Novel Directions in Free Energy Methods and Applications

Understanding the impact of binding free energy and kinetics calculations in modern drug discovery

INTRODUCTION

For rational drug design, it is crucial to understand the receptor-drug binding processes and mechanisms. A new era for the use of computer simulations in predicting drug-receptor interactions at an atomic level has begun with remarkable advances in supercomputing and methodological breakthroughs.

AREAS COVERED

End-point free energy calculation methods such as Molecular Mechanics/Poisson Boltzmann Surface Area (MM/PBSA) or Molecular-Mechanics/Generalized Born Surface Area (MM/GBSA), free energy perturbation (FEP), and thermodynamic integration (TI) are commonly used for binding free energy calculations in drug discovery. In addition, kinetic dissociation and association rate constants (k off and k on ) play critical roles in the function of drugs. Nowadays, Molecular Dynamics (MD) and enhanced sampling simulations are increasingly being used in drug discovery. Here, the authors provide a review of the computational techniques used in drug binding free energy and kinetics calculations.

EXPERT OPINION

The applications of computational methods in drug discovery and design are expanding, thanks to improved predictions of the binding free energy and kinetic rates of drug molecules. Recent microsecond-timescale enhanced sampling simulations have made it possible to accurately capture repetitive ligand binding and dissociation, facilitating more efficient and accurate calculations of ligand binding free energy and kinetics.

Kartograf: A Geometrically Accurate Atom Mapper for Hybrid-Topology Relative Free Energy Calculations

Relative binding free energy (RBFE) calculations have emerged as a powerful tool that supports ligand optimization in drug discovery. Despite many successes, the use of RBFEs can often be limited by automation problems, in particular, the setup of such calculations. Atom mapping algorithms are an essential component in setting up automatic large-scale hybrid-topology RBFE calculation campaigns. Traditional algorithms typically employ a 2D subgraph isomorphism solver (SIS) in order to estimate the maximum common substructure. SIS-based approaches can be limited by time-intensive operations and issues with capturing geometry-linked chemical properties, potentially leading to suboptimal solutions. To overcome these limitations, we have developed Kartograf, a geometric-graph-based algorithm that uses primarily the 3D coordinates of atoms to find a mapping between two ligands. In free energy approaches, the ligand conformations are usually derived from docking or other previous modeling approaches, giving the coordinates a certain importance. By considering the spatial relationships between atoms related to the molecule coordinates, our algorithm bypasses the computationally complex subgraph matching of SIS-based approaches and reduces the problem to a much simpler bipartite graph matching problem. Moreover, Kartograf effectively circumvents typical mapping issues induced by molecule symmetry and stereoisomerism, making it a more robust approach for atom mapping from a geometric perspective. To validate our method, we calculated mappings with our novel approach using a diverse set of small molecules and used the mappings in relative hydration and binding free energy calculations. The comparison with two SIS-based algorithms showed that Kartograf offers a fast alternative approach. The code for Kartograf is freely available on GitHub (https://github.com/OpenFreeEnergy/kartograf). While developed for the OpenFE ecosystem, Kartograf can also be utilized as a standalone Python package.

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

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

What to Make of Zero: Resolving the Statistical Noise from Conformational Reorganization in Alchemical Binding Free Energy Estimates with Metadynamics Sampling

We introduce the self-relative binding free energy (self-RBFE) approach to evaluate the intrinsic statistical variance of dual-topology alchemical binding free energy estimators. The self-RBFE is the relative binding free energy between a ligand and a copy of the same ligand, and its true value is zero. Nevertheless, because the two copies of the ligand move independently, the self-RBFE value produced by a finite-length simulation fluctuates and can be used to measure the variance of the model. The results of this validation provide evidence that a significant fraction of the errors observed in benchmark studies reflect the statistical fluctuations of unconverged estimates rather than the models' accuracy. Furthermore, we find that ligand reorganization is a significant contributing factor to the statistical variance of binding free energy estimates and that metadynamics-accelerated conformational sampling of the torsional degrees of freedom of the ligand can drastically reduce the time to convergence.

