FtsZ filament structures in different nucleotide states reveal the mechanism of assembly dynamics

Treadmilling protein filaments perform essential cellular functions by growing from one end while shrinking from the other, driven by nucleotide hydrolysis. Bacterial cell division relies on the primitive tubulin homolog FtsZ, a target for antibiotic discovery that assembles into single treadmilling filaments that hydrolyse GTP at an active site formed upon subunit association. We determined high-resolution filament structures of FtsZ from the pathogen Staphylococcus aureus in complex with different nucleotide analogs and cations, including mimetics of the ground and transition states of catalysis. Together with mutational and biochemical analyses, our structures reveal interactions made by the GTP γ-phosphate and Mg2+ at the subunit interface, a K+ ion stabilizing loop T7 for co-catalysis, new roles of key residues at the active site and a nearby crosstalk area, and rearrangements of a dynamic water shell bridging adjacent subunits upon GTP hydrolysis. We propose a mechanistic model that integrates nucleotide hydrolysis signaling with assembly-associated conformational changes and filament treadmilling. Equivalent assembly mechanisms may apply to more complex tubulin and actin cytomotive filaments that share analogous features with FtsZ.


Introduction
FtsZ is an assembling GTPase that plays a key role during bacterial cell division [1]. This widely conserved protein polymerizes in the presence of GTP and metal cations into polar filaments that gather at the center of dividing cells to form a dynamic Z-ring [2]. FtsZ filaments associate with a variable set of partner proteins into the divisome, which coordinates membrane invagination and cell wall peptidoglycan synthesis during cytokinesis [3,4]. As such, bacterial cell division proteins are targets for discovering new antibiotics [5], needed to fight resistant bacterial pathogens [6].
Translocational head-to-tail polymerization dynamics, discovered in actin filaments [7] and termed treadmilling in microtubule studies [8], has been demonstrated for FtsZ filaments both in vitro [9,10] and in vivo [11][12][13]. Treadmilling depends on two major properties of FtsZ (see scheme in Fig 1A). First, GTP hydrolysis only occurs within the filament, as the complete catalytic site is formed at the interface between adjacent FtsZ monomers [14,15]. Second, FtsZ can adopt two distinct conformations with different affinities for the filament [16,17]. The relaxed (R) conformation, which is present in free monomers irrespective of the bound nucleotide [17], exhibits low filament-binding affinity, while the tense (T) conformation is acquired by filament subunits. Switching between these two conformations [18] explains cooperative assembly of single-stranded FtsZ filaments [19,20] and creates different pairs of encountering interfaces at each filament end, thus enabling kinetic polarity for treadmilling [17,21]. GTP-bound FtsZ monomers associate to the filament growing end and, once inside the filament, are retained in the T conformation due to simultaneous contact with subunits on both of its sides, even after GTP hydrolysis. The subunit at the shrinking end dissociates due to weakened contact with its only neighboring GDP-bound subunit [17] (Fig 1A). FtsZ filaments shrink from the exposed nucleotide end, as deduced from mutational studies [21,22]. A recent numerical model generates populations of treadmilling filaments that accurately reproduce experimental results, thus unifying the described FtsZ properties [23]. FtsZ consists of an enzymatic core followed by a flexible C-terminal tail that contains binding motifs for membrane-tethering proteins [3]. The primitive enzymatic core of FtsZ, conserved with tubulin [24], comprises an N-terminal nucleotide-binding domain (NBD) and a C-terminal GTPase-activating domain (GAD) connected by the long central H7 α-helix [15,25]. The nucleotide occupies a pocket in the NBD, where loops T1 to T4 contact the phosphate groups, loop T5 interacts with the ribose moiety, and loop T6 contributes to guanine binding. At the opposite face of the monomer, the T7 synergy loop contains two conserved catalytic aspartates that promote GTP hydrolysis of the nucleotide placed in the adjacent subunit within the filament [14,15]. While loop T7 exhibits remarkable plasticity in FtsZ structures in the R conformation [16,17,[26][27][28], it adopts a defined arrangement by coordinating a metal ion in the T conformation [29]. Concomitant rotation of the neighboring GAD enables the formation of straight filaments where the nucleotide is buried from the solvent. The antibacterial compound PC190723 and chemically related FtsZ inhibitors bind in a cleft between NBD and GAD of subunits in the T conformation, thus blocking filament disassembly [29][30][31]. A reduced interaction area in the R conformation leads to monomers [17] or pseudofilaments where the nucleotide is partly exposed to the solvent [16,27,28]. Crystal structures of FtsZ filaments in the T conformation are only available with bound GDP [16,17,29,30], GTP with a truncated noncatalytic T7 loop [32], or the nonhydrolysable GTP analog guanosine-5 0 -(γthio)-triphosphate (GTPγS) [32]. Therefore, mechanistic information on GTP hydrolysis and its implication in filament assembly dynamics is currently largely missing.
We report a dozen filament structures of the FtsZ core (residues 12 to 316) from the pathogen S. aureus [6], hereafter SaFtsZ, in complex with various GTP mimetics and metal ions. The high resolution of these structures enables description of key interactions at the interface of adjacent monomers forming the catalytic site with unprecedented detail. Together with structure-based mutational analysis of critical residues around the active site, our results shed light on the mechanisms of FtsZ filament assembly, GTP hydrolysis, and treadmilling.

