Session Q27: Biological Active Matter II

Locomotion of flagellated bacteria: the influence of complex fluids and the role of multiflagellarit

A flagellated bacterium inhabits and swims in fluids of low Reynolds number, a world, though foreign to us, is of ultimately importance to many aspects of our daily lives ranging from food production, disease prevention to environmental health. In this talk, I discuss two recent experimental works in my group on the fascinating swimming behaviors of a prominent example of flagellated bacteria, Escherichia coli. First, we study the motility of E. coli in colloidal suspensions of varying sizes and volume fractions. We find that bacteria in dilute colloidal suspensions display the quantitatively same motile behaviors as those in dilute polymer solutions, where a size-dependent motility enhancement up to 80% is observed accompanied by a strong suppression of bacterial wobbling. We then develop a simple hydrodynamic model incorporating the colloidal nature of complex fluids, which quantitatively explains bacterial wobbling dynamics and mobility enhancement in both colloidal and polymeric fluids. Second, we explore the role of multiflagellarity in maintaining the constant swimming of E. coli of different lengths. By synergizing experiments of immense sample sizes with quantitative hydrodynamic modeling and simulations, we reveal how bacteria utilize the increasing number of flagella to regulate the flagellar motor load, which leads to faster flagellar rotation neutralizing the higher fluid drag on their larger bodies. Without such a collective balancing mechanism, the swimming speed of uniflagellar bacteria generically decreases with increasing body size. Our study provides new insights into the selective advantage of multiflagellarity as a ubiquitous cellular feature of bacteria. The uncovered difference between uniflagellar and multiflagellar swimming is also important for understanding environmental influence on bacterial morphology and useful for designing artificial flagellated microswimmers.   

Self-Regulation of Minimal Contractile Active Systems

Minimal reconstituted systems of cytoskeletal filaments and molecular motors have proven a valuable platform for understanding spontaneous self-organization in active matter systems. Recent experimental results have highlighted the diverse set of behaviors systems of reconstituted cytoskeleton networks and motors can take on, and their ability to create self-organized structures that can regulate their behavior in the absence of biochemical signaling. However, even in minimal cytoskeletal systems, teasing out mechanisms for phenomena from experimental results remains challenging due to competing effects introduced by integrating multiple interacting cytoskeletal components and due to feedback mechanisms by which the macro-scale dynamics of these systems influence the agent-scale behavior. Here, we perform fluorescence microscopy assays on a minimal system of stabilized filaments and molecular motors. We show that the most minimal possible cytoskeletal active system is sufficient to generate self-regulating contractile structures, and map the dependence of the behavior of the system given different concentrations of components of the system. Our results represent an important step forward in understanding the physical origins of spatiotemporal self-regulation in active matter systems, as well as informing principles for minimal requirements for autonomous spatiotemporal control of bio-inspired active materials.   

Analysis of elastic strains reveals shape selection pathways in active gels

Myosin motor-induced forces in the actin cytoskeleton are responsible for cell and tissue shape changes in living systems. We consider in vitro experiments where a set of actomyosin gel disks spontaneously contract and buckle into a family of initial-geometry dependent, 3D shapes ranging from domes to wrinkled [1]. We perform particle imaging velocimetry (PIV) analysis on gels of different initial shapes to obtain the in-plane distribution of elastic strains. Resolving the radial and azimuthal components of strain reveals the robust occurrence of an inner isotropic contracting region, surrounded by an outer region with radial stretching. Comparison with a model for active stresses in elastic disks allows us to infer an outer region with aligned force dipoles representing myosin activity. Our findings support the hypothesis that this differential distribution of active stresses arises from the contraction-induced local alignment of actin bundles along the gel boundary. Future work will reveal how the in-plane strain distribution determines the final 3D buckled shapes.

1. “Artificial contractile actomyosin gels recreate the curved and wrinkling shapes of cells and tissues” by G. Livne et al., biorXiv 2023.03.21.533327   

Heterogenous Population of Kinesin-Streptavidin Complex Revealed by Mass Photometry

The kinesin-streptavidin complex is widely used to drive filament-filament sliding in microtubule-based active matter studies. Although the stoichiometry of the kinesin-streptavidin complex is generally assumed to be 2:1, this assumption has not been experimentally verified. Here we employ mass photometry, a label-free single-molecule technique, to determine the mass of individual kinesin-streptavidin complexes in solution. We found that the complex population is heterogenous, although the relative abundance of different complexes depends sensitively on the kinesin:streptavidin incubation ratio. We identify an incubation ratio that maximizes the 2:1 complex stoichiometry optimal for filament-filament sliding in active matter studies.   

