Interrogating the Escherichia coli cell cycle by cell dimension perturbations

1.2 MB·

by  Hai Zheng

E. coli
Interrogating the cell cycle by cell
dimension perturbations
HaiZhenga,b,Po-YiHoc,MeilingJianga,BinTangd,WeirongLiua,b,DengjinLia,XuefengYue,NancyKlecknerf,ArielAmirc,1,
andChenliLiua,b,1
aCenterforSyntheticBiologyEngineeringResearch,ShenzhenInstitutesofAdvancedTechnology,ChineseAcademyofSciences,Shenzhen518055,P.R.China;
bUniversityofChineseAcademyofSciences,Beijing,100049,P.R.China;cSchoolofEngineeringandAppliedSciences,HarvardUniversity,Cambridge,MA02138,USA;
dDepartmentofMaterialsScienceandEngineering,SouthernUniversityofScienceandTechnology,Shenzhen518055,P.R.China;eInstituteofBiomedicineand
Biotechnology,ShenzhenInstitutesofAdvancedTechnology,ChineseAcademyofSciences,Shenzhen518055,P.R.China;fDepartmentofMolecularandCellularBiology,
HarvardUniversity,Cambridge,MA02138,USA
7 ThismanuscriptwascompiledonJanuary4,2017
1
0 Bacteriatightlyregulateandcoordinatethevariouseventsintheir wheretheconstantv0 setstheaveragecellsizeatbirth. This
2 cell cycles to duplicatethemselves accuratelyand to controltheir is known as the “incremental" or “adder" model, and cells
cellsizes.GrowthofEscherichiacoli,inparticular,followsarelation followingthisbehavioraresaidtoexhibit“addercorrelations”
n
a knownasSchaechter’sgrowthlaw. Thislawsaysthattheaverage [1–7]. Importantly,thesemodelspostulatethatcelldivisionis
J cellvolumescalesexponentiallywithgrowthrate,withascalingex- governedbyaphenomenologicalsizevariable,withnoexplicit
3 ponentequaltothetimefrominitiationofaroundofDNAreplication reference to DNAreplication.
tothecelldivisionatwhichthecorrespondingsisterchromosomes A second class of models for control of cell division pos-

] segregate.Here,wesoughttotesttherobustnessofthegrowthlaw tulates that cell division is governed by the process of DNA
B
tosystematicperturbationsincelldimensionsasachievedbyvary- replication,whichcanbedescribedasfollows. Thetimefrom
C ingtheexpressionlevelsofmreBandftsZ.Wefoundthatdecreas- a replication initiation event to the cell division that segre-
. ingmreBlevelresultedinincreasedcellwidth,withlittlechangein gates thecorresponding sister chromosomes can be split into
o
celllength,whereasdecreasingftsZ levelresultedinincreasedcell the C period, from initiation to termination of replication,
i
b length. Furthermore,thetimefromreplicationterminationtocelldi- and the D period, from termination of replication to cell di-
- visionincreasedwiththeperturbeddimensioninbothcases. More- vision [8, 9]. Both the C and D periods remain constant at
q
over, thegrowthlawremained validovera rangeof growthcondi- approximately40and20minutes,respectively,forcellsgrown
[
tionsanddimensionperturbations. Thegrowthlawcanbequanti- invariousgrowthmediasupportingarangeofdoublingtimes

1 tativelyinterpretedasaconsequenceofatightcouplingofcelldivi- between 20 and 60 minutes [10, 11]. We will refer to growth
v siontoreplicationinitiation. Thus,itsrobustnesstoperturbations rateswithinthisrangeasfast. Allexperimentsdescribedhere
7 incelldimensionsstronglysupportsmodelsinwhichthetimingof are carried out under such fast growth conditions. Note that
8
replicationinitiationgovernsthatofcelldivision,andcellvolumeis C+D is approximately 60 minutes and larger than thetime
5
thekeyphenomenologicalvariablegoverningthetimingofreplica- between divisions at fast growth. This situation is achieved
0
tion initiation. These conclusionsare discussed in the context of by the occurrence of multiple ongoing rounds of replication.
0
ourrecentlyproposed“adder-per-origin”model,inwhichcellsadda Thatis,undertheseconditions,acellinitiatesaroundofrepli-
.