Stabilization of FtsZ polymers by GTP mimetics and cations
In preparation for structural studies based on our previous SaFtsZ-GDP filament structure [33], we analyzed the effect of several GTP mimetics on SaFtsZ assembly in solution, monitoring polymer formation with light scattering and sedimentation assays (Fig 1B and 1C). SaFtsZ assembly required GTP plus MgCl 2 and polymers disassembled upon nucleotide exhaustion, as reported [33]. BeF 3 − is a close chemical mimetic of phosphate that has been employed in mechanistic studies of G-proteins [34,35] and tubulin [36,37] as a reversibly binding analog of the GTP γ-phosphate, whose interaction with FtsZ has not been documented. On the other hand, GTP analogs bearing modified triphosphate moieties are frequently employed in FtsZ studies, including GMPCPP (guanosine-5 0 -[(α,β)-methyleno] triphosphate), GMPPCP (guanosine-5 0 -[(β,γ)-methyleno] triphosphate), and GTPγS [10,15,17,19,26,[31][32][33]. We found that addition of BeF 3 − stabilizes SaFtsZ polymers against disassembly, suggesting that BeF 3 − replaces the γ-phosphate in SaFtsZ filaments following GTP hydrolysis. Fast depolymerization can be induced by Mg 2+ chelation with EDTA, which supports an essential role for Mg 2+ in filament stability. BeF 3 − with GDP and Mg 2+ was ineffective for polymer assembly, indicating a filament-stabilizing rather than a nucleating effect of BeF 3 − . Negative-staining electron microscopy showed that GTP plus BeF 3 − forms bundles of SaFtsZ filaments ( Fig 1D) similar to those induced by GTP or by the slowly hydrolysing GTP analog GMPCPP [33]. In contrast, the nonhydrolysable GTP analogs GMPPCP and GTPγS fail to induce SaFtsZ assembly in these experiments, similarly to GDP and its analog GMPCP (guanosine-5 0 -[(α,β)-methyleno] diphosphate), highlighting their inability to mimic GTP function on SaFtsZ (Fig 1C and 1D). This is likely due to altered chemistry of the scissile bond in GMPPCP and GTPγS. We then confirmed that BeF 3 − stabilizes the assembly of full-length FtsZ from S. aureus in a qualitatively similar manner to the SaFtsZ core, as well as that of distant homologs from Escherichia coli (EcFtsZ) and Methanocaldococcus jannaschii (MjFtsZ) (S1 Fig). Repolymerization with BeF 3 − after disassembly was observed for MjFtsZ, possibly related to residual GTP. Aluminum fluoride, AlF 3 /AlF 4 − (AlF x ), is a mimetic of the transition state of GTP catalysis, as described for classical GTPases [35,38]. We observed that, in contrast to BeF 3 − , AlF x with GDP and Mg 2+ induces SaFtsZ to form short, C-shaped, single, and double filaments of approximately 100 nm in diameter (S2 Fig). These distinct AlF x polymers form rapidly with GDP and more slowly with GTP, possibly reflecting the need of GTP hydrolysis for AlF x binding in place of the γ-phosphate. The striking filament curvature induced by AlF x , reported previously for EcFtsZ [39] and similar to the approximately 150 nm circular filaments observed during EcFtsZ disassembly [40], likely relates to structural alterations at the association interface between SaFtsZ monomers in solution.

