Accounting for Solvation Correlation Effects on the Thermodynamics of Water Networks in Protein Cavities.

Macromolecular recognition and ligand binding are at the core of biological function and drug discovery efforts. Water molecules play a significant role in mediating the protein-ligand interaction, acting as more than just the surrounding medium by affecting the thermodynamics and thus the outcome of the binding process. As individual water contributions are impossible to measure experimentally, a range of computational methods have emerged to identify hydration sites in protein pockets and characterize their energetic contributions for drug discovery applications. Even though several methods model solvation effects explicitly, they focus on determining the stability of specific water sites independently and neglect solvation correlation effects upon replacement of clusters of water molecules, which typically happens in hit-to-lead optimization. In this work, we rigorously determine the conjoint effects of replacing all combinations of water molecules in protein binding pockets through the use of the RE-EDS multistate free-energy method, which combines Hamiltonian replica exchange (RE) and enveloping distribution sampling (EDS). Applications on the small bovine pancreatic trypsin inhibitor and four proteins of the bromodomain family illustrate the extent of solvation correlation effects on water thermodynamics, with the favorability of replacement of the water sites by pharmacophore probes highly dependent on the composition of the water network and the pocket environment. Given the ubiquity of water networks in biologically relevant protein targets, we believe our approach can be helpful for computer-aided drug discovery by providing a pocket-specific and a priori systematic consideration of solvation effects on ligand binding and selectivity.

Accelerating Alchemical Free Energy Prediction Using a Multistate Method: Application to Multiple Kinases.

Alchemical free-energy methods based on molecular dynamics (MD) simulations have become important tools to identify modifications of small organic molecules that improve their protein binding affinity during lead optimization. The routine application of pairwise free-energy methods to rank potential binders from best to worst is impacted by the combinatorial increase in calculations to perform when the number of molecules to assess grows. To address this fundamental limitation, our group has developed replica-exchange enveloping distribution sampling (RE-EDS), a pathway-independent multistate method, enabling the calculation of alchemical free-energy differences between multiple ligands (N > 2) from a single MD simulation. In this work, we apply the method to a set of four kinases with diverse binding pockets and their corresponding inhibitors (42 in total), chosen to showcase the general applicability of RE-EDS in prospective drug design campaigns. We show that for the targets studied, RE-EDS is able to model up to 13 ligands simultaneously with high sampling efficiency, leading to a substantial decrease in computational cost when compared to pairwise methods.

Replica-Exchange Enveloping Distribution Sampling Using Generalized AMBER Force-Field Topologies: Application to Relative Hydration Free-Energy Calculations for Large Sets of Molecules.

Free-energy differences between pairs of end-states can be estimated based on molecular dynamics (MD) simulations using standard pathway-dependent methods such as thermodynamic integration (TI), free-energy perturbation, or Bennett's acceptance ratio. Replica-exchange enveloping distribution sampling (RE-EDS), on the other hand, allows for the sampling of multiple end-states in a single simulation without the specification of any pathways. In this work, we use the RE-EDS method as implemented in GROMOS together with generalized AMBER force-field (GAFF) topologies, converted to a GROMOS-compatible format with a newly developed GROMOS++ program amber2gromos, to compute relative hydration free energies for a series of benzene derivatives. The results obtained with RE-EDS are compared to the experimental data as well as calculated values from the literature. In addition, the estimated free-energy differences in water and in vacuum are compared to values from TI calculations carried out with GROMACS. The hydration free energies obtained using RE-EDS for multiple molecules are found to be in good agreement with both the experimental data and the results calculated using other free-energy methods. While all considered free-energy methods delivered accurate results, the RE-EDS calculations required the least amount of total simulation time. This work serves as a validation for the use of GAFF topologies with the GROMOS simulation package and the RE-EDS approach. Furthermore, the performance of RE-EDS for a large set of 28 end-states is assessed with promising results.

Leveraging the sampling efficiency of RE-EDS in OpenMM using a shifted reaction-field with an atom-based cutoff.

