The Min system as a general cell geometry detection mechanism: branch lengths in Y-shaped Escherichia coli cells affect Min oscillation patterns and division dynamics

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.

Feedback linking cell envelope stiffness, curvature, and synthesis enables robust rod-shaped bacterial growth

Bacterial growth is remarkably robust to environmental fluctuations, yet the mechanisms of growth-rate homeostasis are poorly understood. Here, we combine theory and experiment to infer mechanisms by which Escherichia coli adapts its growth rate in response to changes in osmolarity, a fundamental physicochemical property of the environment. The central tenet of our theoretical model is that cell-envelope expansion is only sensitive to local information, such as enzyme concentrations, cell-envelope curvature, and mechanical strain in the envelope. We constrained this model with quantitative measurements of the dynamics of E. coli elongation rate and cell width after hyperosmotic shock. Our analysis demonstrated that adaptive cell-envelope softening is a key process underlying growth-rate homeostasis. Furthermore, our model correctly predicted that softening does not occur above a critical hyperosmotic shock magnitude and precisely recapitulated the elongation-rate dynamics in response to shocks with magnitude larger than this threshold. Finally, we found that, to coordinately achieve growth-rate and cell-width homeostasis, cells employ direct feedback between cell-envelope curvature and envelope expansion. In sum, our analysis points to cellular mechanisms of bacterial growth-rate homeostasis and provides a practical theoretical framework for understanding this process.

The E. coli MinCDE system in the regulation of protein patterns and gradients

Molecular self-organziation, also regarded as pattern formation, is crucial for the correct distribution of cellular content. The processes leading to spatiotemporal patterns often involve a multitude of molecules interacting in complex networks, so that only very few cellular pattern-forming systems can be regarded as well understood. Due to its compositional simplicity, the Escherichia coli MinCDE system has, thus, become a paradigm for protein pattern formation. This biological reaction diffusion system spatiotemporally positions the division machinery in E. coli and is closely related to ParA-type ATPases involved in most aspects of spatiotemporal organization in bacteria. The ATPase MinD and the ATPase-activating protein MinE self-organize on the membrane as a reaction matrix. In vivo, these two proteins typically oscillate from pole-to-pole, while in vitro they can form a variety of distinct patterns. MinC is a passenger protein supposedly operating as a downstream cue of the system, coupling it to the division machinery. The MinCDE system has helped to extract not only the principles underlying intracellular patterns, but also how they are shaped by cellular boundaries. Moreover, it serves as a model to investigate how patterns can confer information through specific and non-specific interactions with other molecules. Here, we review how the three Min proteins self-organize to form patterns, their response to geometric boundaries, and how these patterns can in turn induce patterns of other molecules, focusing primarily on experimental approaches and developments.

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.

Self-organization principles of intracellular pattern formation

Dynamic patterning of specific proteins is essential for the spatio-temporal regulation of many important intracellular processes in prokaryotes, eukaryotes and multicellular organisms. The emergence of patterns generated by interactions of diffusing proteins is a paradigmatic example for self-organization. In this article, we review quantitative models for intracellular Min protein patterns in Escherichia coli, Cdc42 polarization in Saccharomyces cerevisiae and the bipolar PAR protein patterns found in Caenorhabditis elegans. By analysing the molecular processes driving these systems we derive a theoretical perspective on general principles underlying self-organized pattern formation. We argue that intracellular pattern formation is not captured by concepts such as ‘activators’, ‘inhibitors’ or ‘substrate depletion’. Instead, intracellular pattern formation is based on the redistribution of proteins by cytosolic diffusion, and the cycling of proteins between distinct conformational states. Therefore, mass-conserving reaction–diffusion equations provide the most appropriate framework to study intracellular pattern formation. We conclude that directed transport, e.g. cytosolic diffusion along an actively maintained cytosolic gradient, is the key process underlying pattern formation. Thus the basic principle of self-organization is the establishment and maintenance of directed transport by intracellular protein dynamics.

This article is part of the theme issue ‘Self-organization in cell biology’.

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'.

