Resolving coupled pH titrations using alchemical free energy calculations.

In a protein, nearby titratable sites can be coupled: the (de)protonation of one may affect the other. The degree of this interaction depends on several factors and can influence the measured p K a . Here, we derive a formalism based on double free energy differences ( Δ Δ G ) for quantifying the individual site p K a values of coupled residues. As Δ Δ G values can be obtained by means of alchemical free energy calculations, the presented approach allows for a convenient estimation of coupled residue p K a s in practice. We demonstrate that our approach and a previously proposed microscopic p K a formalism, can be combined with alchemical free energy calculations to resolve pH-dependent protein p K a values. Toy models and both, regular and constant-pH molecular dynamics simulations, alongside experimental data, are used to validate this approach. Our results highlight the insights gleaned when coupling and microstate probabilities are analyzed and suggest extensions to more complex enzymatic contexts. Furthermore, we find that naïvely computed p K a values that ignore coupling, can be significantly improved when coupling is accounted for, in some cases reducing the error by half. In short, alchemical free energy methods can resolve the p K a values of both uncoupled and coupled residues.

Guidelines for Free-Energy Calculations Involving Charge Changes.

The Coulomb interactions in molecular simulations are inherently approximated due to the finite size of the molecular box sizes amenable to current-day compute power. Several methods exist for treating long-range electrostatic interactions, yet these approaches are subject to various finite-size-related artifacts. Lattice-sum methods are frequently used to approximate long-range interactions; however, these approaches also suffer from artifacts which become particularly pronounced for free-energy calculations that involve charge changes. The artifacts, however, also affect the sampling when plain simulations are performed, leading to a biased ensemble. Here, we investigate two previously described model systems to determine if artifacts continue to play a role when overall neutral boxes are considered, in the context of both free-energy calculations and sampling. We find that ensuring that no net-charge changes take place, while maintaining a neutral simulation box, may be sufficient provided that the simulation boxes are large enough. Addition of salt to the solution (when appropriate) can further alleviate the remaining artifacts in the sampling or the calculated free-energy differences. We provide practical guidelines to avoid finite-size artifacts.

Accurately Predicting Protein pKa Values Using Nonequilibrium Alchemy.

The stability, solubility, and function of a protein depend on both its net charge and the protonation states of its individual residues. pKa is a measure of the tendency for a given residue to (de)protonate at a specific pH. Although pKa values can be resolved experimentally, theory and computation provide a compelling alternative. To this end, we assess the applicability of a nonequilibrium (NEQ) alchemical free energy method to the problem of pKa prediction. On a data set of 144 residues that span 13 proteins, we report an average unsigned error of 0.77 ± 0.09, 0.69 ± 0.09, and 0.52 ± 0.04 pK for aspartate, glutamate, and lysine, respectively. This is comparable to current state-of-the-art predictors and the accuracy recently reached using free energy perturbation methods (e.g., FEP+). Moreover, we demonstrate that our open-source, pmx-based approach can accurately resolve the pKa values of coupled residues and observe a substantial performance disparity associated with the lysine partial charges in Amber14SB/Amber99SB*-ILDN, for which an underused fix already exists.

Broadening the Scope of Binding Free Energy Calculations Using a Separated Topologies Approach.

