Kilohertz serial crystallography with the JUNGFRAU detector at a fourth-generation synchrotron source.

Serial and time-resolved macromolecular crystallography are on the rise. However, beam time at X-ray free-electron lasers is limited and most third-generation synchrotron-based macromolecular crystallography beamlines do not offer the necessary infrastructure yet. Here, a new setup is demonstrated, based on the JUNGFRAU detector and Jungfraujoch data-acquisition system, that enables collection of kilohertz serial crystallography data at fourth-generation synchrotrons. More importantly, it is shown that this setup is capable of collecting multiple-time-point time-resolved protein dynamics at kilohertz rates, allowing the probing of microsecond to second dynamics at synchrotrons in a fraction of the time needed previously. A high-quality complete X-ray dataset was obtained within 1 min from lysozyme microcrystals, and the dynamics of the light-driven sodium-pump membrane protein KR2 with a time resolution of 1 ms could be demonstrated. To make the setup more accessible for researchers, downstream data handling and analysis will be automated to allow on-the-fly spot finding and indexing, as well as data processing.

Reconstructing the infrared spectrum of a peptide from representative conformers of the full canonical ensemble.

Leucine enkephalin (LeuEnk), a biologically active endogenous opioid pentapeptide, has been under intense investigation because it is small enough to allow efficient use of sophisticated computational methods and large enough to provide insights into low-lying minima of its conformational space. Here, we reproduce and interpret experimental infrared (IR) spectra of this model peptide in gas phase using a combination of replica-exchange molecular dynamics simulations, machine learning, and ab initio calculations. In particular, we evaluate the possibility of averaging representative structural contributions to obtain an accurate computed spectrum that accounts for the corresponding canonical ensemble of the real experimental situation. Representative conformers are identified by partitioning the conformational phase space into subensembles of similar conformers. The IR contribution of each representative conformer is calculated from ab initio and weighted according to the population of each cluster. Convergence of the averaged IR signal is rationalized by merging contributions in a hierarchical clustering and the comparison to IR multiple photon dissociation experiments. The improvements achieved by decomposing clusters containing similar conformations into even smaller subensembles is strong evidence that a thorough assessment of the conformational landscape and the associated hydrogen bonding is a prerequisite for deciphering important fingerprints in experimental spectroscopic data.

How do interfaces alter the dynamics of supercooled water?

The structure of liquid water in the proximity of an interface can deviate significantly from that of bulk water, with surface-induced structural perturbations typically converging to bulk values at about ∼1 nm from the interface. While these structural changes are well established it is, in contrast, less clear how an interface perturbs the dynamics of water molecules within the liquid. Here, through an extensive set of molecular dynamics simulations of supercooled bulk and interfacial water films and nano-droplets, we observe the formation of persistent, spatially extended dynamical domains in which the average mobility varies as a function of the distance from the interface. This is in stark contrast with the dynamical heterogeneity observed in bulk water, where these domains average out spatially over time. We also find that the dynamical response of water to an interface depends critically on the nature of the interface and on the choice of interface definition. Overall these results reveal a richness in the dynamics of interfacial water that opens up the prospect of tuning the dynamical response of water through specific modifications of the interface structure or confining material.

Simulating the ghost: quantum dynamics of the solvated electron.

The nature of the bulk hydrated electron has been a challenge for both experiment and theory due to its short lifetime and high reactivity, and the need for a high-level of electronic structure theory to achieve predictive accuracy. The lack of a classical atomistic structural formula makes it exceedingly difficult to model the solvated electron using conventional empirical force fields, which describe the system in terms of interactions between point particles associated with atomic nuclei. Here we overcome this problem using a machine-learning model, that is sufficiently flexible to describe the effect of the excess electron on the structure of the surrounding water, without including the electron in the model explicitly. The resulting potential is not only able to reproduce the stable cavity structure but also recovers the correct localization dynamics that follow the injection of an electron in neat water. The machine learning model achieves the accuracy of the state-of-the-art correlated wave function method it is trained on. It is sufficiently inexpensive to afford a full quantum statistical and dynamical description and allows us to achieve accurate determination of the structure, diffusion mechanisms, and vibrational spectroscopy of the solvated electron.

