RodZ modulates geometric localization of the bacterial actin MreB to regulate cell shape

In the rod-shaped bacterium Escherichia coli, the actin-like protein MreB localizes in a curvature-dependent manner and spatially coordinates cell-wall insertion to maintain cell shape, although the molecular mechanism by which cell width is regulated remains unknown. Here we demonstrate that the membrane protein RodZ regulates the biophysical properties of MreB and alters the spatial organization of E. coli cell-wall growth. The relative expression levels of MreB and RodZ change in a manner commensurate with variations in growth rate and cell width, and RodZ systematically alters the curvature-based localization of MreB and cell width in a concentration-dependent manner. We identify MreB mutants that alter the bending properties of MreB filaments in molecular dynamics simulations similar to RodZ binding, and show that these mutants rescue rod-like shape in the absence of RodZ alone or in combination with wild-type MreB. Thus, E. coli can control its shape and dimensions by differentially regulating RodZ and MreB to alter the patterning of cell-wall insertion, highlighting the rich regulatory landscape of cytoskeletal molecular biophysics.

B acterial shape is determined by the cell wall, a cross-linked sugar network that is constantly remodeled as cells grow 1,2 . In several rod-shaped organisms, cell-wall insertion is controlled by the cytoskeletal protein MreB 3,4 , a structural homolog of eukaryotic actin 5 . In Escherichia coli, MreB forms oligomers 6 that bind the inner surface of the cytoplasmic membrane 7 , rotate around the cell's long axis in a manner that is dependent on activity of the essential cell-wall synthesis enzyme PBP2 6,8 , and control the spatiotemporal pattern of cell-wall insertion 5,[9][10][11] . Disruption of MreB through point mutations [12][13][14][15] , depletion 16 , overexpression 16,17 , or antibiotics 16,18,19 can lead to subtle size changes or aberrant morphological phenotypes. Quantification of the pattern of MreB fluorescence as a function of geometry in exponentially growing cells 11 or in cell walldeficient spheroplasts 20 revealed that MreB preferentially localizes to invaginations of the cell surface. Molecular dynamics simulations predicted that MreB polymers have nucleotide-dependent intrinsic curvature and substantial resistance to bending 21 , both of which are key ingredients for sensing curvature. Moreover, simulations based on a mechanochemical model of cell-wall growth demonstrated that preferential localization to regions of negative Gaussian curvature is sufficient to straighten a bent cell 11 . Thus, biophysical feedback between cell shape and MreBmediated wall growth appears to be crucial for cell-shape maintenance, although it remains unknown whether E. coli cells actively regulate the biophysical properties of MreB polymers to adjust cell shape and size.
E. coli cell shape has long been recognized to vary across growth phases, with cells becoming shorter as population optical density increases past~0.3; cells become nearly round in stationary phase 22 . Moreover, the steady-state cellular dimensions of many rod-shaped bacteria adjust in response to nutrientdetermined changes in growth rate 23,24 , with faster-growing cells having increased volume. The molecular mechanisms underlying changes in length and width are only partially understood, and there may be several pathways that indirectly affect cell size [24][25][26] . Nonetheless, mutation of a single residue of MreB to various amino acids was sufficient to drive a wide range of cell-size changes and to increase competitive fitness via decreases in lag time 14 , suggesting that modification of MreB is a robust mechanism for determining cellular dimensions and thereby altering cellular physiology. Chemical inhibition of MreB polymerization by sublethal levels of the small molecule A22 resulted in dose-dependent changes to cell width and the chirality of cell-wall architecture 3 , indicating that MreB polymeric properties may be biophysical parameters that can be exploited by the cell as tuning knobs for regulating cell width. Since MreB is located in the cytoplasm, other proteins are needed to couple its activity to regulation of cell-wall synthesis. One potential factor is RodZ, a bitopic membrane protein that directly binds to MreB 17,27,28 . Deletion of RodZ causes cells to lose rod shape despite the presence of MreB 17,28 . How the geometric sensing function of MreB, which we define as MreB localization in response to morphological features such as surface curvature, is connected with cell size has not been systematically investigated.
To elucidate the precise relationship between the molecular biophysics of the MreB cytoskeleton and the diverse landscape of cell shape requires both molecular-level structural investigations and precise single-cell experiments.
Here we establish that the spatial organization of MreB in E. coli changes systematically across phases of growth, suggesting that the biophysical properties of MreB filaments alter in a manner commensurate with the nutrient-regulated changes in growth rate. Using single-cell microscopy, we determine that the protein RodZ regulates the geometric sensing of MreB. Molecular dynamics simulations prompt us to propose that RodZ binding directly alters the conformational dynamics and intrinsic curvature of MreB polymers. We study several MreB mutations that complement rod-like shape in the absence of RodZ when expressed alone or in combination with wild-type MreB (MreB WT ). These mutants display enrichment of MreB to curvatures distinct from wild-type cells, and result in longer polymers. Simulations predict that these MreB mutations alter polymer bending dynamics in a manner consistent with the behavior of wild-type MreB bound to RodZ. Together, our findings demonstrate that regulation of RodZ tunes the geometric localization of MreB and thereby alters cell shape.

