Best Practices for Quantification of Uncertainty and Sampling Quality in Molecular Simulations [Article v1.0]

Pathogenic mutation impairs functional dynamics of Hsp60 in mono- and oligomeric states

Mitochondrial chaperonin Heat Shock Protein 60 kDa (Hsp60) oversees the correct folding of client proteins in cooperation with Hsp10. Hsp60 monomers M first form 7-meric Single rings (S), which then pair into 14-meric Double rings (D) that accommodate clients in their lumen. Recruitment of 7 Hsp10 molecules per pole yields a sealed 28-meric Football-shaped complex (F). ATP hydrolysis in each Hsp60 unit drives client folding and F disassembly. The V72I mutation in hereditary spastic paraplegia form SPG13 impairs Hsp60 function despite being distant from the active site. We here investigate this impairment with atomistic molecular dynamics (MD) simulations of M, S, D, and F for both WT and mutant Hsp60, considering catalytic aspartates in D and F in different protonation states (even simulating one such state of D post-hydrolysis). Our findings show that-as observed experimentally-V72I rigidifies Hsp60 assemblies, significantly impacting internal dynamics. In monomers, V72I introduces a new allosteric route that bypasses the ATP binding site and affects mechanisms driving reactivity. These insights highlight a multiscale complexity of Hsp60 that could inspire the design of experiments to better understand both its WT and V72I variants.

Structure-Based Experimental Datasets for Benchmarking Protein Simulation Force Fields [Article v0.1]

This review article provides an overview of structurally oriented experimental datasets that can be used to benchmark protein force fields, focusing on data generated by nuclear magnetic resonance (NMR) spectroscopy and room temperature (RT) protein crystallography. We discuss what the observables are, what they tell us about structure and dynamics, what makes them useful for assessing force field accuracy, and how they can be connected to molecular dynamics simulations carried out using the force field one wishes to benchmark. We also touch on statistical issues that arise when comparing simulations with experiment. We hope this article will be particularly useful to computational researchers and trainees who develop, benchmark, or use protein force fields for molecular simulations.

Disentangling Folding from Energetic Traps in Simulations of Disordered Proteins

Protein conformational heterogeneity plays an essential role in a myriad of different biological processes. Extensive conformational heterogeneity is especially characteristic of intrinsically disordered proteins and protein regions (collectively IDRs), which lack a well-defined three-dimensional structure and instead rapidly exchange between a diverse ensemble of configurations. An emerging paradigm recognizes that the conformational biases encoded in IDR ensembles can play a central role in their biological function, necessitating understanding these sequence-ensemble relations. All-atom simulations have provided critical insight into our modern understanding of the solution behavior of IDRs. However, effectively exploring the accessible conformational space associated with large, heterogeneous ensembles is challenging. In particular, identifying poorly sampled or energetically trapped regions of disordered proteins in simulations often relies on qualitative assessment based on visual inspection of simulations and/or analysis data. These approaches, while convenient, run the risk of masking poorly sampled simulations. In this work, we present an algorithm for quantifying per-residue local conformational heterogeneity in protein simulations. Our work builds on prior work and compares the similarity between backbone dihedral angle distributions generated from molecular simulations in a limiting polymer model and across independent all-atom simulations. In this regime, the polymer model serves as a statistical reference model for extensive conformational heterogeneity in a real chain. Quantitative comparisons of probability vectors generated from these simulations reveal the extent of conformational sampling in a simulation, enabling us to distinguish between situations in which protein regions are well-sampled, poorly sampled, or folded. To demonstrate the effectiveness of this approach, we apply our algorithm to several toy, synthetic, and biological systems. Accurately assessing local conformational sampling in simulations of IDRs will help better quantify new enhanced sampling methods, ensure force field comparisons are equivalent, and provide confidence that conclusions drawn from simulations are robust.

Prospective Evaluation of Structure-Based Simulations Reveal Their Ability to Predict the Impact of Kinase Mutations on Inhibitor Binding

Small molecule kinase inhibitors are critical in the modern treatment of cancers, evidenced by the existence of over 80 FDA-approved small-molecule kinase inhibitors. Unfortunately, intrinsic or acquired resistance, often causing therapy discontinuation, is frequently caused by mutations in the kinase therapeutic target. The advent of clinical tumor sequencing has opened additional opportunities for precision oncology to improve patient outcomes by pairing optimal therapies with tumor mutation profiles. However, modern precision oncology efforts are hindered by lack of sufficient biochemical or clinical evidence to classify each mutation as resistant or sensitive to existing inhibitors. Structure-based methods show promising accuracy in retrospective benchmarks at predicting whether a kinase mutation will perturb inhibitor binding, but comparisons are made by pooling disparate experimental measurements across different conditions. We present the first prospective benchmark of structure-based approaches on a blinded dataset of in-cell kinase inhibitor affinities to Abl kinase mutants using a NanoBRET reporter assay. We compare NanoBRET results to structure-based methods and their ability to estimate the impact of mutations on inhibitor binding (measured as ΔΔG). Comparing physics-based simulations, Rosetta, and previous machine learning models, we find that structure-based methods accurately classify kinase mutations as inhibitor-resistant or inhibitor-sensitizing, and each approach has a similar degree of accuracy. We show that physics-based simulations are best suited to estimate ΔΔG of mutations that are distal to the kinase active site. To probe modes of failure, we retrospectively investigate two clinically significant mutations poorly predicted by our methods, T315A and L298F, and find that starting configurations and protonation states significantly alter the accuracy of our predictions. Our experimental and computational measurements provide a benchmark for estimating the impact of mutations on inhibitor binding affinity for future methods and structure-based models. These structure-based methods have potential utility in identifying optimal therapies for tumor-specific mutations, predicting resistance mutations in the absence of clinical data, and identifying potential sensitizing mutations to established inhibitors.

Protein misfolding involving entanglements providesa structural explanation for the origin of stretched-exponential refolding kinetics

Stretched-exponential protein refolding kinetics, first observed decades ago, were attributed to a nonnative ensemble of structures with parallel, non-interconverting folding pathways. However, the structural origin of the large energy barriers preventing interconversion between these folding pathways is unknown. Here, we combine simulations with limited proteolysis (LiP) and cross-linking (XL) mass spectrometry (MS) to study the protein phosphoglycerate kinase (PGK). Simulations recapitulate its stretched-exponential folding kinetics and reveal that misfolded states involving changes of entanglement underlie this behavior: either formation of a nonnative, noncovalent lasso entanglement or failure to form a native entanglement. These misfolded states act as kinetic traps, requiring extensive unfolding to escape, which results in a distribution of free energy barriers and pathway partitioning. Using LiP-MS and XL-MS, we propose heterogeneous structural ensembles consistent with these data that represent the potential long-lived misfolded states PGK populates. This structural and energetic heterogeneity creates a hierarchy of refolding timescales, explaining stretched-exponential kinetics.

Prospective evaluation of structure-based simulations reveal their ability to predict the impact of kinase mutations on inhibitor binding

Small molecule kinase inhibitors are critical in the modern treatment of cancers, evidenced by the existence of over 80 FDA-approved small-molecule kinase inhibitors. Unfortunately, intrinsic or acquired resistance, often causing therapy discontinuation, is frequently caused by mutations in the kinase therapeutic target. The advent of clinical tumor sequencing has opened additional opportunities for precision oncology to improve patient outcomes by pairing optimal therapies with tumor mutation profiles. However, modern precision oncology efforts are hindered by lack of sufficient biochemical or clinical evidence to classify each mutation as resistant or sensitive to existing inhibitors. Structure-based methods show promising accuracy in retrospective benchmarks at predicting whether a kinase mutation will perturb inhibitor binding, but comparisons are made by pooling disparate experimental measurements across different conditions. We present the first prospective benchmark of structure-based approaches on a blinded dataset of in-cell kinase inhibitor affinities to Abl kinase mutants using a NanoBRET reporter assay. We compare NanoBRET results to structure-based methods and their ability to estimate the impact of mutations on inhibitor binding (measured as ΔΔG). Comparing physics-based simulations, Rosetta, and previous machine learning models, we find that structure-based methods accurately classify kinase mutations as inhibitor-resistant or inhibitor-sensitizing, and each approach has a similar degree of accuracy. We show that physics-based simulations are best suited to estimate ΔΔG of mutations that are distal to the kinase active site. To probe modes of failure, we retrospectively investigate two clinically significant mutations poorly predicted by our methods, T315A and L298F, and find that starting configurations and protonation states significantly alter the accuracy of our predictions. Our experimental and computational measurements provide a benchmark for estimating the impact of mutations on inhibitor binding affinity for future methods and structure-based models. These structure-based methods have potential utility in identifying optimal therapies for tumor-specific mutations, predicting resistance mutations in the absence of clinical data, and identifying potential sensitizing mutations to established inhibitors.

