Alchemical Free Energy Calculations Research Articles

Design of protein fold-switches using alchemical mutation free energy calculations

Design of protein fold-switches using alchemical mutation free energy calculations

Ligand-binding affinity prediction for membrane proteins with alchemical free-energy calculation methods

Ligand-binding affinity prediction for membrane proteins with alchemical free-energy calculation methods

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.

Implementation and Validation of an OpenMM Plugin for the Deep Potential Representation of Potential Energy.

Machine learning potentials, particularly the deep potential (DP) model, have revolutionized molecular dynamics (MD) simulations, striking a balance between accuracy and computational efficiency. To facilitate the DP model's integration with the popular MD engine OpenMM, we have developed a versatile OpenMM plugin. This plugin supports a range of applications, from conventional MD simulations to alchemical free energy calculations and hybrid DP/MM simulations. Our extensive validation tests encompassed energy conservation in microcanonical ensemble simulations, fidelity in canonical ensemble generation, and the evaluation of the structural, transport, and thermodynamic properties of bulk water. The introduction of this plugin is expected to significantly expand the application scope of DP models within the MD simulation community, representing a major advancement in the field.

Identification of novel LRRK2 inhibitors by structure-based virtual screening and alchemical free energy calculation.

The Leucine-rich repeat kinase 2 (LRRK2) target has been identified as a promising drug target for Parkinson's disease (PD) treatment. This study focuses on optimizing the activity of LRRK2 inhibitors using alchemical relative binding free energy (RBFE) calculations. Initially, we assessed various free energy calculation methods across different LRRK2 kinase inhibitor scaffolds. The results indicate that alchemical free energy calculations are promising for prospective predictions on LRRK2 inhibitors, especially for the aminopyrimidine scaffold with an RMSE of 1.15 kcal mol-1 and Rp of 0.83. Following this, we optimized a potent LRRK2 kinase inhibitor identified from previous virtual screenings, featuring a novel scaffold. Guided by RBFE predictions using alchemical methods, this optimization led to the discovery of compound LY2023-001. This compound, with a [1,2,4]triazolo[5,6-b]indole scaffold, exhibited enhanced inhibitory activity against G2019S LRRK2 (IC50 = 12.9 nM). Molecular dynamics (MD) simulations revealed that LY2023-001 formed stable hydrogen bonds with Glu1948, and Ala1950 in the G2019S LRRK2 protein. Additionally, its phenyl substituents engage in strong electrostatic interactions with Lys1906 and van der Waals interactions with Leu1885, Phe1890, Val1893, Ile1933, Met1947, Leu1949, Leu2001, Ala2016, and Asp2017. Our findings underscore the potential of computational methods in the successful optimization of small molecules, offering important insights for the development of novel LRRK2 inhibitors.

Solvent effects on extractant conformational energetics in liquid-liquid extraction: a simulation study of molecular solvents and ionic liquids.

Extractant design in liquid-liquid extraction (LLE) is a research frontier of metal ion separations that typically focuses on the direct extractant-metal interactions. However, a more detailed understanding of energetic drivers of separations beyond primary metal coordination is often lacking, including the role of solvent in the extractant phase. In this work, we propose a new mechanism for enhancing metal-complexant energetics with nanostructured solvents. Using molecular dynamics simulations with umbrella sampling, we find that the organic solvent can reshape the energetics of the extractant's intramolecular conformational landscape. We calculate free energy profiles of different conformations of a representative bidentate extractant, n-octyl(phenyl)-N,N-diisobutyl carbamoyl methyl phosphinoxide (CMPO), in four different solvents: dodecane, tributyl phosphate (TBP), and dry and wet ionic liquid (IL) 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIM][Tf2N]). By promoting reorganization of the extractant molecule into its binding conformation, our findings reveal how particular solvents can ameliorate this unfavorable step of the metal separation process. In particular, the charge alternating nanodomains formed in ILs substantially reduce the free energy penalty associated with extractant reorganization. Importantly, using alchemical free energy calculations, we find that this stabilization persists even when we explicitly include the extracted cation. These findings provide insight into the energetic drivers of metal ion separations and potentially suggest a new approach to designing effective separations using a molecular-level understanding of solvent effects.

