Ligand Affinities Estimated by Quantum Chemical Calculations

Binding Free Energy Calculation Based on the Fragment Molecular Orbital Method and Its Application in Designing Novel SHP-2 Allosteric Inhibitors

The accurate prediction of binding free energy is a major challenge in structure-based drug design. Quantum mechanics (QM)-based approaches show promising potential in predicting ligand-protein binding affinity by accurately describing the behavior and structure of electrons. However, traditional QM calculations face computational limitations, hindering their practical application in drug design. Nevertheless, the fragment molecular orbital (FMO) method has gained widespread application in drug design due to its ability to reduce computational costs and achieve efficient ab initio QM calculations. Although the FMO method has demonstrated its reliability in calculating the gas phase potential energy, the binding of proteins and ligands also involves other contributing energy terms, such as solvent effects, the 'deformation energy' of a ligand's bioactive conformations, and entropy. Particularly in cases involving ionized fragments, the calculation of solvation free energy becomes particularly crucial. We conducted an evaluation of some previously reported implicit solvent methods on the same data set to assess their potential for improving the performance of the FMO method. Herein, we develop a new QM-based binding free energy calculation method called FMOScore, which enhances the performance of the FMO method. The FMOScore method incorporates linear fitting of various terms, including gas-phase potential energy, deformation energy, and solvation free energy. Compared to other widely used traditional prediction methods such as FEP+, MM/PBSA, MM/GBSA, and Autodock vina, FMOScore showed good performance in prediction accuracies. By constructing a retrospective case study, it was observed that incorporating calculations for solvation free energy and deformation energy can further enhance the precision of FMO predictions for binding affinity. Furthermore, using FMOScore-guided lead optimization against Src homology-2-containing protein tyrosine phosphatase 2 (SHP-2), we discovered a novel and potent allosteric SHP-2 inhibitor (compound 8).

Evaluating the ability of end-point methods to predict the binding affinity tendency of protein kinase inhibitors

Because of the high economic cost of exploring the experimental impact of mutations occurring in kinase proteins, computational approaches have been employed as alternative methods for evaluating the structural and energetic aspects of kinase mutations. Among the main computational methods used to explore the affinity linked to kinase mutations are docking procedures and molecular dynamics (MD) simulations combined with end-point methods or alchemical methods. Although it is known that end-point methods are not able to reproduce experimental binding free energy (ΔG) values, it is also true that they are able to discriminate between a better or a worse ligand through the estimation of ΔG. In this contribution, we selected ten wild-type and mutant cocrystallized EGFR-inhibitor complexes containing experimental binding affinities to evaluate whether MMGBSA or MMPBSA approaches can predict the differences in affinity between the wild type and mutants forming a complex with a similar inhibitor. Our results show that a long MD simulation (the last 50 ns of a 100 ns-long MD simulation) using the MMGBSA method without considering the entropic components reproduced the experimental affinity tendency with a Pearson correlation coefficient of 0.779 and an R2 value of 0.606. On the other hand, the correlation between theoretical and experimental ΔΔG values indicates that the MMGBSA and MMPBSA methods are helpful for obtaining a good correlation using a short rather than a long simulation period.

Revisiting MMPBSA by Adoption of MC-Based Surface Area/Volume, ANI-ML Potentials, and Two-Valued Interior Dielectric Constant

Here, we report the accuracy improvements of molecular mechanics Poisson-Boltzmann surface area (MMPBSA) calculations by adoption of ANI-ML potentials in replacement of MM terms, the use of solvent-accessible surface area (SASA) and volume (SAV) values from the Monte Carlo sampling of the probe, and introducing two different interior dielectric constants for electrostatic interactions of protein-ligand (P-L) and polar solvation term in the MMPBSA calculations. Our results show that the Pearson correlation coefficients of MMPBSA-calculated values with respect to experimental binding free energies can be drastically improved from 0.48 to 0.90 by adoption of ANI-ML potentials in replacement of MM energy terms in the equation, referred to as ANI-PBSA. Moreover, we show that the SASA/SAV-combined equation in the scaled particle theory (SPT) can be a better choice to model nonpolar solvation term, reaching nearly the same accuracy by ANI-PBSA calculations. Finally, we introduce two different values of interior dielectric constants, which could be an alternative strategy between the single and variable constant definitions.