Minimal in vitro systems shed light on cell polarity

Cell polarity - the morphological and functional differentiation of cellular compartments in a directional manner - is required for processes such as orientation of cell division, directed cellular growth and motility. How the interplay of components within the complexity of a cell leads to cell polarity is still heavily debated. In this Review, we focus on one specific aspect of cell polarity: the non-uniform accumulation of proteins on the cell membrane. In cells, this is achieved through reaction-diffusion and/or cytoskeleton-based mechanisms. In reaction-diffusion systems, components are transformed into each other by chemical reactions and are moving through space by diffusion. In cytoskeleton-based processes, cellular components (i.e. proteins) are actively transported by microtubules (MTs) and actin filaments to specific locations in the cell. We examine how minimal systems - in vitro reconstitutions of a particular cellular function with a minimal number of components - are designed, how they contribute to our understanding of cell polarity (i.e. protein accumulation), and how they complement in vivo investigations. We start by discussing the Min protein system from Escherichia coli, which represents a reaction-diffusion system with a well-established minimal system. This is followed by a discussion of MT-based directed transport for cell polarity markers as an example of a cytoskeleton-based mechanism. To conclude, we discuss, as an example, the interplay of reaction-diffusion and cytoskeleton-based mechanisms during polarity establishment in budding yeast.

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.

Multi-Algorithm Particle Simulations with Spatiocyte

As quantitative biologists get more measurements of spatially regulated systems such as cell division and polarization, simulation of reaction and diffusion of proteins using the data is becoming increasingly relevant to uncover the mechanisms underlying the systems. Spatiocyte is a lattice-based stochastic particle simulator for biochemical reaction and diffusion processes. Simulations can be performed at single molecule and compartment spatial scales simultaneously. Molecules can diffuse and react in 1D (filament), 2D (membrane), and 3D (cytosol) compartments. The implications of crowded regions in the cell can be investigated because each diffusing molecule has spatial dimensions. Spatiocyte adopts multi-algorithm and multi-timescale frameworks to simulate models that simultaneously employ deterministic, stochastic, and particle reaction-diffusion algorithms. Comparison of light microscopy images to simulation snapshots is supported by Spatiocyte microscopy visualization and molecule tagging features. Spatiocyte is open-source software and is freely available at http://spatiocyte.org .

Stability analysis in spatial modeling of cell signaling

Advances in high-resolution microscopy and other techniques have emphasized the spatio-temporal nature of information transfer through signal transduction pathways. The compartmentalization of signaling molecules and the existence of microdomains are now widely acknowledged as key features in biochemical signaling. To complement experimental observations of spatio-temporal dynamics, mathematical modeling has emerged as a powerful tool. Using modeling, one can not only recapitulate experimentally observed dynamics of signaling molecules, but also gain an understanding of the underlying mechanisms in order to generate experimentally testable predictions. Reaction-diffusion systems are commonly used to this end; however, the analysis of coupled nonlinear systems of partial differential equations, generated by considering large reaction networks is often challenging. Here, we aim to provide an introductory tutorial for the application of reaction-diffusion models to the spatio-temporal dynamics of signaling pathways. In particular, we outline the steps for stability analysis of such models, with a focus on biochemical signal transduction. WIREs Syst Biol Med 2018, 10:e1395. doi: 10.1002/wsbm.1395 This article is categorized under: Biological Mechanisms > Cell Signaling Analytical and Computational Methods > Dynamical Methods Models of Systems Properties and Processes > Mechanistic Models.

Characterization of C-terminal structure of MinC and its implication in evolution of bacterial cell division

Proper cell division at the mid-site of Gram-negative bacteria reflects stringent regulation by the min system (MinC, MinD and MinE). Herein we report crystal structure of the C-terminal domain of MinC from Escherichia coli (EcMinC_CTD). The MinC_CTD beta helical domain is engaged in a tight homodimer, similar to Thermotoga maritima MinC_CTD (TmMinC_CTD). However, both EcMinC_CTD and TmMinC_CTD lack an α-helix (helix3) at their C-terminal tail, in comparison to Aquifex aerolicu MinC_CTD (AaMinC_CTD) which forms an extra interaction interface with MinD. To understand the role of this extra binding element in MinC/MinD interactions, we fused this helix (Aahelix3) to the C-terminus of EcMinC and examined its effect on cell morphology and cell growth. Our results revealed that Aahelix3 impaired normal cell division in vivo. Furthermore, results of a co-pelleting assay and binding free energy calculation suggested that Aahelix3 plays an essential role in AaMinCD complex formation, under the circumstance of lacking MinE in A. aerolicu. Combining these results with sequence analysis of MinC and MinD in different organisms, we propose an evolutionary relationship to rationalize different mechanisms in cell division positioning in various organisms.

Mode Selection in Compressible Active Flow Networks

Coherent, large-scale dynamics in many nonequilibrium physical, biological, or information transport networks are driven by small-scale local energy input. Here, we introduce and explore an analytically tractable nonlinear model for compressible active flow networks. In contrast to thermally driven systems, we find that active friction selects discrete states with a limited number of oscillation modes activated at distinct fixed amplitudes. Using perturbation theory, we systematically predict the stationary states of noisy networks and find good agreement with a Bayesian state estimation based on a hidden Markov model applied to simulated time series data. Our results suggest that the macroscopic response of active network structures, from actomyosin force networks to cytoplasmic flows, can be dominated by a significantly reduced number of modes, in contrast to energy equipartition in thermal equilibrium. The model is also well suited to study topological sound modes and spectral band gaps in active matter.

