Session W34: Topological Defects in Soft/Active/Biological Matter I

Topological defects in cell monolayers controlled by topography

The organization of cells influences many key processes such as migration, cell-cell communication and morphogenesis. It is well known that some cells types have a naturally elongated shape and spontaneously align with their neighbors like nematic liquid crystals. However, cells have capabilities that liquid crystals do not have, such as the ability to divide and to change shape. This changes the types of configurations available to this active nematic system and, consequently, its response to confining boundaries. 

We induce topological defects and distortions in monolayers of fibroblasts using micro-patterned ridges with varying height, spacing and shape. This constitutes a useful platform to characterize the alignment and the organization of the fibroblasts. For example, we investigate the cell density inhomogeneities within the monolayers and their correlation with the defect locations. We hypothesize that the density difference is mainly not driven by collective cell migration, but by a different rate of cell division in the defects' proximity, and we test the hypothesis by suppressing cell migration using high ridges. Furthermore, we confine cells near defects with fractional topological charge using corners with edges and thus we characterize the cells' tendency to splay or bend near corners. Finally, we investigate the role of the cell-substrate interaction in suppressing or promoting collective cell motion.   

Statistical Correlations of Topological Defects in a Model Monolayer Confluent Tissue

There is a recent interest in studying confluent cells as active matter. The Active Vertex Model (AVM), which represents cells as Voronoi polygons, has been instrumental in elucidating various dynamical phenomena in confluent tissues, including solid-liquid phase transition as a function of cell motility and cell shape. On the other hand, treating confluent tissues as active nematic liquid crystals has provided valuable insights into the collective dynamics and stress distributions within tissues. However, how to reconcile the two views of point, and what role nematic order plays in Voronoi cells, remain unclear, which hinders our further understanding of such biological systems. To bridge this research gap, we employ the AVM to investigate the statistical correlations between lattice defects (cell shapes deviating from hexagons) and orientational defects. Our findings demonstrate that collective active fluctuations of cells can lead to extensile-like stresses and give rise to strong spatial and orientational correlations between lattice defects and +1/2 defects. We also examine the directional motion of individual cells to further reveal how orientational defects mediate local cell rearrangements. Taken together, we have shed light on the role of defects in confluent cells.   

Coupling 3D reaction-diffusion and active matter to investigate morphogenesis

This project aims at unraveling the physical mechanisms by which pattern formation coupled with active matter can lead to robust morphogenesis.

Engineering machines and materials that imitate living organisms has been a persistent challenge in science. While recent advances in biochemistry allow the extraction of molecular building blocks from cells, reproducing complex structures such as a developing organism is still out-of-reach. In nature, morphogenesis often results from the interplay between biochemical, mechanical processes and topology, with mutual feedback. These processes are coordinated across scales to form robust, functional outcomes such as cell division, motility, and development. Yet, building efficient chemomechanical couplings in vitro remains a challenge.

To address this, I use biochemistry and microfabrication tools to couple membrane-binding morphogen proteins (MinDE proteins) with microtubule-based active matter. In this talk, I will first explain how I extended 2D chemical gradients formed by Min proteins into a reaction-diffusion-based 3D structure. I characterize this complex dynamical structure by detecting topological defects and studying their organization and dynamics. I will then reveal how to successfully combine this system with an active gel and demonstrate how active flows affect reaction-diffusion patterns in 3D. Future steps involve controlling molecular motor behavior using kinesin inhibitors governed by Min pattern and quantifying how chemical and activity gradients cooperate in selecting patterns.

Unraveling these interactions will enhance our ability to control pattern selection and defects localization in active gels.   

