Overcoming dissipation in the calculation of standard binding free energies by ligand extraction

The SAMPL9 host-guest blind challenge: an overview of binding free energy predictive accuracy

We report the results of the SAMPL9 host-guest blind challenge for predicting binding free energies. The challenge focused on macrocycles from pillar[n]-arene and cyclodextrin host families, including WP6, and bCD and HbCD. A variety of methods were used by participants to submit binding free energy predictions. A machine learning approach based on molecular descriptors achieved the highest accuracy (RMSE of 2.04 kcal mol-1) among the ranked methods in the WP6 dataset. Interestingly, predictions for WP6 obtained via docking tended to outperform all methods (RMSE of 1.70 kcal mol-1), most of which are MD based and computationally more expensive. In general, methods applying force fields achieved better correlation with experiments for WP6 opposed to the machine learning and docking models. In the cyclodextrin-phenothiazine challenge, the ATM approach emerged as the top performing method with RMSE less than 1.86 kcal mol-1. Correlation metrics of ranked methods in this dataset were relatively poor compared to WP6. We also highlight several lessons learned to guide future work and help improve studies on the systems discussed. For example, WP6 may be present in other microstates other than its -12 state in the presence of certain guests. Machine learning approaches can be used to fine tune or help train force fields for certain chemistry (i.e. WP6-G4). Certain phenothiazines occupy distinct primary and secondary orientations, some of which were considered individually for accurate binding free energies. The accuracy of predictions from certain methods while starting from a single binding pose/orientation demonstrates the sensitivity of calculated binding free energies to the orientation, and in some cases the likely dominant orientation for the system. Computational and experimental results suggest that guest phenothiazine core traverses both the secondary and primary faces of the cyclodextrin hosts, a bulky cationic side chain will primarily occupy the primary face, and the phenothiazine core substituent resides at the larger secondary face.

Tuning Potential Functions to Host-Guest Binding Data

Software to more rapidly and accurately predict protein-ligand binding affinities is of high interest for early-stage drug discovery, and physics-based methods are among the most widely used technologies for this purpose. The accuracy of these methods depends critically on the accuracy of the potential functions that they use. Potential functions are typically trained against a combination of quantum chemical and experimental data. However, although binding affinities are among the most important quantities to predict, experimental binding affinities have not to date been integrated into the experimental data set used to train potential functions. In recent years, the use of host-guest complexes as simple and tractable models of binding thermodynamics has gained popularity due to their small size and simplicity, relative to protein-ligand systems. Host-guest complexes can also avoid ambiguities that arise in protein-ligand systems such as uncertain protonation states. Thus, experimental host-guest binding data are an appealing additional data type to integrate into the experimental data set used to optimize potential functions. Here, we report the extension of the Open Force Field Evaluator framework to enable the systematic calculation of host-guest binding free energies and their gradients with respect to force field parameters, coupled with the curation of 126 host-guest complexes with available experimental binding free energies. As an initial application of this novel infrastructure, we optimized generalized Born (GB) cavity radii for the OBC2 GB implicit solvent model against experimental data for 36 host-guest systems. This refitting led to a dramatic improvement in accuracy for both the training set and a separate test set with 90 additional host-guest systems. The optimized radii also showed encouraging transferability from host-guest systems to 59 protein-ligand systems. However, the new radii are significantly smaller than the baseline radii and lead to excessively favorable hydration free energies (HFEs). Thus, users of the OBC2 GB model currently may choose between GB cavity radii that yield more accurate binding affinities and GB cavity radii that yield more accurate HFEs. We suspect that achieving good accuracy on both will require more far-reaching adjustments to the GB model. We note that binding free-energy calculations using the OBC2 model in OpenMM gain about a 10× speedup relative to corresponding explicit solvent calculations, suggesting a future role for implicit solvent absolute binding free-energy (ABFE) calculations in virtual compound screening. This study proves the principle of using host-guest systems to train potential functions that are transferrable to protein-ligand systems and provides an infrastructure that enables a range of applications.

Performance and Analysis of the Alchemical Transfer Method for Binding-Free-Energy Predictions of Diverse Ligands

The Alchemical Transfer Method (ATM) is herein validated against the relative binding-free energies (RBFEs) of a diverse set of protein-ligand complexes. We employed a streamlined setup workflow, a bespoke force field, and AToM-OpenMM software to compute the RBFEs of the benchmark set prepared by Schindler and collaborators at Merck KGaA. This benchmark set includes examples of standard small R-group ligand modifications as well as more challenging scenarios, such as large R-group changes, scaffold hopping, formal charge changes, and charge-shifting transformations. The novel coordinate perturbation scheme and a dual-topology approach of ATM address some of the challenges of single-topology alchemical RBFE methods. Specifically, ATM eliminates the need for splitting electrostatic and Lennard-Jones interactions, atom mapping, defining ligand regions, and postcorrections for charge-changing perturbations. Thus, ATM is simpler and more broadly applicable than conventional alchemical methods, especially for scaffold-hopping and charge-changing transformations. Here, we performed well over 500 RBFE calculations for eight protein targets and found that ATM achieves accuracy comparable to that of existing state-of-the-art methods, albeit with larger statistical fluctuations. We discuss insights into the specific strengths and weaknesses of the ATM method that will inform future deployments. This study confirms that ATM can be applied as a production tool for RBFE predictions across a wide range of perturbation types within a unified, open-source framework.

Standard Binding Free-Energy Calculations: How Far Are We from Automation?

Recent success stories suggest that in silico protein-ligand binding free-energy calculations are approaching chemical accuracy. However, their widespread application remains limited by the extensive human intervention required, posing challenges for the neophyte. As such, it is critical to develop automated workflows for estimating protein-ligand binding affinities with minimum personal involvement. Key human efforts include setting up and tuning enhanced-sampling or alchemical-transformation algorithms as a preamble to computational binding free-energy estimations. Additionally, preparing input files, bookkeeping, and postprocessing represent nontrivial tasks. In this Perspective, we discuss recent progress in automating standard binding free-energy calculations, featuring the development of adaptive or parameter-free algorithms, standardization of binding free-energy calculation workflows, and the implementation of user-friendly software. We also assess the current state of automated standard binding free-energy calculations and evaluate the limitations of existing methods. Last, we outline the requirements for future algorithms and workflows to facilitate automated free-energy calculations for diverse protein-ligand complexes.

Interplay of structure and photophysics of individualized rod-shaped graphene quantum dots with up to 132 sp² carbon atoms

Nanographene materials are promising building blocks for the growing field of low-dimensional materials for optics, electronics and biophotonics applications. In particular, bottom-up synthesized 0D graphene quantum dots show great potential as single quantum emitters. To fully exploit their exciting properties, the graphene quantum dots must be of high purity; the key parameter for efficient purification being the solubility of the starting materials. Here, we report the synthesis of a family of highly soluble and easily processable rod-shaped graphene quantum dots with fluorescence quantum yields up to 94%. This is uncommon for a red emission. The high solubility is directly related to the design of the structure, allowing for an accurate description of the photophysical properties of the graphene quantum dots both in solution and at the single molecule level. These photophysical properties were fully predicted by quantum-chemical calculations.

