Perspective on Free-Energy Perturbation Calculations for Chemical Equilibria

Antibiotic resistance challenge: evaluating anthraquinones as rifampicin monooxygenase inhibitors through integrated bioinformatics analysis

OBJECTIVE

Antibiotic resistance poses a pressing and crucial global public health challenge, leading to significant clinical and health-related consequences. Substantial evidence highlights the pivotal involvement of rifampicin monooxygenase (RIFMO) in the context of antibiotic resistance. Hence, inhibiting RIFMO could offer potential in the treatment of various infections. Anthraquinones, a group of organic compounds, have shown promise in addressing tuberculosis. This study employed integrated bioinformatics approaches to evaluate the potential inhibitory effects of a selection of anthraquinones on RIFMO. The findings were subsequently compared with those of rifampicin (RIF), serving as a positive control inhibitor.

METHODS

The AutoDock 4.0 tool assessed the binding free energy between 21 anthraquinones and the RIFMO catalytic cleft. The ligands were ranked based on the most favorable scores derived from ΔGbinding. The docking analyses for the highest-ranked anthraquinone and RIF underwent a cross-validation process. This validation procedure utilized the SwissDock server and the Schrödinger Maestro docking software. Molecular dynamics simulations were conducted to scrutinize the stability of the backbone atoms in free RIFMO, RIFMO-RIF, and RIFMO complexed with the top-ranked anthraquinone throughout a 100-ns computer simulation. The Discovery Studio Visualizer tool visualized interactions between RIFMO residues and ligands. An evaluation of the pharmacokinetics and toxicity profiles of the tested compounds was also conducted.

RESULTS

Five anthraquinones were indicated with ΔGbinding scores less than - 10 kcal/mol. Hypericin emerged as the most potent RIFMO inhibitor, boasting a ΔGbinding score and inhibition constant value of - 12.11 kcal/mol and 798.99 pM, respectively. The agreement across AutoDock 4.0, SwissDock, and Schrödinger Maestro results highlighted hypericin's notable binding affinity to the RIFMO catalytic cleft. The RIFMO-hypericin complex achieved stability after a 70-ns computer simulation, exhibiting a root-mean-square deviation of 0.55 nm. Oral bioavailability analysis revealed that all anthraquinones except hypericin, sennidin A, and sennidin B may be suitable for oral administration. Furthermore, the carcinogenicity prediction analysis indicated a favorable safety profile for all examined anthraquinones.

CONCLUSION

Inhibiting RIFMO, particularly with anthraquinones such as hypericin, holds promise as a potential therapeutic strategy for infectious diseases.

A Comprehensive Study of Factors Affecting the Prediction of the pKa Shift of Asp26 in Thioredoxin Protein

The stable protonation state of ionizable amino acids in a protein can be predicted by computing the pKa shift of that residue within the protein environment. Thermodynamic Integration (TI) is an ideal molecular dynamics-based approach for predicting the pKa shift of ionizable protein residues. Here, we probe TI-based simulation protocols for their ability to accurately predict the pKa shift of Asp26 in thioredoxin. While implicit solvent models can predict the pKa shift accurately, explicit solvent models result in substantial errors. To understand the underlying reason for this surprising discrepancy, we investigate the role of various factors such as solvent models, conformational sampling, background charges, and polarization.

Assessing the Accuracy and Efficiency of Free Energy Differences Obtained from Reweighted Flow-Based Probabilistic Generative Models

Computing free energy differences between metastable states characterized by nonoverlapping Boltzmann distributions is often a computationally intensive endeavor, usually requiring chains of intermediate states to connect them. Targeted free energy perturbation (TFEP) can significantly lower the computational cost of FEP calculations by choosing a set of invertible maps used to directly connect the distributions of interest, achieving the necessary statistically significant overlaps without sampling any intermediate states. Probabilistic generative models (PGMs) based on normalizing flow architectures can make it much easier via machine learning to train invertible maps needed for TFEP. However, the accuracy and applicability of approaches based on empirically learned maps depend crucially on the choice of reweighting method adopted to estimate the free energy differences. In this work, we assess the accuracy, rate of convergence, and data efficiency of different free energy estimators, including exponential averaging, Bennett acceptance ratio (BAR), and multistate Bennett acceptance ratio (MBAR), in reweighting PGMs trained by maximum likelihood on limited amounts of molecular dynamics data sampled only from end-states of interest. We carry out the comparisons on a set of simple but representative case studies, including conformational ensembles of alanine dipeptide and ibuprofen. Our results indicate that BAR and MBAR are both data efficient and robust, even in the presence of significant model overfitting in the generation of invertible maps. This analysis can serve as a stepping stone for the deployment of efficient and quantitatively accurate ML-based free energy calculation methods in complex systems.

GENESIS 2.1: High-Performance Molecular Dynamics Software for Enhanced Sampling and Free-Energy Calculations for Atomistic, Coarse-Grained, and Quantum Mechanics/Molecular Mechanics Models

GENeralized-Ensemble SImulation System (GENESIS) is a molecular dynamics (MD) software developed to simulate the conformational dynamics of a single biomolecule, as well as molecular interactions in large biomolecular assemblies and between multiple biomolecules in cellular environments. To achieve the latter purpose, the earlier versions of GENESIS emphasized high performance in atomistic MD simulations on massively parallel supercomputers, with or without graphics processing units (GPUs). Here, we implemented multiscale MD simulations that include atomistic, coarse-grained, and hybrid quantum mechanics/molecular mechanics (QM/MM) calculations. They demonstrate high performance and are integrated with enhanced conformational sampling algorithms and free-energy calculations without using external programs except for the QM programs. In this article, we review new functions, molecular models, and other essential features in GENESIS version 2.1 and discuss ongoing developments for future releases.

Convergence criteria for single-step free-energy calculations: the relation between the Π bias measure and the sample variance

Free energy calculations play a crucial role in simulating chemical processes, enzymatic reactions, and drug design. However, assessing the reliability and convergence of these calculations remains a challenge. This study focuses on single-step free-energy calculations using thermodynamic perturbation. It explores how the sample distributions influence the estimated results and evaluates the reliability of various convergence criteria, including Kofke's bias measure Π and the standard deviation of the energy difference ΔU, σ ΔU . The findings reveal that for Gaussian distributions, there is a straightforward relationship between Π and σ ΔU , free energies can be accurately approximated using a second-order cumulant expansion, and reliable results are attainable for σ ΔU up to 25 kcal mol-1. However, interpreting non-Gaussian distributions is more complex. If the distribution is skewed towards more positive values than a Gaussian, converging the free energy becomes easier, rendering standard convergence criteria overly stringent. Conversely, distributions that are skewed towards more negative values than a Gaussian present greater challenges in achieving convergence, making standard criteria unreliable. We propose a practical approach to assess the convergence of estimated free energies.