Boundary geometry drives three-dimensional defect transitions in a polar fluid

Confinement is a prominent driver of collective phenomena in anisotropic matter. Hence, understanding its role in the emergence of order is crucial for the control of complex structures such as topological defects. Using a minimal continuum model, we address the role of boundaries—with emphasis on their geometry—in the surface induced ordering of a 3D confined polar fluid. We define a dimensionless parameter that allows us to adjust the geometry of the system continuously, and use a weak anchoring energy to account for nonuniform boundary conditions. We find that, although material parameters are responsible for the creation of defects in the order parameter field, their location and structure are determined by the system geometry. We test our results in the experimental context of the mouse epiblast, where cells gradually align along their apico-basal axis and eventually form a fluid filled cavity (lumen) at their apical sides. Since field defects represent regions where the apical sides of the cells meet, changes in defect position can be relevant to lumen formation in the biological system. We compare our predictions with imaging data of the morphogenetic process for wildtype and genetically perturbed mice, finding a remarkable quantitative agreement without any fitting parameters. Our work provides insights into luminogenesis and embryonic viability, while paving the way for defect control by geometry manipulation in more general settings.   

Chaotic control of active nematics

Active fluids are a class of materials in which individual subunits consume locally available energy to create coherent motion at larger scales. In active nematics, the phase exhibits liquid crystal-like ordering and as a result gives rise to mobile topological defects. These defects can be considered as virtual stirring rods, driving chaotic mixing in the active phase. In recent work, our group has characterized an active nematic comprised of biological filaments and molecular motors. We have developed analysis techniques inspired by non-linear dynamics and chaos theory to describe the system. In this presentation, I will introduce experiments that demonstrate how geometrical confinement can influence the braiding dynamics of the topological defects. Notably, we show that confinement in cardioid-shaped wells leads to realization of the golden braid, a maximally efficient mixing state. The active nematic system naturally settles into the state of maximal fluid stretching per unit time when the boundary is appropriately engineered. Increasing the size of the confining cardioid produces a transition from the golden braid, to the fully chaotic, or active turbulent state. We show that this transition can be described using different measures of topological entropy and explore new concepts for control of defect braiding.   

Self-organized dynamics of viscous drops with surface nematic activity

Biological surfaces are often active, signifying that they are driven internally by chemical reactions at microscopic scales. In addition, they typically exhibit a form of in-plane order, such as nematic or polar alignment, facilitating extensive hydrodynamic interactions and self-organized behavior. It has been evidenced that nematic order emerges in various crucial biological processes such as cytokinesis and tissue morphogenesis. In this work, we study morphological dynamics in a freely-suspended viscous drop with surface nematic activity that drives the system out of equilibrium. This system serves as a simplified model for understanding complex active living systems, such as cells. Using a spectral boundary integral solver for Stokes flow coupled with a hydrodynamic evolution equation for the nematic tensor, we uncover the intricate interplay between flow, nematic order, and mechanics of deformations, leading to self-organized behaviors and symmetry-breaking phenomena, consistent with experimental observations under small and finite deformations. Diverse dynamical behaviors are observed, from periodic braiding motion of topological defects to chaotic creation and annihilation of defects under high activity levels, and translational motion under finite deformations. Our study offers valuable insights into the emergent dynamics observed in biological and biomimetic systems characterized by active fluid surfaces.   

Acoustically powered active liquid crystals

Active nematics are materials composed of mobile, elongated particles that can transform energy from the environment into a mechanical motion. Current experimental realizations of the active nematics are of biological origin and include cell layers, suspensions of elongated bacteria in liquid crystal, and combinations of bio-filaments with molecular motors. In this talk, we report the discovery of a fully synthetic active nematic system comprised of a lyotropic chromonic liquid crystal externally energized by ultrasonic waves. This synthetic active liquid crystal is free from biological degradation and variability, exhibits stable material properties, and enables a precise and rapid control of activity over an extended range. The energy of the acoustic field is converted into microscopic extensile stresses that disrupt long-range nematic order and give rise to an undulation instability, proliferation of topological defects, and the development of turbulent-like stress. We also reveal the emergence of unconventional free-standing persistent vortices in the nematic director field at high activity levels. Development of active nematic systems with stable and well-controlled material properties and turnable topological dynamics is crucial for both investigating the complex phenomenology of active nematics and unlocking their potential practical applications.   

