Kinetic modeling of the assembly, dynamic steady state, and contraction of the FtsZ ring in prokaryotic cytokinesis

Dynamics of interdomain rotation facilitates FtsZ filament assembly

FtsZ, the tubulin homolog essential for bacterial cell division, assembles as the Z-ring at the division site, and directs peptidoglycan synthesis by treadmilling. It is unclear how FtsZ achieves kinetic polarity that drives treadmilling. To obtain insights into fundamental features of FtsZ assembly dynamics independent of peptidoglycan synthesis, we carried out structural and biochemical characterization of FtsZ from the cell wall-less bacteria, Spiroplasma melliferum (SmFtsZ). Interestingly the structures of SmFtsZ, bound to GDP and GMPPNP respectively, were captured as domain swapped dimers. SmFtsZ was found to be a slower GTPase with a higher critical concentration (CC) compared to Escherichia coli FtsZ (EcFtsZ). In FtsZs, a conformational switch from R-state (close) to T-state (open) favors polymerization. We identified that Phe224, located at the interdomain cleft of SmFtsZ, is crucial for R- to T-state transition. SmFtsZF224M exhibited higher GTPase activity and lower CC, whereas the corresponding EcFtsZM225F resulted in cell division defects in E. coli. Our results demonstrate that relative rotation of the domains is a rate-limiting step of polymerization. Our structural analysis suggests that the rotation is plausibly triggered upon addition of a GTP-bound monomer to the filament through interaction of the preformed N-terminal domain (NTD). Hence, addition of monomers to the NTD-exposed end of filament is slower in comparison to the C-terminal domain (CTD) end, thus explaining kinetic polarity. In summary, the study highlights the importance of interdomain interactions and conformational changes in regulating FtsZ assembly dynamics.

Data integration strategies for whole-cell modeling

Data makes the world go round-and high quality data is a prerequisite for precise models, especially for whole-cell models (WCM). Data for WCM must be reusable, contain information about the exact experimental background, and should-in its entirety-cover all relevant processes in the cell. Here, we review basic requirements to data for WCM and strategies how to combine them. As a species-specific resource, we introduce the Yeast Cell Model Data Base (YCMDB) to illustrate requirements and solutions. We discuss recent standards for data as well as for computational models including the modeling process as data to be reported. We outline strategies for constructions of WCM despite their inherent complexity.

Recent progress of bacterial FtsZ inhibitors with a focus on peptides

In recent years, the rise of antibiotic resistance has become a primary health problem. With the emergence of bacterial resistance, the need to explore and develop novel antibacterial drugs has become increasingly urgent. Filamentous temperature-sensitive mutant Z (FtsZ), a crucial cell division protein of bacteria, has become a vital antibacterial target. FtsZ is a filamentous GTPase; it is highly conserved in bacteria and shares less than 20% sequence identity with the eukaryotic cytoskeleton protein tubulin, indicating that FtsZ-targeting antibacterial agents may have a low cytotoxicity toward eukaryotes. FtsZ can form a dynamic Z-ring in the center of the cell resulting in cell division. Furthermore, disturbance in the assembly of FtsZ may affect cellular dynamics and bacterial cell survival, making it a fascinating target for drug development. This review focuses on the recent discovery of FtsZ inhibitors, including peptides, natural products, and other synthetic small molecules, as well as their mechanism of action, which could facilitate the discovery of novel FtsZ-targeting clinical drugs in the future.

Towards Design of Self-Organizing Biomimetic Systems

The ability of designing biosynthetic systems with well-defined functional biomodules from scratch is an ambitious and revolutionary goal to deliver innovative, engineered solutions to future challenges in biotechnology and process systems engineering. In this work, several key challenges including modularization, functional biomodule identification, and assembly are discussed. In addition, an in silico protocell modeling approach is presented as a foundation for a computational model-based toolkit for rational analysis and modular design of biomimetic systems.

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.

Quantification of Predictive Uncertainty in Models of FtsZ ring assembly in Escherichia coli

Quantitative predictions of FtsZ protein polymerization are essential for understanding the self-regulating mechanisms in biochemical systems. Due to structural complexity and parametric uncertainty, existing kinetic models remain incomplete and their predictions error-prone. To address such challenges, we perform probabilistic uncertainty quantification and global sensitivity analysis of the concentrations of various protein species predicted with a recent FtsZ protein polymerization model. Our results yield a ranked list of modeling shortcomings that can be improved in order to develop more accurate predictions and more realistic representations of key mechanisms of such biochemical systems and their response to changes in internal or external conditions. Our conclusions and improvement recommendations can be extended to other kinetics models.