E. coli Cell Cycle Machinery

Cytokinesis in E. coli is organized by a cytoskeletal element designated the Z ring. The Z ring is formed at midcell by the coalescence of FtsZ filaments tethered to the membrane by interaction of FtsZ's conserved C-terminal peptide (CCTP) with two membrane-associated proteins, FtsA and ZipA. Although interaction between an FtsZ monomer and either of these proteins is of low affinity, high affinity is achieved through avidity - polymerization linked CCTPs interacting with the membrane tethers. The placement of the Z ring at midcell is ensured by antagonists of FtsZ polymerization that are positioned within the cell and target FtsZ filaments through the CCTP. The placement of the ring is reinforced by a protein network that extends from the terminus (Ter) region of the chromosome to the Z ring. Once the Z ring is established, additional proteins are recruited through interaction with FtsA, to form the divisome. The assembled divisome is then activated by FtsN to carry out septal peptidoglycan synthesis, with a dynamic Z ring serving as a guide for septum formation. As the septum forms, the cell wall is split by spatially regulated hydrolases and the outer membrane invaginates in step with the aid of a transenvelope complex to yield progeny cells.

Robust Min-system oscillation in the presence of internal photosynthetic membranes in cyanobacteria

The oscillatory Min system of Escherichia coli defines the cell division plane by regulating the site of FtsZ-ring formation and represents one of the best-understood examples of emergent protein self-organization in nature. The oscillatory patterns of the Min-system proteins MinC, MinD and MinE (MinCDE) are strongly dependent on the geometry of membranes they bind. Complex internal membranes within cyanobacteria could disrupt this self-organization by sterically occluding or sequestering MinCDE from the plasma membrane. Here, it was shown that the Min system in the cyanobacterium Synechococcus elongatus PCC 7942 oscillates from pole-to-pole despite the potential spatial constraints imposed by their extensive thylakoid network. Moreover, reaction-diffusion simulations predict robust oscillations in modeled cyanobacterial cells provided that thylakoid network permeability is maintained to facilitate diffusion, and suggest that Min proteins require preferential affinity for the plasma membrane over thylakoids to correctly position the FtsZ ring. Interestingly, in addition to oscillating, MinC exhibits a midcell localization dependent on MinD and the DivIVA-like protein Cdv3, indicating that two distinct pools of MinC are coordinated in S. elongatus. Our results provide the first direct evidence for Min oscillation outside of E. coli and have broader implications for Min-system function in bacteria and organelles with internal membrane systems.

Mapping out Min protein patterns in fully confined fluidic chambers

The bacterial Min protein system provides a major model system for studying reaction-diffusion processes in biology. Here we present the first in vitro study of the Min system in fully confined three-dimensional chambers that are lithography-defined, lipid-bilayer coated and isolated through pressure valves. We identify three typical dynamical behaviors that occur dependent on the geometrical chamber parameters: pole-to-pole oscillations, spiral rotations, and traveling waves. We establish the geometrical selection rules and show that, surprisingly, Min-protein spiral rotations govern the larger part of the geometrical phase diagram. Confinement as well as an elevated temperature reduce the characteristic wavelength of the Min patterns, although even for confined chambers with a bacterial-level viscosity, the patterns retain a ~5 times larger wavelength than in vivo. Our results provide an essential experimental base for modeling of intracellular Min gradients in bacterial cell division as well as, more generally, for understanding pattern formation in reaction-diffusion systems.

DOI:http://dx.doi.org/10.7554/eLife.19271.001

Some proteins can spontaneously organize themselves into ordered patterns within living cells. One widely studied pattern is made in a rod-shaped bacterium called Escherichia coli by a group of proteins called the Min proteins. The pattern formed by the Min proteins allows an E. coli cell to produce two equally sized daughter cells when it divides by ensuring that the division machinery correctly assembles at the center of the parent cell. These proteins move back and forth between the two ends of the parent cell so that the levels of Min proteins are highest at the ends and lowest in the middle. Since the Min proteins act to inhibit the assembly of the cell division machinery, this machinery only assembles in locations where the level of Min proteins is at its lowest, that is, at the middle of the cell.

When Min proteins are purified and placed within an artificial compartment that contains a source of chemical energy and is covered by a membrane similar to the membranes that surround cells, they spontaneously form traveling waves on top of the membrane in many directions along to surface. It is not clear how these waves relate to the oscillations seen in E. coli. Caspi and Dekker now analyze the behavior of purified Min proteins inside chambers of various sizes that are fully enclosed by a membrane.

