Development of the knowledge-based and empirical combined scoring algorithm (KECSA) to score protein-ligand interactions

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.

GSScore: a novel Graphormer-based shell-like scoring method for protein-ligand docking

Protein-ligand interactions (PLIs) are essential for cellular activities and drug discovery. But due to the complexity and high cost of experimental methods, there is a great demand for computational approaches to recognize PLI patterns, such as protein-ligand docking. In recent years, more and more models based on machine learning have been developed to directly predict the root mean square deviation (RMSD) of a ligand docking pose with reference to its native binding pose. However, new scoring methods are pressingly needed in methodology for more accurate RMSD prediction. We present a new deep learning-based scoring method for RMSD prediction of protein-ligand docking poses based on a Graphormer method and Shell-like graph architecture, named GSScore. To recognize near-native conformations from a set of poses, GSScore takes atoms as nodes and then establishes the docking interface of protein-ligand into multiple bipartite graphs within different shell ranges. Benefiting from the Graphormer and Shell-like graph architecture, GSScore can effectively capture the subtle differences between energetically favorable near-native conformations and unfavorable non-native poses without extra information. GSScore was extensively evaluated on diverse test sets including a subset of PDBBind version 2019, CASF2016 as well as DUD-E, and obtained significant improvements over existing methods in terms of RMSE, $R$ (Pearson correlation coefficient), Spearman correlation coefficient and Docking power.

ViTScore: A Novel Three-Dimensional Vision Transformer Method for Accurate Prediction of Protein-Ligand Docking Poses

Protein-ligand interactions (PLIs) are essential for cellular activities and drug discovery, and due to the complexity and high cost of experimental methods, there is a great demand for computational approaches, such as protein-ligand docking, to decipher PLI patterns. One of the most challenging aspects of protein-ligand docking is to identify near-native conformations from a set of poses, but traditional scoring functions still have limited accuracy. Therefore, new scoring methods are urgently needed for methodological and/or practical implications. We present a novel deep learning-based scoring function for ranking protein-ligand docking poses based on Vision Transformer (ViT), named ViTScore. To recognize near-native poses from a set of poses, ViTScore voxelizes the protein-ligand interactional pocket into a 3D grid labeled by the occupancy contribution of atoms in different physicochemical classes. This allows ViTScore to capture the subtle differences between spatially and energetically favorable near-native poses and unfavorable non-native poses without needing extra information. After that, ViTScore will output the prediction of the root mean square deviation (rmsd) of a docking pose with reference to the native binding pose. ViTScore is extensively evaluated on diverse test sets including PDBbind2019 and CASF2016, and obtains significant improvements over existing methods in terms of RMSE, R and docking power. Moreover, the results demonstrate that ViTScore is a promising scoring function for protein-ligand docking, and it can be used to accurately identify near-native poses from a set of poses. Furthermore, the results suggest that ViTScore is a powerful tool for protein-ligand docking, and it can be used to accurately identify near-native poses from a set of poses. Additionally, ViTScore can be used to identify potential drug targets and to design new drugs with improved efficacy and safety.

Molecular docking in organic, inorganic, and hybrid systems: a tutorial review

Molecular docking simulation is a very popular and well-established computational approach and has been extensively used to understand molecular interactions between a natural organic molecule (ideally taken as a receptor) such as an enzyme, protein, DNA, RNA and a natural or synthetic organic/inorganic molecule (considered as a ligand). But the implementation of docking ideas to synthetic organic, inorganic, or hybrid systems is very limited with respect to their use as a receptor despite their huge popularity in different experimental systems. In this context, molecular docking can be an efficient computational tool for understanding the role of intermolecular interactions in hybrid systems that can help in designing materials on mesoscale for different applications. The current review focuses on the implementation of the docking method in organic, inorganic, and hybrid systems along with examples from different case studies. We describe different resources, including databases and tools required in the docking study and applications. The concept of docking techniques, types of docking models, and the role of different intermolecular interactions involved in the docking process to understand the binding mechanisms are explained. Finally, the challenges and limitations of dockings are also discussed in this review.

