The FtsLB subcomplex of the bacterial divisome is a tetramer with an uninterrupted FtsL helix linking the transmembrane and periplasmic regions

In Escherichia coli, FtsLB plays a central role in the initiation of cell division, possibly transducing a signal that will eventually lead to the activation of peptidoglycan remodeling at the forming septum. The molecular mechanisms by which FtsLB operates in the divisome, however, are not understood. Here, we present a structural analysis of the FtsLB complex, performed with biophysical, computational, and in vivo methods, that establishes the organization of the transmembrane region and proximal coiled coil of the complex. FRET analysis in vitro is consistent with formation of a tetramer composed of two FtsL and two FtsB subunits. We predicted subunit contacts through co-evolutionary analysis and used them to compute a structural model of the complex. The transmembrane region of FtsLB is stabilized by hydrophobic packing and by a complex network of hydrogen bonds. The coiled coil domain probably terminates near the critical constriction control domain, which might correspond to a structural transition. The presence of strongly polar amino acids within the core of the tetrameric coiled coil suggests that the coil may split into two independent FtsQ-binding domains. The helix of FtsB is interrupted between the transmembrane and coiled coil regions by a flexible Gly-rich linker. Conversely, the data suggest that FtsL forms an uninterrupted helix across the two regions and that the integrity of this helix is indispensable for the function of the complex. The FtsL helix is thus a candidate for acting as a potential mechanical connection to communicate conformational changes between periplasmic, membrane, and cytoplasmic regions.

The cell envelope of Gram-negative bacteria, such as Escherichia coli, consists of three layers: a cytoplasmic membrane, an outer membrane, and a rigid cell wall formed by a mesh of peptidoglycan located in the intervening periplasmic space. Cell division requires mechanisms for the separation of these three layers. The first step is the establishment of a division site and the segregation of the duplicated chromosome. This allows for the beginning of constriction, during which the coordinated activities of numerous peptidoglycan synthases and hydrolases remodel the cell wall. Finally, the process leads to membrane fusion and to the separation of two daughter cells. The large multiprotein complex that supports a majority of these functions is called the divisome.
At least 3 dozen proteins are known to participate in cell division in E. coli, but the essential components of the divisome consist of a core of 12 proteins. Their recruitment to mid-cell follows a hierarchical order of dependence (FtsZ 3 FtsA-ZipA 3 FtsE-FtsX 3 FtsK 3 FtsQ 3 FtsL-FtsB 3 FtsW 3 FtsI 3 FtsN; Fig. 1a), which also reflects, in part, the timing and interactions that occur in the complex assembly (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12). The divisome assembles around the tubulin homolog FtsZ, which forms a ringlike structure at mid-cell (the Z-ring) (13)(14)(15). FtsZ protofilaments treadmill around the circumference of the cell, providing a scaffold for the recruitment and movement of the components around the cell and ultimately leading to incorporation of new peptidoglycan around the forming septum (16,17). FtsZ is tethered to the plasma membrane by the cooperative action of ZipA, a single-pass transmembrane (TM) 11 protein (18,19), and of FtsA, an actin homolog and peripheral membrane protein able to form protofilaments (20). Other early components of the divisome include FtsEX, an ABC transporter-like complex that controls cell wall hydrolysis and possibly divisome assembly (21,22), as well as FtsK, a DNA translocase important for chromosome segregation (23).
The late components of the divisome (FtsQ, FtsB, FtsL, FtsW, FtsI, and FtsN) localize approximately at the beginning of constriction (24). FtsQ, FtsB, and FtsL are three bitopic (singlepass) membrane proteins that form a complex whose exact function is not well understood (6). The FtsQLB complex is required for the recruitment of FtsW, a large multispan membrane protein, and FtsI, a bitopic protein. FtsW and FtsI work in coordination to synthesize septal cell wall (8); FtsI is a penicillin-binding protein (PBP3) with transpeptidase activity (25), and FtsW is most likely its cognate glycosyltransferase (26 -28) (FtsW has also been proposed to be a flippase for peptidoglycan precursors (29, 30)). The last protein in the recruitment hierarchy is FtsN, a bitopic protein with an N-terminal TM domain, a predicted disordered region, and a C-terminal domain capable of recognizing septal peptidoglycan (31). The precise role of FtsN is not understood, but its accumulation at the septal ring represents a key event for triggering constriction. This activation may be mediated by some of the interactions that have been postulated for FtsN, which include FtsA, the peptidoglycan synthase complex (FtsW, FtsI, and PBP1B), and the FtsQLB complex (32)(33)(34)(35)(36).
Here we focus on the structural organization of the FtsL-FtsB subcomplex (FtsLB), which has been implicated as a critical player in triggering constriction (41,42). Topologically, FtsL and FtsB are both small bitopic proteins with a nearly identical domain organization, which suggests that they may derive from a common evolutionary ancestor. Both proteins have short (or absent) N-terminal cytoplasmic tails, one TM domain, a juxtamembrane coiled coil, and C-terminal tails in the periplasm (Fig. 1a). Peptides corresponding to the TM helices form a stable higher-order oligomer in vitro, with an equal number of FtsL and FtsB subunits, indicating that the TM region is an important contributor to the stability of the complex (43). This is consistent with the observation that the TM domains are biologically important (6,44,45). FtsL and FtsB associate in vivo even in the absence of FtsQ (11, 46), although FtsQ is required for their recruitment to mid-cell (6). The association with FtsQ to form the FtsQLB complex is primarily mediated by the C-terminal tails of FtsLB, which bind to the C-terminal end of FtsQ, as evidenced by truncation functional analysis (45, 47) as well as cross-linking performed in vivo (48). The periplasmic domains of the three proteins are sufficient to form soluble complexes with submicromolar binding affinities, as established for E. coli (49) and Streptococcus pneumoniae (50,51) proteins. Notably, these studies have been performed using solubilized FtsLB constructs that were fused to a stable heterodimeric coiled coil and thus forced into a dimeric state. However, FtsLB is likely to be a higher-order oligomer (such as a tetramer), as evidenced by biophysical analysis of their TM helices in isolation (43). The tight binding affinity of these 1:1:1 FtsQLB soluble constructs therefore suggests that independent FtsQ-binding sites exist in FtsLB, each formed by one FtsL and one FtsB subunit.
The precise function of FtsLB has not yet been determined. It was originally hypothesized that FtsLB could have a structural role in stabilizing the divisome (45, 47). The finding that FtsL is subject to active degradation unless it is stabilized by interaction with FtsB in Bacillus subtilis (52)(53)(54) and E. coli (45) suggested that FtsL levels may be rate-limiting for division (54). More recent evidence indicates that FtsLB is an active participant in the decision making that controls the cell division process, playing a central role in triggering of septal peptidoglycan synthesis. This hypothesis is supported by observations that point mutations in a particular region of FtsL and FtsB alter the tightly regulated cell division process, allowing it to proceed even in situations in which normally it would not occur (41,42). Tsang and Bernhardt (41) discovered that a single point mutation in FtsL (E88K) allows the cells to bypass the normally strict requirements for other division proteins, namely FtsK, ZipA, FtsN, and FtsA (although residual levels of FtsA expression appear to be still necessary). Independently, De Boer and colleagues (42) identified a series of mutants that bypass the need for FtsN. These mutants map to two short regions of the coiled coil of FtsL (residues 88 -94) and FtsB (residues 55-59). These regions, which are located ϳ30 residues past the TM domain, were named the "constriction control domain" (CCD) (42).
The observed properties of these CCD mutants are consistent with a conformational change in FtsLB that has become deregulated. In other words, an OFF/ON structural transition in FtsLB may be part of the events that control the beginning of Figure 1. The essential proteins of the divisome. a, schematic representation of the divisome of E. coli. The complex assembles around a polymeric scaffold formed by FtsZ. With a few exceptions (FtsZ, FtsA, and FtsE), all essential components are integral membrane proteins. As reported in this work, the FtsLB complex is a heterotetramer formed by two FtsL subunits (yellow) and two FtsB subunits (blue). The complex forms an extended helical bundle that comprises the transmembrane helices and the periplasmic coiled coil. The C-terminal periplasmic tails of FtsLB mediate the binding to FtsQ. The cytoplasmic tail of FtsL has been hypothesized to bind to FtsW. Description of the function of the various components is provided in the Introduction. b, the divisome of E. coli displays a characteristic hierarchy of recruitment at the division site, with the arrows indicating a dependence of a component on the one that precedes it in the sequence. The hierarchy also roughly corresponds to the order of recruitment, which can be subdivided into early and late components.