Performance and Analysis of the Alchemical Transfer Method for Binding-Free-Energy Predictions of Diverse Ligands

The Alchemical Transfer Method (ATM) is herein validated against the relative binding-free energies (RBFEs) of a diverse set of protein-ligand complexes. We employed a streamlined setup workflow, a bespoke force field, and AToM-OpenMM software to compute the RBFEs of the benchmark set prepared by Schindler and collaborators at Merck KGaA. This benchmark set includes examples of standard small R-group ligand modifications as well as more challenging scenarios, such as large R-group changes, scaffold hopping, formal charge changes, and charge-shifting transformations. The novel coordinate perturbation scheme and a dual-topology approach of ATM address some of the challenges of single-topology alchemical RBFE methods. Specifically, ATM eliminates the need for splitting electrostatic and Lennard-Jones interactions, atom mapping, defining ligand regions, and postcorrections for charge-changing perturbations. Thus, ATM is simpler and more broadly applicable than conventional alchemical methods, especially for scaffold-hopping and charge-changing transformations. Here, we performed well over 500 RBFE calculations for eight protein targets and found that ATM achieves accuracy comparable to that of existing state-of-the-art methods, albeit with larger statistical fluctuations. We discuss insights into the specific strengths and weaknesses of the ATM method that will inform future deployments. This study confirms that ATM can be applied as a production tool for RBFE predictions across a wide range of perturbation types within a unified, open-source framework.

Alchemical Free Energy Calculations on Membrane-Associated Proteins

Membrane proteins have diverse functions within cells and are well-established drug targets. The advances in membrane protein structural biology have revealed drug and lipid binding sites on membrane proteins, while computational methods such as molecular simulations can resolve the thermodynamic basis of these interactions. Particularly, alchemical free energy calculations have shown promise in the calculation of reliable and reproducible binding free energies of protein-ligand and protein-lipid complexes in membrane-associated systems. In this review, we present an overview of representative alchemical free energy studies on G-protein-coupled receptors, ion channels, transporters as well as protein-lipid interactions, with emphasis on best practices and critical aspects of running these simulations. Additionally, we analyze challenges and successes when running alchemical free energy calculations on membrane-associated proteins. Finally, we highlight the value of alchemical free energy calculations calculations in drug discovery and their applicability in the pharmaceutical industry.

Learned mappings for targeted free energy perturbation between peptide conformations

Targeted free energy perturbation uses an invertible mapping to promote configuration space overlap and the convergence of free energy estimates. However, developing suitable mappings can be challenging. Wirnsberger et al. [J. Chem. Phys. 153, 144112 (2020)] demonstrated the use of machine learning to train deep neural networks that map between Boltzmann distributions for different thermodynamic states. Here, we adapt their approach to the free energy differences of a flexible bonded molecule, deca-alanine, with harmonic biases and different spring centers. When the neural network is trained until "early stopping"-when the loss value of the test set increases-we calculate accurate free energy differences between thermodynamic states with spring centers separated by 1 Å and sometimes 2 Å. For more distant thermodynamic states, the mapping does not produce structures representative of the target state, and the method does not reproduce reference calculations.

Validation of the Alchemical Transfer Method for the Estimation of Relative Binding Affinities of Molecular Series

The accurate prediction of protein-ligand binding affinities is crucial for drug discovery. Alchemical free energy calculations have become a popular tool for this purpose. However, the accuracy and reliability of these methods can vary depending on the methodology. In this study, we evaluate the performance of a relative binding free energy protocol based on the alchemical transfer method (ATM), a novel approach based on a coordinate transformation that swaps the positions of two ligands. The results show that ATM matches the performance of more complex free energy perturbation (FEP) methods in terms of Pearson correlation but with marginally higher mean absolute errors. This study shows that the ATM method is competitive compared to more traditional methods in speed and accuracy and offers the advantage of being applicable with any potential energy function.

