Elucidation of Nonadditive Effects in Protein–Ligand Binding Energies: Thrombin as a Case Study

Comparison of Methodologies for Absolute Binding Free Energy Calculations of Ligands to Intrinsically Disordered Proteins

Modulating the function of Intrinsically Disordered Proteins (IDPs) with small molecules is of considerable importance given the crucial roles of IDPs in the pathophysiology of numerous diseases. Reported binding affinities for ligands to diverse IDPs vary broadly, and little is known about the detailed molecular mechanisms that underpin ligand efficacy. Molecular simulations of IDP ligand binding mechanisms can help us understand the mode of action of small molecule inhibitors of IDP function, but it is still unclear how binding energies can be modeled rigorously for such a flexible class of proteins. Here, we compare alchemical absolute binding free energy calculations (ABFE) and Markov-State Modeling (MSM) protocols to model the binding of the small molecule 10058-F4 to a disordered peptide extracted from a segment of the oncoprotein c-Myc. The ABFE results produce binding energy estimates that are sensitive to the choice of reference structure. In contrast, the MSM results produce more reproducible binding energy estimates consistent with weak mM binding affinities and transient intermolecular contacts reported in the literature.

Automated Adaptive Absolute Binding Free Energy Calculations

Alchemical absolute binding free energy (ABFE) calculations have substantial potential in drug discovery, but are often prohibitively computationally expensive. To unlock their potential, efficient automated ABFE workflows are required to reduce both computational cost and human intervention. We present a fully automated ABFE workflow based on the automated selection of λ windows, the ensemble-based detection of equilibration, and the adaptive allocation of sampling time based on inter-replicate statistics. We find that the automated selection of intermediate states with consistent overlap is rapid, robust, and simple to implement. Robust detection of equilibration is achieved with a paired t-test between the free energy estimates at initial and final portions of a an ensemble of runs. We determine reasonable default parameters for all algorithms and show that the full workflow produces equivalent results to a nonadaptive scheme over a variety of test systems, while often accelerating equilibration. Our complete workflow is implemented in the open-source package A3FE (https://github.com/michellab/a3fe).

Sire: An interoperability engine for prototyping algorithms and exchanging information between molecular simulation programs

Sire is a Python/C++ library that is used both to prototype new algorithms and as an interoperability engine for exchanging information between molecular simulation programs. It provides a collection of file parsers and information converters that together make it easier to combine and leverage the functionality of many other programs and libraries. This empowers researchers to use sire to write a single script that can, for example, load a molecule from a PDBx/mmCIF file via Gemmi, perform SMARTS searches via RDKit, parameterize molecules using BioSimSpace, run GPU-accelerated molecular dynamics via OpenMM, and then display the resulting dynamics trajectory in a NGLView Jupyter notebook 3D molecular viewer. This functionality is built on by BioSimSpace, which uses sire's molecular information engine to interconvert with programs such as GROMACS, NAMD, Amber, and AmberTools for automated molecular parameterization and the running of molecular dynamics, metadynamics, and alchemical free energy workflows. Sire comes complete with a powerful molecular information search engine, plus trajectory loading and editing, analysis, and energy evaluation engines. This, when combined with an in-built computer algebra system, gives substantial flexibility to researchers to load, search for, edit, and combine molecular information from multiple sources and use that to drive novel algorithms by combining functionality from other programs. Sire is open source (GPL3) and is available via conda and at a free Jupyter notebook server at https://try.openbiosim.org. Sire is supported by the not-for-profit OpenBioSim community interest company.

Comparison of Receptor-Ligand Restraint Schemes for Alchemical Absolute Binding Free Energy Calculations

Alchemical absolute binding free energy calculations are of increasing interest in drug discovery. These calculations require restraints between the receptor and ligand to restrict their relative positions and, optionally, orientations. Boresch restraints are commonly used, but they must be carefully selected in order to sufficiently restrain the ligand and to avoid inherent instabilities. Applying multiple distance restraints between anchor points in the receptor and ligand provides an alternative framework without inherent instabilities which may provide convergence benefits by more strongly restricting the relative movements of the receptor and ligand. However, there is no simple method to calculate the free energy of releasing these restraints due to the coupling of the internal and external degrees of freedom of the receptor and ligand. Here, a method to rigorously calculate free energies of binding with multiple distance restraints by imposing intramolecular restraints on the anchor points is proposed. Absolute binding free energies for the human macrophage migration inhibitory factor/MIF180, system obtained using a variety of Boresch restraints and rigorous and nonrigorous implementations of multiple distance restraints are compared. It is shown that several multiple distance restraint schemes produce estimates in good agreement with Boresch restraints. In contrast, calculations without orientational restraints produce erroneously favorable free energies of binding by up to approximately 4 kcal mol-1. These approaches offer new options for the deployment of alchemical absolute binding free energy calculations.

