Accurate measurements of dynamics and reproducibility in small genetic networks.

1.7 MB·English

by  Dubuis, Julien O

MolecularSystemsBiology9;Articlenumber639;doi:10.1038/msb.2012.72
Citation:MolecularSystemsBiology9:639
www.molecularsystemsbiology.com
Accurate measurements of dynamics and
reproducibility in small genetic networks
JulienODubuis1,2,RebaSamanta3andThomasGregor1,2,*
1 JosephHenryLaboratoriesofPhysics,PrincetonUniversity,Princeton,NJ,USA,2 LewisSiglerInstituteforIntegrativeGenomics,PrincetonUniversity,
Princeton,NJ,USAand3 HowardHughesMedicalInstitute,PrincetonUniversity,Princeton,NJ,USA
* Correspondingauthor.JosephHenryLaboratoriesofPhysics,LewisSiglerInstituteforIntegrativeGenomics,PrincetonUniversity,WashingtonRoad,Princeton,
NJ08544,USA.Tel.: þ16092584335;Fax: þ16092586360;E-mail:[email protected]
Received10.9.12;accepted10.12.12
Quantificationofgeneexpressionhasbecomeacentraltoolforunderstandinggeneticnetworks.
Inmanysystems,theonlyviablewaytomeasureproteinlevelsisbyimmunofluorescence,whichis
notoriousforitslimitedaccuracy.UsingtheearlyDrosophilaembryoasanexample,weshowthat
carefulidentificationandcontrolofexperimentalerrorallowsforhighlyaccurategeneexpression
measurements. We generated antibodies in different host species, allowing for simultaneous
stainingoffourDrosophilagapgenesinindividualembryos.Carefulerroranalysisofhundredsof
expression profiles reveals that less than B20% of the observed embryo-to-embryo fluctuations
stem from experimental error. These measurements make it possible to extract not only very
accuratemeangeneexpressionprofilesbutalsotheirnaturallyoccurringfluctuationsofbiological
origin and corresponding cross-correlations. We use this analysis to extract gap gene profile
dynamics with B1min accuracy. The combination of these new measurements and analysis
techniques reveals a twofold increase in profile reproducibility owing to a collective network
dynamicsthatrelayspositionalaccuracyfromthematernalgradientstothepair-rulegenes.
MolecularSystemsBiology9:639;publishedonline22January2013;doi:10.1038/msb.2012.72
SubjectCategories:development
Keywords: Drosophilagapgenes;dynamics;erroranalysis;immunofluorescence;reproducibility
Introduction concepts (Schro¨dinger, 1944). In one view, each step in the
processisnoisyandvariable,andnoisereductiononlyoccurs
Thefinalmacroscopicoutcomeofdevelopmentalprocessesin through integration of many elements or collectively within
multicellularorganismsresultsinstructuresthatareremark- thewholenetworkofelements.Intheotherview,eachstepin
ably similar between individuals of a given species theprocesshasbeentunedtoenhanceitsreliability,attimes
(Thompson,1917;Held,1991).Ininsects,thishaslongbeen maybeevendowntothelimitssetbybasicphysicalprinciples
observedforthedeterminationofsensorybristlesoftheadult (Gregor et al, 2007a). Can the precise and reproducible
(Wigglesworth, 1940; Richelle and Ghysen, 1979; Whittle, features observed in the patterning system be sufficient to
1998).Inflyembryos,inparticular,thesegmentallyrepeated account for the precision observed in morphology? Focusing
denticlepatternoftheventralepidermisishomologousfrom on these quantitative features of the network will ultimately
oneregiontothenextandidenticalfromoneindividualtothe lead to our understanding of which network properties
next (Alexandre et al, 1999; Hatini et al, 2000; Jones and aretrulyreliable,whichonesarevariable,howtheyrelateto
Bejsovec, 2005). The earliest macroscopic manifestation networkarchitecture,andhowtheyrespondtoenvironmental
ofreproduciblepatternintheflyembryocanbeidentifiedas andgeneticvariation.