Results
E. coli cells rapidly change size as nutrients are depleted. Based on previous reports 22 that E. coli cell mass decreases dramatically as the population increases beyond an optical density of~0.3, we hypothesized that passage through a typical growth curve would yield insights into the mechanisms of cell-size determination across a range of cell sizes in a single-genotypic background. We interrogated a strain expressing the mreBCD operon under control of the native promoter on a plasmid, with a sandwich fusion of MreB to monomeric superfolder GFP (msfGFP) 11 . To monitor cell shape as a function of cell density, we back-diluted a 24 h, stationary-phase culture grown in lysogeny broth (LB) 1:200 into fresh LB in a test tube. Every 15 min, we extracted a small sample and imaged cells on an agarose pad with phase-contrast and epifluorescence microscopy to measure cell shape and MreB localization (Methods section). We extracted cell contours 11,14 and computed the mean length and width of the population at each time point (Methods section). Concurrently, we measured optical density from a parallel culture to quantify bulk growth rate (Fig. 1a).
Along the growth curve of the cell culture's exit from stationary phase, the mean cell length and width of the population rapidly changed. Within 1 h, there was a detectable increase in both mean width and length (Fig. 1b). Changes in width and length were not synchronized, with width initially increasing for the first 45 min, followed by a gradual decrease back to a value typical of stationary-phase cultures over the growth curve (Fig. 1b). In contrast, length continuously increased for the first 1.5 h, plateaued for 45 min, and then gradually decreased (Fig. 1b). The cell population had not reached stationary-phase dimensions after 3 h, as the culture was still growing at a slow rate (Fig. 1a). Similar changes to cellular dimensions occurred in wild-type (unlabeled MreBCD at the native chromosomal locus) E. coli MG1655 cells (Supplementary Fig. 1). Thus, cellular dimensions change in an asynchronous, non-trivial manner as nutrients are consumed, providing the opportunity to reveal connected changes in the behavior of the molecular mechanisms that construct the cell wall and determine shape.
Curvature-based enrichment of MreB varies with cell density.
To correlate MreB localization with features of a cell's shape, we computed two curvature-related features at every point along the contour. Contour curvature describes bending along the cell outline (Fig. 1c). By our convention, the poles are regions of highpositive contour curvature (small blue circle, Fig. 1c), while invaginations such as division-site constrictions are regions of high-negative contour curvature (red circle, Fig. 1c). Although most of the cell away from the poles is approximately cylindrical, there are fluctuations in contour curvature (large blue circle, Fig. 1c) that we previously exploited to determine that MreB preferentially localizes to regions of negative contour curvature during exponential growth 11,20 . The second curvature feature captures the local width, which is the distance of closest approach to the cell midline. We defined the inverse of this distance as the radial curvature (Fig. 1d), which approximates the out-of-plane curvature along the circumferential direction under the assumption of cylindrical symmetry. Thus, as cell width changes throughout the growth curve, straight regions have zero contour curvature regardless of cell width and smaller or larger radial curvature as cell width increases or decreases, respectively.
Throughout the growth curve after exit from stationary phase, cells adopted wide distributions of contour and radial curvatures ( Fig. 1e). We computed the enrichment of MreB fluorescence as a function of contour and radial curvature across thousands of cells at each time point (Supplementary Fig. 2). First, we calculated the distribution of curvatures as a two-dimensional (2D) histogram with fixed bin widths and bin positions for all cells in a given sample. Next, for each curvature bin, the intensity values of MreB localized at curvature values between the bin edges were averaged and normalized by the average fluorescence expected under the null hypothesis that MreB was randomly distributed along the contour of each cell. At 1.5 h (OD 600~0 .05), MreB was generally localized to negative contour curvature, as expected (Fig. 1f). However, the specific shape of the enrichment profile depended on the local radial curvature: MreB was more likely to be found at wider regions (lower radial curvature) with negative contour curvature (Fig. 1f). Simulated microscopy 29 showed that this width-dependent enrichment could not be accounted for by optical artifacts due to the variable cell width ( Supplementary  Fig. 3). Thus, for a fixed contour curvature, MreB prefers wider regions of the cell. By contrast, at t = 0 (the beginning of the exit from stationary phase), MreB displayed a qualitatively distinct enrichment profile. Most notably, in the shorter and thinner stationary-phase cells (Fig. 1e, Supplementary Fig. 2), MreB localized preferentially to the poles (high-positive contour curvature) (Fig. 1f). Since the spatiotemporal patterns of MreB and of new cell-wall synthesis are highly correlated 11 , this polar localization during stationary phase is consistent with our observation of rapid cell widening as cells exit stationary phase (Fig. 1b). To examine how the enrichment profile varied over time, we compressed the 2D curvature into a measure that we term average curvature (computed as the average of contour and radial curvature, an estimate of the 3D mean curvature in rod-like cells), binned average curvatures into a one-dimensional histogram, and recomputed the observation-weighted average of MreB enrichment as a function of average curvature (Fig. 1g). To estimate the confidence of enrichment measurements, the enrichment profile was calculated 10 times from data bootstrapped from the original dataset with replacement, and the standard deviation of enrichment across resampled datasets was calculated for each bin. MreB localization was initially enriched in regions of highaverage curvature (cell poles), but steadily decreased at later time points (Fig. 1h). Across the entire time course after the initial measurement (t = 0), there was a consistent enrichment of MreB at lower average curvature (negative contour curvature). However, the enrichment profile varied quantitatively throughout the growth curve, with variations in enrichment on similar time scales as the changes in cellular dimensions (Fig. 1b). For example, cell width and length (Fig. 1b) were relatively constant between~60 and 90 min (OD 600~0 .02-0.05), as was MreB enrichment (Fig. 1h). Moreover, MreB enrichment continued to change throughout the 3-h time course, as did cellular dimensions (Fig. 1b). Thus, MreB curvature sensing and cell shape both change dramatically as cells exit from stationary phase. Given the relationship between MreB and patterning of the insertion of cell wall material, we hypothesized that a direct relationship exists between curvature sensing and cell shape.
