Monte Carlo study of a phase‐separating liquid mixture by umbrella sampling

Energy landscapes-Past, present, and future: A perspective

Energy landscapes and the closely related cost function landscapes have been recognized in science, mathematics, and various other fields such as economics as being highly useful paradigms and tools for the description and analysis of the properties of many systems, ranging from glasses, proteins, and abstract global optimization problems to business models. A multitude of algorithms for the exploration and exploitation of such landscapes have been developed over the past five decades in the various fields of applications, where many re-inventions but also much cross-fertilization have occurred. Twenty-five years ago, trying to increase the fruitful interactions between workers in different fields led to the creation of workshops and small conferences dedicated to the study of energy landscapes in general instead of only focusing on specific applications. In this perspective, I will present some history of the development of energy landscape studies and try to provide an outlook on in what directions the field might evolve in the future and what larger challenges are going to lie ahead, both from a conceptual and a practical point of view, with the main focus on applications of energy landscapes in chemistry and physics.

The role of electrostatic potential in the translocation of triangulene across membranes

Triangulene and its derivatives show broad application prospects in the fields of biological imaging and biosensing. However, its interaction with cell membranes is still poorly studied. In this study, classical molecular dynamics simulations were used to adjust the electrostatic potential of triangulene to observe its interactions with cell membranes. We found that electrostatic potential not only affects the behavior as it enters the cell membrane, but also spatial distribution within the cell membrane. The angle distribution of inside-0 and all-0 triangulene when penetrating the membrane is more extensive than that of ESP triangulene. However, inside-0 triangulene could cross the midline of the cell membrane and prefers to stay in the upper leaflet, while all-0 triangulene and ESP triangulene can reach the lower leaflet. These findings can help us regulate the distribution of nanoparticles in cells, so as to design functional nanoparticles that conform to the requirements.

Nuclear quantum effects on zeolite proton hopping kinetics explored with machine learning potentials and path integral molecular dynamics

Proton hopping is a key reactive process within zeolite catalysis. However, the accurate determination of its kinetics poses major challenges both for theoreticians and experimentalists. Nuclear quantum effects (NQEs) are known to influence the structure and dynamics of protons, but their rigorous inclusion through the path integral molecular dynamics (PIMD) formalism was so far beyond reach for zeolite catalyzed processes due to the excessive computational cost of evaluating all forces and energies at the Density Functional Theory (DFT) level. Herein, we overcome this limitation by training first a reactive machine learning potential (MLP) that can reproduce with high fidelity the DFT potential energy surface of proton hopping around the first Al coordination sphere in the H-CHA zeolite. The MLP offers an immense computational speedup, enabling us to derive accurate reaction kinetics beyond standard transition state theory for the proton hopping reaction. Overall, more than 0.6 μs of simulation time was needed, which is far beyond reach of any standard DFT approach. NQEs are found to significantly impact the proton hopping kinetics up to ~473 K. Moreover, PIMD simulations with deuterium can be performed without any additional training to compute kinetic isotope effects over a broad range of temperatures.

In silico study of selective inhibition mechanism of S-adenosyl-L-methionine analogs for human DNA methyltransferase 3A

Epigenetic mechanisms leading to transcriptional regulation, including DNA methylation, are frequently dysregulated in diverse cancers. Interfering with aberrant DNA methylation performed by DNA cytosine methyltransferases (DNMTs) is a clinically validated approach. In particular, the selective inhibition of the de novo DNMT3A and DNMT3B enzymes, whose expression is limited to early embryogenesis, adult stem cells, and in cancers, is particularly attractive; such selectivity is likely to attenuate the dose limiting toxicity shown by current, non-selective DNMT inhibitors. We use molecular dynamics (MD) based computational analysis to study known small molecule binders of DNMT3A, then propose reversible, tight binding, and selective inhibitors that exploit the Asn¹¹⁹²/Arg⁶⁸⁸ difference between the maintenance DNMT1 and DNMT3A near the active site. A similar strategy exploiting the presence of a unique active site cysteine Cys⁶⁶⁶ is used to propose DNMT3A-selective irreversible inhibitors. We report our results of relative binding energies of the known and proposed compounds estimated using MM/GBSA and umbrella sampling (US) techniques, and our evaluation of other end-point binding free energy calculation methods for these receptors. These calculations offer insight into the potential for small molecules to selectively target the active site of DNMT3A.

