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

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