A mechanical explanation for cytoskeletal rings and helices in bacteria

Several bacterial proteins have been shown to polymerize into coils or rings on cell membranes. These include the cytoskeletal proteins MreB, FtsZ, and MinD, which together with other cell components make up what is being called the bacterial cytoskeleton. We believe that these shapes arise, at least in part, from the interaction of the inherent mechanical properties of the protein polymers and the constraints imposed by the curved cell membrane. This hypothesis, presented as a simple mechanical model, was tested with numerical energy-minimization methods from which we found that there are five low-energy polymer morphologies on a rod-shaped membrane: rings, lines, helices, loops, and polar-targeted circles. Analytic theory was used to understand the possible structures and to create phase diagrams that show which parameter combinations lead to which structures. Inverting the results, it is possible to infer the effective mechanical bending parameters of protein polymers from fluorescence images of their shapes. This theory also provides a plausible explanation for the morphological changes exhibited by the Z ring in a sporulating Bacillus subtilis; is used to calculate the mechanical force exerted on a cell membrane by a polymer; and allows predictions of polymer shapes in mutant cells.