Determination of the proper site for division in Escherichia coli and other bacteria involves a unique spatial oscillatory system in which membrane-associated structures composed of the MinC, MinD and MinE proteins oscillate rapidly between the two cell poles. In vitro evidence indicates that this involves ordered cycles of assembly and disassembly of MinD polymers. We propose a mathematical model to explain this behavior. Unlike previous attempts, the present approach is based on the expected behavior of polymerization-depolymerization systems and incorporates current knowledge of the biochemical properties of MinD and MinE. Simulations based on the model reproduce all of the known topological and temporal characteristics of the in vivo oscillatory system.Min ͉ cell division ͉ cytoskeleton M ost bacteria divide by forming a division septum at the midpoint of the cell. Accurate placement of the division site is required to permit the equidistribution of genetic and cytoplasmic components between daughter cells. In Escherichia coli and related organisms, placement of the septum is regulated by a system of negative control, mediated by the three proteins of the MinCDE system (reviewed in ref. 1). The Min system prevents septation at potential division sites near cell poles without blocking septum formation at the desired midcell location. The MinC protein is responsible for the septation block. MinD and MinE prevent MinC from blocking division at the desired midcell site while permitting it to act at other potential division sites, thereby giving topological specificity to the division inhibitor. This process involves a unique oscillatory system in which membrane-associated MinC, -D, and -E oscillate rapidly from pole to pole.The oscillation process is initiated by assembly of a membraneassociated polar zone consisting of MinC, MinD, and MinE (2-5), which first appears near a cell pole and grows toward midcell (Fig. 1). As the growing polar zone approaches midcell, MinE forms an annular structure (the E-ring) at its leading edge. The polar zone then disassembles, retracting from midcell back to the original pole. The E-ring remains associated with the medial edge of the zone during the disassembly stage (6, 7).As the polar zone retracts from one pole, a new cycle of assembly and disassembly is initiated at the opposite end of the cell. In this way, MinC, -D, and -E oscillate from pole-to-pole with a periodicity of Ϸ1 min (2, 4-7). As a result, the timeaveraged concentration of the MinC division inhibitor is kept low at midcell, thereby permitting assembly of the new septum at this site. Although MinC normally accompanies MinD throughout the oscillation cycle, MinC is not required for the oscillation phenomenon, which requires only MinD and MinE (2, 3).In vitro, MinD binds to phospholipid vesicles in the presence of ATP (8). MinE destabilizes the phospholipid-MinD-ATP interaction by binding to the vesicle-bound MinD; this activates the MinD ATPase (9), leading to release of MinD-ADP and MinE from the vesicles.MinD ...