Taming Rugged Free Energy Landscapes Using an Average Force

Atomic-Resolution Experimental Structural Biology and Molecular Dynamics Simulations of Hyaluronan and Its Complexes

This review summarizes the atomic-resolution structural biology of hyaluronan and its complexes available in the Protein Data Bank, as well as published studies of atomic-resolution explicit-solvent molecular dynamics simulations on these and other hyaluronan and hyaluronan-containing systems. Advances in accurate molecular mechanics force fields, simulation methods and software, and computer hardware have supported a recent flourish in such simulations, such that the simulation publications now outnumber the structural biology publications by an order of magnitude. In addition to supplementing the experimental structural biology with computed dynamic and thermodynamic information, the molecular dynamics studies provide a wealth of atomic-resolution information on hyaluronan-containing systems for which there is no atomic-resolution structural biology either available or possible. Examples of these summarized in this review include hyaluronan pairing with other hyaluronan molecules and glycosaminoglycans, with ions, with proteins and peptides, with lipids, and with drugs and drug-like molecules. Despite limitations imposed by present-day computing resources on system size and simulation timescale, atomic-resolution explicit-solvent molecular dynamics simulations have been able to contribute significant insight into hyaluronan's flexibility and capacity for intra- and intermolecular non-covalent interactions.

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.

Predicting the structural basis of targeted protein degradation by integrating molecular dynamics simulations with structural mass spectrometry

Targeted protein degradation (TPD) is a promising approach in drug discovery for degrading proteins implicated in diseases. A key step in this process is the formation of a ternary complex where a heterobifunctional molecule induces proximity of an E3 ligase to a protein of interest (POI), thus facilitating ubiquitin transfer to the POI. In this work, we characterize 3 steps in the TPD process. (1) We simulate the ternary complex formation of SMARCA2 bromodomain and VHL E3 ligase by combining hydrogen-deuterium exchange mass spectrometry with weighted ensemble molecular dynamics (MD). (2) We characterize the conformational heterogeneity of the ternary complex using Hamiltonian replica exchange simulations and small-angle X-ray scattering. (3) We assess the ubiquitination of the POI in the context of the full Cullin-RING Ligase, confirming experimental ubiquitinomics results. Differences in degradation efficiency can be explained by the proximity of lysine residues on the POI relative to ubiquitin.

Meta-Analysis Reveals That Absolute Binding Free-Energy Calculations Approach Chemical Accuracy

Systematic and quantitative analysis of the reliability of formally exact methods that in silico calculate absolute protein-ligand binding free energies remains lacking. Here, we provide, for the first time, evidence-based information on the reliability of these methods by statistically studying 853 cases from 34 different research groups through meta-analysis. The results show that formally exact methods approach chemical accuracy (error = 1.58 kcal/mol), even if people are challenging difficult tasks such as blind drug screening in recent years. The geometrical-pathway-based methods prove to possess a better convergence ability than the alchemical ones, while the latter have a larger application range. We also reveal the importance of always using the latest force fields to guarantee reliability and discuss the pros and cons of turning to an implicit solvent model in absolute binding free-energy calculations. Moreover, based on the meta-analysis, an evidence-based guideline for in silico binding free-energy calculations is provided.

From free-energy profiles to activation free energies

Given a chemical reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) discriminating between R and P, we define the free-energy profile (FEP) as the logarithm of the marginal Boltzmann distribution of the CV. This FEP is not a true free energy. Nevertheless, it is common to treat the FEP as the “free-energy” analog of the minimum potential energy path and to take the activation free energy, [Formula: see text], as the difference between the maximum at the transition state and the minimum at R. We show that this approximation can result in large errors. The FEP depends on the CV and is, therefore, not unique. For the same reaction, different discriminating CVs can yield different [Formula: see text]. We derive an exact expression for the activation free energy that avoids this ambiguity. We find [Formula: see text] to be a combination of the probability of the system being in the reactant state, the probability density on the dividing surface, and the thermal de Broglie wavelength associated with the transition. We apply our formalism to simple analytic models and realistic chemical systems and show that the FEP-based approximation applies only at low temperatures for CVs with a small effective mass. Most chemical reactions occur on complex, high-dimensional PES that cannot be treated analytically and pose the added challenge of choosing a good CV. We study the influence of that choice and find that, while the reaction free energy is largely unaffected, [Formula: see text] is quite sensitive.

Markov state models elucidate the stability of DNA influenced by the chiral 5S-Tg base

The static and dynamic structures of DNA duplexes affected by 5S-Tg (Tg, Thymine glycol) epimers were studied using MD simulations and Markov State Models (MSMs) analysis. The results show that the 5S,6S-Tg base caused little perturbation to the helix, and the base-flipping barrier was determined to be 4.4 kcal mol-1 through the use of enhanced sampling meta-eABF calculations, comparable to 5.4 kcal mol-1 of the corresponding thymine flipping. Two conformations with the different hydrogen bond structures between 5S,6R-Tg and A19 were identified in several independent MD trajectories. The 5S,6R-Tg:O6HO6•••N1:A19 hydrogen bond is present in the high-energy conformation displaying a clear helical distortion, and near barrier-free Tg base flipping. The low-energy conformation always maintains Watson-Crick base pairing between 5S,6R-Tg and A19, and 5S-Tg base flipping is accompanied by a small barrier of ca. 2.0 KBT (T = 298 K). The same conformations are observed in the MSMs analysis. Moreover, the transition path and metastable structures of the damaged base flipping are for the first time verified through MSMs analysis. The data clearly show that the epimers have completely different influence on the stability of the DNA duplex, thus implying different enzymatic mechanisms for DNA repair.