the formation of the cephalic furrow (Namba et al, 1997), Studies of the emergence of reproducible patterns during
which forms only 3h after the egg is fertilized. The swift embryogenesistypicallyutilizegenetictoolstodisruptentire
appearanceofenduringreproduciblefeaturessuggeststhatthe nodes of the regulatory network (e.g., Driever et al, 1989;
observedsimilaritiesmayhavetheiroriginsatthemolecular Hu¨lskampetal,1990;KrautandLevine,1991;Capovillaetal,
level in the reproducible spatial patterns of morphogen 1992;Struhletal,1992;Rivera-Pomaretal,1995.SeeSa´nchez
concentrations in the early embryo (Lawrence, 1992, Arias andThieffry,2001forafullreview).Thesubsequentresponse
and Hayward, 2006; Kerszberg and Wolpert, 2007; Lander, of the system is then used to infer interactions between
2007;Gregoretal,2007a). the remaining network components. As a complementary
Uncoveringtheoriginofpreciseandreproduciblestructures approach, precise measurements in an intact, wild-type
in biological processes is a fundamentally quantitative system can reveal the quantitative relationships within the
question,theanswertowhichcanbeoneoftwoverydistinct network in an unperturbed, natural state (Mjolsness et al,
&2013EMBOandMacmillanPublishersLimited MolecularSystemsBiology2013 1
Dynamicsandreproducibilityingeneticnetworks
JODubuisetal
1991;ReinitzandSharp,1995;Reinitzetal,1998;Jaegeretal, polarity genes. These genes interact with each other in a
2004b; Crombach et al, 2012). It is challenging to perform complex network (Nu¨sslein-Volhard and Wieschaus, 1980;
experiments that take advantage of the latter approach as it Akam,1987;Ingham,1988;Hu¨lskampetal,1990;Krautand
requires extreme care to minimize sources of experimental Levine, 1991; Papatsenko, 2009; Jaeger, 2011), resulting 3h
error that allow for the data to be accurately quantified. afterfertilizationintheformationofprecisepatternsinwhich
Nevertheless, such measurements are essential both neighboring cells have readily distinguishable levels of gene
for mathematical modeling of gene interactions and for expression (Gergen and Wieschaus, 1986), and which are
understandingincreasinglycomplexdevelopmentsystems. reproducible from embryo-to-embryo (Houchmandzadeh
To fully understand the source and maintenance of et al, 2002; Gregor et al, 2007a). In order to understand the
developmentalreproducibility,andthelevelofreproducibility strategiesthatnatureusestomakeembryonicdevelopmentso
thatisactuallyrelevanttobiologicalprocesses(i.e.,thelevelof reproducible,itiscrucialtopreciselyrecordthevariationsin
variationthatistoleratedbythesystemwhilestillmaintaining geneexpressionlevelsacrossembryosovertime(Gregoretal,
function), a number of conceptual and technical challenges 2007b). In particular, what is the final gene expression level
need to be overcome (Kudoh et al, 2001; Myasnikova et al, reproducibility at the time of gastrulation and how does it
2001; Visel et al, 2004; Tassy et al, 2006; Lein et al, 2007; compare with the initial reproducibility of the Bcd gradient
Tomancaketal,2007;Fakhourietal,2010).Conceptually,we (Gregor et al, 2007a)? What is the response of the gap gene
are seeking to uncover novel quantitative traits in develop- network to the Bcd input (Ochoa-Espinosa et al, 2009); and
mentalregulatorynetworks,such asthetimedependenceof how is reproducibility transmitted from Bcd to the pair-rule
simultaneously measured expression levels, and their posi- genes(Houchmandzadehetal,2002;Gregoretal,2007a)?
tion-dependent variances and cross-correlations across Inthispaper,wepresentasetoftoolsandanumberofcareful
populationsofcomparableembryos.Technically,suchquan- controlmeasurementsthatclearlydemonstratetowhatextent
tities cannot be determined precisely in the presence of antibodystainingscanbeusedforquantitativeanalysis.First,
systematicexperimentalbiasormeasurementerror. we developed a new set of antibodies for the four major gap
Quantitative data in this context is largely based on genes, Hb, Kru¨ppel(Kr), Giant (Gt), and Knirps (Kni),which
immunofluorescence staining (Ay et al, 2008; Fowlkes et al, allowsustostainindividualembryoswithallfourantibodiesat
2008;Surkovaetal,2008;Pisarevetal,2009),atechniquethat once, and hence to preserve temporal correlations between
is restricted to fixed tissue and induces systematic errors thesegenes.Second,wemeasurethedevelopmentaltimepoint
inherenttotheexperimentalprocedure.Thesefluctuationsare ofembryosattheinstantoffixationwithaprecisionof1–2min
thoughttohaveonlyaminoreffectonthemeasurementofthe usingthemembranefurrowinvaginationasacalibrator.Third,
meanexpressionprofiles(Myasnikovaetal,2009).However, weidentifyeightsourcesofexperimentalmeasurementerror,
ifoneisinterestedinquantifyingthevariationsthatnaturally andshowthatthecombinedsumoftheseerrorsforanygeneis
arise from embryo-to-embryo, such experimental error will o20%ofthetotalvarianceinourdataset,leavingover80%of
distort the signal. Moreover, using fixed tissues makes it thevarianceavailableforbiologicalinterpretation.
difficulttoreconstructgeneexpressiondynamics(Myasnikova Todemonstratethepotentialofthisapproach,weconnectthe
et al, 2001). Finally, because the number of simultaneously dynamics and reproducibility of the gap gene expression
stainable genes is limited, comparisons of different genes patterns with the positional precision of various position
atanygiventimepointarerestricted. markers. Specifically, we compute the positional error of 20
Here,weaddresstheseissuesofthefixed-tissueapproachin individual position markers (such as boundary positions and
thecontextofthegapgenenetworkintheearlyflyembryo.We thepositions of the peakconcentrations ofall four majorgap
show that precise measurements in conjunction with proper genes)inasetof163embryos.Weshowthatatanytimeduring
quantification of experimental error enable (i) simultaneous nuclearcycle(n.c.)14allmarkersofallgenesarereproducible
spatial and temporal tracking of gene expression levels; below one internuclear distance. We further see a dynamic
(ii)quantificationofreproducibilityatanunprecedentedlevel increaseofthisreproducibility(averagedoverallmarkers)from
ofprecision;and(iii)hithertounmatchedaccesstoquestions oneinternucleardistanceatthebeginningofn.c.14tohalfan
abouttheinteractionsbetweenthegenes. internucleardistance40–45minlater.Thisreductioncoincides
In embryos of the fruit fly Drosophila melanogaster, the withan overall zenith of thegapgene network,whenallgap
earliestsignofareproduciblepatternisthegradientofbicoid genessimultaneouslypeakintheirmaximumconcentrationas
(Bcd), the primary anterior determinant of patterning along wellastheirmaximumboundaryslopes.Theseresultsleadusto
the major body axis (Driever and Nu¨sslein-Volhard, 1988; postulatethat along thecentral 80% of theembryo collective
Craukand Dostatni, 2005; He et al, 2008; de Lachapelle and network dynamics increase positional accuracy twofold from
Bergmann, 2010), and which is established by maternally thelevelofreproducibilityinherenttotheBcdgradienttothat
depositedmRNAattheanteriorpoleoftheegg(Ephrussiand observedinthepair-rulegenes.
