Leveraging uncertainty estimates and derivative information in Gaussian process regression for efficient collection and use of molecular simulation data.

We introduce Gaussian Process Regression (GPR) as an enhanced method of thermodynamic extrapolation and interpolation. The heteroscedastic GPR models that we introduce automatically weight provided information by its estimated uncertainty, allowing for the incorporation of highly uncertain, high-order derivative information. By the linearity of the derivative operator, GPR models naturally handle derivative information and, with appropriate likelihood models that incorporate heterogeneous uncertainties, are able to identify estimates of functions for which the provided observations and derivatives are inconsistent due to the sampling bias that is common in molecular simulations. Since we utilize kernels that form complete bases on the function space to be learned, the estimated uncertainty in the model takes into account that of the functional form itself, in contrast to polynomial interpolation, which explicitly assumes the functional form to be fixed. We apply GPR models to a variety of data sources and assess various active learning strategies, identifying when specific options will be most useful. Our active-learning data collection based on GPR models incorporating derivative information is finally applied to tracing vapor-liquid equilibrium for a single-component Lennard-Jones fluid, which we show represents a powerful generalization to previous extrapolation strategies and Gibbs-Duhem integration. A suite of tools implementing these methods is provided at https://github.com/usnistgov/thermo-extrap.

Systematic control of collective variables learned from variational autoencoders.

Variational autoencoders (VAEs) are rapidly gaining popularity within molecular simulation for discovering low-dimensional, or latent, representations, which are critical for both analyzing and accelerating simulations. However, it remains unclear how the information a VAE learns is connected to its probabilistic structure and, in turn, its loss function. Previous studies have focused on feature engineering, ad hoc modifications to loss functions, or adjustment of the prior to enforce desirable latent space properties. By applying effectively arbitrarily flexible priors via normalizing flows, we focus instead on how adjusting the structure of the decoding model impacts the learned latent coordinate. We systematically adjust the power and flexibility of the decoding distribution, observing that this has a significant impact on the structure of the latent space as measured by a suite of metrics developed in this work. By also varying weights on separate terms within each VAE loss function, we show that the level of detail encoded can be further tuned. This provides practical guidance for utilizing VAEs to extract varying resolutions of low-dimensional information from molecular dynamics and Monte Carlo simulations.

Learning Efficient, Collective Monte Carlo Moves with Variational Autoencoders.

Discovering meaningful collective variables for enhancing sampling, via applied biasing potentials or tailored MC move sets, remains a major challenge within molecular simulation. While recent studies identifying collective variables with variational autoencoders (VAEs) have focused on the encoding and latent space discovered by a VAE, the impact of the decoding and its ability to act as a generative model remains unexplored. We demonstrate how VAEs may be used to learn (on-the-fly and with minimal human intervention) highly efficient, collective Monte Carlo moves that accelerate sampling along the learned collective variable. In contrast to many machine learning-based efforts to bias sampling and generate novel configurations, our methods result in exact sampling in the ensemble of interest and do not require reweighting. In fact, we show that the acceptance rates of our moves approach unity for a perfect VAE model. While this is never observed in practice, VAE-based Monte Carlo moves still enhance sampling of new configurations. We demonstrate, however, that the form of the encoding and decoding distributions, in particular the extent to which the decoder reflects the underlying physics, greatly impacts the performance of the trained VAE.

Evidence for Entropically Controlled Interfacial Hydration in Mesoporous Organosilicas.

At aqueous interfaces, the distribution and dynamics of adsorbates are modulated by the behavior of interfacial water. Hydration of a hydrophobic surface can store entropy via the ordering of interfacial water, which contributes to the Gibbs energy of solute binding. However, there is little experimental evidence for the existence of such entropic reservoirs, and virtually no precedent for their rational design in systems involving extended interfaces. In this study, two series of mesoporous silicas were modified in distinct ways: (1) progressively deeper thermal dehydroxylation, via condensation of surface silanols, and (2) increasing incorporation of nonpolar organic linkers into the silica framework. Both approaches result in decreasing average surface polarity, manifested in a blue-shift in the fluorescence of an adsorbed dye. For the inorganic silicas, hydrogen-bonding of water becomes less extensive as the number of surface silanols decreases. Overhauser dynamic nuclear polarization (ODNP) relaxometry indicates enhanced surface water diffusivity, reflecting a loss of enthalpic hydration. In contrast, organosilicas show a monotonic decrease in surface water diffusivity with decreasing polarity, reflecting enhanced hydrophobic hydration. Molecular dynamics simulations predict increased tetrahedrality of interfacial water for the organosilicas, implying increased ordering near the nm-size organic domains (relative to inorganic silicas, which necessarily lack such domains). These findings validate the prediction that hydrophobic hydration at interfaces is controlled by the microscopic length scale of the hydrophobic regions. They further suggest that the hydration thermodynamics of structurally heterogeneous silica surfaces can be tuned to promote adsorption, which in turn tunes the selectivity in catalytic reactions.