Effects of Lipid Headgroups on the Mechanical Properties and In Vitro Cellular Internalization of Liposomes

We performed all-atom and coarse-grained simulations of lipid bilayer mixtures of the unsaturated lipid DOPC, with saturated lipids having the same 18-carbon acyl tails and different headgroups, to understand their mechanical properties. The secondary lipids were DSPG, DSPA, DSPS, DSPC, and DSPE. The DOPC:DSPG system with 65:35 molar ratio was the softest, with area compressibility modulus KA ∼ 22% smaller than the pure DOPC value. Raising the mole % of DOPC leads to increases in KA, yet at any given composition the KA trend is DSPG < DSPA < DSPS < DSPC < DSPE. Lipid-lipid interactions are weaker in DOPC:DSPG mixtures and stronger in DSPE systems. The head and phosphate groups of the secondary lipids DSPG, DSPA, and DSPS interact strongly with salt ions. Adding secondary lipids leads to DOPC having more ordered acyl tails relative to pure DOPC systems. No evidence of phase separation or inhomogeneities was observed in our simulations. We synthesized three liposomal formulations, L-DOPC (pure DOPC) and L-DOPC/DSPG and L-DOPC/DSPA, both with 15 mol % of secondary lipid. L-DOPC/DSPA had approximately 3- and 2-times higher in vitro internalization by normal epithelial (EpH4-Ev) and metastatic breast cancer (4T1) cells, compared with L-DOPC. The uptake of L-DOPC/DSPG by EpH4-Ev cells was almost 2-fold compared to L-DOPC, but both liposomes had similar uptakes by cancer cells. As L-DOPC/DSPG and L-DOPC/DSPA have similar KA values, we presumed that the mechanical properties, possibly in combination with the higher negative surface charges in L-DOPC/DSPA and differences in effective liposome diameters and diffusivities, contributed to these observations.

Toward Grid-Based Models for Molecular Association

This paper presents a grid-based approach to model molecular association processes as an alternative to sampling-based Markov models. Our method discretizes the six-dimensional space of relative translation and orientation into grid cells. By discretizing the Fokker-Planck operator governing the system dynamics via the square-root approximation, we derive analytical expressions for the transition rate constants between grid cells. These expressions depend on geometric properties of the grid, such as the cell surface area and volume, which we provide. In addition, one needs only the molecular energy at the grid cell center, circumventing the need for extensive MD simulations and reducing the number of energy evaluations to the number of grid cells. The resulting rate matrix is closely related to the Markov state model transition matrix, offering insights into metastable states and association kinetics. We validate the accuracy of the model in identifying metastable states and binding mechanisms, though improvements are necessary to address limitations like ignoring bulk transitions and anisotropic rotational diffusion. The flexibility of this grid-based method makes it applicable to a variety of molecular systems and energy functions, including those derived from quantum mechanical calculations. The software package MolGri, which implements this approach, offers a systematic and computationally efficient tool for studying molecular association processes.

Robust Automated Truncation Point Selection for Molecular Simulations

Quantities calculated from molecular simulations are often subject to an initial bias due to unrepresentative starting configurations. Initial data are usually discarded to reduce bias. Chodera's method for automated truncation point selection [J. Chem. Theory Comput. 2016, 12, 4, 1799-1805] is popular but has not been thoroughly assessed. We reformulate White's marginal standard error rule to provide a spectrum of truncation point selection heuristics that differ in their treatment of autocorrelation. These include a method effectively equivalent to Chodera's. We test these methods on ensembles of synthetic time series modeled on free energy change estimates from long absolute binding free energy calculations. Methods that more thoroughly account for autocorrelation often show late and variable truncation times, while methods that less thoroughly account for autocorrelation often show early truncation, relative to the optimal truncation point. This increases variance and bias, respectively. We recommend a method that achieves robust performance across our test sets by balancing these two extremes. None of the methods reliably detected insufficient sampling. All heuristics tested are implemented in the open-source Python package RED (github.com/fjclark/red).

Improving the Computational Efficiency of the Adaptive Biasing Force Sampling by Leveraging the Telescopic-Solvation Scheme

The number of solvent molecules present in the system during molecular dynamics is the balancing act between the need to remove the boundary effects present in the system and the computational cost. Application of the telescopic-solvation box scheme during the estimation of the potential of mean force (PMF) can be advantageous in situations where the contribution of solvent far from the site of interest toward the whole PMF is negligible, as previously demonstrated in the case of adaptive steered molecular dynamics and umbrella sampling. This work explores the application of the telescopic-solvation box scheme during enhanced sampling by the stratified adaptive biasing force (ABF) family of methods, including ABF, extended ABF, well-tempered-metadynamics extended ABF, and multiwalker extended ABF. During this scheme, the number of water molecules differed in each stratified window, whose number depended on the value of the collective variable being sampled in that window. Two systems were used to verify the viability of the telescopic scheme: unfolding (Ala)10 peptide in water and insertion of α-tocopherol in a bilayer membrane. In the first system, the 1D and 2D PMFs obtained by the telescopic-solvation scheme matched well with the benchmark PMFs estimated with a standard solvation box. The minimal energy path connecting the α-helical and extended conformational states revealed that the unfolding process of (Ala)10 in water involved multiple closely spaced metastable states. As for the second system, the PMF, equilibrium location of α-tocopherol, and the free energy associated with the desorption and flipping of α-tocopherol obtained within the scope of the telescopic-solvation box scheme agreed with their standard solvation box values. Enhanced sampling with ABF and its variants in conjunction with the telescopic-solvation scheme results in a similar quality of the estimated PMF compared to sampling with a standard solvation box, albeit with reduced computational cost.

Machine learning-driven investigation of the structure and dynamics of the BMIM-BF4 room temperature ionic liquid

Room-temperature ionic liquids are an exciting group of materials with the potential to revolutionize energy storage. Due to their chemical structure and means of interaction, they are challenging to study computationally. Classical descriptions of their inter- and intra-molecular interactions require time intensive parametrization of force-fields which is prone to assumptions. While ab initio molecular dynamics approaches can capture all necessary interactions, they are too slow to achieve the time and length scales required. In this work, we take a step towards addressing these challenges by applying state-of-the-art machine-learned potentials to the simulation of 1-butyl-3-methylimidazolium tetrafluoroborate. We demonstrate a learning-on-the-fly procedure to train machine-learned potentials from single-point density functional theory calculations before performing production molecular dynamics simulations. Obtained structural and dynamical properties are in good agreement with computational and experimental references. Furthermore, our results show that hybrid machine-learned potentials can contribute to an improved prediction accuracy by mitigating the inherent shortsightedness of the models. Given that room-temperature ionic liquids necessitate long simulations to address their slow dynamics, achieving an optimal balance between accuracy and computational cost becomes imperative. To facilitate further investigation of these materials, we have made our IPSuite-based training and simulation workflow publicly accessible, enabling easy replication or adaptation to similar systems.

