Estimates of ligand-binding affinities supported by quantum mechanical methods

How are N-methylcarbamates encapsulated by β-cyclodextrin: insight into the binding mechanism

Guest molecules containing chromophore groups encapsulated by β-cyclodextrin (β-CD) generate circular dichroism (CD) signals, which enables a preliminary prediction of their binding modes. However, the accurate determination of the representative binding conformation (RC) remains a challenging task due to the complex conformational space of these host-guest systems. Here, we combine a molecular dynamics/quantum mechanics/continuum solvent model (MD/QM/CSM) with induced circular dichroism (ICD) data (N. L. Pacioni, A. B. Pierini and A. V. Veglia, Spectrochim. Acta A Mol. Biomol. Spectrosc., 2013, 103, 319-324.) to explore the binding mechanism of β-CD with four N-methylcarbamate molecules: promecarb (PC), bendiocarb (BC), carbaryl (CY) and carbofuran (CF). In aqueous solution, their stability decreases as: PC > BC > CY > CF. Comparing the ECD spectra computed from TD-DFT with the ICD data can help eliminate many common binding configurations and identify the RC. The host-guest binding affinities (BAs) estimated using a ONIOM2(B971:PM6)/SMD model reproduce the measured binding trend, reveal the competition between the non-covalent interaction and solvent effect and explain the large difference in their binding modes. We also examine the fluctuations in the computed BA using similar structures.

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.

Fragment-based quantum mechanical approach to biomolecules, molecular clusters, molecular crystals and liquids

To study large molecular systems beyond the system size that the current state-of-the-art ab initio electronic structure methods could handle, fragment-based quantum mechanical (QM) approaches have been developed over the past years, and proved to be efficient in dealing with large molecular systems at various ab initio levels. According to the fragmentation approach, a large molecular system can be divided into subsystems (fragments), and subsequently the property of the whole system can be approximately obtained by taking a proper combination of the corresponding terms of individual fragments. Therefore, the standard QM calculation of a large system could be circumvented by carrying out a series of calculations on small fragments, which significantly promotes computational efficiency. The electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method is one of the fragment-based QM approaches which has been developed by our research group in recent years. This Perspective presents the theoretical framework of this fragmentation method and its applications in biomolecules, molecular clusters, molecular crystals and liquids, including total energy calculation, protein-ligand/protein binding affinity prediction, geometry optimization, vibrational spectrum simulation, ab initio molecular dynamics simulation, and prediction of excited-state properties.

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?

Binding free energies in the SAMPL5 octa-acid host-guest challenge calculated with DFT-D3 and CCSD(T)

We have tried to calculate the free energy for the binding of six small ligands to two variants of the octa-acid deep cavitand host in the SAMPL5 blind challenge. We employed structures minimised with dispersion-corrected density-functional theory with small basis sets and energies were calculated using large basis sets. Solvation energies were calculated with continuum methods and thermostatistical corrections were obtained from frequencies calculated at the HF-3c level. Care was taken to minimise the effects of the flexibility of the host by keeping the complexes as symmetric and similar as possible. In some calculations, the large net charge of the host was reduced by removing the propionate and benzoate groups. In addition, the effect of a restricted molecular dynamics sampling of structures was tested. Finally, we tried to improve the energies by using the DLPNO-CCSD(T) approach. Unfortunately, results of quite poor quality were obtained, with no correlation to the experimental data, systematically too positive affinities (by ~50 kJ/mol) and a mean absolute error (after removal of the systematic error) of 11-16 kJ/mol. DLPNO-CCSD(T) did not improve the results, so the accuracy is not limited by the energy function. Instead, four likely sources of errors were identified: first, the minimised structures were often incorrect, owing to the omission of explicit solvent. They could be partly improved by performing the minimisations in a continuum solvent with four water molecules around the charged groups of the ligands. Second, some ligands could bind in several different conformations, requiring sampling of reasonable structures. Third, there is an indication the continuum-solvation model has problems to accurately describe the binding of both the negatively and positively charged guest molecules. Fourth, different methods to calculate the thermostatistical corrections gave results that differed by up to 30 kJ/mol and there is an indication that HF-3c overestimates the entropy term. In conclusion, it is a challenge to calculate binding affinities for this octa-acid system with quantum-mechanical methods.

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.

Receptor-ligand molecular docking

Docking methodology aims to predict the experimental binding modes and affinities of small molecules within the binding site of particular receptor targets and is currently used as a standard computational tool in drug design for lead compound optimisation and in virtual screening studies to find novel biologically active molecules. The basic tools of a docking methodology include a search algorithm and an energy scoring function for generating and evaluating ligand poses. In this review, we present the search algorithms and scoring functions most commonly used in current molecular docking methods that focus on protein-ligand applications. We summarise the main topics and recent computational and methodological advances in protein-ligand docking. Protein flexibility, multiple ligand binding modes and the free-energy landscape profile for binding affinity prediction are important and interconnected challenges to be overcome by further methodological developments in the docking field.

