Langevin computer simulations of bacterial protein filaments and the force-generating mechanism during cell division

How Does the Spatial Confinement of FtsZ to a Membrane Surface Affect Its Polymerization Properties and Function?

FtsZ is the cytoskeletal protein that organizes the formation of the septal ring and orchestrates bacterial cell division. Its association to the membrane is essential for its function. In this mini-review I will address the question of how this association can interfere with the structure and dynamic properties of the filaments and argue that its dynamics could also remodel the underlying lipid membrane through its activity. Thus, lipid rearrangement might need to be considered when trying to understand FtsZ’s function. This new element could help understand how FtsZ assembly coordinates positioning and recruitment of the proteins forming the septal ring inside the cell with the activity of the machinery involved in peptidoglycan synthesis located in the periplasmic space.

Biomolecular response to hour-long ultralow field microwave radiation: An effective coarse-grained model simulation

Various electronic devices, which we commonly use, radiate microwaves. Such external perturbation influences the functionality of biomolecules. In an ultralow field, the cumulative response of a molecule is expected only over a time scale of hours. To study the structural dynamics of biomolecules over hours, we adopt a simple methodology for constructing the coarse-grained structure of the protein molecule and solve the Langevin equation under different working potentials. In this approach, each amino acid residue of a biomolecule is mapped onto a number of beads, a few for the backbone, and few for the side chain, depending on the complexity of its chemical structure. We choose the force field in such a way that the dynamics of the protein molecule in the presence of ultralow radiation field of microvolt/nm could be followed over the time frame of 2 h. We apply the model to describe a biomolecule, hen egg white lysozyme, and simulate its structural evolution under ultralow strength electromagnetic radiation. The simulation revealed the finer structural details, like the extent of exposure of bioactive residues and the state of the secondary structures of the molecule, further confirmed from spectroscopic measurements [details are available in Phys. Rev. E 97, 052416 (2018)10.1103/PhysRevE.97.052416 and briefly described here]. Though tested for a specific system, the model is quite general. We believe that it harnesses the potential in studying the structural dynamics of any biopolymer under external perturbation over an extended time scale.

Simulations of Proposed Mechanisms of FtsZ-Driven Cell Constriction

FtsZ is thought to generate constrictive force to divide the cell, possibly via one of two predominant models in the field. In one, FtsZ filaments overlap to form complete rings which constrict as filaments slide past each other to maximize lateral contact.

To divide, bacteria must constrict their membranes against significant force from turgor pressure. A tubulin homolog, FtsZ, is thought to drive constriction, but how FtsZ filaments might generate constrictive force in the absence of motor proteins is not well understood. There are two predominant models in the field. In one, FtsZ filaments overlap to form complete rings around the circumference of the cell, and attractive forces cause filaments to slide past each other to maximize lateral contact. In the other, filaments exert force on the membrane by a GTP-hydrolysis-induced switch in conformation from straight to bent. Here, we developed software, ZCONSTRICT, for quantitative three-dimensional (3D) simulations of Gram-negative bacterial cell division to test these two models and identify critical conditions required for them to work. We find that the avidity of any kind of lateral interactions quickly halts the sliding of filaments, so a mechanism such as depolymerization or treadmilling is required to sustain constriction by filament sliding. For filament bending, we find that a mechanism such as the presence of a rigid linker is required to constrain bending to within the division plane and maintain the distance observed in vivo between the filaments and the membrane. Of these two models, only the filament bending model is consistent with our lab’s recent observation of constriction associated with a single, short FtsZ filament.

IMPORTANCE FtsZ is thought to generate constrictive force to divide the cell, possibly via one of two predominant models in the field. In one, FtsZ filaments overlap to form complete rings which constrict as filaments slide past each other to maximize lateral contact. In the other, filaments exert force on the membrane by switching conformation from straight to bent. Here, we developed software, ZCONSTRICT, for three-dimensional (3D) simulations to test these two models. We find that a mechanism such as depolymerization or treadmilling are required to sustain constriction by filament sliding. For filament bending, we find that a mechanism that constrains bending to within the division plane is required to maintain the distance observed in vivo between the filaments and the membrane.

