Origin of contractile force during cell division of bacteria

Self-organization of mortal filaments and its role in bacterial division ring formation

Filaments in the cell commonly treadmill. Driven by energy consumption, they grow on one end while shrinking on the other, causing filaments to appear motile even though individual proteins remain static. This process is characteristic of cytoskeletal filaments and leads to collective filament self-organization. Here we show that treadmilling drives filament nematic ordering by dissolving misaligned filaments. Taking the bacterial FtsZ protein involved in cell division as an example, we show that this mechanism aligns FtsZ filaments in vitro and drives the organization of the division ring in living Bacillus subtilis cells. We find that ordering via local dissolution also allows the system to quickly respond to chemical and geometrical biases in the cell, enabling us to quantitatively explain the ring formation dynamics in vivo. Beyond FtsZ and other cytoskeletal filaments, our study identifies a mechanism for self-organization via constant birth and death of energy-consuming filaments.

Insights into the Structure, Function, and Dynamics of the Bacterial Cytokinetic FtsZ-Ring

The FtsZ protein is a highly conserved bacterial tubulin homolog. In vivo, the functional form of FtsZ is the polymeric, ring-like structure (Z-ring) assembled at the future division site during cell division. While it is clear that the Z-ring plays an essential role in orchestrating cytokinesis, precisely what its functions are and how these functions are achieved remain elusive. In this article, we review what we have learned during the past decade about the Z-ring's structure, function, and dynamics, with a particular focus on insights generated by recent high-resolution imaging and single-molecule analyses. We suggest that the major function of the Z-ring is to govern nascent cell pole morphogenesis by directing the spatiotemporal distribution of septal cell wall remodeling enzymes through the Z-ring's GTP hydrolysis-dependent treadmilling dynamics. In this role, FtsZ functions in cell division as the counterpart of the cell shape-determining actin homolog MreB in cell elongation.

The dynamics of shapes of vesicle membranes with time dependent spontaneous curvature

We study the time evolution of the shape of a vesicle membrane under time-dependent spontaneous curvature by means of phase-field model. We introduce the variation in time of the spontaneous curvature via a second field which represents the concentration of a substance that anchors with the lipid bilayer thus changing the local curvature and producing constriction. This constriction is mediated by the action on the membrane of an structure resembling the role of a Z ring. Our phase-field model is able to reproduce a number of different shapes that have been experimentally observed. Different shapes are associated with different constraints imposed upon the model regarding conservation of membrane area. In particular, we show that if area is conserved our model reproduces the so-called L-form shape. By contrast, if the area of the membrane is allowed to grow, our model reproduces the formation of a septum in the vicinity of the constriction. Furthermore, we propose a new term in the free energy which allows the membrane to evolve towards eventual pinching.

Minimal coarse-grained models for molecular self-organisation in biology

The molecular machinery of life is largely created via self-organisation of individual molecules into functional assemblies. Minimal coarse-grained models, in which a whole macromolecule is represented by a small number of particles, can be of great value in identifying the main driving forces behind self-organisation in cell biology. Such models can incorporate data from both molecular and continuum scales, and their results can be directly compared to experiments. Here we review the state of the art of models for studying the formation and biological function of macromolecular assemblies in living organisms. We outline the key ingredients of each model and their main findings. We illustrate the contribution of this class of simulations to identifying the physical mechanisms behind life and diseases, and discuss their future developments.

Tubulation pattern of membrane vesicles coated with biofilaments

Narrow membrane tubes are commonly pulled out from the surface of phospholipid vesicles using forces applied either through laser or magnetic tweezers or through the action of processive motor proteins. Recent examples have emerged in which an array of such tubes grows spontaneously from vesicles coated with bioactive cytoskeletal filaments (e.g., FtsZ, microtubule) in the presence GTP or ATP. We show how a soft vesicle deforms as a result of the interplay between its topology, local curvature, and the forces due to filament bundles. We present results from dynamically triangulated Monte Carlo simulations of a closed membrane vesicle coated with a nematic field (the filaments), and we show how the intrinsic curvature of the filaments and their bundling interactions drive membrane tubulation. We predict interesting patterns consisting of a large number of nematic defects that accompany tubulation. A common theme emerges: defect locations on vesicle surfaces are hot spots of membrane deformation activity, which could be useful for vesicle origami. Although our equilibrium model is not applicable to the nonequilibrium shape dynamics exhibited by active microtubule-coated vesicles, we show that some of the features, such as the size-dependent vesicle shape and the number of tubes, can still be understood from our equilibrium model.

