A new class of models for computing receptor-ligand binding affinities

graphLambda: Fusion Graph Neural Networks for Binding Affinity Prediction

Predicting the binding affinity of protein-ligand complexes is crucial for computer-aided drug discovery (CADD) and the identification of potential drug candidates. The deep learning-based scoring functions have emerged as promising predictors of binding constants. Building on recent advancements in graph neural networks, we present graphLambda for protein-ligand binding affinity prediction, which utilizes graph convolutional, attention, and isomorphism blocks to enhance the predictive capabilities. The graphLambda model exhibits superior performance across CASF16 and CSAR HiQ NRC benchmarks and demonstrates robustness with respect to different types of train-validation set partitions. The development of graphLambda underscores the potential of graph neural networks in advancing binding affinity prediction models, contributing to more effective CADD methodologies.

Computational methods for calculation of protein-ligand binding affinities in structure-based drug design

Drug design is an expensive and time-consuming process. Any method that allows reducing the time the costs of the drug development project can have great practical value for the pharmaceutical industry. In structure-based drug design, affinity prediction methods are of great importance. The majority of methods used to predict binding free energy in protein-ligand complexes use molecular mechanics methods. However, many limitations of these methods in describing interactions exist. An attempt to go beyond these limits is the application of quantum-mechanical description for all or only part of the analyzed system. However, the extensive use of quantum mechanical (QM) approaches in drug discovery is still a demanding challenge. This chapter briefly reviews selected methods used to calculate protein-ligand binding affinity applied in virtual screening (VS), rescoring of docked poses, and lead optimization stage, including QM methods based on molecular simulations.

3-Thienylboronic Acid as a Receptor for Diol-Containing Compounds: A Study by Isothermal Titration Calorimetry

The electrochemical activity of 3-thienylboronic acid and its feature to form polymer films makes it a perspective receptor material for sensor applications. The affinity properties of this compound were studied here by isothermal titration calorimetry. A number of different analytes were tested, and the highest binding enthalpy was observed for sorbitol and fructose. An increase of pH in the range of 5.5–10.6 results in the rise of the binding enthalpy with an increase of the binding constant to ~8400 L/mol for sorbitol or ~3400 L/mol for fructose. The dependence of the binding constant on pH has an inflection point at pH 7.6 with a slope that is a ten-fold binding constant per one pH unit. The binding properties of 3-thienylboronic acid were evaluated to be very close to that of the phenylboronic acid, but the electrochemical activity of 3-thienylboronic acid provides a possibility of external electrical control: dependence of the affinity of 3-thienylboronic acid on its redox state defined by the presence of ferro/ferricyanide in different ratios was demonstrated. The results show that 3-thienylboronic acid can be applied in smart chemical sensors with electrochemically controllable receptor affinity.

Using diverse potentials and scoring functions for the development of improved machine-learned models for protein-ligand affinity and docking pose prediction

The advent of computational drug discovery holds the promise of significantly reducing the effort of experimentalists, along with monetary cost. More generally, predicting the binding of small organic molecules to biological macromolecules has far-reaching implications for a range of problems, including metabolomics. However, problems such as predicting the bound structure of a protein-ligand complex along with its affinity have proven to be an enormous challenge. In recent years, machine learning-based methods have proven to be more accurate than older methods, many based on simple linear regression. Nonetheless, there remains room for improvement, as these methods are often trained on a small set of features, with a single functional form for any given physical effect, and often with little mention of the rationale behind choosing one functional form over another. Moreover, it is not entirely clear why one machine learning method is favored over another. In this work, we endeavor to undertake a comprehensive effort towards developing high-accuracy, machine-learned scoring functions, systematically investigating the effects of machine learning method and choice of features, and, when possible, providing insights into the relevant physics using methods that assess feature importance. Here, we show synergism among disparate features, yielding adjusted R² with experimental binding affinities of up to 0.871 on an independent test set and enrichment for native bound structures of up to 0.913. When purely physical terms that model enthalpic and entropic effects are used in the training, we use feature importance assessments to probe the relevant physics and hopefully guide future investigators working on this and other computational chemistry problems.

DockingApp RF: A State-of-the-Art Novel Scoring Function for Molecular Docking in a User-Friendly Interface to AutoDock Vina

Motivation: Bringing a new drug to the market is expensive and time-consuming. To cut the costs and time, computer-aided drug design (CADD) approaches have been increasingly included in the drug discovery pipeline. However, despite traditional docking tools show a good conformational space sampling ability, they are still unable to produce accurate binding affinity predictions. This work presents a novel scoring function for molecular docking seamlessly integrated into DockingApp, a user-friendly graphical interface for AutoDock Vina. The proposed function is based on a random forest model and a selection of specific features to overcome the existing limits of Vina’s original scoring mechanism. A novel version of DockingApp, named DockingApp RF, has been developed to host the proposed scoring function and to automatize the rescoring procedure of the output of AutoDock Vina, even to nonexpert users. Results: By coupling intermolecular interaction, solvent accessible surface area features and Vina’s energy terms, DockingApp RF’s new scoring function is able to improve the binding affinity prediction of AutoDock Vina. Furthermore, comparison tests carried out on the CASF-2013 and CASF-2016 datasets demonstrate that DockingApp RF’s performance is comparable to other state-of-the-art machine-learning- and deep-learning-based scoring functions. The new scoring function thus represents a significant advancement in terms of the reliability and effectiveness of docking compared to AutoDock Vina’s scoring function. At the same time, the characteristics that made DockingApp appealing to a wide range of users are retained in this new version and have been complemented with additional features.