Expression of RodZ alters MreB curvature enrichment. The large, systematic changes in MreB curvature-based localization suggest that molecular factors could be responsible for altering the subcellular behavior of MreB. Based on evidence from previous studies, a strong candidate for the regulation of MreB a The ratio of MreB to RodZ protein abundance consistently increases in a manner concordant with growth rate across multiple independent studies. d: chemostat dilution rate. b For a strain in which the native promoter of rodZ was replaced by P ara, RodZ expression is driven by arabinose (Ara). In the absence of arabinose, cells became spheroidal. Scale bar is 5 µm. c Schematic of experimental approach in d. Overnight cultures grown in the absence of arabinose were further incubated after adding varying amounts of arabinose. The distribution of MreB fluorescence was measured after 60 min. d After 1 h of growth, induction of RodZ by arabinose enhanced the depletion of MreB at high-average curvature in a dose-dependent manner. By contrast, the enrichment profile was more uniform after induction with 0.2% xylose (Xyl) or 0% arabinose. Shaded areas represent the standard deviation of enrichment from resampled data for each condition. All bins include at least 50 observations. e Overnight cultures grown in 0% arabinose and back-diluted 1:10,000 into fresh LB with varying levels of arabinose exhibited dose-dependent steadystate widths after 4 h of growth. Black lines represent standard error of mean (n > 50 cells) patterning is the bitopic membrane protein RodZ 17,27,28 . In E. coli, deletion of RodZ causes cells to become round 17,28 . Changes to RodZ levels also tune cell shape: both underexpression and overexpression increase cell width, and overexpression also results in larger width variations 17 . Suppressor mutations of rodZ deletion that recover rod-like shape occur in mreB and mrdA (which encodes PBP2) 30 . Interestingly, most suppressors isolated in rich media die in minimal media, suggesting sensitivity to changes in a cellular quantity such as cell shape connected with growth rate 30 . Ribosomal profiling data indicated that there is approximately fivefold more MreB than RodZ in rich media, and that the ratio of MreB to RodZ abundance decreases in minimal media 31 . Similarly, mass spectrometry data from a variety of nutrient conditions showed that the ratio of MreB to RodZ generally decreases in nutrient-limited conditions 32 . Our mass spectrometry measurements of the strain used for our curvature enrichment measurements (Fig. 1) were consistent with these previous studies, and indicated that the MreB:RodZ ratio was 30% higher in exponential phase than in stationary phase (Fig. 2a, Methods section). Thus, we hypothesized that the MreB localization changes along the growth curve were driven by changes in RodZ expression relative to that of MreB.
To test how RodZ expression changes the curvature sensing of MreB and cell shape, we constructed a strain in which the native promoter of rodZ was replaced by P ara (Methods section). The strain background has a chromosomally integrated sandwich fusion of MreB to msfGFP as the sole copy of mreB 11 ; the chromosomally integrated msfGFP fusion provides the best complementation of cell size of all MreB fusions studied to date 15 . As expected, after 12 h of growth in the absence of arabinose, cells were round (Fig. 2b), similar to ΔrodZ cells 17 , whereas cells grown in the presence of arabinose were rod-shaped (Fig. 2b), albeit with larger cell widths than wild-type cells (Supplementary Table 2).
