Under special conditions bacteria excrete an attractant and aggregate. The high density regions initially collapse into cylindrical structures, which subsequently destabilize and break up into spherical aggregates. This paper presents a theoretical description of the process, from the structure of the collapsing cylinder to the spacing of the final aggregates. We show that cylindrical collapse involves a delicate balance in which bacterial attraction and diffusion nearly cancel, leading to corrections to the collapse laws expected from dimensional analysis. The instability of a collapsing cylinder is composed of two distinct stages: Initially, slow modulations to the cylinder develop, which correspond to a variation of the collapse time along the cylinder axis. Ultimately, one point on the cylinder pinches off. At this final stage of the instability, a front propagates from the pinch into the remainder of the cylinder. The spacing of the resulting spherical aggregates is determined by the front propagation.

33 pages, 15 figures