The results show that in narrow chambers, Min proteins move back and forth (i.e. oscillate) from one side to the other. However, in wider containers the wave motion is more common. In containers of medium width the Min proteins rotate in a spiral fashion. Caspi and Dekker propose that the spiral rotations are the underlying pattern formed by Min proteins and that the back and forth motion is caused by spirals being cut short. In other words, if a spiral cannot form because the compartment is too small then the back and forth motion emerges. Similarly, Caspi and Dekker propose that the waves emerge in larger containers when multiple spirals come together.

These findings suggest that the different patterns that Min proteins form in bacterial cells and artificial compartments arise from different underlying mechanisms. The next step will be to investigate other differences in how the patterns of Min proteins form in E. coli and in artificial compartments.

DOI:http://dx.doi.org/10.7554/eLife.19271.002

Multistability and dynamic transitions of intracellular Min protein patterns

Cells owe their internal organization to self-organized protein patterns, which originate and adapt to growth and external stimuli via a process that is as complex as it is little understood. Here, we study the emergence, stability, and state transitions of multistable Min protein oscillation patterns in live Escherichia coli bacteria during growth up to defined large dimensions. De novo formation of patterns from homogenous starting conditions is observed and studied both experimentally and in simulations. A new theoretical approach is developed for probing pattern stability under perturbations. Quantitative experiments and simulations show that, once established, Min oscillations tolerate a large degree of intracellular heterogeneity, allowing distinctly different patterns to persist in different cells with the same geometry. Min patterns maintain their axes for hours in experiments, despite imperfections, expansion, and changes in cell shape during continuous cell growth. Transitions between multistable Min patterns are found to be rare events induced by strong intracellular perturbations. The instances of multistability studied here are the combined outcome of boundary growth and strongly nonlinear kinetics, which are characteristic of the reaction-diffusion patterns that pervade biology at many scales.

Geometry-induced protein pattern formation

Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in [Formula: see text] EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems.

Stochasticity and homeostasis in the E. coli replication and division cycle

How cells correct for stochasticity to coordinate the chromosome replication and cellular division cycle is poorly understood. We used time-lapse microscopy and fluorescently labelled SeqA to determine the timing of birth, initiation, termination, and division, as well as cell size throughout the cell cycle. We found that the time between birth and initiation (B-period) compensates for stochastic variability in birth size and growth rate. The time between termination and division (D-period) also compensates for size and growth variability, invalidating the notion that replication initiation is the principal trigger for cell division. In contrast, the time between initiation and termination (C-period) did not display such compensations. Interestingly, the C-period did show small but systematic decreases for cells that spontaneously grew faster, which suggests a coupling between metabolic fluctuations and replication. An auto-regressive theoretical framework was employed to compare different possible models of sub-period control.

Theoretical Prediction of Disrupted Min Oscillation in Flattened Escherichia coli

The dynamics of the Min-protein system help Escherichia coli regulate the process of cell division by identifying the center of the cell. While this system exhibits robust bipolar oscillations in wild-type cell shapes, recent experiments have shown that when the cells are mechanically deformed into wide, flattened out, irregular shapes, the spatial regularity of these oscillations breaks down. We employ widely used stochastic and deterministic models of the Min system to simulate cells with flattened shapes. The deterministic model predicts strong bipolar oscillations, in contradiction with the experimentally observed behavior, while the stochastic model, which is based on the same reaction-diffusion equations, predicts more spatially irregular oscillations. We further report simulations of flattened but more symmetric shapes, which suggest that the flattening and lateral expansion may contribute as much to the irregular oscillation behavior as the asymmetry of the cell shapes.

Symmetry and scale orient Min protein patterns in shaped bacterial sculptures

The boundary of a cell defines the shape and scale of its subcellular organization. However, the effects of the cell's spatial boundaries as well as the geometry sensing and scale adaptation of intracellular molecular networks remain largely unexplored. Here, we show that living bacterial cells can be 'sculpted' into defined shapes, such as squares and rectangles, which are used to explore the spatial adaptation of Min proteins that oscillate pole-to-pole in rod-shaped Escherichia coli to assist cell division. In a wide geometric parameter space, ranging from 2 × 1 × 1 to 11 × 6 × 1 μm(3), Min proteins exhibit versatile oscillation patterns, sustaining rotational, longitudinal, diagonal, stripe and even transversal modes. These patterns are found to directly capture the symmetry and scale of the cell boundary, and the Min concentration gradients scale with the cell size within a characteristic length range of 3-6 μm. Numerical simulations reveal that local microscopic Turing kinetics of Min proteins can yield global symmetry selection, gradient scaling and an adaptive range, when and only when facilitated by the three-dimensional confinement of the cell boundary. These findings cannot be explained by previous geometry-sensing models based on the longest distance, membrane area or curvature, and reveal that spatial boundaries can facilitate simple molecular interactions to result in far more versatile functions than previously understood.

