Simulations suggest a constrictive force is required for Gram-negative bacterial cell division

To divide, Gram-negative bacterial cells must remodel cell wall at the division site. It remains debated, however, whether this cell wall remodeling alone can drive membrane constriction, or if a constrictive force from the tubulin homolog FtsZ is required. Previously, we constructed software (REMODELER 1) to simulate cell wall remodeling during growth. Here, we expanded this software to explore cell wall division (REMODELER 2). We found that simply organizing cell wall synthesis complexes at the midcell is not sufficient to cause invagination, even with the implementation of a make-before-break mechanism, in which new hoops of cell wall are made inside the existing hoops before bonds are cleaved. Division can occur, however, when a constrictive force brings the midcell into a compressed state before new hoops of relaxed cell wall are incorporated between existing hoops. Adding a make-before-break mechanism drives division with a smaller constrictive force sufficient to bring the midcell into a relaxed, but not necessarily compressed, state.


35
Bacterial cells are protected from turgor pressure by a peptidoglycan (PG) cell wall that is composed of 36 long glycan strands crosslinked by short peptides (Vollmer et al., 2008). This relatively rigid sacculus 37 allows cells to adopt specialized shapes, such as the rod shape of many Gram-negative bacteria. In order 38 for the cell to change size or shape during growth and division, the pressurized sacculus must be 39 carefully remodeled. This is accomplished by a set of cell wall remodeling enzymes including 40 transglycosylases, transpeptidases, and endopeptidases. Experimental insights into the exact molecular 41 mechanisms of these remodeling enzymes and how their functions are coordinated remain limited. 42 Previously, we gained insight into these questions by building simulation software, REMODELER 1, to 43 study cell wall synthesis during cell elongation (Nguyen et al., 2015). In this software, a cylindrical cell 44 wall is coarse-grained as chains of tetrasaccharide beads running circumferentially around the cylinder 45 and connected by peptide crosslinks. The functions of transglycosylases, transpeptidases, and 46 endopeptidases are explicitly modeled as beads. Using this software, we found that in order to maintain 47 the integrity and rod shape of the cell, these remodeling enzymes have to coordinate with one another 48 locally in synthetic complexes, but that no long-range coordination of the independent complexes is 49 required. We also found that these complexes must contain a lytic transglycosylase to remove long, 50 uncrosslinked glycan tails to clear the path for enzyme movement (Nguyen et al., 2015). (Such an 51 enzyme was independently identified experimentally (Cho et al., 2014).) 52 53 During cell elongation, the diameter of a rod-shaped cell is conserved. In contrast, during division, the 54 diameter of the cell wall at the division site must become smaller and smaller. How the cell overcomes 55 turgor pressure to remodel its cell wall to a smaller diameter remains unclear (Osawa and Erickson, 56 2018). It is unlikely to be due to a fundamentally different mode of synthesis, since (a) partially 57 elongated the cylinder without changing its radius (Fig. 1C-D Since FtsZ filaments have been proposed to exert a constrictive force on the membrane, we implemented 128 a constrictive force at the midcell to see if this allowed new PG to be incorporated in smaller hoops at 129 the constriction site (see Methods/Constriction force). Initially, the constrictive force made the midcell 130 smaller before new PG was inserted ( Fig. 2A). As new PG was inserted, further reduction of the midcell 131 radius did not occur if & , the constrictive force divided by the sacculus circumference, was smaller than 132 20 pN/nm (Fig. 2B, 2D). The midcell did continue to reduce in size if & was larger than 20 pN/nm (Fig.  133 2C, 2D). We found that at the transition point & ~ 20 pN/nm, the force initially constricted the midcell 134 into a relaxed state where its radius was equivalent to that of an unpressurized cell, 127.5 nm (Fig. 2E). 135 Therefore, a constrictive force alone can drive division if it is sufficiently large to initially bring the 136 midcell into a compressed state, i.e. reduce the midcell radius to less than that of a relaxed sacculus. 137 Note also that our findings were limited to & less than ~32 pN/nm since a larger force buckled the cell 138 wall, making the simulation unstable.

