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We study how the three-dimensional shape of rigid filaments determines the microscopic dynamics and macroscopic rheology of entangled semidilute Brownian suspensions. To control the filament shape we use bacterial flagella, which are microns-long helical or straight filaments assembled from flagellin monomers. We compare the dynamics of straight rods, helical filaments, and shape-diblock copolymers composed of seamlessly joined straight and helical segments. Caged by their neighbors, straight rods preferentially diffuse along their long axis, but exhibit significantly suppressed rotational diffusion. Entangled helical filaments escape their confining tube by corkscrewing through the dense obstacles created by other filaments. By comparison, the adjoining segments of the rod-helix shape-diblocks suppress both the translation and the corkscrewing dynamics. Consequently, the shape-diblock filaments become permanently jammed at exceedingly low densities. We also measure the rheological properties of semidilute suspensions and relate their mechanical properties to the microscopic dynamics of constituent filaments. In particular, rheology shows that an entangled suspension of shape rod-helix copolymers forms a low-density glass whose elastic modulus can be estimated by accounting for how shear deformations reduce the entropic degrees of freedom of constrained filaments. Our results demonstrate that the three-dimensional shape of rigid filaments can be used to design rheological properties of semidilute fibrous suspensions. 

Living systems are intrinsically nonequilibrium: They use metabolically derived chemical energy to power their emergent dynamics and self-organization. A crucial driver of these dynamics is the cellular cytoskeleton, a defining example of an active material where the energy injected by molecular motors cascades across length scales, allowing the material to break the constraints of thermodynamic equilibrium and display emergent nonequilibrium dynamics only possible due to the constant influx of energy. Notwithstanding recent experimental advances in the use of local probes to quantify entropy production and the breaking of detailed balance, little is known about the energetics of active materials or how energy propagates from the molecular to emergent length scales. Here, we use a recently developed picowatt calorimeter to experimentally measure the energetics of an active microtubule gel that displays emergent large-scale flows. We find that only approximately one-billionth of the system’s total energy consumption contributes to these emergent flows. We develop a chemical kinetics model that quantitatively captures how the system’s total thermal dissipation varies with ATP and microtubule concentrations but that breaks down at high motor concentration, signaling an interference between motors. Finally, we estimate how energy losses accumulate across scales. Taken together, these results highlight energetic efficiency as a key consideration for the engineering of active materials and are a powerful step toward developing a nonequilibrium thermodynamics of living systems.

 

Active interfaces exhibit giant fluctuations and propagating waves that power wetting transitions and droplet shape shifting. 

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. 

Microtubule-based active matter provides insight into the self-organization of motile interacting constituents. We describe several formulations of microtubule-based 3D active isotropic fluids. Dynamics of these fluids is powered by three types of kinesin motors: a processive motor, a non-processive motor, and a motor which is permanently linked to a microtubule backbone. Another modification uses a specific microtubule crosslinker to induce bundle formation instead of a non-specific polymer depletant. In comparison to the already established system, each formulation exhibits distinct properties. These developments reveal the temporal stability of microtubule-based active fluids while extending their reach and the applicability. 

Cytoskeletal active nematics exhibit striking nonequilibrium dynamics that are powered by energy-consuming molecular motors. To gain insight into the structure and mechanics of these materials, we design programmable clusters in which kinesin motors are linked by a double-stranded DNA linker. The efficiency by which DNA-based clusters power active nematics depends on both the stepping dynamics of the kinesin motors and the chemical structure of the polymeric linker. Fluorescence anisotropy measurements reveal that the motor clusters, like filamentous microtubules, exhibit local nematic order. The properties of the DNA linker enable the design of force-sensing clusters. When the load across the linker exceeds a critical threshold, the clusters fall apart, ceasing to generate active stresses and slowing the system dynamics. Fluorescence readout reveals the fraction of bound clusters that generate interfilament sliding. In turn, this yields the average load experienced by the kinesin motors as they step along the microtubules. DNA-motor clusters provide a foundation for understanding the molecular mechanism by which nanoscale molecular motors collectively generate mesoscopic active stresses, which in turn power macroscale nonequilibrium dynamics of active nematics.

 

Adhesive interactions between elastic structures such as graphene sheets, carbon nanotubes, and microtubules have been shown to exhibit hysteresis due to irrecoverable energy loss associated with bond breakage, even in static (rate-independent) experiments. To understand this phenomenon, we start with a minimal theory for the peeling of a thin sheet from a substrate, coupling the local event of bond breaking to the nonlocal elastic relaxation of the sheet and show that this can drive static adhesion hysteresis over a bonding/debonding cycle. Using this model we quantify hysteresis in terms of the adhesion and elasticity parameters of the system. This allows us to derive a scaling relation that preserves hysteresis at different levels of granularity while resolving a seeming paradox of lattice trapping in the continuum limit of a discrete fracture process. Finally, to verify our theory, we use new experiments to demonstrate and measure adhesion hysteresis in bundled microtubules.