Coiled-coil domains are sufficient to drive liquid-liquid phase separation in protein models.

Liquid-liquid phase separation (LLPS) is thought to be a main driving force in the formation of membraneless organelles. Examples of such organelles include the centrosome, central spindle, and stress granules. Recently, it has been shown that coiled-coil (CC) proteins, such as the centrosomal proteins pericentrin, spd-5, and centrosomin, might be capable of LLPS. CC domains have physical features that could make them the drivers of LLPS, but it is unknown if they play a direct role in the process. We developed a coarse-grained simulation framework for investigating the LLPS propensity of CC proteins, in which interactions that support LLPS arise solely from CC domains. We show, using this framework, that the physical features of CC domains are sufficient to drive LLPS of proteins. The framework is specifically designed to investigate how the number of CC domains, as well as the multimerization state of CC domains, can affect LLPS. We show that small model proteins with as few as two CC domains can phase separate. Increasing the number of CC domains up to four per protein can somewhat increase LLPS propensity. We demonstrate that trimer-forming and tetramer-forming CC domains have a dramatically higher LLPS propensity than dimer-forming coils, which shows that multimerization state has a greater effect on LLPS than the number of CC domains per protein. These data support the hypothesis of CC domains as drivers of protein LLPS, and have implications in future studies to identify the LLPS-driving regions of centrosomal and central spindle proteins.

Parameterization of General Organic Polymers within the Open Force Field Framework.

Polymer and chemically modified biopolymer systems present unique challenges to traditional molecular simulation preparation workflows. First, typical polymer and biomolecular input formats, such as Protein Data Bank (PDB) files, lack adequate chemical information needed for the parameterization of new chemistries. Second, polymers are typically too large for accurate partial charge generation methods. In this work, we employ direct chemical perception through the Open Force Field toolkit to create a flexible polymer simulation workflow for organic polymers, encompassing everything from biopolymers to soft materials. We propose and test a new input specification for monomer information that can, along with a 3D conformational geometry, parametrize and simulate most soft-material systems within the same workflow used for smaller ligands. The monomer format encompasses a subset of the SMIRKS substructure query language to uniquely identify chemical information and repeating charges in underspecified systems through matching atomic connectivity. This workflow is combined with several different approaches for automatic partial-charge generation for larger systems. As an initial proof of concept, a variety of diverse polymeric systems were parametrized with the Open Force Field toolkit, including functionalized proteins, DNA, homopolymers, cross-linked systems, and sugars. Additionally, shape properties and radial distribution functions were computed from molecular dynamics simulations of poly(ethylene glycol), polyacrylamide, and poly(N-isopropylacrylamide) homopolymers in aqueous solution and compared to previous simulation results in order to demonstrate a start-to-finish workflow for simulation and property prediction. We expect that these tools will greatly expedite the day-to-day computational research of soft-matter simulations and create a robust atomic-scale polymer specification in conjunction with existing polymer structural notations.

Bayesian-Inference-Driven Model Parametrization and Model Selection for 2CLJQ Fluid Models.

A high level of physical detail in a molecular model improves its ability to perform high accuracy simulations but can also significantly affect its complexity and computational cost. In some situations, it is worthwhile to add complexity to a model to capture properties of interest; in others, additional complexity is unnecessary and can make simulations computationally infeasible. In this work, we demonstrate the use of Bayesian inference for molecular model selection, using Monte Carlo sampling techniques accelerated with surrogate modeling to evaluate the Bayes factor evidence for different levels of complexity in the two-centered Lennard-Jones + quadrupole (2CLJQ) fluid model. Examining three nested levels of model complexity, we demonstrate that the use of variable quadrupole and bond length parameters in this model framework is justified only for some chemistries. Through this process, we also get detailed information about the distributions and correlation of parameter values, enabling improved parametrization and parameter analysis. We also show how the choice of parameter priors, which encode previous model knowledge, can have substantial effects on the selection of models, penalizing careless introduction of additional complexity. We detail the computational techniques used in this analysis, providing a roadmap for future applications of molecular model selection via Bayesian inference and surrogate modeling.

