Discovering dynamic laws from observations: The case of self-propelled, interacting colloids.

Active matter spans a wide range of time and length scales, from groups of cells and synthetic self-propelled colloids to schools of fish and flocks of birds. The theoretical framework describing these systems has shown tremendous success in finding universal phenomenology. However, further progress is often burdened by the difficulty of determining forces controlling the dynamics of individual elements within each system. Accessing this local information is pivotal for the understanding of the physics governing an ensemble of active particles and for the creation of numerical models capable of explaining the observed collective phenomena. In this work, we present ActiveNet, a machine-learning tool consisting of a graph neural network that uses the collective motion of particles to learn active and two-body forces controlling their individual dynamics. We verify our approach using numerical simulations of active Brownian particles, active particles undergoing underdamped Langevin dynamics, and chiral active Brownian particles considering different interaction potentials and values of activity. Interestingly, ActiveNet can equally learn conservative or nonconservative forces as well as torques. Moreover, ActiveNet has proven to be a useful tool to learn the stochastic contribution to the forces, enabling the estimation of the diffusion coefficients. Therefore, all coefficients of the equation of motion of Active Brownian Particles are captured. Finally, we apply ActiveNet to experiments of electrophoretic Janus particles, extracting the active and two-body forces controlling colloids' dynamics. On the one side, we have learned that the active force depends on the electric field and area fraction. On the other side, we have also discovered a dependence of the two-body interaction with the electric field that leads us to propose that the dominant force between active colloids is a screened electrostatic interaction with a constant length scale. We believe that the proposed methodological tool, ActiveNet, might open a new avenue for the study and modeling of experimental suspensions of active particles.

Geometrically frustrated interactions drive structural complexity in amorphous calcium carbonate.

Amorphous calcium carbonate is an important precursor for biomineralization in marine organisms. Key outstanding problems include understanding the structure of amorphous calcium carbonate and rationalizing its metastability as an amorphous phase. Here we report high-quality atomistic models of amorphous calcium carbonate generated using state-of-the-art interatomic potentials to help guide fits to X-ray total scattering data. Exploiting a recently developed inversion approach, we extract from these models the effective Ca⋯Ca interaction potential governing the structure. This potential contains minima at two competing distances, corresponding to the two different ways that carbonate ions bridge Ca2+-ion pairs. We reveal an unexpected mapping to the Lennard-Jones-Gauss model normally studied in the context of computational soft matter. The empirical model parameters for amorphous calcium carbonate take values known to promote structural complexity. We thus show that both the complex structure and its resilience to crystallization are actually encoded in the geometrically frustrated effective interactions between Ca2+ ions.

Measuring many-body distribution functions in fluids using test-particle insertion.

We derive a hierarchy of equations, which allow a general n-body distribution function to be measured by test-particle insertion of between 1 and n particles. We apply it to measure the pair and three-body distribution functions in a simple fluid using snapshots from Monte Carlo simulations in the grand canonical ensemble. The resulting distribution functions obtained from insertion methods are compared with the conventional distance-histogram method: the insertion approach is shown to overcome the drawbacks of the histogram method, offering enhanced structural resolution and a more straightforward normalization. At high particle densities, the insertion method starts breaking down, which can be delayed by utilizing the underlying hierarchical structure of the insertion method. Our method will be especially useful in characterizing the structure of inhomogeneous fluids and investigating closure approximations in liquid state theory.

Ion binding with charge inversion combined with screening modulates DEAD box helicase phase transitions.

Membraneless organelles, or biomolecular condensates, enable cells to compartmentalize material and processes into unique biochemical environments. While specific, attractive molecular interactions are known to stabilize biomolecular condensates, repulsive interactions, and the balance between these opposing forces, are largely unexplored. Here, we demonstrate that repulsive and attractive electrostatic interactions regulate condensate stability, internal mobility, interfaces, and selective partitioning of molecules both in vitro and in cells. We find that signaling ions, such as calcium, alter repulsions between model Ddx3 and Ddx4 condensate proteins by directly binding to negatively charged amino acid sidechains and effectively inverting their charge, in a manner fundamentally dissimilar to electrostatic screening. Using a polymerization model combined with generalized stickers and spacers, we accurately quantify and predict condensate stability over a wide range of pH, salt concentrations, and amino acid sequences. Our model provides a general quantitative treatment for understanding how charge and ions reversibly control condensate stability.