A stochastic model for dynamics of FtsZ filaments and the formation of Z -ring

Understanding the mechanisms responsible for the formation and growth of FtsZ polymers and their subsequent formation of the Z -ring is important for gaining insight into the cell division in prokaryotic cells. In this work, we present a minimal stochastic model that qualitatively reproduces in vitro observations of polymerization, formation of dynamic contractile ring that is stable for a long time and depolymerization shown by FtsZ polymer filaments. In this stochastic model, we explore different mechanisms for ring breaking and hydrolysis. In addition to hydrolysis, which is known to regulate the dynamics of other tubulin polymers like microtubules, we find that the presence of the ring allows for an additional mechanism for regulating the dynamics of FtsZ polymers. Ring breaking dynamics in the presence of hydrolysis naturally induce rescue and catastrophe events in this model irrespective of the mechanism of hydrolysis.

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.

Surface Orientation and Binding Strength Modulate Shape of FtsZ on Lipid Surfaces

We have used a simple model system to test the prediction that surface attachment strength of filaments presenting a torsion would affect their shape and properties. FtsZ from E. coli containing one cysteine in position 2 was covalently attached to a lipid bilayer containing maleimide lipids either in their head group (to simulate tight attachment) or at the end of a polyethylene glycol molecule attached to the head group (to simulate loose binding). We found that filaments tightly attached grew straight, growing from both ends, until they formed a two-dimensional lattice. Further monomer additions to their sides generated a dense layer of oriented filaments that fully covered the lipid membrane. After this point the surface became unstable and the bilayer detached from the surface. Filaments with a loose binding were initially curved and later evolved into straight thicker bundles that destabilized the membrane after reaching a certain surface density. Previously described theoretical models of FtsZ filament assembly on surfaces that include lateral interactions, spontaneous curvature, torsion, anchoring to the membrane, relative geometry of the surface and the filament ‘living-polymer’ condition in the presence of guanosine triphosphate (GTP) can offer some clues about the driving forces inducing these filament rearrangements.

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.

Microwave-radiation-induced molecular structural rearrangement of hen egg-white lysozyme

We have investigated the nonthermal effect of 10 GHz/22 dBm microwave radiation on hen egg-white lysozyme (HEWL) over different irradiation times, ranging from 2 min to 1 h. To ensure a control over the radiation parameters, a pair of microwave rectangular waveguides is used to irradiate the samples. Optical spectroscopic measurements, which include UV-visible absorption spectroscopy, Raman spectroscopy, and far UV CD spectroscopy, reveal the exposure of the buried tryptophan (Trp) residues of the native molecule between 15 and 30 min of radiation. The higher duration of the perturbation leads to a compact structure of the protein and Trp residues are buried again. Interestingly, we do not find any change in the secondary structure of the protein even for 1 h duration of radiation. The relaxation dynamics of the irradiated molecules also has been discussed. We have shown that the molecules relax to their native configuration in 7-8 h after the radiation field is turned off. The structural rearrangement over the above timescale has further been probed by a model calculation, based on a modified Langevin equation. Our coarse-grained simulation approach utilizes the mean of atomic positions and net atomic charge of each amino acid of native HEWL to mimic the initial conformation of the molecule. The modified positions of the residues are then calculated for the given force fields. The simulation results reveal the nonmonotonous change in overall size of the molecule, as observed experimentally. The radiation parameters used in our experiments are very similar to those of some of the electronic devices we often come across. Thus, we believe that the results of our studies on a simple protein structure may help us in understanding the effect of radiation on complex biological systems as well.

Short FtsZ filaments can drive asymmetric cell envelope constriction at the onset of bacterial cytokinesis

FtsZ, the bacterial homologue of eukaryotic tubulin, plays a central role in cell division in nearly all bacteria and many archaea. It forms filaments under the cytoplasmic membrane at the division site where, together with other proteins it recruits, it drives peptidoglycan synthesis and constricts the cell. Despite extensive study, the arrangement of FtsZ filaments and their role in division continue to be debated. Here, we apply electron cryotomography to image the native structure of intact dividing cells and show that constriction in a variety of Gram-negative bacterial cells, including Proteus mirabilis and Caulobacter crescentus, initiates asymmetrically, accompanied by asymmetric peptidoglycan incorporation and short FtsZ-like filament formation. These results show that a complete ring of FtsZ is not required for constriction and lead us to propose a model for FtsZ-driven division in which short dynamic FtsZ filaments can drive initial peptidoglycan synthesis and envelope constriction at the onset of cytokinesis, later increasing in length and number to encircle the division plane and complete constriction.

