RodZ promotes MreB polymer formation and curvature localization to determine the cylindrical uniformity of E. coli shape

Cell shape in bacteria is determined by the cell wall, which is synthesized by a variety of proteins whose actions are coordinated by the actin-like MreB protein. MreB uses local geometric cues of envelope curvature to avoid the cell poles and localize to specific regions of the cell body. However, it remains unclear whether MreB’s curvature preference is regulated by additional factors, and which features of MreB are essential for specific aspects of rod shape growth, such as cylindrical uniformity. Here we show that in addition to its previously-described role in mediating MreB motion, RodZ also modulates MreB polymer number and curvature preference. MreB polymer number and curvature localization can be regulated independently. Quantitative 3D measurements and a series of mutant strains show that among various properties of MreB, polymer number, total length of MreB polymers, and MreB curvature preference are the key determinants of cylindrical uniformity, a measure of the variability in radius within a single cell. Changes in the values of these parameters are highly predictive of the resulting changes in cell shape (r2=0.93). Our data suggest a model for rod shape in which RodZ promotes the assembly of multiple long MreB polymers that ensure the growth of a uniform cylinder.


Results 125
RodZ is required for MreB curvature localization. 126 We recently showed that the transmembrane protein RodZ interacts with both 127 MreB and the cell wall synthesis machinery to couple MreB rotation to cell wall 128 synthesis 1 . RodZ is necessary for MreB rotation and specific point mutations in 129 mreB can roughly restore rod-like shape without restoring MreB rotation 1 . While 130 these data indicated that MreB rotation is not necessary for rod shape, the 131 resulting cells had an irregular morphology distinct from wild-type (WT) cells, 132 suggesting that RodZ could play an important role in the cylindrical uniformity of 133 cell shape independently of its role in MreB rotation. Consequently, we examined 134 the role of RodZ in controlling the biophysical properties of MreB that are thought 135 to be important for shape determination, like curvature preference. 136 To quantify the effect of RodZ on MreB curvature preference we 137 measured the 3D cell shape and curvature enrichment of MreB in a strain 138 expressing MreB-GFP sw (internal msGFP sandwich fusion) as the sole copy of 139 MreB (Fig. 1B). We previously showed that this fusion fully complements the 140 shape of WT E. coli under a wide range of conditions 5 and all mutants described 141 below were generated in this strain background. Generating 3D cell-shape 142 reconstructions with roughly 50 nm precision from the raw fluorescence images 143 allowed us to calculate the Gaussian curvature, which is the product of the two 144 principal curvatures, at every location on the 3D surface of the cell 21  Interestingly, we found that deletion of rodZ strongly reduced the curvature 158 preference of MreB (Fig. 1CD). In ΔrodZ cells, MreB is no longer enriched near 159 zero Gaussian curvature or excluded from the poles. The shape of ΔrodZ cells 160 can be complemented by expressing full-length RodZ from a plasmid (RodZ 1-337 ). 161 and ΔrodZ cells lack rod-like shape but only ΔrodZ cells lack geometrically 179 localized MreB, the lack of MreB enrichment in ΔrodZ must not be a failure in our 180 3D analysis. These data show that RodZ specifically promotes MreB's curvature 181 localization in a manner that is not merely secondary to its role in cell shape cytoplasmic domain (Fig. 1A). We hypothesized that these two domains of RodZ 187 could play distinct roles, with the periplasmic domain binding the PG synthesis 188 machinery to promote MreB rotation, and the cytoplasmic domain binding MreB 189 to promote its curvature preference. In order to determine how RodZ regulates 190 MreB curvature localization, we thus examined MreB curvature enrichment in 191 RodZ truncations from both its periplasmic and cytoplasmic termini. Gaussian curvature preference measurements reported in this study, we take 212 into account the distributions of curvatures observed such that changes in 213 curvature preference are not due to changes in the available curvatures in the 214 cell ( Fig. S1-S3). 215