StJohnston, 2004). Initsmainregionofactivity between10
and60%egglength(EL;where0%correspondstotheanterior
Results
pole of the egg), the gradient has been shown to be
reproducible to B10% in Bcd concentration across different
Quadruple antibody stainings in individual
embryos,whichtranslatesintoapositionalaccuracyof1–2%
embryos
EL(Gregoretal,2007a).Bcd,actingasatranscriptionfactor,
triggers the expression of Hunchback (Hb) and other down- Whenlabelingdifferentproteinswithfluorescentprobesinthe
streamzygoticgenessuchasthegap,pair-rule,andsegment sametissue,therearetwomainlimitations.Thefirstlimitation
2 MolecularSystemsBiology2013 &2013EMBOandMacmillanPublishersLimited
Dynamicsandreproducibilityingeneticnetworks
JODubuisetal
isbiochemical:antibodiesareraisedinspecifichostanimals, temporally staged in a very precise way. During this time,
soeachantibodyusedtolabelagiventissuehastobemadein cell membranes form in an apical–basal direction across the
a different animal, of which only a limited number exist entire embryo surface, and we can use the progression
commercially. The second limitation is optical: secondary ofthiscellularizationprocess(bymeasuringthedepthd of
FC
antibodies are conjugated with fluorophores whose absorp- themembranefurrowcanal(FC))asa‘clock’toestimatethe
tion and emission spectra can significantly overlap, which ageoftheembryo(seeFigure2AandLecuitetal,2002).
leads to crosstalk between the different optical channels, To evaluate the precision of this method, we start by
making quantification of co-labeled proteins challenging. comparing d across live-imaged embryos as shown in
FC
Someattemptshavebeenmadeinthepasttotrytoovercome Figure2BandSupplementaryVideo1.Afterprofilealignment
thoselimitations(directlabeling(Kosmanetal,2004),useof (seeMaterialsandmethods),wefindthatthes.d.s ofd
dFC FC
quantumdotsasfluorescentprobes(Choietal,2009),spectral across live-imaged embryos never exceeds 1mm, which
imaging(Dickinson etal,2001),andblindsourceseparation translatesintoatemporalprecisionofB2minduringthefirst
(Neheretal,2009))buttoourknowledgetherehasbeenno 30minofn.c.14andinto o1minduring thenext30minas
attempt to use the classic immunofluorescence staining shown in Figure 2B (inset). Finally, the clock is rescaled to
protocol to simultaneously quantify more than three account for embryo shrinkage owing to the heat fixation
co-labeledproteinswithhighprecision. protocol (5% EL, see green right axis of Figure 2B and
To overcome the biochemical limitation, we developed a Materials and methods). This method allows us to precisely
newsetofprimarypolyclonalantibodiesagainstthreeofthe select embryos for any given developmental time point
fourmaingapgenes(Kosmanetal,1998).Allantibodieswere duringn.c.14,effectivelyreducingthevariabilityofintensity
raisedinadifferenthostspecies(ratanti-Kni,guineapiganti- profilesacrossembryosinagivenwell-definedtimewindow
Gt, and mouse anti-Hb), allowing us to use them in (Figure2C).
combinationwitharabbitanti-Krantibody(giftofCRushlow) Previous quantitative studies of expression in this system
tosimultaneouslystainallfourmajorgapgenesinthesame have used roughly 10-min time intervals (Myasnikova et al,
embryowithouttheriskofcross-reactivitybetweenreagents. 2001).Bystagingembryosin1–2minintervals,wedetermined
To ensure that our immunofluorescence protocol would that10–20%ofthevarianceinthese10-mintimeintervalsis
potentiallybesuitableforgeneexpressionprofilequantifica- due to underlying expression dynamics (Supplementary
tion with these new antibodies, we verified their linearity Figure 2A). We correct embryo-to-embryo intensity
by comparing immunofluorescence intensities and protein profile fluctuations that are due to the underlying pattern
concentrations nucleus per nucleus in individual embryos dynamics bycomputing the average time dependence of the
(seeMaterialsandmethodsandSupplementaryFigure1). expression level at each position, and use it to detrend our
Toovercometheopticallimitation, wechosefluorophores expression profiles by this systematic gene expression drift
that maximized the span of the employable laser excitation (Figure2D),effectivelyreducingtheoverallprofilevariance.
wavelengths to limit simultaneous excitation of multiple For example, for profiles of embryos pooled together in the
fluorophores,andweadjustedthebandwidthsoftheemission particulartimewindowof37–49mininton.c.14(correspond-
channels in order to minimize simultaneous emission from ing to d ¼10–20mm), we find that in the case of Gt this
FC
multiple fluorophores in the same imaging channel (see correction is on average 15% of the original variance
Figure1A).Weusedthissetuptostainandimageabatchof (Figure2E).
