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Surface-to-volume scaling and aspect ratio preservation in rod-shaped bacteria

  1. Nikola Ojkic
  2. Diana Serbanescu
  3. Shiladitya Banerjee  Is a corresponding author
  1. University College London, United Kingdom
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Cite this article as: eLife 2019;8:e47033 doi: 10.7554/eLife.47033

Abstract

Rod-shaped bacterial cells can readily adapt their lengths and widths in response to environmental changes. While many recent studies have focused on the mechanisms underlying bacterial cell size control, it remains largely unknown how the coupling between cell length and width results in robust control of rod-like bacterial shapes. In this study we uncover a conserved surface-to-volume scaling relation in Escherichia coli and other rod-shaped bacteria, resulting from the preservation of cell aspect ratio. To explain the mechanistic origin of aspect-ratio control, we propose a quantitative model for the coupling between bacterial cell elongation and the accumulation of an essential division protein, FtsZ. This model reveals a mechanism for why bacterial aspect ratio is independent of cell size and growth conditions, and predicts cell morphological changes in response to nutrient perturbations, antibiotics, MreB or FtsZ depletion, in quantitative agreement with experimental data.

https://doi.org/10.7554/eLife.47033.001

Introduction

Cell morphology is an important adaptive trait that is crucial for bacterial growth, motility, nutrient uptake, and proliferation (Young, 2006). When rod-shaped bacteria grow in media with different nutrient availability, both cell length and width increase with growth rate (Schaechter et al., 1958; Si et al., 2017). At the single-cell level, control of cell volume in many rod-shaped cells is achieved via an adder mechanism, whereby cells elongate by a fixed length per division cycle (Amir, 2014; Campos et al., 2014; Taheri-Araghi et al., 2015Deforet et al., 2015Wallden et al., 2016; Banerjee et al., 2017). A recent study has linked the determination of cell size to a condition-dependent regulation of cell surface-to-volume ratio (Harris and Theriot, 2016). However, it remains largely unknown how cell length and width are coupled to regulate rod-like bacterial shapes in diverse growth conditions (Volkmer and Heinemann, 2011; Belgrave and Wolgemuth, 2013; Colavin et al., 2018; Shi et al., 2018).

Results

Here we investigated the relation between cell surface area (S) and cell volume (V) for E. coli cells grown under different nutrient conditions, challenged with antibiotics, protein overexpression or depletion, and single gene deletions (Nonejuie et al., 2013; Harris and Theriot, 2016; Si et al., 2017; Vadia et al., 2017Campos et al., 2018Gray et al., 2019). Collected surface and volume data span two orders of magnitude and exhibit a single power law in this regime: S=γV2/3 (Figure 1A). Specifically, during steady-state growth (Si et al., 2017), γ = 6.24 ± 0.04, suggesting an elegant geometric relation: S2πV2/3. This surface-to-volume scaling with a constant prefactor, γ, is a consequence of tight control of cell aspect ratio η (length/width) (Figure 1D), whose mechanistic origin has been puzzling for almost half a century (Zaritsky, 1975Zaritsky, 2015). Specifically, for a sphero-cylindrical bacterium, S=γV2/3 implies γ=ηπ(ηπ4-π12)-2/3. A constant γ thus defines a constant aspect ratio η = 4.14 ± 0.17 (Figure 1B-inset), with a coefficient of variation ∼14% (Figure 1B).

Figure 1 with 1 supplement see all
Surface-to-volume scaling in E. coli and other rod-shaped bacteria.

(A) E. coli cells subjected to different antibiotics, nutrient conditions, protein overexpression/depletion, and single gene deletions (Nonejuie et al., 2013; Si et al., 2017; Harris and Theriot, 2016; Vadia et al., 2017; Campos et al., 2018; Gray et al., 2019), follow the scaling relation between population-averaged surface area (S) and volume (V): S=γV2/3 (legend on the right, 5011 data points; Supplementary file 1). Best fit shown in dashed black line for steady-state data from Si et al. (2017) gives γ = 6.24 ± 0.04, and a power law exponent 0.671 ± 0.006. For single deletion Keio set (Campos et al., 2018), the best fit curve is S=5.79V2/3. (B) Aspect-ratio distribution for cells growing in steady-state, corresponding to the data in (A) (Si et al., 2017). (Inset) Relationship between γ and aspect ratio η for a sphero-cylinder (red line). Best fit from (A) shown with horizontal green band gives aspect ratio 4.14 ± 0.17. (C) S/V vs growth rate. Model line uses S=2πV2/3 and the nutrient growth law (Equation 1). Data from Si et al. (2017). (D) S-V relation for various bacterial cell shapes. Black dashed line: Small, medium, and large rod-shaped cells with a conserved aspect ratio of 4 follow the relation: S=2πV2/3. Gray dashed line: Filamentous cells with constant cell width follow the scaling law: SV. Red dashed line: Spheres follow S=62/3π1/3V2/3. (E) S vs V for 49 different bacterial species (Sato, 2000; Trachtenberg, 2004; Pelling et al., 2005; Wright et al., 2015; Deforet et al., 2015; Desmarais et al., 2015; Harris and Theriot, 2016; Ojkic et al., 2016; Quach et al., 2016; Carabetta et al., 2016; Chattopadhyay et al., 2017; Lopez-Garrido et al., 2018; Gray et al., 2019), and one rod-shaped Archaea (H. volcanii) (Supplementary file 2). Rod-shaped cells lie on S=2πV2/3 line, above the line are Spirochete and below the line are coccoid. For coccoid S. aureus exposed to different antibiotics best fit is S=4.92V2/3, with preserved aspect ratio η = 1.38 ± 0.18. Red dashed line is for spheres.

https://doi.org/10.7554/eLife.47033.002

The surface-to-volume relation for steady-state growth, S2πV2/3, results in a simple expression for cell surface-to-volume ratio: S/V2πV-1/3. Using the phenomenological nutrient growth law V=V0eακ (Schaechter et al., 1958), where κ is the population growth rate, a negative correlation emerges between S/V and κ:

(1) S/V2πV0-1/3e-ακ/3,

with V0 the cell volume at κ=0, and α is the relative rate of increase in V with κ (Figure 1C). In Equation (1) underlies an adaptive feedback response of the cell — at low nutrient concentrations, cells increase their surface-to-volume ratio to promote nutrient influx (Si et al., 2017; Harris and Theriot, 2018). Prediction from Equation (1) is in excellent agreement with the best fit to the experimental data. Furthermore, a constant aspect ratio of ≈4 implies V8w3 and S4πw2, where w is the cell width, suggesting stronger geometric constraints than recently proposed (Harris and Theriot, 2018; Shi et al., 2018). Thus, knowing cell volume as a function of cell cycle parameters (Si et al., 2017) we can directly predict cell width and length under changes in growth media, in agreement with experimental data (Figure 1—figure supplement 1A–B). We further analysed cell shape data for 48 rod-shaped bacteria, one rod-shaped Archaea (H. vulcanii), two long spiral Spirochete, and one coccoid bacteria (Figure 1E). Collected data for all rod-shaped cells follow closely the relationship S2πV2/3, while the long Spirochetes deviate from this curve (Figure 1D–E). Coccoid S. aureus also follows the universal scaling relation S=γV2/3 (with γ = 4.92), but maintains a much lower aspect ratio η = 1.38 ± 0.18 (Quach et al., 2016) when exposed to different antibiotics (Figure 1D–E). Therefore, aspect-ratio preservation likely emerges from a mechanism that is common to diverse rod-shaped and coccoid bacterial species.