Alchemical approach performance in calculating the ligand-binding free energy.

Alchemical binding free energy calculations are one of the most accurate methods for estimating ligand-binding affinity. Assessing the accuracy of the approach over protein targets is one of the most interesting issues. The free energy difference of binding between a protein and a ligand was calculated via the alchemical approach. The alchemical approach exhibits satisfactory accuracy over four targets, including AmpC beta-lactamase (AmpC); glutamate receptor, ionotropic kainate 1 (GluK1); heat shock protein 90 (Hsp90); and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) main protease (Mpro). In particular, the correlation coefficients between calculated binding free energies and the respective experiments over four targets range from 0.56 to 0.86. The affinity computed via free energy perturbation (FEP) simulations is overestimated over the experimental value. Particularly, the electrostatic interaction free energy rules the binding process of ligands to AmpC and GluK1. However, the van der Waals (vdW) interaction free energy plays an important role in the ligand-binding processes of HSP90 and SARS-CoV-2 Mpro. The obtained results associate with the hydrophilic or hydrophobic properties of the ligands. This observation may enhance computer-aided drug design.

Probing the formation of a hetero-dimeric membrane transport complex with dual in vitro and in silico mutagenesis.

The reversible association of transmembrane helices is a fundamental mechanism in how living cells convey information and respond to physiological events. The cardiac calcium transport regulator phospholamban (PLN) is an example of a single-span transmembrane protein that populates a variety of reversible and competing oligomeric states. PLN primarily forms monomers and pentamers in the membrane, where the PLN pentamer is a storage form and the PLN monomer forms a hetero-dimeric inhibitory complex with SERCA. The binding affinity and free-energy of formation of the SERCA-PLN complex in a membrane have not been determined. As is the case for most transmembrane protein interactions, measuring these quantities experimentally is extremely challenging. In this study, we estimated binding affinities by employing in silico alchemical free-energy calculations for all PLN transmembrane alanine substitutions in a membrane bilayer. The binding affinities were calculated separately for the SERCA-PLN complex, a PLN monomer, and a PLN pentamer and compared to in vitro functional measurements of SERCA regulation by the PLN alanine substitutions. Initially, the changes in SERCA inhibition by PLN alanine substitutions were compared to the changes in free energy for the SERCA-PLN complex formed from the PLN monomer. However, the functional data for the PLN alanine substitutions were better explained by the formation of the SERCA-PLN complex directly from the PLN pentamer. This finding points to an inhibitory mechanism favoring conformational selection of SERCA and the interaction of a PLN pentamer with SERCA for 'delivery' of a PLN monomer to the inhibitory site. The implications of these findings suggest that the energetics of helix exchange between homo- and hetero-oligomeric signaling complexes is favored over an intermediate involving a free monomeric helix in the membrane bilayer.

Assessment of Halogen Off-Center Point-Charge Models Using Explicit Solvent Simulations.

Compounds containing halogens can form halogen bonds (XBs) with biological targets such as proteins and membranes due to their anisotropic electrostatic potential. To accurately describe this anisotropy, off-center point-charge (EP) models are commonly used in force field methods, allowing the description of XBs at the molecular mechanics and molecular dynamics level. Various EP implementations have been documented in the literature, and despite being efficient in reproducing protein-ligand geometries and sampling of XBs, it is unclear how well these EP models predict experimental properties such as hydration free energies (ΔGhyd), which are often used to validate force field performance. In this work, we report the first assessment of three EP models using alchemical free energy calculations to predict ΔGhyd values. We show that describing the halogen anisotropy using some EP models can lead to a slight improvement in the prediction of the ΔGhyd when compared with the models without EP, especially for the chlorinated compounds; however, this improvement is not related to the establishment of XBs but is most likely due to the improvement of the sampling of hydrogen bonds. We also highlight the importance of the choice of the EP model, especially for the iodinated molecules, since a slight tendency to improve the prediction is observed for compounds with a larger σ-hole but significantly worse results were obtained for compounds that are weaker XB donors.

