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.

Emergent ultra–long-range interactions between active particles in hybrid active–inactive systems

“…Sea urchin sperm cells have been found to phase separate and organize into arrays of vortices when the density of spermatozoa is large enough (10). In fact, a myriad of biological systems, and experimental systems with biological components, have reported swarming (11)(12)(13), flocking (6,14,15), spiraling (13,16), and many more nonequilibrium steady states (17,18). It is clear that, in all these systems, a combination of the activity, shape of the active agents, and the environment lead to effective out-ofequilibrium interactions that determine their steady states.…”

Formation of spiral coils among self-propelled chains

“…We cannot entirely rule out other effects that resemble attraction in a real biological system, for example, the entanglement of lateral flagella in the swarm of V. alginolyticus. Nevertheless, we specify that the exclude volume interaction is the only interaction between the chains in this work as it appears to be the most significant effect observed in the experiments [19,24].…”

“…Therefore, the bending elasticity of the cell envelope shall play a role in the in-plane rotational dynamics and the formation of clusters among the bacteria. Meanwhile, some of the very long bacteria (> 100 µm) in the swarm fold into an ordered, compact conformation called the spiral-coil [19] in spite of the stiff cell envelope. It is speculated that the onset of forming the spiral-coil is triggered by collision events from a number of clusters formed by the shorter bacteria.…”

Shelter in a Swarm

“…Also, placing bacteria between two no-slip boundaries creates an environment that is different from a natural swarm whose upper surface is not stationary [25]. The best platform on which to observe the swarm would be the natural open one, where the bacteria have themselves initiated movement [26-28]. …”