1 constantvolumeperoriginbetweeninitiationsanddivideaconstant cationsimultaneouslyatmultipleoriginsthatultimatelygive
0 timeafterinitiation. rise to the chromsomes of their grand- or even great-grand-
7
daughters[12]. ExtendingthebasicdefinitionoftheC andD
1 Cellcycle|Cellgrowth|E. coli|DNAreplication
periods,CooperandHelmstetterspecificallyproposedthatan
:
v
i Bacteria can regulate tightly and coordinate the various
X
events in their cell cycles in order to accurately dupli-
r cate their genomes and to homeostatically regulate their cell
a
sizes. This is a particular challenge under fast growth condi- SignificanceStatement
tions where cells are undergoing multiple concurrent rounds How bacteria regulate cell division toachieve cell size home-
of DNA replication. Despite much progress, we still have ostasis, with concomitant coordination of DNA replication, is
anincompleteunderstandingoftheprocessesthatcoordinate afundamentalquestion. Currently,thereexistseveralcompet-
DNA replication, cell growth, and cell division. This lack ingmodelsforcellcycleregulationinE.coli.Weperformedex-
of understandingis manifested, for instance, in discrepancies perimentswherewesystematicallyperturbedcelldimensions,
among various recent studies that propose different models
and found that average cell volume scales exponentially with
for control of cell division in thebacterium Escherichia coli.
the product of the growth rate and the time from initiation of
Oneclass of modelssuggests that cell division istriggered DNA replication to the corresponding cell division. Our data
bytheaccumulationofaconstantsize(e.g. volume,length,or support a model inwhich cells initiatereplication on average
surface-area) between birth and division [1–3]. Such models at a constant volume per origin, and divide a constant time
aresupportedbyexperimentsmeasuringcorrelationsbetween thereafter.
cell size at birth and cell size at division, which showed that, ..
HZ,MJ,BT,WL,DL,XY,andCLperformedtheexperiments.PH,NK,AA,andCLanalyzedthe
when averaged over all cells of a given birth size vB, cell size dataandwrotethemanuscript.CLdesignedtheresearch.
at division vD approximately follows: Theauthorsdeclarenoconflictsofinterests.
1Towhomcorrespondenceshouldbeaddressed.E-mail:[email protected],CL-
vD =vB+v0, [1] [email protected]
www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX PNAS | January4,2017 | vol.XXX | no.XX | 1–7
initiation [15]. Becausecells growexponentiallyatthesingle-
celllevel[16],cellswillthendivideonaverageatavolume∆
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)∆ ,becausethecellvolumeaveragedoveran
I
exponentially growing population is the average cell volume
at birth times 2log(2) [17]. In Schaechter’s experiments, the
C and D periods were approximately constant, giving rise to
theexponentialscalingobserved. However,thederivationfor
Eq. 2 holds regardless of the values of the C and D periods,
andincaseswheretheyarenotconstant,averagecellvolume
is not expected to scale exponentially with growth rate. Eq.
2isknownasSchaechter’sgrowthlaw,butwillbereferredto
simply as thegrowth law for the rest of this manuscript.
Recent single-cell analyses found that cells indeed initiate
replication on average at aconstant volumeper origin orper
somelocusclosetotheorigin[11]. Whilefurtherexperiments
are required, the fact that introduction of an origin onto a
plasmid doesnot affect cellcycletimingsorcell size suggests
thatthelatterpossibilityiscorrect[11,18,19](SI).Below,for
Fig.1. (A)Schematicillustrationoftheexperiment. MreBandFtsZareinvolvedin simplicity, we will use the phrase “per origin,” while keeping
cellwallsynthesisandseptumformation,respectively.UsingmreB-orftsZ-titratable thiscomplexity in mind.
strains,weareabletotunetheirexpressionlevelscontinuously,andperturbcelldi-
Clearly, the two classes of models for control of cell divi-
mensions. Inbothexperiments,theDperiodincreasedwithcellwidthandlength.
sion differ fundamentally. In the first class, division depends
TheCperiodanddoublingtimeτremainedconstant. (B)Schematicillustrationof
ourmodel. TheperturbedDperiodsetstheaveragenumberoforiginspercell, only on the accumulation of size from birth, and DNA repli-
whichisequaltothescalingfactorSbecausereplicationinitiationtriggerscelldi- cation plays no explicit role. In the second class, division is
vision. Theaveragenumberoforiginspercellthensetstheaveragecellvolume downstream of the preceding initiation of DNA replication.
followingthegrowthlaw. FortitratedmreBlevels,cellvolumechangesmanifested
Importantly,also,theexperimentsleadingtothefirstclassof
mostlyascellwidthchanges. FortitratedftsZ levels,celllengthchangedinstead,
becauseFtsZdidnotaffectcellwidth. models defined cell size differences by measuring cell length.
