Bringing Clarity to the Prediction of Protein-Ligand Binding Free Energies via "Blurring"

Machine Learning Methods as a Cost-Effective Alternative to Physics-Based Binding Free Energy Calculations

The rank ordering of ligands remains one of the most attractive challenges in drug discovery. While physics-based in silico binding affinity methods dominate the field, they still have problems, which largely revolve around forcefield accuracy and sampling. Recent advances in machine learning have gained traction for protein-ligand binding affinity predictions in early drug discovery programs. In this article, we perform retrospective binding free energy evaluations for 172 compounds from our internal collection spread over four different protein targets and five congeneric ligand series. We compared multiple state-of-the-art free energy methods ranging from physics-based methods with different levels of complexity and conformational sampling to state-of-the-art machine-learning-based methods that were available to us. Overall, we found that physics-based methods behaved particularly well when the ligand perturbations were made in the solvation region, and they did not perform as well when accounting for large conformational changes in protein active sites. On the other end, machine-learning-based methods offer a good cost-effective alternative for binding free energy calculations, but the accuracy of their predictions is highly dependent on the experimental data available for training the model.

Ligand binding free energy evaluation by Monte Carlo Recursion

The correct evaluation of ligand binding free energies by computational methods is still a very challenging active area of research. The most employed methods for these calculations can be roughly classified into four groups: (i) the fastest and less accurate methods, such as molecular docking, designed to sample a large number of molecules and rapidly rank them according to the potential binding energy; (ii) the second class of methods use a thermodynamic ensemble, typically generated by molecular dynamics, to analyze the endpoints of the thermodynamic cycle for binding and extract differences, in the so-called 'end-point' methods; (iii) the third class of methods is based on the Zwanzig relationship and computes the free energy difference after a chemical change of the system (alchemical methods); and (iv) methods based on biased simulations, such as metadynamics, for example. These methods require increased computational power and as expected, result in increased accuracy for the determination of the strength of binding. Here, we describe an intermediate approach, based on the Monte Carlo Recursion (MCR) method first developed by Harold Scheraga. In this method, the system is sampled at increasing effective temperatures, and the free energy of the system is assessed from a series of terms W(b,T), computed from Monte Carlo (MC) averages at each iteration. We show the application of the MCR for ligand binding with datasets of guest-hosts systems (N = 75) and we observed that a good correlation is obtained between experimental data and the binding energies computed with MCR. We also compared the experimental data with an end-point calculation from equilibrium Monte Carlo calculations that allowed us to conclude that the lower-energy (lower-temperature) terms in the calculation are the most relevant to the estimation of the binding energies, resulting in similar correlations between MCR and MC data and the experimental values. On the other hand, the MCR method provides a reasonable view of the binding energy funnel, with possible connections with the ligand binding kinetics, as well. The codes developed for this analysis are publicly available on GitHub as a part of the LiBELa/MCLiBELa project (https://github.com/alessandronascimento/LiBELa).

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.

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.

Alchemical Grid Dock (AlGDock): Binding Free Energy Calculations between Flexible Ligands and Rigid Receptors

Alchemical Grid Dock (AlGDock) is open-source software designed to compute the binding potential of mean force-the binding free energy between a flexible ligand and a rigid receptor-for a small organic ligand and a biological macromolecule. Multiple BPMFs can be used to rigorously compute binding affinities between flexible partners. AlGDock uses replica exchange between thermodynamic states at different temperatures and receptor-ligand interaction strengths. Receptor-ligand interaction energies are represented by interpolating precomputed grids. Thermodynamic states are adaptively initialized and adjusted on-the-fly to maintain adequate replica exchange rates. In demonstrative calculations, when the bound ligand is treated as fully solvated, AlGDock estimates BPMFs with a precision within 4 kT in 65% and within 8 kT for 91% of systems. It correctly identifies the native binding pose in 83% of simulations. Performance is sometimes limited by subtle differences in the important configuration space of sampled and targeted thermodynamic states. © 2019 Wiley Periodicals, Inc.

