Alchemical Binding Free Energy Calculations Research Articles

PopShift: A Thermodynamically Sound Approach to Estimate Binding Free Energies by Accounting for Ligand-Induced Population Shifts from a Ligand-Free Markov State Model.

Obtaining accurate binding free energies from in silico screens has been a long-standing goal for the computational chemistry community. However, accuracy and computational cost are at odds with one another, limiting the utility of methods that perform this type of calculation. Many methods achieve massive scale by explicitly or implicitly assuming that the target protein adopts a single structure, or undergoes limited fluctuations around that structure, to minimize computational cost. Others simulate each protein-ligand complex of interest, accepting lower throughput in exchange for better predictions of binding affinities. Here, we present the PopShift framework for accounting for the ensemble of structures a protein adopts and their relative probabilities. Protein degrees of freedom are enumerated once, and then arbitrarily many molecules can be screened against this ensemble. Specifically, we use Markov state models (MSMs) as a compressed representation of a protein's thermodynamic ensemble. We start with a ligand-free MSM and then calculate how addition of a ligand shifts the populations of each protein conformational state based on the strength of the interaction between that protein conformation and the ligand. In this work we use docking to estimate the affinity between a given protein structure and ligand, but any estimator of binding affinities could be used in the PopShift framework. We test PopShift on the classic benchmark pocket T4 Lysozyme L99A. We find that PopShift is more accurate than common strategies, such as docking to a single structure and traditional ensemble docking─producing results that compare favorably with alchemical binding free energy calculations in terms of RMSE but not correlation─and may have a more favorable computational cost profile in some applications. In addition to predicting binding free energies and ligand poses, PopShift also provides insight into how the probability of different protein structures is shifted upon addition of various concentrations of ligand, providing a platform for predicting affinities and allosteric effects of ligand binding. Therefore, we expect PopShift will be valuable for hit finding and for providing insight into phenomena like allostery.

Alchemical approach performance in calculating the ligand-binding free energy.

Alchemical binding free energy calculations are one of the most accurate methods for estimating ligand-binding affinity. Assessing the accuracy of the approach over protein targets is one of the most interesting issues. The free energy difference of binding between a protein and a ligand was calculated via the alchemical approach. The alchemical approach exhibits satisfactory accuracy over four targets, including AmpC beta-lactamase (AmpC); glutamate receptor, ionotropic kainate 1 (GluK1); heat shock protein 90 (Hsp90); and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) main protease (Mpro). In particular, the correlation coefficients between calculated binding free energies and the respective experiments over four targets range from 0.56 to 0.86. The affinity computed via free energy perturbation (FEP) simulations is overestimated over the experimental value. Particularly, the electrostatic interaction free energy rules the binding process of ligands to AmpC and GluK1. However, the van der Waals (vdW) interaction free energy plays an important role in the ligand-binding processes of HSP90 and SARS-CoV-2 Mpro. The obtained results associate with the hydrophilic or hydrophobic properties of the ligands. This observation may enhance computer-aided drug design.

Identifying and Overcoming the Sampling Challenges in Relative Binding Free Energy Calculations of a Model Protein:Protein Complex.

Relative alchemical binding free energy calculations are routinely used in drug discovery projects to optimize the affinity of small molecules for their drug targets. Alchemical methods can also be used to estimate the impact of amino acid mutations on protein:protein binding affinities, but these calculations can involve sampling challenges due to the complex networks of protein and water interactions frequently present in protein:protein interfaces. We investigate these challenges by extending a graphics processing unit (GPU)-accelerated open-source relative free energy calculation package (Perses) to predict the impact of amino acid mutations on protein:protein binding. Using the well-characterized model system barnase:barstar, we describe analyses for identifying and characterizing sampling problems in protein:protein relative free energy calculations. We find that mutations with sampling problems often involve charge-changes, and inadequate sampling can be attributed to slow degrees of freedom that are mutation-specific. We also explore the accuracy and efficiency of current state-of-the-art approaches─alchemical replica exchange and alchemical replica exchange with solute tempering─for overcoming relevant sampling problems. By employing sufficiently long simulations, we achieve accurate predictions (RMSE 1.61, 95% CI: [1.12, 2.11] kcal/mol), with 86% of estimates within 1 kcal/mol of the experimentally determined relative binding free energies and 100% of predictions correctly classifying the sign of the changes in binding free energies. Ultimately, we provide a model workflow for applying protein mutation free energy calculations to protein:protein complexes, and importantly, catalog the sampling challenges associated with these types of alchemical transformations. Our free open-source package (Perses) is based on OpenMM and is available at https://github.com/choderalab/perses.

