Sampling Conformational Changes of Bound Ligands Using Nonequilibrium Candidate Monte Carlo and Molecular Dynamics

Predicting binding events in very flexible, allosteric, multi-domain proteins

Knowledge of the structures formed by proteins and small molecules is key to understand the molecular principles of chemotherapy and for designing new and more effective drugs. During the early stage of a drug discovery program, it is customary to predict ligand-protein complexes in silico , particularly when screening large compound databases. While virtual screening based on molecular docking is widely used for this purpose, it generally fails in mimicking binding events associated with large conformational changes in the protein, particularly when the latter involve multiple domains. In this work, we describe a new methodology to generate bound-like conformations of very flexible and allosteric proteins bearing multiple binding sites by exploiting only information on the unbound structure and the putative binding sites. The protocol is validated on the paradigm enzyme adenylate kinase, for which we generated a significant fraction of bound-like structures. A fraction of these conformations, employed in ensemble-docking calculations, allowed to find native-like poses of substrates and inhibitors (binding to the active form of the enzyme), as well as catalytically incompetent analogs (binding the inactive form). Our protocol provides a general framework for the generation of bound-like conformations of challenging drug targets that are suitable to host different ligands, demonstrating high sensitivity to the fine chemical details that regulate protein's activity. We foresee applications in virtual screening, in the prediction of the impact of amino acid mutations on structure and dynamics, and in protein engineering.

Cryptate binding energies towards high throughput chelator design: metadynamics ensembles with cluster-continuum solvation

A tiered forcefield/semiempirical/meta-GGA pipeline together with a thermodynamic scheme designed with error cancellation in mind was developed to calculate binding energies of [2.2.2] cryptate complexes of mono- and divalent cations. Stable complexes of Na, K, Rb, Ca, Zn and Pb were generated, revealing consistent cation-N lengths but highly variable cation-O lengths and an amine stacking mechanism potentially augmenting the cation size selectivity. Metadynamics, used for searching the high-dimensional potential energy surface, together with a cluster-continuum model for affordable - yet accurate - solvation modeling, enabled the discovery of more stable geometries than those previously reported. Similar solvation energy curve shapes for lone vs. coordinated ions enabled rapid solvation convergence via the cancellation of errors stemming from finite cluster sizes. An R2 of 0.850 vs. experimental aqueous binding energies was obtained, validating this scheme as the backbone of a high-throughput workflow for chelator design.

Reliability of AlphaFold2 Models in Virtual Drug Screening: A Focus on Selected Class A GPCRs

Protein three-dimensional (3D) structure prediction is one of the most challenging issues in the field of computational biochemistry, which has overwhelmed scientists for almost half a century. A significant breakthrough in structural biology has been established by developing the artificial intelligence (AI) system AlphaFold2 (AF2). The AF2 system provides a state-of-the-art prediction of protein structures from nearly all known protein sequences with high accuracy. This study examined the reliability of AF2 models compared to the experimental structures in drug discovery, focusing on one of the most common protein drug-targeted classes known as G protein-coupled receptors (GPCRs) class A. A total of 32 representative protein targets were selected, including experimental structures of X-ray crystallographic and Cryo-EM structures and their corresponding AF2 models. The quality of AF2 models was assessed using different structure validation tools, including the pLDDT score, RMSD value, MolProbity score, percentage of Ramachandran favored, QMEAN Z-score, and QMEANDisCo Global. The molecular docking was performed using the Genetic Optimization for Ligand Docking (GOLD) software. The AF2 models' reliability in virtual drug screening was determined by their ability to predict the ligand binding poses closest to the native binding pose by assessing the Root Mean Square Deviation (RMSD) metric and docking scoring function. The quality of the docking and scoring function was evaluated using the enrichment factor (EF). Furthermore, the capability of using AF2 models in molecular docking to identify hits with key protein-ligand interactions was analyzed. The posing power results showed that the AF2 models successfully predicted ligand binding poses (RMSD < 2 Å). However, they exhibited lower screening power, with average EF values of 2.24, 2.42, and 1.82 for X-ray, Cryo-EM, and AF2 structures, respectively. Moreover, our study revealed that molecular docking using AF2 models can identify competitive inhibitors. In conclusion, this study found that AF2 models provided docking results comparable to experimental structures, particularly for certain GPCR targets, and could potentially significantly impact drug discovery.