Unraveling Copper Exchange in the Atox1-Cu(I)-Mnk1 Heterodimer: A Simulation Approach

Copper, an essential metal for various cellular processes, requires tight regulation to prevent cytotoxicity. Intracellular pathways crucial for maintaining optimal copper levels involve soluble and membrane transporters, namely, metallochaperones and P-type ATPases, respectively. In this study, we used a simulation workflow based on free-energy perturbation (FEP) theory and parallel bias metadynamics (PBMetaD) to predict the Cu(I) exchange mechanism between the human Cu(I) chaperone, Atox1, and one of its two physiological partners, ATP7A. ATP7A, also known as the Menkes disease protein, is a transmembrane protein and one of the main copper-transporting ATPases. It pumps copper into the trans-Golgi network for the maturation of cuproenzymes and is also essential for the efflux of excess copper across the plasma membrane. In this analysis, we utilized the nuclear magnetic resonance (NMR) structure of the Cu(I)-mediated complex between Atox1 and the first soluble domain of the Menkes protein (Mnk1) as a starting point. Independent free-energy simulations were conducted to investigate the dissociation of both Atox1 and Mnk1. The calculations revealed that the two dissociations require free energy values of 6.3 and 6.2 kcal/mol, respectively, following a stepwise dissociation mechanism.

How exascale computing can shape drug design: A perspective from multiscale QM/MM molecular dynamics simulations and machine learning-aided enhanced sampling algorithms

Molecular simulations are an essential asset in the first steps of drug design campaigns. However, the requirement of high-throughput limits applications mainly to qualitative approaches with low computational cost, but also low accuracy. Unlocking the potential of more rigorous quantum mechanical/molecular mechanics (QM/MM) models combined with molecular dynamics-based free energy techniques could have a tremendous impact. Indeed, these two relatively old techniques are emerging as promising methods in the field. This has been favored by the exponential growth of computer power and the proliferation of powerful data-driven methods. Here, we briefly review recent advances and applications, and give our perspective on the impact that QM/MM and free-energy methods combined with machine learning-aided algorithms can have on drug design.

Binding Sites of Bicarbonate in Phosphoenolpyruvate Carboxylase

Phosphoenolpyruvate carboxylase (PEPC) is used in plant metabolism for fruit maturation or seed development as well as in the C4 and crassulacean acid metabolism (CAM) mechanisms in photosynthesis, where it is used for the capture of hydrated CO2 (bicarbonate). To find the yet unknown binding site of bicarbonate in this enzyme, we have first identified putative binding sites with nonequilibrium molecular dynamics simulations and then ranked these sites with alchemical free energy calculations with corrections of computational artifacts. Fourteen pockets where bicarbonate could bind were identified, with three having realistic binding free energies with differences with the experimental value below 1 kcal/mol. One of these pockets is found far from the active site at 14 Å and predicted to be an allosteric binding site. In the two other binding sites, bicarbonate is in direct interaction with the magnesium ion; neither sequence alignment nor the study of mutant K606N allowed to discriminate between these two pockets, and both are good candidates as the binding site of bicarbonate in phosphoenolpyruvate carboxylase.

A comprehensive review of the recent advances on predicting drug-target affinity based on deep learning

Accurate calculation of drug-target affinity (DTA) is crucial for various applications in the pharmaceutical industry, including drug screening, design, and repurposing. However, traditional machine learning methods for calculating DTA often lack accuracy, posing a significant challenge in accurately predicting DTA. Fortunately, deep learning has emerged as a promising approach in computational biology, leading to the development of various deep learning-based methods for DTA prediction. To support researchers in developing novel and highly precision methods, we have provided a comprehensive review of recent advances in predicting DTA using deep learning. We firstly conducted a statistical analysis of commonly used public datasets, providing essential information and introducing the used fields of these datasets. We further explored the common representations of sequences and structures of drugs and targets. These analyses served as the foundation for constructing DTA prediction methods based on deep learning. Next, we focused on explaining how deep learning models, such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Transformer, and Graph Neural Networks (GNNs), were effectively employed in specific DTA prediction methods. We highlighted the unique advantages and applications of these models in the context of DTA prediction. Finally, we conducted a performance analysis of multiple state-of-the-art methods for predicting DTA based on deep learning. The comprehensive review aimed to help researchers understand the shortcomings and advantages of existing methods, and further develop high-precision DTA prediction tool to promote the development of drug discovery.

Development of CHARMM compatible force field parameters and molecular dynamics simulations for the pesticide flupyradifurone

Flupyradifurone (FLU) is a novel butenolide insecticide with partial agonist activity for insect nicotinic acetylcholine receptors. Its safety for non-target organisms has been questioned in the literature, despite initial claims of its harmlessness. Detailed understanding of its toxicity and related molecular mechanisms remain under discussion. Thus, in this work, an optimized set of CHARMM compatible parameters for FLU is presented. CHARMM General Force Field program was used as a starting point while the non-bonded and bonded parameters were adjusted and optimized to reproduce MP2/6-31G(d) accuracy level results. For the validity assessment of these parameters, infrared spectrum, water-octanol partition coefficient, and normal modes were computed and compared to experimental values found in the literature. Several MD simulations of FLU in water and FLU in complex with an acetylcholine-binding protein were performed to estimate the ability of the optimized parameters to correctly describe its torsional space and reproduce observed crystallographic trends respectively.