Free-Energy Profiles for Membrane Permeation of Compounds Calculated Using Rare-Event Sampling Methods

The free-energy profile of a compound is an essential measurement in evaluating the membrane permeation process by means of theoretical methods. Computationally, molecular dynamics (MD) simulation allows the free-energy profile calculation. However, MD simulations frequently fail to sample membrane permeation because they are rare events induced in longer timescales than the accessible timescale of MD, leading to an insufficient conformational search to calculate an incorrect free-energy profile. To achieve a sufficient conformational search, several enhanced sampling methods have been developed and elucidated the membrane permeation process. In addition to these enhanced sampling methods, we proposed a simple yet powerful free-energy calculation of a compound for the membrane permeation process based on originally rare-event sampling methods developed by us. Our methods have a weak dependency on external biases and their optimizations to promote the membrane permeation process. Based on distributed computing, our methods only require the selection of initial structures and their conformational resampling, whereas the enhanced sampling methods may be required to adjust external biases. Furthermore, our methods efficiently search membrane permeation processes with simple scripts without modifying any MD program. As demonstrations, we calculated the free-energy profiles of seven linear compounds for their membrane permeation based on a hybrid conformational search using two rare-event sampling methods, that is, (1) parallel cascade selection MD (PaCS-MD) and (2) outlier flooding method (OFLOOD), combined with a Markov state model (MSM) construction. In the first step, PaCS-MD generated initial membrane permeation paths of a compound. In the second step, OFLOOD expanded the unsearched conformational area around the initial paths, allowing for a broad conformational search. Finally, the trajectories were employed to construct reliable MSMs, enabling correct free-energy profile calculations. Furthermore, we estimated the membrane permeability coefficients of all compounds by constructing the reliable MSMs for their membrane permeation. In conclusion, the calculated coefficients were qualitatively correlated with the experimental measurements (correlation coefficient (R²) = 0.8689), indicating that the hybrid conformational search successfully calculated the free-energy profiles and membrane permeability coefficients of the seven compounds.

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.

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.

Mechanistic Characterization of Zeolite-Catalyzed Aromatic Electrophilic Substitution at Realistic Operating Conditions

Zeolite-catalyzed benzene ethylation is an important industrial reaction, as it is the first step in the production of styrene for polymer manufacturing. Furthermore, it is a prototypical example of aromatic electrophilic substitution, a key reaction in the synthesis of many bulk and fine chemicals. Despite extensive research, the reaction mechanism and the nature of elusive intermediates at realistic operating conditions is not properly understood. More in detail, the existence of the elusive arenium ion (better known as Wheland complex) formed upon electrophilic attack on the aromatic ring is still a matter of debate. Temperature effects and the presence of protic guest molecules such as water are expected to impact the reaction mechanism and lifetime of the reaction intermediates. Herein, we used enhanced sampling ab initio molecular dynamics simulations to investigate the complete mechanism of benzene ethylation with ethene and ethanol in the H-ZSM-5 zeolite. We show that both the stepwise and concerted mechanisms are active at reaction conditions and that the Wheland intermediate spontaneously appears as a shallow minimum in the free energy surface after the electrophilic attack on the benzene ring. Addition of water enhances the protonation kinetics by about 1 order of magnitude at coverages of one water molecule per Brønsted acidic site. In the fully solvated regime, an overstabilization of the BAS as hydronium ion occurs and the rate enhancement disappears. The obtained results give critical atomistic insights in the role of water to selectively tune the kinetics of protonation reactions in zeolites.

Evaluation of Constrained and Restrained Molecular Dynamics Simulation Methods for Predicting Skin Lipid Permeability

Recently, molecular dynamics (MD) simulations have been utilized to investigate the barrier properties of human skin stratum corneum (SC) lipid bilayers. Different MD methods and force fields have been utilized, with predicted permeabilities varying by few orders of magnitude. In this work, we compare constrained MD simulations with restrained MD simulations to obtain the potential of the mean force and the diffusion coefficient profile for the case of a water molecule permeating across an SC lipid bilayer. Corresponding permeabilities of the simulated lipid bilayer are calculated via the inhomogeneous solubility diffusion model. Results show that both methods perform similarly, but restrained MD simulations have proven to be the more robust approach for predicting the potential of the mean force profile. Critical to both methods are the sampling of the whole trans-bilayer axis and the following symmetrization process. Re-analysis of the previously reported free energy profiles showed that some of the discrepancies in the reported permeability values is due to misquotation of units, while some are due to the inaccurately obtained potential of the mean force. By using the existing microscopic geometrical models via the intercellular lipid pathway, the permeation through the whole SC is predicted from the MD simulation results, and the predicted barrier properties have been compared to experimental data from the literature with good agreement.

Crocin Inhibits the Fibrillation of Human α-synuclein and Disassembles Mature Fibrils: Experimental Findings and Mechanistic Insights from Molecular Dynamics Simulation

The aggregation of human alpha-synuclein (hαS) is pivotally implicated in the development of most types of synucleinopathies. Molecules that can inhibit or reverse the aggregation process of amyloidogenic proteins have potential therapeutic value. The anti-aggregating activity of multiple carotenoid compounds has been reported over the past decades against a growing list of amyloidogenic polypeptides. Here, we aimed to determine whether crocin, the main carotenoid glycoside component of saffron, would inhibit hαS aggregation or could disassemble its preformed fibrils. By employing a series of biochemical and biophysical techniques, crocin was exhibited to inhibit hαS fibrillation in a dose-dependent fashion by stabilizing very early aggregation intermediates in off-pathway non-toxic conformations with little β-sheet content. We also observed that crocin at high concentrations could efficiently destabilize mature fibrils and disassemble them into seeding-incompetent intermediates by altering their β-sheet conformation and reshaping their structure. Our atomistic molecular dynamics (MD) simulations demonstrated that crocin molecules bind to both the non amyloid-β component (NAC) region and C-terminal domain of hαS. These interactions could thereby stabilize the autoinhibitory conformation of the protein and prevent it from adopting aggregation-prone structures. MD simulations further suggested that ligand molecules prefer to reside longitudinally along the fibril axis onto the edges of the inter-protofilament interface where they establish hydrogen and hydrophobic bonds with steric zipper stabilizing residues. These interactions turned out to destabilize hαS fibrils by altering the interstrand twist angles, increasing the rigidity of the fibril core, and elevating its radius of gyration. Our findings suggest the potential pharmaceutical implication of crocin in synucleinopathies.