Structural analysis of the FtsLB tetrameric complex
cell constriction. This transition may be triggered allosterically by FtsN itself, as suggested by the observation that the essential region of FtsN ( E FtsN, a short stretch of sequence that is separated by ϳ20 amino acids from the C-terminal side of the TM domain) is in a position that is topologically equivalent with the location of the CCD in FtsLB (41,42).
To elucidate the effect of the CCD mutants and the overall function of the FtsQLB complex in molecular detail, it is necessary to understand its structural organization. So far, two partial structures have been obtained. The structure of the periplasmic domain of FtsQ has been solved by X-ray crystallography, without the TM and cytoplasmic domains (39). Additionally, we previously determined the crystal structure of the coiled coil domain of FtsB and also produced a computational model of the TM domain of the same protein, based on mutagenesis data (38). Both structures were obtained in the absence of FtsL and in a homodimeric form. In addition, computational models of the FtsQLB periplasmic region (both in the trimeric and hexameric state) have also been reported (55). These models were based on available experimental data regarding contacts between FtsQ and FtsLB, whereas the FtsLB component was predicted ab initio. Additionally, these models lacked the TM region.
Here, we present a structural analysis of the TM domain and periplasmic coiled coil of FtsLB, based on a combination of biophysical and computational methods with in vivo validation. The work includes in vitro FRET to determine the oligomerization state of FtsLB; a co-evolutionary analysis of sequence alignments to provide an extensive set of predicted contacts between positions in FtsL and FtsB; molecular modeling to compute a three-dimensional structural model of the complex; molecular dynamics in lipid bilayers to evaluate stability and dynamics of the model; and a functional analysis of mutants in vivo to experimentally test the model and investigate the biological relevance of the predicted structural features.
Our results confirm that FtsLB is a higher oligomer and point to an L 2 B 2 tetramer. Overall, the phenotypic analysis is in good agreement with structural features identified computationally. The distribution of deleterious phenotypes among the TM region mutants is consistent with the predicted interface. We confirm that the helix of FtsB breaks between the TM and periplasmic regions, with the formation of a flexible linker, as hypothesized previously (38). In contrast, we show that FtsL forms a continuous helix and that the integrity of this helix is crucial for function. We also found indications that the coiled coil might not be built for structural stability, at least not in the form of a canonical tetrameric helical bundle assembly, suggesting that the coil may either serve as a dynamic structural unit or else split into two independent domains.

Co-evolutionary analysis identifies potential quaternary contacts consistent with an extended helical bundle
To predict the positions that mediate the association of the FtsLB complex, we analyzed a paired alignment of FtsL and FtsB sequences from proteobacteria species using the EV-Couplings algorithm (56). EV-Couplings uses a maximum-entropy model of the evolutionary history of a protein (or protein complex) to infer potential tertiary (56) and quaternary (57) contacts in its structure. It is based on the notion that, to maintain complementary interactions, amino acid changes influence the variation of positions that are in close proximity. The results of our EV-Couplings analysis are shown in Fig. 2a. The figure displays the top 95 pairs of positions identified between FtsL and FtsB. The complete ranked list is provided in Table S1. FtsB-FtsB and FtsL-FtsL pairs are displayed in Fig. S1.
A notable diagonal pattern of co-evolving positions starts in the TM region of both proteins and continues in the coiled coil  Table S1. The TM region and coiled coil are highlighted by boxes. Marked in the sequence of FtsB is also the position of a Gly-rich region between the TM and coil domains (G). b, predicted contacts in the coiled coil domain between FtsB (blue) and FtsL (yellow) displayed using a helical-wheel projection. The contacts are in excellent agreement with the expected contacts for a canonical coiled coil. c, similar map for the TM region. The contacts are also consistent with the formation of a helical bundle. The interfacial positions of FtsL are on the same face of the interfacial position in the coiled coil, suggesting that FtsL forms a continuous helix. The positions in FtsB are rotated by ϳ60°with respect to those of the coiled coil (white arrow), indicating that a discontinuity is probably present between the two helical domains.

Structural analysis of the FtsLB tetrameric complex
region, which is consistent with the contact map expected for an extended parallel helical bundle. As shown in the helical wheel diagram of Fig. 2b, the co-evolving positions in the periplasmic region are also consistent with the expected geometry of a coiled coil (7,50,58), occurring at positions of the "heptad repeat" (abcdefg) that are interfacial, at either the buried a and d positions or at the partially solvent exposed e and g positions. Moreover, these predicted contacts occur between pairs that are in proximity in a canonical coiled coil (e.g. a-a, a-d, and g-e, but not a-e). The pattern of connectivity remains in good agreement with a coiled coil contact map until positions 61 in FtsB and 91 in FtsL, after which it loses this periodicity. This range covers approximately five heptad repeats, which for FtsB is ϳ10 -20 amino acids shorter than the consensus of the sequence-based predictors Paircoil (59), Multicoil (60), Marcoil (61), and Coils (62, 63) (inferring the length of the coiled coil of FtsL with the same methods is difficult because it is poorly predicted (58)). The coiled coil predicted by the evolutionary analysis approximately reaches the CCD (55-59 in FtsB, 88 -94 in FtsL, highlighted in yellow in Fig. 2, a and d), suggesting that it is possible that this critical regulatory region occurs toward the end of the coil and thus in proximity of a structural transition.

A continuous FtsL helix and a discontinuous FtsB
As illustrated in the helical wheel diagram of Fig. 2c, the TM region also displays a pattern of predicted contacts consistent with a bundle of parallel helices. The co-evolving positions are clustered toward the C-terminal side of the TM domains. Remarkably, the interfacial positions of the TM domain FtsB are in excellent agreement with those identified previously from their sensitivity to mutagenesis in a self-association assay (38).
Comparison of the contact maps ( Fig. 2, b and c) indicates that, in FtsL, the predicted interfaces of coiled coil and TM domains occur on the same face of the helix (involving the a, d, and g positions in the TM domain and the a, d, e, and g positions in the coil). This pattern indicates that FtsL forms a continuous helix across the membrane and the periplasmic region. A different outcome is observed for FtsB, for which the TM domain interface involves a and e but also b positions (versus a, d, e, and g positions in the coil) and thus appears rotated by ϳ60°with respect to the periplasmic region (as indicated by the arrow in Fig. 2c). This rotation suggests the presence of a helical break. Rearrangements of the periodicity from the canonical heptad repeat are not uncommon in long coils. The 60°shift of the relative orientation of the interface between the TM and coiled coil regions of FtsB would correspond to the insertion of four amino acids (abcdabcdefg), which is designated as a "stutter" (64,65). Such mismatches influence the coil's local structure and can possibly facilitate conformational changes necessary for function (66,67). In this particular case, however, the presence of a conserved Gly-rich region ( 22 GKNG 25 in E. coli and 22 GKGG 25 in the consensus sequence of ␣-, ␤-, and ␥-proteobacteria (38)) suggests that the juxtamembrane linker of FtsB is more likely to adopt a flexible and extended conformation instead of a local distortion of the helix.