Surface tension measurement and calculation of model biomolecular condensates.

The surface tension of liquid-like protein-rich biomolecular condensates is an emerging physical principle governing the mesoscopic interior organisation of biological cells. In this study, we present a method to evaluate the surface tension of model biomolecular condensates, through straighforward sessile drop measurements of capillary lengths and condensate densities. Our approach bypasses the need for characterizing condensate viscosities, which was required in previously reported techniques. We demonstrate this method using model condensates comprising two mutants of the intrinsically disordered protein Ddx4N. Notably, we uncover a detrimental impact of increased protein net charge on the surface tension of Ddx4N condensates. Furthermore, we explore the application of Scheutjens-Fleer theory, calculating condensate surface tensions through a self-consistent mean-field framework using Flory-Huggins interaction parameters. This relatively simple theory provides semi-quantitative accuracy in predicting Ddx4N condensate surface tensions and enables the evaluation of molecular organisation at condensate surfaces. Our findings shed light on the molecular details of fluid-fluid interfaces in biomolecular condensates.

Topology of Orientational Defects in Confined Smectic Liquid Crystals.

We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization, this charge is distributed in pointlike units of quarter-integer magnitude, which we identify with tetratic disclinations located at the end points and nodes. This coexisting nematic and tetratic order is analyzed with the help of extensive Monte Carlo simulations for a broad range of two-dimensional confining geometries as well as colloidal experiments, showing how the observed defect networks can be universally reconstructed from simple building blocks. We further find that the curvature of the confining wall determines the anchoring behavior of grain boundaries, such that the number of nodes in the emerging networks and the location of their end points can be tuned by changing the number and smoothness of corners, respectively.

Characterization of MIPS in a suspension of repulsive active Brownian particles through dynamical features.

We study a two-dimensional system composed by Active Brownian Particles (ABPs), focusing on the onset of Motility Induced Phase Separation (MIPS), by means of molecular dynamics simulations. For a pure hard-disk system with no translational diffusion, the phase diagram would be completely determined by their density and Péclet number. In our model, two additional effects are present: translational noise and the overlap of particles; we study the effects of both in the phase space. As we show, the second effect can be mitigated if we use, instead of the standard Weeks-Chandler-Andersen potential, a stiffer potential: the pseudo-hard sphere potential. Moreover, in determining the boundary of our phase space, we explore different approaches to detect MIPS and conclude that observing dynamical features, via the non-Gaussian parameter, is more efficient than observing structural ones, such as through the local density distribution function. We also demonstrate that the Vogel-Fulcher equation successfully reproduces the decay of the diffusion as a function of density, with the exception of very high densities. Thus, in this regard, the ABP system behaves similar to a fragile glass.

Stabilisation of hollow colloidal TiO2 particles by partial coating with evenly distributed lobes.

Photo-catalytically active crystalline TiO2 has attracted special attention due to its relevance for renewable energy and is typically obtained by the calcination of amorphous TiO2. However, stabilising hollow colloidal TiO2 particles against aggregation during calcination without compromising their photocatalytic activity poses two conflicting demands: to be stable their surface needs to be coated, while efficient photocatalysis requires an exposed TiO2 surface. Here, this incompatibility is resolved by partially coating TiO2 shells with evenly distributed 3-trimethoxysilyl propyl methacrylate (TPM) lobes. These lobes act both as steric barriers and surface charge enhancers that efficiently stabilise the TiO2 shells against aggregation during calcination. The morphology of the TPM lobes and their coverage, and the associated particle stability during the calcination-induced TiO2 crystallization, can be controlled by the pH and the contact angle between TPM and TiO2. The crystal structure and the grain size of the coated TiO2 shells are controlled by varying the calcination temperature, which allows tuning their photocatalytic activity. Finally, the durable photocatalytic activity over many usage cycles of the coated TiO2 compared to uncoated shells is demonstrated in a simple way by measuring the photo-degradation of a fluorescent dye. Our approach offers a general strategy for stabilising colloidal materials, without compromising access to their active surfaces.