Independent Nontargeted Parallel Cascade Selection Molecular Dynamics (Ino-PaCS-MD) to Enhance the Conformational Sampling of Proteins

Biological functions are related to long-time protein dynamics (rare events) that are induced over microseconds. Such protein dynamics can be investigated using molecular dynamics (MD) simulations. However, the detection of rare events remains challenging using conventional MD (cMD) since the accessible timescales of cMD are shorter than those of the biological functions. Recently, the parallel cascade selection MD (PaCS-MD) has been proposed to detect such rare events, wherein transition paths are generated between a given reactant and product. As an extension, the nontargeted PaCS-MD (nt-PaCS-MD) has been proposed to predict the transition paths without requiring reference to any product. Thus, as a further extension, we herein propose independent nt-PaCS-MD, namely, Ino-PaCS-MD, wherein multiple walkers are launched from a set of different starting configurations. Each walker repeats a cycle of restarting short-time MD simulations from configurations with high potentials for making transitions to neighboring metastable states. To further enhance the sampling ability, Ino-PaCS-MD temporarily stops the conformational search and periodically resets the starting configurations so that they are uniformly distributed in a conformational subspace, thereby preventing a given protein from being trapped in one of the metastable states. As a demonstration, Ino-PaCS-MD successfully detects rare events of a maltose-binding protein as open-close transitions with a nanosecond-order simulation time, although a microsecond-order cMD simulation failed to detect these rare events, showing the high sampling efficiency of Ino-PaCS-MD.

Simulation of protein pulling dynamics on second time scale with boxed molecular dynamics

We demonstrate how recently developed Boxed Molecular Dynamics (BXD) and kinetics [D. V. Shalashilin et al., J. Chem. Phys. 137, 165102 (2012)] can provide a kinetic description of protein pulling experiments, allowing for a connection to be made between experiment and the atomistic protein structure. BXD theory applied to atomic force microscopy unfolding is similar in spirit to the kinetic two-state model [A. Noy and R. W. Friddle, Methods 60, 142 (2013)] but with some differences. First, BXD uses a large number of boxes, and therefore, it is not a two-state model. Second, BXD rate coefficients are obtained from atomistic molecular dynamics simulations. BXD can describe the dependence of the pulling force on pulling speed. Similar to Shalashilin et al. [J. Chem. Phys. 137, 165102 (2012)], we show that BXD is able to model the experiment at a very long time scale up to seconds, which is way out of reach for standard molecular dynamics.

Complex Reaction Network Thermodynamic and Kinetic Autoconstruction Based on Ab Initio Statistical Mechanics: A Case Study of O2 Activation on Ag4 Clusters

An approach based on ab initio statistical mechanics is demonstrated for autoconstructing complex reaction networks. Ab initio molecular dynamics combined with Markov state models are employed to study relevant transitions and corresponding thermodynamic and kinetic properties of a reaction. To explore the capability and flexibility of this approach, we present a study of oxygen activation on Ag4 as a model reaction. Specifically, with the same sampled trajectories, it is possible to study the structural effects and the reaction rate of the cited reaction. The results show that this approach is suitable for automatized construction of reaction networks, especially for non-well-studied reactions, which can benefit from this ab initio molecular dynamics based approach to construct comprehensive reaction networks with Markov state models without prior knowledge about the potential energy landscape.

Exploring the concerted mechanistic pathway for HIV-1 PR-substrate revealed by umbrella sampling simulation

HIV-1 protease (HIV-1 PR) is an essential enzyme for the replication process of its virus, and therefore considered an important target for the development of drugs against the acquired immunodeficiency syndrome (AIDS). Our previous study shows that the catalytic mechanism of subtype B/C-SA HIV-1 PR follows a one-step concerted acyclic hydrolysis reaction process using a two-layered ONIOM B3LYP/6-31++G(d,p) method. This present work is aimed at exploring the proposed mechanism of the proteolysis catalyzed by HIV-1 PR and to ensure our proposed mechanism is not an artefact of a single theoretical technique. Hence, we present umbrella sampling method that is suitable for calculating potential mean force (PMF) for non-covalent ligand/substrate-enzyme association/dissociation interactions which provide thermodynamic details for molecular recognition. The free activation energy results were computed in terms of PMF analysis within the hybrid QM(DFTB)/MM approach. The theoretical findings suggest that the proposed mechanism corresponds in principle with experimental data. Given our observations, we suggest that the QM/MM MD method can be used as a reliable computational technique to rationalize lead compounds against specific targets such as the HIV-1 protease.