Recent Advances in Alchemical Binding Free Energy Calculations for Drug Discovery.

Rigorous physics-based methods to calculate binding free energies of protein-ligand complexes have become a valued component of structure-based drug design. Relative and absolute binding free energy calculations have been deployed prospectively in support of solving diverse drug discovery challenges. Here we review recent applications of binding free energy calculations to fragment growing and linking, scaffold hopping, binding pose validation, virtual screening, covalent enzyme inhibition, and positional analogue scanning. Furthermore, we discuss the merits of using protein models and highlight recent efforts to replace costly binding free energy calculations with predictions from machine learning models trained on a limited number of free energy perturbation or thermodynamic integration calculations thereby allowing for extended chemical space exploration.

Dual A1/A3 Adenosine Receptor Antagonists: Binding Kinetics and Structure-Activity Relationship Studies Using Mutagenesis and Alchemical Binding Free Energy Calculations.

Drugs targeting adenosine receptors (AR) can provide treatment for diseases. We report the identification of 7-(phenylamino)-pyrazolo[3,4-c]pyridines L2-L10, A15, and A17 as low-micromolar to low-nanomolar A1R/A3R dual antagonists, with 3-phenyl-5-cyano-7-(trimethoxyphenylamino)-pyrazolo[3,4-c]pyridine (A17) displaying the highest affinity at both receptors with a long residence time of binding, as determined using a NanoBRET-based assay. Two binding orientations of A17 produce stable complexes inside the orthosteric binding area of A1R in molecular dynamics (MD) simulations, and we selected the most plausible orientation based on the agreement with alanine mutagenesis supported by affinity experiments. Interestingly, for drug design purposes, the mutation of L2506.51 to alanine increased the binding affinity of A17 at A1R. We explored the structure-activity relationships against A1R using alchemical binding free energy calculations with the thermodynamic integration coupled with the MD simulation (TI/MD) method, applied on the whole G-protein-coupled receptor-membrane system, which showed a good agreement (r = 0.73) between calculated and experimental relative binding free energies.

Alchemical binding free energy calculations guided design of novel human topoisomerase II inhibitors

Human topoisomerase II (topoII) enzymes are critical in DNA topology modulation within the cell. Importantly, topoII are validated anticancer drug targets due to their association with cancer cell proliferation. The clinically available topoII targeted anticancer drugs such as etoposide, often show harmful side effects and drug resistance. Therefore, new studies revolving around the design of topoII inhibitors are crucial for the discovery of novel, potent and safer anti-cancer therapeutics. We present an ongoing drug design campaign to optimize compounds centered on a recently patented chemical class of topoIIα inhibitors.

Precise Binding Free Energy Calculations for Multiple Molecules Using an Optimal Measurement Network of Pairwise Differences

Alchemical binding free energy (BFE) calculations offer an efficient and thermodynamically rigorous approach to in silico binding affinity predictions. As a result of decades of methodological improvements and recent advances in computer technology, alchemical BFE calculations are now widely used in drug discovery research. They help guide the prioritization of candidate drug molecules by predicting their binding affinities for a biomolecular target of interest (and potentially selectivity against undesirable antitargets). Statistical variance associated with such calculations, however, may undermine the reliability of their predictions, introducing uncertainty both in ranking candidate molecules and in benchmarking their predictive accuracy. Here, we present a computational method that substantially improves the statistical precision in BFE calculations for a set of ligands binding to a common receptor by dynamically allocating computational resources to different BFE calculations according to an optimality objective established in a previous work from our group and extended in this work. Our method, termed Network Binding Free Energy (NetBFE), performs adaptive BFE calculations in iterations, re-optimizing the allocations in each iteration based on the statistical variances estimated from previous iterations. Using examples of NetBFE calculations for protein binding of congeneric ligand series, we demonstrate that NetBFE approaches the optimal allocation in a small number (≤5) of iterations and that NetBFE reduces the statistical variance in the BFE estimates by approximately a factor of 2 when compared to a previously published and widely used allocation method at the same total computational cost.

Accounting for the Central Role of Interfacial Water in Protein-Ligand Binding Free Energy Calculations.

