Accurate Free Energy Research Articles

Accurate protein-ligand binding free energy estimation using QM/MM on multi-conformers predicted from classical mining minima

Accurate prediction of binding free energy is crucial for the rational design of drug candidates and understanding protein-ligand interactions. To address this, we have developed four protocols that combine QM/MM calculations and the mining minima (M2) method, tested on 9 targets and 203 ligands. Our protocols carry out free energy processing with or without conformational search on the selected conformers obtained from M2 calculations, where their force field atomic charge parameters are substituted with those obtained from a QM/MM calculation. The method achieved a high Pearson’s correlation coefficient (0.81) with experimental binding free energies across diverse targets, demonstrating its generality. Using a differential evolution algorithm with a universal scaling factor of 0.2, we achieved a low mean absolute error of 0.60 kcal mol-1. This performance surpasses many existing methods and is comparable to popular relative binding free energy techniques but at significantly lower computational cost.

The Discovery of MORF-627, a Highly Selective Conformationally-Biased Zwitterionic Integrin αvβ6 Inhibitor for Fibrosis.

Inhibition of integrin αvβ6 is a promising approach to the treatment of fibrotic disease such as idiopathic pulmonary fibrosis. Screening a small library combining head groups that stabilize the bent-closed conformation of integrin αIIbβ3 with αv integrin binding motifs resulted in the identification of hit compounds that bind the bent-closed conformation of αvβ6. Crystal structures of these compounds bound to αvβ6 and related integrins revealed opportunities to increase potency and selectivity, and these efforts were accelerated using accurate free energy perturbation (FEP+) calculations. Optimization of PK parameters including permeability, bioavailability, clearance, and half-life resulted in the discovery of development candidate MORF-627, a highly selective inhibitor of αvβ6 that stabilizes the bent-closed conformation and has good oral PK. Unfortunately, the compound showed toxicity in a 28-day NHP safety study, precluding further development. Nevertheless, MORF-627 is a useful tool compound for studying the biology of integrin αvβ6.

A Method for Treating Significant Conformational Changes in Alchemical Free Energy Simulations of Protein-Ligand Binding.

Relative binding free energy (RBFE) simulation is a rigorous approach to the calculation of quantitatively accurate binding free energy values for protein-ligand binding in which a reference binder is gradually converted to a target binder through alchemical transformation during the simulation. The success of such simulations relies on being able to accurately sample the correct conformational phase space for each alchemical state; however, this becomes a challenge when a significant conformation change occurs between the reference and target binder-receptor complexes. Increasing the simulation time and using enhanced sampling methods can be helpful, but effects can be limited, especially when the free energy barrier between conformations is high or when the correct target complex conformation is difficult to find and maintain. Current RBFE protocols seed the reference complex structure into every alchemical window of the simulation. In our study, we describe an improved protocol in which the reference structure is seeded into the first half of the alchemical windows, and the target structure is seeded into the second half of the alchemical windows. By applying information about the relevant correct end point conformations to different simulation windows from the beginning, the need for large barrier crossings or simulation prediction of the correct structures during an alchemical simulation is in many cases obviated. In the diverse cases we examine below, the simulations yielded free energy predictions that are satisfactory as compared to experiment and superior to running the simulations utilizing the conventional protocol. The method is straightforward to implement for publicly available FEP workflows.

Rapid, Accurate, Ranking of Protein-Ligand Binding Affinities with VM2, the Second-Generation Mining Minima Method.

The structure-based technologies most widely used to rank the affinities of candidate small molecule drugs for proteins range from faster but less reliable docking methods to slower but more accurate explicit solvent free energy methods. In recent years, we have advanced another technology, which is called mining minima because it "mines" out the main contributions to the chemical potentials of the free and bound molecular species by identifying and characterizing their main local energy minima. The present study provides systematic benchmarks of the accuracy and computational speed of mining minima, as implemented in the VeraChem Mining Minima Generation 2 (VM2) code, across two well-regarded protein-ligand benchmark data sets, for which there are already benchmark data for docking, free energy, and other computational methods. A core result is that VM2's accuracy approaches that of explicit solvent free energy methods at a far lower computational cost. In finer-grained analyses, we also examine the influence of various run settings, such as the treatment of crystallographic water molecules, on the accuracy, and define the costs in time and dollars of representative runs on Amazon Web Services (AWS) compute instances with various CPU and GPU combinations. We also use the benchmark data to determine the importance of VM2's correction from generalized Born to finite-difference Poisson-Boltzmann results for each energy well and find that this correction affords a remarkably consistent improvement in accuracy at a modest computational cost. The present results establish VM2 as a distinctive technology for early-stage drug discovery, which provides a strong combination of efficiency and predictivity.

