Parallelized-over-parts computation of absolute binding free energy with docking and molecular dynamics

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

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

Taming multiple binding poses in alchemical binding free energy prediction: the β-cyclodextrin host-guest SAMPL9 blinded challenge

We apply the Alchemical Transfer Method (ATM) and a bespoke fixed partial charge force field to the SAMPL9 bCD host-guest binding free energy prediction challenge that comprises a combination of complexes formed between five phenothiazine guests and two cyclodextrin hosts. Multiple chemical forms, competing binding poses, and computational modeling challenges pose significant obstacles to obtaining reliable computational predictions for these systems. The phenothiazine guests exist in solution as racemic mixtures of enantiomers related by nitrogen inversions that bind the hosts in various binding poses, each requiring an individual free energy analysis. Due to the large size of the guests and the conformational reorganization of the hosts, which prevent a direct absolute binding free energy route, binding free energies are obtained by a series of absolute and relative binding alchemical steps for each chemical species in each binding pose. Metadynamics-accelerated conformational sampling was found to be necessary to address the poor convergence of some numerical estimates affected by conformational trapping. Despite these challenges, our blinded predictions quantitatively reproduced the experimental affinities for the β-cyclodextrin host and, to a lesser extent, those with a methylated derivative. The work illustrates the challenges of obtaining reliable free energy data in in silico drug design for even seemingly simple systems and introduces some of the technologies available to tackle them.

Enhancing Hit Discovery in Virtual Screening through Absolute Protein-Ligand Binding Free-Energy Calculations

In the hit identification stage of drug discovery, a diverse chemical space needs to be explored to identify initial hits. Contrary to empirical scoring functions, absolute protein-ligand binding free-energy perturbation (ABFEP) provides a theoretically more rigorous and accurate description of protein-ligand binding thermodynamics and could, in principle, greatly improve the hit rates in virtual screening. In this work, we describe an implementation of an accurate and reliable ABFEP method in FEP+. We validated the ABFEP method on eight congeneric compound series binding to eight protein receptors including both neutral and charged ligands. For ligands with net charges, the alchemical ion approach is adopted to avoid artifacts in electrostatic potential energy calculations. The calculated binding free energies correlate with experimental results with a weighted average of R² = 0.55 for the entire dataset. We also observe an overall root-mean-square error (RMSE) of 1.1 kcal/mol after shifting the zero-point of the simulation data to match the average experimental values. Through ABFEP calculations using apo versus holo protein structures, we demonstrated that the protein conformational and protonation state changes between the apo and holo proteins are the main physical factors contributing to the protein reorganization free energy manifested by the overestimation of raw ABFEP calculated binding free energies using the holo structures of the proteins. Furthermore, we performed ABFEP calculations in three virtual screening applications for hit enrichment. ABFEP greatly improves the hit rates as compared to docking scores or other methods like metadynamics. The good performance of ABFEP in rank ordering compounds demonstrated in this work confirms it as a useful tool to improve the hit rates in virtual screening, thus facilitating hit discovery.

Meta-Analysis Reveals That Absolute Binding Free-Energy Calculations Approach Chemical Accuracy

Systematic and quantitative analysis of the reliability of formally exact methods that in silico calculate absolute protein-ligand binding free energies remains lacking. Here, we provide, for the first time, evidence-based information on the reliability of these methods by statistically studying 853 cases from 34 different research groups through meta-analysis. The results show that formally exact methods approach chemical accuracy (error = 1.58 kcal/mol), even if people are challenging difficult tasks such as blind drug screening in recent years. The geometrical-pathway-based methods prove to possess a better convergence ability than the alchemical ones, while the latter have a larger application range. We also reveal the importance of always using the latest force fields to guarantee reliability and discuss the pros and cons of turning to an implicit solvent model in absolute binding free-energy calculations. Moreover, based on the meta-analysis, an evidence-based guideline for in silico binding free-energy calculations is provided.

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.

Comparing the Performance of Different AMBER Protein Forcefields, Partial Charge Assignments, and Water Models for Absolute Binding Free Energy Calculations

Identifying chemical starting points is a vital first step in small molecule drug discovery and can take significant time and money. For this reason, computational approaches to virtual screening are of great interest as they can lower the cost and shorten timeframes. However, simple approaches such as molecular docking and pharmacophore screening are of limited accuracy and provide a low probability of success. Alchemical binding free energies represent a promising approach for virtual screening as they naturally incorporate the key effects of water molecules, protein flexibility, and binding entropy. However, the calculations are technically very challenging, with performance depending on the specific forcefield used. For this reason, it is important that the community has access to benchmark test sets to assess prediction accuracy. In this paper, we present an approach to alchemical binding free energies using OpenMM. We identify effective simulation parameters using an existing BRD4(1) test set and present two new benchmark sets (cMET and PDE2A) that can be used in the community for validation purposes. Our findings also highlight the effectiveness of some AMBER forcefields, in particular, AMBER ff15ipq.