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.

Predicting the mutation effects of protein–ligand interactions via end-point binding free energy calculations: strategies and analyses

Protein mutations occur frequently in biological systems, which may impact, for example, the binding of drugs to their targets through impairing the critical H-bonds, changing the hydrophobic interactions, etc. Thus, accurately predicting the effects of mutations on biological systems is of great interests to various fields. Unfortunately, it is still unavailable to conduct large-scale wet-lab mutation experiments because of the unaffordable experimental time and financial costs. Alternatively, in silico computation can serve as a pioneer to guide the experiments. In fact, numerous pioneering works have been conducted from computationally cheaper machine-learning (ML) methods to the more expensive alchemical methods with the purpose to accurately predict the mutation effects. However, these methods usually either cannot result in a physically understandable model (ML-based methods) or work with huge computational resources (alchemical methods). Thus, compromised methods with good physical characteristics and high computational efficiency are expected. Therefore, here, we conducted a comprehensive investigation on the mutation issues of biological systems with the famous end-point binding free energy calculation methods represented by MM/GBSA and MM/PBSA. Different computational strategies considering different length of MD simulations, different value of dielectric constants and whether to incorporate entropy effects to the predicted total binding affinities were investigated to provide a more accurate way for predicting the energetic change upon protein mutations. Overall, our result shows that a relatively long MD simulation (e.g. 100 ns) benefits the prediction accuracy for both MM/GBSA and MM/PBSA (with the best Pearson correlation coefficient between the predicted ∆∆G and the experimental data of ~ 0.44 for a challenging dataset). Further analyses shows that systems involving large perturbations (e.g. multiple mutations and large number of atoms change in the mutation site) are much easier to be accurately predicted since the algorithm works more sensitively to the large change of the systems. Besides, system-specific investigation reveals that conformational adjustment is needed to refine the micro-environment of the manually mutated systems and thus lead one to understand why longer MD simulation is necessary to improve the predicting result. The proposed strategy is expected to be applied in large-scale mutation effects investigation with interpretation.

Accurate Binding Free Energy Method from End-State MD Simulations

Herein, we introduce a new strategy to estimate binding free energies using end-state molecular dynamics simulation trajectories. The method is adopted from linear interaction energy (LIE) and ANI-2x neural network potentials (machine learning) for the atomic simulation environment (ASE). It predicts the single-point interaction energies between ligand–protein and ligand–solvent pairs at the accuracy of the wb97x/6-31G* level for the conformational space that is sampled by molecular dynamics (MD) simulations. Our results on 54 protein–ligand complexes show that the method can be accurate and have a correlation of R = 0.87–0.88 to the experimental binding free energies, outperforming current end-state methods with reduced computational cost. The method also allows us to compare BFEs of ligands with different scaffolds. The code is available free of charge (documentation and test files) at https://github.com/otayfuroglu/deepQM.

Protein–ligand free energies of binding from full-protein DFT calculations: convergence and choice of exchange–correlation functional

Quantum mechanical binding free energies based on thousands of full-protein DFT calculations are tractable, reproducible and converge well.

SQM/COSMO Scoring Function: Reliable Quantum-Mechanical Tool for Sampling and Ranking in Structure-Based Drug Design

Quantum mechanical (QM) methods have been gaining importance in structure-based drug design where a reliable description of protein-ligand interactions is of utmost significance. However, strategies i. e. QM/MM, fragmentation or semiempirical (SQM) methods had to be pursued to overcome the unfavorable scaling of QM methods. Various SQM-based approaches have significantly contributed to the accuracy of docking and improvement of lead compounds. Parametrizations of SQM and implicit solvent methods in our laboratory have been instrumental to obtain a reliable SQM-based scoring function. The experience gained in its application for activity ranking of ligands binding to tens of protein targets resulted in setting up a faster SQM/COSMO scoring approach, which outperforms standard scoring methods in native pose identification for two dozen protein targets with ten thousand poses. Recently, SQM/COSMO was effectively applied in a proof-of-concept study of enrichment in virtual screening. Due to its superior performance, feasibility and chemical generality, we propose the SQM/COSMO approach as an efficient tool in structure-based drug design.