To investigate how aspect ratio is regulated at the single cell level we analysed the morphologies of E. coli cells grown in the mother machine (Taheri-Araghi et al., 2015) (Figure 2A,B). For five different growth media, mean volume and surface area of newborn cells also follow the relationship S=2πV2/3, suggesting that a fixed aspect ratio is maintained on average. In the single-cell data, slight deviation from the 2/3 scaling is a consequence of large fluctuations in newborn cell lengths for a given cell width (Figure 2—figure supplement 1A–B). Importantly, the probability distribution of aspect ratio is independent of the growth media (Figure 2B), implying that cellular aspect ratio is independent of cell size as well as growth rate.

Figure 2 with 1 supplement see all
Aspect ratio control in E. coli at the single cell level.

(A) S vs V for newborn E. coli cells grown in mother machine (Taheri-Araghi et al., 2015). Single cell data (small circles) binned in volume follow population averages (large circles). For sample size refer to Supplementary file 1. (B) Probability distribution of newborn cell aspect ratio is independent of growth rate, fitted by a log-normal distribution (solid line) (C) Model schematic. Cell length L increases exponentially during the division cycle at a rate k. Division proteins (P) are produced at a rate kP, and assembles a ring in the mid-cell region. At birth, cells contain P* molecules in the cytoplasm. Amount of FtsZ recruited in the ring is Pr. Cells divide when Pr=P0w, where w is cell width. P vs time and L vs time are reproduced from model simulations. (D) Ratio of the added length (ΔL) and cell width (w) during one cell cycle is constant and independent of growth rate. Error bars: ±1 standard deviation.

https://doi.org/10.7554/eLife.47033.004

To explain the origin of aspect ratio homeostasis we developed a quantitative model for cell shape dynamics that accounts for the coupling between cell elongation and the accumulation of cell division proteins FtsZ (Figure 2C). Our model is thus only applicable to bacteria that divide using the FtsZ machinery. E. coli and other rod-like bacteria maintain a constant width during their cell cycle while elongating exponentially in length L (Donachie et al., 1976; Taheri-Araghi et al., 2015): dL/dt=kL, with k the elongation rate. Cell division is triggered when a constant length is added per division cycle — a mechanism that is captured by a model for threshold accumulation of division initiator proteins, produced at a rate proportional to cell size (Basan et al., 2015; Deforet et al., 2015; Ghusinga et al., 2016). While many molecular candidates have been suggested as initiators of division (Adams and Errington, 2009), a recent study (Si et al., 2019) has identified FtsZ as the key initiator protein that assembles a ring-like structure in the mid-cell region to trigger septation.

Dynamics of division protein accumulation can be described using a two-component model. First, a cytoplasmic component with abundance Pc grows in proportion to cell size (L), as ribosome content increases with cell size (Marguerat and Bähler, 2012). Second, a ring-bound component, Pr, is assembled from the cytoplasmic pool at a constant rate. Dynamics of the cytoplasmic and ring-bound FtsZ are given by:

(2) dPcdt=-kbPc+kdPr+kPL,
(3) dPrdt=kbPc-kdPr,

where kP is the constant production rate of cytoplasmic FtsZ, kb is the rate of binding of cytoplasmic FtsZ to the Z-ring, and kd is the rate of disassembly of Z-ring bound FtsZ. At the start of the cell cycle, we have Pc=P* (a constant) and Pr=0. Cell divides when Pr reaches a threshold amount, P0, required for the completion of ring assembly. A key ingredient of our model is that P0 scales linearly with the cell circumference, P0=ρπw, preserving the density ρ of FtsZ in the ring. This is consistent with experimental findings that the total FtsZ scales with the cell width (Shi et al., 2017). Accumulation of FtsZ proteins, P=Pc+Pr-P*, follows the equation: dP/dt=kPL, where kP is the production rate of division proteins, with P=0 at the start of the division cycle. We assume that kbkd, such that all the newly synthesized cytoplasmic proteins are recruited to the Z-ring at a rate much faster than growth rate (Söderström et al., 2018). As a result, cell division occurs when P=P0 (Figure 2C). Upon division P is reset to 0 for the two daughter cells. It is reasonable to assume that all the FtsZ proteins are in filamentous form at cell division, as the concentration of FtsZ in an average E. coli cell is in the range 4–10 μM, much higher than the critical concentration 1 μM (Erickson et al., 2010).

From the model it follows that during one division cycle cells grow by adding a length ΔL=P0k/kP, which equals the homeostatic length of newborn cells. Furthermore, recent experiments suggest that the amount of FtsZ synthesised per unit cell length, dP/dL, is constant (Si et al., 2019). This implies,

(4) dLdP=kkP=ΔLP0ΔLw=const.

Aspect ratio homeostasis is thus achieved via a balance between the rates of cell elongation and division protein production, consistent with observations that FtsZ overexpression leads to minicells and FtsZ depletion induces elongated phenotypes (Potluri et al., 2012; Zheng et al., 2016). Indeed single cell E. coli data (Taheri-Araghi et al., 2015) show that ΔL/w is constant on average and independent of growth conditions (Figure 2D). Furthermore, added length correlates with cell width during one cell cycle implying that the cell width is a good predictor for added cell length (Figure 2—figure supplement 1C–D).

To predict cell-shape dynamics under perturbations to growth conditions we simulated our single-cell model (Figure 3, Materials and methods) with an additional equation for cell width that we derived from a recent model proposed by Harris and Theriot (2016): dS/dt=βV, where β is the rate of surface area synthesis relative to volume and is a linearly increasing function of k (Figure 3—figure supplement 1A). This model leads to an equation for the control of cell width for a sphero-cylinder shaped bacterium,

(5) dwdt=w(k-βw/4)1-w/3L1-w/L,

such that w=4k/β at steady-state. It then follows from Equation (4) that the added cell length ΔLk2/βkP. However, our model for division control is mechanistically different from Harris and Theriot (2016). In the latter, cells accumulate a threshold amount of excess surface area material to trigger septation, which does not lead to aspect ratio preservation. By contrast, we propose that cells divide when they accumulate a threshold amount of division proteins in the Z-ring, proportional to the cell diameter.