Molecular Mechanism Exploration of Potent Fluorinated PI3K Inhibitors with a Triazine Scaffold: Unveiling the Unusual Synergistic Effect of Pyridine-to-Pyrimidine Ring Interconversion and CF3 Defluorination

The phosphatidylinostitol-3-kinase (PI3K)/AKT/mammalian target of rapamycin signaling pathway is a vital regulator of cell proliferation, growth, and survival, which is frequently overactivated in many human cancers. To this effect, PI3K, which is an important mediator of this pathway, has been pinpointed as a crucial target in cancer therapy and hence the importance of PI3K inhibitors. It was recently reported that defluorination and pyridine-to-pyrimidine ring interconversion increase the potency of specific small-molecule inhibitors of PI3K. Compound 4, an inhibitor with the difluorinated pyrimidine motif, was found to be eight times more potent against PI3K than compound 1, an inhibitor with the trifluorinated pyridine motif. This observation presents the need to rationally resolve the differential inhibitory mechanisms exhibited by both compounds. In this present work, we employed multiple computational approaches to investigate and distinguish the binding modes of 1 and 4 in addition to the effects they mediate on the secondary structure of PI3K. Likewise, we evaluated two other derivatives, compounds 2 with the difluorinated pyridine motif and 3 with the trifluorinated pyrimidine motif, to investigate the cooperativity effect between the defluorination of CF₃ and pyridine-to-pyrimidine ring interconversion. Findings revealed that PI3K, upon interaction with 4, exhibited a series of structural changes that favored the binding of the inhibitor at the active-site region. Furthermore, a positive (synergistic) cooperativity effect was observed between CF₃ defluorination and pyridine-to-pyrimidine ring interconversion. Moreover, there was a good correlation between the binding free energy estimated and the biological activity reported experimentally. Energy decomposition analysis revealed that the major contributing force to binding affinity variations between 1 and 4 is the electrostatic energy. Per-residue energy-based hierarchical clustering analysis further identified four hot-spot residues ASP841, TYR867, ASP964, and LYS833 and four warm-spot residues ASP836, SER806, ASP837, and LYS808, which essentially mediate the optimal and higher-affinity binding of compound 4 to PI3K relative to 1. This study therefore provides rational insights into the mechanisms by which 4 exhibited superior PI3K-inhibitory activities over 1, which is vital for future structure-based drug discovery efforts in PI3K targeting.

Kinetics and thermodynamics of thermal inactivation for recombinant Escherichia coli cellulases, cel12B, cel8C, and polygalacturonase, peh28; biocatalysts for biofuel precursor production

Lignocellulosic biomass conversion using cellulases/polygalacturonases is a process that can be progressively influenced by several determinants involved in cellulose microfibril degradation. This article focuses on the kinetics and thermodynamics of thermal inactivation of recombinant Escherichia coli cellulases, cel12B, cel8C and a polygalacturonase, peh 28, derived from Pectobacterium carotovorum sub sp. carotovorum. Several consensus motifs conferring the enzymes' thermal stability in both cel12B and peh28 model structures have been detailed earlier, which were confirmed for the three enzymes through the current study of their thermal inactivation profiles over the 20-80°C range using the respective activities on carboxymethylcellulose and polygalacturonic acid. Kinetic constants and half-lives of thermal inactivation, inactivation energy, plus inactivation entropies, enthalpies and Gibbs free energies, revealed high stability, less conformational change and protein unfolding for cel12B and peh28 due to thermal denaturation compared to cel8C. The apparent thermal stability of peh28 and cel12B, along with their hydrolytic efficiency on a lignocellulosic biomass conversion as reported previously, makes these enzymes candidates for various industrial applications. Analysis of the Gibbs free energy values suggests that the thermal stabilities of cel12B and peh28 are entropy-controlled over the tested temperature range.

A Multi-target Drug Designing for BTK, MMP9, Proteasome and TAK1 for the Clinical Treatment of Mantle Cell Lymphoma

BACKGROUND

Mantle cell lymphoma (MCL) is a type of non-Hodgkin lymphoma characterized by the mutation and overexpression of the cyclin D1 protein by the reciprocal chromosomal translocation t(11;14)(q13:q32).

AIM

The present study aims to identify potential inhibition of MMP9, Proteasome, BTK, and TAK1 and determine the most suitable and effective protein target for the MCL.

