Can a Flux-Based Mechanism Explain Protein Cluster Positioning in a Three-Dimensional Cell Geometry?

The plane of bacterial cell division must be precisely positioned. In the bacterium Myxococcus xanthus, the proteins PomX and PomY form a large cluster, which is tethered to the nucleoid by the ATPase PomZ and moves in a stochastic but biased manner toward midcell where it initiates cell division. Previously, a positioning mechanism based on the fluxes of PomZ on the nucleoid was proposed. However, the cluster dynamics was analyzed in a reduced, one-dimensional geometry. Here, we introduce a mathematical model that accounts for the three-dimensional shape of the nucleoid, such that nucleoid-bound PomZ dimers can diffuse past the cluster without interacting with it. Using stochastic simulations, we find that the cluster still moves to and localizes at midcell. Redistribution of PomZ by diffusion in the cytosol is essential for this cluster dynamics. Our mechanism also positions two clusters equidistantly on the nucleoid, as observed for low-copy-number plasmid partitioning. We conclude that a flux-based mechanism allows for cluster positioning in a biologically realistic three-dimensional cell geometry.