To determine whether induction of RodZ changes MreB curvature sensing, we added various concentrations of arabinose (0-0.2%) directly to the 12-h culture of cells depleted of RodZ (0% arabinose), and imaged cells after 60 min (Fig. 2c). Since cells had already depleted the nutrients, little to no increase in optical density took place during the 60 min of arabinose treatment ( Supplementary Fig. 4a). For all cultures, there was enough cellshape variability to measure average curvature enrichment profiles of MreB fluorescence. The culture grown without arabinose had a relatively flat enrichment profile, signifying approximately random localization. As the arabinose concentration was increased, we measured increased enrichment of MreB to lower average curvature and depletion at high curvature (Fig. 2d). Importantly, the increased range of enrichment with arabinose induction (−25% to 25%) was in quantitative agreement with the wild-type profiles after~180 min outgrowth from stationary phase (Fig. 1h). Moreover, overnight cultures grown in the absence of arabinose and then back-diluted 1:10,000 in fresh LB with varying levels of arabinose exhibited a dosedependent average width after 4 h, with higher arabinose concentrations leading to wild-type-like widths (Fig. 2e). By contrast, cells grown in xylose rather than arabinose exhibited MreB curvature enrichment similar to the original overnight culture (0% arabinose) (Fig. 2d). In addition, cells grown with xylose exhibited more diffuse MreB fluorescence than cells grown with arabinose, as measured by the difference in the distribution of peripheral fluorescence values across the population (Supplementary Fig. 4b).
Although it is possible that RodZ expression acts indirectly on cell morphology, these results show that different RodZ expression levels correspond to MreB localization changes in a dose-dependent manner, leading to enhanced curvature sensitivity, which further regulates cell shape.
ΔrodZ suppressor mutants alter cell shape and curvature sensing. A previous study identified several mutations in MreB that were selected as suppressors of the slow-growth phenotype of ΔrodZ cells 30 . All of these mutants were able to grow as rods in the absence of rodZ 30 . We were interested to determine whether these mutations also modify the curvature sensing of MreB. We introduced three of these MreB mutations (D83E, R124C, and A174T) into E. coli MG1655 cells expressing the msfGFP sandwich fusion to MreB as the sole copy at the native mreB locus (Methods section). These three mutations were selected to cover multiple regions of MreB; A174 is near the RodZ binding interface in domain IIA, R124 is near the membrane binding interface in subdomain IA, and D83 is at the double-protofilament interface in subdomain IB 33 (Fig. 3a). We also investigated a fusion of MreB E276D to msfGFP, since E276 is located at the polymer interface and near the RodZ binding interface (Fig. 3a). MreB D83E and MreB R124C cells had a small, but significant, decrease in maximal growth rate compared to wild-type cells, while the maximal growth rate of MreB A174T cells was almost twofold lower than MreB WT cells ( Supplementary Fig. 5a,b). These three strains also had significantly longer lag times than wild-type cells (Supplementary Fig. 5c). We measured the cellular dimensions of each strain at the time of reaching maximal growth rate (Fig. 3b, c). MreB D83E and MreB A174T cells were somewhat and much wider and shorter than MreB WT cells, respectively (Fig. 3b, c), while MreB 124C cells had an average width and length similar to wild-type cells (Fig. 3c) but exhibited substantial tapering and occasional branching (Fig. 3b). These shape phenotypes are in good agreement with the study in which they were originally identified 30 . MreB E276D cells had quantitatively similar growth (Supplementary Fig. 5a) and shape (Fig. 3b, c) phenotypes to those of wild-type cells.
We next quantified the localization of MreB fluorescence as a function of curvature at the time when each strain reached its maximum growth rate. Since some of the strains exhibited more aberrant shapes than MreB WT (MreB R124C and MreB A174T in particular), we normalized the MreB enrichment ( Supplementary  Fig. 6a) by the enrichment calculated from the fluorescence signal from the membrane dye FM4-64 ( Supplementary Fig. 6b), and observed qualitatively similar results without (Fig. 3d, Supplementary Fig. 6a) and with ( Supplementary Fig. 6c) normalization. MreB E276D cells had a curvature enrichment profile that was very similar to that of MreB WT (Fig. 3d). MreB D83E and MreB A174T cells had profiles shifted such that the crossover average curvature at which localization was random (enrichment = 0) was lower for wider cells (Fig. 3d) 34 . MreB R124C cells had a flatter enrichment profile than any of the other strains, indicating less curvature sensitivity; this finding suggests that the branching that we observed in MreB R124C cells (Fig. 3b) is due to increased potential for growth at the polar (high curvature) regions during cell division, as has been observed in various cell-wall mutants 35 . Thus, while the three ΔrodZ suppressor mutants drive rod-shaped growth in the absence of RodZ, they have non-wild-type growth, shape, and localization phenotypes.