Comparative Interaction Studies of Quercetin with 2-Hydroxyl-propyl-β-cyclodextrin and 2,6-Methylated-β-cyclodextrin

Quercetin (QUE) is a well-known natural product that can exert beneficial properties on human health. However, due to its low solubility its bioavailability is limited. In the present study, we examine whether its formulation with two cyclodextrins (CDs) may enhance its pharmacological profile. Comparative interaction studies of quercetin with 2-hydroxyl-propyl-β-cyclodextrin (2HP-β-CD) and 2,6-methylated cyclodextrin (2,6Me-β-CD) were performed using NMR spectroscopy, DFT calculations, and in silico molecular dynamics (MD) simulations. Using T1 relaxation experiments and 2D DOSY it was illustrated that both cyclodextrin vehicles can host quercetin. Quantum mechanical calculations showed the formation of hydrogen bonds between QUE with 2HP-β-CD and 2,6Μe-β-CD. Six hydrogen bonds are formed ranging between 2 to 2.8 Å with 2HP-β-CD and four hydrogen bonds within 2.8 Å with 2,6Μe-β-CD. Calculations of absolute binding free energies show that quercetin binds favorably to both 2,6Me-β-CD and 2HP-β-CD. MM/GBSA results show equally favorable binding of quercetin in the two CDs. Fluorescence spectroscopy shows moderate binding of quercetin in 2HP-β-CD (520 M-1) and 2,6Me-β-CD (770 M-1). Thus, we propose that both formulations (2HP-β-CD:quercetin, 2,6Me-β-CD:quercetin) could be further explored and exploited as small molecule carriers in biological studies.

Leveraging the Sampling Efficiency of RE-EDS in OpenMM Using a Shifted Reaction-Field With an Atom-Based Cutoff

Replica-exchange enveloping distribution sampling (RE-EDS) is a pathway-independent multistate free-energy method, currently implemented in the GROMOS software package for molecular dynamics (MD) simulations. It has a high intrinsic sampling efficiency as the interactions between the unperturbed particles have to be calculated only once for multiple end-states. As a result, RE-EDS is an attractive method for the calculation of relative solvation and binding free energies. An essential requirement for reaching this high efficiency is the separability of the nonbonded interactions into solute-solute, solute-environment, and environment-environment contributions. Such a partitioning is trivial when using a Coulomb term with a reaction-field (RF) correction to model the electrostatic interactions, but not when using lattice- sum schemes. To avoid cutoff artifacts, the RF correction is typically used in combination with a charge-group based cutoff, which is not supported by most small-molecule force fields and other MD engines. To address this issue, we investigate the combination of RE-EDS simulations with a recently introduced RF scheme including a shifting function that enables the rigorous calculation of RF electrostatics with atom-based cutoffs. The resulting approach is validated by calculating solvation free energies with the generalized AMBER force field (GAFF) in water and chloroform using both the GROMOS software package and a proof-of-concept implementation in OpenMM.

Replica-Exchange Enveloping Distribution Sampling Using Generalized AMBER Force-Field Topologies: Application to Relative Hydration Free-Energy Calculations for Large Sets of Molecules

Free-energy differences between pairs of end-states can be estimated based on molecular dynamics (MD) simulations using standard pathway-dependent methods such as thermodynamic integration (TI), free-energy perturbation, or Bennett’s acceptance ratio. Replica-exchange enveloping distribution sampling (RE-EDS), on the other hand, allows for the sampling of multiple end-states in a single simulation without the specification of any pathways. In this work, we use the RE-EDS method as implemented in GROMOS together with generalized AMBER force-field (GAFF) topologies, converted to a GROMOS-compatible format with a newly developed GROMOS++ program amber2gromos, to compute relative hydration free energies for a series of benzene derivatives. The results obtained with RE-EDS are compared to the experimental data as well as calculated values from the literature. In addition, the estimated free-energy differences in water and in vacuum are compared to values from TI calculations carried out with GROMACS. The hydration free energies obtained using RE-EDS for multiple molecules are found to be in good agreement with both the experimental data and the results calculated using other free-energy methods. While all considered free-energy methods delivered accurate results, the RE-EDS calculations required the least amount of total simulation time. This work serves as a validation for the use of GAFF topologies with the GROMOS simulation package and the RE-EDS approach. Furthermore, the performance of RE-EDS for a large set of 28 end-states is assessed with promising results.

