Comparison of Equilibrium and Nonequilibrium Approaches for Relative Binding Free Energy Predictions

Alchemical relative binding free energy calculations have recently found important applications in drug optimization. A series of congeneric compounds are generated from a preidentified lead compound, and their relative binding affinities to a protein are assessed in order to optimize candidate drugs. While methods based on equilibrium thermodynamics have been extensively studied, an approach based on nonequilibrium methods has recently been reported together with claims of its superiority. However, these claims pay insufficient attention to the basis and reliability of both methods. Here we report a comparative study of the two approaches across a large data set, comprising more than 500 ligand transformations spanning in excess of 300 ligands binding to a set of 14 diverse protein targets. Ensemble methods are essential to quantify the uncertainty in these calculations, not only for the reasons already established in the equilibrium approach but also to ensure that the nonequilibrium calculations reside within their domain of validity. If and only if ensemble methods are applied, we find that the nonequilibrium method can achieve accuracy and precision comparable to those of the equilibrium approach. Compared to the equilibrium method, the nonequilibrium approach can reduce computational costs but introduces higher computational complexity and longer wall clock times. There are, however, cases where the standard length of a nonequilibrium transition is not sufficient, necessitating a complete rerun of the entire set of transitions. This significantly increases the computational cost and proves to be highly inconvenient during large-scale applications. Our findings provide a key set of recommendations that should be adopted for the reliable implementation of nonequilibrium approaches to relative binding free energy calculations in ligand-protein systems

High-throughput Binding Affinity Calculations at Extreme Scales

Resistance to chemotherapy and molecularly targeted therapies is a major factor in limiting the effectiveness of cancer treatment. In many cases, resistance can be linked to genetic changes in target proteins, either pre-existing or evolutionarily selected during treatment. Key to overcoming this challenge is an understanding of the molecular determinants of drug binding. Using multi-stage pipelines of molecular simulations we can gain insights into the binding free energy and the residence time of a ligand, which can inform both stratified and personal treatment regimes and drug development. To support the scalable, adaptive and automated calculation of the binding free energy on high-performance computing resources, we introduce the High- throughput Binding Affinity Calculator (HTBAC). HTBAC uses a building block approach in order to attain both workflow flexibility and performance. We demonstrate close to perfect weak scaling to hundreds of concurrent multi-stage binding affinity calculation pipelines. This permits a rapid time-to-solution that is essentially invariant of the calculation protocol, size of candidate ligands and number of ensemble simulations. As such, HTBAC advances the state of the art of binding affinity calculations and protocols

Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy, Precision, and Reproducibility

The binding free energy between a ligand and its target protein is an essential quantity to know at all stages of the drug discovery pipeline. Assessing this value computationally can offer insight into where efforts should be focused in the pursuit of effective therapeutics to treat a myriad of diseases. In this work, we examine the computation of alchemical relative binding free energies with an eye for assessing reproducibility across popular molecular dynamics packages and free energy estimators. The focus of this work is on 54 ligand transformations from a diverse set of protein targets: MCL1, PTP1B, TYK2, CDK2, and thrombin. These targets are studied with three popular molecular dynamics packages: OpenMM, NAMD2, and NAMD3 alpha. Trajectories collected with these packages are used to compare relative binding free energies calculated with thermodynamic integration and free energy perturbation methods. The resulting binding free energies show good agreement between molecular dynamics packages with an average mean unsigned error between them of 0.50 kcal/mol. The correlation between packages is very good, with the lowest Spearman's, Pearson's and Kendall's tau correlation coefficients being 0.92, 0.91, and 0.76, respectively. Agreement between thermodynamic integration and free energy perturbation is shown to be very good when using ensemble averaging

Ensemble-Based Approaches Ensure Reliability and Reproducibility

It is increasingly widely recognized that ensemble-based approaches are required to achieve reliability, accuracy, and precision in molecular dynamics calculations. The purpose of the present article is to address a frequently raised question: what is the optimal way to perform ensemble simulation to calculate quantities of interest

