Towards full Quantum-Mechanics-based Protein-Ligand Binding Affinities

Benchmarking Quantum Mechanical Levels of Theory for Valence Parametrization in Force Fields

A wide range of density functional methods and basis sets are available to derive the electronic structure and properties of molecules. Quantum mechanical calculations are too computationally intensive for routine simulation of molecules in the condensed phase, prompting the development of computationally efficient force fields based on quantum mechanical data. Parametrizing general force fields, which cover a vast chemical space, necessitates the generation of sizable quantum mechanical data sets with optimized geometries and torsion scans. To achieve this efficiently, choosing a quantum mechanical method that balances computational cost and accuracy is crucial. In this study, we seek to assess the accuracy of quantum mechanical theory for specific properties such as conformer energies and torsion energetics. To comprehensively evaluate various methods, we focus on a representative set of 59 diverse small molecules, comparing approximately 25 combinations of functional and basis sets against the reference level coupled cluster calculations at the complete basis set limit.

Recent advances in computational and experimental protein-ligand affinity determination techniques

INTRODUCTION

Modern drug discovery revolves around designing ligands that target the chosen biomolecule, typically proteins. For this, the evaluation of affinities of putative ligands is crucial. This has given rise to a multitude of dedicated computational and experimental methods that are constantly being developed and improved.

AREAS COVERED

In this review, the authors reassess both the industry mainstays and the newest trends among the methods for protein - small-molecule affinity determination. They discuss both computational affinity predictions and experimental techniques, describing their basic principles, main limitations, and advantages. Together, this serves as initial guide to the currently most popular and cutting-edge ligand-binding assays employed in rational drug design.

EXPERT OPINION

The affinity determination methods continue to develop toward miniaturization, high-throughput, and in-cell application. Moreover, the availability of data analysis tools has been constantly increasing. Nevertheless, cross-verification of data using at least two different techniques and careful result interpretation remain of utmost importance.

Target-ligand binding affinity from single point enthalpy calculation and elemental composition

Reliable target-ligand binding thermodynamics data are essential for successful drug design and molecular engineering projects. Besides experimental methods, a number of theoretical approaches have been introduced for the generation of binding thermodynamics data. However, available approaches often neglect electronic effects or explicit water molecules influencing target-ligand interactions. To handle electronic effects within a reasonable time frame, we introduce a fast calculator QMH-L using a single target-ligand complex structure pre-optimized at the molecular mechanics level. QMH-L is composed of the semi-empirical quantum mechanics calculation of binding enthalpy with predicted explicit water molecules at the complex interface, and a simple descriptor based on the elemental composition of the ligand. QMH-L estimates the target-ligand binding free energy with a root mean square error (RMSE) of 0.94 kcal mol-1. The calculations also provide binding enthalpy values and they were compared with experimental binding thermodynamics data collected from the most reliable isothermal titration calorimetry studies of systems including various protein targets and challenging, large peptide ligands with a molecular weight of up to 2-3 thousand. The single point enthalpy calculations of QMH-L require modest computational resources and are based on short runs with open source and/or free software like Gromacs, Mopac, MobyWat, and Fragmenter. QMH-L can be applied for fast, automated scoring of drug candidates during a virtual screen, enthalpic engineering of new ligands or thermodynamic explanation of complex interactions.

Understanding the Structure-Activity Relationship through Density Functional Theory: A Simple Method Predicts Relative Binding Free Energies of Metalloenzyme Fragment-like Inhibitors

Despite being involved in several human diseases, metalloenzymes are targeted by a small percentage of FDA-approved drugs. Development of novel and efficient inhibitors is required, as the chemical space of metal binding groups (MBGs) is currently limited to four main classes. The use of computational chemistry methods in drug discovery has gained momentum thanks to accurate estimates of binding modes and binding free energies of ligands to receptors. However, exact predictions of binding free energies in metalloenzymes are challenging due to the occurrence of nonclassical phenomena and interactions that common force field-based methods are unable to correctly describe. In this regard, we applied density functional theory (DFT) to predict the binding free energies and to understand the structure-activity relationship of metalloenzyme fragment-like inhibitors. We tested this method on a set of small-molecule inhibitors with different electronic properties and coordinating two Mn²⁺ ions in the binding site of the influenza RNA polymerase PA_N endonuclease. We modeled the binding site using only atoms from the first coordination shell, hence reducing the computational cost. Thanks to the explicit treatment of electrons by DFT, we highlighted the main contributions to the binding free energies and the electronic features differentiating strong and weak inhibitors, achieving good qualitative correlation with the experimentally determined affinities. By introducing automated docking, we explored alternative ways to coordinate the metal centers and we identified 70% of the highest affinity inhibitors. This methodology provides a fast and predictive tool for the identification of key features of metalloenzyme MBGs, which can be useful for the design of new and efficient drugs targeting these ubiquitous proteins.

