Spontaneous motion in hierarchically assembled active matter

Abstract

With remarkable precision and reproducibility, cells orchestrate the cooperative action of thousands of nanometre-sized molecular motors to carry out mechanical tasks at much larger length scales, such as cell motility, division and replication. Besides their biological importance, such inherently non-equilibrium processes suggest approaches for developing biomimetic active materials from microscopic components that consume energy to generate continuous motion. Being actively driven, these materials are not constrained by the laws of equilibrium statistical mechanics and can thus exhibit sought-after properties such as autonomous motility, internally generated flows and self-organized beating. Here, starting from extensile microtubule bundles, we hierarchically assemble far-from-equilibrium analogues of conventional polymer gels, liquid crystals and emulsions. At high enough concentration, the microtubules form a percolating active network characterized by internally driven chaotic flows, hydrodynamic instabilities, enhanced transport and fluid mixing. When confined to emulsion droplets, three-dimensional networks spontaneously adsorb onto the droplet surfaces to produce highly active two-dimensional nematic liquid crystals whose streaming flows are controlled by internally generated fractures and self-healing, as well as unbinding and annihilation of oppositely charged disclination defects. The resulting active emulsions exhibit unexpected properties, such as autonomous motility, which are not observed in their passive analogues. Taken together, these observations exemplify how assemblages of animate microscopic objects exhibit collective biomimetic properties that are very different from those found in materials assembled from inanimate building blocks, challenging us to develop a theoretical framework that would allow for a systematic engineering of their far-from-equilibrium material properties.

Fig. 1. Active MT networks exhibit internally-generated flows

(a) Schematic illustration of an extensile MT-kinesin bundle, the basic building block used for the assembly of active matter. Kinesin clusters exert inter-filament sliding forces while depleting PEG polymers induce MT bundling. (b) Two MT bundles merge and the resultant bundle immediately extends, eventually falling apart. Time interval, 5 seconds, 15 μm bar. (c) In a percolating MT network, bundles constantly merge (red arrows), extend, buckle (green dashed lines), fracture, and self-heal to produce a robust and highly dynamic steady-state. Time interval, 11.5 seconds, 15 μm bar. (d) An active MT network viewed on a large scale. Arrows indicate local bundle velocity direction. 80 μm bar.

Fig. 2. ATP concentration controls dynamics of active MT networks

(a) Tracer particles embedded in BANs indicate local fluid flow. Trajectories of the particles (red paths) reveal highly non-Brownian motion. 80 μm bar. (b) Mean square displacements of tracer beads plotted as a function of time for different ATP concentrations, shown in the legend. Lines indicate a diffusive exponent of 1.0 and a ballistic exponent of 2.0. (c) Normalized spatial velocity-velocity correlation functions as a function of lateral separation for varying concentrations of ATP. The velocities were determined using equal-time intervals of 5 seconds. When normalized by the peak velocity 〈V(O)²〉, the correlation functions rescale onto a universal curve, revealing a characteristic lengthscale that is independent of ATP concentration. Inset: Bare spatial correlation functions reveal that average velocity depends on ATP concentration.

Fig. 3. Dynamics of 2D streaming nematics confined to fluid interfaces

(a) Schematic illustrations of the nematic director configuration around disclination defects of charge ½ and minus;½. (b–c) Active liquid crystals exhibit disclinations of both ½ and −½ charge, indicating the presence of nematic order. 15μm bar. (d) A sequence of images demonstrates buckling, folding and internal fracture of a nematic domain. The fracture line terminates with a pair of oppositely charged disclination defects. After the fracture line self-heals, the disclination pair remains unbound. 15 second time lapse. 20μm bar.

Fig. 4. Motile water-in-oil emulsion droplets

(a) Droplets containing extensile MT bundles exhibit spontaneous autonomous motility, when partially compressed between chamber surfaces. A droplet trajectory taken over a time interval of 33 minutes is overlaid onto a brightfield droplet image. (b) In the absence of ATP, passive droplets exert no internal forces, and the only contribution to their movement is minor drift. 80 μm bar. (c) Fluorescence image of active MT bundles which spontaneously adsorb onto the oil-water interface. The resulting active liquid crystalline phase exhibits streaming flows, indicated with blue arrows. Red arrow indicates instantaneous droplet velocity. The image is focused on the droplet surface that is in contact with the coverslip. 100 μm bar. (d) Image of the droplet taken at a midplane indicates that the droplet interior is largely devoid of MT bundles. 100 μm bar.