Figure 3 with 1 supplement see all
Simulations of aspect ratio preservation during nutrient upshift or downshift.

(A–C) At t = 0 h cells are exposed to nutrient upshift or downshift. Population average of n = 105 simulated cells. (A) Growth rate (k) vs time used as input for our simulations. (B) Population-averaged cell length and width vs time. (C) Population-averaged aspect ratio of newborn cells vs time. Changes in cell width and length result in a transient increase in aspect ratio during nutrient downshift, or a transient decrease during nutrient upshift.

https://doi.org/10.7554/eLife.47033.006

We simulated nutrient shift experiments using the coupled equations for cell length, width and division protein production (Materials and methods). When simulated cells are exposed to new nutrient conditions (Figure 3—figure supplement 1B–E), changes in cell width result in a transient increase in aspect ratio (η=L/w) during nutrient downshift, or a transient decrease in η during nutrient upshift (Figure 3C). After nutrient shift, aspect ratio reaches its pre-stimulus homeostatic value over multiple generations. Typical timescale for transition to the new steady-state is controlled by the growth rate of the new medium (k-1), such that the cell shape parameters reach a steady state faster in media with higher growth rate. This result is consistent with the experimental observation that newborn aspect ratio reaches equilibrium faster in fast growing media (Taheri-Araghi et al., 2015) (Figure 3—figure supplement 1F). In our model, cell shape changes are controlled by two parameters: the ratio k/kP that determines cell aspect ratio, and k/β that controls cell width (Figure 4A). Nutrient upshift or downshift only changes the ratio k/β while keeping the steady-state aspect ratio (k/kP) constant.

Figure 4 with 1 supplement see all
Model predictions for aspect ratio and shape control under perturbations.

(A) Model parameters that control changes in cell aspect ratio (k/kP) or width (k/β). For quantification see Figure 4—figure supplement 1A. (B) Surface area vs volume for cells under antibiotic treatment (Nonejuie et al., 2013), FtsZ knockdown and MreB depletion (Si et al., 2017; Zheng et al., 2016). Solid lines are best fit obtained using our model and data from Zheng et al. (2016) (see Materials and methods). Cells with depleted FtsZ have elongated phenotypes, while depleted MreB have smaller aspect ratio and larger width. Cell wall or DNA targeting antibiotics induce filamentation. Dashed green line: S=2πV2/3, dashed black line: spheres.

https://doi.org/10.7554/eLife.47033.008

We further used our model to predict drastic shape changes leading to deviations from the homeostatic aspect ratio when cells are perturbed by FtsZ knockdown, MreB depletion, and antibiotic treatments that induce non steady state filamentation (Figure 4B). First, FtsZ depletion results in long cells while the width stays approximately constant, SV0.95 (Figure 4—figure supplement 1C), data from Zheng et al. (2016). We modelled FtsZ knockdown by decreasing kP and simulations quantitatively agree with experimental data. Second, MreB depletion increases the cell width and slightly decreases cell length while keeping growth rate constant (Zheng et al., 2016). We modelled MreB knockdown by decreasing β as expected for disruption in cell wall synthesis machinery, while simultaneously increasing kP (Materials and methods). This increase in kP is consistent with a prior finding that in MreB mutant cells of various sizes, the total FtsZ scales with the cell width (Shi et al., 2017). Furthermore, cells treated with MreB inhibitor A22 induce envelope stress response system (Rcs) that in turn activates FtsZ overproduction (Carballès et al., 1999; Cho et al., 2014). Third, transient long filamentous cells result from exposure to high dosages of cell-wall targeting antibiotics that prevent cell division, or DNA-targeting antibiotics that induce filamentation via SOS response (Nonejuie et al., 2013). Cell-wall targeting antibiotics inhibit the activity of essential septum forming penicillin binding proteins, preventing cell septation. We modelled this response as an effective reduction in kP, while slightly decreasing surface synthesis rate β (Materials and methods). For DNA targeting antibiotics, FtsZ is directly sequestered during SOS response resulting in delayed ring formation and septation (Chen et al., 2012). Surprisingly all filamentous cells have a similar aspect ratio of 11.0 ± 1.4, represented by a single curve in the S-V plane (Figure 4B).

Discussion

The conserved surface-to-volume scaling in diverse bacterial species, SV2/3, is a direct consequence of aspect-ratio homeostasis at the single-cell level. We present a regulatory model (Figure 2C) where aspect-ratio control is the consequence of a constant ratio between the rate of cell elongation (k) and division protein accumulation (kP). Deviation from the homeostatic aspect ratio is a consequence of altered k/kP, as observed in filamentous cells, FtsZ or MreB depleted cells (Figure 4B). By contrast, drugs that target cell wall biogenesis, for example Fosfomycin, do not alter k/kP and maintain cellular aspect ratio (Figure 4—figure supplement 1C).

Our study suggests that cell width is an essential shape parameter for determining cell length in E. coli (Figure 2—figure supplement 1C–D). This is to be contrasted with B. subtilis, where cell width stays approximately constant across different media, while elongating in length (Sharpe et al., 1998). However, FtsZ recruitment in B. subtilis is additionally controlled by effector UgtP, which localises to the division site in a nutrient-dependent manner and prevents Z-ring assembly (Weart et al., 2007). This can be interpreted as a reduction in kP with increasing k, within the framework of our model. As a result, B. subtilis aspect ratio (k/kP) is predicted to increase with increasing growth rate.

Aspect ratio control may have several adaptive benefits. For instance, increasing cell surface-to-volume ratio under low nutrient conditions can result in an increased nutrient influx to promote cell growth (Figure 1C). Under translation inhibition by ribosome-targeting antibiotics, bacterial cells increase their volume while preserving aspect ratio (Harris and Theriot, 2016; Si et al., 2017). This leads to a reduction in surface-to-volume ratio to counter further antibiotic influx. Furthermore, recent studies have shown that the efficiency of swarming bacteria strongly depends on their aspect ratio (Ilkanaiv et al., 2017; Jeckel et al., 2019). The highest foraging speed has been observed for aspect ratios in the range 4–6 (Ilkanaiv et al., 2017), suggesting that the maintenance of an optimal aspect ratio may have evolutionary benefits for cell swarmers.

Materials and methods

Cell shape analysis

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Bacterial cell surface area and volume are obtained directly from previous publications where these values were reported (Si et al., 2017; Campos et al., 2018; Gray et al., 2019), or they are calculated assuming a sphero-cylindrical cell geometry using reported values for population-averaged cell length and width (Vadia et al., 2017; Nonejuie et al., 2013; Zheng et al., 2016; Wright et al., 2015; Deforet et al., 2015; Desmarais et al., 2015; Ojkic et al., 2016; Carabetta et al., 2016; Lopez-Garrido et al., 2018). Single cell data are obtained from Suckjoon Jun lab (UCSD) (Taheri-Araghi et al., 2015). For number of cells analyzed per growth condition see Supplementary file 1. Intergeneration autocorrelation function (Figure 2—figure supplement 1D) of average cell width during one cell cycle is calculated using expression in Ojkic et al. (2014). For a spherocylinder of pole-to-pole length L and width w, the surface area is S=wLπ, and volume is given by V=π4w2L-π12w3. In the case of S. aureus, surface area and volume are computed assuming prolate spheroidal shape using reported population averaged values of cell major axis, c, and minor axis a (Quach et al., 2016). Surface area of a prolate spheroid is S=2πa2+2πac2c2-a2arcsin(c2-a2c), and volume is V=4π3a2c.