Structure and Dynamics of the CCCH-Type Tandem Zinc Finger Domain of POS-1 and Implications for RNA Binding Specificity

CCCH-type tandem zinc finger (TZF) motifs are found in many RNA-binding proteins involved in regulating mRNA stability, translation, and splicing. In Caenorhabditis elegans, several RNA-binding proteins that regulate embryonic development and cell fate determination contain CCCH TZF domains, including POS-1. Previous biochemical studies have shown that despite high levels of sequence conservation, POS-1 recognizes a broader set of RNA sequences compared to the human homologue tristetraprolin. However, the molecular basis of these differences remains unknown. In this study, we refined the consensus RNA sequence and determined the differing binding specificities of the two zinc fingers of POS-1. We also determined the solution structure and characterized the internal dynamics of the TZF domain of POS-1. From the structure, we identified unique features that define the RNA binding specificity of POS-1. We also observed that the TZF domain of POS-1 is in equilibrium between interconverting conformations. Transitions between these conformations require internal motions involving many residues with correlated dynamics in each ZF. We propose that the correlated dynamics are necessary to allow allosteric communication between the nucleotide-binding pockets observed in the N-terminal ZF. Our study shows that both the structure and conformational plasticity of POS-1 are important in ensuring recognition of its RNA binding targets.

Monte Carlo molecular simulations with FEASST version 0.25.1

FEASST is an open-source Monte Carlo software package for particle-based simulations. This software, which was released in 2017, has been used to study phase equilibrium, self-assembly, aggregation or gelation in biological materials, colloids, polymers, ionic liquids, and adsorption in porous networks. We highlight some of the unique features available in FEASST, such as flat-histogram grand canonical ensemble, Gibbs ensemble, and Mayer-sampling simulations with support for anisotropic models and parallelization with flat-histogram and prefetching. We also discuss how the challenges of supporting a variety of Monte Carlo algorithms were overcome by an object-oriented design. This also allows others to extend classes, which improves software interoperability, as inspired by LAMMPS classes and user packages. This article describes version 0.25.1 with benchmarks, compilation instructions, and introductory tutorials for running, restarting, and testing simulations, user guidelines, software design strategies, alternative interfaces, and the test-driven development strategy.

Estimating Free-Energy Surfaces and Their Convergence from Multiple, Independent Static and History-Dependent Biased Molecular-Dynamics Simulations with Mean Force Integration

Addressing the sampling problem is central to obtaining quantitative insight from molecular dynamics simulations. Adaptive biased sampling methods, such as metadynamics, tackle this issue by perturbing the Hamiltonian of a system with a history-dependent bias potential, enhancing the exploration of the ensemble of configurations and estimating the corresponding free energy surface (FES). Nevertheless, efficiently assessing and systematically improving their convergence remains an open problem. Here, building on mean force integration (MFI), we develop and test a metric for estimating the convergence of FESs obtained by combining asynchronous, independent simulations subject to diverse biasing protocols, including static biases, different variants of metadynamics, and various combinations of static and history-dependent biases. The developed metric and the ability to combine independent simulations granted by MFI enable us to devise strategies to systematically improve the quality of FES estimates. We demonstrate our approach by computing FES and assessing the convergence of a range of systems of increasing complexity, including one- and two-dimensional analytical FESs, alanine dipeptide, a Lennard-Jones supersaturated vapor undergoing liquid droplet nucleation, and the model of a colloidal system crystallizing via a two-step mechanism. The methods presented here can be generally applied to biased simulations and are implemented in pyMFI, a publicly accessible, open-source Python library.

Synthesis, molecular dynamics simulation, and evaluation of biological activity of novel flurbiprofen and ibuprofen-like compounds

The frequent use of anti-inflammatory drugs and the side effects of existing drugs keep the need for new compounds constant. For this purpose, flurbiprofen and ibuprofen-like compounds, which are frequently used anti-inflammatory compounds in this study, were synthesized and their structures were elucidated. Like ibuprofen and flurbiprofen, the compounds contain a residue of phenylacetic acid. On the other hand, it contains a secondary amine residue. Thus, it is planned to reduce the acidity, which is the biggest side effect of NSAI drugs, even a little bit. The estimated ADME parameters of the compounds were evaluated. Apart from internal use, local use of anti-inflammatory compounds is also very important. For this reason, the skin permeability values of the compounds were also calculated. And it has been found to be compatible with reference drugs. The COX enzyme inhibitory effects of the obtained compounds were tested by in vitro experiments. Compound 2a showed significant activity against COX-1 enzyme with an IC50 = 0.123 + 0.005 μM. The interaction of the compound with the enzyme active site was clarified by molecular dynamics studies.

Interaction of MRI Contrast Agent [Gd(DOTA)]- with Lipid Membranes: A Molecular Dynamics Study

Contrast agents are important imaging probes in clinical MRI, allowing the identification of anatomic changes that otherwise would not be possible. Intensive research on the development of new contrast agents is being made to image specific pathological markers or sense local biochemical changes. The most widely used MRI contrast agents are based on gadolinium(III) complexes. Due to their very high charge density, they have low permeability through tight biological barriers such as the blood-brain barrier, hampering their application in the diagnosis of neurological disorders. In this study, we explore the interaction between the widely used contrast agent [Gd(DOTA)]- (Dotarem) and POPC lipid bilayers by means of molecular dynamics simulations. This metal complex is a standard reference where several chemical modifications have been introduced to improve key properties such as bioavailability and targeting. The simulations unveil detailed insights into the agent's interaction with the lipid bilayer, offering perspectives beyond experimental methods. Various properties, including the impact on global and local bilayer properties, were analyzed. As expected, the results indicate a low partition coefficient (KP) and high permeation barrier for this reference compound. Nevertheless, favorable interactions are established with the membrane leading to moderately long residence times. While coordination of one inner-sphere water molecule is maintained for the membrane-associated chelate, the physical-chemical attributes of [Gd(DOTA)]- as a MRI contrast agent are affected. Namely, increases in the rotational correlation times and in the residence time of the inner-sphere water are observed, with the former expected to significantly increase the water proton relaxivity. This work establishes a reference framework for the use of simulations to guide the rational design of new contrast agents with improved relaxivity and bioavailability and for the development of liposome-based formulations for use as imaging probes or theranostic agents.

Bayesian Mechanistic Inference, Statistical Mechanics, and a New Era for Monte Carlo

On the one hand, much of computational chemistry is concerned with "bottom-up" calculations which elucidate observable behavior starting from exact or approximated physical laws, a paradigm exemplified by typical quantum mechanical calculations and molecular dynamics simulations. On the other hand, "top down" computations aiming to formulate mathematical models consistent with observed data, e.g., parametrizing force fields, binding or kinetic models, have been of interest for decades but recently have grown in sophistication with the use of Bayesian inference (BI). Standard BI provides an estimation of parameter values, uncertainties, and correlations among parameters. Used for "model selection," BI can also distinguish between model structures such as the presence or absence of individual states and transitions. Fortunately for physical scientists, BI can be formulated within a statistical mechanics framework, and indeed, BI has led to a resurgence of interest in Monte Carlo (MC) algorithms, many of which have been directly adapted from or inspired by physical strategies. Certain MC algorithms─notably procedures using an "infinite temperature" reference state─can be successful in a 5-20 parameter BI context which would be unworkable in molecular spaces of 103 coordinates and more. This Review provides a pedagogical introduction to BI and reviews key aspects of BI through a physical lens, setting the computations in terms of energy landscapes and free energy calculations and describing promising sampling algorithms. Statistical mechanics and basic probability theory also provide a reference for understanding intrinsic limitations of Bayesian inference with regard to model selection and the choice of priors.