Graphical abstract

Binding and selectivity studies of phosphatidylinositol 3-kinase (PI3K) inhibitors

Overexpression of the Phosphatidylinositol 3-kinase (PI3K) proteins have been observed in cancer cells. Targeting the phosphatidylinositol 3-kinase (PI3K) signaling transduction pathway by inhibition of the PI3K substrate recognition sites has been proved to be an effective approach to block cancer progression. Many PI3K inhibitors have been developed. Seven drugs have been approved by the US FDA with a mechanism of targeting the phosphatidylinositol 3-kinase/protein kinase-B/mammalian target of rapamycin (PI3K/AKT/mTOR) signaling pathway. In this study, we used docking tools to investigate selective binding of ligands toward four different subtypes of PI3Ks (PI3Kα, PI3Kβ, PI3Kγ and PI3Kδ). The affinity predicted from both the Glide dock and the Movable-Type (MT)-based free energy calculations agreed well with the experimental data. The validation of our predicted methods with a large dataset of 147 ligands showed very small mean errors. We identified residues that may dictate the subtype-specific binding. Particularly, residues Asp964, Ser806, Lys890 and Thr886 of PI3Kγ might be utilized for PI3Kγ-selective inhibitor design. Residues Val828, Trp760, Glu826 and Tyr813 may be important for PI3Kδ-selective inhibitor binding.

Scoring Functions for Protein-Ligand Binding Affinity Prediction using Structure-Based Deep Learning: A Review

The rapid and accurate in silico prediction of protein-ligand binding free energies or binding affinities has the potential to transform drug discovery. In recent years, there has been a rapid growth of interest in deep learning methods for the prediction of protein-ligand binding affinities based on the structural information of protein-ligand complexes. These structure-based scoring functions often obtain better results than classical scoring functions when applied within their applicability domain. Here we review structure-based scoring functions for binding affinity prediction based on deep learning, focussing on different types of architectures, featurization strategies, data sets, methods for training and evaluation, and the role of explainable artificial intelligence in building useful models for real drug-discovery applications.

RNA-ligand molecular docking: advances and challenges

With rapid advances in computer algorithms and hardware, fast and accurate virtual screening has led to a drastic acceleration in selecting potent small molecules as drug candidates. Computational modeling of RNA-small molecule interactions has become an indispensable tool for RNA-targeted drug discovery. The current models for RNA-ligand binding have mainly focused on the docking-and-scoring method. Accurate docking and scoring should tackle four crucial problems: (1) conformational flexibility of ligand, (2) conformational flexibility of RNA, (3) efficient sampling of binding sites and binding poses, and (4) accurate scoring of different binding modes. Moreover, compared with the problem of protein-ligand docking, predicting ligand binding to RNA, a negatively charged polymer, is further complicated by additional effects such as metal ion effects. Thermodynamic models based on physics-based and knowledge-based scoring functions have shown highly encouraging success in predicting ligand binding poses and binding affinities. Recently, kinetic models for ligand binding have further suggested that including dissociation kinetics (residence time) in ligand docking would result in improved performance in estimating in vivo drug efficacy. More recently, the rise of deep-learning approaches has led to new tools for predicting RNA-small molecule binding. In this review, we present an overview of the recently developed computational methods for RNA-ligand docking and their advantages and disadvantages.

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.

