Session A05: Active Matter and Liquid Crystals in Biological and Bio-Inspired Systems

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Active cilia are prototypical engines of motility at the micron scale. They undergo spontaneous oscillations in viscous fluids by continuously consuming chemical energy and dissipating them through mechanical motion. Therefore, stable oscillations require that the active energy input must be balanced by a significant source of dissipation. Conventionally, it stems from the ambient fluid because cilia operate at a low-Reynolds regime. However, we show that external fluid friction is negligibly small to counteract the passive elastic stresses generated within the filament due to the active drive. This counter-intuitive result is borne out of experiments by simultaneously measuring the waveform and flow field of an isolated and reactivated Chlamydomonas cilia, beating near the instability threshold, for one-shot determination of both elastic and frictional components of the system. Consequently, it is the internal friction of cilium that controls the dynamical steady state in ciliary oscillations. We combine these experimental insights with theoretical modeling of active filaments to illustrate that ciliary oscillations indeed exist in the presence of internal friction as the sole source of dissipation.   

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Activity invalidates many of the traditional assumptions of hydrodynamics. So far, many studies have been limited to characterizing and simulating activity-driven flows: few have measured forces and torques exerted by an active fluid on an external body. Yet quantitative measurements of active stresses are required to test active hydrodynamics theories and conceive practical applications of active fluids. Here, we experimentally measure the drag force on a sphere sedimenting in a 3D active fluid powered by the continuous extension and buckling of kinesin-microtubules bundles. The sphere sediments under the combined effects of large-scale spontaneous coherent flows, mesoscopic turbulence and gravity. Its motion can be described by a nonlinear Stokes drag characterized by an effective viscosity and an effective diffusivity. Using a custom-built bright-field microscope, we track active sedimentation with micron resolution, even for large bead diameters up to 100 microns, in 3D microfluidic chambers, through continuous scanning of a moving volume with a piezo-driven objective. Combined with theoretical and numerical frameworks, we present the statistics of the bead trajectories and develop the form of the Stokes drag for active media.   

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Extensive efforts over the past few years have focused on understanding the non-equilibrium
macroscale behaviors of filamentous biopolymers such as microtubules and actin filaments that
are driven by associated molecular motors. Previously studied systems exhibited either robust
contractions or extensile stresses that powered turbulent flows. Despite these effort our
understanding of how various microscopic parameters determine the symmetries of the emergent
active stresses remains incomplete. To connect microscopic dynamics to macroscale behaviors
we measured the phase diagram of a new system of microtubule filaments and end-accumulating
kinesin molecular motors. Our results demonstrate mechanisms that can be used to switch
between extensile and contractile stresses, as well as a range of new dynamical pathways and
structures that are reminiscent of those observed in equilibrium amphiphilic systems.   

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Confined active nematic systems exhibit an array of intriguing dynamical states, including spontaneous unidirectional flow, nontrivial periodic trajectories, and chaotic "active turbulence". In this work, we explore these states and the transitions between them in a 2D channel from a dynamical systems point of view using the nemato-hydrodynamic equations. In the low-moderate activity regime, we identify the sequences of bifurcations leading to the development of steady and periodic coherent flows. Moving towards the large activity regime, we calculate new unstable equilibria and periodic orbits, and discuss their role in characterizing the phenomenon of active turbulence.   

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We are investigating the origin of self-amplifying deformations in 3D active networks composed of cytoskeletal filaments (microtubules), crosslinkers and molecular motors. The motors hydrolyze ATP and convert chemical energy into mechanical work as they slide adjacent microtubules. This input of energy drives the cytoskeletal network away from thermodynamic equilibrium. We shear-aligned this suspension in thin microfluidic channels and investigate how the kinematics of the instability can reveal the underlying rheology of the network. In particular, we investigate the role of microtubule length on the rheology of the network and show that increasing the length of the polymer leads to a transition from an active liquid to an active solid.   