Accurate Description of Solvent-Exposed Salt Bridges with a Non-polarizable Force Field Incorporating Solvent Effects

The strength of salt bridges resulting from the interaction of cations and anions is modulated by their environment. However, polarization of the solvent molecules by the charged moieties makes the accurate description of cation-anion interactions in an aqueous solution by means of a pairwise additive potential energy function and classical combination rules particularly challenging. In this contribution, aiming at improving the representation of solvent-exposed salt-bridge interactions with an all-atom non-polarizable force field, we put forth here a parametrization strategy. First, the interaction of a cation and an anion is characterized by hybrid quantum mechanical/molecular mechanics (QM/MM) potential of mean force (PMF) calculations, whereby constantly exchanging solvent molecules around the ions are treated at the quantum mechanical level. The Lennard-Jones (LJ) parameters describing the salt-bridge ion pairs are then optimized to match the reference QM/MM PMFs through the so-called nonbonded FIX, or NBFIX, feature of the CHARMM force field. We apply the new set of parameters, coined CHARMM36m-SBFIX, to the calculation of association constants for the ammonium-acetate and guanidinium-acetate complexes, the osmotic pressures for glycine zwitterions, guanidinium, and acetate ions, and to the simulation of both folded and intrinsically disordered proteins. Our findings indicate that CHARMM36m-SBFIX improves the description of solvent-exposed salt-bridge interactions, both structurally and thermodynamically. However, application of this force field to the standard binding free-energy calculation of a protein-ligand complex featuring solvent-excluded salt-bridge interactions leads to a poor reproduction of the experimental value, suggesting that the parameters optimized in an aqueous solution cannot be readily transferred to describe solvent-excluded salt-bridge interactions. Put together, owing to their sensitivity to the environment, modeling salt-bridge interactions by means of a single, universal set of LJ parameters remains a daunting theoretical challenge.

Statistically optimal analysis of the extended-system adaptive biasing force (eABF) method

The extended-system adaptive biasing force (eABF) method and its newer variants offer rapid exploration of the configuration space of chemical systems. Instead of directly applying the ABF bias to collective variables, they are harmonically coupled to fictitious particles, which separates the problem of enhanced sampling from that of free energy estimation. The prevalent analysis method to obtain the potential of mean force (PMF) from eABF is thermodynamic integration. However, besides the PMF, most information is lost as the unbiased probability of visited configurations is never recovered. In this contribution, we show how statistical weights of individual frames can be computed using the Multistate Bennett's Acceptance Ratio (MBAR), putting the post-processing of eABF on one level with other frequently used sampling methods. In addition, we apply this formalism to the prediction of nuclear magnetic resonance shieldings, which are very sensitive to molecular geometries and often require extensive sampling. The results show that the combination of enhanced sampling by means of extended-system dynamics with the MBAR estimator is a highly useful tool for the calculation of ensemble properties. Furthermore, the extension of the presented scheme to the recently published Gaussian-accelerated molecular dynamics eABF hybrid is straightforward and approximation free.

Hazardous Shortcuts in Standard Binding Free Energy Calculations

Calculating the standard binding free energies of protein-protein and protein-ligand complexes from atomistic molecular dynamics simulations in explicit solvent is a problem of central importance in computational biophysics. A rigorous strategy for carrying out such calculations is the so-called "geometrical route". In this method, two molecular objects are progressively separated from one another in the presence of orientational and conformational restraints serving to control the change in configurational entropy that accompanies the dissociation process, thereby allowing the computations to converge within simulations of affordable length. Although the geometrical route provides a rigorous theoretical framework, a tantalizing computational shortcut consists of simply leaving out such orientational and conformational degrees of freedom during the separation process. Here the accuracy and convergence of the two approaches are critically compared in the case of two protein-ligand complexes (Abl kinase-SH3:p41 and MDM2-p53:NVP-CGM097) and three protein-protein complexes (pig insulin dimer, SARS-CoV-2 spike RBD:ACE2, and CheA kinase-P2:CheY). The results of the simulations that strictly follow the geometrical route match the experimental standard binding free energies within chemical accuracy. In contrast, simulations bereft of geometrical restraints converge more poorly, yielding inconsistent results that are at variance with the experimental measurements. Furthermore, the orientational and positional time correlation functions of the protein in the unrestrained simulations decay over several microseconds, a time scale that is far longer than the typical simulation times of the geometrical route, which explains why those simulations fail to sample the relevant degrees of freedom during the separation process of the complexes.