An accurate free energy estimator: based on MM/PBSA combined with interaction entropy for protein-ligand binding affinity

The molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) method is constantly used to calculate the binding free energy of protein-ligand complexes, and has been shown to effectively balance computational cost against accuracy. The relative binding affinities obtained by the MM/PBSA approach are acceptable, while it usually overestimates the absolute binding free energy. This paper proposes four free energy estimators based on the MM/PBSA for enthalpy change combined with interaction entropy (IE) for entropy change using different weights for individual energy terms. The ΔG_{PBSA_IE} method is determined to be an optimal estimator based on its performance in terms of the correlation between experimental and theoretical values and error estimations. This approach is optimized using high-quality experimental values from a training set containing 84 protein-ligand systems, and the coefficients for the sum of electrostatic energy and polar solvation free energy, van der Waals (vdW) energy, non-polar solvation energy and entropy change are obtained by multivariate linear fitting to the corresponding experimental values. A comparison between the traditional MM/PBSA method and this method shows that the correlation coefficient is improved from 0.46 to 0.72 and the slope of the regression line increases from 0.10 to 1.00. More importantly, the mean absolute error (MAE) is significantly reduced from 22.52 to 1.59 kcal mol^-1. Furthermore, the numerical stability of this method is validated on a test set with a similar correlation coefficient, slope and MAE to those of the training set. Based on the above advantages, the ΔG_{PBSA_IE} method can be a powerful tool for a reliable and accurate estimation of binding free energy and plays a significant role in a detailed energetic investigation of protein-ligand interaction.

QM Implementation in Drug Design: Does It Really Help?

Computational chemistry allows one to characterize the structure, dynamics, and energetics of protein-ligand interactions, which makes it a valuable tool in drug discovery in both academic research and pharmaceutical industry. Molecular mechanics (MM)-based approaches are widely utilized to assist the discovery of new drug candidates. However, the complexity of protein-ligand interactions challenges the accuracy and efficiency of the commonly used empirical methods. Aiming to provide better accuracy in the description of protein-ligand interactions, quantum mechanics (QM)-based approaches are becoming increasingly explored. In principle, QM calculation includes all contributions to the energy, accounting for terms usually missing in empirical force fields, and provides a greater degree of transferability. The usefulness of QM in drug design cannot be overemphasized. In this chapter, we present recent developments and applications of fragment-based QM method in studying the protein-ligand and protein-protein interactions. We critically discuss the performance of the fragment-based QM method at different ab initio levels while trying to answer a critical question: do QM-based methods really help in drug design?

Taking Water into Account with the Fragment Molecular Orbital Method

This chapter describes the current status of development of the fragment molecular orbital (FMO) method for analyzing the electronic state and intermolecular interactions of biomolecular systems in solvent. The orbital energies and the inter-fragment interaction energies (IFIEs) for a specific molecular structure can be obtained directly by performing FMO calculations by exposing water molecules and counterions around biomolecular systems. Then, it is necessary to pay attention to the thickness of the water shell surrounding the biomolecules. The single-point calculation for snapshots from MD trajectory does not incorporate the effects of temperature and configurational fluctuation, but the SCIFIE (statistically corrected IFIE) method is proposed as a many-body correlated method that partially compensates for this deficiency. Furthermore, implicit continuous dielectric models have been developed as effective approaches to incorporating the screening effect of the solvent in thermal equilibrium, and we illustrate their usefulness for theoretical evaluation of IFIEs and ligand-binding free energy on the basis of the FMO-PBSA (Poisson-Boltzmann surface area) method and other computational methods.

Solvent Screening in Zwitterions Analyzed with the Fragment Molecular Orbital Method

Based on induced solvent charges, a new model of solvent screening is developed in the framework of the fragment molecular orbital combined with the polarizable continuum model. The developed model is applied to analyze interactions in a prototypical zwitterionic system, sodium chloride in water, and it is shown that the large underestimation of the interaction in the original solvent screening based on local charges is successfully corrected. The model is also applied to a complex of the Trp-cage (PDB: 1L2Y ) miniprotein with an anionic ligand, and the physical factors determined protein-ligand binding in solution are unraveled.