Binding free energy calculations predict the potency of compounds to protein binding sites in a physically rigorous manner and see broad application in prioritizing the synthesis of novel drug candidates. Relative binding free energy (RBFE) calculations have emerged as an industry-standard approach to achieve highly accurate rank-order predictions of the potency of related compounds; however, this approach requires that the ligands share a common scaffold and a common binding mode, restricting the methods' domain of applicability. This is a critical limitation since complex modifications to the ligands, especially core hopping, are very common in drug design. Absolute binding free energy (ABFE) calculations are an alternate method that can be used for ligands that are not congeneric. However, ABFE suffers from a known problem of long convergence times due to the need to sample additional degrees of freedom within each system, such as sampling rearrangements necessary to open and close the binding site. Here, we report on an alternative method for RBFE, called Separated Topologies (SepTop), which overcomes the issues in both of the aforementioned methods by enabling large scaffold changes between ligands with a convergence time comparable to traditional RBFE. Instead of only mutating atoms that vary between two ligands, this approach performs two absolute free energy calculations at the same time in opposite directions, one for each ligand. Defining the two ligands independently allows the comparison of the binding of diverse ligands without the artificial constraints of identical poses or a suitable atom-atom mapping. This approach also avoids the need to sample the unbound state of the protein, making it more efficient than absolute binding free energy calculations. Here, we introduce an implementation of SepTop. We developed a general and efficient protocol for running SepTop, and we demonstrated the method on four diverse, pharmaceutically relevant systems. We report the performance of the method, as well as our practical insights into the strengths, weaknesses, and challenges of applying this method in an industrial drug design setting. We find that the accuracy of the approach is sufficiently high to rank order ligands with an accuracy comparable to traditional RBFE calculations while maintaining the additional flexibility of SepTop.

Development and Benchmarking of Open Force Field 2.0.0: The Sage Small Molecule Force Field.

We introduce the Open Force Field (OpenFF) 2.0.0 small molecule force field for drug-like molecules, code-named Sage, which builds upon our previous iteration, Parsley. OpenFF force fields are based on direct chemical perception, which generalizes easily to highly diverse sets of chemistries based on substructure queries. Like the previous OpenFF iterations, the Sage generation of OpenFF force fields was validated in protein-ligand simulations to be compatible with AMBER biopolymer force fields. In this work, we detail the methodology used to develop this force field, as well as the innovations and improvements introduced since the release of Parsley 1.0.0. One particularly significant feature of Sage is a set of improved Lennard-Jones (LJ) parameters retrained against condensed phase mixture data, the first refit of LJ parameters in the OpenFF small molecule force field line. Sage also includes valence parameters refit to a larger database of quantum chemical calculations than previous versions, as well as improvements in how this fitting is performed. Force field benchmarks show improvements in general metrics of performance against quantum chemistry reference data such as root-mean-square deviations (RMSD) of optimized conformer geometries, torsion fingerprint deviations (TFD), and improved relative conformer energetics (ΔΔE). We present a variety of benchmarks for these metrics against our previous force fields as well as in some cases other small molecule force fields. Sage also demonstrates improved performance in estimating physical properties, including comparison against experimental data from various thermodynamic databases for small molecule properties such as ΔHmix, ρ(x), ΔGsolv, and ΔGtrans. Additionally, we benchmarked against protein-ligand binding free energies (ΔGbind), where Sage yields results statistically similar to previous force fields. All the data is made publicly available along with complete details on how to reproduce the training results at https://github.com/openforcefield/openff-sage.

Automated relative binding free energy calculations from SMILES to ΔΔG.

In drug discovery, computational methods are a key part of making informed design decisions and prioritising experiments. In particular, optimizing compound affinity is a central concern during the early stages of development. In the last 10 years, alchemical free energy (FE) calculations have transformed our ability to incorporate accurate in silico potency predictions in design decisions, and represent the 'gold standard' for augmenting experiment-driven drug discovery. However, relative FE calculations are complex to set up, require significant expert intervention to prepare the calculation and analyse the results or are provided only as closed-source software, not allowing for fine-grained control over the underlying settings. In this work, we introduce an end-to-end relative FE workflow based on the non-equilibrium switching approach that facilitates calculation of binding free energies starting from SMILES strings. The workflow is implemented using fully modular steps, allowing various components to be exchanged depending on licence availability. We further investigate the dependence of the calculated free energy accuracy on the initial ligand pose generated by various docking algorithms. We show that both commercial and open-source docking engines can be used to generate poses that lead to good correlation of free energies with experimental reference data.

Chemical Space Exploration with Active Learning and Alchemical Free Energies.