Identifying signatures of proteolytic stability and monomeric propensity in O-glycosylated insulin using molecular simulation.

Insulin has been commonly adopted as a peptide drug to treat diabetes as it facilitates the uptake of glucose from the blood. The development of oral insulin remains elusive over decades owing to its susceptibility to the enzymes in the gastrointestinal tract and poor permeability through the intestinal epithelium upon dimerization. Recent experimental studies have revealed that certain O-linked glycosylation patterns could enhance insulin's proteolytic stability and reduce its dimerization propensity, but understanding such phenomena at the molecular level is still difficult. To address this challenge, we proposed and tested several structural determinants that could potentially influence insulin's proteolytic stability and dimerization propensity. We used these metrics to assess the properties of interest from [Formula: see text] aggregate molecular dynamics of each of 12 targeted insulin glyco-variants from multiple wild-type crystal structures. We found that glycan-involved hydrogen bonds and glycan-dimer occlusion were useful metrics predicting the proteolytic stability and dimerization propensity of insulin, respectively, as was in part the solvent-accessible surface area of proteolytic sites. However, other plausible metrics were not generally predictive. This work helps better explain how O-linked glycosylation influences the proteolytic stability and monomeric propensity of insulin, illuminating a path towards rational molecular design of insulin glycoforms.

The SAMPL6 SAMPLing challenge: assessing the reliability and efficiency of binding free energy calculations.

Approaches for computing small molecule binding free energies based on molecular simulations are now regularly being employed by academic and industry practitioners to study receptor-ligand systems and prioritize the synthesis of small molecules for ligand design. Given the variety of methods and implementations available, it is natural to ask how the convergence rates and final predictions of these methods compare. In this study, we describe the concept and results for the SAMPL6 SAMPLing challenge, the first challenge from the SAMPL series focusing on the assessment of convergence properties and reproducibility of binding free energy methodologies. We provided parameter files, partial charges, and multiple initial geometries for two octa-acid (OA) and one cucurbit[8]uril (CB8) host-guest systems. Participants submitted binding free energy predictions as a function of the number of force and energy evaluations for seven different alchemical and physical-pathway (i.e., potential of mean force and weighted ensemble of trajectories) methodologies implemented with the GROMACS, AMBER, NAMD, or OpenMM simulation engines. To rank the methods, we developed an efficiency statistic based on bias and variance of the free energy estimates. For the two small OA binders, the free energy estimates computed with alchemical and potential of mean force approaches show relatively similar variance and bias as a function of the number of energy/force evaluations, with the attach-pull-release (APR), GROMACS expanded ensemble, and NAMD double decoupling submissions obtaining the greatest efficiency. The differences between the methods increase when analyzing the CB8-quinine system, where both the guest size and correlation times for system dynamics are greater. For this system, nonequilibrium switching (GROMACS/NS-DS/SB) obtained the overall highest efficiency. Surprisingly, the results suggest that specifying force field parameters and partial charges is insufficient to generally ensure reproducibility, and we observe differences between seemingly converged predictions ranging approximately from 0.3 to 1.0 kcal/mol, even with almost identical simulations parameters and system setup (e.g., Lennard-Jones cutoff, ionic composition). Further work will be required to completely identify the exact source of these discrepancies. Among the conclusions emerging from the data, we found that Hamiltonian replica exchange-while displaying very small variance-can be affected by a slowly-decaying bias that depends on the initial population of the replicas, that bidirectional estimators are significantly more efficient than unidirectional estimators for nonequilibrium free energy calculations for systems considered, and that the Berendsen barostat introduces non-negligible artifacts in expanded ensemble simulations.

Configurational mapping significantly increases the efficiency of solid-solid phase coexistence calculations via molecular dynamics: Determining the FCC-HCP coexistence line of Lennard-Jones particles.