Bacterial cell division: modeling FtsZ assembly and force generation from single filament experimental data

The bacterial cytoskeletal protein FtsZ binds and hydrolyzes GTP, self-aggregates into dynamic filaments and guides the assembly of the septal ring on the inner side of the membrane at midcell. This ring constricts the cell during division and is present in most bacteria. Despite exhaustive studies undertaken in the last 25 years after its discovery, we do not yet know the mechanism by which this GTP-dependent self-aggregating protein exerts force on the underlying membrane. This paper reviews recent experiments and theoretical models proposed to explain FtsZ filament dynamic assembly and force generation. It highlights how recent observations of single filaments on reconstituted model systems and computational modeling are contributing to develop new multiscale models that stress the importance of previously overlooked elements as monomer internal flexibility, filament twist and flexible anchoring to the cell membrane. These elements contribute to understand the rich behavior of these GTP consuming dynamic filaments on surfaces. The aim of this review is 2-fold: (1) to summarize recent multiscale models and their implications to understand the molecular mechanism of FtsZ assembly and force generation and (2) to update theoreticians with recent experimental results.

Z-ring Structure and Constriction Dynamics in E. coli

The Z-ring plays a central role in bacterial division. It consists of FtsZ filaments, but the way these reorganize in the ring-like structure during septation remains largely unknown. Here, we measure the effective constriction dynamics of the ring. Using an oscillating optical trap, we can switch individual rod-shaped E. coli cells between horizontal and vertical orientations. In the vertical orientation, the fluorescent Z-ring image appears as a symmetric circular structure that renders itself to quantitative analysis. In the horizontal orientation, we use phase-contrast imaging to determine the extent of the cell constriction and obtain the effective time of division. We find evidence that the Z-ring constricts at a faster rate than the cell envelope such that its radial width (inwards from the cytoplasmic membrane) grows during septation. In this respect, our results differ from those recently obtained using photoactivated localization microscopy (PALM) where the radial width of the Z-ring was found to be approximately constant as the ring constricts. A possible reason for the different behavior of the constricting Z-rings could be the significant difference in the corresponding cell growth rates.

Mutations on FtsZ lateral helix H3 that disrupt cell viability hamper reorganization of polymers on lipid surfaces

FtsZ filaments localize at the middle of the bacterial cell and participate in the formation of a contractile ring responsible for cell division. Previous studies demonstrated that the highly conserved negative charge of glutamate 83 and the positive charge of arginine 85 located in the lateral helix H3 bend of Escherichia coli FtsZ are required for in vivo cell division. In order to understand how these lateral mutations impair the formation of a contractile ring,we extend previous in vitro characterization of these mutants in solution to study their behavior on lipid modified surfaces. We study their interaction with ZipAand look at their reorganization on the surface. We found that the dynamic bundling capacity of the mutant proteins is deficient, and this impairment increases the more the composition and spatial arrangement of the reconstituted system resembles the situation inside the cell: mutant proteins completely fail to reorganize to form higher order aggregates when bound to an E.coli lipid surface through oriented ZipA.We conclude that these surface lateral point mutations affect the dynamic reorganization of FtsZ filaments into bundles on the cell membrane, suggesting that this event is relevant for generating force and completing bacterial division.

Beyond force generation: Why is a dynamic ring of FtsZ polymers essential for bacterial cytokinesis?

We propose that the essential function of the most highly conserved protein in bacterial cytokinesis, FtsZ, is not to generate a mechanical force to drive cell division. Rather, we suggest that FtsZ acts as a signal-processing hub to coordinate cell wall synthesis at the division septum with a diverse array of cellular processes, ensuring that the cell divides smoothly at the correct time and place, and with the correct septum morphology. Here, we explore how the polymerization properties of FtsZ, which have been widely attributed to force generation, can also be advantageous in this signal processing role. We suggest mechanisms by which FtsZ senses and integrates both mechanical and biochemical signals, and conclude by proposing experiments to investigate how FtsZ contributes to the remarkable spatial and temporal precision of bacterial cytokinesis.

Membrane remodelling in bacteria

In bacteria the ability to remodel membrane underpins basic cell processes such as growth, and more sophisticated adaptations like inter-cell crosstalk, organelle specialisation, and pathogenesis. Here, selected examples of membrane remodelling in bacteria are presented and the diverse mechanisms for inducing membrane fission, fusion, and curvature discussed. Compared to eukaryotes, relatively few curvature-inducing proteins have been characterised so far. Whilst it is likely that many such proteins remain to be discovered, it also reflects the importance of alternative membrane remodelling strategies in bacteria where passive mechanisms for generating curvature are utilised.

Redefining the roles of the FtsZ-ring in bacterial cytokinesis

In most bacteria, cell division relies on the functions of an essential protein, FtsZ. FtsZ polymerizes at the future division site to form a ring-like structure, termed the Z-ring, that serves as a scaffold to recruit all other division proteins, and possibly generates force to constrict the cell. The scaffolding function of the Z-ring is well established, but the force generating function has recently been called into question. Additionally, new findings have demonstrated that the Z-ring is more directly linked to cell wall metabolism than simply recruiting enzymes to the division site. Here we review these advances and suggest that rather than generating a rate-limiting constrictive force, the Z-ring's function may be redefined as an orchestrator of septum synthesis.