Molecular Determinants of EphA2 and EphB2 Antagonism Enable the Design of Ligands with Improved Selectivity

With the aim of identifying novel antagonists selective for the EphA receptor family, a combined experimental and computational approach was taken to investigate the molecular basis of the recognition between a prototypical Eph-ephrin antagonist (UniPR1447) and two representative receptors of the EphA and EphB subfamilies, namely, EphA2 and EphB2 receptors. The conformational free-energy surface (FES) of the binding state of UniPR1447 within the ligand binding domain of EphA2 and EphB2, reconstructed from molecular dynamics (MD) simulations performed on the microsecond time scale, was exploited to drive the design and synthesis of a novel antagonist selective for EphA2 over the EphB2 receptor. The availability of compounds with this pharmacological profile will help discriminate the importance of these two receptors in the insurgence and progression of cancer.

Grand-canonical molecular dynamics simulations powered by a hybrid 4D nonequilibrium MD/MC method: Implementation in LAMMPS and applications to electrolyte solutions

Molecular simulations in an open environment, involving ion exchange, are necessary to study various systems, from biosystems to confined electrolytes. However, grand-canonical simulations are often computationally demanding in condensed phases. A promising method [L. Belloni, J. Chem. Phys. 151, 021101 (2019)], one of the hybrid nonequilibrium molecular dynamics/Monte Carlo algorithms, was recently developed, which enables efficient computation of fluctuating number or charge density in dense fluids or ionic solutions. This method facilitates the exchange through an auxiliary dimension, orthogonal to all physical dimensions, by reducing initial steric and electrostatic clashes in three-dimensional systems. Here, we report the implementation of the method in LAMMPS with a Python interface, allowing facile access to grand-canonical molecular dynamics simulations with massively parallelized computation. We validate our implementation with two electrolytes, including a model Lennard-Jones electrolyte similar to a restricted primitive model and aqueous solutions. We find that electrostatic interactions play a crucial role in the overall efficiency due to their long-range nature, particularly for water or ion-pair exchange in aqueous solutions. With properly screened electrostatic interactions and bias-based methods, our approach enhances the efficiency of salt-pair exchange in Lennard-Jones electrolytes by approximately four orders of magnitude, compared to conventional grand-canonical Monte Carlo. Furthermore, the acceptance rate of NaCl-pair exchange in aqueous solutions at moderate concentrations reaches about 3% at the maximum efficiency.

WaterKit: Thermodynamic Profiling of Protein Hydration Sites

Water desolvation is one of the key components of the free energy of binding of small molecules to their receptors. Thus, understanding the energetic balance of solvation and desolvation resulting from individual water molecules can be crucial when estimating ligand binding, especially when evaluating different molecules and poses as done in High-Throughput Virtual Screening (HTVS). Over the most recent decades, several methods were developed to tackle this problem, ranging from fast approximate methods (usually empirical functions using either discrete atom-atom pairwise interactions or continuum solvent models) to more computationally expensive and accurate ones, mostly based on Molecular Dynamics (MD) simulations, such as Grid Inhomogeneous Solvation Theory (GIST) or Double Decoupling. On one hand, MD-based methods are prohibitive to use in HTVS to estimate the role of waters on the fly for each ligand. On the other hand, fast and approximate methods show an unsatisfactory level of accuracy, with low agreement with results obtained with the more expensive methods. Here we introduce WaterKit, a new grid-based sampling method with explicit water molecules to calculate thermodynamic properties using the GIST method. Our results show that the discrete placement of water molecules is successful in reproducing the position of crystallographic waters with very high accuracy, as well as providing thermodynamic estimates with accuracy comparable to more expensive MD simulations. Unlike these methods, WaterKit can be used to analyze specific regions on the protein surface, (such as the binding site of a receptor), without having to hydrate and simulate the whole receptor structure. The results show the feasibility of a general and fast method to compute thermodynamic properties of water molecules, making it well-suited to be integrated in high-throughput pipelines such as molecular docking.