Capturing the Recognition Dynamics of para-Sulfonato-calix[4]arenes by Cytochrome c: Toward a Quantitative Free Energy Assessment

Calix[n]arenes' selective recognition of protein surfaces covers a broad range of timely applications, from controlling protein assembly and crystallization to trapping partially disordered proteins. Here, the interaction of para-sulfonated calix-[4]-arenes with cytochrome c is investigated through all-atom, explicit water molecular dynamics simulations which allow characterization of two binding sites in quantitative agreement with experimental evidence. Free energy calculations based on the MM-PBSA and the attach-pull-release (APR) methods highlight key residues implicated in the recognition process and provide binding free energy results in quantitative agreement with isothermal titration calorimetry. Our study emphasizes the role of MD simulations to capture and describe the "walk" of sulfonated calix-[4]-arenes on the cytochrome c surface, with the arginine R13 as a pivotal interacting residue. Our MD investigation allows, through the quasi-harmonic multibasin (QHMB) method, probing an allosteric reinforcement of several per-residue interactions upon calixarene binding, which suggests a more complex mode of action of these supramolecular auxiliaries.

Adsorption of rhodamine 6G and choline on gold electrodes: a molecular dynamics study

The adsorption of analyte molecules on nano-optoelectrodes (e.g. a combined nanoantenna and nanoelectrode device) significantly affects the signal characteristics in surface-enhanced Raman scattering (SERS) measurements. Understanding how different molecules adsorb on electrodes and their electrical potential modulation helps interpret SERS measurements better. We use molecular dynamics simulations to investigate the adsorption of prototypical analyte molecules (rhodamine 6G and choline) on gold electrodes with negative, neutral, and positive surface charges. We show that both molecules can readily adsorb on gold surfaces at all surface charge densities studied. Nevertheless, the configurations of the adsorbed molecules can differ for different surface charge densities, and adsorption can also change a molecule's conformation. Rhodamine 6G molecules adsorb more strongly than choline molecules, and the adsorption of both molecules is affected by electrode charge in 0.25 M NaCl solutions. The mechanisms of these observations are elucidated, and their implications for voltage-modulated SERS measurements are discussed.

An overview of the SAMPL8 host-guest binding challenge

The SAMPL series of challenges aim to focus the community on specific modeling challenges, while testing and hopefully driving progress of computational methods to help guide pharmaceutical drug discovery. In this study, we report on the results of the SAMPL8 host–guest blind challenge for predicting absolute binding affinities. SAMPL8 focused on two host–guest datasets, one involving the cucurbituril CB8 (with a series of common drugs of abuse) and another involving two different Gibb deep-cavity cavitands. The latter dataset involved a previously featured deep cavity cavitand (TEMOA) as well as a new variant (TEETOA), both binding to a series of relatively rigid fragment-like guests. Challenge participants employed a reasonably wide variety of methods, though many of these were based on molecular simulations, and predictive accuracy was mixed. As in some previous SAMPL iterations (SAMPL6 and SAMPL7), we found that one approach to achieve greater accuracy was to apply empirical corrections to the binding free energy predictions, taking advantage of prior data on binding to these hosts. Another approach which performed well was a hybrid MD-based approach with reweighting to a force matched QM potential. In the cavitand challenge, an alchemical method using the AMOEBA-polarizable force field achieved the best success with RMSE less than 1 kcal/mol, while another alchemical approach (ATM/GAFF2-AM1BCC/TIP3P/HREM) had RMSE less than 1.75 kcal/mol. The work discussed here also highlights several important lessons; for example, retrospective studies of reference calculations demonstrate the sensitivity of predicted binding free energies to ethyl group sampling and/or guest starting pose, providing guidance to help improve future studies on these systems.

Absolute binding free energy calculations improve enrichment of actives in virtual compound screening

We determined the effectiveness of absolute binding free energy (ABFE) calculations to refine the selection of active compounds in virtual compound screening, a setting where the more commonly used relative binding free energy approach is not readily applicable. To do this, we conducted baseline docking calculations of structurally diverse compounds in the DUD-E database for three targets, BACE1, CDK2 and thrombin, followed by ABFE calculations for compounds with high docking scores. The docking calculations alone achieved solid enrichment of active compounds over decoys. Encouragingly, the ABFE calculations then improved on this baseline. Analysis of the results emphasizes the importance of establishing high quality ligand poses as starting points for ABFE calculations, a nontrivial goal when processing a library of diverse compounds without informative co-crystal structures. Overall, our results suggest that ABFE calculations can play a valuable role in the drug discovery process.

Drug Discovery by Automated Adaptation of Chemical Structure and Identity

Computer-aided drug design offers the potential to dramatically reduce the cost and effort required for drug discovery. While screening-based methods are valuable in the early stages of hit identification, they are frequently succeeded by iterative, hypothesis-driven computations that require recurrent investment of human time and intuition. To increase automation, we introduce a computational method for lead refinement that combines concerted dynamics of the ligand/protein complex via molecular dynamics simulations with integrated Monte Carlo-based changes in the chemical formula of the ligand. This approach, which we refer to as ligand-exchange Monte Carlo molecular dynamics, accounts for solvent- and entropy-based contributions to competitive binding free energies by coupling the energetics of bound and unbound states during the ligand-exchange attempt. Quantitative comparison of relative binding free energies to reference values from free energy perturbation, conducted in vacuum, indicates that ligand-exchange Monte Carlo molecular dynamics simulations sample relevant conformational ensembles and are capable of identifying strongly binding compounds. Additional simulations demonstrate the use of an implicit solvent model. We speculate that the use of chemical graphs in which exchanges are only permitted between ligands with sufficient similarity may enable an automated search to capture some of the benefits provided by human intuition during hypothesis-guided lead refinement.

Molecular Modeling of ABHD5 Structure and Ligand Recognition

Alpha/beta hydrolase domain-containing 5 (ABHD5), also termed CGI-58, is the key upstream activator of adipose triglyceride lipase (ATGL), which plays an essential role in lipid metabolism and energy storage. Mutations in ABHD5 disrupt lipolysis and are known to cause the Chanarin-Dorfman syndrome. Despite its importance, the structure of ABHD5 remains unknown. In this work, we combine computational and experimental methods to build a 3D structure of ABHD5. Multiple comparative and machine learning-based homology modeling methods are used to obtain possible models of ABHD5. The results from Gaussian accelerated molecular dynamics and experimental data of the apo models and their mutants are used to select the most likely model. Moreover, ensemble docking is performed on representative conformations of ABHD5 to reveal the binding mechanism of ABHD5 and a series of synthetic ligands. Our study suggests that the ABHD5 models created by deep learning-based methods are the best candidate structures for the ABHD5 protein. The mutations of E41, R116, and G328 disturb the hydrogen bonding network with nearby residues and suppress membrane targeting or ATGL activation. The simulations also reveal that the hydrophobic interactions are responsible for binding sulfonyl piperazine ligands to ABHD5. Our work provides fundamental insight into the structure of ABHD5 and its ligand-binding mode, which can be further applied to develop ABHD5 as a therapeutic target for metabolic disease and cancer.