Defining the rate-limiting processes of bacterial cytokinesis

Bacterial cytokinesis is accomplished by the essential 'divisome' machinery. The most widely conserved divisome component, FtsZ, is a tubulin homolog that polymerizes into the 'FtsZ-ring' ('Z-ring'). Previous in vitro studies suggest that Z-ring contraction serves as a major constrictive force generator to limit the progression of cytokinesis. Here, we applied quantitative superresolution imaging to examine whether and how Z-ring contraction limits the rate of septum closure during cytokinesis in Escherichia coli cells. Surprisingly, septum closure rate was robust to substantial changes in all Z-ring properties proposed to be coupled to force generation: FtsZ's GTPase activity, Z-ring density, and the timing of Z-ring assembly and disassembly. Instead, the rate was limited by the activity of an essential cell wall synthesis enzyme and further modulated by a physical divisome-chromosome coupling. These results challenge a Z-ring-centric view of bacterial cytokinesis and identify cell wall synthesis and chromosome segregation as limiting processes of cytokinesis.

Phase-field modelling of the dynamics of Z-ring formation in liposomes: Onset of constriction and coarsening

We propose a model for the dynamics of the formation of rings of FtsZ on tubular liposomes which produce constriction on the corresponding membrane. Our phase-field model is based on a simple bending energy that captures the dynamics of the interplay between the protein and the membrane. The short-time regime is analyzed by a linear dispersion relation, with which we are able to predict the number of rings per unit length on a tubular liposome. We study numerically the long-time dynamics of the system in the non-linear regime where we observe coarsening of Z-rings on tubular liposomes. In particular, our numerical results show that, during the coarsening process, the number of Z-rings decreases as the radius of tubular liposome increases. This is consistent with the experimental observation that the separation between rings is proportional to the radius of the liposome. Our model predicts that the mechanism for the increased rate of coarsening in liposomes of larger radius is a consequence of the increased interface energy.

Effects of various kinetic rates of FtsZ filaments on bacterial cytokinesis

Cell morphodynamics during bacterial cytokinesis is extensively investigated by a combination of phase field model for rod-shaped cells and a kinetic description for FtsZ ring maintenance.

Torsion and curvature of FtsZ filaments

FtsZ filaments participate in bacterial cell division, but it is still not clear how their dynamic polymerization and shape exert force on the underlying membrane. We present a theoretical description of individual filaments that incorporates information from molecular dynamic simulations. The structure of the crystallized Methanococcus jannaschii FtsZ dimer was used to model a FtsZ pentamer that showed a curvature and a twist. The estimated bending and torsion angles between monomers and their fluctuations were included in the theoretical description. The MD data also permitted positioning the curvature with respect to the protein coordinates and allowed us to explore the effect of the relative orientation of the preferred curvature with respect to the surface plane. We find that maximum tension is attained when filaments are firmly attached and oriented with their curvature perpendicular to the surface and that the twist serves as a valve to release or to tighten the tension exerted by the curved filaments on the membrane. The theoretical model also shows that the presence of torsion can explain the shape distribution of short filaments observed by Atomic Force Microscopy in previously published experiments. New experiments with FtsZ covalently attached to lipid membranes show that the filament on-plane curvature depends on lipid head charge, confirming the predicted monomer orientation effects. This new model underlines the fact that the combination of the three elements, filament curvature, twist and the strength and orientation of its surface attachment, can modulate the force exerted on the membrane during cell division.

Coupling FtsZ filaments and morphodynamics during bacterial cell division

Cell morphodynamics during bacterial cell division is extensively investigated by a combination of a phase field model for rod-shaped cells and a kinetic description for FtsZ ring maintenance.

Cell shape can mediate the spatial organization of the bacterial cytoskeleton

The bacterial cytoskeleton guides the synthesis of cell wall and thus regulates cell shape. Because spatial patterning of the bacterial cytoskeleton is critical to the proper control of cell shape, it is important to ask how the cytoskeleton spatially self-organizes in the first place. In this work, we develop a quantitative model to account for the various spatial patterns adopted by bacterial cytoskeletal proteins, especially the orientation and length of cytoskeletal filaments such as FtsZ and MreB in rod-shaped cells. We show that the combined mechanical energy of membrane bending, membrane pinning, and filament bending of a membrane-attached cytoskeletal filament can be sufficient to prescribe orientation, e.g., circumferential for FtsZ or helical for MreB, with the accuracy of orientation increasing with the length of the cytoskeletal filament. Moreover, the mechanical energy can compete with the chemical energy of cytoskeletal polymerization to regulate filament length. Notably, we predict a conformational transition with increasing polymer length from smoothly curved to end-bent polymers. Finally, the mechanical energy also results in a mutual attraction among polymers on the same membrane, which could facilitate tight polymer spacing or bundling. The predictions of the model can be verified through genetic, microscopic, and microfluidic approaches.

