Abstract
Self-organized pattern formation is common in biological systems. Microbial populations can generate spatiotemporal patterns through various mechanisms, such as chemotaxis, quorum sensing, and mechanical interactions. When their motile behavior is coupled to a gravitational potential field, swimming microorganisms display a phenomenon known as bioconvection, which is characterized by the pattern formation of active cellular plumes that enhance material mixing in the fluid. While bioconvection patterns have been characterized in various organisms, including eukaryotic and bacterial microswimmers, the dynamics of bioconvection pattern formation in bacteria is less explored. Here, we study this phenomenon using suspensions of a chemotactic bacterium Bacillus subtilis confined in closed three-dimensional (3D) fluid chambers. We discovered an active plume lattice pattern that displays hexagonal order and emerges via a self-organization process. By flow field measurement, we revealed a toroidal flow structure associated with individual plumes. We also uncovered a power-law scaling relation between the lattice pattern's wavelength and the dimensionless Rayleigh number that characterizes the ratio of buoyancy-driven convection to diffusion. Taken together, this study highlights that coupling between chemotaxis and external potential fields can promote the self-assembly of regular spatial structures in bacterial populations. The findings are also relevant to material transport in surface water environments populated by swimming microorganisms.