Computational Modeling of Supramolecular Metallo-organic Cages-Challenges and Opportunities

Self-assembled metallo-organic cages have emerged as promising biomimetic platforms that can encapsulate whole substrates akin to an enzyme active site. Extensive experimental work has enabled access to a variety of structures, with a few notable examples showing catalytic behavior. However, computational investigations of metallo-organic cages are scarce, not least due to the challenges associated with their modeling and the lack of accurate and efficient protocols to evaluate these systems. In this review, we discuss key molecular principles governing the design of functional metallo-organic cages, from the assembly of building blocks through binding and catalysis. For each of these processes, computational protocols will be reviewed, considering their inherent strengths and weaknesses. We will demonstrate that while each approach may have its own specific pitfalls, they can be a powerful tool for rationalizing experimental observables and to guide synthetic efforts. To illustrate this point, we present several examples where modeling has helped to elucidate fundamental principles behind molecular recognition and reactivity. We highlight the importance of combining computational and experimental efforts to speed up supramolecular catalyst design while reducing time and resources.

Accurate determination of protein:ligand standard binding free energies from molecular dynamics simulations

Designing a reliable computational methodology to calculate protein:ligand standard binding free energies is extremely challenging. The large change in configurational enthalpy and entropy that accompanies the association of ligand and protein is notoriously difficult to capture in naive brute-force simulations. Addressing this issue, the present protocol rests upon a rigorous statistical mechanical framework for the determination of protein:ligand binding affinities together with the comprehensive Binding Free-Energy Estimator 2 (BFEE2) application software. With the knowledge of the bound state, available from experiments or docking, application of the BFEE2 protocol with a reliable force field supplies in a matter of days standard binding free energies within chemical accuracy, for a broad range of protein:ligand complexes. Limiting undesirable human intervention, BFEE2 assists the end user in preparing all the necessary input files and performing the post-treatment of the simulations towards the final estimate of the binding affinity.

Relative Binding Free Energy Calculations for Ligands with Diverse Scaffolds with the Alchemical Transfer Method

We present an extension of the alchemical transfer method (ATM) for the estimation of relative binding free energies of molecular complexes applicable to conventional, as well as scaffold-hopping, alchemical transformations. Named ATM-RBFE, the method is implemented in the free and open-source OpenMM molecular simulation package and aims to provide a simpler and more generally applicable route to the calculation of relative binding free energies than what is currently available. ATM-RBFE is based on sound statistical mechanics theory and a novel coordinate perturbation scheme designed to swap the positions of a pair of ligands such that one is transferred from the bulk solvent to the receptor binding site while the other moves simultaneously in the opposite direction. The calculation is conducted directly in a single solvent box with a system prepared with conventional setup tools, without splitting of electrostatic and nonelectrostatic transformations, and without pairwise soft-core potentials. ATM-RBFE is validated here against the absolute binding free energies of the SAMPL8 GDCC host-guest benchmark set and against protein-ligand benchmark sets that include complexes of the estrogen receptor ERα and those of the methyltransferase EZH2. In each case the method yields self-consistent and converged relative binding free energy estimates in agreement with absolute binding free energies and reference literature values, as well as experimental measurements.

Modeling Kinetics and Thermodynamics of Guest Encapsulation into the [M4L6]12- Supramolecular Organometallic Cage

The encapsulation of molecular guests into supramolecular hosts is a complex molecular recognition process in which the guest displaces the solvent from the host cavity, while the host deforms to let the guest in. An atomistic description of the association would provide valuable insights on the physicochemical properties that guide it. This understanding may be used to design novel host assemblies with improved properties (i.e., affinities) toward a given class of guests. Molecular simulations may be conveniently used to model the association processes. It is thus of interest to establish efficient protocols to trace the encapsulation process and to predict the associated magnitudes ΔG_bind and ΔG_bind^⧧. Here, we report the calculation of the Gibbs energy barrier and Gibbs binding energy by means of explicit solvent molecular simulations for the [Ga₄L₆]^12– metallocage encapsulating a series of cationic molecules. The ΔG_bind^⧧ for encapsulation was estimated by means of umbrella sampling simulations. The steps involved were identified, including ion-pair formation and naphthalene rotation (from L ligands of the metallocage) during the guest’s entrance. The ΔG_bind values were computed using the attach–pull–release method. The results reveal the sensitivity of the estimates on the force field parameters, in particular on atomic charges, showing that higher accuracy is obtained when charges are derived from implicit solvent quantum chemical calculations. Correlation analysis identified some indicators for the binding affinity trends. All computed magnitudes are in very good agreement with experimental observations. This work provides, on one side, a benchmarked way to computationally model a highly charged metallocage encapsulation process. This includes a nonstandard parameterization and charge derivation procedure. On the other hand, it gives specific mechanistic information on the binding processes of [Ga₄L₆]^12– at the molecular level where key motions are depicted. Taken together, the study provides an interesting option for the future design of metal–organic cages.

Alchemical Transfer Approach to Absolute Binding Free Energy Estimation

The alchemical transfer method (ATM) for the calculation of standard binding free energies of noncovalent molecular complexes is presented. The method is based on a coordinate displacement perturbation of the ligand between the receptor binding site and the explicit solvent bulk and a thermodynamic cycle connected by a symmetric intermediate in which the ligand interacts with the receptor and solvent environments with equal strength. While the approach is alchemical, the implementation of the ATM is as straightforward as that for physical pathway methods of binding. The method is applicable, in principle, with any force field, as it does not require splitting the alchemical transformations into electrostatic and nonelectrostatic steps, and it does not require soft-core pair potentials. We have implemented the ATM as a freely available and open-source plugin of the OpenMM molecular dynamics library. The method and its implementation are validated on the SAMPL6 SAMPLing host-guest benchmark set. The work paves the way to streamlined alchemical relative and absolute binding free energy implementations on many molecular simulation packages and with arbitrary energy functions including polarizable, quantum-mechanical, and artificial neural network potentials.

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.

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.

