On Calculating Free Energy Differences Using Ensembles of Transition Paths

Multimerization of TREM2 is impaired by Alzheimer's disease-associated variants

INTRODUCTION

The immune receptor triggering receptor expressed on myeloid cells 2 (TREM2) is among the strongest genetic risk factors for Alzheimer's disease (AD) and is a therapeutic target. TREM2 multimers have been identified in crystallography and implicated in the efficacy of antibody therapeutics; however, the molecular basis for TREM2 multimerization remains poorly understood.

METHODS

We used molecular dynamics simulations and binding energy analysis to determine the effects of AD-associated variants on TREM2 multimerization and validated with experimental results.

RESULTS

TREM2 trimers remained stably bound, driven primarily by salt bridge between residues D87 and R76 at the interface of TREM2 units. This salt bridge was disrupted by the AD-associated variants R47H and R98W and nearly ablated by the D87N variant. This decreased binding among TREM2 multimers was validated with co-immunoprecipitation assays.

DISCUSSION

This study uncovers a molecular basis for TREM2 forming stable trimers and unveils a novel mechanism by which TREM2 variants may increase AD risk by disrupting TREM2 oligomerization to impair TREM2 normal function.

HIGHLIGHTS

Triggering receptor expressed on myeloid cells 2 (TREM2) multimerization could regulate TREM2 activation and function. D87-R76 salt bridges at the interface of TREM2 units drive the formation of stable TREM2 dimers and trimers. Alzheimer's disease (AD)-associated R47H and R98W variants disrupt the D87-R76 salt bridge. The AD-associated D87N variant leads to complete loss of the D87-R76 salt bridge.

Calculating Binding Free Energies in Model Host-Guest Systems with Unrestrained Advanced Sampling

Host-guest interactions are important to the design of pharmaceuticals and, more broadly, to soft materials as they can enable targeted, strong, and specific interactions between molecules. The binding process between the host and guest may be classified as a "rare event" when viewing the system at atomic scales, such as those explored in molecular dynamics simulations. To obtain equilibrium binding conformations and dissociation constants from these simulations, it is essential to resolve these rare events. Advanced sampling methods such as the adaptive biasing force (ABF) promote the occurrence of less probable configurations in a system, therefore facilitating the sampling of essential collective variables that characterize the host-guest interactions. Here, we present the application of ABF to a rod-cavitand coarse-grained model of host-guest systems to acquire the potential of mean force. We show that the employment of ABF enables the computation of the configurational and thermodynamic properties of bound and unbound states, including the free energy landscape. Moreover, we identify important dynamic bottlenecks that limit sampling and discuss how these may be addressed in more general systems.

Virtual screening and molecular dynamics investigations using natural compounds against autotaxin for the treatment of chronic pain

Chronic pain is a common and debilitating condition with a huge social and economic burden worldwide. Currently, available drugs in clinics are not adequately effective and possess a variety of severe side effects leading to treatment withdrawal and poor quality of life. Recent findings highlight the potential role of autotaxin (ATX) as a promising novel target for chronic pain management, extending beyond its previously established involvement in arthritis and other neurological disorders, such as Alzheimer's disease. In the present study, we used a virtual screening strategy by targeting ATX against commercially available natural compounds (enamine- phenotypic screening library) to identify the potential inhibitors for the treatment of chronic pain. After initial identification using molecular docking based virtual screening, molecular mechanics (MM/GBSA), ADMET profiling and molecular dynamics simulation were performed to verify top hits. The computational screening resulted in the identification of fifteen top scoring structurally diverse hits that have free energy of binding (ΔG) values in the range of -25.792 (for compound Enamine_1850) to -74.722 Kcal/mol (for compound Enamine_1687). Moreover, the top-scoring hits have favourable ADME properties as calculated using in-silico algorithms. Additionally, the molecular dynamics simulation revealed the stable nature of protein-ligand interaction and provided information about amino acid residues involved in binding. This study led to the identification of potential autotaxin inhibitors with favourable pharmacokinetic properties. Identified hits may further be investigated for their safety and efficacy potential using in-vitro and in-vivo models of chronic pain.Communicated by Ramaswamy H. Sarma.