RodZ alters MreB filament properties in simulations. Since the cytoplasmic tail of RodZ directly binds MreB 7 , we hypothesized that the altered curvature sensing of MreB due to RodZ expression is driven by a direct biophysical interaction that alters the conformation of MreB filaments. We previously used all-atom molecular dynamics (MD) simulations to demonstrate that Thermotoga maritima MreB subunits adopt a range of conformations connected with filament properties 21 , and predicted a polymerization-induced flattening of MreB subunits that was subsequently verified using X-ray crystallography 33 . The conformations of MreB filaments can be described by the intermolecular bending (out-of-plane θ 1 , in-plane θ 2 ) and twisting (θ 3 ) between two adjacent MreB subunits (Fig. 4a, b). To investigate whether RodZ binding alters the conformations of MreB filaments, we used the T. maritima MreB-RodZ cocrystal structure (PDB ID: 2WUS) to simulate MreB dimers with RodZ bound to both subunits (Methods section, Fig. 4c). In the absence of RodZ, an ATP-bound MreB dimer exhibited significant bending along θ 2 compared to ADP-bound dimers ( Supplementary Fig. 7), as we previously reported 21 Fig. 4 RodZ binding and MreB mutations may alter the bending properties of MreB filaments. a Schematic of an MreB dimer (PDB ID: 1JCG) and its orientation relative to the membrane. The bending of MreB protofilaments is captured by the relative orientation along three orthogonal axes (cylinders) of adjacent MreB subunits, colored light (top) and dark gray (bottom). The membrane binding interface of the MreB protofilament is shown as a green plane. b Schematic of MreB dimer bending angles out of the plane of the membrane (θ 1 , top) and in the plane of the membrane (θ 2 , bottom). In the crystal structures that form the initial states of our MD simulations, these bending angles are zero. c MD simulation system comprised of a nucleotide-bound T. maritima MreB dimer, with each subunit bound to the cytoplasmic tail of RodZ. d D72E, R112C, A162T, and E266D mutations in ATP-bound T. maritima MreB shift the θ 1 bending angles toward that of a RodZ-bound ATP dimer, signifying filament straightening some bending along θ 1 (Fig. 4d). In contrast, in the presence of RodZ, dimer bending was drastically reduced along both the θ 1 and θ 2 bending axes (Fig. 4d, Supplementary Fig. 7). These results were consistent across replicate simulations (Supplementary Fig. 7). Thus, since RodZ directly alters the spectrum of conformations adopted by MreB dimers in silico, we predict that the binding of RodZ to a fraction of the MreB subunits, which will be related at least in part to the stoichiometry of MreB and RodZ (Fig. 2a), causes altered curvature sensing of MreB in vivo.

Mutations in MreB mimic RodZ-bound MreB in simulations.
Since RodZ expression modulates MreB curvature enrichment, and since our simulations predicted that RodZ-binding alters MreB filament mechanics, we asked whether the ΔrodZ suppressor mutants we studied in vivo also exhibit smaller bending angles than MreB WT , indicating straighter polymers. Since all three positions are conserved in E. coli and T. maritima, as is E276, we carried out all-atom MD simulations of dimers of the corresponding T. maritima mutants (D72E, R112C, A162T, E266D; Fig. 3a) bound to ATP, in the absence of RodZ. For all mutants, we observed shifts in the bending angles θ 1 and θ 2 toward zero (the approximate bending angle for MreB WT bound to RodZ; Fig. 4d, Supplementary Fig. 7), with a high degree of reproducibility in replicate simulations ( Supplementary Fig. 7). The MreB A162T (MreB A174T ) mutant, which had a shape phenotype (Fig. 3b) closer to that of spherical RodZ-cells (Fig. 2b) Combination of MreB WT and MreB E276D suppresses loss-ofrod shape. In our MD simulations, MreB E266D (MreB E276D ) dimers displayed intermediate straightening ( Supplementary  Fig. 7), suggesting that the mechanical properties of polymers of this mutant are different from those of MreB WT despite having similar growth and shape phenotypes to wild type in the presence of RodZ (Fig. 3b-d, Supplementary Fig. 5). Thus, we wondered whether MreB E276D cells would be rod-shaped in the absence of RodZ. We constructed a ΔrodZ strain with MreB E276D fused to msfGFP 15 . Like MreB WT cells, MreB E276D cells were round in the absence of RodZ (Supplementary Fig. 5g) and grew as slowly as ΔrodZ MreB WT cells, indicating that MreB E276D is not a suppressor of ΔrodZ growth defects. Thus, we hypothesized that the mutant imitates a scenario in which MreB constitutively binds RodZ, similar to overexpression of RodZ, which is known to disrupt rod-like shape and result in round cells 17 .
To test this hypothesis, we sought to create a genetic background in which only a fraction of MreB is bound to RodZ. We constructed a strain expressing MreB WT from the chromosome and MreB E276D -msfGFP from a plasmid with the otherwise wild-type mre operon driven by the native mreB promoter (Methods section) in a ΔrodZ background; we will refer to this strain as ΔrodZ MreB WT + MreB E276D* (the asterisk indicates the presence of msfGFP), and use similar notation for strains with other mreB alleles on the chromosome and fused to sfGFP on the plasmid, with the rest of the mre operon included on the plasmid in all such strains. The ΔrodZ MreB WT + MreB E276D* strain formed larger colonies and grew more quickly than ΔrodZ MreB WT cells ( Supplementary Fig. 5d,e). ΔrodZ MreB WT + MreB E276D* cells were rod-shaped (Fig. 5a), albeit wider than MreB WT cells ( Supplementary Fig. 8, Supplementary Table 2), indicating that complementation was not perfect. To determine whether the MreB copy number is important for recovering of rod-shape, we constructed ΔrodZ MreB WT + MreB WT* and ΔrodZ MreB E276D + MreB E276D* strains. ΔrodZ MreB WT + MreB WT* cells were slow-growing spheres (Fig. 5b, Supplementary Fig. 5d,e), unlike ΔrodZ MreB WT + MreB E276D* cells that displayed a contour curvature profile representative of rodshaped cells (Fig. 5b). After 90 min of growth, the ΔrodZ MreB WT + MreB E276D* strain exhibited a wider range of MreB enrichment than the ΔrodZ MreB WT + MreB WT* strain (Fig. 5c). While some ΔrodZ MreB E276D + MreB E276D* cells were rodshaped (Supplementary Table 2), this strain displayed significantly longer lag time ( Supplementary Fig. 5d,f) and lower growth rate ( Supplementary Fig. 5d,e) than ΔrodZ MreB WT + MreB E276D* or ΔrodZ MreB WT cells ( Supplementary Fig. 5a,e,f).