Particle-resolved topological defects of smectic colloidal liquid crystals in extreme confinement.

Confined samples of liquid crystals are characterized by a variety of topological defects and can be exposed to external constraints such as extreme confinements with nontrivial topology. Here we explore the intrinsic structure of smectic colloidal layers dictated by the interplay between entropy and an imposed external topology. Considering an annular confinement as a basic example, a plethora of competing states is found with nontrivial defect structures ranging from laminar states to multiple smectic domains and arrays of edge dislocations, which we refer to as Shubnikov states in formal analogy to the characteristic of type-II superconductors. Our particle-resolved results, gained by a combination of real-space microscopy of thermal colloidal rods and fundamental-measure-based density functional theory of hard anisotropic bodies, agree on a quantitative level.

Shaping colloidal bananas to reveal biaxial, splay-bend nematic, and smectic phases.

Understanding the impact of curvature on the self-assembly of elongated microscopic building blocks, such as molecules and proteins, is key to engineering functional materials with predesigned structure. We develop model "banana-shaped" colloidal particles with tunable dimensions and curvature, whose structure and dynamics are accessible at the particle level. By heating initially straight rods made of SU-8 photoresist, we induce a controllable shape deformation that causes the rods to buckle into banana-shaped particles. We elucidate the phase behavior of differently curved colloidal bananas using confocal microscopy. Although highly curved bananas only form isotropic phases, less curved bananas exhibit very rich phase behavior, including biaxial nematic phases, polar and antipolar smectic-like phases, and even the long-predicted, elusive splay-bend nematic phase.

Phage liquid crystalline droplets form occlusive sheaths that encapsulate and protect infectious rod-shaped bacteria.

The opportunistic pathogen Pseudomonas aeruginosa is a major cause of antibiotic-tolerant infections in humans. P. aeruginosa evades antibiotics in bacterial biofilms by up-regulating expression of a symbiotic filamentous inoviral prophage, Pf4. We investigated the mechanism of phage-mediated antibiotic tolerance using biochemical reconstitution combined with structural biology and high-resolution cellular imaging. We resolved electron cryomicroscopy atomic structures of Pf4 with and without its linear single-stranded DNA genome, and studied Pf4 assembly into liquid crystalline droplets using optical microscopy and electron cryotomography. By biochemically replicating conditions necessary for antibiotic protection, we found that phage liquid crystalline droplets form phase-separated occlusive compartments around rod-shaped bacteria leading to increased bacterial survival. Encapsulation by these compartments was observed even when inanimate colloidal rods were used to mimic rod-shaped bacteria, suggesting that shape and size complementarity profoundly influences the process. Filamentous inoviruses are pervasive across prokaryotes, and in particular, several Gram-negative bacterial pathogens including Neisseria meningitidis, Vibrio cholerae, and Salmonella enterica harbor these prophages. We propose that biophysical occlusion mediated by secreted filamentous molecules such as Pf4 may be a general strategy of bacterial survival in harsh environments.

Detection of magnetic field effects by confocal microscopy.

Certain pairs of paramagnetic species generated under conservation of total spin angular momentum are known to undergo magnetosensitive processes. Two prominent examples of systems exhibiting these so-called magnetic field effects (MFEs) are photogenerated radical pairs created from either singlet or triplet molecular precursors, and pairs of triplet states generated by singlet fission. Here, we showcase confocal microscopy as a powerful technique for the investigation of such phenomena. We first characterise the instrument by studying the field-sensitive chemistry of two systems in solution: radical pairs formed in a cryptochrome protein and the flavin mononucleotide/hen egg-white lysozyme model system. We then extend these studies to single crystals. Firstly, we report temporally and spatially resolved MFEs in flavin-doped lysozyme single crystals. Anisotropic magnetic field effects are then reported in tetracene single crystals. Finally, we discuss the future applications of confocal microscopy for the study of magnetosensitive processes with a particular focus on the cryptochrome-based chemical compass believed to lie at the heart of animal magnetoreception.