Since for a constant growth environment the widths of bac-
terial cells are very narrowly distributed with a coefficient of
initiationeventtriggersadivisionafteratimeC+D,thereby variation (CV) less than 0.05 [2], these analyses cannot dis-
ensuringthatcellsdivideonlyafterthecompletionofaround tinguish whether cell size in a given environment is set by
ofDNAreplication[8,10]. ThisCooper-Helmstetter(CH)for- a constant volume, surface-area, or length. This ambiguity
mulation,hereaftertheCHmodel,belongstothesecondclass raises the question of what is the key phenomenological vari-
of models for control of cell division. able governing cell cycle progression.
The CH model is supported by the phenomenon of rate Here, we sought to test these models by perturbing cell
maintenance [13]: after a change from one growth medium dimensionsinE.coli,andassayingtheeffectsofthosepertur-
to a richer one (a shift-up), cells continue to divide at the bations on both replication events and cell division. In our
rate associated with the poorer medium for a period of 60 study, shape perturbations were achieved by systematically
minutes. According to the CH model, in which division is varying expression levels of the protein MreB, an actin ho-
triggered by initiation, all cells that have already initiated mologue involvedincell wall synthesis,and theprotein FtsZ,
replication beforeashift-upwillhavealsoalreadycommitted a tubulin homologue involved in the formation of the divi-
to their ensuing divisions, and thus the rate of division will sionseptum[20,21]. Ourapproachisindicatedschematically
remain unchanged for a time C+D following a shift-up. in Fig. 1A. It extends and complements Schaechter’s experi-
Thesamevalueof60minuteshadalso emergedinaseem-
ingly different context a decade earlier, in the seminal study
ofSchaechteretal. [14]. Intheirwork,cellvolumes,averaged A %*5# B 2.5 mreB
couveltruarengerxopwoinnegntuianldlyergdroowzeinngs opfopduifflaetrieonnt,gwreorwetmhemaseudriaedsufopr- "#$%& level AN12..50 ftsZ
wpoarstiwngellfadsetscgrriobwetdh.byItanwaesxpfoounnednttiahlatrealvateiroangewcietlhl vgoroluwmthe *+# !!"*!$#*+# ()#’()#*,# .,/0#1# Rm .leR01..50
rate V = ∆eλT, where V is the average cell volume, ∆ is /0)1#234## ,-%&-.!"# $%&’"#"#$%& 0.01 10 100
a constant with dimensions of volume, λ is the growth rate, ()#’()& aTc (ng ml-1)
τ =log(2)/λ is the doublingtime, and T ≈60 mins.
Fig.2. TitratablemreBorftsZ expression. (A)ThegeneticcircuitofthemreB-or
Donachie showed that this exponential scaling of average
ftsZ-titratablestrains.TheexpressionofmreBorftsZisunderthecontrolofaPtet-
cellvolumewithgrowthratecanalsobeexplainedbytheCH tetR feedbackloopandthenativemreB orftsZ wasseamlesslyreplacedwitha
modelifitisfurtherassumedthatcellsinitiatereplicationon kanamycinresistancegene.(B)RelativemreBandftsZmRNAlevelinthetitratable
average at a constant volume ∆ per origin of replication at strainsinbulkculturecontainingvariousconcentrationsofaTc(3-50ngml−1).
I
2 | www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Zheng etal.
ments,inwhichgrowthratewasperturbed,andisreminiscent volume growth rates, or OD doubling rates (Fig. S1), of
600
of thework of Harris et al. [3], in which cell dimensions were the titratable strain remained approximately constant (CV
perturbed, but with the important addition to both studies of 0.03) (Fig. 3D). Together, these results suggest that the
thatwealsomeasuredthecellcycleperiodsC andDbecause titratable system is suitable for characterizing the functions
theyplayanimportantroleintheCHmodel. Forthispaper, of MreB in a quantitative manner with no need to consider
we definedivision as completion of septation. complications dueto differing growth rates.
