Advances in the calculation of binding free energies

An Efficient Approach to the Accurate Prediction of Mutational Effects in Antigen Binding to the MHC1

The major histocompatibility complex (MHC) can recognize and bind to external peptides to generate effective immune responses by presenting the peptides to T cells. Therefore, understanding the binding modes of peptide-MHC complexes (pMHC) and predicting the binding affinity of pMHCs play a crucial role in the rational design of peptide vaccines. In this study, we employed molecular dynamics (MD) simulations and free energy calculations with an Alanine Scanning with Generalized Born and Interaction Entropy (ASGBIE) method to investigate the protein-peptide interaction between HLA-A*02:01 and the G9209 peptide derived from the melanoma antigen gp100. The energy contribution of individual residue was calculated using alanine scanning, and hotspots on both the MHC and the peptides were identified. Our study shows that the pMHC binding is dominated by the van der Waals interactions. Furthermore, we optimized the ASGBIE method, achieving a Pearson correlation coefficient of 0.91 between predicted and experimental binding affinity for mutated antigens. This represents a significant improvement over the conventional MM/GBSA method, which yields a Pearson correlation coefficient of 0.22. The computational protocol developed in this study can be applied to the computational screening of antigens for the MHC1 as well as other protein-peptide binding systems.

Biomolecular dynamics in the 21st century

The relevance of motions in biological macromolecules has been clear since the early structural analyses of proteins by X-ray crystallography. Computer simulations have been applied to provide a deeper understanding of the dynamics of biological macromolecules since 1976, and are now a standard tool in many labs working on the structure and function of biomolecules. In this mini-review we highlight some areas of current interest and active development for simulations, in particular all-atom molecular dynamics simulations.

Introduction to Computational Biomedicine

The domain of computational biomedicine is a new and burgeoning one. Its areas of concern cover all scales of human biology, physiology, and pathology, commonly referred to as medicine, from the genomic to the whole human and beyond, including epidemiology and population health. Computational biomedicine aims to provide high-fidelity descriptions and predictions of the behavior of biomedical systems of both fundamental scientific and clinical importance. Digital twins and virtual humans aim to reproduce the extremely accurate duplicate of real-world human beings in cyberspace, which can be used to make highly accurate predictions that take complicated conditions into account. When that can be done reliably enough for the predictions to be actionable, such an approach will make an impact in the pharmaceutical industry by reducing or even replacing the extremely laboratory-intensive preclinical process of making and testing compounds in laboratories, and in clinical applications by assisting clinicians to make diagnostic and treatment decisions.

Improving Speed and Affordability without Compromising Accuracy: Standard Binding Free-Energy Calculations Using an Enhanced Sampling Algorithm, Multiple-Time Stepping, and Hydrogen Mass Repartitioning

Accurate evaluation of protein-ligand binding free energies in silico is of paramount importance for understanding the mechanisms of biological regulation and providing a theoretical basis for drug design and discovery. Based on a series of atomistic molecular dynamics simulations in an explicit solvent, using well-tempered metadynamics extended adaptive biasing force (WTM-eABF) as an enhanced sampling algorithm, the so-called "geometrical route" offers a rigorous theoretical framework for binding affinity calculations that match experimental values. However, although robust, this strategy remains expensive, requiring substantial computational time to achieve convergence of the simulations. Improving the efficiency of the geometrical route, while preserving its reliability through improved ergodic sampling, is, therefore, highly desirable. In this contribution, having identified the computational bottleneck of the geometrical route, to accelerate the calculations we combine (i) a longer time step for the integration of the equations of motion with hydrogen-mass repartitioning (HMR), and (ii) multiple time-stepping (MTS) for collective-variable and biasing-force evaluation. Altogether, we performed 50 independent WTM-eABF simulations in triplicate for the "physical" separation of the Abl kinase-SH3 domain:p41 complex, following different HMR and MTS schemes, while tuning, in distinct protocols, the parameters of the enhanced-sampling algorithm. To demonstrate the consistency and reliability of the results obtained with the best-performing setups, we carried out quintuple simulations. Furthermore, we demonstrated the transferability of our method to other complexes by triplicating a 200 ns separation simulation of nine chosen protocols for the MDM2-p53:NVP-CGM097 complex. [Holzer et al. J. Med. Chem. 2015, 58, 6348-6358.] Our results, based on an aggregate simulation time of 14.4 μs, allowed an optimal set of parameters to be identified, able to accelerate convergence by a factor of three without any noticeable loss of accuracy.

The nucleotide excision repair proteins through the lens of molecular dynamics simulations

Mutations that affect the proteins responsible for the nucleotide excision repair (NER) pathway can lead to diseases such as xeroderma pigmentosum, trichothiodystrophy, Cockayne syndrome, and Cerebro-oculo-facio-skeletal syndrome. Hence, understanding their molecular behavior is needed to elucidate these diseases' phenotypes and how the NER pathway is organized and coordinated. Molecular dynamics techniques enable the study of different protein conformations, adaptable to any research question, shedding light on the dynamics of biomolecules. However, as important as they are, molecular dynamics studies focused on DNA repair pathways are still becoming more widespread. Currently, there are no review articles compiling the advancements made in molecular dynamics approaches applied to NER and discussing: (i) how this technique is currently employed in the field of DNA repair, focusing on NER proteins; (ii) which technical setups are being employed, their strengths and limitations; (iii) which insights or information are they providing to understand the NER pathway or NER-associated proteins; (iv) which open questions would be suited for this technique to answer; and (v) where can we go from here. These questions become even more crucial considering the numerous 3D structures published regarding the NER pathway's proteins in recent years. In this work, we tackle each one of these questions, revising and critically discussing the results published in the context of the NER pathway.