Uncovering the Mechanism of Drug Resistance Caused by the T790M Mutation in EGFR Kinase From Absolute Binding Free Energy Calculations

The emergence of drug resistance may increase the death rates in advanced non-small cell lung cancer (NSCLC) patients. The resistance of erlotinib, the effective first-line antitumor drug for NSCLC with the L858R mutation of epidermal growth factor receptor (EGFR), happens after the T790M mutation of EGFR, because this mutation causes the binding of adenosine triphosphate (ATP) to EGFR more favorable than erlotinib. However, the mechanism of the enhancement of the binding affinity of ATP to EGFR, which is of paramount importance for the development of new inhibitors, is still unclear. In this work, to explore the detailed mechanism of the drug resistance due to the T790M mutation, molecular dynamics simulations and absolute binding free energy calculations have been performed. The results show that the binding affinity of ATP with respect to the L858R/T790M mutant is higher compared with the L858R mutant, in good agreement with experiments. Further analysis demonstrates that the T790M mutation significantly changes the van der Waals interaction of ATP and the binding site. We also find that the favorable binding of ATP to the L858R/T790M mutant, compared with the L858R mutant, is due to a conformational change of the αC-helix, the A-loop and the P-loop of the latter induced by the T790M mutation. This change makes the interaction of ATP and P-loop, αC-helix in the L858R/T790M mutant higher than that in the L858R mutant, therefore increasing the binding affinity of ATP to EGFR. We believe the drug-resistance mechanism proposed in this study will provide valuable guidance for the design of drugs for NSCLC.

Mechanism and biomass association of glucuronoyl esterase: an α/β hydrolase with potential in biomass conversion

Glucuronoyl esterases (GEs) are α/β serine hydrolases and a relatively new addition in the toolbox to reduce the recalcitrance of lignocellulose, the biggest obstacle in cost-effective utilization of this important renewable resource. While biochemical and structural characterization of GEs have progressed greatly recently, there have yet been no mechanistic studies shedding light onto the rate-limiting steps relevant for biomass conversion. The bacterial GE OtCE15A possesses a classical yet distinctive catalytic machinery, with easily identifiable catalytic Ser/His completed by two acidic residues (Glu and Asp) rather than one as in the classical triad, and an Arg side chain participating in the oxyanion hole. By QM/MM calculations, we identified deacylation as the decisive step in catalysis, and quantified the role of Asp, Glu and Arg, showing the latter to be particularly important. The results agree well with experimental and structural data. We further calculated the free-energy barrier of post-catalysis dissociation from a complex natural substrate, suggesting that in industrial settings non-catalytic processes may constitute the rate-limiting step, and pointing to future directions for enzyme engineering in biomass utilization.

Zong and coworkers combine computational and experimental methods to decipher in detail the mechanism of action of glucuronoyl esterases, enzymes with significant biotechnological potential for decoupling lignin from polysaccharides in biomass.

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

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

A Companion Guide to the String Method with Swarms of Trajectories: Characterization, Performance, and Pitfalls

The string method with swarms of trajectories (SMwST) is an algorithm that identifies a physically meaningful transition pathway─a one-dimensional curve, embedded within a high-dimensional space of selected collective variables. The SMwST algorithm leans on a series of short, unbiased molecular dynamics simulations spawned at different locations of the discretized path, from whence an average dynamic drift is determined to evolve the string toward an optimal pathway. However conceptually simple in both its theoretical formulation and practical implementation, the SMwST algorithm is computationally intensive and requires a careful choice of parameters for optimal cost-effectiveness in applications to challenging problems in chemistry and biology. In this contribution, the SMwST algorithm is presented in a self-contained manner, discussing with a critical eye its theoretical underpinnings, applicability, inherent limitations, and use in the context of path-following free-energy calculations and their possible extension to kinetics modeling. Through multiple simulations of a prototypical polypeptide, combining the search of the transition pathway and the computation of the potential of mean force along it, several practical aspects of the methodology are examined with the objective of optimizing the computational effort, yet without sacrificing accuracy. In light of the results reported here, we propose some general guidelines aimed at improving the efficiency and reliability of the computed pathways and free-energy profiles underlying the conformational transitions at hand.

Conformational Change from U- to I-Shape of Ion Transporters Facilitates K+ Transport across Lipid Bilayers

We have investigated, at the atomic level, the ion-fishing mechanism underlying the ion transport across membranes mediated by an artificial ion transporter composed of a hydroxyl-rich cholesterol group, a flexible alkyl chain, and a crown ether. Our results show that the transporter can spontaneously insert into the membrane and switch between the folded (U-shaped) and extended (I-shaped) conformations. The free-energy profile associated with the conformational transition indicates that compared with the U-shaped conformation of the transporter, the I-shaped one is thermodynamically more favorable. Furthermore, the free-energy profiles describing the ion translocation reveal that the transporter capturing the ion in U-shape on one side of the membrane and releasing it in I-shape on the other side constitutes a key way for the highly efficient transport of K⁺ ions. We present herewith a rigorous and rational framework to decipher the detailed ion-fishing mechanism of transmembrane ion transport with exceptionally high activity.