Empirical Scoring Functions for Structure-Based Virtual Screening: Applications, Critical Aspects, and Challenges

Structure-based virtual screening (VS) is a widely used approach that employs the knowledge of the three-dimensional structure of the target of interest in the design of new lead compounds from large-scale molecular docking experiments. Through the prediction of the binding mode and affinity of a small molecule within the binding site of the target of interest, it is possible to understand important properties related to the binding process. Empirical scoring functions are widely used for pose and affinity prediction. Although pose prediction is performed with satisfactory accuracy, the correct prediction of binding affinity is still a challenging task and crucial for the success of structure-based VS experiments. There are several efforts in distinct fronts to develop even more sophisticated and accurate models for filtering and ranking large libraries of compounds. This paper will cover some recent successful applications and methodological advances, including strategies to explore the ligand entropy and solvent effects, training with sophisticated machine-learning techniques, and the use of quantum mechanics. Particular emphasis will be given to the discussion of critical aspects and further directions for the development of more accurate empirical scoring functions.

Multi-physics interactions drive VEGFR2 relocation on endothelial cells

Vascular Endothelial Growth Factor Receptor-2 (VEGFR2) is a pro-angiogenic receptor, expressed on endothelial cells (ECs). Although biochemical pathways that follow the VEGFR2 activation are well established, knowledge about the dynamics of receptors on the plasma membrane remains limited. Ligand stimulation induces the polarization of ECs and the relocation of VEGFR2, either in cell protrusions or in the basal aspect in cells plated on ligand-enriched extracellular matrix (ECM). We develop a mathematical model in order to simulate the relocation of VEGFR2 on the cell membrane during the mechanical adhesion of cells onto a ligand-enriched substrate. Co-designing the in vitro experiments with the simulations allows identifying three phases of the receptor dynamics, which are controlled respectively by the high chemical reaction rate, by the mechanical deformation rate, and by the diffusion of free receptors on the membrane. The identification of the laws that regulate receptor polarization opens new perspectives toward developing innovative anti-angiogenic strategies through the modulation of EC activation.

Accuracy comparison of several common implicit solvent models and their implementations in the context of protein-ligand binding

In this study several commonly used implicit solvent models are compared with respect to their accuracy of estimating solvation energies of small molecules and proteins, as well as desolvation penalty in protein-ligand binding. The test set consists of 19 small proteins, 104 small molecules, and 15 protein-ligand complexes. We compared predicted hydration energies of small molecules with their experimental values; the results of the solvation and desolvation energy calculations for small molecules, proteins and protein-ligand complexes in water were also compared with Thermodynamic Integration calculations based on TIP3P water model and Amber12 force field. The following implicit solvent (water) models considered here are: PCM (Polarized Continuum Model implemented in DISOLV and MCBHSOLV programs), GB (Generalized Born method implemented in DISOLV program, S-GB, and GBNSR6 stand-alone version), COSMO (COnductor-like Screening Model implemented in the DISOLV program and the MOPAC package) and the Poisson-Boltzmann model (implemented in the APBS program). Different parameterizations of the molecules were examined: we compared MMFF94 force field, Amber12 force field and the quantum-chemical semi-empirical PM7 method implemented in the MOPAC package. For small molecules, all of the implicit solvent models tested here yield high correlation coefficients (0.87-0.93) between the calculated solvation energies and the experimental values of hydration energies. For small molecules high correlation (0.82-0.97) with the explicit solvent energies is seen as well. On the other hand, estimated protein solvation energies and protein-ligand binding desolvation energies show substantial discrepancy (up to 10kcal/mol) with the explicit solvent reference. The correlation of polar protein solvation energies and protein-ligand desolvation energies with the corresponding explicit solvent results is 0.65-0.99 and 0.76-0.96 respectively, though this difference in correlations is caused more by different parameterization and less by methods and indicates the need for further improvement of implicit solvent models parameterization. Within the same parameterization, various implicit methods give practically the same correlation with results obtained in explicit solvent model for ligands and proteins: e.g. correlation values of polar ligand solvation energies and the corresponding energies in the frame of explicit solvent were 0.953-0.966 for the APBS program, the GBNSR6 program and all models used in the DISOLV program. The DISOLV program proved to be on a par with the other used programs in the case of proteins and ligands solvation energy calculation. However, the solution of the Poisson-Boltzmann equation (APBS program) and Generalized Born method (implemented in the GBNSR6 program) proved to be the most accurate in calculating the desolvation energies of complexes.