Computational approaches for the design of modulators targeting protein-protein interactions

BACKGROUND

Protein-protein interactions (PPIs) are intriguing targets for designing novel small-molecule inhibitors. The role of PPIs in various infectious and neurodegenerative disorders makes them potential therapeutic targets . Despite being portrayed as undruggable targets, due to their flat surfaces, disorderedness, and lack of grooves. Recent progresses in computational biology have led researchers to reconsider PPIs in drug discovery.

AREAS COVERED

In this review, we introduce in-silico methods used to identify PPI interfaces and present an in-depth overview of various computational methodologies that are successfully applied to annotate the PPIs. We also discuss several successful case studies that use computational tools to understand PPIs modulation and their key roles in various physiological processes.

EXPERT OPINION

Computational methods face challenges due to the inherent flexibility of proteins, which makes them expensive, and result in the use of rigid models. This problem becomes more significant in PPIs due to their flexible and flat interfaces. Computational methods like molecular dynamics (MD) simulation and machine learning can integrate the chemical structure data into biochemical and can be used for target identification and modulation. These computational methodologies have been crucial in understanding the structure of PPIs, designing PPI modulators, discovering new drug targets, and predicting treatment outcomes.

Structural predictions of protein-DNA binding: MELD-DNA

Structural, regulatory and enzymatic proteins interact with DNA to maintain a healthy and functional genome. Yet, our structural understanding of how proteins interact with DNA is limited. We present MELD-DNA, a novel computational approach to predict the structures of protein-DNA complexes. The method combines molecular dynamics simulations with general knowledge or experimental information through Bayesian inference. The physical model is sensitive to sequence-dependent properties and conformational changes required for binding, while information accelerates sampling of bound conformations. MELD-DNA can: (i) sample multiple binding modes; (ii) identify the preferred binding mode from the ensembles; and (iii) provide qualitative binding preferences between DNA sequences. We first assess performance on a dataset of 15 protein-DNA complexes and compare it with state-of-the-art methodologies. Furthermore, for three selected complexes, we show sequence dependence effects of binding in MELD predictions. We expect that the results presented herein, together with the freely available software, will impact structural biology (by complementing DNA structural databases) and molecular recognition (by bringing new insights into aspects governing protein-DNA interactions).

Prioritizing Small Sets of Molecules for Synthesis through in-silico Tools: A Comparison of Common Ranking Methods

Prioritizing molecules for synthesis is a key role of computational methods within medicinal chemistry. Multiple tools exist for ranking molecules, from the cheap and popular molecular docking methods to more computationally expensive molecular-dynamics (MD)-based methods. It is often questioned whether the accuracy of the more rigorous methods justifies the higher computational cost and associated calculation time. Here, we compared the performance on ranking the binding of small molecules for seven scoring functions from five docking programs, one end-point method (MM/GBSA), and two MD-based free energy methods (PMX, FEP+). We investigated 16 pharmaceutically relevant targets with a total of 423 known binders. The performance of docking methods for ligand ranking was strongly system dependent. We observed that MD-based methods predominantly outperformed docking algorithms and MM/GBSA calculations. Based on our results, we recommend the application of MD-based free energy methods for prioritization of molecules for synthesis in lead optimization, whenever feasible.

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.

A Physics-Guided Neural Network for Predicting Protein–Ligand Binding Free Energy: From Host–Guest Systems to the PDBbind Database

Calculation of protein–ligand binding affinity is a cornerstone of drug discovery. Classic implicit solvent models, which have been widely used to accomplish this task, lack accuracy compared to experimental references. Emerging data-driven models, on the other hand, are often accurate yet not fully interpretable and also likely to be overfitted. In this research, we explore the application of Theory-Guided Data Science in studying protein–ligand binding. A hybrid model is introduced by integrating Graph Convolutional Network (data-driven model) with the GBNSR6 implicit solvent (physics-based model). The proposed physics-data model is tested on a dataset of 368 complexes from the PDBbind refined set and 72 host–guest systems. Results demonstrate that the proposed Physics-Guided Neural Network can successfully improve the “accuracy” of the pure data-driven model. In addition, the “interpretability” and “transferability” of our model have boosted compared to the purely data-driven model. Further analyses include evaluating model robustness and understanding relationships between the physical features.

Improving the Potential of Mean Force and Nonequilibrium Pulling Simulations by Simultaneous Alchemical Modifications

We present an approach combining alchemical modifications and physical-pathway methods to calculate absolute binding free energies. The employed physical-pathway method is either a stratified umbrella sampling to calculate a potential of mean force or nonequilibrium pulling. We devised two basic approaches: the simultaneous approach (S-approach), where, along the physical unbinding pathway, an alchemical transformation of ligand-protein interactions is installed and deinstalled, and the prior-plus-simultaneous approach (PPS-approach), where, prior to the physical-pathway simulation, an alchemical transformation of ligand-protein interactions is installed in the binding site and deinstalled during the physical-pathway simulation. Using a mutant of T4 lysozyme with a benzene ligand as an example, we show that installation and deinstallation of soft-core interactions concurrent with physical ligand unbinding (S-approach) allow successful potential of mean force calculations and nonequilibrium pulling simulations despite the problems posed by the occluded nature of the lysozyme binding pocket. Good agreement between the potential of the mean-force-based S-approach and double decoupling simulations as well as a remarkable efficiency and accuracy of the nonequilibrium-pulling-based S-approach is found. The latter turned out to be more compute-efficient than the potential of mean force calculation by approximately 70%. Furthermore, we illustrate the merits of reducing ligand-protein interactions prior to potential of mean force calculations using the murine double minute homologue protein MDM2 with a p53-derived peptide ligand (PPS-approach). Here, the problem of breaking strong interactions in the binding pocket is transferred to a prior alchemical transformation that reduces the free-energy barrier between the bound and unbound state in the potential of mean force. Besides, disentangling physical ligand displacement from the deinstallation of ligand-protein interactions was seen to allow a more uniform sampling of distance histograms in the umbrella sampling. In the future, physical ligand unbinding combined with simultaneous alchemical modifications may prove useful in the calculation of protein-protein binding free energies, where sampling problems posed by multiple, possibly sticky interactions and potential steric clashes can thus be reduced.

