A polymerization-depolymerization model that accurately generates the self-sustained oscillatory system involved in bacterial division site placement

Forceful patterning: theoretical principles of mechanochemical pattern formation

Biological pattern formation is essential for generating and maintaining spatial structures from the scale of a single cell to tissues and even collections of organisms. Besides biochemical interactions, there is an important role for mechanical and geometrical features in the generation of patterns. We review the theoretical principles underlying different types of mechanochemical pattern formation across spatial scales and levels of biological organization.

Molecular interactions and their predictive roles in cell pole determination in bacteria

Bacterial cell cycle is divided into well-coordinated phases; chromosome duplication and segregation, cell elongation, septum formation, and cytokinesis. The temporal separation of these phases depends upon the growth rates and doubling time in different bacteria. The entire process of cell division starts with the assembly of divisome complex at mid-cell position followed by constriction of the cell wall and septum formation. In the mapping of mid-cell position for septum formation, the gradient of oscillating Min proteins across the poles plays a pivotal role in several bacteria genus. The cues in the cell that defines the poles and plane of cell division are not fully characterized in cocci. Recent studies have shed some lights on molecular interactions at the poles and the underlying mechanisms involved in pole determination in non-cocci. In this review, we have brought forth recent findings on these aspects together, which would suggest a model to explain the mechanisms of pole determination in rod shaped bacteria and could be extrapolated as a working model in cocci.

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.

Organization and function of anionic phospholipids in bacteria

In addition to playing a central role as a permeability barrier for controlling the diffusion of molecules and ions in and out of bacterial cells, phospholipid (PL) membranes regulate the spatial and temporal position and function of membrane proteins that play an essential role in a variety of cellular functions. Based on the very large number of membrane-associated proteins encoded in genomes, an understanding of the role of PLs may be central to understanding bacterial cell biology. This area of microbiology has received considerable attention over the past two decades, and the local enrichment of anionic PLs has emerged as a candidate mechanism for biomolecular organization in bacterial cells. In this review, we summarize the current understanding of anionic PLs in bacteria, including their biosynthesis, subcellular localization, and physiological relevance, discuss evidence and mechanisms for enriching anionic PLs in membranes, and conclude with an assessment of future directions for this area of bacterial biochemistry, biophysics, and cell biology.

Effect of the Min system on timing of cell division in Escherichia coli

In Escherichia coli the Min protein system plays an important role in positioning the division site. We show that this system also has an effect on timing of cell division. We do this in a quantitative way by measuring the cell division waiting time (defined as time difference between appearance of a division site and the division event) and the Z-ring existence time. Both quantities are found to be different in WT and cells without functional Min system. We develop a series of theoretical models whose predictions are compared with the experimental findings. Continuous improvement leads to a final model that is able to explain all relevant experimental observations. In particular, it shows that the chromosome segregation defect caused by the absence of Min proteins has an important influence on timing of cell division. Our results indicate that the Min system affects the septum formation rate. In the absence of the Min proteins this rate is reduced, leading to the observed strongly randomized cell division events and the longer division waiting times.

Differential affinities of MinD and MinE to anionic phospholipid influence Min patterning dynamics in vitro

The E. coli Min system forms a cell-pole-to-cell-pole oscillator that positions the divisome at mid-cell. The MinD ATPase binds the membrane and recruits the cell division inhibitor MinC. MinE interacts with and releases MinD (and MinC) from the membrane. The chase of MinD by MinE creates the in vivo oscillator that maintains a low level of the division inhibitor at mid-cell. In vitro reconstitution and visualization of Min proteins on a supported lipid bilayer has provided significant advances in understanding Min patterns in vivo. Here we studied the effects of flow, lipid composition, and salt concentration on Min patterning. Flow and no-flow conditions both supported Min protein patterns with somewhat different characteristics. Without flow, MinD and MinE formed spiraling waves. MinD and, to a greater extent MinE, have stronger affinities for anionic phospholipid. MinD-independent binding of MinE to anionic lipid resulted in slower and narrower waves. MinE binding to the bilayer was also more susceptible to changes in ionic strength than MinD. We find that modulating protein diffusion with flow, or membrane binding affinities with changes in lipid composition or salt concentration, can differentially affect the retention time of MinD and MinE, leading to spatiotemporal changes in Min patterning.

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.

