Enhancing Protein-Ligand Binding Affinity Predictions using Neural Network Potentials.

This letter gives results on improving protein-ligand binding affinity predictions based on molecular dynamics simulations using machine learning potentials with a hybrid neural network potential and molecular mechanics methodology (NNP/MM). We compute relative binding free energies (RBFE) with the Alchemical Transfer Method (ATM) and validate its performance against established benchmarks and find significant enhancements compared to conventional MM force fields like GAFF2.

Enhancing Protein-Ligand Binding Affinity Predictions Using Neural Network Potentials.

This letter gives results on improving protein-ligand binding affinity predictions based on molecular dynamics simulations using machine learning potentials with a hybrid neural network potential and molecular mechanics methodology (NNP/MM). We compute relative binding free energies with the Alchemical Transfer Method and validate its performance against established benchmarks and find significant enhancements compared with conventional MM force fields like GAFF2.

What to Make of Zero: Resolving the Statistical Noise from Conformational Reorganization in Alchemical Binding Free Energy Estimates with Metadynamics Sampling.

We introduce the self-relative binding free energy (self-RBFE) approach to evaluate the intrinsic statistical variance of dual-topology alchemical binding free energy estimators. The self-RBFE is the relative binding free energy between a ligand and a copy of the same ligand, and its true value is zero. Nevertheless, because the two copies of the ligand move independently, the self-RBFE value produced by a finite-length simulation fluctuates and can be used to measure the variance of the model. The results of this validation provide evidence that a significant fraction of the errors observed in benchmark studies reflect the statistical fluctuations of unconverged estimates rather than the models' accuracy. Furthermore, we find that ligand reorganization is a significant contributing factor to the statistical variance of binding free energy estimates and that metadynamics-accelerated conformational sampling of the torsional degrees of freedom of the ligand can drastically reduce the time to convergence.

OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials.

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features in simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations with only a modest increase in cost.

Studies on the Configurational Stability of Tropolone-Ketone-, Ester-, and Aldehyde-Based Chiral Axes.

Recent studies have revealed that tropolone-amide aryl C-C(O) rotational barriers are dramatically higher than those of analogous benzamide-based systems, and as a result, they have an increased likelihood of displaying high configurational stability. Studies on other tropolone-based chiral axes are important to assess the generality of this phenomenon. Herein, we describe a series of studies on the rotational barriers of tropolone-ketone, tropolone-ester, and tropolone-aldehyde chiral axes. These studies are complemented with computational modeling of the dynamics of these and analogous benzenoid variants to illuminate the impact that tropolone may have on aryl-C(O) configurational stability.

Performance and Analysis of the Alchemical Transfer Method for Binding-Free-Energy Predictions of Diverse Ligands.

The Alchemical Transfer Method (ATM) is herein validated against the relative binding-free energies (RBFEs) of a diverse set of protein-ligand complexes. We employed a streamlined setup workflow, a bespoke force field, and AToM-OpenMM software to compute the RBFEs of the benchmark set prepared by Schindler and collaborators at Merck KGaA. This benchmark set includes examples of standard small R-group ligand modifications as well as more challenging scenarios, such as large R-group changes, scaffold hopping, formal charge changes, and charge-shifting transformations. The novel coordinate perturbation scheme and a dual-topology approach of ATM address some of the challenges of single-topology alchemical RBFE methods. Specifically, ATM eliminates the need for splitting electrostatic and Lennard-Jones interactions, atom mapping, defining ligand regions, and postcorrections for charge-changing perturbations. Thus, ATM is simpler and more broadly applicable than conventional alchemical methods, especially for scaffold-hopping and charge-changing transformations. Here, we performed well over 500 RBFE calculations for eight protein targets and found that ATM achieves accuracy comparable to that of existing state-of-the-art methods, albeit with larger statistical fluctuations. We discuss insights into the specific strengths and weaknesses of the ATM method that will inform future deployments. This study confirms that ATM can be applied as a production tool for RBFE predictions across a wide range of perturbation types within a unified, open-source framework.

OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials.