Advances in Docking

BACKGROUND

Design of small molecules which are able to bind to the protein responsible for a disease is the key step of the entire process of the new medicine discovery. Atomistic computer modeling can significantly improve effectiveness of such design. The accurate calculation of the free energy of binding a small molecule (a ligand) to the target protein is the most important problem of such modeling. Docking is one of the most popular molecular modeling methods for finding ligand binding poses in the target protein and calculating the protein-ligand binding energy. This energy is used for finding the most active compounds for the given target protein. This short review aims to give a concise description of distinctive features of docking programs focusing on computation methods and approximations influencing their accuracy.

METHODS

This review is based on the peer-reviewed research literature including author's own publications. The main features of several representative docking programs are briefly described focusing on their characteristics influencing docking accuracy: force fields, energy calculations, solvent models, algorithms of the best ligand pose search, global and local optimizations, ligand and target protein flexibility, and the simplifications made for the docking accelerating. Apart from other recent reviews focused mainly on the performance of different docking programs, in this work, an attempt is made to extract the most important functional characteristics defining the docking accuracy. Also a roadmap for increasing the docking accuracy is proposed. This is based on the new generation of docking programs which have been realized recently. These programs and respective new global optimization algorithms are described shortly.

RESULTS

Several popular conventional docking programs are considered. Their search of the best ligand pose is based explicitly or implicitly on the global optimization problem. Several algorithms are used to solve this problem, and among them, the heuristic genetic algorithm is distinguished by its popularity and an elaborate design. All conventional docking programs for their acceleration use the preliminary calculated grids of protein-ligand interaction potentials or preferable points of protein and ligand conjugation. These approaches and commonly used fitting parameters restrict strongly the docking accuracy. Solvent is considered in exceedingly simplified approaches in the course of the global optimization and the search for the best ligand poses. More accurate approaches on the base of implicit solvent models are used frequently for more careful binding energy calculations after docking. The new generation of docking programs are developed recently. They find the spectrum of low energy minima of a protein-ligand complex including the global minimum. These programs should be more accurate because they do not use a preliminary calculated grid of protein-ligand interaction potentials and other simplifications, the energy of any conformation of the molecular system is calculated in the frame of a given force field and there are no fitting parameters. A new docking algorithm is developed and fulfilled specially for the new docking programs. This algorithm allows docking a flexible ligand into a flexible protein with several dozen mobile atoms on the base of the global energy minimum search. Such docking results in improving the accuracy of ligand positioning in the docking process. The adequate choice of the method of molecular energy calculations also results in the better docking positioning accuracy. An advancement in the application of quantum chemistry methods to docking and scoring is revealed.

CONCLUSION

The findings of this review confirm the great demand in docking programs for discovery of new medicine substances with the help of molecular modeling. New trends in docking programs design are revealed. These trends are focused on the increase of the docking accuracy at the expense of more accurate molecular energy calculations without any fitting parameters, including quantum-chemical methods and implicit solvent models, and by using new global optimization algorithms which make it possible to treat flexibility of ligands and mobility of protein atoms simultaneously. Finally, it is shown that all the necessary prerequisites for increasing the docking accuracy can be accomplished in practice.

Mechanisms for Benzene Dissociation through the Excited State of T4 Lysozyme L99A Mutant

The atomic-level mechanisms that coordinate ligand release from protein pockets are only known for a handful of proteins. Here, we report results from accelerated molecular dynamics simulations for benzene dissociation from the buried cavity of the T4 lysozyme Leu99Ala mutant (L99A). In these simulations, benzene is released through a previously characterized, sparsely populated room-temperature excited state of the mutant, explaining the coincidence for experimentally measured benzene off rate and apo protein slow-timescale NMR relaxation rates between ground and excited states. The path observed for benzene egress is a multistep ligand migration from the buried cavity to ultimate release through an opening between the F/G-, H-, and I-helices and requires a number of cooperative multiresidue and secondary-structure rearrangements within the C-terminal domain of L99A. These rearrangements are identical to those observed along the ground state to excited state transitions characterized by molecular dynamic simulations run on the Anton supercomputer. Analyses of the molecular properties of the residues lining the egress path suggest that protein surface electrostatic potential may play a role in the release mechanism. Simulations of wild-type T4 lysozyme also reveal that benzene-egress-associated dynamics in the L99A mutant are potentially exaggerations of the substrate-processivity-related dynamics of the wild type.