Affinity of small-molecule solutes to hydrophobic, hydrophilic, and chemically patterned interfaces in aqueous solution.

Performance of membranes for water purification is highly influenced by the interactions of solvated species with membrane surfaces, including surface adsorption of solutes upon fouling. Current efforts toward fouling-resistant membranes often pursue surface hydrophilization, frequently motivated by macroscopic measures of hydrophilicity, because hydrophobicity is thought to increase solute-surface affinity. While this heuristic has driven diverse membrane functionalization strategies, here we build on advances in the theory of hydrophobicity to critically examine the relevance of macroscopic characterizations of solute-surface affinity. Specifically, we use molecular simulations to quantify the affinities to model hydroxyl- and methyl-functionalized surfaces of small, chemically diverse, charge-neutral solutes represented in produced water. We show that surface affinities correlate poorly with two conventional measures of solute hydrophobicity, gas-phase water solubility and oil-water partitioning. Moreover, we find that all solutes show attraction to the hydrophobic surface and most to the hydrophilic one, in contrast to macroscopically based hydrophobicity heuristics. We explain these results by decomposing affinities into direct solute interaction energies (which dominate on hydroxyl surfaces) and water restructuring penalties (which dominate on methyl surfaces). Finally, we use an inverse design algorithm to show how heterogeneous surfaces, with multiple functional groups, can be patterned to manipulate solute affinity and selectivity. These findings, importantly based on a range of solute and surface chemistries, illustrate that conventional macroscopic hydrophobicity metrics can fail to predict solute-surface affinity, and that molecular-scale surface chemical patterning significantly influences affinity-suggesting design opportunities for water purification membranes and other engineered interfaces involving aqueous solute-surface interactions.

Extrapolation and interpolation strategies for efficiently estimating structural observables as a function of temperature and density.

Thermodynamic extrapolation has previously been used to predict arbitrary structural observables in molecular simulations at temperatures (or relative chemical potentials in open-system mixtures) different from those at which the simulation was performed. This greatly reduces the computational cost in mapping out phase and structural transitions. In this work, we explore the limitations and accuracy of thermodynamic extrapolation applied to water, where qualitative shifts from anomalous to simple-fluid-like behavior are manifested through shifts in the liquid structure that occur as a function of both temperature and density. We present formulas for extrapolating in volume for canonical ensembles and demonstrate that linear extrapolations of water's structural properties are only accurate over a limited density range. On the other hand, linear extrapolation in temperature can be accurate across the entire liquid state. We contrast these extrapolations with classical perturbation theory techniques, which are more conservative and slowly converging. Indeed, we show that such behavior is expected by demonstrating exact relationships between extrapolation of free energies and well-known techniques to predict free energy differences. An ideal gas in an external field is also studied to more clearly explain these results for a toy system with fully analytical solutions. We also present a recursive interpolation strategy for predicting arbitrary structural properties of molecular fluids over a predefined range of state conditions, demonstrating its success in mapping qualitative shifts in water structure with density.

Performing solvation free energy calculations in LAMMPS using the decoupling approach.

The decoupling approach to solvation free energy calculations requires scaling the interactions between the solute and the solution with all intramolecular interactions preserved. This paper reports a new procedure that makes it possible to these calculations in LAMMPS. The procedure is tested against built-in GROMACS capabilities. The model compounds chosen to test our methodology are ethanol and biphenyl. The LAMMPS and GROMACS results obtained are in good agreement with each other. This work should help perform solvation free energy calculations in LAMMPS and/or other molecular dynamics software having no built-in functions to implement the decoupling approach.

Best Practices for Foundations in Molecular Simulations [Article v1.0].

This document provides a starting point for approaching molecular simulations, guiding beginning practitioners to what issues they need to know about before and while starting their first simulations, and why those issues are so critical. This document makes no claims to provide an adequate introduction to the subject on its own. Instead, our goal is to help people know what issues are critical before beginning, and to provide references to good resources on those topics. We also provide a checklist of key issues to consider before and while setting up molecular simulations which may serve as a foundation for other best practices documents.

Decoding signatures of structure, bulk thermodynamics, and solvation in three-body angle distributions of rigid water models.