FFENCODER-PL: Pair Wise Energy Descriptors for Protein-Ligand Pose Selection

Scoring functions are the essential component in molecular docking methods. An accurate scoring function is expected to distinguish the native ligand pose from decoy poses. Our previous experience (Pei et al. J. Chem. Inf. Model. 2019, 59 (7), 3305-3315) proved that combining the random forest (RF) algorithm with knowledge-based potential functions can emphasize germane pair wise interactions and improve the performance of original knowledge-based potential functions on protein-ligand decoy detection. One of the most important potential function classes is the force field (FF) potential with one example being the Amber collection of FFs, which are widely available in the AMBER suite of simulation programs. However, for use in RF modeling studies, one needs pair wise energies that are hard to directly extract from Amber. To address this issue, FFENCODER-PL was constructed to calculate the pair wise energies based on the FF14SB and GAFF2 FFs in Amber. FFENCODER-PL was validated using 275 ligand and 21 protein-ligand structures. RF models were built by combining an RF classification algorithm with the pair wise energies calculated from FFENCODER-PL. CASF-2016 (Su et al. J. Chem. Inf. Model. 2019, 59, 895-913) was employed to test the performance of the resultant RF models, which outperformed 33 scoring functions on accuracy and native ranking tests. For the best decoy RMSD test, RF models give a best decoy with an RMSD of around 2 Å from the native pose after including the best decoy-decoy comparisons in the RF model. The relative importance of the RF algorithm and force field potentials was also tested with the results suggesting that both the RF algorithm and force field potentials are important and combining them is the only way to achieve high accuracy. Finally, FFENCODER-PL makes force field-based pair wise energies available for further development of machine learning-based scoring functions. The codes and data used in this paper can be found at https://github.com/JunPei000/Amber_protein_ligand_encoding.

DeepBSP-a Machine Learning Method for Accurate Prediction of Protein-Ligand Docking Structures

In recent years, machine-learning-based scoring functions have significantly improved the scoring power. However, many of these methods do not perform well in distinguishing the native structure from docked decoy poses due to the lack of decoy structural information in their training data. Here, we developed a machine-learning model, named DeepBSP, that can directly predict the root mean square deviation (rmsd) of a ligand docking pose with reference to its native binding pose. Unlike the binding affinity, the rmsd between the docking poses with reference to their native structures can be straightforwardly determined. By training on a generated data set with 11,925 native complexes and more than 165,000 docked poses, our model shows excellent docking power on our test set and also on the CASF-2016 docking decoy set compared to other major scoring functions. Thus, by combining molecular dockings that generate many poses with the application of DeepBSP, one can more accurately predict the best binding pose that is closest to the native complex structure. This DeepBSP model shall be very useful in picking out poses close to their natives from many poses generated from a dock application.

Refinement of pairwise potentials via logistic regression to score protein-protein interactions

Protein-protein interactions (PPIs) are ubiquitous and functionally of great importance in biological systems. Hence, the accurate prediction of PPIs by protein-protein docking and scoring tools is highly desirable in order to characterize their structure and biological function. Ab initio docking protocols are divided into the sampling of docking poses to produce at least one near-native structure, and then to evaluate the vast candidate structures by scoring. Concurrent development in both sampling and scoring is crucial for the deployment of protein-protein docking software. In the present work, we apply a machine learning model on pairwise potentials to refine the task of protein quaternary structure native structure detection among decoys. A decoy set was featurized using the Knowledge and Empirical Combined Scoring Algorithm 2 (KECSA2) pairwise potential. The highly unbalanced decoy set was then balanced using a comparison concept between native and decoy structures. The resultant comparison descriptors were used to train a logistic regression (LR) classifier. The LR model yielded the optimal performance for native detection among decoys compared with conventional scoring functions, while exhibiting lesser performance for the detection of low root mean square deviation decoy structures. Its deployment on an independent benchmark set confirms that the scoring function performs competitively relative to other scoring functions. The scripts used are available at https://github.com/TanemuraKiyoto/PPI-native-detection-via-LR.

Improving the binding affinity estimations of protein-ligand complexes using machine-learning facilitated force field method

Scoring functions are routinely deployed in structure-based drug design to quantify the potential for protein-ligand (PL) complex formation. Here, we present a new scoring function Bappl+ that is designed to predict the binding affinities of non-metallo and metallo PL complexes. Bappl+ outperforms other state-of-the-art scoring functions, achieving a high Pearson correlation coefficient of up to ~ 0.76 with low standard deviations. The biggest contributors to the increased performance are the use of a machine-learning model and the enlarged training dataset. We have also evaluated the performance of Bappl+ on target-specific proteins, which highlighted the limitations of our function and provides a way for further improvements. We believe that Bappl+ methodology could prove valuable in ranking candidate molecules against a target metallo or non-metallo protein by reliably predicting their binding affinities, thus helping in the drug discovery process.