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features on simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein (GFP) chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations at only a modest increase in cost.

Taming multiple binding poses in alchemical binding free energy prediction: the ß-cyclodextrin host-guest SAMPL9 blinded challenge.

We apply the Alchemical Transfer Method (ATM) and a bespoke fixed partial charge force field to the SAMPL9 bCD host-guest binding free energy prediction challenge that comprises a combination of complexes formed between five phenothiazine guests and two cyclodextrin hosts. Multiple chemical forms, competing binding poses, and computational modeling challenges pose significant obstacles to obtaining reliable computational predictions for these systems. The phenothiazine guests exist in solution as racemic mixtures of enantiomers related by nitrogen inversions that bind the hosts in various binding poses, each requiring an individual free energy analysis. Due to the large size of the guests and the conformational reorganization of the hosts, which prevent a direct absolute binding free energy route, binding free energies are obtained by a series of absolute and relative binding alchemical steps for each chemical species in each binding pose. Metadynamics-accelerated conformational sampling was found to be necessary to address the poor convergence of some numerical estimates affected by conformational trapping. Despite these challenges, our blinded predictions quantitatively reproduced the experimental affinities for the ß-cyclodextrin host and, to a lesser extent, those with a methylated derivative. The work illustrates the challenges of obtaining reliable free energy data in in silico drug design for even seemingly simple systems and introduces some of the technologies available to tackle them.

Validation of the Alchemical Transfer Method for the Estimation of Relative Binding Affinities of Molecular Series.

The accurate prediction of protein-ligand binding affinities is crucial for drug discovery. Alchemical free energy calculations have become a popular tool for this purpose. However, the accuracy and reliability of these methods can vary depending on the methodology. In this study, we evaluate the performance of a relative binding free energy protocol based on the alchemical transfer method (ATM), a novel approach based on a coordinate transformation that swaps the positions of two ligands. The results show that ATM matches the performance of more complex free energy perturbation (FEP) methods in terms of Pearson correlation but with marginally higher mean absolute errors. This study shows that the ATM method is competitive compared to more traditional methods in speed and accuracy and offers the advantage of being applicable with any potential energy function.

Validation of the Alchemical Transfer Method for the Estimation of Relative Binding Affinities of Molecular Series.

The accurate prediction of protein-ligand binding affinities is crucial for drug discovery. Alchemical free energy calculations have become a popular tool for this purpose. However, the accuracy and reliability of these methods can vary depending on the methodology. In this study, we evaluate the performance of a relative binding free energy protocol based on the alchemical transfer method (ATM), a novel approach based on a coordinate transformation that swaps the positions of two ligands. The results show that ATM matches the performance of more complex free energy perturbation (FEP) methods in terms of Pearson correlation, but with marginally higher mean absolute errors. This study shows that the ATM method is competitive compared to more traditional methods in speed and accuracy and offers the advantage of being applicable with any potential energy function.

Free Energy-Based Computational Methods for the Study of Protein-Peptide Binding Equilibria.

This chapter discusses the theory and application of physics-based free energy methods to estimate protein-peptide binding free energies. It presents a statistical mechanics formulation of molecular binding, which is then specialized in three methodologies: (1) alchemical absolute binding free energy estimation with implicit solvation, (2) alchemical relative binding free energy estimation with explicit solvation, and (3) potential of mean force binding free energy estimation. Case studies of protein-peptide binding application taken from the recent literature are discussed for each method.

Developing end-point methods for absolute binding free energy calculation using the Boltzmann-quasiharmonic model.