Structure-Based Optimization of Carbendazim-Derived Tubulin Polymerization Inhibitors through Alchemical Free Energy Calculations.

Carbendazim derivatives, commonly used as antiparasitic drugs, have shown potential as anticancer agents due to their ability to induce cell cycle arrest and apoptosis in human cancer cells by inhibiting tubulin polymerization. Crystallographic structures of α/β-tubulin multimers complexed with nocodazole and mebendazole, two carbendazim derivatives with potent anticancer activity, highlighted the possibility of designing compounds that occupy both benzimidazole- and colchicine-binding sites. In addition, previous studies have demonstrated that the incorporation of a phenoxy group at position 5/6 of carbendazim increases the antiproliferative activity in cancer cell lines. Despite the significant progress made in identifying new tubulin-targeting anticancer compounds, further modifications are needed to enhance their potency and safety. In this study, we explored the impact of modifying the phenoxy substitution pattern on antiproliferative activity. Alchemical free energy calculations were used to predict the binding free energy difference upon ligand modification and define the most viable path for structure optimization. Based on these calculations, seven compounds were synthesized and evaluated against lung and colon cancer cell lines. Our results showed that compound 5a, which incorporates an α-naphthyloxy substitution, exhibits the highest antiproliferative activity against both cancer lines (SK-LU-1 and SW620, IC50 < 100 nM) and induces morphological changes in the cells associated with mitotic arrest and mitotic catastrophe. Nevertheless, the tubulin polymerization assay showed that 5a has a lower inhibitory potency than nocodazole. Molecular dynamics simulations suggested that this low antitubulin activity could be associated with the loss of the key H-bond interaction with V236. This study provides insights into the design of novel carbendazim derivatives with anticancer activity.

Alchemical Free Energy Calculations on Membrane-Associated Proteins.

Membrane proteins have diverse functions within cells and are well-established drug targets. The advances in membrane protein structural biology have revealed drug and lipid binding sites on membrane proteins, while computational methods such as molecular simulations can resolve the thermodynamic basis of these interactions. Particularly, alchemical free energy calculations have shown promise in the calculation of reliable and reproducible binding free energies of protein-ligand and protein-lipid complexes in membrane-associated systems. In this review, we present an overview of representative alchemical free energy studies on G-protein-coupled receptors, ion channels, transporters as well as protein-lipid interactions, with emphasis on best practices and critical aspects of running these simulations. Additionally, we analyze challenges and successes when running alchemical free energy calculations on membrane-associated proteins. Finally, we highlight the value of alchemical free energy calculations calculations in drug discovery and their applicability in the pharmaceutical industry.

Comparison of Equilibrium and Nonequilibrium Approaches for Relative Binding Free Energy Predictions.

Alchemical relative binding free energy calculations have recently found important applications in drug optimization. A series of congeneric compounds are generated from a preidentified lead compound, and their relative binding affinities to a protein are assessed in order to optimize candidate drugs. While methods based on equilibrium thermodynamics have been extensively studied, an approach based on nonequilibrium methods has recently been reported together with claims of its superiority. However, these claims pay insufficient attention to the basis and reliability of both methods. Here we report a comparative study of the two approaches across a large data set, comprising more than 500 ligand transformations spanning in excess of 300 ligands binding to a set of 14 diverse protein targets. Ensemble methods are essential to quantify the uncertainty in these calculations, not only for the reasons already established in the equilibrium approach but also to ensure that the nonequilibrium calculations reside within their domain of validity. If and only if ensemble methods are applied, we find that the nonequilibrium method can achieve accuracy and precision comparable to those of the equilibrium approach. Compared to the equilibrium method, the nonequilibrium approach can reduce computational costs but introduces higher computational complexity and longer wall clock times. There are, however, cases where the standard length of a nonequilibrium transition is not sufficient, necessitating a complete rerun of the entire set of transitions. This significantly increases the computational cost and proves to be highly inconvenient during large-scale applications. Our findings provide a key set of recommendations that should be adopted for the reliable implementation of nonequilibrium approaches to relative binding free energy calculations in ligand-protein systems.