Mechanotransduction in cells

Cell-matrix and cell-cell adhesions critically influence cell metabolism, protein synthesis, cell survival, cytoskeletal architecture and consequently cell mechanical properties such as migration, spreading and contraction. An important group of adhesive transmembrane receptors that mechanically link the ECM (extracellular matrix) with the internal cytoskeleton are integrins which are intimately connected with the FAs (focal adhesions) which consists of many proteins. The transient formation of FAs is greatly augmented either through externally applied tension to the cell or internally through myosin II-driven cell contractility. Exactly which protein(s) within FAs sense, transmit and respond to mechanical stress is currently debated and numerous candidates have been proposed.

Stuttering Min oscillations within E. coli bacteria: a stochastic polymerization model

We have developed a 3D off-lattice stochastic polymerization model to study the subcellular oscillation of Min proteins in the bacteria Escherichia coli, and used it to investigate the experimental phenomenon of Min oscillation stuttering. Stuttering was affected by the rate of immediate rebinding of MinE released from depolymerizing filament tips (processivity), protection of depolymerizing filament tips from MinD binding and fragmentation of MinD filaments due to MinE. Processivity, protection and fragmentation each reduce stuttering, speed oscillations and MinD filament lengths. Neither processivity nor tip protection were, on their own, sufficient to produce fast stutter-free oscillations. While filament fragmentation could, on its own, lead to fast oscillations with infrequent stuttering; high levels of fragmentation degraded oscillations. The infrequent stuttering observed in standard Min oscillations is consistent with short filaments of MinD, while we expect that mutants that exhibit higher stuttering frequencies will exhibit longer MinD filaments. Increased stuttering rate may be a useful diagnostic to find observable MinD polymerization under experimental conditions.

Highly canalized MinD transfer and MinE sequestration explain the origin of robust MinCDE-protein dynamics

Min-protein oscillations in Escherichia coli are characterized by the remarkable robustness with which spatial patterns dynamically adapt to variations of cell geometry. Moreover, adaption, and therefore proper cell division, is independent of temperature. These observations raise fundamental questions about the mechanisms establishing robust Min oscillations, and about the role of spatial cues, as they are at odds with present models. Here, we introduce a robust model based on experimental data, consistently explaining the mechanisms underlying pole-to-pole, striped, and circular patterns, as well as the observed temperature dependence of the oscillation period. Contrary to prior conjectures, the model predicts that MinD and cardiolipin domains are not colocalized. The transient sequestration of MinE and highly canalized transfer of MinD between polar zones are the key mechanisms underlying oscillations. MinD channeling enhances midcell localization and facilitates stripe formation, revealing the potential optimization process from which robust Min-oscillations originally arose.

An oscillating Min system in Bacillus subtilis influences asymmetrical septation during sporulation

The Min system plays an important role in ensuring that cell division occurs at mid-cell in rod-shaped bacteria. In Escherichia coli, pole-to-pole oscillation of the Min proteins specifically inhibits polar septation. This system also prevents polar division in Bacillus subtilis during vegetative growth; however, the Min proteins do not oscillate in this organism. The Min system of B. subtilis plays a distinct role during sporulation, a process of differentiation which begins with an asymmetrical cell division. Here, we show that oscillation of the E. coli Min proteins can be reproduced following their introduction into B. subtilis cells. Further, we present evidence that the oscillatory behaviour of the Min system inhibits sporulation. We propose that an alternative Min system mechanism avoiding oscillation is evolutionarily important because oscillation of the Min system is incompatible with efficient asymmetrical septum formation and sporulation.

Chemophoresis as a driving force for intracellular organization: Theory and application to plasmid partitioning

Biological units such as macromolecules, organelles, and cells are directed to a proper location by gradients of chemicals. We consider a macroscopic element with surface binding sites where chemical adsorption reactions can occur and show that a thermodynamic force generated by chemical gradients acts on the element. By assuming local equilibrium and adopting the grand potential used in thermodynamics, we derive a formula for the “chemophoresis” force, which depends on chemical potential gradients and the Langmuir isotherm. The conditions under which the formula is applicable are shown to occur in intracellular reactions. Further, the role of the chemophoresis in the partitioning of bacterial chromosomal loci/plasmids during cell division is discussed. By performing numerical simulations, we demonstrate that the chemophoresis force can contribute to the regular positioning of plasmids observed in experiments.

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.