How Robust Is the Ligand Binding Transition State?

For many drug targets, it has been shown that the kinetics of drug binding (e.g., on rate and off rate) is more predictive of drug efficacy than thermodynamic quantities alone. This motivates the development of predictive computational models that can be used to optimize compounds on the basis of their kinetics. The structural details underpinning these computational models are found not only in the bound state but also in the short-lived ligand binding transition states. Although transition states cannot be directly observed experimentally due to their extremely short lifetimes, recent successes have demonstrated that modeling the ligand binding transition state is possible with the help of enhanced sampling molecular dynamics methods. Previously, we generated unbinding paths for an inhibitor of soluble epoxide hydrolase (sEH) with a residence time of 11 min. Here, we computationally modeled unbinding events with the weighted ensemble method REVO (resampling of ensembles by variation optimization) for five additional inhibitors of sEH with residence times ranging from 14.25 to 31.75 min, with average prediction accuracy within an order of magnitude. The unbinding ensembles are analyzed in detail, focusing on features of the ligand binding transition state ensembles (TSEs). We find that ligands with similar bound poses can show significant differences in their ligand binding TSEs, in terms of their spatial distribution and protein-ligand interactions. However, we also find similarities across the TSEs when examining more general features such as ligand degrees of freedom. Together these findings show significant challenges for rational, kinetics-based drug design.

Reinforcing supramolecular hyaluronan hydrogels via kinetically interlocking multiple-units strategy

Supramolecular hydrogels exhibit promising potential in biological and clinical fields due to their special dynamic properties. However, most existing supramolecular hydrogels suffer from poor mechanical strength, which severely limits their applications. Here in this study, the Kinetically Interlocking Multiple-Units (KIMU) strategy was applied to the hyaluronan networks by introducing different supramolecular interaction motifs in an organized and alternative manner. Our strategy successfully elevated the energy barrier of crosslinker dissociation to 103.0 kJ mol^-1 and increased the storage modulus of hydrogels by 78 % with the intrinsic dynamic properties preserved. It can be expected that this method would bring a convenient and effective route to fabricate novel supramolecular materials with excellent mechanical properties.

Assessment of binding interaction to salmon sperm DNA of two antiviral agents and ecofriendly nanoparticles: comprehensive spectroscopic study

The direct binding of antiviral agents; Daclatasvir and valacyclovir and green synthesized nanoparticles to salmon sperm DNA have been assessed in a comparative study. The nanoparticles were synthesized by the hydrothermal autoclave method and have been fully characterized. The interactive behavior and competitive binding of the analytes to DNA in addition to the thermodynamic properties were deeply investigated by the UV-visible spectroscopy. The binding constants were monitored in the physiological pH conditions to be 1.65 × 10⁶, 4.92 × 10⁵ and 3.12 × 10⁵ for daclatasvir,valacyclovir and quantum dots, respectively. The significant changes in the spectral features of all analytes have proven intercalative binding. The competitive study has confirmed that, daclatasvir, valacyclovir, and the quantum dots have exhibited groove binding. All analytes have shown good entropy and enthalpy values indicating stable interactions. The electrostatic and non-electrostatic kinetic parameters have been determined through studying the binding interactions at different concentrations of KCl solutions. A molecular modelling study has been applied to demonstrate the binding interactions and their mechanisms. The obtained results were complementary and afforded new eras for the therapeutic applications.