Surface Characteristics Control the Attachment and Functionality of (Chimeric) Avidin

The physical adsorption (physisorption) of proteins to surfaces is an important but incompletely understood factor in many biological processes and is of increasing significance in bionanotechnology as well. Avidin is an important protein because of strong avidin-biotin binding, which has been exploited in numerous applications. We have undertaken thorough experimentation on the physisorption of avidin, to chemically different flat surfaces of Si and graphite and also to the curved version of the latter, on multiwalled carbon nanotubes (MWNTs) of different diameters. The difference in the behavior of avidin on Si versus graphite is drastic; on Si, avidin deposits as single globular tetrameric units and maintains functionality, whereas on graphite, it forms irregular networks of two-layer thick filaments, where the first layer has lost its biological activity. On MWNTs, avidin also deposits as one-dimensional formations, or stripes, but these appear to order in a perpendicular arrangement to the MWNT axis. A better understanding of protein-surface interactions is essential for the development of robust and reliable methods for biofunctionalization of materials. This work also provides insights into the importance of the nanoscale surface architecture.

Use of the Multilayer Fragment Molecular Orbital Method to Predict the Rank Order of Protein-Ligand Binding Affinities: A Case Study Using Tankyrase 2 Inhibitors

In computational drug discovery, ranking a series of compound analogues in the order that is consistent with the experimental binding affinities remains a challenge. Many of the computational methods available for evaluating binding affinities have adopted molecular mechanics (MM)-based force fields, although they cannot completely describe protein-ligand interactions. By contrast, quantum mechanics (QM) calculations play an important role in understanding the protein-ligand interactions; however, their huge computational costs hinder their application in drug discovery. In this study, we have evaluated the ability to rank the binding affinities of tankyrase 2 ligands by combining both MM and QM calculations. Our computational approach uses the protein-ligand binding energies obtained from a cost-effective multilayer fragment molecular orbital (MFMO) method combined with the solvation energy obtained from the MM-Poisson-Boltzmann/surface area (MM-PB/SA) method to predict the binding affinity. This approach enabled us to rank tankyrase 2 inhibitor analogues, outperforming several MM-based methods, including rescoring by molecular docking and the MM-PB/SA method alone. Our results show that this computational approach using the MFMO method is a promising tool for predicting the rank order of the binding affinities of inhibitor analogues.

Outlining migrainous through dihydroergotamine–serotonin receptor interactions using quantum biochemistry

We present the electronic structure of the complex dihydroergotamine–serotonin receptor to unveil new medications to treat migraine and related diseases.

Statistical Analysis on the Performance of Molecular Mechanics Poisson-Boltzmann Surface Area versus Absolute Binding Free Energy Calculations: Bromodomains as a Case Study

Binding free energy calculations that make use of alchemical pathways are becoming increasingly feasible thanks to advances in hardware and algorithms. Although relative binding free energy (RBFE) calculations are starting to find widespread use, absolute binding free energy (ABFE) calculations are still being explored mainly in academic settings due to the high computational requirements and still uncertain predictive value. However, in some drug design scenarios, RBFE calculations are not applicable and ABFE calculations could provide an alternative. Computationally cheaper end-point calculations in implicit solvent, such as molecular mechanics Poisson-Boltzmann surface area (MMPBSA) calculations, could too be used if one is primarily interested in a relative ranking of affinities. Here, we compare MMPBSA calculations to previously performed absolute alchemical free energy calculations in their ability to correlate with experimental binding free energies for three sets of bromodomain-inhibitor pairs. Different MMPBSA approaches have been considered, including a standard single-trajectory protocol, a protocol that includes a binding entropy estimate, and protocols that take into account the ligand hydration shell. Despite the improvements observed with the latter two MMPBSA approaches, ABFE calculations were found to be overall superior in obtaining correlation with experimental affinities for the test cases considered. A difference in weighted average Pearson ([Formula: see text]) and Spearman ([Formula: see text]) correlations of 0.25 and 0.31 was observed when using a standard single-trajectory MMPBSA setup ([Formula: see text] = 0.64 and [Formula: see text] = 0.66 for ABFE; [Formula: see text] = 0.39 and [Formula: see text] = 0.35 for MMPBSA). The best performing MMPBSA protocols returned weighted average Pearson and Spearman correlations that were about 0.1 inferior to ABFE calculations: [Formula: see text] = 0.55 and [Formula: see text] = 0.56 when including an entropy estimate, and [Formula: see text] = 0.53 and [Formula: see text] = 0.55 when including explicit water molecules. Overall, the study suggests that ABFE calculations are indeed the more accurate approach, yet there is also value in MMPBSA calculations considering the lower compute requirements, and if agreement to experimental affinities in absolute terms is not of interest. Moreover, for the specific protein-ligand systems considered in this study, we find that including an explicit ligand hydration shell or a binding entropy estimate in the MMPBSA calculations resulted in significant performance improvements at a negligible computational cost.