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.

Binding of Phosphate Species to Ca2+ and Mg2+ in Aqueous Solution.

Phosphate derivatives and their interaction with metal cations are involved in many important biological phenomena, so an accurate characterization of the phosphate-metal interaction is necessary to properly understand the role of phosphate-metal contacts in mediating biological function. Herein, we improved the standard 12-6 Lennard-Jones (LJ) potential via the usage of the 12-6-4 LJ model, which incorporates ion-induced dipole interactions. Via parameter scanning, we fine-tuned the 12-6-4 LJ polarizability values to obtain accurate absolute binding free energies for the phosphate anions H2PO4-, HPO42-, PO43- coordinating with Ca2+ and Mg2+. First, we modified the phosphate 12-6-4 LJ parameters to reproduce the solvation free energies of the series of phosphate anions using the thermodynamic integration (TI) method. Then, using the potential mean force (PMF) method, the polarizability of the metal-phosphate interaction was obtained. We show that the free energy profiles of phosphate ions coordinated to Ca2+ and Mg2+ generally show similar trends at longer metal-phosphate distances, while the absolute binding energy values increased with deprotonation. The resulting parameters demonstrate the flexibility of the 12-6-4 LJ-type nonbonded model and its usefulness in accurately describing cation-anion interactions.

QM, molecular docking and molecular dynamics investigation on acidic phospholipase A2 2 protein and acidic phospholipase A2 3 protein with silane dimethyl

Phytochemicals and non-nutritive plant substances can protect humans from various diseases by possessing anti-inflammatory or anti-disease properties. The Andrographis Paniculata species has been the primary focus of extensive pharmacological and phytochemical research. QM concepts are being applied scientifically in chemical and biological problems, with molecular docking and molecular dynamics techniques being crucial in-silico drug development. Absorptions in Andrographis Paniculata come from charge transfer due to visible light's energy emissions, with GCMS– results indicating its chemical components possess antibacterial properties. The PES concept aids in the intuitive understanding of mathematical concepts, while RDG recreates the complete distribution of electronic pairings, including interatomic bonding regions, lone pairs, and cores. Molecular dynamics is crucial for protein-ligand docking due to its accurate binding free energy calculations and profound understanding of the dynamic nature of protein-ligand interactions.

Accurate Free Energies of Aqueous Electrolyte Solutions from Molecular Simulations with Non-polarizable Force Fields.

Non-polarizable force fields fail to accurately predict free energies of aqueous electrolytes without compromising the predictive ability for densities and transport properties. A new approach is presented in which (1) TIP4P/2005 water and scaled charge force fields are used to describe the interactions in the liquid phase and (2) an additional Effective Charge Surface (ECS) is used to compute free energies at zero additional computational expense. The ECS is obtained using a single temperature-independent charge scaling parameter per species. Thereby, the chemical potential of water and the free energies of hydration of various aqueous salts (e.g., NaCl and LiCl) are accurately described (deviations less than 5% from experiments), in sharp contrast to calculations where the ECS is omitted (deviations larger than 20%). This approach enables accurate predictions of free energies of aqueous electrolyte solutions using non-polarizable force fields, without compromising liquid-phase properties.

Reweighting from Molecular Mechanics Force Fields to the ANI-2x Neural Network Potential.