Seeding the multi-dimensional nonequilibrium pulling for Hamiltonian variation: indirect nonequilibrium free energy simulations at QM levels

The combination of free energy simulations in the alchemical and configurational spaces provides a feasible route to access the thermodynamic profiles under a computationally demanding target Hamiltonian. Normally, due to the significant differences between the computational cost of ab initio quantum mechanics (QM) calculations and those of semi-empirical quantum mechanics (SQM) and molecular mechanics (MM), this indirect method could be used to obtain the QM thermodynamics by combining the SQM or MM results and the SQM-to-QM or MM-to-QM corrections. In our previous work, a multi-dimensional nonequilibrium pulling framework for Hamiltonian variations was introduced based on bidirectional pulling and bidirectional reweighting. The method performs nonequilibrium free energy simulations in the configurational space to obtain the thermodynamic profile along the conformational change pathway under a selected computationally efficient Hamiltonian, and uses the nonequilibrium alchemical method to correct or perturb the thermodynamic profile to that under the target Hamiltonian. The BAR-based method is designed to achieve the best generality and transferability and thus leads to modest (∼20 fold) speedup. In this work, we explore the possibility of further accelerating the nonequilibrium free energy simulation by employing unidirectional pulling and using the selection criterion to obtain the initial configurations used to initiate nonequilibrium trajectories following the idea of adaptive steered molecular dynamics (ASMD). A single initial condition is used to seed the whole multi-dimensional nonequilibrium free energy simulation and the sampling is performed fully in the nonequilibrium ensemble. Introducing very short ps-length equilibrium sampling to grab more initial seeds could also be helpful. The ASMD scheme estimates the free energy difference with the unidirectional exponential average (EXP), but it does not follow exactly the requirements of the EXP estimator. Another deficiency of the seeding simulation is the inherently sequential or serial pulling due to the inter-segment dependency, which triggers some problems in the parallelizability of the simulation. Numerical tests are performed to grasp some insights and guidelines for using this selection-criterion-based ASMD scheme. The presented selection-criterion-based multi-dimensional ASMD scheme follows the same perturbation network of the BAR-based method, and thus could be used in various Hamiltonian-variation cases.

Accurate determination of protein:ligand standard binding free energies from molecular dynamics simulations

Designing a reliable computational methodology to calculate protein:ligand standard binding free energies is extremely challenging. The large change in configurational enthalpy and entropy that accompanies the association of ligand and protein is notoriously difficult to capture in naive brute-force simulations. Addressing this issue, the present protocol rests upon a rigorous statistical mechanical framework for the determination of protein:ligand binding affinities together with the comprehensive Binding Free-Energy Estimator 2 (BFEE2) application software. With the knowledge of the bound state, available from experiments or docking, application of the BFEE2 protocol with a reliable force field supplies in a matter of days standard binding free energies within chemical accuracy, for a broad range of protein:ligand complexes. Limiting undesirable human intervention, BFEE2 assists the end user in preparing all the necessary input files and performing the post-treatment of the simulations towards the final estimate of the binding affinity.

Computational Tools for Accurate Binding Free-Energy Prediction

A quantitative thermodynamic understanding of the noncovalent association of (bio)molecules is of central importance in molecular life sciences. An important quantity characterizing (bio)molecular association is the binding affinity or absolute binding free energy. In recent years, the computational prediction of absolute binding free energies has evolved considerably in terms of accuracy, computational speed, and user-friendliness. In this chapter, we first give an overview of how absolute free energies are defined and how they can be determined with computational means. We proceed with an outline of the theoretical basis of the two most reliable methods, potential of mean force, and double decoupling calculations. In particular, we describe how the sampling problem can be alleviated by application of restraints. Finally, we provide step-by-step instructions of how to set up corresponding molecular simulations with a commonly employed molecular dynamics simulation engine.

Explicit solvation thermodynamics in ionic solution: extending grid inhomogeneous solvation theory to solvation free energy of salt-water mixtures

Hydration thermodynamics play a fundamental role in fields ranging from the pharmaceutical industry to environmental research. Numerous methods exist to predict solvation thermodynamics of compounds ranging from small molecules to large biomolecules. Arguably the most precise methods are those based on molecular dynamics (MD) simulations in explicit solvent. One theory that has seen increased use is inhomogeneous solvation theory (IST). However, while many applications require accurate description of salt-water mixtures, no implementation of IST is currently able to estimate solvation properties involving more than one solvent species. Here, we present an extension to grid inhomogeneous solvation theory (GIST) that can take salt contributions into account. At the example of carbazole in 1 M NaCl solution, we compute the solvation energy as well as first and second order entropies. While the effect of the first order ion entropy is small, both the water-water and water-ion entropies contribute strongly. We show that the water-ion entropies are efficiently approximated using the Kirkwood superposition approximation. However, this approach cannot be applied to the water-water entropy. Furthermore, we test the quantitative validity of our method by computing salting-out coefficients and comparing them to experimental data. We find a good correlation to experimental salting-out constants, while the absolute values are overpredicted due to the approximate second order entropy. Since ions are frequently used in MD, either to neutralize the system or as a part of the investigated process, our method greatly extends the applicability of GIST. The use-cases range from biopharmaceuticals, where many assays require high salt concentrations, to environmental research, where solubility in sea water is important to model the fate of organic substances.