Cellular quantitative structure-activity relationship (Cell-QSAR): conceptual dissection of receptor binding and intracellular disposition in antifilarial activities of Selwood antimycins

We present the cellular quantitative structure–activity relationship (cell-QSAR) concept that adapts ligand-based and receptor-based 3D-QSAR methods for use with cell-level activities. The unknown intracellular drug disposition is accounted for by the disposition function (DF), a model-based, nonlinear function of a drug’s lipophilicity, acidity, and other properties. We conceptually combined the DF with our multispecies, multimode version of the frequently used ligand-based comparative molecular field analysis (CoMFA) method, forming a single correlation function for fitting the cell-level activities. The resulting cell-QSAR model was applied to the Selwood data on filaricidal activities of antimycin analogues. Their molecules are flexible, ionize under physiologic conditions, form different intramolecular H-bonds for neutral and ionized species, and cross several membranes to reach unknown receptors. The calibrated cell-QSAR model is significantly more predictive than other models lacking the disposition part and provides valuable structure optimization clues by factorizing the cell-level activity of each compound into the contributions of the receptor binding and disposition.

Statistical mechanics and molecular dynamics in evaluating thermodynamic properties of biomolecular recognition

Molecular recognition plays a central role in biochemical processes. Although well studied, understanding the mechanisms of recognition is inherently difficult due to the range of potential interactions, the molecular rearrangement associated with binding, and the time and length scales involved. Computational methods have the potential for not only complementing experiments that have been performed, but also in guiding future ones through their predictive abilities. In this review, we discuss how molecular dynamics (MD) simulations may be used in advancing our understanding of the thermodynamics that drive biomolecular recognition. We begin with a brief review of the statistical mechanics that form a basis for these methods. This is followed by a description of some of the most commonly used methods: thermodynamic pathways employing alchemical transformations and potential of mean force calculations, along with end-point calculations for free energy differences, and harmonic and quasi-harmonic analysis for entropic calculations. Finally, a few of the fundamental findings that have resulted from these methods are discussed, such as the role of configurational entropy and solvent in intermolecular interactions, along with selected results of the model system T4 lysozyme to illustrate potential and current limitations of these methods.

Molecular motions in drug design: the coming age of the metadynamics method

Metadynamics is emerging as a useful free energy method in physics, chemistry and biology. Recently, it has been applied also to investigate ligand binding to biomolecules of pharmacological interest. Here, after introducing the basic idea of the method, we review applications to challenging targets for pharmaceutical intervention. We show that this methodology, especially when combined with a variety of other computational approaches such as molecular docking and/or molecular dynamics simulation, may be useful to predict structure and energetics of ligand/target complexes even when the targets lack a deep binding cavity, such as DNA and proteins undergoing fibrillation in neurodegenerative diseases. Furthermore, the method allows investigating the routes of molecular recognition and the associated binding energy profiles, providing a molecular interpretation to experimental data.

Modeling Protein-Ligand Binding by Mining Minima

We present the first application of the mining minima algorithm to protein-small molecule binding. This end-point approach use an empirical force field and implicit solvent models, treats the protein binding-site as fully flexible and estimates free energies as sums over local energy wells. The calculations are found to yield encouraging agreement with experiment for three sets of HIV-1protease inhibitors and a set of phosphodiesterase 10a inhibitors. The contributions of various aspects of the model to its accuracy are examined, and the Poisson-Boltzmann correction is found to be the most critical. Interestingly, the computed changes in configurational entropy upon binding fall roughly along the same entropy-energy correlation previously observed for smaller host-guest systems. Strengths and weaknesses of the method are discussed, as are the prospects for enhancing accuracy and speed.

Path-integral method for predicting relative binding affinities of protein-ligand complexes

We present a novel approach for computing biomolecular interaction binding affinities based on a simple path integral solution of the Fokker-Planck equation. Computing the free energy of protein-ligand interactions can expedite structure-based drug design. Traditionally, the problem is seen through the lens of statistical thermodynamics. The computations can become, however, prohibitively long for the change in the free energy upon binding to be determined accurately. In this work, we present a different approach based on a stochastic kinetic formalism. Inspired by Feynman's path integral formulation, we extend the theory to classical interacting systems. The ligand is modeled as a Brownian particle subjected to the effective nonbonding interaction potential of the receptor. This allows the calculation of the relative binding affinities of interacting biomolecules in water to be computed as a function of the ligand's diffusivity and the curvature of the potential surface in the vicinity of the binding minimum. The calculation is thus exceedingly rapid. In test cases, the correlation coefficient between actual and computed free energies is >0.93 for accurate data sets.

Effects of protein conformation in docking: improved pose prediction through protein pocket adaptation

Computational methods for docking ligands have been shown to be remarkably dependent on precise protein conformation, where acceptable results in pose prediction have been generally possible only in the artificial case of re-docking a ligand into a protein binding site whose conformation was determined in the presence of the same ligand (the "cognate" docking problem). In such cases, on well curated protein/ligand complexes, accurate dockings can be returned as top-scoring over 75% of the time using tools such as Surflex-Dock. A critical application of docking in modeling for lead optimization requires accurate pose prediction for novel ligands, ranging from simple synthetic analogs to very different molecular scaffolds. Typical results for widely used programs in the "cross-docking case" (making use of a single fixed protein conformation) have rates closer to 20% success. By making use of protein conformations from multiple complexes, Surflex-Dock yields an average success rate of 61% across eight pharmaceutically relevant targets. Following docking, protein pocket adaptation and rescoring identifies single pose families that are correct an average of 67% of the time. Consideration of the best of two pose families (from alternate scoring regimes) yields a 75% mean success rate.

