Relative Binding Free Energy Calculations Research Articles

Impact of protein conformations on binding free energy calculations in the beta-secretase 1 system.

In binding free energy calculations, simulations must sample all relevant conformations of the system in order to obtain unbiased results. For instance, different ligands can bind to different metastable states of a protein, and if these protein conformational changes are not sampled in relative binding free energy calculations, the contribution of these states to binding is not accounted for and thus calculated binding free energies are inaccurate. In this work, we investigate the impact of different beta-sectretase 1 (BACE1) protein conformations obtained from x-ray crystallography on the binding of BACE1 inhibitors. We highlight how these conformational changes are not adequately sampled in typical molecular dynamics simulations. Furthermore, we show that insufficient sampling of relevant conformations induces substantial error in relative binding free energy calculations, as judged by a variation in calculated relative binding free energies up to 2kcal/mol depending on the starting protein conformation. These results emphasize the importance of protein conformational sampling and pose this BACE1 system as a challenge case for further method development in the area of enhanced protein conformational sampling, either in combination with binding calculations or as an endpoint correction.

Development of a Series of Pyrrolopyridone MAT2A Inhibitors.

The optimization of an allosteric fragment, discovered by differential scanning fluorimetry, to an in vivo MAT2a tool inhibitor is discussed. The structure-based drug discovery approach, aided by relative binding free energy calculations, resulted in AZ'9567 (21), a potent inhibitor in vitro with excellent preclinical pharmacokinetic properties. This tool showed a selective antiproliferative effect on methylthioadenosine phosphorylase (MTAP) KO cells, both in vitro and in vivo, providing further evidence to support the utility of MAT2a inhibitors as potential anticancer therapies for MTAP-deficient tumors.

Kartograf: A Geometrically Accurate Atom Mapper for Hybrid-Topology Relative Free Energy Calculations.

Relative binding free energy (RBFE) calculations have emerged as a powerful tool that supports ligand optimization in drug discovery. Despite many successes, the use of RBFEs can often be limited by automation problems, in particular, the setup of such calculations. Atom mapping algorithms are an essential component in setting up automatic large-scale hybrid-topology RBFE calculation campaigns. Traditional algorithms typically employ a 2D subgraph isomorphism solver (SIS) in order to estimate the maximum common substructure. SIS-based approaches can be limited by time-intensive operations and issues with capturing geometry-linked chemical properties, potentially leading to suboptimal solutions. To overcome these limitations, we have developed Kartograf, a geometric-graph-based algorithm that uses primarily the 3D coordinates of atoms to find a mapping between two ligands. In free energy approaches, the ligand conformations are usually derived from docking or other previous modeling approaches, giving the coordinates a certain importance. By considering the spatial relationships between atoms related to the molecule coordinates, our algorithm bypasses the computationally complex subgraph matching of SIS-based approaches and reduces the problem to a much simpler bipartite graph matching problem. Moreover, Kartograf effectively circumvents typical mapping issues induced by molecule symmetry and stereoisomerism, making it a more robust approach for atom mapping from a geometric perspective. To validate our method, we calculated mappings with our novel approach using a diverse set of small molecules and used the mappings in relative hydration and binding free energy calculations. The comparison with two SIS-based algorithms showed that Kartograf offers a fast alternative approach. The code for Kartograf is freely available on GitHub (https://github.com/OpenFreeEnergy/kartograf). While developed for the OpenFE ecosystem, Kartograf can also be utilized as a standalone Python package.

Development and Comprehensive Benchmark of a High-Quality AMBER-Consistent Small Molecule Force Field with Broad Chemical Space Coverage for Molecular Modeling and Free Energy Calculation.

