types in the solute or if only ε is changed.

Alchemical Free-Energy Calculations by Multiple-Replica λ-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme

A new method is proposed to calculate alchemical free-energy differences based on molecular dynamics (MD) simulations, called the conveyor belt thermodynamic integration (CBTI) scheme. As in thermodynamic integration (TI), K replicas of the system are simulated at different values of the alchemical coupling parameter λ. The number K is taken to be even, and the replicas are equally spaced on a forward-turn-backward-turn path, akin to a conveyor belt (CB) between the two physical end-states; and as in λ-dynamics (λD), the λ-values associated with the individual systems evolve in time along the simulation. However, they do so in a concerted fashion, determined by the evolution of a single dynamical variable Λ of period 2π controlling the advance of the entire CB. Thus, a change of Λ is always associated with K/2 equispaced replicas moving forward and K/2 equispaced replicas moving backward along λ. As a result, the effective free-energy profile of the replica system along Λ is periodic of period 2 πK^-1, and the magnitude of its variations decreases rapidly upon increasing K, at least as K^-1 in the limit of large K. When a sufficient number of replicas is used, these variations become small, which enables a complete and quasi-homogeneous coverage of the λ-range by the replica system, without application of any biasing potential. If desired, a memory-based biasing potential can still be added to further homogenize the sampling, the preoptimization of which is computationally inexpensive. The final free-energy profile along λ is calculated similarly to TI, by binning of the Hamiltonian λ-derivative as a function of λ considering all replicas simultaneously, followed by quadrature integration. The associated quadrature error can be kept very low owing to the continuous and quasi-homogeneous λ-sampling. The CBTI scheme can be viewed as a continuous/deterministic/dynamical analog of the Hamiltonian replica-exchange/permutation (HRE/HRP) schemes or as a correlated multiple-replica analog of the λD or λ-local elevation umbrella sampling (λ-LEUS) schemes. Compared to TI, it shares the advantage of the latter schemes in terms of enhanced orthogonal sampling, i.e. the availability of variable-λ paths to circumvent conformational barriers present at specific λ-values. Compared to HRE/HRP, it permits a deterministic and continuous sampling of the λ-range, is expected to be less sensitive to possible artifacts of the thermo- and barostating schemes, and bypasses the need to carefully preselect a λ-ladder and a swapping-attempt frequency. Compared to λ-LEUS, it eliminates (or drastically reduces) the dead time associated with the preoptimization of a biasing potential. The goal of this article is to provide the mathematical/physical formulation of the proposed CBTI scheme, along with an initial application of the method to the calculation of the hydration free energy of methanol.

Comparison of RESP and IPolQ-Mod Partial Charges for Solvation Free Energy Calculations of Various Solute/Solvent Pairs

The calculation of solvation free energies ΔG_solv by molecular simulations is of great interest as they are linked to other physical properties such as relative solubility, partition coefficient, and activity coefficient. However, shortcomings in molecular models can lead to ΔG_solv deviations from experimental data. Various studies have demonstrated the impact of partial charges on free energy results. Consequently, calculation methods for partial charges aimed at more accurate ΔG_solv predictions are the subject of various studies in the literature. Here we compare two methods to derive partial charges for the general AMBER force field (GAFF), i.e. the default RESP as well as the physically motivated IPolQ-Mod method that implicitly accounts for polarization costs. We study 29 solutes which include characteristic functional groups of drug-like molecules, and 12 diverse solvents were examined. In total, we consider 107 solute/solvent pairs including two water models TIP3P and TIP4P/2005. Comparison with experimental results yields better agreement for TIP3P, regardless of the partial charge scheme. The overall performance of GAFF/RESP and GAFF/IPolQ-Mod is similar, though specific shortcomings in the description of ΔG_solv for both RESP and IPolQ-Mod can be identified. However, the high correlation between free energies obtained with GAFF/RESP and GAFF/IPolQ-Mod demonstrates the compatibility between the modified charges and remaining GAFF parameters.