Reconstitution of Protein Dynamics Involved in Bacterial Cell Division

Even simple cells like bacteria have precisely regulated cellular anatomies, which allow them to grow, divide and to respond to internal or external cues with high fidelity. How spatial and temporal intracellular organization in prokaryotic cells is achieved and maintained on the basis of locally interacting proteins still remains largely a mystery. Bulk biochemical assays with purified components and in vivo experiments help us to approach key cellular processes from two opposite ends, in terms of minimal and maximal complexity. However, to understand how cellular phenomena emerge, that are more than the sum of their parts, we have to assemble cellular subsystems step by step from the bottom up. Here, we review recent in vitro reconstitution experiments with proteins of the bacterial cell division machinery and illustrate how they help to shed light on fundamental cellular mechanisms that constitute spatiotemporal order and regulate cell division.

FtsZ Constriction Force - Curved Protofilaments Bending Membranes

FtsZ assembles in vitro into protofilaments (pfs) that are one subunit thick and ~50 subunits long. In vivo these pfs assemble further into the Z ring, which, along with accessory division proteins, constricts to divide the cell. We have reconstituted Z rings in liposomes in vitro, using pure FtsZ that was modified with a membrane targeting sequence to directly bind the membrane. This FtsZ-mts assembled Z rings and constricted the liposomes without any accessory proteins. We proposed that the force for constriction was generated by a conformational change from straight to curved pfs. Evidence supporting this mechanism came from switching the membrane tether to the opposite side of the pf. These switched-tether pfs assembled "inside-out" Z rings, and squeezed the liposomes from the outside, as expected for the bending model. We propose three steps for the full process of cytokinesis: (a) pf bending generates a constriction force on the inner membrane, but the rigid peptidoglycan wall initially prevents any invagination; (b) downstream proteins associate to the Z ring and remodel the peptidoglycan, permitting it to follow the constricting FtsZ to a diameter of ~250 nm; the final steps of closure of the septum and membrane fusion are achieved by excess membrane synthesis and membrane fluctuations.

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.

Collective effects of torsion in FtsZ filaments

Recent evidence points to the presence of torsion in FtsZ bonds. In addition, experiments with FtsZ mutants on surfaces resulted in new aggregates that cannot be explained by older models for FtsZ dynamics. We use an interaction model for FtsZ derived from molecular dynamics simulations and expand a fine-grained lattice model used to describe FtsZ aggregates on a surface. This new model includes different anchoring angles for the monomers and allows bond twist, two ingredients that oppose each other resulting in a more dynamic and interesting system. We study the role and importance of these conflicting elements and how the aggregates are characterized by the different interaction parameters.

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.

Architecture of the ring formed by the tubulin homologue FtsZ in bacterial cell division

Membrane constriction is a prerequisite for cell division. The most common membrane constriction system in prokaryotes is based on the tubulin homologue FtsZ, whose filaments in E. coli are anchored to the membrane by FtsA and enable the formation of the Z-ring and divisome. The precise architecture of the FtsZ ring has remained enigmatic. In this study, we report three-dimensional arrangements of FtsZ and FtsA filaments in C. crescentus and E. coli cells and inside constricting liposomes by means of electron cryomicroscopy and cryotomography. In vivo and in vitro, the Z-ring is composed of a small, single-layered band of filaments parallel to the membrane, creating a continuous ring through lateral filament contacts. Visualisation of the in vitro reconstituted constrictions as well as a complete tracing of the helical paths of the filaments with a molecular model favour a mechanism of FtsZ-based membrane constriction that is likely to be accompanied by filament sliding.

DOI:http://dx.doi.org/10.7554/eLife.04601.001

Cell division is the process by which new cells are made. It is therefore vital for the growth and development, and the regeneration and repair of damaged tissues. When bacterial and animal cells divide, they must constrict their membrane inwards to split a single cell into two. In most bacteria, this constriction is guided by a ring-like structure that contains filaments of a protein called FtsZ. During cell division, this structure forms around the inside edge of the cell and when it contracts, it pulls the membrane inwards and causes the cell to constrict and eventually divide.

In recent years, this arrangement of FtsZ filaments has been intensively investigated, giving rise to various theories about how it is made and how it works: for example, some recent studies suggested that FtsZ does not form a continuous ring. Nevertheless, many details about the cell division process remain unknown.

Szwedziak, Wang et al. have now investigated this protein ring in two species of bacteria by turning to advanced forms of microscopy to closely observe its structure and how it works. This included mapping the ring in three dimensions. Contrary to earlier reports that the FtsZ ring is discontinuous, in both a bacterium called Caulobacter crescentus and another called Escherichia coli, the ring forms a continuous shape made up of overlapping filaments.