Explicit treatment of active-site waters enhances quantum mechanical/implicit solvent scoring: Inhibition of CDK2 by new pyrazolo[1,5-a]pyrimidines

We present comprehensive testing of solvent representation in quantum mechanics (QM)-based scoring of protein-ligand affinities. To this aim, we prepared 21 new inhibitors of cyclin-dependent kinase 2 (CDK2) with the pyrazolo[1,5-a]pyrimidine core, whose activities spanned three orders of magnitude. The crystal structure of a potent inhibitor bound to the active CDK2/cyclin A complex revealed that the biphenyl substituent at position 5 of the pyrazolo[1,5-a]pyrimidine scaffold was located in a previously unexplored pocket and that six water molecules resided in the active site. Using molecular dynamics, protein-ligand interactions and active-site water H-bond networks as well as thermodynamics were probed. Thereafter, all the inhibitors were scored by the QM approach utilizing the COSMO implicit solvent model. Such a standard treatment failed to produce a correlation with the experiment (R² = 0.49). However, the addition of the active-site waters resulted in significant improvement (R² = 0.68). The activities of the compounds could thus be interpreted by taking into account their specific noncovalent interactions with CDK2 and the active-site waters. In summary, using a combination of several experimental and theoretical approaches we demonstrate that the inclusion of explicit solvent effects enhance QM/COSMO scoring to produce a reliable structure-activity relationship with physical insights. More generally, this approach is envisioned to contribute to increased accuracy of the computational design of novel inhibitors.

Converging ligand-binding free energies obtained with free-energy perturbations at the quantum mechanical level

In this article, the convergence of quantum mechanical (QM) free-energy simulations based on molecular dynamics simulations at the molecular mechanics (MM) level has been investigated. We have estimated relative free energies for the binding of nine cyclic carboxylate ligands to the octa-acid deep-cavity host, including the host, the ligand, and all water molecules within 4.5 Å of the ligand in the QM calculations (158-224 atoms). We use single-step exponential averaging (ssEA) and the non-Boltzmann Bennett acceptance ratio (NBB) methods to estimate QM/MM free energy with the semi-empirical PM6-DH2X method, both based on interaction energies. We show that ssEA with cumulant expansion gives a better convergence and uses half as many QM calculations as NBB, although the two methods give consistent results. With 720,000 QM calculations per transformation, QM/MM free-energy estimates with a precision of 1 kJ/mol can be obtained for all eight relative energies with ssEA, showing that this approach can be used to calculate converged QM/MM binding free energies for realistic systems and large QM partitions. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Recent Progress in Treating Protein-Ligand Interactions with Quantum-Mechanical Methods

We review the first successes and failures of a “new wave” of quantum chemistry-based approaches to the treatment of protein/ligand interactions. These approaches share the use of “enhanced”, dispersion (D), and/or hydrogen-bond (H) corrected density functional theory (DFT) or semi-empirical quantum mechanical (SQM) methods, in combination with ensemble weighting techniques of some form to capture entropic effects. Benchmark and model system calculations in comparison to high-level theoretical as well as experimental references have shown that both DFT-D (dispersion-corrected density functional theory) and SQM-DH (dispersion and hydrogen bond-corrected semi-empirical quantum mechanical) perform much more accurately than older DFT and SQM approaches and also standard docking methods. In addition, DFT-D might soon become and SQM-DH already is fast enough to compute a large number of binding modes of comparably large protein/ligand complexes, thus allowing for a more accurate assessment of entropic effects.

The SQM/COSMO filter: reliable native pose identification based on the quantum-mechanical description of protein–ligand interactions and implicit COSMO solvation

Strictly uphill – in cognate docking experiments we show that a quantum mechanical description of interaction and solvation outperforms established scoring functions in sharply distinguishing the native state from decoy poses.

