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>

A Heuristic Approach for Precipitation Data Assimilation: Effect of Forecast Errors and Assimilation of NCEP Stage IV Precipitation Analyses

Recently, Pérez Hortal et al. introduced a simple data assimilation (DA) technique named localized ensemble mosaic assimilation (LEMA) for the assimilation of radar-derived precipitation observations. The method constructs an analysis by assigning to each model grid point the information from the ensemble member that is locally closest to the precipitation observations. This study explores the effects of the forecasts errors in the performance of the method using a series of observing system simulation experiments (OSSEs) with different magnitudes of forecast errors employing a small ensemble of 20 members. The ideal experiments show that LEMA is able to produce forecasts with considerable and long-lived error reductions in the fields of precipitation, temperature, humidity, and wind. Nonetheless, the quality of the analysis deteriorates with increasing forecast errors beyond the spread of the ensemble. To overcome this limitation, we expand the spread of the ensemble used to construct the analysis mosaic by considering states at different times and states from forecasts initialized at different times (lagged forecasts). The ideal experiments show that the additional information in the expanded ensemble improves the performance of LEMA, producing larger and long-lived improvements in the state variables and in the precipitation forecast quality. Finally, the potential of LEMA is explored in real DA experiments using actual Stage IV precipitation observations. When LEMA uses only the background members, the quality of the precipitation forecast shows small or no improvements. However, the expanded ensemble improves the LEMA’s effectiveness, producing larger and more persistent improvements in precipitation forecasts.

The SAMPL6 SAMPLing challenge: Assessing the reliability and efficiency of binding free energy calculations

Approaches for computing small molecule binding free energies based on molecular simulations are now regularly being employed by academic and industry practitioners to study receptor-ligand systems and prioritize the synthesis of small molecules for ligand design. Given the variety of methods and implementations available, it is natural to ask how the convergence rates and final predictions of these methods compare. In this study, we describe the concept and results for the SAMPL6 SAMPLing challenge, the first challenge from the SAMPL series focusing on the assessment of convergence properties and reproducibility of binding free energy methodologies. We provided parameter files, partial charges, and multiple initial geometries for two octa-acid (OA) and one cucurbit[8]uril (CB8) host-guest systems. Participants submitted binding free energy predictions as a function of the number of force and energy evaluations for seven different alchemical and physical-pathway (i.e., potential of mean force and weighted ensemble of trajectories) methodologies implemented with the GROMACS, AMBER, NAMD, or OpenMM simulation engines. To rank the methods, we developed an efficiency statistic based on bias and variance of the free energy estimates. For the two small OA binders, the free energy estimates computed with alchemical and potential of mean force approaches show relatively similar variance and bias as a function of the number of energy/force evaluations, with the attach-pull-release (APR), GROMACS expanded ensemble, and NAMD double decoupling submissions obtaining the greatest efficiency. The differences between the methods increase when analyzing the CB8-quinine system, where both the guest size and correlation times for system dynamics are greater. For this system, nonequilibrium switching (GROMACS/NS-DS/SB) obtained the overall highest efficiency. Surprisingly, the results suggest that specifying force field parameters and partial charges is insufficient to generally ensure reproducibility, and we observe differences between seemingly converged predictions ranging approximately from 0.3 to 1.0 kcal/mol, even with almost identical simulations parameters and system setup (e.g., Lennard-Jones cutoff, ionic composition). Further work will be required to completely identify the exact source of these discrepancies. Among the conclusions emerging from the data, we found that Hamiltonian replica exchange—while displaying very small variance—can be affected by a slowly-decaying bias that depends on the initial population of the replicas, that bidirectional estimators are significantly more efficient than unidirectional estimators for nonequilibrium free energy calculations for systems considered, and that the Berendsen barostat introduces non-negligible artifacts in expanded ensemble simulations.

Gain Form of the Ensemble Transform Kalman Filter and Its Relevance to Satellite Data Assimilation with Model Space Ensemble Covariance Localization

To ameliorate suboptimality in ensemble data assimilation, methods have been introduced that involve expanding the ensemble size. Such expansions can incorporate model space covariance localization and/or estimates of climatological or model error covariances. Model space covariance localization in the vertical overcomes problematic aspects of ensemble-based satellite data assimilation. In the case of the ensemble transform Kalman filter (ETKF), the expanded ensemble size associated with vertical covariance localization would also enable the simultaneous update of entire vertical columns of model variables from hyperspectral and multispectral satellite sounders. However, if the original formulation of the ETKF were applied to an expanded ensemble, it would produce an analysis ensemble that was the same size as the expanded forecast ensemble. This article describes a variation on the ETKF called the gain ETKF (GETKF) that takes advantage of covariances from the expanded ensemble, while producing an analysis ensemble that has the required size of the unexpanded forecast ensemble. The approach also yields an inflation factor that depends on the localization length scale that causes the GETKF to perform differently to an ensemble square root filter (EnSRF) using the same expanded ensemble. Experimentation described herein shows that the GETKF outperforms a range of alternative ETKF-based solutions to the aforementioned problems. In cycling data assimilation experiments with a newly developed storm-track version of the Lorenz-96 model, the GETKF analysis root-mean-square error (RMSE) matches the EnSRF RMSE at shorter than optimal localization length scales but is superior in that it yields smaller RMSEs for longer localization length scales.