Active Spaghetti: Collective Organization in Cyanobacteria.

Filamentous cyanobacteria can show fascinating examples of nonequilibrium self-organization, which, however, are not well understood from a physical perspective. We investigate the motility and collective organization of colonies of these simple multicellular lifeforms. As their area density increases, linear chains of cells gliding on a substrate show a transition from an isotropic distribution to bundles of filaments arranged in a reticulate pattern. Based on our experimental observations of individual behavior and pairwise interactions, we introduce a nonreciprocal model accounting for the filaments' large aspect ratio, fluctuations in curvature, motility, and nematic interactions. This minimal model of active filaments recapitulates the observations, and rationalizes the appearance of a characteristic length scale in the system, based on the Péclet number of the cyanobacteria filaments.

Complex-tensor theory of simple smectics.

Matter self-assembling into layers generates unique properties, including structures of stacked surfaces, directed transport, and compact area maximization that can be highly functionalized in biology and technology. Smectics represent the paradigm of such lamellar materials - they are a state between fluids and solids, characterized by both orientational and partial positional ordering in one layering direction, making them notoriously difficult to model, particularly in confining geometries. We propose a complex tensor order parameter to describe the local degree of lamellar ordering, layer displacement and orientation of the layers for simple, lamellar smectics. The theory accounts for both dislocations and disclinations, by regularizing singularities within defect cores and so remaining continuous everywhere. The ability to describe disclinations and dislocation allows this theory to simulate arrested configurations and inclusion-induced local ordering. This tensorial theory for simple smectics considerably simplifies numerics, facilitating studies on the mesoscopic structure of topologically complex systems.

Phenotyping single-cell motility in microfluidic confinement.

The movement trajectories of organisms serve as dynamic read-outs of their behaviour and physiology. For microorganisms this can be difficult to resolve due to their small size and fast movement. Here, we devise a novel droplet microfluidics assay to encapsulate single micron-sized algae inside closed arenas, enabling ultralong high-speed tracking of the same cell. Comparing two model species - Chlamydomonas reinhardtii (freshwater, 2 cilia), and Pyramimonas octopus (marine, 8 cilia), we detail their highly-stereotyped yet contrasting swimming behaviours and environmental interactions. By measuring the rates and probabilities with which cells transition between a trio of motility states (smooth-forward swimming, quiescence, tumbling or excitable backward swimming), we reconstruct the control network that underlies this gait switching dynamics. A simplified model of cell-roaming in circular confinement reproduces the observed long-term behaviours and spatial fluxes, including novel boundary circulation behaviour. Finally, we establish an assay in which pairs of droplets are fused on demand, one containing a trapped cell with another containing a chemical that perturbs cellular excitability, to reveal how aneural microorganisms adapt their locomotor patterns in real-time.

Self-generated oxygen gradients control collective aggregation of photosynthetic microbes.

For billions of years, photosynthetic microbes have evolved under the variable exposure to sunlight in diverse ecosystems and microhabitats all over our planet. Their abilities to dynamically respond to alterations of the luminous intensity, including phototaxis, surface association and diurnal cell cycles, are pivotal for their survival. If these strategies fail in the absence of light, the microbes can still sustain essential metabolic functionalities and motility by switching their energy production from photosynthesis to oxygen respiration. For suspensions of motile C. reinhardtii cells above a critical density, we demonstrate that this switch reversibly controls collective microbial aggregation. Aerobic respiration dominates over photosynthesis in conditions of low light, which causes the microbial motility to sensitively depend on the local availability of oxygen. For dense microbial populations in self-generated oxygen gradients, microfluidic experiments and continuum theory based on a reaction-diffusion mechanism show that oxygen-regulated motility enables the collective emergence of highly localized regions of high and low cell densities.

Emergent probability fluxes in confined microbial navigation.

