Umbrella sampling: a powerful method to sample tails of distributions
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Charles Matthews↗
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Results for “umbrella sampling”
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Supervised learning and the finite-temperature string method for computing committor functions and reaction rates
A central object in the computational studies of rare events is the committor function. Though costly to compute, the committor function encodes complete mechanistic information of the processes involving rare events, including reaction rates and transition-state ensembles. Under the framework of transition path theory, Rotskoff et al. [Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, Proceedings of Machine Learning Research (PLMR, 2022), Vol. 145, pp. 757–780] proposes an algorithm where a feedback loop couples a neural network that models the committor function with importance sampling, mainly umbrella sampling, which collects data needed for adaptive training. Here, in this work, we show additional modifications are needed to improve the accuracy of the algorithm. The first modification adds elements of supervised learning, which allows the neural network to improve its prediction by fitting to sample-mean estimates of committor values obtained from short molecular dynamics trajectories. The second modification replaces the committor-based umbrella sampling with the finite-temperature string (FTS) method, which enables homogeneous sampling in regions where transition pathways are located. We test our modifications on low-dimensional systems with non-convex potential energy where reference solutions can be found via analytical or finite element methods, and show how combining supervised learning and the FTS method yields accurate computation of committor functions and reaction rates. We also provide an error analysis for algorithms that use the FTS method, using which reaction rates can be accurately estimated during training with a small number of samples. The methods are then applied to a molecular system in which no reference solution is known, where accurate computations of committor functions and reaction rates can still be obtained.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Computing equilibrium free energies through a nonequilibrium quench
Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium “quench” process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications.
Chemistry↗
Towards the Accurate Thermodynamic Characterization of Enzyme Reaction Mechanisms
We employed QM/MM molecular dynamics (MD) simulations to characterize the rate-limiting step of the glycosylation reaction of pancreatic α-amylase with combined DFT/molecular dynamics methods (PBE/def2-SVP : AMBER). Upon careful choice of four starting active site conformations based on thorough reactivity criteria, Gibbs energy profiles were calculated with umbrella sampling simulations within a statistical convergence of 1 -2 kcal · mol -1 . Nevertheless, Gibbs activation barriers and reaction energies still varied from 11.0 to 16.8 kcal · mol -1 and -6.3 to +3.8 kcal · mol -1 depending on the starting conformations, showing that despite significant state-of-the-art QM/MM MD sampling (0.5 ns/profile) the result still depends on the starting structure. In conclusion, the results supported the one step dissociative mechanism of Asp197 glycosylation preceded by an acid-base reaction by the Glu233, which are qualitatively similar to those from multi-PES QM/MM studies, and thus support the use of the latter to determine enzyme reaction mechanisms.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Computing Potential of the Mean Force Profiles for Ion Permeation Through Channelrhodopsin Chimera, C1C2
Umbrella sampling, coupled with a weighted histogram analysis method (US-WHAM), can be used to construct potentials of mean force (PMFs) for studying the complex ion permeation pathways of membrane transport proteins. Despite the widespread use of US-WHAM, obtaining a physically meaningful PMF can be challenging. Here, we provide a protocol to resolve that issue. Then, we apply that protocol to compute a meaningful PMF for sodium ion permeation through channelrhodopsin chimera, C1C2, for illustration.
59 BASIC BIOLOGICAL SCIENCES↗
Molecular Mechanisms Underlying Surfactant-Based Plastics De-Inking
Surfactant-mediated binder removal is critical for de-inking pretreatment in plastics recycling, yet the molecular mechanisms governing surfactant performance remain poorly understood. We used all-atom (AA) and coarse-grained (CG) molecular dynamics (MD) simulations alongside alkaline surfactant washing experiments to investigate interactions between a series of surfactants and a polyether urethane (PEU) binder in solution and on a polyethylene (PE) surface. Experiments reveal a range of de-inking efficiencies, ranging from <25 to >95% depending upon surfactant headgroup charge and tail length. AA simulations reveal that charged surfactants reach stable levels of surfactant coverage, while nonionic surfactants aggregate on the binder. CG umbrella sampling calculations quantify the thermodynamics of binder desorption in water. In ∼0.25 M surfactant solutions, up to a 52% reduction in the free energy barrier is computed, with trends in good agreement (R 2 = 0.92, Pearson’s r = –0.96, Spearman’s ρ = –0.83) with experimental de-inking efficiencies. We find that charged surfactants are more effective than nonionic surfactants for de-inking and propose three regimes of surfactant de-inking processes: good de-inking occurs in surfactants that promote PEU desorption with a low radius of gyration (R g ); moderate de-inking occurs when surfactants stabilize PEU but increase R g ; poor de-inking occurs in surfactants that aggregate on the binder and promote extensive anchoring to the surface. Overall, these molecular-level insights have the potential to guide the design of surfactant formulations for plastics recycling applications.