Freely Accessible Chemical Database Resources of Compounds for In Silico Drug Discovery

BACKGROUND

In silico drug discovery has been proved to be a solidly established key component in early drug discovery. However, this task is hampered by the limitation of quantity and quality of compound databases for screening. In order to overcome these obstacles, freely accessible database resources of compounds have bloomed in recent years. Nevertheless, how to choose appropriate tools to treat these freely accessible databases is crucial. To the best of our knowledge, this is the first systematic review on this issue.

OBJECTIVE

The existed advantages and drawbacks of chemical databases were analyzed and summarized based on the collected six categories of freely accessible chemical databases from literature in this review.

RESULTS

Suggestions on how and in which conditions the usage of these databases could be reasonable were provided. Tools and procedures for building 3D structure chemical libraries were also introduced.

CONCLUSION

In this review, we described the freely accessible chemical database resources for in silico drug discovery. In particular, the chemical information for building chemical database appears as attractive resources for drug design to alleviate experimental pressure.

Molecular Modeling Studies on the Binding Mode of the PD-1/PD-L1 Complex Inhibitors

The programmed cell death protein 1 (PD-1)/programmed cell death ligand 1 (PD-L1) is an immune checkpoint (ICP) overexpressed in various types of tumors; thus, it has been considered as an important target for cancer therapy. To determine important residues for ligand binding, we applied molecular docking studies to PD-1/PD-L1 complex inhibitors against the PD-L1 protein. Our data revealed that the residues Tyr56, Asp122, and Lys124 play critical roles in ligand binding to the PD-L1 protein and they could be used to design ligands that are active against the PD-1/PD-L1 complex. The formation of H-bonds with Arg125 of the PD-L1 protein may enhance the potency of the PD-1/PD-L1 binding.

An Overview of Scoring Functions Used for Protein-Ligand Interactions in Molecular Docking

Currently, molecular docking is becoming a key tool in drug discovery and molecular modeling applications. The reliability of molecular docking depends on the accuracy of the adopted scoring function, which can guide and determine the ligand poses when thousands of possible poses of ligand are generated. The scoring function can be used to determine the binding mode and site of a ligand, predict binding affinity and identify the potential drug leads for a given protein target. Despite intensive research over the years, accurate and rapid prediction of protein-ligand interactions is still a challenge in molecular docking. For this reason, this study reviews four basic types of scoring functions, physics-based, empirical, knowledge-based, and machine learning-based scoring functions, based on an up-to-date classification scheme. We not only discuss the foundations of the four types scoring functions, suitable application areas and shortcomings, but also discuss challenges and potential future study directions.

Evaluation of Predicted Protein-Protein Complexes by Binding Free Energy Simulations

The accurate prediction of protein-protein complex geometries is of major importance to ultimately model the complete interactome of interacting proteins in a cell. A major bottleneck is the realistic free energy evaluation of predicted docked structures. Typically, simple scoring functions applied to single-complex structures are employed that neglect conformational entropy and often solvent effects completely. The binding free energy of a predicted protein-protein complex can, however, be calculated using umbrella sampling (US) along a predefined dissociation/association coordinate of a complex. We employed atomistic US-molecular dynamics simulations including appropriate conformational and axial restraints and an implicit generalized Born solvent model to calculate binding free energies of a large set of docked decoys for 20 different complexes. Free energies associated with the restraints were calculated separately. In principle, the approach includes all energetic and entropic contributions to the binding process. The evaluation of docked complexes based on binding free energy calculation was in better agreement with experiment compared to a simple scoring based on energy minimization or MD refinement using exactly the same force field description. Even calculated absolute binding free energies of structures close to the native binding geometry showed a reasonable correlation to experiment. However, still for a number of complexes docked decoys of lower free energy than near-native geometries were found indicating inaccuracies in the force field or the implicit solvent model. Although time consuming the approach may open up a new route for realistic ranking of predicted geometries based on calculated free energy of binding.

