Absolute Alchemical Free Energy Calculations for Ligand Binding: A Beginner's Guide

Structural Dynamics of the Methyl-Coenzyme M Reductase Active Site Are Influenced by Coenzyme F430 Modifications

Methyl-coenzyme M reductase (MCR) is a central player in methane biogeochemistry, governing methanogenesis and the anaerobic oxidation of methane (AOM) in methanogens and anaerobic methanotrophs (ANME), respectively. The prosthetic group of MCR is coenzyme F430, a nickel-containing tetrahydrocorphin. Several modified versions of F430 have been discovered, including the 172-methylthio-F430 (mtF430) used by ANME-1 MCR. Here, we employ molecular dynamics (MD) simulations to investigate the active site dynamics of MCR from Methanosarcina acetivorans and ANME-1 when bound to the canonical F430 compared to 172-thioether coenzyme F430 variants and substrates (methyl-coenzyme M and coenzyme B) for methane formation. Our simulations highlight the importance of the Gln to Val substitution in accommodating the 172 methylthio modification in ANME-1 MCR. Modifications at the 172 position disrupt the canonical substrate positioning in M. acetivorans MCR. However, in some replicates, active site reorganization to maintain substrate positioning suggests that the modified F430 variants could be accommodated in a methanogenic MCR. We additionally report the first quantitative estimate of MCR intrinsic electric fields that are pivotal in driving methane formation. Our results suggest that the electric field aligned along the CH3-S-CoM thioether bond facilitates homolytic bond cleavage, coinciding with the proposed catalytic mechanism. Structural perturbations, however, weaken and misalign these electric fields, emphasizing the importance of the active site structure in maintaining their integrity. In conclusion, our results deepen the understanding of MCR active site dynamics, the enzyme's organizational role in intrinsic electric fields for catalysis, and the interplay between active site structure and electrostatics.

Current State of Open Source Force Fields in Protein-Ligand Binding Affinity Predictions

In drug discovery, the in silico prediction of binding affinity is one of the major means to prioritize compounds for synthesis. Alchemical relative binding free energy (RBFE) calculations based on molecular dynamics (MD) simulations are nowadays a popular approach for the accurate affinity ranking of compounds. MD simulations rely on empirical force field parameters, which strongly influence the accuracy of the predicted affinities. Here, we evaluate the ability of six different small-molecule force fields to predict experimental protein-ligand binding affinities in RBFE calculations on a set of 598 ligands and 22 protein targets. The public force fields OpenFF Parsley and Sage, GAFF, and CGenFF show comparable accuracy, while OPLS3e is significantly more accurate. However, a consensus approach using Sage, GAFF, and CGenFF leads to accuracy comparable to OPLS3e. While Parsley and Sage are performing comparably based on aggregated statistics across the whole dataset, there are differences in terms of outliers. Analysis of the force field reveals that improved parameters lead to significant improvement in the accuracy of affinity predictions on subsets of the dataset involving those parameters. Lower accuracy can not only be attributed to the force field parameters but is also dependent on input preparation and sampling convergence of the calculations. Especially large perturbations and nonconverged simulations lead to less accurate predictions. The input structures, Gromacs force field files, as well as the analysis Python notebooks are available on GitHub.

Accelerating and Automating the Free Energy Perturbation Absolute Binding Free Energy Calculation with the RED-E Function

The accurate prediction of the binding affinities between small molecules and biological macromolecules plays a fundamental role in structure-based drug design, which is still challenging. The free energy perturbation-based absolute binding free energy (FEP-ABFE) approach has shown potential in its reliability. To correctly calculate the energy related to the ligand being restrained by the receptor, additional restraints between the ligand and the receptor are needed. However, determining the restraint parameters for individual ligands empirically is too trivial to be automated, and usually gives rise to numerical instabilities, which set back the applications of FEP-ABFE. To address these issues, we derived the analytical expression for the probability distribution of energy differences, P(ΔU), during the process of restraint addition, which is called the RED-E (restraint energy distribution at equilibrium position) function. Simulations indicated that the RED-E function can accurately describe P(ΔU) when restraints are added at the equilibrium position. Based on the RED-E function, an automatic restraint selection method was proposed to select the best restraint. With this method, there is a high phase-space overlap between the free and restrained states, such that using a 2-λ perturbation can accurately calculate the free energy of the restraint addition, which is a nearly 6 times acceleration compared with current widely used 12-λ perturbation method. The RED-E function gives insight into the non-Gaussian behavior of the sampled P(ΔU) in certain FEP processes in an analytical way. The highly automated and accelerated restraint selection also makes it possible for the large-scale application of FEP-ABFE in real drug discovery practices.