Energetics of a protein disorder-order transition in small molecule recognition

Many proteins recognise other proteins via mechanisms that involve the folding of intrinsically disordered regions upon complex formation. Here we investigate how the selectivity of a drug-like small molecule arises from its modulation of a protein disorder-to-order transition. Binding of the compound AM-7209 has been reported to confer order upon an intrinsically disordered ‘lid’ region of the oncoprotein MDM2. Calorimetric measurements revealed that truncation of the lid region of MDM2 increases the apparent dissociation constant of AM-7209 250-fold. By contrast, lid truncation has little effect on the binding of the ligand Nutlin-3a. Insights into these differential binding energetics were obtained via a complete thermodynamic analysis that featured adaptive absolute alchemical free energy of binding calculations with enhanced-sampling molecular dynamics simulations. The simulations reveal that in apo MDM2 the ordered lid state is energetically disfavoured. AM-7209, but not Nutlin-3a, shows a significant energetic preference for ordered lid conformations, thus shifting the balance towards ordering of the lid in the AM-7209/MDM2 complex. The methodology reported herein should facilitate broader targeting of intrinsically disordered regions in medicinal chemistry.

Molecular simulations and biophysical measurements elucidate why the ligand AM-7209 orders a disordered region of the protein MDM2 on binding. This work expands strategies available to medicinal chemists for targeting disordered proteins.

Implementation of the QUBE Force Field in SOMD for High-Throughput Alchemical Free-Energy Calculations

The quantum mechanical bespoke (QUBE) force-field approach has been developed to facilitate the automated derivation of potential energy function parameters for modeling protein-ligand binding. To date, the approach has been validated in the context of Monte Carlo simulations of protein-ligand complexes. We describe here the implementation of the QUBE force field in the alchemical free-energy calculation molecular dynamics simulation package SOMD. The implementation is validated by demonstrating the reproducibility of absolute hydration free energies computed with the QUBE force field across the SOMD and GROMACS software packages. We further demonstrate, by way of a case study involving two series of non-nucleoside inhibitors of HIV-1 reverse transcriptase, that the availability of QUBE in a modern simulation package that makes efficient use of graphics processing unit acceleration will facilitate high-throughput alchemical free-energy calculations.

Synthesis, biochemical evaluation and molecular modeling studies of nonpeptidic nitrile-based fluorinated compounds

Aim: Compounds that block enzyme activity can kill pathogens and help develop effective and safe drugs for Chagas disease and leishmaniasis. Materials & methods: A library of nonpeptidic nitrile-based compounds was synthesized and had their inhibitory affinity tested against cruzain, Leishmania mexicana cysteine protease B and cathepsin L. Isothermal titration calorimetry experiments and molecular simulations were performed for selected compounds to obtain thermodynamic fingerprints and identify main interactions and putative modes of binding with cruzain. Results: The derivatives provided increased affinity against all enzymes compared with the lead, and thermodynamic and computational studies showed improved thermodynamic properties and a possible different mode of binding. Conclusion: Our studies culminated in 1b, a compound 60-fold more potent in cruzain than its lead that also showed entropic and enthalpic contributions favorable to Gibbs binding energy.

Hybrid Alchemical Free Energy/Machine-Learning Methodology for the Computation of Hydration Free Energies

A methodology that combines alchemical free energy calculations (FEP) with machine learning (ML) has been developed to compute accurate absolute hydration free energies. The hybrid FEP/ML methodology was trained on a subset of the FreeSolv database and retrospectively shown to outperform most submissions from the SAMPL4 competition. Compared to pure machine-learning approaches, FEP/ML yields more precise estimates of free energies of hydration and requires a fraction of the training set size to outperform standalone FEP calculations. The ML-derived correction terms are further shown to be transferable to a range of related FEP simulation protocols. The approach may be used to inexpensively improve the accuracy of FEP calculations and to flag molecules which will benefit the most from bespoke force field parametrization efforts.

Optimization strategy of single-digit nanomolar cross-class inhibitors of mammalian and protozoa cysteine proteases

Cysteine proteases (CPs) are involved in a myriad of actions that include not only protein degradation, but also play an essential biological role in infectious and systemic diseases such as cancer. CPs also act as biomarkers and can be reached by active-based probes for diagnostic and mechanistic purposes that are critical in health and disease. In this paper, we present the modulation of a CP panel of parasites and mammals (Trypanosoma cruzi cruzain, LmCPB, CatK, CatL and CatS), whose inhibition by nitrile peptidomimetics allowed the identification of specificity and selectivity for a given CP. The activity cliffs identified at the CP inhibition level are useful for retrieving trends through multiple structure-activity relationships. For two of the cruzain inhibitors (10g and 4e), both enthalpy and entropy are favourable to Gibbs binding energy, thus overcoming enthalpy-entropy compensation (EEC). Group contribution of individual molecular modification through changes in enthalpy and entropy results in a separate partition on the relative differences of Gibbs binding energy (ΔΔG). Overall, this study highlights the role of CPs in polypharmacology and multi-target screening, which represents an imperative trend in the actual drug discovery effort.