Peptide Dynamics and Metadynamics: Leveraging Enhanced Sampling Molecular Dynamics to Robustly Model Long-Timescale Transitions

Molecular dynamics simulations can in theory reveal the thermodynamics and kinetics of peptide conformational transitions at atomic-level resolution. However, even with modern computing power, they are limited in the timescales they can sample, which is especially problematic for peptides that are fully or partially disordered. Here, we discuss how the enhanced sampling methods accelerated molecular dynamics (aMD) and metadynamics can be leveraged in a complementary fashion to quickly explore conformational space and then robustly quantify the underlying free energy landscape. We apply these methods to two peptides that have an intrinsically disordered nature, the histone H3 and H4 N-terminal tails, and use metadynamics to compute the free energy landscape along collective variables discerned from aMD simulations. Results show that these peptides are largely disordered, with a slight preference for α-helical structures.

Computer-aided design of molecular machines: techniques, paradigms and difficulties

With their development in the past decade, molecular machines, which achieve specific tasks by responding to external stimuli, have gradually come to be regarded as powerful tools for a wide range of applications, rather than interesting molecular toys. This conceptual change in turn motivates scientists to design molecular machines with complex architectures. Due to the lack of general principles bridging the functions and the chemical structures of molecular machines, experience-based design becomes difficult with the increase of size and complexity of the architectures. Computer-aided molecular-machine design, therefore, has attracted widespread attention on account of its ability to model and investigate complex molecular architectures without too much time and expense required for synthetic experiments. Using leading-edge numerical-simulation techniques, the mechanisms underlying achieving tasks through response to external stimuli of a large number of existing molecular machines have been successfully explored. Based on the experience of studying existing molecular machines, generalized methodologies of predicting the properties and working principles of molecular candidates have been established, paving the way for de novo computer-aided design of molecular machines. In this perspective, we introduce cutting-edge techniques that have been applied for investigating and designing molecular machines. We show paradigms of computer-aided design of molecular machines, which can serve as guidelines for the investigation of new supramolecular architectures. Moreover, we discuss the limitations and possible future developments of current techniques and methodologies in the field of computer-aided design of molecular machines.

MLCV: Bridging Machine-Learning-Based Dimensionality Reduction and Free-Energy Calculation

Importance-sampling algorithms leaning on the definition of a model reaction coordinate (RC) are widely employed to probe processes relevant to chemistry and biology alike, spanning time scales not amenable to common, brute-force molecular dynamics (MD) simulations. In practice, the model RC often consists of a handful of collective variables (CVs) chosen on the basis of chemical intuition. However, constructing manually a low-dimensional RC model to describe an intricate geometrical transformation for the purpose of free-energy calculations and analyses remains a daunting challenge due to the inherent complexity of the conformational transitions at play. To solve this issue, remarkable progress has been made in employing machine-learning techniques, such as autoencoders, to extract the low-dimensional RC model from a large set of CVs. Implementation of the differentiable, nonlinear machine-learned CVs in common MD engines to perform free-energy calculations is, however, particularly cumbersome. To address this issue, we present here a user-friendly tool (called MLCV) that facilitates the use of machine-learned CVs in importance-sampling simulations through the popular Colvars module. Our approach is critically probed with three case examples consisting of small peptides, showcasing that through hard-coded neural network in Colvars, deep-learning and enhanced-sampling can be effectively bridged with MD simulations. The MLCV code is versatile, applicable to all the CVs available in Colvars, and can be connected to any kind of dense neural networks. We believe that MLCV provides an effective, powerful, and user-friendly platform accessible to experts and nonexperts alike for machine-learning (ML)-guided CV discovery and enhanced-sampling simulations to unveil the molecular mechanisms underlying complex biochemical processes.

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.

Fast and Accurate Multidimensional Free Energy Integration

Enhanced sampling and free energy calculation algorithms of the thermodynamic integration family (such as the adaptive biasing force (ABF) method) are not based on the direct computation of a free energy surface but rather of its gradient. Integrating the free energy surface is nontrivial in dimensions higher than one. Here, the author introduces a flexible, portable implementation of a Poisson equation formalism to integrate free energy surfaces from estimated gradients in dimensions 2 and 3 using any combination of periodic and nonperiodic (Neumann) boundary conditions. The algorithm is implemented in portable C++ and provided as a standalone tool that can be used to integrate multidimensional gradient fields estimated on a grid using any algorithm, such as umbrella integration as a post-treatment of umbrella sampling simulations. It is also included in the implementation of ABF (and its extended-system variant eABF) in the Collective Variables Module, enabling the seamless computation of multidimensional free energy surfaces within ABF and eABF simulations. A Python-based analysis toolchain is provided to easily plot and analyze multidimensional ABF simulation results, including metrics to assess their convergence. The Poisson integration algorithm can also be used to perform Helmholtz decomposition of noisy gradient estimates on the fly, resulting in an efficient implementation of the projected ABF (pABF) method proposed by Leliévre and co-workers. In numerical tests, pABF is found to lead to faster convergence with respect to ABF in simple cases of low intrinsic dimension but seems detrimental to convergence in a more realistic case involving degenerate coordinates and hidden barriers due to slower exploration. This suggests that variance reduction schemes do not always yield convergence improvements when applied to enhanced sampling methods.