Polymorphism of FtsZ filaments on lipid surfaces: role of monomer orientation

FtsZ is a bacterial cytoskeletal protein involved in cell division. It forms a ringlike structure that attaches to the membrane to complete bacterial division. It binds and hydrolyzes GTP, assembling into polymers in a GTP-dependent manner. To test how the orientation of the monomers affects the curvature of the filaments on a surface, we performed site-directed mutagenesis on the E. coli FtsZ protein to insert cysteine residues at lateral locations to orient FtsZ on planar lipid bilayers. The E93C and S255C mutants were overproduced, purified, and found to be functionally active in solution, as well as being capable of sustaining cell division in vivo in complementation assays. Atomic force microscopy was used to observe the shape of the filament fibers formed on the surface. The FtsZ mutants were covalently linked to the lipids and could be polymerized on the bilayer surface in the presence of GTP. Unexpectedly, both mutants assembled into straight structures. E93C formed a well-defined lattice with monomers interacting at 60° and 120° angles, whereas S255C formed a more open array of straight thicker filament aggregates. These results indicate that filament curvature and bending are not fixed and that they can be modulated by the orientation of the monomers with respect to the membrane surface. As filament curvature has been associated with the force generation mechanism, these results point to a possible role of filament membrane attachment in lateral association and curvature, elements currently identified as relevant for force generation.

In the beginning, Escherichia coli assembled the proto-ring: an initial phase of division

Cell division in Escherichia coli begins by assembling three proteins, FtsZ, FtsA, and ZipA, to form a proto-ring at midcell. These proteins nucleate an assembly of at least 35 components, the divisome. The structuring of FtsZ to form a ring and the processes that effect constriction have been explained by alternative but not mutually exclusive mechanisms. We discuss how FtsA and ZipA provide anchoring of the cytoplasmic FtsZ to the membrane and how a temporal sequence of alternative protein interactions may operate in the maturation and stability of the proto-ring. How the force needed for constriction is generated and how the proto-ring proteins relate to peptidoglycan synthesis remain as the main challenges for future research.

Membrane reconstitution of FtsZ-ZipA complex inside giant spherical vesicles made of E. coli lipids: large membrane dilation and analysis of membrane plasticity

During the division process of Escherichia coli, the globular protein FtsZ is early recruited at the constriction site. The Z-ring, based on FtsZ filaments associated to the inner cell membrane, has been postulated to exert constriction forces. Membrane anchoring is mediated by ZipA, an essential transmembrane protein able to specifically bind FtsZ. In this work, an artificial complex of FtsZ-ZipA has been reconstituted at the inner side of spherical giant unilamellar vesicles made of E. coli lipids. Under these conditions, FtsZ polymerization, triggered when a caged GTP analogue is UV-irradiated, was followed by up to 40% vesicle inflation. The homogeneous membrane dilation was accompanied by the visualization of discrete FtsZ assemblies at the membrane. Complementary rheological data revealed enhanced elasticity under lateral dilation. This explains why vesicles can undergo large dilations in the regime of mechanical stability. A mechanical role for FtsZ polymers as promoters of membrane softening and plasticization is hypothesized.

Depolymerization dynamics of individual filaments of bacterial cytoskeletal protein FtsZ

We report observation and analysis of the depolymerization filaments of the bacterial cytoskeletal protein FtsZ (filament temperature-sensitive Z) formed on a mica surface. At low concentration, proteins adsorbed on the surface polymerize forming curved filaments that close into rings that remain stable for some time before opening irreversibly and fully depolymerizing. The distribution of ring lifetimes (T) as a function of length (N), shows that the rate of ring aperture correlates with filament length. If this ring lifetime is expressed as a bond survival time, (T(b) ≡ NT), this correlation is abolished, indicating that these rupture events occur randomly and independently at each monomer interface. After rings open irreversibly, depolymerization of the remaining filaments is fast, but can be slowed down and followed using a nonhydrolyzing GTP analogue. The histogram of depolymerization velocities of individual filaments has an asymmetric distribution that can be fit with a computer model that assumes two rupture rates, a slow one similar to the one observed for ring aperture, affecting monomers in the central part of the filaments, and a faster one affecting monomers closer to the open ends. From the quantitative analysis, we conclude that the depolymerization rate is affected both by nucleotide hydrolysis rate and by its exchange along the filament, that all monomer interfaces are equally competent for hydrolysis, although depolymerization is faster at the open ends than in central filament regions, and that all monomer-monomer interactions, regardless of the nucleotide present, can adopt a curved configuration.