We next measured cell dimensions by phase contrast mi-
croscopy (Fig. 3A), and found that with decreasing mreB
Results
expression level, the cell width increased (Fig. 3B). The cell
Decreased mreB level resulted in increased cell width, with lengthchangedslightly,whichwediscussbelow(Fig. 3C,SI).
littlechangeincelllength.Cell length and cell width are two Although the software used for image processing is designed
majorcharacteristicsofarod-shapedcell. Asacellgrows,cell to define bacterial cell dimensions to subpixel precision [25],
length increases exponentially, while cell width remains con- wewantedtoverifyourresultsusinganindependentmethod.
stant. Howcellwidthisdeterminedandmaintainedislargely WeshowedthattheODpercellislinearlycorrelatedwiththe
unknown. However,severalmutationsofmreB werereported cell volume in µm3 (Fig. S1). We also verified that neither
to result in altered cell dimensions [20, 23, 24], thus raising thepresenceofinducernorthepresenceofthegeneticcircuit
thepossibilitythatalterationsinmreBexpressionlevelwould construct has any effect on wild type cells within the ranges
altercellwidth. Tocontinuouslyandsystematically varycell of inducer concentrations studied here (Fig. 3BC, and SI).
width, we constructed a strain in which the level of mreB Similar results were obtained in all other growth media, sup-
could be experimentally controlled. We employed a system porting various fast growth rates, tested in this study (Fig.
inwhichaP -tetR feedbacklooptriggeredmreB expression S2). All of our experiments, and thus the resultant conclu-
tet
(Fig. 2A, and SI). The modulated copy of mreB was the sions, concern fast growth conditions as definedabove.
sole version of the gene in the genome as the native copy of
mreB was replaced by a kanamycin-resistance gene. In this Cellwidthmaintenancebycellwallstiffness.Lastly,we char-
construct, expression of mreB could be tightly controlled by acterized in detail the morphological properties of the mreB
adjustingtheconcentrationofanappropriateinducerofPtet- titratedcellsusingscanningelectronmicroscopy. Here,wider
tetR, anhydrotetracycline (aTc). cells showed a slightly flattened, dumpling-like morphology
We found that cell size increased with decreasing inducer (Fig. S3A). It is known that MreB is involved in bacterial
concentration until, at very low mreB levels, the cells even- cell wall synthesis [20, 23, 24]. Thus it seemed possible that
tually lysed (at an aTc concentration below 1 ng ml−1 in thecell wall might havebecomesofter in cells expressinglow
Rich Defined Medium (RDM) + glucose). Above this mini- levels of MreB. Due to the difficulty in directly measuring
mum threshold, the expression level of mreB varied linearly cell wall elasticity, we instead measured the effective cellular
with the concentration of inducer (Fig. 2B). We also found stiffness (ECS) of the mreB titrated cells using atomic force
that within a certain range of mreB expression levels, the microscopy. As expected, the ECS significantly decreased as
Fig.3.TitratablemreBorftsZexpressiontosystematicallyperturbcellwidthorcelllength,respectively,withoutaffectingthevolumegrowthrates.(C)Representativephase
contrastimagesofthemreB-titratableandwildtypestrains. (DandE)Scatterplotpresentstheaverage,meancellwidth(averagedalongthelongaxisofacell)(D)or
averagecelllength(E)oftheindividualwildtype(WT)ormreB-titratablecells.(F)VolumegrowthratesinbulkcultureversusmeancellwidthformreB-titratablecells.(G,H,
I,andJ)Thesameas(C,D,E,andF)butfortheftsZ-titratablestrain.ErrorbarsrepresenttheSEMofthreereplicates.