When the motion of a motile cell is observed closely, it appears erratic, and yet the combination of nonequilibrium forces and surfaces can produce striking examples of organization in microbial systems. While most of our current understanding is based on bulk systems or idealized geometries, it remains elusive how and at which length scale self-organization emerges in complex geometries. Here, using experiments and analytical and numerical calculations, we study the motion of motile cells under controlled microfluidic conditions and demonstrate that probability flux loops organize active motion, even at the level of a single cell exploring an isolated compartment of nontrivial geometry. By accounting for the interplay of activity and interfacial forces, we find that the boundary's curvature determines the nonequilibrium probability fluxes of the motion. We theoretically predict a universal relation between fluxes and global geometric properties that is directly confirmed by experiments. Our findings open the possibility to decipher the most probable trajectories of motile cells and may enable the design of geometries guiding their time-averaged motion.

Flow-assisted self-healing of the helical structure in a cholesteric liquid crystal.

We employ nonequilibrium molecular dynamics simulations to investigate the structure and dynamics of a cholesteric liquid crystal confined between atomically corrugated solid walls. By choosing walls normal to the helical axis, we can study systems with an arbitrary cholesteric pitch without exposing the cholesteric helix to a spurious stress. We investigate the effects of local heating and flow and their joint effects. A steady-state laminar Poiseuille flow is initiated by means of an external body force. Flow alone (i.e., without local heating) in a direction normal to the helical axis does not affect the cholesteric pitch. If the liquid crystal is heated in a small region, the cholesteric helix becomes unstable and melts locally. However, if local heating and flow are combined, a nontrivial synergistic effect is observed in that the helical structure recuperates the better, the higher the speed of the flow is.

Multiparticle collision dynamics simulations of a squirmer in a nematic fluid.

We study the dynamics of a squirmer in a nematic liquid crystal using the multiparticle collision dynamics (MPCD) method. A recently developed nematic MPCD method [Phys. Rev. E 99, 063319 (2019)] which employs a tensor order parameter to describe the spatial and temporal variations of the nematic order is used to simulate the suspending anisotropic fluid. Considering both nematodynamic effects (anisotropic viscosity and elasticity) and thermal fluctuations, in the present study, we couple the nematic MPCD algorithm with a molecular dynamics (MD) scheme for the squirmer. A unique feature of the proposed method is that the nematic order, the fluid, and the squirmer are all represented in a particle-based framework. To test the applicability of this nematic MPCD-MD method, we simulate the dynamics of a spherical squirmer with homeotropic surface anchoring conditions in a bulk domain. The importance of anisotropic viscosity and elasticity on the squirmer's speed and orientation is studied for different values of self-propulsion strength and squirmer type (pusher, puller or neutral). In sharp contrast to Newtonian fluids, the speed of the squirmer in a nematic fluid depends on the squirmer type. Interestingly, the speed of a strong pusher is smaller in the nematic fluid than for the Newtonian case. The orientational dynamics of the squirmer in the nematic fluid also shows a non-trivial dependence on the squirmer type. Our results compare well with existing experimental and numerical data. The full particle-based framework could be easily extended to model the dynamics of multiple squirmers in anisotropic fluids.

Hybrid sideways/longitudinal swimming in the monoflagellate Shewanella oneidensis: from aerotactic band to biofilm.

Shewanella oneidensis MR-1 are facultative aerobic electroactive bacteria with an appealing potential for sustainable energy production and bioremediation. They gather around air sources, forming aerotactic bands and biofilms. Here, we experimentally follow the evolution of the band around an air bubble, and we find good agreement with the numerical solutions of the pertinent transport equations. Video microscopy reveals a transition between motile and non-motile MR-1 upon oxygen depletion, preventing further development of the biofilm. We discover that MR-1 can alternate between longitudinal fast and sideways slow swimming. The resulting bimodal velocity distributions change in response to different oxygen concentrations and gradients, supporting the biological functions of aerotaxis and confinement.

Self-assembly of liquid crystals in nanoporous solids for adaptive photonic metamaterials.