METHODOLOGY

Nine known inhibitors for MMP9, 24 for proteasome, 15 for BTK and 14 for TAK1 were screened. SB-3CT (PubChem ID: 9883002), oprozomib (PubChem ID: 25067547), zanubrutinib (PubChem ID: 135565884) and TAK1 inhibitor (PubChem ID: 66760355) were recognized as drugs with high binding capacity with their respective protein receptors. 41, 72, 102 and 3 virtual screened compounds were obtained after the similarity search with compound (PubChem ID:102173753), PubChem compound SCHEMBL15569297 (PubChem ID:72374403), PubChem compound SCHEMBL17075298 (PubChem ID:136970120) and compound CID: 71814473 with best virtual screened compounds.

RESULT

MMP9 inhibitors show commendable affinity and good interaction profile of compound holding PubChem ID:102173753 over the most effective established inhibitor SB-3CT. The pharmacophore study of the best virtual screened compound reveals its high efficacy based on various interactions. The virtual screened compound's better affinity with the target MMP9 protein was deduced using toxicity and integration profile studies.

CONCLUSION

Based on the ADMET profile, the compound (PubChem ID: 102173753) could be a potent drug for MCL treatment. Similar to the established SB-3CT, the compound was non-toxic with LD50 values for both the compounds lying in the same range.

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

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

A new method for estimating the relative binding free energy, derived from a free energy variational principle for the Pim-1-kinase-ligand and FKBP-ligand systems

In this study, a new method is proposed for calculating the relative binding free energy between a ligand and a protein, derived from a free energy variational principle (FEVP). To address the shortcomings of the method used in our previous study, we incorporate the dynamical fluctuation of a ligand in the FEVP calculation. The present modified method is applied to the Pim-1-kinase-ligand system and also to the FKBP-ligand system as a comparison with our previous work. Any inhibitor of Pim-1 kinase is expected to function as an anti-cancer drug. Some improvements are observed in the results compared to the previous study. The present work also shows comparable or better results than approaches using a standard technique of binding free energy calculations, such as the LIE and the MM-PB/SA methods. The possibility of applying the present method in the drug discovery process is also discussed.

Free-energy landscape of molecular interactions between endothelin 1 and human endothelin type B receptor: fly-casting mechanism

The free-energy landscape of interaction between a medium-sized peptide, endothelin 1 (ET1), and its receptor, human endothelin type B receptor (hETB), was computed using multidimensional virtual-system coupled molecular dynamics, which controls the system's motions by introducing multiple reaction coordinates. The hETB embedded in lipid bilayer was immersed in explicit solvent. All molecules were expressed as all-atom models. The resultant free-energy landscape had five ranges with decreasing ET1-hETB distance: completely dissociative, outside-gate, gate, binding pocket, and genuine-bound ranges. In the completely dissociative range, no ET1-hETB interaction appeared. In the outside-gate range, an ET1-hETB attractive interaction was the fly-casting mechanism. In the gate range, the ET1 orientational variety decreased rapidly. In the binding pocket range, ET1 was in a narrow pathway with a steep free-energy slope. In the genuine-bound range, ET1 was in a stable free-energy basin. A G-protein-coupled receptor (GPCR) might capture its ligand from a distant place.

Variational selection of features for molecular kinetics

The modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long time-scale kinetics from molecular dynamics simulations. However, one yet-unoptimized step of the pipeline involves choosing the features, or collective variables, from which the model should be constructed. In order to build intuitive models, these collective variables are often sought to be interpretable and familiar features, such as torsional angles or contact distances in a protein structure. However, previous approaches for evaluating the chosen features rely on constructing a full MSM, which in turn requires additional hyperparameters to be chosen, and hence leads to a computationally expensive framework. Here, we present a method to optimize the feature choice directly, without requiring the construction of the final kinetic model. We demonstrate our rigorous preprocessing algorithm on a canonical set of 12 fast-folding protein simulations and show that our procedure leads to more efficient model selection.

Massive-Scale Binding Free Energy Simulations of HIV Integrase Complexes Using Asynchronous Replica Exchange Framework Implemented on the IBM WCG Distributed Network