Szwedziak, Wang et al. then increased the levels of two of the ring's main components: the FtsZ protein that forms the filaments and a protein that anchors these filaments to the cell membrane. This caused the modified cells to constrict and divide at extra sites, which resulted in the formation of abnormally small cells. These findings suggest that these two ring components by themselves are able to generate both the structures and force required for cell constriction. This is supported by the fact that when they were introduced into artificial cell-like structures, these proteins spontaneously self-organised into rings and triggered constriction where they formed.

Szwedziak, Wang et al. propose that constriction only starts once the FtsZ protein forms a closed ring and that the ring's overlapping filaments slide along each other to further decrease its diameter and constrict the cell. The degree of filament overlap likely also increases with constriction, requiring filaments to be shortened to maintain sliding. This shortening, along with sliding, could provide a mechanism by which to drive the constriction process.

This work will be followed by even more detailed studies in order to understand the process of bacterial cell division at the atomic scale and how the cell's wall is reshaped during the process. In the long run, intricate knowledge of how a bacterial cell divides might enable the design of new classes of antibiotics targeting the molecular machinery involved.

DOI:http://dx.doi.org/10.7554/eLife.04601.002

Modeling the interplay between protein and lipid aggregation in supported membranes

We present a theoretical model that deals with the complex interplay between lipid segregation and the self-aggregation of lipid-attached proteins. The model, in contrast to previous ones that consider proteins only as passive elements affecting the lipid distribution, describes the system including three terms: the dynamic interactions between protein monomers, the interactions between lipid components, and a mixed term considering protein-lipid interactions. It is used to explain experimental results performed on a well-defined system in which a self-aggregating soluble bacterial cytoskeletal protein polymerizes on a lipid bilayer containing two lipid components. All the elements considered in a previously described protein model, including torsion of the monomers within the filament, are needed to account for the observed filament shapes. The model also points out that lipid segregation can affect the length and curvature of the filaments and that the dynamic behavior of the lipids and proteins can have different time scales, giving rise to memory effects. This simple model that considers a dynamic protein assembly on a fluid and active lipid surface can be easily extended to other biologically relevant situations in which the interplay between protein and lipid aggregation is needed to fully describe the system.

Divided we stand: splitting synthetic cells for their proliferation

With the recent dawn of synthetic biology, the old idea of man-made artificial life has gained renewed interest. In the context of a bottom-up approach, this entails the de novo construction of synthetic cells that can autonomously sustain themselves and proliferate. Reproduction of a synthetic cell involves the synthesis of its inner content, replication of its information module, and growth and division of its shell. Theoretical and experimental analysis of natural cells shows that, whereas the core synthesis machinery of the information module is highly conserved, a wide range of solutions have been realized in order to accomplish division. It is therefore to be expected that there are multiple ways to engineer division of synthetic cells. Here we survey the field and review potential routes that can be explored to accomplish the division of bottom-up designed synthetic cells. We cover a range of complexities from simple abiotic mechanisms involving splitting of lipid-membrane-encapsulated vesicles due to physical or chemical principles, to potential division mechanisms of synthetic cells that are based on prokaryotic division machineries.

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.

Methods for modeling cytoskeletal and DNA filaments

This review summarizes the models that researchers use to represent the conformations and dynamics of cytoskeletal and DNA filaments. It focuses on models that address individual filaments in continuous space. Conformation models include the freely jointed, Gaussian, angle-biased chain (ABC), and wormlike chain (WLC) models, of which the first three bend at discrete joints and the last bends continuously. Predictions from the WLC model generally agree well with experiment. Dynamics models include the Rouse, Zimm, stiff rod, dynamic WLC, and reptation models, of which the first four apply to isolated filaments and the last to entangled filaments. Experiments show that the dynamic WLC and reptation models are most accurate. They also show that biological filaments typically experience strong hydrodynamic coupling and/or constrained motion. Computer simulation methods that address filament dynamics typically compute filament segment velocities from local forces using the Langevin equation and then integrate these velocities with explicit or implicit methods; the former are more versatile and the latter are more efficient. Much remains to be discovered in biological filament modeling. In particular, filament dynamics in living cells are not well understood, and current computational methods are too slow and not sufficiently versatile. Although primarily a review, this paper also presents new statistical calculations for the ABC and WLC models. Additionally, it corrects several discrepancies in the literature about bending and torsional persistence length definitions, and their relations to flexural and torsional rigidities.

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.