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.

Efficient models of polymerization applied to FtsZ ring assembly in Escherichia coli

High protein concentrations complicate modeling of polymer assembly kinetics by introducing structural complexity and a large variety of protein forms. We present a modeling approach that achieves orders of magnitude speed-up by replacing distributions of lengths and widths with their average counterparts and by introducing a hierarchical classification of species and reactions into sets. We have used this model to study FtsZ ring assembly in Escherichia coli The model's prediction of key features of the ring formation, such as time to reach the steady state, total concentration of FtsZ species in the ring, total concentration of monomers, and average dimensions of filaments and bundles, are all in agreement with the experimentally observed values. Besides validating our model against the in vivo observations, this study fills some knowledge gaps by proposing a specific structure of the ring, describing the influence of the total concentration in short and long kinetics processes, determining some characteristic mechanisms in polymer assembly regulation, and providing insights about the role of ZapA proteins, critical components for both positioning and stability of the ring.

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.

Efficient Multiscale Models of Polymer Assembly

Protein polymerization and bundling play a central role in cell physiology. Predictive modeling of these processes remains an open challenge, especially when the proteins involved become large and their concentrations high. We present an effective kinetics model of filament formation, bundling, and depolymerization after GTP hydrolysis, which involves a relatively small number of species and reactions, and remains robust over a wide range of concentrations and timescales. We apply this general model to study assembly of FtsZ protein, a basic element in the division process of prokaryotic cells such as Escherichia coli, Bacillus subtilis, or Caulobacter crescentus. This analysis demonstrates that our model outperforms its counterparts in terms of both accuracy and computational efficiency. Because our model comprises only 17 ordinary differential equations, its computational cost is orders-of-magnitude smaller than the current alternatives consisting of up to 1000 ordinary differential equations. It also provides, to our knowledge, a new insight into the characteristics and functioning of FtsZ proteins at high concentrations. The simplicity and versatility of our model render it a powerful computational tool, which can be used either as a standalone descriptor of other biopolymers' assembly or as a component in more complete kinetic models.

GTPase activity-coupled treadmilling of the bacterial tubulin FtsZ organizes septal cell wall synthesis

The bacterial tubulin FtsZ is the central component of the cell division machinery, coordinating an ensemble of proteins involved in septal cell wall synthesis to ensure successful constriction. How cells achieve this coordination is unknown. We found that in Escherichia coli cells, FtsZ exhibits dynamic treadmilling predominantly determined by its guanosine triphosphatase activity. The treadmilling dynamics direct the processive movement of the septal cell wall synthesis machinery but do not limit the rate of septal synthesis. In FtsZ mutants with severely reduced treadmilling, the spatial distribution of septal synthesis and the molecular composition and ultrastructure of the septal cell wall were substantially altered. Thus, FtsZ treadmilling provides a mechanism for achieving uniform septal cell wall synthesis to enable correct polar morphology.

WhmD promotes the assembly of Mycobacterium smegmatis FtsZ: A possible role of WhmD in bacterial cell division

WhmD is considered to have a role in the septation and division of Mycobacterium smegmatis cells. Since FtsZ is the central protein of the septum, we determined the effect of WhmD on the assembly of Mycobacterium smegmatis FtsZ (MsFtsZ) in vitro. WhmD increased both the rate and extent of the assembly of MsFtsZ in vitro. WhmD also increased the amount of polymerized MsFtsZ as evident from a sedimentation assay. Further, the assembly promoting activity of WhmD occurred in the presence of GTP. MsFtsZ polymerized to form thin filaments in the absence of WhmD while MsFtsZ formed thick filaments in the presence of WhmD suggesting that WhmD enhanced the bundling of MsFtsZ filaments. Interestingly, WhmD neither suppressed the dilution-induced disassembly of FtsZ filaments nor significantly altered the GTPase activity of FtsZ. Using size exclusion chromatography, circular dichroism and fluorescence spectroscopy, WhmD was found to bind to MsFtsZ in vitro. The results showed that WhmD can promote the assembly of FtsZ and indicated that WhmD may play a role in the division of M. smegmatis cells by assisting the polymerization of FtsZ.

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.

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.