Dissociation Pathways of the p53 DNA Binding Domain from DNA and Critical Roles of Key Residues Elucidated by dPaCS-MD/MSM

p53 is a transcriptional factor that regulates cell response to a variety of stresses. About a half of all human tumors contain p53 mutations, and the accumulation of mutations in the DNA binding domain of p53 (p53-DBD) can cause destabilization of p53 and its complex with DNA. To identify the key residues of the p53-DBD/DNA binding and to understand the dissociation mechanisms of the p53-DBD/DNA complex, the dissociation process of p53-DBD from a DNA duplex that contains the consensus sequence (the specific target of p53-DBD) was investigated by a combination of dissociation parallel cascade selection molecular dynamics (dPaCS-MD) and the Markov state model (MSM). This combination (dPaCS-MD/MSM) enabled us to simulate dissociation of the two large molecules based on an all-atom model with a short simulation time (11.2 ± 2.2 ns per trial) and to analyze dissociation pathways, free energy landscape (FEL), and binding free energy. Among 75 trials of dPaCS-MD, p53-DBD dissociated first from the major groove and then detached from the minor groove in 93% of the cases, while 7% of the cases unbinding from the minor groove occurred first. Minor groove binding is mainly stabilized by R248, identified as the most important residue that tightly binds deep inside the minor groove. The standard binding free energy calculated from the FEL was -10.9 ± 0.4 kcal/mol, which agrees with an experimental value of -11.1 kcal/mol. These results indicate that the dPaCS-MD/MSM combination can be a powerful tool to investigate dissociation mechanisms of two large molecules. Analysis of the p53 key residues for DNA binding indicates high correlations with cancer-related mutations, confirming that impairment of the interactions between p53-DBD and DNA can be frequently related to cancer.

RestraintMaker: a graph-based approach to select distance restraints in free-energy calculations with dual topology

The calculation of relative binding free energies (RBFE) involves the choice of the end-state/system representation, of a sampling approach, and of a free-energy estimator. System representations are usually termed "single topology" or "dual topology". As the terminology is often used ambiguously in the literature, a systematic categorization of the system representations is proposed here. In the dual-topology approach, the molecules are simulated as separate molecules. Such an approach is relatively easy to automate for high-throughput RBFE calculations compared to the single-topology approach. Distance restraints are commonly applied to prevent the molecules from drifting apart, thereby improving the sampling efficiency. In this study, we introduce the program RestraintMaker, which relies on a greedy algorithm to find (locally) optimal distance restraints between pairs of atoms based on geometric measures. The algorithm is further extended for multi-state methods such as enveloping distribution sampling (EDS) or multi-site [Formula: see text]-dynamics. The performance of RestraintMaker is demonstrated for toy models and for the calculation of relative hydration free energies. The Python program can be used in script form or through an interactive GUI within PyMol. The selected distance restraints can be written out in GROMOS or GROMACS file formats. Additionally, the program provides a human-readable JSON format that can easily be parsed and processed further. The code of RestraintMaker is freely available on GitHub https://github.com/rinikerlab/restraintmaker.

Binding free energy of protein/ligand complexes calculated using dissociation Parallel Cascade Selection Molecular Dynamics and Markov state model

We recently proposed a computational procedure to simulate the dissociation of protein/ligand complexes using the dissociation Parallel Cascade Selection Molecular Dynamics simulation (dPaCS-MD) method and to analyze the generated trajectories using the Markov state model (MSM). This procedure, called dPaCS-MD/MSM, enables calculation of the dissociation free energy profile and the standard binding free energy. To examine whether this method can reproduce experimentally determined binding free energies for a variety of systems, we used it to investigate the dissociation of three protein/ligand complexes: trypsin/benzamine, FKBP/FK506, and adenosine A_2A receptor/T4E. First, dPaCS-MD generated multiple dissociation pathways within a reasonable computational time for all the complexes, although the complexes differed significantly in the size of the molecules and in intermolecular interactions. Subsequent MSM analyses produced free energy profiles for the dissociations, which provided insights into how each ligand dissociates from the protein. The standard binding free energies obtained by dPaCS-MD/MSM are in good agreement with experimental values for all the complexes. We conclude that dPaCS-MD/MSM can accurately calculate the binding free energies of these complexes.