Enthalpies and entropies of hydration from Monte Carlo simulations

The changes in free energy, enthalpy, and entropy for transfer of a solute from the gas phase into solution are the fundamental thermodynamic quantities that characterize the solvation process. Owing to the development of methods based on free-energy perturbation theory, computation of free energies of solvation has become routine in conjunction with Monte Carlo (MC) statistical mechanics and molecular dynamics (MD) simulations. Computation of the enthalpy change and by inference the entropy change is more challenging. Two methods are considered in this work corresponding to direct averaging for the solvent and solution and to computing the temperature derivative of the free energy in the van't Hoff approach. The application is for neutral organic solutes in TIP4P water using long MC simulations to improve precision. Definitive results are also provided for pure TIP4P water. While the uncertainty in computed free energies of hydration is ca. 0.05 kcal mol-1, it is ca. 0.4 kcal mol-1 for the enthalpy changes from either van't Hoff plots or the direct method with sampling for 5 billion MC configurations. Partial molar volumes of hydration are also computed by the direct method; they agree well with experimental data with an average deviation of 3 cm3 mol-1. In addition, the results permit breakdown of the errors in the free energy changes from the OPLS-AA force field into their enthalpic and entropic components. The excess hydrophobicity of organic solutes is enthalpic in origin.

Landscape of In Silico Tools for Modeling Covalent Modification of Proteins: A Review on Computational Covalent Drug Discovery

Covalent drug discovery has been a challenging research area given the struggle of finding a sweet balance between selectivity and reactivity for these drugs, the lack of which often leads to off-target activities and hence undesirable side effects. However, there has been a resurgence in covalent drug design following the success of several covalent drugs such as boceprevir (2011), ibrutinib (2013), neratinib (2017), dacomitinib (2018), zanubrutinib (2019), and many others. Design of covalent drugs includes many crucial factors, where "evaluation of the binding affinity" and "a detailed mechanistic understanding on covalent inhibition" are at the top of the list. Well-defined experimental techniques are available to elucidate these factors; however, often they are expensive and/or time-consuming and hence not suitable for high throughput screens. Recent developments in in silico methods provide promise in this direction. In this report, we review a set of recent publications that focused on developing and/or implementing novel in silico techniques in "Computational Covalent Drug Discovery (CCDD)". We also discuss the advantages and disadvantages of these approaches along with what improvements are required to make it a great tool in medicinal chemistry in the near future.

Integrated Molecular Modeling and Machine Learning for Drug Design

Modern therapeutic development often involves several stages that are interconnected, and multiple iterations are usually required to bring a new drug to the market. Computational approaches have increasingly become an indispensable part of helping reduce the time and cost of the research and development of new drugs. In this Perspective, we summarize our recent efforts on integrating molecular modeling and machine learning to develop computational tools for modulator design, including a pocket-guided rational design approach based on AlphaSpace to target protein-protein interactions, delta machine learning scoring functions for protein-ligand docking as well as virtual screening, and state-of-the-art deep learning models to predict calculated and experimental molecular properties based on molecular mechanics optimized geometries. Meanwhile, we discuss remaining challenges and promising directions for further development and use a retrospective example of FDA approved kinase inhibitor Erlotinib to demonstrate the use of these newly developed computational tools.

Comparison of Equilibrium and Nonequilibrium Approaches for Relative Binding Free Energy Predictions

Alchemical relative binding free energy calculations have recently found important applications in drug optimization. A series of congeneric compounds are generated from a preidentified lead compound, and their relative binding affinities to a protein are assessed in order to optimize candidate drugs. While methods based on equilibrium thermodynamics have been extensively studied, an approach based on nonequilibrium methods has recently been reported together with claims of its superiority. However, these claims pay insufficient attention to the basis and reliability of both methods. Here we report a comparative study of the two approaches across a large data set, comprising more than 500 ligand transformations spanning in excess of 300 ligands binding to a set of 14 diverse protein targets. Ensemble methods are essential to quantify the uncertainty in these calculations, not only for the reasons already established in the equilibrium approach but also to ensure that the nonequilibrium calculations reside within their domain of validity. If and only if ensemble methods are applied, we find that the nonequilibrium method can achieve accuracy and precision comparable to those of the equilibrium approach. Compared to the equilibrium method, the nonequilibrium approach can reduce computational costs but introduces higher computational complexity and longer wall clock times. There are, however, cases where the standard length of a nonequilibrium transition is not sufficient, necessitating a complete rerun of the entire set of transitions. This significantly increases the computational cost and proves to be highly inconvenient during large-scale applications. Our findings provide a key set of recommendations that should be adopted for the reliable implementation of nonequilibrium approaches to relative binding free energy calculations in ligand-protein systems.

Cheminformatics-based discovery of new organoselenium compounds with potential for the treatment of cutaneous and visceral leishmaniasis

Leishmaniasis affects more than 12 million humans globally and a further 1 billion people are at risk in leishmaniasis endemic areas. The lack of a vaccine for leishmaniasis coupled with the limitations of existing anti-leishmanial therapies prompted this study. Cheminformatic techniques are widely used in screening large libraries of compounds, studying protein-ligand interactions, analysing pharmacokinetic properties, and designing new drug molecules with great speed, accuracy, and precision. This study was undertaken to evaluate the anti-leishmanial potential of some organoselenium compounds by quantitative structure-activity relationship (QSAR) modeling, molecular docking, pharmacokinetic analysis, and molecular dynamic (MD) simulation. The built QSAR model was validated (R2train = 0.8646, R2test = 0.8864, Q2 = 0.5773) and the predicted inhibitory activity (pIC50) values of the newly designed compounds were higher than that of the template (Compound 6). The new analogues (6a, 6b, and 6c) showed good binding interactions with the target protein (Pyridoxal kinase, PdxK) while also presenting excellent drug-likeness and pharmacokinetic profiles. The results of density functional theory, MD simulation, and molecular mechanics generalized Born surface area (MM/GBSA) analyses suggest the favourability and stability of protein-ligand interactions of the new analogues with PdxK, comparing favourably well with the reference drug (Pentamidine). Conclusively, the newly designed compounds could be synthesized and tested experimentally as potential anti-leishmanial drug molecules.Communicated by Ramaswamy H. Sarma.

Application of Machine Learning Algorithms to Metadynamics for the Elucidation of the Binding Modes and Free Energy Landscape of Drug/Target Interactions: a Case Study

In the context of drug discovery, computational methods were able to accelerate the challenging process of designing and optimizing a new drug candidate. Amongst the possible atomistic simulation approaches, metadynamics (metaD) has proven very powerful. However, the choice of collective variables (CVs) is not trivial for complex systems. To automate the process of CVs identification, two different machine learning algorithms were applied in this study, namely DeepLDA and Autoencoder, to the metaD simulation of a well-researched drug/target complex, consisting in a pharmacologically relevant non-canonical DNA secondary structure (G-quadruplex) and a metallodrug acting as its stabilizer, as well as solvent molecules.