163 Drosophila embryos at the blastoderm stage. A typical Hence,ascouldbeinferredfrompreviousstudiesandisnow
embryoimagedinallfourchannelsisdepictedinFigure1B. madeclearbyclassifyingembryosintosmallertimeclasses,an
Typical intensity profiles extracted from these images are overwhelmingmajorityoftherawprofile-to-profilevariability
shown in Figure 1C, and cross-talk between channels is seen in Figure 2C can be attributed to the dynamics of the
quantifiedinFigure1D.Thisapproachallowsustomeasure expressionlevels.Precisestaging,grouping,anddetrendingof
expressionprofilesofallfourmajorgapgenessimultaneously expressionprofilesinrelativelysmalltimewindowsallowsus
in individual embryos, an indispensable requirement to thentoconvertintensityvaluesintogeneexpressionlevelsg
measurenaturalfluctuationsandcross-correlationsofprofile (Figure2C)andtodecomposetheresidualvariances2within
g
variabilitiesacrossgenesandtoguaranteetemporalorderand a given time window (Figure 2E) into its various sources of
correlationsforthesemeasurements. experimental error with the goal to ultimately expose the
remainingbiologicalvariance.
Developmental time measurements in fixed
embryos Experimental error quantification
TheDrosophilagapgenesareendogenouslytranscribedfora Inordertoextractsignificantinformationfromthemeansthe
time span of 1–2h, peaking roughly 2.5h after the onset of variances, and the cross-correlations of gene expression
embryonicdevelopment.Duringthisentiretime,geneexpres- profiles, we have to utilize the fraction of the observed
sionpatternschangesignificantly, makingthedetermination profile variance that is due to actual biological fluctuations
of each individual embryo’s age with high fidelity a crucial resultingfromthenaturalembryo-to-embryovarianceacrossa
prerequisiteforanyquantitativepurposesuchasassessingthe populationofembryos.Theobservedvariance,however,isa
profiles’reproducibility.Fortunately,intheDrosophilaembryo combination of (1) the natural variation in the system and
the1-htimewindowbeforegastrulation(i.e.,n.c.14)canbe (2)theexperimentalerror.
&2013EMBOandMacmillanPublishersLimited MolecularSystemsBiology2013 3
Dynamicsandreproducibilityingeneticnetworks
JODubuisetal
Filter: 520/40 575/20 620/40 670/40
Laser: 488 546 594 633
1
u.)
a.
y (
sit
n
e
nt
I
0
500 550 600 650 700
Wavelength (nm)
Kni (488 nm) Kr (546 nm) Gt (594 nm) Hb (633 nm)
4000
u.)
a.
y ( 2000
sit
n
e
nt
I 0
104
u.)
a. 102
y (
sit
n 100
e
nt
I
10–2
0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1
x/L x/L x/L x/L
Figure1 Simultaneousimmunostainingofthefourmaingapgenes.(A)Spectralimagingsettingsforsimultaneousmeasurementsoffourfluorescentdyes.Absorption
(dashedlines)andemission(solidlines)spectraofthedyesusedforfoursimultaneousimmunostainings;laserexcitationwavelengths(blackarrows)andbandwidthsof
theemissionfiltersforeachdetectionchannel(lightcolorpatches)areindicated.(B)OpticalsectionsthroughthemidsagittalplaneofasingleDrosophilaembryowith
co-immunofuorescencestainingagainstthefourgapgenesKni(green),Kr(yellow),Gt(orange),andHb(red);scalebar100mm.(C)Rawintensityprofiles(dorsalside)
of23selectedembryos(lightcolors);embryodepictedaboveishighlightedindarkercolor(anteriorpoleatx/L¼0;posteriorpoleatx/L¼1).(D)Quantificationof
spectralcrosstalkandfluorophorebleed-through.Foreachchannel,theaverageintensityprofileIof10embryosimmunofluorescentlylabeledwiththreeantibodies
lackingthespecificantibodycorrespondingtothatopticalchannelisshowningray.Blackdashedlineshowsacross-talkestimateusingareconstructionalgorithm
(seeMaterialsandmethods).AverageprofilesfromBareshownincolor.
Hence, for an analysis of gap gene reproducibility to be effect of the latter on our results we only work with single-
meaningful, we need to identify and precisely measure our batchexperiments.
sources of experimental error in order to minimize their Here,weassessthecontributionsofsixpossiblesourcesof
contributions to the overall variance s2. Only when the experimentalerrorinourexperimentsthatarelikelytoperturb
g
varianceowingtomeasurementerrorisasmallfractionofs2 themeasurementofs2:
g g
canwehopetoextractknowledgeaboutthesystemfromthe
1. Thegapgeneexpressionprofileschangeduringthecourse
underlying natural fluctuations. We can then choose to
ofn.c.14suchthattheuncertaintyinourestimationofa
subtract this fraction from s2, or work with s2 directly,
g g givenembryo’sexactageinducesasystematiccontribution
knowingthatitrepresentsanupperbound.
s to s (see Figure 2Fand Supplementary Figure 2B).