To achieve chemical accuracy in free energy calculations, it is necessary to accurately describe the system's potential energy surface and efficiently sample configurations from its Boltzmann distribution. While neural network potentials (NNPs) have shown significantly higher accuracy than classical molecular mechanics (MM) force fields, they have a limited range of applicability and are considerably slower than MM potentials, often by orders of magnitude. To address this challenge, Rufa et al. [Rufa et al. bioRxiv 2020, 10.1101/2020.07.29.227959.] suggested a two-stage approach that uses a fast and established MM alchemical energy protocol, followed by reweighting the results using NNPs, known as endstate correction or indirect free energy calculation. This study systematically investigates the accuracy and robustness of reweighting from an MM reference to a neural network target potential (ANI-2x) for an established data set in vacuum, using single-step free-energy perturbation (FEP) and nonequilibrium (NEQ) switching simulation. We assess the influence of longer switching lengths and the impact of slow degrees of freedom on outliers in the work distribution and compare the results to those of multistate equilibrium free energy simulations. Our results demonstrate that free energy calculations between NNPs and MM potentials should be preferably performed using NEQ switching simulations to obtain accurate free energy estimates. NEQ switching simulations between the MM potentials and NNPs are efficient, robust, and trivial to implement.

Efficient and accurate binding free energy calculation of Aβ9-40 protofilament propagation.

Self-assembled aggregation of peptides and proteins into regular amyloid fibrils is associated with several neurodegenerative diseases. In case of Alzheimer's disease proteolytic cleavage products of the amyloid precursor protein form pathological amyloid-beta fibrils in a nucleation and propagation phase. The molecular details and thermodynamic driving forces of amyloid formation are not well understood, but are of high relevance for potential pharmacological interference. We used atomistic binding free energy simulations to calculate the free energy of protofilament propagation by an additional Aβ9-40 peptide binding to the protofilament tip. It requires sampling of relevant conformational transitions which is challenging since the monomeric Aβ9-40 peptide is intrinsically disordered. However, the convergence of umbrella simulations can be enhanced by applying additional restraining potentials on the axial, orientational and conformational degrees of freedom. The improved convergence leads to a much closer agreement with experimental binding free energy data compared to unrestrained umbrella sampling. Moreover, the restraining approach results in a separation of contributions to the total binding free energy. The calculated contributions indicate that the free energy change associated with the restriction of conformational freedom upon propagation makes a large opposing contribution of higher magnitude than the total binding free energy. Finally, optimization of the approach leads to further significant reduction of the computational demand which is crucial for systematic studies on mutations, denaturants and inhibitors in the fibril propagation step.

Structure of the Bacterial Cell Envelope and Interactions with Antimicrobials: Insights from Molecular Dynamics Simulations.

Bacteria have evolved over 3 billion years, shaping our intrinsic and symbiotic coexistence with these single-celled organisms. With rising populations of drug-resistant strains, the search for novel antimicrobials is an ongoing area of research. Advances in high-performance computing platforms have led to a variety of molecular dynamics simulation strategies to study the interactions of antimicrobial molecules with different compartments of the bacterial cell envelope of both Gram-positive and Gram-negative species. In this review, we begin with a detailed description of the structural aspects of the bacterial cell envelope. Simulations concerned with the transport and associated free energy of small molecules and ions through the outer membrane, peptidoglycan, inner membrane and outer membrane porins are discussed. Since surfactants are widely used as antimicrobials, a section is devoted to the interactions of surfactants with the cell wall and inner membranes. The review ends with a discussion on antimicrobial peptides and the insights gained from the molecular simulations on the free energy of translocation. Challenges involved in developing accurate molecular models and coarse-grained strategies that provide a trade-off between atomic details with a gain in sampling time are highlighted. The need for efficient sampling strategies to obtain accurate free energies of translocation is also discussed. Molecular dynamics simulations have evolved as a powerful tool that can potentially be used to design and develop novel antimicrobials and strategies to effectively treat bacterial infections.

SparseRNAfolD: optimized sparse RNA pseudoknot-free folding with dangle consideration

MotivationComputational RNA secondary structure prediction by free energy minimization is indispensable for analyzing structural RNAs and their interactions. These methods find the structure with the minimum free energy (MFE) among exponentially many possible structures and have a restrictive time and space complexity (O(n3)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^3)$$\\end{document} time and O(n2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(n^2)$$\\end{document} space for pseudoknot-free structures) for longer RNA sequences. Furthermore, accurate free energy calculations, including dangle contributions can be difficult and costly to implement, particularly when optimizing for time and space requirements.ResultsHere we introduce a fast and efficient sparsified MFE pseudoknot-free structure prediction algorithm, SparseRNAFolD, that utilizes an accurate energy model that accounts for dangle contributions. While the sparsification technique was previously employed to improve the time and space complexity of a pseudoknot-free structure prediction method with a realistic energy model, SparseMFEFold, it was not extended to include dangle contributions due to the complexity of computation. This may come at the cost of prediction accuracy. In this work, we compare three different sparsified implementations for dangle contributions and provide pros and cons of each method. As well, we compare our algorithm to LinearFold, a linear time and space algorithm, where we find that in practice, SparseRNAFolD has lower memory consumption across all lengths of sequence and a faster time for lengths up to 1000 bases.ConclusionOur SparseRNAFolD algorithm is an MFE-based algorithm that guarantees optimality of result and employs the most general energy model, including dangle contributions. We provide a basis for applying dangles to sparsified recursion in a pseudoknot-free model that has the potential to be extended to pseudoknots.