Rigorous binding free energy methods in drug discovery are growing in popularity because of a combination of methodological advances, improvements in computer hardware, and workflow automation. These calculations typically use molecular dynamics (MD) to sample from the Boltzmann distribution of conformational states. However, when part or all of the binding sites is inaccessible to the bulk solvent, the time needed for water molecules to equilibrate between bulk solvent and the binding site can be well beyond what is practical with standard MD. This sampling limitation is problematic in relative binding free energy calculations, which compute the reversible work of converting ligand 1 to ligand 2 within the binding site. Thus, if ligand 1 is smaller and/or more polar than ligand 2, the perturbation may allow additional water molecules to occupy a region of the binding site. However, this change in hydration may not be captured by standard MD simulations and may therefore lead to errors in the computed free energy. We recently developed a hybrid Monte Carlo/MD (MC/MD) method, which speeds up the equilibration of water between bulk solvent and buried cavities, while sampling from the intended distribution of states. Here, we report on the use of this approach in the context of alchemical binding free energy calculations. We find that using MC/MD markedly improves the accuracy of the calculations and also reduces hysteresis between the forward and reverse perturbations, relative to matched calculations using only MD with or without the crystallographic water molecules. The present method is available for use in AMBER simulation software.

Alchemical Binding Free Energy Calculations in AMBER20: Advances and Best Practices for Drug Discovery.

Predicting protein-ligand binding affinities and the associated thermodynamics of biomolecular recognition is a primary objective of structure-based drug design. Alchemical free energy simulations offer a highly accurate and computationally efficient route to achieving this goal. While the AMBER molecular dynamics package has successfully been used for alchemical free energy simulations in academic research groups for decades, widespread impact in industrial drug discovery settings has been minimal because of the previous limitations within the AMBER alchemical code, coupled with challenges in system setup and postprocessing workflows. Through a close academia-industry collaboration we have addressed many of the previous limitations with an aim to improve accuracy, efficiency, and robustness of alchemical binding free energy simulations in industrial drug discovery applications. Here, we highlight some of the recent advances in AMBER20 with a focus on alchemical binding free energy (BFE) calculations, which are less computationally intensive than alternative binding free energy methods where full binding/unbinding paths are explored. In addition to scientific and technical advances in AMBER20, we also describe the essential practical aspects associated with running relative alchemical BFE calculations, along with recommendations for best practices, highlighting the importance not only of the alchemical simulation code but also the auxiliary functionalities and expertise required to obtain accurate and reliable results. This work is intended to provide a contemporary overview of the scientific, technical, and practical issues associated with running relative BFE simulations in AMBER20, with a focus on real-world drug discovery applications.

Perturbation potentials to overcome order/disorder transitions in alchemical binding free energy calculations.

We investigate the role of order/disorder transitions in alchemical simulations of protein-ligand absolute binding free energies. We show, in the context of a potential of mean force description, that for a benchmarking system (the complex of the L99A mutant of T4 lysozyme with 3-iodotoluene) and for a more challenging system relevant for medicinal applications (the complex of the farnesoid X receptor with inhibitor 26 from a recent D3R challenge) that order/disorder transitions can significantly hamper Hamiltonian replica exchange sampling efficiency and slow down the rate of equilibration of binding free energy estimates. We further show that our analytical model of alchemical binding combined with the formalism developed by Straub et al. for the treatment of order/disorder transitions of molecular systems can be successfully employed to analyze the transitions and help design alchemical schedules and soft-core functions that avoid or reduce the adverse effects of rare binding/unbinding transitions. The results of this work pave the way for the application of these techniques to the alchemical estimation with explicit solvation of hydration free energies and absolute binding free energies of systems undergoing order/disorder transitions.

Analytical Model of the Free Energy of Alchemical Molecular Binding.

We present a parametrized analytic statistical model of the thermodynamics of alchemical molecular binding within the solvent potential of mean force formalism. The model describes the free energy profiles of linear single-decoupling alchemical binding free energy calculations accurately. The parameters of the model, which are physically motivated, are derived by maximum likelihood inference from data obtained from alchemical molecular simulations. The validity of the model has been assessed on a set of host-guest complexes. The model faithfully reproduces both the binding free energy profiles and the probability densities of the perturbation energy as a function of the alchemical progress parameter. The model offers a rationalization for the characteristic shape of binding free energy profiles. The parameters obtained from the model are potentially useful descriptors of the association equilibrium of molecular complexes. Potential applications of the model for the classification of molecular complexes and the design of alchemical molecular simulations are envisioned.