Biological Insights from a Simulation Model of the Critical FtsZ Accumulation Required for Prokaryotic Cell Division

A simulation model of prokaryotic Z-ring assembly, based on the observed behavior of FtsZ in vitro as well as on in vivo parameters, is used to integrate critical processes in cell division. According to the model, the cell's ability to divide depends on a "contraction parameter" (χ) that links the force of contraction to the dynamics of FtsZ. This parameter accurately predicts the outcome of division. Evaluating the GTP binding strength, the FtsZ polymerization rate, and the intrinsic GTP hydrolysis/dissociation activity, we find that inhibition of GTP-FtsZ binding is an inefficient antibacterial target. Furthermore, simulations indicate that the temperature sensitivity of the ftsZ84 mutation arises from the conversion of FtsZ to a dual-specificity NTPase. Finally, the sensitivity to temperature of the rate of ATP hydrolysis, over the critical temperature range, leads us to conclude that the ftsZ84 mutation affects the turnover rate of the Z-ring much less strongly than previously reported.

FtsZ filament capping by MciZ, a developmental regulator of bacterial division

Cytoskeletal structures are dynamically remodeled with the aid of regulatory proteins. FtsZ (filamentation temperature-sensitive Z) is the bacterial homolog of tubulin that polymerizes into rings localized to cell-division sites, and the constriction of these rings drives cytokinesis. Here we investigate the mechanism by which the Bacillus subtilis cell-division inhibitor, MciZ (mother cell inhibitor of FtsZ), blocks assembly of FtsZ. The X-ray crystal structure reveals that MciZ binds to the C-terminal polymerization interface of FtsZ, the equivalent of the minus end of tubulin. Using in vivo and in vitro assays and microscopy, we show that MciZ, at substoichiometric levels to FtsZ, causes shortening of protofilaments and blocks the assembly of higher-order FtsZ structures. The findings demonstrate an unanticipated capping-based regulatory mechanism for FtsZ.

Bacterial cell division: experimental and theoretical approaches to the divisome

Cell division is a key event in the bacterial life cycle. It involves constriction at the midcell, so that one cell can give rise to two daughter cells. This constriction is mediated by a ring composed offibrous multimers of the protein FtsZ. However a host of additional factors is involved in the formation and dynamics of this "Z-ring" and this complicated apparatus is collectively known as the "divisome". We review the literature, with an emphasis on mathematical modelling, and show how such theoretical efforts have helped experimentalists to make sense of the at times bewildering data, and plan further experiments.

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.

Probing the conformational flexibility of monomeric FtsZ in GTP-bound, GDP-bound, and nucleotide-free states

The mechanism of nucleotide-regulated assembly and disassembly of the prokaryotic cell division protein FtsZ is not yet clearly understood. In this work, we attempt to characterize the functional motions in monomeric FtsZ through molecular dynamics simulations and essential dynamics (ED) analyses and correlate those motions to FtsZ assembly and disassembly. Results suggest that the nucleotide binding subdomain of FtsZ can switch between multitudes of curved conformations in all nucleotide states, but it prefers to be in an assembly competent less curved conformation in the GTP-bound state. Further, the GDP to GTP exchange invokes a subtle conformational change in the nucleotide binding pocket that tends to align the top portion of core helix H7 along the longitudinal axis of the protein. ED analyses suggest that the longitudinal movements of H7 and the adjacent H6-H7 region modulate the motions of C-domain elements coherently. These longitudinal movements of functionally relevant H7, H6-H7, T3, T7, and H10 regions are likely to facilitate the assembly of GTP-FtsZ into straight filament. On the other hand, the observed radial or random movements of FtsZ residues in the GDP state might not allow the monomers to assemble as efficiently as GTP-bound monomers and could produce curved filaments. Our results correlate very well with recent mutagenesis data that inferred FtsZ conformational flexibility and the involvement of the H6-H7 region in assembly.

An equilibrium model for the Mg(2+)-linked self-assembly of FtsZ in the presence of GTP or a GTP analogue

The concerted formation of a narrow distribution of oligomeric FtsZ species in the presence of GTP or a GTP analogue under close to physiological conditions (neutral pH and 0.5 M K(+)) has been characterized recently by various biophysical methods [Monterroso, B., et al. (2012) Biochemistry 51, 4541-4550]. An equilibrium model may semiquantitatively account for the results of this study; in the model, FtsZ self-associates in a noncooperative fashion to form linear fibrils, that upon increasing to a certain size exhibit an increasing tendency to form closed cyclic fibrils, as previously suggested [González, J. M., et al. (2005) Proc. Natl. Acad. Sci. U.S.A. 102, 1895-1900]. The closed cyclic fibrils are formed when the natural curvature and flexibility of a linear oligomer bring the ends of a linear fiber sufficiently close to overcome the entropic barrier to loop closure. The size distribution of cyclic oligomers is thus a reflection of the tendency toward curvature of linear fibrils of FtsZ under the conditions used in these experiments.

