Identification and analysis of 3D pores in packed particulate materials

We took the classic 'guess the number of beans in a jar game' and amplified the research question. Rather than estimate the quantity of particles in the jar, we sought to characterize the spaces between them. Here we present an approach for delineating the pockets of empty space (three-dimensional pores) between packed particles, which are hotspots for activity in applications and natural phenomena that deal with particulate materials. We utilize techniques from graph theory to exploit information about particle configuration that allows us to locate important spatial landmarks within the void space. These landmarks are the basis for our pore segmentation, where we consider both interior pores as well as entrance and exit pores into and out of the structure. Our method is robust for particles of varying size, form, stiffness and configuration, which allows us to study and compare three-dimensional pores across a range of packed particle types. We report striking relationships between particles and pores that are described mathematically, and we offer a visual library of pore types. With a meaningful discretization of void space, we demonstrate that packed particles can be understood not by their solid space, but by their empty space.

Mixing properties of bi-disperse ellipsoid assemblies: mean-field behaviour in a granular matter experiment

The structure and spatial statistical properties of amorphous ellipsoid assemblies have profound scientific and industrial significance in many systems, from cell assays to granular materials. This paper uses a fundamental theoretical relationship for mixture distributions to explain the observations of an extensive X-ray computed tomography study of granular ellipsoidal packings. We study a size-bi-disperse mixture of two types of ellipsoids of revolutions that have the same aspect ratio of α ≈ 0.57 and differ in size, by about 10% in linear dimension, and compare these to mono-disperse systems of ellipsoids with the same aspect ratio. Jammed configurations with a range of packing densities are achieved by employing different tapping protocols. We numerically interrogate the final packing configurations by analyses of the local packing fraction distributions calculated from the Voronoi diagrams. Our main finding is that the bi-disperse ellipsoidal packings studied here can be interpreted as a mixture of two uncorrelated mono-disperse packings, insensitive to the compaction protocol. Our results are consolidated by showing that the local packing fraction shows no correlation beyond their first shell of neighbours in the binary mixtures. We propose a model of uncorrelated binary mixture distribution that describes the observed experimental data with high accuracy. This analysis framework will enable future studies to test whether the observed mean-field behaviour is specific to the particular granular system or the specific parameter values studied here or if it is observed more broadly in other bi-disperse non-spherical particle systems.

Core packing of well-defined X-ray and NMR structures is the same

Numerous studies have investigated the differences and similarities between protein structures determined by solution NMR spectroscopy and those determined by X-ray crystallography. A fundamental question is whether any observed differences are due to differing methodologies or to differences in the behavior of proteins in solution versus in the crystalline state. Here, we compare the properties of the hydrophobic cores of high-resolution protein crystal structures and those in NMR structures, determined using increasing numbers and types of restraints. Prior studies have reported that many NMR structures have denser cores compared with those of high-resolution X-ray crystal structures. Our current work investigates this result in more detail and finds that these NMR structures tend to violate basic features of protein stereochemistry, such as small non-bonded atomic overlaps and few Ramachandran and sidechain dihedral angle outliers. We find that NMR structures solved with more restraints, and which do not significantly violate stereochemistry, have hydrophobic cores that have a similar size and packing fraction as their counterparts determined by X-ray crystallography at high resolution. These results lead us to conclude that, at least regarding the core packing properties, high-quality structures determined by NMR and X-ray crystallography are the same, and the differences reported earlier are most likely a consequence of methodology, rather than fundamental differences between the protein in the two different environments.

Analyses of protein cores reveal fundamental differences between solution and crystal structures

There have been several studies suggesting that protein structures solved by NMR spectroscopy and X-ray crystallography show significant differences. To understand the origin of these differences, we assembled a database of high-quality protein structures solved by both methods. We also find significant differences between NMR and crystal structures-in the root-mean-square deviations of the C α atomic positions, identities of core amino acids, backbone, and side-chain dihedral angles, and packing fraction of core residues. In contrast to prior studies, we identify the physical basis for these differences by modeling protein cores as jammed packings of amino acid-shaped particles. We find that we can tune the jammed packing fraction by varying the degree of thermalization used to generate the packings. For an athermal protocol, we find that the average jammed packing fraction is identical to that observed in the cores of protein structures solved by X-ray crystallography. In contrast, highly thermalized packing-generation protocols yield jammed packing fractions that are even higher than those observed in NMR structures. These results indicate that thermalized systems can pack more densely than athermal systems, which suggests a physical basis for the structural differences between protein structures solved by NMR and X-ray crystallography.

Using physical features of protein core packing to distinguish real proteins from decoys

The ability to consistently distinguish real protein structures from computationally generated model decoys is not yet a solved problem. One route to distinguish real protein structures from decoys is to delineate the important physical features that specify a real protein. For example, it has long been appreciated that the hydrophobic cores of proteins contribute significantly to their stability. We used two sources to obtain datasets of decoys to compare with real protein structures: submissions to the biennial Critical Assessment of protein Structure Prediction competition, in which researchers attempt to predict the structure of a protein only knowing its amino acid sequence, and also decoys generated by 3DRobot, which have user-specified global root-mean-squared deviations from experimentally determined structures. Our analysis revealed that both sets of decoys possess cores that do not recapitulate the key features that define real protein cores. In particular, the model structures appear more densely packed (because of energetically unfavorable atomic overlaps), contain too few residues in the core, and have improper distributions of hydrophobic residues throughout the structure. Based on these observations, we developed a feed-forward neural network, which incorporates key physical features of protein cores, to predict how well a computational model recapitulates the real protein structure without knowledge of the structure of the target sequence. By identifying the important features of protein structure, our method is able to rank decoy structures with similar accuracy to that obtained by state-of-the-art methods that incorporate many additional features. The small number of physical features makes our model interpretable, emphasizing the importance of protein packing and hydrophobicity in protein structure prediction.