Nanoporous media exhibit structures significantly smaller than the wavelengths of visible light and can thus act as photonic metamaterials. Their optical functionality is not determined by the properties of the base materials, but rather by tailored, multiscale structures, in terms of precise pore shape, geometry, and orientation. Embedding liquid crystals in pore space provides additional opportunities to control light-matter interactions at the single-pore, meta-atomic scale. Here, we present temperature-dependent 3D reciprocal space mapping using synchrotron-based X-ray diffraction in combination with high-resolution birefringence experiments on disk-like mesogens (HAT6) imbibed in self-ordered arrays of parallel cylindrical pores 17 to 160 nm across in monolithic anodic aluminium oxide (AAO). In agreement with Monte Carlo computer simulations we observe a remarkably rich self-assembly behaviour, unknown from the bulk state. It encompasses transitions between the isotropic liquid state and discotic stacking in linear columns as well as circular concentric ring formation perpendicular and parallel to the pore axis. These textural transitions underpin an optical birefringence functionality, tuneable in magnitude and in sign from positive to negative via pore size, pore surface-grafting and temperature. Our study demonstrates that the advent of large-scale, self-organised nanoporosity in monolithic solids along with confinement-controllable phase behaviour of liquid-crystalline matter at the single-pore scale provides a reliable and accessible tool to design materials with adjustable optical anisotropy, and thus offers versatile pathways to fine-tune polarisation-dependent light propagation speeds in materials. Such a tailorability is at the core of the emerging field of transformative optics, allowing, e.g., adjustable light absorbers and extremely thin metalenses.

Crystallization via shaking in a granular gas with van der Waals interactions.

We investigate the effect of van der Waals forces on a collection of granular particles by means of molecular dynamics simulations of a vibrated system in three dimensions. The van der Waals interactions introduce two phase coexistences: one between a random close packing and a gas and a second between a polycrystalline dense state and a gas, where the dense, disordered component crystallizes when the driving amplitude exceeds a threshold value. The region of stability of the ordered state in the nonequilibrium phase diagram grows in size as the Hamaker constant increases or the degree of dissipation increases.

Structural transition in the collective behavior of cognitive agents.

Living organisms process information to interact and adapt to their surroundings with the goal of finding food, mating, or averting hazards. The structure of their environment has profound repercussions through both selecting their internal architecture and also inducing adaptive responses to environmental cues and stimuli. Adaptive collective behavior underpinned by specialized optimization strategies is ubiquitous in the natural world. We develop a minimal model of agents that explore their environment by means of sampling trajectories. The spatial information stored in the sampling trajectories is our minimal definition of a cognitive map. We find that, as cognitive agents build and update their internal, cognitive representation of the causal structure of their environment, complex patterns emerge in the system, where the onset of pattern formation relates to the spatial overlap of cognitive maps. Exchange of information among the agents leads to an order-disorder transition. As a result of the spontaneous breaking of translational symmetry, a Goldstone mode emerges, which points at a collective mechanism of information transfer among cognitive organisms. These findings may be generally applicable to the design of decentralized, artificial-intelligence swarm systems.

Multiparticle collision dynamics for tensorial nematodynamics.

Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects come together is the mesoscopic (micron) scale. It is then important to develop models aimed at capturing this variety of dynamics. We have generalized the particle-based multiparticle collision dynamics (MPCD) method to model the dynamics of nematic liquid crystals. Following the Qian-Sheng theory [Phys. Rev. E 58, 7475 (1998)1063-651X10.1103/PhysRevE.58.7475] of nematics, the spatial and temporal variations of the nematic director field and order parameter are described by a tensor order parameter. The key idea is to assign tensorial degrees of freedom to each MPCD particle, whose mesoscopic average is the tensor order parameter. This nematic MPCD method includes backflow effect, velocity-orientation coupling, and thermal fluctuations. We validate the applicability of this method by testing (i) the nematic-isotropic phase transition, (ii) the flow alignment of the director in shear and Poiseuille flows, and (iii) the annihilation dynamics of a pair of line defects. We find excellent agreement with existing literature. We also investigate the flow field around a force dipole in a nematic liquid crystal, which represents the leading-order flow field around a force-free microswimmer. The anisotropy of the medium not only affects the magnitude of velocity field around the force dipole, but can also induce hydrodynamic torques depending on the orientation of dipole axis relative to director field. A force dipole experiences a hydrodynamic torque when the dipole axis is tilted with respect to the far-field director. The direction of hydrodynamic torque is such that the pusher- (or puller-) type force dipole tends to orient along (or perpendicular to) the director field. Our nematic MPCD method can have far-reaching implications not only in modeling of nematic flows, but also to study the motion of colloids and microswimmers immersed in an anisotropic medium.