Simulation workflows to predict the circular dichroism and circularly polarized luminescence of chiral materials

Chiral materials are attracting considerable interest in various fields in view of their unique properties and optical activity. Indeed, the peculiar features of chiral materials to absorb and emit circularly polarized light enable their use in an extensive range of applications. Motivated by the interest in boosting the development of chiral materials characterized by enhanced chiroptical properties such as circular dichroism (CD) and circular polarized luminescence (CPL), we herein illustrate in this tutorial how theoretical simulations can be used for the predictions and interpretations of chiroptical data and for the identification of chiral geometries. We are focusing on computational frameworks that can be used to investigate the theoretical aspects of chiral materials' photophysical and conformational characteristics. We will then illustrate ab initio methods based on density functional theory (DFT) and its time-dependent extension (TD-DFT) to simulate CD and CPL signals, and we will exemplify a variety of enhanced sampling techniques useful for an adequate sampling of the configurational space for chiral systems.

CrystalClear: an open, modular protocol for predicting molecular crystal growth from solution

We present a new protocol for the prediction of free energies that determine the growth of sites in molecular crystals for subsequent use in Monte Carlo simulations using tools such as CrystalGrower [Hill et al., Chemical Science, 2021, 12, 1126-1146]. Key features of the proposed approach are that it requires minimal input, namely the crystal structure and solvent only, and provides automated, rapid generation of the interaction energies. The constituent components of this protocol, namely interactions between molecules (growth units) in the crystal, solvation contributions and treatment of long-range interactions are described in detail. The power of this method is shown via prediction of crystal shapes for ibuprofen grown from ethanol, ethyl acetate, toluene and acetonitrile, adipic acid grown from water, and five polymorphs (ON, OP, Y, YT04 and R) of ROY (5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile), with promising results. The predicted energies may be used directly or subsequently refined against experimental data, facilitating insight into the interactions governing crystal growth, while also providing a prediction of the solubility of the material. The protocol has been implemented in standalone, open-source software made available alongside this publication.

Predicting bioactivity of antibiotic metabolites by molecular docking and dynamics

Antibiotics enter the environment through waste streams, where they can exert selective pressure for antimicrobial resistance in bacteria. However, many antibiotics are excreted as partly metabolized forms, or can be subject to partial breakdown in wastewater treatment, soil, or through natural processes in the environment. If a metabolite is bioactive, even at sub-lethal levels, and also stable in the environment, then it could provide selection pressure for resistance. (5S)-penicilloic acid of piperacillin has previously been found complexed to the binding pocket of penicillin binding protein 3 (PBP3) of Pseudomonas aeruginosa. Here, we predicted the affinities of all potentially relevant antibiotic metabolites of ten different penicillins to that target protein, using molecular docking and molecular dynamics simulations. Docking predicts that, in addition to penicilloic acid, pseudopenicillin derivatives of these penicillins, as well as 6-aminopenicillanic acid (6APA), could also bind to this target. MD simulations further confirmed that (5R)-pseudopenicillin and 6APA bind the target protein, in addition to (5S)-penicilloic acid. Thus, it is possible that these metabolites are bioactive, and, if stable in the environment, could be contaminants selective for antibiotic resistance. This could have considerable significance for environmental surveillance for antibiotics as a means to reduce antimicrobial resistance, because targeted mass spectrometry could be required for relevant metabolites as well as the native antibiotics.

Binding and Dynamics Demonstrate the Destabilization of Ligand Binding for the S688Y Mutation in the NMDA Receptor GluN1 Subunit

Encephalopathies are brain dysfunctions that lead to cognitive, sensory, and motor development impairments. Recently, the identification of several mutations within the N-methyl-D-aspartate receptor (NMDAR) have been identified as significant in the etiology of this group of conditions. However, a complete understanding of the underlying molecular mechanism and changes to the receptor due to these mutations has been elusive. We studied the molecular mechanisms by which one of the first mutations within the NMDAR GluN1 ligand binding domain, Ser688Tyr, causes encephalopathies. We performed molecular docking, randomly seeded molecular dynamics simulations, and binding free energy calculations to determine the behavior of the two major co-agonists: glycine and D-serine, in both the wild-type and S688Y receptors. We observed that the Ser688Tyr mutation leads to the instability of both ligands within the ligand binding site due to structural changes associated with the mutation. The binding free energy for both ligands was significantly more unfavorable in the mutated receptor. These results explain previously observed in vitro electrophysiological data and provide detailed aspects of ligand association and its effects on receptor activity. Our study provides valuable insight into the consequences of mutations within the NMDAR GluN1 ligand binding domain.

Protein-protein interfaces in molecular glue-induced ternary complexes: classification, characterization, and prediction

Molecular glues are a class of small molecules that stabilize the interactions between proteins. Naturally occurring molecular glues are present in many areas of biology where they serve as central regulators of signaling pathways. Importantly, several clinical compounds act as molecular glue degraders that stabilize interactions between E3 ubiquitin ligases and target proteins, leading to their degradation. Molecular glues hold promise as a new generation of therapeutic agents, including those molecular glue degraders that can redirect the protein degradation machinery in a precise way. However, rational discovery of molecular glues is difficult in part due to the lack of understanding of the protein-protein interactions they stabilize. In this review, we summarize the structures of known molecular glue-induced ternary complexes and the interface properties. Detailed analysis shows different mechanisms of ternary structure formation. Additionally, we also review computational approaches for predicting protein-protein interfaces and highlight the promises and challenges. This information will ultimately help inform future approaches for rational molecular glue discovery.