Structure determination of FtsZ filaments with GTP mimetics
Our attempts to determine the structure of SaFtsZ with bound GTP in the T conformation employing X-ray crystallography yielded filament structures where density in the active site only accounted for GDP, like in reported structures [29,33]. Therefore, we solved 12 crystal structures of SaFtsZ in complex with different GTP mimetics, analogs and metal ions, at resolutions ranging from 1.4 to 1.9 Å (S1 Table), which enabled unambiguous assignment of ligand densities (S3 Fig). We complemented this study with 4 additional structures of single-residue mutants complexed to GDP (S1 Table). In all cases, SaFtsZ adopts the T conformation forming straight filaments with minor but relevant differences between them, as detailed below. Subsequent description displays the filament in an orientation where nucleotide-binding loops T1 to T6 in the NBD face upwards, while the T7 synergy loop in the GAD looks downwards (Fig  2A), without further assumptions at this stage on which is the growing (plus) or the shrinking (minus) filament end. Four major contact regions can be defined in longitudinal contacts between adjacent monomers ( Fig 2B)

Structures mimicking the precatalytic state of GTP hydrolysis
The filament structure of SaFtsZ complexed to GDP and BeF 3 − in the presence of Mg 2+ reveals that BeF 3 − adopts a tetrahedral configuration with beryllium lying 2.7 Å apart from GDP ( Fig   3). Two fluorine atoms contact the bottom FtsZ monomer through hydrogen bonds (H-bond) with residues A71 and A73 in loop T3, G108 in loop T4, and T109 in helix H4 (Fig 3A). The third fluorine atom coordinates Mg 2+ , together with the β-phosphate of GDP. This configuration suggests that, in the canonical precatalytic state bound to GTP, the positive charge of Mg 2+ deprives in electrons the link between the β-and γ-phosphates in GTP, thus providing the main activating charge. Mg Comparison with the reported structure of GTP-bound SaFtsZ in the R conformation [17] shows that switching into the filament-prone T conformation involves small rearrangements of GTP and Mg 2+ within their binding pocket, whose geometry is essentially maintained, especially around loops T2 and T3 (S4B Fig).
An intricate network of solvent molecules surrounds BeF 3 − and Mg 2+ ions and contributes to stabilize the interactions between adjacent monomers. Four water molecules complete the octahedral coordination sphere of Mg 2+ (Fig 3A). Three of these waters (M1 to M3) form Hbonds with the sidechains of N44 and D46 in loop T2 of the bottom monomer, while the fourth (M4) connects BeF 3 − and the GDP α-and β-phosphates with the backbone of N208 in loop T7 of the top monomer ( Fig 3B). In addition, BeF 3 − establishes H-bonds with 3 other water molecules ( Fig 3C): (i) the precatalytic water ( Fig 3C, (Fig 3B and 3C). The K + ion is further coordinated by the backbone of residues L200, V203, and L209 in the top monomer, plus a solvent molecule (K1). Additionally, the sidechain of Q48 in bottom helix H2 lies 3.1 Å apart from K + , which is within the 3.6 Å coordination limit of this cation [41], whereas a second water molecule (K2) connected to Q48 lies 4.2 Å away from the cation. The high resolution of our structures enabled us to assign density for this ion to K + supported by results from various analysis, instead of a previously assigned Ca 2+ ion [29,33]. First, validation using Check My Metal [42] of atomic models refined with each of these ions favors K + . Second, crystals obtained in the presence of divalent cation chelators showed density for this ion that is identical to that observed in the original KCl buffer (S5 Fig). Third, free Ca 2+ in solution was below 1 ion per 50 SaFtsZ molecules, as determined with a fluorescent probe (Materials and methods). Finally, substitution of KCl by NaCl during protein purification yielded a structure where the T7 loop is occupied by Na + (S5D Fig). The presence of Na + in the T7 loop alters the configuration of ion-coordinating residues, especially V203. Notably, Q48 lies outside the Na + coordination sphere, whereas water K2 lies within and forms an H-bond with Q48. These changes, likely associated with increased filament stability, correlate with a 10-fold reduction in GTPase activity upon substitution of KCl by NaCl (S3 Table).
We also sought to solve the structure of SaFtsZ complexed to GMPCPP, as it induces filament formation with Mg 2+ (Fig 1C and 1D). However, the resulting structure only showed density for GMPCP, which binds SaFtsZ as GDP does [33]   Overall, our results indicate that the GTP γ-phosphate provides a chemical environment for Mg 2+ binding, reinforces interactions with the solvent network at the subunit interface, and enables bottom helix H2 to entrap a K + cation within the top T7 loop.