Organization of Cytoskeletal Networks Creates Non-Equilibrium Energy Gradients Through Space and Time

Active matter systems consume fuel to form organized, dynamic structures and patterns. These ordered states do not exist in the absence of an energy source. To gain insight into the energetic cost of structure formation, we investigate the assembly of an ordered aster from a disordered, uniform mixture of microtubules and kinesin motors. This self-organization occurs due to optogenetically-controllable crosslinking of motor proteins that walk on microtubules and hydrolyze ATP. Here, we perform the first careful measurement of ATP consumption, and power usage, through space and time on an in vitro cytoskeletal network. We additionally develop reaction-diffusion models and corresponding finite element simulations to predict how a given motor profile results in non-equilibrium ATP distributions. Our experiments and models both reveal radial spatial gradients in ATP, with the lowest ATP concentration in the aster core, where the motors are most dense. The expended power correlates with aster contraction, where the largest changes in aster radius accompany the greatest power usage. These results suggest that loading of motors, due to high motor densities at small aster radii, creates slower contraction. This work is a step toward understanding the role of energy consumption through space and time to produce organization in this active matter system. More broadly, our work provides a case study towards developing generalized theories of non-equilibrium systems connecting energy, entropy, and order.   

Activity-driven phase transition causes coherent flows of chromatin

We discover a new type of nonequilibrium phase transition in a model of chromatin dynamics, which accounts for the coherent motions that have been observed in experiment. The coherent motion is due to the long-range cooperation of molecular motors tethered to chromatin. Cooperation occurs if each motor acts simultaneously on the polymer and the surrounding solvent, exerting on them equal and opposite forces. This drives the flow of solvent past the polymer, which in turn affects the orientation of nearby motors and, if the drive is strong enough, an active polar (``ferromagnetic'') phase of motors can spontaneously form. Depending on boundary conditions, either transverse flows, or sustained longitudinal oscillations and waves are possible. Predicted time and length scales are consistent with experiments. We now have in hand a coarse-grained description of chromatin dynamics which reproduces the directed coherent flows of chromatin seen in experiments. This field-theoretic description can be analytically coupled to other features of the nuclear environment such as fluctuating or porous boundaries, local heterogeneities in the distribution of chromatin or its activity, leading to insights on the effects of activity on the cell nucleus and its contents.   

Controlling an elastic network's structure, mechanics and dynamics with an active fluid

In vitro experiments have shown that the structure and mechanics of actin networks depend dramatically on both actin and concentration and type of actin crosslinkers. Previous studies have explored networks whose assembly kinetics was driven by thermal motion.  We investigate the behavior of actin networks whose assembly is driven by turbulent-like flows generated by extensile microtubule-kinesin active fluids. Using both widefield and confocal microscopy, we study the structure and dynamics of this composite system across several length and time scales. Our work demonstrates how active fluids can be used to control shape, structure, mechanics and dynamics of elastic filamentous networks.   

Shape change and orientational order in contractile active gels

Biological active gels comprising cytoskeletal filaments and molecular motors can show complex shape changes driven by mechanical forces.  Here, we consider a general theoretical model for the feedback between active forces (generated by molecular motors such as myosin) and orientational order of fibers (such as actin bundles).  The model combines active and elastic stresses with strain-induced alignment leading to orientational order which in turn directs the active contractile forces. We are motivated by in vitro experiments on contractile actomyosin gel disks with same composition but different initial geometry, that spontaneously self-organize into various shapes like dome, saddle and wrinkled, with varying degrees of actin alignment at the gel boundary. By solving  the model analytically in a 2D annular geometry for axially symmetric contraction, we show the spontaneous emergence of orientational order and strain gradients. By combining linear stability analysis with numeric solution of the coupled dynamics of orientational order and elastic deformation, we show how such deformation and ordering arises from an initial random, undeformed state. The resulting in-plane distribution of strains may indicate the complex pathway of 3D shape selection. Overall, we predict how active force driven alignment in elastic materials determines shape change.   

