Modeling partitioning of Min proteins between daughter cells after septation in Escherichia coli

The mechanism of MinD stability modulation by MinE in Min protein dynamics

The patterns formed both in vivo and in vitro by the Min protein system have attracted much interest because of the complexity of their dynamic interactions given the apparent simplicity of the component parts. Despite both the experimental and theoretical attention paid to this system, the details of the biochemical interactions of MinD and MinE, the proteins responsible for the patterning, are still unclear. For example, no model consistent with the known biochemistry has yet accounted for the observed dual role of MinE in the membrane stability of MinD. Until now, a statistical comparison of models to the time course of Min protein concentrations on the membrane has not been carried out. Such an approach is a powerful way to test existing and novel models that are difficult to test using a purely experimental approach. Here, we extract time series from previously published fluorescence microscopy time lapse images of in vitro experiments and fit two previously described and one novel mathematical model to the data. We find that the novel model, which we call the Asymmetric Activation with Bridged Stability Model, fits the time-course data best. It is also consistent with known biochemistry and explains the dual MinE role via MinE-dependent membrane stability that transitions under the influence of rising MinE to membrane instability with positive feedback. Our results reveal a more complex network of interactions between MinD and MinE underlying Min-system dynamics than previously considered.

Molecular Interactions of the Min Protein System Reproduce Spatiotemporal Patterning in Growing and Dividing Escherichia coli Cells

Oscillations of the Min protein system are involved in the correct midcell placement of the divisome during Escherichia coli cell division. Based on molecular interactions of the Min system, we formulated a mathematical model that reproduces Min patterning during cell growth and division. Specifically, the increase in the residence time of MinD attached to the membrane as its own concentration increases, is accounted for by dimerisation of membrane-bound MinD and its interaction with MinE. Simulation of this system generates unparalleled correlation between the waveshape of experimental and theoretical MinD distributions, suggesting that the dominant interactions of the physical system have been successfully incorporated into the model. For cells where MinD is fully-labelled with GFP, the model reproduces the stationary localization of MinD-GFP for short cells, followed by oscillations from pole to pole in larger cells, and the transition to the symmetric distribution during cell filamentation. Cells containing a secondary, GFP-labelled MinD display a contrasting pattern. The model is able to account for these differences, including temporary midcell localization just prior to division, by increasing the rate constant controlling MinD ATPase and heterotetramer dissociation. For both experimental conditions, the model can explain how cell division results in an equal distribution of MinD and MinE in the two daughter cells, and accounts for the temperature dependence of the period of Min oscillations. Thus, we show that while other interactions may be present, they are not needed to reproduce the main characteristics of the Min system in vivo.

Self-organized partitioning of dynamically localized proteins in bacterial cell division

The Min proteins are equally partitioned between daughter cells at division.

The mechanism allowing this accurate distribution is intrinsic to the Min system.

Individual oscillations appear in each daughter cell before cytokinesis is completed.

Diffusion through the gradually constricting septum is key to this process.

One of the central problems of cell division is the proper distribution of all components to the progeny, which is essential to avoid the adverse effects that an unequal distribution—when not actively sought for differentiation purposes—would have on cell growth and regulation. Fast-growing bacterial cells are particularly exposed to this problem, as corrections of inequalities in protein distribution by biosynthesis could be too slow compared with the generation time. Moreover, bacterial proteins are usually stable and, therefore, their levels are not easily adjustable in one generation. Although for homogeneously distributed proteins an equal partitioning at division is readily achieved, dedicated mechanisms must exist to segregate proteins or cellular structures that possess a specific cellular location, but these mechanisms are largely unknown.

An extremely challenging case is represented by the Min proteins—MinC, MinD and MinE—that in Escherichia coli oscillate from pole to pole to inhibit the assembly of the cytokinetic ring anywhere except at mid-cell. The oscillations stem solely from local interactions among the proteins at the cytoplasmic membrane. In this work, we show that self-organization is also responsible for the distribution of Min proteins between daughter cells at division. Our combined experimental and computational results demonstrate that the equal protein partitioning stems from interplay between the self-organized oscillations and changes in the cell geometry during division, with no need for any additional regulatory network.