In this study, we incorporate configuration mapping between simulation ensembles into the successive interpolation of multistate reweighting (SIMR) method in order to increase phase space overlap between neighboring simulation ensembles. This significantly increases computational efficiency over the original SIMR method in many situations. We use this approach to determine the coexistence curve of face-centered cubic-hexagonal close-packed Lennard-Jones spheres using direct molecular dynamics and SIMR. As previously noted, the coexistence curve is highly sensitive to the treatment of the van der Waals cutoff. Using a cutoff treatment, the chemical potential difference between phases is moderate and SIMR quickly finds the phase equilibrium lines with good statistical uncertainty. Using a smoothed cutoff results in nonphysical errors in the phase diagram, while the use of particle mesh Ewald for the dispersion term results in a phase equilibrium curve that is comparable with previous results. The drastically closer free energy surfaces for this case test the limits of this configuration mapping approach to phase diagram prediction.

Uncertainty quantification confirms unreliable extrapolation toward high pressures for united-atom Mie λ-6 force field.

Molecular simulation results at extreme temperatures and pressures can supplement experimental data when developing fundamental equations of state. Since most force fields are optimized to agree with vapor-liquid equilibria (VLE) properties, however, the reliability of the molecular simulation results depends on the validity/transferability of the force field at higher temperatures and pressures. As demonstrated in this study, although state-of-the-art united-atom Mie λ-6 potentials for normal and branched alkanes provide accurate estimates for VLE, they tend to over-predict pressures for dense supercritical fluids and compressed liquids. The physical explanation for this observation is that the repulsive barrier is too steep for the "optimal" united-atom Mie λ-6 potential parameterized with VLE properties. Bayesian inference confirms that no feasible combination of non-bonded parameters (ϵ, σ, and λ) is capable of simultaneously predicting saturated vapor pressures, saturated liquid densities, and pressures at high temperatures and densities. This conclusion has both practical and theoretical ramifications, as more realistic non-bonded potentials may be required for accurate extrapolation to high pressures of industrial interest.

Using reweighting and free energy surface interpolation to predict solid-solid phase diagrams.

Many physical properties of small organic molecules are dependent on the current crystal packing, or polymorph, of the material, including bioavailability of pharmaceuticals, optical properties of dyes, and charge transport properties of semiconductors. Predicting the most stable crystalline form at a given temperature and pressure requires determining the crystalline form with the lowest relative Gibbs free energy. Effective computational prediction of the most stable polymorph could save significant time and effort in the design of novel molecular crystalline solids or predict their behavior under new conditions. In this study, we introduce a new approach using multistate reweighting to address the problem of determining solid-solid phase diagrams and apply this approach to the phase diagram of solid benzene. For this approach, we perform sampling at a selection of temperature and pressure states in the region of interest. We use multistate reweighting methods to determine the reduced free energy differences between T and P states within a given polymorph and validate this phase diagram using several measures. The relative stability of the polymorphs at the sampled states can be successively interpolated from these points to create the phase diagram by combining these reduced free energy differences with a reference Gibbs free energy difference between polymorphs. The method also allows for straightforward estimation of uncertainties in the phase boundary. We also find that when properly implemented, multistate reweighting for phase diagram determination scales better with the size of the system than previously estimated.

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

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

Lessons learned from comparing molecular dynamics engines on the SAMPL5 dataset.

We describe our efforts to prepare common starting structures and models for the SAMPL5 blind prediction challenge. We generated the starting input files and single configuration potential energies for the host-guest in the SAMPL5 blind prediction challenge for the GROMACS, AMBER, LAMMPS, DESMOND and CHARMM molecular simulation programs. All conversions were fully automated from the originally prepared AMBER input files using a combination of the ParmEd and InterMol conversion programs. We find that the energy calculations for all molecular dynamics engines for this molecular set agree to better than 0.1 % relative absolute energy for all energy components, and in most cases an order of magnitude better, when reasonable choices are made for different cutoff parameters. However, there are some surprising sources of statistically significant differences. Most importantly, different choices of Coulomb's constant between programs are one of the largest sources of discrepancies in energies. We discuss the measures required to get good agreement in the energies for equivalent starting configurations between the simulation programs, and the energy differences that occur when simulations are run with program-specific default simulation parameter values. Finally, we discuss what was required to automate this conversion and comparison.

