  The spatiotemporal oscillation patterns of the proteins MinD and MinE are
used by the bacterium E. coli to sense its own geometry. Strikingly, both
computer simulations and experiments have recently shown that for the same
geometry of the reaction volume, different oscillation patterns can be stable,
with stochastic switching between them. Here we use particle-based Brownian
dynamics simulations to predict the relative frequency of different oscillation
patterns over a large range of three-dimensional compartment geometries, in
excellent agreement with experimental results. Fourier analyses as well as
pattern recognition algorithms are used to automatically identify the different
oscillation patterns and the switching rates between them. We also identify
novel oscillation patterns in three-dimensional compartments with
membrane-covered walls and identify a linear relation between the bound
Min-protein densities and the volume-to-surface ratio. In general, our work
shows how geometry sensing is limited by multistability and stochastic
fluctuations.