Physics of bacterial morphogenesis

Bacterial cells utilize three-dimensional (3D) protein assemblies to perform important cellular functions such as growth, division, chemoreception, and motility. These assemblies are composed of mechanoproteins that can mechanically deform and exert force. Sometimes, small-nucleotide hydrolysis is coupled to mechanical deformations. In this review, we describe the general principle for an understanding of the coupling of mechanics with chemistry in mechanochemical systems. We apply this principle to understand bacterial cell shape and morphogenesis and how mechanical forces can influence peptidoglycan cell wall growth. We review a model that can potentially reconcile the growth dynamics of the cell wall with the role of cytoskeletal proteins such as MreB and crescentin. We also review the application of mechanochemical principles to understand the assembly and constriction of the FtsZ ring. A number of potential mechanisms are proposed, and important questions are discussed.

Active membrane viscoelasticity by the bacterial FtsZ-division protein

At the early stages of the division process in Escherichia coli, the protein FtsZ forms a septal ring at the midcell. This Z-ring causes membrane constriction during bacterial division. The Z-ring associates to the lipid membrane through several membrane proteins, ZipA among them. Here, a simplified FtsZ-ZipA model was reconstituted onto Langmuir monolayers based in E. coli polar lipid extract. Brewster angle and atomic force microscopy have revealed membrane FtsZ-polymerization upon GTP hydrolysis. The compression viscoelasticity of these monolayers has been also investigated. The presence of protein induced softening and fluidization with respect to the bare lipid membrane. An active mechanism, based on the internal forces stressed by FtsZ filaments and transduced to the lipid membrane by ZipA, was suggested to underlie the observed behavior.

Supramolecular cellular filament systems: how and why do they form?

All cells, from simple bacteria to complex human tissues, rely on extensive networks of protein fibers to help maintain their proper form and function. These filament systems usually do not operate as single filaments, but form complex suprastructures, which are essential for specific cellular functions. Here, we describe the progress in determining the architectures of molecular filamentous suprastructures, the principles leading to their formation, and the mechanisms by which they may facilitate function. The complex eukaryotic cytoskeleton is tightly regulated by a large number of actin- or microtubule-associated proteins. In contrast, recently discovered bacterial actins and tubulins have few associated regulatory proteins. Hence, the quest to find basic principles that govern the formation of filamentous suprastructures is simplified in bacteria. Three common principles, which have been probed extensively during evolution, can be identified that lead to suprastructures formation: cationic counterion fluctuations; self-association into liquid crystals; and molecular crowding. The underlying physics of these processes will be discussed with respect to physiological circumstance.

Estimating the bending modulus of a FtsZ bacterial-division protein filament

FtsZ, a cytoskeletal protein homologous to tubulin, is the principle constituent of the division ring in bacterial cells. It is known to have force-generating capacity in vitro and has been conjectured to be the source of the constriction force in vivo. Several models have been proposed to explain the generation of force by the Z ring. Here we re-examine data from in vitro experiments in which Z rings formed and constricted inside tubular liposomes, and we carry out image analysis on previously published data with which to better estimate important model parameters that have proven difficult to measure by direct means. We introduce a membrane-energy-based model for the dynamics of multiple Z rings moving and colliding inside a tubular liposome and a fluid model for the drag of a Z ring as it moves through the tube. Using this model, we estimate an effective membrane bending modulus of 500-700 pN nm. If we assume that FtsZ force generation is driven by hydrolysis into a highly curved conformation, we estimate the FtsZ filament bending modulus to be 310-390 pN nm(2). If we assume instead that force is generated by the non-hydrolysis-dependent intermediate curvature conformation, we find that B(f)>1400 pN nm(2). The former value sits at the lower end of the range of previously estimated values and, if correct, may raise challenges for models that rely on filament bending to generate force.

FtsZ polymers bound to lipid bilayers through ZipA form dynamic two dimensional networks

Bacteria divide by forming a contractile ring around their midcell region. FtsZ, a cytoskeletal soluble protein structurally related to tubulin, is the main component of this division machinery. It forms filaments that bundle at the inner side of the cytoplasmic membrane. These FtsZ bundles do not attach to bare lipid surfaces. In Escherichia coli they remain near the membrane surface by attaching to the membrane protein ZipA and FtsA. In order to study the structure and dynamics of the ZipA-FtsZ bundles formed on a lipid surface, we have oriented a soluble form of ZipA (sZipA), with its transmembrane domain substituted by a histidine tag, on supported lipid membranes. Atomic force microscopy has been used to visualize the polymers formed on top of this biomimetic surface. In the presence of GTP, when sZipA is present, FtsZ polymers restructure forming higher order structures. The lipid composition of the underlying membrane affects the aggregation kinetics and the shape of the structures formed. On the negatively charged E. coli lipid membranes, filaments condense from initially disperse material to form a network that is more dynamic and flexible than the one formed on phosphatidyl choline bilayers. These FtsZ-ZipA filament bundles are interconnected, retain their capacity to dynamically restructure, to fragment, to anneal and to condense laterally.

