Active matter is a field that continues to grow in interest because of its widespread relevance to fields such as biology and nanotechnology. Active matter describes systems composed of individual entities that consume energy leading to complex motion. Often, active matter systems exhibit collective motion with emerging patterns, structures, and flows. Active materials can span large length scales ranging from macroscopic (i.e. bird flocks, schools of fish, and marching locusts) to microscopic (i.e. bacterial colonies, self-propelled colloidal particles and proteins). This dissertation explores active matter systems using cytoskeletal proteins, microtubules and kinesin motors.

The first project in this dissertation explores microtubules propelled by kinesin motors that self-assemble into rotating spools. These structures are an example of a potential bio-actuator that can convert chemical energy into mechanical work. Understanding the underlying mechanisms of how to control the spool formation is vital to further development in bio-inspired applications. We explore the role of microtubule gliding velocity during initial spool assembly and once it has reached steady state. Our results show that microtubule spool assembly occurs at a faster rate at higher gliding velocities. Also, slower gliding velocities lead to a lower average spool circumference size. At lower velocities, microtubules do not disperse away from their initial isotropic state as quickly, therefore microtubules are confined to a smaller space when initial spool formation occurs. Once the system has reached a steady state, ~120 minutes later, the gliding velocity no longer plays a role in in spool size or spool density. These results build upon prior work in understanding the fundamental parameters contributing to spool formation.

The second project in this dissertation explores a microtubule-kinesin based active system in a different geometry. Here, kinesin motor clusters crosslink microtubule bundles and form an active network. As the kinesin motors move, the microtubule bundles extend, bend, buckle, fracture and recombine with neighboring bundles. This continuous activity generates complex fluid flows in the network. When confined in two dimensions (2D) at an oil/water interface, spontaneous active ±1/2 topological defects emerge. The ±1/2 defects are reminiscent of defects observed in the nematic liquid crystal phase, which is why the term 2D active nematic was coined to describe the confined network. The topological defects are created and annihilated constantly, which generates fluid flows. Until now, only turbulence was considered to characterize the rich dynamics seen in the network. We take a new approach to study this system from the perspective of chaos and introduce concepts from chaos theory to describe the dynamics generated by the defects. Additionally, we propose to consider the fluid as an active fluid, where the fluid material is the microtubule, that is self-mixed.

We use topological entropy and Lyapunov exponents to quantify the complexities generated in the active nematic. Using two methods to measure the local stretching of the active nematic, our results show there is exponential stretching at the local level which is a characteristic of chaotic advection. Our results show three independent measures of topological entropy that probe the system at different length scales are all consistent and agree with the computed Lyapunov exponent. This consistency demonstrates these measures of chaos are robust across varying length scales in the system. We then vary the activity in the active nematic by changing the energy injected at the local level (ATP concentration) to study how changes in the dynamics affects mixing. There is a non-monotonic dependence of topological entropy and Lyapunov exponent on the activity level; however, nondimensionalizing these quantities with a time-constant derived from the network velocity and characteristic length scale leads to remarkably constant values for all levels of activity. The insensitivity of the dimensionless topological entropy and dimensionless Lyapunov exponent to activity level indicates that this may be a universal feature.

In the third project of this dissertation, we expand on the second project and explore how the active fluid responds to external changes in its environment. To probe this, we change the viscosity of the bounding oil that the active nematic is in contact with at the oil/water interface. We observe both changes in the dynamics and morphology of the active nematic with changing viscosity. We measure defect pair separations for all viscosities to probe local stretching dynamics in the active nematic. Defect pair separations show exponential stretching at the local level which is consistent behavior to our previous work. Again, there are nonmonotonic relationships observed for both topological entropy and Lyapunov exponent as a function of viscosity; however, dimensionless topological entropy and dimensionless Lyapunov exponents result in relatively constant values. The dimensionless topological entropy is about three times the Lyapunov exponent. The source of this discrepancy is still unclear. We speculate that changes in the morphology that result in defect fracturing may enhance defect stretching but may not be captured in computations for the Lyapunov exponent. More work must be done to fully understand this difference.

Overall in this dissertation we explore interesting structures and collective behavior that arise from active microtubules driven by kinesin motors. In the first project, we contribute to some fundamental understandings for the mechanism behind spool formation that may be useful for future development of bio-inspired nanomachines. In the last two projects we have introduced a new concept to create a bridge between chaotic advection and active nematics. This new perspective introduces possibilities of new analysis methods to understand the fundamental dynamics in the system. Additionally, we have shown early evidence that the active nematic can be considered to be a self-mixing active fluid.

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