Molecular Insights into the Covalent Binding of Zoxamide to the β-Tubulin of Botrytis cinerea.

Botrytis cinerea is a fungal plant pathogen that causes significant economic losses in the agricultural industry worldwide. Fungicides that target microtubules, such as carbendazim (CBZ), diethofencarb (DEF), and zoxamide (ZOX), are widely used in crop protection against this pathogen. These groups of compounds exert their fungicidal activity by disrupting the microtubule assembly by binding to the β-tubulin subunit, provoking cell-cycle arrest and cell death. However, with the appearance of isolates resistant to these compounds, it is necessary to search for new alternatives to control this pathogenic fungus. In this work, we gained insight into the binding and stability of these fungicides in the benzimidazole binding site of B. cinerea β-tubulin through different computational approaches. Our molecular dynamics simulation replicas showed that R enantiomers of ZOX and its analog RH-4032 had better interaction profiles at the site compared to S enantiomers. The simulations also revealed that while the R-isomer fungicides formed H-bonds with the main chain carbonyl of V236 or the side chain residue of S314, only CBZ interacted with E198. Previous experimental data have identified key mutations in B. cinerea's β-tubulin gene that lead to the development of resistance or, on the contrary, increased sensitivity for treatment with these fungicide compounds. In agreement with experimental findings, alchemical free energy calculations showed that E198A and E198V mutations in B. cinerea β-tubulin have high sensitivity to (R)-ZOX, whereas the E198K mutation decreased its affinity. Similarly, the results obtained explain the resistance to CBZ of B. cinerea isolates with E198A/V/K mutations and the insensitivity of the wild-type organism to DEF. Our work provides a deeper insight into the molecular mechanism of action of these fungicides, highlighting the importance of understanding the interaction profiles to develop more effective antifungal agents.

Chemical accuracy prediction of molecular solvation and partition in ionic liquids with educated estimators

Ionic liquids (ILs) derivatives as novel green solvents are widely employed in laboratory and industrial applications. Many computational tools have been developed to compute various physiochemical properties of ILs species, e.g., mass density and viscosity. However, despite their central role as solvents, predictive tools for the solvation of external agents and the partition between water and ILs phases are rather limited. Common selections are atomistic simulations, especially the alchemical method. However, the relatively high computational costs could be harmful to large-scale applications. In this work, we develop a series of low-cost machine-learning estimators to exploit further the chemical-accuracy frontier. 1764 solvation and 1764 water-ILs transfer free energies involving 120 gaseous or drug-like solutes and many commonly applied ILs families are gathered from experimental references to form the dataset with a diverse coverage of chemical spaces. The best-performing tree-based method could predict simultaneously solvation and water-ILs biphasic partition thermodynamics with a state-of-the-art performance of ∼ 0.13 kcal/mol MAE, ∼0.25 kcal/mol RMSE, ∼0.98 Pearson r and ∼ 0.94 Kendall τ, beating transferable tools such as alchemical free energy calculations in a series of face-to-face comparisons.

Revisiting the pseudo-supercritical path method: An improved formulation for the alchemical calculation of solid-liquid coexistence.

