Anti-Diffusion in an Algae-Bacteria Microcosm: Photosynthesis, Chemotaxis, and Expulsion

In Nature there are significant relationships known between microorganisms from two kingdoms of life, as in the supply of vitamin B$_{12}$ by bacteria to algae. Such interactions motivate general investigations into the spatio-temporal dynamics of metabolite exchanges. Here we study by experiment and theory a model system: a coculture of the bacterium $B. subtilis$, an obligate aerobe that is chemotactic to oxygen, and a nonmotile mutant of the alga $C. reinhardtii$, which photosynthetically produces oxygen when illuminated. Strikingly, when a shaft of light illuminates a thin, initially uniform suspension of the two, the chemotactic influx of bacteria to the photosynthetically active region leads to expulsion of the algae from that area. This effect arises from algal transport due to spatially-varying collective behavior of bacteria, and is mathematically related to the ``turbulent diamagnetism" associated with magnetic flux expulsion in stars.