The Drug-Induced Interface That Drives HIV-1 Integrase Hypermultimerization and Loss of Function

Allosteric HIV-1 integrase (IN) inhibitors (ALLINIs) are an emerging class of small molecules that disrupt viral maturation by inducing the aberrant multimerization of IN. Here, we present cocrystal structures of HIV-1 IN with two potent ALLINIs, namely, BI-D and the drug candidate Pirmitegravir. The structures reveal atomistic details of the ALLINI-induced interface between the HIV-1 IN catalytic core and carboxyl-terminal domains (CCD and CTD). Projecting from their principal binding pocket on the IN CCD dimer, the compounds act as molecular glue by engaging a triad of invariant HIV-1 IN CTD residues, namely, Tyr226, Trp235, and Lys266, to nucleate the CTD-CCD interaction. The drug-induced interface involves the CTD SH3-like fold and extends to the beginning of the IN carboxyl-terminal tail region. We show that mutations of HIV-1 IN CTD residues that participate in the interface with the CCD greatly reduce the IN-aggregation properties of Pirmitegravir. Our results explain the mechanism of the ALLINI-induced condensation of HIV-1 IN and provide a reliable template for the rational development of this series of antiretrovirals through the optimization of their key contacts with the viral target. IMPORTANCE Despite the remarkable success of combination antiretroviral therapy, HIV-1 remains among the major causes of human suffering and loss of life in poor and developing nations. To prevail in this drawn-out battle with the pandemic, it is essential to continue developing advanced antiviral agents to fight drug resistant HIV-1 variants. Allosteric integrase inhibitors (ALLINIs) are an emerging class of HIV-1 antagonists that are orthogonal to the current antiretroviral drugs. These small molecules act as highly specific molecular glue, which triggers the aggregation of HIV-1 integrase. In this work, we present high-resolution crystal structures that reveal the crucial interactions made by two potent ALLINIs, namely, BI-D and Pirmitegravir, with HIV-1 integrase. Our results explain the mechanism of drug action and will inform the development of this promising class of small molecules for future use in antiretroviral regimens.

Hydrophilic Versus Hydrophobic Coupling in the Pressure Dependence of the Chemical Potential of Alkali Metal and Halide Ions in Water

We computed the chemical potential for some alkali metal ions (K⁺, Rb⁺, and Cs⁺) and two halide ions (Br^- and I^-) in aqueous solution at ambient T and various pressures in the range 1-8000 atm. Results were obtained from classic Monte Carlo simulations in the NPT ensemble by means of the free energy perturbation method. Here, the chemical potential is computed as the sum of a term relative to a Lennard-Jones solute and a term relative to the process in which this solute is transformed into the ion. Hydrophobic and hydrophilic features of these two components of the chemical potential show opposite behaviors under isothermal compression. The increase in pressure determines an increase in the hydrophobic component, which becomes more positive with a stronger effect for larger ions. Correspondingly, the values of the hydrophilic component become more negative for alkali ions, whereas they are only slightly affected by compression for halide ions. Hydrophobic-hydrophilic quasi-compensation in the slopes is observed for Rb⁺. For a smaller ion, such as K⁺, the dependence on pressure of the hydrophilic component is slightly dominant. For a larger ion, as observed in the cases of Cs⁺, Br^-, and I^-, the hydrophobic component assumes the determinant role. Pressure dependence of the chemical potential is little affected by corrections introduced for molecular potential truncation. This view can change for possible boundary artifacts that could have affected the static electrostatic potential. Some inference is obtained from comparison with experimental data at 1 atm on the free energy of hydration. Discrepancies show the characteristic asymmetry between cations and anions. The further addition of a correction based on the static potential significantly reduces these discrepancies with important error cancellation on the sum of chemical potentials of ions of opposite charge. The correction is applied also at higher pressures, and results are compared with those obtained by adding an alternative correction that is based on the water number density. Regardless of the ion, changes of the chemical potential induced by an increase in pressure appear to be dominated by the hydrophobic component, in particular when using the alternative correction. For bromide and iodide electrolytes, the two corrections give chemical potentials in good agreement.

When the Dust Has Settled: Calculation of Binding Affinities from First Principles for SARS-CoV-2 Variants with Quantitative Accuracy

Accurate determination of binding free energy is pivotal for the study of many biological processes and has been applied in a number of theoretical investigations to compare the affinity of severe acute respiratory syndrome coronavirus 2 variants toward the host cell. Diversity of these variants challenges the development of effective general therapies, their transmissibility relying either on an increased affinity toward their dedicated human receptor, the angiotensin-converting enzyme 2 (ACE2), or on escaping the immune response. Now that robust structural data are available, we have determined with utmost accuracy the standard binding free energy of the receptor-binding domain to the most widespread variants, namely, Alpha, Beta, Delta, and Omicron BA.2, as well as the wild type (WT) in complex either with ACE2 or with antibodies, namely, S2E12 and H11-D4, using a rigorous theoretical framework that combines molecular dynamics and potential-of-mean-force calculations. Our results show that an appropriate starting structure is crucial to ensure appropriate reproduction of the binding affinity, allowing the variants to be compared. They also emphasize the necessity to apply the relevant methodology, bereft of any shortcut, to account for all the contributions to the standard binding free energy. Our estimates of the binding affinities support the view that while the Alpha and Beta variants lean on an increased affinity toward the host cell, the Delta and Omicron BA.2 variants choose immune escape. Moreover, the S2E12 antibody, already known to be active against the WT (Starr et al., 2021; Mlcochova et al., 2021), proved to be equally effective against the Delta variant. In stark contrast, H11-D4 retains a low affinity toward the WT compared to that of ACE2 for the latter. Assuming robust structural information, the methodology employed herein successfully addresses the challenging protein-protein binding problem in the context of coronavirus disease 2019 while offering promising perspectives for predictive studies of ever-emerging variants.

Refinement of the Optimized Potentials for Liquid Simulations Force Field for Thermodynamics and Dynamics of Liquid Alkanes

Torsion and Lennard-Jones parameters of the optimized potentials for liquid simulations (OPLS) all-atom force field have been refined for describing thermodynamics and dynamics of a wide range of liquid alkanes. Monte Carlo statistical mechanics (MC) and molecular dynamics (MD) simulations were carried out. For thermodynamics properties, MC simulations with truncated electrostatic interactions performed very closely to MD simulations with a Verlet neighbor list and the particle mesh Ewald algorithm. The average errors in comparison with experimental data for computed properties were improved with the modified force field (OPLS/2020), especially for long-chain alkanes. For liquid densities, heats of vaporization, and free energies of hydration, the average errors are 0.01 g/cm³, 0.2 kcal/mol, and ca. 0.5 kcal/mol, respectively; significant gains were made for relative heats of vaporization of isomeric series. Results for self-diffusion coefficients also reproduce experimental data well for linear alkane liquids up to hexadecane. The new force field is suitable for use in improved modeling of myriad systems of importance in chemistry, biology, and materials science.