Quality over quantity: Sampling high probability rare events with the weighted ensemble algorithm

The prediction of (un)binding rates and free energies is of great significance to the drug design process. Although many enhanced sampling algorithms and approaches have been developed, there is not yet a reliable workflow to predict these quantities. Previously we have shown that free energies and transition rates can be calculated by directly simulating the binding and unbinding processes with our variant of the WE algorithm "Resampling of Ensembles by Variation Optimization", or "REVO". Here, we calculate binding free energies retrospectively for three SAMPL6 host-guest systems and prospectively for a SAMPL9 system to test a modification of REVO that restricts its cloning behavior in quasi-unbound states. Specifically, trajectories cannot clone if they meet a physical requirement that represents a high likelihood of unbinding, which in the case of this work is a center-of-mass to center-of-mass distance. The overall effect of this change was difficult to predict, as it results in fewer unbinding events each of which with a much higher statistical weight. For all four systems tested, this new strategy produced either more accurate unbinding free energies or more consistent results between simulations than the standard REVO algorithm. This approach is highly flexible, and any feature of interest for a system can be used to determine cloning eligibility. These findings thus constitute an important improvement in the calculation of transition rates and binding free energies with the weighted ensemble method.

Accuracy and precision of binding free energy prediction for a tacrine related lead inhibitor of acetylcholinesterase with an arsenal of supercomputerized molecular modelling methods: a comparative study

Nowadays, advanced computational chemistry methods offer various strategies for revealing prospective hit structures in drug development essentially through accurate binding free energy predictions. After the era of molecular docking and quantitative structure-activity relationships, much interest has been lately oriented to perturbed molecular dynamic approaches like replica exchange with solute tempering and free energy perturbation (REST/FEP) and the potential of the mean force with adaptive biasing and accelerated weight histograms (PMF/AWH). Both of these receptor-based techniques can exploit exascale CPU&GPU supercomputers to achieve high throughput performance. In this fundamental study, we have compared the predictive power of a panel of supercomputerized molecular modelling methods to distinguish the major binding modes and the corresponding binding free energies of a promising tacrine related potential antialzheimerics in human acetylcholinesterase. The binding free energies were estimated using flexible molecular docking, molecular mechanics/generalized Born surface area/Poisson-Boltzmann surface area (MM/GBSA/PBSA), transmutation REST/FEP with 12 x 5 ns/λ windows, annihilation FEP with 20 x 5 ns/λ steps, PMF with weight histogram analysis method (WHAM) and 40 x 5 ns samples, and PMF/AWH with 10 x 100 ns replicas. Confrontation of the classical approaches such as canonical molecular dynamics and molecular docking with alchemical calculations and steered molecular dynamics enabled us to show how large errors in ΔG predictions can be expected if these in silico methods are employed in the elucidation of a common case of enzyme inhibition.Communicated by Ramaswamy H. Sarma.

Water Network in the Binding Pocket of Fluorinated BPTI-Trypsin Complexes─Insights from Simulation and Experiment

Structural waters in the S1 binding pocket of β-trypsin are critical for the stabilization of the complex of β-trypsin with its inhibitor bovine pancreatic trypsin inhibitor (BPTI). The inhibitor strength of BPTI can be modulated by replacing the critical lysine residue at the P1 position by non-natural amino acids. We study BPTI variants in which the critical Lys15 in BPTI has been replaced by α-aminobutyric acid (Abu) and its fluorinated derivatives monofluoroethylglycine (MfeGly), difluoroethylglycine (DfeGly), and trifluoroethylglycine (TfeGly). We investigate the hypothesis that additional water molecules in the binding pocket can form specific noncovalent interactions with the fluorinated side chains and thereby act as an extension of the inhibitors. We report potentials of mean force (PMF) of the unbinding process for all four complexes and enzyme activity inhibition assays. Additionally, we report the protein crystal structure of the Lys15MfeGly-BPTI-β-trypsin complex (pdb: 7PH1). Both experimental and computational data show a stepwise increase in inhibitor strength with increasing fluorination of the Abu side chain. The PMF additionally shows a minimum for the encounter complex and an intermediate state just before the bound state. In the bound state, the computational analysis of the structure and dynamics of the water molecules in the S1 pocket shows a highly dynamic network of water molecules that does not indicate a rigidification or stabilizing trend in regard to energetic properties that could explain the increase in inhibitor strength. The analysis of the energy and the entropy of the water molecules in the S1 binding pocket using grid inhomogeneous solvation theory confirms this result. Overall, fluorination systematically changes the binding affinity, but the effect cannot be explained by a persistent water network in the binding pocket. Other effects, such as the hydrophobicity of fluorinated amino acids and the stability of the encounter complex as well as the additional minimum in the potential of mean force in the bound state, likely influence the affinity more directly.

