Stochastic switching between multistable oscillation patterns of the Min-system

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 threedimensional 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.

Effects of geometry and topography on Min-protein dynamics

“…Coexistence of several Min-protein patterns has been reported before for the dynamic equations introduced in Ref. [ 49 ], see [ 50 , 51 ]. All of the patterns can be decomposed into standing wave patterns along the rectangles’ symmetry axes with appropriate relative phases.…”

“…To obtain the symmetric patterns shown in Fig 7 , we chose the initial distribution of proteins to be inhomogeneous along one of the symmetry axes. In presence of molecular noise, one expects stochastic switches between the different stable patterns [ 51 ] similar to the stochastic switching between the two cell poles in short bacteria with over-expressed Min proteins [ 52 ].…”

Test Models for Statistical Inference: Two-Dimensional Reaction Systems Displaying Limit Cycle Bifurcations and Bistability

“…In this section, we show that systems (12) and (15) (see below), the latter of which is known to display bicyclicity and a multiple limit cycle bifurcation, are topologically equivalent near the corresponding critical points, provided conditions (14) are satisfied. In Figures 2(c) and 2(d), we show the phase plane diagram of (12) for a particular choice of the parameters satisfying (14), and it can be seen that the system also displays bicyclicity and a multiple limit cycle bifurcation, with Figures 2(c) and 2(d) showing the cases before and after the bifurcation, respectively. In Figure 2(c), the only stable invariant set is the limit cycle shown in red, while in Figure 2(d) there are two additional limit cyclesa stable one, shown in purple, and an unstable one, shown in black.…”

Large-scale modulation of reconstituted Min protein patterns and gradients by defined mutations in MinE’s membrane targeting sequence

“…Even though MinE’s MTS has been investigated previously, its precise role in pattern and gradient formation has remained ambiguous. While it was suggested theoretically that MinE membrane interaction is important for robust pattern formation [ 23 , 33 ], many mathematical models display regular Min protein dynamics even in its absence [ 34 – 36 ]. On the other hand, in vivo experiments showed that mutations in MinE’s MTS are associated with severe cell division defects [ 31 ].…”