Drug discovery can be thought of as a search for a needle in a haystack: searching through a large chemical space for the most active compounds. Computational techniques can narrow the search space for experimental follow up, but even they become unaffordable when evaluating large numbers of molecules. Therefore, machine learning (ML) strategies are being developed as computationally cheaper complementary techniques for navigating and triaging large chemical libraries. Here, we explore how an active learning protocol can be combined with first-principles based alchemical free energy calculations to identify high affinity phosphodiesterase 2 (PDE2) inhibitors. We first calibrate the procedure using a set of experimentally characterized PDE2 binders. The optimized protocol is then used prospectively on a large chemical library to navigate toward potent inhibitors. In the active learning cycle, at every iteration a small fraction of compounds is probed by alchemical calculations and the obtained affinities are used to train ML models. With successive rounds, high affinity binders are identified by explicitly evaluating only a small subset of compounds in a large chemical library, thus providing an efficient protocol that robustly identifies a large fraction of true positives.

Pre-exascale HPC approaches for molecular dynamics simulations. Covid-19 research: A use case.

Exascale computing has been a dream for ages and is close to becoming a reality that will impact how molecular simulations are being performed, as well as the quantity and quality of the information derived for them. We review how the biomolecular simulations field is anticipating these new architectures, making emphasis on recent work from groups in the BioExcel Center of Excellence for High Performance Computing. We exemplified the power of these simulation strategies with the work done by the HPC simulation community to fight Covid-19 pandemics. This article is categorized under:Data Science > Computer Algorithms and ProgrammingData Science > Databases and Expert SystemsMolecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods.

A litmus test for classifying recognition mechanisms of transiently binding proteins.

Partner recognition in protein binding is critical for all biological functions, and yet, delineating its mechanism is challenging, especially when recognition happens within microseconds. We present a theoretical and experimental framework based on straight-forward nuclear magnetic resonance relaxation dispersion measurements to investigate protein binding mechanisms on sub-millisecond timescales, which are beyond the reach of standard rapid-mixing experiments. This framework predicts that conformational selection prevails on ubiquitin's paradigmatic interaction with an SH3 (Src-homology 3) domain. By contrast, the SH3 domain recognizes ubiquitin in a two-state binding process. Subsequent molecular dynamics simulations and Markov state modeling reveal that the ubiquitin conformation selected for binding exhibits a characteristically extended C-terminus. Our framework is robust and expandable for implementation in other binding scenarios with the potential to show that conformational selection might be the design principle of the hubs in protein interaction networks.

GROMACS in the Cloud: A Global Supercomputer to Speed Up Alchemical Drug Design.

We assess costs and efficiency of state-of-the-art high-performance cloud computing and compare the results to traditional on-premises compute clusters. Our use case is atomistic simulations carried out with the GROMACS molecular dynamics (MD) toolkit with a particular focus on alchemical protein-ligand binding free energy calculations. We set up a compute cluster in the Amazon Web Services (AWS) cloud that incorporates various different instances with Intel, AMD, and ARM CPUs, some with GPU acceleration. Using representative biomolecular simulation systems, we benchmark how GROMACS performs on individual instances and across multiple instances. Thereby we assess which instances deliver the highest performance and which are the most cost-efficient ones for our use case. We find that, in terms of total costs, including hardware, personnel, room, energy, and cooling, producing MD trajectories in the cloud can be about as cost-efficient as an on-premises cluster given that optimal cloud instances are chosen. Further, we find that high-throughput ligand-screening can be accelerated dramatically by using global cloud resources. For a ligand screening study consisting of 19 872 independent simulations or ∼200 µs of combined simulation trajectory, we made use of diverse hardware available in the cloud at the time of the study. The computations scaled-up to reach peak performance using more than 4 000 instances, 140 000 cores, and 3 000 GPUs simultaneously. Our simulation ensemble finished in about 2 days in the cloud, while weeks would be required to complete the task on a typical on-premises cluster consisting of several hundred nodes.

Pre-Exascale Computing of Protein-Ligand Binding Free Energies with Open Source Software for Drug Design.