Ligand Unbinding Pathway and Mechanism Analysis Assisted by Machine Learning and Graph Methods

We present two methods to reveal protein-ligand unbinding mechanisms in biased unbinding simulations by clustering trajectories into ensembles representing unbinding paths. The first approach is based on a contact principal component analysis for reducing the dimensionality of the input data, followed by identification of unbinding paths and training a machine learning model for trajectory clustering. The second approach clusters trajectories according to their pairwise mean Euclidean distance employing the neighbor-net algorithm, which takes into account input data bias in the distances set and is superior to dendrogram construction. Finally, we describe a more complex case where the reaction coordinate relevant for path identification is a single intraligand hydrogen bond, highlighting the challenges involved in unbinding path reaction coordinate detection.

Computationally Elucidating the Binding Kinetics for Different AChE Inhibitors to Access the Rationale for Improving the Drug Efficacy

Traditional drug discovery is based on a binding affinity (thermodynamics)-driven paradigm. Numerous examples, however, demonstrated that drug efficacy does not always depend only on binding affinity but positively correlates with binding kinetics, that is, the dissociation rate constant (k_off). Binding free energy landscape (BFEL) constructor is a computational binding kinetics prediction method, previously developed by us, that estimates the binding kinetics for ligand-protein based on their constructed binding free energy landscape, but it also reveals the detailed molecular mechanism of the binding event, hence, providing the position of transition states at the molecular level to modify/improve the binding kinetics. Acetylcholinesterase (AChE) is a well-known Alzheimer's disease (AD) target for which there is still not an ideal drug on the market. Therefore, to improve the drug design strategy for AD, the binding kinetics and binding molecular mechanisms of the four inhibitors of AChE, that is, E2020 (Aricept), HupA, Rivastigmine, and Galantamine, were studied. Also, the differentiation of the binding kinetics between mAChE and TcAChE was studied to evaluate the sensitiveness of BFEL constructor. The flexibility of molecules has a noticeable effect on the nature of BFEL. To the same target, flexible molecules (i.e., E2020 and Rivastigmine) which contain more rotatable bonds tend to have more complicated BFELs reflecting more complicated molecular action mechanisms than the rigid ones (i.e., HupA and Galantamine), which therefore could be more challenging to be optimized. The binding kinetics is highly dependent on the structure of the molecules, such as the length and the functional groups. Therefore, E2020 presents better binding kinetic and thermodynamic properties with either TcAChE or mAChE. Therefore, it is the most promising lead drug for binding kinetics-based drug design. In addition, the binding kinetics of a drug may present different values in the proteins of different organisms because the residue compositions of the binding gorges of the targets are variant, that is, E2020 shows lower binding affinity and association energy barrier in binding with mAChE than TcAChE. However, HupA presents a better binding property with TcAChE than mAChE.

LINES: Log-Probability Estimation via Invertible Neural Networks for Enhanced Sampling

It is very challenging to sample a molecular process with large activation energies using molecular dynamics simulations. Current enhanced sampling methodologies, such as umbrella sampling and metadynamics, rely on the identification of appropriate reaction coordinates for a system. In this paper, we developed a method for log-probability estimation via invertible neural networks for enhanced sampling (LINES). This iterative scheme utilizes a normalizing flow machine learning model to learn the underlying free energy surface (FES) of a system as a function of molecular coordinates and then applies a gradient-based optimization method to the learned normalizing flow to identify reaction coordinates. A biasing potential is then evaluated over a tabulated grid of the reaction coordinate values, which can be applied to the next round of simulations for enhanced sampling, resulting in more efficient sampling. We tested the accuracy and efficiency of the LINES method in sampling the FES using the alanine dipeptide system. We also demonstrated the effectiveness of identification of reaction coordinates through simulation of cyclobutanol unbinding from β-cyclodextrin and the folding/unfolding of CLN025─a variant of the peptide Chignolin. The LINES method can be extended to the study of large-scale protein systems with complex nonlinear reaction pathways.