A simple and consistent quantum-chemical fragmentation scheme for proteins that includes two-body contributions

The Molecular Fractionation with Conjugate Caps (MFCC) method is a popular fragmentation method for the quantum-chemical treatment of proteins. However, it does not account for interactions between the amino acid fragments, such as intramolecular hydrogen bonding. Here, we present a combination of the MFCC fragmentation scheme with a second-order many-body expansion (MBE) that consistently accounts for all fragment-fragment, fragment-cap, and cap-cap interactions, while retaining the overall simplicity of the MFCC scheme with its chemically meaningful fragments. We show that with the resulting MFCC-MBE(2) scheme, the errors in the total energies of selected polypeptides and proteins can be reduced by up to one order of magnitude and relative energies of different protein conformers can be predicted accurately.

Quantum harmonic free energies for biomolecules and nanomaterials

Obtaining the free energy of large molecules from quantum mechanical energy functions is a long-standing challenge. We describe a method that allows us to estimate, at the quantum mechanical level, the harmonic contributions to the thermodynamics of molecular systems of large size, with modest cost. Using this approach, we compute the vibrational thermodynamics of a series of diamond nanocrystals, and show that the error per atom decreases with system size in the limit of large systems. We further show that we can obtain the vibrational contributions to the binding free energies of prototypical protein-ligand complexes where exact computation is too expensive to be practical. Our work raises the possibility of routine quantum mechanical estimates of thermodynamic quantities in complex systems.

Protein-ligand binding affinity prediction with edge awareness and supervised attention

Accurate prediction of protein-ligand binding affinity is crucial in structure-based drug design but remains some challenges even with recent advances in deep learning: (1) Existing methods neglect the edge information in protein and ligand structure data; (2) current attention mechanisms struggle to capture true binding interactions in the small dataset. Herein, we proposed SEGSA_DTA, a SuperEdge Graph convolution-based and Supervised Attention-based Drug-Target Affinity prediction method, where the super edge graph convolution can comprehensively utilize node and edge information and the multi-supervised attention module can efficiently learn the attention distribution consistent with real protein-ligand interactions. Results on the multiple datasets show that SEGSA_DTA outperforms current state-of-the-art methods. We also applied SEGSA_DTA in repurposing FDA-approved drugs to identify potential coronavirus disease 2019 (COVID-19) treatments. Besides, by using SHapley Additive exPlanations (SHAP), we found that SEGSA_DTA is interpretable and further provides a new quantitative analytical solution for structure-based lead optimization.

Efficient Computation of the Interaction Energies of Very Large Non-covalently Bound Complexes

We present a new benchmark set consisting of 16 large non-covalently bound systems (LNCI16) ranging from 380 up to 1988 atoms and featuring diverse interaction motives. Gas-phase interaction energies are calculated with various composite DFT, semi-empirical quantum mechanical (SQM), and force field (FF) methods and are evaluated using accurate DFT reference values. Of the employed QM methods, PBEh-3c proves to be the most robust for large systems with a relative mean absolute deviation (relMAD) of 8.5% with respect to the reference interaction energies. r2SCAN-3c yields an even smaller relMAD, at least for the subset of complexes for which the calculation could be converged, but is less robust for systems with smaller HOMO–LUMO gaps. The inclusion of Fock-exchange is therefore important for the description of very large non-covalent interaction (NCI) complexes in the gas phase. GFN2-xTB was found to be the best performer of the SQM methods with an excellent result of only 11.1% deviation. From the assessed force fields, GFN-FF and GAFF achieve the best accuracy. Considering their low computational costs, both can be recommended for routine calculations of very large NCI complexes, with GFN-FF being clearly superior in terms of general applicability. Hence, GFN-FF may be routinely applied in supramolecular synthesis planning.