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We next analyzed in detail how a constrictive force might drive cell wall division. Without the 152 constrictive force, the cell wall radius was maintained as new glycan beads were perfectly matched one-153 to-one with the existing template (Fig. 3A). Applying a small constrictive force ( & < 20 pN/nm) 154 squeezed the midcell and pulled the enzymes and the two new strand tips closer to the default template 155 crosslink, but this did not interrupt the one-to-one template matching between the new beads and the 156 existing beads and therefore did not reduce the midcell radius (Fig. 3B). On the other hand, in the 157 presence of a large force ( & > 20 pN/nm), the enzymes were pulled past the default template crosslink, 158 skipping it and crosslinking the two new beads to a new template that was upstream of the skipped 159 template (Fig. 3C). Due to these skipping events, the two new PG hoops had fewer PG beads than the 160 existing hoops, making the midcell radius smaller.

PG remodeling under a make-before-break mechanism 169
Next, we explored if and how cell wall growth alone could be sufficient to drive cell division without 170 the presence of a constriction force. Conceptually, this can occur with a make-before-break mechanism, 171 in which the cell wall synthesis machinery adds one or several new PG layers that form a temporary 172 septum underneath the existing PG layer (make) before hydrolases cleave the constraining peptide 173 crosslinks above these new PG layers (break). If many layers are built in before any bond on the surface 174 is hydrolyzed, the hoops of PG in the inner layer can potentially be made from fewer PG beads. While it 175 is clear that Gram-positive bacteria divide by making a thick septum across the width of the cell, it has 176 only recently been speculated that Gram-negative bacteria might also adopt this septation scheme, but 177 with a thinner septum (Erickson, 2017). (For clarity, we use septum here to refer to the new PG layers 178 beneath, but not including, the existing layer.) 179

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To determine if such a septum exists in dividing Gram-negative bacterial cells, we examined 3D 181 electron cryotomograms of intact frozen-hydrated cells of six species: Caulobacter crescentus, 182 Escherichia coli, Proteus mirabilis, Myxococcus xanthus, Cupriavidus necator, and Shewanella 183 oneidensis. In all cases, we could not discern any thickening of the wall at the dividing midcell that 184 might indicate the existence of a thin septum ( Fig. 4A; Fig. S2). We also observed that the distance 185 between the inner and outer membranes remained constant throughout the midcell (Fig. 4B). We 186 therefore concluded that if a thin septum exists at the dividing midcell, it must be thinner than ~4 nm, 187 the resolution of the electron cryotomograms (Gan and Jensen, 2012). Accordingly, in our simulations, 188 we limited septum thickness to one layer of PG. 189

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We simulated a make-before-break mechanism by decoupling PG synthesis (transglycosylation and 197 transpeptidation) from PG hydrolysis (endopeptidation). Specifically, cleavage of existing peptide 198 crosslinks was blocked until complete hoops of new glycan strands were crosslinked into the PG 199 network underneath these crosslinks ( Fig. 5A-D). Note that how this might occur at a molecular level 200 remains unclear. The rate of endopeptidases was controlled so that only ~one layer of new PG was 201 present underneath the existing layer (see Methods/Make-before-break mechanism). To mimic the 202 volume exclusion effect between the outer and inner layers, before existing peptide crosslinks were 203 cleaved, a repulsive force between these crosslinks and the new glycan strands was applied to separate 204 them to a distance of 2 nm, the estimated thickness of one PG layer. To study the effect of the make-205 before-break mechanism alone, we did not apply a constrictive force. Simulation results showed, 206 however, that this make-before-break mechanism did not reduce the midcell radius (Fig. 5E, 5F). We 207 found that once the existing crosslinks above the new PG hoops were cut, the inner hoops expanded to 208 the size of the existing hoops ( In the presence of turgor pressure, however, the cell wall expanded as peptide crosslinks were stretched 239 and tilted away from the long axis of the cylinder (Fig. 6). As a result, beads were no longer evenly 240 spaced on the same hoop. At breaks between glycan strands in the hoop, the gap between the adjacent 241 peptide crosslinks expanded from 2 " = 4 nm (Fig. 6A) to ~ 6.2 nm (Fig. 6B) as terminal peptides tilted 242 an average of 30° (SD = 15°) (Fig. 6C). We observed that right before encountering a glycan break on 243 the existing strands, which occurred every ~14 beads, the new strand tips had gotten ahead of their 244 templates by an accumulated distance : = 14∆ = 0.44 nm (Fig. 6D). At the glycan break, though, 245 this small progress was more than offset by the 2.2-nm turgor pressure-induced expansion of the gap 246 ( Fig. 6E). At this stage, the new strand tips even fell behind their templates (Fig. 6F). This lag did not 247 accumulate, however, because new strands also terminated, at which point the next new strands were 248 pulled forward (Fig. 6G). This meant that template beads were not skipped, the new hoops had the same 249 number of beads as the existing hoops, and constriction did not occur.