Computation of the Binding Energies between Human ACE2 and Spike RBDs of the Original Strain, Delta and Omicron Variants of the SARS-CoV-2: A DFT Simulation Approach

The receptor binding domain (RBD) of SARS-CoV-2 binds to human ACE2 leading to infection. In this study, the complexes that are formed by the attachment of the SARS-CoV-2 spike RBDs of the original strain, delta and omicron variants to the human ACE2 are investigated via density functional theory (DFT) simulations to obtain binding energies. The DFT computations are performed without fragmenting the interfaces to involve longer-range interactions for improved accuracy, which is one of the primary features of the approach used in this study. Basis set superposition error corrections and van der Waals dispersions are also included in the DFT simulations. The binding energies of the SARS-CoV-2 spike RBDs of the original strain, delta and omicron variants to the human ACE2 are computed as -4.76, -6.68, and -11.77 eV, respectively. These binding energy values indicate that the binding of the omicron variant to the ACE2 is much more favorable than the binding of the original strain and the delta variant, which constitute a molecular reason for the takeover of the omicron variant. The binding energies and the decomposition of these energies found in this study are expected to aid in the development of neutralizing agents.

Density functional theory computation of the binding free energies between various mutations of SARS-CoV-2 RBD and human ACE2: molecular level roots of the contagiousness

The receptor-binding domain (RBD) of SARS-CoV-2 attaches to the human ACE2 to initiate binding of SARS-CoV-2 to human cell and leads to the infection process afterwards. In this study, various mutations of SARS-CoV-2 spike RBD and human ACE2 complexes are investigated via density functional theory (DFT) computations to obtain binding free energies. The DFT computations are performed without fragmenting the interfaces to involve longer-range quantum mechanical interactions for improving accuracy. The vibrational free energies, van der Waals dispersion forces and basis set superposition error corrections are also included in the calculations. The results show that the absolute value of the binding energy of B.1.1.7 mutated spike RBD-ACE2 complex is more than five times higher than that of the original strain. The results of this study are expected to be useful for a deeper understanding of the relation of the binding free energies and the level of contagiousness.

Binding reactions at finite systems

A perpetual yearn exists among computational scientists to scale down the size of physical systems, a desire shared as well with experimentalists able to track single molecules. A question then arises whether averages observed at small systems are the same as those observed at large or macroscopic systems. Utilizing statistical-mechanics formulations in ensembles in which the total numbers of particles are fixed, we demonstrate that properties of binding reactions are not homogeneous functions. This means that averages of intensive parameters, such as the concentration of the bound-state, at finite systems are different than those at large systems. The discrepancy increases with decreasing temperature, volume, and to some extent, numbers of particles. As perplexing as it may sound, despite variations in average quantities, extracting the equilibrium constant from systems of different sizes does yield the same value. The reason is that correlations in reactants' concentrations ought to be accounted for in the expression of the equilibrium constant, being negligible at large-scale but significant at small-scale. Similar arguments pertain to the calculations of the reaction rate constants, more specifically, the bimolecular rate of the forward reaction is related to the average of the product (and not to the product of the averages) of the reactants' concentrations. Furthermore, we derive relations aiming to predict the composition only from the equilibrium constant and the system's size. All predictions are validated by Monte-Carlo and molecular dynamics simulations. An important consequence of these findings is that the expression of the equilibrium constant at finite systems is not dictated solely by the chemical equation of the reaction but requires knowledge of the elementary processes involved.