Toward a molecular understanding of the interaction of dual specificity phosphatases with substrates: insights from structure-based modeling and high throughput screening

Dual-specificity phosphatases (DSPs) are important, but poorly understood, cell signaling enzymes that remove phosphate groups from tyrosine and serine/threonine residues on their substrate. Deregulation of DSPs has been implicated in cancer, obesity, diabetes, inflammation, and Alzheimer's disease. Due to their biological and biomedical significance, DSPs have increasingly become the subject of drug discovery high-throughput screening (HTS) and focused compound library development efforts. Progress in identifying selective and potent DSP inhibitors has, however, been restricted by the lack of sufficient structural data on inhibitor-bound DSPs. The shallow, almost flat, substrate binding sites in DSPs have been a major factor in hampering the rational design and the experimental development of active site inhibitors. Recent experimental and virtual HTS studies, as well as advances in molecular modeling, provide new insights into the potential mechanisms for substrate recognition and binding by this important class of enzymes. We present herein an overview of the progress, along with a brief description of applications to two types of DSPs: Cdc25 and MAP kinase phosphatase (MKP) family members. In particular, we focus on combined computational and experimental efforts for designing Cdc25B and MKP-1 inhibitors and understanding their mechanisms of interactions with their target proteins. These studies emphasize the utility of developing computational models and methods that meet the two major challenges currently faced in structure-based in silico design of lead compounds: the conformational flexibility of the target protein and the entropic contribution to the selection and stabilization of particular bound conformers.

Daunomycin Binding to Detergent Micelles: A Model System for Evaluating the Hydrophobic Contribution to Drug−DNA Interactions

The interaction of daunomycin with sodium dodecyl sulfate and Triton X-100 micelles was investigated as a model for the hydrophobic contribution to the free energy of DNA intercalation reactions. Measurements of visible absorbance, fluorescence lifetime, steady-state fluorescence emission intensity, and fluorescence anisotropy indicate that the anthraquinone ring partitions into the hydrophobic micelle interior. Fluorescence quenching experiments using both steady-state and lifetime measurements demonstrate reduced accessibility of daunomycin in sodium dodecyl sulfate micelles to the anionic quencher iodide and to the neutral quencher acrylamide. Quenching of daunomycin fluorescence by iodide in Triton X-100 micelles was similar to that seen with free daunomycin. Studies of the energetics of the interaction of daunomycin with micelles by fluorescence and absorbance titration methods and by isothermal titration calorimetry in the presence of excess micelles revealed that association with sodium dodecyl sulfate and Triton X-100 micelles is driven by a large negative enthalpy. Association of the drug with both types of micelles also has a favorable entropic contribution, which is larger in magnitude for Triton X-100 micelles than for sodium dodecyl sulfate micelles. The thermodynamic profile for the interaction of daunomycin with both types of micelles is characteristic of the "nonclassical" hydrophobic effect. The enthalpy for the interaction of daunomycin with sodium dodecyl sulfate micelles increases nonlinearly with temperature, indicating a positive (and temperature dependent) heat capacity change. The binding isotherm for daunomycin association with sodium dodecyl sulfate micelles was cooperative, with a Hill coefficient of 1.6. The cooperative behavior and the positive heat capacity change suggest that the drug alters micelle size or imposes order on the hydrocarbon interior of the micelle.

Stochastic approach to molecular interactions and computational theory of metabolic and genetic regulations

The underlying molecular mechanisms of metabolic and genetic regulations are computationally identical and can be described by a finite state Markov process. We establish a common computational model for both regulations based on the stationary distribution of the Markov process with the aim of establishing a unified, quantitative model of general biological regulations. Various existing results regarding intracellular regulations are derived including the classical Michaelis-Menten equation and its generalization to more complex allosteric enzymes in a systematic way. The notion of probability flow is introduced to distinguish the equilibrium stationary distribution from the non-equilibrium one; it plays a crucial role in the analysis of stationary state equations. A graphical criterion to guarantee the existence of an equilibrium stationary distribution is derived, which turns out to be identical to the classical Wegscheider condition. Simple graphical methods to compute the equilibrium and non-equilibrium stationary distributions are derived based crucially on the probability flow, which dramatically simplifies the classical methods still used in enzymology.

Role of binding entropy in the refinement of protein-ligand docking predictions: analysis based on the use of 11 scoring functions

We present results of testing the ability of eleven popular scoring functions to predict native docked positions using a recently developed method (Ruvinsky and Kozintsev, J Comput Chem 2005, 26, 1089) for estimation the entropy contributions of relative motions to protein-ligand binding affinity. The method is based on the integration of the configurational integral over clusters obtained from multiple docked positions. We use a test set of 100 PDB protein-ligand complexes and ensembles of 101 docked positions generated by (Wang et al. J Med Chem 2003, 46, 2287) for each ligand in the test set. To test the suggested method we compared the averaged root-mean square deviations (RMSD) of the top-scored ligand docked positions, accounting and not accounting for entropy contributions, relative to the experimentally determined positions. We demonstrate that the method increases docking accuracy by 10-21% when used in conjunction with the AutoDock scoring function, by 2-25% with G-Score, by 7-41% with D-Score, by 0-8% with LigScore, by 1-6% with PLP, by 0-12% with LUDI, by 2-8% with F-Score, by 7-29% with ChemScore, by 0-9% with X-Score, by 2-19% with PMF, and by 1-7% with DrugScore. We also compared the performance of the suggested method with the method based on ranking by cluster occupancy only. We analyze how the choice of a clustering-RMSD and a low bound of dense clusters impacts on docking accuracy of the scoring methods. We derive optimal intervals of the clustering-RMSD for 11 scoring functions.