Timing of Z-ring localization in Escherichia coli

Bacterial cell division takes place in three phases: Z-ring formation at midcell, followed by divisome assembly and building of the septum per se. Using time-lapse microscopy of live bacteria and a high-precision cell edge detection method, we have previously found the true time for the onset of septation, τ(c), and the time between consecutive divisions, τ(g). Here, we combine the above method with measuring the dynamics of the FtsZ-GFP distribution in individual Escherichia coli cells to determine the Z-ring positioning time, τ(z). To analyze the FtsZ-GFP distribution along the cell, we used the integral fluorescence profile (IFP), which was obtained by integrating the fluorescence intensity across the cell width. We showed that the IFP may be approximated by an exponential peak and followed the peak evolution throughout the cell cycle, to find a quantitative criterion for the positioning of the Z-ring and hence the value of τ(z). We defined τ(z) as the transition from oscillatory to stable behavior of the mean IFP position. This criterion was corroborated by comparison of the experimental results to a theoretical model for the FtsZ dynamics, driven by Min oscillations. We found that τ(z) < τ(c) for all the cells that were analyzed. Moreover, our data suggested that τ(z) is independent of τ(c), τ(g) and the cell length at birth, L(0). These results are consistent with the current understanding of the Z-ring positioning and cell septation processes.

Force generation in bacteria without nucleotide-dependent bending of cytoskeletal filaments

Binary cell division in bacteria occurs via the formation and subsequent contraction of a polymeric ring, the so-called Z ring, at the middle of the cell. This ring is made of filamenting temperature-sensitive Z (FtsZ) proteins and it shrinks in radius to generate a contractile radial force on the cell membrane. Although a few models have been proposed, the ring contraction mechanism still remains a mystery. The models rely on various physical properties of the FtsZ filaments, some of which have been verified through in vitro experiments and some of which remain unclear. A feature common to all these models is the hydrolysis-driven transition of FtsZ filaments from straight to curved conformations. While the intrinsic curvature of FtsZ filaments has been experimentally established beyond doubt, evidence has been mounting against the existence of any transition between the straight FtsZ-GTP and the curved FtsZ-GDP conformations. Preliminary results from our earlier work [B. Ghosh and A. Sain, Phys. Rev. Lett. 101, 178101 (2008)] indicated that hydrolysis-induced bending is not necessary for Z-ring contraction. Since then many new experimental observations have been reported on this subject and in view of these here we argue that our model appears even more plausible than before. In addition, we have explored more realistic features, such as how the length distribution of FtsZ filaments in the cytoplasm may influence the contraction dynamics, and we have also demonstrated that the Z ring retains approximately the same number of monomers, although not the same monomers, during the course of contraction as reported by fluorescence experiments.

Imaging-based identification of a critical regulator of FtsZ protofilament curvature in Caulobacter

FtsZ is an essential bacterial GTPase that polymerizes at midcell, recruits the division machinery, and may generate constrictive forces necessary for cytokinesis. However, many of the mechanistic details underlying these functions are unknown. We sought to identify FtsZ-binding proteins that influence FtsZ function in Caulobacter crescentus. Here, we present a microscopy-based screen through which we discovered two FtsZ-binding proteins, FzlA and FzlC. FzlA is conserved in α-proteobacteria and was found to be functionally critical for cell division in Caulobacter. FzlA altered FtsZ structure both in vivo and in vitro, forming stable higher-order structures that were resistant to depolymerization by MipZ, a spatial determinant of FtsZ assembly. Electron microscopy revealed that FzlA organizes FtsZ protofilaments into striking helical bundles. The degree of curvature induced by FzlA depended on the nucleotide bound to FtsZ. Induction of FtsZ curvature by FzlA carries implications for regulating FtsZ function by modulating its superstructure.

Strong FtsZ is with the force: mechanisms to constrict bacteria

FtsZ, the best-known prokaryotic division protein, assembles at midcell with other proteins forming a ring during septation. Widely conserved in bacteria, FtsZ represents the ancestor of tubulin. In the presence of GTP it forms polymers able to associate into multi-stranded flexible structures. FtsZ research is aimed at determining the role of the Z-ring in division, describing the polymerization and potential force-generating mechanisms and evaluating the roles of nucleotide exchange and hydrolysis. Systems to reconstruct the FtsZ ring in vitro have been described and some of its mechanical properties have been reproduced using in silico modeling. We discuss current research in FtsZ, some of the controversies, and finally propose further research needed to complete a model of FtsZ action that reconciles its in vitro properties with its role in division.

