Downloaded by guest on September 29, 2021 n hsbhvo r adt xii adrcreain”(1–7). governed correlations” is division “adder cell exhibit that postulate to models follow- these said cells Importantly, are and behavior model, this “adder” or ing “incremental” the as known constant the where cycle cell time constant a divide initiation. and after initiations constant between a origin add per cells volume which recently in our model, of “adder-per-origin” context the proposed phe- in key discussed are the initia- conclusions replication is These of volume tion. timing cell the and governing division, variable cell nomenological initia- of replication that of governs timing the tion which dimensions in cell replication models in to supports perturbations strongly division to cell robustness of its coupling Thus, tight initiation. interpreted a of quantitatively consequence be a can dimension as and law conditions growth growth The of perturbations. range a law growth over with the valid Moreover, increased remained cases. both division in cell dimension perturbed to the termination decreasing replication whereas from length, time cell in change the little with the width, decreasing cell that of levels found dimen- expression cell We the in varying perturbations by systematic achieved to sions law growth robust- the round the of corresponding test a ness to the sought of which we at Here, initiation segregate. division from chromosomes cell sister time the to the replication to DNA with of equal rate, growth exponent with scaling exponentially a the scales that volume says law cell This average law. growth Schaechter’s as in control known of relation to events Growth and sizes. accurately various 2016) cell themselves 30, the their duplicate September to review coordinate for cycles (received cell and 2016 their 14, regulate November approved tightly and MD, Bacteria Bethesda, Health, of Institutes National Mizuuchi, Kiyoshi by Edited and China; of Republic People’s 518055, Shenzhen Sciences, China; of Republic People’s 518055, 02138; MA Cambridge, University, Harvard China; of Republic a Amir Ariel Zheng Hai perturbations dimension the Interrogating www.pnas.org/cgi/doi/10.1073/pnas.1617932114 aver- size when birth that, given follows showed a approximately which of cells division, all at over size aged size cell cell and between birth correlations at measuring sup- are experiments models sur- by Such or (1–3). ported length, division and volume, birth (e.g., between size area) face constant a of accumulation the bacterium the in division coli. cell Escherichia of for control pro- manifested, for that models growth, studies is different recent pose understanding cell various among of discrepancies replication, lack of in instance, This DNA understanding division. incomplete coordinate cell an and that have processes still Despite the replication. under- we DNA are progress, of cells particular much rounds where a concurrent conditions is multiple growth This going fast sizes. cell under their challenge regulate homeostatically to B etrfrSnhtcBooyEgneigRsac,Seze ntttso dacdTcnlg,CieeAaeyo cecs hnhn585,People’s 518055, Shenzhen Sciences, of Academy Chinese Technology, Advanced of Institutes Shenzhen Research, Engineering Biology Synthetic for Center n ls fmdl ugssta eldvso stigrdby triggered is division cell that suggests models of class One ftsZ ntercl ylst cuaeydpiaetergnmsand genomes their duplicate accurately to cycles events cell various their the in coordinate and tightly regulate can acteria | ee eutdi nrae ellnt.Frhroe the Furthermore, length. cell increased in resulted level elgrowth cell c,1 a,b n hniLiu Chenli and , oY Ho Po-Yi , b nvriyo hns cdm fSine,Biig104,Pol’ eulco China; of Republic People’s 100049, Beijing Sciences, of Academy Chinese of University | v .coli E. 0 esteaeaecl iea it.Ti is This birth. at size cell average the sets c v eln Jiang Meiling , D npriua,flosa follows particular, in coli, Escherichia | N replication DNA = a,b,1 e v nttt fBoeiieadBoehooy hnhnIsiue fAvne ehooy hns cdm of Academy Chinese Technology, Advanced of Institutes Shenzhen Biotechnology, and Biomedicine of Institute mreB B + v d eateto aeil cec n niern,Suhr nvriyo cec n ehooy Shenzhen Technology, and Science of University Southern Engineering, and Science Materials of Department 0 ee eutdi increased in resulted level v , B elsz tdivision at size cell , a | i Tang Bin , shrci coli Escherichia eldimension cell mreB f eateto oeua n ellrBooy avr nvriy abig,M 02138 MA Cambridge, University, Harvard Biology, Cellular and Molecular of Department d ern Liu Weirong , and ftsZ. [1] v D 1073/pnas.1617932114/-/DCSupplemental at online information supporting contains article This option. access open 1 PNAS the through online available Freely Submission. Direct PNAS a is article This P.H., interest. of and conflict data; no declare analyzed authors C.L. The paper. and the A.A., wrote N.E.K., C.L. 