Notethatthesourcesofexperimentalerrorweaddresshere gage g
We find that this source of error represents 2–7% of the
onlydealwitherrorwithinagivenembryo(i.e.,fluctuationsof
totalvariances2,dependingonthegeneconsidered.
successivegeneexpressionmeasurementsofthesamespeci- g
men) and with error across embryos within a given experi- 2. Laserfluctuationsandphotondetectioninducenoiseinthe
ment. We ignore error that arises from pooling different imagingprocessandperturbtheintensitymeasurementin
experimentalbatchesasthiswouldgobeyondthescopeofthe each embryo. We quantified their contribution to the
presentwork,andwillbetreatedelsewhere.Tocircumventthe variancebycomparingsuccessiveintensitymeasurements
4 MolecularSystemsBiology2013 &2013EMBOandMacmillanPublishersLimited
Dynamicsandreproducibilityingeneticnetworks
JODubuisetal
546 nm 488 nm Anti-Rat
40 13 34 40
δμ (m)FC 123000 Mitosis δFC σ(T)t0120 20T4060 123000 δμfixed (m)FC Excitation GP anti-Hb Hb
0 0 Rat anti-Hb
60 80 100 120 0 20 40 60
Time (min) Time (min) 488 nm 546 nm Anti-GP
×103 ×103
4
4 4 0.06
T
Gt intensity 123 10 I 02 10δFC 20 T−@Hb / 488−@R 123 σI148200000 1 2 3×103 σσ=/(I−I)gImax minIS 000...000124
0 0.5 1 0 10 20 30 R 0 I ×103 0
x/L δ (μm) 0 1 2 3 4 0 0.2 0.4 0.6 0.8 1
FC
GP−@Hb / 546−@GP g
0.04 10−1
Figure 3 Quantification of imaging noise and antibody nonspecificities.
2)min 0.03 10−2 (pAri)mSacryheamntai-tHicbreapnrteibsoednietastiaonndotfhaeisrirmeuspltaencteivoeussesctaoinndinagryparonctiebsosdibeystcwoonjduigsatitnecdt
σσ22=/(I−IgImax 00..0012 σσ22, ggage 1100−−34 mppwhrieotohactesodusnisrfecfeedosrueifnnontrtielnypagrcicmahonaloodrpyreltaiadcsnaedldrcysihneeatsce.nonnnsTedihtlayecrflyousmacynetsutstieabfmtorioodanmitesics)i.mae(saBrrg)woinrSegcllsanatIotseiisnrthepenl(omurtacaonleifdnatolhyrmeoinnwbtuieinncndglseiniattgoyr
intensities from two channels with different anti-Hb antibodies and Alexa-
0 10−5 conjugateddyes(anti-rat(488)andanti-guineapig(546)).Asthetwochannels
0 0.5 1 0 0.5 1
x/L x/L aredetectedseparatelyandhavedifferentprimaryandsecondaryantibodies,the
scatter of gray dots results from the combined errors owing to imaging and
Figure 2 Staging of gene expression profiles in fixed embryos with minute staining(primaryandsecondary).Twodashedlinesdefinetheminimum(reddot)
precision. (A) Depth of FC (dFC) during blastoderm cellularization measured andthemaximumgeneexpressionlevels,IminandImax,respectively.Insetshows
alinloengcothrreesdpoorsnadlssitdoeooufraelivsetim-imataegeodfwmilidto-tsyipse1e3m.bInrysoetdusrhinogwsn.ca.1b4r.igDhatsfiheeldd ddeiapgeonndaelndciveidoefdmbeyaspurffi2effiffi)maesntanfouinscetisonI(osf.dt.heofmtheeandisintatenncseityofI,thceompopiunttesdtootvheer
microscopyimageofafraction(40–50%EL)ofthedorsalsideoftheembryoata 40equallyspacedbinsalongthewholeintensityrange(onlydatapointswithfive
timepointindicatedbyreddot;scalebar10mm.dFC,definedasthedistance ormorenucleiareshown).S.d.ofzeroexpressionlevelregionshownasared
betweentheFCandtheedgeoftheembryo,wasmeasuredasindicatedbyred dot.(C)Rescaledmeasurementnoisecontributionfromimagingandstaining
mbaera.n(Bs)aInndvasg.din.’astiionnbolafctkh.eTmheemmberaanneoffothreeoignhsteetsmobfryno.cs.(1g4raisyilnindeicsa)twedithabsiannreedd sfugnISct¼ionsIo=fðtIhmeaxge(cid:2)neImeinxÞpr(ecsosmiopnutleedvefrlogm.RtheedddaotatsshhoowwnsitnheinsbeatcokfgproaunnedlBn)oaissea,
dashedlineandtheirs.d.isrepresentedbytheerrorbaroftheredsquare.The and two dashed lines represent the 1 and 4% measurement noise levels,
profileinAisshowninbluehere.Scaleontherightshowstheadjustedlength respectively.Errorbarscomputedbybootstrapping.
measuredinfixedembryos(onaverage5%ELshrinkagew.r.t.livingembryos).
Inset shows the measurement error of the embryo age estimation s as a
dFC
functionoftime.(C)RawdorsalGtintensityprofilesof80embryosimagedintheir 3. Primary and secondary antibodies have nonspecific bind-
midsagittalplane(DVorientation)withT¼0–60min(gray)andasubsetof23
ing properties (Figure 3A) that affect the overall staining
embryoswithT¼37–49min(lightorange).Themeanintensityprofileofthe23
quality. The ensuing measurement error was determined
embryosisshowninblackanditsminimumandmaximuminthe10–90%EL
regionareshownasdashedlines(definingtheminimum(0)andmaximum(1) by simultaneously staining a single embryo with two Hb
gene expression levels g, respectively). (D) Intensity measured at position x/ antibodies raised in different animals and with two
L¼0.72 (vertical gray dotted line in C) as a function of dFC, each point differently colored secondary antibodies (see Figure 3B
representingadifferentembryo.The23pointsofthe10–20mmbatchareplotted
and C and Supplementary Figure 3). We find that the
inlightorange.Theblacklinerepresentsanearestneighboraveragingwitha
Gaussianfilter(s¼5mm).Insetshowsdetrendedlightorangedatapointswith combined variance s2gIS, induced by imaging and staining
weighted average subtracted, i.e., time-corrected. (E) Variance of Gt gene (primary and secondary) error, contributes 4–10% to the
expression levels sg2 computed for the same 23 embryos shown in panel C totalvariancesg2,dependingonthegeneconsidered.