ink removal↗
Multitask Machine Learning of Collective Variables for Enhanced Sampling of Rare Events
Computing accurate reaction rates is a central challenge in computational chemistry and biology because of the high cost of free energy estimation with unbiased molecular dynamics. In this work, a data-driven machine learning algorithm is devised to learn collective variables with a multitask neural network, where a common upstream part reduces the high dimensionality of atomic configurations to a low dimensional latent space and separate downstream parts map the latent space to predictions of basin class labels and potential energies. Here, the resulting latent space is shown to be an effective low-dimensional representation, capturing the reaction progress and guiding effective umbrella sampling to obtain accurate free energy landscapes. This approach is successfully applied to model systems including a 5D Müller Brown model, a 5D three-well model, the alanine dipeptide in vacuum, and an Au(110) surface reconstruction unit reaction. It enables automated dimensionality reduction for energy controlled reactions in complex systems, offers a unified and data-efficient framework that can be trained with limited data, and outperforms single-task learning approaches, including autoencoders.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
An interoperable implementation of collective‐variable based enhanced sampling methods in extended phase space within the OpenMM package
Collective variable (CV)-based enhanced sampling techniques are widely used today for accelerating barrier-crossing events in molecular simulations. A class of these methods, which includes temperature accelerated molecular dynamics (TAMD)/driven-adiabatic free energy dynamics (d-AFED), unified free energy dynamics (UFED), and temperature accelerated sliced sampling (TASS), uses an extended variable formalism to achieve quick exploration of conformational space. These techniques are powerful, as they enhance the sampling of a large number of CVs simultaneously compared to other techniques. Extended variables are kept at a much higher temperature than the physical temperature by ensuring adiabatic separation between the extended and physical subsystems and employing rigorous thermostatting. Here, in this work, we present a computational platform to perform extended phase space enhanced sampling simulations using the open-source molecular dynamics engine OpenMM. The implementation allows users to have interoperability of sampling techniques, as well as employ state-of-the-art thermostats and multiple time-stepping. This work also presents protocols for determining the critical parameters and procedures for reconstructing high-dimensional free energy surfaces. As a demonstration, we present simulation results on the high dimensional conformational landscapes of the alanine tripeptide in vacuo, tetra-N-methylglycine (tetra-sarcosine) peptoid in implicit solvent, and the Trp-cage mini protein in explicit water.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Molecular simulation of lignin-related aromatic compound permeation through gram-negative bacterial outer membranes
Lignin, an abundant aromatic heteropolymer in secondary plant cell walls, is the single largest source of renewable aromatics in the biosphere. Leveraging this resource for renewable bioproducts through targeted microbial action depends on lignin fragment uptake by microbial hosts and subsequent enzymatic action to obtain the desired product. Recent computational work has emphasized that bacterial inner membranes are permeable to many aromatic compounds expected from lignin depolymerization processes. In this study, we expand on these findings through simulations for 42 lignin-related compounds across a gram-negative bacterial outer membrane model. Unbiased simulation trajectories indicate that spontaneous crossing for the full outer membrane is relatively rare at molecular simulation timescales, primarily due to preferential membrane partitioning and slow diffusion within the lipopolysaccharide layer within the outer membrane. Membrane partitioning and permeability coefficients were determined through replica exchange umbrella sampling simulations to overcome sampling limitations. We find that the glycosylated lipopolysaccharides found in the outer membrane increase the permeation barrier to many lignin-related compounds, particularly the most hydrophobic compounds. However, the effect is relatively modest; at industrially relevant concentrations, uncharged lignin-related compounds will readily diffuse across the outer membrane without the need for specific porins. Together, our results provide insight into the permeability of the bacterial outer membrane for assessing lignin fragment uptake and the future production of renewable bioproducts.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Atomistic Characterization of Gramicidin Channel Formation
We investigated gramicidin A (gA) subunit dimerization in lipid bilayers using microsecond-long replica-exchange umbrella sampling simulations, millisecond-long unbiased molecular dynamics simulations, and machine learning. Our simulations led to a dimer structure that is indistinguishable from the experimentally determined gA channel structures, with the two gA subunits joined by six hydrogen bonds (6HB). The simulations also uncovered two additional dimer structures, with different gA–gA stacking orientations that were stabilized by four or two hydrogen bonds (4HB or 2HB). When examining the temporal evolution of the dimerization, we found that two bilayer-inserted gA subunits can form the 6HB dimer directly, with no discernible intermediate states, as well as through paths that involve the 2HB and 4HB dimers.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Thermodynamic Analysis of Silk Fibroin–Graphite Hybrid Materials and Their Morphology