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Since cell expansion due to turgor pressure varies with cell size (Fig. S4A), the difference in radius of 264 the cell wall ∆ between a relaxed cell and a pressurized cell can be negligible for cells of sufficiently 265 small sizes. For example, for cells with circumference of fewer than 150 tetrasaccharides (corresponding 266 to a diameter of ~100 nm), ∆ would be smaller than 2 nm, which is the assumed thickness of one PG 267 layer (Fig. S4B). In this case, a make-before-break mechanism could plausibly drive division in the 268 absence of a constrictive force. In addition to cell width, turgor pressure may vary between cells. While 269 most studies report turgor pressure in the range of 2-4 atm in Gram-negative bacteria ( tetrasaccharides would expand less than 2 nm in radius (Fig. S4B). Still, for a make-before-break 273 mechanism to be effective in a cell the size of an E. coli (~1500 tetrasaccharides in circumference), the 274 turgor pressure would need to be on the order of 0.03 atm to make the radius expansion negligible (Fig.  275   S4C). 276 277

Make-before-break in the presence of a constrictive force 278
Our observations suggested that in order for the make-before-break PG remodeling mechanism to be 279 effective in constriction, the midcell must be in a relaxed state. We reasoned that a constrictive force 280 squeezing the midcell could create this condition by restoring the gaps between adjacent peptide 281 crosslinks at glycan breaks from ~6.2 nm to their relaxed size of ~4 nm (Fig. 7A). Implementing a 282 constrictive force per circumference length & smaller than ~20 pN/nm resulted in an initial constriction 283 that did not completely relax the midcell. Predictably, in this scenario, insertion of new PG with a make-284 before-break mechanism did not cause further constriction (Fig. 7C). When & was ≳ 20 pN/nm, the 285 midcell was completely relaxed or even squeezed to a smaller radius than the unpressurized cell (Fig.  286   2E). As we expected, in this condition make-before-break PG remodeling could now reduce the midcell 287 radius (Fig. 7B, 7C). Note that while the constriction force alone could drive division if the magnitude of 288 & was larger than 20 pN/nm, reducing the midcell to a compressed state (Fig. 2E), in the presence of the 289 make-before-break mechanism, division started to occur at & = 20 pN/nm since reducing the midcell to 290 a relaxed state was sufficient.  Together, our results demonstrate how 3D modeling of molecular details can provide insights into 303 complex symmetry-breaking processes such as cell division. By simulating how rod-shaped Gram-304 negative bacteria could divide their cell walls, we found that a constrictive force is the key factor driving 305 constriction, while cell wall remodeling by a make-before-break mechanism can only facilitate the 306 process. We note, however, that our results are limited by three assumptions: (1) PG synthesis enzymes 307 only act on substrates locally in a complex, (2) a force generator (presumably FtsZ) provides a 308 constrictive force at the midcell during cell division, and (3) the cell can remodel its cell wall by a make-309 before-break mechanism in which new hoops of PG are made inside the existing hoops before peptide 310 crosslinks on the old hoops are cleaved. Note that the original make-before-break model was proposed 311 for individual glycan strands, not complete hoops of strands (Koch, 1990;Höltje, 1993). While 312 experiments are needed to validate or refute these assumptions, our work provides, to our knowledge, 313 the first in silico insights into how cells might employ different driving forces to divide their cell walls. 314 315