Conformational effects on the pro-S hydrogen abstraction reaction in cyclooxygenase-1: an integrated QM/MM and MD study

A key step in the cyclooxygenase reaction cycle of cyclooxygenase 1 (COX-1) is abstraction of the pro-S hydrogen atom of the arachidonic acid by a radical that is formed at the protein residue Tyr-385. Here we investigate this reaction step by a quantum-mechanics/molecular-mechanics approach in combination with molecular-dynamics simulations. The simulations identify the hydrogen abstraction angle as a crucial geometric determinant of the reaction, thus revealing the importance of the cyclooxygenase active site for calculating the potential energy surface of the reaction

T-cell epitope prediction and immune complex simulation using molecular dynamics: state of the art and persisting challenges

Atomistic Molecular Dynamics provides powerful and flexible tools for the prediction and analysis of molecular and macromolecular systems. Specifically, it provides a means by which we can measure theoretically that which cannot be measured experimentally: the dynamic time-evolution of complex systems comprising atoms and molecules. It is particularly suitable for the simulation and analysis of the otherwise inaccessible details of MHC-peptide interaction and, on a larger scale, the simulation of the immune synapse. Progress has been relatively tentative yet the emergence of truly high-performance computing and the development of coarse-grained simulation now offers us the hope of accurately predicting thermodynamic parameters and of simulating not merely a handful of proteins but larger, longer simulations comprising thousands of protein molecules and the cellular scale structures they form. We exemplify this within the context of immunoinformatics

The performance of ensemble-based free energy protocols in computing binding affinities to ROS1 kinase

Optimization of binding affinities for compounds to their target protein is a primary objective in drug discovery. Herein we report on a collaborative study that evaluates a set of compounds binding to ROS1 kinase. We use ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent) and TIES (thermodynamic integration with enhanced sampling) protocols to rank the binding free energies. The predicted binding free energies from ESMACS simulations show good correlations with experimental data for subsets of the compounds. Consistent binding free energy differences are generated for TIES and ESMACS. Although an unexplained overestimation exists, we obtain excellent statistical rankings across the set of compounds from the TIES protocol, with a Pearson correlation coefficient of 0.90 between calculated and experimental activities

Ensemble Simulations and Experimental Free Energy Distributions: Evaluation and Characterization of Isoxazole Amides as SMYD3 Inhibitors

Optimization of binding affinities for ligands to their target protein is a primary objective in rational drug discovery. Herein, we report on a collaborative study that evaluates various compounds designed to bind to the SET and MYND domain-containing protein 3 (SMYD3). SMYD3 is a histone methyltransferase and plays an important role in transcriptional regulation in cell proliferation, cell cycle, and human carcinogenesis. Experimental measurements using the scintillation proximity assay show that the distributions of binding free energies from a large number of independent measurements exhibit non-normal properties. We use ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent) and TIES (thermodynamic integration with enhanced sampling) protocols to predict the binding free energies and to provide a detailed chemical insight into the nature of ligand-protein binding. Our results show that the 1-trajectory ESMACS protocol works well for the set of ligands studied here. Although one unexplained outlier exists, we obtain excellent statistical ranking across the set of compounds from the ESMACS protocol and good agreement between calculations and experiments for the relative binding free energies from the TIES protocol. ESMACS and TIES are again found to be powerful protocols for the accurate comparison of the binding free energies

Ensembles are required to handle aleatoric and parametric uncertainty in molecular dynamics simulation

Classical molecular dynamics is a computer simulation technique that is in widespread use across many areas of science, from physics and chemistry to materials, biology, and medicine. The method continues to attract criticism due its oft-reported lac

Non-Gaussian distributions of absolute free energies in ensemble molecular dynamics simulations

Significantly more ‘outliers’ can be produced from a non-Gaussian distribution than one would anticipate were the statistics to conform to a normal distribution. Using ensemble simulations consisting of 25 replicas, we have previously identified a considerable percentage of ligand-protein systems which present non-Gaussian distributions in calculated binding free energies. Here we report on the statistics of much larger ensemble and find that the free energy distributions are definitively non-Gaussian for these systems