Toward Atomistic Modeling of Irreversible Covalent Inhibitor Binding Kinetics.

Covalent inhibitors have emerged as an important drug class in recent years, largely due to their many unique advantages as compared to noncovalent inhibitors, including longer duration of action, lower prolonged systemic exposure, higher potency, and selectivity. However, the potential off-target toxicity of covalent inhibitors, particularly of irreversible covalent inhibitors, represents a great challenge in covalent drug development. Therefore, accurate calculation of protein covalent inhibitor reaction kinetics to guide the design of selective inhibitors would greatly benefit covalent drug discovery efforts. In the present paper, we present a computational method to calculate the relative reaction kinetics between congeneric irreversible covalent inhibitors and their protein receptors. The method combines density functional theory calculations of the transition state barrier height of the rate-limiting step for reaction between the warhead of the inhibitor and a single protein residue, and molecular-mechanics-based free energy calculations to account for the interactions between the ligand in the transition state and the protein environment. The method was tested on four pharmaceutically interesting irreversible covalent binding systems involving 28 ligands; the mean unsigned error (MUE) of the relative reaction rate for all pairs of ligands between the predictions and experimental results for these tested systems is 0.79 log unit. This is to our knowledge the first time where the reaction kinetics of protein irreversible covalent inhibition have been directly calculated with physics-based free energy calculation methods and transition state theory. We anticipate the outstanding accuracy demonstrated here across a broad range of target classes will have a strong impact on the design of selective covalent inhibitors.

Advancing Drug Discovery through Enhanced Free Energy Calculations.

A principal goal of drug discovery project is to design molecules that can tightly and selectively bind to the target protein receptor. Accurate prediction of protein-ligand binding free energies is therefore of central importance in computational chemistry and computer aided drug design. Multiple recent improvements in computing power, classical force field accuracy, enhanced sampling methods, and simulation setup have enabled accurate and reliable calculations of protein-ligands binding free energies, and position free energy calculations to play a guiding role in small molecule drug discovery. In this Account, we outline the relevant methodological advances, including the REST2 (Replica Exchange with Solute Temperting) enhanced sampling, the incorporation of REST2 sampling with convential FEP (Free Energy Perturbation) through FEP/REST, the OPLS3 force field, and the advanced simulation setup that constitute our FEP+ approach, followed by the presentation of extensive comparisons with experiment, demonstrating sufficient accuracy in potency prediction (better than 1 kcal/mol) to substantially impact lead optimization campaigns. The limitations of the current FEP+ implementation and best practices in drug discovery applications are also discussed followed by the future methodology development plans to address those limitations. We then report results from a recent drug discovery project, in which several thousand FEP+ calculations were successfully deployed to simultaneously optimize potency, selectivity, and solubility, illustrating the power of the approach to solve challenging drug design problems. The capabilities of free energy calculations to accurately predict potency and selectivity have led to the advance of ongoing drug discovery projects, in challenging situations where alternative approaches would have great difficulties. The ability to effectively carry out projects evaluating tens of thousands, or hundreds of thousands, of proposed drug candidates, is potentially transformative in enabling hard to drug targets to be attacked, and in facilitating the development of superior compounds, in various dimensions, for a wide range of targets. More effective integration of FEP+ calculations into the drug discovery process will ensure that the results are deployed in an optimal fashion for yielding the best possible compounds entering the clinic; this is where the greatest payoff is in the exploitation of computer driven design capabilities. A key conclusion from the work described is the surprisingly robust and accurate results that are attainable within the conventional classical simulation, fixed charge paradigm. No doubt there are individual cases that would benefit from a more sophisticated energy model or dynamical treatment, and properties other than protein-ligand binding energies may be more sensitive to these approximations. We conclude that an inflection point in the ability of MD simulations to impact drug discovery has now been attained, due to the confluence of hardware and software development along with the formulation of "good enough" theoretical methods and models.

Polarizable Force Field for Molecular Ions Based on the Classical Drude Oscillator.