1 Introduction

2 The LNCI16 Benchmark Set

3 Computational Details

4 Generation of Reference Values

5 Results and Discussion

6 Conclusions

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.

Nonadiabatic Molecular Dynamics with Extended Density Functional Tight-Binding: Application to Nanocrystals and Periodic Solids

In this work, we report a new methodology for nonadiabatic molecular dynamics calculations within the extended tight-binding (xTB) framework. We demonstrate the applicability of the developed approach to finite and periodic systems with thousands of atoms by modeling "hot" electron relaxation dynamics in silicon nanocrystals and electron-hole recombination in both a graphitic carbon nitride monolayer and a titanium-based metal-organic framework (MOF). This work reports the nonadiabatic dynamic simulations in the largest Si nanocrystals studied so far by the xTB framework, with diameters up to 3.5 nm. For silicon nanocrystals, we find a non-monotonic dependence of "hot" electron relaxation rates on the nanocrystal size, in agreement with available experimental reports. We rationalize this relationship by a combination of decreasing nonadiabatic couplings related to system size and the increase of available coherent transfer pathways in systems with higher densities of states. We emphasize the importance of proper treatment of coherences for obtaining such non-monotonic dependences. We characterize the electron-hole recombination dynamics in the graphitic carbon nitride monolayer and the Ti-containing MOF. We demonstrate the importance of spin-adaptation and proper sampling of surface hopping trajectories in modeling such processes. We also assess several trajectory surface hopping schemes and highlight their distinct qualitative behavior in modeling the excited-state dynamics in superexchange-like models depending on how they handle coherences between nearly parallel states.

ET-score: Improving Protein-ligand Binding Affinity Prediction Based on Distance-weighted Interatomic Contact Features Using Extremely Randomized Trees Algorithm

The molecular docking simulation is a key computational tool in modern drug discovery research that its predictive performance strongly depends on the employed scoring functions. Many recent studies have shown that the application of machine learning algorithms in the development of scoring functions has led to a significant improvement in docking performance. In this work, we introduce a new machine learning (ML) based scoring function called ET-Score, which employs the distance-weighted interatomic contacts between atom type pairs of the ligand and the protein for featurizing protein-ligand complexes and Extremely Randomized Trees algorithm for the training process. The performance of ET-Score is compared with some successful ML-based scoring functions and several popular classical scoring functions on the PDBbind 2016v core set. It is shown that our ET-Score model (with Pearson's correlation of 0.827 and RMSE of 1.332) achieves very good performance in comparison with most of the ML-based scoring functions and all classical scoring functions despite its extremely low computational cost. ET-Score's codes are freely available on the web at https://github.com/miladrayka/ET_Score.

Docking Paradigm in Drug Design

Docking is in demand for the rational computer aided structure based drug design. A review of docking methods and programs is presented. Different types of docking programs are described. They include docking of non-covalent small ligands, protein-protein docking, supercomputer docking, quantum docking, the new generation of docking programs and the application of docking for covalent inhibitors discovery. Taking into account the threat of COVID-19, we present here a short review of docking applications to the discovery of inhibitors of SARS-CoV and SARS-CoV-2 target proteins, including our own result of the search for inhibitors of SARS-CoV-2 main protease using docking and quantum chemical post-processing. The conclusion is made that docking is extremely important in the fight against COVID-19 during the process of development of antivirus drugs having a direct action on SARS-CoV-2 target proteins.

Sensory Perception of Non-Deuterated and Deuterated Organic Compounds

The chemical background of olfactory perception has been subject of intensive research, but no available model can fully explain the sense of smell. There are also inconsistent results on the role of the isotopology of molecules. In experiments with human subjects it was found that the isotope effect is weak with acetone and D6 -acetone. In contrast, clear differences were observed in the perception of octanoic acid and D15 -octanoic acid. Furthermore, a trained sniffer dog was initially able to distinguish between these isotopologues of octanoic acid. In chromatographic measurements, the respective deuterated molecule showed weaker interaction with a non-polar liquid phase. Quantum chemical calculations give evidence that deuterated octanoic acid binds more strongly to a model receptor than non-deuterated. In contrast, the binding of the non-deuterated molecule is stronger with acetone. The isotope effect is calculated in the framework of statistical mechanics. It results from a complicated interplay between various thermostatistical contributions to the non-covalent free binding energies and it turns out to be very molecule-specific. The vibrational terms including non-classical zero-point energies play about the same role as rotational/translational contributions and are larger than bond length effects for the differential isotope perception of odor for which general rules cannot be derived.