To perform massive-scale replica exchange molecular dynamics (REMD) simulations for calculating binding free energies of protein-ligand complexes, we implemented the asynchronous replica exchange (AsyncRE) framework of the binding energy distribution analysis method (BEDAM) in implicit solvent on the IBM World Community Grid (WCG) and optimized the simulation parameters to reduce the overhead and improve the prediction power of the WCG AsyncRE simulations. We also performed the first massive-scale binding free energy calculations using the WCG distributed computing grid and 301 ligands from the SAMPL4 challenge for large-scale binding free energy predictions of HIV-1 integrase complexes. In total there are ∼10000 simulated complexes, ∼1 million replicas, and ∼2000 μs of aggregated MD simulations. Running AsyncRE MD simulations on the WCG requires accepting a trade-off between the number of replicas that can be run (breadth) and the number of full RE cycles that can be completed per replica (depth). As compared with synchronous Replica Exchange (SyncRE) running on tightly coupled clusters like XSEDE, on the WCG many more replicas can be launched simultaneously on heterogeneous distributed hardware, but each full RE cycle requires more overhead. We compared the WCG results with that from AutoDock and more advanced RE simulations including the use of flattening potentials to accelerate sampling of selected degrees of freedom of ligands and/or receptors related to slow dynamics due to high energy barriers. We propose a suitable strategy of RE simulations to refine high throughput docking results which can be matched to corresponding computing resources: from HPC clusters, to small or medium-size distributed campus grids, and finally to massive-scale computing networks including millions of CPUs like the resources available on the WCG.

Binding Modes of Ligands Using Enhanced Sampling (BLUES): Rapid Decorrelation of Ligand Binding Modes via Nonequilibrium Candidate Monte Carlo

Accurately predicting protein-ligand binding affinities and binding modes is a major goal in computational chemistry, but even the prediction of ligand binding modes in proteins poses major challenges. Here, we focus on solving the binding mode prediction problem for rigid fragments. That is, we focus on computing the dominant placement, conformation, and orientations of a relatively rigid, fragment-like ligand in a receptor, and the populations of the multiple binding modes which may be relevant. This problem is important in its own right, but is even more timely given the recent success of alchemical free energy calculations. Alchemical calculations are increasingly used to predict binding free energies of ligands to receptors. However, the accuracy of these calculations is dependent on proper sampling of the relevant ligand binding modes. Unfortunately, ligand binding modes may often be uncertain, hard to predict, and/or slow to interconvert on simulation time scales, so proper sampling with current techniques can require prohibitively long simulations. We need new methods which dramatically improve sampling of ligand binding modes. Here, we develop and apply a nonequilibrium candidate Monte Carlo (NCMC) method to improve sampling of ligand binding modes. In this technique, the ligand is rotated and subsequently allowed to relax in its new position through alchemical perturbation before accepting or rejecting the rotation and relaxation as a nonequilibrium Monte Carlo move. When applied to a T4 lysozyme model binding system, this NCMC method shows over 2 orders of magnitude improvement in binding mode sampling efficiency compared to a brute force molecular dynamics simulation. This is a first step toward applying this methodology to pharmaceutically relevant binding of fragments and, eventually, drug-like molecules. We are making this approach available via our new Binding modes of ligands using enhanced sampling (BLUES) package which is freely available on GitHub.

Ligand binding to telomeric G-quadruplex DNA investigated by funnel-metadynamics simulations

A thorough characterization of the binding interaction between a drug and its molecular target is fundamental to successfully lead drug design. We demonstrate that this characterization is also possible using the recently developed method of funnel-metadynamics (FM), here applied to investigate the binding of berberine to DNA G-quadruplex. We computed a quantitatively well-characterized free-energy landscape that allows identifying two low-energy ligand binding modes and the presence of higher energy prebinding states. We validated the accuracy of our calculations by steady-state fluorescence experiments. The good agreement between the theoretical and experimental binding free-energy value demonstrates that FM is a most reliable method to study ligand/DNA interaction.

G-quadruplexes (G4s) are higher-order DNA structures typically present at promoter regions of genes and telomeres. Here, the G4 formation decreases the replicative DNA at each cell cycle, finally leading to apoptosis. The ability to control this mitotic clock, particularly in cancer cells, is fascinating and passes through a rational understanding of the ligand/G4 interaction. We demonstrate that an accurate description of the ligand/G4 binding mechanism is possible using an innovative free-energy method called funnel-metadynamics (FM), which we have recently developed to investigate ligand/protein interaction. Using FM simulations, we have elucidated the binding mechanism of the anticancer alkaloid berberine to the human telomeric G4 (d[AG₃(T₂AG₃)₃]), computing also the binding free-energy landscape. Two ligand binding modes have been identified as the lowest energy states. Furthermore, we have found prebinding sites, which are preparatory to reach the final binding mode. In our simulations, the ions and the water molecules have been explicitly represented and the energetic contribution of the solvent during ligand binding evaluated. Our theoretical results provide an accurate estimate of the absolute ligand/DNA binding free energy (ΔGb0 = −10.3 ± 0.5 kcal/mol) that we validated through steady-state fluorescence binding assays. The good agreement between the theoretical and experimental value demonstrates that FM is a most powerful method to investigate ligand/DNA interaction and can be a useful tool for the rational design also of G4 ligands.