Silk fibroin (SF) is a β-sheet-rich protein that is responsible for the remarkable tensile strength of silk. In addition to its mechanical properties, SF is biocompatible and biodegradable, making it an attractive candidate for use in biotic/abiotic hybrid materials. A pairing of particular interest is the use of SF with graphene-based nanomaterials (GBNs). The properties of this interface drive the formation of well-ordered nanostructures and can improve the electronic properties of the resulting hybrid. It was previously demonstrated that SF can form lamellar nanostructures in the presence of graphite; however, the equilibrium morphology and associated driving interactions are not fully understood. Here, in this study, we characterize these interactions between SF and SF lamellar with graphite using molecular dynamics (MD) simulations and umbrella sampling (US). We find that SF lamellar nanostructures have strong orientational and spatial preferences on graphite that are driven by the hydrophobic effect, destabilizing solvent–protein interactions and stabilizing protein–protein and protein–graphite interactions. Finally, we show how careful consideration of these underlying interactions can be applied to rationally modify the nanostructure morphology.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Molecular Modeling and Molecular Dynamics Simulation of a Packed and Intact Bacterial Microcompartment
Bacterial microcompartments (BMCs) are protein-bound organelles found in some bacteria which encapsulate enzymes for enhanced catalytic activity. These compartments spatially sequester enzymes within semipermeable shell proteins and are packed full of enzyme cargoes and metabolites as they fulfill their function. Coupling together recent SAXS and proteomics work, it is possible to develop molecular models for these microcompartments and interrogate enzyme and metabolite dynamics within. Our primary goal of this study is to quantify the permeability of metabolite glyceraldehyde-3-phosphate (G3P) and dihydroxyacetone phosphate (DHAP) across the BMC shell through classical molecular dynamics simulation. The Haliangium ochraceum model of BMC shell (PDB: 6MZX) was used to model an intact BMC of approximately 10 million atoms. Working at this scale presented its own challenges in managing large data sets, with multiple challenges and hardware advances discussed that facilitated this work. Over approximately 750 ns of aggregate simulation, we see multiple permeation events for these metabolites that were added at high concentration through the pores present within BMC shell tiles. When compared to independent permeability estimates for the same metabolites determined through replica exchange umbrella sampling simulations, the permeabilities varied by approximately 3 orders of magnitude. Regardless, the permeability coefficients for both G3P and DHAP are highly similar and very high, such that only very small concentration gradients can be maintained across the BMC shell between the cytosol and BMC interior. The large simulation systems also facilitated comparisons for molecular diffusivity in the crowded environment within the BMC shell. By our estimates, the viscosity within a packed BMC shell is at least 10-fold higher than it would be in neat solution and is the real driver for varying permeability estimates we obtained through simulation. These findings will be used as design inputs for future bioengineering efforts to make products from BMCs, highlighting how permeable BMC shells can be.
Diffusion↗
Molecular dynamics simulations of the secondary-binding site in disaccharide-modified glycopeptide antibiotics
Oritavancin is a semisynthetic glycopeptide antibiotic used to treat severe infections by multidrug-resistant Gram-positive pathogens. Oritavancin is known to be a thousand times more potent than vancomycin against Gram-positive bacteria due to the additional interactions with bacterial peptidoglycan (PG) facilitated by a secondary-binding site. The presence of this secondary-binding site is evident in desleucyl-oritavancin, an Edman degradation product of oritavancin, still retaining its potency against Gram-positive bacteria, whereas desleucyl-vancomycin is devoid of any antimicrobial activities. Herein, using explicit solvent molecular dynamics (MD) simulations, steered MD simulations, and umbrella sampling, we show evidence of a secondary-binding site mediated by the disaccharide-modified hydrophobic sidechain of oritavancin interactions with the pentaglycyl-bridge segment of the PG. The interactions were characterized through comparison to the interaction of PG with chloroeremomycin, vancomycin, and the desleucyl analogs of the glycopeptides. Our results show that the enhanced binding of oritavancin to PG over the binding of the other complexes studied is due to an increase in the hydrophobic effect, electrostatic and van der Waals interactions, and not the average number of hydrogen bonds. Our ranking of the binding interactions of the biomolecular complexes directly correlates with the order based on their experimental minimum inhibitory concentrations. The results of our simulations provide insight into the modification of glycopeptides to increase their antimicrobial activities or the design of novel antibiotics against pathogenic Gram-positive bacteria.