Stable glassy configurations of the Kob-Andersen model using swap Monte Carlo

The swap Monte Carlo algorithm allows the preparation of highly stable glassy configurations for a number of glass-formers but is inefficient for some models, such as the much studied binary Kob-Andersen (KA) mixture. We have recently developed generalizations to the KA model where swap can be very effective. Here, we show that these models can, in turn, be used to considerably enhance the stability of glassy configurations in the original KA model at no computational cost. We successfully develop several numerical strategies both in and out of equilibrium to achieve this goal and show how to optimize them. We provide several physical measurements indicating that the proposed algorithms considerably enhance mechanical and thermodynamic stability in the KA model, including a transition toward brittle yielding behavior. Our results thus pave the way for future studies of stable glasses using the KA model.

Random-field Ising model criticality in a glass-forming liquid

We use computer simulations to investigate the extended phase diagram of a supercooled liquid linearly coupled to a quenched reference configuration. An extensive finite-size scaling analysis demonstrates the existence of a random-field Ising model (RFIM) critical point and of a first-order transition line, in agreement with recent field-theoretical approaches. The dynamics in the vicinity of this critical point resembles the peculiar activated scaling of RFIM-like systems, and the overlap autocorrelation displays a logarithmic stretching. Our study demonstrates RFIM criticality in the thermodynamic limit for a three-dimensional supercooled liquid at equilibrium.

Enhanced Conformational Sampling Method Based on Anomaly Detection Parallel Cascade Selection Molecular Dynamics: ad-PaCS-MD

In the present study, we propose a rare-event sampling method called anomaly detection parallel cascade selection molecular dynamics (ad-PaCS-MD). The original PaCS-MD was designed to generate conformational transition pathways from a given reactant to a product when the latter is known a priori. As an extension of the original method, ad-PaCS-MD has been designed to efficiently search transition pathways from a given reactant without referring to a given product. In ad-PaCS-MD, rarely occurring but essential states (configurations) of proteins for the transitions are identified based on the degrees of an anomaly. In more detail, ad-PaCS-MD adopts an algorithm called an anomaly detection generative adversarial network (anoGAN) as a measure for detecting rarely occurring states to be resampled. Here, the essential configurations with higher degrees of the anomaly are selected with anoGAN and intensively resampled by restarting short-time MD simulations from the selected configurations. By repeating the detections and resampling of configurations with the higher degrees of the anomaly, ad-PaCS-MD automatically and efficiently promotes the rare events and gives a wide range of the free energy landscape by combining with the Markov state model construction. As demonstrations, open-closed transitions of two globular proteins (T4 lysozyme and maltose-binding protein) were promoted with ad-PaCS-MD by referring only to the given starting configurations. In each demonstration, ad-PaCS-MD promoted the large-amplitude open-closed transitions with nanosecond-order simulation times. In conclusion, our demonstrations showed a higher conformational sampling efficiency for ad-PaCS-MD than conventional MD (CMD) because CMD required computational costs of more than microsecond-order simulation times to promote the rare events.

MD simulation reveals differential binding of Cm(III) and Th(IV) with serum transferrin at acidic pH

The iron carrier human serum transferrin (sTf) is known to transport other metals, including some actinides (An). Radiotoxic An are routinely involved in the nuclear fuel cycle and the possibility of their accidental exposure cannot be ruled out. Understanding An interaction with sTf assumes a greater significance for the development of safe and efficacious chelators for their removal from the blood stream. Here we report several 100 ns equilibrium MD simulations of Cm(III)- and Th(IV)-loaded sTf at various protonation states of the protein to explore the possibility of the two An ions release and speciation. The results demonstrate variation in protonation state of dilysine pair (K206 and K296) and the tyrosine (Y188) residue is necessary for the opening of Cm(III)-bound protein and the release of the ion. For the tetravalent thorium, protonation of dilysine pair suffices to cause conformational changes of protein. However, in none of the protonation states, Th(IV) releases from sTf because of its strong electrostatic interaction with D63 in the first shell of the sTf binding cleft. Analysis of hydrogen bond, water bridge, and the evaluation of potential of mean forces of the An ions' release from sTf, substantiate the differential behavior of Cm(III) and Th(IV) at endosomal pH. The results provide insight in the regulation of Cm(III) and Th(IV) bioavailability that may prove useful for effective design of their decorporating agents and as well may help the future design of radiotherapy based on tetravalent ions.