Replica exchange molecular dynamics study of the amyloid beta (11–40) trimer penetrating a membrane

The transmembrane Aβ_11–40 trimer is investigated for the first time using REMD and FEP.

Anti-arrhythmic Medication Propafenone a Potential Drug for Alzheimer's Disease Inhibiting Aggregation of Aβ: In Silico and in Vitro Studies

Alzheimer's disease (AD) is the most common form of dementia caused by the formation of Aβ aggregates. So far, no effective medicine for the treatment of AD is available. Many efforts have been made to find effective medicine to cope with AD. Curcumin is a drug candidate for AD, being a potent anti-amyloidogenic compound, but the results of clinical trials for it were either negative or inclusive. In the present study, we took advantages from accumulated knowledge about curcumin and have screened out four compounds that have chemical and structural similarity with curcumin more than 80% from all FDA-approved oral drugs. Using all-atom molecular dynamics simulation and the free energy perturbation method we showed that among predicted compounds anti-arrhythmic medication propafenone shows the best anti-amyloidogenic activity. The in vitro experiment further revealed that it can inhibit Aβ aggregation and protect cells against Aβ induced cytotoxicity to almost the same extent as curcumin. Our results suggest that propafenone may be a potent drug for the treatment of Alzheimer's disease.

I. Dissociation free energies of drug–receptor systems via non-equilibrium alchemical simulations: a theoretical framework

In this contribution I critically discuss the alchemical approach for evaluating binding free energies in drug–receptor systems, placing this methodology into the broader context of non-equilibrium thermodynamics.

Using docking and alchemical free energy approach to determine the binding mechanism of eEF2K inhibitors and prioritizing the compound synthesis

A-484954 is a known eEF2K inhibitor with submicromolar IC₅₀ potency. However, the binding mechanism and the crystal structure of the kinase remains unknown. Here, we employ a homology eEF2K model, docking and alchemical free energy simulations to probe the binding mechanism of eEF2K, and in turn, guide the optimization of potential lead compounds. The inhibitor was docked into the ATP-binding site of a homology model first. Three different binding poses, hypothesis 1, 2, and 3, were obtained and subsequently applied to molecular dynamics (MD) based alchemical free energy simulations. The calculated relative binding free energy of the analogs of A-484954 using the binding pose of hypothesis 1 show a good correlation with the experimental IC₅₀ values, yielding an r² coefficient of 0.96 after removing an outlier (compound 5). Calculations using another two poses show little correlation with experimental data, (r² of less than 0.5 with or without removing any outliers). Based on hypothesis 1, the calculated relative free energy suggests that bigger cyclic groups, at R1 e.g., cyclobutyl and cyclopentyl promote more favorable binding than smaller groups, such as cyclopropyl and hydrogen. Moreover, this study also demonstrates the ability of the alchemical free energy approach in combination with docking and homology modeling to prioritize compound synthesis. This can be an effective means of facilitating structure-based drug design when crystal structures are not available.

Site Identification by Ligand Competitive Saturation (SILCS) simulations for fragment-based drug design

Fragment-based drug design (FBDD) involves screening low molecular weight molecules ("fragments") that correspond to functional groups found in larger drug-like molecules to determine their binding to target proteins or nucleic acids. Based on the principle of thermodynamic additivity, two fragments that bind nonoverlapping nearby sites on the target can be combined to yield a new molecule whose binding free energy is the sum of those of the fragments. Experimental FBDD approaches, like NMR and X-ray crystallography, have proven very useful but can be expensive in terms of time, materials, and labor. Accordingly, a variety of computational FBDD approaches have been developed that provide different levels of detail and accuracy.The Site Identification by Ligand Competitive Saturation (SILCS) method of computational FBDD uses all-atom explicit-solvent molecular dynamics (MD) simulations to identify fragment binding. The target is "soaked" in an aqueous solution with multiple fragments having different identities. The resulting computational competition assay reveals what small molecule types are most likely to bind which regions of the target. From SILCS simulations, 3D probability maps of fragment binding called "FragMaps" can be produced. Based on the probabilities relative to bulk, SILCS FragMaps can be used to determine "Grid Free Energies (GFEs)," which provide per-atom contributions to fragment binding affinities. For essentially no additional computational overhead relative to the production of the FragMaps, GFEs can be used to compute Ligand Grid Free Energies (LGFEs) for arbitrarily complex molecules, and these LGFEs can be used to rank-order the molecules in accordance with binding affinities.