A tetrahedral structure resulting from hydrogen bonding is a hallmark of liquid water and plays a significant role in determining its unique thermophysical properties. This water feature has helped understand anomalous properties and physically interpret and model hydrophobic solvation thermodynamics. Tetrahedrality is well described by the geometric relationship of any central water molecule with two of its nearest neighbors in the first coordination shell, as defined by the corresponding "three-body" angle. While order parameters and even full water models have been developed using specific or average features of the three-body angle distribution, here we examine the distribution holistically, tracking its response to changes in temperature, density, and the presence of model solutes. Surprisingly, we find that the three-body distribution responds by varying primarily along a single degree of freedom, suggesting a remarkably simplified view of water structure. We characterize three-body angle distributions across temperature and density space and identify principal components of the variations with state conditions. We show that these principal components embed physical significance and trace out transitions between tetrahedral and simple-fluid-like behavior. Moreover, we find that the ways three-body angles vary within the hydration shells of model colloids of different types and sizes are nearly identical to the variations seen in bulk water across density and temperature. Importantly, through the principal directions of these variations, we find that perturbations to the hydration-water distributions well predict the thermodynamics associated with colloid solvation, in particular, the relative entropy of this process that captures indirect, solvent-mediated contributions to the hydration free energy.

Computational discovery of chemically patterned surfaces that effect unique hydration water dynamics.

The interactions of water with solid surfaces govern their apparent hydrophobicity/hydrophilicity, influenced at the molecular scale by surface coverage of chemical groups of varied nonpolar/polar character. Recently, it has become clear that the precise patterning of surface groups, and not simply average surface coverage, has a significant impact on the structure and thermodynamics of hydration layer water, and, in turn, on macroscopic interfacial properties. Here we show that patterning also controls the dynamics of hydration water, a behavior frequently thought to be leveraged by biomolecules to influence functional dynamics, but yet to be generalized. To uncover the role of surface heterogeneities, we couple a genetic algorithm to iterative molecular dynamics simulations to design the patterning of surface functional groups, at fixed coverage, to either minimize or maximize proximal water diffusivity. Optimized surface configurations reveal that clustering of hydrophilic groups increases hydration water mobility, while dispersing them decreases it, but only if hydrophilic moieties interact with water through directional, hydrogen-bonding interactions. Remarkably, we find that, across different surfaces, coverages, and patterns, both the chemical potential for inserting a methane-sized hydrophobe near the interface and, in particular, the hydration water orientational entropy serve as strong predictors for hydration water diffusivity, suggesting that these simple thermodynamic quantities encode the way surfaces control water dynamics. These results suggest a deep and intriguing connection between hydration water thermodynamics and dynamics, demonstrating that subnanometer chemical surface patterning is an important design parameter for engineering solid-water interfaces with applications spanning separations to catalysis.

Surface chemical heterogeneity modulates silica surface hydration.

An in-depth knowledge of the interaction of water with amorphous silica is critical to fundamental studies of interfacial hydration water, as well as to industrial processes such as catalysis, nanofabrication, and chromatography. Silica has a tunable surface comprising hydrophilic silanol groups and moderately hydrophobic siloxane groups that can be interchanged through thermal and chemical treatments. Despite extensive studies of silica surfaces, the influence of surface hydrophilicity and chemical topology on the molecular properties of interfacial water is not well understood. In this work, we controllably altered the surface silanol density, and measured surface water diffusivity using Overhauser dynamic nuclear polarization (ODNP) and complementary silica-silica interaction forces across water using a surface forces apparatus (SFA). The results show that increased silanol density generally leads to slower water diffusivity and stronger silica-silica repulsion at short aqueous separations (less than ∼4 nm). Both techniques show sharp changes in hydration properties at intermediate silanol densities (2.0-2.9 nm-2). Molecular dynamics simulations of model silica-water interfaces corroborate the increase in water diffusivity with silanol density, and furthermore show that even on a smooth and crystalline surface at a fixed silanol density, adjusting the spatial distribution of silanols results in a range of surface water diffusivities spanning ∼10%. We speculate that a critical silanol cluster size or connectivity parameter could explain the sharp transition in our results, and can modulate wettability, colloidal interactions, and surface reactions, and thus is a phenomenon worth further investigation on silica and chemically heterogeneous surfaces.

Unraveling Hydrophobic Interactions at the Molecular Scale Using Force Spectroscopy and Molecular Dynamics Simulations.