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.

Molecular Dynamics Simulation Framework to Probe the Binding Hypothesis of CYP3A4 Inhibitors

The Cytochrome P450 family of heme-containing proteins plays a major role in catalyzing phase I metabolic reactions, and the CYP3A4 subtype is responsible for the metabolism of many currently marketed drugs. Additionally, CYP3A4 has an inherent affinity for a broad spectrum of structurally diverse chemical entities, often leading to drug-drug interactions mediated by the inhibition or induction of the metabolic enzyme. The current study explores the binding of selected highly efficient CYP3A4 inhibitors by docking and molecular dynamics (MD) simulation protocols and their binding free energy calculated using the WaterSwap method. The results indicate the importance of binding pocket residues including Phe57, Arg105, Arg106, Ser119, Arg212, Phe213, Thr309, Ser312, Ala370, Arg372, Glu374, Gly481 and Leu483 for interaction with CYP3A4 inhibitors. The residue-wise decomposition of the binding free energy from the WaterSwap method revealed the importance of binding site residues Arg106 and Arg372 in the stabilization of all the selected CYP3A4-inhibitor complexes. The WaterSwap binding energies were further complemented with the MM(GB/PB)SA results and it was observed that the binding energies calculated by both methods do not differ significantly. Overall, our results could guide towards the use of multiple computational approaches to achieve a better understanding of CYP3A4 inhibition, subsequently leading to the design of highly specific and efficient new chemical entities with suitable ADMETox properties and reduced side effects.

Synthesis and structure-activity relationship of nitrile-based cruzain inhibitors incorporating a trifluoroethylamine-based P2 amide replacement

The structure-activity relationship for nitrile-based cruzain inhibitors incorporating a P2 amide replacement based on trifluoroethylamine was explored by deconstruction of a published series of inhibitors. It was demonstrated that the P3 biphenyl substituent present in the published inhibitor structures could be truncated to phenyl with only a small loss of affinity. The effects of inverting the configuration of the P2 amide replacement and linking a benzyl substituent at P1 were observed to be strongly nonadditive. We show that plotting affinity against molecular size provides a means to visualize both the molecular size efficiency of structural transformations and the nonadditivity in the structure-activity relationship. We also show how the relationship between affinity and lipophilicity, measured by high-performance liquid chromatography with an immobilized artificial membrane stationary phase, may be used to normalize affinity with respect to lipophilicity.

Visualizing protein-ligand binding with chemical energy-wise decomposition (CHEWD): application to ligand binding in the kallikrein-8 S1 Site

Kallikrein-8, a serine protease, is a target for structure-based drug design due to its therapeutic potential in treating Alzheimer's disease and is also useful as a biomarker in ovarian cancer. We present a binding assessment of ligands to kallikrein-8 using a residue-wise decomposition of the binding energy. Binding of four putative inhibitors of kallikrein-8 is investigated through molecular dynamics simulation and ligand binding energy evaluation with two methods (MM/PBSA and WaterSwap). For visualization of the residue-wise decomposition of binding energies, chemical energy-wise decomposition or CHEWD is introduced as a plugin to UCSF Chimera and Pymol. CHEWD allows easy comparison between ligands using individual residue contributions to the binding energy. Molecular dynamics simulations indicate one ligand binds stably to the kallikrein-8 S1 binding site. Comparison with other members of the kallikrein family shows that residues responsible for binding are specific to kallikrein-8. Thus, ZINC02927490 is a promising lead for development of novel kallikrein-8 inhibitors.

Effect of set up protocols on the accuracy of alchemical free energy calculation over a set of ACK1 inhibitors

Hit-to-lead virtual screening frequently relies on a cascade of computational methods that starts with rapid calculations applied to a large number of compounds and ends with more expensive computations restricted to a subset of compounds that passed initial filters. This work focuses on set up protocols for alchemical free energy (AFE) scoring in the context of a Docking–MM/PBSA–AFE cascade. A dataset of 15 congeneric inhibitors of the ACK1 protein was used to evaluate the performance of AFE set up protocols that varied in the steps taken to prepare input files (using previously docked and best scored poses, manual selection of poses, manual placement of binding site water molecules). The main finding is that use of knowledge derived from X-ray structures to model binding modes, together with the manual placement of a bridging water molecule, improves the R² from 0.45 ± 0.06 to 0.76 ± 0.02 and decreases the mean unsigned error from 2.11 ± 0.08 to 1.24 ± 0.04 kcal mol^-1. By contrast a brute force automated protocol that increased the sampling time ten-fold lead to little improvements in accuracy. Besides, it is shown that for the present dataset hysteresis can be used to flag poses that need further attention even without prior knowledge of experimental binding affinities.