Identifying Selectivity Filters in Protein Biosensor for Ligand Screening

Specialized sensing mechanisms in bacteria enable the identification of cognate ligands with remarkable selectivity in highly xenobiotic-polluted environments where these ligands are utilized as energy sources. Here, via integrating all-atom computer simulation, biochemical assay, and isothermal titration calorimetry measurements, we determine the molecular basis of MopR, a phenol biosensor's complex selection process of ligand entry. Our results reveal a set of strategically placed selectivity filters along the ligand entry pathway of MopR. These filters act as checkpoints, screening diverse aromatic ligands at the protein surface based on their chemical features and sizes. Ligands meeting specific criteria are allowed to enter the sensing site in an orientation-dependent manner. Sequence and structural analyses demonstrate the conservation of this ligand entry mechanism across the sensor class, with individual amino acids along the selectivity filter path playing a critical role in ligand selection. Together, this investigation highlights the importance of interactions with the ligand entry pathway, in addition to interactions within the binding pocket, in achieving ligand selectivity in biological sensing. The findings enhance our understanding of ligand selectivity in bacterial phenol biosensors and provide insights for rational expansion of the biosensor repertoire, particularly for the biotechnologically relevant class of aromatic pollutants.

The energetics and ion coupling of cholesterol transport through Patched1

Patched1 (PTCH1) is a tumor suppressor protein of the mammalian Hedgehog (HH) signaling pathway, implicated in embryogenesis and tissue homeostasis. PTCH1 inhibits the G protein-coupled receptor Smoothened (SMO) via a debated mechanism involving modulating ciliary cholesterol accessibility. Using extensive molecular dynamics simulations and free energy calculations to evaluate cholesterol transport through PTCH1, we find an energetic barrier of ~15 to 20 kilojoule per mole for cholesterol export. In silico data are coupled to in vivo biochemical assays of PTCH1 mutants to probe coupling between cation binding sites, transmembrane motions, and PTCH1 activity. Using complementary simulations of Dispatched1, we find that transition between "inward-open" and solvent "occluded" states is accompanied by Na+-induced pinching of intracellular helical segments. Thus, our findings illuminate the energetics and ion coupling stoichiometries of PTCH1 transport mechanisms, whereby one to three Na+ or two to three K+ couple to cholesterol export, and provide the first molecular description of transitions between distinct transport states.

Molecular dynamics and absolute binding free energy studies of piperine derivatives as potential inhibitors of SARS-CoV-2 main protease

The work presents a library of piperine derivatives as potential inhibitors of the main protease protein (Mpro) functionality using Docking Studies, Molecular Dynamics (MD) Simulations and Absolute Binding Free-Energy calculations. 342 ligands were selected for this work and docked with Mpro protein. Among all the ligands studied, PIPC270, PIPC299, PIPC252, PIPC63, PIPC311 were the top five docked conformations having significant hydrogen bonding and hydrophobic interactions inside the active pocket of Mpro. These top five ligands were subjected to MD simulations for 100 ns using GROMACS. Root Mean Square Deviation (RMSD), Root Mean Square Fluctuation (RMSF), Radius of Gyration (Rg), Solvent Accessible Surface Area (SASA) and hydrogen bond analysis revealed that the ligands bounded to protein remain stable without significant deviations during the course of MD simulations. Absolute binding free energy (ΔGb) was calculated for theses complexes and found that the ligand PIPC299 shows the prevalent binding affinity with binding free-energy of about -113.05 Kcal/mol. Thus, these molecules can be further tested by in vitro and in vivo studies on Mpro. This study lays a path to explore the new functionality of piperine derivatives as novel drug like molecules.Communicated by Ramaswamy H. Sarma.