Ligand-receptor affinities computed by an adapted linear interaction model for continuum electrostatics and by protein conformational averaging

Accurate calculations of free energies involved in small-molecule binding to a receptor are challenging. Interactions between ligand, receptor, and solvent molecules have to be described precisely, and a large number of conformational microstates has to be sampled, particularly for ligand binding to a flexible protein. Linear interaction energy models are computationally efficient methods that have found considerable success in the prediction of binding free energies. Here, we parametrize a linear interaction model for implicit solvation with coefficients adapted by ligand and binding site relative polarities in order to predict ligand binding free energies. Results obtained for a diverse series of ligands suggest that the model has good predictive power and transferability. We also apply implicit ligand theory and propose approximations to average contributions of multiple ligand-receptor poses built from a protein conformational ensemble and find that exponential averages require proper energy discrimination between plausible binding poses and false-positives (i.e., decoys). The linear interaction model and the averaging procedures presented can be applied independently of each other and of the method used to obtain the receptor structural representation.

Converging free energies of binding in cucurbit[7]uril and octa-acid host-guest systems from SAMPL4 using expanded ensemble simulations

Molecular containers such as cucurbit[7]uril (CB7) and the octa-acid (OA) host are ideal simplified model test systems for optimizing and analyzing methods for computing free energies of binding intended for use with biologically relevant protein-ligand complexes. To this end, we have performed initially blind free energy calculations to determine the free energies of binding for ligands of both the CB7 and OA hosts. A subset of the selected guest molecules were those included in the SAMPL4 prediction challenge. Using expanded ensemble simulations in the dimension of coupling host-guest intermolecular interactions, we are able to show that our estimates in most cases can be demonstrated to fully converge and that the errors in our estimates are due almost entirely to the assigned force field parameters and the choice of environmental conditions used to model experiment. We confirm the convergence through the use of alternative simulation methodologies and thermodynamic pathways, analyzing sampled conformations, and directly observing changes of the free energy with respect to simulation time. Our results demonstrate the benefits of enhanced sampling of multiple local free energy minima made possible by the use of expanded ensemble molecular dynamics and may indicate the presence of significant problems with current transferable force fields for organic molecules when used for calculating binding affinities, especially in non-protein chemistries.

Absolute Free Energy of Binding and Entropy of the FKBP12-FK506 Complex: Effects of the Force Field

The hypothetical scanning molecular dynamics (HSMD) method combined with thermodynamic integration (HSMD-TI) has been extended recently for calculating ΔA(0)-the absolute free energy of binding of a ligand to a protein. With HSMD-TI, ΔA(0) is obtained in a new way as a sum of several components, among them is ΔSligand-the change in the conformational entropy as the ligand is transferred from the bulk solvent to the active site-this entropy is obtained by a specific reconstruction procedure. This unique aspect of HSMD (which is useful in rational drug design) is in particular important for treating large ligands, where ΔSligand might be significant. Technically, one should verify that the results for ΔSligand converge-a property that might become more difficult for large ligands; therefore, studying ligands of increasing size would define the range of applicability of HSMD-TI for binding. In this paper, we check the performance of HSMD-TI by applying it to the relatively large ligand FK506 (126 atoms) complexed with the protein FKBP12, where ΔA(0) = -12.8 kcal/mol is known experimentally as well as the crystal structure of the complex. This structure was initially equilibrated by carrying out a 100 ns molecular dynamics trajectory, where the system is modeled by the AMBER force field, TIP3P water, and Particle Mesh Ewald. HSMD-TI calculations were carried out in three conformational regions defined by the intervals [0.2,2], [2,5], and [5,100] ns along the trajectory, where local equilibration of the total energy has been observed; we obtained ΔA(0) = -13.6 ± 1.1, -16.6 ± 1.4, and -16.7 ± 1.4 kcal/mol, respectively indicating the following: (1) The second and third regions belong to the same conformational subspace of the complex, which is different from the [0.2,2] ns subspace. (2) The unsatisfactory result for ΔA(0) obtained in the well equilibrated (hence theoretically preferred) latter regions reflects the nonperfect modeling used, which however (3) has led to the experimental ΔA(0) in the [0.2,2] ns region close to the crystal structure. Keeping the complex near its crystal structure has been a successful approach in the literature. To check this avenue further, we applied harmonic restraints on backbone atoms and obtained unsatisfactory results for ΔA(0), suggesting that implementation of this approach is not straightforward. Converging results for ΔSligand were obtained in all regions, where the result ΔSligand([0.2,2]) = 7.1 ± 1.2 kcal/mol is less region dependent than ΔA(0) and is relatively large probably due to the large ligand.