An overview of the SAMPL8 host-guest binding challenge

The SAMPL series of challenges aim to focus the community on specific modeling challenges, while testing and hopefully driving progress of computational methods to help guide pharmaceutical drug discovery. In this study, we report on the results of the SAMPL8 host–guest blind challenge for predicting absolute binding affinities. SAMPL8 focused on two host–guest datasets, one involving the cucurbituril CB8 (with a series of common drugs of abuse) and another involving two different Gibb deep-cavity cavitands. The latter dataset involved a previously featured deep cavity cavitand (TEMOA) as well as a new variant (TEETOA), both binding to a series of relatively rigid fragment-like guests. Challenge participants employed a reasonably wide variety of methods, though many of these were based on molecular simulations, and predictive accuracy was mixed. As in some previous SAMPL iterations (SAMPL6 and SAMPL7), we found that one approach to achieve greater accuracy was to apply empirical corrections to the binding free energy predictions, taking advantage of prior data on binding to these hosts. Another approach which performed well was a hybrid MD-based approach with reweighting to a force matched QM potential. In the cavitand challenge, an alchemical method using the AMOEBA-polarizable force field achieved the best success with RMSE less than 1 kcal/mol, while another alchemical approach (ATM/GAFF2-AM1BCC/TIP3P/HREM) had RMSE less than 1.75 kcal/mol. The work discussed here also highlights several important lessons; for example, retrospective studies of reference calculations demonstrate the sensitivity of predicted binding free energies to ethyl group sampling and/or guest starting pose, providing guidance to help improve future studies on these systems.

Best practices for constructing, preparing, and evaluating protein-ligand binding affinity benchmarks [Article v0.1]

Free energy calculations are rapidly becoming indispensable in structure-enabled drug discovery programs. As new methods, force fields, and implementations are developed, assessing their expected accuracy on real-world systems (benchmarking) becomes critical to provide users with an assessment of the accuracy expected when these methods are applied within their domain of applicability, and developers with a way to assess the expected impact of new methodologies. These assessments require construction of a benchmark-a set of well-prepared, high quality systems with corresponding experimental measurements designed to ensure the resulting calculations provide a realistic assessment of expected performance when these methods are deployed within their domains of applicability. To date, the community has not yet adopted a common standardized benchmark, and existing benchmark reports suffer from a myriad of issues, including poor data quality, limited statistical power, and statistically deficient analyses, all of which can conspire to produce benchmarks that are poorly predictive of real-world performance. Here, we address these issues by presenting guidelines for (1) curating experimental data to develop meaningful benchmark sets, (2) preparing benchmark inputs according to best practices to facilitate widespread adoption, and (3) analysis of the resulting predictions to enable statistically meaningful comparisons among methods and force fields. We highlight challenges and open questions that remain to be solved in these areas, as well as recommendations for the collection of new datasets that might optimally serve to measure progress as methods become systematically more reliable. Finally, we provide a curated, versioned, open, standardized benchmark set adherent to these standards (PLBenchmarks) and an open source toolkit for implementing standardized best practices assessments (arsenic) for the community to use as a standardized assessment tool. While our main focus is free energy methods based on molecular simulations, these guidelines should prove useful for assessment of the rapidly growing field of machine learning methods for affinity prediction as well.

Enhancing Sampling of Water Rehydration on Ligand Binding: A Comparison of Techniques

Water often plays a key role in protein structure, molecular recognition, and mediating protein-ligand interactions. Thus, free energy calculations must adequately sample water motions, which often proves challenging in typical MD simulation time scales. Thus, the accuracy of methods relying on MD simulations ends up limited by slow water sampling. Particularly, as a ligand is removed or modified, bulk water may not have time to fill or rearrange in the binding site. In this work, we focus on several molecular dynamics (MD) simulation-based methods attempting to help rehydrate buried water sites: BLUES, using nonequilibrium candidate Monte Carlo (NCMC); grand, using grand canonical Monte Carlo (GCMC); and normal MD. We assess the accuracy and efficiency of these methods in rehydrating target water sites. We selected a range of systems with varying numbers of waters in the binding site, as well as those where water occupancy is coupled to the identity or binding mode of the ligand. We analyzed the rehydration of buried water sites in binding pockets using both clustering of trajectories and direct analysis of electron density maps. Our results suggest both BLUES and grand enhance water sampling relative to normal MD and grand is more robust than BLUES, but also that water sampling remains a major challenge for all of the methods tested. The lessons we learned for these methods and systems are discussed.