Calculations of protein-ligand binding entropy of relative and overall molecular motions

In the context of virtual database screening, calculations of protein-ligand binding entropy of relative and overall molecular motions are challenging, owing to the inherent structural complexity of the ligand binding well in the energy landscape of protein-ligand interactions and computing time limitations. We describe a fast statistical thermodynamic method for estimation the binding entropy to address the challenges. The method is based on the integration of the configurational integral over clusters obtained from multiple docked positions. We apply the method in conjunction with 11 popular scoring functions (AutoDock, ChemScore, DrugScore, D-Score, F-Score, G-Score, LigScore, LUDI, PLP, PMF, X-Score) to evaluate the binding entropy of 100 protein-ligand complexes. The averaged values of binding entropy contribution vary from 6.2 to 9.1 kcal/mol, showing good agreement with literature. We calculate positional sizes and the angular volume of the native ligand wells. The averaged geometric mean of positional sizes in principal directions varies from 0.8 to 1.4 A. The calculated range of angular volumes is 3.3-11.8 rad(2). Then we demonstrate that the averaged six-dimensional volume of the native well is larger than the volume of the most populated non-native well in energy landscapes described by all of 11 scoring functions.

Novel statistical-thermodynamic methods to predict protein-ligand binding positions using probability distribution functions

We present two novel methods to predict native protein-ligand binding positions. Both methods identify the native binding position as the most probable position corresponding to a maximum of a probability distribution function (PDF) of possible binding positions in a protein active site. Possible binding positions are the origins of clusters composed, on the basis of root-mean square deviations (RMSD), from the multiple ligand positions determined by a docking algorithm. The difference between the methods lies in the ways the PDF is derived. To validate the suggested methods, we compare the averaged RMSD of the predicted ligand docked positions relative to the experimentally determined positions for a set of 135 PDB protein-ligand complexes. We demonstrate that the suggested methods improve docking accuracy by as much as 21-24% in comparison with a method that simply identifies the binding position as the energy top-scored ligand position.

Can Configuration Entropy Losses Be Predicted from the Binding Affinities of Hydrogen-Bonded Complexes with Varying Numbers of Single Bonds?

The design of new supramolecular complexes often depends on reducing entropic contributions to improve binding. However, few studies provide reliable values for the cost of entropic contributions. Here, the binding affinities of a series of six alpha,omega-diamides to alpha,omega-dicarboxylates are calculated using a predominant states method and an implicit solvent model based upon finite difference solutions of the Poisson-Boltzmann equation. The calculations are able to reproduce the observed increase in binding free energy as the number of single bonds increases. However, calculations show that the increase in binding free energy is not due to an increase in entropy. Instead, the increase is due to the changing ability of the alpha,omega-diamides to form internal hydrogen bonds that must be disrupted to bind to the dicarboxylate receptors. This suggests that interpreting experimental free-energy trends to give rotational entropy contributions may be problematic.

Calculation of absolute protein-ligand binding affinity using path and endpoint approaches

A comparative analysis is provided of rigorous and approximate methods for calculating absolute binding affinities of two protein-ligand complexes: the FKBP protein bound with small molecules 4-hydroxy-2-butanone and FK506. Our rigorous approach is an umbrella sampling technique where a potential of mean force is determined by pulling the ligand out of the protein active site over several simulation windows. The results of this approach agree well with experimentally observed binding affinities. Also assessed is a commonly used approximate endpoint approach, which separately estimates enthalpy, solvation free energy, and entropy. We show that this endpoint approach has numerous variations, all of which are prone to critical shortcomings. For example, conventional harmonic and quasiharmonic entropy estimation procedures produce disparate results for the relatively simple protein-ligand systems studied in this work.

New and fast statistical-thermodynamic method for computation of protein-ligand binding entropy substantially improves docking accuracy

We present a novel method to estimate the contributions of translational and rotational entropy to protein-ligand binding affinity. The method is based on estimates of the configurational integral through the sizes of clusters obtained from multiple docking positions. Cluster sizes are defined as the intervals of variation of center of ligand mass and Euler angles in the cluster. Then we suggest a method to consider the entropy of torsional motions. We validate the suggested methods on a set of 135 PDB protein-ligand complexes by comparing the averaged root-mean square deviations (RMSD) of the top-scored ligand docked positions, accounting and not accounting for entropy contributions, relative to the experimentally determined positions. We demonstrate that the method increases docking accuracy by 10-21% when used in conjunction with the AutoDock docking program, thus reducing the percent of incorrectly docked ligands by 1.4-fold to four-fold, so that in some cases the percent of ligands correctly docked to within an RMSD of 2 A is above 90%. We show that the suggested method to account for entropy of relative motions is identical to the method based on the Monte Carlo integration over intervals of variation of center of ligand mass and Euler angles in the cluster.