Single-Molecule, Super-Resolution, and Functional Analysis of G Protein-Coupled Receptor Behavior Within the T Cell Immunological Synapse.

A central process in immunity is the activation of T cells through interaction of T cell receptors (TCRs) with agonistic peptide-major histocompatibility complexes (pMHC) on the surface of antigen presenting cells (APCs). TCR-pMHC binding triggers the formation of an extensive contact between the two cells termed the immunological synapse, which acts as a platform for integration of multiple signals determining cellular outcomes, including those from multiple co-stimulatory/inhibitory receptors. Contributors to this include a number of chemokine receptors, notably CXC-chemokine receptor 4 (CXCR4), and other members of the G protein-coupled receptor (GPCR) family. Although best characterized as mediators of ligand-dependent chemotaxis, some chemokine receptors are also recruited to the synapse and contribute to signaling in the absence of ligation. How these and other GPCRs integrate within the dynamic structure of the synapse is unknown, as is how their normally migratory Gαi-coupled signaling is terminated upon recruitment. Here, we report the spatiotemporal organization of several GPCRs, focusing on CXCR4, and the G protein Gαi2 within the synapse of primary human CD4+ T cells on supported lipid bilayers, using standard- and super-resolution fluorescence microscopy. We find that CXCR4 undergoes orchestrated phases of reorganization, culminating in recruitment to the TCR-enriched center. This appears to be dependent on CXCR4 ubiquitination, and does not involve stable interactions with TCR microclusters, as viewed at the nanoscale. Disruption of this process by mutation impairs CXCR4 contributions to cellular activation. Gαi2 undergoes active exclusion from the synapse, partitioning from centrally-accumulated CXCR4. Using a CRISPR-Cas9 knockout screen, we identify several diverse GPCRs with contributions to T cell activation, most significantly the sphingosine-1-phosphate receptor S1PR1, and the oxysterol receptor GPR183. These, and other GPCRs, undergo organization similar to CXCR4; including initial exclusion, centripetal transport, and lack of receptor-TCR interactions. These constitute the first observations of GPCR dynamics within the synapse, and give insights into how these receptors may contribute to T cell activation. The observation of broad GPCR contributions to T cell activation also opens the possibility that modulating GPCR expression in response to cell status or environment may directly regulate responsiveness to pMHC.

Model-Free Measurement of the Pair Potential in Colloidal Fluids Using Optical Microscopy.

We report a straightforward, model-free approach for measuring pair potentials from particle-coordinate data, based on enforcing consistency between the pair distribution function measured separately by the distance-histogram and test-particle insertion routes. We demonstrate the method's accuracy and versatility in simulations of simple fluids, before applying it to an experimental system composed of superparamagnetic colloidal particles. The method will enable experimental investigations into many-body interactions and allow for effective coarse graining of interactions from simulations.

Interrupted Motility Induced Phase Separation in Aligning Active Colloids.

Switching on high activity in a relatively dense system of active Janus colloids, we observe fast clustering, followed by cluster aggregation towards full phase separation. The phase separation process is however interrupted when large enough clusters start breaking apart. Following the cluster size distribution as a function of time, we identify three successive dynamical regimes. Tracking both the particle positions and orientations, we characterize the structural ordering and alignment in the growing clusters and thereby unveil the mechanisms at play in these regimes. In particular, we identify how alignment between the neighboring particles is responsible for the interruption of the full phase separation. Our large scale quantification of the phase separation kinetics in active colloids points towards the new physics observed when both alignment and short-range repulsions are present.

Dynamics of individual Brownian rods in a microchannel flow.