Electrification in granular gases leads to constrained fractal growth.

The empirical observation of aggregation of dielectric particles under the influence of electrostatic forces lies at the origin of the theory of electricity. The growth of clusters formed of small grains underpins a range of phenomena from the early stages of planetesimal formation to aerosols. However, the collective effects of Coulomb forces on the nonequilibrium dynamics and aggregation process in a granular gas - a model representative of the above physical processes - have so far evaded theoretical scrutiny. Here, we establish a hydrodynamic description of aggregating granular gases that exchange charges upon collisions and interact via the long-ranged Coulomb forces. We analytically derive the governing equations for the evolution of granular temperature, charge variance, and number density for homogeneous and quasi-monodisperse aggregation. We find that, once the aggregates are formed, the granular temperature of the cluster population, the charge variance of the cluster population and the number density of the cluster population evolve in such a way that their non-dimensional combination obeys a physical constraint of nearly constant dimensionless ratio of characteristic electrostatic to kinetic energy. This constraint on the collective evolution of charged clusters is confirmed both by  our theory and our detailed molecular dynamics simulations. The inhomogeneous aggregation of monomers and clusters in their mutual electrostatic field proceeds in a fractal manner. Our theoretical framework is extendable to more precise charge exchange mechanisms, a current focus of extensive experimentation. Furthermore, it illustrates the collective role of long-ranged interactions in dissipative gases and can lead to novel designing principles in particulate systems.

Hydrodynamic interactions dominate the structure of active swimmers' pair distribution functions.

Microswimmers often exhibit surprising patterns due to the nonequilibrium nature of their dynamics. Collectively, suspensions of microswimmers appear as a liquid whose properties set it apart from its passive counterpart. To understand the impact of hydrodynamic interactions on the basic statistical features of a microswimmer's liquid, we investigate its structure by means of the pair distribution function. We perform particle-based simulations of microswimmers that include steric effects, shape anisotropy, and hydrodynamic interactions. We find that hydrodynamic interactions considerably alter the orientation-dependent pair distribution function compared to purely excluded-volume models like active Brownian particles and generally decrease the structure of the liquid. Depletion regions are dominant at lower filling fractions, while at larger filling fraction, the microswimmer liquid develops a stronger first shell of neighbors in specific directions, while losing structure at larger distances. Our work is a first step toward a statistico-mechanical treatment of the structure of microswimmer suspensions.

Dynamics of sedimenting active Brownian particles.

We investigate the stochastic dynamics of one sedimenting active Brownian particle in three dimensions under the influence of gravity and passive fluctuations in the translational and rotational motion. We present an analytical solution of the Fokker-Planck equation for the stochastic process which allows us to describe the dynamics of one active Brownian particle in three dimensions. We address the time evolution of the density, the polarization, and the steady-state solution. We also perform Brownian dynamics simulations and study the effect of the activity of the particles on their collective motion. These results qualitatively agree with our model. Finally, we compare our results with experiments (J. Palacci et al., Phys. Rev. Lett. 105, 088304 (2010)) and find very good agreement.

Emergence of phytoplankton patchiness at small scales in mild turbulence.