Understanding the physical forces underlying receptor-ligand binding requires robust methods for analyzing the binding thermodynamics. In end-point binding free energy methods the binding free energy is naturally decomposable into physically intuitive contributions such as the solvation free energy and configurational entropy that can provide insights. Here we present a new end-point method called EE-BQH (Effective Energy-Boltzmann-Quasiharmonic) which combines the Boltzmann-Quasiharmonic model for configurational entropy with different solvation free energy methods, such as the continuum solvent PBSA model and the integral equation-based 3D-RISM, to estimate the absolute binding free energy. We compare EE-BQH with other treatments of configurational entropy such as Quasiharmonic models in internal coordinates (QHIC) and in Cartesian coordinates (QHCC), and Normal Mode analysis (NMA), by testing them on the octa acids host-guest complexes from the SAMPL8 blind challenge. The accuracies in the calculated absolute binding free energies strongly depend on the configurational entropy and solvation free energy methods used. QHIC and BQH yield the best agreements with the established potential of mean force (PMF) estimates, with R2 of ∼0.7 and mean unsigned error of ∼1.7 kcal mol-1. These results from the end-point calculations are also in similar agreement with experiments. While 3D-RISM in combination with QHIC or BQH lead to reasonable correlations with the PMF results and experiments, the calculated absolute binding free energies are underestimated by ∼5 kcal mol-1. While the binding is accompanied by a significant reduction in the ligand translational/rotational entropy, the change in the torsional entropy in these host-guest systems is slightly positive. Compared with BQH, QHIC underestimates the reduction of configurational entropy because of the non-Gaussian probability distributions in the ligand rotation and a small number of torsions. The study highlights the crucial role of configurational entropy in determining binding and demonstrates the potential of using the new end-point method to provide insights in more complex protein-ligand systems.

Relative Binding Free Energy Calculations for Ligands with Diverse Scaffolds with the Alchemical Transfer Method.

We present an extension of the alchemical transfer method (ATM) for the estimation of relative binding free energies of molecular complexes applicable to conventional, as well as scaffold-hopping, alchemical transformations. Named ATM-RBFE, the method is implemented in the free and open-source OpenMM molecular simulation package and aims to provide a simpler and more generally applicable route to the calculation of relative binding free energies than what is currently available. ATM-RBFE is based on sound statistical mechanics theory and a novel coordinate perturbation scheme designed to swap the positions of a pair of ligands such that one is transferred from the bulk solvent to the receptor binding site while the other moves simultaneously in the opposite direction. The calculation is conducted directly in a single solvent box with a system prepared with conventional setup tools, without splitting of electrostatic and nonelectrostatic transformations, and without pairwise soft-core potentials. ATM-RBFE is validated here against the absolute binding free energies of the SAMPL8 GDCC host-guest benchmark set and against protein-ligand benchmark sets that include complexes of the estrogen receptor ERα and those of the methyltransferase EZH2. In each case the method yields self-consistent and converged relative binding free energy estimates in agreement with absolute binding free energies and reference literature values, as well as experimental measurements.

Application of the alchemical transfer and potential of mean force methods to the SAMPL8 host-guest blinded challenge.

We report the results of our participation in the SAMPL8 GDCC Blind Challenge for host-guest binding affinity predictions. Absolute binding affinity prediction is of central importance to the biophysics of molecular association and pharmaceutical discovery. The blinded SAMPL series have provided an important forum for assessing the reliability of binding free energy methods in an objective way. In this challenge, we employed two binding free energy methods, the newly developed alchemical transfer method (ATM) and the well-established potential of mean force (PMF) physical pathway method, using the same setup and force field model. The calculated binding free energies from the two methods are in excellent quantitative agreement. Importantly, the results from the two methods were also found to agree well with the experimental binding affinities released subsequently, with R values of 0.89 (ATM) and 0.83 (PMF). These results were ranked among the best of the SAMPL8 GDCC challenge and second only to those obtained with the more accurate AMOEBA force field. Interestingly, the two host molecules included in the challenge (TEMOA and TEETOA) displayed distinct binding mechanisms, with TEMOA undergoing a dehydration transition whereas guest binding to TEETOA resulted in the opening of the binding cavity that remains essentially dry during the process. The coupled reorganization and hydration equilibria observed in these systems is a useful prototype for the study of these phenomena often observed in the formation of protein-ligand complexes. Given that the two free energy methods employed here are based on entirely different thermodynamic pathways, the close agreement between the two and their general agreement with the experimental binding free energies are a testament to the high quality and precision achieved by theory and methods. The study provides further validation of the novel ATM binding free energy estimation protocol and paves the way to further extensions of the method to more complex systems.