Rod-shaped cells have WT-like MreB localization but WT-like MreB 217 localization is not sufficient for proper cell shape 218
Deleting rodZ results in a loss of cylindrical uniformity that can be suppressed by 219 a point mutant in mreB (MreB S14A ) without restoring MreB rotation 1,23 . Because 220 RodZ is needed for MreB's proper curvature localization, we determined whether 221 MreB S14A can also suppress the loss of MreB's curvature enrichment in the 222 absence of rodZ. In contrast to its effects on MreB rotation, the curvature 223 enrichment profile of MreB S14A was restored to a WT-like profile in ΔrodZ cells 224 To test whether the correlation between shape and MreB localization 227 observed for MreB S14A ΔrodZ is generalizable, we examined additional MreB 228 point mutations that were originally identified as resistant to an MreB targeting 229 drug, A22, and previously characterized 5 . We confirmed that the steady state  Table S4). Analysis of another point mutant, MreB Y183N, reinforced the conclusion 237 that proper curvature localization is insufficient for proper rod shape (Fig. S5). observed that there were not substantial changes in polymer length (Fig. 3) or 250 average polymer angle (Fig. S4A). There was a statistically-significant change in 251 the fraction of MreB associated with the cell periphery (Fig. S4D), but this change 252 was small (~5%) and also observed in mecillinam-rounded cells, such that it does 253 not appear to be a major component of RodZ's influence on MreB. We note that decrease of the number of MreB polymers per cell (Fig. 3D). Surprisingly, we 279 also saw a dramatic reduction in the number of MreB polymers per cell when we 280 truncated the periplasmic domain of RodZ (Fig. 3E). Since the periplasmic 281 domain of RodZ is needed to interact with the cell wall synthesis machinery, 282 these data suggest RodZ could integrate signals from the process of cell growth 283 to feed back on MreB and control polymer number. 284 We also compared MreB polymer properties in MreB point mutants with or 285 without rodZ. We found that specific point mutations altered specific properties of 286 MreB. For example, MreB E143A polymers are longer than WT but have the same 287 MreB polymer angle, while MreB S14A polymers are the same length as WT but the 288 polymer angle is different ( Fig. 3A and S4). Interestingly, when comparing 289 MreB S14A in the presence or absence of RodZ, MreB S14A suppressed the RodZ-290 dependent properties of MreB (curvature localization, polymer number, and 291 membrane-association) ( Fig. 3A and S4). MreB S14A was also the strongest 292 suppressor of ΔrodZ cell shape, suggesting that MreB S14A functionally restores a 293 majority of the effect of the WT MreB-RodZ interaction. In contrast, MreB E143A , a 294 partial suppressor of ΔrodZ cell shape, suppresses the effects of RodZ on MreB 295 curvature localization but does not suppress the effects of RodZ on MreB 296 polymer number or membrane fraction. MreB E143A also has longer polymers than 297 MreB WT and the length of these polymers increases in the absence of RodZ. 298 Together our results suggest that the different properties of MreB can be 299 modulated independently. 300 301

Cells need multiple, long, and geometrically-localized MreB polymers to 302 grow as uniform rods. 303
Because MreB curvature preference did not always correlate with 304 cylindrical uniformity and MreB parameters can be independently controlled, we 305 sought to determine which properties of MreB best predict cylindrical uniformity. 306 To this end we quantified cell shape and compared MreB properties across a 307 large set of mreB and rodZ mutants (Supplemental Table 4-mutants and 308 properties). To quantify cylindrical uniformity we relied on our previous analysis 1 showing that the variation of cell diameter within a single cell (intracellular 310 diameter deviation, IDD) is a quantitative measure of cylindrical uniformity (Fig.  311   S7). We confirmed that the IDD measured from 3D reconstructions also shows a 312 clear separation between cells that are qualitatively classified as uniform rods, 313 irregular rods, and round cells (note that IDD is inversely related to cylindrical 314 uniformity, Fig. S7). We then built a collection of shape comparisons by 315 computing the difference in IDD between two strains (ΔIDD = IDD strain1 -316 IDD strain2 ) ( Table 1) with different normalizations. However, a leave-one-out analysis of the data 343 revealed that this was an over fit model (Table S2). To determine which version 344 of normalization was most predictive across different subsampled datasets, we 345 used two different analysis methods (see Materials and Methods). Both methods 346 converged on the same terms: MreB enrichment in regions of low Gaussian 347 curvature (<2 μm -2 ), the total length of MreB polymer in each cell normalized by 348 cell volume, and the number of polymers per cell (Fig. 4, Table S2). The 349 combination of these three parameters was very predictive of the change in cell MreB E143A ΔrodZ background increased MreB polymer number (Fig. S8). 364 Importantly, we observed the LASSO-predicted change in shape upon increasing 365 MreB polymer number, as ectopic expression of MreB E143 made the cells more 366 rod-like, even though rodZ was still absent (Fig. S8, Fig. 4A, Table 1). We also 367 ectopically expressed MreB WT in a MreB WT ΔrodZ background, which is not 368 properly curvature-localized. This strain did not restore rod shape, confirming that 369 the MreB E143 effect is not a generic consequence of ectopic expression (Fig. S8). 370 These results support our conclusion that MreB-dependent uniform rod shape formation of new polymers, as a severing protein that cuts single polymers into 416 two separate polymers, or as a capping factor that limits polymer growth. We 417 note that a simple polymer stabilization mechanism is unlikely because that 418 would have led to significantly-increased polymer length. Regardless of the 419 mechanistic details, whose dissection will require future in vitro studies, our 420 findings represent the first identification of a factor that enhances MreB polymer 421

