PHYSICAL-MECHANISMS FOR CHEMOTACTIC PATTERN-FORMATION BY BACTERIA

This paper formulates a theory for chemotactic pattern formation by th e bacteria Escherichia coli in the presence of excreted attractant. In a chemotactically neutral background, through chemoattractant signali ng, the bacteria organize into swarm rings and aggregates. The analysi s invokes only those physical processes that are both justifiable by k nown biochemistry and necessary and sufficient for swarm ring migratio n and aggregate formation. Swarm rings migrate in the absence of an ex ternal chemoattractant gradient. The ring motion is caused by the depl etion of a substrate that is necessary to produce attractant. Several scaling laws are proposed and are demonstrated to be consistent with e xperimental data. Aggregate formation corresponds to finite time singu larities in which the bacterial density diverges at a point. Instabili ties of swarm rings leading to aggregate formation occur via a mechani sm similar to aggregate formation itself: when the mass density of the swarm ring exceeds a threshold, the ring collapses cylindrically and then destabilizes into aggregates. This sequence of events is demonstr ated both in the theoretical model and in the experiments.