The fragment molecular orbital method combined with density-functional tight-binding and the polarizable continuum model

The electronic gap in proteins is analyzed in detail, and it is shown that FMO-DFTB/PCM is efficient and accurate in describing the molecular structure of proteins in solution.

Predicting the relative binding affinity of mineralocorticoid receptor antagonists by density functional methods

In drug discovery, prediction of binding affinity ahead of synthesis to aid compound prioritization is still hampered by the low throughput of the more accurate methods and the lack of general pertinence of one method that fits all systems. Here we show the applicability of a method based on density functional theory using core fragments and a protein model with only the first shell residues surrounding the core, to predict relative binding affinity of a matched series of mineralocorticoid receptor (MR) antagonists. Antagonists of MR are used for treatment of chronic heart failure and hypertension. Marketed MR antagonists, spironolactone and eplerenone, are also believed to be highly efficacious in treatment of chronic kidney disease in diabetes patients, but is contra-indicated due to the increased risk for hyperkalemia. These findings and a significant unmet medical need among patients with chronic kidney disease continues to stimulate efforts in the discovery of new MR antagonist with maintained efficacy but low or no risk for hyperkalemia. Applied on a matched series of MR antagonists the quantum mechanical based method gave an R(2) = 0.76 for the experimental lipophilic ligand efficiency versus relative predicted binding affinity calculated with the M06-2X functional in gas phase and an R(2) = 0.64 for experimental binding affinity versus relative predicted binding affinity calculated with the M06-2X functional including an implicit solvation model. The quantum mechanical approach using core fragments was compared to free energy perturbation calculations using the full sized compound structures.

Binding affinities by alchemical perturbation using QM/MM with a large QM system and polarizable MM model

The most general way to improve the accuracy of binding-affinity calculations for protein-ligand systems is to use quantum-mechanical (QM) methods together with rigorous alchemical-perturbation (AP) methods. We explore this approach by calculating the relative binding free energy of two synthetic disaccharides binding to galectin-3 at a reasonably high QM level (dispersion-corrected density functional theory with a triple-zeta basis set) and with a sufficiently large QM system to include all short-range interactions with the ligand (744-748 atoms). The rest of the protein is treated as a collection of atomic multipoles (up to quadrupoles) and polarizabilities. Several methods for evaluating the binding free energy from the 3600 QM calculations are investigated in terms of stability and accuracy. In particular, methods using QM calculations only at the endpoints of the transformation are compared with the recently proposed non-Boltzmann Bennett acceptance ratio (NBB) method that uses QM calculations at several stages of the transformation. Unfortunately, none of the rigorous approaches give sufficient statistical precision. However, a novel approximate method, involving the direct use of QM energies in the Bennett acceptance ratio method, gives similar results as NBB but with better precision, ∼3 kJ/mol. The statistical error can be further reduced by performing a greater number of QM calculations.

The MM/PBSA and MM/GBSA methods to estimate ligand-binding affinities

INTRODUCTION

The molecular mechanics energies combined with the Poisson-Boltzmann or generalized Born and surface area continuum solvation (MM/PBSA and MM/GBSA) methods are popular approaches to estimate the free energy of the binding of small ligands to biological macromolecules. They are typically based on molecular dynamics simulations of the receptor-ligand complex and are therefore intermediate in both accuracy and computational effort between empirical scoring and strict alchemical perturbation methods. They have been applied to a large number of systems with varying success.

AREAS COVERED

The authors review the use of MM/PBSA and MM/GBSA methods to calculate ligand-binding affinities, with an emphasis on calibration, testing and validation, as well as attempts to improve the methods, rather than on specific applications.

EXPERT OPINION

MM/PBSA and MM/GBSA are attractive approaches owing to their modular nature and that they do not require calculations on a training set. They have been used successfully to reproduce and rationalize experimental findings and to improve the results of virtual screening and docking. However, they contain several crude and questionable approximations, for example, the lack of conformational entropy and information about the number and free energy of water molecules in the binding site. Moreover, there are many variants of the method and their performance varies strongly with the tested system. Likewise, most attempts to ameliorate the methods with more accurate approaches, for example, quantum-mechanical calculations, polarizable force fields or improved solvation have deteriorated the results.

