Cooperative behavior of Escherichia coli cell-division protein FtsZ assembly involves the preferential cyclization of long single-stranded fibrils

Abstract

A mechanism of noncooperative (isodesmic) assembly coupled with preferential cyclization of long polymers is proposed to explain the previously posed question of how a single-stranded filament of the bacterial cell-division protein FtsZ can assemble in an apparently cooperative manner. This proposal is based on results of GTP-mediated assembly of FtsZ from Escherichia coli that was studied under physiologically relevant steady-state solution conditions by a combination of methods including measurement of sedimentation velocity, atomic force and electron microscopy, and precipitation assays. Sedimentation-velocity experiments carried out at multiple protein concentrations reveal an essentially bimodal distribution of slowly sedimenting species and a relatively narrow distribution of rapidly sedimenting species that appears only above an apparent “critical concentration” of protein. In a precipitation assay, the amount of protein that pellets, which correlates with the fraction of rapidly sedimenting species observed in sedimentation-velocity experiments, increases linearly with the total concentration of protein in excess of the critical concentration. Sedimentation coefficients of the rapidly sedimenting fraction are qualitatively consistent with the presence of single-stranded cyclic oligomers with a size range of ≈50–150 protomers, similar to polymeric single-stranded rings observed in atomic force and electron micrographs. The proposed model is in accord with the results obtained from our experimental observations.

The GTP-mediated assembly and disassembly of FtsZ, a bacterial homolog of tubulin, are thought to be essential for the formation of the dynamic septal ring during cell division (reviewed in refs. 1–3). However, the detailed structure of the septal ring and mechanism of ring assembly in vivo is presently not known, and most of the information on FtsZ polymerization has been obtained from in vitro studies. In the presence of GDP, FtsZ oligomerizes after a Mg²⁺-linked noncooperative, nearly isodesmic process (4), whereas in the presence of physiologically relevant concentrations of GTP, FtsZ forms a variety of polymers [thin filaments, bundles, ribbons, and rings (5–9)] depending on solution conditions. The multiplicity of possible oligomeric motifs, together with the relatively high intrinsic GTPase activity of FtsZ, which is linked to polymer disassembly (10), has complicated efforts to elucidate the structure and assembly of biologically relevant FtsZ complexes.

The simplest known aggregates of Escherichia coli FtsZ, identified by means of negative-staining EM and quantitative mass measurement by scanning transmission microscopy, are single-stranded filaments (9, 11). Observations of thin FtsZ fibrils compatible with either a single- or double-stranded structure have been reported (4, 6). Thicker multistranded filaments were observed more frequently after increasing protein concentration or lowering the pH (8, 12–14), suggesting that these conditions favor lateral contacts between FtsZ filaments that are important for assembly. Formation of larger FtsZ polymers (i.e., bundles, ribbons) in vitro is promoted by the polycation DEAE-dextran or cationic phospholipids (5), high concentrations of calcium (7), glutamate (15), or ruthenium red (16), the presence of either of two proteins that stabilize the septal ring, ZipA (17) and ZapA (18), and high concentrations of inert polymers, mimicking the crowded bacterial cytoplasm (6). The strong tendency of FtsZ to form these multistranded polymers, together with the fact that at least some of these promoting agents are likely to be present in vivo, has led to the suggestion that the dynamic filament bundles or ribbons observed in vitro represent the basic structure that FtsZ adopts within the septal ring (6, 19, 20).

Centrifugation and light-scattering assays carried out by using FtsZ from different organisms indicate that FtsZ assembly proceeds as a highly cooperative process analogous to a first-order transition or condensation (6, 8, 10, 21, 22). According to these assays, there exists a critical protein concentration below which all of the protein is soluble; protein present in excess of this critical concentration is present in a distinct fraction that scatters light more intensely and is substantially more sedimentable than the soluble fraction. These observations suggest that the basic FtsZ polymer structure must be a multistranded filament, because cooperative assembly of linear polymers requires that two or more strands interact both laterally and longitudinally to form a helical or a two-dimensional/three-dimensional array (23–25), as in the case of F-actin and microtubules (26). However, EM and scanning transmission microscopy images of the FtsZ preparations under the same solution conditions indicate that the protein is present partially or predominantly as single-stranded filaments (6, 9, 11). These observations leave open the question on how a single-stranded filament can assemble in a cooperative manner (2, 9, 11). The present study was undertaken to explore further the mechanism of FtsZ assembly in solution and resolve the apparent contradiction between the observations noted above.