To Design Scalable Free Energy Perturbation Networks, Optimal Is Not Enough

Drug discovery is accelerated with computational methods such as alchemical simulations to estimate ligand affinities. In particular, relative binding free energy (RBFE) simulations are beneficial for lead optimization. To use RBFE simulations to compare prospective ligands in silico, researchers first plan the simulation experiment, using graphs where nodes represent ligands and graph edges represent alchemical transformations between ligands. Recent work demonstrated that optimizing the statistical architecture of these perturbation graphs improves the accuracy of the predicted changes in the free energy of ligand binding. Therefore, to improve the success rate of computational drug discovery, we present the open-source software package High Information Mapper (HiMap)─a new take on its predecessor, Lead Optimization Mapper (LOMAP). HiMap removes heuristics decisions from design selection and instead finds statistically optimal graphs over ligands clustered with machine learning. Beyond optimal design generation, we present theoretical insights for designing alchemical perturbation maps. Some of these results include that for n number of nodes, the precision of perturbation maps is stable at n·ln(n) edges. This result indicates that even an "optimal" graph can result in unexpectedly high errors if a plan includes too few alchemical transformations for the given number of ligands and edges. And, as a study compares more ligands, the performance of even optimal graphs will deteriorate with linear scaling of the edge count. In this sense, ensuring an A- or D-optimal topology is not enough to produce robust errors. We additionally find that optimal designs will converge more rapidly than radial and LOMAP designs. Moreover, we derive bounds for how clustering reduces cost for designs with a constant expected relative error per cluster, invariant of the size of the design. These results inform how to best design perturbation maps for computational drug discovery and have broader implications for experimental design.

The Energetics and Ion Coupling of Cholesterol Transport Through Patched1

Patched1 (PTCH1) is the principal tumour suppressor protein of the mammalian Hedgehog (HH) signalling pathway, implicated in embryogenesis and tissue homeostasis. PTCH1 inhibits the Class F G protein-coupled receptor Smoothened (SMO) via a debated mechanism involving modulating accessible cholesterol levels within ciliary membranes. Using extensive molecular dynamics (MD) simulations and free energy calculations to evaluate cholesterol transport through PTCH1, we find an energetic barrier of ~15-20 kJ mol -1 for cholesterol export. In simulations we identify cation binding sites within the PTCH1 transmembrane domain (TMD) which may provide the energetic impetus for cholesterol transport. In silico data are coupled to in vivo biochemical assays of PTCH1 mutants to probe coupling between transmembrane motions and PTCH1 activity. Using complementary simulations of Dispatched1 (DISP1) we find that transition between 'inward-open' and solvent 'occluded' states is accompanied by Na + induced pinching of intracellular helical segments. Thus, our findings illuminate the energetics and ion-coupling stoichiometries of PTCH1 transport mechanisms, whereby 1-3 Na + or 2-3 K + couple to cholesterol export, and provide the first molecular description of transitions between distinct transport states.

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

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

Electrostatic Contributions to the Binding Free Energy of Nicotine to the Acetylcholine Binding Protein

Biomolecular binding relies on specific attractive interactions between two partner molecules, including electrostatics, dispersion, hydrophobicity, and solvation. Assessing the contributions of electrostatic interactions to binding is key to the understanding of ligand binding mechanisms and the design of improved biomolecular binders. For example, nicotine is a well-known agonist of nicotinic acetylcholine receptors (nAChRs), but the molecular mechanisms for the differential action of nicotine on brain and muscle nAChRs remain elusive. In this work, we have chosen the acetylcholine binding protein (AChBP) in complex with nicotine as a model system to interrogate the electrostatic contributions to nicotine binding. Our absolute binding free energy simulations confirm that nicotine binds AChBP predominantly in its protonated (charged) form. By comparing energetic contributions from decomposed interactions for either neutral or charged nicotine, our calculations shed light on the nature of the binding of nicotine to the AChBP. The preferred binding of charged nicotine over neutral nicotine originates from its stronger electrostatic interactions with AChBP, a cation-π interaction to a tryptophan residue and a hydrogen bond between nicotine and the backbone carbonyl of the tryptophan, whereas the major force driving the binding process appears to be van der Waals interactions. The various nonelectrostatic terms can also indirectly modulate the electrostatic interactions through fine-tuning the binding pose of the ligand in the binding site, providing an explanation of why the binding specificity of nicotine to the brain versus muscle nAChRs is driven by electrostatic interaction, given that the immediate binding site residues, including the key tryptophan residue, are identical in the two receptors.