The nature of ligand efficiency

Ligand efficiency is a widely used design parameter in drug discovery. It is calculated by scaling affinity by molecular size and has a nontrivial dependency on the concentration unit used to express affinity that stems from the inability of the logarithm function to take dimensioned arguments. Consequently, perception of efficiency varies with the choice of concentration unit and it is argued that the ligand efficiency metric is not physically meaningful nor should it be considered to be a metric. The dependence of ligand efficiency on the concentration unit can be eliminated by defining efficiency in terms of sensitivity of affinity to molecular size and this is illustrated with reference to fragment-to-lead optimizations. Group efficiency and fit quality are also examined in detail from a physicochemical perspective. The importance of examining relationships between affinity and molecular size directly is stressed throughout this study and an alternative to ligand efficiency for normalization of affinity with respect to molecular size is presented.

A computationally designed binding mode flip leads to a novel class of potent tri-vector cyclophilin inhibitors

Cyclophilins (Cyps) are a major family of drug targets that are challenging to prosecute with small molecules because the shallow nature and high degree of conservation of the active site across human isoforms offers limited opportunities for potent and selective inhibition. Herein a computational approach based on molecular dynamics simulations and free energy calculations was combined with biophysical assays and X-ray crystallography to explore a flip in the binding mode of a reported urea-based Cyp inhibitor. This approach enabled access to a distal pocket that is poorly conserved among key Cyp isoforms, and led to the discovery of a new family of sub-micromolar cell-active inhibitors that offer unprecedented opportunities for the development of next-generation drug therapies based on Cyp inhibition. The computational approach is applicable to a broad range of organic functional groups and could prove widely enabling in molecular design.

Blinded predictions of standard binding free energies: lessons learned from the SAMPL6 challenge

In the context of the SAMPL6 challenges, series of blinded predictions of standard binding free energies were made with the SOMD software for a dataset of 27 host-guest systems featuring two octa-acids hosts (OA and TEMOA) and a cucurbituril ring (CB8) host. Three different models were used, ModelA computes the free energy of binding based on a double annihilation technique; ModelB additionally takes into account long-range dispersion and standard state corrections; ModelC additionally introduces an empirical correction term derived from a regression analysis of SAMPL5 predictions previously made with SOMD. The performance of each model was evaluated with two different setups; buffer explicitly matches the ionic strength from the binding assays, whereas no-buffer merely neutralizes the host-guest net charge with counter-ions. ModelC/no-buffer shows the lowest mean-unsigned error for the overall dataset (MUE 1.29 < 1.39 < 1.50 kcal mol^-1, 95% CI), while explicit modelling of the buffer improves significantly results for the CB8 host only. Correlation with experimental data ranges from excellent for the host TEMOA (R² 0.91 < 0.94 < 0.96), to poor for CB8 (R² 0.04 < 0.12 < 0.23). Further investigations indicate a pronounced dependence of the binding free energies on the modelled ionic strength, and variable reproducibility of the binding free energies between different simulation packages.

Impact of domain knowledge on blinded predictions of binding energies by alchemical free energy calculations

The Drug Design Data Resource (D3R) consortium organises blinded challenges to address the latest advances in computational methods for ligand pose prediction, affinity ranking, and free energy calculations. Within the context of the second D3R Grand Challenge several blinded binding free energies predictions were made for two congeneric series of Farsenoid X Receptor (FXR) inhibitors with a semi-automated alchemical free energy calculation workflow featuring FESetup and SOMD software tools. Reasonable performance was observed in retrospective analyses of literature datasets. Nevertheless, blinded predictions on the full D3R datasets were poor due to difficulties encountered with the ranking of compounds that vary in their net-charge. Performance increased for predictions that were restricted to subsets of compounds carrying the same net-charge. Disclosure of X-ray crystallography derived binding modes maintained or improved the correlation with experiment in a subsequent rounds of predictions. The best performing protocols on D3R set1 and set2 were comparable or superior to predictions made on the basis of analysis of literature structure activity relationships (SAR)s only, and comparable or slightly inferior, to the best submissions from other groups.

Using the fast fourier transform in binding free energy calculations

According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc.

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.