Efficient Conformational Sampling of Collective Motions of Proteins with Principal Component Analysis-Based Parallel Cascade Selection Molecular Dynamics

Molecular dynamics (MD) simulation has become a powerful tool because it provides a time series of protein dynamics at high temporal-spatial resolution. However, the accessible timescales of MD simulation are shorter than those of the biologically rare events. Generally, long-time MD simulations over microseconds are required to detect the rare events. Therefore, it is desirable to develop rare-event-sampling methods. For a rare-event-sampling method, we have developed parallel cascade selection MD (PaCS-MD). PaCS-MD generates transition pathways from a given source structure to a target structure by repeating short-time MD simulations. The key point in PaCS-MD is how to select reasonable candidates (protein configurations) with high potentials to make transitions toward the target structure. In the present study, based on principal component analysis (PCA), we propose PCA-based PaCS-MD to detect rare events of collective motions of a given protein. Here, the PCA-based PaCS-MD is composed of the following two steps. At first, as a preliminary run, PCA is performed using an MD trajectory from the target structure to define a principal coordinate (PC) subspace for describing the collective motions of interest. PCA provides principal modes as eigenvectors to project a protein configuration onto the PC subspace. Then, as a production run, all the snapshots of short-time MD simulations are ranked by inner products (IPs), where an IP is defined between a snapshot and the target structure. Then, snapshots with higher values of the IP are selected as reasonable candidates, and short-time MD simulations are independently restarted from them. By referring to the values of the IP, the PCA-based PaCS-MD repeats the short-time MD simulations from the reasonable candidates that are highly correlated with the target structure. As a demonstration, we applied the PCA-based PaCS-MD to adenylate kinase and detected its large-amplitude (open-closed) transition with a nanosecond-order 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.

Comparison of Free-Energy Methods to Calculate the Barriers for the Nucleophilic Substitution of Alkyl Halides by Hydroxide

Calculating the free-energy barriers of liquid-phase chemical reactions with explicit solvent is a considerable challenge. Most studies use the energy and entropy of minimized single-point geometries of the reactants and transition state in implicit solvent using normal mode analysis (NMA). Explicit-solvent methods instead make use of the potential of mean force (PMF). Here, we propose a new energy-entropy (EE) method to calculate the Gibbs free energy of reactants and transition states in explicit solvent by combining quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations with multiscale cell correlation (MCC). We apply it to six nucleophilic substitution reactions of the hydroxide transfer to methyl and ethyl halides in water, where the halides are F, Cl, and Br. We compare EE-MCC Gibbs free energy barriers using two Hamiltonians, self-consistent charge density functional based tight-binding (SCC-DFTB) and B3LYP/6-31+G* density functional theory (DFT) with respective PMF values, EE-NMA values using B3LYP/6-31+G* and M06/6-31+G* DFT in implicit solvent and experimental values derived via transition state theory. The barriers using SCC-DFTB are found to agree well with the PMF and experiment and previous computational studies, being slightly higher but improving on the lower values obtained for the implicit solvent. Achieving convergence over many degrees of freedom remains a challenge for EE-MCC in explicit-solvent QM/MM systems, particularly for the more expensive B3LYP/6-31+G* and M06/6-31+G* DFT methods, but the insightful decomposition of entropy over all degrees of freedom should make EE-MCC a valuable tool for deepening the understanding of chemical reactions.

Dimerization energetics of the G-protein coupled bile acid receptor TGR5 from all-atom simulations

We describe the first extensive energetic evaluation of GPCR dimerization on the atomistic level by means of potential of mean force (PMF) computations and implicit solvent/implicit membrane end-point free energy calculations (MM-PBSA approach). Free energies of association computed from the PMFs show that the formation of both the 1/8 and 4/5 interface is energetically favorable for TGR5, the first GPCR known to be activated by hydrophobic bile acids and neurosteroids. Furthermore, formation of the 1/8 interface is favored over that of the 4/5 interface. Both results are in line with our previous FRET experiments in live cells. Differences in lipid-protein interactions are identified to contribute to the observed differences in free energies of association. A per-residue decomposition of the MM-PBSA effective binding energy reveals hot spot residues specific for both interfaces that form clusters. This knowledge may be used to guide the design of dimerization inhibitors or perform mutational studies to explore physiological consequences of distorted TGR5 association. Finally, we characterized the role of Y111, located in the conserved (D/E)RY motif, as a facilitator of TGR5 interactions. The types of computations performed here should be transferable to other transmembrane proteins that form dimers or higher oligomers as long as good structural models of the dimeric or oligomeric states are available. Such computations may help to overcome current restrictions due to an imperfect energetic representation of protein association at the coarse-grained level. © 2019 Wiley Periodicals, Inc.

Nontargeted Parallel Cascade Selection Molecular Dynamics Based on a Nonredundant Selection Rule for Initial Structures Enhances Conformational Sampling of Proteins

Nontargeted parallel cascade selection molecular dynamics (nt-PaCS-MD) is a method for enhanced conformational sampling of proteins. To search a broad conformational subspace, nt-PaCS-MD repeats cycles of conformational resampling from relevant initial structures. Generally, the conformational sampling efficiency of nt-PaCS-MD depends on a selection rule for the initial structures. In the original nt-PaCS-MD, the initial structures were selected by referring to structural distributions of protein configurations generated by conformational resampling (multiple short-time MD simulations). However, their structural redundancy among the initial structures was neglected for the cycles of conformational resampling, indicating that similar protein configurations might be frequently specified and resampled in every cycle in the original nt-PaCS-MD. To reduce the possibility of resampling from redundant initial structures, we propose an alternative selection rule that accounts for structural similarity among the initial structures. Specifically, a pairwise root-mean-square deviation (RMSD) is defined for all of the initial structures selected for all of the past cycles. Then a set of protein configurations with a larger pairwise RMSD is sequentially specified and resampled in the next cycle, which is regarded to as a history-dependent selection of initial structures by considering a profile of the past specified initial structures. The present scheme, termed extended nt-PaCS-MD, prevents us from resampling a set of redundant protein configurations. To check the conformational sampling efficiency of the extended nt-PaCS-MD, we used a middle-sized protein, T4 lysozyme, in explicit water. Through the assessment, this extended nt-PaCS-MD identified the open-closed transitions of T4 lysozyme more efficiently than the original nt-PaCS-MD.