Development of accurate force field parameters for molecular ions in the context of a polarizable energy function based on the classical Drude oscillator is a crucial step toward an accurate polarizable model for modeling and simulations of biological macromolecules. Toward this goal we have undertaken a hierarchical approach in which force field parameter optimization is initially performed for small molecules for which experimental data exists that serve as building blocks of macromolecular systems. Small molecules representative of the ionic moieties of biological macromolecules include the cationic ammonium and methyl substituted ammonium derivatives, imidazolium, guanidinium and methylguanidinium, and the anionic acetate, phenolate, and alkanethiolates. In the present work, parameters for molecular ions in the context of the Drude polarizable force field are optimized and compared to results from the nonpolarizable additive CHARMM general force field (CGenFF). Electrostatic and Lennard-Jones parameters for the model compounds are developed in the context of the polarizable SWM4-NDP water model, with emphasis on assuring that the hydration free energies are consistent with previously reported parameters for atomic ions. The final parameters are shown to be in good agreement with the selected quantum mechanical (QM) and experimental target data. Analysis of the structure of water around the ions reveals substantial differences between the Drude and additive force fields indicating the important role of polarization in dictating the molecular details of aqueous solvation. The presented parameters represent the foundation for the charged functionalities in future generations of the Drude polarizable force field for biological macromolecules as well as for drug-like molecules.

Docking covalent inhibitors: a parameter free approach to pose prediction and scoring.

Although many popular docking programs include a facility to account for covalent ligands, large-scale systematic docking validation studies of covalent inhibitors have been sparse. In this paper, we present the development and validation of a novel approach for docking and scoring covalent inhibitors, which consists of conventional noncovalent docking, heuristic formation of the covalent attachment point, and structural refinement of the protein-ligand complex. This approach combines the strengths of the docking program Glide and the protein structure modeling program Prime and does not require any parameter fitting for the study of additional covalent reaction types. We first test this method by predicting the native binding geometry of 38 covalently bound complexes. The average RMSD of the predicted poses is 1.52 Å, and 76% of test set inhibitors have an RMSD of less than 2.0 Å. In addition, the apparent affinity score constructed herein is tested on a virtual screening study and the characterization of the SAR properties of two different series of congeneric compounds with satisfactory success.

The maximal and current accuracy of rigorous protein-ligand binding free energy calculations.

Computational techniques can speed up the identification of hits and accelerate the development of candidate molecules for drug discovery. Among techniques for predicting relative binding affinities, the most consistently accurate is free energy perturbation (FEP), a class of rigorous physics-based methods. However, uncertainty remains about how accurate FEP is and can ever be. Here, we present what we believe to be the largest publicly available dataset of proteins and congeneric series of small molecules, and assess the accuracy of the leading FEP workflow. To ascertain the limit of achievable accuracy, we also survey the reproducibility of experimental relative affinity measurements. We find a wide variability in experimental accuracy and a correspondence between binding and functional assays. When careful preparation of protein and ligand structures is undertaken, FEP can achieve accuracy comparable to experimental reproducibility. Throughout, we highlight reliable protocols that can help maximize the accuracy of FEP in prospective studies.

Transferable Neural Network Potential Energy Surfaces for Closed-Shell Organic Molecules: Extension to Ions.

Transferable high dimensional neural network potentials (HDNNPs) have shown great promise as an avenue to increase the accuracy and domain of applicability of existing atomistic force fields for organic systems relevant to life science. We have previously reported such a potential (Schrödinger-ANI) that has broad coverage of druglike molecules. We extend that work here to cover ionic and zwitterionic druglike molecules expected to be relevant to drug discovery research activities. We report a novel HDNNP architecture, which we call QRNN, that predicts atomic charges and uses these charges as descriptors in an energy model that delivers conformational energies within chemical accuracy when measured against the reference theory it is trained to. Further, we find that delta learning based on a semiempirical level of theory approximately halves the errors. We test the models on torsion energy profiles, relative conformational energies, geometric parameters, and relative tautomer errors.

Reliable and Accurate Prediction of Single-Residue pKa Values through Free Energy Perturbation Calculations.

Accurate prediction of the pKa's of protein residues is crucial to many applications in biological simulation and drug discovery. Here, we present the use of free energy perturbation (FEP) calculations for the prediction of single-protein residue pKa values. We begin with an initial set of 191 residues with experimentally determined pKa values. To isolate sampling limitations from force field inaccuracies, we develop an algorithm to classify residues whose environments are significantly affected by crystal packing effects. We then report an approach to identify buried histidines that require significant sampling beyond what is achieved in typical FEP calculations. We therefore define a clean data set not requiring algorithms capable of predicting major conformational changes on which other pKa prediction methods can be tested. On this data set, we report an RMSE of 0.76 pKa units for 35 ASP residues, 0.51 pKa units for 44 GLU residues, and 0.67 pKa units for 76 HIS residues.