FtsLB is a higher oligomer, probably an L 2 B 2 tetrameric complex
To build a structural model for the FtsLB complex based on the evolutionary constraints, it was necessary to establish its oligomeric state. In previous work, we demonstrated that the isolated TM region of the FtsLB complex assembles to form a higher-order oligomer consisting of an equal number of FtsL and FtsB subunits, but we were unable to distinguish between heterotetrameric (L 2 B 2 ), heterohexameric (L 3 B 3 ), or even higher oligomeric forms (43). Here, we assessed the stoichiometry of a construct that includes both periplasmic and TM domains by FRET analysis in vitro.
The FtsLB complex was overexpressed in E. coli, consisting of an N-terminally His-tagged FtsB and an N-terminally Streptagged FtsL. FtsL and FtsB were co-expressed. The proteins co-purify over sequential Ni-NTA and streptavidin columns in DM and DDM detergents, indicating that they form a stable complex with a density over Coomassie staining compatible with a 1:1 stoichiometric ratio (Fig. S2a). A C-terminal Cys residue was introduced in either FtsB or FtsL, and protein samples were separately labeled with either donor (Cyanine 3; Cy3) or acceptor (Cyanine 5; Cy5) fluorophores. Because the stoichiometric analysis is performed separately for the two proteins, to further confirm interaction between FtsL and FtsB in the experimental conditions, we mixed and equilibrated FtsL unlabeled -FtsB Cy3 and FtsL Cy5 -FtsB unlabeled samples, which produced a distinct FRET signal (Fig. S2b).
We analyzed the stoichiometry of FtsLB by adopting a FRET method based on changing the relative fraction of donor-and acceptor-labeled molecules while the total protein concentration was maintained constant (68). In these conditions, the theoretical variation of donor quenching (Q) depends on the oligomeric state of the complex, being proportional to (1 Ϫ P D n Ϫ 1 ), where P D is the relative fraction of donor-labeled protein, and n is the number of subunits in the complex (see Equation 4 under "Experimental procedures"). Due to the power law, no variation of donor quenching is expected for monomers as the donor fraction decreases, a linear increase of Q is expected for dimers, and a curved relationship is expected for trimers and higher oligomers. We performed two independent experiments, labeling only one of the two proteins with donor and acceptor fluorophores while leaving the other unlabeled. By labeling only either the FtsL or the FtsB moieties of the FtsLB complex, the procedure allowed us to calculate the number of subunits of FtsL and of FtsB individually.
As illustrated in Fig. 3 (left), donor quenching increased linearly for FtsL-labeled samples when the acceptor fraction was increased. We used the sum of residuals between the experimental data and the models to compare the fits. The residual of the two-subunit linear model (dashed line, residual (r) ϭ 0.001) is 10-fold smaller than the residuals of the three-subunit model (continuous line, r ϭ 0.01), indicating that two FtsL molecules are present in the FtsLB complex. The quenching data of FtsB (Fig. 3, right) also display a progressive increase of donor quenching, establishing that at least two FtsB subunits are present in the FtsLB complex. However, the fit to two subunits (r ϭ 0.0055) is only marginally better than the fit to three subunits

Structural analysis of the FtsLB tetrameric complex
(r ϭ 0.0064); therefore, the data cannot differentiate between these two models, as in the case of FtsL. The fit, however, can reasonably rule out a four-subunit model (dotted line, r ϭ 0.02).
Overall, the analysis confirms that the FtsLB complex is a higher-order oligomer. Considering the entire body of available evidence, the most likely model is an L 2 B 2 heterotetramer. Because FtsL fits well to a model containing two subunits, the possible states supported by the data are L 2 B 2 or L 2 B 3 stoichiometries. However, a 2:3 stoichiometry is in disagreement with previous FRET data that indicated that the FtsLB complex has an equivalent number of FtsL and FtsB subunits (43). A 2:3 pentamer is also a less common oligomeric form in nature than a 2:2 heterotetramer (69). In addition, a 2:3 pentamer would be necessarily asymmetrical, whereas the co-evolutionary contacts are strongly consistent with a standard symmetrical organization ( Fig. 2, b and c). Finally, 2:2 would also be consistent with a previous estimate of the stoichiometry of the divisome based on ribosome profiling data (70).

Molecular modeling of the FtsLB helical bundle
We used a Monte Carlo docking procedure guided by the evolutionarily based distance constraints to create an all-atom computational model of the structure of the TM and coiled coil domains of the tetrameric complex (residues 1-61 of FtsB and 35-91 of FtsL). The model, which is illustrated in Fig. 4a, consists of a four-helix bundle that spans the membrane and projects into the periplasmic region for ϳ55 Å. The structure is well packed, with the exception of a small void (ϳ12 Å 3 ) present at the level of the juxtamembrane linker region. A majority of the co-evolutionary distance constraints used to derive the model (dashed lines in the figure, listed in Table S1) are satisfied; of the 27 side chain pairs involved, 22 are in contact (minimal distance between heavy atoms (d min ) Ͻ 5 Å), four are in proximity (d min Ͻ 10 Å), and only one pair is separated by over 10 Å (FtsL Gln-66 with FtsB Ile-26). Because an L 3 B 3 hexamer could not be entirely excluded, we also modeled this stoichiometry. The coevolutionary restraints were well satisfied by the resulting model, but the model is significantly underpacked, with the presence of an incomplete pore spanning parts of the TM and coiled coil domains (Fig. S3). For this reason, the L 3 B 3 model was no longer pursued.
The TM region of the L 2 B 2 model forms a helical bundle characterized by a left-handed crossing angle (7°for FtsB and 10°for FtsL, tilt angle of the helices with respect to the membrane normal). The two TM helices of FtsB are in closer proximity to each other compared with the two helices of FtsL (interhelical distance of 13.6 and 15.2 Å, respectively). Remarkably, the conformation of FtsB is similar to a model of a FtsB dimer that we obtained previously (RMSD of 2.5 Å; Fig. S4). This previous model was obtained from the effect of point mutations on the homodimerization of the TM domain of FtsB in the absence of FtsL, as assayed with TOXCAT (38). The convergence of two completely independent sets of data, evolutionary information and experimental mutagenesis, to a similar model is a strong indication that the conformation and interface of the TM helices of FtsB are correctly predicted.
The C-terminal side of the TM region contains a number of side chains that can form hydrogen bonds, including the polar Gln-16. In the lowest-energy model, Gln-16 acts as a hydrogen bond donor to the side chain hydroxyl group of Thr-49 of FtsL (Fig. 4b). Small changes in conformation would allow alternative interactions of Gln-16 with a number of other donor and acceptor groups. In particular, Gln-16 could form self-interactions with Gln-16 from the opposing chain as well as potential hydrogen bonds with Thr-52 of FtsL and Trp-20 of FtsB. Analysis of the stoichiometry of Cy3-and Cy5-labeled FtsLB complexes was performed in DDM detergent. Two independent analyses were performed to count the subunits of FtsL (left) and FtsB (right) by labeling only one of the two proteins of the complex. Left, the FRET data of FtsL fit well to a two-subunit stoichiometry (dashed line, sum of residuals r ϭ 0.0010) with respect to a three-subunit model (continuous line, r ϭ 0.0111). Right, the fit for FtsB establishes that there are at least two subunits but does not differentiate between two-and three-subunit models (r ϭ 0.0055 and 0.0064, respectively). A four-subunit model can be excluded (dotted line, r ϭ 0.0224). Considering prior evidence and likely symmetry, the most likely model for FtsLB is a 2:2 heterotetramer.

Structural analysis of the FtsLB tetrameric complex
As expected, FtsL was modeled as a continuous helix across the TM and coiled coil domains. Also as expected, the change of orientation of the interface between the same two domains of FtsB required the introduction of a break in the ␣-helix in the juxtamembrane region (red in Fig. 4). We opted to model the linker in the least perturbing conformation (an unwound helix), although the Gly-rich linker is likely to adopt a more extended conformation. The relative flexibility of the linker regions of FtsL and FtsB will be addressed later using molecular dynamics. The dashed lines represent the co-evolutionary constraints applied to obtain the model. FtsL (yellow) consists of continuous helices that traverse the membrane into the periplasmic region. The helix of FtsB (blue) is modeled in an unwound conformation in the juxtamembrane Gly-rich region (red). c, detail of the CCD region. If the coiled coil conformation persists beyond this region, the polar side chain of Glu-88 would be buried in the coil's core. d, the lower coiled coil also contains a cluster of very polar amino acids buried in the core (Gln-39 and Asn-41 from FtsB; Arg-67 and Arg-74 from FtsL). These amino acids are likely to be destabilizing if buried in a canonical coiled coil, as represented by the model. e, the TM region contains a cluster of amino acids able to form hydrogen bonds (Gln-16, Tyr-17, and Trp-20 from FtsB; Thr-49, Thr-52, and Thr-56 from FtsL), which may contribute to stabilize this domain.

