Active nematics are out-of-equilibrium fluids composed of rod-like subunits, which can generate large-scale, self-driven flows. We examine a microtubule-kinesin-based active nematic confined to two-dimensions, exhibiting chaotic flows with moving topological defects. Applying tools from chaos theory, we investigate self-driven advection and mixing on different length scales. Local fluid stretching is quantified by the Lyapunov exponent. Global mixing is quantified by the topological entropy, calculated from both defect braiding and curve extension rates. We find excellent agreement between these independent measures of chaos, demonstrating that the extensile stretching between microtubules directly translates into macroscopic braiding of positive defects. Remarkably, increasing extensile activity (via ATP concentration) does not increase the dimensionless topological entropy. This study represents the first application of chaotic advection to the emerging field of active nematics and the first time that the collective motion of an ensemble of defects has been quantified (via topological entropy) in a liquid crystal.

Microtubules are rigid, proteinaceous filaments required to organize and rearrange the interior of cells. They organize space by two mechanisms, including acting as the tracks for long-distance cargo transporters, such as kinesin-1, and by forming a network that supports the shape of the cell. The microtubule network is composed of microtubules and a bevy of associated proteins and enzymes that self-organize using non-equilibrium dynamic processes. In order to address the effects of self-organization of microtubules, we have utilized the filament-gliding assay with kinesin-1 motors driving microtubule motion. To further enhance the complexity of the system and determine if new patterns are formed, we added the microtubule crosslinking protein MAP65-1. MAP65-1 is a microtubule-associated protein from plants that crosslinks antiparallel microtubules, similar to mammalian PRC1 and fission yeast Ase1. We find that MAP65 can slow and halt the velocity of microtubules in gliding assays, but when pre-formed microtubule bundles are added to gliding assays, kinesin-1 motors can pull apart the bundles and reconstitute cell-like protrusions.

We examined the sensitivity of microtubule spools to transport velocity. Perhaps surprisingly, we determined that the steady-state number and size of spools remained constant over a seven-fold range of velocities. Our data on the kinetics of spool assembly further suggest that the main mechanisms underlying spool growth vary during assembly.