Alchemical Transfer Approach to Absolute Binding Free Energy Estimation.

The alchemical transfer method (ATM) for the calculation of standard binding free energies of noncovalent molecular complexes is presented. The method is based on a coordinate displacement perturbation of the ligand between the receptor binding site and the explicit solvent bulk and a thermodynamic cycle connected by a symmetric intermediate in which the ligand interacts with the receptor and solvent environments with equal strength. While the approach is alchemical, the implementation of the ATM is as straightforward as that for physical pathway methods of binding. The method is applicable, in principle, with any force field, as it does not require splitting the alchemical transformations into electrostatic and nonelectrostatic steps, and it does not require soft-core pair potentials. We have implemented the ATM as a freely available and open-source plugin of the OpenMM molecular dynamics library. The method and its implementation are validated on the SAMPL6 SAMPLing host-guest benchmark set. The work paves the way to streamlined alchemical relative and absolute binding free energy implementations on many molecular simulation packages and with arbitrary energy functions including polarizable, quantum-mechanical, and artificial neural network potentials.

New tetrahydroisoquinoline-based D3R ligands with an o-xylenyl linker motif.

The effect of rigidification of the n-butyl linker region of tetrahydroisoquinoline-containing D3R ligands via inclusion of an o-xylenyl motif was examined in this study. Generally, rigidification with an o-xylenyl linker group reduces D3R affinity and negatively impacts selectivity versus D2R for compounds possessing a 6-methoxy-1,2,3,4,-tetrahydroisoquinolin-7-ol primary pharmacophore group. However, D3R affinity appears to be regulated by the primary pharmacophore group and high affinity D3R ligands with 6,7-dihydroxy-1,2,3,4-tetrahydroisoquinoline and 6,7-dimethoxy-1,2,3,4-tetrahydroisoquinoline primary pharmacophore groups were identified. The results of this study also indicate that D3R selectivity versus the σ2R is dictated by the benzamide secondary pharmacophore group, this being facilitated with 4-substituted benzamides. Compounds 5s and 5t were identified as high affinity (Ki < 4 nM) D3R ligands. Docking studies revealed that the added phenyl ring moiety interacts with the Cys181 in D3R which partially accounts for the strong D3R affinity of the ligands.

Alchemical transformations for concerted hydration free energy estimation with explicit solvation.

We present a family of alchemical perturbation potentials that enable the calculation of hydration free energies of small- to medium-sized molecules in a single concerted alchemical coupling step instead of the commonly used sequence of two distinct coupling steps for Lennard-Jones and electrostatic interactions. The perturbation potentials we employ are non-linear functions of the solute-solvent interaction energy designed to focus sampling near entropic bottlenecks along the alchemical pathway. We present a general framework to optimize the parameters of alchemical perturbation potentials of this kind. The optimization procedure is based on the λ-function formalism and the maximum-likelihood parameter estimation procedure we developed earlier to avoid the occurrence of multi-modal distributions of the coupling energy along the alchemical path. A novel soft-core function applied to the overall solute-solvent interaction energy rather than individual interatomic pair potentials critical for this result is also presented. Because it does not require modifications of core force and energy routines, the soft-core formulation can be easily deployed in molecular dynamics simulation codes. We illustrate the method by applying it to the estimation of the hydration free energy in water droplets of compounds of varying size and complexity. In each case, we show that convergence of the hydration free energy is achieved rapidly. This work paves the way for the ongoing development of more streamlined algorithms to estimate free energies of molecular binding with explicit solvation.

3,7-Dihydroxytropolones Inhibit Initiation of Hepatitis B Virus Minus-Strand DNA Synthesis.