Structural analysis of the FtsLB tetrameric complex
The periplasmic region (residues 27-61 in FtsB and 58 -91 in FtsL) produced a well-packed canonical coiled coil. The coil is approximately five heptad repeats long (ϳ35 amino acids). Interestingly, the domain is unusually rich in polar amino acids occurring at a and d buried positions, with a total of 12. These polar amino acids are equally contributed by both proteins (three per subunit), although FtsB contains only neutral side chains (Gln-39, Asn-43, and Asn-50), whereas FtsL contains amino acids that are normally charged (Arg-67, Arg-74, and Glu-80). A region around the second and third heptad repeats of the coiled coil is particularly polar, where Arg-67 and Arg-74 from FtsL and Gln-39 and Asn-43 from FtsB occur in close proximity. The presence of so many buried hydrophilic side chains is interesting because they are likely to destabilize the coiled coil. In particular, the four Arg residues contributed by FtsL would be charged even if buried inside the protein core and thus very costly to desolvate (71). Another potentially charged side chain, Glu-80 in FtsL, is in the core in the modeled complex, but it is placed toward the end of the predicted coiled coil, near the CCD region, and thus it may be solvent-accessible.

Molecular dynamics suggest a stable TM region with an intricate network of hydrogen bonding
Two features, the presence of a flexible linker and a potentially destabilized coiled coil, raise questions about the dynamic properties of the FtsLB complex. To address them, we per-formed molecular dynamics (MD) simulations of the FtsLB model in explicit POPE bilayers. For this simulation, we extended the coiled coil conformation by ϳ20 amino acids beyond the region predicted by the co-evolutionary contacts, to avoid end effects and to test the coil boundaries. We will refer to this added region as the "extended coil" (residues 92-110 for FtsL and 62-79 for FtsB) and to the section predicted by the co-evolutionary analysis as the "lower coil" (residues 29 -61 of FtsB and 57-91 of FtsL). Three replica MD simulations were run for 260 ns (run 1; Fig. 5) and for 200 ns (runs 2 and 3; Fig. S5).
During the simulation, the RMSD from the initial structure increases to ϳ4, 5, and 6 Å in the three replica runs (black traces in Fig. 5a and Fig. S5). The majority of these changes are localized to the "extended coil" section (red traces), which quickly separates and partially unfolds. The lower coil remains relatively stable during the run (final RMSD around 2.3, 3.4, and 2.9 Å; green traces). The most stable region is the TM domain, which remains stable for the entire run across all three simulations, with average RMSDs around 1.6, 1.9, and 2.3 Å during the three runs (blue traces).
A slight rearrangement of the relative orientation of the TM helices is observed, which brings the two FtsB helices closer to each other by ϳ1-2 Å and, consequently, further separates the FtsL helices by a similar distance. This rearrangement gives the . The CCD, which separates the lower from the extended coil, is in orange. As evident from the RMSD traces, the TM and lower coil are stable during the simulation, whereas the upper coil diverges, although it retains some helicity and interaction between pairs of FtsL and FtsB chains. The unfolding of the Gly-rich linker in the juxtamembrane region of FtsB is also evident. b, the TM region seen from above the membrane; the region rearranges during the simulation to bring the two FtsB helices (blue) closer to each other and in contact, whereas the FtsL helices are now separated from each other. c, a configuration of the extended hydrogen bonding network present in the C-terminal side of the TM region, involving Gln-16, Tyr-17, and Trp-20 of FtsB and three threonine residues (Thr-49, -52, and -56) of FtsL. d, a view of the water that invades the core of the lower coiled coil, hydrating otherwise buried side chains or Arg-67, Arg-74, Gln-39, and Asn-43.

Structural analysis of the FtsLB tetrameric complex
bundle a less "square" and more "rhomboid" configuration, one in which extensive packing occurs not only between FtsL and FtsB but also between the two FtsB helices, whereas the contacts between the two FtsL helices become reduced (Fig. 5b). With the two helices of FtsB in closer proximity, their conformation becomes even more similar to our previous model of an FtsB dimer (RMSD ϳ2 Å; Fig. S4b) (38).
A second important change that occurs in the TM region during the MD runs is a rearrangement and expansion of the hydrogen-bonding network. In the C-terminal section of FtsLB, there are 12 side chains in close proximity that are able to hydrogen-bond (three from each helix: Gln-16, Tyr-17, and Trp-20 in FtsB and three threonines, Thr-49, -52, and -56, in FtsL). With the exception of Trp-20, all of these side chains have both donor and acceptor groups. In addition, Gln-16 is also very flexible. Therefore, the network can rearrange in multiple configurations. Fig. 5c illustrates one of the configurations observed, which displays a total of seven interhelical hydrogen bonds. The configuration of the hydrogen-bonding network varies over the simulations, but some interactions are predominant during the runs (Table S2). The most persistent interaction is between Tyr-17 of FtsB subunit A and the side chain of Thr-52 of FtsL subunit C (Tyr-17 of subunit B prefers to interact with the backbone carbonyl of Leu-48). Gln-16 interacts primarily with the side chain hydroxyl groups of Thr-49 and Thr-52 from FtsL and with Gln-16 from the opposed FtsB helix. Trp-20 primarily donates to the side chain hydroxyl group of FtsL Thr-56, but it can also donate to the carbonyl group of Gln-16 side chain. This extended network of hydrogen bonds is likely to contribute significantly to the association of the TM region, which can form a stable oligomer in isolation in vitro (43).
As a control, we also performed a 160-ns simulation of a structural model that has comparably low energy but does not satisfy the evolutionary constraints in the TM region ("bad" model; Fig. S5d). The TM region rearranges away from the initial model relatively quickly, reaching an RMSD of Ͼ3 Å in the first 60 ns. Its average (2.8 Å) and maximum (3.5 Å) are higher than the RMSD of the TM region in the three replica runs of the "good" model (1.6, 1.9 and 2.3 Å, with maxima of 2.1, 2.4, and 2.7 Å, respectively).

A continuous FtsL helix and a dynamic coiled coil
Different sections of the coiled coil behave differently during the MD runs. These are notable in the helicity analysis presented in Fig. S6. The "extended coil" (the region that extends beyond the pattern of co-evolutionary contacts consistent with a coiled coil (Fig. 2)) unfolds partially as a bundle during the runs, although the region retains substantial helicity, and interactions still occur between pairs of FtsL and FtsB helices. The likely occurrence of a breakage of the helix between the "lower" and the "extended" coil regions was also hypothesized by a previous modeling analysis of the periplasmic region of the FtsLBQ complex (55). Interestingly, the location of the transition between these two regions roughly corresponds to the CCD.
The lower coil remains more stable during the run (final RMSD around 2.3, 3.4, and 2.9 Å). However, notable changes occur even in this region, providing further indication that the FtsLB complex may not be built to form a rigid, canonical, tetrameric coiled coil. Partial unfolding of the FtsL helix is observed in subunit C, and occasional unfolding is also notable in both FtsL subunits in the third replica run.
In the transition between the TM and coiled coil domains, the segment of 5-10 amino acids centered around the Gly-rich section of FtsB rapidly unfolds from the "unwound helix" conformation imposed by the modeling, unlinking the two domains and adopting a flexible and extended conformation (Fig. 5a). Conversely, the juxtamembrane region of FtsL remains stable as a continuous helix throughout the duration of all three replica runs. The unfolding of the Gly-rich linker of FtsB creates an opening that allows water to access the core of the four-helix bundle (Fig. 5d). Water molecules penetrate deeply up into the core of the coil, solvating the strongly polar side chains that would otherwise be buried in the structure (Arg-67 and Arg-74 from FtsL and Gln-39 and Asn-43 from FtsB, "polar core" in Fig. 5d). In this region near the membrane, the coil becomes essentially separated by the water into two two-helix bundles. Water is excluded from the above layer, where the four-helix bundle becomes compact again around a hydrophobic core consisting of Leu-46 from FtsB and Leu-77 and Trp-81 from FtsL ("hydrophobic core" in Fig. 5d).
With all caution in drawing conclusions from a theoretical model, it appears unlikely that a core so enriched in strongly polar amino acids would produce a very stable coiled coil. A possibility is that the stability of the coil is purposely "detuned" because the function of the FtsLB complex requires a weak coil, possibly to allow for a conformational change. A second hypothesis is that the region is actually designed to split into two separate two-helix coils. This split is most evident, as illustrated in the last frame of MD run number 3 (Fig. S5). A "split" coiled coil would be consistent with the observation that a solubilized version of the periplasmic region of FtsLB forced into a heterodimeric form binds to FtsQ with high affinity (49 -51), suggesting that association with FtsQ may be mediated by two independent binding domains of FtsLB. Such an organization would designate the TM region as the major factor driving tetramerization.