Ultrasmall Au clusters supported on pristine and defected CeO2: Structure and stability

The atomistic simulation of supported metal catalysts has long been challenging due to the increased complexity of dual components. In order to determine the metal/support interface, efficient theoretical tools to map out the potential energy surface (PES) are generally required. This work represents the first attempt to apply the recently developed SSW-NN method, stochastic surface walking (SSW) global optimization based on global neural network potential (G-NN), to explore the PES of a highly controversial supported metal catalyst, Au/CeO₂, system. By establishing the ternary Au-Ce-O G-NN potential based on first principles global dataset, we have searched for the global minima for a series of Au/CeO₂ systems. The segregation and diffusion pathway for Au clusters on CeO₂(111) are then explored by using enhanced molecular dynamics. Our results show that the ultrasmall cationic Au clusters, e.g., Au₄O₂, attaching to surface structural defects are the only stable structural pattern and the other clusters on different CeO₂ surfaces all have a strong energy preference to grow into a bulky Au metal. Despite the thermodynamics tendency of sintering, Au clusters on CeO₂ have a high kinetics barrier (>1.4 eV) in segregation and diffusion. The high thermodynamics stability of ultrasmall cationic Au clusters and the high kinetics stability for Au clusters on CeO₂ are thus the origin for the high activity of Au/CeO₂ catalysts in a range of low temperature catalytic reactions. We demonstrate that the global PES exploration is critical for understanding the morphology and kinetics of metal clusters on oxide support, which now can be realized via the SSW-NN method.

Why are some Enzymes Dimers? Flexibility and Catalysis in Thermotoga Maritima Dihydrofolate Reductase

Dihydrofolate reductase from Thermotoga maritima (TmDFHFR) is a dimeric thermophilic enzyme that catalyzes the hydride transfer from the cofactor NADPH to dihydrofolate less efficiently than other DHFR enzymes, such as the mesophilic analogue Escherichia coli DHFR (EcDHFR). Using QM/MM potentials, we show that the reduced catalytic efficiency of TmDHFR is most likely due to differences in the amino acid sequence that stabilize the M20 loop in an open conformation, which prevents the formation of some interactions in the transition state and increases the number of water molecules in the active site. However, dimerization provides two advantages to the thermophilic enzyme: it protects its structure against denaturation by reducing thermal fluctuations and it provides a less negative activation entropy, toning down the increase of the activation free energy with temperature. Our molecular picture is confirmed by the analysis of the temperature dependence of enzyme kinetic isotope effects in different DHFR enzymes.

Insight into the selective binding mechanism of DNMT1 and DNMT3A inhibitors: a molecular simulation study

DNA methyltransferases (DNMTs), responsible for the regulation of DNA methylation, have been regarded as promising drug targets for cancer therapy. However, high structural conservation of the catalytic domains of DNMTs poses a big challenge to design selective inhibitors for a specific DNMT isoform. In this study, molecular dynamics (MD) simulations, end-point free energy calculations and umbrella sampling (US) simulations were performed to reveal the molecular basis of the binding selectivity of three representative DNMT inhibitors towards DNMT1 and DNMT3A, including SFG (DNMT1 and DNMT3A dual inhibitors), DC-05 (DNMT1 selective inhibitor) and GSKex1 (DNMT3A selective inhibitor). The binding selectivity of the studied inhibitors reported in previous experiments is reproduced by the MD simulation and binding free energy prediction. The simulation results also suggest that the driving force to determine the binding selectivity of the studied inhibitors stems from the difference in the protein-inhibitor van der Waals interactions. Meanwhile, the per-residue free energy decomposition reveals that the contributions from several non-conserved residues in the binding pocket of DNMT1/DNMT3A, especially Val1580/Trp893, Asn1578/Arg891 and Met1169/Val665, are the key factors responsible for the binding selectivity of DNMT inhibitors. In addition, the binding preference of the studied inhibitors was further validated by the potentials of mean force predicted by the US simulations. This study will provide valuable information for the rational design of novel selective inhibitors targeting DNMT1 and DNMT3A.

Selective enhanced sampling in dihedral energy facilitates overcoming the dihedral energy increase in protein folding and accelerates the searching for protein native structure

A dihedral-energy-based selective enhanced sampling method (D-SITSMD) is presented with improved capabilities for searching a protein's natively folded structure and for providing the underlying folding pathway.