Ligand binding free-energy calculations with funnel metadynamics

The accurate resolution of the binding mechanism of a ligand to its molecular target is fundamental to develop a successful drug design campaign. Free-energy calculations, which provide the energy value of the ligand-protein binding complex, are essential for resolving the binding mode of the ligand. The accuracy of free-energy calculation methods is counteracted by their poor user-friendliness, which hampers their broad application. Here we present the Funnel-Metadynamics Advanced Protocol (FMAP), which is a flexible and user-friendly graphical user interface (GUI)-based protocol to perform funnel metadynamics, a binding free-energy method that employs a funnel-shape restraint potential to reveal the ligand binding mode and accurately calculate the absolute ligand-protein binding free energy. FMAP guides the user through all phases of the free-energy calculation process, from preparation of the input files, to production simulation, to analysis of the results. FMAP delivers the ligand binding mode and the absolute protein-ligand binding free energy as outputs. Alternative binding modes and the role of waters are also elucidated, providing a detailed description of the ligand binding mechanism. The entire protocol on the paradigmatic system benzamidine-trypsin, composed of ~105 k atoms, took ~2.8 d using the Cray XC50 piz Daint cluster at the Swiss National Supercomputing Centre.

On Restraints in End-Point Protein-Ligand Binding Free Energy Calculations

The impact of harmonic restraints on protein heavy atoms and ligand atoms on end-point free energy calculations is systematically characterized for 54 protein-ligand complexes. We observe that stronger restraints reduce the equilibration time and statistical inefficiency, suppress conformational sampling, influence correlation with experiment, and monotonically decrease the estimated loss of entropy upon binding, leading to stronger estimated binding free energies in most systems. A statistical estimator that reweights for the biasing potential and includes data prior to the estimated equilibration time has the highest correlation with experiment. A spring constant of 20 cal mol-1 Å-2 maintains a near-native energy landscape and suppresses artifactual energy minima while minimally limiting thermal fluctuations about the crystal structure. © 2019 Wiley Periodicals, Inc.

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.

Best Practices for Alchemical Free Energy Calculations [Article v1.0]

Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of "bridging" potential energy functions representing alchemical intermediate states that cannot exist as real chemical species. The data collected from these bridging alchemical thermodynamic states allows the efficient computation of transfer free energies (or differences in transfer free energies) with orders of magnitude less simulation time than simulating the transfer process directly. While these methods are highly flexible, care must be taken in avoiding common pitfalls to ensure that computed free energy differences can be robust and reproducible for the chosen force field, and that appropriate corrections are included to permit direct comparison with experimental data. In this paper, we review current best practices for several popular application domains of alchemical free energy calculations performed with equilibrium simulations, in particular relative and absolute small molecule binding free energy calculations to biomolecular targets.

Binding Thermodynamics of Host-Guest Systems with SMIRNOFF99Frosst 1.0.5 from the Open Force Field Initiative

Designing ligands that bind their target biomolecules with high affinity and specificity is a key step in small-molecule drug discovery, but accurately predicting protein-ligand binding free energies remains challenging. Key sources of errors in the calculations include inadequate sampling of conformational space, ambiguous protonation states, and errors in force fields. Noncovalent complexes between a host molecule with a binding cavity and a druglike guest molecule have emerged as powerful model systems. As model systems, host-guest complexes reduce many of the errors in more complex protein-ligand binding systems, as their small size greatly facilitates conformational sampling, and one can choose systems that avoid ambiguities in protonation states. These features, combined with their ease of experimental characterization, make host-guest systems ideal model systems to test and ultimately optimize force fields in the context of binding thermodynamics calculations. The Open Force Field Initiative aims to create a modern, open software infrastructure for automatically generating and assessing force fields using data sets. The first force field to arise out of this effort, named SMIRNOFF99Frosst, has approximately one tenth the number of parameters, in version 1.0.5, compared to typical general small molecule force fields, such as GAFF. Here, we evaluate the accuracy of this initial force field, using free energy calculations of 43 α and β-cyclodextrin host-guest pairs for which experimental thermodynamic data are available, and compare with matched calculations using two versions of GAFF. For all three force fields, we used TIP3P water and AM1-BCC charges. The calculations are performed using the attach-pull-release (APR) method as implemented in the open source package, pAPRika. For binding free energies, the root-mean-square error of the SMIRNOFF99Frosst calculations relative to experiment is 0.9 [0.7, 1.1] kcal/mol, while the corresponding results for GAFF 1.7 and GAFF 2.1 are 0.9 [0.7, 1.1] kcal/mol and 1.7 [1.5, 1.9] kcal/mol, respectively, with 95% confidence ranges in brackets. These results suggest that SMIRNOFF99Frosst performs competitively with existing small molecule force fields and is a parsimonious starting point for optimization.

Using AMBER18 for Relative Free Energy Calculations

With renewed interest in free energy methods in contemporary structure-based drug design, there is a pressing need to validate against multiple targets and force fields to assess the overall ability of these methods to accurately predict relative binding free energies. We computed relative binding free energies using graphics processing unit accelerated thermodynamic integration (GPU-TI) on a data set originally assembled by Schrödinger, Inc. Using their GPU free energy code (FEP+) and the OPLS2.1 force field combined with the REST2 enhanced sampling approach, these authors obtained an overall MUE of 0.9 kcal/mol and an overall RMSD of 1.14 kcal/mol. In our study using GPU-TI from AMBER with the AMBER14SB/GAFF1.8 force field but without enhanced sampling, we obtained an overall MUE of 1.17 kcal/mol and an overall RMSD of 1.50 kcal/mol for the 330 perturbations contained in this data set. A more detailed analysis of our results suggested that the observed differences between the two studies arise from differences in sampling protocols along with differences in the force fields employed. Future work should address the problem of establishing benchmark quality results with robust statistical error bars obtained through multiple independent runs and enhanced sampling, which is possible with the GPU-accelerated features in AMBER.

Detailed potential of mean force studies on host-guest systems from the SAMPL6 challenge

Accurately predicting receptor-ligand binding free energies is one of the holy grails of computational chemistry with many applications in chemistry and biology. Many successes have been reported, but issues relating to sampling and force field accuracy remain significant issues affecting our ability to reliably calculate binding free energies. In order to explore these issues in more detail we have examined a series of small host-guest complexes from the SAMPL6 blind challenge, namely octa-acids (OAs)-guest complexes and Curcurbit[8]uril (CB8)-guest complexes. Specifically, potential of mean force studies using umbrella sampling combined with the weighted histogram method were carried out on both systems with both known and unknown binding affinities. We find that using standard force fields and straightforward simulation protocols we are able to obtain satisfactory results, but that simply scaling our results allows us to significantly improve our predictive ability for the unknown test sets: the overall RMSD of the binding free energy versus experiment is reduced from 5.59 to 2.36 kcal/mol; for the CB8 test system, the RMSD goes from 8.04 to 3.51 kcal/mol, while for the OAs test system, the RSMD goes from 2.89 to 0.95 kcal/mol. The scaling approach was inspired by studies on structurally related known benchmark sets: by simply scaling, the RMSD was reduced from 6.23 to 1.19 kcal/mol and from 2.96 to 0.62 kcal/mol for the CB8 benchmark system and the OA benchmark system, respectively. We find this scaling procedure to correct absolute binding affinities to be highly effective especially when working across a "congeneric" series with similar charge states. It is less successful when applied to mixed ligands with varied charges and chemical characteristics, but improvement is still realized in the present case. This approach suggests that there are large systematic errors in absolute binding free energy calculations that can be straightforwardly accounted for using a scaling procedure. Random errors are still an issue, but near chemical accuracy can be obtained using the present strategy in select cases.