Absolute binding free energies of mucroporin and its analog mucroporin-M1 with the heptad repeat 1 domain and RNA-dependent RNA polymerase of SARS-CoV-2

The peptide Mucroporin and its analog Mucroporin-M1 were studied using the molecular docking and molecular dynamics simulation of their complexation with two protein targets, the Heptad Repeat 1 (HR1) domain and RNA-dependent RNA polymerase (RdRp) of SARS-CoV-2. The molecular docking of the peptide-protein complexes was performed using the glowworm swarm optimization algorithm. The lowest energy poses were submitted to molecular dynamics simulation. Then, the binding free energies of Mucroporin and its analog Mucroporin-M1 with these two protein targets were calculated using the Multistate Bennett Acceptance Ratio (MBAR) method. It was verified that the peptides/HR1 domain complex showed stability in the interaction site determined by molecular docking. It was also found that Mucroporin-M1 has a much higher affinity than Mucroporin to the HR1 protein target. The peptides showed similar stability and affinity at the NTP binding site in the RdRp protein. Additional experimental studies are needed to confirm the antiviral activity of Mucroporin-M1 and a possible mechanism of action against SARS-CoV-2. However, here we indicate that Mucroporin-M1 may have potential antiviral activity against the HR1 domain with the possibility for further peptide optimization.Communicated by Ramaswamy H. Sarma.

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.

Finding alternatives to 5-fluorouracil: application of ensemble-based virtual screening for drug repositioning against human thymidylate synthase

5-fluorouracil and analogs are used in the treatment of many solid tumours. However, there are many cases of resistance and high toxicity associated with 5-fluorouracil chemotherapy. Repurposing FDA drugs against human thymidylate synthase revealed a number of FDA drugs that have a potential to be further developed for the treatment of various cancers for which 5-fluorouracil and analogs have been used for chemotherapy. Four FDA drugs prioritized for further validation included Erismodegib, Irinotecan, Conivaptan and Ergotamine. The role of water in mediating drug interactions and its contribution to the total binding energy was also shown. MM-PBSA calculations revealed that the binding affinity was the lowest for the hTS-Ergotamine complex (-66.702 ± 1.807 kJ/mol) suggesting moderate inhibition despite a large energetic contribution from van der Waal interactions (-190.889 ± 1.027 kJ/mol).Communicated by Ramaswamy H. Sarma.

Optimizing the Calculation of Free Energy Differences in Nonequilibrium Work SQM/MM Switching Simulations

A key step during indirect alchemical free energy simulations using quantum mechanical/molecular mechanical (QM/MM) hybrid potential energy functions is the calculation of the free energy difference ΔAlow→high between the low level (e.g., pure MM) and the high level of theory (QM/MM). A reliable approach uses nonequilibrium work (NEW) switching simulations in combination with Jarzynski's equation; however, it is computationally expensive. In this study, we investigate whether it is more efficient to use more shorter switches or fewer but longer switches. We compare results obtained with various protocols to reference free energy differences calculated with Crooks' equation. The central finding is that fewer longer switches give better converged results. As few as 200 sufficiently long switches lead to ΔAlow→high values in good agreement with the reference results. This optimized protocol reduces the computational cost by a factor of 40 compared to earlier work. We also describe two tools/ways of analyzing the raw data to detect sources of poor convergence. Specifically, we find it helpful to analyze the raw data (work values from the NEW switching simulations) in a quasi-time series-like manner. Principal component analysis helps to detect cases where one or more conformational degrees of freedom are different at the low and high level of theory.

Computational Tools for Accurate Binding Free-Energy Prediction

A quantitative thermodynamic understanding of the noncovalent association of (bio)molecules is of central importance in molecular life sciences. An important quantity characterizing (bio)molecular association is the binding affinity or absolute binding free energy. In recent years, the computational prediction of absolute binding free energies has evolved considerably in terms of accuracy, computational speed, and user-friendliness. In this chapter, we first give an overview of how absolute free energies are defined and how they can be determined with computational means. We proceed with an outline of the theoretical basis of the two most reliable methods, potential of mean force, and double decoupling calculations. In particular, we describe how the sampling problem can be alleviated by application of restraints. Finally, we provide step-by-step instructions of how to set up corresponding molecular simulations with a commonly employed molecular dynamics simulation engine.