The Min system and other nucleoid-independent regulators of Z ring positioning

Rod-shaped bacteria such as E. coli have mechanisms to position their cell division plane at the precise center of the cell, to ensure that the daughter cells are equal in size. The two main mechanisms are the Min system and nucleoid occlusion (NO), both of which work by inhibiting assembly of FtsZ, the tubulin-like scaffold that forms the cytokinetic Z ring. Whereas NO prevents Z rings from constricting over unsegregated nucleoids, the Min system is nucleoid-independent and even functions in cells lacking nucleoids and thus NO. The Min proteins of E. coli and B. subtilis form bipolar gradients that inhibit Z ring formation most at the cell poles and least at the nascent division plane. This article will outline the molecular mechanisms behind Min function in E. coli and B. subtilis, and discuss distinct Z ring positioning systems in other bacterial species.

Dynamic tuning of lymphocytes: physiological basis, mechanisms, and function

Dynamic tuning of cellular responsiveness as a result of repeated stimuli improves the ability of cells to distinguish physiologically meaningful signals from each other and from noise. In particular, lymphocyte activation thresholds are subject to tuning, which contributes to maintaining tolerance to self-antigens and persisting foreign antigens, averting autoimmunity and immune pathogenesis, but allowing responses to strong, structured perturbations that are typically associated with acute infection. Such tuning is also implicated in conferring flexibility to positive selection in the thymus, in controlling the magnitude of the immune response, and in generating memory cells. Additional functional properties are dynamically and differentially tuned in parallel via subthreshold contact interactions between developing or mature lymphocytes and self-antigen-presenting cells. These interactions facilitate and regulate lymphocyte viability, maintain their functional integrity, and influence their responses to foreign antigens and accessory signals, qualitatively and quantitatively. Bidirectional tuning of T cells and antigen-presenting cells leads to the definition of homeostatic set points, thus maximizing clonal diversity.

Reconstitution of self-organizing protein gradients as spatial cues in cell-free systems

Intracellular protein gradients are significant determinants of spatial organization. However, little is known about how protein patterns are established, and how their positional information directs downstream processes. We have accomplished the reconstitution of a protein concentration gradient that directs the assembly of the cell division machinery in E.coli from the bottom-up. Reconstituting self-organized oscillations of MinCDE proteins in membrane-clad soft-polymer compartments, we demonstrate that distinct time-averaged protein concentration gradients are established. Our minimal system allows to study complex organizational principles, such as spatial control of division site placement by intracellular protein gradients, under simplified conditions. In particular, we demonstrate that FtsZ, which marks the cell division site in many bacteria, can be targeted to the middle of a cell-like compartment. Moreover, we show that compartment geometry plays a major role in Min gradient establishment, and provide evidence for a geometry-mediated mechanism to partition Min proteins during bacterial development.

Peptidoglycan synthesis machinery in Agrobacterium tumefaciens during unipolar growth and cell division

The synthesis of peptidoglycan (PG) in bacteria is a crucial process controlling cell shape and vitality. In contrast to bacteria such as Escherichia coli that grow by dispersed lateral insertion of PG, little is known of the processes that direct polar PG synthesis in other bacteria such as the Rhizobiales. To better understand polar growth in the Rhizobiales Agrobacterium tumefaciens, we first surveyed its genome to identify homologs of (~70) well-known PG synthesis components. Since most of the canonical cell elongation components are absent from A. tumefaciens, we made fluorescent protein fusions to other putative PG synthesis components to assay their subcellular localization patterns. The cell division scaffolds FtsZ and FtsA, PBP1a, and a Rhizobiales- and Rhodobacterales-specific l,d-transpeptidase (LDT) all associate with the elongating cell pole. All four proteins also localize to the septum during cell division. Examination of the dimensions of growing cells revealed that new cell compartments gradually increase in width as they grow in length. This increase in cell width is coincident with an expanded region of LDT-mediated PG synthesis activity, as measured directly through incorporation of exogenous d-amino acids. Thus, unipolar growth in the Rhizobiales is surprisingly dynamic and represents a significant departure from the canonical growth mechanism of E. coli and other well-studied bacilli.