An experimentally representative in-silico protocol for dynamical studies of lyophilised and weakly hydrated amorphous proteins

Characterization of biopolymers in both dry and weakly hydrated amorphous states has implications for the pharmaceutical industry since it provides understanding of the effect of lyophilisation on stability and biological activity. Atomistic Molecular Dynamics (MD) simulations probe structural and dynamical features related to system functionality. However, while simulations in homogenous aqueous environments are routine, dehydrated model assemblies are a challenge with systems investigated in-silico needing careful consideration; simulated systems potentially differing markedly despite seemingly negligible changes in procedure. Here we propose an in-silico protocol to model proteins in lyophilised and weakly hydrated amorphous states that is both more experimentally representative and routinely applicable. Since the outputs from MD align directly with those accessed by neutron scattering, the efficacy of the simulation protocol proposed is shown by validating against experimental neutron data for apoferritin and insulin. This work also highlights that without cooperative experimental and simulative data, development of simulative procedures using MD alone would prove most challenging.

Coil-Helix Block Copolymers Can Exhibit Divergent Thermodynamics in the Disordered Phase

Chiral building blocks have the ability to self-assemble and transfer chirality to larger hierarchical length scales, which can be leveraged for the development of novel nanomaterials. Chiral block copolymers, where one block is made completely chiral, are prime candidates for studying this phenomenon, but fundamental questions regarding the self-assembly are still unanswered. For one, experimental studies using different chemistries have shown unexplained diverging shifts in the order-disorder transition temperature. In this study, particle-based molecular simulations of chiral block copolymers in the disordered melt were performed to uncover the thermodynamic behavior of these systems. A wide range of helical models were selected, and several free energy calculations were performed. Specifically, we aimed to understand (1) the thermodynamic impact of changing the conformation of one block in chemically identical block copolymers and (2) the effect of the conformation on the Flory-Huggins interaction parameter, χ, when chemical disparity was introduced. We found that the effective block repulsion exhibits diverging behavior, depending on the specific conformational details of the helical block. Commonly used conformational metrics for flexible or stiff block copolymers do not capture the effective block repulsion because helical blocks are semiflexible and aspherical. Instead, pitch can quantitatively capture the effective block repulsion. Quite remarkably, the shift in χ for chemically dissimilar block copolymers can switch sign with small changes in the pitch of the helix.

Investigating Biomolecules in Deep Eutectic Solvents with Molecular Dynamics Simulations: Current State, Challenges and Future Perspectives

Deep eutectic solvents (DESs) have recently gained increased attention for their potential in biotechnological applications. DESs are binary mixtures often consisting of a hydrogen bond acceptor and a hydrogen bond donor, which allows for tailoring their properties for particular applications. If produced from sustainable resources, they can provide a greener alternative to many traditional organic solvents for usage in various applications (e.g., as reaction environment, crystallization agent, or storage medium). To navigate this large design space, it is crucial to comprehend the behavior of biomolecules (e.g., enzymes, proteins, cofactors, and DNA) in DESs and the impact of their individual components. Molecular dynamics (MD) simulations offer a powerful tool for understanding thermodynamic and transport processes at the atomic level and offer insights into their fundamental phenomena, which may not be accessible through experiments. While the experimental investigation of DESs for various biotechnological applications is well progressed, a thorough investigation of biomolecules in DESs via MD simulations has only gained popularity in recent years. Within this work, we aim to provide an overview of the current state of modeling biomolecules with MD simulations in DESs and discuss future directions with a focus for optimizing the molecular simulations and increasing our fundamental knowledge.

Molecular Dynamics Simulations for Rationalizing Polymer Bioconjugation Strategies: Challenges, Recent Developments, and Future Opportunities

The covalent modification of proteins with polymers is a well-established method for improving the pharmacokinetic properties of therapeutically valuable biologics. The conjugated polymer chains of the resulting hybrid represent highly flexible macromolecular structures. As the dynamics of such systems remain rather elusive for established experimental techniques from the field of protein structure elucidation, molecular dynamics simulations have proven as a valuable tool for studying such conjugates at an atomistic level, thereby complementing experimental studies. With a focus on new developments, this review aims to provide researchers from the polymer bioconjugation field with a concise and up to date overview of such approaches. After introducing basic principles of molecular dynamics simulations, as well as methods for and potential pitfalls in modeling bioconjugates, the review illustrates how these computational techniques have contributed to the understanding of bioconjugates and bioconjugation strategies in the recent past and how they may lead to a more rational design of novel bioconjugates in the future.

Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime

We derive general bounds on the probability that the empirical first-passage time τ[over ¯]_{n}≡∑_{i=1}^{n}τ_{i}/n of a reversible ergodic Markov process inferred from a sample of n independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct nonasymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.

Peptide Power: Mechanistic Insights into the Effect of Mitochondria-Targeted Tetrapeptides on Membrane Electrostatics from Molecular Simulations

Mitochondrial dysfunction is implicated in nine of the ten leading causes of death in the US, yet there are no FDA-approved therapeutics to treat it. Synthetic mitochondria-targeted peptides (MTPs), including the lead compound SS-31, offer promise, as they have been shown to restore healthy mitochondrial function and treat a variety of common diseases. At the cellular level, research has shown that MTPs accumulate strongly at the inner mitochondrial membrane (IMM), slow energy sinks (e.g., proton leaks), and improve ATP production. Modulation of electrostatic fields around the IMM has been implicated as a key aspect in the mechanism of action (MoA) of these peptides; however, molecular and mechanistic details have remained elusive. In this study, we employed all-atom molecular dynamics simulations (MD) to investigate the interactions of four MTPs with lipid bilayers and calculate their effect on structural and electrostatic properties. In agreement with previous experimental findings, we observed the modulation of the membrane surface and dipole potentials by MTPs. The simulations reveal that the MTPs achieve a reduction in the dipole potential by acting to disorder both lipid head groups and water layers proximal to the bilayer surface. We also find that MTPs decrease the bilayer thickness and increase the membrane's capacitance. These changes suggest that MTPs may enhance how much potential energy can be stored across the IMM at a given transmembrane potential difference. The MTPs also displace cations away from the bilayer surface, modulating the surface potential and offering an alternative mechanism for how these MTPs reduce mitochondrial energy sinks like proton leaks and mitigate Ca2+ accumulation stress. In conclusion, this study highlights the therapeutic potential of MTPs and underlines how interactions of MTPs with lipid bilayers serve as a fundamental component of their MoA.

Physical limits to membrane curvature sensing by a single protein

Membrane curvature sensing is essential for a diverse range of biological processes. Recent experiments have revealed that a single nanometer-sized septin protein has different binding rates to membrane-coated glass beads of 1-µm and 3-µm diameters, even though the septin is orders of magnitude smaller than the beads. This sensing ability is especially surprising since curvature-sensing proteins must deal with persistent thermal fluctuations of the membrane, leading to discrepancies between the bead's curvature and the local membrane curvature sensed instantaneously by a protein. Using continuum models of fluctuating membranes, we investigate whether it is feasible for a protein acting as a perfect observer of the membrane to sense micron-scale curvature either by measuring local membrane curvature or by using bilayer lipid densities as a proxy. To do this, we develop algorithms to simulate lipid density and membrane shape fluctuations. We derive physical limits to the sensing efficacy of a protein in terms of protein size, membrane thickness, membrane bending modulus, membrane-substrate adhesion strength, and bead size. To explain the experimental protein-bead association rates, we develop two classes of predictive models: (i) for proteins that maximally associate to a preferred curvature and (ii) for proteins with enhanced association rates above a threshold curvature. We find that the experimentally observed sensing efficacy is close to the theoretical sensing limits imposed on a septin-sized protein. Protein-membrane association rates may depend on the curvature of the bead, but the strength of this dependence is limited by the fluctuations in membrane height and density.