In this work we characterized the GTP-mediated FtsZ assembly in solution by means of sedimentation velocity combined with other structural [EM and atomic force microscopy (AFM)] and biochemical polymerization assays. Sedimentation velocity is a powerful tool for the quantitative characterization of the degree of homogeneity and distribution of macromolecular species in reversible associating systems (27) that has been used previously to study FtsZ oligomer formation in the presence of GDP (4, 6, 28) but not to follow FtsZ polymerization in the presence of physiological millimolar concentrations of GTP. The use of a GTP-regenerating system to maintain constant the GTP pool and the stability of the polymers (6) throughout the duration of sedimentation experiments allows us to study the GTP-mediated FtsZ assembly under steady state as well as physiologically relevant (neutral pH and relatively high ionic strength) solution conditions. In Materials and Experimental Methods these experimental approaches are described briefly, and in Experimental Results we summarize the results obtained by using each of these methods. Next, a model of noncooperative (isodesmic) assembly of single-stranded filaments in combination with preferential cyclization of long polymers is then proposed. The validity of this mechanism for the assembly of FtsZ is supported by results of quantitative simulations based on a simplified version of the model that exhibits the basic features of the data reported here. These results suggest that the proposed mechanism resolves the apparent contradiction between observations of single-strandedness on the one hand and the existence of a critical concentration for higher-order assembly on the other.

Materials and Experimental Methods

Materials. E. coli FtsZ was purified as described (4). All the experiments described in this work were carried out at 25°C in 50 mM Tris·HCl/500 mM KCl/5 mM MgCl₂, pH 7.5 (Tris-500KCl-Mg buffer) with either 1 mM GDP or GTP. The GTP was regenerated by using a GTP-regenerating system (1 unit/ml acetate kinase and 15 mM acetyl phosphate) as described (6) to maintain FtsZ in its polymeric state for at least 1 h (6).

Sedimentation Velocity. The experiments were conducted in a Beckman Optima XL-I ultracentrifuge (Beckman Coulter) equipped with an interference optical detection system that allowed us to monitor the sedimentation of FtsZ at physiologically high (millimolar) concentrations of nucleotide. Samples were studied at different speeds (ranging from 10,000 to 50,000 rpm) by using an An50Ti eight-hole rotor and double-sector Epon-charcoal centerpieces. After dialysis of the protein against Tris-500KCl-Mg buffer, samples and the corresponding reference buffers were supplemented with 1 mM nucleotide and, in the case of GTP, with the GTP-regenerating system. Differential sedimentation-coefficient distributions, c(s), were calculated by least-squares boundary modeling of sedimentation-velocity data by using the program sedfit (29). The time intervals between successive scans shown in Fig. 1 A and B were 5 and 1 min, respectively.

Fig. 1.

FtsZ sedimentation velocity data and analysis. Summary of sedimentation velocity data and derived distributions of sedimentation coefficient obtained from experiments conducted in GDP (A) and GTP (B). (C) The dependence of the derived distribution of sedimentation coefficients upon total concentration in the presence of GTP is shown.

Other FtsZ Assembly Assays. Pelleting assays, 90° light scattering, EM, and AFM analysis were done essentially as described (6). AFM images were obtained by using a Nanotec microscope (Nanotec Electrónica, Madrid) operated in the jump mode with the sample maintained under solution while imaging. A few microliters of a solution containing FtsZ polymers, formed in the same conditions as the ones used for the sedimentation-velocity studies, were incubated on top of a piece of freshly cleaved mica for a few minutes. The surface then was washed to remove the excess of protein and the mica surface image under the buffer solution.

