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

Location of the axon initial segment assembly can be predicted from neuronal shape

The axon initial segment (AIS) is located at the proximal axon demarcating the boundary between axonal and somatodendritic compartments. The AIS facilitates the generation of action potentials and maintenance of neuronal polarity. In this study, we show that the location of AIS assembly, as marked by Ankyrin G, corresponds to the nodal plane of the lowest-order harmonic of the Laplace-Beltrami operator solved over the neuronal shape. This correlation establishes a coupling between location of AIS assembly and neuronal cell morphology. We validate this correlation for neurons with atypical morphology and neurons containing multiple AnkG clusters on distinct neurites, where the nodal plane selects the appropriate axon showing enriched Tau. Based on our findings, we propose that Turing patterning systems are candidates for dynamically governing AIS location. Overall, this study highlights the importance of neuronal cell morphology in determining the precise localization of the AIS within the proximal axon.

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.

Division plane placement in pleomorphic archaea is dynamically coupled to cell shape

One mechanism for achieving accurate placement of the cell division machinery is via Turing patterns, where nonlinear molecular interactions spontaneously produce spatiotemporal concentration gradients. The resulting patterns are dictated by cell shape. For example, the Min system of Escherichia coli shows spatiotemporal oscillation between cell poles, leaving a mid-cell zone for division. The universality of pattern-forming mechanisms in divisome placement is currently unclear. We examined the location of the division plane in two pleomorphic archaea, Haloferax volcanii and Haloarcula japonica, and showed that it correlates with the predictions of Turing patterning. Time-lapse analysis of H. volcanii shows that divisome locations after successive rounds of division are dynamically determined by daughter cell shape. For H. volcanii, we show that the location of DNA does not influence division plane location, ruling out nucleoid occlusion. Triangular cells provide a stringent test for Turing patterning, where there is a bifurcation in division plane orientation. For the two archaea examined, most triangular cells divide as predicted by a Turing mechanism; however, in some cases multiple division planes are observed resulting in cells dividing into three viable progeny. Our results suggest that the division site placement is consistent with a Turing patterning system in these archaea.

Active Transport of Membrane Components by Self-Organization of the Min Proteins

Heterogeneous distribution of components in the biological membrane is critical in the process of cell polarization. However, little is known about the mechanisms that can generate and maintain the heterogeneous distribution of the membrane components. Here, we report that the propagating wave patterns of the bacterial Min proteins can impose steric pressure on the membrane, resulting in transport and directional accumulation of the component in the membrane. Therefore, the membrane component waves represent transport of the component in the membrane that is caused by the steric pressure gradient induced by the differential levels of binding and dissociation of the Min proteins in the propagating waves on the membrane surface. The diffusivity, majorly influenced by the membrane anchor of the component, and the repulsed ability, majorly influenced by the steric property of the membrane component, determine the differential spatial distribution of the membrane component. Thus, transportation of the membrane component by the Min proteins follows a simple physical principle, which resembles a linear peristaltic pumping process, to selectively segregate and maintain heterogeneous distribution of materials in the membrane. VIDEO ABSTRACT.

The Min-protein oscillations in Escherichia coli: an example of self-organized cellular protein waves

In the rod-shaped bacterium Escherichia coli, selection of the cell centre as the division site involves pole-to-pole oscillations of the proteins MinC, MinD and MinE. This spatio-temporal pattern emerges from interactions among the Min proteins and with the cytoplasmic membrane. Combining experimental studies in vivo and in vitro together with theoretical analysis has led to a fairly good understanding of Min-protein self-organization. In different geometries, the system can, in addition to standing waves, also produce travelling planar and spiral waves as well as coexisting stable stationary distributions. Today it stands as one of the best-studied examples of cellular self-organization of proteins.This article is part of the theme issue 'Self-organization in cell biology'.

Effects of geometry and topography on Min-protein dynamics

In the rod-shaped bacterium Escherichia coli, the center is selected by the Min-proteins as the site of cell division. To this end, the proteins periodically translocate between the two cell poles, where they suppress assembly of the cell division machinery. Ample evidence notably obtained from in vitro reconstitution experiments suggests that the oscillatory pattern results from self-organization of the proteins MinD and MinE in presence of a membrane. A mechanism built on cooperative membrane attachment of MinD and persistent MinD removal from the membrane induced by MinE has been shown to be able to reproduce the observed Min-protein patterns in rod-shaped E. coli and on flat supported lipid bilayers. Here, we report our results of a numerical investigation of patterns generated by this mechanism in various geoemtries. Notably, we consider the dynamics on membrane patches of different forms, on topographically structured lipid bilayers, and in closed geometries of various shapes. We find that all previously described patterns can be reproduced by the mechanism. However, it requires different parameter sets for reproducing the patterns in closed and in open geometries.