Comparing alchemical and physical pathway methods for computing the absolute binding free energy of charged ligands

Accurately predicting absolute binding free energies of protein-ligand complexes is important as a fundamental problem in both computational biophysics and pharmaceutical discovery. Calculating binding free energies for charged ligands is generally considered to be challenging because of the strong electrostatic interactions between the ligand and its environment in aqueous solution. In this work, we compare the performance of the potential of mean force (PMF) method and the double decoupling method (DDM) for computing absolute binding free energies for charged ligands. We first clarify an unresolved issue concerning the explicit use of the binding site volume to define the complexed state in DDM together with the use of harmonic restraints. We also provide an alternative derivation for the formula for absolute binding free energy using the PMF approach. We use these formulas to compute the binding free energy of charged ligands at an allosteric site of HIV-1 integrase, which has emerged in recent years as a promising target for developing antiviral therapy. As compared with the experimental results, the absolute binding free energies obtained by using the PMF approach show unsigned errors of 1.5-3.4 kcal mol-1, which are somewhat better than the results from DDM (unsigned errors of 1.6-4.3 kcal mol-1) using the same amount of CPU time. According to the DDM decomposition of the binding free energy, the ligand binding appears to be dominated by nonpolar interactions despite the presence of very large and favorable intermolecular ligand-receptor electrostatic interactions, which are almost completely cancelled out by the equally large free energy cost of desolvation of the charged moiety of the ligands in solution. We discuss the relative strengths of computing absolute binding free energies using the alchemical and physical pathway methods.

Bind3P: Optimization of a Water Model Based on Host-Guest Binding Data

We report a water model, Bind3P (Version 0.1), which was obtained by using sensitivity analysis to readjust the Lennard-Jones parameters of the TIP3P model against experimental binding free energies for six host-guest systems, along with pure liquid properties. Tests of Bind3P against >100 experimental binding free energies and enthalpies for host-guest systems distinct from the training set show a consistent drop in the mean signed error, relative to matched calculations with TIP3P. Importantly, Bind3P also yields some improvement in the hydration free energies of small organic molecules and preserves the accuracy of bulk water properties, such as density and the heat of vaporization. The same approach can be applied to more sophisticated water models that can better represent pure water properties. These results lend further support to the concept of integrating host-guest binding data into force field parametrization.

BFEE: A User-Friendly Graphical Interface Facilitating Absolute Binding Free-Energy Calculations

Quantifying protein-ligand binding has attracted the attention of both theorists and experimentalists for decades. Many methods for estimating binding free energies in silico have been reported in recent years. Proper use of the proposed strategies requires, however, adequate knowledge of the protein-ligand complex, the mathematical background for deriving the underlying theory, and time for setting up the simulations, bookkeeping, and postprocessing. Here, to minimize human intervention, we propose a toolkit aimed at facilitating the accurate estimation of standard binding free energies using a geometrical route, coined the binding free-energy estimator (BFEE), and introduced it as a plug-in of the popular visualization program VMD. Benefitting from recent developments in new collective variables, BFEE can be used to generate the simulation input files, based solely on the structure of the complex. Once the simulations are completed, BFEE can also be utilized to perform the post-treatment of the free-energy calculations, allowing the absolute binding free energy to be estimated directly from the one-dimensional potentials of mean force in simulation outputs. The minimal amount of human intervention required during the whole process combined with the ergonomic graphical interface makes BFEE a very effective and practical tool for the end-user.

Accurate Estimation of the Standard Binding Free Energy of Netropsin with DNA

DNA is the target of chemical compounds (drugs, pollutants, photosensitizers, etc.), which bind through non-covalent interactions. Depending on their structure and their chemical properties, DNA binders can associate to the minor or to the major groove of double-stranded DNA. They can also intercalate between two adjacent base pairs, or even replace one or two base pairs within the DNA double helix. The subsequent biological effects are strongly dependent on the architecture of the binding motif. Discriminating between the different binding patterns is of paramount importance to predict and rationalize the effect of a given compound on DNA. The structural characterization of DNA complexes remains, however, cumbersome at the experimental level. In this contribution, we employed all-atom molecular dynamics simulations to determine the standard binding free energy of DNA with netropsin, a well-characterized antiviral and antimicrobial drug, which associates to the minor groove of double-stranded DNA. To overcome the sampling limitations of classical molecular dynamics simulations, which cannot capture the large change in configurational entropy that accompanies binding, we resort to a series of potentials of mean force calculations involving a set of geometrical restraints acting on collective variables.

Modern drug design: the implication of using artificial neuronal networks and multiple molecular dynamic simulations

We report the implementation of molecular modeling approaches developed as a part of the 2016 Grand Challenge 2, the blinded competition of computer aided drug design technologies held by the D3R Drug Design Data Resource ( https://drugdesigndata.org/ ). The challenge was focused on the ligands of the farnesoid X receptor (FXR), a highly flexible nuclear receptor of the cholesterol derivative chenodeoxycholic acid. FXR is considered an important therapeutic target for metabolic, inflammatory, bowel and obesity related diseases (Expert Opin Drug Metab Toxicol 4:523-532, 2015), but in the context of this competition it is also interesting due to the significant ligand-induced conformational changes displayed by the protein. To deal with these conformational changes we employed multiple simulations of molecular dynamics (MD). Our MD-based protocols were top-ranked in estimating the free energy of binding of the ligands and FXR protein. Our approach was ranked second in the prediction of the binding poses where we also combined MD with molecular docking and artificial neural networks. Our approach showed mediocre results for high-throughput scoring of interactions.

Resolving the Ligand-Binding Specificity in c-MYC G-Quadruplex DNA: Absolute Binding Free Energy Calculations and SPR Experiment

We report the absolute binding free energy calculation and surface plasmon resonance (SPR) experiment for ligand binding with the c-MYC G-quadruplex DNA. The unimolecular parallel DNA G-quadruplex formed in nuclease hypersensitivity element III₁ of the c-MYC gene promoter regulates the c-MYC transcription and is recognized as an emerging drug target for cancer therapy. Quindoline derivatives have been shown to stabilize the G-quadruplex and inhibit the c-MYC expression in cancer cells. NMR revealed two binding sites located at the 5' and 3' termini of the G-quadruplex. Questions about which site is more favored and the basis for the ligand-induced binding site formation remain unresolved. Here, we employ two absolute binding free energy methods, the double decoupling and the potential of mean force methods, to dissect the ligand-binding specificity in the c-MYC G-quadruplex. The calculated absolute binding free energies are in general agreement with the SPR result and suggest that quindoline has a slight preference for the 5' site. The flanking residues around the two sites undergo significant reorganization as the ligand unbinds, which provides evidence for ligand-induced binding pocket formation. The results help interpret experimental data and inform rational design of small molecules targeting the c-MYC G-quadruplex.