How much can physics do for protein design?

Physics and physical chemistry are an important thread in computational protein design, complementary to knowledge-based tools. They provide molecular mechanics scoring functions that need little or no ad hoc parameter readjustment, methods to thoroughly sample equilibrium ensembles, and different levels of approximation for conformational flexibility. They led recently to the successful redesign of a small protein using a physics-based folded state energy. Adaptive Monte Carlo or molecular dynamics schemes were discovered where protein variants are populated as per their ligand-binding free energy or catalytic efficiency. Molecular dynamics have been used for backbone flexibility. Implicit solvent models have been refined, polarizable force fields applied, and many physical insights obtained.

Enhancing water sampling of buried binding sites using nonequilibrium candidate Monte Carlo

Water molecules can be found interacting with the surface and within cavities in proteins. However, water exchange between bulk and buried hydration sites can be slow compared to simulation timescales, thus leading to the inefficient sampling of the locations of water. This can pose problems for free energy calculations for computer-aided drug design. Here, we apply a hybrid method that combines nonequilibrium candidate Monte Carlo (NCMC) simulations and molecular dynamics (MD) to enhance sampling of water in specific areas of a system, such as the binding site of a protein. Our approach uses NCMC to gradually remove interactions between a selected water molecule and its environment, then translates the water to a new region, before turning the interactions back on. This approach of gradual removal of interactions, followed by a move and then reintroduction of interactions, allows the environment to relax in response to the proposed water translation, improving acceptance of moves and thereby accelerating water exchange and sampling. We validate this approach on several test systems including the ligand-bound MUP-1 and HSP90 proteins with buried crystallographic waters removed. We show that our BLUES (NCMC/MD) method enhances water sampling relative to normal MD when applied to these systems. Thus, this approach provides a strategy to improve water sampling in molecular simulations which may be useful in practical applications in drug discovery and biomolecular design.

Reversibly Sampling Conformations and Binding Modes Using Molecular Darting

Sampling multiple binding modes of a ligand in a single molecular dynamics simulation is difficult. A given ligand may have many internal degrees of freedom, along with many different ways it might orient itself in a binding site or across several binding sites, all of which might be separated by large energy barriers. We have developed a novel Monte Carlo move called molecular darting (MolDarting) to reversibly sample between predefined binding modes of a ligand. Here, we couple this with nonequilibrium candidate Monte Carlo (NCMC) to improve acceptance of moves. We apply this technique to a simple dipeptide system, a ligand binding to T4 lysozyme L99A, and ligand binding to HIV integrase to test this new method. We observe significant increases in acceptance compared to uniformly sampling the internal and rotational/translational degrees of freedom in these systems.

Binding-Induced Unfolding of 1-Bromopropane in α-Cyclodextrin

Raman multivariate curve resolution vibrational spectroscopy and X-ray crystallography are used to quantify changes in the gauche-trans conformational equilibrium of 1-bromopropane (1-BP) upon binding to α-cyclodextrin (α-CD). Both conformers of 1-BP are found to bind to α-CD, although binding favors the unfolded trans conformation. Temperature-dependent measurements of the binding-induced change in the 1-BP conformation equilibrium constant indicate that the trans conformer is both enthalpically and entropically stabilized in the host cavity.

Best Practices for Alchemical Free Energy Calculations [Article v1.0]

Alchemical free energy calculations are a useful tool for predicting free energy differences associated with the transfer of molecules from one environment to another. The hallmark of these methods is the use of "bridging" potential energy functions representing alchemical intermediate states that cannot exist as real chemical species. The data collected from these bridging alchemical thermodynamic states allows the efficient computation of transfer free energies (or differences in transfer free energies) with orders of magnitude less simulation time than simulating the transfer process directly. While these methods are highly flexible, care must be taken in avoiding common pitfalls to ensure that computed free energy differences can be robust and reproducible for the chosen force field, and that appropriate corrections are included to permit direct comparison with experimental data. In this paper, we review current best practices for several popular application domains of alchemical free energy calculations performed with equilibrium simulations, in particular relative and absolute small molecule binding free energy calculations to biomolecular targets.