Poisson-Boltzmann-based machine learning model for electrostatic analysis

Electrostatics is of paramount importance to chemistry, physics, biology, and medicine. The Poisson-Boltzmann (PB) theory is a primary model for electrostatic analysis. However, it is highly challenging to compute accurate PB electrostatic solvation free energies for macromolecules due to the nonlinearity, dielectric jumps, charge singularity, and geometric complexity associated with the PB equation. The present work introduces a PB-based machine learning (PBML) model for biomolecular electrostatic analysis. Trained with the second-order accurate MIBPB solver, the proposed PBML model is found to be more accurate and faster than several eminent PB solvers in electrostatic analysis. The proposed PBML model can provide highly accurate PB electrostatic solvation free energy of new biomolecules or new conformations generated by molecular dynamics with much reduced computational cost.

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.

Machine learning thermodynamic perturbation theory offers accurate activation free energies at the RPA level for alkene isomerization in zeolites

Thanks to Machine Learning Perturbation Theory, a combination of AIMD with RPA was made to accurately predict the activation energy of alkene isomerization into Brønsted acidic zeolite.

The SAMPL9 host-guest blind challenge: an overview of binding free energy predictive accuracy.

We report the results of the SAMPL9 host-guest blind challenge for predicting binding free energies. The challenge focused on macrocycles from pillar[n]-arene and cyclodextrin host families, including WP6, and bCD and HbCD. A variety of methods were used by participants to submit binding free energy predictions. A machine learning approach based on molecular descriptors achieved the highest accuracy (RMSE of 2.04 kcal mol-1) among the ranked methods in the WP6 dataset. Interestingly, predictions for WP6 obtained via docking tended to outperform all methods (RMSE of 1.70 kcal mol-1), most of which are MD based and computationally more expensive. In general, methods applying force fields achieved better correlation with experiments for WP6 opposed to the machine learning and docking models. In the cyclodextrin-phenothiazine challenge, the ATM approach emerged as the top performing method with RMSE less than 1.86 kcal mol-1. Correlation metrics of ranked methods in this dataset were relatively poor compared to WP6. We also highlight several lessons learned to guide future work and help improve studies on the systems discussed. For example, WP6 may be present in other microstates other than its -12 state in the presence of certain guests. Machine learning approaches can be used to fine tune or help train force fields for certain chemistry (i.e. WP6-G4). Certain phenothiazines occupy distinct primary and secondary orientations, some of which were considered individually for accurate binding free energies. The accuracy of predictions from certain methods while starting from a single binding pose/orientation demonstrates the sensitivity of calculated binding free energies to the orientation, and in some cases the likely dominant orientation for the system. Computational and experimental results suggest that guest phenothiazine core traverses both the secondary and primary faces of the cyclodextrin hosts, a bulky cationic side chain will primarily occupy the primary face, and the phenothiazine core substituent resides at the larger secondary face.

Development and test of highly accurate endpoint free energy methods. 3: partition coefficient prediction using a Poisson-Boltzmann method combined with a solvent accessible surface area model for SAMPL challenges.