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.

ATP control of dynamic P1 ParA-DNA interactions: a key role for the nucleoid in plasmid partition

P1 ParA is a member of the Walker-type family of partition ATPases involved in the segregation of plasmids and bacterial chromosomes. ATPases of this class interact with DNA non-specifically in vitro and colocalize with the bacterial nucleoid to generate a variety of reported patterns in vivo. Here, we directly visualize ParA binding to DNA using total internal reflection fluorescence microscopy. This activity depends on, and is highly specific for ATP. DNA-binding activity is not coupled to ATP hydrolysis. Rather, ParA undergoes a slow multi-step conformational transition upon ATP binding, which licenses ParA to bind non-specific DNA. The kinetics provide a time-delay switch to allow slow cycling between the DNA binding and non-binding forms of ParA. We propose that this time delay, combined with stimulation of ParA's ATPase activity by ParB bound to the plasmid DNA, generates an uneven distribution of the nucleoid-associated ParA, and provides the motive force for plasmid segregation prior to cell division.

Multiple modes of interconverting dynamic pattern formation by bacterial cell division proteins

Min proteins of the Escherichia coli cell division system oscillate between the cell poles in vivo. In vitro on a solid-surface supported lipid bilayer, these proteins exhibit a number of interconverting modes of collective ATP-driven dynamic pattern formation including not only the previously described propagating waves, but also near uniformity in space surface concentration oscillation, propagating filament like structures with a leading head and decaying tail and moving and dividing amoeba-like structures with sharp edges. We demonstrate that the last behavior most closely resembles in vivo system behavior. The simple reaction-diffusion models previously proposed for the Min system fail to explain the results of the in vitro self-organization experiments. We propose the hypotheses that initiation of MinD binding to the surface is controlled by counteraction of initiation and dissociation complexes; the binding of MinD/E is stimulated by MinE and involves polymerization-depolymerization dynamics; polymerization of MinE over MinD oligomers triggers dynamic instability leading to detachment from the membrane. The physical properties of the lipid bilayer are likely to be one of the critical determinants of certain aspects of the dynamic patterns observed.

A new multicompartmental reaction-diffusion modeling method links transient membrane attachment of E. coli MinE to E-ring formation

Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally.

Predictions from a stochastic polymer model for the MinDE protein dynamics in Escherichia coli

The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations--both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.

The dynamic nature of the bacterial cytoskeleton

Three of the four well-established bacterial cytoskeletal systems-the MreB, MinCDE, and FtsZ systems-undergo a variety of short-range and long-range dynamic behaviors. These include the cellular reorganization of the cytoskeletal elements, in which the proteins redistribute from a predominantly helical pole-to-pole pattern into annular structures near midcell. Despite their apparent similarity, these dramatic redistributional events in the three systems are in large part independent of each other. In addition, some of the cytoskeletal structures undergo oscillatory behavior in which the helical elements move repetitively back-and-forth between the two ends of the cell. The details and mechanisms underlying these dynamic cellular events are just now being revealed by fluorescence microscopy of intact cells, fluorescence photobleaching recovery studies, single molecule tracking techniques, and in vitro studies of the purified proteins.

Self-organization of the MinE protein ring in subcellular Min oscillations

We model the self-organization of the MinE ring that is observed during subcellular oscillations of the proteins MinD and MinE within the rod-shaped bacterium Escherichia coli. With a steady-state approximation, we can study the MinE ring generically--apart from the other details of the Min oscillation. Rebinding of MinE to depolymerizing MinD-filament tips controls MinE-ring formation through a scaled cell shape parameter r. We find two types of E-ring profiles near the filament tip: either a strong plateaulike E ring controlled by one-dimensional diffusion of MinE along the bacterial length or a weak cusplike E ring controlled by three-dimensional diffusion near the filament tip. While the width of a strong E ring depends on r, the occupation fraction of MinE at the MinD-filament tip is saturated and hence the depolymerization speed does not depend strongly on r. Conversely, for weak E rings both r and the MinE to MinD stoichiometry strongly control the tip occupation and hence the depolymerization speed. MinE rings in vivo are close to the threshold between weak and strong, and so MinD-filament depolymerization speed should be sensitive to cell shape, stoichiometry, and MinE-rebinding rate. We also find that the transient to MinE-ring formation is quite long in the appropriate open geometry for assays of ATPase activity in vitro, explaining the long delays of ATPase activity observed for smaller MinE concentrations in those assays without the need to invoke cooperative MinE activity.