60 APPLIED LIFE SCIENCES↗
Probing remdesivir nucleotide analogue insertion to SARS-CoV-2 RNA dependent RNA polymerase in viral replication
Remdesivir (RDV) prodrug can be metabolized into a triphosphate form nucleotide analogue (RDV-TP) to bind and insert into the active site of viral RNA dependent RNA polymerase (RdRp) to further interfere with viral genome replication. Here in this work, we computationally studied how RDV-TP binds and inserts to the SARS-CoV-2 RdRp active site, in comparison with natural nucleotide substrate adenosine triphosphate (ATP). To do that, we first constructed atomic structural models of an initial binding complex (active site open) and a substrate insertion complex (active site closed), based on high-resolution cryo-EM structures determined recently for SARS-CoV-2 RdRp or non-structural protein (nsp) 12, in complex with accessory protein factors nsp7 and nsp8. By conducting all-atom molecular dynamics simulation with umbrella sampling strategies on the nucleotide insertion between the open and closed state RdRp complexes, our studies show that RDV-TP can initially bind in a comparatively stabilized state to the viral RdRp active site, as it primarily forms base stacking with the template uracil nucleotide (nt +1), which under freely fluctuations supports a low free energy barrier of the RDV-TP insertion (~1.5 kcal mol -1 ). In comparison, the corresponding natural substrate ATP binds initially to the RdRp active site in Watson–Crick base pairing with the template nt, and inserts into the active site with a medium low free energy barrier (~2.6 kcal mol -1 ), when the fluctuations of the template nt are well quenched. The simulations also show that the initial base stacking of RDV-TP with the template can be specifically stabilized by motif C-S759, S682 (near motif B) with the base, and motif G-K500 with the template backbone. Although the RDV-TP insertion can be hindered by motif F-R555/R553 interaction with the triphosphate, the ATP insertion seems to be facilitated by such interactions. The inserted RDV-TP and ATP can be further distinguished by specific sugar interaction with motif B-T687 and motif A-D623, respectively.
36 MATERIALS SCIENCE↗
Solvent effects on extractant conformational energetics in liquid–liquid extraction: a simulation study of molecular solvents and ionic liquids
Extractant design in liquid–liquid extraction (LLE) is a research frontier of metal ion separations that typically focuses on the direct extractant–metal interactions. However, a more detailed understanding of energetic drivers of separations beyond primary metal coordination is often lacking, including the role of solvent in the extractant phase. In this work, we propose a new mechanism for enhancing metal-complexant energetics with nanostructured solvents. Using molecular dynamics simulations with umbrella sampling, we find that the organic solvent can reshape the energetics of the extractant's intramolecular conformational landscape. Here, we calculate free energy profiles of different conformations of a representative bidentate extractant, n-octyl(phenyl)-N,N-diisobutyl carbamoyl methyl phosphinoxide (CMPO), in four different solvents: dodecane, tributyl phosphate (TBP), and dry and wet ionic liquid (IL) 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIM][Tf 2 N]). By promoting reorganization of the extractant molecule into its binding conformation, our findings reveal how particular solvents can ameliorate this unfavorable step of the metal separation process. In particular, the charge alternating nanodomains formed in ILs substantially reduce the free energy penalty associated with extractant reorganization. Importantly, using alchemical free energy calculations, we find that this stabilization persists even when we explicitly include the extracted cation. These findings provide insight into the energetic drivers of metal ion separations and potentially suggest a new approach to designing effective separations using a molecular-level understanding of solvent effects.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Uranium (VI) Adsorbate Structures on Portlandite [Ca(OH)2] Type Surfaces Determined by Computational Modelling and X-ray Absorption Spectroscopy
Portlandite [Ca(OH) 2 ] is a potentially dominant solid phase in the high pH fluids expected within the cementitious engineered barriers of Geological Disposal Facilities (GDF). This study combined X-ray Absorption Spectroscopy with computational modelling in order to provide atomic-scale data which improves our understanding of how a critically important radionuclide (U) will be adsorbed onto this phase under conditions relevant to a GDF environment. Such data are fundamental for predicting radionuclide mass transfer. Surface coordination chemistry and speciation of uranium with portlandite [Ca(OH) 2 ] under alkaline groundwater conditions (ca. pH 12) were determined by both in situ and ex situ grazing incidence extended X-ray absorption fine structure analysis (EXAFS) and by computational modelling at the atomic level. Free energies of sorption of aqueous uranyl hydroxides, [UO 2 (OH) n ] 2–n (n = 0–5) with the (001), (100) and (203) or (101) surfaces of portlandite are predicted