Experimental Results

Preliminary Characterization of FtsZ Fibers. Before sedimentation-velocity analysis of GTP-mediated FtsZ assembly, a series of experiments were performed to confirm the behavior of FtsZ, previously reported by our group, under very similar assembly promoting solutions, i.e., neutral pH, high ionic strength, and millimolar concentrations of GTP in the presence of an enzymatic GTP-regenerating system (6). Assays of concentration-dependent precipitation of FtsZ confirmed the first-order transition behavior typical of a cooperative assembly: no FtsZ was found in the precipitate up to a critical concentration (≈0.06 g/liter), and all of the protein added in excess of this concentration appears in the precipitate fraction. Microscopic analysis (EM and AFM) confirmed the nature of the polymers as thin filaments (see below). Finally, the stability of the polymer species during the time scale required in sedimentation-velocity experiments (60–90 min) was checked by 90° light scattering, confirming previous results (6).

Sedimentation-Velocity Analysis. Fig. 1A shows the sedimentation-velocity profiles of E. coli FtsZ (1.5 g/liter) in Tris-500K-Mg buffer with 1 mM GDP. The corresponding sedimentation-coefficient distribution revealed that GDP-FtsZ sediments primarily as two species with apparent sedimentation coefficients of ≈2.5 and 3.5 S. We identify these two peaks as monomeric and dimeric FtsZ, respectively, although the maxima in the sedimentation-coefficient distribution do not necessarily correspond to the precise values of the actual sedimentation coefficients of each species, because the positions of these maxima are sensitive to the rate of monomer–dimer association/dissociation (J. Dam, C. A. Velikovsky, R. A. Mariuzza, C. Urbanke, and P.S., unpublished data). The absence of larger sedimenting species is in agreement with previous work under comparable conditions (but at lower nucleotide concentration, 0.05 mM), which demonstrated that FtsZ in its GDP-bound state has a weak tendency to oligomerize in solution and no polymers were found (6).

In the presence of GTP the sedimentation-velocity behavior of FtsZ (1.5 g/liter) changed dramatically (Fig. 1B). Unexpectedly, almost all of the FtsZ appears in a sharp, rapidly sedimenting peak with an apparent sedimentation coefficient of ≈12 S. To correct for nonideal effects, results obtained at the three highest protein concentrations were extrapolated to zero concentration to obtain a limiting estimate of 13.5 S (30). This result was independent of rotor speed (between 10,000 and 40,000 rpm), ruling out an effect of pressure on the protein behavior (31). Concentration-dependent experiments (Fig. 1C) indicated that FtsZ exists primarily, although not exclusively, in one of two states of sedimentation: a slowly sedimenting fraction (2.5 S) that is predominant at low protein concentration (0.05 g/liter, in agreement with the apparent critical concentration determined in the pelleting assays; see above and ref. 6) and the rapidly sedimenting fraction previously described that appears at higher concentrations. Although significant amounts of intermediates were visible over a narrow range of protein concentration (≈0.1 g/liter), at concentrations of 0.05 and >0.2 g/liter virtually all the material is in the monomer and the fast-sedimenting peak, respectively. In the limit of high concentration (1.5 g/liter) all protein appears in the rapidly sedimenting fraction (see Fig. 1A), which has a sedimentation coefficient of somewhere between five and six times that of the slowly sedimenting fraction.‡‡

EM and AFM Analysis. Parallel samples to those used in the sedimentation-velocity experiments, after negative staining, were visualized at the electron microscope. The morphology of the FtsZ fibers confirmed that the main species found were filaments of variable length and curvature, 5–6 nm wide (6), compatible with single-stranded FtsZ filaments. At high fractional surface occupancy, the filaments tend to be linear and wider filaments are often observed (data not shown), as reported previously (8, 12). However, when images were taken at very low fractional surface occupancy (<0.1), single-stranded closed rings were clearly visible (Fig. 2 A and B). The contour length of these rings is variable, ranging from 500 to 800 nm. Assuming that the diameter of a single molecule of FtsZ is ≈4 nm, these rings contain 125–200 protomers. These rings are comparable to those reported recently by Erickson and co-workers using a tryptophan mutant of E. coli FtsZ (11).

Fig. 2.

Morphology of the FtsZ fibers, obtained at low fractional surface occupancy, using either EM (A and B) or AFM (C). (Bars, 100 nm.)