Absolute Binding Free Energies between T4 Lysozyme and 141 Small Molecules: Calculations Based on Multiple Rigid Receptor Configurations.

We demonstrate the feasibility of estimating protein-ligand binding free energies using multiple rigid receptor configurations. On the basis of T4 lysozyme snapshots extracted from six alchemical binding free energy calculations with a flexible receptor, binding free energies were estimated for a total of 141 ligands. For 24 ligands, the calculations reproduced flexible-receptor estimates with a correlation coefficient of 0.90 and a root-mean-square error of 1.59 kcal/mol. The accuracy of calculations based on Poisson-Boltzmann/surface area implicit solvent was comparable to that of previously reported free energy calculations.

Reweighting the Apo to the Holo Ensemble

Molecular dynamics (MD) simulations have become a powerful and popular method for the study of protein allostery, the widespread phenomenon in which a stimulus at one site on a protein influences the properties of another site. Simulations can enable the discovery of allosteric binding sites and elucidate the mechanism of allostery, providing a foundation for applications including rational drug design and protein engineering. However, performing a separate simulation for every ligand can be computationally expensive. Here we demonstrate a proof of principle that conformations sampled from the apo state can be reweighted according to the binding potential of mean force (BPMF) to predict ensemble averages in the holo state. Using BPMFs for the binding of AMP and ADP to adenylate kinase, an enzyme that plays an important role in the process of energy homeostasis, we construct a hinge angle distribution consistent with alchemical binding free energy calculations.

Dissecting the Contribution of Kinase Conformational Reorganization Energies to Inhibitor Selectivity

Kinases are an important target for many cancer therapies. However, they can be difficult to selectively target without hitting one of the other ∼500 kinases in the human genome. Recent experimental and computational evidence suggests that the cost of confining the kinase to the binding-competent conformation could play a large role in determining inhibitor selectivity, specifically in the case of Src and Abl kinase and the ligand imatinib (also known as the paradigm shifting targeted cancer drug ‘Gleevec’). To test this hypothesis on a larger scale, and to dissect the contribution of this reorganization energy to kinase inhibitor affinity and selectivity, we have developed an approach that combines massively distributed molecular simulations with automated experimental biophysical measurements. Atomistic molecular simulations are run on the Folding@home worldwide distributed computing platform to collect ∼ms of simulation data. Markov state models are then constructed of this data to determine the accessible conformations and relative free energies. Alchemical binding free energy calculations are used to assess the ligand binding free energies of selective kinase inhibitors to individual kinetically metastable conformations, and automated biophysical experiments using a novel fluorescence-based assay are used to directly measure binding affinities of kinase inhibitors to a variety of kinases. By analyzing this data together, we believe this work provides a more global picture of the role that kinase conformational reorganization energies play in selectivity, pushing us toward a better understanding of the requirements for selective inhibitor design.

Evaluation of Selected Classical Force Fields for Alchemical Binding Free Energy Calculations of Protein-Carbohydrate Complexes.

Protein-carbohydrate recognition is crucial in many vital biological processes including host-pathogen recognition, cell-signaling, and catalysis. Accordingly, computational prediction of protein-carbohydrate binding free energies is of enormous interest for drug design. However, the accuracy of current force fields (FFs) for predicting binding free energies of protein-carbohydrate complexes is not well understood owing to technical challenges such as the highly polar nature of the complexes, anomerization, and conformational flexibility of carbohydrates. The present study evaluated the performance of alchemical predictions of binding free energies with the GAFF1.7/AM1-BCC and GLYCAM06j force fields for modeling protein-carbohydrate complexes. Mean unsigned errors of 1.1 ± 0.06 (GLYCAM06j) and 2.6 ± 0.08 (GAFF1.7/AM1-BCC) kcal·mol(-1) are achieved for a large data set of monosaccharide ligands for Ralstonia solanacearum lectin (RSL). The level of accuracy provided by GLYCAM06j is sufficient to discriminate potent, moderate, and weak binders, a goal that has been difficult to achieve through other scoring approaches. Accordingly, the protocols presented here could find useful applications in carbohydrate-based drug and vaccine developments.