Solvents to Fragments to Drugs: MD Applications in Drug Design

Simulations of molecular dynamics (MD) are playing an increasingly important role in structure-based drug discovery (SBDD). Here we review the use of MD for proteins in aqueous solvation, organic/aqueous mixed solvents (MDmix) and with small ligands, to the classic SBDD problems: Binding mode and binding free energy predictions. The simulation of proteins in their condensed state reveals solvent structures and preferential interaction sites (hot spots) on the protein surface. The information provided by water and its cosolvents can be used very effectively to understand protein ligand recognition and to improve the predictive capability of well-established methods such as molecular docking. The application of MD simulations to the study of the association of proteins with drug-like compounds is currently only possible for specific cases, as it remains computationally very expensive and labor intensive. MDmix simulations on the other hand, can be used systematically to address some of the common tasks in SBDD. With the advent of new tools and faster computers we expect to see an increase in the application of mixed solvent MD simulations to a plethora of protein targets to identify new drug candidates.

Overview of the SAMPL6 host-guest binding affinity prediction challenge

Accurately predicting the binding affinities of small organic molecules to biological macromolecules can greatly accelerate drug discovery by reducing the number of compounds that must be synthesized to realize desired potency and selectivity goals. Unfortunately, the process of assessing the accuracy of current computational approaches to affinity prediction against binding data to biological macromolecules is frustrated by several challenges, such as slow conformational dynamics, multiple titratable groups, and the lack of high-quality blinded datasets. Over the last several SAMPL blind challenge exercises, host-guest systems have emerged as a practical and effective way to circumvent these challenges in assessing the predictive performance of current-generation quantitative modeling tools, while still providing systems capable of possessing tight binding affinities. Here, we present an overview of the SAMPL6 host-guest binding affinity prediction challenge, which featured three supramolecular hosts: octa-acid (OA), the closely related tetra-endo-methyl-octa-acid (TEMOA), and cucurbit[8]uril (CB8), along with 21 small organic guest molecules. A total of 119 entries were received from ten participating groups employing a variety of methods that spanned from electronic structure and movable type calculations in implicit solvent to alchemical and potential of mean force strategies using empirical force fields with explicit solvent models. While empirical models tended to obtain better performance than first-principle methods, it was not possible to identify a single approach that consistently provided superior results across all host-guest systems and statistical metrics. Moreover, the accuracy of the methodologies generally displayed a substantial dependence on the system considered, emphasizing the need for host diversity in blind evaluations. Several entries exploited previous experimental measurements of similar host-guest systems in an effort to improve their physical-based predictions via some manner of rudimentary machine learning; while this strategy succeeded in reducing systematic errors, it did not correspond to an improvement in statistical correlation. Comparison to previous rounds of the host-guest binding free energy challenge highlights an overall improvement in the correlation obtained by the affinity predictions for OA and TEMOA systems, but a surprising lack of improvement regarding root mean square error over the past several challenge rounds. The data suggests that further refinement of force field parameters, as well as improved treatment of chemical effects (e.g., buffer salt conditions, protonation states), may be required to further enhance predictive accuracy.