Dynamics of Passive and Active Microtubules in Entangled Actin Networks

Rigid rods placed in a viscoelastic network exhibit caged dynamics. They escape their effective cage by passive diffusion along their long axis. We study these escape dynamics by visualizing 3D trajectories of individual microtubules confined in a network of semiflexible actin filaments. Due to their rod-like diffusive properties, longer microtubules are caged on longer timescales than shorter microtubules. To overcome this diffusion-limited escape timescale, we actively drive the microtubules with molecular motors coupled to the background network. Active rods within a network exhibit fundamentally different dynamics. In contrast to the passive case, driven microtubules with longer contour length move through the network and escape their cages more efficiently than shorter microtubules.   

Form Follows Function - Morphodynamics in single-celled Algae

Photosynthesis is essential for all life on Earth. However, the ever-changing light conditions in the environment of organisms are continuously challenging the photosynthetic performance. We show how non-motile organisms, like single-celled marine algae, can adapt to changes in light by morphing their photosynthetic material. As this highly dynamic process occurs in confinement by the rigid cell wall, the drastic intracellular re-arrangement needs "smart" logistics strategies. We show how the cell exploits meta-material properties to adapt to environmental changes efficiently. Exposing the cell to different physiological light conditions and applying temporal illumination sequences shows that the morpho-dynamics follow simple rules, allowing the use of coarse-grained equations of motion to describe this biological system. Our study shows how topologically complex metamaterials are applied in critical life-sustaining processes in nature and that simple dynamical rules can account for complex material transport in a crowded intracellular environment.   

Pattern formation in active droplets

Many morphogenic processes in biology -- from embryogenesis to mitosis -- involve a dynamic competition between bulk active stresses and interfacial tension. We mimic this competition experimentally to understand how activity and capillarity compete to generate functionalized structures. A microtubule-driven active liquid is embedded in a binary, polymeric liquid that phase separates, forming active droplets surrounded by a passive background. Fluctuations in active stress near the boundary induce spontaneous curvature changes of the soft interface. We report active analogs of the viscous fingering and Rayleigh-Plateau instabilities in passive liquids: activity competes against surface tension to destabilize the interface. After the nonequilibrium instability occurs, asymmetries between active and capillary stresses break detailed balance, hence breaking time-reversal and up/down symmetry of the interface. We quantify statistical signatures of these symmetries to understand how activity drives far-from-equilibrium pattern formation. Our work shows active droplets display key morphogenic signatures of living cells, a step toward building functional, bioinspired materials.   

Geometric computation of finite, disordered mineral lattices through topologically complex active confinements

Mineralization involves surface growth which successively records contour geometries of the crystal in a history dependent manner. It leads to the evolution of a crystal shape towards an energetically favorable equilibrium that is determined by the species concentration and gradients which are dependent on the boundary conditions. Living systems can however continuously alter these boundary conditions and guide mineral growth along desired pathways to create functional structures. Sea cucumbers grow ~100 µm length scale calcite-based skeletal structures called ossicles in diverse forms. Each ossicle can be described as a finite-disordered polygonal lattice with mineral deposits along the edges, making it equivalent to a multi-genus torus. We demonstrate that ossicles grow from an initial seed crystal that transforms into a multi-holed lattice through 4 steps - symmetry breaking in the seed, tip elongation to extend branches, tip splitting or budding to create new branches, and the fusion of two tips create closed loops. We find that the computation of final geometry of such a topologically complex rigid object is achieved through the unique cellular physiology of the cells continuously wrapping the structure as it evolves. This wrapping restricts transport of mineral precursors through microtubule networks along the surface of the existing geometry, thus coupling shape and material transport. The continuous extension of this wrapping around growing tips makes growth of actin filament based membranous projections possible. This endows otherwise passive mineral tips with activity, enabling them to execute a local search algorithm to find other tips nearby and perform fusion based loop closure. We also identify distinct modes of participating cell-cluster dispersion, which acts as an additional layer of control over the underlying growth process. Through reduced-order models of transport on self-closing active branching networks, we demonstrate that globally observed broken symmetries can be replicated through a simple parameter tuning and thus highlight the hidden universality in the diversity of shapes. The system thus serves as a unique playground merging aspects of cellular physiology, non-equilibrium growth processes, and classical branching morphogenesis in living systems.