The mechanics of FtsZ fibers

Inhibition of the Fts family of proteins causes the growth of long filamentous cells, indicating that they play some role in cell division. FtsZ polymerizes into protofilaments and assembles into the Z-ring at the future site of the septum of cell division. We analyze the rigidity of GTP-bound FtsZ protofilaments by using cryoelectron microscopy to sample their bending fluctuations. We find that the FtsZ-GTP filament rigidity is κ=4.7±1.0×10(-27) Nm(2), with a corresponding thermal persistence length of l(p)=1.15±0.25μm, much higher than previous estimates. In conjunction with other model studies, our new higher estimate for FtsZ rigidity suggests that contraction of the Z-ring may generate sufficient force to facilitate cell division. The good agreement between the measured mode amplitudes and that predicted by equipartition of energy supports our use of a simple mechanical model for FtsZ fibers. The study also provides evidence that the fibers have no intrinsic global or local curvatures, such as might be caused by partial hydrolysis of the GTP.

Targeting the assembly of bacterial cell division protein FtsZ with small molecules

FtsZ is the key protein of bacterial cell division and an emergent target for new antibiotics. It is a filament-forming GTPase and a structural homologue of eukaryotic tubulin. A number of FtsZ-interacting compounds have been reported, some of which have powerful antibacterial activity. Here we review recent advances and new approaches in modulating FtsZ assembly with small molecules. This includes analyzing their chemical features, binding sites, mechanisms of action, the methods employed, and computational insights, aimed at a better understanding of their molecular recognition by FtsZ and at rational antibiotic design.

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.

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.

FtsZ in bacterial cytokinesis: cytoskeleton and force generator all in one

FtsZ, a bacterial homolog of tubulin, is well established as forming the cytoskeletal framework for the cytokinetic ring. Recent work has shown that purified FtsZ, in the absence of any other division proteins, can assemble Z rings when incorporated inside tubular liposomes. Moreover, these artificial Z rings can generate a constriction force, demonstrating that FtsZ is its own force generator. Here we review light microscope observations of how Z rings assemble in bacteria. Assembly begins with long-pitch helices that condense into the Z ring. Once formed, the Z ring can transition to short-pitch helices that are suggestive of its structure. FtsZ assembles in vitro into short protofilaments that are ∼30 subunits long. We present models for how these protofilaments might be further assembled into the Z ring. We discuss recent experiments on assembly dynamics of FtsZ in vitro, with particular attention to how two regulatory proteins, SulA and MinC, inhibit assembly. Recent efforts to develop antibacterial drugs that target FtsZ are reviewed. Finally, we discuss evidence of how FtsZ generates a constriction force: by protofilament bending into a curved conformation.

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.

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.

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.

Curved FtsZ protofilaments generate bending forces on liposome membranes

We have created FtsZ-YFP-mts where an amphipathic helix on the C-terminus tethers FtsZ to the membrane. When incorporated inside multi-lamellar tubular liposomes, FtsZ-YFP-mts can assemble Z rings that generate a constriction force. When added to the outside of liposomes, FtsZ-YFP-mts bound and produced concave depressions, bending the membrane in the same direction as the Z ring inside liposomes. Prominent membrane tubules were then extruded at the intersections of concave depressions. We tested the effect of moving the membrane-targeting sequence (mts) from the C-terminus to the N-terminus, which is approximately 180 degrees from the C-terminal tether. When mts-FtsZ-YFP was applied to the outside of liposomes, it generated convex bulges, bending the membrane in the direction opposite to the concave depressions. We conclude that FtsZ protofilaments have a fixed direction of curvature, and the direction of membrane bending depends on which side of the bent protofilament the mts is attached to. This supports models in which the FtsZ constriction force is generated by protofilament bending.

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.

Structural and functional model for ionic (K(+)/Na(+)) and pH dependence of GTPase activity and polymerization of FtsZ, the prokaryotic ortholog of tubulin

Bacterial cell division occurs through the formation of a protein ring (division ring) at the site of division, with FtsZ being its main component in most bacteria. FtsZ is the prokaryotic ortholog of eukaryotic tubulin; it shares GTPase activity properties and the ability to polymerize in vitro. To study the mechanism of action of FtsZ, we used molecular dynamics simulations of the behavior of the FtsZ dimer in the presence of GTP-Mg(2+) and monovalent cations. The presence of a K(+) ion at the GTP binding site allows the positioning of one water molecule that interacts with catalytic residues Asp235 and Asp238, which are also involved in the coordination sphere of K(+). This arrangement might favor dimer stability and GTP hydrolysis. Contrary to this, Na(+) destabilizes the dimer and does not allow the positioning of the catalytic water molecule. Protonation of the GTP gamma-phosphate, simulating low pH, excludes both monovalent cations and the catalytic water molecule from the GTP binding site and stabilizes the dimer. These molecular dynamics predictions were contrasted experimentally by analyzing the GTPase and polymerization activities of purified Methanococcus jannaschii and Escherichia coli FtsZ proteins in vitro.