Generation of Pairwise Potentials Using Multidimensional Data Mining

The rapid development of molecular structural databases provides the chemistry community access to an enormous array of experimental data that can be used to build and validate computational models. Using radial distribution functions collected from experimentally available X-ray and NMR structures, a number of so-called statistical potentials have been developed over the years using the structural data mining strategy. These potentials have been developed within the context of the two-particle Kirkwood equation by extending its original use for isotropic monatomic systems to anisotropic biomolecular systems. However, the accuracy and the unclear physical meaning of statistical potentials have long formed the central arguments against such methods. In this work, we present a new approach to generate molecular energy functions using structural data mining. Instead of employing the Kirkwood equation and introducing the "reference state" approximation, we model the multidimensional probability distributions of the molecular system using graphical models and generate the target pairwise Boltzmann probabilities using the Bayesian field theory. Different from the current statistical potentials that mimic the "knowledge-based" PMF based on the 2-particle Kirkwood equation, the graphical-model-based structure-derived potential developed in this study focuses on the generation of lower-dimensional Boltzmann distributions of atoms through reduction of dimensionality. We have named this new scoring function GARF, and in this work we focus on the mathematical derivation of our novel approach followed by validation studies on its ability to predict protein-ligand interactions.

Free-Energy-Based Protein Design: Re-Engineering Cellular Retinoic Acid Binding Protein II Assisted by the Moveable-Type Approach

How to fine-tune the binding free energy of a small-molecule to a receptor site by altering the amino acid residue composition is a key question in protein engineering. Indeed, the ultimate solution to this problem, to chemical accuracy (±1 kcal/mol), will result in profound and wide-ranging applications in protein design. Numerous tools have been developed to address this question using knowledge-based models to more computationally intensive molecular dynamics simulations-based free energy calculations, but while some success has been achieved there remains room for improvement in terms of overall accuracy and in the speed of the methodology. Here we report a fast, knowledge-based movable-type (MT)-based approach to estimate the absolute and relative free energy of binding as influenced by mutations in a small-molecule binding site in a protein. We retrospectively validate our approach using mutagenesis data for retinoic acid binding to the Cellular Retinoic Acid Binding Protein II (CRABPII) system and then make prospective predictions that are borne out experimentally. The overall performance of our approach is supported by its success in identifying mutants that show high or even sub-nano-molar binding affinities of retinoic acid to the CRABPII system.

Conformation Generation: The State of the Art

The generation of conformations for small molecules is a problem of continuing interest in cheminformatics and computational drug discovery. This review will present an overview of methods used to sample conformational space, focusing on those methods designed for organic molecules commonly of interest in drug discovery. Different approaches to both the sampling of conformational space and the scoring of conformational stability will be compared and contrasted, with an emphasis on those methods suitable for conformer sampling of large numbers of drug-like molecules. Particular attention will be devoted to the appropriate utilization of information from experimental solid-state structures in validating and evaluating the performance of these tools. The review will conclude with some areas worthy of further investigation.

On the fly estimation of host-guest binding free energies using the movable type method: participation in the SAMPL5 blind challenge

We review our performance in the SAMPL5 challenge for predicting host-guest binding affinities using the movable type (MT) method. The challenge included three hosts, acyclic Cucurbit[2]uril and two octa-acids with and without methylation at the entrance to their binding cavities. Each host was associated with 6-10 guest molecules. The MT method extrapolates local energy landscapes around particular molecular states and estimates the free energy by Monte Carlo integration over these landscapes. Two blind submissions pairing MT with variants of the KECSA potential function yielded mean unsigned errors of 1.26 and 1.53 kcal/mol for the non-methylated octa-acid, 2.83 and 3.06 kcal/mol for the methylated octa-acid, and 2.77 and 3.36 kcal/mol for Cucurbit[2]uril host. While our results are in reasonable agreement with experiment, we focused on particular cases in which our estimates gave incorrect results, particularly with regard to association between the octa-acids and an adamantane derivative. Working on the hypothesis that differential solvation effects play a role in effecting computed binding affinities for the parent octa-acid and the methylated octa-acid and that the ligands bind inside the pockets (rather than on the surface) we devised a new solvent accessible surface area term to better quantify solvation energy contributions in MT based studies. To further explore this issue a, molecular dynamics potential of mean force (PMF) study indicates that, as found by our docking calculations, the stable binding mode for this ligand is inside (rather than surface bound) the octa-acid cavity whether the entrance is methylated or not. The PMF studies also obtained the correct order for the methylation-induced change in binding affinities and associated the difference, to a large extent to differential solvation effects. Overall, the SAMPL5 challenge yielded in improvements our solvation modeling and also demonstrated the need for thorough validation of input data integrity prior to any computational analysis.

