In the bacterium E. coli, a spatiotemporal oscillation of specific proteins guarantees a reliable division of the cell at its center. Confocal fluorescence microscopy shows that these proteins form helices on the inner wall of the cell membrane. We describe this dynamics in terms of the growing and shrinking of two interacting protein polymers. The effect of cytosolic diffusion of the proteins as well as spatial patterns in long cells are investigated. The theoretical results are presented in a way that allows direct comparison with experimentally obtained pictures.