Cell growth simulations

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We simulated the single-cell model using the coupled equations for the dynamics of cell length L, cell width w, and division protein production P (Figure 2C). In simulations, when P reaches the threshold P0=ρπw, the mother cell divides into two daughter cells whose lengths are 0.5 ± δ of the mother cell. Parameter δ is picked from Gaussian distribution (μ=0, σ=0.05).

For nutrient shift simulations we simulated 105 asynchronous cells growing at a rate k=0.75h-1 (Figure 3). In Equation 5, parameter β=4k/w is obtained from the fit to experimental data for 4k/w vs k (Figure 3—figure supplement 1A) (Si et al., 2017), giving β=3.701k+0.996, where k is in units of h–1, and β in h-1 μm-1. At t = 0 h we change k corresponding to nutrient upshift (k= 1.25, 2 h-1) or nutrient downshift (k= 0.75, 0.25 h-1). We calculated population average of length and width (Figure 3B), and population average of aspect ratio of newborn cells (Figure 3C). Aspect ratio of newborn cells are binned in time and the bin average is calculated for a temporal bin size of 10 min. Examples of single cell traces during the nutrient shift are shown in Figure 3—figure supplement 1B–E.

FtsZ depletion experiment (Zheng et al., 2016) was simulated for w=1μm while kP was reduced to 40% of its initial value. This is consistent with the reduction of relative mRNA to ∼40% corresponding to addition of 3 ng/ml of aTc to reduce ftsZ expression (Zheng et al., 2016). Our model predictions for the dependence of cell aspect ratio on kb/kd is shown in Figure 4—figure supplement 1B.

Best fit for MreB depletion experiment (Zheng et al., 2016) was obtained for η ≈ 2.7, by simulating reduction in division protein production rate, kP, and by varying β so that width spans range from 0.9 to 1.8 μm. The best fit for long filamentous cells (resulting from DNA or cell-wall targeting antibiotics) was obtained for η ≈ 11.0 . Filamentation was simulated by decreasing kP and β so that w spans the range from 0.9 to 1.4 μm as experimentally observed (Nonejuie et al., 2013).

Open Source Physics (www.compadre.org) Java was used for executing the simulations and Mathematica 11 for data analysis, model fitting, and data presentation.

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Decision letter

  1. Raymond E Goldstein
    Reviewing Editor; University of Cambridge, United Kingdom
  2. Naama Barkai
    Senior Editor; Weizmann Institute of Science, Israel
  3. Charles W Wolgemuth
    Reviewer

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

[Editors’ note: this article was originally rejected after discussions between the reviewers, but the authors were invited to resubmit after an appeal against the decision.]

Thank you for submitting your work entitled "Universal surface-to-volume scaling and aspect ratio homeostasis in rod-shaped bacteria" for consideration by eLife. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Charles W Wolgemuth (Reviewer #1).

The reviewers had no doubt that the subject matter of your paper is both interesting and timely, but both have raised questions about its significance, the nature of the underlying assumptions, and the level of "universality" that can be claimed. Our decision on your manuscript has been reached after consultation between the reviewers. Based on these discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in eLife.

Reviewer #1:

This manuscript compiles data on the length, width, and growth rate of E. coli under a number of experimental perturbations, such as changes in growth medium, incubation in antibiotics, inhibited protein synthesis, etc. and shows that the surface area to volume ratio is strongly conserved. This result is consistent with recent work from Julie Theriot's group (which is cited in Harris and Theriot, 2016; 2018). In this manuscript, the author's also add data from other rod-shaped bacteria that show similar behavior (Figure 1G). The authors use this result to develop a model for aspect ratio regulation that is based on exponential growth of the bacterial length at fixed width, FtsZ production at a rate proportional to volume growth rate (which by assuming constant width also assumes that the FtsZ production is proportional to the length growth rate), and division that occurs when FtsZ production reaches a critical value that is proportional to the width. This model predicts a constant aspect ratio and the authors then go on to predict the dynamics under impulse type perturbations.

I have two main concerns with the manuscript.

First, the only novelty of the model is the assumption that there is a critical amount of FtsZ required to divide the cell and that this depends on the width. I think that this is a reasonable assumption, but I also feel that the overall results are fairly obvious. That is, it is not clear that the model provides a significant advance in our understanding. That said, there is also a small problem with the model, in that we would expect the binding rate of FtsZ to depend on the surface to volume ratio (which turns out not to matter, because the authors end up making assumptions that the rate the ring is built is equal to the protein production rate). Note also that there is a typo in the equation fordPrdt, which has kd multiplying both rates.

Second, and more important, is that while the results match well with the data, there are a number of aspects of the presentation that are misleading. The title claims that the results/model presented here are universal. In Figure 1G, the authors select 7 bacteria to claim that the scaling of SA = 2 π V(2/3) is ubiquitous among bacteria. As noted, this also suggests that an aspect ratio of ~4 is the rule for rod-shaped bacteria. This is not true. As an example, myxococcus xanthus has an aspect ratio around 7-8 and spirochetes have aspect ratios of ~30! Even more importantly, single species don't always maintain the same aspect ratio. In B. subtilis, the aspect ratio can vary between at least 3.8 – 8 (see Ilkanaiv et al., 2017). Therefore, this model may be applicable to E. coli (and possibly some other bacteria), but it is not universal.

Reviewer #2:

In this study the authors set out to study the size and shape of a wide range of 'rod-shaped' cells by collecting image data from at least seven different species and thousands to total conditions (genotype x nutrients x antibiotics). Across all these conditions, the authors find a simple scaling law to the surface area/volume ratio, namely a scaling that preserves the aspect ratio of the cell at roughly 4:1. Given this observation, they build a simple, mechanistically inspired, quantitative model for the growth of the cell. Using this model, they are able to tune three parameters (k, kp, β) to match a collection of genetic knockdown and antibiotic treatment experiments.