Functional analysis: The effect of mutations in the TM region is consistent with the predicted interface
To investigate how the model's structural features support the function of FtsLB, a series of rationally designed variants of the complex were tested in vivo for their ability to support cell division. Because FtsL and FtsB are essential proteins, the mutant proteins were introduced into strains in which a chromosomal copy of the wildtype protein is under the control of a repressible promoter (45, 47). This allows for the depletion of the wildtype copy and the induction of the mutant version to reveal its phenotype. The expectation is that the most severe mutations will produce cells that elongate but are unable to divide, resulting in the formation of very long filaments, whereas less severe mutations will allow the cells to divide but will produce subpopulations of elongated cells. To assess each mutant, we measured the distri-

Structural analysis of the FtsLB tetrameric complex
bution of cell lengths, as exemplified in Fig. 6a for the L15A mutant of FtsB. The data for each individual mutant are reported in Fig. S7.
Although none of the point mutations caused filamentous phenotypes, many produced elongated cells. To determine whether the difference between each mutant's and the wildtype's length distributions was significant, we used the Mann-Whitney U test (72). However, as a consequence of the very large sample size of each experiment (500 to Ͼ1,000 cells), minuscule differences can be statistically significant even if they are not biologically relevant. To overcome this issue, we adopted an operative classification based on the fraction of elongated cells observed for each variant. We defined as "elongated" those cells that are longer than the 95th percentile in the distribution of wildtype cell length (Fig. 6a). Based on this threshold, we defined phenotypes as "mild temperature-sensitive" (Mild T.S.) when Ͼ15% (i.e. Ͼ3-fold compared with the wildtype) of cells were elongated only at the less permissive temperature of 42°C; as "mild" when Ͼ15% of cells were elongated at 37°C; as "intermediate" when Ͼ25% of cells were elongated (Ͼ5-fold); as "severe" when over 50% of the cells were elongated (Ͼ10 fold); and, finally, as "filamentous" when all cells were filamentous. The example of Fig. 6a, which has 72% elongated cells at 37°C, is therefore classified as "severe." The fractions of elongated cells for each variant in the TM region of FtsL and FtsB are reported in Fig. 6b, with the relative classification reported at the bottom. The variants include a variety of drastic small-to-large amino acid changes (such as A10F in FtsB and L38W in FtsL), large-to-small changes (such as W14A and L8A in FtsB), and some conservative mutations (such as L19I in FtsB). We expected to observe division phenotypes when mutations affected the packing or hydrogen bonding at positions that mediate interaction between the helices. The results are in good agreement with this prediction. First, all positions that displayed impaired cell division phenotypes (Leu-8, Leu-12, Leu-15, Gln-16, and Trp-20 in FtsB; Leu-38 and Leu-42 in FtsL (Fig. 6b)) occur at the helix-helix interfaces, as illustrated schematically in Fig. 6c. In addition, all positions predicted to be away from the interface and exposed solely to lipids are classified as indistinguishable from wildtype (Leu-7, Ala-10, and Trp-14 in FtsB; Phe-43 and Ile-47 in FtsL). However, some of the TM region mutations that were predicted to be detrimental displayed little or no effect (e.g. Q16M, W20A, C45W, and T49W). This is particularly noticeable for the C-terminal side of the TM bundle, a section characterized by an extensive hydrogen bonding network (Fig. 5c). Mutations of Thr-49, Thr-52, and Thr-55 of FtsL and Tyr-17 of FtsB have no effect, and those of Gln-16 and Trp-20 of FtsB have little or no phenotype. Even a double mutation (Q16M/Y17F or Q16A/ Y17F) that removes two hydrogen bonding groups is completely tolerated.
The finding is surprising because the C-terminal side of the TM bundle is the region with the highest number of co-evolutionary "connections," suggesting that these positions would be structurally or functionally important. Moreover, Gln-16 and Trp-20 of FtsB, are nearly absolutely conserved in proteobacteria (38). A potential explanation is that the hydrogen bonding network may be sufficiently robust, extensive, and plastic to accommodate changes. Because of the large network, the removal of some donors and acceptors may not be sufficiently detrimental to destabilize the complex. Conversely, the N-terminal region, which is mediated exclusively by packing of hydrophobic residues, could be more sensitive to disruption of the complementary side chain packing. It is also possible that thermodynamic stability of the TM region is not strictly required for function, at least in the conditions tested.
To investigate whether there is an overall correspondence between the observed biological phenotypes and predictions based on the structural model, we calculated mutational energies in silico for all TM mutants and compared them with the fraction of elongated cells observed for each variant (using the 42°C data to maximize the dynamic range of the experimental observations). We calculated the energies using a rigid-body model without backbone movement as well as with FoldX, a method specifically calibrated to calculate the folding stability of protein mutants (73). The data are plotted in Fig. S8. The energies produced by FoldX statistically correlate with the severity of the phenotypes by rank order Spearman correlation coefficient analysis (r ϭ 0.4631, n ϭ 29, p Ͻ 0.01) (74). We conclude that perturbation of stability estimated on the basis of the structural model is a reasonably good predictor of the functional state of FtsLB.

The juxtamembrane and coiled coil of FtsB are tolerant to mutation
We applied a similar mutational approach to investigate the functional importance of the coiled coil and of the juxtamembrane region. The results are reported in Fig. 7 (and Fig. S7). We first tested whether the evolutionarily conserved Gly-rich juxtamembrane linker of FtsB ( 22 GKNG 25 ) is essential. A potential role for Gly is to provide structural flexibility, as suggested by our MD simulations. Alternatively, because of glycine's less restrictive Ramachandran distribution, this amino acid can also be required in a rigid structure to enable conformations of the backbone that are forbidden to all other amino acids.
We tested individual and double Gly-to-Ala mutations at positions 22 and 25. They presented either no defects (G22A and G22A/G25A) or a mild TS phenotype (G25A) (Fig. 7a). A possible explanation is that the structure of the linker retains sufficient flexibility even when Gly-22 and Gly-25 are substituted by Ala. To further test the flexibility of the linker, we inserted a series of Ala residues (up to three) between the TM domain and the coiled coil region (between positions Phe-21 and Gly-22), with the rationale that insertions should be better tolerated in a flexible region. The cells appear largely unaffected by the changes (only the two-Ala insertion mutation displays a mild TS phenotype; Fig. 7b). The outcome is therefore consistent with a flexible FtsB linker and confirms the presence of a helical break between the membrane and periplasmic domains of FtsB. These observations are not consistent with the alternative hypothesis that Gly is required to enable a rigid backbone conformation.
We also applied this Ala insertion strategy to test the coiled coil region of FtsB. A single additional Ala residue was inserted between the b and c positions (i.e. in a position that is solvent-Structural analysis of the FtsLB tetrameric complex exposed) of each of the five heptad repeats. Most of these five insertion mutants did not display any impairment, with the exception of a mild TS phenotype for the second heptad insertion after position Ala-37 (Fig. 7c). Overall, the analysis suggests that the coiled coil of FtsB is likely to be quite plastic and able to tolerate insertion mutations all along its length.