Similar structures were observed in atomic force micrographs of protein adsorbed on a mica surface in contact with the parent solution. Clear images are obtained of FtsZ filaments that appear to be only one protein molecule wide, i.e., they are not multi-stranded (M. Vélez, J.M.G., and G.R., unpublished data). At high fractional surface occupancy of filaments, the extent of their curvature is limited by lateral interactions with neighboring filaments, and most of them are roughly linear. As the fractional surface occupancy decreases, highly curved filaments were readily observed (Fig. 2C). The smallest rings observed have a contour length between 290 and 360 nm, compatible with rings containing between 73 and 90 FtsZ protomers. Because the distribution of rings is heterogeneous, structures with sizes comparable to those seen in the electron micrographs are also often found.

Model for Steady-State Assembly of FtsZ in GTP-Containing Solution

The model presented here, and expressed quantitatively in Appendix 1, is based on the following assumptions§§:

1. Under conditions such that the concentration of free GTP is independent of time, the rates of GTP binding, hydrolysis, GDP dissociation, and any protein–protein association and dissociation constants that are linked to these processes are likewise independent of time. Thus, we treat the steady-state system as if it were at equilibrium, with apparent equilibrium constants that depend on the steady-state concentration of free GTP. Similar assumptions have been applied in the analysis of other protein-assembly systems that are modulated by nucleotide hydrolysis (23, 26).

2. It is assumed that at low protein concentration, fibrils assemble as linear oligomers and that the apparent equilibrium constant for addition of individual monomers to a growing oligomer is insensitive to the size of the oligomer. For the purpose of a simple qualitative demonstration of the behavior of the model (as opposed to an attempt to quantitatively fit actual data), we shall additionally assume that all stepwise equilibrium constants are equal and that the equilibrium distribution of linear oligomers may be described by an isodesmic scheme (4, 9), although in the most general case, assembly need not be strictly isodesmic (32).

3. Although the fibrils are assumed to be linear in the sense of being single-stranded, they are composed of individual protein molecules that lack a symmetry axis. Thus, the fibrils formed are likely to have an intrinsic curvature that would ultimately lead to a helical fiber (Fig. 3). Although a favored geometry corresponding to a potential energy minimum of a particular i-mer exists, the fibers are assumed to be flexible and that the distance between the two ends of an i-mer may be described by a distribution about the most probable end-to-end distance. When the degree of polymerization of the fibril reaches a certain size, the natural curvature brings the ends of the fiber into close juxtaposition. At this point the entropy loss associated with the formation of a closed ring reaches a minimum, and it is suggested that this minimum entropy loss is far smaller than that associated with binding of an additional monomer from the bulk solution (Fig. 3). Thus, it is proposed that over a certain range of fibril length, the equilibrium probability of forming a closed ring is much greater than the probability of further linear extension of the fibril by either addition of monomer or end-to-end association of existing fibrils. Although polymer elongation can be studied as a kinetic process, the experiments in the present study reflect a steady-state distribution of populations, including those resulting from bond forming and chain breaking, and are analyzed in the context of an equilibrium model that makes allowance for linear oligomers of indefinite length.

Fig. 3.

Scheme to summarize the model of noncooperative (isodesmic) assembly coupled to preferential cyclization of long polymers (see Model for Steady-State Assembly of FtsZ in GTP-containing Solution and Appendix 1).

The assumptions described above are expressed quantitatively in Appendix 1, and the resulting relations permit calculation of the equilibrium distribution of both linear and cyclic polymers as a function of total protein concentration, the equilibrium association constant for stepwise addition of monomer, and the equilibrium constants for cyclization of various linear i-mers.

Comparison of Experimental Data and Model Simulations

The simple observation that the fast-sedimenting fraction observed in this study has a certain range of s values would not enable one to distinguish linear from cyclic polymers. Our proposal that the fast-sedimenting fraction corresponds to a population of cyclic polymers is based on the observation that as total protein concentration increases, the fast-sedimenting fraction becomes progressively populated at the expense of smaller species but does not significantly increase in size. The formation of linear polymers in the absence of a cyclization reaction would lead to a monotonic increase in average s value and substantial broadening of the sedimentation-coefficient distribution with increasing total protein concentration (33). Our data clearly indicate the existence of preferred oligomers with an upper size limit, an observation that we believe is most readily accounted for in the context of the model proposed here.