Relative Binding Free Energy Calculations for Ligands with Diverse Scaffolds with the Alchemical Transfer Method

We present an extension of the alchemical transfer method (ATM) for the estimation of relative binding free energies of molecular complexes applicable to conventional, as well as scaffold-hopping, alchemical transformations. Named ATM-RBFE, the method is implemented in the free and open-source OpenMM molecular simulation package and aims to provide a simpler and more generally applicable route to the calculation of relative binding free energies than what is currently available. ATM-RBFE is based on sound statistical mechanics theory and a novel coordinate perturbation scheme designed to swap the positions of a pair of ligands such that one is transferred from the bulk solvent to the receptor binding site while the other moves simultaneously in the opposite direction. The calculation is conducted directly in a single solvent box with a system prepared with conventional setup tools, without splitting of electrostatic and nonelectrostatic transformations, and without pairwise soft-core potentials. ATM-RBFE is validated here against the absolute binding free energies of the SAMPL8 GDCC host-guest benchmark set and against protein-ligand benchmark sets that include complexes of the estrogen receptor ERα and those of the methyltransferase EZH2. In each case the method yields self-consistent and converged relative binding free energy estimates in agreement with absolute binding free energies and reference literature values, as well as experimental measurements.

Relative free-energy calculations for scaffold hopping-type transformations with an automated RE-EDS sampling procedure

The calculation of relative free-energy differences between different compounds plays an important role in drug design to identify potent binders for a given protein target. Most rigorous methods based on molecular dynamics simulations estimate the free-energy difference between pairs of ligands. Thus, the comparison of multiple ligands requires the construction of a “state graph”, in which the compounds are connected by alchemical transformations. The computational cost can be optimized by reducing the state graph to a minimal set of transformations. However, this may require individual adaptation of the sampling strategy if a transformation process does not converge in a given simulation time. In contrast, path-free methods like replica-exchange enveloping distribution sampling (RE-EDS) allow the sampling of multiple states within a single simulation without the pre-definition of alchemical transition paths. To optimize sampling and convergence, a set of RE-EDS parameters needs to be estimated in a pre-processing step. Here, we present an automated procedure for this step that determines all required parameters, improving the robustness and ease of use of the methodology. To illustrate the performance, the relative binding free energies are calculated for a series of checkpoint kinase 1 inhibitors containing challenging transformations in ring size, opening/closing, and extension, which reflect changes observed in scaffold hopping. The simulation of such transformations with RE-EDS can be conducted with conventional force fields and, in particular, without soft bond-stretching terms.

Application of the alchemical transfer and potential of mean force methods to the SAMPL8 host-guest blinded challenge

We report the results of our participation in the SAMPL8 GDCC Blind Challenge for host-guest binding affinity predictions. Absolute binding affinity prediction is of central importance to the biophysics of molecular association and pharmaceutical discovery. The blinded SAMPL series have provided an important forum for assessing the reliability of binding free energy methods in an objective way. In this challenge, we employed two binding free energy methods, the newly developed alchemical transfer method (ATM) and the well-established potential of mean force (PMF) physical pathway method, using the same setup and force field model. The calculated binding free energies from the two methods are in excellent quantitative agreement. Importantly, the results from the two methods were also found to agree well with the experimental binding affinities released subsequently, with R values of 0.89 (ATM) and 0.83 (PMF). These results were ranked among the best of the SAMPL8 GDCC challenge and second only to those obtained with the more accurate AMOEBA force field. Interestingly, the two host molecules included in the challenge (TEMOA and TEETOA) displayed distinct binding mechanisms, with TEMOA undergoing a dehydration transition whereas guest binding to TEETOA resulted in the opening of the binding cavity that remains essentially dry during the process. The coupled reorganization and hydration equilibria observed in these systems is a useful prototype for the study of these phenomena often observed in the formation of protein-ligand complexes. Given that the two free energy methods employed here are based on entirely different thermodynamic pathways, the close agreement between the two and their general agreement with the experimental binding free energies are a testament to the high quality and precision achieved by theory and methods. The study provides further validation of the novel ATM binding free energy estimation protocol and paves the way to further extensions of the method to more complex systems.