Progress in Free Energy Perturbation: Options for Evolving Fragments

One of the remaining bottlenecks in fragment-based drug design (FBDD) is the initial exploration and optimization of the identified hit fragments. There is a growing interest in computational approaches that can guide these efforts by predicting the binding affinity of newly designed analogues. Among others, alchemical free energy (AFE) calculations promise high accuracy at a computational cost that allows their application during lead optimization campaigns. In this review, we discuss how AFE could have a strong impact in fragment evolution, and we raise awareness on the challenges that could be encountered applying this methodology in FBDD studies.

Disruption of Water Networks is the Cause of Human/Mouse Species Selectivity in Urokinase Plasminogen Activator (uPA) Inhibitors Derived from Hexamethylene Amiloride (HMA)

The urokinase plasminogen activator (uPA) plays a critical role in tumor cell invasion and migration and is a promising antimetastasis target. 6-Substituted analogues of 5-N,N-(hexamethylene)amiloride (HMA) are potent and selective uPA inhibitors that lack the diuretic and antikaliuretic properties of the parent drug amiloride. However, the compounds display pronounced selectivity for human over mouse uPA, thus confounding interpretation of data from human xenograft mouse models of cancer. Here, computational and experimental findings reveal that residue 99 is a key contributor to the observed species selectivity, whereby enthalpically unfavorable expulsion of a water molecule by the 5-N,N-hexamethylene ring occurs when residue 99 is Tyr (as in mouse uPA). Analogue 7 lacking the 5-N,N-hexamethylene ring maintained similar water networks when bound to human and mouse uPA and displayed reduced selectivity, thus supporting this conclusion. The study will guide further optimization of dual-potent human/mouse uPA inhibitors from the amiloride class as antimetastasis drugs.

Multiscale Approach for Computing Gated Ligand Binding from Molecular Dynamics and Brownian Dynamics Simulations

We develop an approach to characterize the effects of gating by a multiconformation protein consisting of macrostate conformations that are either accessible or inaccessible to ligand binding. We first construct a Markov state model of the apo-protein from atomistic molecular dynamics simulations from which we identify macrostates and their conformations, compute their relative macrostate populations and interchange kinetics, and structurally characterize them in terms of ligand accessibility. We insert the calculated first-order rate constants for conformational transitions into a multistate gating theory from which we derive a gating factor γ that quantifies the degree of conformational gating. Applied to HIV-1 protease, our approach yields a kinetic network of three accessible (semi-open, open, and wide-open) and two inaccessible (closed and a newly identified, "parted") macrostate conformations. The parted conformation sterically partitions the active site, suggesting a possible role in product release. We find that the binding kinetics of drugs and drug-like inhibitors to HIV-1 protease falls in the slow gating regime. However, because γ = 0.75, conformational gating only modestly slows ligand binding. Brownian dynamics simulations of the diffusional association of eight inhibitors to the protease─having a wide range of experimental association constants (∼10⁴-10¹⁰ M^-1 s^-1)─yields gated rate constants in the range of ∼0.5-5.7 × 10⁸ M^-1 s^-1. This indicates that, whereas the association rate of some inhibitors could be described by the model, for many inhibitors either subsequent conformational transitions or alternate binding mechanisms may be rate-limiting. For systems known to be modulated by conformational gating, the approach could be scaled computationally efficiently to screen association kinetics for a large number of ligands.

Perturbation Free-Energy Toolkit: An Automated Alchemical Topology Builder

Free-energy calculations play an important role in the application of computational chemistry to a range of fields, including protein biochemistry, rational drug design, or materials science. Importantly, the free-energy difference is directly related to experimentally measurable quantities such as partition and adsorption coefficients, water activity, and binding affinities. Among several techniques aimed at predicting free-energy differences, perturbation approaches, involving the alchemical transformation of one molecule into another through intermediate states, stand out as rigorous methods based on statistical mechanics. However, despite the importance of free-energy calculations, the applicability of the perturbation approaches is still largely impeded by a number of challenges, including the definition of the perturbation path, i.e., alchemical changes leading to the transformation of one molecule to the other. To address this, an automatic perturbation topology builder based on a graph-matching algorithm is developed, which can identify the maximum common substructure (MCS) of two or multiple molecules and provide the perturbation topologies suitable for free-energy calculations using the GROMOS and the GROMACS simulation packages. Various MCS search options are presented leading to alternative definitions of the perturbation pathway. Moreover, perturbation topologies generated using the default multistate MCS search are used to calculate the changes in free energy between lysine and its two post-translational modifications, 3-methyllysine and acetyllysine. The pairwise free-energy calculations performed on this test system led to a cycle closure of 0.5 ± 0.3 and 0.2 ± 0.2 kJ mol-1, with GROMOS and GROMACS simulation packages, respectively. The same relative free energies between the three states are obtained by employing the enveloping distribution sampling (EDS) approach when compared to the pairwise perturbations. Importantly, this toolkit is made available online as an open-source Python package (https://github.com/drazen-petrov/SMArt).