Zheng etal. PNAS | January4,2017 | vol.XXX | no.XX | 3
X = 2(C(1−m)+D)/τ [26]. We used this relation to extract
A 60 B 50 the lengths of the C and D periods from qPCR data of the
)n50 )n40 copy numbers of different chromosome loci (including oriC,
im im
( d40 ( d30 terC and a series of different loci between them; SI). The
oire30 oire20 C period was also measured independently by the methods
Dp 20 Cp 10 in Refs. [27, 28] which gave values consistent with those ob-
tainedbytheqPCRmethod(SI).WealsomeasuredhOiusing
10 0
0.8 1.0 1.2 1.4 0.8 1.0 1.2 1.4 replication-run-out experiments (SI).
Mean cell width (µm) Mean cell width (µm)
These analyses revealed that, over the analyzed ranges in
C 60 D 50 thelevelsof bothmreB andftsZ expression, theC period re-
)n50 )n40 mained unchanged (CV of 0.09 and 0.05 for mreB- and ftsZ-
im im titratablestrains, respectively),while theD period increased
( do40 ( do30 with increasing cell width or length, respectively (Fig. 4).
irep30 irep20 Note that the relation between the D period and cell length
D 20 C 10
predicted by our model below is not linear, but appears ap-
10 0
3 4 5 6 7 3 4 5 6 7 proximately linear given the particular values of the relevant
Cell length (µm) Cell length (µm) parameters undertheconditions of these experiments.
Thegrowthlawholds inface ofperturbations tocell dimen-
Fig.4. Changesinthecellcycleparametersascelldimensionsareperturbed. (A)
sions.We find that the growth law, Eq. (2), holds in our
TheDperiodincreasedmonotonicallywithcellwidthinmreB-titratablestrains.The
lineisthebestlinearfit.(B)TheCperiodremainedapproximatelyconstantascell experiments, both across a range of growth media (Fig. 4)
widthchangedinresponsetotitratedmreBexpressionlevels.Thelineisthemean andacrossthetwotitratableperturbationsthatdrasticallyaf-
valueofC averagedovermreB expressionlevels. (C)TheD periodincreased fectedcellwidthandcelllength(Fig. 5A).Thebestfitpropor-
monotonicallywithcelllengthinftsZ-titratablestrains. (D)TheCperiodremained tionality constant is ∆=0.55±0.04µm3. Theplus-minusin-
approximatelyconstantascelllengthchangedinresponsetotitratedftsZ expres-
sionlevels.Thecircle,triangle,andsquareindicatesmreB-titratable,ftsZ-titratable, dicatesthe95%confidenceintervalofthefit. Fromthederiva-
andwildtypestrains, respectively. Differentcolorsdenotegrowthmedia: redis tionofthegrowthlawintheIntroduction,wefindtheaverage
RDM+glucose,blueRDM+glycerol.TheSEMsofthreereplicatesweresmallerthan cellsizeperoriginatinitiationtobe∆ =0.79±0.06µm3. In
I
thesizeofthesymbols.
contrast, theaverage cell area, cell length, andcell widthare
not proportional to thescaling factor S (Fig. 5B, Fig. S4).
cellwidthincreased(Fig. S3B).Thisresultraisesthepossibil- Wefurthertested thevalidity of aconstant ∆ byfixing∆
itythatincreasedcellwidthreflectstheforcebalancebetween to 0.55µm3 and calculating the ratio of log2(V/∆) and τ−1,
turgor pressure and thetensile resistance of thecell wall. 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
DecreasedftsZ levelresultedinincreasedcelllength,andno well with independent measurements in both the titratable,
changeincellwidth.Weconstructedandcharacterized,using as well as wild type, strains (Fig. 6B).