Hybrid Cascade-Type Molecular Dynamics with a Markov State Model for Efficient Free Energy Calculations

A protocol for calculating free energy landscapes (FELs) is proposed based on a combination of two cascade-type molecular dynamics (MD) methods, parallel cascade selection MD (PaCS-MD) and outlier flooding method (OFLOOD), with the help of a Markov state model (MSM). The former rapidly generates approximated transition paths directly connecting reactants with products, and the latter complementary resamples marginal conformational subspaces. Trajectories obtained by them give reliable microstates in MSM providing accurate FEL with low computational costs. As a demonstration, the present method was applied to a miniprotein (Chignolin and Trp-cage) in explicit water and successfully elucidated multiple folding paths on their free energy landscapes. Our method could be applicable to a wide variety of biological systems to estimate their free energy profiles.

Detailed potential of mean force studies on host-guest systems from the SAMPL6 challenge

Accurately predicting receptor-ligand binding free energies is one of the holy grails of computational chemistry with many applications in chemistry and biology. Many successes have been reported, but issues relating to sampling and force field accuracy remain significant issues affecting our ability to reliably calculate binding free energies. In order to explore these issues in more detail we have examined a series of small host-guest complexes from the SAMPL6 blind challenge, namely octa-acids (OAs)-guest complexes and Curcurbit[8]uril (CB8)-guest complexes. Specifically, potential of mean force studies using umbrella sampling combined with the weighted histogram method were carried out on both systems with both known and unknown binding affinities. We find that using standard force fields and straightforward simulation protocols we are able to obtain satisfactory results, but that simply scaling our results allows us to significantly improve our predictive ability for the unknown test sets: the overall RMSD of the binding free energy versus experiment is reduced from 5.59 to 2.36 kcal/mol; for the CB8 test system, the RMSD goes from 8.04 to 3.51 kcal/mol, while for the OAs test system, the RSMD goes from 2.89 to 0.95 kcal/mol. The scaling approach was inspired by studies on structurally related known benchmark sets: by simply scaling, the RMSD was reduced from 6.23 to 1.19 kcal/mol and from 2.96 to 0.62 kcal/mol for the CB8 benchmark system and the OA benchmark system, respectively. We find this scaling procedure to correct absolute binding affinities to be highly effective especially when working across a "congeneric" series with similar charge states. It is less successful when applied to mixed ligands with varied charges and chemical characteristics, but improvement is still realized in the present case. This approach suggests that there are large systematic errors in absolute binding free energy calculations that can be straightforwardly accounted for using a scaling procedure. Random errors are still an issue, but near chemical accuracy can be obtained using the present strategy in select cases.

On-the-Fly Specifications of Reaction Coordinates in Parallel Cascade Selection Molecular Dynamics Accelerate Conformational Transitions of Proteins

Parallel Cascade Selection Molecular Dynamics (PaCS-MD) is an efficient conformational sampling method for generating a set of reactive trajectories that connect a given reactant and a product. In PaCS-MD, initial structures relevant to conformational transitions are reasonably selected by referring to a set of reaction coordinates (RCs), and short-time molecular dynamics (MD) simulations are independently launched from them. To efficiently perform PaCS-MD, specifications of RCs are essential, but specifying reasonable RCs is generally nontrivial. In the present study, we propose on-the-fly specifications of RCs as an extended PaCS-MD. In the present method, n types of RCs are provided as candidates a priori as follows: RC = (X₁, X₂, ..., X _n), and one of the RCs is specified in a cycle-dependent manner, i.e. the reasonable RC is searched at every cycle by evaluating gradients of the RCs, i.e. RC with the steepest gradient for cycle is regarded as the reasonable RC, and conformational resampling proceeds along it, promoting conformational transition of a given protein. For a demonstration, the extended PaCS-MD was applied to reproduce the open-closed conformational transition of T4 lysozyme (T4L). As candidates of possible RCs, (1) root-mean square distance, (2) principal coordinates, (3) accessible surface area, (4) radius of gyration, and (5) end-to-end distance were adopted in the cycle-dependent specifications of RCs. Through the demonstration, the extended PaCS-MD successfully reproduced the conformational transition from the open to closed states of T4L. As a more complicated practice, a dimerization process of diubiquitin was efficiently reproduced with the extended PaCS-MD, showing the high conformational sampling efficiency of the present algorithm. In contrast, the conventional PaCS-MD with a fixed RC sometimes failed to generate a set of reactive trajectories when an unreasonable RC was specified, i.e. the conformational sampling efficiency of PaCS-MD might more or less depend on the specified RCs. Judging from the present demonstrations, on-the-fly specifications of RCs might be effective in reproducing/predicting essential transitions of a given protein.

Dimer Interface of the Human Serotonin Transporter and Effect of the Membrane Composition

The oligomeric state of membrane proteins has recently emerged in many cases as having an effect on their function. However, the intrinsic dynamics of their spatial organization in cells and model systems makes it challenging to characterize. Here we use molecular dynamics (MD) simulations at multiple resolutions to determine the dimer conformation of the human serotonin transporter (hSERT). From self-assembly simulations we predict dimer candidates and subsequently quantify their relative strength. We use umbrella sampling (US) replica exchange MD simulations for which we present extensive analysis of their efficiency and improved sampling compared to regular US MD simulations. The data shows that the most stable hSERT dimer interface is symmetrical and involves transmembrane helix 12 (TM12), similar to the crystal structure of the bacterial homologue LeuT, but with a slightly different orientation. We also describe the supramolecular organization of hSERT from a 250 μs self-assembly simulation. Finally, the effects of the presence of phosphatidylinositol bisphosphate or cholesterol in the membrane model has been quantified for the TM12-TM12 predicted interface. Collectively, the presented data bring new insight to the area of protein and lipid interplay in biological membranes.