Using high-resolution time-lapse microscopy, we detected changes in the Min oscillatory regime that correlate with the amount of septal constriction (Figure 3A, B, E and F). When the cell is unconstricted, oscillations run from pole to pole (Figure 3A). When the constriction reaches a certain degree, typically corresponding to a septum of 600–500 nm, the oscillations change into a ‘half-cell to half-cell' mode during which the fluorescence covers, alternatively, the entire membrane of one daughter cell (Figure 3A, B and E). This mode persists for several minutes and, just before cell division when the septum is smaller than 200 nm, gives way to yet another oscillatory pattern wherein oscillations split and run independently in each daughter cell (Figure 3A, B and F).

Our 3D stochastic computer simulations revealed that these different regimes are an outcome of impaired diffusion through the closing septum and that oscillations finally split because protein exchange between the two future daughter cells becomes critically slow, so that independent oscillations on both sides of the septum become the stable solution (Figure 6A and E). FRAP experiments confirmed that the presence of the septum is enough to slow down the passage of molecules from one side of the cell to the other (Figure 6F). As oscillations become independent in each daughter cell before completion of cytokinesis, diffusion through the septum can still occur, which further equilibrates the levels of the Min proteins in the daughter cells (Figure 3C and D and Figure 6B, C and D).

In summary, our results suggest that E. coli cells have evolved a very simple and elegant way to ensure equal concentrations of the Min proteins in the progeny, based entirely on the intrinsic self-organizing properties of the Min system. This provides a clear example of self-organizing partitioning, which we expect to be a widely used strategy given its simplicity and low evolutionary cost.

How cells manage to get equal distribution of their structures and molecules at cell division is a crucial issue in biology. In principle, a feedback mechanism could always ensure equality by measuring and correcting the distribution in the progeny. However, an elegant alternative could be a mechanism relying on self-organization, with the interplay between system properties and cell geometry leading to the emergence of equal partitioning. The problem is exemplified by the bacterial Min system that defines the division site by oscillating from pole to pole. Unequal partitioning of Min proteins at division could negatively impact system performance and cell growth because of loss of Min oscillations and imprecise mid-cell determination. In this study, we combine live cell and computational analyses to show that known properties of the Min system together with the gradual reduction of protein exchange through the constricting septum are sufficient to explain the observed highly precise spontaneous protein partitioning. Our findings reveal a novel and effective mechanism of protein partitioning in dividing cells and emphasize the importance of self-organization in basic cellular processes.

Changes in the Min oscillation pattern before and after cell birth

The Min system regulates the positioning of the cell division site in many bacteria. In Escherichia coli, MinD migrates rapidly from one cell pole to the other. In conjunction with MinC, MinD helps to prevent unwanted FtsZ rings from assembling at the poles and to stabilize their positioning at midcell. Using time-lapse microscopy of growing and dividing cells expressing a gfp-minD fusion, we show that green fluorescent protein (GFP)-MinD often paused at midcell in addition to at the poles, and the frequency of midcell pausing increased as cells grew longer and cell division approached. At later stages of septum formation, GFP-MinD often paused specifically on only one side of the septum, followed by migration to the other side of the septum or to a cell pole. About the time of septum closure, this irregular pattern often switched to a transient double pole-to-pole oscillation in the daughter cells, which ultimately became a stable double oscillation. The splitting of a single MinD zone into two depends on the developing septum and is a potential mechanism to explain how MinD is distributed equitably to both daughter cells. Septal pausing of GFP-MinD did not require MinC, suggesting that MinC-FtsZ interactions do not drive MinD-septal interactions, and instead MinD recognizes a specific geometric, lipid, and/or protein target at the developing septum. Finally, we observed regular end-to-end oscillation over very short distances along the long axes of minicells, supporting the importance of geometry in MinD localization.

Cardiolipin membrane domains in prokaryotes and eukaryotes

Cardiolipin (CL) plays a key role in dynamic organization of bacterial and mitochondrial membranes. CL forms membrane domains in bacterial cells, and these domains appear to participate in binding and functional regulation of multi-protein complexes involved in diverse cellular functions including cell division, energy metabolism, and membrane transport. Visualization of CL domains in bacterial cells by the fluorescent dye 10-N-nonyl acridine orange is critically reviewed. Possible mechanisms proposed for CL dynamic localization in bacterial cells are discussed. In the mitochondrial membrane CL is involved in organization of multi-subunit oxidative phosphorylation complexes and in their association into higher order supercomplexes. Evidence suggesting a possible role for CL in concert with ATP synthase oligomers in establishing mitochondrial cristae morphology is presented. Hypotheses on CL-dependent dynamic re-organization of the respiratory chain in response to changes in metabolic states and CL dynamic re-localization in mitochondria during the apoptotic response are briefly addressed.