Integrity of the juxtamembrane and coiled coil regions of FtsL is essential for function
Whereas the juxtamembrane and coiled coil domains of FtsB appeared tolerant to insertion, the opposite was observed for FtsL. We first introduced single, double, and triple Ala insertion mutations in the juxtamembrane region of FtsL (between positions Ala-57 and His-58). If the helix of FtsL is uninterrupted, the insertions should introduce strain into the structure because they would either produce a 100°rotation of the helix for each additional Ala or, more likely, introduce distortions into the helix. We observed that all insertion mutants, even the single Ala insertion, produced cells that were completely filamentous (Fig. 7, b and cell images in c). These are the most dramatic phenotypes observed in the whole study. The results are consistent with the hypothesis that FtsL forms an uninterrupted helix that runs through the membrane and periplasmic regions.
We also tested the juxtamembrane linker of FtsL with a series of point substitutions (H58A, H59A, and T60A; Fig. 7a). Interestingly, we observed some degree of functional disruption, particularly with the H59A mutation, which displays a 7-fold increase in the number of elongated cells compared with wildtype at 37°C. In our model, His-59 is solvent-exposed and engaged only in minor interactions with the FtsB helix. It is possible that this position is important for interactions with other components of the divisome, possibly with the periplasmic domain of FtsQ, which was shown to cross-link with this region of FtsL (48).
Finally, we scanned the entire coiled coil region of FtsL by Ala insertion (Fig. 7c), as we did with FtsB. We observed a severe phenotype for the first heptad insertion, a mild phenotype for the second heptad insertion, and a wildtype phenotype for the third heptad insertion. A completely filamentous phenotype is then observed when Ala is inserted in the fourth heptad repeat (after position Arg-82). It is difficult to speculate what might cause such a dramatic defect, but we note that the mutation is in proximity to the CCD region of FtsL (residues 88 -94, highlighted in orange in Fig. 7e). Insertion at position 89, which is within the CCD and which would correspond to the fifth heptad, if the coiled coil persisted in this region, produced a mild phenotype (ϳ4-fold increase in elongated cells). Overall, the periplasmic coiled coil of FtsL is sensitive to mutation, whereas the same domain of FtsB is tolerant, as schematically illustrated in Fig. 7e. Interestingly, this outcome is the opposite of that observed for the mutagenesis of the TM region, where FtsB was the sensitive subunit, compared with the much milder phenotype displayed by FtsL (Fig. 6).

Conclusions
The topology of the FtsLB complex, a helical bundle spanning the membrane and periplasmic space, with terminal tails available for binding other components, is widely conserved evolutionarily (6,50). The widespread occurrence of FtsLB across a broad variety of bacterial species with different cellular envelopes implies that this specific domain organization fulfills some important functional purpose, which is still unknown. To investigate this question, we have analyzed the structure-function relationship of the extended helical region of FtsLB, revealing a number of important features regarding the organization of the complex.
This study confirms that FtsLB is a higher-order oligomer and provides evidence that the complex consists of a heterotetramer. It identifies with a high degree of confidence the interface of the helical bundle region of the complex. It also produces a structural model of FtsLB validated experimentally through functional analysis. Further validation is also provided by a notable convergence of features in FtsB (the conformation of the TM helices and the presence of a flexible linker) that were also predicted in a prior model of FtsB based on a completely orthogonal set of experimental data (38).
The number of strongly polar, and even charged, amino acids that are predicted to be buried in the core of the coiled coil is a surprising and probably important finding, suggesting that the coil region may not be built for enhanced structural stability. A structural alternative to a monolithic four-helix coil could be the formation of two independent "dimeric" branches formed by one FtsL and one FtsB subunit. This possibility is consistent with previous observations that FtsLB fragments can bind to FtsQ with high affinity even when forced in a heterodimeric state (49 -51).
We found that the integrity of the extended helix of FtsL is essential for the complex. A continuous helix is probably important for structural stability; given that the juxtamembrane linker of FtsB is disordered, a stable FtsL helix is probably necessary for nucleating the coiled coil. This hypothesis is in good agreement with the observation that amino acid insertions are most detrimental at the base of this domain. The helix of FtsL is also an interesting candidate for acting as a mechanical connection that could propagate a postulated allosteric conformational change (41,42) across the periplasmic, TM, and cytoplasmic regions. For example, the cytoplasmic region of FtsL is important for the recruitment of FtsW (47); therefore, it is possible that FtsLB could control the activation of the The distribution of cells lengths is compared between the wildtype (aqua) and the mutant (magenta). L15A displays 72% of cells that are longer than the 95th percentile in the wildtype distribution (colored areas, past the dotted line). As such, it is classified as a "severe" mutation. Graphs for each individual mutant are provided and explained in detail in Fig. S7. Scale bar, 5 m. b, phenotypes of TM domain mutants at 37 and 42°C growth conditions. Classification is indicated using filled circles below. Filamentous, all cells are elongated at 37°C; Severe, Ͼ50% of the cells are elongated; Intermediate, Ͼ25% of cells are elongated at 42°C; Mild, Ͼ15% of cells are elongated at 42°C; mild temperature-sensitive (Mild T. -S.), Ͼ15% of cells are elongated at 42°C. c, location of the mutations within the structure of the TM domain. All mutations that display a cell division phenotype map within the interface of the helical bundle. All mutations on the outer surface of the bundle display As WT phenotypes.  Fig. 6. Graphs for each individual mutant are provided in Fig. S7. b, alanine insertion mutation (1-3 extra residues) in the same region. c, Ala insertion mutations in the coiled coil region (operated between positions b and c in the heptad repeats). d, representative images of Ala insertion mutants in the linker and periplasmic coiled coil of FtsB and FtsL. Images for all mutants are provided in Fig. S7. e, observed phenotype of the mutants mapped onto the molecular model. Constriction control domain is displayed in orange. The evidence is consistent with a flexible linker in FtsB, with the presence of a helical break, and with an uninterrupted helix that runs through the membrane and periplasmic regions for FtsL.

Structural analysis of the FtsLB tetrameric complex
FtsWI peptidoglycan synthase complex through direct interaction by coordinating a signal from the periplasm (i.e. interaction with FtsN). This study provides the structural groundwork necessary for investigating this and other hypotheses with coordinated biophysical and functional studies, which are necessary to finally clarify the precise role and the molecular mechanisms of the FtsLB complex in bacterial cell division.

Co-evolutionary analysis
Sequences of FtsL and FtsB homologues were collected using the DELTA-BLAST algorithm on the RefSeq database (75). These sequences were filtered to include only proteobacterial species and then concatenated by matching the organism name in each record. The paired sequences were then aligned using the ClustalW algorithm with five guide tree and five hidden Markov model iterations (76). Columns in the alignment with a gap fraction higher than 0.3 were masked. This paired multisequence alignment was analyzed with the EV-Couplings algorithm (56) using default parameters and ignoring membrane topology, which would otherwise assume that sequential TM domains are anti-parallel. The top 95 (the number of unmasked columns in the multisequence alignment divided by 2) evolutionary constraints (i.e. the co-varying residues) predicted by EV-Fold between FtsL and FtsB were used for analysis and molecular modeling. The paired alignment is provided as a supplementary FASTA file. A total of 1291 sequences were used in the alignment. The number of effective sequences after reweighting for similarity is 883.1, corresponding ϳ4.6 sequences/residue. From this, ϳ40% of the top 95 contacts are estimated to be false positive pairs in the co-evolutionary analysis (77).