Accurately predicting solvation free energy is the key to predict protein-ligand binding free energy. In addition, the partition coefficient (log P), which is an important physicochemical property that determines the distribution of a drug in vivo, can be derived directly from transfer free energies, i.e., the difference between solvation free energies (SFEs) in different solvents. Within the Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL) 9 challenge, we applied the Poisson-Boltzmann (PB) surface area (SA) approach to predict the toluene/water transfer free energy and partition coefficient (log Ptoluene/water) from SFEs. For each solute, only a single conformation automatically generated by the free software Open Babel was used. The PB calculation directly adopts our previously optimized boundary definition - a set of general AMBER force field 2 (GAFF2) atom-type based sphere radii for solute atoms. For the non-polar SA model, we newly developed the solvent-related molecular surface tension parameters γ and offset b for toluene and cyclohexane targeting experimental SFEs. This approach yielded the highest predictive accuracy in terms of root mean square error (RMSE) of 1.52 kcal mol-1 in transfer free energy for 16 small drug molecules among all 18 submissions in the SAMPL9 blind prediction challenge. The re-evaluation of the challenge set using multi-conformation strategies based on molecular dynamics (MD) simulations further reduces the prediction RMSE to 1.33 kcal mol-1. At the same time, an additional evaluation of our PBSA method on the SAMPL5 cyclohexane/water distribution coefficient (log Dcyclohexane/water) prediction revealed that our model outperformed COSMO-RS, the best submission model with RMSEPBSA = 1.88 versus RMSECOSMO-RS = 2.11 log units. Two external log Ptoluene/water and log Pcyclohexane/water datasets that contain 110 and 87 data points, respectively, are collected for extra validation and provide an in-depth insight into the error source of the PBSA method.

Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields.

The rational design of alloys and solid solutions relies on accurate computational predictions of phase diagrams. The cluster expansion method has proven to be a valuable tool for studying disordered crystals. However, the effects of vibrational entropy are commonly neglected due to the computational cost. Here, we devise a method for including the vibrational free energy in cluster expansions with a low computational cost by fitting a machine learning force field (MLFF) to the relaxation trajectories available from cluster expansion construction. We demonstrate our method for two (pseudo)binary systems, Na1-xKxCl and Ag1-xPdx, for which accurate phonon dispersions and vibrational free energies are derived from the MLFF. For both systems, the inclusion of vibrational effects results in significantly better agreement with miscibility gaps in experimental phase diagrams. This methodology can allow routine inclusion of vibrational effects in calculated phase diagrams and thus more accurate predictions of properties and stability for mixtures of materials.

OGRe: Optimal Grid Refinement Protocol for Accurate Free Energy Surfaces and Its Application in Proton Hopping in Zeolites and 2D COF Stacking.

While free energy surfaces are the crux of our understanding of many chemical and biological processes, their accuracy is generally unknown. Moreover, many developments to improve their accuracy are often complicated, limiting their general use. Luckily, several tools and guidelines are already in place to identify these shortcomings, but they are typically lacking in flexibility or fail to systematically determine how to improve the accuracy of the free energy calculation. To overcome these limitations, this work introduces OGRe, a Python package for optimal grid refinement in an arbitrary number of dimensions. OGRe is based on three metrics that gauge the confinement, consistency, and overlap of each simulation in a series of umbrella sampling (US) simulations, an enhanced sampling technique ubiquitously adopted to construct free energy surfaces for hindered processes. As these three metrics are fundamentally linked to the accuracy of the weighted histogram analysis method adopted to generate free energy surfaces from US simulations, they facilitate the systematic construction of accurate free energy profiles, where each metric is driven by a specific umbrella parameter. This allows for the derivation of a consistent and optimal collection of umbrellas for each simulation, largely independent of the initial values, thereby dramatically increasing the ease-of-use toward accurate free energy surfaces. As such, OGRe is particularly suited to determine complex free energy surfaces with large activation barriers and shallow minima, which underpin many physical and chemical transformations and hence to further our fundamental understanding of these processes.

Learned mappings for targeted free energy perturbation between peptide conformations.

Targeted free energy perturbation uses an invertible mapping to promote configuration space overlap and the convergence of free energy estimates. However, developing suitable mappings can be challenging. Wirnsberger et al. [J. Chem. Phys. 153, 144112 (2020)] demonstrated the use of machine learning to train deep neural networks that map between Boltzmann distributions for different thermodynamic states. Here, we adapt their approach to the free energy differences of a flexible bonded molecule, deca-alanine, with harmonic biases and different spring centers. When the neural network is trained until "early stopping"-when the loss value of the test set increases-we calculate accurate free energy differences between thermodynamic states with spring centers separated by 1 Å and sometimes 2 Å. For more distant thermodynamic states, the mapping does not produce structures representative of the target state, and the method does not reproduce reference calculations.