Simple Adjustment of Intranucleotide Base-Phosphate Interaction in the OL3 AMBER Force Field Improves RNA Simulations

Molecular dynamics (MD) simulations represent an established tool to study RNA molecules. The outcome of MD studies depends, however, on the quality of the force field (ff). Here we suggest a correction for the widely used AMBER OL3 ff by adding a simple adjustment of the nonbonded parameters. The reparameterization of the Lennard-Jones potential for the -H8···O5'- and -H6···O5'- atom pairs addresses an intranucleotide steric clash occurring in the type 0 base-phosphate interaction (0BPh). The nonbonded fix (NBfix) modification of 0BPh interactions (NBfix0BPh modification) was tuned via a reweighting approach and subsequently tested using an extensive set of standard and enhanced sampling simulations of both unstructured and folded RNA motifs. The modification corrects minor but visible intranucleotide clash for the anti nucleobase conformation. We observed that structural ensembles of small RNA benchmark motifs simulated with the NBfix0BPh modification provide better agreement with experiments. No side effects of the modification were observed in standard simulations of larger structured RNA motifs. We suggest that the combination of OL3 RNA ff and NBfix0BPh modification is a viable option to improve RNA MD simulations.

Computation of Shear Viscosity by a Consistent Method in Equilibrium Molecular Dynamics Simulations: Applications to 1-Decene Oligomers

Accurate computation of shear viscosity is fundamental for describing fluid flow and designing and developing new processes. Poly-α-olefins (PAO's), particularly from 1-decene, have been applied to a variety of industrial processes. Recently, these molecules have been applied as carbon dioxide thickeners, enhancing carbon dioxide viscosity, which is important in carbon dioxide injection, either for enhanced oil recovery or sequestration in geological formations. For these applications, knowledge of the pure oligomer viscosity is crucial to design and operate the oligomer upstream pipelines before mixing them with carbon dioxide. Using Green-Kubo formalism with equilibrium molecular dynamics simulations, two methods are presented in the literature to generate the traceless, symmetric pressure tensor. In this work, we show that these two methods provide different values of shear viscosity, from the analysis of how the diagonal components of the traceless, symmetric pressure tensor are computed in each method. Then, we examine the consistency and correctness of each method: one is found to be consistent. The other is corrected by scaling the fluctuations of the diagonal components. Shear viscosities of supercritical carbon dioxide, vapor and liquid n-pentane, and liquid n-decane are computed to illustrate the analysis. We also apply the consistent method to compute the viscosity of 1-decene oligomers, including for the first time larger-than-dimer oligomers (trimer, tetramer, hexamer, and decamer).

Understanding the Mechanical Properties of Ultradeformable Liposomes Using Molecular Dynamics Simulations

Improving drug delivery efficiency to solid tumor sites is a central challenge in anticancer therapeutic research. Our previous experimental study (Guo et al., Nat. Commun. 2018, 9, 130) showed that soft, elastic liposomes had increased uptake and accumulation in cancer cells and tumors in vitro and in vivo respectively, relative to rigid particles. As a first step toward understanding how liposomes' molecular structure and composition modulates their elasticity, we performed all-atom and coarse-grained classical molecular dynamics (MD) simulations of lipid bilayers formed by mixing a long-tailed unsaturated phospholipid with a short-tailed saturated lipid with the same headgroup. The former types of phospholipids considered were 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1,2-dipalmitoleoyl-sn-glycero-3-phosphocholine (termed here DPMPC). The shorter saturated lipids examined were 1,2-diheptanoyl-sn-glycero-3-phosphocholine (DHPC), 1,2-didecanoyl-sn-glycero-3-phosphocholine (DDPC), 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC), and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). Several lipid concentrations and surface tensions were considered. Our results show that DOPC or DPMPC systems having 25-35 mol % of the shortest lipids DHPC or DDPC are the least rigid, having area compressibility moduli KA that are ∼10% smaller than the values observed in pure DOPC or DPMPC bilayers. These results agree with experimental measurements of the stretching modulus and lysis tension in liposomes with the same compositions. These mixed systems also have lower areas per lipid and form more uneven x-y interfaces with water, the tails of both primary and secondary lipids are more disordered, and the terminal methyl groups in the tails of the long lipid DOPC or DPMPC wriggle more in the vertical direction, compared to pure DOPC or DPMPC bilayers or their mixtures with the longer saturated lipid DLPC or DMPC. These observations confirm our hypothesis that adding increasing concentrations of the short unsaturated lipid DHPC or DDPC to DOPC or DPMPC bilayers alters lipid packing and thus makes the resulting liposomes more elastic and less rigid. No formation of lipid nanodomains was noted in our simulations, and no clear trends were observed in the lateral diffusivities of the lipids as the concentration, type of secondary lipid, and surface tension were varied.

Modulation of Structure and Dynamics of Cardiac Troponin by Phosphorylation and Mutations Revealed by Molecular Dynamics Simulations

Adrenaline acts on β1 receptors in the heart muscle to enhance contractility, increase the heart rate, and increase the rate of relaxation (lusitropy) via activation of the cyclic AMP-dependent protein kinase, PKA. Phosphorylation of serines 22 and 23 in the N-terminal peptide of cardiac troponin I is responsible for lusitropy. Mutations associated with cardiomyopathy suppress the phosphorylation-dependent change. Key parts of troponin responsible for this modulatory system are disordered and cannot be resolved by conventional structural approaches. We performed all-atom molecular dynamics simulations (5 × 1.5 μs runs) of the troponin core (419 amino acids) in the presence of Ca2+ in the bisphosphorylated and unphosphorylated states for both wild-type troponin and the troponin C (cTnC) G159D mutant. PKA phosphorylation affects troponin dynamics. There is significant rigidification of the structure involving rearrangement of the cTnI(1-33)-cTnC interaction and changes in the distribution of the cTnC helix A/B angle, troponin I (cTnI) switch peptide (149-164) docking, and the angle between the regulatory head and ITC arm domains. The familial dilated cardiomyopathy cTnC G159D mutation whose Ca2+ sensitivity is not modulated by cTnI phosphorylation exhibits a structure inherently more rigid than the wild type, with phosphorylation reversing the direction of all metrics relative to the wild type.

Biophysical Determinants for the Viscosity of Concentrated Monoclonal Antibody Solutions

Monoclonal antibodies (mAbs) are particularly relevant for therapeutics due to their high specificity and versatility, and mAb-based drugs are hence used to treat numerous diseases. The increased patient compliance of self-administration motivates the formulation of products for subcutaneous (SC) administration. The associated challenge is to formulate highly concentrated antibody solutions to achieve a significant therapeutic effect, while limiting their viscosity and preserving their physicochemical stability. Protein-protein interactions (PPIs) are in fact the root cause of several potential problems concerning the stability, manufacturability, and delivery of a drug product. The understanding of macroscopic viscosity requires an in-depth knowledge on protein diffusion, PPIs, and self-association/aggregation. Here, we study the self-diffusion of different mAbs of the IgG1 subtype in aqueous solution as a function of the concentration and temperature by quasi-elastic neutron scattering (QENS). QENS allows us to probe the short-time self-diffusion of the molecules and therefore to determine the hydrodynamic mAb cluster size and to gain information on the internal mAb dynamics. Small-angle neutron scattering (SANS) is jointly employed to probe structural details and to understand the nature and intensity of PPIs. Complementary information is provided by molecular dynamics (MD) simulations and viscometry, thus obtaining a comprehensive picture of mAb diffusion.

BICePs v2.0: Software for Ensemble Reweighting Using Bayesian Inference of Conformational Populations

Bayesian Inference of Conformational Populations (BICePs) version 2.0 (v2.0) is a free, open-source Python package that reweights theoretical predictions of conformational state populations using sparse and/or noisy experimental measurements. In this article, we describe the implementation and usage of the latest version of BICePs (v2.0), a powerful, user-friendly and extensible package which makes several improvements upon the previous version. The algorithm now supports many experimental NMR observables (NOE distances, chemical shifts, J-coupling constants, and hydrogen-deuterium exchange protection factors), and enables convenient data preparation and processing. BICePs v2.0 can perform automatic analysis of the sampled posterior, including visualization, and evaluation of statistical significance and sampling convergence. We provide specific coding examples for these topics, and present a detailed example illustrating how to use BICePs v2.0 to reweight a theoretical ensemble using experimental measurements.