OPLS4: Improving Force Field Accuracy on Challenging Regimes of Chemical Space.

We report on the development and validation of the OPLS4 force field. OPLS4 builds upon our previous work with OPLS3e to improve model accuracy on challenging regimes of drug-like chemical space that includes molecular ions and sulfur-containing moieties. A novel parametrization strategy for charged species, which can be extended to other systems, is introduced. OPLS4 leads to improved accuracy on benchmarks that assess small-molecule solvation and protein-ligand binding.

Advancing Free-Energy Calculations of Metalloenzymes in Drug Discovery via Implementation of LFMM Potentials.

To address some of the inherent challenges in modeling metalloenzymes, we here report an extension to the functional form of the OPLS3e force field to include terms adopted from the ligand field molecular mechanics (LFMM) model, including the angular overlap and Morse potential terms. The integration of these terms with OPLS3e, herein referred to as OPLS3e+M, improves the description of metal-ligand interactions and provides accurate relative binding energies and geometric preferences of transition-metal complexes by training to gas-phase density functional theory (DFT) energies. For [Cu(H2O)4]2+, OPLS3e+M significantly improves H2O binding energies and the geometric preference of the tetra-aqua Cu2+ complex. In addition, we conduct free-energy perturbation calculations on two pharmaceutically relevant metalloenzyme targets, which include chemical modifications at varying proximity to the binding-site metals, including changes to the metal-binding moiety of the ligand itself. The extensions made to OPLS3e lead to accurate predicted relative binding free energies for these series (mean unsigned error of 1.29 kcal mol-1). Our results provide evidence that integration of the LFMM model with OPLS3e can be utilized to predict thermodynamic quantities for such systems near chemical accuracy. With these improvements, we anticipate that robust free-energy perturbation calculations can be employed to accelerate the drug development efforts for metalloenzyme targets.

Enhancing Water Sampling in Free Energy Calculations with Grand Canonical Monte Carlo.

The prediction of protein-ligand binding affinities using free energy perturbation (FEP) is becoming increasingly routine in structure-based drug discovery. Most FEP packages use molecular dynamics (MD) to sample the configurations of proteins and ligands, as MD is well-suited to capturing coupled motion. However, MD can be prohibitively inefficient at sampling water molecules that are buried within binding sites, which has severely limited the domain of applicability of FEP and its prospective usage in drug discovery. In this paper, we present an advancement of FEP that augments MD with grand canonical Monte Carlo (GCMC), an enhanced sampling method, to overcome the problem of sampling water. We accomplished this without degrading computational performance. On both old and newly assembled data sets of protein-ligand complexes, we show that the use of GCMC in FEP is essential for accurate and robust predictions for ligand perturbations that disrupt buried water.

Many-body polarization effects and the membrane dipole potential.

Molecular dynamics simulations of a lipid monolayer at a water-air interface are used to investigate the dipole potential that arises at the water-lipid interface. One simulation explicitly accounts for many-body polarization effects by using a model based on classical Drude oscillators. The dipole potential of the Drude model monolayer is 0.35V in excellent agreement with experimental estimates that range between 0.3 and 0.4V, whereas, a simulation using a nonpolarizable model significantly overestimates the potential with a calculated value of 0.8V. Induced polarization effects in the nonpolar region of the monolayer are found to buffer the residual positive lipid potential that results from competing polarization effects at the polar water/monolayer interface. These results, indicate the utility of the inclusion of many-body polarization effects in empirical force field models of lipids.

Molecular dynamics study of a polymeric reverse osmosis membrane.

Molecular dynamics (MD) simulations are used to investigate the properties of an atomic model of an aromatic polyamide reverse osmosis membrane. The monomers forming the polymeric membrane are cross-linked progressively on the basis of a heuristic distance criterion during MD simulations until the system interconnectivity reaches completion. Equilibrium MD simulations of the hydrated membrane are then used to determine the density and diffusivity of water within the membrane. Given a 3 MPa pressure differential and a 0.125 microm width membrane, the simulated water flux is calculated to be 1.4x10(-6) m/s, which is in fair agreement with an experimental flux measurement of 7.7x10(-6) m/s.