A Markovian Approach towards Bacterial Size Control and Homeostasis in Anomalous Growth Processes

Regardless of the progress achieved during recent years, the mechanisms coupling growth and division to attain cell size homeostasis in bacterial populations are still not well understood. In particular, there is a gap of knowledge about the mechanisms controlling anomalous growth events that are ubiquitous even in wild-type phenotypes. Thus, when cells exceed the doubling size the divisome dynamics sets a characteristic length scale that suggests a sizer property. Yet, it has been recently shown that the size at birth and the size increment still satisfy an adder-like correlation. Herein we propose a Markov chain model, that we complement with computational and experimental approaches, to clarify this issue. In this context, we show that classifying cells as a function of the characteristic size set by the divisome dynamics provides a compelling framework to understand size convergence, growth, and division at the large length scale, including the adaptation to, and rescue from, filamentation processes. Our results reveal the independence of size homeostasis on the division pattern of long cells and help to reconcile sizer concepts at the single cell level with an adder-like behavior at a population level.

Mathematical modeling of spatiotemporal protein localization patterns in C. crescentus bacteria: A mechanism for asymmetric FtsZ ring positioning

We examine the localization patterns of ParA, ParB, PopZ, and MipZ, which are key division proteins in C. crescentus bacteria. While Par and PopZ proteins have been implicated in the physical segregation of the replicated chromosome, MipZ dimers control the placement of the cell division plane by preventing FtsZ proteins from assembling into a Z-ring. MipZ proteins generate bipolar gradients that are sensitive to Par protein localization, however, it is not understood how the MipZ gradient is shaped so as to allow for the correct Z-ring placement during asymmetric cell division in C. crescentus. In this paper, we develop and analyze a mathematical model that incorporates the known interactions between Par, PopZ, and MipZ proteins and use it to test mechanisms for MipZ gradient formation. Using our model, we show that gradient-dependent ParB advection velocities in conjunction with a ParA polar recycling mechanism are sufficient to maintain a robust new pole-directed ParA dimer gradient during segregation. A "saturation of binding site" hypothesis limiting access of ParA and MipZ to the ParB complex is then necessary and sufficient to generate time-averaged bipolar MipZ protein gradients with minima that are skewed toward ParA gradient peaks at the new pole, in agreement with data. By analyzing reduced versions of the model, we show the existence of oscillatory ParA localization regimes provided that cytoplasmic PopZ oligomers interact with ParA and ParA is over-expressed. We use our model to study mechanisms by which these protein patterns may simultaneously direct proper chromosome segregation and division site placement in C. crescentus.

Dissecting the role of conformational change and membrane binding by the bacterial cell division regulator MinE in the stimulation of MinD ATPase activity

The bacterial cell division regulators MinD and MinE together with the division inhibitor MinC localize to the membrane in concentrated zones undergoing coordinated pole-to-pole oscillation to help ensure that the cytokinetic division septum forms only at the mid-cell position. This dynamic localization is driven by MinD-catalyzed ATP hydrolysis, stimulated by interactions with MinE's anti-MinCD domain. This domain is buried in the 6-β-stranded MinE "closed" structure, but is liberated for interactions with MinD, giving rise to a 4-β-stranded "open" structure through an unknown mechanism. Here we show that MinE-membrane interactions induce a structural change into a state resembling the open conformation. However, MinE mutants lacking the MinE membrane-targeting sequence stimulated higher ATP hydrolysis rates than the full-length protein, indicating that binding to MinD is sufficient to trigger this conformational transition in MinE. In contrast, conformational change between the open and closed states did not affect stimulation of ATP hydrolysis rates in the absence of membrane binding, although the MinD-binding residue Ile-25 is critical for this conformational transition. We therefore propose an updated model where MinE is brought to the membrane through interactions with MinD. After stimulation of ATP hydrolysis, MinE remains bound to the membrane in a state that does not catalyze additional rounds of ATP hydrolysis. Although the molecular basis for this inhibited state is unknown, previous observations of higher-order MinE self-association may explain this inhibition. Overall, our findings have general implications for Min protein oscillation cycles, including those that regulate cell division in bacterial pathogens.

Non-linear Min protein interactions generate harmonics that signal mid-cell division in Escherichia coli

The Min protein system creates a dynamic spatial pattern in Escherichia coli cells where the proteins MinD and MinE oscillate from pole to pole. MinD positions MinC, an inhibitor of FtsZ ring formation, contributing to the mid-cell localization of cell division. In this paper, Fourier analysis is used to decompose experimental and model MinD spatial distributions into time-dependent harmonic components. In both experiment and model, the second harmonic component is responsible for producing a mid-cell minimum in MinD concentration. The features of this harmonic are robust in both experiment and model. Fourier analysis reveals a close correspondence between the time-dependent behaviour of the harmonic components in the experimental data and model. Given this, each molecular species in the model was analysed individually. This analysis revealed that membrane-bound MinD dimer shows the mid-cell minimum with the highest contrast when averaged over time, carrying the strongest signal for positioning the cell division ring. This concurs with previous data showing that the MinD dimer binds to MinC inhibiting FtsZ ring formation. These results show that non-linear interactions of Min proteins are essential for producing the mid-cell positioning signal via the generation of second-order harmonic components in the time-dependent spatial protein distribution.