Detailed potential of mean force studies on host-guest systems from the SAMPL6 challenge

Accurately predicting receptor-ligand binding free energies is one of the holy grails of computational chemistry with many applications in chemistry and biology. Many successes have been reported, but issues relating to sampling and force field accuracy remain significant issues affecting our ability to reliably calculate binding free energies. In order to explore these issues in more detail we have examined a series of small host-guest complexes from the SAMPL6 blind challenge, namely octa-acids (OAs)-guest complexes and Curcurbit[8]uril (CB8)-guest complexes. Specifically, potential of mean force studies using umbrella sampling combined with the weighted histogram method were carried out on both systems with both known and unknown binding affinities. We find that using standard force fields and straightforward simulation protocols we are able to obtain satisfactory results, but that simply scaling our results allows us to significantly improve our predictive ability for the unknown test sets: the overall RMSD of the binding free energy versus experiment is reduced from 5.59 to 2.36 kcal/mol; for the CB8 test system, the RMSD goes from 8.04 to 3.51 kcal/mol, while for the OAs test system, the RSMD goes from 2.89 to 0.95 kcal/mol. The scaling approach was inspired by studies on structurally related known benchmark sets: by simply scaling, the RMSD was reduced from 6.23 to 1.19 kcal/mol and from 2.96 to 0.62 kcal/mol for the CB8 benchmark system and the OA benchmark system, respectively. We find this scaling procedure to correct absolute binding affinities to be highly effective especially when working across a "congeneric" series with similar charge states. It is less successful when applied to mixed ligands with varied charges and chemical characteristics, but improvement is still realized in the present case. This approach suggests that there are large systematic errors in absolute binding free energy calculations that can be straightforwardly accounted for using a scaling procedure. Random errors are still an issue, but near chemical accuracy can be obtained using the present strategy in select cases.

Absolute Binding Free Energies between T4 Lysozyme and 141 Small Molecules: Calculations Based on Multiple Rigid Receptor Configurations

We demonstrate the feasibility of estimating protein-ligand binding free energies using multiple rigid receptor configurations. On the basis of T4 lysozyme snapshots extracted from six alchemical binding free energy calculations with a flexible receptor, binding free energies were estimated for a total of 141 ligands. For 24 ligands, the calculations reproduced flexible-receptor estimates with a correlation coefficient of 0.90 and a root-mean-square error of 1.59 kcal/mol. The accuracy of calculations based on Poisson-Boltzmann/surface area implicit solvent was comparable to that of previously reported free energy calculations.

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.

Homologous ligands accommodated by discrete conformations of a buried cavity

Conformational change in protein-ligand complexes is widely modeled, but the protein accommodation expected on binding a congeneric series of ligands has received less attention. Given their use in medicinal chemistry, there are surprisingly few substantial series of congeneric ligand complexes in the Protein Data Bank (PDB). Here we determine the structures of eight alkyl benzenes, in single-methylene increases from benzene to n-hexylbenzene, bound to an enclosed cavity in T4 lysozyme. The volume of the apo cavity suffices to accommodate benzene but, even with toluene, larger cavity conformations become observable in the electron density, and over the series two other major conformations are observed. These involve discrete changes in main-chain conformation, expanding the site; few continuous changes in the site are observed. In most structures, two discrete protein conformations are observed simultaneously, and energetic considerations suggest that these conformations are low in energy relative to the ground state. An analysis of 121 lysozyme cavity structures in the PDB finds that these three conformations dominate the previously determined structures, largely modeled in a single conformation. An investigation of the few congeneric series in the PDB suggests that discrete changes are common adaptations to a series of growing ligands. The discrete, but relatively few, conformational states observed here, and their energetic accessibility, may have implications for anticipating protein conformational change in ligand design.

