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Microtubule-kinesin active fluids consume ATP to generate internal active stresses, driving spontaneous and complex flows. While numerous studies have explored the fluid's autonomous behavior, its response to external mechanical forces remains less understood. This study explores how moving boundaries affect the flow dynamics of this active fluid when confined in a thin cuboidal cavity. Our experiments demonstrate a transition from chaotic, disordered vortices to a single, coherent system-wide vortex as boundary speed increases, resembling the behavior of passive fluids like water. Furthermore, our confocal microscopy revealed that boundary motion altered the microtubule network structure near the moving boundary. In the absence of motion, the network exhibited a disordered, isotropic configuration. However, as the boundary moved, microtubule bundles aligned with the shear flow, resulting in a thicker, tilted nematic layer extending over a greater distance from the moving boundary. These findings highlight the competing influences of external shear stress and internal active stress on both flow kinematics and microtubule network structure. This work provides insight into the mechanical properties of active fluids, with potential applications in areas such as adaptive biomaterials that respond to mechanical stimuli in biological environments. *We acknowledge support from the National Science Foundation (NSF-CBET-2045621). This research is performed with computational resources supported by the Academic & Research Computing Group at Worcester Polytechnic Institute. We acknowledge the Brandeis Materials Research Science and Engineering Center (NSF-MRSEC-DMR-2011846) for use of the Biological Materials Facility. 

Bacteria thrive in anisotropic media such as biofilms, biopolymer solutions, and soil pores. In strongly mechanically anisotropic media, physical interactions force bacteria to swim along a preferred direction rather than to execute the three-dimensional random walk due to their run-and-tumble behavior. Despite their ubiquity in nature and importance for human health, there is little understanding of bacterial mechanisms to navigate these media while constrained to one-dimensional motion. Using a biocompatible liquid crystal, we discovered two mechanisms used by bacteria to switch directions in anisotropic media. First, the flagella assemble in bundles that work against each other from opposite ends of the cell body, and the dominating side in this flagellar “Tug-of-Oars” propels the bacterium along the nematic direction. Bacteria frequently revert their swimming direction ${180}^{\circ }$by a mechanism of flagellar buckling and reorganization on the opposite side of the cell. The Frank elastic energies of the liquid crystal dictate the minimum compression for the Euler buckling of a flagellum. Beyond a critical elasticity of the medium, flagellar motors cannot generate the necessary torque for flagellar buckling, and bacteria are stuck in their configuration. However, we found that bacteria can still switch swimming directions using a second mechanism where individual bundles alternate their rotation. Our results shed light on bacterial strategies to navigate anisotropic media and give rise to questions about sensing environmental cues and adapting at the level of flagellar bundles. The two adaptation mechanisms found here support the use of biocompatible liquid crystals as a synthetic model for bacterial natural environments. Published by the American Physical Society2024 

Using a minimal hydrodynamic model, we theoretically and computationally study the Couette flow of active gels in straight and annular two-dimensional channels subject to an externally imposed shear. 

We carry out Monte Carlo simulations on fluid membranes with orientational order and multiple edges in the presence and absence of external forces. The membrane resists bending and has an edge tension, the orientational order couples with the membrane surface normal through a cost for tilting, and there is a chiral liquid crystalline interaction. In the absence of external forces, a membrane initialized as a vesicle will form a disk at low chirality, with the directors forming a smectic-A phase with alignment perpendicular to the membrane surface except near the edge. At large chirality a catenoid-like shape or a trinoid-like shape is formed, depending on the number of edges in the initial vesicle. This shape change is accompanied by cholesteric ordering of the directors and multiple p walls connecting the membrane edges and wrapping around the membrane neck. If the membrane is initialized instead in a cylindrical shape and stretched by an external force, it maintains a nearly cylindrical shape but additional liquid crystalline phases appear. For large tilt coupling and low chirality, a smectic-A phase forms where the directors are normal to the surface of the membrane. For lower values of the tilt coupling, a nematic phase appears at zero chirality with the average director oriented perpendicular to the long axis of the membrane, while for nonzero chirality a cholesteric phase appears. The p walls are tilt walls at low chirality and transition to twist walls as chirality is increased. We construct a continuum model of the director field to explain this behavior. 

Changes in the geometry and topology of self-assembled membranes underlie diverse processes across cellular biology and engineering. Similar to lipid bilayers, monolayer colloidal membranes have in-plane fluid-like dynamics and out-of-plane bending elasticity. Their open edges and micrometer-length scale provide a tractable system to study the equilibrium energetics and dynamic pathways of membrane assembly and reconfiguration. Here, we find that doping colloidal membranes with short miscible rods transforms disk-shaped membranes into saddle-shaped surfaces with complex edge structures. The saddle-shaped membranes are well approximated by Enneper’s minimal surfaces. Theoretical modeling demonstrates that their formation is driven by increasing the positive Gaussian modulus, which in turn, is controlled by the fraction of short rods. Further coalescence of saddle-shaped surfaces leads to diverse topologically distinct structures, including shapes similar to catenoids, trinoids, four-noids, and higher-order structures. At long timescales, we observe the formation of a system-spanning, sponge-like phase. The unique features of colloidal membranes reveal the topological transformations that accompany coalescence pathways in real time. We enhance the functionality of these membranes by making their shape responsive to external stimuli. Our results demonstrate a pathway toward control of thin elastic sheets’ shape and topology—a pathway driven by the emergent elasticity induced by compositional heterogeneity. 

Motivated by experiments on colloidal membranes composed of chiral rod-like viruses, we use Monte Carlo methods to simulate these systems and determine the phase diagram for the liquid crystalline order of the rods and the membrane shape. We generalize the Lebwohl–Lasher model for a nematic with a chiral coupling to a curved surface with edge tension and a resistance to bending, and include an energy cost for tilting of the rods relative to the local membrane normal. The membrane is represented by a triangular mesh of hard beads joined by bonds, where each bead is decorated by a director. The beads can move, the bonds can reconnect and the directors can rotate at each Monte Carlo step. When the cost of tilt is small, the membrane tends to be flat, with the rods only twisting near the edge for low chiral coupling, and remaining parallel to the normal in the interior of the membrane. At high chiral coupling, the rods twist everywhere, forming a cholesteric state. When the cost of tilt is large, the emergence of the cholesteric state at high values of the chiral coupling is accompanied by the bending of the membrane into a saddle shape. Increasing the edge tension tends to flatten the membrane. These results illustrate the geometric frustration arising from the inability of a surface normal to have twist. 

We use theory and numerical computation to determine the shape of an axisymmetric fluid membrane with a resistance to bending and constant area. The membrane connects two rings in the classic geometry that produces a catenoidal shape in a soap film. In our problem, we find infinitely many branches of solutions for the shape and external force as functions of the separation of the rings, analogous to the infinite family of eigenmodes for the Euler buckling of a slender rod. Special attention is paid to the catenoid, which emerges as the shape of maximal allowable separation when the area is less than a critical area equal to the planar area enclosed by the two rings. A perturbation theory argument directly relates the tension of catenoidal membranes to the stability of catenoidal soap films in this regime. When the membrane area is larger than the critical area, we find additional cylindrical tether solutions to the shape equations at large ring separation, and that arbitrarily large ring separations are possible. These results apply for the case of vanishing Gaussian curvature modulus; when the Gaussian curvature modulus is nonzero and the area is below the critical area, the force and the membrane tension diverge as the ring separation approaches its maximum value. We also examine the stability of our shapes and analytically show that catenoidal membranes have markedly different stability properties than their soap film counterparts.