An Atomistic Statistically Effective Energy Function for Computational Protein Design

Shortcomings in the definition of effective free-energy surfaces of proteins are recognized to be a major contributory factor responsible for the low success rates of existing automated methods for computational protein design (CPD). The formulation of an atomistic statistically effective energy function (SEEF) suitable for a wide range of CPD applications and its derivation from structural data extracted from protein domains and protein-ligand complexes are described here. The proposed energy function comprises nonlocal atom-based and local residue-based SEEFs, which are coupled using a novel atom connectivity number factor to scale short-range, pairwise, nonbonded atomic interaction energies and a surface-area-dependent cavity energy term. This energy function was used to derive additional SEEFs describing the unfolded-state ensemble of any given residue sequence based on computed average energies for partially or fully solvent-exposed fragments in regions of irregular structure in native proteins. Relative thermal stabilities of 97 T4 bacteriophage lysozyme mutants were predicted from calculated energy differences for folded and unfolded states with an average unsigned error (AUE) of 0.84 kcal mol(-1) when compared to experiment. To demonstrate the utility of the energy function for CPD, further validation was carried out in tests of its capacity to recover cognate protein sequences and to discriminate native and near-native protein folds, loop conformers, and small-molecule ligand binding poses from non-native benchmark decoys. Experimental ligand binding free energies for a diverse set of 80 protein complexes could be predicted with an AUE of 2.4 kcal mol(-1) using an additional energy term to account for the loss in ligand configurational entropy upon binding. The atomistic SEEF is expected to improve the accuracy of residue-based coarse-grained SEEFs currently used in CPD and to extend the range of applications of extant atom-based protein statistical potentials.

KECSA-Movable Type Implicit Solvation Model (KMTISM)

Computation of the solvation free energy for chemical and biological processes has long been of significant interest. The key challenges to effective solvation modeling center on the choice of potential function and configurational sampling. Herein, an energy sampling approach termed the “Movable Type” (MT) method, and a statistical energy function for solvation modeling, “Knowledge-based and Empirical Combined Scoring Algorithm” (KECSA) are developed and utilized to create an implicit solvation model: KECSA-Movable Type Implicit Solvation Model (KMTISM) suitable for the study of chemical and biological systems. KMTISM is an implicit solvation model, but the MT method performs energy sampling at the atom pairwise level. For a specific molecular system, the MT method collects energies from prebuilt databases for the requisite atom pairs at all relevant distance ranges, which by its very construction encodes all possible molecular configurations simultaneously. Unlike traditional statistical energy functions, KECSA converts structural statistical information into categorized atom pairwise interaction energies as a function of the radial distance instead of a mean force energy function. Within the implicit solvent model approximation, aqueous solvation free energies are then obtained from the NVT ensemble partition function generated by the MT method. Validation is performed against several subsets selected from the Minnesota Solvation Database v2012. Results are compared with several solvation free energy calculation methods, including a one-to-one comparison against two commonly used classical implicit solvation models: MM-GBSA and MM-PBSA. Comparison against a quantum mechanics based polarizable continuum model is also discussed (Cramer and Truhlar’s Solvation Model 12).

Flexible CDOCKER: Development and application of a pseudo-explicit structure-based docking method within CHARMM

Protein-ligand docking is a commonly used method for lead identification and refinement. While traditional structure-based docking methods represent the receptor as a rigid body, recent developments have been moving toward the inclusion of protein flexibility. Proteins exist in an interconverting ensemble of conformational states, but effectively and efficiently searching the conformational space available to both the receptor and ligand remains a well-appreciated computational challenge. To this end, we have developed the Flexible CDOCKER method as an extension of the family of complete docking solutions available within CHARMM. This method integrates atomically detailed side chain flexibility with grid-based docking methods, maintaining efficiency while allowing the protein and ligand configurations to explore their conformational space simultaneously. This is in contrast to existing approaches that use induced-fit like sampling, such as Glide or Autodock, where the protein or the ligand space is sampled independently in an iterative fashion. Presented here are developments to the CHARMM docking methodology to incorporate receptor flexibility and improvements to the sampling protocol as demonstrated with re-docking trials on a subset of the CCDC/Astex set. These developments within CDOCKER achieve docking accuracy competitive with or exceeding the performance of other widely utilized docking programs.