Structure mimicking the transition state of GTP hydrolysis
To gain further insight into the FtsZ catalytic mechanism, we determined the filament struc- ture, which is accompanied by a 30˚rotation of catalytic residue D210. A square bipyramid is, thus, formed between AlF 4 − , the linking oxygen in the GDP β-phosphate, and the catalytic water. In addition, the geometry of K + coordination is rearranged on both sides of the subunit interface. On one hand, the N208 sidechain contacts the Mg 2+ coordination sphere while keeping direct contact with K + . On the other hand, the Q48 sidechain shifts 2.1 Å away from its K + coordination position in the BeF 3 − structure, while D46 moves 0.8 Å away from the Mg 2+ ion. As a result, D46 loses an H-bond with the Mg 2+ coordination sphere, compensated by H-bond formation with a new solvent molecule that also contacts top residue N208 ( Fig 4B).

Nucleotide-dependent structural rearrangements and interfacial bonding
Differences between the BeF 3 − and AlF 4 − complexes at the residue level entail minor structural rearrangements at the subunit interface. The top T7 loop flattens toward the γ-phosphate position, while the neighboring top GAD rotates by approximately 5˚toward top helix H7 (S1 and S2 Movies). This movement is coordinated with opening of bottom monomer motifs that surround the nucleotide, including helix H2, loop T3, loop T5, and the N-terminal end of helix H7. As a result, the interaction between top strand S9 and bottom loop T5 (Region B, Fig 2B) is reinforced, while the contact between top loop T7 and bottom helix H2 (Region D, Fig 2B) is Further comparison with the structure of SaFtsZ bound to only GDP in the same T conformation [33] shows that both the top and bottom monomers exhibit a configuration that is similar to that observed in the BeF 3 − structure (S3, S4, S5, and S6 Movies). Nevertheless, several interactions are absent in the GDP structure that likely destabilize the association interface. First, nine water-mediated H-bonds involving BeF 3 − and Mg 2+ ions are lost from the association interface, despite the presence of two solvent molecules in the BeF 3 − site (S2 Table).