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.

Analyses of mechanisms for force generation during cell septation in Escherichia coli

Escherichia coli is a rod-shaped bacterium that divides at its midplane, partitioning its cellular material into two roughly equal parts. At the appropriate time, a septum forms, creating the two daughter cells. Septum formation starts with the appearance of a ring of FtsZ proteins on the cell membrane at midplane. This Z-ring causes an invagination in the membrane, which is followed by growth of two new endcaps for the daughter cells. Invagination occurs against a cell overpressure of several atmospheres. A model is presented for the shape of the cell as determined by the tension in the Z-ring. This model allows the calculation of the force required for invagination. Then three possible models to generate the force necessary to achieve invagination are presented and analyzed. These models are based on converting GTP-bound FtsZ polymeric structures to GDP-bound FtsZ structures, which then leave the polymer. Each model is able to generate the force by relating the hydrolyzation to an irreversible molecular binding event, resulting in a net motion of putative anchors for the structures. All three models show that cross-linking the FtsZ protofilaments into a polymer structure allows the removal of GDP-FtsZ without interrupting the structure during force generation, as would happen for a simple polymeric chain.

Phosphatidic acid and N-acylphosphatidylethanolamine form membrane domains in Escherichia coli mutant lacking cardiolipin and phosphatidylglycerol

The pgsA null Escherichia coli strain, UE54, lacks the major anionic phospholipids phosphatidylglycerol and cardiolipin. Despite these alterations the strain exhibits relatively normal cell division. Analysis of the UE54 phospholipids using negativeion electrospray ionization mass spectrometry resulted in identification of a new anionic phospholipid, N-acylphosphatidylethanolamine. Staining with the fluorescent dye 10-N-nonyl acridine orange revealed anionic phospholipid membrane domains at the septal and polar regions. Making UE54 null in minCDE resulted in budding off of minicells from polar domains. Analysis of lipid composition by mass spectrometry revealed that minicells relative to parent cells were significantly enriched in phosphatidic acid and N-acylphosphatidylethanolamine. Thus despite the absence of cardiolipin, which forms membrane domains at the cell pole and division sites in wild-type cells, the mutant cells still maintain polar/septal localization of anionic phospholipids. These three anionic phospholipids share common physical properties that favor polar/septal domain formation. The findings support the proposed role for anionic phospholipids in organizing amphitropic cell division proteins at specific sites on the membrane surface.

Modelling of processes governing subcellular localisation of MinD in Escherichia coli

Recent research has highlighted several examples wherein bacterial cell fate is determined by precise subcellular localisation of proteins. A prominent example is the polar localisation and oscillation of the Min proteins which is necessary for accurate cell division in Escherichia coli. Several computational models have been proposed which reproduce the oscillatory behaviour and observed phenotypes. However, these models use varying assumptions to do so leading to different mechanisms for precise polar localisation of MinD zones. To gain further insight, the authors extend a simplified model which focused on some key processes to explain the observed length scale for MinD zone formation. Using analytical approaches and numerical simulations, the authors explore cellular MinD distributions produced by these processes and propose a mechanism for precise polar localisation of MinD.

Lipid spirals in Bacillus subtilis and their role in cell division

The fluid mosaic model of membrane structure has been revised in recent years as it has become evident that domains of different lipid composition are present in eukaryotic and prokaryotic cells. Using membrane binding fluorescent dyes, we demonstrate the presence of lipid spirals extending along the long axis of cells of the rod-shaped bacterium Bacillus subtilis. These spiral structures are absent from cells in which the synthesis of phosphatidylglycerol is disrupted, suggesting an enrichment in anionic phospholipids. Green fluorescent protein fusions of the cell division protein MinD also form spiral structures and these were shown by fluorescence resonance energy transfer to be coincident with the lipid spirals. These data indicate a higher level of membrane lipid organization than previously observed and a primary role for lipid spirals in determining the site of cell division in bacterial cells.