To ascertain whether ΔrodZ MreB WT + MreB E276D* and ΔrodZ MreB E276D + MreB E276D* cells were truly undergoing rod-like growth, we grew them in the presence of cephalexin, which inhibits the division-specific cell wall-synthesis enzyme PBP3 36 . In the presence of cephalexin, round E. coli cells lyse due to the inability to divide 37 , whereas rod-shaped E. coli cells elongate to tens of microns 11 . Many ΔrodZ MreB WT + MreB E276D* cells (80%) elongated by more than twofold over 70 min without dramatically changing cell width, whereas only 50% of ΔrodZ MreB E276D + MreB E276D* cells were able to double in length as opposed to halting growth (Fig. 5d, n ≥ 50 cells). Taken together, these ΔrodZ MreB WT + MreB E276D* data demonstrate recovery of rod-like shape in the absence of RodZ; the enhanced recovery compared with ΔrodZ MreB E276D + MreB E276D* cells suggest the importance of the relative levels of RodZ-bound and unbound MreB in wild-type cells.
RodZ-related MreB mutant filaments are longer than WT filaments. How are the biophysical properties of MreB connected to the cellular-scale properties of filaments and intracellular patterning? Since our MD simulations predicted that RodZ binding and various MreB mutations alter curvature enrichment by changing filament bending, and moreover since some perturbations (A174T, E276D) occurred near the polymerization interface of the MreB filament structure, we wondered whether these changes manifested in part as increased MreB polymer length. MreB usually forms diffraction-limited puncta 9,10 ; thus, to measure the patterning of MreB, we carried out super-resolution imaging using structured illumination microscopy (Methods section). Strikingly, some cells expressing MreB E276D alone contained filaments that were much longer than filaments in MreB WT cells, extending several microns in many cases (Fig. 5e). In contrast, MreB WT formed small structures, presumably consisting of short filaments, with sizes consistent with structures imaged using epifluorescence microscopy (Fig. 5e). MreB R124C , MreB D83E , and MreB A174T cells displayed fluorescence patch sizes (Methods section) intermediate between those of MreB WT and MreB E276D cells (Fig. 5f), suggesting that all mutations stabilized filaments compared to MreB WT . Neither MreB E276D nor MreB WT structure sizes were significantly smaller when rodZ was deleted (Fig. 5g), suggesting that RodZ does not alter MreB oligomerization. MreB WT + MreB E276D* cells contained MreB structures of intermediate size (Fig. 5g), consistent with the hypothesis that MreB WT and MreB E276D subunits form hybrid filaments. Consistent with previous observations, cells that were more rod-like (Methods section) had larger MreB structures than did less-rod-like cells ( Supplementary Fig. 10, p < 0.0001 by the two-sample Kolmogorov-Smirnov test), suggesting that intermediate polymer size is required for the recovery of rod-shaped cells in the absence of RodZ.

Discussion
Here we demonstrate that E. coli dynamically modulates the geometric sensing of MreB via RodZ to drive changes in cell shape. Increased RodZ expression systematically enhanced the enrichment of MreB in regions of negative contour curvature (Fig. 2d), suggesting that RodZ alters the biophysical properties of MreB filaments, and decreased cell width (Fig. 2e), indicating that the changes in MreB localization affect cell morphology. Our MD simulations predicted that the bending of ATP-bound MreB filaments is reduced by RodZ binding (Fig. 4d), which could stabilize filaments on the relatively flat membrane. Nonetheless, it is also likely that filament mechanics is intrinsically coupled to biochemical parameters such as hydrolysis state 21 , which in turn affect polymer size. Although structured illumination microscopy suggested that the formation of larger MreB oligomers is necessary for rod-shaped growth in ΔrodZ cells (Fig. 5f), the observation that MreB E276D did not rescue rod-like shape in ΔrodZ cells ( Supplementary Fig. 5g) may be due to the inability of very long filaments (Fig. 5g) to adjust to local variations in cell shape. By contrast, the combination of MreB WT and MreB E276D was sufficient to recover rod-shaped growth in the absence of RodZ ( Fig. 5a-d), implying the need for balance between the polymeric properties of RodZ-bound and unbound MreB WT filaments. The three ΔrodZ suppressor MreB mutants that we studied have different curvature enrichment profiles (Fig. 3d) and larger polymer patch sizes (Fig. 5f) than wild-type cells in vivo, and while these changes enable growth in the absence of ΔrodZ, potentially due to the capacity of these mutant filaments to mimic the effects of RodZ binding on MreB polymer mechanics (Fig. 4d), all three mutants have a fitness cost and altered shape relative to MreB WT that we suggest results from the inability to properly modulate MreB filament length and mechanics in a wild-type manner. A previous study reported that the only ΔrodZ suppressor MreB mutant that had higher self-interaction than MreB WT was also the only mutant that rescued rod-like shape in minimal medium 30 , possibly due to the need for longer MreB filaments in minimal medium, further highlighting the links between regulation of MreB polymerization and shape determination. Although it remains possible that some effects of RodZ expression on MreB and cell shape are indirect, the inducible RodZ expression system and MreB mutations we have analyzed here should prove powerful and complementary tuning knobs for further dissection of the variables dictating MreB localization and cell-shape determination.