We study the orientational dynamics of heavy silica microrods flowing through a microfluidic channel. Comparing experiments and Brownian dynamics simulations we identify different particle orbits, in particular in-plane tumbling behavior, which cannot be explained by classical Jeffery theory, and we relate this behavior to the rotational diffusion of the rods. By constructing the full, three-dimensional, orientation distribution, we describe the rod trajectories and quantify the persistence of Jeffery orbits using temporal correlation functions of the Jeffery constant. We find that our colloidal rods lose memory of their initial configuration in about a second, corresponding to half a Jeffery period.

Synthesis of Colloidal SU-8 Polymer Rods Using Sonication.

The bulk synthesis of fluorescent colloidal SU-8 polymer rods with tunable dimensions is described. The colloidal SU-8 rods are prepared by shearing an emulsion of SU-8 polymer droplets and then exposing the resulting non-Brownian rods to ultrasonic waves, which breaks them into colloidal rods with typical lengths of 3.5-10 µm and diameters of 0.4-1 µm. The rods are stable in both aqueous and apolar solvents, and by varying the composition of apolar solvent mixtures both the difference in refractive index and mass density between particles and solvent can be independently controlled. Consequently, these colloidal SU-8 rods can be used in both 3D confocal microscopy and optical trapping experiments while carefully tuning the effect of gravity. This is demonstrated by using confocal microscopy to image the liquid crystalline phases and the isotropic-nematic interface formed by the colloidal SU-8 rods and by optically trapping single rods in water. Finally, the simultaneous confocal imaging and optical manipulation of multiple SU-8 rods in the isotropic phase is shown.

Colloidal Liquid Crystals Confined to Synthetic Tactoids.

When a liquid crystal forming particles are confined to a spatial volume with dimensions comparable to that of their own size, they face a complex trade-off between their global tendency to align and the local constraints imposed by the boundary conditions. This interplay may lead to a non-trivial orientational patterns that strongly depend on the geometry of the confining volume. This novel regime of liquid crystalline behavior can be probed with colloidal particles that are macro-aggregates of biomolecules. Here we study director fields of filamentous fd-viruses in quasi-2D lens-shaped chambers that mimic the shape of tactoids, the nematic droplets that form during isotropic-nematic phase separation. By varying the size and aspect ratio of the chambers we force these particles into confinements that vary from circular to extremely spindle-like shapes and observe the director field using fluorescence microscopy. In the resulting phase diagram, next to configurations predicted earlier for 3D tactoids, we find a number of novel configurations. Using Monte Carlo Simulations, we show that these novel states are metastable, yet long-lived. Their multiplicity can be explained by the co-existence of multiple dynamic relaxation pathways leading to the final stable states.

A new family of urea-based low molecular-weight organogelators for environmental remediation: the influence of structure.

Gelation processes grant access to a wealth of soft materials with tailorable properties, in applications as diverse as environmental remediation, biomedicine and electronics. Several classes of self-assembling gelators have been studied and employ non-covalent bonds to direct assembly, but recently attention has come to focus on how the overall shape of the gelator molecule impacts its gelation. Here we study a new sub-family of low molecular weight organogelators and explore how steric rearrangement influences their gelation. The gels produced are characterised with X-ray diffraction and small-angle neutron scattering (SANS) to probe their ex situ and in situ gelation mechanisms. The best examples were then tested for environmental remediation applications, gelling petrol and oils in the presence of water and salts.

Communication: Contact values of pair distribution functions in colloidal hard disks by test-particle insertion.

We apply Henderson's method for measuring the cavity distribution function y(r) [J. Henderson, Mol. Phys. 48, 389 (1983)] to obtain the pair distribution function at contact, g(σ+). In contrast to the conventional distance-histogram method, no approximate extrapolation to contact is required. The resulting equation of state from experiments and simulations of hard disks agrees well with the scaled particle theory prediction up to high fluid packing fractions. We also provide the first experimental measurement of y(r) inside the hard core, which will allow for a more complete comparison with theory. The method's flexibility is further illustrated by measuring the partial pair distribution functions of binary hard-disk mixtures in simulation. The equation for the contact values can be used to derive familiar results from statistical geometry.