Estimation of the Size of Cyclic FtsZ Polymers. The sedimentation coefficient of cyclic polymers, relative to that of monomer, calculated according to Eqs. A2-1–A2-3, is plotted as a function of the degree of polymerization in Fig. 4. The experimental data shown in Fig. 2C indicate that the rapidly sedimenting fraction has a sedimentation coefficient between five and six times that of the slower sedimenting species (which is compatible with FtsZ monomer). Thus, we estimate that the sedimentation behavior of the rapidly sedimenting fraction is consistent with that of a distribution of cyclic polymers containing between 50 and 150 monomers. These values agree with estimates of the sizes of FtsZ rings observed in EM and AFM images (see above). Hence, the hypothetical circles are a physically realizable species.

Fig. 4.

Dependence of the sedimentation coefficient of polymer rings on the degree of polymerization i (see Appendix 2).

Cooperative Behavior of the Isodesmic Growth Plus Cyclization Model. Results of simulations performed by using the relations presented in Appendix 1 are presented in Figs. 5 and 6. We observe the following behavior. At low concentration, all of the protein is present as small oligomers. Above a certain critical concentration (for this parameter set, c* ≈ 50), cyclic polymers with degrees of polymerization in the vicinity of the optimal value i* (Fig. 3) begin to accumulate, but few if any linear polymers of intermediate size are observed. With increasing concentration, the amount of cyclic polymer increases nearly linearly with total protein concentration, whereas the total amount of small polymer remains nearly constant. Within the precision of a typical pelleting assay, such behavior would be interpreted as evidence of a highly cooperative and possibly first-order condensation process.

Fig. 5.

Size distribution of oligomers (mass fraction vs. degree of polymerization), calculated for i* = 150, σ_cyc = 20, K_c(i*) = 10⁴, and c* = 10 (red), 100 (black), 1,000 (green), and 10,000 (blue).

Fig. 6.

Simulated pelleting assay, calculated with the values of i*, σ_cyc, and K_c(i*) as in the example shown in Fig. 5, assuming that pelleted material consists of all species with i > ≈100.

Although the quantitative results clearly depend on the choice of parameter values, the qualitative characteristics of Figs. 5 and 6 are robust, as long as i* ≫ 1 and K_c(i*) ≫ 1, i.e., as long as cyclization is highly favored over linear growth once the linear polymer reaches an appropriately large contour length.

Concluding Remarks

In this work we characterized GTP-mediated FtsZ assembly in solution by means of sedimentation velocity. The experiments were carried out by using wild-type protein under physiologically relevant solution conditions (neutral pH and relatively high ionic strength). The presence of an enzymatic GTP-regenerating system allowed us to conduct experiments under steady-state conditions. The concentration-dependent sedimentation of FtsZ exhibits a relatively narrow distribution of rapidly sedimenting species that occurs only above an apparent “critical concentration” of protein and cannot be accounted for by any mechanism that postulates only linear polymers, whether single or multistranded (33). These experimental observations, together with the ring-like structures seen by EM and AFM, may be explained by a model that invokes noncooperative lengthening of single-stranded FtsZ filaments, coupled with preferential cyclization of higher polymers deriving from the intrinsic curvature of the fibrils. This simple model can also account for the condensation-like behavior observed in the pelleting assays. The behavior shown in Fig. 6 is quite similar to, and probably experimentally indistinguishable from, the behavior of FtsZ undergoing a first-order phase transition to a condensed phase, as occurs in a cooperative assembly. The proposed model thus resolves the apparent contradiction between the observation of single-stranded fibers on the one hand and the appearance of a critical concentration for appearance of a high molecular weight and highly sedimentable fraction of protein.