Understanding how cell size and shape homeostasis is maintained throughout the bacterial kingdom is a very interesting and important problem and these authors should be commended for pushing the community to consider that these mechanisms may be conserved across a wide phylogenetic range. However, given the extensive body of literature already available about cell size/shape homeostasis, and, in particular the review mentioned by the authors by Harris and Theriot, the scientific bar for productive engagement on this topic is already quite high. Much of the intellectual driving force for this work seems to follow directly from the hypothesis from Harris and Theriot that "While many studies have treated volume as the actively controlled parameter in this scenario, our recent work suggests that it is likely the other way around, and that SA/V is the actively regulated variable, with size following along as necessary [13]." The current work seeks to extend or provide alternatives for the mechanistic models presented in Harris and Theriot as well as integrate additional data in other species. However, given that the idea of SA/V scaling conservation is not new, appealing to a broad audience such as that of eLife would require experimental validation of their mechanistic model.

In addition to the core concerns around novelty of the central hypothesis and validity of the mechanistic model, there are a few issues the authors might choose to consider:

Major points:

1) The authors should clearly explain how their mechanistic model contrasts with the cell wall-focused model proposed by Harris and Theriot and should strive to propose experiments with predicted outcomes that would differentiate a peptidoglycan centric model from an FtsZ centric model. If the data already exist to rule out one of them, this should be clearly presented. As one such example, the authors show that tuning one parameter (kp) is consistent with the experimental notion of knocking down the production of FtsZ. However, they fail to show if there is quantitative agreement between the production rate of FtsZ and the amount they expect to need to change kp(40%).

2) The use of 'universal' in the paper's title significantly oversells of the breadth of species included in the observations and a power law describing data which span roughly one order of magnitude. While the authors do include a large collection of data, the collection is far from comprehensive for all size/shape data available and the authors do not clearly indicate why they limited themselves to the data they did. A quick literature search reveals anecdotal evidence of bacterial sizes that are much smaller than a micron such as Brevundimonas (PDA J Pharm Sci Technol. 2002 Mar-Apr;56(2):99-108.) to nearly a millimeter in length Epulopiscium (J. Protozoal., 35(4), 1988, pp. 565-569). Granted, these publications may not have the same type of data necessary to integrate it directly into their model, but for a discussion of the 'universal scaling', the authors should push themselves to cover as large of a length-scale as possible. When choosing a set of species for inclusion in this study, it seems like the microbiology community may have already picked an aspect ratio of about 4:1 in its definition of rod-shaped bacteria. For example, cells that have a much shorter aspect ratio are given the term ovoid or lancet (Streptococcus pneumoniae) or spherical (Staphylococcus aureus included here) and ones that are much longer are called filamentous (Sphaerotilus natans). Confusingly, these authors do not include species that have been traditionally classified as rod-shaped cells with a longer aspect ratio such as (Helicobacter, Spiroplasma, Spirochetes, Myxobacter).

3) I'm not entirely convinced that the universal scaling applies within the single cell data (Figure 1D). By plotting the single cell data from a variety of experiments, the range of the data seems to put a larger priority on the averages. However, within each condition there seems to be clear deviations from the 'single aspect ratio', consistent with the author's single cell growth model that cells grow without changing their diameter before dividing. This should result in a roughly factor of two change in aspect ratio from birth to division. I think this is what the authors refer to in the fourth paragraph of the Introduction but should discuss more fully.

4) I do not understand Figure 2B at all. In particular, the binning of the data that I have been able to find in Taheri-Araghi et al., 2015, is binned by the size of cells at birth, not the individual cell growth rate. Further, the authors do not describe how they go from the data in Taheri-Araghi et al., 2015, to the data in Figure 2B, but it could be that they obtained the raw data from the authors and performed a new type of analysis. If so, a description of this process should be included.

5) I am unclear about why the MreB and FtsZ knockdown data from Si et al. is included in the bulk Figure 1A data but the MreB and FtsZ knockdown data from Zheng et al. is treated as a completely separate experiment. If the approach that these two studies used was different, it may be helpful to explain why some data are included in one place and others are not.

https://doi.org/10.7554/eLife.47033.014

Author response

[Editors’ note: the author responses to the first round of peer review follow.]

The mechanistic or molecular origin of bacterial aspect ratio control has remained an unsolved problem for more than four decades (see e.g. Zaritsky,2015; Zaritsky, 1975). In our manuscript we provide the first biophysical model for aspect-ratio homeostasis in rod-like bacteria and elucidate the underlying molecular mechanism that will inform future experimental studies. Our findings push the field of ‘bacterial cell size control’ to a new direction, which has so far focused on the individual control of cell volume, length or width, neglecting how bacterial length and width are coupled to give rise to rod-like cell shapes.

To support our model, we collected a large number of cell shape data (~5000 conditions) from many different laboratories, which indeed confirm that aspect ratio is conserved in E. coli (and 7 other organisms) under many different perturbations to the growth conditions (Figure 1). Importantly, our model also predicts under what conditions E. coli cells may deviate from their homeostatic aspect ratio of 4:1, and we tested our quantitative predictions for filamentous and spherical cell shapes against experimental data (Figure 2). Therefore, our thesis is not solely about the maintenance of 4:1 aspect ratio in E. coli, but more broadly about the control of bacterial cell shapes under many different perturbations.

It is evident from the reviewer comments that the principal issues with our manuscript lie in the presentation of results (e.g. claim of ‘universality’), and concerns about the novelty of our model in the context of previous studies. This is in part due to inadequate communication on our part. Having carefully read and deliberated on the reviewer comments, we believe that an improvement in the presentation of our results, an increased clarity of writing, and expanded description of the model will address all reviewer comments thoroughly and completely.

Reviewer #1:

This manuscript compiles data on the length, width, and growth rate of E. coli under a number of experimental perturbations, such as changes in growth medium, incubation in antibiotics, inhibited protein synthesis, etc. and shows that the surface area to volume ratio is strongly conserved. This result is consistent with recent work from Julie Theriot's group (which is cited in Harris and Theriot, 2016; 2018). In this manuscript, the author's also add data from other rod-shaped bacteria that show similar behavior (Figure 1G). The authors use this result to develop a model for aspect ratio regulation that is based on exponential growth of the bacterial length at fixed width, FtsZ production at a rate proportional to volume growth rate (which by assuming constant width also assumes that the FtsZ production is proportional to the length growth rate), and division that occurs when FtsZ production reaches a critical value that is proportional to the width. This model predicts a constant aspect ratio and the authors then go on to predict the dynamics under impulse type perturbations.

We appreciate the succinct summary of our work. While our findings are consistent with a recent model proposed by Julie Theriot’s group, it is important to note the key difference: Harris and Theriot showed that rod-shaped bacteria (E. coli, C. crescentus) maintain a homeostatic surface-to-volume ratio (S/V) in a growth-rate dependent manner. Here we uncover a much stronger geometric constraint that bacteria (especially E. coli) maintain the relationship S=γV2/3 (with a constant γ), independent of growth rate. Furthermore Harris and Theriot model does not lead to aspect ratio control, as addressed in response to a comment from Reviewer #2.

I have two main concerns with the manuscript.