the same method as above, an ftsZ-titratable strain to allow
perturbationofcelllength(SI).Wefound,inagreementwith Discussion
previous work [21], that cell length increased with decreased
ftsZ expression levels, but that both cell width and growth Here,we perturbedcell dimensions and thenobserved theef-
rateremainedrelativelyconstantwithintherangesofinducer fectsoftheseperturbationsonthecellcycleinordertointer-
concentration studied here (CV of 0.01 and 0.03 respectively, rogate the mechanism of cell cycle regulation in E. coli. The
across different experiments, Fig. 3EFGH). most important finding of this work is that the growth law,
that average cell volume is proportional to the scaling factor
Correlationsbetweenperturbedcelldimensionsandcellcy- S = 2(C+D)/τ, remained valid across large perturbations in
cletimings.We next investigated how the mreB and ftsZ ex- celldimensions. AsdiscussedintheIntroduction,thegrowth
pressionlevelsaffecttheC andDperiods. Forabulkculture law can bequantitativelyderived undertwo assumptions: (i)
in steady-state exponential growth, the CH model predicts theCHmodel,thatreplicationinitiationtriggerscelldivision
that the average number of origins per cell, hOi, scales expo- after a constant time C +D, and (ii) that the average cell
nentiallywithgrowth rate[22,26]. Thisisbecauseinsteady- volumeatinitiationofDNAreplicationisproportionaltothe
state exponential growth, the number of cells and the total numberoforiginsatinitiation. Therobustnessofthegrowth
number of origins in the population must both grow expo- lawasdocumentedabovesuggeststhatbothassumptionshold
nentially at the same rate. However, because the CH model in face of theperturbations studied here.
postulatesthatdivisiononlyoccursafteratimeC+Dfollow- Correspondingly,giventhefirstassumption,thepresented
ing the corresponding initiation, the total number of origins results support the second class of models for control of cell
will be larger than the number of cells by the scaling factor division (Introduction) in which the timing of initiation gov-
S, defined above. Therefore, hOi = S. This relation holds erns that of division, and opposes the first class of models
regardless of the valueof C+D. in which the timing of division is governed by the accumula-
An expression for the average number of copies X of a tionofcell sizewithnoexplicitreference toDNAreplication.
gene per cell as a function of the location m of the gene The presented findings do not rule out models in which, op-
along the chromosome (m = 0 for oriC and m = 1 for positely to the CH model, division triggers initiation. How-
terC) can be derived similarly. Under the assumption that ever, these models are heavily challenged by the finding that
replication forks travel at a constant speed, theexpression is C+Disessentiallyconstant(CVofapproximately0.1)onthe
4 | www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Zheng etal.
A 6 B 6 A 3 8273 B100
3)mµ( emulov lleC0240 2 ∆4=0.565 µm8310 2)m( aera lleCµ 0240 2 4 6 8 10 logemuloVgoL2∆2-00121.00 0.02 0.04 6516 DC)nim( [phone]
S S 1/τ (min-1) Slope in panel A
Fig.5. Thegrowthlawholdsinfaceofperturbationtocelldimensions. (A)The Fig.6.Theaveragecellvolumeperoriginatinitiationisconstantinfaceofperturba-
averagecellvolumeisproportionalto thescalingfactorS = 2(C+D)/τ. The tionsincelldimensions.(A)Coloredlinesconnectlog2(∆)toboldedsymbolsasex-
blacklineshowsthegrowthlawV = S∆forthebestfitproportionalityconstant amples.Therespectiveslopesofthelinesarecomputedastheratiooflog2(V/∆)
∆ = 0.55±0.04µm3. Theplus-minusindicatesthe95%confidenceintervalof over1/τ,andshownasnumbers(minutes).(C)MeasuredC+Dvaluesareplotted
thefit. ThecoefficientofdeterminationR2ofthefitis0.81. (B)Theaveragecell againsttheratioscalculatedinpanel(A).Thecircle,triangle,andsquareindicates
areaisnotproportionaltothescalingfactor. Theblacklineshowsthebestfitwith mreB-titratable, ftsZ-titratable, andwildtypestrains,respectively. Differentcolors
interceptforcedtozero. TheR2ofthefitis0.40. Thecircle,triangle,andsquare denotegrowthmedia:redisRDM+glucose,blueRDM+glycerol.TheSEMsofthree
indicatesmreB-titratable,ftsZ-titratable,andwildtypestrains,respectively.Different replicatesweresmallerthanthesizeofthesymbols.
colorsdenotegrowthmedia:redisRDM+glucose,blueRDM+glycerol. TheSEMs
ofthreereplicatesweresmallerthanthesizeofthesymbols.
this situation, happens to manifest as an increase in length
alone, with no change in width. This asymmetric change in
single-celllevelatfastgrowth[11]. Tobeconsistentwiththis length,versuswidth,matchesthefactthatcellwidthismain-
finding,thesemodelsmustsomehowcoordinatethetriggered tained normally even in filamentous cells where septation is
initiationeventwiththedivisioneventinthenextgeneration. completely eliminated [21, 29].