Efficient Computation of Free Energy Contributions for Association Reactions of Large Molecules

Modern density functional theory (DFT) methods are capable of providing accurate association energies for supramolecular systems and even protein-ligand complexes. However, the calculation of the essential harmonic vibrational frequencies needed to obtain free energies is often too computationally demanding. In this work, the corresponding thermostatistical contributions are computed in the well-established (modified) rigid-rotor-harmonic-oscillator approximation with structures and frequencies taken from low-cost quantum chemical methods, namely, GFN2-xTB and PM6-D3H4. Additionally, a recently developed new general force field (GFN-FF) is tested for this purpose. DFT reference values for 59 complexes composed of three standard noncovalent and supramolecular benchmark sets (S22, L7, and S30L) are used in the evaluation. Overall, the accuracy of the low-cost methods is remarkable with typical deviations of only 0.5-2 kcal mol^-1 (5-10%) from the DFT reference values. In particular, the performance of the GFN-FF is promising considering the acceleration of 5 and 2-3 orders of magnitude compared to DFT and GFN2-xTB, respectively. This opens new perspectives for computing thermodynamic properties of, e.g., biomacromolecules as shown, for example, for the binding of retinol and rivaroxaban in protein complexes consisting of ≤4700 atoms.

Machine learning classification can reduce false positives in structure-based virtual screening

With the recent explosion in the size of libraries available for screening, virtual screening is positioned to assume a more prominent role in early drug discovery's search for active chemical matter. In typical virtual screens, however, only about 12% of the top-scoring compounds actually show activity when tested in biochemical assays. We argue that most scoring functions used for this task have been developed with insufficient thoughtfulness into the datasets on which they are trained and tested, leading to overly simplistic models and/or overtraining. These problems are compounded in the literature because studies reporting new scoring methods have not validated their models prospectively within the same study. Here, we report a strategy for building a training dataset (D-COID) that aims to generate highly compelling decoy complexes that are individually matched to available active complexes. Using this dataset, we train a general-purpose classifier for virtual screening (vScreenML) that is built on the XGBoost framework. In retrospective benchmarks, our classifier shows outstanding performance relative to other scoring functions. In a prospective context, nearly all candidate inhibitors from a screen against acetylcholinesterase show detectable activity; beyond this, 10 of 23 compounds have IC₅₀ better than 50 μM. Without any medicinal chemistry optimization, the most potent hit has IC₅₀ 280 nM, corresponding to K_i of 173 nM. These results support using the D-COID strategy for training classifiers in other computational biology tasks, and for vScreenML in virtual screening campaigns against other protein targets. Both D-COID and vScreenML are freely distributed to facilitate such efforts.

Xanthine oxidoreductase inhibition – A review of computational aspect

Xanthine Oxidoreductase (XOR) exists in a variety of organisms from bacteria to humans and catalyzes the oxidation of hypoxanthine to xanthine and from xanthine to uric acid. Excessive uric acid could lead to gout and hyperuricemia. In this paper, we have reviewed the recent computational studies on xanthine oxidase inhibition. Computational methods, such as molecular dynamics (molecular mechanics), quantum mechanics, and quantum mechanics/molecular mechanics (QM/MM), have been employed to investigate the binding affinity of xanthine oxidase with synthesized and isolated nature inhibitors. The limitations of different computational methods for xanthine oxidase inhibition studies were also discussed. Implications of the computational approach could be used to help to understand the existing arguments on substrate/product orientation in xanthine oxidase inhibition, which allows designing new inhibitors with higher efficacy.

Quantum Chemical Calculation of Molecular and Periodic Peptide and Protein Structures

Special-purpose classical force fields (FFs) provide good accuracy at very low computational cost, but their application is limited to systems for which potential energy functions are available. This excludes most metal-containing proteins or those containing cofactors. In contrast, the GFN2-xTB semiempirical quantum chemical method is parametrized for almost the entire periodic table. The accuracy of GFN2-xTB is assessed for protein structures with respect to experimental X-ray data. Furthermore, the results are compared with those of two special-purpose FFs, HF-3c, PM6-D3H4X, and PM7. The test sets include proteins without any prosthetic groups as well as metalloproteins. Crystal packing effects are examined for a set of smaller proteins to validate the molecular approach. For the proteins without prosthetic groups, the special purpose FF OPLS-2005 yields the smallest overall RMSD to the X-ray data but GFN2-xTB provides similarly good structures with even better bond-length distributions. For the metalloproteins with up to 5000 atoms, a good overall structural agreement is obtained with GFN2-xTB. The full geometry optimizations of protein structures with on average 1000 atoms in wall-times below 1 day establishes the GFN2-xTB method as a versatile tool for the computational treatment of various biomolecules with a good accuracy/computational cost ratio.