The Iron Maiden. Cytosolic Aconitase/IRP1 Conformational Transition in the Regulation of Ferritin Translation and Iron Hemostasis

Maintaining iron homeostasis is fundamental for almost all living beings, and its deregulation correlates with severe and debilitating pathologies. The process is made more complicated by the omnipresence of iron and by its role as a fundamental component of a number of crucial metallo proteins. The response to modifications in the amount of the free-iron pool is performed via the inhibition of ferritin translation by sequestering consensus messenger RNA (mRNA) sequences. In turn, this is regulated by the iron-sensitive conformational equilibrium between cytosolic aconitase and IRP1, mediated by the presence of an iron-sulfur cluster. In this contribution, we analyze by full-atom molecular dynamics simulation, the factors leading to both the interaction with mRNA and the conformational transition. Furthermore, the role of the iron-sulfur cluster in driving the conformational transition is assessed by obtaining the related free energy profile via enhanced sampling molecular dynamics simulations.

Correlation of membrane protein conformational and functional dynamics

Conformational changes in ion channels lead to gating of an ion-conductive pore. Ion flux has been measured with high temporal resolution by single-channel electrophysiology for decades. However, correlation between functional and conformational dynamics remained difficult, lacking experimental techniques to monitor sub-millisecond conformational changes. Here, we use the outer membrane protein G (OmpG) as a model system where loop-6 opens and closes the β-barrel pore like a lid in a pH-dependent manner. Functionally, single-channel electrophysiology shows that while closed states are favored at acidic pH and open states are favored at physiological pH, both states coexist and rapidly interchange in all conditions. Using HS-AFM height spectroscopy (HS-AFM-HS), we monitor sub-millisecond loop-6 conformational dynamics, and compare them to the functional dynamics from single-channel recordings, while MD simulations provide atomistic details and energy landscapes of the pH-dependent loop-6 fluctuations. HS-AFM-HS offers new opportunities to analyze conformational dynamics at timescales of domain and loop fluctuations.

Overcoming Free-Energy Barriers with a Seamless Combination of a Biasing Force and a Collective Variable-Independent Boost Potential

Amid collective-variable (CV)-based importance-sampling algorithms, a hybrid of the extended adaptive biasing force and the well-tempered metadynamics algorithms (WTM-eABF) has proven particularly cost-effective for exploring the rugged free-energy landscapes that underlie biological processes. However, as an inherently CV-based algorithm, this hybrid scheme does not explicitly accelerate sampling in the space orthogonal to the chosen CVs, thereby limiting its efficiency and accuracy, most notably in those cases where the slow degrees of freedom of the process at hand are not accounted for in the model transition coordinate. Here, inspired by Gaussian-accelerated molecular dynamics (GaMD), we introduce the same CV-independent harmonic boost potential into WTM-eABF, yielding a hybrid algorithm coined GaWTM-eABF. This algorithm leans on WTM-eABF to explore the transition coordinate with a GaMD-mollified potential and recovers the unbiased free-energy landscape through thermodynamic integration followed by proper reweighting. As illustrated in our numerical tests, GaWTM-eABF effectively overcomes the free-energy barriers in orthogonal space and correctly recovers the unbiased potential of mean force (PMF). Furthermore, applying both GaWTM-eABF and WTM-eABF to two biologically relevant processes, namely, the reversible folding of (i) deca-alanine and (ii) chignolin, our results indicate that GaWTM-eABF reduces the uncertainty in the PMF calculation and converges appreciably faster than WTM-eABF. Obviating the need of multiple-copy strategies, GaWTM-eABF is a robust, computationally efficient algorithm to surmount the free-energy barriers in orthogonal space and maps with utmost fidelity the free-energy landscape along selections of CVs. Moreover, our strategy that combines WTM-eABF with GaMD can be easily extended to other biasing-force algorithms.

Accuracy of Alternate Nonpolarizable Force Fields for the Determination of Protein-Ligand Binding Affinities Dominated by Cation-π Interactions

Modifying pair-specific Lennard-Jones parameters through the nonbonded FIX (NBFIX) feature of the CHARMM36 force field has proven cost-effective for improving the description of cation-π interactions in biological objects by means of pairwise additive potential energy functions. Here, two sets of newly optimized CHARMM36 force-field parameters including NBFIX corrections, coined CHARMM36m-NBF and CHARMM36-WYF, and the original force fields, namely CHARMM36m and Amber ff14SB, are used to determine the standard binding free energies of seven protein-ligand complexes containing cation-π interactions. Compared with precise experimental measurements, our results indicate that the uncorrected, original force fields significantly underestimate the binding free energies, with a mean error of 5.3 kcal/mol, while the mean errors of CHARMM36m-NBF and CHARMM36-WYF amount to 0.8 and 2.1 kcal/mol, respectively. The present study cogently demonstrates that the use of modified parameters jointly with NBFIX corrections dramatically increases the accuracy of the standard binding free energy of protein-ligand complexes dominated by cation-π interactions, most notably with CHARMM36m-NBF.