Biomolecular simulations have become an essential tool in contemporary drug discovery, and molecular mechanics force fields (FFs) constitute its cornerstone. Developing a high quality and broad coverage general FF is a significant undertaking that requires substantial expert knowledge and computing resources, which is beyond the scope of general practitioners. Existing FFs originate from only a limited number of groups and organizations, and they either suffer from limited numbers of training sets, lower than desired quality because of oversimplified representations, or are costly for the molecular modeling community to access. To address these issues, in this work, we developed an AMBER-consistent small molecule FF with extensive chemical space coverage, and we provide Open Access parameters for the entire modeling community. To validate our FF, we carried out benchmarks of quantum mechanics (QM)/molecular mechanics conformer comparison and free energy perturbation calculations on several benchmark data sets. Our FF achieves a higher level of performance at reproducing QM energies and geometries than two popular open-source FFs, OpenFF2 and GAFF2. In relative binding free energy calculations for 31 protein-ligand data sets, comprising 1079 pairs of ligands, the new FF achieves an overall root-mean-square error of 1.19 kcal/mol for ΔΔG and 0.92 kcal/mol for ΔG on a subset of 463 ligands without bespoke fitting to the data sets. The results are on par with those of the leading commercial series of OPLS FFs.

Binding of Cholesterol to the N-Terminal Domain of the NPC1L1 Transporter: Analysis of the Epimerization-Related Binding Selectivity and Loop Mutations.

Cholesterol is a fat-like substance with a pivotal physiological relevance in humans, and its homeostasis is tightly regulated by various cellular processes, including the import in the small intestine and the reabsorption in the biliary ducts by the Niemann-Pick C1 Like 1 (NPC1L1) importer. NPC1L1 can mediate the absorption of a variety of sterols but strikingly exhibits a large sensitivity to cholesterol epimerization. This study examines the molecular basis of the epimerization-related selective binding of cholesterol by combining extended unbiased molecular dynamics simulations of the apo and holo species of the N-terminal domain of wild-type NPC1L1, in conjunction with relative binding free energy, umbrella sampling, and well-tempered metadynamics calculations. The analysis of the results discloses the existence of two distinct binding modes for cholesterol and epi-cholesterol. The former binds deeper in the cavity, forming key hydrogen-bond interactions with Q95, S56, and a water molecule. In contrast, epi-cholesterol is shifted ca. 3 Å to the mouth of the cavity and the transition to the Q95 site is prevented by an energetic barrier of 4.1 kcal·mol-1. Thus, the configuration of the hydroxyl group of cholesterol, together with the presence of a structural water molecule, is a key feature for effective absorption. Finally, whereas these findings may seemingly be challenged by single-point mutations that impair cholesterol transport but have a mild impact on the binding of cholesterol to the Q95 binding site, our results reveal that they have a drastic influence on the conformational landscape of the α8/β7 loop in the apo species compared to the wild-type protein. Overall, the results give support to the functional role played by the α8/β7 loop in regulating the access of ligands to NPC1L1, and hence to interpreting the impact of these mutations on diseases related to disruption of sterol absorption, paving the way to understanding certain physiological dysfunctions.

Fast free energy estimates from λ-dynamics with bias-updated Gibbs sampling

Relative binding free energy calculations have become an integral computational tool for lead optimization in structure-based drug design. Classical alchemical methods, including free energy perturbation or thermodynamic integration, compute relative free energy differences by transforming one molecule into another. However, these methods have high operational costs due to the need to perform many pairwise perturbations independently. To reduce costs and accelerate molecular design workflows, we present a method called λ-dynamics with bias-updated Gibbs sampling. This method uses dynamic biases to continuously sample between multiple ligand analogues collectively within a single simulation. We show that many relative binding free energies can be determined quickly with this approach without compromising accuracy. For five benchmark systems, agreement to experiment is high, with root mean square errors near or below 1.0 kcal mol−1. Free energy results are consistent with other computational approaches and within statistical noise of both methods (0.4 kcal mol−1 or less). Notably, large efficiency gains over thermodynamic integration of 18–66-fold for small perturbations and 100–200-fold for whole aromatic ring substitutions are observed. The rapid determination of relative binding free energies will enable larger chemical spaces to be more readily explored and structure-based drug design to be accelerated.

