Paths and patterns: the biology and physics of swimming bacterial populations

The velocity distribution of swimming micro-organisms depends on directional cues supplied by the environment. Directional swimming within a bounded space results in the accumulation of organisms near one or more surfaces. Gravity, gradients of chemical concentration and illumination affect the motile behaviour of individual swimmers. Concentrated populations of organisms scatter and absorb light or consume molecules, such as oxygen. When supply is one-sided, consumption creates gradients; the presence of the population alters the intensity and the symmetry of the environmental cues. Patterns of cues interact dynamically with patterns of the consumer population. In suspensions, spatial variations in the concentration of organisms are equivalent to variations of mean mass density of the fluid. When organisms accumulate in one region whilst moving away from another region, the force of gravity causes convection that translocates both organisms and dissolved substances. The geometry of the resulting concentration-convection patterns has features that are remarkably reproducible. Of interest for biology are (1) the long-range organisation achieved by organisms that do not communicate, and (2) that the entire system, consisting of fluid, cells, directional supply of consumables, boundaries and gravity, generates a dynamic that improves the organisms' habitat by enhancing transport and mixing. Velocity distributions of the bacterium Bacillus subtilis have been measured within the milieu of the spatially and temporally varying oxygen concentration which they themselves create. These distributions of swimming speed and direction are the fundamental ingredients required for a quantitative mathematical treatment of the patterns. The quantitative measurement of swimming behaviour also contributes to our understanding of aerotaxis of individual cells.