Improved Sampling and Free Energy Estimates for Antibiotic Permeation through Bacterial Porins

Antibiotics enter into bacterial cells via protein channels that serve as low-energy pathways through the outer membrane, which is otherwise impenetrable. Insights into the molecular mechanisms underlying the transport processes are vital for the development of effective antibacterials. A much-desired prerequisite is an accurate and reproducible determination of free energy surfaces for antibiotic translocation, enabling quantitative and meaningful comparisons of permeation mechanisms for different classes of antibiotics. Inefficient sampling along the orthogonal degrees of freedom, for example, in umbrella sampling and metadynamics approaches, is however a key limitation affecting the accuracy and the convergence of free energy estimates. To overcome this limitation, two sampling methods have been employed in the present study that, respectively, combine umbrella sampling and metadynamics-style biasing schemes with temperature acceleration for improved sampling along orthogonal degrees of freedom. As a model for the transport of bulky solutes, the ciprofloxacin-OmpF system has been selected. The well-tempered metadynamics approach with multiple walkers is compared with its "temperature-accelerated" variant in terms of improvements in sampling and convergence of free energy estimates. We find that the inclusion of collective variables governing solute degrees of freedom and solute-water interactions within the sampling scheme largely alleviates sampling issues. Concerning improved sampling and convergence of free energy estimates from independent simulations, the temperature-accelerated sliced sampling approach that combines umbrella sampling with temperature-accelerated molecular dynamics performs even better as shown for the ciprofloxacin-OmpF system.

"Dividing and Conquering" and "Caching" in Molecular Modeling

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

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

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

Nanomachine-Assisted Ion Transport Across Membranes: From Mechanism to Rational Design and Applications

Assisting ion transport across membranes by means of sophisticated molecular machines has promising applications in the treatment of diseases induced by dysregulated ion transport. To develop such nanoscale devices imbued with specific functions, rational de novo design, upstream from costly syntheses, is eminently desirable but would require the atomic detail of the translocation mechanism, which is still largely missing. We have explored the full ion capture-transport-release process over an aggregate simulation time of 60 μs, employing leading-edge enhanced-sampling algorithms to disentangle with unprecedented detail the mechanism that underlies ion transport mediated by a membrane-spanning [2]rotaxane composed of an ion carrier linked to a wheel threaded onto an axle. Beyond validating the reliability of our methodology through careful examination of the clockwork of a documented nanomachine, we put forth an original pH-controlled nano-object that can assist transient unidirectional ion transport across membranes.

Identifying the natural polyphenol catechin as a multi-targeted agent against SARS-CoV-2 for the plausible therapy of COVID-19: an integrated computational approach

The global pandemic crisis, coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has claimed the lives of millions of people across the world. Development and testing of anti-SARS-CoV-2 drugs or vaccines have not turned to be realistic within the timeframe needed to combat this pandemic. Here, we report a comprehensive computational approach to identify the multi-targeted drug molecules against the SARS-CoV-2 proteins, whichare crucially involved in the viral-host interaction, replication of the virus inside the host, disease progression and transmission of coronavirus infection. Virtual screening of 75 FDA-approved potential antiviral drugs against the target proteins, spike (S) glycoprotein, human angiotensin-converting enzyme 2 (hACE2), 3-chymotrypsin-like cysteine protease (3CLpro), cathepsin L (CTSL), nucleocapsid protein, RNA-dependent RNA polymerase (RdRp) and non-structural protein 6 (NSP6), resulted in the selection of seven drugs which preferentially bind to the target proteins. Further, the molecular interactions determined by molecular dynamics simulation revealed that among the 75 drug molecules, catechin can effectively bind to 3CLpro, CTSL, RBD of S protein, NSP6 and nucleocapsid protein. It is more conveniently involved in key molecular interactions, showing binding free energy (ΔGbind) in the range of -5.09 kcal/mol (CTSL) to -26.09 kcal/mol (NSP6). At the binding pocket, catechin is majorly stabilized by the hydrophobic interactions, displays ΔEvdW values: -7.59 to -37.39 kcal/mol. Thus, the structural insights of better binding affinity and favorable molecular interaction of catechin toward multiple target proteins signify that catechin can be potentially explored as a multi-targeted agent against COVID-19.

Repurposing Existing Molecular Machines through Accurate Regulation of Cooperative Motions

To understand how different external stimuli affect the cooperative motions in a molecular machine consisting of multiple components, we have investigated at the atomic level the effects of pH, solvent, and ionic strength on the mechanism underlying the ring-through-ring movement in a saturated [3]rotaxane. Our results indicate that different external stimuli regulate the stable states, the shuttling rate, and the mechanism that governs the ring-through-ring motion by controlling the cooperative movement of the components and triggering a gamut of responses, thereby opening to a vast number of potential applications, such as quaternary logical calculations. The present work cogently demonstrates that with existing nanomachines possessing a simple topology, but using different external stimuli-an approach coined multidimensional regulation-challenging tasks requiring precise control of the molecular motions at play can be achieved, and our methodology is particularly germane for de novo design of intelligent molecular machines.