Cell wall synthesis is necessary for membrane dynamics during sporulation of Bacillus subtilis

During Bacillus subtilis sporulation, an endocytic-like process called engulfment results in one cell being entirely encased in the cytoplasm of another cell. The driving force underlying this process of membrane movement has remained unclear, although components of the machinery have been characterized. Here we provide evidence that synthesis of peptidoglycan, the rigid, strength bearing extracellular polymer of bacteria, is a key part of the missing force-generating mechanism for engulfment. We observed that sites of peptidoglycan synthesis initially coincide with the engulfing membrane and later with the site of engulfment membrane fission. Furthermore, compounds that block muropeptide synthesis or polymerization prevented membrane migration in cells lacking a component of the engulfment machinery (SpoIIQ), and blocked the membrane fission event at the completion of engulfment in all cells. In addition, these compounds inhibited bulge and vesicle formation that occur in spoIID mutant cells unable to initiate engulfment, as did genetic ablation of a protein that polymerizes muropeptides. This is the first report to our knowledge that peptidoglycan synthesis is necessary for membrane movements in bacterial cells and has implications for the mechanism of force generation during cytokinesis.

Constricting force of filamentary protein rings evaluated from experimental results

We present a model of Z -ring constriction in bacteria based on different experimental in vitro results. The forces produced by the Z ring due to lateral attraction of its constituent parts, estimated in previous studies that were based on FtsZ filaments observed by atomic force microscopy, are in good agreement with an estimation of the force required for recently found deformations in liposomes caused by FtsZ. These forces are calculated within the usual Helfrich energy formalism. In this context, we also explain the apparent attraction of multiple Z rings in the liposomes initially separated by small distances, as well as the stable distribution of rings separated by distances greater than approximately twice the diameter of the cylindrical liposomes. We adapted the model to the in vivo conditions imposed by the bacterial cell wall, concluding that the proposed mechanism gives a qualitative explanation for the force generation during bacterial division.

Stretching weakly bending filaments with spontaneous curvature in two dimensions

Some important biomolecules (for instance, bacterial FtsZ and eukaryotic DNA) are known to posses spontaneous (intrinsic) curvature. Using a simple extension of the wormlike chain model, we study the response of a weakly bending filament in two dimensions to a pulling force applied at its ends (a configuration common in classical in-vitro experiments and relevant to several in-vivo cell cases). The spontaneous curvature of such a chain or filament can in general be arc-length dependent and we study a case of sinusoidal variation, from which an arbitrary case can be reconstructed via Fourier transformation. We obtain analytic results for the force-extension relationship and the width of transverse fluctuations. We show that spontaneous-curvature undulations can affect the force-extension behavior even in relatively flexible filaments with a persistence length smaller than the contour length.

Arabidopsis FtsZ2-1 and FtsZ2-2 are functionally redundant, but FtsZ-based plastid division is not essential for chloroplast partitioning or plant growth and development

FtsZ1 and FtsZ2 are phylogenetically distinct families of FtsZ in plants that co-localize to mid-plastid rings and facilitate division of chloroplasts. In plants, altered levels of either FtsZ1 or FtsZ2 cause dose-dependent defects in chloroplast division; thus, studies on the functional relationship between FtsZ genes require careful manipulation of FtsZ levels in vivo. To define the functional relationship between the two FtsZ2 genes in Arabidopsis thaliana, FtsZ2-1 and FtsZ2-2, we expressed FtsZ2-1 in an ftsZ2-2 null mutant, and vice versa, and determined whether the chloroplast division defects were rescued in plants expressing different total levels of FtsZ2. Full rescue was observed when either the FtsZ2-1 or FtsZ2-2 level approximated total FtsZ2 levels in wild-type (WT). Additionally, FtsZ2-2 interacts with ARC6, as shown previously for FtsZ2-1. These data indicate that FtsZ2-1 and FtsZ2-2 are functionally redundant for chloroplast division in Arabidopsis. To rigorously validate the requirement of each FtsZ family for chloroplast division, we replaced FtsZ1 with FtsZ2 in vivo, and vice versa, while maintaining the FtsZ level in the transgenic plants equal to that of the total level in WT. Chloroplast division defects were not rescued, demonstrating conclusively that FtsZ1 and FtsZ2 are non-redundant for maintenance of WT chloroplast numbers. Finally, we generated ftsZ triple null mutants and show that plants completely devoid of FtsZ protein are viable and fertile. As plastids are presumably essential organelles, these findings suggest that an FtsZ-independent mode of plastid partitioning may occur in higher plants.