Towards the development of Bacillus subtilis as a cell factory for membrane proteins and protein complexes

Background

The Gram-positive bacterium Bacillus subtilis is an important producer of high quality industrial enzymes and a few eukaryotic proteins. Most of these proteins are secreted into the growth medium, but successful examples of cytoplasmic protein production are also known. Therefore, one may anticipate that the high protein production potential of B. subtilis can be exploited for protein complexes and membrane proteins to facilitate their functional and structural analysis. The high quality of proteins produced with B. subtilis results from the action of cellular quality control systems that efficiently remove misfolded or incompletely synthesized proteins. Paradoxically, cellular quality control systems also represent bottlenecks for the production of various heterologous proteins at significant concentrations.

Conclusion

While inactivation of quality control systems has the potential to improve protein production yields, this could be achieved at the expense of product quality. Mechanisms underlying degradation of secretory proteins are nowadays well understood and often controllable. It will therefore be a major challenge for future research to identify and modulate quality control systems of B. subtilis that limit the production of high quality protein complexes and membrane proteins, and to enhance those systems that facilitate assembly of these proteins.

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

In Escherichia coli, division site placement is regulated by the dynamic behavior of the MinCDE proteins, which oscillate from pole to pole and confine septation to the centers of normal rod-shaped cells. Some current mathematical models explain these oscillations by considering interactions among the Min proteins without recourse to additional localization signals. So far, such models have been applied only to regularly shaped bacteria, but here we test these models further by employing aberrantly shaped E. coli cells as miniature reactors. The locations of MinCDE proteins fused to derivatives of green fluorescent protein were monitored in branched cells with at least three conspicuous poles. MinCDE most often moved from one branch to another in an invariant order, following a nonreversing clockwise or counterclockwise direction over the time periods observed. In cells with two short branches or nubs, the proteins oscillated symmetrically from one end to the other. The locations of FtsZ rings were consistent with a broad MinC-free zone near the branch junctions, and Min rings exhibited the surprising behavior of moving quickly from one possible position to another. Using a reaction-diffusion model that reproduces the observed MinCD oscillations in rod-shaped and round E. coli, we predict that the oscillation patterns in branched cells are a natural response of Min behavior in cellular geometries having different relative branch lengths. The results provide further evidence that Min protein oscillations act as a general cell geometry detection mechanism that can locate poles even in branched cells.

An experimentalist's guide to computational modelling of the Min system

Spatio-temporal oscillations of the Min proteins are essential for selecting the cell division site in Escherichia coli. These oscillations are a key example of a biological phenomenon that can only be understood on a systems level rather than on the level of its individual components. Here, we review the key concepts that mathematical modelling has added to our understanding of the Min system. While several different mechanisms have been proposed, in all cases the oscillations emerge from a dynamic instability of a uniform protein distribution. To generate this instability, however, the various mechanisms rely on different features of Min protein interactions and transport. We critically evaluate these mechanisms in light of recent experimental evidence. We also review the effects of fluctuations caused by low cellular concentration of Min proteins, and describe how stochastic effects may potentially influence Min protein dynamics.

Assembly dynamics of the bacterial MinCDE system and spatial regulation of the Z ring

The positioning of a cytoskeletal element that dictates the division plane is a fundamental problem in biology. The assembly and positioning of this cytoskeletal element has to be coordinated with DNA segregation and cell growth to ensure that equal-sized progeny cells are produced, each with a copy of the chromosome. In most prokaryotes, cytokinesis involves positioning a Z ring assembled from FtsZ, the ancestral homologue of tubulin. The position of the Z ring is determined by a gradient of negative regulators of Z-ring assembly. In Escherichia coli, the Min system consists of three proteins that cooperate to position the Z ring through a fascinating oscillation, which inhibits the formation of the Z ring away from midcell. Additional gradients of negative regulators of FtsZ assembly are used by E. coli and other bacteria to achieve spatial control of Z-ring assembly.

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

Ongoing sub-cellular oscillation of Min proteins is required to block minicelling in Escherichia coli. Experimentally, Min oscillations are seen in newly divided cells and no minicells are produced. In model Min systems many daughter cells do not oscillate following septation because of unequal partitioning of Min proteins between the daughter cells. Using the 3D model of Huang et al, we investigate the septation process in detail to determine the cause of the asymmetric partitioning of Min proteins between daughter cells. We find that this partitioning problem arises at certain phases of the MinD and MinE oscillations with respect to septal closure and it persists independently of parameter variation. At most 85% of the daughter cells exhibit Min oscillation following septation. Enhanced MinD binding at the static polar and dynamic septal regions, consistent with cardiolipin domains, does not substantially increase this fraction of oscillating daughters. We believe that this problem will be shared among all existing Min models and discuss possible biological mechanisms that may minimize partitioning errors of Min proteins following septation.