Functional properties and structure of FtsZ interfacial mutants
Our structural studies identified D46, Q48, R143, N208, D210, and D213, all conserved across species, as key residues for subunit association or GTP hydrolysis. We constructed individual SaFtsZ mutants in these positions, which in EcFtsZ functionally inactivate the protein as observed using in vivo complementation tests [22]. Mutations D46A, R143Q, N208L, D210N, and D213N all suppress SaFtsZ assembly as monitored by light scattering and polymer sedimentation ( Fig 5A and 5B), supporting a prominent role in filament formation. In accordance, the crystal structures of mutants D46A and D210N exhibit altered configurations at Region D ( Fig 5C). In the D46A mutant, bottom residue Q48 shifts 3 Å away from the K + site, while the whole top T7 loop is distorted, underscoring the relevance of D46 in the connection between the top and bottom subunits in the vicinity of Mg 2+ . In the D210N mutant, the top T7 loop lacks K + and moves 2 Å away from the bottom monomer, while the bottom T3 loop is severely rearranged. Interestingly, mutants Q48A and R143K supported assembly, forming polymers that are stabilized against disassembly by GTP consumption as compared to the wild-type protein ( Fig  5A and 5B). This correlates with reduced GTPase activity by about 6-fold in both mutants (S3 Table). The structure of the Q48A mutant shows that its K + coordination position is occupied by water K2 (Fig 5C), indicating a role for this residue in securing K + within the T7 loop for efficient catalysis. In the structure of the R143K mutant, K143 occupies an equivalent position to that of R143 in the wild-type protein but its positive charge lies 3 Å further from the GDP αand γ-phosphates ( Fig 5C). As the R143Q mutant is incompetent for polymerization and catalysis, our results indicate that a positively charged residue in this position is required for GTP hydrolysis. The polymers formed by the Q48A and R143K mutants were mostly filamentous ribbons (Fig 5D), rather than the bundles observed for the wild-type protein (Fig 1D). Because the employed concentration of 8 mM Mg 2+ slows polymer nucleation (notice lag times in Fig  5A), the effects of the mutations on assembly were confirmed at 2 mM Mg 2+ (S8 Fig). While the wild-type protein forms rapidly depolymerizing, single and double, wavy filaments, Q48A and R143K form stabilized, straight, thin filaments that slowly evolve into filamentous ribbons. These properties, which are strikingly similar to the effects of Na + on wild-type SaFtsZ assembly (S5 Fig), suggest that inhibition of GTP hydrolysis favors more rigid, straight SaFtsZ filaments that associate into ribbons.

Discussion
Cytomotive proteins such as actins and tubulins self-assemble into nucleotide-hydrolyzing dynamic filaments that serve as rails for motor proteins and are also able to perform mechanical work by themselves [43]. Treadmilling of FtsZ filaments, driven by GTP hydrolysis, is essential for correct cell division in bacteria, which lack homologs of cytoskeletal motor proteins. In this work, we reveal the detailed mechanism of interfacial nucleotide hydrolysis by FtsZ filaments, by determining crystal filament structures in complex with different GTP mimetics and metal ions, combined with functional and structural characterization of individual mutants. Our results, together with previous structures, uncover the structural mechanism of FtsZ assembly dynamics at an unmatched resolution among cytomotive filaments.

A composite active site with two labile metal ions
Our structures reveal new features of FtsZ as an atypical GTPase [24]. First, we identified swinging of D210 in the top T7 loop as a key event to position the catalytic water for attack over the γ-phosphate of GTP. In contrast, top residue D213 and bottom residue G72 essentially preserve their position during catalysis and rather provide a chemical environment for nucleophilic attack. Second, we found that bottom residue R143, which connects to both D213 and the nucleotide γ-phosphate through bridging water B1, contributes to catalysis and that the position of its positive charge is critical for efficient GTP hydrolysis. Accordingly, R143K and not R143Q mutation allows assembly but presents reduced GTPase activity (Fig 5 and S3  Table). The equivalent residue in MjFtsZ, R169, was suggested to stabilize the transition state [15]. The role of R143 is likely equivalent to that of the arginine finger in Ras-like GTPases, while in these enzymes, the finger residue contacts the nucleotide directly [44]. Third, we showed that a two-cation mechanism involving Mg 2+ and K + operates in FtsZ for GTP hydrolysis. While Mg 2+ contacts the β-and γ-phosphates of GTP and has a direct role in catalysis, K + locates in the top T7 loop and contacts the substrate indirectly through its coordinating residue N208, which forms H-bonds with solvent molecules connected to Mg 2+ and the γ-phosphate. Accordingly, mutation N208L abolishes polymerization. Taken together, SaFtsZ can be classified as a type II Mg 2+ /K + enzyme, as the monovalent cation has an allosteric role in catalysis [45]. This differs from most type I GTPases, where K + assists catalysis through direct contact with the nucleotide phosphates, thus providing the activating charge that in other GTPases is supplied by the arginine finger [44]. Fourth, we found that locking of K + within the top T7 loop by bottom residue Q48 plays a role in catalysis. In agreement, the Q48A mutant allows assembly but exhibits reduced GTPase activity (Fig 5 and S3 Table). K + is bound weakly and can be evicted from its binding site by subtle changes around the T7 loop, as observed in the structures of mutant Q48A and wild-type SaFtsZ complexed to GMPPCP and Mg 2+ . Moreover, substitution of K + by Na + strongly reduces the GTPase activity ( S5 Fig and S3 Table), similarly to FtsZ from other species, with some exceptions [46]. This K + preference for hydrolysis correlates with estimated concentrations in the bacterial cytosol of 200 mM K + and 5 mM Na + [47].