Phytoplankton often encounter turbulence in their habitat. As most toxic phytoplankton species are motile, resolving the interplay of motility and turbulence has fundamental repercussions on our understanding of their own ecology and of the entire ecosystems they inhabit. The spatial distribution of motile phytoplankton cells exhibits patchiness at distances of decimeter to millimeter scales for numerous species with different motility strategies. The explanation of this general phenomenon remains challenging. Furthermore, hydrodynamic cell-cell interactions, which grow more relevant as the density in the patches increases, have been so far ignored. Here, we combine particle simulations and continuum theory to study the emergence of patchiness in motile microorganisms in three dimensions. By addressing the combined effects of motility, cell-cell interaction, and turbulent flow conditions, we uncover a general mechanism: The coupling of cell-cell interactions to the turbulent dynamics favors the formation of dense patches. Identification of the important length and time scales, independent from the motility mode, allows us to elucidate a general physical mechanism underpinning the emergence of patchiness. Our results shed light on the dynamical characteristics necessary for the formation of patchiness and complement current efforts to unravel planktonic ecological interactions.

Correction: In Situ Analysis of a Silver Nanoparticle-Precipitating Shewanella Biofilm by Surface Enhanced Confocal Raman Microscopy.

[This corrects the article DOI: 10.1371/journal.pone.0145871.].

Maximum in density heterogeneities of active swimmers.

Suspensions of unicellular microswimmers such as flagellated bacteria or motile algae can exhibit spontaneous density heterogeneities at large enough concentrations. We introduce a novel model for biological microswimmers that creates the flow field of the corresponding microswimmers, and takes into account the shape anisotropy of the swimmer's body and stroke-averaged flagella. By employing multiparticle collision dynamics, we directly couple the swimmer's dynamics to the fluid's. We characterize the nonequilibrium phase diagram, as the filling fraction and Péclet number are varied, and find density heterogeneities in the distribution of both pullers and pushers, due to hydrodynamic instabilities. We find a maximum degree of clustering at intermediate filling fractions and at large Péclet numbers resulting from a competition of hydrodynamic and steric interactions between the swimmers. We develop an analytical theory that supports these results. This maximum might represent an optimum for the microorganisms' colonization of their environment.

Early-stage aggregation in three-dimensional charged granular gas.

Neutral grains made of the same dielectric material can attain considerable charges due to collisions and generate long-range interactions. We perform molecular dynamic simulations in three dimensions for a dilute, freely cooling granular gas of viscoelastic particles that exchange charges during collisions. As compared to the case of clustering of viscoelastic particles solely due to dissipation, we find that the electrostatic interactions due to collisional charging alter the characteristic size, morphology, and growth rate of the clusters. The average cluster size grows with time as a power law, whose exponent is relatively larger in the charged gas than the neutral case. The growth of the average cluster size is found to be independent of the ratio of characteristic Coulomb to kinetic energy, or equivalently, of the typical Bjerrum length. However, this ratio alters the crossover time of the growth. Both simulations and mean-field calculations based on Smoluchowski's equation suggest that a suppression of particle diffusion due to the electrostatic interactions helps in the aggregation process.

Quantized Self-Assembly of Discotic Rings in a Liquid Crystal Confined in Nanopores.

Disklike molecules with aromatic cores spontaneously stack up in linear columns with high, one-dimensional charge carrier mobilities along the columnar axes, making them prominent model systems for functional, self-organized matter. We show by high-resolution optical birefringence and synchrotron-based x-ray diffraction that confining a thermotropic discotic liquid crystal in cylindrical nanopores induces a quantized formation of annular layers consisting of concentric circular bent columns, unknown in the bulk state. Starting from the walls this ring self-assembly propagates layer by layer towards the pore center in the supercooled domain of the bulk isotropic-columnar transition and thus allows one to switch on and off reversibly single, nanosized rings through small temperature variations. By establishing a Gibbs free energy phase diagram we trace the phase transition quantization to the discreteness of the layers' excess bend deformation energies in comparison to the thermal energy, even for this near room-temperature system. Monte Carlo simulations yielding spatially resolved nematic order parameters, density maps, and bond-orientational order parameters corroborate the universality and robustness of the confinement-induced columnar ring formation as well as its quantized nature.