PyAutoFEP: An Automated Free Energy Perturbation Workflow for GROMACS Integrating Enhanced Sampling Methods

Free energy perturbation (FEP) calculations are now routinely used in drug discovery to estimate the relative FEB (RFEB) of small molecules to a biomolecular target of interest. Using enhanced sampling can improve the correlation between predictions and experimental data, especially in systems with conformational changes. Due to the large number of perturbations required in drug discovery campaigns, the manual setup of FEP calculations is no longer viable. Here, we introduce PyAutoFEP, a flexible and open-source tool to aid the setup of RFEB FEP. PyAutoFEP is written in Python3, and automates the generation of perturbation maps, dual topologies, system building and molecular dynamics (MD), and analysis. PyAutoFEP supports multiple force fields, incorporates replica exchange with solute tempering (REST) and replica exchange with solute scaling (REST2) enhanced sampling methods, and allows flexible λ values along perturbation windows. To validate PyAutoFEP, it was applied to a set of 14 Farnesoid X receptor ligands, a system included in the drug design data resource grand challenge 2. An 88% mean correct sign prediction was achieved, and 75% of the predictions had an error below 1.5 kcal/mol. Results using Amber03/GAFF, CHARMM36m/CGenFF, and OPLS-AA/M/LigParGen had Pearson's r values of 0.71 ± 0.13, 0.30 ± 0.27, and 0.66 ± 0.20, respectively. The Amber03/GAFF and OPLS-AA/M/LigParGen results were on par with the top grand challenge 2 submissions. Applying REST2 improved the results using CHARMM36m/CGenFF (Pearson's r = 0.43 ± 0.21) but had little impact on the other force fields. CHARMM36-YF and CHARMM36-WYF modifications did not yield improved predictions compared to CHARMM36m. Finally, we estimated the probability of finding a molecule 1 pK_i better than a lead when using PyAutoFEP to screen 10 or 100 analogues. The probabilities, when compared to random sampling, increased up to sevenfold when 100 molecules were to be screened, suggesting that PyAutoFEP would likely be useful for lead optimization. PyAutoFEP is available on GitHub at https://github.com/lmmpf/PyAutoFEP.

Computational Modeling as a Tool to Investigate PPI: From Drug Design to Tissue Engineering

Protein-protein interactions (PPIs) mediate a large number of important regulatory pathways. Their modulation represents an important strategy for discovering novel therapeutic agents. However, the features of PPI binding surfaces make the use of structure-based drug discovery methods very challenging. Among the diverse approaches used in the literature to tackle the problem, linear peptides have demonstrated to be a suitable methodology to discover PPI disruptors. Unfortunately, the poor pharmacokinetic properties of linear peptides prevent their direct use as drugs. However, they can be used as models to design enzyme resistant analogs including, cyclic peptides, peptide surrogates or peptidomimetics. Small molecules have a narrower set of targets they can bind to, but the screening technology based on virtual docking is robust and well tested, adding to the computational tools used to disrupt PPI. We review computational approaches used to understand and modulate PPI and highlight applications in a few case studies involved in physiological processes such as cell growth, apoptosis and intercellular communication.

Uncertainty quantification in classical molecular dynamics

Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach has begun to advance from being a computer-based means of rationalizing experimental observations to producing apparently credible predictions for a number of real-world applications within industrial sectors such as advanced materials and drug discovery. However, key aspects concerning the reproducibility of the method have not kept pace with the speed of its uptake in the scientific community. Here, we present a discussion of uncertainty quantification for molecular dynamics simulation designed to endow the method with better error estimates that will enable it to be used to report actionable results. The approach adopted is a standard one in the field of uncertainty quantification, namely using ensemble methods, in which a sufficiently large number of replicas are run concurrently, from which reliable statistics can be extracted. Indeed, because molecular dynamics is intrinsically chaotic, the need to use ensemble methods is fundamental and holds regardless of the duration of the simulations performed. We discuss the approach and illustrate it in a range of applications from materials science to ligand-protein binding free energy estimation. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

An affinity prediction approach for the ligand of E3 ligase Cbl-b and an insight into substrate binding pattern

Protein-protein interactions (PPIs) are essentially fundamental to all cellular processes, so that developing small molecule inhibitors of PPIs have great significance despite representing a huge challenge. Studying PPIs with the help of peptide motifs could obtain the structural information and reference significance to reduce the difficulty in the development of small molecules. Computational methods are powerful tools to characterize peptide-protein interactions, especially molecular dynamics simulation and binding free energy calculation. Here, we established an affinity prediction model suitable for Casitas B lymphoma-b (Cbl-b) and phosphorylated motif system. According to the affinity data set of multiple truncated peptides, the force field, solvent model, and internal dielectric constant of molecular mechanics/generalized Born surface area (MM/GBSA) method were optimized. Further, we predicted the affinity of the rationally designed new sequences through this model and obtained a new 6-mer motif with a 7-fold increase in affinity and the comprehensive structure-activity relationship. Moreover, we proposed an insight of unexpected activity of the truncated 5-mer peptide and revealed the possible binding mode of the new highly active 6-mer motif by extended simulation. Our results showed that the activity enhancement of the truncated peptide was caused by the acetyl-mediated conformation change. The side chain of Arg and pTyr in the 6-mer motif co-occupied the site p1 to form numerous hydrogen bond interactions and increased hydrophobic interaction formed with Tyr266, leading to the higher affinity. The present work provided a reference to investigate the PPI of Cbl-b and phosphorylated substrates and guided the development of Cbl-b inhibitors.