Conceptual models of cell wall division 316
To decrease the radius of the midcell, the cell needs to add smaller and smaller hoops of new PG. 317 Conceptually, this can occur by three models. (1) Because existing PG hoops are stretched by turgor 318 pressure, if by some unknown mechanism new PG hoops are stretched even further at the time they are 319 incorporated between existing hoops, the new hoops would have fewer PG beads and therefore become 320 smaller as the system relaxes.
(2) If a mechanism exists to initially compress existing hoops at the 321 midcell and new, relaxed PG hoops are incorporated between these existing hoops, the new hoops would 322 have fewer beads and become smaller upon relaxation. (3) If a mechanism exists to initially relax 323 existing hoops at the midcell and new, also relaxed, PG hoops are made inside existing PG hoops, the 324 new hoops would again have fewer beads. Here we showed that Model 2 is plausible with a constriction 325 force alone and Model 3 is plausible with a combination of a constriction force and a make-before-break 326 mechanism. We did not simulate Model 1 as we judge it unlikely to occur in real cells. Nevertheless, we 327 cannot currently rule out the possibility that an unknown force pulls the enzymes forward, stretching the 328 new glycan strands before incorporating them. Nor can we rule out the possibility that cells might divide 329 by a completely different mechanism that has not yet been discussed in the literature. division. Here we found in silico that to make new PG hoops smaller than existing hoops, the midcell 335 needs to be initially constricted to at least a relaxed state, with further constriction occurring only after 336 new PG is inserted. In this model, the constriction rate is limited by the slower of either the force 337 generator (presumably FtsZ) or the PG synthesis rate. Therefore, the finding by Coltharp et al. that the 338 inward growth rate of the cell wall is limited by the rate of PG synthesis but did not change even when 339 the GTP hydrolysis rate of FtsZ was reduced 90% (Coltharp et al., 2016) might simply reflect that the 340 PG synthesis rate is much slower than the action of FtsZ. Indeed, it has been reported that an FtsZ 341 mutant with a GTP hydrolysis rate 3% that of wild type FtsZ resulted in very slow growth of colonies 342 (Redick et al., 2005). 343 344 In our model, the total initial constriction force needed to be at least ~15 nN (corresponding to a force 345 per circumference & ~20 pN/nm) to enable cell wall division. Assuming that the constrictive force is 346 generated by FtsZ, each monomer of which has been estimated by molecular dynamics simulations to 347 generate 30 pN (Hsin et al., 2012), our estimated force is equivalent to the action of 500 FtsZ monomers, 348 which could form a continuous filament ~2.2 μm long or 15 filaments of an average length of 150 nm. 349 This is reasonable, considering an estimated ~5-7,000 FtsZ molecules per cell measured in E. coli 350 (Erickson et al., 2010) and the fact that our simulated sacculus is a third the size of an E. coli cell. Note 351 that it has recently been speculated that excess membrane synthesis might also generate a constrictive 352 force (Osawa and Erickson, 2018). via a make-before-break mechanism failed to cause cell division in the absence of a constriction force. 358 We found that for the make-before-break mechanism to have an effect, the new PG hoops must be made 359 inside relaxed existing hoops and therefore a constriction force is needed to initially relax the midcell. In 360 theory, the need for a constriction force could be bypassed if the enzymes could make a multi-layered 361 septum. Once the septum thickness was equal to or larger than the difference in radius between the 362 pressurized cell and the relaxed cell, the innermost layer of the septum would be in a relaxed state, 363 allowing the next PG layer to be made of hoops containing fewer PG beads (Fig. S5). For this scenario 364 to occur, in the case of our modeled cell wall, which had a radius of 127.5 nm when relaxed and 137.5 365 nm when pressurized, the septum would have to contain at least five PG layers (assuming each layer is 2 366 nm thick). By this logic, a cell the size of an E. coli, whose circumference is ~1500 tetrasaccharides, 367 would need a septum ~65 nm thick for this mechanism to drive division (Fig. S4A-B). However, we saw 368 no such septa in our electron cryotomograms of dividing cells. We therefore think it unlikely that this 369 mechanism is the primary driver of cell division. 370