Benchmark of electronic structure methods for protein–ligand interactions based on high-level reference data

The accurate prediction of the strength of protein–ligand interactions is a very difficult problem despite impressive advances in the field of biomolecular modeling. There are good reasons to believe that quantum mechanical methods can help with this task, but the application of such methods in the context of scoring is still in its infancy. Here we benchmark several wave function theory (WFT), density functional theory (DFT) and semiempirical quantum mechanical (SQM) approaches against high-level theoretical references for realistic test cases. Based on our findings for systematically generated model systems of real protein/ligand complexes from the PDB-bind database, we can recommend SCS-MP2 and B2-PLYP-D3 as reference methods, TPSS-D3+Dabc/def-TZVPP as the best DFT approach and PM6-DH+ as a fast and accurate alternative to full ab initio treatments.

Calculation of protein–ligand binding affinities based on a fragment quantum mechanical method

An efficient fragment-based quantum mechanical method has been successfully applied for reliable prediction of protein–ligand binding affinities.

Induced fit docking, and the use of QM/MM methods in docking

Docking methods are popular computational techniques in drug discovery to identify new active molecules that bind to a given biological target. Although widely used, the predictive reliability of docking methods is often limited by the inability to accurately and efficiently model protein flexibility and quantify binding strength. We highlight several emerging concepts that address those methodological issues including a discussion on the incorporation of QM/MM methodologies in the scoring process.

Potency prediction of β-secretase (BACE-1) inhibitors using density functional methods

Scoring potency is a main challenge for structure based drug design. Inductive effects of subtle variations in the ligand are not possible to accurately predict by classical computational chemistry methods. In this study, the problem of predicting potency of ligands with electronic variations participating in key interactions with the protein was addressed. The potency was predicted for a large set of cyclic amidine and guanidine cores extracted from β-secretase (BACE-1) inhibitors. All cores were of similar size and had equal interaction motifs but were diverse with respect to electronic substitutions. A density functional theory approach, in combination with a representation of the active site of a protein using only key residues, was shown to be predictive. This computational approach was used to guide and support drug design, within the time frame of a normal drug discovery design cycle.

Hybrid RHF/MP2 geometry optimizations with the effective fragment molecular orbital method

The frozen domain effective fragment molecular orbital method is extended to allow for the treatment of a single fragment at the MP2 level of theory. The approach is applied to the conversion of chorismate to prephenate by Chorismate Mutase, where the substrate is treated at the MP2 level of theory while the rest of the system is treated at the RHF level. MP2 geometry optimization is found to lower the barrier by up to 3.5 kcal/mol compared to RHF optimzations and ONIOM energy refinement and leads to a smoother convergence with respect to the basis set for the reaction profile. For double zeta basis sets the increase in CPU time relative to RHF is roughly a factor of two.

Quantum mechanics-based scoring rationalizes the irreversible inactivation of parasitic Schistosoma mansoni cysteine peptidase by vinyl sulfone inhibitors

The quantum mechanics (QM)-based scoring function that we previously developed for the description of noncovalent binding in protein-ligand complexes has been modified and extended to treat covalent binding of inhibitory ligands. The enhancements are (i) the description of the covalent bond breakage and formation using hybrid QM/semiempirical QM (QM/SQM) restrained optimizations and (ii) the addition of the new ΔG(cov)' term to the noncovalent score, describing the "free" energy difference between the covalent and noncovalent complexes. This enhanced QM-based scoring function is applied to a series of 20 vinyl sulfone-based inhibitory compounds inactivating the cysteine peptidase cathepsin B1 of the Schistosoma mansoni parasite (SmCB1). The available X-ray structure of the SmCB1 in complex with a potent vinyl sulfone inhibitor K11017 is used as a template to build the other covalently bound complexes and to model the derived noncovalent complexes. We present the correlation of the covalent score and its constituents with the experimental binding data. Four outliers are identified. They contain bulky R1' substituents structurally divergent from the template, which might induce larger protein rearrangements than could be accurately modeled. In summary, we propose a new computational approach and an optimal protocol for the rapid evaluation and prospective design of covalent inhibitors with a conserved binding mode.