OPLS3e: Extending Force Field Coverage for Drug-Like Small Molecules.

Building upon the OPLS3 force field we report on an enhanced model, OPLS3e, that further extends its coverage of medicinally relevant chemical space by addressing limitations in chemotype transferability. OPLS3e accomplishes this by incorporating new parameter types that recognize moieties with greater chemical specificity and integrating an on-the-fly parametrization approach to the assignment of partial charges. As a consequence, OPLS3e leads to greater accuracy against performance benchmarks that assess small molecule conformational propensities, solvation, and protein-ligand binding.

Understanding the dielectric properties of liquid amides from a polarizable force field.

The role played by electronic polarization in the dielectric properties of liquid N-methyl acetamide (NMA) is examined using molecular dynamics simulations with a polarizable force field based on classical Drude oscillators. The model presented is the first force field shown to reproduce the anomalously large dielectric constant of liquid NMA. Details of the molecular polarizability are found to be important. For instance, all elements of the polarizability tensor, rather then just the trace, impact on the condensed phase properties. Two factors related to electronic polarizability are found to contribute to this large dielectric constant. First is the significant enhancement of the mean amide molecular dipole magnitude, which is 50% larger in the liquid than in the gas phase. Second is the consequent strong hydrogen bonding between molecular neighbors that enhances the orientational alignment of the molecular dipoles. Polarizable models of amide compounds that have two (acetamide) and zero (N,N-dimethyl acetamide) polar hydrogen-bond donor atoms are also investigated. Experimentally, the neat liquid dielectric constants at 373 K are 100 for NMA, 66 for acetamide and 26 for N,N-dimethyl acetamide. The polarizable models replicate this trend, predicting a dielectric constant of 92+/-5 for NMA, 66+/-3 for acetamide and 23+/-1 for N,N-dimethyl acetamide.

On the origin of the electrostatic potential difference at a liquid-vacuum interface.

The microscopic origin of the interface potential calculated from computer simulations is elucidated by considering a simple model of molecules near an interface. The model posits that molecules are isotropically oriented and their charge density is Gaussian distributed. Molecules that have a charge density that is more negative toward their interior tend to give rise to a negative interface potential relative to the gaseous phase, while charge densities more positive toward their interior give rise to a positive interface potential. The interface potential for the model is compared to the interface potential computed from molecular dynamics simulations of the nonpolar vacuum-methane system and the polar vacuum-water interface system. The computed vacuum-methane interface potential from a molecular dynamics simulation (-220 mV) is captured with quantitative precision by the model. For the vacuum-water interface system, the model predicts a potential of -400 mV compared to -510 mV, calculated from a molecular dynamics simulation. The physical implications of this isotropic contribution to the interface potential is examined using the example of ion solvation in liquid methane.

High Energy Density in Azobenzene-based Materials for Photo-Thermal Batteries via Controlled Polymer Architecture and Polymer-Solvent Interactions.

Energy densities of ~510 J/g (max: 698 J/g) have been achieved in azobenzene-based syndiotactic-rich poly(methacrylate) polymers. The processing solvent and polymer-solvent interactions are important to achieve morphologically optimal structures for high-energy density materials. This work shows that morphological changes of solid-state syndiotactic polymers, driven by different solvent processings play an important role in controlling the activation energy of Z-E isomerization as well as the shape of the DSC exotherm. Thus, this study shows the crucial role of processing solvents and thin film structure in achieving higher energy densities.

OPLS3: A Force Field Providing Broad Coverage of Drug-like Small Molecules and Proteins.

The parametrization and validation of the OPLS3 force field for small molecules and proteins are reported. Enhancements with respect to the previous version (OPLS2.1) include the addition of off-atom charge sites to represent halogen bonding and aryl nitrogen lone pairs as well as a complete refit of peptide dihedral parameters to better model the native structure of proteins. To adequately cover medicinal chemical space, OPLS3 employs over an order of magnitude more reference data and associated parameter types relative to other commonly used small molecule force fields (e.g., MMFF and OPLS_2005). As a consequence, OPLS3 achieves a high level of accuracy across performance benchmarks that assess small molecule conformational propensities and solvation. The newly fitted peptide dihedrals lead to significant improvements in the representation of secondary structure elements in simulated peptides and native structure stability over a number of proteins. Together, the improvements made to both the small molecule and protein force field lead to a high level of accuracy in predicting protein-ligand binding measured over a wide range of targets and ligands (less than 1 kcal/mol RMS error) representing a 30% improvement over earlier variants of the OPLS force field.

