E. coli is a rod-shaped bacterium that grows and divides into two equivalent daughter cells. One mechanism that regulates the central placement of the division site is the Min-protein system, which prevents division near the cell ends. A surprising discovery in recent years is that the Min system is an oscillator involving wholesale shifts of proteins from one end of the cell to the other. We present a complete model of the Min system, using only known properties of the proteins, which accurately reproduces the observed oscillations. The oscillations are driven by hydrolysis of ATP: (1) MinD binds ATP and the complex binds to the membrane; (2) MinE binds to the MinD:ATP, induces ATP hydrolysis, and all constituents are released from the membrane; (3) MinD:ADP releases ADP, completing the cycle. 

The model correctly reproduces the central experimental observations: (1) In each oscillation, the protein MinD accumulates in the cell membrane in a ``polar zone'' at the end of the cell. This polar zone then shrinks toward the end of the cell, as a new accumulation forms at the opposite pole; (2) the protein MinE forms a ring at the boundary of the MinD endcap; and (3) the oscillation period is proportional to the ratio of the total amounts of MinD and MinE in the cell. Our model explains why MinD accumulates at the poles of the cell without special targets at the cell ends and predicts the formation of a MinE ring without any MinE-MinE interaction. Another success of the model is  the doubling of the spatial oscillation pattern in long cells (>10 microns).  Our model also predicts that Min-protein oscillations can select the long axis in nearly round cells, a potentially important factor in division-plane selection in round bacteria such as Neisseria gonnorhoeae Finally, we propose an answer to the fundamental question of why E. coli needs an oscillator.