Fast Equilibration of Water between Buried Sites and the Bulk by Molecular Dynamics with Parallel Monte Carlo Water Moves on Graphical Processing Units

Molecular dynamics (MD) simulations of proteins are commonly used to sample from the Boltzmann distribution of conformational states, with wide-ranging applications spanning chemistry, biophysics, and drug discovery. However, MD can be inefficient at equilibrating water occupancy for buried cavities in proteins that are inaccessible to the surrounding solvent. Indeed, the time needed for water molecules to equilibrate between the bulk solvent and the binding site can be well beyond what is practical with standard MD, which typically ranges from hundreds of nanoseconds to a few microseconds. We recently introduced a hybrid Monte Carlo/MD (MC/MD) method, which speeds up the equilibration of water between buried cavities and the surrounding solvent, while sampling from the thermodynamically correct distribution of states. While the initial implementation of the MC functionality led to considerable slowing of the overall simulations, here we address this problem with a parallel MC algorithm implemented on graphical processing units. This results in speed-ups of 10-fold to 1000-fold over the original MC/MD algorithm, depending on the system and simulation parameters. The present method is available for use in the AMBER simulation software.

Exploring the binding mechanism of positive allosteric modulators in human metabotropic glutamate receptor 2 using molecular dynamics simulations

Positive allosteric modulators (PAMs) of human metabotropic glutamate receptor 2 (hmGlu₂) are well-known in the treatment of psychiatric disorders for their higher selectivity and lower tolerance risk. A variety of PAMs have been reported over the last decade and two compounds were in Phase II clinical trials for schizophrenia and anxiety. These trials were discontinued on account of the unsatisfactory therapeutic efficacy, but PAMs were explored as novel treatments for addiction and epilepsy. Thus, it is still important to explore novel hmGlu₂ PAMs in the near future. Nowadays, the challenges in optimizing drug potency and improving scaffold diversity for PAMs are the noncomprehensive character analyses of multiple scaffolds; the exploration of the binding modes of PAMs in the allosteric binding site have been proposed to reduce this difficulty. However, there has been no comprehensive research about the binding profiles of PAMs in the hmGlu₂ receptor. To address this issue, this work explores the binding characters of eight PAMs representing five chemical series by multiple computational methods. As a result, the shared binding modes of the eight studied PAMs interacting with 15 residues in the allosteric binding site were defined. In addition, the reduced hydrophobicity with low electronegativity of R₁, increased hydrophobicity with low negative electron density of R₂ and the electronegativity of the linker were identified as indicators that regulate the affinity of PAMs. This finding agrees well with the physicochemical properties of reported multiple series PAMs. This comprehensive work sheds additional light on the binding mechanism and physicochemical regularity underlining PAMs affinity and could be further utilized as a structural and energetic blueprint for discovering and assessing novel PAMs for hmGlu₂.

From Bench to Biomolecular Simulation: Phospholipid Modulation of Potassium Channels

Potassium (K+) ion channels are crucial in numerous cellular processes as they hyperpolarise a cell through K+ conductance, returning a cell to its resting potential. K+ channel mutations result in multiple clinical complications such as arrhythmia, neonatal diabetes and migraines. Since 1995, the regulation of K+ channels by phospholipids has been heavily studied using a range of interdisciplinary methods such as cellular electrophysiology, structural biology and computational modelling. As a result, K+ channels are model proteins for the analysis of protein-lipid interactions. In this review, we will focus on the roles of lipids in the regulation of K+ channels, and how atomic-level structures, along with experimental techniques and molecular simulations, have helped guide our understanding of the importance of phospholipid interactions.

Learning protein-ligand binding affinity with atomic environment vectors

Scoring functions for the prediction of protein-ligand binding affinity have seen renewed interest in recent years when novel machine learning and deep learning methods started to consistently outperform classical scoring functions. Here we explore the use of atomic environment vectors (AEVs) and feed-forward neural networks, the building blocks of several neural network potentials, for the prediction of protein-ligand binding affinity. The AEV-based scoring function, which we term AEScore, is shown to perform as well or better than other state-of-the-art scoring functions on binding affinity prediction, with an RMSE of 1.22 pK units and a Pearson’s correlation coefficient of 0.83 for the CASF-2016 benchmark. However, AEScore does not perform as well in docking and virtual screening tasks, for which it has not been explicitly trained. Therefore, we show that the model can be combined with the classical scoring function AutoDock Vina in the context of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta$$\end{document}Δ-learning, where corrections to the AutoDock Vina scoring function are learned instead of the protein-ligand binding affinity itself. Combined with AutoDock Vina, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta$$\end{document}Δ-AEScore has an RMSE of 1.32 pK units and a Pearson’s correlation coefficient of 0.80 on the CASF-2016 benchmark, while retaining the docking and screening power of the underlying classical scoring function.