Furtherstudieswill berequiredtoinvestigate thispossibility. Reduced mreB expression also increases the D period. In
Our findings also provide information about the question one possibility, MreB would have two direct roles: both in
of what keyphenomenological variablegovernscell cyclepro- septation via local effects at the division site [30], and in de-
gression. Wefindthatonlycellvolume,andnotsurface-area, termining cell width. Here, at reduced MreB levels, delayed
length, or width, is proportional to the scaling factor S (Fig. septation would increase the D period. Due to the second
5, Fig. S4). Together with the second assumption (above), roleofMreB,thecorrespondingincreaseincellvolumeinthis
therobustnessofthegrowthlawthensupportsthehypothesis case is implemented mostly by the increase in cell width. Al-
that volume per origin, rather than other geometric features, ternatively,MreBmightplayonlytheroleofdeterminingcell
is the key phenomenological variable that is invariant at ini- width. In this scenario, the increased cell width then results
tiation. Hence, cell volume governs the timing of initiation in aprolonged septation process andthus,alonger D period.
and, bythe CH model, thetiming of division. In both scenarios, however, given experimentally-determined
Figs. 5 and 6 also show that the proportionality constant values for the D period and cell width, the cell volume pre-
∆, which links average cell volume to the scaling factor S in dicted by the growth law also dictates small changes in cell
thegrowth law (Eq. 2), remained constant across thepertur- length. Themagnitudesofthesepredictedchangesarejustat
bationsstudiedhere. Inthederivationofthegrowthlaw,∆is the level of detection of the current study but are consistent
proportionalto∆ ,ortheaveragevolumeperoriginrequired with observed values (Fig. S5).
I
forinitiation. Theconstancyof∆thereforesuggestthatnone In general, the growth law specifies cell volume without
oftheperturbationsstudied(MreB,FtsZ,andvariousgrowth referencetotheaspectratiooftherod-shapemorphology. As
media) affected themolecular mechanism underlyingthereg- aresult,agivenchangeincellvolumeduetoachangeinthe
ulation of initiation. Despite drastic changes in cell shape, parameters of the growth law can be manifested as diverse
thetitratablestrainsstillinitiatedreplicationonaverageata combinations of changes in cell length and cell width.
constant 0.79±0.06µm3 perorigin just asin wild type. This Ouranalysishasshownthat,inanalyzingsize-relatedmea-
value for the average cell volume per origin at initiation is surements, the growth law and its underlying tenets imply
similar to the recently reported valueof 0.9−1.0µm3 [11]. thatanyperturbationstotheC orD periods,orgrowthrate
Althoughthepresentstudyexaminedalteredgeneticcondi- will affect cell volume - even if the perturbations are not af-
tionsthatresultinalteredcelllengthandcellwidth,ouranal- fectingthecoremechanismofsizeregulation thatdetermines
ysis implies that these changes in cell length and cell width the value of the invariant average cell volume per origin at
did not affect cell volume directly. Rather - since neither ge- initiation. Thus, with respect to determining cell size, an
netic perturbation affected growth rate, the C period, or ∆ important distinction can be made between “primary” and
- changes in the D period alone were responsible for the ob- “secondary” regulators, as highlighted in Ref. [31]. In the
served changes in cell volume, which in turn are manifested context of the above analysis, MreB and FtsZ appear to be
as changes in cell length and cell width. secondary regulators in E. coli because ∆ remained constant
Fig. 1B illustrates schematically how the two genetic per- across titrated mreB and ftsZ levels.
turbationsmightexerttheireffects. Inonecase,reducedftsZ Alloftheconsiderationsabovebuildontheclassicalworks
expression increases the D period. Since FtsZ is a direct me- of Schaechter, CH, and Donachie, which consider population
diator of septum formation, this effect could result directly average behaviors. Donachie further proposed a single-cell
from a prolongation of the septation process. The increased interpretation of his idea in which initiation occurs in a cell
D period dictatesanincreasedaveragecellvolume,which,in whenthecellreachesaconstantvolumeperorigin [15]. How-
Zheng etal. PNAS | January4,2017 | vol.XXX | no.XX | 5
ever,theproposalisnotcompatiblewithexperimentalsingle- References
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