Fully ab initio protein-ligand interaction energies with dispersion corrected density functional theory

Dispersion corrected density functional theory (DFT-D3) is used for fully ab initio protein-ligand (PL) interaction energy calculation via molecular fractionation with conjugated caps (MFCC) and applied to PL complexes from the PDB comprising 3680, 1798, and 1060 atoms. Molecular fragments with n amino acids instead of one in the original MFCC approach are considered, thereby allowing for estimating the three-body and higher many-body terms. n > 1 is recommended both in terms of accuracy and efficiency of MFCC. For neutral protein side-chains, the computed PL interaction energy is visibly independent of the fragment length n. The MFCC fractionation error is determined by comparison to a full-system calculation for the 1060 atoms containing PL complex. For charged amino acid side-chains, the variation of the MFCC result with n is increased. For these systems, using a continuum solvation model with a dielectricity constant typical for protein environments (ϵ = 4) reduces both the variation with n and improves the stability of the DFT calculations considerably. The PL interaction energies for two typical complexes obtained ab initio for the first time are found to be rather large (-30 and -54 kcal/mol).

Protein-ligand interaction energies with dispersion corrected density functional theory and high-level wave function based methods

With dispersion-corrected density functional theory (DFT-D3) intermolecular interaction energies for a diverse set of noncovalently bound protein-ligand complexes from the Protein Data Bank are calculated. The focus is on major contacts occurring between the drug molecule and the binding site. Generalized gradient approximation (GGA), meta-GGA, and hybrid functionals are used. DFT-D3 interaction energies are benchmarked against the best available wave function based results that are provided by the estimated complete basis set (CBS) limit of the local pair natural orbital coupled-electron pair approximation (LPNO-CEPA/1) and compared to MP2 and semiempirical data. The size of the complexes and their interaction energies (ΔE(PL)) varies between 50 and 300 atoms and from -1 to -65 kcal/mol, respectively. Basis set effects are considered by applying extended sets of triple- to quadruple-ζ quality. Computed total ΔE(PL) values show a good correlation with the dispersion contribution despite the fact that the protein-ligand complexes contain many hydrogen bonds. It is concluded that an adequate, for example, asymptotically correct, treatment of dispersion interactions is necessary for the realistic modeling of protein-ligand binding. Inclusion of the dispersion correction drastically reduces the dependence of the computed interaction energies on the density functional compared to uncorrected DFT results. DFT-D3 methods provide results that are consistent with LPNO-CEPA/1 and MP2, the differences of about 1-2 kcal/mol on average (<5% of ΔE(PL)) being on the order of their accuracy, while dispersion-corrected semiempirical AM1 and PM3 approaches show a deviating behavior. The DFT-D3 results are found to depend insignificantly on the choice of the short-range damping model. We propose to use DFT-D3 as an essential ingredient in a QM/MM approach for advanced virtual screening approaches of protein-ligand interactions to be combined with similarly "first-principle" accounts for the estimation of solvation and entropic effects.

A QM/MM study of the binding of RAPTA ligands to cathepsin B

We have carried out quantum mechanical (QM) and QM/MM (combined QM and molecular mechanics) calculations, as well as molecular dynamics (MD) simulations to study the binding of a series of six RAPTA (Ru(II)-arene-1,3,5-triaza-7-phosphatricyclo-[3.3.1.1] decane) complexes with different arene substituents to cathepsin B. The recently developed QM/MM-PBSA approach (QM/MM combined with Poisson-Boltzmann solvent-accessible surface area solvation) has been used to estimate binding affinities. The QM calculations reproduce the antitumour activities of the complexes with a correlation coefficient (r (2)) of 0.35-0.86 after a conformational search. The QM/MM-PBSA method gave a better correlation (r (2) = 0.59) when the protein was fixed to the crystal structure, but more reasonable ligand structures and absolute binding energies were obtained if the protein was allowed to relax, indicating that the ligands are strained when the protein is kept fixed. In addition, the best correlation (r (2) = 0.80) was obtained when only the QM energies were used, which suggests that the MM and continuum solvation energies are not accurate enough to predict the binding of a charged metal complex to a charged protein. Taking into account the protein flexibility by means of MD simulations slightly improves the correlation (r (2) = 0.91), but the absolute energies are still too large and the results are sensitive to the details in the calculations, illustrating that it is hard to obtain stable predictions when full flexible protein is included in the calculations.

An MM/3D-RISM approach for ligand binding affinities

We have modified the popular MM/PBSA or MM/GBSA approaches (molecular mechanics for a biomolecule, combined with a Poisson-Boltzmann or generalized Born electrostatic and surface area nonelectrostatic solvation energy) by employing instead the statistical-mechanical, three-dimensional molecular theory of solvation (also known as 3D reference interaction site model, or 3D-RISM-KH) coupled with molecular mechanics or molecular dynamics ( Blinov , N. ; et al. Biophys. J. 2010 ; Luchko , T. ; et al. J. Chem. Theory Comput. 2010 ). Unlike the PBSA or GBSA semiempirical approaches, the 3D-RISM-KH theory yields a full molecular picture of the solvation structure and thermodynamics from the first principles, with proper account of chemical specificities of both solvent and biomolecules, such as hydrogen bonding, hydrophobic interactions, salt bridges, etc. We test the method on the binding of seven biotin analogues to avidin in aqueous solution and show it to work well in predicting the ligand-binding affinities. We have compared the results of 3D-RISM-KH with four different generalized Born and two Poisson-Boltzmann methods. They give absolute binding energies that differ by up to 208 kJ/mol and mean absolute deviations in the relative affinities of 10-43 kJ/mol.