Many rod-shaped bacteria, including pathogens such as Brucella and Mycobacterium, grow by adding new material to their cell poles, and yet the proteins and mechanisms contributing to this process are not yet well defined. The polarly growing plant pathogen Agrobacterium tumefaciens was used as a model bacterium to explore these polar growth mechanisms. The results obtained indicate that polar growth in this organism is facilitated by repurposed cell division components and an otherwise obscure class of alternative peptidoglycan transpeptidases (l,d-transpeptidases). This growth results in dynamically changing cell widths as the poles expand to maturity and contrasts with the tightly regulated cell widths characteristic of canonical rod-shaped growth. Furthermore, the abundance and/or activity of l,d-transpeptidases appears to associate with polar growth strategies, suggesting that these enzymes may serve as attractive targets for specifically inhibiting growth of Rhizobiales, Actinomycetales, and other polarly growing bacterial pathogens.

Oscillations of Min-proteins in micropatterned environments: a three-dimensional particle-based stochastic simulation approach

The Min-proteins from E. coli and other bacteria are the best characterized pattern forming system in cells and their spatiotemporal oscillations have been successfully reconstituted in vitro. Different mathematical and computational models have been used to better understand these oscillations. Here we use particle-based stochastic simulations to study Min-oscillations in patterned environments. We simulate a rectangular box of length 10 μm and width 5 μm that is filled with grid or checkerboard patterns of different patch sizes and distances. For this geometry, we find different stable oscillation patterns, typically pole-to-pole oscillations along the minor axis and striped oscillations along the major axis. The Min-oscillations can switch from one pattern to the other, either effected by changes in pattern geometry or stochastically. By automatic analysis of large-scale computer simulations, we show quantitatively how the perturbing effect of increased patch distance can be rescued by increased patch size. We also show that striped oscillations occur robustly in arbitrarily shaped filamentous E. coli cells. Our results highlight the robustness and variability of Min-oscillations, put limits on the effect of putative division sites, and provide a powerful computational framework for future studies of protein self-organization in patterned environments.

How do bacteria localize proteins to the cell pole?

It is now well appreciated that bacterial cells are highly organized, which is far from the initial concept that they are merely bags of randomly distributed macromolecules and chemicals. Central to their spatial organization is the precise positioning of certain proteins in subcellular domains of the cell. In particular, the cell poles - the ends of rod-shaped cells - constitute important platforms for cellular regulation that underlie processes as essential as cell cycle progression, cellular differentiation, virulence, chemotaxis and growth of appendages. Thus, understanding how the polar localization of specific proteins is achieved and regulated is a crucial question in bacterial cell biology. Often, polarly localized proteins are recruited to the poles through their interaction with other proteins or protein complexes that were already located there, in a so-called diffusion-and-capture mechanism. Bacteria are also starting to reveal their secrets on how the initial pole 'recognition' can occur and how this event can be regulated to generate dynamic, reproducible patterns in time (for example, during the cell cycle) and space (for example, at a specific cell pole). Here, we review the major mechanisms that have been described in the literature, with an emphasis on the self-organizing principles. We also present regulation strategies adopted by bacterial cells to obtain complex spatiotemporal patterns of protein localization.

Membrane binding of MinE allows for a comprehensive description of Min-protein pattern formation

The rod-shaped bacterium Escherichia coli selects the cell center as site of division with the help of the proteins MinC, MinD, and MinE. This protein system collectively oscillates between the two cell poles by alternately binding to the membrane in one of the two cell halves. This dynamic behavior, which emerges from the interaction of the ATPase MinD and its activator MinE on the cell membrane, has become a paradigm for protein self-organization. Recently, it has been found that not only the binding of MinD to the membrane, but also interactions of MinE with the membrane contribute to Min-protein self-organization. Here, we show that by accounting for this finding in a computational model, we can comprehensively describe all observed Min-protein patterns in vivo and in vitro. Furthermore, by varying the system's geometry, our computations predict patterns that have not yet been reported. We confirm these predictions experimentally.

Cellular protein structures have long been suggested to form by protein self-organization. A particularly clear example is provided by the proteins MinC, MinD, and MinE selecting the center as site of cell division in the rod-shaped bacterium Escherichia coli. Based on binding of MinD to the cytoplasmic membrane and an antagonistic action of MinE, which induces the release of MinD into the cytoplasm, these proteins oscillate from pole to pole, where they inhibit cell division. Supporting the idea of self-organization being the cause of the Min oscillations, purified Min proteins were found to spontaneously form traveling waves on supported lipid bilayers. A comprehensive understanding of the Min patterns formed under various conditions remains elusive. We have performed a computational analysis of Min-protein dynamics taking into account the recently discovered persistent action of MinE. We show that this property allows to reproduce all observed Min-protein patterns in a unified framework. Furthermore, our analysis predicts new structures, which we observed experimentally. Our study highlights that mechanisms underlying the spontaneous formation of protein patterns under purified in vitro conditions can also generate patterns inside complex intracellular environments.