Large-Scale Validation of a Quantum Mechanics Based Scoring Function: Predicting the Binding Affinity and the Binding Mode of a Diverse Set of Protein−Ligand Complexes

Computational methods to calculate binding affinity in protein-ligand interaction are of immense interest because of obvious practical applications in structure-based drug design. Scoring functions attempt to calculate the variation in binding affinity of ligands-inhibitors bound to protein targets at various levels of theory. In this study we use semiempirical quantum mechanics to design a scoring function that can calculate the electrostatic interactions and solvation free energy expected during complexation. This physically based approach has the ability to capture binding affinity trends in a diverse range of protein-ligand complexes. We also show the predictive power of this scoring function within protein targets and its ability to score ligand poses docked to a protein target. We also demonstrate the ability of this scoring function to discriminate between native and decoy poses and highlight the crucial role played by electrostatic interactions in molecular recognition. Finally we compare the performance of our scoring function with other available scoring functions in the literature.

Calculation of cyclodextrin binding affinities: energy, entropy, and implications for drug design

The second generation Mining Minima method yields binding affinities accurate to within 0.8 kcal/mol for the associations of alpha-, beta-, and gamma-cyclodextrin with benzene, resorcinol, flurbiprofen, naproxen, and nabumetone. These calculations require hours to a day on a commodity computer. The calculations also indicate that the changes in configurational entropy upon binding oppose association by as much as 24 kcal/mol and result primarily from a narrowing of energy wells in the bound versus the free state, rather than from a drop in the number of distinct low-energy conformations on binding. Also, the configurational entropy is found to vary substantially among the bound conformations of a given cyclodextrin-guest complex. This result suggests that the configurational entropy must be accounted for to reliably rank docked conformations in both host-guest and ligand-protein complexes. In close analogy with the common experimental observation of entropy-enthalpy compensation, the computed entropy changes show a near-linear relationship with the changes in mean potential plus solvation energy.

Calculation of ligand-nucleic acid binding free energies with the generalized-born model in DOCK

The calculation of ligand-nucleic acid binding free energies is investigated by including solvation effects computed with the generalized-Born model. Modifications of the solvation module in DOCK, including introduction of all-atom parameters and revision of coefficients in front of different terms, are shown to improve calculations involving nucleic acids. This computing scheme is capable of calculating binding energies, with reasonable accuracy, for a wide variety of DNA-ligand complexes, RNA-ligand complexes, and even for the formation of double-stranded DNA. This implementation of GB/SA is also shown to be capable of discriminating strong ligands from poor ligands for a series of RNA aptamers without sacrificing the high efficiency of the previous implementation. These results validate this approach to screening large databases against nucleic acid targets.

Tork: Conformational analysis method for molecules and complexes

A conformational search method for organic molecules and bimolecular complexes is presented. The method, termed Tork, uses normal-mode analysis in bond-angle-torsion coordinates and focuses on a key subset of torsional coordinates to identify natural molecular motions that lead the initial conformation to new energy minima. New conformations are generated via distortion along these modes and their pairwise combinations, followed by energy minimization. For complexes, special treatment is accorded to the six coordinates that specify the position and orientation of one molecule relative to the other. Tests described here show that Tork is highly efficient for cyclic, acyclic, and mixed single molecules, as well as for host-guest complexes.

Interpreting trends in the binding of cyclic ureas to HIV-1 protease

The design of new HIV protease inhibitors requires an improved understanding of the physical basis of inhibitor/protein binding. Here, the binding affinities of seven aliphatic cyclic ureas to HIV-1 protease are calculated using a predominant states method and an implicit solvent model based upon finite difference solutions of the Poisson-Boltzmann equation. The calculations are able to reproduce the observed U-shaped trend of binding free energy as a function of aliphatic chain length. Interestingly, the decrease in affinity for the longest chains is attributable primarily to the energy cost of partly desolvating charged aspartic and arginine groups at the mouths of the active site. Even aliphatic chains too short to contact these charged groups directly are subject to considerable desolvation penalties. We are not aware of other systems where binding affinity trends have been attributed to long-ranged electrostatic desolvation of ionized groups. A generalized Born/surface area solvation model yields a much smaller change in desolvation energy with chain length and, therefore, does not reproduce the experimental binding affinity trends. This result suggests that the generalized Born model should be used with caution for complex, partly desolvated systems like protein binding sites. We also find that changing the assumed protonation state of the active site aspartyl dyad significantly affects the computed binding affinity trends. The protonation state of the aspartyl dyad in the presence of cyclic ureas is discussed in light of the observation that the monoprotonated state reproduces the experimental results best.