Local Ion Densities can Influence Transition Paths of Molecular Binding

Improper reaction coordinates can pose significant problems for path-based binding free energy calculations. Particularly, omission of long timescale motions can lead to over-estimation of the energetic barriers between the bound and unbound states. Many methods exist to construct the optimal reaction coordinate using a pre-defined basis set of features. Although simulations are typically conducted in explicit solvent, the solvent atoms are often excluded by these feature sets—resulting in little being known about their role in reaction coordinates, and ultimately, their role in determining (un)binding rates and free energies. In this work, analysis is done on an extensive set of host-guest unbinding trajectories, working to characterize differences between high and low probability unbinding trajectories with a focus on solvent-based features, including host-ion interactions, guest-ion interactions and location-dependent ion densities. We find that differences in ion densities as well as guest-ion interactions strongly correlate with differences in the probabilities of reactive paths that are used to determine free energies of (un)binding and play a significant role in the unbinding process.

Estimation of binding rates and affinities from multiensemble Markov models and ligand decoupling

Accurate and efficient simulation of the thermodynamics and kinetics of protein-ligand interactions is crucial for computational drug discovery. Multiensemble Markov Model (MEMM) estimators can provide estimates of both binding rates and affinities from collections of short trajectories but have not been systematically explored for situations when a ligand is decoupled through scaling of non-bonded interactions. In this work, we compare the performance of two MEMM approaches for estimating ligand binding affinities and rates: (1) the transition-based reweighting analysis method (TRAM) and (2) a Maximum Caliber (MaxCal) based method. As a test system, we construct a small host-guest system where the ligand is a single uncharged Lennard-Jones (LJ) particle, and the receptor is an 11-particle icosahedral pocket made from the same atom type. To realistically mimic a protein-ligand binding system, the LJ ϵ parameter was tuned, and the system was placed in a periodic box with 860 TIP3P water molecules. A benchmark was performed using over 80 µs of unbiased simulation, and an 18-state Markov state model was used to estimate reference binding affinities and rates. We then tested the performance of TRAM and MaxCal when challenged with limited data. Both TRAM and MaxCal approaches perform better than conventional Markov state models, with TRAM showing better convergence and accuracy. We find that subsampling of trajectories to remove time correlation improves the accuracy of both TRAM and MaxCal and that in most cases, only a single biased ensemble to enhance sampled transitions is required to make accurate estimates.

How Do Modulators Affect the Orthosteric and Allosteric Binding Pockets?

Allosteric modulators (AMs) that bind allosteric sites can exhibit greater selectivity than the orthosteric ligands and can either enhance agonist-induced receptor activity (termed positive allosteric modulator or PAM), inhibit agonist-induced activity (negative AM or NAM), or have no effect on activity (silent AM or SAM). Until now, it is not clear what the exact effects of AMs are on the orthosteric active site or the allosteric binding pocket(s). In the present work, we collected both the three-dimensional (3D) structures of receptor-orthosteric ligand and receptor-orthosteric ligand-AM complexes of a specific target protein. Using our novel algorithm toolset, molecular complex characterizing system (MCCS), we were able to quantify the key residues in both the orthosteric and allosteric binding sites along with potential changes of the binding pockets. After analyzing 21 pairs of 3D crystal or cryo-electron microscopy (cryo-EM) complexes, including 4 pairs of GPCRs, 5 pairs of ion channels, 11 pairs of enzymes, and 1 pair of transcription factors, we found that the binding of AMs had little impact on both the orthosteric and allosteric binding pockets. In return, given the accurately predicted allosteric binding pocket(s) of a drug target of medicinal interest, we can confidently conduct the virtual screening or lead optimization without concern that the huge conformational change of the pocket could lead to the low accuracy of virtual screening.

A particle-based computational model to analyse remodelling of the red blood cell cytoskeleton during malaria infections

Red blood cells can withstand the harsh mechanical conditions in the vasculature only because the bending rigidity of their plasma membrane is complemented by the shear elasticity of the underlying spectrin-actin network. During an infection by the malaria parasite Plasmodium falciparum, the parasite mines host actin from the junctional complexes and establishes a system of adhesive knobs, whose main structural component is the knob-associated histidine rich protein (KAHRP) secreted by the parasite. Here we aim at a mechanistic understanding of this dramatic transformation process. We have developed a particle-based computational model for the cytoskeleton of red blood cells and simulated it with Brownian dynamics to predict the mechanical changes resulting from actin mining and KAHRP-clustering. Our simulations include the three-dimensional conformations of the semi-flexible spectrin chains, the capping of the actin protofilaments and several established binding sites for KAHRP. For the healthy red blood cell, we find that incorporation of actin protofilaments leads to two regimes in the shear response. Actin mining decreases the shear modulus, but knob formation increases it. We show that dynamical changes in KAHRP binding affinities can explain the experimentally observed relocalization of KAHRP from ankyrin to actin complexes and demonstrate good qualitative agreement with experiments by measuring pair cross-correlations both in the computer simulations and in super-resolution imaging experiments.