Initiation of protein-primed (-) strand DNA synthesis in hepatitis B virus (HBV) requires interaction of the viral reverse transcriptase with epsilon (ε), a cis-acting regulatory signal located at the 5' terminus of pre-genomic RNA (pgRNA), and several host-encoded chaperone proteins. Binding of the viral polymerase (P protein) to ε is necessary for pgRNA encapsidation and synthesis of a short primer covalently attached to its terminal domain. Although we identified small molecules that recognize HBV ε RNA, these failed to inhibit protein-primed DNA synthesis. However, since initiation of HBV (-) strand DNA synthesis occurs within a complex of viral and host components (e.g., Hsp90, DDX3 and APOBEC3G), we considered an alternative therapeutic strategy of allosteric inhibition by disrupting the initiation complex or modifying its topology. To this end, we show here that 3,7-dihydroxytropolones (3,7-dHTs) can inhibit HBV protein-primed DNA synthesis. Since DNA polymerase activity of a ribonuclease (RNase H)-deficient HBV reverse transcriptase that otherwise retains DNA polymerase function is also abrogated, this eliminates direct involvement of RNase (ribonuclease) H activity of HBV reverse transcriptase and supports the notion that the HBV initiation complex might be therapeutically targeted. Modeling studies also provide a rationale for preferential activity of 3,7-dHTs over structurally related α-hydroxytropolones (α-HTs).

Exploring the Free-Energy Landscape and Thermodynamics of Protein-Protein Association.

We report the free-energy landscape and thermodynamics of the protein-protein association responsible for the drug-induced multimerization of HIV-1 integrase (IN). Allosteric HIV-1 integrase inhibitors promote aberrant IN multimerization by bridging IN-IN intermolecular interactions. However, the thermodynamic driving forces and kinetics of the multimerization remain largely unknown. Here, we explore the early steps in the IN multimerization by using umbrella sampling and unbiased molecular dynamics simulations in explicit solvent. In direct simulations, the two initially separated dimers spontaneously associate to form near-native complexes that resemble the crystal structure of the aberrant tetramer. Most strikingly, the effective interaction of the protein-protein association is very short-ranged: the two dimers associate rapidly within tens of nanoseconds when their binding surfaces are separated by d ≤ 4.3 Å (less than two water diameters). Beyond this distance, the oligomerization kinetics appears to be diffusion controlled with a much longer association time. The free-energy profile also captured the crucial role of allosteric IN inhibitors in promoting multimerization and explained why several C-terminal domain mutations are remarkably resistant to the drug-induced multimerization. The results also show that at small separation, the protein-protein binding process contains two consecutive phases with distinct thermodynamic signatures. First, interprotein water molecules are expelled to the bulk, resulting in a small increase in entropy, as the solvent entropy gain from the water release is nearly cancelled by the loss of side-chain entropies as the two proteins approach each other. At shorter distances, the two dry binding surfaces adapt to each other to optimize their interaction energy at the expense of further protein configurational entropy loss. Although the binding interfaces feature clusters of hydrophobic residues, overall, the protein-protein association in this system is driven by enthalpy and opposed by entropy.

Amide-containing α-hydroxytropolones as inhibitors of hepatitis B virus replication.

The Hepatitis B Virus (HBV) ribonuclease H (RNaseH) is a promising but unexploited drug target. Here, we synthesized and analyzed a library of 57 amide-containing α-hydroxytropolones (αHTs) as potential leads for HBV drug development. Fifty percent effective concentrations ranged from 0.31 to 54 µM, with selectivity indexes in cell culture of up to 80. Activity against the HBV RNaseH was confirmed in semi-quantitative enzymatic assays with recombinant HBV RNaseH. The compounds were overall poorly active against human ribonuclease H1, with 50% inhibitory concentrations of 5.1 to >1,000 µM. The αHTs had modest activity against growth of the fungal pathogen Cryptococcus neoformans, but had very limited activity against growth of the Gram - bacterium Escherichia coli and the Gram + bacterium Staphylococcus aureus, indicating substantial selectivity for HBV. A molecular model of the HBV RNaseH templated against the Ty3 RNaseH was generated. Docking the compounds to the RNaseH revealed the anticipated binding pose with the divalent cation coordinating motif on the compounds chelating the two Mn++ ions modeled into the active site. These studies reveal that that amide αHTs can be strong, specific HBV inhibitors that merit further assessment toward becoming anti-HBV drugs.