A dynamic water shell mediates assembly and catalysis
The high resolution of the structures reported here enables location of solvent molecules at the subunit interface that contribute to filament assembly and catalysis (S2 Table). Water molecules M1 to M4, located between the nucleotide phosphates and the bottom T2 loop, coordinate Mg 2+ binding, with water M4 playing a prominent role as it also bridges the nucleotide phosphates with the residue N208 in the top T7 loop (Fig 3). Notably, waters M1 to M4 rearrange to accommodate the planar transition intermediate analog AlF 4 − and the sidechain of catalytic residue D210, thus enabling correct positioning of the catalytic water and minor opening of bottom residue Q48 and helix H2 (Fig 4B and S2 Movie). Besides, waters B1 to B5 connect the nucleotide phosphates with the top T7 loop and strand S9. Moreover, relocation of waters B2 to B4 upon Mg 2+ binding enables bridging of R143 with the nucleotide phosphates, which arises as a key event to position its positive charge to assist catalysis. Furthermore, bridging waters B1 to B3 rearrange to accommodate the catalysis intermediate, thus inducing slightly retraction of the R143 charge in the transition state. Solvent rearrangements also occur at the interface between bottom T2 and top T7 loops, which in the transition intermediate allow disengagement of bottom helix H2 from the top T7 loop.

A crosstalk region modulates catalysis and disassembly
In spite of the rigid context of our structures, concerted rearrangements are observed between the structures complexed to BeF 3 − or AlF 4 − (S1 and S2 Movies), while additional changes arise in the absence of the γ-phosphate (S3, S4, S5 and S6 Movies). We distinguish two major interacting areas in the straight filament interface. On one hand, contact Regions A and B ( Fig 2B) constitute a pivoting area that would allow partial opening of the subunit interface, as observed in molecular dynamics simulations of SaFtsZ filaments [48]. While rearranged, contact around this area is roughly maintained in R conformation structures of SaFtsZ pseudofilaments [16,27,28]. On the other hand, we define a crosstalk area around the γ-phosphate site, which encompasses interface contact Regions C and D ( Fig 2B) and is specific of straight filaments in the T conformation. The relevance of this crosstalk area is highlighted by mutational analysis showing that D46A, N208L, D210N, and D213N, all impair filament formation in solution. In agreement, the structures of mutants D46A and D210N exhibit an altered configuration around this area. A similar effect can be expected for N208 and D213N, which are both critical to maintain the T7 loop conformation and its interaction with the bottom monomer. Our structures in complex with GMPPCP in the presence and absence of Mg 2+ further underscore the plasticity of the crosstalk interface within straight filaments.