Reconstitution of pole-to-pole oscillations of min proteins in microengineered polydimethylsiloxane compartments

Cell division in bacteria is highly regulated in time and space. The use of micrometer-sized sample volumes and model membranes allows the pole-to-pole oscillations of spatial regulators for bacterial cell division to be reconstituted in a synthetic minimal system.

MinD and MinE interact with anionic phospholipids and regulate division plane formation in Escherichia coli

The Min proteins (MinC, MinD, and MinE) form a pole-to-pole oscillator that controls the spatial assembly of the division machinery in Escherichia coli cells. Previous studies identified that interactions of MinD with phospholipids positioned the Min machinery at the membrane. We extend these studies by measuring the affinity, kinetics, and ATPase activity of E. coli MinD, MinE, and MinDE binding to supported lipid bilayers containing varying compositions of anionic phospholipids. Using quartz crystal microbalance measurements, we found that the binding affinity (K(d)) for the interaction of recombinant E. coli MinD and MinE with lipid bilayers increased with increasing concentration of the anionic phospholipids phosphatidylglycerol and cardiolipin. The K(d) for MinD (1.8 μM) in the presence of ATP was smaller than for MinE (12.1 μM) binding to membranes consisting of 95:5 phosphatidylcholine/cardiolipin. The simultaneous binding of MinD and MinE to membranes revealed that increasing the concentration of anionic phospholipid stimulates the initial rate of adsorption (k(on)). The ATPase activity of MinD decreased in the presence of anionic phospholipids. These results indicate that anionic lipids, which are concentrated at the poles, increase the retention of MinD and MinE and explain its dwell time at this region of bacterial cells. These studies provide insight into interactions between MinD and MinE and between these proteins and membranes that are relevant to understanding the process of bacterial cell division, in which the interaction of proteins and membranes is essential.

Geometry sensing by self-organized protein patterns

In the living cell, proteins are able to organize space much larger than their dimensions. In return, changes of intracellular space can influence biochemical reactions, allowing cells to sense their size and shape. Despite the possibility to reconstitute protein self-organization with only a few purified components, we still lack knowledge of how geometrical boundaries affect spatiotemporal protein patterns. Following a minimal systems approach, we used purified proteins and photolithographically patterned membranes to study the influence of spatial confinement on the self-organization of the Min system, a spatial regulator of bacterial cytokinesis, in vitro. We found that the emerging protein pattern responds even to the lateral, two-dimensional geometry of the membrane such that, as in the three-dimensional cell, Min protein waves travel along the longest axis of the membrane patch. This shows that for spatial sensing the Min system does not need to be enclosed in a three-dimensional compartment. Using a computational model we quantitatively analyzed our experimental findings and identified persistent binding of MinE to the membrane as requirement for the Min system to sense geometry. Our results give insight into the interplay between geometrical confinement and biochemical patterns emerging from a nonlinear reaction-diffusion system.

The ParA/MinD family puts things in their place

Bacteria must segregate their DNA and position a septum to grow and divide. In many bacteria, MinD is involved in spatial regulation of the cytokinetic Z ring, and ParAs are involved in chromosome and plasmid segregation. The use of the MinD/ParA family to provide positional information for spatial organization continues to expand with the recognition that orphan ParAs are required for segregating cytoplasmic protein clusters and the polar localization of chemotaxis proteins, conjugative transfer machinery, type IV pili, and cellulose synthesis. Also, some bacteria lacking MinD use orphan ParAs to regulate cell division. Positioning of MinD/ParA proteins is either due to self-organization on a surface or reliance on a landmark protein that functions as a molecular beacon.

Robustness and accuracy of cell division in Escherichia coli in diverse cell shapes

Cell division in typical rod-shaped bacteria such as Escherichia coli shows a remarkable plasticity in being able to adapt to a variety of irregular cell shapes. Here, we investigate the roles of the Min system and the nucleoid-occlusion factor SlmA in supporting this adaptation. We study "squeezed" E. coli in narrow nanofabricated channels where these bacteria exhibit highly irregular shapes and large volumes. Despite the severely anomalous morphologies we find that most of these bacteria maintain their ability to divide into two equally sized daughters with an accuracy comparable to that of normal rod-shaped cells (about 4%). Deletion of either slmA or minC shows that the molecular systems associated with these genes are largely dispensable for accurate cell division in these irregular cell shapes. Using fluorescence time-lapse microscopy, we determine that the functionality of the Min system is affected by the cell shape, whereas the localization of a nucleoid relative to the cell division proteins (the divisome) remains unperturbed in a broad spectrum of morphologies, consistent with nucleoid occlusion. The observed positioning of the nucleoid relative to the divisome appears not to be affected by the nucleoid-occlusion factor SlmA. The current study underscores the importance of nucleoid occlusion in positioning the divisome and shows that it is robust against shape irregularities.