Interactions between hydrophobic moieties steer ubiquitous processes in aqueous media, including the self-organization of biologic matter. Recent decades have seen tremendous progress in understanding these for macroscopic hydrophobic interfaces. Yet, it is still a challenge to experimentally measure hydrophobic interactions (HIs) at the single-molecule scale and thus to compare with theory. Here, we present a combined experimental-simulation approach to directly measure and quantify the sequence dependence and additivity of HIs in peptide systems at the single-molecule scale. We combine dynamic single-molecule force spectroscopy on model peptides with fully atomistic, both equilibrium and nonequilibrium, molecular dynamics (MD) simulations of the same systems. Specifically, we mutate a flexible (GS)5 peptide scaffold with increasing numbers of hydrophobic leucine monomers and measure the peptides' desorption from hydrophobic self-assembled monolayer surfaces. Based on the analysis of nonequilibrium work-trajectories, we measure an interaction free energy that scales linearly with 3.0-3.4 kBT per leucine. In good agreement, simulations indicate a similar trend with 2.1 kBT per leucine, while also providing a detailed molecular view into HIs. This approach potentially provides a roadmap for directly extracting qualitative and quantitative single-molecule interactions at solid/liquid interfaces in a wide range of fields, including interactions at biointerfaces and adhesive interactions in industrial applications.

Are AMBER Force Fields and Implicit Solvation Models Additive? A Folding Study with a Balanced Peptide Test Set.

Implicit solvation models have long been sought as routes to significantly increase the speed and capabilities of biomolecular simulations. However, it has not always been clear that force fields developed independently of solvation models can together accurately predict secondary structure and folding, and whether the separate influences of the solvation and force field models can be described as independent and additive (versus synergistic). Here, we test two implicit solvation models with several recently developed protein force fields, within the AMBER simulation package. We create a representative set of five helical and five hairpin peptides, 11-20 amino acid residues in length, and calculate folded structures using replica exchange molecular dynamics simulations for all force field/solvent/peptide combinations, each with two instances using distinct starting configurations. In general, we find that no force field/solvent combination successfully folds all peptides and that the hairpin peptides are more difficult to capture. That being said, the older ff96/igb5* combination does a reasonable job in folding multiple secondary structures, while ff14SB/igb5* and ff14ipq/igb8 work well for helical and hairpin motifs, respectively. All combinations give rise to similar numbers of salt bridges, except for solvent models paired with ff14ipq, which slightly enhances them. Interestingly, we are unable statistically to decouple the effects of force field, solvent model, and peptide secondary structure on performance, such that particular combinations can have specific effects. These results suggest that future efforts might benefit from codevelopment of implicit models with force fields or from the use of emerging coarse-graining strategies that extract solvation effects in a bottom-up manner.

Converging free energies of binding in cucurbit[7]uril and octa-acid host-guest systems from SAMPL4 using expanded ensemble simulations.

Molecular containers such as cucurbit[7]uril (CB7) and the octa-acid (OA) host are ideal simplified model test systems for optimizing and analyzing methods for computing free energies of binding intended for use with biologically relevant protein-ligand complexes. To this end, we have performed initially blind free energy calculations to determine the free energies of binding for ligands of both the CB7 and OA hosts. A subset of the selected guest molecules were those included in the SAMPL4 prediction challenge. Using expanded ensemble simulations in the dimension of coupling host-guest intermolecular interactions, we are able to show that our estimates in most cases can be demonstrated to fully converge and that the errors in our estimates are due almost entirely to the assigned force field parameters and the choice of environmental conditions used to model experiment. We confirm the convergence through the use of alternative simulation methodologies and thermodynamic pathways, analyzing sampled conformations, and directly observing changes of the free energy with respect to simulation time. Our results demonstrate the benefits of enhanced sampling of multiple local free energy minima made possible by the use of expanded ensemble molecular dynamics and may indicate the presence of significant problems with current transferable force fields for organic molecules when used for calculating binding affinities, especially in non-protein chemistries.

Investigating the mutation resistance of nonnucleoside inhibitors of HIV-RT using multiple microsecond atomistic simulations.

Inhibiting HIV reverse transcriptase through the use of nonnucleoside reverse transcriptase inhibitors (NNRTIs) has become an essential component in drug regimens for the treatment of HIV. Older NNRTIs, such as nevirapine, are structurally rigid, exhibiting decreased inhibitory function on development of common mutations in the NNRTI-binding pocket, which is located around 10 Å from the catalytically active binding site. The newer generation of drugs, such as rilpivirine, are more flexible and resistant to binding pocket mutations but the mechanism by which they actually inhibit protein function and avoid mutations is not well-understood. To this end, we have performed 2-2.4 µs simulations with explicit solvent in an isobaric-isothermal ensemble of six different systems: apo wild-type, apo K103N/Y181C mutant, nevirapine-bound wild-type, nevirapine-bound mutant, rilpivirine-bound wild type, and rilpivirine-bound mutant. Analysis of protein conformations, principal components of motion, and mutual information between residues points to an inhibitory mechanism in which the primer grip stretches away from the catalytic triad of aspartic acids necessary for polymerization of HIV-encoding DNA, but is still unable to reveal a specific structural mechanism behind mutation resistance.