Scoring docked conformations generated by rigid-body protein-protein docking

Rigid-body methods, particularly Fourier correlation techniques, are very efficient for docking bound (co-crystallized) protein conformations using measures of surface complementarity as the target function. However, when docking unbound (separately crystallized) conformations, the method generally yields hundreds of false positive structures with good scores but high root mean square deviations (RMSDs). This paper describes a two-step scoring algorithm that can discriminate near-native conformations (with less than 5 A RMSD) from other structures. The first step includes two rigid-body filters that use the desolvation free energy and the electrostatic energy to select a manageable number of conformations for further processing, but are unable to eliminate all false positives. Complete discrimination is achieved in the second step that minimizes the molecular mechanics energy of the retained structures, and re-ranks them with a combined free-energy function which includes electrostatic, solvation, and van der Waals energy terms. After minimization, the improved fit in near-native complex conformations provides the free-energy gap required for discrimination. The algorithm has been developed and tested using docking decoys, i.e., docked conformations generated by Fourier correlation techniques. The decoy sets are available on the web for testing other discrimination procedures. Proteins 2000;40:525-537.

Structure/thermodynamics relationships of lectin-saccharide complexes: the Erythrina corallodendron case

Molecular dynamics (MD) simulations of Erythrina corallodendron lectin binding to a monosaccharide, alpha-galactose, and a disaccharide, N-acetyl lactosamine, have been performed in order to investigate the relationship between structure and thermodynamics. A simulated annealing protocol has been used to generate ensembles of structures for the two complexes, from which both qualitative and quantitative information on binding dynamics have been extracted. The ensembled averaged lectin-saccharide interaction enthalpy is equivalent for both sugars, whereas the calculation based on the X-ray structures does show a difference. Within large statistical errors, the calculated 'binding enthalpy' is also the same for the two systems. These errors arise largely from terms involving solvent and are a typical limitation of current MD simulations. Significant qualitative differences in binding between the two complexes are, however, observed over the ensembles. These could be important for unraveling the structure/thermodynamic relationship. Stated simply, there are a greater number of binding options available to the disaccharide compared to the monosaccharide. The implications of alternative binding states on thermodynamic parameters and the 'breaking of enthalpy-entropy compensation' are discussed. The role of solvent in lectin-saccharide complex formation is suggested to be significant.

Energetics of drug-DNA interactions

Understanding the thermodynamics of drug binding to DNA is of both practical and fundamental interest. The practical interest lies in the contribution that thermodynamics can make to the rational design process for the development of new DNA targeted drugs. Thermodynamics offer key insights into the molecular forces that drive complex formation that cannot be obtained by structural or computational studies alone. The fundamental interest in these interactions lies in what they can reveal about the general problems of parsing and predicting ligand binding free energies. For these problems, drug-DNA interactions offer several distinct advantages, among them being that the structures of many drug-DNA complexes are known at high resolution and that such structures reveal that in many cases the drug acts as a rigid body, with little conformational change upon binding. Complete thermodynamic profiles (delta G, delta H, delta S, delta Cp) for numerous drug-DNA interactions have been obtained, with the help of high-sensitivity microcalorimetry. The purpose of this article is to offer a perspective on the interpretation of these thermodynamics parameters, and in particular how they might be correlated with known structural features. Obligatory conformational changes in the DNA to accommodate intercalators and the loss of translational and rotational freedom upon complex formation both present unfavorable free energy barriers for binding. Such barriers must be overcome by favorable free energy contributions from the hydrophobic transfer of ligand from solution into the binding site, polyelectrolyte contributions from coupled ion release, and molecular interactions (hydrogen and ionic bonds, van der Waals interactions) that form within the binding site. Theoretical and semiempirical tools that allow estimates of these contributions to be made will be discussed, and their use in dissecting experimental data illustrated. This process, even at the current level of approximation, can shed considerable light on the drug-DNA binding process.

Structure-based library design: molecular modelling merges with combinatorial chemistry

Recent advances in both computational and experimental techniques now allow a very fruitful interplay of computational and combinatorial chemistry in the structure-based design of combinatorial libraries.

Structural determinants of trypsin affinity and specificity for cationic inhibitors

The binding free energies of four inhibitors to bovine beta-trypsin are calculated. The inhibitors use either ornithine, lysine, or arginine to bind to the S1 specificity site. The electrostatic contribution to binding free energy is calculated by solving the finite difference Poisson-Boltzmann equation, the contribution of nonpolar interactions is calculated using a free energy-surface area relationship and the loss of conformational entropy is estimated both for trypsin and ligand side chains. Binding free energy values are of a reasonable magnitude and the relative affinity of the four inhibitors for trypsin is correctly predicted. Electrostatic interactions are found to oppose binding in all cases. However, in the case of ornithine- and lysine-based inhibitors, the salt bridge formed between their charged group and the partially buried carboxylate of Asp189 is found to stabilize the complex. Our analysis reveals how the molecular architecture of the trypsin binding site results in highly specific recognition of substrates and inhibitors. Specifically, partially burying Asp189 in the inhibitor-free enzyme decreases the penalty for desolvation of this group upon complexation. Water molecules trapped in the binding interface further stabilize the buried ion pair, resulting in a favorable electrostatic contribution of the ion pair formed with ornithine and lysine side chains. Moreover, all side chains that form the trypsin specificity site are partially buried, and hence, relatively immobile in the inhibitor-free state, thus reducing the entropic cost of complexation. The implications of the results for the general problem of recognition and binding are considered. A novel finding in this regard is that like charged molecules can have electrostatic contributions to binding that are more favorable than oppositely charged molecules due to enhanced interactions with the solvent in the highly charged complex that is formed.