before(lightorange)andafter(darkorange)timecorrection,respectively.Error
4. Theprofiles dependon the azimuthalembryoorientation
barsobtainedbybootstrapping;s2isthevarianceoftherawintensities(across
I j, which is hard to precisely control when mounting the
orangeprofilesinC).(F)Estimationofresidualvarianceinagedetermination
s (gray)duetomeasurementuncertaintys afterprofiletimecorrection samples.Asthissourceofundesiredvarianceturnsoutto
(ggraagey line); for comparison, in dark orangdeFC the variance s2 of the be one of the most important, we estimated it using two
g
time-correctednormalizedprofiles.Forasimilaranalysisoftheothergapgenes independent methods (see Figure 4 and Supplementary
seeSupplementaryFigure2.
Figure4).Withbothmethods,wefindthatouruncertainty
inestimatingembryoorientations2 rangesfrom2–13%of
inthreeopticalchannels,andweshowthatthiscontribu- thetotalvariances2,dependingongfthegeneconsidered.
g
tiondependsonthemeansignalandperturbsitbyB1% 5. As the absorption and emission spectra of the four
(seeSupplementaryFigure3). fluorophoresoverlap,thereispotentialcross-talkbetween
&2013EMBOandMacmillanPublishersLimited MolecularSystemsBiology2013 5
Dynamicsandreproducibilityingeneticnetworks
JODubuisetal
Midpslaangeittal x/L=0.2 ×1034 crfreoosmmulbteiinnmegbderryiromoroargisiienlngatragateinoldyngsset2gnaf,ienadigneegpdepenrtdeoercnmetsi,snneasotinosen2gIiSss.2glaWager,ghaeinlredthttahhnee
D 22.5° 3 y 13%ofsg2(seeFigure5C).
67.5° nsit Weconcludethatnaturalfluctuationsintheprofilesarethe
Coronal 2 nte largest contributor to the overall variance sg2 (B80%) that
plane I occursacrossembryos.Therefore,ourexperimentalmethodis
1
suitable not only to precisely calculate the average gap gene
V expressionpatterns,butalsothefluctuationsinthesepatterns
0 0.5 1
x/L and cross-correlations between them. In the remaining
sections, we will continue to work with the measured total
×103
4 10−1 variancesg2;thisisacautiouschoice,assubtractingmeasure-
ment error from raw data is only feasible if there are no
3 10−2 correlations among thevarious errorsources,which is often
ensity 2 σ2, gφ 10−3 utinmkencoowrrne.cTtihone(odneltyresnydstinemg)abtieccaeurrsoerwtheaktnwowe ttahkeeuonudterislytinhge
nt σ2g
I 10−4 model. Hence, given our upper bound on the measurement
1 error(B20%),weoverestimatetheactualbiologicalvariance
10−5 and therefore our measures of reproducibility are lower
0 45 90 0 0.5 1
boundsonwhatthesystemcanpotentiallyachieve.
φ (deg) x/L
Figure4 ContributionofazimuthalembryoorientationuncertaintytoGtgene
expressionprofilereproducibility.(A)Schematicrepresentationoftheabsolute
azimuthalangledistributionoftheembryosdependingontheirimagingplane. Dynamics of gap gene expression profiles
(B)Meanands.d.ofdorsaltime-correctedGtintensityprofilesofembryoswhose
imagingplaneisclosertothemidsagittalplane(darkorange,DVorientation, The results in the preceding three sections allow us to fully
23 samples, d ¼10–20mm) or closer to the coronal plane (light orange, reconstruct the dynamics of the four major gap gene
FC
LR orientation, 23 samples, dFC¼10–20mm). (C) Linear estimate of the expression profiles from fixed tissue: simultaneous labeling
DVdependenceofrawdorsalGtintensityatthefractionalELx/L¼0.2.The of all fourgenes in single embryospreservestemporalorder
systematicerrorinintensityowingtoembryoorientationuncertaintyofthedark
embryoscanbestagedwithatemporalprecisionof1–2min;
brownprofiless (showninblack)isestimatedbypropagatingtheuncertaintyon
I
theazimuthalangles (uniformdistributionf¼0–451),s¼s (cid:3)dI/dj,where andexperimentalerrorislowandcontrollable.Wemergedand
j I j
dI/df is the slope of the dashed line (see text). (D) Variance of Gt gene age-classifiedthedorsalintensityprofilesofHb,Kr,Gt,andKni
expressionprofilesduetoembryoorientationuncertainty(inblack),computedas simultaneously extracted from 80 embryos during n.c. 14.
sco2grfre¼ctsed2I=dðoIrmsaaxlp(cid:2)roIfimleinsÞi2s;sthootawlnvainriadnacrkeoorfagnegneefoerxpcoremspsiaornisporno,figlerasyolfinteheshtiomwes- Profileswererescaledsuchthattheirmaximumlevelofgene
anestimationofthevarianceinducedbytheembryoorientationuncertaintyby expression over the course of n.c. 14 is 1 foreach gap gene.
thealternativemethodofSupplementaryFigure4. Chronologically ordered 1min snapshots were generated by
time-averagingintensitiesateachpositionwitha3-min-wide
gaussiandistributiontoproduceamovieofthegapgenetime
neighboringopticalchannels.Thecorrespondingcontribu- dependenceduringtheentirecourseofn.c.14(Supplementary
tion to profile accuracy can be estimated by performing Video2).
independentcontrolexperimentsforwhichallsecondaries Foreachembryoandeachgene,wetrackedthepositionof
but the one whose channel is tested are present the peaks in gene expression as well as the position of the
inflection points (i.e., pattern boundaries) in the region
(see Figure 1D). Using finely tuned microscope settings
oftransitionbetweenhighandlowlevelsofgeneexpression.
