The position of a division site in the rod-shaped bacterium E. coli is partially determined by pole-to-pole oscillations of the Min-family of proteins—MinC, MinD, and MinE. Furthermore, experiments reveal that MinD protein polymerizes on the membrane into filaments and that MinE protein forms an oscillating ring. We assume that MinD filaments are single-stranded (two-stranded hypothesis has been already tested in our previous paper [20]). In the filamentous cells zebra-striped MinD oscillation pattern, fully formed oscillating MinE rings, and weakly fluorescent, rapidly moving MinE rings are experimentally observed. All these phenomena are reproduced by our three-dimensional off-lattice stochastic reaction-diffusion model. An algorithm with adaptive time steps is implemented in order to speed up the time-consuming process of tracking each protein in the computer simulation.