Approaches for calculating solvation free energies and enthalpies demonstrated with an update of the FreeSolv database.

Solvation free energies can now be calculated precisely from molecular simulations, providing a valuable test of the energy functions underlying these simulations. Here, we briefly review "alchemical" approaches for calculating the solvation free energies of small, neutral organic molecules from molecular simulations, and illustrate by applying them to calculate aqueous solvation free energies (hydration free energies). These approaches use a non-physical pathway to compute free energy differences from a simulation or set of simulations and appear to be a particularly robust and general-purpose approach for this task. We also present an update (version 0.5) to our FreeSolv database of experimental and calculated hydration free energies of neutral compounds and provide input files in formats for several simulation packages. This revision to FreeSolv provides calculated values generated with a single protocol and software version, rather than the heterogeneous protocols used in the prior version of the database. We also further update the database to provide calculated enthalpies and entropies of hydration and some experimental enthalpies and entropies, as well as electrostatic and nonpolar components of solvation free energies.

Blind prediction of cyclohexane-water distribution coefficients from the SAMPL5 challenge.

In the recent SAMPL5 challenge, participants submitted predictions for cyclohexane/water distribution coefficients for a set of 53 small molecules. Distribution coefficients (log D) replace the hydration free energies that were a central part of the past five SAMPL challenges. A wide variety of computational methods were represented by the 76 submissions from 18 participating groups. Here, we analyze submissions by a variety of error metrics and provide details for a number of reference calculations we performed. As in the SAMPL4 challenge, we assessed the ability of participants to evaluate not just their statistical uncertainty, but their model uncertainty-how well they can predict the magnitude of their model or force field error for specific predictions. Unfortunately, this remains an area where prediction and analysis need improvement. In SAMPL4 the top performing submissions achieved a root-mean-squared error (RMSE) around 1.5 kcal/mol. If we anticipate accuracy in log D predictions to be similar to the hydration free energy predictions in SAMPL4, the expected error here would be around 1.54 log units. Only a few submissions had an RMSE below 2.5 log units in their predicted log D values. However, distribution coefficients introduced complexities not present in past SAMPL challenges, including tautomer enumeration, that are likely to be important in predicting biomolecular properties of interest to drug discovery, therefore some decrease in accuracy would be expected. Overall, the SAMPL5 distribution coefficient challenge provided great insight into the importance of modeling a variety of physical effects. We believe these types of measurements will be a promising source of data for future blind challenges, especially in view of the relatively straightforward nature of the experiments and the level of insight provided.

Identifying Differences and Similarities in Static and Dynamic Contact Angles between Nanoscale and Microscale Textured Surfaces Using Molecular Dynamics Simulations.

We quantify some of the effects of patterned nanoscale surface texture on static contact angles, dynamic contact angles, and dynamic contact angle hysteresis using molecular dynamics simulations of a moving Lennard-Jones droplet in contact with a solid surface. We observe static contact angles that change with the introduction of surface texture in a manner consistent with theoretical and experimental expectations. However, we find that the introduction of nanoscale surface texture at the length scale of 5-10 times the fluid particle size does not affect dynamic contact angle hysteresis even though it changes both the advancing and receding contact angles significantly. This result differs significantly from microscale experimental results where dynamic contact angle hysteresis decreases with the addition of surface texture due to an increase in the receding contact angle. Instead, we find that molecular-kinetic theory, previously applied only to nonpatterned surfaces, accurately describes dynamic contact angle and dynamic contact angle hysteresis behavior as a function of terminal fluid velocity. Therefore, at length scales of tens of nanometers, the kinetic phenomena such as contact line pinning observed at larger scales become insignificant in comparison to the effects of molecular fluctuations for moving droplets, even though the static properties are essentially scale-invariant. These findings may have implications for the design of highly hierarchical structures with particular wetting properties. We also find that quantitatively determining the trends observed in this article requires the careful selection of system and analysis parameters in order to achieve sufficient accuracy and precision in calculated contact angles. Therefore, we provide a detailed description of our two-surface, circular-fit approach to calculating static and dynamic contact angles on surfaces with nanoscale texturing.