Chromosome segregation in Escherichia coli division: a free energy-driven string model

Although the mechanisms of eukaryotic chromosome segregation and cell division have been elucidated to a certain extent, those for bacteria remain largely unknown. Here we present a computational string model for simulating the dynamics of Escherichia coli chromosome segregation. A novel thermal-average force field accounting for stretching, bending, volume exclusion, friction and random fluctuation is introduced. A Langevin equation is used to simulate the chromosome structural changes. The mechanism of chromosome segregation is thereby postulated as a result of free energy-driven structural optimization with replication introduced chromosomal mass increase. Predictions of the model agree well with observations of fluorescence labeled chromosome loci movement in living cells. The results demonstrate the possibility of a mechanism of chromosome segregation that does not involve cytoskeletal guidance or advanced apparatus in an E. coli cell. The model also shows that DNA condensation of locally compacted domains is a requirement for successful chromosome segregation. Simulations also imply that the shape-determining protein MreB may play a role in the segregation via modification of the membrane pressure.

A mechanical explanation for cytoskeletal rings and helices in bacteria

Several bacterial proteins have been shown to polymerize into coils or rings on cell membranes. These include the cytoskeletal proteins MreB, FtsZ, and MinD, which together with other cell components make up what is being called the bacterial cytoskeleton. We believe that these shapes arise, at least in part, from the interaction of the inherent mechanical properties of the protein polymers and the constraints imposed by the curved cell membrane. This hypothesis, presented as a simple mechanical model, was tested with numerical energy-minimization methods from which we found that there are five low-energy polymer morphologies on a rod-shaped membrane: rings, lines, helices, loops, and polar-targeted circles. Analytic theory was used to understand the possible structures and to create phase diagrams that show which parameter combinations lead to which structures. Inverting the results, it is possible to infer the effective mechanical bending parameters of protein polymers from fluorescence images of their shapes. This theory also provides a plausible explanation for the morphological changes exhibited by the Z ring in a sporulating Bacillus subtilis; is used to calculate the mechanical force exerted on a cell membrane by a polymer; and allows predictions of polymer shapes in mutant cells.

A multistranded polymer model explains MinDE dynamics in E. coli cell division

In Escherichia coli, the location of the site for cell division is regulated by the action of the Min proteins. These proteins undergo a periodic pole-to-pole oscillation that involves polymerization and ATPase activity of MinD under the controlling influence of MinE. This oscillation suppresses division near the poles while permitting division at midcell. Here, we propose a multistranded polymer model for MinD and MinE dynamics that quantitatively agrees with the experimentally observed dynamics in wild-type cells and in several well-studied mutant phenotypes. The model also provides new explanations for several phenotypes that have never been addressed by previous modeling attempts. In doing so, the model bridges a theoretical gap between protein structure, biochemistry, and mutant phenotypes. Finally, the model emphasizes the importance of nonequilibrium polymer dynamics in cell function by demonstrating how behavior analogous to the dynamic instability of microtubules is used by E. coli to achieve a sufficiently rapid timescale in controlling division site selection.

Self-sustained spatiotemporal oscillations induced by membrane-bulk coupling

We propose a novel mechanism leading to spatiotemporal oscillations in extended systems that does not rely on local bulk instabilities. Instead, oscillations arise from the interaction of two subsystems of different spatial dimensionality. Specifically, we show that coupling a passive diffusive bulk of dimension d with an excitable membrane of dimension d-1 produces a self-sustained oscillatory behavior. An analytical explanation of the phenomenon is provided for d=1. Moreover, in-phase and antiphase synchronization of oscillations are found numerically in one and two dimensions. This novel dynamic instability could be used by biological systems such as cells, where the dynamics on the cellular membrane is necessarily different from that of the cytoplasmic bulk.

