Abstract
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.
Highlights
The bacterial Min-proteins are a well studied example of a pattern-forming protein system that gives rise to rich spatiotemporal oscillations
The dynamic nature of this protein system was demonstrated by live cell imaging in E. coli bacteria, where these proteins oscillate along the longitudinal axis between the cell poles of the rod-shaped bacterium, forming so-called polar zones [2,3,4,5]
With this particular choice the width of the system approximately matches the typical length of wild-type E. coli cells and the length of the system corresponds to the length of a grown E. coli cell which can roughly double in length before septum formation and division
Summary
The bacterial Min-proteins are a well studied example of a pattern-forming protein system that gives rise to rich spatiotemporal oscillations. Most bacteria use a cytoskeletal structure, a so-called Z-ring, for the completion of bacterial cytokinesis [6] This Z-ring self-assembles from filaments of polymerized FtsZ-proteins, the prokaryotic homolog of the eukaryotic protein tubulin [7], which serve as a scaffold structure for midcell constriction and the eventual septum formation in the midplane. If successful, this process creates two sized daughter cells with an identical set of genetic information [8]. While nucleoid occlusion prevents division near the chromosome, the Min-system actively keeps the divisome away from the cell poles through the MinC-protein acting as FtsZ-polymerization inhibitor [5]. MinC is indispensable for correct division site placement, it acts only as a passenger molecule, passively following the oscillatory dynamics of MinD and MinE [2, 3, 11]
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