Molecular Basis of SARS-CoV-2 Infection and Rational Design of Potential Antiviral Agents: Modeling and Simulation Approaches

The emergence in late 2019 of the coronavirus SARS-CoV-2 has resulted in the breakthrough of the COVID-19 pandemic that is presently affecting a growing number of countries. The development of the pandemic has also prompted an unprecedented effort of the scientific community to understand the molecular bases of the virus infection and to propose rational drug design strategies able to alleviate the serious COVID-19 morbidity. In this context, a strong synergy between the structural biophysics and molecular modeling and simulation communities has emerged, resolving at the atomistic level the crucial protein apparatus of the virus and revealing the dynamic aspects of key viral processes. In this Review, we focus on how in silico studies have contributed to the understanding of the SARS-CoV-2 infection mechanism and the proposal of novel and original agents to inhibit the viral key functioning. This Review deals with the SARS-CoV-2 spike protein, including the mode of action that this structural protein uses to entry human cells, as well as with nonstructural viral proteins, focusing the attention on the most studied proteases and also proposing alternative mechanisms involving some of its domains, such as the SARS unique domain. We demonstrate that molecular modeling and simulation represent an effective approach to gather information on key biological processes and thus guide rational molecular design strategies.

Thermodynamics of the Interaction between the Spike Protein of Severe Acute Respiratory Syndrome Coronavirus-2 and the Receptor of Human Angiotensin-Converting Enzyme 2. Effects of Possible Ligands

Since the end of 2019, the coronavirus SARS-CoV-2 has caused more than 1000000 deaths all over the world and still lacks a medical treatment despite the attention of the whole scientific community. Human angiotensin-converting enzyme 2 (ACE2) was recently recognized as the transmembrane protein that serves as the point of entry of SARS-CoV-2 into cells, thus constituting the first biomolecular event leading to COVID-19 disease. Here, by means of a state-of-the-art computational approach, we propose a rational evaluation of the molecular mechanisms behind the formation of the protein complex. Moreover, the free energy of binding between ACE2 and the active receptor binding domain of the SARS-CoV-2 spike protein is evaluated quantitatively, providing for the first time the thermodynamics of virus-receptor recognition. Furthermore, the action of different ACE2 ligands is also examined in particular in their capacity to disrupt SARS-CoV-2 recognition, also providing via a free energy profile the quantification of the ligand-induced decreased affinity. These results improve our knowledge on molecular grounds of the SARS-CoV-2 infection and allow us to suggest rationales that could be useful for the subsequent wise molecular design for the treatment of COVID-19 cases.

Cryo-EM and MD infer water-mediated proton transport and autoinhibition mechanisms of Vo complex

Rotary vacuolar adenosine triphosphatases (V-ATPases) drive transmembrane proton transport through a V_o proton channel subcomplex. Despite recent high-resolution structures of several rotary ATPases, the dynamic mechanism of proton pumping remains elusive. Here, we determined a 2.7-Å cryo-electron microscopy (cryo-EM) structure of yeast V_o proton channel in nanodisc that reveals the location of ordered water molecules along the proton path, details of specific protein-lipid interactions, and the architecture of the membrane scaffold protein. Moreover, we uncover a state of V_o that shows the c-ring rotated by ~14°. Molecular dynamics simulations demonstrate that the two rotary states are in thermal equilibrium and depict how the protonation state of essential glutamic acid residues couples water-mediated proton transfer with c-ring rotation. Our cryo-EM models and simulations also rationalize a mechanism for inhibition of passive proton transport as observed for free V_o that is generated as a result of V-ATPase regulation by reversible disassembly in vivo.

Accurate Description of Cation-π Interactions in Proteins with a Nonpolarizable Force Field at No Additional Cost

Cation-π interactions play a significant role in a host of processes eminently relevant to biology. However, polarization effects arising from the interaction of cations with aromatic moieties have long been recognized to be inadequately described by pairwise additive force fields. In the present work, we address this longstanding shortcoming through the nonbonded FIX (NBFIX) feature of the CHARMM36 force field, modifying pair-specific Lennard-Jones (LJ) parameters, while circumventing the limitations of the Lorentz-Berthelot combination rules. The potentials of mean force (PMFs) characterizing prototypical cation-π interactions in aqueous solutions are first determined using a hybrid quantum mechanical/molecular mechanics (QM/MM) strategy in conjunction with an importance-sampling algorithm. The LJ parameters describing the cation-π pairs are then optimized to match the QM/MM PMFs. The standard binding free energies of nine cation-π complexes, i.e., toluene, para-cresol, and 3-methyl-indole interacting with either ammonium, guanidinium, or tetramethylammonium, determined with this new set of parameters agree well with the experimental measurements. Additional simulations were carried out on three different classes of biological objects featuring cation-π interactions, including five individual proteins, three protein-ligand complexes, and two protein-protein complexes. Our results indicate that the description of cation-π interactions is overall improved using NBFIX corrections, compared with the standard pairwise additive force field. Moreover, an accurate binding free energy calculation for a protein-ligand complex containing cation-π interactions (2BOK) shows that using the new parameters, the experimental binding affinity can be reproduced quantitatively. Put together, the present work suggests that the NBFIX parameters optimized here can be broadly utilized in the simulation of proteins in an aqueous solution to enhance the representation of cation-π interactions, at no additional computational cost.