Division site recognition inEscherichia coliandBacillus subtilis

The process of cell division has been intensively studied at the molecular level for decades but some basic questions remain unanswered. The mechanisms of cell division are probably best characterized in the rod-shaped bacteria Escherichia coli and Bacillus subtilis. Many of the key players are known, but detailed descriptions of the molecular mechanisms which determine where, how and when cells form the division septum are lacking. Different models have been proposed to account for the high precision with which the septum is constructed at the midcell and these models have been evaluated and refined against new data emerging from the fast improving methodologies of cell biology. This review summarizes important advances in our understanding of how the cell positions the division septum, whether it be vegetative or asymmetric. It also describes how the asymmetric septum forms and how this septation event is linked to chromosome segregation and subsequent asymmetric gene expression during spore formation in B. subtilis.

Surface waves of Min-proteins

In the bacterium Escherichia coli, the Min-proteins show pronounced pole-to-pole oscillations. They are functional for suppressing cell division at the cell ends, leaving the center as the only possible site for division. Analyzing different models of Min-protein dynamics in a bacterial geometry, we find waves on the cytoplasmic membrane. Interestingly, the surface wave solutions of different models belong to different symmetry classes. We suggest that experiments on Min-protein surface waves in vitro are helpful in distinguishing between different classes of models of Min-protein dynamics.

Dynamic filaments of the bacterial cytoskeleton

Bacterial cells contain a variety of structural filamentous proteins necessary for the spatial regulation of cell shape, cell division, and chromosome segregation, analogous to the eukaryotic cytoskeletal proteins. The molecular mechanisms by which these proteins function are beginning to be revealed, and these proteins show numerous three-dimensional structural features and biochemical properties similar to those of eukaryotic actin and tubulin, revealing their evolutionary relationship. Recent technological advances have illuminated links between cell division and chromosome segregation, suggesting a higher complexity and organization of the bacterial cell than was previously thought.

Z ring as executor of bacterial cell division

It has become apparent that bacteria possess ancestors of the major eukaryotic cytoskeletal proteins. FtsZ, the ancestral homologue of tubulin, assembles into a cytoskeletal structure associated with cell division, designated the Z ring. Formation of the Z ring represents a major point of both spatial and temporal regulation of cell division. Here we discuss findings concerning the structure and the formation of the ring as well as its spatial and temporal regulation.

Mobility of Min-proteins in Escherichia coli measured by fluorescence correlation spectroscopy

In the bacterium Escherichia coli, selection of the division site involves pole-to-pole oscillations of the proteins MinD and MinE. Different oscillation mechanisms based on cooperative effects between Min-proteins and on the exchange of Min-proteins between the cytoplasm and the cytoplasmic membrane have been proposed. The parameters characterizing the dynamics of the Min-proteins in vivo are not known. It has therefore been difficult to compare the models quantitatively with experiments. Here, we present in vivo measurements of the mobility of MinD and MinE using fluorescence correlation spectroscopy. Two distinct timescales are clearly visible in the correlation curves. While the faster timescale can be attributed to cytoplasmic diffusion, the slower timescale could result from diffusion of membrane-bound proteins or from protein exchange between the cytoplasm and the membrane. We determine the diffusion constant of cytoplasmic MinD to be approximately 16 microm(2) s(-1), while for MinE we find about 10 microm(2) s(-1), independently of the processes responsible for the slower time-scale. The implications of the measured values for the oscillation mechanism are discussed.

The bacterial cytoskeleton

In recent years it has been shown that bacteria contain a number of cytoskeletal structures. The bacterial cytoplasmic elements include homologs of the three major types of eukaryotic cytoskeletal proteins (actin, tubulin, and intermediate filament proteins) and a fourth group, the MinD-ParA group, that appears to be unique to bacteria. The cytoskeletal structures play important roles in cell division, cell polarity, cell shape regulation, plasmid partition, and other functions. The proteins self-assemble into filamentous structures in vitro and form intracellular ordered structures in vivo. In addition, there are a number of filamentous bacterial elements that may turn out to be cytoskeletal in nature. This review attempts to summarize and integrate the in vivo and in vitro aspects of these systems and to evaluate the probable future directions of this active research field.

Temperature dependence of MinD oscillation in Escherichia coli: running hot and fast

We observed that the oscillation period of MinD within rod-like and filamentous cells of Escherichia coli varied by a factor of 4 in the temperature range from 20 degrees C to 40 degrees C. The detailed dependence was Arrhenius, with a slope similar to the overall temperature-dependent growth curve of E. coli. The detailed pattern of oscillation, including the characteristic wavelength in filamentous cells, remained independent of temperature. A quantitative model of MinDE oscillation exhibited similar behavior, with an activated temperature dependence of the MinE-stimulated MinD-ATPase rate.