Simulation of cell wall synthesis 372
Here we only briefly describe our simulation system. For a more detailed description, please see our 373 previous paper (Nguyen et al., 2015). 374 375

Cell wall 376
We coarse-grained the cell wall such that each glycan strand is represented as a chain of beads, each 377 bead represents one tetrasaccharide, and the peptides attached to the beads alternate between the left and 378 right sides. Adjacent glycan beads are connected by springs of a relaxed length " = 2 nm and a spring 379 constant " = 5.57 nN/nm. The bending stiffness of the strand is 4 = 8.36 • 10 BCD J and the relaxed 380 angle at the beads is D = 3.14 rad. We modeled peptide crosslinks as worm-like chains such that if the 381 peptide end-to-end extension is larger than D = 1.0 nm the following force is applied: Previously, in order to reduce the computational cost, most of our simulations started with a small 387 sacculus with a circumference composed of 100 tetrasaccharides (Nguyen et al., 2015). In the current 388 simulations, to allow the midcell radius to constrict over time, we used a starting sacculus with a 389 circumference of 400 tetrasaccharides. To reduce the computational cost, since PG remodeling only 390 occurs at the midcell during cell division, we removed the two caps of the starting sacculus and built a 391 cylinder only 40 glycan hoops wide. 392

PG remodeling enzymes 393
Four enzyme complexes were added at the midcell. In each complex, three types of PG remodeling 394 enzymes are explicitly represented as beads and a house-keeping enzyme that cleaves the long tails of 395 glycan strands is implicitly implemented. Specifically, there are two transglycosylases that each 396 synthesizes a glycan strand (so two strands emerge from the complex) (Fig. S1). On average, each 397 transglycosylase adds a tetrasaccharide bead every 10 Q time steps. Transglycosylase then translocates to 398 the strand tip to be ready to add another bead. Note that previously we hypothesized that 399 transpeptidation facilitates translocation. Specifically, the probability of translocation is once every 2 • 400 10 R time steps if the last-added bead is not crosslinked, but this probability becomes once every 3 • 10 S 401 time steps after the last-added bead is crosslinked (these numbers were arbitrarily chosen because we 402 were not aware of experimentally-reported enzyme rates) (Nguyen et al., 2015). Considering that the 403 modeled sacculi in our current simulations were 4 times larger than those in our previous simulations, to 404 speed up the current simulations, we increased the probability of transpeptidation-facilitated 405 translocation 10 times to become once every 3 • 10 Q time steps. To maintain an average glycan strand 406 length of 14 tetrasaccharides, the termination probability of strand elongation is also increased two-fold 407 to once every 2 • 10 R time steps. Note also that in our previous simulations, interactions between 408 transglycosylases and outer-membrane lipoproteins LpoA and LpoB were implemented that prevented 409 the transglycosylase-lipoprotein complex from crossing through glycan strands or peptide crosslinks. To 410 enable the make-before-break mechanism, these transglycosylase-lipoprotein interactions were removed 411 from the current model, allowing transglycosylases to freely move across strands and crosslinks. To implement the make-before-break mechanism, existing peptide crosslinks are marked as 444 "constraining crosslinks" once new glycan strands are formed underneath the crosslinks. Cleavage of a 445 constraining crosslink is delayed for 10 R time steps. After that, cleavage can occur by four scenarios: (a) 446 an endopeptidase is within 2 nm of the constraining crosslink, (b) two PG layers exist beneath the 447 crosslink, (c) a random cleavage with a probability of once every 10 h time steps, or (d) the constraining 448 crosslink has existed for 10 i time steps. We found that these probabilities resulted in a septum ~1 PG 449 layer thick.

Measurement of the distance between the inner and outer membranes 465
A tomographic slice 10 nm thick through a central plane along the long axis of the cell was captured 466 using the IMOD software (Kremer et al., 1996). Each membrane (inner and outer) was manually traced 467 and represented by a set of points evenly spaced along the line. This process was repeated for the 468 membranes on the opposite side of the cell. The location of the midcell was determined by the shortest 469 distance between the two traces of the inner membrane. The distance between the inner and outer 470 membrane on each side was then calculated for points up to 500 nm from the midcell in both directions. 471 472