A model for FtsZ filament dynamics
We propose a model for the FtsZ catalytic assembly cycle (Fig 6). Our description starts with a filament where all subunits are in the T conformation and the association interface contains GTP. We reason that Mg 2+ requirement for FtsZ polymerization is mainly related to its shielding effect over the acidic charge of the triphosphate nucleotide, while it also contributes to accurate positioning of the γ-phosphate for catalysis (Figs 3 and S4D). Additionally, K + within the filament T7 loop is secured through labile coordination with residue Q48 from the neighboring subunit. In such configuration, nucleophilic attack by the catalytic water over the γphosphate occurs through a transition state where key residues and solvent molecules around the crosstalk region are rearranged. GTP hydrolysis proceeds at slow rate due to unique catalytic properties of FtsZ described above, followed by fast Mg 2+ release through the exit pore, which likely rearranges to also liberate inorganic phosphate. This generates the assembled GDP-bound filament interface in the T conformation, where absence of key interfacial ionic interactions mediated by the γ-phosphate and Mg 2+ destabilizes filament contacts, which is accompanied by minor structural rearrangements. We speculate that this allows detachment around the crosstalk region while contacts around the pivoting area are roughly maintained.
This eventually allows structural relaxation into the R conformation, likely accompanied by K + release from loop T7 as density for ion is absent across FtsZ structures in the R conformation, altogether leading to interfacial dissociation at the filament minus end. The antibacterial compound PC190723 inhibits FtsZ filament treadmilling and cell division [11] by stabilizing the T conformation [29][30][31]. Free FtsZ monomers in the R conformation spontaneously exchangein GTP and Mg 2+ to enter a new assembly cycle at the filament plus end. While this model does not imply a defined filament kinetic polarity, our findings combined with existing structural data enable a tentative assignment. The nucleotide γ-phosphate and Mg 2+ stabilize the crosstalk region of the R monomer such that its top surface is preorganized similar to the T conformation ( S4B Fig). However, the bottom surface of this R monomer is substantially different from the T conformation including a flexible T7 loop [16,17]. The exposed bottom surface, including the T7 loop, in an all-T single-filament model has to adopt the association-prone configuration for assembly to be cooperative [19,20]. Altogether, this suggests that an incoming R monomer should preferentially associate through its preorganized GTP-bound top surface, that is, with the bottom end of the T filament exposing the T7 loop, which constitutes the growing end. This correlates with the reported effects of mutations at the bottom association interface, which block cell division and are toxic, as opposed to mutations on the top interface [21,22]. The same polarity of FtsZ filaments is supported by the effects of the Bacillus subtilis cell division inhibitor MciZ, which forms a complex with the bottom interface of FtsZ monomers in the R conformation and caps FtsZ filaments [49]. Bottom capping would reduce filament growth and annealing, in agreement with the observed decrease in filament length [49], which, together with a striking increase in treadmilling velocity in cells [11], is captured by Monte Carlo model simulations of treadmilling FtsZ filaments growing from the bottom end [23].
Our proposed mechanism unifies slow nucleotide hydrolysis with conformational switch and treadmilling, all essential properties for FtsZ function in bacterial cell division. It has been pointed out [23,50] that, analogously to FtsZ, tubulin [51] and actin [52,53] both show relatively small nucleotide-induced rearrangements associated to nucleotide hydrolysis in cryo-EM filament structures, compared to the larger structural changes between their unassembled (relaxed) and assembled (tense) states. The primitive assembly mechanism of single-stranded FtsZ filaments might thus help to better understand those of more complex, multistranded cytomotive filaments.