formation. 422
Interestingly, our RodZ truncation and MreB mutant analyses suggest that 423 the functions of RodZ in promoting MreB rotation, polymer formation, and 424 geometric localization are genetically separable. Thus, RodZ appears to use its 425 cytoplasmic and periplasmic domains to coordinate multiple aspects of MreB, 426 including acting upstream of MreB assembly to regulate its polymer properties 427 and downstream of MreB assembly to regulate its coupling to the movement of 428 the cell wall synthesis machinery. Such modularity in a transmembrane protein is 429 an appealing way for the cell to tune the properties of MreB, perhaps enabling 430 optimization of MreB in response to different growth conditions. 431

Cylindrical uniformity requires multiple long and curvature-localized 433 polymers 434
In previous studies, our lab and others determined that MreB mediates 435 multiple aspects of rod shape determination 1,2,4,5 . MreB localization helps 436 straighten rods and initiate new rods out of spheres, while MreB angle is 437 correlated with the average width of a rod 2,5 , even in the absence of RodZ (Fig.  438   S9). Here we show that MreB also determines the cylindrical uniformity of rods 439 (Fig. 5). Specifically, a machine learning analysis (LASSO) of the correlations 440 between MreB properties and rod shape revealed that a combination of 441 modulating polymer number and total polymer length, along with the correct 442 curvature localization is sufficient to accurately predict rod shape changes. While of independent cells that contributed to the enrichment plots is indicated in gray.

589
Shaded areas of the curves indicate ± 1 standard error of the mean and dotted 590 lines indicate strains deleted of rodZ. The curve for each strain is a cubic 591 smoothing spline and is truncated using a probability threshold for extreme 592 curvatures of p>5x10 -3 (Fig. S3)  RodZ (solid red bar). For other comparisons see Table S3. The number above 615 the bars is the number of polymers (B) and the number of cells (C-E) analyzed. 616 Error bars represent 95% confidence intervals. ns P > 0.05, ** P ≤ 0.01, *** P ≤ 617 0.001 618 619 620 Figure 4. LASSO analysis reveals that rod shape requires many long and 621 geometrically-localized MreB polymers. A) The correlation between observed 622 and predicted cell shape when using the LASSO model combining parameters. 623 See Table 1 for all the strains used and the observed and predicted IDD values. 624 Note that to preserve its use as a test of the model, overexpression of MreB E143A 625 was not used for model selection and training. r 2 value represents the square of 626 the Pearson correlation coefficient. B) Left-the correlation between observed and 627 predicted cell shape when only using polymer length normalized by volume. 628 Middle-the correlation between observed and predicted cell shape when only 629 using polymer number. Right-the correlation between observed and predicted 630 cell shape when only using average MreB enrichment at Gaussian curvatures 631 below 2 μm -2 . C) The mean squared error (MSE) of 10-fold cross-validation as a 632 function of the LASSO regularization parameter. The solid curve is the mean 633 MSE and the shaded region represents one standard error of the mean. The dot 634 represents the most compact model within one standard error of the mean from 635 the minimum of the curve. See Table S2 for the coefficients in this model. 636 637 Red-as width increases cells become more sphere like and less rod like. For 646 each of these shape descriptors, a quantitative metric of shape provides a 647 continuous rather than a binary description of rod vs non-rod. 648 649 is the change in cell shape (IDD) that we predict from the regression model, while 653 measured shape change is taken from 3D measurements of cells. ∆-RodZ 654 periplasmic truncations, ∇-RodZ cytoplasmic truncations, -MreB point mutants 655 were strains used to determine the LASSO parameters. Grey circle-comparison 656 used to test the model. 657