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.

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.

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.

Inside-out Z rings--constriction with and without GTP hydrolysis

The bacterial tubulin homologue FtsZ forms a ring-like structure called the Z ring that drives cytokinesis. We showed previously that FtsZ-YFP-mts, which has a short amphipathic helix (mts) on its C terminus that inserts into the membrane, can assemble contractile Z rings in tubular liposomes without any other protein. Here we study mts-FtsZ-YFP, where the membrane tether is switched to the opposite side of the protofilament. This assembled 'inside-out' Z rings that wrapped around the outside surface of tubular liposomes. The inside-out Z rings were highly dynamic, and generated a constriction force that squeezed the tubular liposomes from outside. This is consistent with models where the constriction force is generated by curved protofilaments bending the membrane. We used this system to test how GTP hydrolysis by FtsZ is involved in Z-ring constriction. Without GTP hydrolysis, Z rings could still assemble and generate an initial constriction. However, the constriction quickly stopped, suggesting that Z rings became rigidly stabilized in the absence of GTP hydrolysis. We propose that remodelling of the Z ring, mediated by GTP hydrolysis and exchange of subunits, is necessary for the continuous constriction.

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.

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.

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.

FtsZ filament dynamics at steady state: subunit exchange with and without nucleotide hydrolysis

We have measured three aspects of FtsZ filament dynamics at steady state: rates of GTP hydrolysis, subunit exchange between protofilaments, and disassembly induced by dilution or excess GDP. All three reactions were slowed with an increase in the potassium concentration from 100 to 500 mM, via replacement of potassium with rubidium, or with an increase in the magnesium concentration from 5 to 20 mM. Electron microscopy showed that the polymers assembled under the conditions of fastest assembly were predominantly short, one-stranded protofilaments, whereas under conditions of slower dynamics, the protofilaments tended to associate into long, thin bundles. We suggest that exchange of subunits between protofilaments at steady state involves two separate mechanisms: (1) fragmentation or dissociation of subunits from protofilament ends following GTP hydrolysis and (2) reversible association and dissociation of subunits from protofilament ends independent of hydrolysis. Exchange of nucleotides on these recycling subunits could give the appearance of exchange directly into the polymer. Several of our observations suggest that exchange of nucleotide can take place on these recycling subunits, but not directly into the FtsZ polymer. Annealing of protofilaments was demonstrated for the L68W mutant in EDTA buffer but not in Mg buffer, where rapid cycling of subunits may obscure the effect of annealing. We also reinvestigated the nucleotide composition of FtsZ polymers at steady state. We found that the GDP:GTP ratio was 50:50 for concentrations of GTP >100 microM, significantly higher than the 20:80 ratio previously reported at 20 microM GTP.

Mathematical modeling of a minimal protocell with coordinated growth and division

Self-replication is an essential attribute of life but the molecular-level mechanisms involved are not well understood. Cellular self-replication requires not only duplicating all cellular components and doubling volume and membrane area, but also replicating cellular geometry. A whole-cell modeling framework is presented in which an assumed reaction network determines both concentration changes of cellular components and cell geometry. Cell shape is calculated by minimizing membrane-bending energy. Using this framework, simultaneous doubling of volume, surface area, and all components was found to be insufficient to provide mid-cell "pinching" of the parental cell to form two daughter cells. This prompted the design of a minimal protocell that includes a growing shell, a cell-cycle engine, and a contractile ring to enforce cytokinesis. Kinetic parameters were found such that the system exhibited periodic behavior with fundamental aspects of self-replication. This involved simultaneous doubling of all cellular components during a cell cycle, doubling cell volume and membrane area, achieving periodic changes in surface/volume ratio, and forming daughter cells that were geometrically equivalent to each other and to the "newborn" parental cell. The results presented here impact the design of laboratory protocells and the development of a modular strategy for constructing a comprehensive in silico whole-cell model.

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.

Mica surface promotes the assembly of cytoskeletal proteins

We report the surface-mediated polymerization of FtsZ protein, the prokaryote homologue of tubulin, by AFM. FtsZ protein can form filaments on mica whereas the bulk FtsZ concentration is orders of magnitude lower than the critical concentration. Surface polymerization is favored by a local increase in protein concentration and requires a high mobility of proteins on the surface. To generalize to other cytoskeleton protein, we also show that mica can initiate the formation of tubulin protofilaments. This study is of particular interest for studying cytoskeletal protein dynamics by AFM but also for the surface autoassembly of nanostructures.

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.