Unraveling motion in proteins by combining NMR relaxometry and molecular dynamics simulations: A case study on ubiquitin.

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields.

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.

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.

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.

How does it really move? Recent progress in the investigation of protein nanosecond dynamics by NMR and simulation.

Nuclear magnetic resonance (NMR) spin relaxation experiments currently probe molecular motions on timescales from picoseconds to nanoseconds. The detailed interpretation of these motions in atomic detail benefits from complementarity with the results from molecular dynamics (MD) simulations. In this mini-review, we describe the recent developments in experimental techniques to study the backbone dynamics from 15N relaxation and side-chain dynamics from 13C relaxation, discuss the different analysis approaches from model-free to dynamics detectors, and highlight the many ways that NMR relaxation experiments and MD simulations can be used together to improve the interpretation and gain insights into protein dynamics.

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.

Relative free-energy calculations for scaffold hopping-type transformations with an automated RE-EDS sampling procedure.

The calculation of relative free-energy differences between different compounds plays an important role in drug design to identify potent binders for a given protein target. Most rigorous methods based on molecular dynamics simulations estimate the free-energy difference between pairs of ligands. Thus, the comparison of multiple ligands requires the construction of a "state graph", in which the compounds are connected by alchemical transformations. The computational cost can be optimized by reducing the state graph to a minimal set of transformations. However, this may require individual adaptation of the sampling strategy if a transformation process does not converge in a given simulation time. In contrast, path-free methods like replica-exchange enveloping distribution sampling (RE-EDS) allow the sampling of multiple states within a single simulation without the pre-definition of alchemical transition paths. To optimize sampling and convergence, a set of RE-EDS parameters needs to be estimated in a pre-processing step. Here, we present an automated procedure for this step that determines all required parameters, improving the robustness and ease of use of the methodology. To illustrate the performance, the relative binding free energies are calculated for a series of checkpoint kinase 1 inhibitors containing challenging transformations in ring size, opening/closing, and extension, which reflect changes observed in scaffold hopping. The simulation of such transformations with RE-EDS can be conducted with conventional force fields and, in particular, without soft bond-stretching terms.

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.

Recent developments in multiscale free energy simulations.

Physics-based free energy simulations enable the rigorous calculation of properties, such as conformational equilibria, solvation or binding free energies. While historically most applications have occurred at the atomistic level of resolution, a range of advances in the past years make it possible now to reliably cross the temporal, spatial and theory scales for the modeling of complex systems or the efficient prediction of results at the accuracy level of expensive quantum-mechanical calculations. In this mini-review, we discuss recent methodological advances as well as opportunities opened up by the introduction of machine learning approaches, which tackle the diverse challenges across the different scales, improve the accuracy and feasibility, and push the boundaries of multiscale free energy simulations.

Use of Extended-Hückel Descriptors for Rapid and Accurate Predictions of Conjugated Torsional Energy Barriers.

Over the past few decades, virtual high-throughput screening (vHTS) and molecular dynamics simulations have become effective and widely used tools in the initial stages of drug discovery efforts. These methods allow a great number of druglike molecules to be screened quickly and inexpensively. Unfortunately, however, the accuracies of both these methods rely on the quality of the underlying molecular mechanics force fields (FFs), which are often poor. This major weakness originates from the reliance of FFs on a finite list of specific parameters, called atom types, which have low transferability between molecules. In particular, the torsional energy barriers of druglike molecules are notoriously difficult to predict. Continuing our endeavor to understand factors affecting the torsional energy barriers of small molecules and quantify them, we showed that descriptors calculated using the extended-Hückel method could be used to rapidly assign accurate torsion parameters for conjugated molecules. This method, called H-TEQ 4.5, was developed using a set of 684 conjugated molecules. It was subsequently validated on a test set of 200 diverse molecules and produced an average root-mean-square error (rmse) of 1.01 kcal·mol-1, with respect to the reference quantum mechanic torsional profiles. For comparison, GAFF2, MMFF94, and MAB produced average rmse's of 3.49, 1.50, and 1.77 kcal·mol-1, respectively. H-TEQ 4.5 is also computationally inexpensive, running just under 0.25 ms for a biphenyl molecule on a home computer, allowing it to be used for vHTS of large libraries of compounds. Overall, H-TEQ 4.5 solved the problems associated with the transferability of torsion parameters for conjugated molecules. This method was incorporated into the Molecular Operating Environment and will be available for a wide variety of applications.

Atom Type Independent Modeling of the Conformational Energy of Benzylic, Allylic, and Other Bonds Adjacent to Conjugated Systems.

Applications of computational methods to predict binding affinities for protein/drug complexes are routinely used in structure-based drug discovery. Applications of these methods often rely on empirical force fields (FFs) and their associated parameter sets and atom types. However, it is widely accepted that FFs cannot accurately cover the entire chemical space of drug-like molecules, due to the restrictive cost of parametrization and the poor transferability of existing parameters. To address these limitations, initiatives have been carried out to develop more transferable methods, in order to allow for more rigorous descriptions of any drug-like molecule. We have previously reported H-TEQ, a method which does not rely on atom types and incorporates well established chemical principles to assign parameters to organic molecules. The previous implementation of H-TEQ (a torsional barrier prediction method) only covered saturated and lone pair containing molecules; here, we report our efforts to incorporate conjugated systems into our model. The next step was the evaluation of the introduction of unsaturations. The developed model (H-TEQ3.0) has been validated on a wide variety of molecules containing heteroaromatic groups, alkyls, and fused ring systems. Our method performs on par with one of the most commonly used FFs (GAFF2), without relying on atom types or any prior parametrization.

Torsional Energy Barriers of Biaryls Could Be Predicted by Electron Richness/Deficiency of Aromatic Rings; Advancement of Molecular Mechanics toward Atom-Type Independence.

Biaryl molecules are ubiquitous pharmacophores found in natural products and pharmaceuticals. In spite of this, existing molecular mechanics force fields are unable to accurately reproduce their torsional energy profiles, except for a few well-parametrized cases. This effectively limits the ability of structure-based drug design methods to correctly identify hits involving biaryls with confidence (e.g., during virtual screening, employing docking and/or molecular dynamics simulations). Continuing in our endeavor to quantify organic chemistry principles, we showed that the torsional energy profile of biaryl compounds could be computed on-the-fly based on the electron richness/deficiency of the aromatic rings. This method, called H-TEQ 4.0, was developed using a set of 131 biaryls. It was subsequently validated on a separate set of 100 diverse biaryls, including multisubstituted, bicyclic and tricyclic druglike molecules, and produced an average root-mean-square error (RMSE) of 0.95 kcal·mol-1. For comparison, GAFF2 produced an RMSE of 3.88 kcal·mol-1, owing to problems associated with the transferability of torsion parameters. The success of H-TEQ 4.0 provided further evidence that force fields could transition to become atom-type independent, providing that the correct chemical principles are used. Overall, this method solved the problem of transferability of biaryl torsion parameters, while simultaneously improving the overall accuracy of the force field.