Prediction of the binding affinity of compounds with diverse scaffolds by MP-CAFEE

Accurate methods to predict the binding affinities of compounds for target molecules are powerful tools in structure-based drug design (SBDD). A recently developed method called massively parallel computation of absolute binding free energy with a well-equilibrated system (MP-CAFEE) successfully predicted the binding affinities of compounds with relatively similar scaffolds. We investigate the applicability of MP-CAFEE for predicting the affinity of compounds having more diverse scaffolds for the target p38α, a mitogen-activated protein kinase. The calculated and experimental binding affinities correlate well, showing that MP-CAFEE can accurately rank the compounds with diverse scaffolds. We propose a method to determine the optimal number of sampling runs with respect to a predefined level of accuracy, which is established according to the stage in the SBDD process being considered. The optimal number of sampling runs for two key stages-lead identification and lead optimization-is estimated to be five and eight or more, respectively, in our model system using Cochrans sample size formula.

Accurate calculation of mutational effects on the thermodynamics of inhibitor binding to p38α MAP kinase: a combined computational and experimental study

A major current challenge for drug design efforts focused on protein kinases is the development of drug resistance caused by spontaneous mutations in the kinase catalytic domain. The ubiquity of this problem means that it would be advantageous to develop fast, effective computational methods that could be used to determine the effects of potential resistance-causing mutations before they arise in a clinical setting. With this long-term goal in mind, we have conducted a combined experimental and computational study of the thermodynamic effects of active-site mutations on a well-characterized and high-affinity interaction between a protein kinase and a small-molecule inhibitor. Specifically, we developed a fluorescence-based assay to measure the binding free energy of the small-molecule inhibitor, SB203580, to the p38α MAP kinase and used it measure the inhibitor's affinity for five different kinase mutants involving two residues (Val38 and Ala51) that contact the inhibitor in the crystal structure of the inhibitor-kinase complex. We then conducted long, explicit-solvent thermodynamic integration (TI) simulations in an attempt to reproduce the experimental relative binding affinities of the inhibitor for the five mutants; in total, a combined simulation time of 18.5 μs was obtained. Two widely used force fields - OPLS-AA/L and Amber ff99SB-ILDN - were tested in the TI simulations. Both force fields produced excellent agreement with experiment for three of the five mutants; simulations performed with the OPLS-AA/L force field, however, produced qualitatively incorrect results for the constructs that contained an A51V mutation. Interestingly, the discrepancies with the OPLS-AA/L force field could be rectified by the imposition of position restraints on the atoms of the protein backbone and the inhibitor without destroying the agreement for other mutations; the ability to reproduce experiment depended, however, upon the strength of the restraints' force constant. Imposition of position restraints in corresponding simulations that used the Amber ff99SB-ILDN force field had little effect on their ability to match experiment. Overall, the study shows that both force fields can work well for predicting the effects of active-site mutations on small molecule binding affinities and demonstrates how a direct combination of experiment and computation can be a powerful strategy for developing an understanding of protein-inhibitor interactions.

Perspective: Alchemical free energy calculations for drug discovery

Computational techniques see widespread use in pharmaceutical drug discovery, but typically prove unreliable in predicting trends in protein-ligand binding. Alchemical free energy calculations seek to change that by providing rigorous binding free energies from molecular simulations. Given adequate sampling and an accurate enough force field, these techniques yield accurate free energy estimates. Recent innovations in alchemical techniques have sparked a resurgence of interest in these calculations. Still, many obstacles stand in the way of their routine application in a drug discovery context, including the one we focus on here, sampling. Sampling of binding modes poses a particular challenge as binding modes are often separated by large energy barriers, leading to slow transitions. Binding modes are difficult to predict, and in some cases multiple binding modes may contribute to binding. In view of these hurdles, we present a framework for dealing carefully with uncertainty in binding mode or conformation in the context of free energy calculations. With careful sampling, free energy techniques show considerable promise for aiding drug discovery.

Absolute free energy of binding of avidin/biotin, revisited

The binding of biotin to avidin is one of the strongest in nature with absolute free energy of binding, ΔA(0) = -20.4 kcal/mol. Therefore, this complex became a target for a large number of computational studies, which all, however, are based on approximate techniques or simplified models and have led to a wide range of results Therefore, ΔA(0) is calculated here by rigorous statistical mechanical methods and models that consider long-range electrostatics. (1) We apply our method, "hypothetical scanning molecular dynamics with thermodynamic integration" (HSMD-TI) to avidin-biotin modeled by periodic boundary conditions with particle mesh ewald (PME). (2) We apply the double decoupling method (DDM) to this system modeled by the spherical solvent boundary potential (SSBP) and the generalized solvent boundary potential (GSBP). The corresponding results for neutral biotin, ΔA(0) = -29.1 ± 0.8 and -25.2 ± 0.5 kcal/mol are significantly lower than the experimental value; we also provide the result for a charged biotin, ΔA(0) = -33.3 ± 0.8 kcal/mol. It is plausible to suggest that this disagreement with the experiment may stem from ignoring the (positive) contribution of a mobile loop that changes its structure upon ligand binding.