Improving virtual screening results with MM/GBSA and MM/PBSA rescoring

Virtual screening (VS) based on molecular docking is one of the most useful methods in computer-aided drug design. By allowing to identify computationally putative ligands binding to the proteins of interest, VS dramatically reduces the time and expense of the development of novel therapeutics. Among the limitations of the VS approaches is the low accuracy of scoring functions implemented in docking methods for assessing binding affinity. Many such scoring functions are developed for rapid, high-throughput evaluation of binding energy of multiple conformations generated by a searching algorithm. The methods for more rigorous calculation of binding affinity calculation are generally time-consuming. Even so, in many studies more accurate methods were used for rescoring of the final poses and false-positive hits evaluation. We performed VS for three benchmark sets and used energy minimization with MM/PB(GB)SA methods (molecular mechanics energies combined with the Poisson-Boltzmann or generalized Born and surface area) to rescore binding affinities. The comparison of the area under the curve (AUC), enrichment factor (EF), and Boltzmann-enhanced discrimination of receiver operating characteristics (BEDROC) showed essential improvements in the binding energy prediction after the rescoring. Finally, we provide a program for minimization and rescoring VS results based on freely available AmberTools. The code requires just the final binding poses of the ligand as the input and can be used with any docking program.

BFEE2: Automated, Streamlined, and Accurate Absolute Binding Free-Energy Calculations

Accurate absolute binding free-energy estimation in silico, following either an alchemical or a geometrical route, involves several subprocesses and requires the introduction of geometric restraints. Human intervention, for instance, to define the necessary collective variables, prepare the input files, monitor the simulation, and perform post-treatments is, however, tedious, cumbersome, and prone to errors. With the aim of automating and streamlining free-energy calculations, especially for nonexperts, version 2.0 of the binding free energy estimator (BFEE2) provides both standardized alchemical and geometrical workflows and obviates the need for extensive human intervention to guarantee complete reproducibility of the results. To achieve the largest gamut of protein-ligand and, more generally, of host-guest complexes, BFEE2 supports most academic force fields, such as CHARMM, Amber, OPLS, and GROMOS. Configurational files are generated in the NAMD and Gromacs formats, and all the post-treatments are performed in an automated fashion. Moreover, convergence of the free-energy calculation can be monitored from the intermediate files generated during the simulation. All in all, BFEE2 is a foolproof, versatile tool for accurate absolute binding free-energy calculations, assisting the end-user over a broad range of applications.

An Effective MM/GBSA Protocol for Absolute Binding Free Energy Calculations: A Case Study on SARS-CoV-2 Spike Protein and the Human ACE2 Receptor

The binding free energy calculation of protein-ligand complexes is necessary for research into virus-host interactions and the relevant applications in drug discovery. However, many current computational methods of such calculations are either inefficient or inaccurate in practice. Utilizing implicit solvent models in the molecular mechanics generalized Born surface area (MM/GBSA) framework allows for efficient calculations without significant loss of accuracy. Here, GBNSR6, a new flavor of the generalized Born model, is employed in the MM/GBSA framework for measuring the binding affinity between SARS-CoV-2 spike protein and the human ACE2 receptor. A computational protocol is developed based on the widely studied Ras-Raf complex, which has similar binding free energy to SARS-CoV-2/ACE2. Two options for representing the dielectric boundary of the complexes are evaluated: one based on the standard Bondi radii and the other based on a newly developed set of atomic radii (OPT1), optimized specifically for protein-ligand binding. Predictions based on the two radii sets provide upper and lower bounds on the experimental references: -14.7(ΔGbindBondi)<-10.6(ΔGbindExp.)<-4.1(ΔGbindOPT1) kcal/mol. The consensus estimates of the two bounds show quantitative agreement with the experiment values. This work also presents a novel truncation method and computational strategies for efficient entropy calculations with normal mode analysis. Interestingly, it is observed that a significant decrease in the number of snapshots does not affect the accuracy of entropy calculation, while it does lower computation time appreciably. The proposed MM/GBSA protocol can be used to study the binding mechanism of new variants of SARS-CoV-2, as well as other relevant structures.

Implementing and Assessing an Alchemical Method for Calculating Protein-Protein Binding Free Energy

Protein-protein binding is fundamental to most biological processes. It is important to be able to use computation to accurately estimate the change in protein-protein binding free energy due to mutations in order to answer biological questions that would be experimentally challenging, laborious, or time-consuming. Although nonrigorous free-energy methods are faster, rigorous alchemical molecular dynamics-based methods are considerably more accurate and are becoming more feasible with the advancement of computer hardware and molecular simulation software. Even with sufficient computational resources, there are still major challenges to using alchemical free-energy methods for protein-protein complexes, such as generating hybrid structures and topologies, maintaining a neutral net charge of the system when there is a charge-changing mutation, and setting up the simulation. In the current study, we have used the pmx package to generate hybrid structures and topologies, and a double-system/single-box approach to maintain the net charge of the system. To test the approach, we predicted relative binding affinities for two protein-protein complexes using a nonequilibrium alchemical method based on the Crooks fluctuation theorem and compared the results with experimental values. The method correctly identified stabilizing from destabilizing mutations for a small protein-protein complex, and a larger, more challenging antibody complex. Strong correlations were obtained between predicted and experimental relative binding affinities for both protein-protein systems.

Computational study on the allosteric mechanism of Leishmania major IF4E-1 by 4E-interacting protein-1: Unravelling the determinants of m7GTP cap recognition

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Atomistic details on perturbations induced by Lm4E-IP1 binding are described.