Mapping the Structure of Oxygen-Doped Wurtzite Aluminum Nitride Coatings from Ab Initio Random Structure Search and Experiments.

Machine learning is changing how we design and interpret experiments in materials science. In this work, we show how unsupervised learning, combined with ab initio random structure searching, improves our understanding of structural metastability in multicomponent alloys. We focus on the case of Al-O-N alloys where the formation of aluminum vacancies in wurtzite AlN upon the incorporation of substitutional oxygen can be seen as a general mechanism of solids where crystal symmetry is reduced to stabilize defects. The ideal AlN wurtzite crystal structure occupation cannot be matched due to the presence of an aliovalent hetero-element into the structure. The traditional interpretation of the c-lattice shrinkage in sputter-deposited Al-O-N films from X-ray diffraction (XRD) experiments suggests the existence of a solubility limit at 8 at % oxygen content. Here, we show that such naive interpretation is misleading. We support XRD data with accurate ab initio modeling and dimensionality reduction on advanced structural descriptors to map structure-property relationships. No signs of a possible solubility limit are found. Instead, the presence of a wide range of non-equilibrium oxygen-rich defective structures emerging at increasing oxygen contents suggests that the formation of grain boundaries is the most plausible mechanism responsible for the lattice shrinkage measured in Al-O-N sputtered films. We further confirm our hypothesis using positron annihilation lifetime spectroscopy.

An accurate and transferable machine learning potential for carbon.

We present an accurate machine learning (ML) model for atomistic simulations of carbon, constructed using the Gaussian approximation potential (GAP) methodology. The potential, named GAP-20, describes the properties of the bulk crystalline and amorphous phases, crystal surfaces, and defect structures with an accuracy approaching that of direct ab initio simulation, but at a significantly reduced cost. We combine structural databases for amorphous carbon and graphene, which we extend substantially by adding suitable configurations, for example, for defects in graphene and other nanostructures. The final potential is fitted to reference data computed using the optB88-vdW density functional theory (DFT) functional. Dispersion interactions, which are crucial to describe multilayer carbonaceous materials, are therefore implicitly included. We additionally account for long-range dispersion interactions using a semianalytical two-body term and show that an improved model can be obtained through an optimization of the many-body smooth overlap of atomic positions descriptor. We rigorously test the potential on lattice parameters, bond lengths, formation energies, and phonon dispersions of numerous carbon allotropes. We compare the formation energies of an extensive set of defect structures, surfaces, and surface reconstructions to DFT reference calculations. The present work demonstrates the ability to combine, in the same ML model, the previously attained flexibility required for amorphous carbon [V. L. Deringer and G. Csányi, Phys. Rev. B 95, 094203 (2017)] with the high numerical accuracy necessary for crystalline graphene [Rowe et al., Phys. Rev. B 97, 054303 (2018)], thereby providing an interatomic potential that will be applicable to a wide range of applications concerning diverse forms of bulk and nanostructured carbon.

Identifying and Tracking Defects in Dynamic Supramolecular Polymers.