Replica-exchange enveloping distribution sampling (RE-EDS) is a pathway-independent multistate free-energy method currently implemented in the GROMOS software package for molecular dynamics (MD) simulations. It has a high intrinsic sampling efficiency as the interactions between the unperturbed particles have to be calculated only once for multiple end-states. As a result, RE-EDS is an attractive method for the calculation of relative solvation and binding free energies. An essential requirement for reaching this high efficiency is the separability of the nonbonded interactions into solute-solute, solute-environment, and environment-environment contributions. Such a partitioning is trivial when using a Coulomb term with a reaction-field (RF) correction to model the electrostatic interactions but not when using lattice-sum schemes. To avoid cutoff artifacts, the RF correction is typically used in combination with a charge-group-based cutoff, which is not supported by most small-molecule force fields as well as other MD engines. To address this issue, we investigate the combination of RE-EDS simulations with a recently introduced RF scheme including a shifting function that enables the rigorous calculation of RF electrostatics with atom-based cutoffs. The resulting approach is validated by calculating solvation free energies with the generalized AMBER force field in water and chloroform using both the GROMOS software package and a proof-of-concept implementation in OpenMM.

Replica-Exchange Enveloping Distribution Sampling: Calculation of Relative Free Energies in GROMOS.

Molecular dynamics (MD) simulations have become an important tool to investigate biological systems. Free-energy calculations based on MD are playing an increasingly important role for computer-aided drug design and material discovery in recent years. Free-energy differences between pairs of end-states can be estimated using well-established methods such as thermodynamic integration (TI) or Bennett's acceptance ratio (BAR). An attractive alternative is the recently developed replica-exchange enveloping distribution sampling (RE-EDS) method, which enables estimating relative free-energy differences between multiple molecules from a single simulation. Here, we provide an introduction to the principles underlying RE-EDS and give an overview of the RE-EDS pipeline. In addition, we provide a description of the two complementary tools RestraintMaker and amber2gromos. We briefly discuss the findings of three recent applications of RE-EDS to calculate relative binding or hydration free energies. In all three studies, good agreement was found between the results obtained using RE-EDS and experimental values as well as values obtained using other free-energy methods.

Development of an open-source software for isomer enumeration.

This article documents enu, a freely-downloadable, open-source and stand-alone program written in C++ for the enumeration of the constitutional isomers and stereoisomers of a molecular formula. The program relies on graph theory to enumerate all the constitutional isomers of a given formula on the basis of their canonical adjacency matrix. The stereoisomers of a given constitutional isomer are enumerated as well, on the basis of the automorphism group of this matrix. The isomer list is then reported in the form of canonical SMILES strings within files in XML format. The specification of the molecule family of interest is very flexible and the code is optimized for computational efficiency. The algorithms and implementations underlying enu are described, and simple illustrative applications are presented. The enu code is freely available on GitHub at https://github.com/csms-ethz/CombiFF .

Comparison of the United- and All-Atom Representations of (Halo)alkanes Based on Two Condensed-Phase Force Fields Optimized against the Same Experimental Data Set.

The level of accuracy that can be achieved by a force field is influenced by choices made in the interaction-function representation and in the relevant simulation parameters. These choices, referred to here as functional-form variants (FFVs), include for example the model resolution, the charge-derivation procedure, the van der Waals combination rules, the cutoff distance, and the treatment of the long-range interactions. Ideally, assessing the effect of a given FFV on the intrinsic accuracy of the force-field representation requires that only the specific FFV is changed and that this change is performed at an optimal level of parametrization, a requirement that may prove extremely challenging to achieve in practice. Here, we present a first attempt at such a comparison for one specific FFV, namely the choice of a united-atom (UA) versus an all-atom (AA) resolution in a force field for saturated acyclic (halo)alkanes. Two force-field versions (UA vs AA) are optimized in an automated way using the CombiFF approach against 961 experimental values for the pure-liquid densities ρliq and vaporization enthalpies ΔHvap of 591 compounds. For the AA force field, the torsional and third-neighbor Lennard-Jones parameters are also refined based on quantum-mechanical rotational-energy profiles. The comparison between the UA and AA resolutions is also extended to properties that have not been included as parameterization targets, namely the surface-tension coefficient γ, the isothermal compressibility κT, the isobaric thermal-expansion coefficient αP, the isobaric heat capacity cP, the static relative dielectric permittivity ϵ, the self-diffusion coefficient D, the shear viscosity η, the hydration free energy ΔGwat, and the free energy of solvation ΔGche in cyclohexane. For the target properties ρliq and ΔHvap, the UA and AA resolutions reach very similar levels of accuracy after optimization. For the nine other properties, the AA representation leads to more accurate results in terms of η; comparably accurate results in terms of γ, κT, αP, ϵ, D, and ΔGche; and less accurate results in terms of cP and ΔGwat. This work also represents a first step toward the calibration of a GROMOS-compatible force field at the AA resolution.