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BIOCHEMISTRY The CH model is supported by the phenomenon of rate main- A tenance (13): After a change from one growth medium to a richer one (a shift up), cells continue to divide at the rate associated with the poorer medium for a period of 60 min. According to the CH model, in which division is triggered by initiation, all cells that have already initiated replication before a shift up will have also already committed to their ensuing divisions, and thus the rate of division will remain unchanged for a time C + D follow- ing a shift up. The same value of 60 min also emerged in a seemingly different context a decade earlier, in the seminal study of B Schaechter et al. (14). In their work, cell volumes, averaged over an exponentially growing population, were measured for culture growing under dozens of different growth media supporting fast growth. It was found that average cell volume was well described by an exponential relation with growth rate V = ∆eλT , where V is the average cell volume, ∆ is a constant with dimensions of volume, λ is the growth rate, τ = log(2)/λ is the doubling time, and T ≈ 60 min. Donachie (15) showed that this exponential scaling of average cell volume with growth rate can also be explained by the CH model if it is further assumed that cells initiate replication on average at a constant volume ∆I per origin of replication at ini- tiation. Because cells grow exponentially at the single-cell level (16), cells will then divide on average at a volume ∆I per origin times a scaling factor S = 2(C +D)/τ . The average cell volume then follows V = ∆2(C +D)/τ = S∆, [2]

with ∆ = log(2)∆I , because the cell volume averaged over an exponentially growing population is the average cell volume at birth times 2 log(2) (17). In Schaechter’s experiments, the C and D periods were approximately constant, giving rise to the 2 exponential scaling observed. However, the derivation for Eq. Fig. 1. (A) Schematic illustration of the experiment. MreB and FtsZ are holds regardless of the values of the C and D periods, and involved in cell wall synthesis and septum formation, respectively. Using in cases where they are not constant, average cell volume is mreB- or ftsZ-titratable strains, we are able to tune their expression levels not expected to scale exponentially with growth rate. Eq. 2 is continuously and perturb cell dimensions. In both experiments, the D period known as Schaechter’s growth law, but is referred to simply as increased with cell width and length. The C period and doubling time τ the growth law for the rest of this paper. remained constant. (B) Schematic illustration of our model. The perturbed Recent single-cell analyses found that cells indeed initiate D period sets the average number of origins per cell, which is equal to the replication on average at a constant volume per origin or per scaling factor S because replication initiation triggers cell division. The aver- some locus close to the origin (11). Although further experiments age number of origins per cell then sets the average cell volume, following the growth law. For titrated mreB levels, cell volume changes manifested are required, the fact that introduction of an origin onto a plas- mostly as cell width changes. For titrated ftsZ levels, cell length changed mid does not affect cell cycle timings or cell size suggests that instead, because FtsZ did not affect cell width. the latter possibility is correct (11, 18, 19) (SI Text, Average Cell Volume at Initiation Is Constant per Some Locus Close to the Ori- gin). Below, for simplicity, we use the phrase “per origin,” while the formation of the division septum (20, 21). Our approach is keeping this complexity in mind. indicated schematically in Fig. 1A. It extends and complements Clearly, the two classes of models for control of cell division Schaechter’s experiments, in which growth rate was perturbed, differ fundamentally. In the first class, division depends only on and is reminiscent of the work of Harris et al. (3), in which cell the accumulation of size from birth, and DNA replication plays dimensions were perturbed, but with the important addition to no explicit role. In the second class, division is downstream of both studies that we also measured the cell cycle periods C and the preceding initiation of DNA replication. Importantly, also, D because they play an important role in the CH model. For this the experiments leading to the first class of models defined cell paper, we define division as completion of septation. size differences by measuring cell length. Because for a constant growth environment the widths of bacterial cells are very nar- Results rowly distributed with a coefficient of variation (CV) less than Decreased mreB Level Resulted in Increased Cell Width, with Little 0.05 (2), these analyses cannot distinguish whether cell size in a Change in Cell Length. Cell length and cell width are two major given environment is set by a constant volume, surface area, or characteristics of a rod-shaped cell. As a cell grows, cell length