High-Throughput Docking Using Quantum Mechanical Scoring

Today high-throughput docking is one of the most commonly used computational tools in drug lead discovery. While there has been an impressive methodological improvement in docking accuracy, docking scoring still remains an open challenge. Most docking programs are rooted in classical molecular mechanics. However, to better characterize protein-ligand interactions, the use of a more accurate quantum mechanical (QM) description would be necessary. In this work, we introduce a QM-based docking scoring function for high-throughput docking and evaluate it on 10 protein systems belonging to diverse protein families, and with different binding site characteristics. Outstanding results were obtained, with our QM scoring function displaying much higher enrichment (screening power) than a traditional docking method. It is acknowledged that developments in quantum mechanics theory, algorithms and computer hardware throughout the upcoming years will allow semi-empirical (or low-cost) quantum mechanical methods to slowly replace force-field calculations. It is thus urgently needed to develop and validate novel quantum mechanical-based scoring functions for high-throughput docking toward more accurate methods for the identification and optimization of modulators of pharmaceutically relevant targets.

Modeling of spin–spin distance distributions for nitroxide labeled biomacromolecules

Combining CREST and MD simulations based on GFN-FF for the automated computation of distance distributions for nitroxide labeled (metallo-) proteins.

Binding Free Energy Calculation Using Quantum Mechanics Aimed for Drug Lead Optimization

The routine use of in silico tools is already established in drug lead design. Besides the use of molecular docking methods to screen large chemical libraries and thus prioritize compounds for purchase or synthesis, more accurate calculations of protein-ligand binding free energy has shown the potential to guide lead optimization, thus saving time and resources. Theoretical developments and advances in computing power have allowed quantum mechanical-based methods applied to calculations on biomacromolecules to be increasingly explored and used, with the purpose of providing a more accurate description of protein-ligand interactions and an enhanced level of accuracy in the calculation of binding affinities. It should be noted that the quantum mechanical formulation includes, in principle, all contributions to the energy, considering terms usually neglected in molecular mechanics force fields, such as electronic polarization, metal coordination, and covalent binding; moreover, quantum mechanical approaches are systematically improvable. By treating all elements and interactions on equal footing, and avoiding the need of system-dependent parameterizations, they provide a greater degree of transferability. In this review, we illustrate the increasing relevance of quantum mechanical methods for binding free energy calculation in the context of structure-based drug lead optimization, showing representative applications of the different approaches available.

Molecular Docking Using Quantum Mechanical-Based Methods

Computational methods are a powerful and consolidated tool in the early stage of the drug lead discovery process. Among these techniques, high-throughput molecular docking has proved to be extremely useful in identifying novel bioactive compounds within large chemical libraries. In the docking procedure, the predominant binding mode of each small molecule within a target binding site is assessed, and a docking score reflective of the likelihood of binding is assigned to them. These methods also shed light on how a given hit could be modified in order to improve protein-ligand interactions and are thus able to guide lead optimization. The possibility of reducing time and cost compared to experimental approaches made this technology highly appealing. Due to methodological developments and the increase of computational power, the application of quantum mechanical methods to study macromolecular systems has gained substantial attention in the last decade. A quantum mechanical description of the interactions involved in molecular association of biomolecules may lead to better accuracy compared to molecular mechanics, since there are many physical phenomena that cannot be correctly described within a classical framework, such as covalent bond formation, polarization effects, charge transfer, bond rearrangements, halogen bonding, and others, that require electrons to be explicitly accounted for. Considering the fact that quantum mechanics-based approaches in biomolecular simulation constitute an active and important field of research, we highlight in this work the recent developments of quantum mechanical-based molecular docking and high-throughput docking.