Malaria is one of the deadliest infectious diseases and its symptoms are related to the blood stage, when the parasite multiplies within red blood cells. In order to avoid clearance by the spleen, the parasite produces specific factors like the adhesion receptor PfEMP1 and the multifunctional protein KAHRP that lead to the formation of adhesive knobs on the surface of the red blood cells and thus increase residence time in the vasculature. We have developed a computational model for the parasite-induced remodelling of the actin-spectrin network to quantitatively predict the dynamical changes in the mechanical properties of the infected red blood cells and the spatial distribution of the different protein components of the membrane skeleton. Our simulations show that KAHRP can relocate to actin junctions due to dynamical changes in binding affinities, in good qualitative agreement with super-resolution imaging experiments. In the future, our simulation framework can be used to gain further mechanistic insight into the way malaria parasites attack the red blood cell cytoskeleton.

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.

In silico investigation and surmounting of Lipopolysaccharide barrier in Gram-Negative Bacteria: How far has molecular dynamics Come?

Lipopolysaccharide (LPS), a main component of the outer membrane of Gram-negative bacteria, has crucial implications on both antibiotic resistance and the overstimulation of the host innate immune system. Fighting against these global concerns calls for the molecular understanding of the barrier function and immunostimulatory ability of LPS. Molecular dynamics (MD) simulations have become an invaluable tool for uncovering important findings in LPS research. While the reach of MD simulations for investigating the immunostimulatory ability of LPS has been already outlined, little attention has been paid to the role of MD simulations for exploring its barrier function and synthesis. Herein, we give an overview about the impact of MD simulations on gaining insight into the shield role and synthesis pathway of LPS, which have attracted considerable attention to discover molecules able to surmount antibiotic resistance, either circumventing LPS defenses or disrupting its synthesis. We specifically focus on the enhanced sampling and free energy calculation methods that have been combined with MD simulations to address such research. We also highlight the use of special-purpose MD supercomputers, the importance of appropriate LPS and ions parameterization to obtain reliable results, and the complementary views that MD and wet-lab experiments provide. Thereby, this work, which covers the last five years of research, apart from outlining the phenomena and strategies that are being explored, evidences the valuable insights that are gained by MD, which may be useful to advance antibiotic design, and what the prospects of this in silico method could be in LPS research.

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.

Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories

We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.

In silico Approaches for the Design and Optimization of Interfering Peptides Against Protein-Protein Interactions

Large contact surfaces of protein-protein interactions (PPIs) remain to be an ongoing issue in the discovery and design of small molecule modulators. Peptides are intrinsically capable of exploring larger surfaces, stable, and bioavailable, and therefore bear a high therapeutic value in the treatment of various diseases, including cancer, infectious diseases, and neurodegenerative diseases. Given these promising properties, a long way has been covered in the field of targeting PPIs via peptide design strategies. In silico tools have recently become an inevitable approach for the design and optimization of these interfering peptides. Various algorithms have been developed to scrutinize the PPI interfaces. Moreover, different databases and software tools have been created to predict the peptide structures and their interactions with target protein complexes. High-throughput screening of large peptide libraries against PPIs; "hotspot" identification; structure-based and off-structure approaches of peptide design; 3D peptide modeling; peptide optimization strategies like cyclization; and peptide binding energy evaluation are among the capabilities of in silico tools. In the present study, the most recent advances in the field of in silico approaches for the design of interfering peptides against PPIs will be reviewed. The future perspective of the field and its advantages and limitations will also be pinpointed.