First, the only novelty of the model is the assumption that there is a critical amount of FtsZ required to divide the cell and that this depends on the width. I think that this is a reasonable assumption, but I also feel that the overall results are fairly obvious. That is, it is not clear that the model provides a significant advance in our understanding.

Our model and analysis expand the current state of understanding in many ways:

– We provide the first biophysical model for aspect ratio control in bacteria and identify the molecular origins. We support our model by large population measurements (~5011 growth conditions in E. coli, 50 different bacterial species) and single cell measurements in mother machine (n~80,000). Why E. coli cells maintain a constant aspect ratio has been puzzling for more than half a century (Zaritsky, 1975; Zaritsky, 2015), with no prior existing model.

– The model for aspect ratio homeostasis provides a conceptual leap in the field of bacterial cell size control, by showing that added cell length for rod-like cells is coupled to their diameter. Previous phenomenological models treated cell length and diameter as independent control variables (Taheri-Araghi et al., 2015, Harris and Theriot, 2016).

– We think it’s not obvious that E. coli cells preserve their aspect ratios under multitude of perturbations to the nutrient conditions, ribosomes, protein overexpression or deletion (Figure 1A). Our model not only identifies that the maintenance of aspect ratio emerges from balanced biosynthesis of growth and division proteins (k/kP constant), but also predicts under what perturbations cells may deviate from their homeostatic aspect ratio of 4:1 (Figure 4). We provide a quantitative, experimentally testable model for cell shape control that goes beyond just the regulation of FtsZ kinetics.

That said, there is also a small problem with the model, in that we would expect the binding rate of FtsZ to depend on the surface to volume ratio (which turns out not to matter, because the authors end up making assumptions that the rate the ring is built is equal to the protein production rate).

It is unclear why the FtsZ binding rate should depend on S/V. The rate equations are formulated in terms of the amount of the surface-bound and cytoplasmic FtsZ, and not their concentrations. If only the rate equations were formulated in terms of the concentration of cytoplasmic (c) and surface-bound proteins (cr), then the rate of increase in surface bound concentration of FtsZ would naturally depend on S/V.

dcrdt=kcr+kbVSc-kdcr

Second, if we were to consider changes in FtsZ binding rate with S/V, our simulations show that this has negligible effect on aspect ratio. For rod-shaped cells, S/V ~1/w in the first approximation, where w is cell width. Since during one cell cycle width doesn’t change, S/V stays approximately constant (new Figure 4—figure supplement 1A). If the width of the bacteria is changing due to changes in growth conditions, overall binding rate may be affected by (S/V) since the area of the Z-ring = δw ~δ/(S/V), where δ is the lateral width of the FtsZ ring. E. coli width changes in different growth conditions from approximately 0.5 till 1 μm (Taheri-Araghi et al., 2015), so S/V can change by a maximum factor of 2. To address the effect of changes in binding rate, we simulated our dynamic model by changing the ratio kb/kd across 4 order of magnitude. The figure in Figure 4-figure supplement 1B shows the dependence of cellular newborn aspect ratio (n = 10000, during steady-state growth) on kb/kd. In the limit kb>>kd, aspect ratio~4 as expected. However, the factor of 2 change even for the border line case of kb/kd = 10, has negligible impact on cell aspect ratio.

However, as noted by the reviewer, the rate of FtsZ recruitment to the Z-ring (~10s, Soderstrom et al., Nat Commun 2018) is much faster than the growth rate. As a result, the rate at which the ring is built is determined by the production rate of FtsZ in the cytoplasm.

Note also that there is a typo in the equation fordPrdt, which has kd multiplying both rates.

We corrected the typo in the manuscript and thank the reviewer for pointing this out.

Second, and more important, is that while the results match well with the data, there are a number of aspects of the presentation that are misleading. The title claims that the results/model presented here are universal. In Figure 1G, the authors select 7 bacteria to claim that the scaling of SA = 2 π V(2/3) is ubiquitous among bacteria. As noted, this also suggests that an aspect ratio of ~4 is the rule for rod-shaped bacteria. This is not true. As an example, myxococcus xanthus has an aspect ratio around 7-8 and spirochetes have aspect ratios of ~30! Even more importantly, single species don't always maintain the same aspect ratio. In B. subtilis, the aspect ratio can vary between at least 3.8 – 8 (see Ilkanaiv et al., 2017). Therefore, this model may be applicable to E. coli (and possibly some other bacteria), but it is not universal.

We apologize for the misunderstanding, which may have been triggered by a lack of clarity in our presentation. In our original submission, we did not claim that the 4:1 aspect ratio, or equivalently S = 2πV 2/3, is universal. Instead, we found that a ‘universal’ scaling law SV2/3 is conserved amongst rod-shaped or coccoid bacterial species, implying the maintenance of a fixed aspect ratio (Figure 1A and E, dataset expanded). It is indeed possible for different bacteria to have different values for γ. For instance, in Figure 1E (previously 1G) we show that the coccoid S. aureus under different perturbations maintain the relation S = 4.92 V 2/3, implying preservation of the same scaling factor (2/3) while maintaining a different aspect ratio (1.38 +/- 0.18). In the same figure (1E), we now show data for a total of 48 different rod-shaped bacteria, and 1 rod-shaped Archaea (H. vulcanii), all of which remarkably follow the curve S = 2πV2/3.

Furthermore, our model also predicts how the aspect ratio and cell width can be altered by changing (k/kp) and (k/β), leading to filamentous or spherical cells, in agreement with available experimental data. In Figure 4 (previously Figure 2) we show that our model indeed predicts the breakdown of the 4:1 aspect ratio in E. coli under FtsZ or MreB perturbations.

However, the reviewer has made an excellent point that long filamentous cells, such as Spirochetes, do not necessarily conserve their aspect ratios. In Figure 1E, we now also include the data for Spirochetes, as one of the exceptions to the rule SV2/3. We have therefore removed the term ‘universal’ from the title and Abstract of our paper. The fact, however, remains that E. coli remarkably conserve their aspect ratios under diverse size perturbations spanning two orders of magnitude (Figure 1A), and so do 50 other cell types (Figure 1E).

Motivated by the comments of reviewers 1 and 2, we now include a schematic in Figure 1D to illustrate the expected scaling relations for different bacterial shapes. Filamentous cells (Helicobacter, Spiroplasma, Spirochetes, Myxobacter) would likely follow the relation SμV, whereas coccoid or the rod-shaped cells follow the scaling law: SμV2/3.

Reviewer #2:

In this study the authors set out to study the size and shape of a wide range of 'rod-shaped' cells by collecting image data from at least seven different species and thousands to total conditions (genotype x nutrients x antibiotics). Across all these conditions, the authors find a simple scaling law to the surface area/volume ratio, namely a scaling that preserves the aspect ratio of the cell at roughly 4:1. Given this observation, they build a simple, mechanistically inspired, quantitative model for the growth of the cell. Using this model, they are able to tune three parameters (k, kp, β) to match a collection of genetic knockdown and antibiotic treatment experiments.