Effect of intrinsic curvature on semiflexible polymers

Recently many important biopolymers have been found to possess intrinsic curvature. Tubulin protofilaments in animal cells, FtsZ filaments in bacteria and double stranded DNA are examples. We examine how intrinsic curvature influences the conformational statistics of such polymers. We give exact results for the tangent-tangent spatial correlation function C(r)=<t(s).t(s+r)>, both in two and three dimensions. Contrary to expectation, C(r) does not show any oscillatory behavior, rather decays exponentially and the effective persistence length has strong length dependence for short polymers. We also compute the distribution function P(R) of the end to end distance R and show how curved chains can be distinguished from wormlike chains using loop formation probability.

Simple modeling of FtsZ polymers on flat and curved surfaces: correlation with experimental in vitro observations

FtsZ is a GTPase that assembles at midcell into a dynamic ring that constricts the membrane to induce cell division in the majority of bacteria, in many archea and several organelles. In vitro, FtsZ polymerizes in a GTP-dependent manner forming a variety of filamentous flexible structures. Based on data derived from the measurement of the in vitro polymerization of Escherichia coli FtsZ cell division protein we have formulated a model in which the fine balance between curvature, flexibility and lateral interactions accounts for structural and dynamic properties of the FtsZ polymers observed with AFM. The experimental results have been used by the model to calibrate the interaction energies and the values obtained indicate that the filaments are very plastic. The extension of the model to explore filament behavior on a cylindrical surface has shown that the FtsZ condensates promoted by lateral interactions can easily form ring structures through minor modulations of either filament curvature or longitudinal bond energies. The condensation of short, monomer exchanging filaments into rings is shown to produce enough force to induce membrane deformations.PACS codes: 87.15.ak, 87.16.ka, 87.17.Ee.

Modeling the physics of FtsZ assembly and force generation

The tubulin homolog FtsZ is the major cytoskeletal protein in bacterial cytokinesis. It can generate a constriction force on the bacterial membrane or inside tubular liposomes. Several models have recently been proposed for how this force might be generated. These fall into 2 categories. The first is based on a conformational change from a straight to a curved protofilament. The simplest "hydrolyze and bend" model proposes a 22 degrees bend at every interface containing a GDP. New evidence suggests another curved conformation with a 2.5 degrees bend at every interface and that the relation of curvature to GTP hydrolysis is more complicated than previously thought. However, FtsZ protofilaments do appear to be mechanically rigid enough to bend membranes. A second category of models is based on lateral bonding between protofilaments, postulating that a contraction could be generated when protofilaments slide to increase the number of lateral bonds. Unfortunately these lateral bond models have ignored the contribution of subunit entropy when adding bond energies; if included, the mechanism is seen to be invalid. Finally, I address recent models that try to explain how protofilaments 1-subunit-thick show a cooperative assembly.

FtsN-like proteins are conserved components of the cell division machinery in proteobacteria

In bacteria, cytokinesis is mediated by a ring-shaped multiprotein complex, called divisome. While some of its components are widely conserved, others are restricted to certain bacterial lineages. FtsN is the last essential cell division protein to localize to the division septum in Escherichia coli and is poorly conserved outside the enteric bacteria. We have identified a homologue of FtsN in the alpha-proteobacterium Caulobacter crescentus and show that it is essential for cell division. C. crescentus FtsN is recruited to the divisome significantly after cell division initiates and remains associated with the new cell poles after cytokinesis is finished. All determinants necessary for localization and function are located in a largely unstructured periplasmic segment of the protein. Its conserved SPOR-domain, by contrast, is dispensable for cytokinesis, although it supports targeting of FtsN to the division site. Interestingly, the SPOR-domain is recruited to the division plane when produced in isolated form and retains its localization potential in a heterologous host background. Searching for proteins that share the characteristic features of FtsN from E. coli and C. crescentus, we identified FtsN-like cell division proteins in beta- and delta-proteobacteria, suggesting that FtsN is widespread among bacteria, albeit highly variable at the sequence level.

Condensation of FtsZ filaments can drive bacterial cell division

Forces are important in biological systems for accomplishing key cell functions, such as motility, organelle transport, and cell division. Currently, known force generation mechanisms typically involve motor proteins. In bacterial cells, no known motor proteins are involved in cell division. Instead, a division ring (Z-ring) consists of mostly FtsZ, FtsA, and ZipA is used to exerting a contractile force. The mechanism of force generation in bacterial cell division is unknown. Using computational modeling, we show that Z-ring formation results from the colocalization of FtsZ and FtsA mediated by the favorable alignment of FtsZ polymers. The model predicts that the Z-ring undergoes a condensation transition from a low-density state to a high-density state and generates a sufficient contractile force to achieve division. FtsZ GTP hydrolysis facilitates monomer turnover during the condensation transition, but does not directly generate forces. In vivo fluorescence measurements show that FtsZ density increases during division, in accord with model results. The mechanism is akin to van der Waals picture of gas-liquid condensation, and shows that organisms can exploit microphase transitions to generate mechanical forces.