The interplay between activity and filament flexibility determines the emergent properties of active nematics

Conformation and dynamics of partially active linear polymers

We perform numerical simulations of isolated, partially active polymers, driven out-of-equilibrium by a fraction of their monomers. We show that, if the active beads are all gathered in a contiguous block, the position of the section along the chain determines the conformational and dynamical properties of the system. Notably, one can modulate the diffusion coefficient of the polymer from active-like to passive-like just by changing the position of the active block. Further, we show that a slight modification of the self-propulsion rule may give rise to an enhancement of diffusion under certain conditions, despite a decrease of the overall polymer activity. Our findings may help in the modelisation of active biophysical systems, such as filamentous bacteria or worms.

Elasticity tunes mechanical stress localization around active topological defects

Mechanical stresses are increasingly found to be associated with various biological functionalities. At the same time, topological defects are being identified across a diverse range of biological systems and are points of localized mechanical stress. It is therefore important to ask how mechanical stress localization around topological defects is controlled. Here, we use continuum simulations of nonequilibrium, fluctuating and active nematics to explore the patterns of stress localization, as well as their extent and intensity around topological defects. We find that by increasing the orientational elasticity of the material, the isotropic stress pattern around topological defects is changed substantially, from a stress dipole characterized by symmetric compression-tension regions around the core of the defect, to a localized stress monopole at the defect position. Moreover, we show that elastic anisotropy alters the extent and intensity of the stresses, and can result in the dominance of tension or compression around defects. Finally, including both nonequilibrium fluctuations and active stress generation, we find that the elastic constant tunes the relative effect of each, leading to the flipping of tension and compression regions around topological defects. This flipping of the tension-compression regions only by changing the elastic constant presents an interesting, simple, way of switching the dynamic behavior in active matter by changing a passive material property. We expect these findings to motivate further exploration tuning stresses in active biological materials by varying material properties of the constituent units.

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.

A polymer chain with dipolar active forces in connection to spatial organization of chromatin

A living cell is an active environment where the organization and dynamics of chromatin are affected by different forms of activity. Optical experiments report that loci show subdiffusive dynamics and the chromatin fiber is seen to be coherent over micrometer-scale regions. Using a bead-spring polymer chain with dipolar active forces, we study how the subdiffusive motion of the loci generate large-scale coherent motion of the chromatin. We show that in the presence of extensile (contractile) activity, the dynamics of the loci grows faster (slower) and the spatial correlation length increases (decreases) compared to the case with no dipolar forces. Hence, both the dipolar active forces modify the elasticity of the chain. Interestingly in our model, the dynamics and organization of such dipolar active chains largely differ from the passive chain with renormalized elasticity.

Spontaneous flow created by active topological defects

Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges [Formula: see text] are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive analytically the spontaneous velocity and stall force of self-advected defects in the presence of both shear and rotational viscosities. Applying our formalism to the dynamics of monolayers of elongated cells at confluence, we show that the non-conservation of cell number generically increases the self-advection velocity and could provide an explanation for their observed role in cellular extrusion and multilayering. We finally investigate numerically the influence of the Ericksen stress. Our work paves the way to a generic study of the role of topological defects in active nematics, and in particular in monolayers of elongated cells.

Vesicle shape transformations driven by confined active filaments

In active matter systems, deformable boundaries provide a mechanism to organize internal active stresses. To study a minimal model of such a system, we perform particle-based simulations of an elastic vesicle containing a collection of polar active filaments. The interplay between the active stress organization due to interparticle interactions and that due to the deformability of the confinement leads to a variety of filament spatiotemporal organizations that have not been observed in bulk systems or under rigid confinement, including highly-aligned rings and caps. In turn, these filament assemblies drive dramatic and tunable transformations of the vesicle shape and its dynamics. We present simple scaling models that reveal the mechanisms underlying these emergent behaviors and yield design principles for engineering active materials with targeted shape dynamics.

A strong nonequilibrium bound for sorting of cross-linkers on growing biopolymers

Understanding the role of nonequilibrium driving in self-organization is crucial for developing a predictive description of biological systems, yet it is impeded by their complexity. The actin cytoskeleton serves as a paradigm for how equilibrium and nonequilibrium forces combine to give rise to self-organization. Motivated by recent experiments that show that actin filament growth rates can tune the morphology of a growing actin bundle cross-linked by two competing types of actin-binding proteins [S. L. Freedman et al., Proc. Natl. Acad. Sci. U.S.A. 116, 16192-16197 (2019)], we construct a minimal model for such a system and show that the dynamics of a growing actin bundle are subject to a set of thermodynamic constraints that relate its nonequilibrium driving, morphology, and molecular fluxes. The thermodynamic constraints reveal the importance of correlations between these molecular fluxes and offer a route to estimating microscopic driving forces from microscopy experiments.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Machine learning active-nematic hydrodynamics

Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecular-motor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics.

Machine learning forecasting of active nematics

Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics.

Interplay of Particle Morphology and Director Distortions in Nematic Fluids

The existing microscopic theories for elasticity of nematics are challenged by recent findings on systems, whether bent molecules or semiflexible polymers, which do not comply with the model of rigid rodlike particles. Here, we propose an extension of Onsager-Straley second-virial theory, based on a model for the orientational distribution function that, through explicit account of the director profile along a particle, changes in the presence of deformations. The elastic constants reveal specific effects of particle morphology, which are not captured by the existing theories. This paves the way to microscopic modeling of the elastic properties of semiflexible liquid crystal polymers, which is a longstanding issue.

Filamentous active matter: Band formation, bending, buckling, and defects

Motor proteins drive persistent motion and self-organization of cytoskeletal filaments. However, state-of-the-art microscopy techniques and continuum modeling approaches focus on large length and time scales. Here, we perform component-based computer simulations of polar filaments and molecular motors linking microscopic interactions and activity to self-organization and dynamics from the filament level up to the mesoscopic domain level. Dynamic filament cross-linking and sliding and excluded-volume interactions promote formation of bundles at small densities and of active polar nematics at high densities. A buckling-type instability sets the size of polar domains and the density of topological defects. We predict a universal scaling of the active diffusion coefficient and the domain size with activity, and its dependence on parameters like motor concentration and filament persistence length. Our results provide a microscopic understanding of cytoplasmic streaming in cells and help to develop design strategies for novel engineered active materials.

Self-organized dynamics and the transition to turbulence of confined active nematics

We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements in disks, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates toward the confinement core over multiple rotation cycles, while the associated nematic director field evolves from a distinct double spiral toward a nearly circularly symmetric configuration. The collapse of the defect orbits is punctuated by another boundary-localized nucleation event, that sets up long-term doubly periodic dynamics. Comparing experimental data to a theoretical model of an active nematic reveals that theory captures the fast procession of a pair of [Formula: see text] defects, but not the slow spiral transformation nor the periodic nucleation of defect pairs. Theory also fails to predict the emergence of circular flows in the weak confinement regime. The developed confinement methods are generalized to more complex geometries, providing a robust microfluidic platform for rationally engineering 2D autonomous flows.