Understanding how cell size and shape homeostasis is maintained throughout the bacterial kingdom is a very interesting and important problem and these authors should be commended for pushing the community to consider that these mechanisms may be conserved across a wide phylogenetic range. However, given the extensive body of literature already available about cell size/shape homeostasis, and, in particular the review mentioned by the authors by Harris and Theriot, the scientific bar for productive engagement on this topic is already quite high. Much of the intellectual driving force for this work seems to follow directly from the hypothesis from Harris and Theriot that "While many studies have treated volume as the actively controlled parameter in this scenario, our recent work suggests that it is likely the other way around, and that SA/V is the actively regulated variable, with size following along as necessary [13]." The current work seeks to extend or provide alternatives for the mechanistic models presented in Harris and Theriot as well as integrate additional data in other species. However, given that the idea of SA/V scaling conservation is not new, appealing to a broad audience such as that of eLife would require experimental validation of their mechanistic model.

In addition to the core concerns around novelty of the central hypothesis and validity of the mechanistic model, there are a few issues the authors might choose to consider:

We thank the reviewer for summarising the key aspects of our work and recognizing the importance of the field of study. Below we address some of the key comments raised above. “extensive body of literature already available about cell size/shape homeostasis” –A lot of work has been done over the past five years on developing phenomenological models for cell size control. Phenomenological models for the homeostasis of bacterial cell shape are treated the control of cell length separately from the control of cell width in rod-shaped bacteria. We provide a molecular model to show for the first time that bacterial cell dimensions are coupled to preserve aspect ratio, thereby linking the field of cell size and shape homeostasis.

“Much of the intellectual driving force for this work seems to follow directly from the hypothesis from Harris and Theriot” – Our model draws evidence from multiple recent experimental studies, while questioning the Harris and Theriot (HT) hypothesis. It is important to recognize the key distinctions between the two models. HT model does not lead to conservation of S-to-V scaling or aspect ratio, instead it leads to a model for the control of cell width (Eq. 3). HT model infers that S/V ratio is a function of growth media, such that cells reach a new homeostatic value of S/V upon perturbations in the growth rate. Here instead we propose a much stronger constraint that cells preserve the scaling relation, S = μV 2/3 (μ a constant) under diverse growth perturbations (~5000 conditions) across ~50 different bacterial species. Furthermore, HT model is agnostic about molecular mechanisms. Here we provide an explicit molecular candidate (FtsZ) for bacterial shape control, in agreement with exciting new evidence from Si et al., 2019. Taken together, our model integrates the adder model for cell size homeostasis with the regulation of S/V ratio and FtsZ, providing an integrative framework that successfully predicts bacterial shape control with only three physiological parameters.

“the idea of SA/V scaling conservation is not new” – We are not aware of any other studies that propose conservation of the scaling relation S = μV 2/3 across growth conditions, nor provide a model for it. Others have only shown evidence for the regulation of surface-to volume ratio by growth rate, which is a natural consequence of our model (Figure 1C).

“appealing to a broad audience such as that of eLife would require experimental validation of their mechanistic model” – Our model is tightly grounded in experimental data (see Figures 1-4), and we compare our model predictions extensively to experimental data, throughout the manuscript. As we are not an experimental lab, we have compiled data from a number of different laboratories to show that our model is consistent with all the available cell shape data across ~50 bacterial species and ~5000 growth conditions for E. coli. We definitely welcome suggestions to test our model further.

Major points:

1) The authors should clearly explain how their mechanistic model contrasts with the cell wall-focused model proposed by Harris and Theriot and should strive to propose experiments with predicted outcomes that would differentiate a peptidoglycan centric model from an FtsZ centric model. If the data already exist to rule out one of them, this should be clearly presented.

We agree with the reviewer that clearer discussion of the contrast between our model and that of Harris/Theriot should be articulated in the manuscript. In the revised manuscript, we have expanded the discussion to highlight the key differences between these two models.

Foremost amongst the comparison is that Harris and Theriot proposes a homeostatic regulation of S/V in a growth-rate dependent manner. Whereas we propose a much stronger geometric constraint that the scaling relation S = μV 2/3 is preserved independent of growth rate. This result, however, does not contradict the model of Harris/Theriot.

Second, Harris and Theriot proposed a model where cells divide once a threshold amount of excess surface area material, ΔA, is accumulated in the cell. From this model it follows that, ΔA = ΔV (β/k – 2/r) = constant, where r is the cell radius of cross-section. This in turn 1, which is in contradiction to experimental data (Figure 1).

Third, we can indeed propose several experimental tests for our model, as highlighted in the revised manuscript:

– Our model would predict that FtsZ overexpression leads to minicells while FtsZ deletion would induce elongated phenotypes (Figure 4A). These predictions are consistent with data from Potluri et al., 1999, and Zheng et al., 2016.

– Oscillations in FtsZ amount would lead to cell size oscillations, in agreement with new data from Si et al., 2019.

– Total abundance of FtsZ scales with cell diameter, in agreement with data from Shi et al., 2017.

– We further predict that FtsZ knockdown would break aspect ratio preservation, whereas targeting cell wall precursors would change growth rate, but not alter aspect ratio or the scaling relation S = μV 2/3. Figure 4—figure supplement 1C shows surface-to-volume scaling for E. coli cells treated with Fosfomycin that target MurA (affecting cell wall biogenesis) and FtsZ depletion. We find that Fosfomycin treated cells preserve the S~V2/3 scaling, whereas FtsZ depletion breaks the S~V2/3 scaling. This is a clear contrast between the role of cell wall precursors and FtsZ on cell shape control, implying that a cell wall precursor-based model alone is not sufficient to account for shape changes.

As one such example, the authors show that tuning one parameter (kp) is consistent with the experimental notion of knocking down the production of FtsZ. However, they fail to show if there is quantitative agreement between the production rate of FtsZ and the amount they expect to need to change kp (40%).

Our model predicts that a reduction in FtsZ production rate to 40% of WT leads to observed phenotype in Zheng et al., 2016. This is consistent with reduction of relative mRNA to ~ 40% corresponding to addition of 3 ng/ml of aTc (Figure 2B of the Zheng et al.). We comment on this in our manuscript and thank the reviewer for pointing this out.

