Teaching free energy calculations to learn from experimental data

Alchemical free energy calculations are an important tool in the computational chemistry tool-box, enabling the efficient calculation of quantities critical for drug discovery such as ligand binding affinities, selectivities, and partition coefficients. However, modern alchemical free energy calculations suffer from three significant limitations: (1) modern molecular mechanics force fields are limited in their ability to model complex molecular interactions, (2) classical force fields are unable to treat phenomena that involve rearrangements of chemical bonds, and (3) these calculations are unable to easily learn to improve their performance if readily-available experimental data is available. Here, we show how all three limitations can be overcome through the use of quantum machine learning (QML) potentials capable of accurately modeling quantum chemical energetics even when chemical bonds are made and broken. Because these potentials are based on mathematically convenient deep learning architectures instead of traditional quantum chemical formulations, QML simulations can be run at a fraction of the cost of quantum chemical simulations using modern graphics processing units (GPUs) and machine learning frameworks. We demonstrate that alchemical free energy calculations in explicit solvent are especially simple to implement using QML potentials because these potentials lack singularities and other pathologies typical of molecular mechanics potentials, and that alchemical free energy calculations are highly effective even when bonds are broken or made. Finally, we show how a limited number of experimental free energy measurements can be used to significantly improve the accuracy of computed free energies for unrelated compounds with no significant generalization gap. We illustrate these concepts on the prediction of aqueous tautomer free energies (related to tautomer ratios), which are highly relevant to drug discovery in that more than a quarter of all approved drugs exist as a mixture of tautomers.

Molecular Environment Specific Atomic Charges Improve Binding Affinity Predictions of SAMPL5 Host-Guest Systems

<div> <div> <div> <p>Host-guest systems are widely used in benchmarks as model systems to improve computational methods for absolute binding free energy predictions. Recent advances in sampling algorithms for alchemical free energy calculations and the increase in computational power have made their binding affinity prediction primarily dependent on the quality of the force field. Here, we propose a new methodology to derive the atomic charges of host-guest systems based on QM/MM calculations and the MBIS partitioning of the polarized electron density. A newly developed interface between the OpenMM and ORCA software package provides D-MBIS charges that best represent the guest’s average electrostatic interactions in the hosts or the solvent. The simulation workflow also calculates the average energy required to polarize the guest in the bound and unbound state. Alchemical free energy calculations using the GAFF force field parameters with D-MBIS charges improve the binding affinity prediction of six guests bound to two octa-acid hosts compared to the AM1-BCC charge set after correction with the average energetic polarization cost. This correction results from the difference in the energetic polarization cost between the bound and unbound state and contributes significantly to the binding affinity of anionic guests. </p></div></div></div><div><div><div> </div> </div> </div>

Molecular Environment Specific Atomic Charges Improve Binding Affinity Predictions of SAMPL5 Host-Guest Systems

<div> <div> <div> <p>Host-guest systems are widely used in benchmarks as model systems to improve computational methods for absolute binding free energy predictions. Recent advances in sampling algorithms for alchemical free energy calculations and the increase in computational power have made their binding affinity prediction primarily dependent on the quality of the force field. Here, we propose a new methodology to derive the atomic charges of host-guest systems based on QM/MM calculations and the MBIS partitioning of the polarized electron density. A newly developed interface between the OpenMM and ORCA software package provides D-MBIS charges that best represent the guest’s average electrostatic interactions in the hosts or the solvent. The simulation workflow also calculates the average energy required to polarize the guest in the bound and unbound state. Alchemical free energy calculations using the GAFF force field parameters with D-MBIS charges improve the binding affinity prediction of six guests bound to two octa-acid hosts compared to the AM1-BCC charge set after correction with the average energetic polarization cost. This correction results from the difference in the energetic polarization cost between the bound and unbound state and contributes significantly to the binding affinity of anionic guests. </p></div></div></div><div><div><div> </div> </div> </div>

Expanded Ensemble Methods Can Be Used to Accurately Predict Protein-Ligand Relative Binding Free Energies

<p>Alchemical free energy methods have become indispensable in computational drug discovery for their ability to calculate highly accurate estimates of protein-ligand affinities. Expanded ensemble (EE) methods, which involve single simulations visiting all of the alchemical intermediates, have some key advantages for alchemical free energy calculation. However, there have been relatively few examples published in the literature of using expanded ensemble simulations for free energies of protein-ligand binding. In this paper, as a test of expanded ensemble methods, we computed relative binding free energies using the Open Force Field Initiative force field (codename “Parsley”) for twenty-four pairs of Tyk2 inhibitors derived from a congeneric series of 16 compounds. The EE predictions agree well with the experimental values (RMSE of 0.94 ± 0.13 kcal mol⁻¹ and MUE of 0.75 ± 0.12 kcal mol⁻¹). We find that while increasing the number of alchemical intermediates can improve the phase space overlap, faster convergence can be obtained with fewer intermediates, as long as the acceptance rates are sufficient. We find that convergence can be improved using more aggressive updating of the biases, and that estimates can be improved by performing multiple independent EE calculations. This work demonstrates that EE is a viable option for alchemical free energy calculation. We discuss the implications of these findings for rational drug design, as well as future directions for improvement.</p>

Expanded Ensemble Methods Can Be Used to Accurately Predict Protein-Ligand Relative Binding Free Energies

<p>Alchemical free energy methods have become indispensable in computational drug discovery for their ability to calculate highly accurate estimates of protein-ligand affinities. Expanded ensemble (EE) methods, which involve single simulations visiting all of the alchemical intermediates, have some key advantages for alchemical free energy calculation. However, there have been relatively few examples published in the literature of using expanded ensemble simulations for free energies of protein-ligand binding. In this paper, as a test of expanded ensemble methods, we computed relative binding free energies using the Open Force Field Initiative force field (codename “Parsley”) for twenty-four pairs of Tyk2 inhibitors derived from a congeneric series of 16 compounds. The EE predictions agree well with the experimental values (RMSE of 0.94 ± 0.13 kcal mol⁻¹ and MUE of 0.75 ± 0.12 kcal mol⁻¹). We find that while increasing the number of alchemical intermediates can improve the phase space overlap, faster convergence can be obtained with fewer intermediates, as long as the acceptance rates are sufficient. We find that convergence can be improved using more aggressive updating of the biases, and that estimates can be improved by performing multiple independent EE calculations. This work demonstrates that EE is a viable option for alchemical free energy calculation. We discuss the implications of these findings for rational drug design, as well as future directions for improvement.</p>

Implementation of the QUBE Force Field in SOMD for High-Throughput Alchemical Free Energy Calculations

<div><div><div><p>The quantum mechanical bespoke (QUBE) force field approach has been developed to facilitate the automated derivation of potential energy function parameters for modelling protein-ligand binding. To date the approach has been validated in the context of Monte Carlo simulations of protein-ligand complexes. We describe here the implementation of the QUBE force field in the alchemical free energy calculation molecular dynamics simulation package SOMD. The implementation is validated by demonstrating the reproducibility of absolute hydration free energies computed with the QUBE force field across the SOMD and GROMACS software packages. We further demonstrate, by way of a case study involving two series of non-nucleoside inhibitors of HIV-1 reverse transcriptase, that the availability of QUBE in a modern simulation package that makes efficient use of GPU acceleration will facilitate high-throughput alchemical free energy calculations.</p></div></div></div>