Structural and dynamic determinants of protein-peptide recognition

Protein-peptide interactions play important roles in many cellular processes, including signal transduction, trafficking, and immune recognition. Protein conformational changes upon binding, an ill-defined peptide binding surface, and the large number of peptide degrees of freedom make the prediction of protein-peptide interactions particularly challenging. To address these challenges, we perform rapid molecular dynamics simulations in order to examine the energetic and dynamic aspects of protein-peptide binding. We find that, in most cases, we recapitulate the native binding sites and native-like poses of protein-peptide complexes. Inclusion of electrostatic interactions in simulations significantly improves the prediction accuracy. Our results also highlight the importance of protein conformational flexibility, especially side-chain movement, which allows the peptide to optimize its conformation. Our findings not only demonstrate the importance of sufficient sampling of the protein and peptide conformations, but also reveal the possible effects of electrostatics and conformational flexibility on peptide recognition.

Computation of the binding affinities of catechol-O-methyltransferase inhibitors: multisubstate relative free energy calculations

Alchemical free energy simulations are amongst the most accurate techniques for the computation of the free energy changes associated with noncovalent protein-ligand interactions. A procedure is presented to estimate the relative binding free energies of several ligands to the same protein target where multiple, low-energy configurational substates might coexist, as opposed to one unique structure. The contributions of all individual substates were estimated, explicitly, with the free energy perturbation method, and combined in a rigorous fashion to compute the overall relative binding free energies and dissociation constants. It is shown that, unless the most stable bound forms are known a priori, inaccurate results may be obtained if the contributions of multiple substates are ignored. The method was applied to study the complex formed between human catechol-O-methyltransferase and BIA 9-1067, a newly developed tight-binding inhibitor that is currently under clinical evaluation for the therapy of Parkinson's disease. Our results reveal an exceptionally high-binding affinity (K(d) in subpicomolar range) and provide insightful clues on the interactions and mechanism of inhibition. The inhibitor is, itself, a slowly reacting substrate of the target enzyme and is released from the complex in the form of O-methylated product. By comparing the experimental catalytic rate (k(cat)) and the estimated dissociation rate (k(off)) constants of the enzyme-inhibitor complex, one can conclude that the observed inhibition potency (K(i)) is primarily dependent on the catalytic rate constant of the inhibitor's O-methylation, rather than the rate constant of dissociation of the complex.

Calculation of the Absolute Free Energy of Binding and Related Entropies with the HSMD-TI Method: The FKBP12-L8 Complex

The hypothetical scanning molecular dynamics (HSMD) method is used here for calculating the absolute free energy of binding, ΔA(0) of the complex of the protein FKBP12 with the ligand SB2 (also denoted L8) - a system that has been studied previously for comparing the performance of different methods. Our preliminary study suggests that considering long-range electrostatics is imperative even for a hydrophobic ligand such as L8. Therefore the system is modeled by the AMBER force field using Particle Mesh Ewald (PME). HSMD consists of three stages applied to both the ligand-solvent and ligand-protein systems. (1) A small set of system configurations (frames) is extracted from an MD trajectory. (2) The entropy of the ligand in each frame is calculated by a reconstruction procedure. (3) The contribution of water and protein to ΔA(0) is calculated for each frame by gradually increasing the ligand-environment interactions from zero to their full value using thermodynamic integration (TI). Unlike the conventional methods, the structure of the ligand is kept fixed during TI, and HSMD is thus free from the end-point problem encountered with the double annihilation method (DAM); therefore, the need for applying restraints is avoided. Furthermore, unlike the conventional methods, the entropy of the ligand and water is obtained directly as a byproduct of the simulation. In this paper, in addition to the difference in the internal entropies of the ligand in the two environments, we calculate for the first time the external entropy of the ligand, which provides a measure for the size of the active site. We obtain ΔA(0) = -10.7 ±1.0 as compared to the experimental values -10.9 and -10.6 kcal/mol. However, a protein/water system treated by periodic boundary conditions grows significantly with increasing protein size and the computation of ΔA(0) would become expensive by all methods. Therefore, we also apply HSMD to FKBP12-L8 described by the GSBP/SSBP model of Roux's group (implemented in the software CHARMM) where only part of the protein and water around the active site are considered and long-range electrostatic effects are taken into account. For comparison this model was also treated by the double decoupling method (DDM). The two methods have led to comparable results for ΔA(0) which are somewhat lower than the experimental value. The ligand was found to be more confined in the active site described by GSBP/SSBP than by PME where its entropy in solvent is larger than in the active site by 1.7 and by 5.5 kcal/mol, respectively.