2) The use of 'universal' in the paper's title significantly oversells of the breadth of species included in the observations and a power law describing data which span roughly one order of magnitude. While the authors do include a large collection of data, the collection is far from comprehensive for all size/shape data available and the authors do not clearly indicate why they limited themselves to the data they did. A quick literature search reveals anecdotal evidence of bacterial sizes that are much smaller than a micron such as Brevundimonas (PDA J Pharm Sci Technol. 2002 Mar-Apr;56(2):99-108.) to nearly a millimeter in length Epulopiscium (J. Protozoal., 35(4), 1988, pp. 565-569). Granted, these publications may not have the same type of data necessary to integrate it directly into their model, but for a discussion of the 'universal scaling', the authors should push themselves to cover as large of a length-scale as possible. When choosing a set of species for inclusion in this study, it seems like the microbiology community may have already picked an aspect ratio of about 4:1 in its definition of rod-shaped bacteria. For example, cells that have a much shorter aspect ratio are given the term ovoid or lancet (Streptococcus pneumoniae) or spherical (Staphylococcus aureus included here) and ones that are much longer are called filamentous (Sphaerotilus natans). Confusingly, these authors do not include species that have been traditionally classified as rod-shaped cells with a longer aspect ratio such as (Helicobacter, Spiroplasma, Spirochetes, Myxobacter).

We address this point in response to the first reviewer. Both the reviewers have raised a pertinent point that long filamentous cells, such as Spirochetes, do not necessarily conserve their aspect ratios. In Figure 1E, we now include available shape data for Spirochetes, as one of the exceptions to the rule SV 2/3. We have therefore removed the term ‘universal’ from the title and Abstract of our paper. The fact, however, remains that rod-shaped bacteria (E. coli) remarkably conserve their aspect ratios under diverse size perturbations spanning two orders of magnitude (Figure 1A).

In Figure 1E we have now expanded the dataset to cover two orders of magnitude by including 49 different rod-shaped bacterial species and 1 rod-shaped Archea. All of them lie on the curve SV 2/3, confirming our predictions. In addition, we have also expanded the E. coli dataset by 30 more nutrient growth conditions (Gray et al., 2019), confirming our initial statement of aspect-ratio homeostasis.

We are grateful to the reviewer for providing the papers reporting drastic volume range in bacteria spanning 2 orders of magnitude. Bacteria that we include in Figure 1E are those that are known divide using FtsZ machinery during binary fission. This is to maintain consistency with our model that is based on FtsZ regulation. For this reason, we did not include Epulopiscium in our analysis. We also did not include Sphaerotilus natans in our graph as we could not find good shape measurements for it. In line with reviewer’s comments we have now included longer filamentous cells in Figure 1E. We have also introduced a new cartoon in Figure 1D showing how long filamentous cells that keep their width constant, would have a different scaling law S~V.

3) I'm not entirely convinced that the universal scaling applies within the single cell data (Figure 1D). By plotting the single cell data from a variety of experiments, the range of the data seems to put a larger priority on the averages. However, within each condition there seems to be clear deviations from the 'single aspect ratio', consistent with the author's single cell growth model that cells grow without changing their diameter before dividing. This should result in a roughly factor of two change in aspect ratio from birth to division. I think this is what the authors refer to in the fourth paragraph of the Introduction but should discuss more fully.

In our original submission, we had already explored in detail the deviation from 2/3 scaling in the single-cell data (Figure 2—figure supplement 1A-B). The main reason for the deviation from 2/3 scaling comes from large fluctuations in newborn length for a given width of bacteria. Using our model, we can quantitatively explain the deviation from the universal scaling by incorporating experimentally measured fluctuations in cell width and length, in agreement with experimental data. We have now attempted to explain this better in the manuscript and in the supplementary figure caption.

4) I do not understand Figure 2B at all. In particular, the binning of the data that I have been able to find in Taheri-Araghi et al., 2015, is binned by the size of cells at birth, not the individual cell growth rate. Further, the authors do not describe how they go from the data in Taheri-Araghi et al., 2015, to the data in Figure 2B, but it could be that they obtained the raw data from the authors and performed a new type of analysis. If so, a description of this process should be included.

We were kindly provided with the raw data for single-cell width and length at various growth rates (conditions) by the Suckjoon Jun lab. We reanalysed the data, performed the necessary binning and analysis. We have clearly stated this in the Appendix and in each figure caption.

5) I am unclear about why the MreB and FtsZ knockdown data from Si et al. is included in the bulk Figure 1A data but the MreB and FtsZ knockdown data from Zheng et al. is treated as a completely separate experiment. If the approach that these two studies used was different, it may be helpful to explain why some data are included in one place and others are not.

For consistency, we now plot the MreB and FtsZ knockdown data from Si et al. in Figure 4B. The knockdown data from Si et al. cover a small dynamic range so it is hard to extract a clear trend from these data alone. This is presumably because cells in those knockdown experiments were grown in slow growth media (MOPS glucose + 6 a. a., with growth rate ~0.75 h-1) and small perturbations, whereas the data from Zheng et al. that show drastic cell shape changes (Figure 4B) are obtained from experiments on rich media (RDM + glucose, with growth rate 1.6 h-1) and large perturbations. The trend in Si et al. seems to be consistent with those in Zheng et al.

https://doi.org/10.7554/eLife.47033.015

Article and author information

Author details

  1. Nikola Ojkic

    Department of Physics and Astronomy, Institute for the Physics of Living Systems, University College London, London, United Kingdom
    Contribution
    Conceptualization, Data curation, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing—original draft
    Competing interests
    No competing interests declared
  2. Diana Serbanescu

    Department of Physics and Astronomy, Institute for the Physics of Living Systems, University College London, London, United Kingdom
    Contribution
    Data curation, Investigation, Methodology
    Competing interests
    No competing interests declared
  3. Shiladitya Banerjee

    Department of Physics and Astronomy, Institute for the Physics of Living Systems, University College London, London, United Kingdom
    Present address
    Department of Physics, Carnegie Mellon University, Pittsburgh, United States
    Contribution
    Conceptualization, Resources, Supervision, Funding acquisition, Validation, Investigation, Visualization, Writing—original draft, Project administration
    For correspondence
    shiladitya.banerjee@ucl.ac.uk
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-8000-2556

Funding

Royal Society (URF/R1/180187)

  • Shiladitya Banerjee

Royal Society (RGF/EA/181044)

  • Shiladitya Banerjee

Engineering and Physical Sciences Research Council (EP/R029822/1)

  • Shiladitya Banerjee

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank Suckjoon Jun lab (UCSD) for providing single cell shape data for E. coli, and Javier López-Garrido, Guillaume Charras, and Deb Sankar Banerjee for useful comments. SB gratefully acknowledges funding from EPSRC New Investigator Award EP/R029822/1, Royal Society Tata University Research Fellowship URF/R1/180187, and Royal Society grant RGF/EA/181044.

Senior Editor

  1. Naama Barkai, Weizmann Institute of Science, Israel

Reviewing Editor

  1. Raymond E Goldstein, University of Cambridge, United Kingdom

Reviewer

  1. Charles W Wolgemuth

Publication history

  1. Received: March 20, 2019
  2. Accepted: August 28, 2019
  3. Accepted Manuscript published: August 28, 2019 (version 1)
  4. Version of Record published: September 12, 2019 (version 2)

Copyright

© 2019, Ojkic et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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