Nowadays, drug design projects benefit from highly accurate protein-ligand binding free energy predictions based on molecular dynamics simulations. While such calculations have been computationally expensive in the past, we now demonstrate that workflows built on open source software packages can efficiently leverage pre-exascale computing resources to screen hundreds of compounds in a matter of days. We report our results of free energy calculations on a large set of pharmaceutically relevant targets assembled to reflect industrial drug discovery projects.

Repositioning Food and Drug Administration-Approved Drugs for Inhibiting Biliverdin IXß Reductase B as a Novel Thrombocytopenia Therapeutic Target.

Biliverdin IXß reductase B (BLVRB) has recently been proposed as a novel therapeutic target for thrombocytopenia through its reactive oxygen species (ROS)-associated mechanism. Thus, we aim at repurposing drugs as new inhibitors of BLVRB. Based on IC50 (<5 µM), we have identified 20 compounds out of 1496 compounds from the Food and Drug Administration (FDA)-approved library and have clearly mapped their binding sites to the active site. Furthermore, we show the detailed BLVRB-binding modes and thermodynamic properties (ΔH, ΔS, and KD) with nuclear magnetic resonance (NMR) and isothermal titration calorimetry together with complex structures of eight water-soluble compounds. We anticipate that the results will serve as a novel platform for further in-depth studies on BLVRB effects for related functions such as ROS accumulation and megakaryocyte differentiation, and ultimately treatments of platelet disorders.

Challenges Encountered Applying Equilibrium and Nonequilibrium Binding Free Energy Calculations.

Binding free energy calculations have become increasingly valuable to drive decision making in drug discovery projects. However, among other issues, inadequate sampling can reduce accuracy, limiting the value of the technique. In this paper, we apply absolute binding free energy calculations to ligands binding to T4 lysozyme L99A and HSP90 using equilibrium and nonequilibrium approaches. We highlight sampling problems encountered in these systems, such as slow side chain rearrangements and slow changes of water placement upon ligand binding. These same types of challenges are also likely to show up in other protein-ligand systems, and we propose some strategies to diagnose and test for such problems in alchemical free energy calculations. We also explore similarities and differences in how the equilibrium and the nonequilibrium approaches handle these problems. Our results show the large amount of work still to be done to make free energy calculations robust and reliable and provide insight for future research in this area.

One Plus One Makes Three: Triangular Coupling of Correlated Amino Acid Mutations.

Correlated mutations have played a pivotal role in the recent success in protein fold prediction. Understanding nonadditive effects of mutations is crucial for altering protein structure, as mutations of multiple residues may change protein stability or binding affinity in a manner unforeseen by the investigation of single mutants. While the couplings between amino acids can be inferred from homologous protein sequences, the physical mechanisms underlying these correlations remain elusive. In this work we demonstrate that calculations based on the first-principles of statistical mechanics are capable of capturing the effects of nonadditivities in protein mutations. The identified thermodynamic couplings cover the short-range as well as previously unknown long-range correlations. We further explore a set of mutations in staphyloccocal nuclease to unravel an intricate interaction pathway underlying the correlations between amino acid mutations.

Accurate absolute free energies for ligand-protein binding based on non-equilibrium approaches.

The accurate calculation of the binding free energy for arbitrary ligand-protein pairs is a considerable challenge in computer-aided drug discovery. Recently, it has been demonstrated that current state-of-the-art molecular dynamics (MD) based methods are capable of making highly accurate predictions. Conventional MD-based approaches rely on the first principles of statistical mechanics and assume equilibrium sampling of the phase space. In the current work we demonstrate that accurate absolute binding free energies (ABFE) can also be obtained via theoretically rigorous non-equilibrium approaches. Our investigation of ligands binding to bromodomains and T4 lysozyme reveals that both equilibrium and non-equilibrium approaches converge to the same results. The non-equilibrium approach achieves the same level of accuracy and convergence as an equilibrium free energy perturbation (FEP) method enhanced by Hamiltonian replica exchange. We also compare uni- and bi-directional non-equilibrium approaches and demonstrate that considering the work distributions from both forward and reverse directions provides substantial accuracy gains. In summary, non-equilibrium ABFE calculations are shown to yield reliable and well-converged estimates of protein-ligand binding affinity.