Alchemical free energy calculations via molecular dynamics have been applied to obtain thermodynamic properties related to solid-liquid equilibrium conditions, such as melting points. In recent years, the pseudo-supercritical path (PSCP) method has proved to be an important approach to melting point prediction due to its flexibility and applicability. In the present work, we propose improvements to the PSCP alchemical cycle to make it more compact and efficient through a concerted evaluation of different potential energies. The multistate Bennett acceptance ratio (MBAR) estimator was applied at all stages of the new cycle to provide greater accuracy and uniformity, which is essential concerning uncertainty calculations. In particular, for the multistate expansion stage from solid to liquid, we employed the MBAR estimator with a reduced energy function that allows affine transformations of coordinates. Free energy and mean derivative profiles were calculated at different cycle stages for argon, triazole, propenal, and the ionic liquid 1-ethyl-3-methyl-imidazolium hexafluorophosphate. Comparisons showed a better performance of the proposed method than the original PSCP cycle for systems with higher complexity, especially the ionic liquid. A detailed study of the expansion stage revealed that remapping the centers of mass of the molecules or ions is preferable to remapping the coordinates of each atom, yielding better overlap between adjacent states and improving the accuracy of the methodology.

Identifying and Overcoming the Sampling Challenges in Relative Binding Free Energy Calculations of a Model Protein:Protein Complex.

Relative alchemical binding free energy calculations are routinely used in drug discovery projects to optimize the affinity of small molecules for their drug targets. Alchemical methods can also be used to estimate the impact of amino acid mutations on protein:protein binding affinities, but these calculations can involve sampling challenges due to the complex networks of protein and water interactions frequently present in protein:protein interfaces. We investigate these challenges by extending a graphics processing unit (GPU)-accelerated open-source relative free energy calculation package (Perses) to predict the impact of amino acid mutations on protein:protein binding. Using the well-characterized model system barnase:barstar, we describe analyses for identifying and characterizing sampling problems in protein:protein relative free energy calculations. We find that mutations with sampling problems often involve charge-changes, and inadequate sampling can be attributed to slow degrees of freedom that are mutation-specific. We also explore the accuracy and efficiency of current state-of-the-art approaches─alchemical replica exchange and alchemical replica exchange with solute tempering─for overcoming relevant sampling problems. By employing sufficiently long simulations, we achieve accurate predictions (RMSE 1.61, 95% CI: [1.12, 2.11] kcal/mol), with 86% of estimates within 1 kcal/mol of the experimentally determined relative binding free energies and 100% of predictions correctly classifying the sign of the changes in binding free energies. Ultimately, we provide a model workflow for applying protein mutation free energy calculations to protein:protein complexes, and importantly, catalog the sampling challenges associated with these types of alchemical transformations. Our free open-source package (Perses) is based on OpenMM and is available at https://github.com/choderalab/perses.

Accurate modelling of pyrrolidinium ionic liquids with charge and vdW scaling

Molecular simulation as a complementing tool to experimental measurements has grown to be an instrument with predictive power for ionic liquids (ILs) derivatives. The combination of molecule-specific atomic charges generated with ab initio calculations and bonded and vdW parameters extracted from pre-fitted transferable force fields serves as the common practice in this field. Charge scaling is often applied to account for charge transfer and polarization effects and the scaling factor 0.8 has been concluded as a near-optimal solution in many scientific reports based on detailed analyses of various structural and thermodynamic observables. However, for ILs from the pyrrolidinium family investigated in the current work, we show that the charge scaling treatment cannot really minimize the experiment-simulation deviations to an acceptable level, which calls for further parameter adjustment. Following the modelling protocol summarized in our previous works, we tune the vdW radius of ILs-forming ions with a 298 K density scan and secure a parameter set that satisfactorily reproduces not only the room-temperature properties but also the mass densities in a large temperature range from 288 K to 348 K. The slopes of the vdW-scaling profiles are between −1.9 g/cm3 and −1.6 g/cm3, which are similar to quinuclidinium ILs investigated in our previous work. This phenomenon suggests the similarity of responding behaviors of the two ILs family during vdW scaling, and this range of response strengths could possibly be representative for ILs vdW scaling. Aside from bulk solvents, we further consider the interaction of ILs with a series of external organic agents. Following the previously accumulated experience, a slightly modified vdW scaling factor is picked as an option balancing different interactions within the heterogeneous solution. Nonequilibrium alchemical free energy calculations are conducted to compute solvation free energies in ILs and also the distribution (partition) behaviors of solutes between aqueous and ILs phases. The computed physiochemical properties involving pyrrolidinium ILs agree well with the experimental reference. Another feature of the selected pyrrolidinium ILs is the systematic variation of the length of the alkyl substituting chain, which enables a direct investigation of the chain-length dependence of the prediction accuracies for both bulk density and solvation/partition thermodynamics. Interestingly, with the chain-length variation, the error of bulk density exhibits a monotonic response, while a fluctuating (non-monotonic) behavior is observed for prediction errors of solvation and partition thermodynamics, which is related to the diverse features of solute-solvent interactions. Therefore, the observed behaviors of the properties of bulk solvents cannot be generalized to the solvation/partition behaviors of the same solvent, and accurate reproductions of bulk behaviors do not guarantee accurate calculations of solvation and partition thermodynamics.