(Figure 1A), our data show a cross-talk contribution of
Thelocationsofthesemarkersshiftduringn.c.14,asshownin
o1%ofthesignalineachopticalchannel.
Figure6A,somebyalmost10%EL;however,someboundaries
6. The focal plane in which each embryo is imaged is
donotchangeatall.Notethatgeneexpressionpatternstendto
manually chosen. Hence each independent focal plane
be more dynamic near the edges of the embryo, where the
choiceaffectsourexpressionprofileextraction.Toquantify
terminalgroupgenesareactive.Overall,ouranalysisofthese
thiseffect,weestimatedouruncertaintyinidentifyingthe
shiftsisingoodagreementwithpreviousreports(Jaegeretal,
midsagittalplaneofasingleembryo.Theresultingerroris
2004a,b;Kera¨nenetal,2006).
obtainedbycomputingthevariancesofprofileintensities
To understand how the average levels of gene expression
across 15 images taken at consecutive heights spaced
change with time, we follow the immunofluorescence inten-
by 0.5mm. We find that this source of error contributes
o1% of the total variance sg2, independent of the gene sviatyluoefotfhtehebosluonpdeaartytihneflseecptiooinntpsoaisntasfausncwtieolnlaosftehmebarbysooalugtee.
considered.
In Figure 6B and C, we analyzethe intensityof twoof these
Figure5Ashowsinblueourestimateofthesummedtotal points at x/LC58%, where the expression boundaries of Kr
variance s2 introduced by these sources of experimental andKniintersect.Wefindthattheintensitiesandtheslopesof
gerr
error.Foranyofthegapgenes,itrepresentsonaverageo20% the borders simultaneously reach their maximum around
ofthegeneexpressionvariances2measuredacrossembryos 42min after the onset of n.c. 14. Remarkably, this trend is
g
(Figure 5B). The major sources of experimental error stem conservedforthebordersofallothergapgenes(Figure6Dand
6 MolecularSystemsBiology2013 &2013EMBOandMacmillanPublishersLimited
Dynamicsandreproducibilityingeneticnetworks
JODubuisetal
Kni Kr Gt Hb
1
2gerr 1e−1
σ
2, g 1e−2
σ
2, 1e−3
g
1e−4
0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1
x/L x/L x/L x/L
0.2
σ2gerr 0.1
2, g
σ
0
0 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1
g g g g
0.006
13%
0.004 10% 10%
σ2gerr 0.002 7% 7% 4% 6%
6% 2% 5%
3% 2%
0
0 0.02 0.04 0 0.02 0.04 0 0.02 0.04 0 0.02 0.04
σ2 σ2 σ2 σ2
g g g g
Figure5 Summaryofsystematicerrorsofthegapgeneexpressionprofiles.(A)Squaredmeandorsalprofiles(lightgray)andcorrespondingtime-correctedvariances
(darkcolor)measuredacross23embryos(d ¼10–20mm)asafunctionoffractionalELx/L.Estimatedsummedtotalvariances2 frommajorsourcesofmeasured
systematicerrors(staining,imaging,orientatFioCn,andtime)areshowninblue.(B)S.d.ofgeneexpressionlevelsintime-correctedgenrrormalizedprofiles(color)ands.d.
owingtosystematicerror(blue)asafunctionofgeneexpressionlevelg(for100equallyspacedbinsalongtheAPaxis).(C)Foreachgapgene,weshowascatterplotof
thevariancesowingtothemajorsourcesofsystematicerrorversusthetotalvariancemeasuredacrossembryos:imagingandstaining(lightgray),age(darkgray),and
orientation(black).Foreachsourceofsystematicerror,datapointswerefittedwithastraightline;slopesrepresentestimatedaveragecontributionstotheoverall
variance.Forreference,dashedlinerepresentsthecases2¼s2 .
g gerr
E),exceptfortheintensityofthemainHbborder,whichpeaks divided in eight equally populated (N¼10) time bins T –T
1 8
at34min. whoseaverageagesrangefrom15to55minaftertheonsetof
Observation of these dynamic featuresof the network is a n.c. 14. The binning step is necessary to increase statistical
signatureforthewell-knownmutuallyrepressiveinteractions significance(i.e.,thes.e.onthevariances2isgivenbys2(cid:4)
pffiffiffiffiffiffiffiffiffi
between the gap genes (Hu¨lskamp et al, 1990; Kraut and 2=N for a sample size of N) in order to undoubtedly
Levine, 1991; Struhl et al, 1992; Kosman and Small, 1997; distinguish reproducibilities at the B1% EL level. Using the
Clyde et al, 2003). Although the coordination of the interac- distributionsofthepositionalmarkersdescribedinFigure6,
tions might be expected from the known network topology we define the marker reproducibility s as the s.d. across
x/L
(Jaeger et al, 2004a,b; Manu et al, 2009a,b; Papatsenko and embryosofthemarkers’fractionalpositionsx/L.InFigure7,
Levine, 2011), the precision of the observed synchronicity theses.d.’sareplottedasafunctionoftheirrespectivemean
suggeststhatsomeintrinsiccollectiveorganizationofthegap fractionalpositionfortimebinsT –T .