Protein purification
The enzymatic core (residues 12 to 316) and full-length forms of FtsZ from methycillin-resistant S. aureus Mu50/ATCC 700699 (SaFtsZ and SaFtsZ f , respectively) complexed to GDP, as well as the nucleotide-free form (apo-SaFtsZ), were all affinity-purified as described [33]. SaFtsZ single-residue mutants were prepared using QuikChange II Site-Directed Mutagenesis Kit (Agilent) with primers listed in S4 Table and purified following the same protocol. For wild-type and mutant SaFtsZ, the final gel filtration was performed in 10 mM Tris-HCl (pH 7.5), 50 mM KCl, 100 μM GDP. To obtain SaFtsZ in Na + solution, KCl in the gel filtration buffer was replaced by 50 mM NaCl. To obtain SaFtsZ in complex with GTP, following thrombin cleavage, the sample was adjusted to 2 mM GTP before anion exchange in the absence of MgCl 2 and adjusted again to 2 mM GTP before gel filtration where GDP was replaced by 100 μM GTP. Similarly, to produce SaFtsZ in complex with GMPPCP, the sample was adjusted to 100 μM GMPPCP before anion exchange in the absence of MgCl 2 , and adjusted again to 2 mM GMPPCP before gel filtration where GDP was replaced by 100 μM GMPPCP. To obtain SaFtsZ deprived of divalent cations in the solution, 1 mM EDTA was added to the gel filtration buffer. Full-length FtsZ from E. coli (EcFtsZ) was purified as described [54] and nucleotidedevoid, full-length FtsZ from M. jannnaschii (apo-MjFtsZ) was prepared as reported [55].

FtsZ assembly and GTPase activity
All FtsZ assembly experiments were made in 50 mM MES-KOH (pH 6.5), 50 mM KCl, 1 mM EDTA (MES assembly buffer) at 25˚C, to which 10 mM MgCl 2 and different nucleotide analogs were added, unless otherwise indicated. Polymer formation was monitored by right angle light scattering at 350 nm and by 30-min high-speed centrifugation followed by SDS-PAGE of pellet and supernatant samples and Coomassie blue staining. FtsZ polymers were visualized by negative stain electron microscopy, as described [33].
GTPase rate measurements were made from polymerizing SaFtsZ solutions (1 mM GTP, 10 mM MgCl 2 ) by taking 10 μL aliquots every 3 min for the wild-type and every 15 to 30 min for the mutants and measuring the released phosphate with the malachite green assay at 650 nm [58]. The hydrolysis rate values given are referred to total SaFtsZ concentration (50 μM).

Measurement of Ca 2+ concentration
Free Ca 2+ concentrations were determined with the fluorescent probe Fura-FF pentapotassium salt (AAT Bioquest, Sunnnyvale, California). A Horiba Fluoromax-4 spectroflurometer was employed to measure the excitation spectra of probe (1 μM), with a 1-nm bandwith and emission set at 505 nm with 2 nm bandwith. A maximum at 360 nm was observed in the absence of Ca 2+ that gradually shifted to a higher intensity maximum at 336 nm upon addition of increasing Ca 2+ concentrations (1 to 100 μM) in the buffer. Comparison with these spectra showed that the free Ca 2+ concentration was below 1 Ca 2+ per 50 SaFtsZ molecules in the purified protein, <1 μM in assembly (approximately 50 μM FtsZ) and crystallization (approximately 500 μM FtsZ) buffers and <10 μM in crystallization solutions.

Structure determination
All crystals were flash-cooled by immersion in liquid nitrogen, and diffraction data were collected at the ALBA (Spain) and ESRF (France) synchrotrons. All data were processed using XDS [59] and Aimless from the CCP4 Suite [60]. Data collection and refinement statistics are presented in S1 Table. The structures were determined through molecular replacement using Molrep [60] and the PDB entry 6RVN [33] as search model. Model building and refinement were done using Coot [61] and PHENIX [62], respectively. Refinement statistics are summarized in S1 Table. Structural figures were prepared using PyMOL (Schrödinger). , and Mg 2+ . (E) Light scattering assembly time courses of SaFtsZ (50 μM) in K + (black lines) and Na + -containing (pink lines) MES assembly buffers at 25˚C. GTP (1 mM) was added, and assembly was triggered by addition of 10 mM MgCl 2 (solid lines) or 5 mM MgCl 2 (dashed lines) as indicated by the arrow. Numerical data for each curve can be found in S7 Data. (F) Representative electron micrograph of SaFtsZ in Na + buffer with 10 mM MgCl 2 , to be compared with polymers formed in K + buffer (Fig 1C). The bar indicates 200 nm. Notice the similarity of these scattering and electron microscopy results of SaFtsZ in Na + buffer with those of the Q48A and R143K mutants in K + buffer (Figs 6 and S8).