Identification of potential inhibitors targeting Ebola virus VP35 protein: a computational strategy

Ebola virus (EBOV) poses a severe threat as a highly infectious pathogen, causing devastating hemorrhagic fever in both humans and animals. The EBOV virus VP35 protein plays a crucial role in viral replication and exhibits the ability to suppress the host interferon cascade, leading to immune system depletion. As a potential drug target, VP35 protein inhibition holds promise for combating EBOV. To discover new drug candidates, we employed a computer-aided drug design approach, focusing on compounds capable of inhibiting VP35 protein replication. In this connection, a pharmacophore model was generated using molecular interactions between the VP35 protein and its inhibitor. ZINC and Cambridge database were screened using validated pharmacophore model. Further the compounds were filtered based on Lipinski’s rule of five and subjected to MD simulation and relative binding free energy calculation. Six compounds manifest a significant docking score and strong binding interaction towards VP35 protein. MD simulations further confirmed the remarkable stability of these six complexes. Relative binding free energy calculations also showed significant ΔG value in the range of −132.3 and −49.3 kcal/mol. This study paves the way for further optimization of these compounds as potential inhibitors of VP35, facilitating subsequent experimental in vitro studies. Communicated by Ramaswamy H. Sarma

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.

Broadening the Scope of Binding Free Energy Calculations Using a Separated Topologies Approach.

Binding free energy calculations predict the potency of compounds to protein binding sites in a physically rigorous manner and see broad application in prioritizing the synthesis of novel drug candidates. Relative binding free energy (RBFE) calculations have emerged as an industry-standard approach to achieve highly accurate rank-order predictions of the potency of related compounds; however, this approach requires that the ligands share a common scaffold and a common binding mode, restricting the methods' domain of applicability. This is a critical limitation since complex modifications to the ligands, especially core hopping, are very common in drug design. Absolute binding free energy (ABFE) calculations are an alternate method that can be used for ligands that are not congeneric. However, ABFE suffers from a known problem of long convergence times due to the need to sample additional degrees of freedom within each system, such as sampling rearrangements necessary to open and close the binding site. Here, we report on an alternative method for RBFE, called Separated Topologies (SepTop), which overcomes the issues in both of the aforementioned methods by enabling large scaffold changes between ligands with a convergence time comparable to traditional RBFE. Instead of only mutating atoms that vary between two ligands, this approach performs two absolute free energy calculations at the same time in opposite directions, one for each ligand. Defining the two ligands independently allows the comparison of the binding of diverse ligands without the artificial constraints of identical poses or a suitable atom-atom mapping. This approach also avoids the need to sample the unbound state of the protein, making it more efficient than absolute binding free energy calculations. Here, we introduce an implementation of SepTop. We developed a general and efficient protocol for running SepTop, and we demonstrated the method on four diverse, pharmaceutically relevant systems. We report the performance of the method, as well as our practical insights into the strengths, weaknesses, and challenges of applying this method in an industrial drug design setting. We find that the accuracy of the approach is sufficiently high to rank order ligands with an accuracy comparable to traditional RBFE calculations while maintaining the additional flexibility of SepTop.

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.

Study of SQ109 analogs binding to mycobacterium MmpL3 transporter using MD simulations and alchemical relative binding free energy calculations

N-geranyl-N΄-(2-adamantyl)ethane-1,2-diamine (SQ109) is a tuberculosis drug that has high potency against Mycobacterium tuberculosis (Mtb) and may function by blocking cell wall biosynthesis. After the crystal structure of MmpL3 from Mycobacterium smegmatis in complex with SQ109 became available, it was suggested that SQ109 inhibits Mmpl3 mycolic acid transporter. Here, we showed using molecular dynamics (MD) simulations that the binding profile of nine SQ109 analogs with inhibitory potency against Mtb and alkyl or aryl adducts at C-2 or C-1 adamantyl carbon to MmpL3 was consistent with the X-ray structure of MmpL3 – SQ109 complex. We showed that rotation of SQ109 around carbon–carbon bond in the monoprotonated ethylenediamine unit favors two gauche conformations as minima in water and lipophilic solvent using DFT calculations as well as inside the transporter’s binding area using MD simulations. The binding assays in micelles suggested that the binding affinity of the SQ109 analogs was increased for the larger, more hydrophobic adducts, which was consistent with our results from MD simulations of the SQ109 analogues suggesting that sizeable C-2 adamantyl adducts of SQ109 can fill a lipophilic region between Y257, Y646, F260 and F649 in MmpL3. This was confirmed quantitatively by our calculations of the relative binding free energies using the thermodynamic integration coupled with MD simulations method with a mean assigned error of 0.74 kcal mol−1 compared to the experimental values.Graphical abstract