Simulation of Reversible Protein-Protein Binding and Calculation of Binding Free Energies Using Perturbed Distance Restraints

Virtually all biological processes depend on the interaction between proteins at some point. The correct prediction of biomolecular binding free-energies has many interesting applications in both basic and applied pharmaceutical research. While recent advances in the field of molecular dynamics (MD) simulations have proven the feasibility of the calculation of protein–protein binding free energies, the large conformational freedom of proteins and complex free energy landscapes of binding processes make such calculations a difficult task. Moreover, convergence and reversibility of resulting free-energy values remain poorly described. In this work, an easy-to-use, yet robust approach for the calculation of standard-state protein–protein binding free energies using perturbed distance restraints is described. In the binding process the conformations of the proteins were restrained, as suggested earlier. Two approaches to avoid end-state problems upon release of the conformational restraints were compared. The method was evaluated by practical application to a small model complex of ubiquitin and the very flexible ubiquitin-binding domain of human DNA polymerase ι (UBM2). All computed free energy differences were closely monitored for convergence, and the calculated binding free energies had a mean unsigned deviation of only 1.4 or 2.5 kJ·mol^–1 from experimental values. Statistical error estimates were in the order of thermal noise. We conclude that the presented method has promising potential for broad applicability to quantitatively describe protein–protein and various other kinds of complex formation.

Attach-Pull-Release Calculations of Ligand Binding and Conformational Changes on the First BRD4 Bromodomain

Bromodomains, protein domains involved in epigenetic regulation, are able to bind small molecules with high affinity. In the present study, we report free energy calculations for the binding of seven ligands to the first BRD4 bromodomain, using the attach-pull-release (APR) method to compute the reversible work of removing the ligands from the binding site and then allowing the protein to relax conformationally. We test three different water models, TIP3P, TIP4PEw, and SPC/E, as well as the GAFF and GAFF2 parameter sets for the ligands. Our simulations show that the apo crystal structure of BRD4 is only metastable, with a structural transition happening in the absence of the ligand typically after 20 ns of simulation. We compute the free energy change for this transition with a separate APR calculation on the free protein and include its contribution to the ligand binding free energies, which generally causes an underestimation of the affinities. By testing different water models and ligand parameters, we are also able to assess their influence in our results and determine which one produces the best agreement with the experimental data. Both free energies associated with the conformational change and ligand binding are affected by the choice of water model, with the two sets of ligand parameters affecting their binding free energies to a lesser degree. Across all six combinations of water model and ligand potential function, the Pearson correlation coefficients between calculated and experimental binding free energies range from 0.55 to 0.83, and the root-mean-square errors range from 1.4-3.2 kcal/mol. The current protocol also yields encouraging preliminary results when used to assess the relative stability of ligand poses generated by docking or other methods, as illustrated for two different ligands. Our method takes advantage of the high performance provided by graphics processing units and can readily be applied to other ligands as well as other protein systems.

Predicting Binding Free Energies: Frontiers and Benchmarks

Binding free energy calculations based on molecular simulations provide predicted affinities for biomolecular complexes. These calculations begin with a detailed description of a system, including its chemical composition and the interactions among its components. Simulations of the system are then used to compute thermodynamic information, such as binding affinities. Because of their promise for guiding molecular design, these calculations have recently begun to see widespread applications in early-stage drug discovery. However, many hurdles remain in making them a robust and reliable tool. In this review, we highlight key challenges of these calculations, discuss some examples of these challenges, and call for the designation of standard community benchmark test systems that will help the research community generate and evaluate progress. In our view, progress will require careful assessment and evaluation of new methods, force fields, and modeling innovations on well-characterized benchmark systems, and we lay out our vision for how this can be achieved.

Whole-Cell-Based Assay To Evaluate Structure Permeation Relationships for Carbapenem Passage through the Pseudomonas aeruginosa Porin OprD

The global emergence of antibiotic resistance, especially in Gram-negative bacteria, is an urgent threat to public health. Discovery of novel classes of antibiotics with activity against these pathogens has been impeded by a fundamental lack of understanding of the molecular drivers underlying small molecule uptake. Although it is well-known that outer membrane porins represent the main route of entry for small, hydrophilic molecules across the Gram-negative cell envelope, the structure-permeation relationship for porin passage has yet to be defined. To address this knowledge gap, we developed a sensitive and specific whole-cell approach in Escherichia coli called titrable outer membrane permeability assay system (TOMAS). We used TOMAS to characterize the structure porin-permeation relationships of a set of novel carbapenem analogues through the Pseudomonas aeruginosa porin OprD. Our results show that small structural modifications, especially the number and nature of charges and their position, have dramatic effects on the ability of these molecules to permeate cells through OprD. This is the first demonstration of a defined relationship between specific molecular changes in a substrate and permeation through an isolated porin. Understanding the molecular mechanisms that impact antibiotic transit through porins should provide valuable insights to antibacterial medicinal chemistry and may ultimately allow for the rational design of porin-mediated uptake of small molecules into Gram-negative bacteria.

Computational Studies of Molecular Permeation through Connexin26 Channels

A signal property of connexin channels is the ability to mediate selective diffusive movement of molecules through plasma membrane(s), but the energetics and determinants of molecular movement through these channels have yet to be understood. Different connexin channels have distinct molecular selectivities that cannot be explained simply on the basis of size or charge of the permeants. To gain insight into the forces and interactions that underlie selective molecular permeation, we investigated the energetics of two uncharged derivatized sugars, one permeable and one impermeable, through a validated connexin26 (Cx26) channel structural model, using molecular dynamics and associated analytic tools. The system is a Cx26 channel equilibrated in explicit membrane/solvent, shown by Brownian dynamics to reproduce key conductance characteristics of the native channel. The results are consistent with the known difference in permeability to each molecule. The energetic barriers extend through most of the pore length, rather than being highly localized as in ion-specific channels. There is little evidence for binding within the pore. Force decomposition reveals how, for each tested molecule, interactions with water and the Cx26 protein vary over the length of the pore and reveals a significant contribution from hydrogen bonding and interaction with K(+). The flexibility of the pore width varies along its length, and the tested molecules have differential effects on pore width as they pass through. Potential sites of interaction within the pore are defined for each molecule. The results suggest that for the tested molecules, differences in hydrogen bonding and entropic factors arising from permeant flexibility substantially contribute to the energetics of permeation. This work highlights factors involved in selective molecular permeation that differ from those that define selectivity among atomic ions.