Probing active nematics with in-situ microfabricated elastic inclusions

Synthetic active biomaterials are valuable tools to explore and understand the organization and dynamics of complex living systems. Proposed theories face limitations in their use since they are based on a few parameters that are challenging to measure.  Our work introduces a novel microfabrication method for the in-situ polymerization of hydrogel structures within a tubulin/kinesin active nematic gel. This method allows to imprint columnar objects of any size and shape, and with a wide range of stiffness: from rigid to compliant structures that can be deformed by forces exerted by the active material. 

After callibrating the mechanical properties of the hydrogel, our protocol has allowed us to measure the shear viscosity, activity parameter, and the bend rigidity of the active biofilaments. Our measurements also enable a quantitative mapping of the forces around topological defects in the active material, which not only play a fundamental role in biological organization but also hold the potential to drive advancements in biohybrid machines in the future. 

Beyond these quantitative results, our fabrication method will enable a new generation of experiments where channels and obstacles with arbitrary rigidity can be instantaneously included into encapsulated active soft materials.    

Controlling Active Nematic Topological Chaos Through Defect Pinning on Sharp Boundary Features

In active nematic liquid crystals, topological defects drive chaotic flows in the bulk. Confined geometries with uniform curvature have been shown to produce ordered defect motion and flows. However, little is known about ordered defect motion enabled by boundaries with varying curvature. To explore how varying curvature can control the active steady state, we simulate an active nematic system using active Beris-Edwards nematodynamics with curved boundary walls. In particular, we investigate the effects of varying bulk topological charge via pinning defects on boundary features. We show that locally convex and concave boundary features have defect pinning effects on positive and negative topological charge respectively, and demonstrate a scheme to tune the strength of defect pinning, expanding the possibilities of ordered states. We also examine how fluid-boundary slipping can stimulate defect nucleation, and can in turn destabilize otherwise periodically stable states. Our findings suggest routes to controllable bulk active flows utilizing boundary features.   

Coarsening of topological defects in 2D polar active matter

In this talk, I'll describe how topological defects in 2D polar active materials coarsen and form dynamic patterns. I'll outline the key differences of the active coarsening process from the equilibrium coarsening. Next, I'll discuss the novel scaling that emerges due to the nonlinear interactions between the defects. I'll close the talk by showing several application of our results to biological systems.   

Spatiotemporal control of active topological defects

Topological defects dictate the properties of many materials, from metal plasticity and magnetic frustration to the resistivity of superconductors. In active fluids, defects can spontaneously propel and drive chaotic flows stirring the fluid. But how can we locally control the dynamics of such defects in space and time? I will present an additive design framework to use elementary activity patterns, as active topological tweezers, to create, move and braid individual defects. A hydrodynamic extension of the framework enables us to control defect organization, patterning and transport at the collective level. I will conclude by highlighting future possibilities for the design of programmable active and living metafluids.   

Periodic orbits, pair nucleation, and unbinding of active nematic defects on cones

Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the simultaneous impact of confinement together with curvature singularity by characterizing the dynamics of an active nematic on a cone. Here, the Born-Oppenheimer approximation means that textures can follow defect positions rapidly on the time scales of interest. Upon imposing strong anchoring boundary conditions at the base of a cone, we find a rich phase diagram of multi-defect dynamics including exotic periodic orbits of one or two +1/2 flank defects, depending on activity and non-quantized geometric charge at the cone apex. By characterizing the transitions between these ordered dynamical states, we can understand (i) defect unbinding, (ii) defect absorption and (iii) defect pair nucleation at the apex. Numerical simulations confirm theoretical predictions of not only the nature of the circular orbits but also defect unbinding from the apex.