Energetics Underlying Twist Polymorphisms in Amyloid Fibrils

Amyloid fibrils are highly ordered protein aggregates associated with more than 40 human diseases. The exact conditions under which the fibrils are grown determine many types of reported fibril polymorphism, including different twist patterns. Twist-based polymorphs display unique mechanical properties in vitro, and the relevance of twist polymorphism in amyloid diseases has been suggested. We present transmission electron microscopy images of Aβ42-derived (amyloid β) fibrils, which are associated with Alzheimer's disease, demonstrating the presence of twist variability even within a single long fibril. To better understand the molecular underpinnings of twist polymorphism, we present a structural and thermodynamics analysis of molecular dynamics simulations of the twisting of β-sheet protofilaments of a well-characterized cross-β model: the GNNQQNY peptide from the yeast prion Sup35. The results show that a protofilament model of GNNQQNY is able to adopt twist angles from -11° on the left-hand side to +8° on the right-hand side in response to various external conditions, keeping an unchanged peptide structure. The potential of mean force (PMF) of this cross-β structure upon twisting revealed that only ∼2kBT per peptide are needed to stabilize a straight conformation with respect to the left-handed free-energy minimum. The PMF also shows that the canonical structural core of β-sheets, i.e., the hydrogen-bonded backbone β-strands, favors the straight conformation. However, the concerted effects of the side chains contribute to twisting, which provides a rationale to correlate polypeptide sequence, environmental growth conditions and number of protofilaments in a fibril with twist polymorphisms.

Modelling of immiscible liquid-liquid systems by Smoothed Particle Hydrodynamics

Immiscible fluid systems are ubiquitous in industry, medicine and nature. Understanding the phase morphologies and intraphase fluid motion is often desirable in many of these situations; for example, this will aid improved design of microfluidic platforms for the production of medicinal formulations. In this paper, we detail a Smoothed Particle Hydrodynamics (SPH) approach that facilitates this understanding. The approach includes surface tension and enforces incompressibility. The approach also allows the consideration of an arbitrary number of immiscible phases of differing viscosities and densities. The nature of the phase morphologies can be arbitrary and change in time, including break-up (which is illustrated) and coalescence. The use of different fluid constitutive models, including non-Newtonian models, is also possible. The validity of the model is demonstrated by applying it to a range of model problems with known solutions, including the Young-Laplace problem, confined droplet deformation under a linear shear field, and a droplet falling under gravity through another quiescent liquid. Results are also presented to illustrate how the SPH model can be used to elucidate the behaviour of immiscible liquid systems.

A Blind Test of Computational Technique for Predicting the Likelihood of Peptide Sequences to Cyclize

An in silico computational technique for predicting peptide sequences that can be cyclized by cyanobactin macrocyclases, e.g., PatG_mac, is reported. We demonstrate that the propensity for PatG_mac-mediated cyclization correlates strongly with the free energy of the so-called pre-cyclization conformation (PCC), which is a fold where the cyclizing sequence C and N termini are in close proximity. This conclusion is driven by comparison of the predictions of boxed molecular dynamics (BXD) with experimental data, which have achieved an accuracy of 84%. A true blind test rather than training of the model is reported here as the in silico tool was developed before any experimental data was given, and no parameters of computations were adjusted to fit the data. The success of the blind test provides fundamental understanding of the molecular mechanism of cyclization by cyanobactin macrocyclases, suggesting that formation of PCC is the rate-determining step. PCC formation might also play a part in other processes of cyclic peptides production and on the practical side the suggested tool might become useful for finding cyclizable peptide sequences in general.

An automated method to find reaction mechanisms and solve the kinetics in organometallic catalysis

A novel computational method is proposed in this work for use in discovering reaction mechanisms and solving the kinetics of transition metal-catalyzed reactions. The method does not rely on either chemical intuition or assumed a priori mechanisms, and it works in a fully automated fashion. Its core is a procedure, recently developed by one of the authors, that combines accelerated direct dynamics with an efficient geometry-based post-processing algorithm to find transition states (Martinez-Nunez, E., J. Comput. Chem.2015, 36, 222-234). In the present work, several auxiliary tools have been added to deal with the specific features of transition metal catalytic reactions. As a test case, we chose the cobalt-catalyzed hydroformylation of ethylene because of its well-established mechanism, and the fact that it has already been used in previous automated computational studies. Besides the generally accepted mechanism of Heck and Breslow, several side reactions, such as hydrogenation of the alkene, emerged from our calculations. Additionally, the calculated rate law for the hydroformylation reaction agrees reasonably well with those obtained in previous experimental and theoretical studies.