length. This ambiguity raises the question of what is the key phe- increases exponentially, whereas cell width remains constant. nomenological variable governing cell cycle progression. How cell width is determined and maintained is largely unknown. Here, we sought to test these models by perturbing cell dimen- However, several mutations of mreB were reported to result sions in E. coli and assaying the effects of those perturbations on in altered cell dimensions (20, 23, 24), thus raising the pos- both replication events and cell division. In our study, shape per- sibility that alterations in mreB expression level would alter turbations were achieved by systematically varying expression lev- cell width. To continuously and systematically vary cell width, els of the protein MreB, an actin homologue involved in cell wall we constructed a strain in which the level of mreB could be synthesis, and the protein FtsZ, a tubulin homologue involved in experimentally controlled. We used a system in which a Ptet-tetR

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(Fig. inducer the threshold, of minimum level mL this expression ng Above 1 glucose]. + below (RDM) concentration medium aTc an [at lysed low very at until, concentration of inducer of (aTc). appropriate anhydrotetracycline copy an tetR, of native concentration the the adjusting of as by expression genome construct, this the In in gene the mreB of of copy version modulated sole The Construction). Strain ods, triggered loop feedback con- various containing culture ng·mL bulk (3–50 in aTc strains of titratable centrations the Relative in (B) gene. level resistance mRNA kanamycin a with replaced lessly i.3. Fig. a of control or mreB- 2. Fig. hn tal. et Zheng AB EFGHA enx esrdcl iesosb hs otatmicros- contrast phase by dimensions cell measured next We inducer decreasing with increased size cell that found We xrsinlvl,tevlm rwhrts rOD or rates, growth volume the levels, expression al S1). (Table gene kanamycin-resistance a by replaced was Titratable Titratable ftsZ P ttaal tan.Teepeso of expression The strains. -titratable tet -tetR mreB mreB edaklo n h native the and loop feedback mreB ttaal el.(E–H cells. mreB-titratable or or ftsZ ftsZ aidlnal ihtecnetainof concentration the with linearly varied mreB − 1 ). xrsint ytmtclyprubcl it rcl egh epciey ihu fetn h ouegot rates. growth volume the affecting without respectively, length, cell or width cell perturb systematically to expression h eei ici fthe of circuit genetic The (A) expression. xrsin(i.2A (Fig. expression mreB mreB ol etgtycontrolled tightly be could ees h el eventually cells the levels, ttaal n idtp tan.(B strains. wild-type and mreB-titratable u o the for but (A–D) as same The ) mreB mreB −1 mreB or fteidvda idtp W)or (WT) wild-type individual the of ) or nrc defined rich in ftsZ mreB and ftsZ mreB B expression sudrthe under is a seam- was IMeth- SI 600 a the was and dou- P ftsZ tet - slnal orltdwt h elvlm ncbcmicrometers cubic in volume cell cell per the OD ( with the results, correlated that our showed linearly verify We is to method. dimen- wanted independent we cell an (25), bacterial using precision define subpixel to to designed sions is used processing software image the Although for Strains). mreB-Titratable changed 3C in length (Fig. Changes below cell discuss The we 3B). which (Fig. slightly, increased width cell the level, xetd h C infiatydcesda elwdhincreased width cell as ( decreased significantly ECS the (ECS) expected, elas- stiffness wall cellular the effective cell of the of measuring levels measured directly low instead in we expressing difficulty ticity, cells the cell in the to that Due softer possible MreB. become seemed have it might morphology Thus, 24). wall 23, dumpling-like (20, synthesis flattened, wall slightly wider a Here, ( the microscopy. showed electron of scanning cells properties using morphological cells, Stiffness. the titrated Wall detail Cell in by acterized Maintenance Width Cell above. defined as conditions growth study fast this concern sions, in tested rates, growth growth ( other fast all various in supporting obtained stud- media, were concentrations results inducer Similar effect of Measurement). any 3 ranges (Fig. has the here construct within ied circuit cells genetic WT the on of presence the nor efud nareetwt rvoswr 2) htcell that (21), work previous Construction). with decreased Strain with agreement increased Methods, length in (SI found, length an We cell above, of as perturbation method same Width. the Cell in Change Decreased wall. the cell and the pressure of turgor resistance between tensile balance force the reflects width ohcl it n rwhrt eandrltvl constant relatively remained rate growth and width cell both .I skonta rBi novdi atra cell bacterial in involved is MreB that known is It S3A). 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BIOCHEMISTRY within the ranges of inducer concentration studied here (CV AB of 0.01 and 0.03, respectively, across different experiments, Fig. 3 E–H).