Absolute binding free energies for octa-acids and guests in SAMPL5 : Evaluating binding free energies for octa-acid and guest complexes in the SAMPL5 blind challenge

As part of the SAMPL5 blind prediction challenge, we calculate the absolute binding free energies of six guest molecules to an octa-acid (OAH) and to a methylated octa-acid (OAMe). We use the double decoupling method via thermodynamic integration (TI) or Hamiltonian replica exchange in connection with the Bennett acceptance ratio (HREM-BAR). We produce the binding poses either through manual docking or by using GalaxyDock-HG, a docking software developed specifically for this study. The root mean square deviations for our most accurate predictions are 1.4 kcal mol-1 for OAH with TI and 1.9 kcal mol-1 for OAMe with HREM-BAR. Our best results for OAMe were obtained for systems with ionic concentrations corresponding to the ionic strength of the experimental solution. The most problematic system contains a halogenated guest. Our attempt to model the σ-hole of the bromine using a constrained off-site point charge, does not improve results. We use results from molecular dynamics simulations to argue that the distinct binding affinities of this guest to OAH and OAMe are due to a difference in the flexibility of the host. We believe that the results of this extensive analysis of host-guest complexes will help improve the protocol used in predicting binding affinities for larger systems, such as protein-substrate compounds.

Overview of the SAMPL5 host-guest challenge: Are we doing better?

The ability to computationally predict protein-small molecule binding affinities with high accuracy would accelerate drug discovery and reduce its cost by eliminating rounds of trial-and-error synthesis and experimental evaluation of candidate ligands. As academic and industrial groups work toward this capability, there is an ongoing need for datasets that can be used to rigorously test new computational methods. Although protein-ligand data are clearly important for this purpose, their size and complexity make it difficult to obtain well-converged results and to troubleshoot computational methods. Host-guest systems offer a valuable alternative class of test cases, as they exemplify noncovalent molecular recognition but are far smaller and simpler. As a consequence, host-guest systems have been part of the prior two rounds of SAMPL prediction exercises, and they also figure in the present SAMPL5 round. In addition to being blinded, and thus avoiding biases that may arise in retrospective studies, the SAMPL challenges have the merit of focusing multiple researchers on a common set of molecular systems, so that methods may be compared and ideas exchanged. The present paper provides an overview of the host-guest component of SAMPL5, which centers on three different hosts, two octa-acids and a glycoluril-based molecular clip, and two different sets of guest molecules, in aqueous solution. A range of methods were applied, including electronic structure calculations with implicit solvent models; methods that combine empirical force fields with implicit solvent models; and explicit solvent free energy simulations. The most reliable methods tend to fall in the latter class, consistent with results in prior SAMPL rounds, but the level of accuracy is still below that sought for reliable computer-aided drug design. Advances in force field accuracy, modeling of protonation equilibria, electronic structure methods, and solvent models, hold promise for future improvements.

Hybrid Steered Molecular Dynamics Approach to Computing Absolute Binding Free Energy of Ligand-Protein Complexes: A Brute Force Approach That Is Fast and Accurate

Computing the free energy of binding a ligand to a protein is a difficult task of essential importance for which purpose various theoretical/computational approaches have been pursued. In this paper, we develop a hybrid steered molecular dynamics (hSMD) method capable of resolving one ligand–protein complex within a few wall-clock days with high enough accuracy to compare with the experimental data. This hSMD approach is based on the relationship between the binding affinity and the potential of mean force (PMF) in the established literature. It involves simultaneously steering n (n = 1, 2, 3, ...) centers of mass of n selected segments of the ligand using n springs of infinite stiffness. Steering the ligand from a single initial state chosen from the bound state ensemble to the corresponding dissociated state, disallowing any fluctuations of the pulling centers along the way, one can determine a 3n-dimensional PMF curve connecting the two states by sampling a small number of forward and reverse pulling paths. This PMF constitutes a large but not the sole contribution to the binding free energy. Two other contributors are (1) the partial partition function containing the equilibrium fluctuations of the ligand at the binding site and the deviation of the initial state from the PMF minimum and (2) the partial partition function containing rotation and fluctuations of the ligand around one of the pulling centers that is fixed at a position far from the protein. We implement this hSMD approach for two ligand–protein complexes whose structures were determined and whose binding affinities were measured experimentally: caprylic acid binding to bovine β-lactoglobulin and glutathione binding to Schistosoma japonicum glutathione S-transferase tyrosine 7 to phenylalanine mutant. Our computed binding affinities agree with the experimental data within a factor of 1.5. The total time of computation for these two all-atom model systems (consisting of 96K and 114K atoms, respectively) was less than one wall-clock week using 512 cores (32 Xeon E5-2680 processors).

Blinded predictions of host-guest standard free energies of binding in the SAMPL5 challenge

In the context of the SAMPL5 blinded challenge standard free energies of binding were predicted for a dataset of 22 small guest molecules and three different host molecules octa-acids (OAH and OAMe) and a cucurbituril (CBC). Three sets of predictions were submitted, each based on different variations of classical molecular dynamics alchemical free energy calculation protocols based on the double annihilation method. The first model (model A) yields a free energy of binding based on computed free energy changes in solvated and host-guest complex phases; the second (model B) adds long range dispersion corrections to the previous result; the third (model C) uses an additional standard state correction term to account for the use of distance restraints during the molecular dynamics simulations. Model C performs the best in terms of mean unsigned error for all guests (MUE [Formula: see text]-95 % confidence interval) for the whole data set and in particular for the octa-acid systems (MUE [Formula: see text]). The overall correlation with experimental data for all models is encouraging ([Formula: see text]). The correlation between experimental and computational free energy of binding ranks as one of the highest with respect to other entries in the challenge. Nonetheless the large MUE for the best performing model highlights systematic errors, and submissions from other groups fared better with respect to this metric.

Computing Protein-Protein Association Affinity with Hybrid Steered Molecular Dynamics

Computing protein-protein association affinities is one of the fundamental challenges in computational biophysics/biochemistry. The overwhelming amount of statistics in the phase space of very high dimensions cannot be sufficiently sampled even with today's high-performance computing power. In this article, we extend a potential of mean force (PMF)-based approach, the hybrid steered molecular dynamics (hSMD) approach we developed for ligand-protein binding, to protein-protein association problems. For a protein complex consisting of two protomers, P1 and P2, we choose m (≥3) segments of P1 whose m centers of mass are to be steered in a chosen direction and n (≥3) segments of P2 whose n centers of mass are to be steered in the opposite direction. The coordinates of these m + n centers constitute a phase space of 3(m + n) dimensions (3(m + n)D). All other degrees of freedom of the proteins, ligands, solvents, and solutes are freely subject to the stochastic dynamics of the all-atom model system. Conducting SMD along a line in this phase space, we obtain the 3(m + n)D PMF difference between two chosen states: one single state in the associated state ensemble and one single state in the dissociated state ensemble. This PMF difference is the first of four contributors to the protein-protein association energy. The second contributor is the 3(m + n - 1)D partial partition in the associated state accounting for the rotations and fluctuations of the (m + n - 1) centers while fixing one of the m + n centers of the P1-P2 complex. The two other contributors are the 3(m - 1)D partial partition of P1 and the 3(n - 1)D partial partition of P2 accounting for the rotations and fluctuations of their m - 1 or n - 1 centers while fixing one of the m/n centers of P1/P2 in the dissociated state. Each of these three partial partitions can be factored exactly into a 6D partial partition in multiplication with a remaining factor accounting for the small fluctuations while fixing three of the centers of P1, P2, or the P1-P2 complex, respectively. These small fluctuations can be well-approximated as Gaussian, and every 6D partition can be reduced in an exact manner to three problems of 1D sampling, counting the rotations and fluctuations around one of the centers as being fixed. We implement this hSMD approach to the Ras-RalGDS complex, choosing three centers on RalGDS and three on Ras (m = n = 3). At a computing cost of about 71.6 wall-clock hours using 400 computing cores in parallel, we obtained the association energy, -9.2 ± 1.9 kcal/mol on the basis of CHARMM 36 parameters, which well agrees with the experimental data, -8.4 ± 0.2 kcal/mol.