Surface Roughness Explains the Observed Water Contact Angle and Slip Length on 2D Hexagonal Boron Nitride

Hexagonal boron nitride (hBN) is a two-dimensional (2D) material that is currently being explored in a number of applications, such as atomically thin coatings, water desalination, and biological sensors. In many of these applications, the hBN surface comes into intimate contact with water. In this work, we investigate the wetting and frictional behavior of realistic 2D hBN surfaces with atomic-scale defects and roughness. We combine density functional theory calculations of the charge distribution inside hBN with free energy calculations using molecular dynamics simulations of the hBN-water interface. We find that the presence of surface roughness, but not that of vacancy defects, leads to remarkable agreement with the experimentally observed water contact angle of 66° on freshly synthesized, uncontaminated hBN. Not only that, the inclusion of surface roughness predicts with exceptional accuracy the experimental water slip length of ∼1 nm on hBN. Our results underscore the importance of considering realistic models of 2D materials with surface roughness while modeling nanomaterial-water interfaces in molecular simulations.

Protein-Ligand Docking in the Machine-Learning Era

Molecular docking plays a significant role in early-stage drug discovery, from structure-based virtual screening (VS) to hit-to-lead optimization, and its capability and predictive power is critically dependent on the protein-ligand scoring function. In this review, we give a broad overview of recent scoring function development, as well as the docking-based applications in drug discovery. We outline the strategies and resources available for structure-based VS and discuss the assessment and development of classical and machine learning protein-ligand scoring functions. In particular, we highlight the recent progress of machine learning scoring function ranging from descriptor-based models to deep learning approaches. We also discuss the general workflow and docking protocols of structure-based VS, such as structure preparation, binding site detection, docking strategies, and post-docking filter/re-scoring, as well as a case study on the large-scale docking-based VS test on the LIT-PCBA data set.

Alchemical Free Energy Calculations to Investigate Protein-Protein Interactions: the Case of the CDC42/PAK1 Complex

Here, we show that alchemical free energy calculations can quantitatively compute the effect of mutations at the protein–protein interface. As a test case, we have used the protein complex formed by the small Rho-GTPase CDC42 and its downstream effector PAK1, a serine/threonine kinase. Notably, the CDC42/PAK1 complex offers a wealth of structural, mutagenesis, and binding affinity data because of its central role in cellular signaling and cancer progression. In this context, we have considered 16 mutations in the CDC42/PAK1 complex and obtained excellent agreement between computed and experimental data on binding affinity. Importantly, we also show that a careful analysis of the side-chain conformations in the mutated amino acids can considerably improve the computed estimates, solving issues related to sampling limitations. Overall, this study demonstrates that alchemical free energy calculations can conveniently be integrated into the design of experimental mutagenesis studies.

Toward in Silico Modeling of Dynamic Combinatorial Libraries

Dynamic combinatorial libraries (DCLs) display adaptive behavior, enabled by the reversible generation of their molecular constituents from building blocks, in response to external effectors, e.g., protein receptors. So far, chemoinformatics has not yet been used for the design of DCLs-which comprise a radically different set of challenges compared to classical library design. Here, we propose a chemoinformatic model for theoretically assessing the composition of DCLs in the presence and the absence of an effector. An imine-based DCL in interaction with the effector human carbonic anhydrase II (CA II) served as a case study. Support vector regression models for the imine formation constants and imine-CA II binding were derived from, respectively, a set of 276 imines synthesized and experimentally studied in this work and 4350 inhibitors of CA II from ChEMBL. These models predict constants for all DCL constituents, to feed software assessing equilibrium concentrations. They are publicly available on the dedicated website. Models rationally selected two amines and two aldehydes predicted to yield stable imines with high affinity for CA II and provided a virtual illustration on how effector affinity regulates DCL members.

Modified Hamiltonian in FEP Calculations for Reducing the Computational Cost of Electrostatic Interactions

The free-energy perturbation (FEP) method predicts relative and absolute free-energy changes of biomolecules in solvation and binding with other molecules. FEP is, therefore, one of the most essential tools in in silico drug design. In conventional FEP, to smoothly connect two thermodynamic states, the potential energy is modified as a linear combination of the end-state potential energies by introducing scaling factors. When the particle mesh Ewald is used for electrostatic calculations, conventional FEP requires two reciprocal-space calculations per time step, which largely decreases the computational performance. To overcome this problem, we propose a new FEP scheme by introducing a modified Hamiltonian instead of interpolation of the end-state potential energies. The scheme introduces nonuniform scaling into the electrostatic potential as used in Replica Exchange with Solute Tempering 2 (REST2) and does not require additional reciprocal-space calculations. We tested this modified Hamiltonian in FEP calculations in several biomolecular systems. In all cases, the calculated free-energy changes with the current scheme are in good agreement with those from conventional FEP. The modified Hamiltonian in FEP greatly improves the computational performance, which is particularly marked for large biomolecular systems whose reciprocal-space calculations are the major bottleneck of total computational time.

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.

Exploring the Binding Mechanism of a Supramolecular Tweezer CLR01 to 14-3-3σ Protein via Well-Tempered Metadynamics

Using supramolecules for protein function regulation is an effective strategy in chemical biology and drug discovery. However, due to the presence of multiple binding sites on protein surfaces, protein function regulation via selective binding of supramolecules is challenging. Recently, the functions of 14-3-3 proteins, which play an important role in regulating intracellular signaling pathways via protein–protein interactions, have been modulated using a supramolecular tweezer, CLR01. However, the binding mechanisms of the tweezer molecule to 14-3-3 proteins are still unclear, which has hindered the development of novel supramolecules targeting the 14-3-3 proteins. Herein, the binding mechanisms of the tweezer to the lysine residues on 14-3-3σ (an isoform in 14-3-3 protein family) were explored by well-tempered metadynamics. The results indicated that the inclusion complex formed between the protein and supramolecule is affected by both kinetic and thermodynamic factors. In particular, simulations confirmed that K214 could form a strong binding complex with the tweezer; the binding free energy was calculated to be −10.5 kcal·mol⁻¹ with an association barrier height of 3.7 kcal·mol⁻¹. In addition, several other lysine residues on 14-3-3σ were identified as being well-recognized by the tweezer, which agrees with experimental results, although only K214/tweezer was co-crystallized. Additionally, the binding mechanisms of the tweezer to all lysine residues were analyzed by exploring the representative conformations during the formation of the inclusion complex. This could be helpful for the development of new inhibitors based on tweezers with more functions against 14-3-3 proteins via modifications of CLR01. We also believe that the proposed computational strategies can be extended to understand the binding mechanism of multi-binding sites proteins with supramolecules and will, thus, be useful toward drug design.