Small-sample limit of the Bennett acceptance ratio method and the variationally derived intermediates

Free energy calculations based on atomistic Hamiltonians provide microscopic insight into the thermodynamic driving forces of biophysical or condensed matter systems. Many approaches use intermediate Hamiltonians interpolating between the two states for which the free energy difference is calculated. The Bennett acceptance ratio (BAR) and variationally derived intermediates (VI) methods are optimal estimator and intermediate states in that the mean-squared error of free energy calculations based on independent sampling is minimized. However, BAR and VI have been derived based on several approximations that do not hold for very few sample points. Analyzing one-dimensional test systems, we show that in such cases BAR and VI are suboptimal and that established uncertainty estimates are inaccurate. Whereas for VI to become optimal, less than seven samples per state suffice in all cases; for BAR the required number increases unboundedly with decreasing configuration space densities overlap of the end states. We show that for BAR, the required number of samples is related to the overlap through an inverse power law. Because this relation seems to hold universally and almost independent of other system properties, these findings can guide the proper choice of estimators for free energy calculations.

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.

Calculation of Energy for RNA/RNA and DNA/RNA Duplex Formation by Molecular Dynamics Simulation

Abstract

The development of approaches for predictive calculation of hybridization properties of various nucleic acid (NA) derivatives is the basis for the rational design of the NA-based constructs. Modern advances in computer modeling methods provide the feasibility of these calculations. We have analyzed the possibility of calculating the energy of DNA/RNA and RNA/RNA duplex formation using representative sets of complexes (65 and 75 complexes, respectively). We used the classical molecular dynamics (MD) method, the MMPBSA or MMGBSA approaches to calculate the enthalpy (ΔH°) component, and the quasi-harmonic approximation (Q-Harm) or the normal mode analysis (NMA) methods to calculate the entropy (ΔS°) contribution to the Gibbs energy ($$\Delta G_{{37}}^{^\circ }$$ ) of the NA complex formation. We have found that the MMGBSA method in the analysis of the MD trajectory of only the NA duplex and the empirical linear approximation allow calculation of the enthalpy of formation of the DNA, RNA, and hybrid duplexes of various lengths and GC content with an accuracy of 8.6%. Within each type of complex, the combination of rather efficient MMGBSA and Q-Harm approaches being applied to the trajectory of only the bimolecular complex makes it possible to calculate the $$\Delta G_{{37}}^{^\circ }$$ of the duplex formation with an error value of 10%. The high accuracy of predictive calculation for different types of natural complexes (DNA/RNA, DNA/RNA, and RNA/RNA) indicates the possibility of extending the considered approach to analogs and derivatives of nucleic acids, which gives a fundamental opportunity in the future to perform rational design of new types of NA-targeted sequence-specific compounds.

Polymyxin B1 within the E. coli cell envelope: insights from molecular dynamics simulations

Polymyxins are used as last-resort antibiotics, where other treatments have been ineffectual due to antibiotic resistance. However, resistance to polymyxins has also been now reported, therefore it is instructive to characterise at the molecular level, the mechanisms of action of polymyxins. Here we review insights into these mechanisms from molecular dynamics simulations and discuss the utility of simulations as a complementary technique to  experimental methodologies.

Binding Free Energy Calculations of Bilayer Graphenes Using Molecular Dynamics

Bilayer graphenes are dimeric assemblies of single graphene layers bound together by π-complexation interactions. Controlling these assemblies can be complicated, as the layered compounds disperse in solvents or aggregate into higher columnar configurations and clusters. One way to assess the interactions that contribute to the stability of the layered compounds is to use molecular simulation. We perform pulling molecular dynamics on bilayer graphenes with different sizes and obtain the normal and shear force profiles of dissociation. We generate pathways of dissociation along the two directions and calculate the binding free energies of the structures with umbrella sampling simulations. We show that the dissociation process is direction-dependent. Along the shear direction, we compute the same free energy for the different samples, which validates the consistency of our simulations. We notice that the dissociation is less adiabatic on the normal than the shear direction, having an entropic contribution to the Gibbs energy. This contribution is more enhanced for the larger bilayer graphenes.

