Three-dimensional structure of the Z-ring as a random network of FtsZ filaments

The spatial organization of the Z-ring, the central element of the bacterial division machinery, is not yet fully understood. Using optical tweezers and subpixel image analysis, we have recently shown that the radial width of the Z-ring in unconstricted Escherichia coli is about 100 nm. The relatively large width is consistent with the observations of others. Moreover, simulation of the experimental FtsZ distribution using the theoretical three-dimensional (3D) point spread function was strongly in favour of a toroidal rather than a thin cylindrical model of the Z-ring. Here, we show that the low density of FtsZ filaments in the ring coincides within experimental uncertainty with the critical density of a 3D random network of cylindrical sticks. This suggests that the Z-ring may consist of a percolating network of FtsZ filaments. Several factors that are expected to affect the polymerization state and the extent of self-interaction of FtsZ within the Z-ring, as well as the functional implications of its sparse toroidal structure, are discussed in terms of percolation theory.