Enhanced semiempirical QM methods for biomolecular interactions

Recent successes and failures of the application of 'enhanced' semiempirical QM (SQM) methods are reviewed in the light of the benefits and backdraws of adding dispersion (D) and hydrogen-bond (H) correction terms. We find that the accuracy of SQM-DH methods for non-covalent interactions is very often reported to be comparable to dispersion-corrected density functional theory (DFT-D), while computation times are about three orders of magnitude lower. SQM-DH methods thus open up a possibility to simulate realistically large model systems for problems both in life and materials science with comparably high accuracy.

Using quantum mechanical approaches to study biological systems

Conspectus Quantum mechanics (QM) has revolutionized our understanding of the structure and reactivity of small molecular systems. Given the tremendous impact of QM in this research area, it is attractive to believe that this could also be brought into the biological realm where systems of a few thousand atoms and beyond are routine. Applying QM methods to biological problems brings an improved representation to these systems by the direct inclusion of inherently QM effects such as polarization and charge transfer. Because of the improved representation, novel insights can be gleaned from the application of QM tools to biomacromolecules in aqueous solution. To achieve this goal, the computational bottlenecks of QM methods had to be addressed. In semiempirical theory, matrix diagonalization is rate limiting, while in density functional theory or Hartree-Fock theory electron repulsion integral computation is rate-limiting. In this Account, we primarily focus on semiempirical models where the divide and conquer (D&C) approach linearizes the matrix diagonalization step with respect to the system size. Through the D&C approach, a number of applications to biological problems became tractable. Herein, we provide examples of QM studies on biological systems that focus on protein solvation as viewed by QM, QM enabled structure-based drug design, and NMR and X-ray biological structure refinement using QM derived restraints. Through the examples chosen, we show the power of QM to provide novel insights into biological systems, while also impacting practical applications such as structure refinement. While these methods can be more expensive than classical approaches, they make up for this deficiency by the more realistic modeling of the electronic nature of biological systems and in their ability to be broadly applied. Of the tools and applications discussed in this Account, X-ray structure refinement using QM models is now generally available to the community in the refinement package Phenix. While the power of this approach is manifest, challenges still remain. In particular, QM models are generally applied to static structures, so ways in which to include sampling is an ongoing challenge. Car-Parrinello or Born-Oppenheimer molecular dynamics approaches address the short time scale sampling issue, but how to effectively use QM to study phenomenon covering longer time scales will be the focus of future research. Finally, how to accurately and efficiently include electron correlation effects to facilitate the modeling of, for example, dispersive interactions, is also a major hurdle that a broad range of groups are addressing The use of QM models in biology is in its infancy, leading to the expectation that the most significant use of these tools to address biological problems will be seen in the coming years. It is hoped that while this Account summarizes where we have been, it will also help set the stage for future research directions at the interface of quantum mechanics and biology.

Computer-aided Drug Design: Using Numbers to your Advantage

Computer-aided drug design could benefit from a greater understanding of how errors arise and propagate in biomolecular modeling. With such knowledge, model predictions could be associated with quantitative estimates of their uncertainty. In addition, novel algorithms could be designed to proactively reduce prediction errors. We investigated how errors propagate in statistical mechanical ensembles and found that free energy evaluations based on single molecular configurations yield maximum uncertainties in free energy. Furthermore, increasing the size of the ensemble by sampling and averaging over additional independent configurations reduces uncertainties in free energy dramatically. This finding suggests a general strategy that could be utilized as a post-hoc correction for improved precision in virtual screening and free energy estimation.