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Boundary conditions influence the outcome of fluid dynamics in conventional passive fluid systems. Such an influence also extends to active fluid systems where fluid can flow by itself without an external driving force. For example, an active fluid that is confined in a thin cylinder can self-organize into a circulation along the central axis of the cylinder but thinning the cylinder to a disk-like geometry suppresses the formation of circulation. These phenomena demonstrated the role of confinement geometry on flow patterns of active fluid. Here, we demonstrate two flow patterns induced by confinement. First, we will show that active fluid can convect within a trapezoidal confinement. Such convection was in a temperature-uniform system, in contrast to Rayleigh-Bénard convection which is induced by a temperature gradient. This result suggested the feasibility of developing convection in a temperature-homogeneous system. Second, we demonstrate a confinement-induced stationary vortex near a corner of confinement whose corner angle is below a critical value. This is similar to conventional Moffatt eddies, except the fluid is internally driven. Our work paves the path to controlling self-organization of active fluid using confinement.   

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Recently, experiments have shown that actin filaments which self-organize into tactoids can be deformed and divided by myosin motors. We present a continuum model that accounts for the activity of myosin motors that slide actin filaments according to their polarity. Using simulations and analytical arguments, we demonstrate how our model captures the essential dynamics and morphology observed in experiments. First a single tactoid is formed, then myosin motors bind, accumulate within the tactoid and localize in the droplet midplane. The myosin motors enable the formation of an aster in the tactoids center, which causes the tactoid to deform into two tactoids with myosin motors at their connecting center. By increasing activity we show how a tactoid can fully divide into two and that multiple asters can emerge inside a droplet, dividing it into three daugter tactoids.   

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Millions of enzyme-catalysed reactions happen every second in the compositionally complex crowded environment of a single living cell. Here, we introduce a model system to mimic the high crowding and metabolic rates found in living cytoplasm, while maintaining relatively simple compositions. We demonstrate how this system can be used to study biochemical phenomena in a realistic controlled environment, and to study the novel physics of active liquids.   

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The field of active matter studies materials whose microscopic constituents can consume energy at the particle scale to produce motion. Many biological processes are driven by such internal active components, such as cell migration due to the actin cytoskeleton, where collective motion of active filaments can lead to the cell forming protrusions, and morphogenesis, where topological defects can act as nucleation sites for morphological features. As a minimal model of a cell, we consider a particle-based simulation of an elastic vesicle containing a collection of polar active filaments. The interplay between the internal active stresses and vesicle elasticity leads to a variety of fascinating steady-state behaviors that have not been observed in bulk systems or under rigid confinement, including highly-aligned rings and caps. We discuss simple scaling models that reveal the mechanisms underlying these emergent behaviors.   

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The contraction of the cytokinetic ring during cell division leads to the physical partitioning of a cell into two daughter cells. This contraction involves flows of actin filaments and myosin motors in the growing membrane interface that causes this separation. Within a continuum gel
theory framework, we explore the coupled dynamics of the flow and the degree of alignment in the acto-myosin network (the order parameter). We find that numerical solutions of the coupled equations are close to the exact results obtained with analytic approximations [1]. The results are also consistent with experimental observations [2,3] on the closure rate of the ring. Our theory [1] also captures how the effective tension in the ring decreases with its radius. We show how this effect significantly slows down the contraction process at later times.

[1] Chatterjee Mainak, et al. arXiv preprint arXiv:2007.13441 (2020).
[2] A. Zumdieck, et al. PLoS ONE 2(8): e696 (2007).
[3] A. S. Maddox, et al. Developmental cell 12, 827 (2007).   

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Unlike traditional fluids, “active fluids” spontaneously flow by means of their own internal energy. Although they occur in various shapes and forms, the most studied active fluids are typically two-dimensional and are commonly composed of nematic rod-like constituents, such as a bacterial colonies, shaken granular rods, or films of sub-cellular filament/motor-protein mixtures. However, recent experimental work has produced extensile three-dimensional active nematic systems using kinesin and microtubule bundles dispersed in a passive colloidal liquid crystal. In this talk, I will describe our recent simulations of three-dimensional active nematic flows in microfluidic channels. Through a hybrid lattice Boltzmann and finite difference numerical scheme, we explore the spontaneous active nematohydrodynamic flow states in confining three-dimensional channels. In particular, we show that varying both the channel’s aspect ratio along the third dimension and boundary conditions, the system can enter into highly ordered and periodical flow states. Through observations of correlation functions and by tracking three-dimensional defects, we analyse the periodicity of these ordered states as well as their subsequent collapse over long times.