Much remains to be discovered regarding the links between MreB, its binding partners, and cell-wall insertion. A previous study showed that RodZ is required for processive motion of MreB 37 , while our previous simulations suggested that curvaturemediated patterning could be responsible for processive motion along the circumferential deformations of negative Gaussian curvature induced by cell-wall insertion 11 . Given that RodZ also affects MreB curvature enrichment, the two bases for processivity are not necessarily contradictory. Moreover, while MreB depolymerization by A22 alters the pattern of cell-wall insertion, suggesting that MreB patterning dictates cell shape, it may also be the case that other aspects of cell size changes affect MreB dynamics and localization. In organisms such as Bacillus subtilis that have multiple MreB homologs, it is possible that RodZ differentially modulates the curvature enrichment of each homolog. MreB has been shown to co-localize with MreC/D 16 and FtsZ in E. coli 38 ; in the latter case, FtsZ adopts various filament conformations 39,40 , which could couple mechanically to MreB. Thus, MreB may have as diverse a set of partners as the actin-binding proteins that enable myriad functions 41 . Given that some actinbinding proteins can deform membranes 42 , other bacterial proteins may act similarly to RodZ to specifically modulate MreB's curvature preference.
The rapid changes in cell shape during the progression from stationary phase to exponential growth and back (Fig. 1b) are consistent with the classic Growth Law of a positive relationship between nutrient-determined steady-state growth rate and cell size 23 , as well as with a more recent finding linking relative rates of surface and volume synthesis to cell-size determination 43 . Our discovery that the curvature preference of MreB (Fig. 1h) varies continuously with growth rate (Fig. 1a), cell size (Fig. 1b), and the ratio of MreB to RodZ (Fig. 2d) suggests that RodZ-driven MreB localization may be a major component of the regulation of cell size; MreB enrichment profiles and cellular dimensions both changed gradually over the first 3 h of passaging (Fig. 1b, h), and the variability in enrichment profiles across time points was similar to what we achieved by modulating RodZ levels (Fig. 2d). Our data indicate that for a fixed contour curvature, MreB prefers wider regions of the cell (Fig. 1f), which may provide a homeostasis mechanism for cell width. The rapid dynamics in mean width and length over 1-2 h (Fig. 1b) indicate that both dimensions can be tuned over a few generations in either direction. This rapid size variation should be useful for probing many general physiological questions such as the coupling between DNA replication and cell division 44 . The remarkable ability of bacterial cells to adjust their size, and hence their physiology, with different concentrations of the same molecular components highlights their ability to regulate and exploit the biophysics of their cytoskeletons.

Methods
Strains and growth conditions. All E. coli strains and plasmids used in this study, along with the condition-dependent mean cell length and width of all imaging experiments, are described in Supplementary Table 2. Strain construction was performed using standard transformation or transduction methods. Lysogeny broth (LB) with 5 g/L NaCl was used for all experiments. Strains were grown at 37°C . The antibiotics chloramphenicol (Sigma-Aldrich) and cephalexin (MP Biomedicals) were used at concentrations of 15 μg/mL and 10 μg/mL, respectively. For rodZ induction experiments, xylose or arabinose were supplemented as described in the main text.
ΔrodZ suppressor MreB mutants were generated using λ-Red recombination in the parental strain expressing a sandwich fusion of MreB to msfGFP (NO34) following standard protocols 45 . The resulting colonies were confirmed by colony PCR and sequencing. Mutated MreB-msfGFP alleles were moved to a clean MG1655 background using P1 transduction.
To measure growth curves, cells were cultured in LB to stationary phase for 18 h or 24 h, then back diluted 200-fold into LB. Optical density was measured using an M200 plate reader (Tecan Group).
Morphological time course. To monitor cell shape as a function of population density, we back-diluted a 24-h culture grown in LB 1:200 into fresh LB in a test tube. Every 15 min, we extracted a small sample and imaged cells on an agarose pad. To minimize temperature fluctuations of the growing culture, cultures were immediately returned to the incubator after the brief period of sample extraction. Cells were imaged with phase-contrast and epifluorescence microscopy to measure cell shape and MreB localization.