Dummy Atoms in Alchemical Free Energy Calculations

In calculations of relative free energy differences, the number of atoms of the initial and final states is rarely the same. This necessitates the introduction of dummy atoms. These placeholders interact with the physical system only by bonded energy terms. We investigate the conditions necessary so that the presence of dummy atoms does not influence the result of a relative free energy calculation. On the one hand, one has to ensure that dummy atoms only give a multiplicative contribution to the partition function so that their contribution cancels from double-free energy differences. On the other hand, the bonded terms used to attach a dummy atom (or group of dummy atoms) to the physical system have to maintain it in a well-defined position and orientation relative to the physical system. A detailed theoretical analysis of both aspects is provided, illustrated by 24 calculations of relative solvation free energy differences, for which all four legs of the underlying thermodynamic cycle were computed. Cycle closure (or lack thereof) was used as a sensitive indicator to probing the effects of dummy atom treatment on the resulting free energy differences. We find that a naive (but often practiced) treatment of dummy atoms results in errors of up to kBT when calculating the relative solvation free energy difference between two small solutes, such as methane and ammonia. While our analysis focuses on the so-called single topology approach to set up alchemical transformations, similar considerations apply to dual topology, at least many widely used variants thereof.

A Cloud Computing Platform for Scalable Relative and Absolute Binding Free Energy Predictions: New Opportunities and Challenges for Drug Discovery

Free energy perturbation (FEP) has become widely used in drug discovery programs for binding affinity prediction between candidate compounds and their biological targets. However, limitations of FEP applications also exist, including, but not limited to, high cost, long waiting time, limited scalability, and breadth of application scenarios. To overcome these problems, we have developed XFEP, a scalable cloud computing platform for both relative and absolute free energy predictions using optimized simulation protocols. XFEP enables large-scale FEP calculations in a more efficient, scalable, and affordable way, for example, the evaluation of 5000 compounds can be performed in 1 week using 50-100 GPUs with a computing cost roughly equivalent to the cost for the synthesis of only one new compound. By combining these capabilities with artificial intelligence techniques for goal-directed molecule generation and evaluation, new opportunities can be explored for FEP applications in the drug discovery stages of hit identification, hit-to-lead, and lead optimization based not only on structure exploitation within the given chemical series but also including evaluation and comparison of completely unrelated molecules during structure exploration in a larger chemical space. XFEP provides the basis for scalable FEP applications to become more widely used in drug discovery projects and to speed up the drug discovery process from hit identification to preclinical candidate compound nomination.

Inhibition Mechanism of Antimalarial Drugs Targeting the Cytochrome bc1 Complex

Plasmodium falciparum (P. falciparum) is the main parasite known to cause malaria in humans. The antimalarial drug atovaquone is known to inhibit the Q_o-site of the cytochrome bc₁ complex of P. falciparum, which ultimately blocks ATP synthesis, leading to cell death. Through the years, mutations of the P. falciparum cytochrome bc₁ complex, causing resistance to atovaquone, have emerged. The present investigation applies molecular dynamics (MD) simulations to study how the specific mutations Y279S and L282V, known to cause atovaquone resistance in malarial parasites, affect the inhibition mechanism of two known inhibitors. Binding free energy estimates were obtained through free energy perturbation calculations but were unable to confidently resolve the effects of mutations due to the great complexity of the binding environment. Meanwhile, basic mechanistic considerations from the MD simulations provide a detailed characterization of inhibitor binding modes and indicate that the Y279S mutation weakens the natural binding of the inhibitors, while no conclusive effect of the L282V mutation could be observed.

Automation of absolute protein-ligand binding free energy calculations for docking refinement and compound evaluation

Absolute binding free energy calculations with explicit solvent molecular simulations can provide estimates of protein-ligand affinities, and thus reduce the time and costs needed to find new drug candidates. However, these calculations can be complex to implement and perform. Here, we introduce the software BAT.py, a Python tool that invokes the AMBER simulation package to automate the calculation of binding free energies for a protein with a series of ligands. The software supports the attach-pull-release (APR) and double decoupling (DD) binding free energy methods, as well as the simultaneous decoupling-recoupling (SDR) method, a variant of double decoupling that avoids numerical artifacts associated with charged ligands. We report encouraging initial test applications of this software both to re-rank docked poses and to estimate overall binding free energies. We also show that it is practical to carry out these calculations cheaply by using graphical processing units in common machines that can be built for this purpose. The combination of automation and low cost positions this procedure to be applied in a relatively high-throughput mode and thus stands to enable new applications in early-stage drug discovery.