Predicting Binding Affinities for GPCR Ligands Using Free-Energy Perturbation.

The rapid growth of structural information for G-protein-coupled receptors (GPCRs) has led to a greater understanding of their structure, function, selectivity, and ligand binding. Although novel ligands have been identified using methods such as virtual screening, computationally driven lead optimization has been possible only in isolated cases because of challenges associated with predicting binding free energies for related compounds. Here, we provide a systematic characterization of the performance of free-energy perturbation (FEP) calculations to predict relative binding free energies of congeneric ligands binding to GPCR targets using a consistent protocol and no adjustable parameters. Using the FEP+ package, first we validated the protocol, which includes a full lipid bilayer and explicit solvent, by predicting the binding affinity for a total of 45 different ligands across four different GPCRs (adenosine A2AAR, ß1 adrenergic, CXCR4 chemokine, and δ opioid receptors). Comparison with experimental binding affinity measurements revealed a highly predictive ranking correlation (average spearman ρ = 0.55) and low root-mean-square error (0.80 kcal/mol). Next, we applied FEP+ in a prospective project, where we predicted the affinity of novel, potent adenosine A2A receptor (A2AR) antagonists. Four novel compounds were synthesized and tested in a radioligand displacement assay, yielding affinity values in the nanomolar range. The affinity of two out of the four novel ligands (plus three previously reported compounds) was correctly predicted (within 1 kcal/mol), including one compound with approximately a tenfold increase in affinity compared to the starting compound. Detailed analyses of the simulations underlying the predictions provided insights into the structural basis for the two cases where the affinity was overpredicted. Taken together, these results establish a protocol for systematically applying FEP+ to GPCRs and provide guidelines for identifying potent molecules in drug discovery lead optimization projects.

Hydrogen-bond dynamics in the air-water interface.

Hydrogen-bond (H-bond) dynamics in the air-water interface is studied by molecular dynamics simulations. The analysis reveals that the dynamics of breaking and forming hydrogen bonds in the air-water interface is faster than that in bulk water for the polarizable water models. This is in contrast to the results found on a protein surface. We show that the difference stems from more rapid translational diffusion in the interface. When the effect of pair diffusion is eliminated, the hydrogen-bond dynamics in the interface is observed to be slower than that in the bulk. This occurs because the number of water molecules adjacent to a hydrogen-bonded pair and available to accept or donate a hydrogen bond is smaller in the interface than in the bulk. The comparison between polarizable water models and fixed-charge models highlights the potential importance of the polarization effect in the water-vapor interface.

Structure and dynamics of the solvation of bovine pancreatic trypsin inhibitor in explicit water: a comparative study of the effects of solvent and protein polarizability.

To isolate the effects of the inclusion of polarizability in the force field model on the structure and dynamics of the solvating water in differing electrostatic environments of proteins, we present the results of molecular dynamics simulations of the bovine pancreatic trypsin inhibitor (BPTI) in water with force fields that explicitly include polarization for both the protein and the water. We use three model potentials for water and two model potentials for the protein. Two of the water models and one of the protein models are polarizable. A total of six systems were simulated representing all combinations of these polarizable and nonpolarizable protein and water force fields. We find that all six systems behave in a similar manner in regions of the protein that are weakly electrostatic (either hydrophobic or weakly hydrophilic). However, in the vicinity of regions of the protein with relatively strong electrostatic fields (near positively or negatively charged residues), we observe that the water structure and dynamics are dependent on both the model of the protein and the model of the water. We find that a large part of the dynamical dependence can be described by small changes in the local environments of each region that limit the local density of non-hydrogen-bonded waters, precisely the water molecules that facilitate the dynamical relaxation of the water-water hydrogen bonds. We introduce a simple method for rescaling for this effect. When this is done, we are able to effectively isolate the influence of polarizability on the dynamics. We find that the solvating water's relaxation is most affected when both the protein and the water models are polarizable. However, when only one model (or neither) is polarizable, the relaxation is similar regardless of the models used.