Escherichia coli low-molecular-weight penicillin-binding proteins help orient septal FtsZ, and their absence leads to asymmetric cell division and branching

Escherichia coli cells lacking low-molecular-weight penicillin-binding proteins (LMW PBPs) exhibit morphological alterations that also appear when the septal protein FtsZ is mislocalized, suggesting that peptidoglycan modification and division may work together to produce cell shape. We found that in strains lacking PBP5 and other LMW PBPs, higher FtsZ concentrations increased the frequency of branched cells and incorrectly oriented Z rings by 10- to 15-fold. Invagination of these rings produced improperly oriented septa, which in turn gave rise to asymmetric cell poles that eventually elongated into branches. Branches always originated from the remnants of abnormal septation events, cementing the relationship between aberrant cell division and branch formation. In the absence of PBP5, PBP6 and DacD localized to nascent septa, suggesting that these PBPs can partially substitute for the loss of PBP5. We propose that branching begins when mislocalized FtsZ triggers the insertion of inert peptidoglycan at unusual positions during cell division. Only later, after normal cell wall elongation separates the patches, do branches become visible. Thus, a relationship between the LMW PBPs and cytoplasmic FtsZ ultimately affects cell division and overall shape.

Protein self-organization: lessons from the min system

One of the most fundamental features of biological systems is probably their ability to self-organize in space and time on different scales. Despite many elaborate theoretical models of how molecular self-organization can come about, only a few experimental systems of biological origin have so far been rigorously described, due mostly to their inherent complexity. The most promising strategy of modern biophysics is thus to identify minimal biological systems showing self-organized emergent behavior. One of the best-understood examples of protein self-organization, which has recently been successfully reconstituted in vitro, is represented by the oscillations of the Min proteins in Escherichia coli. In this review, we summarize the current understanding of the mechanism of Min protein self-organization in vivo and in vitro. We discuss the potential of the Min oscillations to sense the geometry of the cell and suggest that spontaneous protein waves could be a general means of intracellular organization. We hypothesize that cooperative membrane binding and unbinding, e.g., as an energy-dependent switch, may act as an important regulatory mechanism for protein oscillations and pattern formation in the cell.

Cardiolipin microdomains localize to negatively curved regions of Escherichia coli membranes

Many proteins reside at the cell poles in rod-shaped bacteria. Several hypotheses have drawn a connection between protein localization and the large cell-wall curvature at the poles. One hypothesis has centered on the formation of microdomains of the lipid cardiolipin (CL), its localization to regions of high membrane curvature, and its interaction with membrane-associated proteins. A lack of experimental techniques has left this hypothesis unanswered. This paper describes a microtechnology-based technique for manipulating bacterial membrane curvature and quantitatively measuring its effect on the localization of CL and proteins in cells. We confined Escherichia coli spheroplasts in microchambers with defined shapes that were embossed into a layer of polymer and observed that the shape of the membrane deformed predictably to accommodate the walls of the microchambers. Combining this technique with epifluorescence microscopy and quantitative image analyses, we characterized the localization of CL microdomains in response to E. coli membrane curvature. CL microdomains localized to regions of high intrinsic negative curvature imposed by microchambers. We expressed a chimera of yellow fluorescent protein fused to the N-terminal region of MinD--a spatial determinant of E. coli division plane assembly--in spheroplasts and observed its colocalization with CL to regions of large, negative membrane curvature. Interestingly, the distribution of MinD was similar in spheroplasts derived from a CL synthase knockout strain. These studies demonstrate the curvature dependence of CL in membranes and test whether these structures participate in the localization of MinD to regions of negative curvature in cells.

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.

Division site selection in rod-shaped bacteria

Rod-shaped bacteria often divide with high precision at midcell to produce two equally sized daughter cells. The positioning of the division machinery in Escherichia coli and Bacillus subtilis is spatially regulated by two inhibitory systems, the nucleoid occlusion and the Min system. The current models suggest that the target of the inhibitory mechanism is the cytoskeletal element FtsZ and that the concerted action of nucleoid occlusion and Min are necessary for correct placement of the division machinery. However, recent advances show that at least the Min system also ensures that division occurs only once in a cell cycle and might also act downstream of FtsZ assembly.