Accurate calculation of absolute free energy of binding for SHP2 allosteric inhibitors using free energy perturbation

Accurate prediction of binding affinity is a primary objective in structure-based drug discovery. A free energy perturbation (FEP) method based on molecular dynamics simulation shows great promise for protein-ligand binding affinity predictions. However, accurate calculation of binding affinity for allosteric inhibitors remains unknown and elusive, which hampers the discovery of allosteric inhibitors. Allosteric inhibitors exhibit several significant advantages over orthosteric inhibitors including higher specificity and lower side effects. Allosteric inhibitors against SHP2 are thought to be beneficial not only for diseases related to metabolism, but also for cancer, which make SHP2 a potential drug target. However, high structural sensitivity makes structural optimization of SHP2 allosteric inhibitors face challenges. Herein, we calculated the absolute binding free energy of SHP2 allosteric inhibitors using the FEP method by employing different λ-windows/simulation time sampling strategies. A simulation run with 32 λ-windows/64 ps sampling strategy delivered an excellent correlation (r = 0.96) and an unprecedented low mean absolute error of 0.5 kcal mol^-1 between predicted binding free energies and experimental ones, outperforming the MM/PBSA method. Our study demonstrates the possibility to accurately calculate the absolute binding free energy of allosteric inhibitors using FEP, which offers exciting prospects for the discovery of more effective allosteric inhibitors.

Parameterization and Application of the General Amber Force Field to Model Fluoro Substituted Furanose Moieties and Nucleosides

Molecular mechanics force field calculations have historically shown significant limitations in modeling the energetic and conformational interconversions of highly substituted furanose rings. This is primarily due to the gauche effect that is not easily captured using pairwise energy potentials. In this study, we present a refinement to the set of torsional parameters in the General Amber Force Field (gaff) used to calculate the potential energy of mono, di-, and gem-fluorinated nucleosides. The parameters were optimized to reproduce the pseudorotation phase angle and relative energies of a diverse set of mono- and difluoro substituted furanose ring systems using quantum mechanics umbrella sampling techniques available in the IpolQ engine in the Amber suite of programs. The parameters were developed to be internally consistent with the gaff force field and the TIP3P water model. The new set of angle and dihedral parameters and partial charges were validated by comparing the calculated phase angle probability to those obtained from experimental nuclear magnetic resonance experiments.

Combined Free-Energy Calculation and Machine Learning Methods for Understanding Ligand Unbinding Kinetics

The determination of drug residence times, which define the time an inhibitor is in complex with its target, is a fundamental part of the drug discovery process. Synthesis and experimental measurements of kinetic rate constants are, however, expensive and time consuming. In this work, we aimed to obtain drug residence times computationally. Furthermore, we propose a novel algorithm to identify molecular design objectives based on ligand unbinding kinetics. We designed an enhanced sampling technique to accurately predict the free-energy profiles of the ligand unbinding process, focusing on the free-energy barrier for unbinding. Our method first identifies unbinding paths determining a corresponding set of internal coordinates (ICs) that form contacts between the protein and the ligand; it then iteratively updates these interactions during a series of biased molecular dynamics (MD) simulations to reveal the ICs that are important for the whole of the unbinding process. Subsequently, we performed finite-temperature string simulations to obtain the free-energy barrier for unbinding using the set of ICs as a complex reaction coordinate. Importantly, we also aimed to enable the further design of drugs focusing on improved residence times. To this end, we developed a supervised machine learning (ML) approach with inputs from unbiased “downhill” trajectories initiated near the transition state (TS) ensemble of the string unbinding path. We demonstrate that our ML method can identify key ligand–protein interactions driving the system through the TS. Some of the most important drugs for cancer treatment are kinase inhibitors. One of these kinase targets is cyclin-dependent kinase 2 (CDK2), an appealing target for anticancer drug development. Here, we tested our method using two different CDK2 inhibitors for the potential further development of these compounds. We compared the free-energy barriers obtained from our calculations with those observed in available experimental data. We highlighted important interactions at the distal ends of the ligands that can be targeted for improved residence times. Our method provides a new tool to determine unbinding rates and to identify key structural features of the inhibitors that can be used as starting points for novel design strategies in drug discovery.

Assessing the Performance of Screening MM/PBSA in Protein-Ligand Interactions

Accurate calculation of the binding free energies between a protein and a ligand is the primary objective of structure-based drug design, but it still remains a challenging problem. In this work, we apply the screening molecular mechanics/Poisson Boltzmann surface area (MM/PBSA) method to calculate the binding affinity of protein-ligand interactions. Our results show that the performance of the screening MM/PBSA is better than that of the standard MM/PBSA, especially in a charged-ligand system. In addition, we also investigate the effect of the solute dielectric constant on the results, and find that the optimal solute dielectric constants are different between the neutral-ligand system and the charged-ligand system. Moreover, we also evaluate the effect of the atomic-charge methods on the performance of the screening MM/PBSA. The present study demonstrates that the screening MM/PBSA should be a reliable method for calculating binding energy of biosystems.

Efficient calculation of protein-ligand binding free energy with GFN methods: the power of cluster model

The protein-ligand interactions are crucial in many biochemical processes and biomedical applications, yet it still remains challenging to accurately calculating the binding free energy of their interactions. In this work,...

Free Energy-Based Computational Methods for the Study of Protein-Peptide Binding Equilibria

This chapter discusses the theory and application of physics-based free energy methods to estimate protein-peptide binding free energies. It presents a statistical mechanics formulation of molecular binding, which is then specialized in three methodologies: (1) alchemical absolute binding free energy estimation with implicit solvation, (2) alchemical relative binding free energy estimation with explicit solvation, and (3) potential of mean force binding free energy estimation. Case studies of protein-peptide binding application taken from the recent literature are discussed for each method.

Ab initio molecular dynamics with enhanced sampling in heterogeneous catalysis

Enhanced sampling ab initio simulations enable to study chemical phenomena in catalytic systems including thermal effects & anharmonicity, & collective dynamics describing enthalpic & entropic contributions, which can significantly impact on reaction free energy landscapes.

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.