User-Friendly Quantum Mechanics: Applications for Drug Discovery

Quantum mechanics (QM) methods provide a fine description of receptor-ligand interactions and of chemical reactions. Their use in drug design and drug discovery is increasing, especially for complex systems including metal ions in the binding sites, for the design of highly selective inhibitors, for the optimization of bi-specific compounds, to understand enzymatic reactions, and for the study of covalent ligands and prodrugs. They are also used for generating molecular descriptors for predictive QSAR/QSPR models and for the parameterization of force fields. Thanks to the continuous increase of computational power offered by GPUs and to the development of sophisticated algorithms, QM methods are becoming part of the standard tools used in computer-aided drug design (CADD). We present the most used QM methods and software packages, and we discuss recent representative applications in drug design and drug discovery.

Extending and assessing composite electronic structure methods to the solid state

A hierarchy of simplified Hartree-Fock (HF), density functional theory (DFT) methods, and their combinations has been recently proposed for the fast electronic structure computation of large systems. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set global hybrid functional (PBEh-3c), and its screened exchange variant (HSE-3c), all augmented with semiclassical correction potentials. Here, we extend their applicability to inorganic covalent and ionic solids as well as layered materials. The new methods have been dubbed HFsol-3c, PBEsol0-3c, and HSEsol-3c, respectively, to indicate their parent functional as well as the correction potentials. They have been implemented in the CRYSTAL code to enable routine application for molecular as well as solid materials. We validate the new methods on diverse sets of solid state benchmarks that cover more than 90 solids ranging from covalent, ionic, semi-ionic, layered, and molecular crystals. While we focus on structural and energetic properties, we also test bandgaps, vibrational frequencies, elastic constants, and dielectric and piezoelectric tensors. HSEsol-3c appears to be most promising with mean absolute error for cohesive energies and unit cell volumes of molecular crystals of 1.5 kcal/mol and 2.8%, respectively. Lattice parameters of inorganic solids deviate by 3% from the references, and vibrational frequencies of α-quartz have standard deviations of 10 cm^-1. Overall, this shows an accuracy competitive to converged basis set dispersion corrected DFT with a substantial increase in computational efficiency.

Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett's Acceptance Ratio Methods

We use the PBE0/6-31G* density functional method to perform ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations under periodic boundary conditions with rigorous electrostatics using the ambient potential composite Ewald method in order to test the convergence of MM → QM/MM free energy corrections for the prediction of 17 small-molecule solvation free energies and eight ligand binding free energies to T4 lysozyme. The "indirect" thermodynamic cycle for calculating free energies is used to explore whether a series of reference potentials improve the statistical quality of the predictions. Specifically, we construct a series of reference potentials that optimize a molecular mechanical (MM) force field's parameters to reproduce the ab initio QM/MM forces from a QM/MM simulation. The optimizations form a systematic progression of successively expanded parameters that include bond, angle, dihedral, and charge parameters. For each reference potential, we calculate benchmark quality reference values for the MM → QM/MM correction by performing the mixed MM and QM/MM Hamiltonians at 11 intermediate states, each for 200 ps. We then compare forward and reverse application of Zwanzig's relation, thermodynamic integration (TI), and Bennett's acceptance ratio (BAR) methods as a function of reference potential, simulation time, and the number of simulated intermediate states. We find that Zwanzig's equation is inadequate unless a large number of intermediate states are explicitly simulated. The TI and BAR mean signed errors are very small even when only the end-state simulations are considered, and the standard deviations of the TI and BAR errors are decreased by choosing a reference potential that optimizes the bond and angle parameters. We find a robust approach for the data sets of fairly rigid molecules considered here is to use bond + angle reference potential together with the end-state-only BAR analysis. This requires QM/MM simulations to be performed in order to generate reference data to parametrize the bond + angle reference potential, and then this same simulation serves a dual purpose as the full QM/MM end state. The convergence of the results with respect to time suggests that computational resources may be used more efficiently by running multiple simulations for no more than 50 ps, rather than running one long simulation.

