# Can a flux-based mechanism explain positioning of protein clusters in a three-dimensional cell geometry?

## TL;DR

This study introduces a three-dimensional mathematical model demonstrating that flux-based mechanisms can effectively position protein clusters in bacterial cells, accounting for realistic cell geometries and diffusion processes.

## Contribution

The paper extends previous flux-based positioning models to three-dimensional cell geometries, showing that cluster localization is robust in more realistic biological contexts.

## Key findings

- Cluster moves to midcell in 3D geometry
- Diffusion in cytosol is crucial for positioning
- Mechanism positions two clusters equidistantly

## Abstract

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 towards 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. We conclude that a flux-based mechanism allows for cluster positioning in a biologically realistic three-dimensional cell geometry.