Intermediate Thermodynamic States Contribute Equally to Free Energy Convergence: A Demonstration with Replica Exchange

We investigate the relationship between the number of intermediate thermodynamic states along a pathway and the precision of free energy estimates. With a sufficient number of states, the asymptotic variance collapses as a function of the total sample size. Our analytical result is corroborated by replica exchange molecular dynamics simulations of model systems in which the neighbor exchange rate exceeds 35%. Precision collapse is also observed in heat capacity estimates based on the multistate Bennett acceptance ratio. In contrast to the relaxation and mean first-passage times, the autocorrelation time of state indices is found to be relevant to free energy convergence.

Computational Calorimetry: High-Precision Calculation of Host-Guest Binding Thermodynamics

We present a strategy for carrying out high-precision calculations of binding free energy and binding enthalpy values from molecular dynamics simulations with explicit solvent. The approach is used to calculate the thermodynamic profiles for binding of nine small molecule guests to either the cucurbit[7]uril (CB7) or β-cyclodextrin (βCD) host. For these systems, calculations using commodity hardware can yield binding free energy and binding enthalpy values with a precision of ∼0.5 kcal/mol (95% CI) in a matter of days. Crucially, the self-consistency of the approach is established by calculating the binding enthalpy directly, via end point potential energy calculations, and indirectly, via the temperature dependence of the binding free energy, i.e., by the van't Hoff equation. Excellent agreement between the direct and van't Hoff methods is demonstrated for both host-guest systems and an ion-pair model system for which particularly well-converged results are attainable. Additionally, we find that hydrogen mass repartitioning allows marked acceleration of the calculations with no discernible cost in precision or accuracy. Finally, we provide guidance for accurately assessing numerical uncertainty of the results in settings where complex correlations in the time series can pose challenges to statistical analysis. The routine nature and high precision of these binding calculations opens the possibility of including measured binding thermodynamics as target data in force field optimization so that simulations may be used to reliably interpret experimental data and guide molecular design.

Toward Improved Force-Field Accuracy through Sensitivity Analysis of Host-Guest Binding Thermodynamics

Improving the capability of atomistic computer models to predict the thermodynamics of noncovalent binding is critical for successful structure-based drug design, and the accuracy of such calculations remains limited by nonoptimal force field parameters. Ideally, one would incorporate protein-ligand affinity data into force field parametrization, but this would be inefficient and costly. We now demonstrate that sensitivity analysis can be used to efficiently tune Lennard-Jones parameters of aqueous host-guest systems for increasingly accurate calculations of binding enthalpy. These results highlight the promise of a comprehensive use of calorimetric host-guest binding data, along with existing validation data sets, to improve force field parameters for the simulation of noncovalent binding, with the ultimate goal of making protein-ligand modeling more accurate and hence speeding drug discovery.

Computing membrane-AQP5-phosphatidylserine binding affinities with hybrid steered molecular dynamics approach

In order to elucidate how phosphatidylserine (PS6) interacts with AQP5 in a cell membrane, we developed a hybrid steered molecular dynamics (hSMD) method that involved: (1) Simultaneously steering two centers of mass of two selected segments of the ligand, and (2) equilibrating the ligand-protein complex with and without biasing the system. Validating hSMD, we first studied vascular endothelial growth factor receptor 1 (VEGFR1) in complex with N-(4-Chlorophenyl)-2-((pyridin-4-ylmethyl)amino)benzamide (8ST), for which the binding energy is known from in vitro experiments. In this study, our computed binding energy well agreed with the experimental value. Knowing the accuracy of this hSMD method, we applied it to the AQP5-lipid-bilayer system to answer an outstanding question relevant to AQP5's physiological function: Will the PS6, a lipid having a single long hydrocarbon tail that was found in the central pore of the AQP5 tetramer crystal, actually bind to and inhibit AQP5's central pore under near-physiological conditions, namely, when AQP5 tetramer is embedded in a lipid bilayer? We found, in silico, using the CHARMM 36 force field, that binding PS6 to AQP5 was a factor of 3 million weaker than "binding" it in the lipid bilayer. This suggests that AQP5's central pore will not be inhibited by PS6 or a similar lipid in a physiological environment.

BEDAM binding free energy predictions for the SAMPL4 octa-acid host challenge

The binding energy distribution analysis method (BEDAM) protocol has been employed as part of the SAMPL4 blind challenge to predict the binding free energies of a set of octa-acid host-guest complexes. The resulting predictions were consistently judged as some of the most accurate predictions in this category of the SAMPL4 challenge in terms of quantitative accuracy and statistical correlation relative to the experimental values, which were not known at the time the predictions were made. The work has been conducted as part of a hands-on graduate class laboratory session. Collectively the students, aided by automated setup and analysis tools, performed the bulk of the calculations and the numerical and structural analysis. The success of the experiment confirms the reliability of the BEDAM methodology and it shows that physics-based atomistic binding free energy estimation models, when properly streamlined and automated, can be successfully employed by non-specialists.

Bridging Calorimetry and Simulation through Precise Calculations of Cucurbituril-Guest Binding Enthalpies

We used microsecond time scale molecular dynamics simulations to compute, at high precision, binding enthalpies for cucurbit[7]uril (CB7) with eight guests in aqueous solution. The results correlate well with experimental data from previously published isothermal titration calorimetry studies, and decomposition of the computed binding enthalpies by interaction type provides plausible mechanistic insights. Thus, dispersion interactions appear to play a key role in stabilizing these complexes, due at least in part to the fact that their packing density is greater than that of water. On the other hand, strongly favorable Coulombic interactions between the host and guests are compensated by unfavorable solvent contributions, leaving relatively modest electrostatic contributions to the binding enthalpies. The better steric fit of the aliphatic guests into the circular host appears to explain why their binding enthalpies tend to be more favorable than those of the more planar aromatic guests. The present calculations also bear on the validity of the simulation force field. Somewhat unexpectedly, the TIP3P water yields better agreement with experiment than the TIP4P-Ew water model, although the latter is known to replicate the properties of pure water more accurately. More broadly, the present results demonstrate the potential for computational calorimetry to provide atomistic explanations for thermodynamic observations.