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.

Integrative Approach to Dissect the Drug Resistance Mechanism of the H172Y Mutation of SARS-CoV-2 Main Protease.

Nirmatrelvir is an orally available inhibitor of SARS-CoV-2 main protease (Mpro) and the main ingredient of Paxlovid, a drug approved by the U.S. Food and Drug Administration for high-risk COVID-19 patients. Recently, a rare natural mutation, H172Y, was found to significantly reduce nirmatrelvir's inhibitory activity. As the COVID-19 cases skyrocket in China and the selective pressure of antiviral therapy builds in the US, there is an urgent need to characterize and understand how the H172Y mutation confers drug resistance. Here, we investigated the H172Y Mpro's conformational dynamics, folding stability, catalytic efficiency, and inhibitory activity using all-atom constant pH and fixed-charge molecular dynamics simulations, alchemical and empirical free energy calculations, artificial neural networks, and biochemical experiments. Our data suggest that the mutation significantly weakens the S1 pocket interactions with the N-terminus and perturbs the conformation of the oxyanion loop, leading to a decrease in the thermal stability and catalytic efficiency. Importantly, the perturbed S1 pocket dynamics weaken the nirmatrelvir binding in the P1 position, which explains the decreased inhibitory activity of nirmatrelvir. Our work demonstrates the predictive power of the combined simulation and artificial intelligence approaches, and together with biochemical experiments, they can be used to actively surveil continually emerging mutations of SARS-CoV-2 Mpro and assist the optimization of antiviral drugs. The presented approach, in general, can be applied to characterize mutation effects on any protein drug targets.

Alchemical Free Energy and Hamiltonian Replica Exchange Molecular Dynamics to Compute Hydrofluorocarbon Isotherms in Imidazolium-Based Ionic Liquids.

Ionic liquids (ILs) have shown promise for applications that leverage differential gas solubility in an IL solvent, e.g., gas separations. Although most available literature provides Henry's law constants, the ability to efficiently estimate full isotherms is important for engineering design calculations. Molecular simulation can be used as a tool to predict full isotherms of gas in ILs. However, particle insertions or deletions in a charge-dense IL medium and the sluggish conformational dynamics of ILs present two sampling challenges for these systems. We therefore devised a method that uses Hamiltonian replica exchange (HREX) molecular dynamics (MD) combined with alchemical free energy calculations to compute full solubility isotherms of two different hydrofluorocarbons (HFCs) in imidazolium-based IL binary mixtures. This workflow is significantly faster than the Gibbs ensemble Monte Carlo (GEMC) simulations which fail to deal with the slow conformational relaxation caused by the sluggish dynamics of ILs. Multiple free energy estimators, including thermodynamic integration, free energy perturbation, and multistate Bennett acceptance ratio method, provided consistent results. Overall, the simulated Henry's law constant, isotherm curvature, and solubility trends match experimental results reasonably well. We close by calculating the full solubility isotherms of two HFCs in IL mixtures that have not been reported in the literature, demonstrating the potential of this method to be used for solubility prediction and setting the stage for future computational screening studies that search for the "best" IL to separate azeotropic HFC mixtures.