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The modulation of LmIF4E-1 affinity for the cap is confirmed by energetic analyses.

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Signaling paths between the allosteric and othosteric sites of LmIF4E-1 are predicted.

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Lm4E-IP1 binding increases the side-chain entropy of W83 and R172 of LmIF4E-1.

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A mechanism of dynamic allostery is proposed for the regulation mediated by Lm4E-IP1.

During their life cycle, Leishmania parasites display a fine-tuned regulation of the mRNA translation through the differential expression of isoforms of eukaryotic translation initiation factor 4E (LeishIF4Es). The interaction between allosteric modulators such as 4E-interacting proteins (4E-IPs) and LeishIF4E affects the affinity of this initiation factor for the mRNA cap. Here, several computational approaches were employed to elucidate the molecular bases of the previously-reported allosteric modulation in L. major exerted by 4E-IP1 (Lm4E-IP1) on eukaryotic translation initiation factor 4E 1 (LmIF4E-1). Molecular dynamics (MD) simulations and accurate binding free energy calculations (ΔG_bind) were combined with network-based modeling of residue-residue correlations. We also describe the differences in internal motions of LmIF4E-1 apo form, cap-bound, and Lm4E-IP1-bound systems. Through community network calculations, the differences in the allosteric pathways of allosterically-inhibited and active forms of LmIF4E-1 were revealed. The ΔG_bind values show significant differences between the active and inhibited systems, which are in agreement with the available experimental data. Our study thoroughly describes the dynamical perturbations of LmIF4E-1 cap-binding site triggered by Lm4E-IP1. These findings are not only essential for the understanding of a critical process of trypanosomatids’ gene expression but also for gaining insight into the allostery of eukaryotic IF4Es, which could be useful for structure-based design of drugs against this protein family.

Efficient In Silico Saturation Mutagenesis of a Member of the Caspase Protease Family

Rational-design methods have proven to be a valuable toolkit in the field of protein design. Numerical approaches such as free-energy calculations or QM/MM methods are fit to widen the understanding of a protein-sequence space but require large amounts of computational time and power. Here, we apply an efficient method for free-energy calculations that combines the one-step perturbation (OSP) with the third-power-fitting (TPF) approach. It is fit to calculate full free energies of binding from three different end states only. The nonpolar contribution to the free energies are calculated for a set of chosen amino acids from a single simulation of a judiciously chosen reference state. The electrostatic contributions, on the other hand, are predicted from simulations of the neutral and charged end states of the individual amino acids. We used this method to perform in silico saturation mutagenesis of two sites in human Caspase-2. We calculated relative binding free energies toward two different substrates that differ in their P1' site and in their affinity toward the unmutated protease. Although being approximate, our approach showed very good agreement upon validation against experimental data. 76% of the predicted relative free energies of amino acid mutations was found to be true positives or true negatives. We observed that this method is fit to discriminate amino acid mutations because the rate of false negatives is very low (<1.5%). The approach works better for a substrate with medium/low affinity with a Matthews correlation coefficient (MCC) of 0.63, whereas for a substrate with very low affinity, the MCC was 0.38. In all cases, the combined TPF + OSP approach outperformed the linear interaction energy method.

Automation of absolute protein-ligand binding free energy calculations for docking refinement and compound evaluation

Absolute binding free energy calculations with explicit solvent molecular simulations can provide estimates of protein-ligand affinities, and thus reduce the time and costs needed to find new drug candidates. However, these calculations can be complex to implement and perform. Here, we introduce the software BAT.py, a Python tool that invokes the AMBER simulation package to automate the calculation of binding free energies for a protein with a series of ligands. The software supports the attach-pull-release (APR) and double decoupling (DD) binding free energy methods, as well as the simultaneous decoupling-recoupling (SDR) method, a variant of double decoupling that avoids numerical artifacts associated with charged ligands. We report encouraging initial test applications of this software both to re-rank docked poses and to estimate overall binding free energies. We also show that it is practical to carry out these calculations cheaply by using graphical processing units in common machines that can be built for this purpose. The combination of automation and low cost positions this procedure to be applied in a relatively high-throughput mode and thus stands to enable new applications in early-stage drug discovery.

Optimization of Alchemical Pathways Using Extended Thermodynamic Integration

Thermodynamic integration (TI) is a commonly used method to determine free-energy differences. One of its disadvantages is that many intermediate λ-states need to be sampled in order to be able to integrate accurately over ⟨∂H/∂λ⟩. Here, we use the recently introduced extended TI to study alternative parameterizations of H(λ) and its influence on the smoothness of the ⟨∂H/∂λ⟩ curves as well as the efficiency of the simulations. We find that the extended TI approach can be used to select curves of low curvature. An optimal parameterization is suggested for the calculation of hydration free energies. For calculations of relative binding free energies, we show that optimized parameterizations of the Hamiltonian in the unbound state also effectively lower the curvature in the bound state of the ligand.

Charge-Changing Perturbations and Path Sampling via Classical Molecular Dynamic Simulations of Simple Guest-Host Systems

Currently, two different methods dominate the field of biomolecular free-energy calculations for the prediction of binding affinities. Pathway methods are frequently used for large ligands that bind on the surface of a host, such as protein-protein complexes. Alchemical methods, on the other hand, are preferably applied for small ligands that bind to deeply buried binding sites. The latter methods are also widely known to be heavily artifacted by the representation of electrostatic energies in periodic simulation boxes, in particular, when net-charge changes are involved. Different methods have been described to deal with these artifacts, including postsimulation correction schemes and instantaneous correction schemes (e.g., co-alchemical perturbation of ions). Here, we use very simple test systems to show that instantaneous correction schemes with no change in the system net charge lower the artifacts but do not eliminate them. Furthermore, we show that free energies from pathway methods suffer from the same artifacts.