Automated relative binding free energy calculations from SMILES to ΔΔG

In drug discovery, computational methods are a key part of making informed design decisions and prioritising experiments. In particular, optimizing compound affinity is a central concern during the early stages of development. In the last 10 years, alchemical free energy (FE) calculations have transformed our ability to incorporate accurate in silico potency predictions in design decisions, and represent the ‘gold standard’ for augmenting experiment-driven drug discovery. However, relative FE calculations are complex to set up, require significant expert intervention to prepare the calculation and analyse the results or are provided only as closed-source software, not allowing for fine-grained control over the underlying settings. In this work, we introduce an end-to-end relative FE workflow based on the non-equilibrium switching approach that facilitates calculation of binding free energies starting from SMILES strings. The workflow is implemented using fully modular steps, allowing various components to be exchanged depending on licence availability. We further investigate the dependence of the calculated free energy accuracy on the initial ligand pose generated by various docking algorithms. We show that both commercial and open-source docking engines can be used to generate poses that lead to good correlation of free energies with experimental reference data.

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.

TIES 2.0: A Dual-Topology Open Source Relative Binding Free Energy Builder with Web Portal

Relative binding free energy (RBFE) calculations are widely used to aid the process of drug discovery. TIES, Thermodynamic Integration with Enhanced Sampling, is a dual-topology approach to RBFE calculations with support for NAMD and OpenMM molecular dynamics engines. The software has been thoroughly validated on publicly available datasets. Here we describe the open source software along with a web portal (https://ccs-ties.org) that enables users to perform such calculations correctly and rapidly.

Anesthesia, Coming of Age in the World of Modern In Silico Drug Design.

Anesthesia, Coming of Age in the World of Modern In Silico Drug Design.

An Open Source Graph-Based Weighted Cycle Closure Method for Relative Binding Free Energy Calculations.

Free energy perturbation-relative binding free energy (FEP-RBFE) prediction has shown its reliability and accuracy in the prediction of protein-ligand binding affinities, which plays a fundamental role in structure-based drug design. In FEP-RBFE predictions, the calculation of each mutation path is associated with a statistical error, and cycle closure (cc) has proven to be an effective method in improving the calculation accuracy by correcting the hysteresis (summation of errors) of each closed cycle to the theoretical value 0. However, a primary hypothesis was made in the current cycle closure method that the hysteresis is evenly distributed to all paths, which is unlikely to be true in practice and may limit the further improvement of the calculation accuracy when better error estimation methods are available. Moreover, being a closed source software makes the current cycle closure method unachievable in many studies. In this paper, a newly implemented open source graph-based weighted cycle closure (wcc) algorithm was developed and introduced, not only including functions from the original cc method but also containing a new wcc method which can consider different error contributions from different paths and further improve the calculation accuracy. The wcc program also provides a new path-independent molecular error calculation method, which can be quite useful in many studies (like structure-activity relationship (SAR)) compared with the path-dependent method of the original cc program.