Free Energy-Based Conformational Search Algorithm Using the Movable Type Sampling Method

In this article, we extend the movable type (MT) sampling method to molecular conformational searches (MT-CS) on the free energy surface of the molecule in question. Differing from traditional systematic and stochastic searching algorithms, this method uses Boltzmann energy information to facilitate the selection of the best conformations. The generated ensembles provided good coverage of the available conformational space including available crystal structures. Furthermore, our approach directly provides the solvation free energies and the relative gas and aqueous phase free energies for all generated conformers. The method is validated by a thorough analysis of thrombin ligands as well as against structures extracted from both the Protein Data Bank (PDB) and the Cambridge Structural Database (CSD). An in-depth comparison between OMEGA and MT-CS is presented to illustrate the differences between the two conformational searching strategies, i.e., energy-based versus free energy-based searching. These studies demonstrate that our MT-based ligand conformational search algorithm is a powerful approach to delineate the conformational ensembles of molecular species on free energy surfaces.

Improvements, trends, and new ideas in molecular docking: 2012-2013 in review

Molecular docking is a computational method for predicting the placement of ligands in the binding sites of their receptor(s). In this review, we discuss the methodological developments that occurred in the docking field in 2012 and 2013, with a particular focus on the more difficult aspects of this computational discipline. The main challenges and therefore focal points for developments in docking, covered in this review, are receptor flexibility, solvation, scoring, and virtual screening. We specifically deal with such aspects of molecular docking and its applications as selection criteria for constructing receptor ensembles, target dependence of scoring functions, integration of higher-level theory into scoring, implicit and explicit handling of solvation in the binding process, and comparison and evaluation of docking and scoring methods.

The Movable Type Method Applied to Protein-Ligand Binding

Accurately computing the free energy for biological processes like protein folding or protein-ligand association remains a challenging problem. Both describing the complex intermolecular forces involved and sampling the requisite configuration space make understanding these processes innately difficult. Herein, we address the sampling problem using a novel methodology we term "movable type". Conceptually it can be understood by analogy with the evolution of printing and, hence, the name movable type. For example, a common approach to the study of protein-ligand complexation involves taking a database of intact drug-like molecules and exhaustively docking them into a binding pocket. This is reminiscent of early woodblock printing where each page had to be laboriously created prior to printing a book. However, printing evolved to an approach where a database of symbols (letters, numerals, etc.) was created and then assembled using a movable type system, which allowed for the creation of all possible combinations of symbols on a given page, thereby, revolutionizing the dissemination of knowledge. Our movable type (MT) method involves the identification of all atom pairs seen in protein-ligand complexes and then creating two databases: one with their associated pairwise distant dependent energies and another associated with the probability of how these pairs can combine in terms of bonds, angles, dihedrals and non-bonded interactions. Combining these two databases coupled with the principles of statistical mechanics allows us to accurately estimate binding free energies as well as the pose of a ligand in a receptor. This method, by its mathematical construction, samples all of configuration space of a selected region (the protein active site here) in one shot without resorting to brute force sampling schemes involving Monte Carlo, genetic algorithms or molecular dynamics simulations making the methodology extremely efficient. Importantly, this method explores the free energy surface eliminating the need to estimate the enthalpy and entropy components individually. Finally, low free energy structures can be obtained via a free energy minimization procedure yielding all low free energy poses on a given free energy surface. Besides revolutionizing the protein-ligand docking and scoring problem this approach can be utilized in a wide range of applications in computational biology which involve the computation of free energies for systems with extensive phase spaces including protein folding, protein-protein docking and protein design.