A central paradigm of self-assembly is to create ordered structures starting from molecular monomers that spontaneously recognize and interact with each other via noncovalent interactions. In recent years, great efforts have been directed toward perfecting the design of a variety of supramolecular polymers and materials with different architectures. The resulting structures are often thought of as ideally perfect, defect-free supramolecular fibers, micelles, vesicles, etc., having an intrinsic dynamic character, which are typically studied at the level of statistical ensembles to assess their average properties. However, molecular simulations recently demonstrated that local defects that may be present or may form in these assemblies, and which are poorly captured by conventional approaches, are key to controlling their dynamic behavior and properties. The study of these defects poses considerable challenges, as the flexible/dynamic nature of these soft systems makes it difficult to identify what effectively constitutes a defect and to characterize its stability and evolution. Here, we demonstrate the power of unsupervised machine-learning techniques to systematically identify and compare defects in supramolecular polymer variants in different conditions, using as a benchmark 5 Å resolution coarse-grained molecular simulations of a family of supramolecular polymers. We show that this approach allows a complete data-driven characterization of the internal structure and dynamics of these complex assemblies and of the dynamic pathways for defects formation and resorption. This provides a useful, generally applicable approach to unambiguously identify defects in these dynamic self-assembled materials and to classify them based on their structure, stability, and dynamics.

Using Data-Reduction Techniques to Analyze Biomolecular Trajectories.

This chapter discusses the way in which dimensionality reduction algorithms such as diffusion maps and sketch-map can be used to analyze molecular dynamics trajectories. The first part discusses how these various algorithms function as well as practical issues such as landmark selection and how these algorithms can be used when the data to be analyzed comes from enhanced sampling trajectories. In the later part a comparison between the results obtained by applying various algorithms to two sets of sample data is performed and discussed. This section is then followed by a summary of how one algorithm in particular, sketch-map, has been applied to a range of problems. The chapter concludes with a discussion on the directions that we believe this field is currently moving.

Using Dimensionality Reduction to Analyze Protein Trajectories.

In recent years the analysis of molecular dynamics trajectories using dimensionality reduction algorithms has become commonplace. These algorithms seek to find a low-dimensional representation of a trajectory that is, according to a well-defined criterion, optimal. A number of different strategies for generating projections of trajectories have been proposed but little has been done to systematically compare how these various approaches fare when it comes to analysing trajectories for biomolecules in explicit solvent. In the following paper, we have thus analyzed a molecular dynamics trajectory of the C-terminal fragment of the immunoglobulin binding domain B1 of protein G of Streptococcus modeled in explicit solvent using a range of different dimensionality reduction algorithms. We have then tried to systematically compare the projections generated using each of these algorithms by using a clustering algorithm to find the positions and extents of the basins in the high-dimensional energy landscape. We find that no algorithm outshines all the other in terms of the quality of the projection it generates. Instead, all the algorithms do a reasonable job when it comes to building a projection that separates some of the configurations that lie in different basins. Having said that, however, all the algorithms struggle to project the basins because they all have a large intrinsic dimensionality.

Atomic Motif Recognition in (Bio)Polymers: Benchmarks From the Protein Data Bank.

Rationalizing the structure and structure-property relations for complex materials such as polymers or biomolecules relies heavily on the identification of local atomic motifs, e.g., hydrogen bonds and secondary structure patterns, that are seen as building blocks of more complex supramolecular and mesoscopic structures. Over the past few decades, several automated procedures have been developed to identify these motifs in proteins given the atomic structure. Being based on a very precise understanding of the specific interactions, these heuristic criteria formulate the question in a way that implies the answer, by defining a list of motifs based on those that are known to be naturally occurring. This makes them less likely to identify unexpected phenomena, such as the occurrence of recurrent motifs in disordered segments of proteins, and less suitable to be applied to different polymers whose structure is not driven by hydrogen bonds, or even to polypeptides when appearing in unusual, non-biological conditions. Here we discuss how unsupervised machine learning schemes can be used to recognize patterns based exclusively on the frequency with which different motifs occur, taking high-resolution structures from the Protein Data Bank as benchmarks. We first discuss the application of a density-based motif recognition scheme in combination with traditional representations of protein structure (namely, interatomic distances and backbone dihedrals). Then, we proceed one step further toward an entirely unbiased scheme by using as input a structural representation based on the atomic density and by employing supervised classification to objectively assess the role played by the representation in determining the nature of atomic-scale patterns.

Recognizing Local and Global Structural Motifs at the Atomic Scale.