Non-equilibrium approach for binding free energies in cyclodextrins in SAMPL7: force fields and software.

In the current work we report on our participation in the SAMPL7 challenge calculating absolute free energies of the host-guest systems, where 2 guest molecules were probed against 9 hosts-cyclodextrin and its derivatives. Our submission was based on the non-equilibrium free energy calculation protocol utilizing an averaged consensus result from two force fields (GAFF and CGenFF). The submitted prediction achieved accuracy of [Formula: see text] in terms of the unsigned error averaged over the whole dataset. Subsequently, we further report on the underlying reasons for discrepancies between our calculations and another submission to the SAMPL7 challenge which employed a similar methodology, but disparate ligand and water force fields. As a result we have uncovered a number of issues in the dihedral parameter definition of the GAFF 2 force field. In addition, we identified particular cases in the molecular topologies where different software packages had a different interpretation of the same force field. This latter observation might be of particular relevance for systematic comparisons of molecular simulation software packages. The aforementioned factors have an influence on the final free energy estimates and need to be considered when performing alchemical calculations.

Polycation-Anionic Lipid Membrane Interactions.

Natural or synthetic polycations are used as biocides or as drug/gene carriers. Understanding the interactions between these macromolecules and cell membranes at the molecular level is therefore of great importance for the design of effective polymer biocides or biocompatible polycation-based delivery systems. Until now, details of the processes at the interface between polycations and biological systems have not been fully recognized. In this study, we consider the effect of strong polycations with quaternary ammonium groups on the properties of anionic lipid membranes that we use as a model system for protein-free cell membranes. For this purpose, we employed experimental measurements and atomic-scale molecular dynamics (MD) simulations. MD simulations reveal that the polycations are strongly hydrated in the aqueous phase and do not lose the water shell after adsorption at the bilayer surface. As a result of strong hydration, the polymer chains reside at the phospholipid headgroup and do not penetrate to the acyl chain region. The polycation adsorption involves the formation of anionic lipid-rich domains, and the density of anionic lipids in these domains depends on the length of the polycation chain. We observed the accumulation of anionic lipids only in the leaflet interacting with the polymer, which leads to the formation of compositionally asymmetric domains. Asymmetric adsorption of the polycation on only one leaflet of the anionic membrane strongly affects the membrane properties in the polycation-membrane contact areas: (i) anionic lipid accumulates in the region near the adsorbed polymer, (ii) acyl chain ordering and lipid packing are reduced, which results in a decrease in the thickness of the bilayer, and (iii) polycation-anionic membrane interactions are strongly influenced by the presence and concentration of salt. Our results provide an atomic-scale description of the interactions of polycations with anionic lipid bilayers and are fully supported by the experimental data. The outcomes are important for understanding the correlation of the structure of polycations with their activity on biomembranes.

On the importance of statistics in molecular simulations for thermodynamics, kinetics and simulation box size.

Computational simulations, akin to wetlab experimentation, are subject to statistical fluctuations. Assessing the magnitude of these fluctuations, that is, assigning uncertainties to the computed results, is of critical importance to drawing statistically reliable conclusions. Here, we use a simulation box size as an independent variable, to demonstrate how crucial it is to gather sufficient amounts of data before drawing any conclusions about the potential thermodynamic and kinetic effects. In various systems, ranging from solvation free energies to protein conformational transition rates, we showcase how the proposed simulation box size effect disappears with increased sampling. This indicates that, if at all, the simulation box size only minimally affects both the thermodynamics and kinetics of the type of biomolecular systems presented in this work.

Non-active site mutants of HIV-1 protease influence resistance and sensitisation towards protease inhibitors.