Exploring the Transferability of Replica Exchange Structure Reservoirs to Accelerate Generation of Ensembles for Alternate Hamiltonians or Protein Mutations

Generating precise ensembles is commonly a prerequisite to understand the energetics of biological processes using Molecular Dynamics (MD) simulations. Previously, we have shown how unweighted reservoirs built from high temperature MD simulations can accelerate convergence of Boltzmann-weighted ensembles by at least 10× with the Reservoir Replica Exchange MD (RREMD) method. Therefore, in this work, we explore whether an unweighted structure reservoir generated with one Hamiltonian (solute force field plus solvent model) can be reused to quickly generate accurately weighted ensembles for Hamiltonians other than the one that was used to generate the reservoir. We also extended this methodology to rapidly estimate the effects of mutations on peptide stability by using a reservoir of diverse structures obtained from wild-type simulations. These results suggest that structures generated via fast methods such as coarse-grained models or structures predicted by Rosetta or deep learning approaches could be integrated into a reservoir to accelerate generation of ensembles using more accurate representations.

IDP Force Fields Applied to Model PPII-Rich 33-mer Gliadin Peptides

The 33-mer gliadin peptide and its deamidated metabolite, 33-mer DGP, are the immunodominant peptides responsible for the adaptive immune response in celiac disease (CD). CD is a complex autoimmune chronic disorder triggered by gluten ingestion that affects the small intestine and affects ∼1% of the global population. The 33-mers are polyproline II-rich (PPII) and intrinsically disordered peptides (IDPs), whose structures remain elusive. We sampled the conformational ensembles of both 33-mer peptides via molecular dynamics simulations employing two force fields (FFs) (Amber ff03ws and Amber ff99SB-disp) specifically validated for other IDPs. Our results show that both FFs allow the extensive exploration of the conformational landscape, which was not possible with the standard FF GROMOS53A6 reported before. Clustering analysis of the trajectories showed that the five largest clusters (78-88% of the total structures) present elongated, semielongated, and curved conformations in both FFs. Large average radius of gyration and solvent-exposed surfaces characterized these structures. While the structures sampled are similar, the Amber ff99SB-disp trajectories explored folded conformations with a higher probability. In addition, PPII secondary structure was preserved throughout the trajectories (58-73%) together with a non-negligible content of β structures (11-23%), in agreement with previous experimental results. This work represents the initial step in studying further the interaction of these peptides with other biologically relevant molecules, which could lead to finally disclose the molecular events that lead to CD.

Sampling rare event energy landscapes via birth-death augmented dynamics

A common problem that affects simulations of complex systems within the computational physics and chemistry communities is the so-called sampling problem or rare event problem where proper sampling of energy landscapes is impeded by the presences of high kinetic barriers that hinder transitions between metastable states on typical simulation time scales. Many enhanced sampling methods have been developed to address this sampling problem and more efficiently sample rare event systems. An interesting idea, coming from the field of statistics, was introduced in a recent work [Lu, Lu, and Nolen, Accelerating Langevin sampling with birth-death, arXiv:1905.09863] in the form of a novel sampling algorithm that augments overdamped Langevin dynamics with a birth-death process. In this work, we expand on this idea and show that this birth-death sampling scheme can efficiently sample prototypical rare event energy landscapes, and that the speed of equilibration is independent of the barrier height. We amend a crucial shortcoming of the original algorithm that leads to incorrect sampling of barrier regions by introducing an alternative approximation of the birth-death term. We establish important theoretical properties of the modified algorithm and prove mathematically that the relevant convergence results still hold. We investigate via numerical simulations the effect of various parameters, and we investigate ways to reduce the computational effort of the sampling scheme. We show that the birth-death mechanism can be used to accelerate sampling in the more general case of underdamped Langevin dynamics that is more commonly used in simulating physical systems. Our results show that this birth-death scheme is a promising method for sampling rare event energy landscapes.

A Suite of Tutorials for the WESTPA 2.0 Rare-Events Sampling Software [Article v2.0]

The weighted ensemble (WE) strategy has been demonstrated to be highly efficient in generating pathways and rate constants for rare events such as protein folding and protein binding using atomistic molecular dynamics simulations. Here we present two sets of tutorials instructing users in the best practices for preparing, carrying out, and analyzing WE simulations for various applications using the WESTPA software. The first set of more basic tutorials describes a range of simulation types, from a molecular association process in explicit solvent to more complex processes such as host-guest association, peptide conformational sampling, and protein folding. The second set ecompasses six advanced tutorials instructing users in the best practices of using key new features and plugins/extensions of the WESTPA 2.0 software package, which consists of major upgrades for larger systems and/or slower processes. The advanced tutorials demonstrate the use of the following key features: (i) a generalized resampler module for the creation of "binless" schemes, (ii) a minimal adaptive binning scheme for more efficient surmounting of free energy barriers, (iii) streamlined handling of large simulation datasets using an HDF5 framework, (iv) two different schemes for more efficient rate-constant estimation, (v) a Python API for simplified analysis of WE simulations, and (vi) plugins/extensions for Markovian Weighted Ensemble Milestoning and WE rule-based modeling for systems biology models. Applications of the advanced tutorials include atomistic and non-spatial models, and consist of complex processes such as protein folding and the membrane permeability of a drug-like molecule. Users are expected to already have significant experience with running conventional molecular dynamics or systems biology simulations.

Inherited IRAK-4 Deficiency in Acute Human Herpesvirus-6 Encephalitis

Human herpesvirus-6 (HHV-6) infection can rarely cause life-threatening conditions, such as encephalitis, in otherwise healthy children, with unclear pathogenesis. We studied a child who presented with acute HHV-6 encephalitis at the age of 10 months and who was homozygous for a novel missense mutation in IRAK4, encoding interleukin-1 receptor-associated kinase 4, identified by whole-exome sequencing. We tested the damaging impact of this mutation in silico by molecular dynamics simulations and in vitro by biochemical and functional experiments utilizing cell lines and patient's cells. We found that the mutation is severely hypomorphic, impairing both the expression and function of IRAK-4. Patient's leukocytes had barely detectable levels of IRAK-4 and diminished anti-viral immune responses to various stimuli inducing different Toll-like receptors and cytosolic nucleic acid sensors. Overall, these findings suggest that acute HHV-6 encephalitis can result from inborn errors of immunity to virus. This study represents the first report of isolated acute HHV-6 infection causing encephalitis in an inherited primary immunodeficiency, notably autosomal recessive (AR) partial IRAK-4 deficiency, and the first report of AR IRAK-4 deficiency presenting with a severe viral disease, notably HHV-6 encephalitis upon an acute infection, thereby expanding the clinical spectrum of IRAK-4 deficiency.

Computer Aided Development of Nucleic Acid Applications in Nanotechnologies

Utilization of nucleic acids (NAs) in nanotechnologies and nanotechnology-related applications is a growing field with broad application potential, ranging from biosensing up to targeted cell delivery. Computer simulations are useful techniques that can aid design and speed up development in this field. This review focuses on computer simulations of hybrid nanomaterials composed of NAs and other components. Current state-of-the-art molecular dynamics simulations, empirical force fields (FFs), and coarse-grained approaches for the description of deoxyribonucleic acid and ribonucleic acid are critically discussed. Challenges in combining biomacromolecular and nanomaterial FFs are emphasized. Recent applications of simulations for modeling NAs and their interactions with nano- and biomaterials are overviewed in the fields of sensing applications, targeted delivery, and NA templated materials. Future perspectives of development are also highlighted.