Force generation by a dynamic Z-ring in Escherichia coli cell division

FtsZ, a bacterial homologue of tubulin, plays a central role in bacterial cell division. It is the first of many proteins recruited to the division site to form the Z-ring, a dynamic structure that recycles on the time scale of seconds and is required for division to proceed. FtsZ has been recently shown to form rings inside tubular liposomes and to constrict the liposome membrane without the presence of other proteins, particularly molecular motors that appear to be absent from the bacterial proteome. Here, we propose a mathematical model for the dynamic turnover of the Z-ring and for its ability to generate a constriction force. Force generation is assumed to derive from GTP hydrolysis, which is known to induce curvature in FtsZ filaments. We find that this transition to a curved state is capable of generating a sufficient force to drive cell-wall invagination in vivo and can also explain the constriction seen in the in vitro liposome experiments. Our observations resolve the question of how FtsZ might accomplish cell division despite the highly dynamic nature of the Z-ring and the lack of molecular motors.

Origin of contractile force during cell division of bacteria

When a bacterium divides, its cell wall at the division site grows radially inward like the shutter of a camera and guillotines the cell into two halves. The wall is pulled upon from inside by a polymeric ring, which itself shrinks in radius. The ring is made of an intracellular protein FtsZ (filamenting temperature sensitive Z) and thus is called the Z ring. It is not understood how the Z ring generates the required contractile force. We propose a theoretical model and simulate it to show how the natural curvature of the FtsZ filaments and lateral attraction among them may facilitate force generation.

In vitro reconstitution of the initial stages of the bacterial cell division machinery

Fission of many prokaryotes as well as some eukaryotic organelles depends on the self-assembly of the FtsZ protein into a membrane-associated ring structure early in the division process. Different components of the machinery are then sequentially recruited. Although the assembly order has been established, the molecular interactions and the understanding of the force-generating mechanism of this dividing machinery have remained elusive. It is desirable to develop simple reconstituted systems that attempt to reproduce, at least partially, some of the stages of the process. High-resolution studies of Escherichia coli FtsZ filaments' structure and dynamics on mica have allowed the identification of relevant interactions between filaments that suggest a mechanism by which the polymers could generate force on the membrane. Reconstituting the membrane-anchoring protein ZipA on E. coli lipid membrane on surfaces is now providing information on how the membrane attachment regulates FtsZ polymer dynamics and indicates the important role played by the lipid composition of the membrane.

High fluidity and soft elasticity of the inner membrane of Escherichia coli revealed by the surface rheology of model Langmuir monolayers

We have studied the equilibrium and linear mechanical properties of model membranes of Escherichia coli built up as Langmuir monolayers of a native lipid extract using surface thermodynamics, fluorescence microscopy, and surface rheology measurements. The experimental study has been carried out at different temperatures across the physiological operative range 15-37 degrees C. Lipid phase coexistence has been revealed over a broad pressure range by fluorescence microscopy. The presence of ordered domains has been invoked to explain the emergence of shear elasticity accompanying the hydrostatic compression elasticity typical of fluid monolayers. The surface rheology measurements point out the soft character of E. coli membranes; i.e., upon deformation they react as a near-ideal compliant body with minimal energy dissipation, thus optimizing the effectiveness of external stresses in producing membrane deformations. These mechanical features appear to be independent of temperature, suggesting the existence of a passive thermoregulation mechanism.

FtsZ bacterial cytoskeletal polymers on curved surfaces: the importance of lateral interactions

A recent theoretical article provided a mechanical explanation for the formation of cytoskeletal rings and helices in bacteria assuming 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 (Andrews, S., and A. P. Arkin. 2007. Biophys. J. 93:1872-1884). Due to the lack of experimental data regarding the bending rigidity and preferential bond angles of bacterial polymers, the authors explored their model over wide ranges of preferred curvature values. In this letter, we present the shape diagram of the FtsZ bacterial polymer on a curved surface but now including recent experimental data on the in vitro formed FtsZ polymers. The lateral interactions between filaments observed experimentally change qualitatively the shape diagram and indicate that the formation of rings over spirals is more energetically favored than estimated in the above-mentioned article.