Metadynamics as a Postprocessing Method for Virtual Screening with Application to the Pseudokinase Domain of JAK2

With standard scoring methods, top-ranked compounds from virtual screening by docking often turn out to be inactive. For this reason, metadynamics, a method used to sample rare events, was studied to further evaluate docking poses with the aim of reducing false positives. Specifically, virtual screening was performed with Glide SP to seek potential molecules to bind to the ATP site in the pseudokinase domain of JAK2 kinase, and promising compounds were selected from the top-ranked 1000 based on visualization. Rescoring with Glide XP, GOLD, and MM/GBSA was unable to differentiate well between active and inactive compounds. Metadynamics was then used to gauge the relative binding affinity from the required time or the potential of mean force needed to dissociate the ligand from the bound complex. With consideration of previously known binders of varying affinities, metadynamics was able to differentiate between the most active compounds and inactive or weakly active ones, and it could identify correctly most of the selected virtual screening compounds as false positives. Thus, metadynamics has the potential to be a viable postprocessing method for virtual screening, minimizing the expense of buying or synthesizing inactive compounds.

Improved Alchemical Free Energy Calculations with Optimized Smoothstep Softcore Potentials

Progress in the development of GPU-accelerated free energy simulation software has enabled practical applications on complex biological systems and fueled efforts to develop more accurate and robust predictive methods. In particular, this work re-examines concerted (a.k.a., one-step or unified) alchemical transformations commonly used in the prediction of hydration and relative binding free energies (RBFEs). We first classify several known challenges in these calculations into three categories: endpoint catastrophes, particle collapse, and large gradient-jumps. While endpoint catastrophes have long been addressed using softcore potentials, the remaining two problems occur much more sporadically and can result in either numerical instability (i.e., complete failure of a simulation) or inconsistent estimation (i.e., stochastic convergence to an incorrect result). The particle collapse problem stems from an imbalance in short-range electrostatic and repulsive interactions and can, in principle, be solved by appropriately balancing the respective softcore parameters. However, the large gradient-jump problem itself arises from the sensitivity of the free energy to large values of the softcore parameters, as might be used in trying to solve the particle collapse issue. Often, no satisfactory compromise exists with the existing softcore potential form. As a framework for solving these problems, we developed a new family of smoothstep softcore (SSC) potentials motivated by an analysis of the derivatives along the alchemical path. The smoothstep polynomials generalize the monomial functions that are used in most implementations and provide an additional path-dependent smoothing parameter. The effectiveness of this approach is demonstrated on simple yet pathological cases that illustrate the three problems outlined. With appropriate parameter selection, we find that a second-order SSC(2) potential does at least as well as the conventional approach and provides vast improvement in terms of consistency across all cases. Last, we compare the concerted SSC(2) approach against the gold-standard stepwise (a.k.a., decoupled or multistep) scheme over a large set of RBFE calculations as might be encountered in drug discovery.

Molecular Structure, Binding Affinity, and Biological Activity in the Epigenome

Development of valid structure–activity relationships (SARs) is a key to the elucidation of pathomechanisms of epigenetic diseases and the development of efficient, new drugs. The present review is based on selected methodologies and applications supplying molecular structure, binding affinity and biological activity data for the development of new SARs. An emphasis is placed on emerging trends and permanent challenges of new discoveries of SARs in the context of proteins as epigenetic drug targets. The review gives a brief overview and classification of the molecular background of epigenetic changes, and surveys both experimental and theoretical approaches in the field. Besides the results of sophisticated, cutting edge techniques such as cryo-electron microscopy, protein crystallography, and isothermal titration calorimetry, examples of frequently used assays and fast screening techniques are also selected. The review features how different experimental methods and theoretical approaches complement each other and result in valid SARs of the epigenome.

Thermodynamic Integration in 3n Dimensions without Biases or Alchemy for Protein Interactions

Thermodynamic integration (TI), a powerful formalism for computing Gibbs free energy, has been implemented for many biophysical processes with alchemical schemes that require delicate human efforts to choose/design biasing potentials for sampling the desired biophysical events and to remove their artifactitious consequences afterwards. Theoretically, an alchemical scheme is exact but practically, an unsophisticated implementation of this exact formula can cause error amplifications. Small relative errors in the input parameters can be amplified many times in their propagation into the computed free energy [due to subtraction of similar numbers such as (105 ± 5)‒(100 ± 5) = 5 ± 7]. In this paper, we present an unsophisticated implementation of TI in 3n dimensions (3nD) (n=1,2,3…) for the potential of mean force along a 3nD path connecting one state in the bound state ensemble to one state in the unbound state ensemble. Fluctuations in these 3nD are integrated in the bound and unbound state ensembles but not along the 3nD path. Using TI3nD, we computed the standard binding free energies of three protein complexes: trometamol in Salmonella effector SpvD (n=1), biotin-avidin (n=2), and Colicin E9 endonuclease with cognate immunity protein Im9 (n=3). We employed three different protocols in three independent computations of E9-Im9 to show TI3nD's robustness. We also computed the hydration energies of ten biologically relevant compounds (n=1 for water, acetamide, urea, glycerol, trometamol, ammonium and n=2 for erythritol, 1,3-propanediol, xylitol, biotin). Each of the 15 computations is accomplishable within one (for hydration) to ten (for E9-Im9) days on an inexpensive GPU workstation. The computed results all agree with the available experimental data.