Topological traps control material flux in self-organizing active filament spirals

Biological active systems regularly construct robust yet dynamic self-organizing structures where individual building blocks can flow in and out while the architecture remains stable over long time scales. Utilizing a novel active matter system of filamentous cyanobacteria spread on two-dimensional agar, we explore the role of topology in controlling material flux in self-organizing systems. We discover a persistent emergent architecture - active spirals - formed by the collective motility of long filaments, with each filament being a chain of up to thousands of bacterial cells that move cooperatively as a single filament. These spiral objects, once formed, remain stable and persist over long times. Within a spiral, wound filaments move in either clockwise or counterclockwise directions, and can reverse direction spontaneously. Through directional reversals and adhesion forces, filaments are able to interweave and exchange order. Using individual filament tracking, we describe the rich material flux within an active spiral and find discrete topological rules of filament interactions that encode these dynamics. We further discover the existence of a "topological trap" formed purely from the geometric chirality of neighboring wound filaments which creates a material flux boundary. Through analogy between filament tips and dislocations on a periodic polar lattice, we devise a simulation framework for an active spiral. In-silico, we demonstrate optimal strategies for how reversal dynamics control material exchange, which may shed light on the physiological role of this dynamical behavior in bacteria.