Ensembler: A Simple Package for Fast Prototyping and Teaching Molecular Simulations

Ensembler is a Python package that enables method prototyping using 1D and 2D model systems and allows deepening of the understanding of different molecular dynamics (MD) methods, starting from basic techniques to enhanced sampling and free-energy approaches. The ease of installing and using the package increases shareability, comparability, and reproducibility of scientific code developments. Here, we describe the implementation and usage of the package and provide an application example for free-energy calculation. The code of Ensembler is freely available on GitHub at https://github.com/rinikerlab/Ensembler.

Characterization of Structural and Energetic Differences between Conformations of the SARS-CoV-2 Spike Protein

The novel coronavirus disease 2019 (COVID-19) pandemic has disrupted modern societies and their economies. The resurgence in COVID-19 cases as part of the second wave is observed across Europe and the Americas. The scientific response has enabled a complete structural characterization of the Severe Acute Respiratory Syndrome-novel Coronavirus 2 (SARS-CoV-2). Among the most relevant proteins required by the novel coronavirus to facilitate the cell entry mechanism is the spike protein. This protein possesses a receptor-binding domain (RBD) that binds the cellular angiotensin-converting enzyme 2 (ACE2) and then triggers the fusion of viral and host cell membranes. In this regard, a comprehensive characterization of the structural stability of the spike protein is a crucial step to find new therapeutics to interrupt the process of recognition. On the other hand, it has been suggested that the participation of more than one RBD is a possible mechanism to enhance cell entry. Here, we discuss the protein structural stability based on the computational determination of the dynamic contact map and the energetic difference of the spike protein conformations via the mapping of the hydration free energy by the Poisson-Boltzmann method. We expect our result to foster the discussion of the number of RBD involved during recognition and the repurposing of new drugs to disable the recognition by discovering new hotspots for drug targets apart from the flexible loop in the RBD that binds the ACE2.

An Alternative to Conventional λ-Intermediate States in Alchemical Free Energy Calculations: λ-Enveloping Distribution Sampling

Alchemical free energy calculations typically rely on intermediate states to bridge between the relevant phase spaces of the two end states. These intermediate states are usually created by mixing the energies or parameters of the end states according to a coupling parameter λ. The choice of the procedure has a strong impact on the efficiency of the calculation, as it affects both the encountered energy barriers and the phase space overlap between the states. The present work builds on the connection between the minimum variance pathway (MVP) and enveloping distribution sampling (EDS). It is shown that both methods can be regarded as special cases of a common scheme referred to as λ-EDS, which can also reproduce the behavior of conventional λ-intermediate states. A particularly attractive feature of λ-EDS is its ability to emulate the use of soft core potentials (SCP) while avoiding the associated computational overhead when applying efficient free energy estimators such as the multistate Bennett's acceptance ratio (MBAR). The method is illustrated for both relative and absolute free energy calculations considering five benchmark systems. The first two systems (charge inversion and cavity creation in a dipolar solvent) demonstrate the use of λ-EDS as an alternative coupling scheme in the context of thermodynamic integration (TI). The three other systems (change of bond length, change of dihedral angles, and cavity creation in water) investigate the efficiency and optimal choice of parameters in the context of free energy perturbation (FEP) and Bennett's acceptance ratio (BAR). It is shown that λ-EDS allows larger steps along the alchemical pathway than conventional intermediate states.

Computational and structural studies of MeCP2 and associated mutants

Rett Syndrome is a rare genetic disorder exclusively seen in girls. Approximately 95% of RTT cases is caused by mutations in the MeCP2 gene which codes for Methyl-CpG-binding protein 2 (MeCP2). In this review, first, a brief introductory review of Rett Syndrome, MeCP2 protein structure and function, mutation types and frequencies, and phenotype–genotype relationships were provided. After that, the current knowledge on the wild-type and mutant MeCP2 protein structure and dynamics as well as its binding to DNA is reviewed. The review particularly focuses on computational (such as molecular dynamics) and experimental (such as electrophoretic mobility shift assays) studies on the MeCP2 binding to different types of DNA as well as the computational and experimental (such as circular dichroism) studies on the stability changes upon mutations. In the end, a brief opinion on future outlook for further computational studies is provided.