Modeling the TM region of FtsLB
All modeling was performed using programs written in the Molecular Software Library (MSL) (78). For the TM domain, ideal helices corresponding to residues 1-21 of FtsB and residues 35-58 of FtsL were generated. C 2 rotational symmetry (or C 3 , in the case of the hexamer) was preserved around the z axis for FtsB helices and FtsL helices. The geometry of the FtsL and FtsB bundles was defined by the following parameters: interhelical distance (d); rotation around the helical axis (); crossing angle (), and position of the crossing point (s). Additionally, the orientation of the FtsL and FtsB bundles were changed by operating a rotation (⍀) and a translation (S) of each helix bundle about the z axis.
Starting from an initial random assignment of the parameters, the FtsLB TM helix complex was optimized using a Monte Carlo procedure that altered the interhelical geometry. The conformation of the side chains was periodically optimized with a 5% probability after each move. Side chain optimization was performed with a greedy trials algorithm using the backbone-dependent Energy-Based Conformer Library (bEBL) applied at the SL80 level (79,80). Energies were calculated using the CHARMM 22 van der Waals function (81) and the hydrogen-bonding function of SCWRL 4 (82) as implemented in MSL. Additionally, sigmoidal distance restraints were placed between the C␣ atoms of each pair of top co-evolving positions (83), using the following form, where E sigmoidal is the additional energy term, w is the weight, a is the slope, C is the intercept, r is the distance between the atoms, and r 0 is the distance cutoff. For these experiments, w was set to 10 kcal/mol, a was set to 0.5 Å Ϫ1 , C was set to Ϫ2.5 kcal/mol, and r 0 was set to 10 Å.
For each pair of co-evolving residues, there are multiple pairs in the complex corresponding to the same residues on different chains. Only the restraints with the lowest energies for each pair were added to the energy score, whereas the remaining ones were masked. The evolutionary constraints are listed in Table  S1. Models were sorted by energy and clustered using a greedy algorithm and a C␣ RMSD threshold of 2.5.
As a negative control for the molecular dynamics simulations, a second model of the TM domain was produced by identifying a conformation with comparable energy of the initial model but with poor agreement with the co-evolutionary data (bad model). In this model, only one pair of co-evolving positions had a minimum heavy atom distance below 5 Å, and only two pairs had C␣ distances below 10 Å, whereas all pairs satisfy these conditions in the good model.
In silico mutational energies for the mutants in the transmembrane region were calculated in two ways. Rigid-backbone repacking was performed using MSL. Point mutations of interest were generated, and neighboring side chains were repacked using 100 rounds of a greedy trials algorithm. Mutated residues were repacked at the SL99 conformer level of the bEBL library; residues within 8, 16, and 20 Å were repacked at the SL95, SL90, and SL80 levels, respectively. van der Waals radii were scaled by 0.8. Energies of the mutants were subtracted from that of the wildtype to calculate their ⌬⌬E. Mutations were also analyzed using the FoldX Suite (73). The models were first energy-minimized using the RepairPDB command with the membrane parameter set to true. Mutant ⌬⌬G calculations were performed using the buildModel command with the membrane parameter set to true.

Modeling the coiled coil domains of FtsL and FtsB
Supercoiled helices corresponding to residues 52-94 of FtsL and 21-63 of FtsB were generated by using a coiled coil generator based on a coiled coil parameterization described previously (84). The superhelical radius (r 1 ), superhelical pitch (P), helical rotation (⌽ 1 ), and z-shift (s) of both FtsL and FtsB were freely altered, whereas the rise per residue (h) and helical radius (r 0 ) were kept constant. Additionally, the orientation of the FtsL and FtsB bundles were changed by operating a rotation (⍀) and a translation (S) of each helix bundle about the z axis. C 2 symmetry (C 3 for the hexamer) was preserved within the FtsL backbones and the FtsB backbones.
The coiled coils were optimized using a Monte Carlo procedure, changing their superhelical parameters starting from an initial assignment of random parameters. Side-chain conformational sampling was performed with a variable number of

Structural analysis of the FtsLB tetrameric complex
conformers with the positions that participate at a canonical coiled coil interface receiving higher sampling; the a and d positions were sampled at the SL80 conformer level of the bEBL library, e and g positions at the SL75 level, b and c at the SL70 level, and f at the SL60 level. Energies were calculated based on CHARMM 22 van der Waals and CHARMM 22 electrostatic terms. Additionally, sigmoidal restraints for each co-evolving pair in the coiled coil region were added, as described above.

Modeling the juxtamembrane regions of FtsL and FtsB
Top models of the TM and coiled coil domains were connected by aligning the helical residues 52-58 of FtsL, which were present in the models of both regions. The RMSD between the C␣ atoms of these residues was minimized while keeping the main axis of both domains parallel to and centered on the z axis. The juxtamembrane regions of FtsL and FtsB were then replaced with loops corresponding to fragments from the PDB, as described previously (38). For FtsB, six-residue loops, corresponding to positions 21-26, with four flanking helical residues on each side, were used, with an additional sequence requirement that the fragment contain at least one glycine. For FtsL, 15-residue fragments with four flanking helical residues on each side were used with the requirement that the loop have helical secondary structure. Long helix fragments were used to better distribute minor deviation in alignment between the transmembrane and coiled coil helices. The connecting regions were optimized based on a greedy trials algorithm to minimize steric clashing, and the final model was minimized using BFGS constrained optimization using CHARMM (85). Structural voids were analyzed using BetaCavityWeb (86). For the creation of the bad model, the TM model that did not satisfy the co-evolutionary constraints was aligned and connected to the same model of the coiled coil domain using an identical procedure.

All-atom molecular dynamic simulations
For the molecular dynamics simulations, the model's coiled coil region was extended, to avoid edge effects, to residues 110 (FtsL) and 79 (FtsB). The cytoplasmic side of FtsL was also extended to include residues 30 -34, modeled in ideal ␣-helix. Four all-atom MD simulations (a 260-ns run, two 200-ns replica runs, and a 160-ns control run on the control bad model) were performed using the CHARMM 36 force field and NAMD version 2.10 software (87,88). CHARMM-GUI membrane builder (89) was used to prepare systems composed of a POPE bilayer consisting of 301 lipids, the FtsLB tetramer, an ionic concentration of 0.150 M NaCl, and 59,034 TIP3P water molecules for hydration. The sizes of the boxes at the beginning of the simulation were ϳ97 ϫ 97 ϫ 242 Å 3 for runs 1, 2, and 3 and 97 ϫ 97 ϫ 245 Å 3 for the control run. The simulations were initially minimized and equilibrated for 75 ps at an integration time of 1 fs/step and for 600 ps at an integration time of 2 fs/step. The integration time step for the production runs of each of the systems was 2.0 fs/step. The simulations were carried out in the NPT ensemble at a pressure of 1 atmosphere and a temperature of 310.15 K, using the Nose-Hoover Langevin piston and Langevin dynamics method. Particle mesh Ewald was used for electrostatic interactions, and a 12-Å cutoff was applied to Lennard-Jones interactions with a switching function from 10 to 12 Å. The RMSD analysis was performed using the RMSD trajectory tool in VMD (90). Hydrogen-bonding analysis was performed with an in-house script.
Helicity analysis was performed by measuring the backbone dihedrals and the distance between O i and N i ϩ 4 for each residue in each selected frame of the simulation. If the O i -N i ϩ 4 distance was between 2.0 and 4.2 Å and the backbone dihedral angles were within the favored ␣-helical region as defined in PROCHECK (91), the residue was classified as helical. If the O i -N i ϩ 4 distance was within 5 Å and the backbone dihedral angles were within either the favored or allowed ␣-helical region, the residue was classified as near-helical. Otherwise, the residue was classified as non-helical.
The plasmids were transformed into BL21 (DE3) cells. Individual colonies were picked and grown overnight in 3 ml of LB broth containing 100 g/ml of ampicillin before being diluted 1:500 in 1 liter of ZYP-5052 autoinduction medium as described (92), and grown at 37°C until reaching an A 600 of 0.8, after which it was incubated for an additional 20 h at 25°C. The cells were then lysed by sonication in 10 ml/g lysis buffer (50 mM NaCl, 50 mM HEPES, 10 mM TCEP, brought to pH 7.0 with NaOH) supplemented with 0.25 mg/ml lysozyme, 5 mM ␤-mercaptoethanol, and 1 mM phenylmethylsulfonyl fluoride. The inclusion body fraction was separated by centrifugation at 10,000 ϫ g for 20 min, followed by ultracentrifugation of the supernatant at 130,000 ϫ g for 30 min to isolate the cell membranes. The FtsLB complex was then extracted from the membrane fraction with lysis buffer supplemented with 18 mM n-decyl-␤-D-maltopyranoside (DM; Anatrace) and 10 mM TCEP, rocking at 4°C overnight. Solubilized protein was added to 3 ml of Ni-NTA-agarose resin (Qiagen) and rocked for 2 h at 4°C before the resin was washed and the complex was labeled oncolumn with either Cy3 or Cy5 maleimide (Lumiprobe) for FtsB or FtsL. On-column fluorophore labeling was performed by running 3 column volumes of Ni wash buffer (300 mM NaCl, 25 mM HEPES, pH 8.0, 50 mM imidazole, 10 mM TCEP, brought to pH 7.0 with NaOH) supplemented with 5.