AMOEBA binding free energies for the SAMPL7 TrimerTrip host-guest challenge

As part of the SAMPL7 host-guest binding challenge, the AMOEBA force field was applied to calculate the absolute binding free energy for 16 charged organic ammonium guests to the TrimerTrip host, a recently reported acyclic cucurbituril-derived clip host structure with triptycene moieties at its termini. Here we report binding free energy calculations for this system using the AMOEBA polarizable atomic multipole force field and double annihilation free energy methodology. Conformational analysis of the host suggests three families of conformations that do not interconvert in solution on a time scale available to nanosecond molecular dynamics (MD) simulations. Two of these host conformers, referred to as the "indent" and "overlap" structures, are capable of binding guest molecules. As a result, the free energies of all 16 guests binding to both conformations were computed separately, and combined to produce values for comparison with experiment. Initial ranked results submitted as part of the SAMPL7 exercise had a mean unsigned error (MUE) from experimental binding data of 2.14 kcal/mol. Subsequently, a rigorous umbrella sampling reference calculation was used to better determine the free energy difference between unligated "indent" and "overlap" host conformations. Revised binding values for the 16 guests pegged to this umbrella sampling reference reduced the MUE to 1.41 kcal/mol, with a correlation coefficient (Pearson R) between calculated and experimental binding values of 0.832 and a rank correlation (Kendall τ) of 0.65. Overall, the AMOEBA results demonstrate no significant systematic error, suggesting the force field provides an accurate energetic description of the TrimerTrip host, and an appropriate balance of solvation and desolvation effects associated with guest binding.

Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation

Computational studies play an increasingly important role in chemistry and biophysics, mainly thanks to improvements in hardware and algorithms. In drug discovery and development, computational studies can reduce the costs and risks of bringing a new medicine to market. Computational simulations are mainly used to optimize promising new compounds by estimating their binding affinity to proteins. This is challenging due to the complexity of the simulated system. To assess the present and future value of simulation for drug discovery, we review key applications of advanced methods for sampling complex free-energy landscapes at near nonergodicity conditions and for estimating the rate coefficients of very slow processes of pharmacological interest. We outline the statistical mechanics and computational background behind this research, including methods such as steered molecular dynamics and metadynamics. We review recent applications to pharmacology and drug discovery and discuss possible guidelines for the practitioner. Recent trends in machine learning are also briefly discussed. Thanks to the rapid development of methods for characterizing and quantifying rare events, simulation's role in drug discovery is likely to expand, making it a valuable complement to experimental and clinical approaches.

Enhanced Jarzynski free energy calculations using weighted ensemble

The free energy of transitions between stable states is the key thermodynamic quantity that governs the relative probabilities of the forward and reverse reactions and the ratio of state probabilities at equilibrium. The binding free energy of a drug and its receptor is of particular interest, as it serves as an optimization function for drug design. Over the years, many computational methods have been developed to calculate binding free energies, and while many of these methods have a long history, issues such as convergence of free energy estimates and the projection of a binding process onto order parameters remain. Over 20 years ago, the Jarzynski equality was derived with the promise to calculate equilibrium free energies by measuring the work applied to short nonequilibrium trajectories. However, these calculations were found to be dominated by trajectories with low applied work that occur with extremely low probability. Here, we examine the combination of weighted ensemble algorithms with the Jarzynski equality. In this combined method, an ensemble of nonequilibrium trajectories are run in parallel, and cloning and merging operations are used to preferentially sample low-work trajectories that dominate the free energy calculations. Two additional methods are also examined: (i) a novel weighted ensemble resampler that samples trajectories directly according to their importance to the work of work and (ii) the diffusion Monte Carlo method using the applied work as the selection potential. We thoroughly examine both the accuracy and efficiency of unbinding free energy calculations for a series of model Lennard-Jones atom pairs with interaction strengths ranging from 2 kcal/mol to 20 kcal/mol. We find that weighted ensemble calculations can more efficiently determine accurate binding free energies, especially for deeper Lennard-Jones well depths.