from the potential of mean force using classical molecular umbrella sampling simulation methods and the structural interactions are further explored using fully periodic density functional theory computations. Although uranyl is predicted to only weakly adsorb to the (001) and (100) clean surfaces, there should be significantly stronger interactions with the (203/101) surface or at hydroxyl vacancies, both prevalent under groundwater conditions. The uranyl surface complex is typically found to include four equatorially coordinated hydroxyl ligands, forming an inner-sphere sorbate by direct interaction of a uranyl oxygen with surface calcium ions in both the (001) and (203/101) cases. In contrast, on the (100) surface, uranyl is sorbed with its axis more parallel to the surface plane. The EXAFS data are largely consistent with a surface structural layer or film similar to calcium uranate, but also show distinct uranyl characteristics, with the uranyl ion exhibiting the classic dioxygenyl oxygens at 1.8 Å and between four and five equatorial oxygen atoms at distances between 2.28 and 2.35 Å from the central U absorber. These experimental data are wholly consistent with the adsorbate configuration predicted by the computational models. These findings suggest that, under the strongly alkaline conditions of a cementitious backfill engineered barrier, there would be significant uptake of uranyl by portlandite to inhibit the mobility of U(VI) from the near field of a geological disposal facility.
36 MATERIALS SCIENCE↗
Hydrothermal Decomposition of Amino Acids and Origins of Prebiotic Meteoritic Organic Compounds
The organic compounds found in carbonaceous chondrite meteorites provide insight into primordial solar system chemistry. Evaluating the formation and decomposition mechanisms of meteoritic amino acids may aid our understanding of the origins of life and homochirality on Earth. The amino acid glycine is widespread in meteorites and other extraterrestrial environments; other amino acids, such as isovaline, are found with enantiomeric excesses in some meteorites. The relationship between meteoritic amino acids and other compounds with similar molecular structures, such as aliphatic monoamines and monocarboxylic acids is unclear; experimental results evaluating the decomposition of amino acids have produced inconclusive results about the preferred pathways, reaction intermediates, and if the conditions applied may be compatible with those occurring inside meteoritic parent bodies. In this work, we performed extensive tandem metadynamics, umbrella sampling, and committor analysis to simulate the neutral mild hydrothermal decomposition mechanisms of glycine and isovaline and put them into context for the origins of meteoritic organic compounds. Our ab initio simulations aimed to determine free energy profiles and decomposition pathways for glycine and isovaline. We found that under our modeled conditions, methylammonium, glycolic acid, and sec-butylamine are the most likely decomposition products. These results suggest that meteoritic aliphatic monocarboxylic acids are not produced from decomposition of meteoritic amino acids. Our results also indicate that the decomposition of L-isovaline prefers an enantioselective pathway resulting in the production of (S)-sec-butylamine.
Enhanced sampling↗
Investigating the Effect of Water on the Mechanical Properties of Cellulose from Multiscale Molecular Dynamics Simulations
Classical molecular dynamics (MD) simulations provide insight into the structure and physicochemical properties of materials with atomic resolution. However, the length and time scales accessible to atomistic MD are orders of magnitude smaller than many relevant processes such as the response of a bulk material to experimentally accessible strain rates, which presents challenges when comparing models to experimental measurements. Bottom-up coarse-graining provides a means for systematically mapping atomistic information to lower resolution models to increase the length and time scales achievable by simulation. Cellulose is an abundant carbohydrate biopolymer with applications to many fields of research, such as materials science and renewable energy, due to its desirable mechanical properties and viability for conversion into biofuel. The effect of moisture content on the Young's modulus of cellulose is of special interest due to its native environment often being in the hydrated secondary plant cell wall and the grinding energy requirements for biomass feedstock preprocessing. The current work investigates the effects of water solvent on the Young's modulus of cellulose calculated from coarse-grained MD mechanical stress simulations. The coarse-grained model was parametrized from atomistic MD calculations of cellulose-cellulose potentials of mean force using umbrella sampling techniques under vacuum and solvated conditions. The Young's moduli of the coarse-grained cellulose assemblies parametrized from cellulose in vacuum or solvated in water were computed via mechanical stress simulations to highlight the importance of capturing solvent interactions for modeling the mechanical behavior of cellulose.
BASIC BIOLOGICAL SCIENCES,RADIATION PROTECTION AND↗