Conformational Heterogeneity of RNA Stem-Loop Hairpins Bound to FUS-RNA Recognition Motif with Disordered RGG Tail Revealed by Unbiased Molecular Dynamics Simulations

RNA-protein complexes use diverse binding strategies, ranging from structurally well-defined interfaces to completely disordered regions. Experimental characterization of flexible segments is challenging and can be aided by atomistic molecular dynamics (MD) simulations. Here, we used an extended set of microsecond-scale MD trajectories (400 μs in total) to study two FUS-RNA constructs previously characterized by nuclear magnetic resonance (NMR) spectroscopy. The FUS protein contains a well-structured RNA recognition motif domain followed by a presumably disordered RGG tail that binds RNA stem-loop hairpins. Our simulations not only provide several suggestions complementing the experiments but also reveal major methodological difficulties in studies of such complex RNA-protein interfaces. Despite efforts to stabilize the binding via system-specific force-field adjustments, we have observed progressive distortions of the RNA-protein interface inconsistent with experimental data. We propose that the dynamics is so rich that its converged description is not achievable even upon stabilizing the system. Still, after careful analysis of the trajectories, we have made several suggestions regarding the binding. We identify substates in the RNA loops, which can explain the NMR data. The RGG tail localized in the minor groove remains disordered, sampling countless transient interactions with the RNA. There are long-range couplings among the different elements contributing to the recognition, which can lead to allosteric communication throughout the system. Overall, the RNA-FUS systems form dynamical ensembles that cannot be fully represented by single static structures. Thus, albeit imperfect, MD simulations represent a viable tool to investigate dynamic RNA-protein complexes.

Thirty years of molecular dynamics simulations on posttranslational modifications of proteins

Posttranslational modifications (PTMs) are an integral component to how cells respond to perturbation. While experimental advances have enabled improved PTM identification capabilities, the same throughput for characterizing how structural changes caused by PTMs equate to altered physiological function has not been maintained. In this Perspective, we cover the history of computational modeling and molecular dynamics simulations which have characterized the structural implications of PTMs. We distinguish results from different molecular dynamics studies based upon the timescales simulated and analysis approaches used for PTM characterization. Lastly, we offer insights into how opportunities for modern research efforts on in silico PTM characterization may proceed given current state-of-the-art computing capabilities and methodological advancements.

End-to-end differentiable construction of molecular mechanics force fields

Molecular mechanics (MM) potentials have long been a workhorse of computational chemistry. Leveraging accuracy and speed, these functional forms find use in a wide variety of applications in biomolecular modeling and drug discovery, from rapid virtual screening to detailed free energy calculations. Traditionally, MM potentials have relied on human-curated, inflexible, and poorly extensible discrete chemical perception rules (atom types) for applying parameters to small molecules or biopolymers, making it difficult to optimize both types and parameters to fit quantum chemical or physical property data. Here, we propose an alternative approach that uses graph neural networks to perceive chemical environments, producing continuous atom embeddings from which valence and nonbonded parameters can be predicted using invariance-preserving layers. Since all stages are built from smooth neural functions, the entire process-spanning chemical perception to parameter assignment-is modular and end-to-end differentiable with respect to model parameters, allowing new force fields to be easily constructed, extended, and applied to arbitrary molecules. We show that this approach is not only sufficiently expressive to reproduce legacy atom types, but that it can learn to accurately reproduce and extend existing molecular mechanics force fields. Trained with arbitrary loss functions, it can construct entirely new force fields self-consistently applicable to both biopolymers and small molecules directly from quantum chemical calculations, with superior fidelity than traditional atom or parameter typing schemes. When adapted to simultaneously fit partial charge models, espaloma delivers high-quality partial atomic charges orders of magnitude faster than current best-practices with low inaccuracy. When trained on the same quantum chemical small molecule dataset used to parameterize the Open Force Field ("Parsley") openff-1.2.0 small molecule force field augmented with a peptide dataset, the resulting espaloma model shows superior accuracy vis-á-vis experiments in computing relative alchemical free energy calculations for a popular benchmark. This approach is implemented in the free and open source package espaloma, available at https://github.com/choderalab/espaloma.

The evolutionary advantage of an aromatic clamp in plant family 3 glycoside exo-hydrolases

In the barley β-D-glucan glucohydrolase, a glycoside hydrolase family 3 (GH3) enzyme, the Trp286/Trp434 clamp ensures β-D-glucosides binding, which is fundamental for substrate hydrolysis during plant growth and development. We employ mutagenesis, high-resolution X-ray crystallography, and multi-scale molecular modelling methods to examine the binding and conformational behaviour of isomeric β-D-glucosides during substrate-product assisted processive catalysis that operates in GH3 hydrolases. Enzyme kinetics reveals that the W434H mutant retains broad specificity, while W434A behaves as a strict (1,3)-β-D-glucosidase. Investigations of reactant movements on the nanoscale reveal that processivity is sensitive to mutation-specific alterations of the tryptophan clamp. While wild-type and W434H utilise a lateral cavity for glucose displacement and sliding of (1,3)-linked hydrolytic products through the catalytic site without dissociation, consistent with their high hydrolytic rates, W434A does not adopt processive catalysis. Phylogenomic analyses of GH3 hydrolases disclose the evolutionary advantage of the tryptophan clamp that confers broad specificity, high catalytic efficiency, and processivity.

All-Atom Molecular Dynamics of Pure Water-Methane Gas Hydrate Systems under Pre-Nucleation Conditions: A Direct Comparison between Experiments and Simulations of Transport Properties for the Tip4p/Ice Water Model

(1) Background: New technologies involving gas hydrates under pre-nucleation conditions such as gas separations and storage have become more prominent. This has necessitated the characterization and modeling of the transport properties of such systems. (2) Methodology: This work explored methane hydrate systems under pre-nucleation conditions. All-atom molecular dynamics simulations were used to quantify the performance of the TIP4P/2005 and TIP4P/Ice water models to predict the viscosity, diffusivity, and thermal conductivity using various formulations. (3) Results: Molecular simulation equilibrium was robustly demonstrated using various measures. The Green–Kubo estimation of viscosity outperformed other formulations when combined with TIP4P/Ice, and the same combination outperformed all TIP4P/2005 formulations. The Green–Kubo TIP4P/Ice estimation of viscosity overestimates (by 84% on average) the viscosity of methane hydrate systems under pre-nucleation conditions across all pressures considered (0–5 MPag). The presence of methane was found to increase the average number of hydrogen bonds over time (6.7–7.8%). TIP4P/Ice methane systems were also found to have 16–19% longer hydrogen bond lifetimes over pure water systems. (4) Conclusion: An inherent limitation in the current water force field for its application in the context of transport properties estimations for methane gas hydrate systems. A re-parametrization of the current force field is suggested as a starting point. Until then, this work may serve as a characterization of the deviance in viscosity prediction.

Microsolvation Effects in the Spectral Tuning of Heliorhodopsin

Heliorhodopsins (HeR) are a new category of heptahelical transmembrane photoactive proteins with a covalently linked all-trans retinal. The protonated Schiff base (PSB) nitrogen in the retinal is stabilized by a negatively charged counterion. It is well-known that stronger or weaker electrostatic interactions with the counterion cause a significant spectral blue- or red-shift, respectively, in both microbial and animal rhodopsins. In HeR, however, while Glu107 acts as the counterion, mutations of this residue are not directly correlated with a spectral shift. A molecular dynamics analysis revealed that a water cluster pocket produces a microsolvation effect on the Schiff base, compensating to various extents the replacement of the native counterion. Using a combination of molecular dynamics and quantum mechanical/molecular mechanics (QM/MM), we study this microsolvation effect on the electronic absorption of the retinylidene Schiff base chromophore of HeR.

