Session R29: Active Matter and Liquid Crystals in Biological Systems II

Defect Ordering and Patterning in Active Nematics

Active nematics combine liquid crystalline orientational order with internal active driving to generate novel dynamical states involving complex spatio-temporal flows along with spontaneous defect pair creation and proliferation. Topological defects acquire self-propulsion due to activity and play a prominent role in driving large scale flows in two-dimensional active nematics. By focusing on defects as the relevant excitations, we develop a hydrodynamic theory of active defects incorporating both defect motility and active torques that align defect orientations. Our model predicts a defect ordered polar flock at high activity and uncovers the underlying physical mechanism for defect ordering. Extending our framework to include spatially inhomogeneous activity, we show how activity gradients act as ''electric fields'' that can sort defects based on their topological charge. Our continuum model hence offers a useful and versatile approach to quantify the patterning of defects and flow in active nematics by the spatial control of activity.   

Ordering and Correlations of Active Nematic Defects in 2D Flat Space

Topological defects are regions in an ordered material where the characteristic order is undefined. These defects are of significant interest in understanding the dynamics of active nematics, which are intrinsically out of equilibrium. One of the aims of our work is to address the orientation of defects in curved geometries. However, in this talk, I will discuss our results in flat space.We first explain how we prepare and image the system and how we identify defects using image analysis techniques. We focus on their orientation calculated directly from the divergence of the nematic tensor order parameter. We then use the defect positions and orientations to define relevant order parameters – polar and nematic order for the +1/2 defects, and a 3-fold bond angle order for the -1/2 defects. These quantities give us insights on the average orientational ordering of our system of defects. We then proceed to look at orientational correlations, and present insights into the configurations adopted by the defects as a function of the inter-defect spacing. Remarkably, we find that the local orientational order persists irrespective of the defect density.   

Defect order in active nematics

Using a recently derived model of active defects as quasi-particles, some of us have reported emergent states where +1/2 defects in active nematics organize in structures with large scale polar order. While ordered states of +1/2 defects have been obtained in both experiments and simulations of active nematic hydrodynamics, both polar and nematic alignment of the +1/2 defects have been seen depending on whether active flows are dissipated by friction with a substrate or by viscous stresses. In this talk, we will discuss the interplay between elastic and active torques, active flows and frictional dissipation in controlling defect patterns in these active liquid crystals.   

Dynamical Behavior of Defects in Circularly Patterned Active Nematics

Active nematics represent a new class of non-equilibrium systems that combine orientational ordering with active stresses applied to elongated particles. Continuum simulations of the active nematic are employed to explain how the interplay of activity-fueled energy injection to the system and frictional damping forces impact the dynamics of topologically imposed self-propelling +1/2 defects. We show that by patterning the activity by imposing active stresses in circular domains near the center of confinement, it is possible to regulate the motion of defects. A phase diagram of the dynamical response of defects based on activity strength and hydrodynamic friction is developed, revealing a wealth of new phenomena. Our results disclose that defects synchronize their dynamics to minimize the elastic distortion energy while being driven out of equilibrium by active stresses. A phase diagram is presented that displays a rich dynamical behavior, including immobile defects, steady rotation, bouncing defects, cruising defects, and a synchronized dancing state.   

Photo-Patterning DNA Structures with Topological Defects and Arbitrary Patterns through Multiple Length Scales

DNA is the building block for all living organisms, hence controlling supramolecular self-assembly of DNA structures is important not only for better understanding its biological properties, but also sheds light to designing new functional materials for biological engineering and material science applications. However, it is still challenging to control the DNA molecular self-assembly structures in the predesigned manner across multiple length scales. In this work, we demonstrate that the orientational order of DNA molecules can be precisely controlled by using photo-patterning technique. This technique imprints various spatially varying patterns into a layer of liquid crystalline polymer which will be further used to control the DNA structures. It is demonstrated that DNA orientations can be patterned with two dimensional lattice of topological defects and arbitrary patterns through length scale from micrometers to millimeters. The resulting programmable and predesigned DNA self-assembly structures will open opportunities in advanced materials and devices for optical and biological applications.   