Our suggestion that individual FtsZ protofibrils formed in the presence of GTP have an intrinsic curvature and can form single-stranded rings may be relevant to the as-yet-unknown structure of the fully formed septation ring. Although the radius of the smallest rings observed in the present study is considerably smaller than the circumference of E. coli, we note that the average radius of ring-like fibrils increases with increased surface density of fibrils, suggesting that lateral interactions between single-stranded protofibrils tend to increase the preferred radius of curvature. Such interactions could result in the formation of large cyclic ribbon-like structures resembling belts, which, if severed and flattened on a surface due to the influence of strong surface attraction, would appear as two-dimensional arrays of the type reported in several previous EM studies (6, 7).

Appendix 1: Simplified Model for Combined Extension and Cyclization of a Single-Stranded Protein Fibril

It is assumed that linear or “open” oligomers are formed according to an isodesmic scheme, i.e., the free-energy change associated with the addition of a monomer to a linear oligomer is independent of the degree of polymerization (i) of the oligomer:

[A1-1]

where denotes the molar concentration of open i-mer at equilibrium. The equilibrium constant for formation of a closed ring from an open oligomer, K_c, is assumed to depend on the size of the oligomer:

[A1-2]

The dependence of K_c on the degree of polymerization is modeled as follows. We assume that the asymmetry of an individual protein molecule leads to a natural radius of curvature (or average radius of curvature), leading to the formation of a helical rather than straight single-stranded oligomer. It is assumed also that the number of protomers required for a single turn of the helix is sufficiently large that the mechanical work of helix deformation required to join the ends of the oligomer corresponding to a single turn of the helix, forming a closed planar ring, is negligible (i.e., small relative to thermal energy). We reason that the propinquity of the ends of the open oligomer of optimal length makes ring closure much more favorable entropically than the alternate process of adding a free monomer from solution to one end of the open oligomer. Because the two processes are essentially equivalent enthalpically, we assume that for the optimal value of i, denoted by i*, K_c(i*) ≫ 1. Because the open oligomer is flexible, other i-mers can also form planar rings but with smaller probability. We shall assume that the free-energy advantage favoring ring formation varies with oligomer length according to a Hooke's-law relationship,

[A1-3]

which is equivalent to the following form for the equilibrium constant:

[A1-4]

The cyclic species with i ≈ i* therefore represent a local free-energy minimum in the pathway to polymer growth. We define the following dimensionless quantities: (i) the mass fraction of species i,

[A1-5]

where c_tot denotes the total (molar) concentration of protein in moles of protomer/liter; and (ii) the scaled concentration,

[A1-6]

Combination of Eqs. A1-1, A1-2, A1-5, and A1-6 leads to the dimensionless equilibrium relations

[A1-7]

for i > 1, and

[A1-8]

Eq. A1-7 may be rewritten as

[A1-9]

for all i. Conservation of mass is then expressed as

[A1-10]

Eq. A1-10 is solved numerically to obtain f₁ as a function of the values of c* and the various K_c(i).¶¶ Then the values of individual and are calculated by using Eqs. A1-8 and A1-9.

Appendix 2: Estimation of Sedimentation Coefficients of Cyclic Polymers

The sedimentation coefficient of arrays of identical quasispherical subunits may be estimated by using the Kirkwood–Riseman relation (30),

[A2-1]

where S_n denotes the sedimentation coefficient of n-mer, R_S denotes the radius of a spherical subunit, and R_ij is the distance between the centers of the ith and jth subunits. Because this ratio is dimensionless, we may take the value of R_S as unity and measure R_ij in units of R_S.

Although a long single-stranded polymer is likely to be flexible and its structure is dynamic, a cyclic polymer of identical subunits would be expected on grounds of symmetry to be planar on average. The sedimentation coefficient of a planar circular ring of identical spherical subunits is estimated as follows. Consider a regular planar polymer with n vertices, representing the centers of each spherical subunit. The angle subtended by two vertices at the center of the polygon is given by θ = 2π /n, and the distance between two adjacent vertices is 2 (in units of R_S). Let r denote the distance between the center of the polygon and each vertex. From the law of cosines we obtain

[A2-2]

Let us number the vertices around the polygon from 1 to n. It then follows from the law of cosines that

[A2-3]

where θ_ij the central angle between the ith and jth vertex, is (j – i)θ.