Calculated protein and proton motions coupled to electron transfer: electron transfer from QA- to QB in bacterial photosynthetic reaction centers

Reaction centers from Rhodobacter sphaeroides were subjected to Monte Carlo sampling to determine the Boltzmann distribution of side-chain ionization states and positions and buried water orientation and site occupancy. Changing the oxidation states of the bacteriochlorophyll dimer electron donor (P) and primary (QA) and secondary (QB) quinone electron acceptors allows preparation of the ground (all neutral), P+QA-, P+QB-, P0QA-, and P0QB- states. The calculated proton binding going from ground to other oxidation states and the free energy of electron transfer from QA-QB to form QAQB- (DeltaGAB) compare well with experiment from pH 5 to pH 11. At pH 7 DeltaGAB is measured as -65 meV and calculated to be -80 meV. With fixed protein positions as in standard electrostatic calculations, DeltaGAB is +170 meV. At pH 7 approximately 0.2 H+/protein is bound on QA reduction. On electron transfer to QB there is little additional proton uptake, but shifts in side chain protonation and position occur throughout the protein. Waters in channels leading from QB to the surface change site occupancy and orientation. A cluster of acids (GluL212, AspL210, and L213) and SerL223 near QB play important roles. A simplified view shows this cluster with a single negative charge (on AspL213 with a hydrogen bond to SerL233) in the ground state. In the QB- state the cluster still has one negative charge, now on the more distant AspL210. AspL213 and SerL223 move so SerL223 can hydrogen bond to QB-. These rearrangements plus other changes throughout the protein make the reaction energetically favorable.

The effect of multiple binding modes on empirical modeling of ligand docking to proteins

A popular approach to the computational modeling of ligand/receptor interactions is to use an empirical free energy like model with adjustable parameters. Parameters are learned from one set of complexes, then used to predict another set. To improve these empirical methods requires an independent way to study their inherent errors. We introduce a toy model of ligand/receptor binding as a workbench for testing such errors. We study the errors incurred from the two state binding assumption--the assumption that a ligand is either bound in one orientation, or unbound. We find that the two state assumption can cause large errors in free energy predictions, but it does not affect rank order predictions significantly. We show that fitting parameters using data from high affinity ligands can reduce two state errors; so can using more physical models that do not use the two state assumption. We also find that when using two state models to predict free energies, errors are more severe on high affinity ligands than low affinity ligands. And we show that two state errors can be diagnosed by systematically adding new binding modes when predicting free energies: if predictions worsen as the modes are added, then the two state assumption in the fitting step may be at fault.

Scoring functions: a view from the bench

Computational approaches to drug design are presently hindered by the complexity of the physical chemistry which underlies weak, non-covalent interactions between protein targets and small molecule ligands. Although a number of programs are now available for the design of novel potential ligands, it remains a key problem to rank these rapidly and reliably by estimated binding affinity. Such a step is necessary to select only the most promising candidates for synthesis and experimental characterisation. To calculate ligand affinity quickly and reliably is an extremely difficult problem, but it may well prove possible to estimate sufficiently accurately given an appropriate set of parameters to 'score' individual protein-ligand interactions. Improvements in the situation will require a wider set of thermodynamically characterised systems than is currently available.

How and why phosphotyrosine-containing peptides bind to the SH2 and PTB domains

BACKGROUND

Specific recognition of phosphotyrosine-containing protein segments by Src homology 2 (SH2) and phosphotyrosine-binding (PTB) domains plays an important role in intracellular signal transduction. Although many SH2/PTB-domain-containing receptor-peptide complex structures have been solved, little has been done to study the problem computationally. Prediction of the binding geometry and the binding constant of any peptide-protein pair is an extremely important problem.

RESULTS

A procedure to predict binding energies of phosphotyrosine-containing peptides with SH2/PTB domains was developed. The average deviation between experimentally measured binding energies and theoretical evaluations was 1.8 kcal/mol. Binding states of unphosphorylated peptides were also predicted reasonably well. Ab initio predictions of binding geometry of fully flexible peptides correctly identified conformations of two pentapeptides and a hexapeptide complexed with a v-Src SH2 domain receptor with root mean square deviations (rmsds) of 0.3 A, 1.2 A and 1.5 A, respectively.

CONCLUSIONS

The binding energies of phosphotyrosine-containing complexes can be effectively predicted using the procedure developed here. It was also possible to predict the bound conformations of flexible short peptides correctly from random starting conformations.

A hierarchical method for generating low-energy conformers of a protein-ligand complex

A novel dynamical protocol for finding the low-energy conformations of a protein-ligand complex is described. The energy functions examined consist of an empirical force field with four different dielectric screening models; the generalized Born/surface area model also is examined. Application of the method to three complexes of known crystal structure provides insights into the energy functions used for selecting low-energy docked conformations and into the structure of the binding-energy surface. Evidence is presented that the local energy minima of a ligand in a binding site are arranged in a hierarchical fashion. This observation motivates the construction of a hierarchical docking algorithm that substantially enriches the population of ligand conformations close to the crystal conformation. The algorithm is also adapted to permit docking into a flexible binding site and preliminary tests of this method are presented.