Cells as liquid crystals, and what happens when they can't align

The organization of cells in tissues is crucial in determining their properties and functionalities. From the embryonic organization to mature tissues, cells are often arranged in well-determined patterns, which control the mechanical properties of the tissue and the ability to sense the environment. Many cell types have a characteristic anisotropic shape, and show an intrinsic ability to align with their neighbors. This behavior is analog to nematic liquid crystals (LCs). One special feature of LCs is the presence of topological defects, regions where the nematic order is lost and where stresses are concentrated in small regions. Monolayers of cells show alignment defects analog to LC topological defects. There is increasing evidence that such defects have a biological role, and their importance has been discussed in processes such as cell apoptosis, formation of 3D protrusions, growth of tumors stroma and cell migrations from tumors.
To better understand the role of these disordered regions in tissues, we induce topological defects in cell monolayers and study the cells behavior. Our goal is to connect biological properties of cells to the LC properties of the monolayers that the cells can form. We use topography to investigate the behavior of cells near induced topological defects, each characterized by their topological charge. Using shallow patterned grooves, we can impose defects with various charges without totally constraining the cells, and we study the cells’ behavior. Our data show a very different behavior of fibroblasts 3T6 and epithelial cells EpH-4 near topological defects with azimuthal or hyperbolic orientation of cells (+1 and -1 topological charge respectively), both in the ability to align and in the distribution of cell density within the monolayers. Finally, the behavior of cells near defects can provide a unique way to determine the size of the defect core.   

Quantifying orientational interactions among defects in active nematics

In passive two-dimensional systems, from superfluid films to nematic layers, topological defects play a key role in controlling continuous order-disorder transitions. Inspired by this, some of us have recently derived an effective description of the dynamics of topological defects in 2D active nematics as quasiparticles, where the unbound defects are modeled as a gas of self-propelled (+1/2) and passive (-1/2) particles with Coulomb interactions and aligning torques. We have now tested this model against defect trajectories obtained from numerical simulations of 2D active nematic hydrodynamics. Specifically, we demonstrate that the polar +1/2 defects interact via torques that tend to align the defect polarization with the elastic force they experience from other defects, as in previously studied models of flocking.   

Effect of active enzyme diffusion on mesoscale particles

Most of the phenomena in a living matter occur far from equilibrium and, therefore, cannot be treated within the framework of classical equilibrium thermodynamics. The elements of active matter, self-propelled particles, can be used to power active baths that can be rectified to recover work from noisy, non-equilibrium systems. Prior work has used bacteria or colloidal active matter to serve as active baths that can turn rotors or be rectified. However, the large size of bacteria creates a lower limit on the size of a material powered by a bacterial active bath. Cell biological studies have implied that metabolism enzymes serve to mix the viscous and complex fluid of the cytoplasm. Using these ideas our prior expertise in studying enzymes, we will focus on how enzyme baths can power the fluctuation spectrum of nano particles, and their effect on the diffusivity and fluctuations of larger particles such as passive proteins, quantum dots, and colloidal particles. Activity of passive elements will be analyzed through single particle tracking and differential dynamic microscopy.   

Collective trapping of flocking particles by asymmetric obstacles

Anisotropic obstacles not only are capable to induce ratchet effects on suspensions of run-and-tumbling particles, but also affect the collective behaviour of active aligning particles, such as Vicsek particles [1, 2]. In this talk, I will show that flocking particles which follow the Vicsek model aligning rules experience a collective trapping in the presence of a wall of funnels made of chevrons, concentrating at the opposite side of a wall of funnels than run-and-tumbling particles. We study the dynamics of this collective self-trapping behaviour and identify two regimes, one static and other dynamical in which particles are effectively trapped by constantly escaping and getting into the channels. Exploiting these two regimes, we engineer a system showing two perpendicular flows of Vicsek particles.

[1] T. Vicsek, A. Czirok, E. Ben-Jacob, I. Cohen, and O. Shochet, Physical review letters 75, 1226 (1995).
[2] J. A. Drocco, C. O. Reichhardt, and C. Reichhardt, Physical Review E 85, 056102 (2012).   

Polar flocking of active clusters

Biological active matter, such as populations of cells and animals, often change between different flocking regimes. One example is shoaling, milling and schooling transitions in fish. Synthetic active matter consist of self-propelled inanimate units and can emulate the flocking behavior of biological active matter. Here we report on a system of electro-propelled rolling granular beads with tuneable interactions. Many active matter regimes is realized in the same experiment as a function of the electric field: including active crystals and clusters with long range polar order, a stripe phase of clusters, and polar liquid flocks. Remarkably, the crystal to liquid transition occurs at a different velocity threshold than the local to global polar order transition. The stripe phase is reminiscent of those seen in quasi two-dimensional matter with competing interactions. The experimental system offers a physical model for flocking transitions in biological active matter, and can also open new routes for controlling self-assembly in soft matter technologies   

Flocking and clustering of self-propelled disks with active reorientation

In this talk we present a numerical investigation of self-propelled disks that integrates a behavior of active reorientation in analogy to collision avoidance in animal herds. The results of our simulations show rich phase dynamics including a flocking state, and a clustering state as a result of the mobility-induced phase separation. With a systematic exploration, our study reveals the unexpected link between the two collective behaviors. This study illustrated the importance of active reorientation on the emergent behaviors of self-propelled particles relevant to many natural and engineered active systems.