Scalable molecular dynamics on CPU and GPU architectures with NAMD

NAMDis a molecular dynamics program designed for high-performance simulations of very large biological objects on CPU- and GPU-based architectures. NAMD offers scalable performance on petascale parallel supercomputers consisting of hundreds of thousands of cores, as well as on inexpensive commodity clusters commonly found in academic environments. It is written in C++ and leans on Charm++ parallel objects for optimal performance on low-latency architectures. NAMD is a versatile, multipurpose code that gathers state-of-the-art algorithms to carry out simulations in apt thermodynamic ensembles, using the widely popular CHARMM, AMBER, OPLS, and GROMOS biomolecular force fields. Here, we review the main features of NAMD that allow both equilibrium and enhanced-sampling molecular dynamics simulations with numerical efficiency. We describe the underlying concepts utilized by NAMD and their implementation, most notably for handling long-range electrostatics; controlling the temperature, pressure, and pH; applying external potentials on tailored grids; leveraging massively parallel resources in multiple-copy simulations; and hybrid quantum-mechanical/molecular-mechanical descriptions. We detail the variety of options offered by NAMD for enhanced-sampling simulations aimed at determining free-energy differences of either alchemical or geometrical transformations and outline their applicability to specific problems. Last, we discuss the roadmap for the development of NAMD and our current efforts toward achieving optimal performance on GPU-based architectures, for pushing back the limitations that have prevented biologically realistic billion-atom objects to be fruitfully simulated, and for making large-scale simulations less expensive and easier to set up, run, and analyze. NAMD is distributed free of charge with its source code at www.ks.uiuc.edu.

Driving Protein Conformational Cycles in Physiology and Disease: "Frustrated" Amino Acid Interaction Networks Define Dynamic Energy Landscapes: Amino Acid Interaction Networks Change Progressively Along Alpha Tryptophan Synthase's Catalytic Cycle

A general framework by which dynamic interactions within a protein will promote the necessary series of structural changes, or "conformational cycle," required for function is proposed. It is suggested that the free-energy landscape of a protein is biased toward this conformational cycle. Fluctuations into higher energy, although thermally accessible, conformations drive the conformational cycle forward. The amino acid interaction network is defined as those intraprotein interactions that contribute most to the free-energy landscape. Some network connections are consistent in every structural state, while others periodically change their interaction strength according to the conformational cycle. It is reviewed here that structural transitions change these periodic network connections, which then predisposes the protein toward the next set of network changes, and hence the next structural change. These concepts are illustrated by recent work on tryptophan synthase. Disruption of these dynamic connections may lead to aberrant protein function and disease states.

Role of RNA Guanine Quadruplexes in Favoring the Dimerization of SARS Unique Domain in Coronaviruses

Coronaviruses may produce severe acute respiratory syndrome (SARS). As a matter of fact, a new SARS-type virus, SARS-CoV-2, is responsible for the global pandemic in 2020 with unprecedented sanitary and economic consequences for most countries. In the present contribution we study, by all-atom equilibrium and enhanced sampling molecular dynamics simulations, the interaction between the SARS Unique Domain and RNA guanine quadruplexes, a process involved in eluding the defensive response of the host thus favoring viral infection of human cells. Our results evidence two stable binding modes involving an interaction site spanning either the protein dimer interface or only one monomer. The free energy profile unequivocally points to the dimer mode as the thermodynamically favored one. The effect of these binding modes in stabilizing the protein dimer was also assessed, being related to its biological role in assisting the SARS viruses to bypass the host protective response. This work also constitutes a first step in the possible rational design of efficient therapeutic agents aiming at perturbing the interaction between SARS Unique Domain and guanine quadruplexes, hence enhancing the host defenses against the virus.

Insights into directional movement in molecular machines from free-energy calculations

A rotaxane composed of a symmetrical axle containing three binding stations and a cone-like macrocycle containing two secondary amines has been investigated at the atomic level. At high pH, the macrocycle binds to the intermediate di(quaternary ammonium) site, while at low pH, the protonated macrocycle selectively moves along the axle to one of the two symmetrical phenyl triazole binding sites facing its upper rim, but does not shuttle backward. The determined free-energy profile characterizing the translocation of the macrocycle indicates that the selected binding site is energetically more favorable than the one facing the lower rim of the macrocycle and the free-energy barrier against translocation to the former site is lower than to the latter one, rationalizing the directional movement. This selectivity mainly stems from the asymmetry of the macrocycle shape. The strong electrostatic repulsion between the ring and the axle is found to constitute the driving force for the shuttling of the ring and also the resistance for its reverse motion. Moreover, the effect of the solvent on the shuttling has been examined, suggesting that increasing the solvent polarity may weaken the directional preference of shuttling, due to the shielding effect of polar solvents on electrostatic interactions. Our study provides a theoretical framework for tuning the selectivity of directional movement in molecular machines.