Increasing the Potential of the Auristatin Cancer-Drug Family by Shifting the Conformational Equilibrium

Monomethyl auristatin E and monomethyl auristatin F are widely used cytotoxic agents in antibody–drug conjugates (ADCs), a group of promising cancer drugs. The ADCs specifically target cancer cells, releasing the auristatins inside, which results in the prevention of mitosis. The auristatins suffer from a potentially serious flaw, however. In solution, the molecules exist in an equal mixture of two conformers, cis and trans. Only the trans-isomer is biologically active and the isomerization process, i.e., the conversion of cis to trans is slow. This significantly diminishes the efficiency of the drugs and their corresponding ADCs, and perhaps more importantly, raises concerns over drug safety. The potency of the auristatins would be enhanced by decreasing the amount of the biologically inactive isomer, either by stabilizing the trans-isomer or destabilizing the cis-isomer. Here, we follow the computer-aided design strategy of shifting the conformational equilibrium and employ high-level quantum chemical modeling to identify promising candidates for improved auristatins. Coupled cluster calculations predict that a simple halogenation in the norephedrine/phenylalanine residues shifts the isomer equilibrium almost completely toward the active trans-conformation, due to enhanced intramolecular interactions specific to the active isomer.

Electrostatic Complementarity as a Fast and Effective Tool to Optimize Binding and Selectivity of Protein-Ligand Complexes

Electrostatic interactions between small molecules and their respective receptors are essential for molecular recognition and are also key contributors to the binding free energy. Assessing the electrostatic match of protein-ligand complexes therefore provides important insights into why ligands bind and what can be changed to improve binding. Ideally, the ligand and protein electrostatic potentials at the protein-ligand interaction interface should maximize their complementarity while minimizing desolvation penalties. In this work, we present a fast and efficient tool to calculate and visualize the electrostatic complementarity (EC) of protein-ligand complexes. We compiled benchmark sets demonstrating electrostatically driven structure-activity relationships (SAR) from literature data, including kinase, protein-protein interaction, and GPCR targets, and used these to demonstrate that the EC method can visualize, rationalize, and predict electrostatically driven ligand affinity changes and help to predict compound selectivity. The methodology presented here for the analysis of EC is a powerful and versatile tool for drug design.

Cost-Effective Quantum Mechanical Approach for Predicting Thermodynamic and Mechanical Stability of Pure-Silica Zeolites

Several computational techniques for solid-state applications have recently been proposed to enlarge the scope of computer simulations of large molecular systems. In this contribution, we focused on two of these, namely, HF-3c and PBEh-3c. They were recently proposed by the Grimme's group, as "low-cost" ab initio-based techniques for electronic structure calculation of large systems and were proved to be effective essentially for organic molecules. HF-3c is based on a Hartree-Fock Hamiltonian with a minimal Gaussian quality basis set, whereas PBEh-3c is a density functional theory (DFT) based method with a hybrid functional and a medium-quality basis set. Both HF-3c and PBEh-3c account for dispersion (London) interactions and are free from the basis set superposition error due to limited basis set size, through several pairwise semiempirical corrections. To the best of our knowledge, despite the promising results on the cost-accuracy side of molecular simulations of organic molecules, these methods have been used only in few cases for solid-state applications. In this contribution, we studied the performance of HF-3c and PBEh-3c for predicting the properties of inorganic crystals to enlarge the applicability of these cheap and fast methodologies. As a testing ground, we have chosen a well-known class of material, e.g., microporous all-silica zeolites. We benchmarked geometries, formation energies, vibrational features, and mechanical properties by comparing the results with literature data from both experiment and computer simulation. For structures, HF-3c is extremely accurate in predicting the zeolites cell volume, albeit we do not include any vibrational contribution, neither zero point nor thermal, on the computed volumes, which may introduce small variations in the predicted values. For the energetic, the relative stability of the zeolites using the DFT//HF-3c approach allows predictions within the experimental error for most of the cases taken into consideration when the experimental enthalpies were corrected back to electronic energies by using the HF-3c thermodynamic contributions computed in the harmonic approximation. This strategy is particularly convenient, as the slow step (geometry optimization) is carried out with the cheapest HF-3c method, whereas the fast step (single point energy evaluation) is carried out with costly DFT methods. In this sense, the use of the DFT//HF-3c approach results to be a promising one to predict the stability and structure of microporous materials. Finally, the HF-3c method predicts the mechanical properties of the zeolite set in reasonable agreement with respect to those computed with the state-of-the-art DFT simulations, indicating the HF-3c method as a possible technique for the mechanical stability screenings of microporous materials.