Influence of water content on the [2σ+2σ+2π] cycloaddition of dimethyl azodicarboxylate with quadricyclane in mixed methanol-water solvents from QM/MM Monte Carlo simulations

Mixed quantum mechanics/molecular mechanics Monte Carlo (QM/MM/MC) simulations combined with the free energy perturbation (FEP) theory have been performed to investigate the mechanism and solvent effect of the [2σ+2σ+2π] cycloaddition reaction between dimethyl azodicarboxylate and quadricyclanes in the binary mixture solvents of methanol and water by varying the water content from 0 to 100 vol%. The two-dimensional potentials of mean force (2D PMF) calculations demonstrated that the mechanism of the reaction is a collaborative asynchronous procedure. The transition structures do not show large variation among different solvents. The calculated free energies of activation indicated that the QM/MM/MC method reproduced well the tendency of rate enhancement from pure methanol to methanol-water mixtures to "on water" with the water content increasing obtained in the experimental observation. The analyses of the energy pair distribution and radial distribution functions illustrated that hydrogen bonding plays an indispensable role in the stabilization of the transition structures. According to the results in methanol-water mixtures at different volume ratios, it is clear that the site-specific hydrogen bond effects are the central reason which leads to fast rate increases in progressing from a methanol-water volume ratio of 3 : 1 to 1 : 1. This work provides a new insight into the solvent effect for the [2σ+2σ+2π] cycloaddition reaction.

Efficient Alchemical Intermediate States in Free Energy Calculations Using λ-Enveloping Distribution Sampling

Alchemical free energy calculations generally require intermediate states along a coupling parameter λ to establish sufficient phase space overlap for obtaining converged results. Such intermediate states can also be engineered to lower the energy barriers and, consequently, reduce the required sampling time. The recently introduced λ-enveloping distribution sampling (λ-EDS) scheme combines the properties of the minimum variance pathway and the EDS methods to improve sampling and allow for larger steps along the alchemical pathway compared to conventional approaches. This scheme also eliminates the need for soft-core potentials and retains the behavior of conventional λ-intermediate states as a limiting case. In this study, an automated procedure is developed to select the parameters of λ-EDS for optimal performance. The underlying theory is illustrated based on simulations of simple test systems (bond length changes in harmonic oscillators, mutations of dihedral angles, and charge creation in water), as well as on the calculation of the absolute hydration free energies of 12 small organic molecules.

Probe into the Molecular Mechanism of Ibuprofen Interaction with Warfarin Bound to Human Serum Albumin in Comparison to Ascorbic and Salicylic Acids: Allosteric Inhibition of Anticoagulant Release

The release of anticoagulant drugs such as warfarin from human serum albumin (HSA) has been important not only mechanistically but also clinically for patients who take multiple drugs simultaneously. In this study, the role of some commonly used drugs, including s-ibuprofen, ascorbic acid, and salicylic acid, was investigated in the release of warfarin bound to HSA in silico. The effects of the aforementioned drugs on the HSA-warfarin complex were investigated with molecular dynamics (MD) simulations using two approaches; in the first perspective, molecular docking was used to model the interaction of each drug with the HSA-warfarin complex, and in the second approach, drugs were positioned randomly and distant from the binary complex (HSA-warfarin) in a physiologically relevant concentration. The results obtained from both approaches indicated that s-ibuprofen and ascorbic acid both displayed allosteric effects on the release of warfarin from HSA. Although ascorbic acid aided in warfarin release, leading to destabilization of HSA, ibuprofen demonstrated a stabilizing effect on releasing the anticoagulant drug through several noncovalent interactions, including hydrophobic, electrostatic, and hydrogen-bonding interactions with the protein. The calculated binding free energy and energy contribution of involved residues using the molecular mechanics-Poisson Boltzmann surface area (MM-PBSA) method, along with root mean square deviation (RMSD) values, protein gyration, and free energy surface (FES) mapping of the protein, provided valuable details on the nature of the interactions of each drug on the release of warfarin from HSA. These results can provide important information on the mechanisms of anticoagulant release that has not been revealed in molecular details previously.

Dynamics-Based Discovery of Novel, Potent Benzoic Acid Derivatives as Orally Bioavailable Selective Estrogen Receptor Degraders for ERα+ Breast Cancer

The estrogen receptor α (ERα) is identified as an effective target for the treatment of ERα+ breast cancer; thus, discovery of novel selective estrogen receptor degraders (SERDs) are developed as an effective method to overcome the resistance of breast cancer. Herein, the hot-spot residues for protein-ligand interaction between SERDs and ERα are analyzed by molecular dynamic simulation technology, focusing on the hot-spot residues for four series of designed and synthesized SERDs. SAR studies revealed that while the acrylic acid moiety of AZD9496 is scaffold hopping into benzoic acid, compound D24 exhibits potent binding affinity with ERα, good degradation efficacy of ERα, and inhibitory effect against the MCF-7 breast cancer cell line. Besides, D24 also displays good antitumor efficacy in the MCF-7 human breast cancer xenograft model in vivo, favorable pharmacokinetic properties, excellent druggability, and good safety property, making D24 as a promising drug candidate of SERD for further evaluation.

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.

Multi-replica biased sampling for photoswitchable π-conjugated polymers

In recent years, π-conjugated polymers are attracting considerable interest in view of their light-dependent torsional reorganization around the π-conjugated backbone, which determines peculiar light-emitting properties. Motivated by the interest in designing conjugated polymers with tunable photoswitchable pathways, we devised a computational framework to enhance the sampling of the torsional conformational space and, at the same time, estimate ground- to excited-state free-energy differences. This scheme is based on a combination of Hamiltonian Replica Exchange Method (REM), parallel bias metadynamics, and free-energy perturbation theory. In our scheme, each REM samples an intermediate unphysical state between the ground and the first two excited states, which are characterized by time-dependent density functional theory simulations at the B3LYP/6-31G^* level of theory. We applied the method to a 5-mer of 9,9-dioctylfluorene and found that upon irradiation, this system can undergo a dihedral inversion from -155° to 155°, crossing a barrier that decreases from 0.1 eV in the ground state (S₀) to 0.05 eV and 0.04 eV in the first (S₁) and second (S₂) excited states. Furthermore, S₁ and even more S₂ were predicted to stabilize coplanar dihedrals, with a local free-energy minimum located at ±44°. The presence of a free-energy barrier of 0.08 eV for the S₁ state and 0.12 eV for the S₂ state can trap this conformation in a basin far from the global free-energy minimum located at 155°. The simulation results were compared with the experimental emission spectrum, showing a quantitative agreement with the predictions provided by our framework.