Effects of polymer graft properties on protein adsorption and transport in ion exchange chromatography: a multiscale modeling study.

Multiscale simulation is used to study the adsorption of lysozyme onto ion exchangers obtained by grafting charged polymers into a porous matrix, in systems with various polymer properties and strengths of electrostatic interaction. Molecular dynamics simulations show that protein partitioning into the polymer-filled pore space increases with the overall charge content of the polymers, while the diffusivity in the pore space decreases. However, the combination of greatly increased partitioning and modestly decreased diffusion results in macroscopic transport rates that increase as a function of charge content, as the large concentration driving force due to enhanced pore space partitioning outweighs the reduction in the pore space diffusivity. Matrices having greater charge associated with the grafted polymers also exhibit more diffuse intraparticle concentration profiles during transient adsorption. In systems with a high charge content per polymer and a low protein loading, the polymers preferentially partition toward the surface due to favorable interactions with the surface-bound protein. These results demonstrate the potential of multiscale modeling to illuminate qualitative trends between molecular properties and the adsorption equilibria and kinetic properties observable on macroscopic scales.

Guidelines for the analysis of free energy calculations.

Free energy calculations based on molecular dynamics simulations show considerable promise for applications ranging from drug discovery to prediction of physical properties and structure-function studies. But these calculations are still difficult and tedious to analyze, and best practices for analysis are not well defined or propagated. Essentially, each group analyzing these calculations needs to decide how to conduct the analysis and, usually, develop its own analysis tools. Here, we review and recommend best practices for analysis yielding reliable free energies from molecular simulations. Additionally, we provide a Python tool, alchemical-analysis.py, freely available on GitHub as part of the pymbar package (located at http://github.com/choderalab/pymbar), that implements the analysis practices reviewed here for several reference simulation packages, which can be adapted to handle data from other packages. Both this review and the tool covers analysis of alchemical calculations generally, including free energy estimates via both thermodynamic integration and free energy perturbation-based estimators. Our Python tool also handles output from multiple types of free energy calculations, including expanded ensemble and Hamiltonian replica exchange, as well as standard fixed ensemble calculations. We also survey a range of statistical and graphical ways of assessing the quality of the data and free energy estimates, and provide prototypes of these in our tool. We hope this tool and discussion will serve as a foundation for more standardization of and agreement on best practices for analysis of free energy calculations.

Investigating the mutation resistance of nonnucleoside inhibitors of HIV-RT using multiple microsecond atomistic simulations.

Inhibiting HIV reverse transcriptase through the use of nonnucleoside reverse transcriptase inhibitors (NNRTIs) has become an essential component in drug regimens for the treatment of HIV. Older NNRTIs, such as nevirapine, are structurally rigid, exhibiting decreased inhibitory function on development of common mutations in the NNRTI-binding pocket, which is located around 10 Å from the catalytically active binding site. The newer generation of drugs, such as rilpivirine, are more flexible and resistant to binding pocket mutations but the mechanism by which they actually inhibit protein function and avoid mutations is not well-understood. To this end, we have performed 2-2.4 µs simulations with explicit solvent in an isobaric-isothermal ensemble of six different systems: apo wild-type, apo K103N/Y181C mutant, nevirapine-bound wild-type, nevirapine-bound mutant, rilpivirine-bound wild type, and rilpivirine-bound mutant. Analysis of protein conformations, principal components of motion, and mutual information between residues points to an inhibitory mechanism in which the primer grip stretches away from the catalytic triad of aspartic acids necessary for polymerization of HIV-encoding DNA, but is still unable to reveal a specific structural mechanism behind mutation resistance.

GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit.

MOTIVATION: Molecular simulation has historically been a low-throughput technique, but faster computers and increasing amounts of genomic and structural data are changing this by enabling large-scale automated simulation of, for instance, many conformers or mutants of biomolecules with or without a range of ligands. At the same time, advances in performance and scaling now make it possible to model complex biomolecular interaction and function in a manner directly testable by experiment. These applications share a need for fast and efficient software that can be deployed on massive scale in clusters, web servers, distributed computing or cloud resources. RESULTS: Here, we present a range of new simulation algorithms and features developed during the past 4 years, leading up to the GROMACS 4.5 software package. The software now automatically handles wide classes of biomolecules, such as proteins, nucleic acids and lipids, and comes with all commonly used force fields for these molecules built-in. GROMACS supports several implicit solvent models, as well as new free-energy algorithms, and the software now uses multithreading for efficient parallelization even on low-end systems, including windows-based workstations. Together with hand-tuned assembly kernels and state-of-the-art parallelization, this provides extremely high performance and cost efficiency for high-throughput as well as massively parallel simulations. AVAILABILITY: GROMACS is an open source and free software available from http://www.gromacs.org. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Thermodynamics of coupled protein adsorption and stability using hybrid Monte Carlo simulations.

A better understanding of changes in protein stability upon adsorption can improve the design of protein separation processes. In this study, we examine the coupling of the folding and the adsorption of a model protein, the B1 domain of streptococcal protein G, as a function of surface attraction using a hybrid Monte Carlo (HMC) approach with temperature replica exchange and umbrella sampling. In our HMC implementation, we are able to use a molecular dynamics (MD) time step that is an order of magnitude larger than in a traditional MD simulation protocol and observe a factor of 2 enhancement in the folding and unfolding rate. To demonstrate the convergence of our systems, we measure the travel of our order parameter the fraction of native contacts between folded and unfolded states throughout the length of our simulations. Thermodynamic quantities are extracted with minimum statistical variance using multistate reweighting between simulations at different temperatures and harmonic distance restraints from the surface. The resultant free energies, enthalpies, and entropies of the coupled unfolding and absorption processes are in qualitative agreement with previous experimental and computational observations, including entropic stabilization of the adsorbed, folded state relative to the bulk on surfaces with low attraction.

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

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

Assessing the Accuracy and Efficiency of Free Energy Differences Obtained from Reweighted Flow-Based Probabilistic Generative Models.

Computing free energy differences between metastable states characterized by nonoverlapping Boltzmann distributions is often a computationally intensive endeavor, usually requiring chains of intermediate states to connect them. Targeted free energy perturbation (TFEP) can significantly lower the computational cost of FEP calculations by choosing a set of invertible maps used to directly connect the distributions of interest, achieving the necessary statistically significant overlaps without sampling any intermediate states. Probabilistic generative models (PGMs) based on normalizing flow architectures can make it much easier via machine learning to train invertible maps needed for TFEP. However, the accuracy and applicability of approaches based on empirically learned maps depend crucially on the choice of reweighting method adopted to estimate the free energy differences. In this work, we assess the accuracy, rate of convergence, and data efficiency of different free energy estimators, including exponential averaging, Bennett acceptance ratio (BAR), and multistate Bennett acceptance ratio (MBAR), in reweighting PGMs trained by maximum likelihood on limited amounts of molecular dynamics data sampled only from end-states of interest. We carry out the comparisons on a set of simple but representative case studies, including conformational ensembles of alanine dipeptide and ibuprofen. Our results indicate that BAR and MBAR are both data efficient and robust, even in the presence of significant model overfitting in the generation of invertible maps. This analysis can serve as a stepping stone for the deployment of efficient and quantitatively accurate ML-based free energy calculation methods in complex systems.