Simplified DFT methods for consistent structures and energies of large systems

Kohn-Sham density functional theory (DFT) is routinely used for the fast electronic structure computation of large systems and will most likely continue to be the method of choice for the generation of reliable geometries in the foreseeable future. Here, we present a hierarchy of simplified DFT methods designed for consistent structures and non-covalent interactions of large systems with particular focus on molecular crystals. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set screened exchange hybrid functional (HSE-3c), and a generalized gradient approximated functional evaluated in a medium-sized basis set (B97-3c), all augmented with semi-classical correction potentials. We give an overview on the methods design, a comprehensive evaluation on established benchmark sets for geometries and lattice energies of molecular crystals, and highlight some realistic applications on large organic crystals with several hundreds of atoms in the primitive unit cell.

Quantum Chemical Approaches in Structure-Based Virtual Screening and Lead Optimization

Today computational chemistry is a consolidated tool in drug lead discovery endeavors. Due to methodological developments and to the enormous advance in computer hardware, methods based on quantum mechanics (QM) have gained great attention in the last 10 years, and calculations on biomacromolecules are becoming increasingly explored, aiming to provide better accuracy in the description of protein-ligand interactions and the prediction of binding affinities. In principle, the QM formulation includes all contributions to the energy, accounting for terms usually missing in molecular mechanics force-fields, such as electronic polarization effects, metal coordination, and covalent binding; moreover, QM methods are systematically improvable, and provide a greater degree of transferability. In this mini-review we present recent applications of explicit QM-based methods in small-molecule docking and scoring, and in the calculation of binding free-energy in protein-ligand systems. Although the routine use of QM-based approaches in an industrial drug lead discovery setting remains a formidable challenging task, it is likely they will increasingly become active players within the drug discovery pipeline.

Reliable and Performant Identification of Low-Energy Conformers in the Gas Phase and Water

Prediction of compound properties from structure via quantitative structure-activity relationship and machine-learning approaches is an important computational chemistry task in small-molecule drug research. Though many such properties are dependent on three-dimensional structures or even conformer ensembles, the majority of models are based on descriptors derived from two-dimensional structures. Here we present results from a thorough benchmark study of force field, semiempirical, and density functional methods for the calculation of conformer energies in the gas phase and water solvation as a foundation for the correct identification of relevant low-energy conformers. We find that the tight-binding ansatz GFN-xTB shows the lowest error metrics and highest correlation to the benchmark PBE0-D3(BJ)/def2-TZVP in the gas phase for the computationally fast methods and that in solvent OPLS3 becomes comparable in performance. MMFF94, AM1, and DFTB+ perform worse, whereas the performance-optimized but far more expensive functional PBEh-3c yields energies almost perfectly correlated to the benchmark and should be used whenever affordable. On the basis of our findings, we have implemented a reliable and fast protocol for the identification of low-energy conformers of drug-like molecules in water that can be used for the quantification of strain energy and entropy contributions to target binding as well as for the derivation of conformer-ensemble-dependent molecular descriptors.

Towards reliable references for electron paramagnetic resonance parameters based on quantum chemistry: the case of verdazyl radicals

We present an efficient and accurate computational procedure to calculate properties measurable by EPR spectroscopy. We simulate a molecular dynamics (MD) trajectory by employing the quantum mechanically derived force field (QMDFF) [S. Grimme, J. Chem. Theory Comput., 2014, 10, 4497] and sample the trajectory at different time steps. For each snapshot EPR properties are calculated with a hybrid density functional theory (DFT) method. EPR spectra are simulated based on the averaged results. We applied the strategy to a number of previously published and novel verdazyl radicals, for which we recorded EPR spectra. The resulting simulated spectra are compatible with experiment already before employing an additional fitting step, in contrast to those from single point electronic-structure calculations. After the refinement, the experimental data are excellently reproduced, and the fitted EPR parameters do not deviate much from the calculated ones. This provides confidence in ascribing a direct physical meaning to the refined data in terms of experimental EPR parameters rather than merely considering them as mathematical fit parameters. We also find that couplings to hydrogen nuclei have a significant influence on the spectra of verdazyl radicals.

Computational Chemistry: The Fate of Current Methods and Future Challenges

"Where do we go from here?" is the underlying question regarding the future (perhaps foreseeable) developments in computational chemistry. Although this young discipline has already permeated practically all of chemistry, it is likely to become even more powerful with the rapid development of computational hard- and software.