Correlations Between Perturbed Cell Dimensions and Cell Cycle Timings. We next investigated how the mreB and ftsZ expression levels affect the C and D periods. For a bulk culture in steady- state exponential growth, the CH model predicts that the average number of origins per cell, hOi, scales exponentially with growth rate (22, 26). This is because in steady-state exponential growth, the number of cells and the total number of origins in the popu- lation must both grow exponentially at the same rate. However, because the CH model postulates that division occurs only after a time C + D following the corresponding initiation, the total Fig. 5. The growth law holds in the face of perturbation to cell dimen- number of origins will be larger than the number of cells by the sions. (A) The average cell volume is proportional to the scaling factor scaling factor S, defined above. Therefore, hOi = S. This rela- S = 2(C+D)/τ . The black line shows the growth law V = S∆ for the best-fit tion holds regardless of the value of C + D. proportionality constant ∆ = 0.55 ± 0.04 µm3. The plus-or-minus symbol An expression for the average number of copies X of a gene indicates the 95% confidence interval of the fit. The coefficient of deter- per cell as a function of the location m of the gene along the mination R2 of the fit is 0.81. (B) The average cell area is not proportional chromosome (m = 0 for oriC and m = 1 for terC) can be to the scaling factor. The black line shows the best fit with intercept forced 2 derived similarly. Under the assumption that replication forks to zero. The R of the fit is 0.40. The circle, triangle, and square indicate X = 2(C (1−m)+D)/τ mreB-titratable, ftsZ-titratable, and WT strains, respectively. Different col- travel at a constant speed, the expression is ors denote growth media: Red is RDM + glucose, and blue is RDM + glycerol. (26). We used this relation to extract the lengths of the C and The SEMs of three replicates were smaller than the size of the symbols. D periods from quantitative PCR (qPCR) data of the copy numbers of different chromosome loci (including oriC, terC, and a series of different loci between them; SI Methods, Char- using replication run-out experiments (SI Methods, Cellular oriC acterization of the C and D Periods by qPCR and Table S2). Characterization). The C period was also measured independently by the meth- These analyses revealed that, over the analyzed ranges in the ods in refs. 27 and 28, which gave values consistent with those levels of both mreB and ftsZ expression, the C period remained obtained by the qPCR method (SI Methods, Characterization unchanged (CV of 0.09 and 0.05 for mreB- and ftsZ-titratable of the C and D Periods by qPCR). We also measured hOi, strains, respectively), whereas the D period increased with increasing cell width or length, respectively (Fig. 4). Note that the relation between the D period and cell length predicted by our model below is not linear, but appears approximately linear ABgiven the particular values of the relevant parameters under the conditions of these experiments.