Most of the current understanding of structure-property relations at the molecular and the supramolecular scales can be formulated in terms of the stability of and the interactions between a limited number of recurring structural motifs (e.g., H-bonds, coordination polyhedra, and protein secondary structure). Here we demonstrate an algorithm to automatically recognize such patterns, based on the identification of local maxima in the probability distributions observed in atomistic computer simulations, which is robust to the dimensionality and the sparsity of the reference atomistic data. We first discuss its main features, demonstrating some on artificial data sets, and then show how it can be applied to identify coordination environments in Lennard-Jones clusters and to recognize secondary-structure patterns in the simulation of an oligopeptide. To assess the applicability of this algorithm for motifs that involve several interdependent degrees of freedom, we also employ it to identify groups of conformers of the cluster and the polypeptide, considered in their entirety. The motifs identified by analyzing atomistic simulations can be used to interpret and rationalize the stability and behavior of the system at hand, and also as a tool to accelerate sampling, in association with biased molecular dynamics schemes.

Anharmonic and Quantum Fluctuations in Molecular Crystals: A First-Principles Study of the Stability of Paracetamol.

Molecular crystals often exist in multiple competing polymorphs, showing significantly different physicochemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful form, a real challenge due to the combinatorial search space, and the complex interplay of subtle effects that work together to determine the relative stability of different structures. Here we take a comprehensive approach based on different flavors of thermodynamic integration in order to estimate all contributions to the free energies of these systems with density-functional theory, including the oft-neglected anharmonic contributions and nuclear quantum effects. We take the two main stable forms of paracetamol as a paradigmatic example. We find that anharmonic contributions, different descriptions of van der Waals interactions, and nuclear quantum effects all matter to quantitatively determine the stability of different phases. Our analysis highlights the many challenges inherent in the development of a quantitative and predictive framework to model molecular crystals. However, it also indicates which of the components of the free energy can benefit from a cancellation of errors that can redeem the predictive power of approximate models, and suggests simple steps that could be taken to improve the reliability of ab initio crystal structure prediction.

Probing Defects and Correlations in the Hydrogen-Bond Network of ab Initio Water.

The hydrogen-bond network of water is characterized by the presence of coordination defects relative to the ideal tetrahedral network of ice, whose fluctuations determine the static and time-dependent properties of the liquid. Because of topological constraints, such defects do not come alone but are highly correlated coming in a plethora of different pairs. Here we discuss in detail such correlations in the case of ab initio water models and show that they have interesting similarities to regular and defective solid phases of water. Although defect correlations involve deviations from idealized tetrahedrality, they can still be regarded as weaker hydrogen bonds that retain a high degree of directionality. We also investigate how the structure and population of coordination defects is affected by approximations to the interatomic potential, finding that, in most cases, the qualitative features of the hydrogen-bond network are remarkably robust.

Recognizing molecular patterns by machine learning: an agnostic structural definition of the hydrogen bond.

The concept of chemical bonding can ultimately be seen as a rationalization of the recurring structural patterns observed in molecules and solids. Chemical intuition is nothing but the ability to recognize and predict such patterns, and how they transform into one another. Here, we discuss how to use a computer to identify atomic patterns automatically, so as to provide an algorithmic definition of a bond based solely on structural information. We concentrate in particular on hydrogen bonding--a central concept to our understanding of the physical chemistry of water, biological systems, and many technologically important materials. Since the hydrogen bond is a somewhat fuzzy entity that covers a broad range of energies and distances, many different criteria have been proposed and used over the years, based either on sophisticate electronic structure calculations followed by an energy decomposition analysis, or on somewhat arbitrary choices of a range of structural parameters that is deemed to correspond to a hydrogen-bonded configuration. We introduce here a definition that is univocal, unbiased, and adaptive, based on our machine-learning analysis of an atomistic simulation. The strategy we propose could be easily adapted to similar scenarios, where one has to recognize or classify structural patterns in a material or chemical compound.