Patchy particles by self-assembly of star copolymers on a spherical substrate: Thomson solutions in a geometric problem with a color constraint

Confinement or geometric frustration is known to alter the structure of soft matter, including copolymeric melts, and can consequently be used to tune structure and properties. Here we investigate the self-assembly of ABC and ABB 3-miktoarm star copolymers confined to a spherical shell using coarse-grained dissipative particle dynamics simulations. In bulk and flat geometries the ABC stars form hexagonal tilings, but this is topologically prohibited in a spherical geometry which normally is alleviated by forming pentagonal tiles. However, the molecular architecture of the ABC stars implies an additional 'color constraint' which only allows even tilings (where all polygons have an even number of edges) and we study the effect of these simultaneous constraints. We find that both ABC and ABB systems form spherical tiling patterns, the type of which depends on the radius of the spherical substrate. For small spherical substrates, all solutions correspond to patterns solving the Thomson problem of placing mobile repulsive electric charges on a sphere. In ABC systems we find three coexisting, possibly different tilings, one in each color, each of them solving the Thomson problem simultaneously. For all except the smallest substrates, we find competing solutions with seemingly degenerate free energies that occur with different probabilities. Statistically, an observer who is blind to the differences between B and C can tell from the structure of the A domains if the system is an ABC or an ABB star copolymer system.

Geometric effects in random assemblies of ellipses

Assemblies of anisotropic particles commonly appear in studies of active many-body systems. However, in two dimensions, the geometric ramifications of the finite density of such objects are not entirely understood. To fully characterize these effects, we perform an in-depth study of random assemblies generated by a slow compression of frictionless elliptical particles. The obtained configurations are then analysed using the Set Voronoi tessellation, which takes the particle shape into account. Not only do we analyse most scalar and vectorial morphological measures, which are commonly discussed in the literature or which have recently been addressed in experiments, but we also systematically explore the correlations between them. While in a limited range of parameters similarities with findings in 3D assemblies could be identified, important differences are found when a broad range of aspect ratios and packing fractions are considered. The data discussed in this study should thus provide a unique reference set such that geometric effects and differences from random assemblies could be clearly identified in more complex systems, including ones with soft and active particles that are typically found in biological systems.

Void distributions reveal structural link between jammed packings and protein cores

Dense packing of hydrophobic residues in the cores of globular proteins determines their stability. Recently, we have shown that protein cores possess packing fraction ϕ≈0.56, which is the same as dense, random packing of amino-acid-shaped particles. In this article, we compare the structural properties of protein cores and jammed packings of amino-acid-shaped particles in much greater depth by measuring their local and connected void regions. We find that the distributions of surface Voronoi cell volumes and local porosities obey similar statistics in both systems. We also measure the probability that accessible, connected void regions percolate as a function of the size of a spherical probe particle and show that both systems possess the same critical probe size. We measure the critical exponent τ that characterizes the size distribution of connected void clusters at the onset of percolation. We find that the cluster size statistics are similar for void percolation in packings of amino-acid-shaped particles and randomly placed spheres, but different from that for void percolation in jammed sphere packings. We propose that the connected void regions are a defining structural feature of proteins and can be used to differentiate experimentally observed proteins from decoy structures that are generated using computational protein design software. This work emphasizes that jammed packings of amino-acid-shaped particles can serve as structural and mechanical analogs of protein cores, and could therefore be useful in modeling the response of protein cores to cavity-expanding and -reducing mutations.

Skinny emulsions take on granular matter

Our understanding of the structural features of foams and emulsions has advanced significantly over the last 20 years. However, with a search for "super-stable" liquid dispersions, foam and emulsion science employs increasingly complex formulations which create solid-like visco-elastic layers at the bubble/drop surfaces. These lead to elastic, adhesive and frictional forces between bubbles/drops, impacting strongly how they pack and deform against each other, asking for an adaptation of the currently available structural description. The possibility to modify systematically the interfacial properties makes these dispersions ideal systems for the exploration of soft granular materials with complex interactions. We present here a first systematic analysis of the structural features of such a system using a model silicone emulsion containing millimetre-sized polyethylene glycol drops (PEG). Solid-like drop surfaces are obtained by polymeric cross-linking reactions at the PEG-silicone interface. Using a novel droplet-micromanipulator, we highlight the presence of elastic, adhesive and frictional interactions between two drops. We then provide for the first time a full tomographic analysis of the structural features of these emulsions. An in-depth analysis of the angle of repose, local volume fraction distributions, pair correlation functions and the drop deformations for different skin formulations allow us to put in evidence the striking difference with "ordinary" emulsions having fluid-like drop surfaces. While strong analogies with frictional hard-sphere systems can be drawn, these systems display a set of unique features due to the high deformability of the drops which await systematic exploration.