The Growth Law Holds in the Face of Perturbations to Cell Dimensions. We find that the growth law, Eq. 2, holds in our experiments, both across a range of growth media (Fig. 4) and across the two titratable perturbations that drastically affected cell width and cell length (Fig. 5A). The best-fit proportionality constant is ∆ = 0.55 ± 0.04 µm3. The plus-or-minus symbol indicates the 95% confidence interval of the fit. From the derivation of the growth law in the Introduction, we find the average cell size per origin at 3 C D initiation to be ∆I = 0.79 ± 0.06 µm . In contrast, the average cell area, cell length, and cell width are not proportional to the scaling factor S (Fig. 5B and Fig. S4). We further tested the validity of a constant ∆ by fixing ∆ to 3 −1 0.55 µm and calculating the ratio of log2(V /∆) and τ , which is equal to C + D according to Eq. 2 (Fig. 6A). We found that the values of C + D obtained in this way agree well with independent measurements in both the titratable and the WT strains (Fig. 6B). Discussion Here, we perturbed cell dimensions and then observed the ef- fects of these perturbations on the cell cycle to interrogate the Fig. 4. Changes in the cell cycle parameters as cell dimensions are per- mechanism of cell cycle regulation in E. coli. The most important turbed. (A) The D period increased monotonically with cell width in mreB- finding of this work is that the growth law, that average cell vol- titratable strains. The line is the best linear fit. (B) The C period remained ume is proportional to the scaling factor S = 2(C +D)/τ , remained approximately constant as cell width changed in response to titrated mreB valid across large perturbations in cell dimensions. As discussed expression levels. The line is the mean value of C averaged over mreB expres- in the Introduction, the growth law can be quantitatively derived sion levels. (C) The D period increased monotonically with cell length in ftsZ- under two assumptions: (i) the CH model, that replication ini- titratable strains. (D) The C period remained approximately constant as cell C + D length changed in response to titrated ftsZ expression levels. The circle, tri- tiation triggers cell division after a constant time , and angle, and square indicate mreB-titratable, ftsZ-titratable, and WT strains, (ii) that the average cell volume at initiation of DNA replica- respectively. Different colors denote growth media: Red is RDM + glucose, tion is proportional to the number of origins at initiation. The and blue is RDM + glycerol. The SEMs of three replicates were smaller than robustness of the growth law documented above suggests that the size of the symbols. both assumptions hold in face of the perturbations studied here.

4 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1617932114 Zheng et al. 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BIOCHEMISTRY observations, it will be important to further study the single-cell Importantly, although our study here has suggested a coarse- physiology of E. coli under cell dimension perturbations at slow grained, phenomenological model on the level of cell dimen- growth. sions, it has not alluded to the molecular players involved. There has recently been much interest in the question of Several hypothetical molecular mechanisms, such as the accu- cell size homeostasis across all domains of life (35), and we mulation of a threshold amount of an initiator protein per note that adder per origin may be applicable to other organ- origin (36) or the dilution of an inhibitor protein (37), were pre- isms as well. For example, it is known that the bacterium Bacil- viously shown to implement molecularly the phenomenological lus subtilis also exhibits the growth law and adder correlations. model discussed here (6, 22). However, despite decades of work, Repeating the experiment here in B. subtilis may help probe the molecular mechanism for cell cycle regulation in bacteria the relations between cell dimensions and cell cycle timings in remains a fundamental unresolved question. a Gram-positive bacterium. Adder correlations in cell volume ACKNOWLEDGMENTS. The authors acknowledge the reviewers, Terry Hwa were also found recently in budding yeast diploid daughter cells and Arieh Zaritsky, for insightful discussions. This work was financially (6). Given the different morphology of these cells, which changes supported by National Nature Science Foundation of China Grant 31471270, dramatically throughout the cell cycle and particularly at bud- 973 Program Grant 2014CB745202, 863 Program Grant SS2015AA020936, the ding, it is plausible that cell volume, and not cell shape, is the key Guangdong Natural Science Funds for Distinguished Young Scholar Grant S2013050016987, Shenzhen Peacock TeamPlan Grant KQTD2015033ll7210153 phenomenological variable governing cell cycle regulation also in (to C.L.), and National Institutes of Health Grant NIH R01 GM025326 (to this case. N.E.K.). A.A. acknowledges support from the A. P. Sloan Foundation.

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