Discovery of Novel Tankyrase Inhibitors through Molecular Docking-Based Virtual Screening and Molecular Dynamics Simulation Studies

Tankyrase enzymes (TNKS), a core part of the canonical Wnt pathway, are a promising target in the search for potential anti-cancer agents. Although several hundreds of the TNKS inhibitors are currently known, identification of their novel chemotypes attracts considerable interest. In this study, the molecular docking and machine learning-based virtual screening techniques combined with the physico-chemical and ADMET (absorption, distribution, metabolism, excretion, toxicity) profile prediction and molecular dynamics simulations were applied to a subset of the ZINC database containing about 1.7 M commercially available compounds. Out of seven candidate compounds biologically evaluated in vitro for their inhibition of the TNKS2 enzyme using immunochemical assay, two compounds have shown a decent level of inhibitory activity with the IC₅₀ values of less than 10 nM and 10 μM. Relatively simple scores based on molecular docking or MM-PBSA (molecular mechanics, Poisson-Boltzmann, surface area) methods proved unsuitable for predicting the effect of structural modification or for accurate ranking of the compounds based on their binding energies. On the other hand, the molecular dynamics simulations and Free Energy Perturbation (FEP) calculations allowed us to further decipher the structure-activity relationships and retrospectively analyze the docking-based virtual screening performance. This approach can be applied at the subsequent lead optimization stages.

Ligand-protein interactions in lysozyme investigated through a dual-resolution model

A fully atomistic (AT) modeling of biological macromolecules at relevant length- and time-scales is often cumbersome or not even desirable, both in terms of computational effort required and a posteriori analysis. This difficulty can be overcome with the use of multiresolution models, in which different regions of the same system are concurrently described at different levels of detail. In enzymes, computationally expensive AT detail is crucial in the modeling of the active site in order to capture, for example, the chemically subtle process of ligand binding. In contrast, important yet more collective properties of the remainder of the protein can be reproduced with a coarser description. In the present work, we demonstrate the effectiveness of this approach through the calculation of the binding free energy of hen egg white lysozyme with the inhibitor di-N-acetylchitotriose. Particular attention is payed to the impact of the mapping, that is, the selection of AT and coarse-grained residues, on the binding free energy. It is shown that, in spite of small variations of the binding free energy with respect to the active site resolution, the separate contributions coming from different energetic terms (such as electrostatic and van der Waals interactions) manifest a stronger dependence on the mapping, thus pointing to the existence of an optimal level of intermediate resolution.

Proton Control of Transitions in an Amino Acid Transporter

Amino acid transport into the cell is often coupled to the proton electrochemical gradient, as found in the solute carrier 36 family of proton-coupled amino acid transporters. Although no structure of a human proton-coupled amino acid transporter exists, the crystal structure of a related homolog from bacteria, GkApcT, has recently been solved in an inward-occluded state and allows an opportunity to examine how protons are coupled to amino acid transport. Our working hypothesis is that release of the amino acid substrate is facilitated by the deprotonation of a key glutamate residue (E115) located at the bottom of the binding pocket, which forms part of the intracellular gate, allowing the protein to transition from an inward-occluded to an inward-open conformation. During unbiased molecular dynamics simulations, we observed a transition from the inward-occluded state captured in the crystal structure to a much more open state, which we consider likely to be representative of the inward-open state associated with substrate release. To explore this and the role of protons in these transitions, we have used umbrella sampling to demonstrate that the transition from inward occluded to inward open is more energetically favorable when E115 is deprotonated. That E115 is likely to be protonated in the inward-occluded state and deprotonated in the inward-open state is further confirmed via the use of absolute binding free energies. Finally, we also show, via the use of absolute binding free energy calculations, that the affinity of the protein for alanine is very similar regardless of either the conformational state or the protonation of E115, presumably reflecting the fact that all the key interactions are deep within the binding cavity. Together, our results give a detailed picture of the role of protons in driving one of the major transitions in this transporter.

Insights into Membrane Protein-Lipid Interactions from Free Energy Calculations

Integral membrane proteins are regulated by specific interactions with lipids from the surrounding bilayer. The structures of protein–lipid complexes can be determined through a combination of experimental and computational approaches, but the energetic basis of these interactions is difficult to resolve. Molecular dynamics simulations provide the primary computational technique to estimate the free energies of these interactions. We demonstrate that the energetics of protein–lipid interactions may be reliably and reproducibly calculated using three simulation-based approaches: potential of mean force calculations, alchemical free energy perturbation, and well-tempered metadynamics. We employ these techniques within the framework of a coarse-grained force field and apply them to both bacterial and mammalian membrane protein–lipid systems. We demonstrate good agreement between the different techniques, providing a robust framework for their automated implementation within a pipeline for annotation of newly determined membrane protein structures.