Optimizing active learning for free energy calculations

While Relative Binding Free Energy (RBFE) calculations have become a mainstay in lead optimization programs, the computational expense of performing these calculations has limited their broader application. Active learning (AL), a machine learning method used to direct a search iteratively, has explored larger chemical libraries using RBFE calculations. While AL has been successfully applied, there has not been a systematic study of the impact of parameter settings on the performance of AL. To address this gap, we have generated an exhaustive dataset of RBFE calculations on 10,000 congeneric molecules. We used this dataset to explore the impact of several AL design choices, including the number of molecules sampled at each iteration, the method used to select an initial sample, the method used to build a machine learning model, and the acquisition function that defines the balance between exploration and exploitation in the search. Our studies demonstrated that the performance of AL is largely insensitive to the specific machine learning method and acquisition functions used. In our studies, the most significant factor impacting performance was the number of molecules sampled at each iteration where selecting too few molecules hurts performance. Under the best conditions, we were able to identify 75% of the 100 top scoring molecules by sampling only 6% of the dataset. We hope that the dataset of 10K molecules will provide the basis for future studies exploring additional AL strategies. The source code and supporting data for the work are available at https://github.com/google-research/google-research/tree/master/al_for_fep.

AMBER Drug Discovery Boost Tools: Automated Workflow for Production Free-Energy Simulation Setup and Analysis (ProFESSA).

We report an automated workflow for production free-energy simulation setup and analysis (ProFESSA) using the GPU-accelerated AMBER free-energy engine with enhanced sampling features and analysis tools, part of the AMBER Drug Discovery Boost package that has been integrated into the AMBER22 release. The workflow establishes a flexible, end-to-end pipeline for performing alchemical free-energy simulations that brings to bear technologies, including new enhanced sampling features and analysis tools, to practical drug discovery problems. ProFESSA provides the user with top-level control of large sets of free-energy calculations and offers access to the following key functionalities: (1) automated setup of file infrastructure; (2) enhanced conformational and alchemical sampling with the ACES method; and (3) network-wide free-energy analysis with the optional imposition of cycle closure and experimental constraints. The workflow is applied to perform absolute and relative solvation free-energy and relative ligand-protein binding free-energy calculations using different atom-mapping procedures. Results demonstrate that the workflow is internally consistent and highly robust. Further, the application of a new network-wide Lagrange multiplier constraint analysis that imposes key experimental constraints substantially improves binding free-energy predictions.

Relative binding free energy calculations with transformato: A molecular dynamics engine-independent tool.

We present the software package transformato for the setup of large-scale relative binding free energy calculations. Transformato is written in Python as an open source project (https://github.com/wiederm/transformato); in contrast to comparable tools, it is not closely tied to a particular molecular dynamics engine to carry out the underlying simulations. Instead of alchemically transforming a ligand L 1 directly into another L 2, the two ligands are mutated to a common core. Thus, while dummy atoms are required at intermediate states, in particular at the common core state, none are present at the physical endstates. To validate the method, we calculated 76 relative binding free energy differences for five protein–ligand systems. The overall root mean squared error to experimental binding free energies is 1.17 kcal/mol with a Pearson correlation coefficient of 0.73. For selected cases, we checked that the relative binding free energy differences between pairs of ligands do not depend on the choice of the intermediate common core structure. Additionally, we report results with and without hydrogen mass reweighting. The code currently supports OpenMM, CHARMM, and CHARMM/OpenMM directly. Since the program logic to choose and construct alchemical transformation paths is separated from the generation of input and topology/parameter files, extending transformato to support additional molecular dynamics engines is straightforward.

Predicting antibiotic resistance in complex protein targets using alchemical free energy methods.

Drug resistant Mycobacterium tuberculosis, which mostly results from single nucleotide polymorphisms in antibiotic target genes, poses a major threat to tuberculosis treatment outcomes. Relative binding free energy (RBFE) calculations can rapidly predict the effects of mutations, but this approach has not been tested on large, complex proteins. We use RBFE calculations to predict the effects of M. tuberculosis RNA polymerase and DNA gyrase mutations on rifampicin and moxifloxacin susceptibility respectively. These mutations encompass a range of amino acid substitutions with known effects and include large steric perturbations and charged moieties. We find that moderate numbers (n = 3–15) of short RBFE calculations can predict resistance in cases where the mutation results in a large change in the binding free energy. We show that the method lacks discrimination in cases with either a small change in energy or that involve charged amino acids, and we investigate how these calculation errors may be decreased.