BACKGROUND: HIV-1 can develop resistance to antiretroviral drugs, mainly through mutations within the target regions of the drugs. In HIV-1 protease, a majority of resistance-associated mutations that develop in response to therapy with protease inhibitors are found in the protease's active site that serves also as a binding pocket for the protease inhibitors, thus directly impacting the protease-inhibitor interactions. Some resistance-associated mutations, however, are found in more distant regions, and the exact mechanisms how these mutations affect protease-inhibitor interactions are unclear. Furthermore, some of these mutations, e.g. N88S and L76V, do not only induce resistance to the currently administered drugs, but contrarily induce sensitivity towards other drugs. In this study, mutations N88S and L76V, along with three other resistance-associated mutations, M46I, I50L, and I84V, are analysed by means of molecular dynamics simulations to investigate their role in complexes of the protease with different inhibitors and in different background sequence contexts. RESULTS: Using these simulations for alchemical calculations to estimate the effects of mutations M46I, I50L, I84V, N88S, and L76V on binding free energies shows they are in general in line with the mutations' effect on [Formula: see text] values. For the primary mutation L76V, however, the presence of a background mutation M46I in our analysis influences whether the unfavourable effect of L76V on inhibitor binding is sufficient to outweigh the accompanying reduction in catalytic activity of the protease. Finally, we show that L76V and N88S changes the hydrogen bond stability of these residues with residues D30/K45 and D30/T31/T74, respectively. CONCLUSIONS: We demonstrate that estimating the effect of both binding pocket and distant mutations on inhibitor binding free energy using alchemical calculations can reproduce their effect on the experimentally measured [Formula: see text] values. We show that distant site mutations L76V and N88S affect the hydrogen bond network in the protease's active site, which offers an explanation for the indirect effect of these mutations on inhibitor binding. This work thus provides valuable insights on interplay between primary and background mutations and mechanisms how they affect inhibitor binding.

The SAMPL6 SAMPLing challenge: assessing the reliability and efficiency of binding free energy calculations.

Approaches for computing small molecule binding free energies based on molecular simulations are now regularly being employed by academic and industry practitioners to study receptor-ligand systems and prioritize the synthesis of small molecules for ligand design. Given the variety of methods and implementations available, it is natural to ask how the convergence rates and final predictions of these methods compare. In this study, we describe the concept and results for the SAMPL6 SAMPLing challenge, the first challenge from the SAMPL series focusing on the assessment of convergence properties and reproducibility of binding free energy methodologies. We provided parameter files, partial charges, and multiple initial geometries for two octa-acid (OA) and one cucurbit[8]uril (CB8) host-guest systems. Participants submitted binding free energy predictions as a function of the number of force and energy evaluations for seven different alchemical and physical-pathway (i.e., potential of mean force and weighted ensemble of trajectories) methodologies implemented with the GROMACS, AMBER, NAMD, or OpenMM simulation engines. To rank the methods, we developed an efficiency statistic based on bias and variance of the free energy estimates. For the two small OA binders, the free energy estimates computed with alchemical and potential of mean force approaches show relatively similar variance and bias as a function of the number of energy/force evaluations, with the attach-pull-release (APR), GROMACS expanded ensemble, and NAMD double decoupling submissions obtaining the greatest efficiency. The differences between the methods increase when analyzing the CB8-quinine system, where both the guest size and correlation times for system dynamics are greater. For this system, nonequilibrium switching (GROMACS/NS-DS/SB) obtained the overall highest efficiency. Surprisingly, the results suggest that specifying force field parameters and partial charges is insufficient to generally ensure reproducibility, and we observe differences between seemingly converged predictions ranging approximately from 0.3 to 1.0 kcal/mol, even with almost identical simulations parameters and system setup (e.g., Lennard-Jones cutoff, ionic composition). Further work will be required to completely identify the exact source of these discrepancies. Among the conclusions emerging from the data, we found that Hamiltonian replica exchange-while displaying very small variance-can be affected by a slowly-decaying bias that depends on the initial population of the replicas, that bidirectional estimators are significantly more efficient than unidirectional estimators for nonequilibrium free energy calculations for systems considered, and that the Berendsen barostat introduces non-negligible artifacts in expanded ensemble simulations.