Structural analysis of the FtsLB tetrameric complex
Labeling efficiency of each fraction was quantified by UVvisible spectroscopy, using absorbance at 280 nm (protein), 550 nm (Cy3), and 650 nm (Cy5). First, the concentration of the protein was calculated, taking into account the absorbance of the fluorophore, where A 280 is the absorbance at 280 nm, A Cy is the absorbance at 550 nm (Cy3-labeled samples) or 650 nm (Cy5-labeled samples), ⑀ 280 is the molar extinction coefficient of FtsLB at 280 nm (32,430 M Ϫ1 cm Ϫ1 ), and CF Cy is the appropriate correction factor (CF Cy3 ϭ 0.11 and CF Cy5 ϭ 0.05) to subtract the contribution of the fluorophore to absorbance at 280 nm. Then the labeling efficiency P Cy was calculated according to the following, where ⑀ Cy is the molar extinction coefficient of the fluorophore (⑀ Cy3 ϭ 150,000 M Ϫ1 cm Ϫ1 at 550 nm, ⑀ Cy5 ϭ 250,000 M Ϫ1 cm Ϫ1 at 650 nm). Cysteine-less versions of the FtsL and FtsB constructs were also purified and labeled three times with the same protocol to determine background labeling, which was negligible.
A second round of purification could be performed by loading the Ni-NTA-purified FtsLB complex over a streptavidin column. The most concentrated Ni-NTA elution fractions were added to 3 ml of streptavidin resin and rocked for 2 h at 4°C before being washed with 3 column volumes of streptavidin buffer (20 mM Tris, 300 mM NaCl, 0.1 mM EDTA, 0.5 mM TCEP, brought to pH 8.0 with NaOH) with 450 M DDM, followed by elution with 3 column volumes of streptavidin buffer plus 2.5 mM desthiobiotin (initially dissolved in 1 ml of DMSO) and 450 M DDM. Samples from each fraction of the nickel and streptavidin column were boiled in 4ϫ SDS-PAGE loading buffer before being run on NuPage 4 -12% BisTris protein gels at 150 V for 1 h (Thermo Fisher Scientific). Because the FtsLB complex obtained after Ni-NTA had sufficient purity for FRET studies, this second chromatography was not routinely performed, but it was used initially to confirm the stability of the FtsLB complex.

FRET measurements
In all experiments, the FtsLB complex was diluted to 1.35 M in FRET buffer, which contains 450 M DDM, for a final protein/detergent molar ratio of 1:333. Experiments were performed by labeling either the FtsL moiety (FtsL-C41A/C45A/ I100C ϩ FtsB) or the FtsB moiety (FtsL-C41A/C45A ϩ FtsB-S97C) in the protein complex. All FRET analysis was performed on an M1000 Tecan plate reader, with excitation set at 550 nm and emission recorded from 560 to 800 nm in 1-nm increments.
The stoichiometric analysis of FtsL was performed by mixing FtsL Cy3 -FtsB unlabeled (donor) and FtsL Cy5 -FtsB unlabeled (acceptor) samples in different ratios, from 20:80 donor/acceptor up to 90:10, in 10% increments. To determine donor fluorescence in the absence of the acceptor, equivalent samples were produced by mixing FtsL Cy3 -FtsB unlabeled (donor) and FtsL unlabeled -FtsB unlabeled (unlabeled) in the same molar ratios. The stoichiometric analysis of FtsB was performed similarly. Donor (Cy3) fluorescence was recorded using its peak emission at 570 nm. Quenching (Q) of the donor fluorophore was calculated, as explained below, according to Equation 6, from donor/acceptor-labeled protein sample mixes (F) and donor/unlabeled protein sample mixes (F 0 ). Each experiment was independently replicated at least five times.

Fitting of experimental FRET data to obtain the number of subunits
Fitting for different oligomeric states was performed as described by Adair and Engelman (68), where Q is related to the molar fluorescence of the quenched donor (f Q ) in the presence of the acceptor, the molar fluorescence of the donor f D in the absence of acceptor, the number of subunits in the oligomer n, and the molar fraction of donorlabeled protein P D . P D was calculated as follows, where [D] is the molar concentration of donor-labeled protein and [A] is the molar concentration of acceptor-labeled protein.
Relative quenching was calculated as follows, where F is the experimentally measured quenched fluorescence for a certain donor/acceptor molar fraction and F 0 is the experimentally measured unquenched fluorescence of the same amount of donor, obtained in the absence of acceptor and in the presence of an equivalent amount of unlabeled protein. In  Equation 4, the quantity related to the molar fluorescence can be treated as an overall unknown constant k.
The parameter k was thus fit using a least square procedure to the experimental data Q as a function of donor fraction P D according to Equation 8 for the different oligomeric states n.

Structural analysis of the FtsLB tetrameric complex
The relative quality of the fits to different oligomeric states was assessed by comparing the sum of the squared residuals between the experimental data and the models.

Bacterial strains, plasmids, and media for in vivo experiments
The phenotypic analysis was performed using depletion strain NB946 for FtsB (7) and MDG277 for FtsL (45). For all experiments described, bacterial cells were grown in LB medium supplemented with 100 g/ml spectinomycin (Dot Scientific) and the appropriate carbon source. Medium was supplemented with 0.2% (w/v) L-arabinose (Sigma) or 0.2% (w/v) D-glucose (Sigma) to induce or repress, respectively, the expression of chromosomal copies of the wildtype genes regulated by the PBAD promoter. 20 M isopropyl-␤-D-1-thiogalactoside was added to the media to induce the expression of mutant genes regulated by the pTrc promoter in the plasmid. Point mutants and insertion mutants of FtsL and FtsB were constructed in plasmid pNG162 (45) using either standard QuikChange mutagenesis or inverse PCR mutagenesis.

Depletion strain experiments
The protocol for the depletion strain experiment was adapted from Gonzalez and Beckwith (45). In short, a mutated copy of FtsB or FtsL was transformed into its respective depletion strain. Strains were grown overnight at 37°C on an LB plate supplemented with arabinose and spectinomycin. A single colony from the plate was grown overnight at 37°C in 3 ml of LB medium supplemented with arabinose and spectinomycin. The overnight culture was then diluted 1:100 into fresh LB medium containing the same supplement and grown to an A 600 of ϳ0.3. An aliquot of 1 ml of culture was washed twice with LB medium lacking any sugar and then diluted 1:100 into 3 ml of fresh LB medium supplemented with glucose and isopropyl-␤-D-1-thiogalactoside to induce the expression of the mutated gene and the repression of the wildtype gene. The cells were then grown at 37 or 42°C for 3.5 h before microscopy, the approximate time necessary to deplete the cells of the wildtype chromosomal copy (45). Depletion strains provided with their respective wildtype copy of the protein in the plasmid were tested as positive controls, and, similarly, depletion strains with no protein in the plasmid (empty vector) were tested as negative controls.

Microscopy and cell length measurement
10 l of cell samples were mounted on a number 1.5, 24 ϫ 50-mm (0.16 -0.19-mm thickness) coverglass slide (Fisher). Cells were cushioned with a 3% (w/v) agarose gel pad to restrict the movement of the live cells. Cells were optically imaged using a Nikon Eclipse Ti inverted microscope equipped with crossed polarizers and a Photometrics CoolSNAP HQ2 CCD camera using a Nikon ϫ100 oil objective lens. Phase-contrast images of bacterial cells were recorded with a 70-ms exposure time using Nikon NIS Elements software. Multiple snapshots were collected for each experiment. All images were analyzed to measure the cell length in Oufti (93) using one single optimized parameter set.

Whole-cell lysate preparation and Western blotting
Expression level across all variants was assessed by Western blot analysis (Fig. S9). 3.0 ml of cells were pelleted and resus-pended in 500 l of sonication buffer (25 mM Tris-HCl, 2 mM EDTA, pH 8.0). The cells were sonicated and centrifuged at 16,000 ϫ g for 5 min before collecting the supernatant. Total protein concentration was determined by BCA assay (Pierce). 150 l of lysates were mixed with 50 l of 4ϫ LDS sample buffer (Novex, Life Technologies) and boiled at 95°C for 5 min. For each sample, the equivalent of 10 g of total protein was separated by SDS-PAGE (Invitrogen) and transferred to polyvinylidene difluoride membrane (VWR). Horseradish peroxidase-tagged anti-FLAG (M2) antibodies (Sigma; 1:1,000) were used for immunoblotting analysis.