Dynamics of self-organized rotating spiral-coils in bacterial swarms

Abstract

Self-propelled particles (SPP) exhibit complex collective motions, mimicking autonomous behaviors that are often seen in the natural world, but essentially are generated by simple mutual interactions. Previous research on SPP systems focuses on collective behaviors of a uniform population. However, very little is known about the evolution of individual particles under the same global influence. Here we show self-organized rotating spiral coils in a two-dimensional (2D) active system. By using swarming bacteria Vibrio alginolyticus as an ideal experimental realization of a well-controlled 2D self-propelled system, we study the interaction between ultra-long cells and short background active cells. The self-propulsion of long cells and their interactions with neighboring short cells leads to a self-organized, stable spiral rotational state in 2D. We find four types of spiral coils with two main features: the rotating direction (clockwise or counter-clockwise) and the central structure (single or double spiral). The body length of the spiral coils falls between 32 and 296 μm and their rotational speed is within a range from 2.22 to 22.96 rad s⁻¹. The dynamics of these spiral coils involves folding and unfolding processes, which require local velocity changes of the long bacterium. This phenomenon can be qualitatively replicated by a Brownian dynamics simulation using a simple rule of the propulsion thrust, imitating the reorientation of bacterial flagella. Apart from the physical and biological interests in swarming cells, the formation of self-organized spiral coils could be useful for the next generation of microfabrication.