Improving the Efficiency of Variationally Enhanced Sampling with Wavelet-Based Bias Potentials

Collective variable-based enhanced sampling methods are routinely used on systems with metastable states, where high free energy barriers impede the proper sampling of the free energy landscapes when using conventional molecular dynamics simulations. One such method is variationally enhanced sampling (VES), which is based on a variational principle where a bias potential in the space of some chosen slow degrees of freedom, or collective variables, is constructed by minimizing a convex functional. In practice, the bias potential is taken as a linear expansion in some basis function set. So far, primarily basis functions delocalized in the collective variable space, like plane waves, Chebyshev, or Legendre polynomials, have been used. However, there has not been an extensive study of how the convergence behavior is affected by the choice of the basis functions. In particular, it remains an open question if localized basis functions might perform better. In this work, we implement, tune, and validate Daubechies wavelets as basis functions for VES. The wavelets construct orthogonal and localized bases that exhibit an attractive multiresolution property. We evaluate the performance of wavelet and other basis functions on various systems, going from model potentials to the calcium carbonate association process in water. We observe that wavelets exhibit excellent performance and much more robust convergence behavior than all other basis functions, as well as better performance than metadynamics. In particular, using wavelet bases yields far smaller fluctuations of the bias potential within individual runs and smaller differences between independent runs. Based on our overall results, we can recommend wavelets as basis functions for VES.

Molecular Mechanism of Protein Arginine Deiminase 2: A Study Involving Multiple Microsecond Long Molecular Dynamics Simulations

Peptidylarginine deiminase 2 (PAD2) is a Ca²⁺-dependent enzyme that catalyzes the conversion of protein arginine residues to citrulline. This kind of structural modification in histone molecules may affect gene regulation, leading to effects that may trigger several diseases, including breast cancer, which makes PAD2 an attractive target for anticancer drug development. To design new effective inhibitors to control activation of PAD2, improving our understanding of the molecular mechanisms of PAD2 using up-to-date computational techniques is essential. We have designed five different PAD2-substrate complex systems based on varying protonation states of the active site residues. To search the conformational space broadly, multiple independent molecular dynamics simulations of the complexes have been performed. In total, 50 replica simulations have been performed, each of 1 μs, yielding a total simulation time of 50 μs. Our findings identify that the protonation states of Cys647, Asp473, and His471 are critical for the binding and localization of the N-α-benzoyl-l-arginine ethyl ester substrate within the active site. A novel mechanism for enzyme activation is proposed according to near attack conformers. This represents an important step in understanding the mechanism of citrullination and developing PAD2-inhibiting drugs for the treatment of breast cancer.

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

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

Toward Convergence in Folding Simulations of RNA Tetraloops: Comparison of Enhanced Sampling Techniques and Effects of Force Field Modifications

Atomistic molecular dynamics simulations represent an established technique for investigation of RNA structural dynamics. Despite continuous development, contemporary RNA simulations still suffer from suboptimal accuracy of empirical potentials (force fields, ffs) and sampling limitations. Development of efficient enhanced sampling techniques is important for two reasons. First, they allow us to overcome the sampling limitations, and second, they can be used to quantify ff imbalances provided they reach a sufficient convergence. Here, we study two RNA tetraloops (TLs), namely the GAGA and UUCG motifs. We perform extensive folding simulations and calculate folding free energies (ΔG_fold^°) with the aim to compare different enhanced sampling techniques and to test several modifications of the nonbonded terms extending the AMBER OL3 RNA ff. We demonstrate that replica-exchange solute tempering (REST2) simulations with 12-16 replicas do not show any sign of convergence even when extended to a timescale of 120 μs per replica. However, the combination of REST2 with well-tempered metadynamics (ST-MetaD) achieves good convergence on a timescale of 5-10 μs per replica, improving the sampling efficiency by at least 2 orders of magnitude. Effects of ff modifications on ΔG_fold^° energies were initially explored by the reweighting approach and then validated by new simulations. We tested several manually prepared variants of the gHBfix potential which improve stability of the native state of both TLs by ∼2 kcal/mol. This is sufficient to conveniently stabilize the folded GAGA TL while the UUCG TL still remains under-stabilized. Appropriate adjustment of van der Waals parameters for C-H···O5' base-phosphate interaction may further stabilize the native states of both TLs by ∼0.6 kcal/mol.

Alteration of lipid bilayer mechanics by volatile anesthetics: Insights from μs-long molecular dynamics simulations

Very few drugs in clinical practice feature the chemical diversity, narrow therapeutic window, unique route of administration, and reversible cognitive effects of volatile anesthetics. The correlation between their hydrophobicity and their potency and the increasing amount of evidence suggesting that anesthetics exert their action on transmembrane proteins, justifies the investigation of their effects on phospholipid bilayers at the molecular level, given the strong functional and structural link between transmembrane proteins and the surrounding lipid matrix. Molecular dynamics simulations of a model lipid bilayer in the presence of ethylene, desflurane, methoxyflurane, and the nonimmobilizer 1,2-dichlorohexafluorocyclobutane (also called F6 or 2N) at different concentrations highlight the structural consequences of VA partitioning in the lipid phase, with a decrease of lipid order and bilayer thickness, an increase in overall lipid lateral mobility and area-per-lipid, and a marked reduction in the mechanical stiffness of the membrane, that strongly correlates with the compounds' hydrophobicity.

Systematic Parameterization of Ion-Surfactant Interactions in Dissipative Particle Dynamics Using Setschenow Coefficients

Dissipative particle dynamics (DPD) simulations of nonionic surfactants with an added salt show that the Setschenow relationship is reproduced; that is, the critical micelle concentration is log-linearly dependent on the added salt concentration. The simulated Setschenow coefficients depend on the DPD bead–bead repulsion amplitudes, and matching to the experimentally determined values provides a systematic method to parameterize the interactions between salt ion beads and surfactant beads. The optimized ion-specific interaction parameters appear to be transferrable and follow the same trends as the empirical Hofmeister series.

Strain-controlled thermoelectric properties of phosphorene-carbon monosulfide hetero-bilayers

The application of strain to 2D materials allows manipulating the electronic, magnetic, and thermoelectric properties. These physical properties are sensitive to slight variations induced by tensile and compressive strain and the uniaxial strain direction. Herein, we take advantage of the reversible semiconductor-metal transition observed in certain monolayers to propose a hetero-bilayer device. We propose to pill up phosphorene (layered black phosphorus) and carbon monosulfide monolayers. In the first, such transition appears for positive strain, while the second appears for negative strain. Our first-principle calculations show that depending on the direction of the applied uniaxial strain; it is possible to achieve reversible control in the layer that behaves as an electronic conductor while the other layer remains as a thermal conductor. The described strain-controlled selectivity could be used in the design of novel devices.

Expanded Ensemble Methods Can be Used to Accurately Predict Protein-Ligand Relative Binding Free Energies

Alchemical free energy methods have become indispensable in computational drug discovery for their ability to calculate highly accurate estimates of protein-ligand affinities. Expanded ensemble (EE) methods, which involve single simulations visiting all of the alchemical intermediates, have some key advantages for alchemical free energy calculation. However, there have been relatively few examples published in the literature of using expanded ensemble simulations for free energies of protein-ligand binding. In this paper, as a test of expanded ensemble methods, we compute relative binding free energies using the Open Force Field Initiative force field (codename "Parsley") for 24 pairs of Tyk2 inhibitors derived from a congeneric series of 16 compounds. The EE predictions agree well with the experimental values (root-mean-square error (RMSE) of 0.94 ± 0.13 kcal mol^-1 and mean unsigned error (MUE) of 0.75 ± 0.12 kcal mol^-1). We find that while increasing the number of alchemical intermediates can improve the phase space overlap, faster convergence can be obtained with fewer intermediates, as long as acceptance rates are sufficient. We also find that convergence can be improved using more aggressive updating of biases, and that estimates can be improved by performing multiple independent EE calculations. This work demonstrates that EE is a viable option for alchemical free energy calculation. We discuss the implications of these findings for rational drug design, as well as future directions for improvement.