Microscopy. Cells were imaged on a Nikon Eclipse Ti-E inverted fluorescence microscope with a 100X (NA 1.40) oil-immersion objective (Nikon Instruments Inc., Melville, NY, USA). Images were collected using an Andor DU885 EMCCD or Neo 5.5 sCMOS camera (Andor Technology, South Windsor, CT, USA). Cells were maintained at 37°C during imaging with an active-control environmental chamber (HaisonTech, Taipei, Taiwan). Images were collected using µManager v. 1.4 46 .
Image analysis. The MATLAB (MathWorks, Natick, MA, USA) image processing software Morphometrics 29 was used to segment cells and to identify cell contours from phase-contrast images. Fluorescence intensity profiles were generated by integrating image fluorescence along lines perpendicular to the contour at points uniformly spaced by approximately one pixel, extending five pixels in either direction. Mid-plane contour curvature was a three-point measurement defined by the arc-length derivative of the vector field formed from the unit normals to the contour, and did not assume any correlation of curvature values on opposite sides of the neutral axis of the cell 11 . Each curvature profile was smoothed with a lowpass Gaussian filter. Cells were categorized as rod-like or non-rod-like based on the success or failure of the Morphometrics meshing function, which determines whether a grid of lines perpendicular to a midline can be used as a coordinate system for the polygon defined by the cell contour.
Equilibrium MD simulations. All simulations were performed as in ref. 21 using the package NAMD 47 with the CHARMM27 force field 48,49 . Water molecules were described with the TIP3P model 50 . Long-range electrostatic forces were evaluated with the particle-mesh Ewald summation approach with a grid spacing of <1 Å. An integration time step of 2 fs was used 51 . Bonded terms and short-range, nonbonded terms were evaluated at every time step, and long-range electrostatics were evaluated at every other time step. Constant temperature (T = 310 K) was maintained using Langevin dynamics, with a damping coefficient of 1.0 ps −1 . A constant pressure of 1 atm was enforced using the Langevin piston algorithm 52 with a decay period of 200 fs and a time constant of 50 fs.
Simulated systems. Twelve MD systems were analyzed (Supplementary Table 3), eight of which were simulated in this study. For all simulations without RodZ, the MreB crystal structure of T. maritima MreB bound to AMP-PNP (PDB ID: 1JCG) 5 was used, with the nucleotide modified to ATP or ADP 21 . For simulations including RodZ, the cytoplasmic tail of RodZ was added to each MreB by aligning the simulated dimer with the co-crystal structure of MreB and RodZ (PDB ID: 2WUS). Water and neutralizing ions were added around each MreB dimer, resulting in final simulation sizes of 95,000-143,000 atoms. All unconstrained simulations were performed for at least 50 ns. Setup, analysis, and rendering of the simulation systems were performed with VMD 53 . To compute average values and distributions of measurements, only the last 30 ns of each simulation trajectory were used. To ensure that the simulations had reached equilibrium, measurement distributions were fit to a Gaussian distribution. A satisfactory fit implies that the system is located within an energy minimum well approximated by a harmonic potential. All simulations were repeated at least twice, and repeat simulations gave similar results (Supplementary Fig. 7). Relative bending orientations of dimer subunits were calculated by determining the rotational transformation required to align the subunits 21 .
Structured illumination microscopy. Overnight, saturated cultures were backdiluted 1:100 into fresh LB and grown at 37°C with shaking until OD~0.1. One milliliter of the cells was fixed in phosphate-buffered saline containing 3% glutaraldehyde/3% paraformaldehyde (Electron Microscopy Sciences) at room temperature for 15 min, with 1 μg/mL FM4-64FX membrane stain (Invitrogen) added during fixation. Cells were washed three times in cold phosphate-buffered saline, and 1 µL of the cell solution was pipetted onto a No. 1.5 coverslip (Zeiss) coated with poly-L-lysine solution (Sigma-Aldrich). After the droplet dried, a small drop of ProLong Diamond AntiFade Mountant (Thermo Fisher) was added on top of the droplet, and the coverslip was mounted on a glass slide (VWR) and sealed with VALAP (equal parts Vaseline, lanolin, and paraffin by weight).
Cell samples were imaged on an OMX V4 microscope platform (GE Life Sciences) with a 100X (NA 1.42) oil-immersion objective (Nikon Instruments). Images from two channels were collected on two Evolve 512 electron-multiplying charged couple device cameras (Photometrics) using DeltaVision microscopy imaging system v. 3.70 (GE Life Sciences).
Image analysis for structured illumination microscopy. Raw images were reconstructed and aligned using SoftWoRx v6.5.2 (GE Life Sciences), and maximum projection images were created using FIJI 54 . Individual cells were segmented from the FM4-64FX signal using Morphometrics. MreB patches within each cell contour were identified from the GFP channel based on intensity, and patches smaller than the diffraction limit for structured illumination microscopy (~0.03 μm 2 ) were excluded from further quantification. The two-sample Kolmogorov-Smirnov test was used to test the null hypothesis that two one-dimensional samples are drawn from the same underlying probability distribution.
Data availability. The datasets generated and/or analyzed during the current study are available from the corresponding author on request.