Noise-induced Min phenotypes in E. coli

The spatiotemporal oscillations of the Escherichia coli proteins MinD and MinE direct cell division to the region between the chromosomes. Several quantitative models of the Min system have been suggested before, but no one of them accounts for the behavior of all documented mutant phenotypes. We analyzed the stochastic reaction-diffusion kinetics of the Min proteins for several E. coli mutants and compared the results to the corresponding deterministic mean-field description. We found that wild-type (wt) and filamentous (ftsZ⁻) cells are well characterized by the mean-field model, but that a stochastic model is necessary to account for several of the characteristics of the spherical (rodA⁻) and phospathedylethanolamide-deficient (PE⁻) phenotypes. For spherical cells, the mean-field model is bistable, and the system can get trapped in a non-oscillatory state. However, when the intrinsic noise is considered, only the experimentally observed oscillatory behavior remains. The stochastic model also reproduces the change in oscillation directions observed in the spherical phenotype and the occasional gliding of the MinD region along the inner membrane. For the PE⁻ mutant, the stochastic model explains the appearance of randomly localized and dense MinD clusters as a nucleation phenomenon, in which the stochastic kinetics at low copy number causes local discharges of the high MinD^ATP to MinD^ADP potential. We find that a simple five-reaction model of the Min system can explain all documented Min phenotypes, if stochastic kinetics and three-dimensional diffusion are accounted for. Our results emphasize that local copy number fluctuation may result in phenotypic differences although the total number of molecules of the relevant species is high.

Many molecules inside a living cell do not have time to diffuse through the whole cell in-between reactions. Furthermore, the chemical reactions are random and discrete events. In this study, the authors study an example in which these aspects of intracellular chemistry need to be considered when we try to understand how a biological system works.

The authors have investigated the spatial oscillation patterns that are displayed by the Min system of Escherichia coli. In wild-type E. coli, the Min proteins oscillate back and forth between the cell poles to help the bacterium find its middle before cell division. The authors used computer simulations to explain why the oscillation patterns change the way they do in different mutants of E. coli. They find that two of the mutant phenotypes can only be explained if one considers the randomness and discreteness of chemical reactions in addition to the spatial characteristics of the process. Particularly interesting is the phospathedylethanolamide-deficient phenotype, in which large dense clusters of MinD protein appear for some time at random locations on the membrane. The authors believe that this phenotype is due to a nucleation phenomenon, in which the stochastic kinetics at low copy number is amplified to macroscopic proportions.

Subcellular Positioning of F Plasmid Mediated by Dynamic Localization of SopA and SopB

SopA, SopB proteins and the cis-acting sopC DNA region of F plasmid are essential for partitioning of the plasmid, ensuring proper subcellular positioning of the plasmid DNA molecules. We have analyzed by immunofluorescence microscopy the subcellular localization of SopA and SopB. The majority of SopB molecules formed foci, which localized frequently with F plasmid DNA molecules. The foci increased in number in proportion to the cell length. Interestingly, beside the foci formation, SopB formed a spiral structure that was dependent on SopA, which also formed a spiral structure, independent of the presence of SopB, and these two structures partially overlapped. On the basis of these results and previous biochemical studies together with our simulations, we propose a theoretical model named "the reaction-diffusion partitioning model", using reaction-diffusion equations that explain the dynamic subcellular localization of SopA and SopB proteins and the subcellular positioning of F plasmid. We hypothesized that sister copies of plasmid DNA compete with each other for sites at which SopB multimer is at the optimum concentration. The plasmid incompatibility mediated by the Sop system might be explained clearly by this hypothesis.

Min-protein oscillations in Escherichia coli with spontaneous formation of two-stranded filaments in a three-dimensional stochastic reaction-diffusion model

We introduce a three-dimensional stochastic reaction-diffusion model to describe MinD/MinE dynamical structures in Escherichia coli. This model spontaneously generates pole-to-pole oscillations of the membrane-associated MinD proteins, MinE ring, as well as filaments of the membrane-associated MinD proteins. Experimental data suggest MinD filaments are two-stranded. In order to model them we assume that each membrane-associated MinD protein can form up to three bonds with adjacent membrane-associated MinD molecules and that MinE induced hydrolysis strongly depends on the number of bonds MinD has established.