Evaluating Classical Force Fields against Experimental Cross-Solvation Free Energies.

Experimental solvation free energies are nowadays commonly included as target properties in the validation and sometimes even in the calibration of condensed-phase force fields. However, this is often done in a nonsystematic fashion, by considering available solvation free energies involving an arbitrary collection of solutes in a limited set of solvents (e.g., water, octanol, chloroform, cyclohexane, or hexane). Here, this approach is made more systematic by introducing the concept of cross-solvation free energies ΔsGA:B⊖ for a set of N molecules that are all in the liquid state under ambient conditions, namely the matrix of N2 entries for ΔsGA:B⊖ considering each of the N molecules either as a solute (A) or as a solvent (B). Relying on available experimental literature followed by careful data curation, a complete ΔsGA:B⊖ matrix of 625 entries is constructed for 25 molecules with one to seven carbon atoms representative for alkanes, chloroalkanes, ethers, ketones, esters, alcohols, amines, and amides. This matrix is then used to compare the relative accuracies of four popular condensed-phase force fields: GROMOS-2016H66, OPLS-AA, AMBER-GAFF, and CHARMM-CGenFF. In broad terms, and in spite of very different force-field functional-form choices and parametrization strategies, the four force fields are found to perform similarly well. Relative to the experimental values, the root-mean-square errors range between 2.9 and 4.0 kJ·mol-1 (lowest value of 2.9 for GROMOS and OPLS), and the average errors range between -0.8 and +1.0 kJ·mol-1 (lowest magnitude of 0.2 for AMBER and CHARMM). These differences are statistically significant but not very pronounced, especially considering the influence of outliers, some of which possibly caused by inaccurate experimental data.

Systematic Optimization of a Fragment-Based Force Field against Experimental Pure-Liquid Properties Considering Large Compound Families: Application to Saturated Haloalkanes.

Direct optimization against experimental condensed-phase properties concerning small organic molecules still represents the most reliable way to calibrate the empirical parameters of a force field. However, compared to a corresponding calibration against quantum-mechanical (QM) calculations concerning isolated molecules, this approach is typically very tedious and time-consuming. The present article describes an integrated scheme for the automated refinement of force-field parameters against experimental condensed-phase data, considering entire classes of organic molecules constructed using a fragment library via combinatorial isomer enumeration. The main steps of the scheme, referred to as CombiFF, are as follows: (i) definition of a molecule family; (ii) combinatorial enumeration of all isomers; (iii) query for experimental data; (iv) automatic construction of the molecular topologies by fragment assembly; and (v) iterative refinement of the force-field parameters considering the entire family. As a first application, CombiFF is used here to design a GROMOS-compatible united-atom force field for the saturated acyclic haloalkane family. This force field relies on an electronegativity-equalization scheme for the atomic partial charges and involves no specific terms for σ-holes and halogen bonding. A total of 749 experimental liquid densities ρliq and vaporization enthalpies ΔHvap concerning 486 haloalkanes are considered for calibration and validation. The resulting root-mean-square deviations from experiment are 49.8 (27.6) kg·m-3 for ρliq and 2.7 (1.8) kJ·mol-1 for ΔHvap for the calibration (validation) set. The values are lower for the validation set which contains larger molecules (stronger influence of purely aliphatic interactions). The trends in the optimized parameters along the halogen series and across the compound family are in line with chemical intuition based on considerations related to size, polarizability, softness, electronegativity, induction, and hyperconjugation. This observation is particularly remarkable considering that the force-field calibration did not involve any QM calculation. Once the time-consuming task of target-data selection/curation has been performed, the optimization of a force field only takes a few days. As a result, CombiFF enables an easy assessment of the consequences of functional-form decisions on the accuracy of a force field at an optimal level of parametrization.