1 8
genenetworkisatplay(Lacallietal,1988;Edgaretal,1989; ForthetimeclassT (41–45min),wenoticethreeinteresting
6
Clyde et al, 2003; Manu et al, 2009a,b; Lander, 2011). In features. First, for all genes, s is independent of position,
x/L
particular, the peak in the slopes at the intersection of the which is onlyobserved in this particular timewindow if the
gene expression profiles of Kr and Kni at 42min might embryoshavebeencorrectlycategorizedbyageandorienta-
be a point where the network is optimized for certain tion (see Supplementary Figure 6A). In particular, the
characteristics, such as the accuracy with which it can constancy of s across the Hb/Kr, Kr/Kni, Kni/Gt, and
x/L
determinecellfates. Gt/Hbbordershintsatamutualregulationofthesegenes,as
hypothesizedpreviously(KrautandLevine,1991;Papatsenko
and Levine, 2011; Crombach et al, 2012), rather than a
Reproducibility of gap gene expression profiles unidirectional repression (Jaeger et al, 2004a,b), in which
Theultimategoaloftheseexpressionprofilequantificationsis casewewouldseeasmallervarianceintheexpressionprofile
toexaminethestatisticalpropertiesofthegapgenedynamics thatisregulatedthanintheexpressionprofilethatregulates.A
over the course of n.c. 14 and to assess how profile fullcharacterizationoftheunderlyingregulatorymechanisms
reproducibility evolves with time. To increase statistical (e.g., direction and strength) extracted from the profile
significance,embryosweresortedaccordingtotheirageand variabilitiesisbeyondthescopeofthecurrentwork,butwe
&2013EMBOandMacmillanPublishersLimited MolecularSystemsBiology2013 7
Dynamicsandreproducibilityingeneticnetworks
JODubuisetal
60 closest neighbors. Although this might not be enough
todistinguishthemselvesunequivocallyfromtheirneighbors,
50 itsuggeststhatthelevelofreproducibilitynecessarytoform
the cephalic furrow at the time of gastrulation (B1% EL) is
n) 40 alreadyachievedearlierduringn.c.14inseveralregionsofthe
mi embryo.
me ( 30 Thethirdfeatureconcernshowthemarkers’reproducibility
Ti changesoverthecourseofn.c.14.Foreachtimewindow,we
averaged the s across all markers and mapped the result
20 x/L
osx/L4 as a function of time, shown in Figure 8. The
reproducibility of the gap genes increases during the first
10
0 0.2 0.4 0.6 0.8 1 35min, is maximal at 42min, and finally decreases until
x/L gastrulation. The dynamics of gap gene reproducibility are
remarkably correlated with the overall gap gene dynamics
0.6
(Figure6),givingusahintofafunctionalsignificanceforthe
15
collectiveculminationofthenetworkdynamics.Inparticular,
0.4 x this synchronous increase in reproducibility from one inter-
max /Ima10 nucleardistancetohalfaninternucleardistancecouldbethe
/I pe resultofspecificregulatoryinteractionsamongthezygoticgap
I 0.2 Slo 5 genes,aspreviouslysuggested(Lacallietal,1988;Edgaretal,
1989; Manu et al, 2009a,b; Gursky et al, 2011). Thus, these
0 0 dynamicscanbeseenasthedrivingelementinarelayprocess
wherethegapgenenetworkobtainsacertainreproducibility
0.6
15 fromtheBcdinputofoneinternucleardistance(Gregoretal,
2007a),andsubsequentlypassesatwofoldhigherreproduci-
x 0.4 max10 bilityontothepair-rulegenestowardtheendofn.c.14.
ma /I Canweunderstandfromourdatahowthisobservedrisein
I/I 0.2 Slope 5 raerpbritordauriclyibcihliotyseinsmaachrkieevrsedat?aTsomoalvlesrectoomfpeotshiteionlims,iwtaetidoenfinoef
a local quantity that can be computed at any position, the
0 0 positional error s^ resulting from the simultaneous position
10 20 30 40 50 60 10 20 30 40 50 60 x
decoding of all four gap genes (Supplementary Figure 7).
Time (min) Time (min)
InFigure7,wecomputeitstemporalprogressionduringn.c.
Figure 6 Dynamics of the main boundaries of the gap gene expression 14.Thisquantityrequirescalculationofthecovariancematrix
profiles.(A)Positionsofanterior(b)andposterior(c)boundaries(inflection
of the four gap gene profiles, for which the simultaneous
points) of the gap gene expression profiles for Kni (green), Kr (yellow),
Gt(orange),andHb(red)asafunctionoftime.Asaguide-to-the-eye,thepeaks stainingofallfourgapgenesisessential.Atearlytimes(T1),
ofthemajorstripesareplottedindashedlinesandtheinterstripelocalminimum the positional error is already less than one internuclear
of Gt is plotted in short-dashed line. (B) Developmental progression of the distanceintheB40–80%ELregion,suggestingthattranscrip-
intensity at the posterior Kr boundary (yellow) and the anterior Kni boundary
tional inputs and gap gene interactions before n.c. 14 have
(green).Foreachembryoandeachgene,intensityattheinflectionpointisplotted
alreadygeneratedreproducibleprofiles.Progressingintimeto
asafunctionofembryoageinn.c.14(dimdots).Darkercirclesrepresentthe
averages and s.d.’s of the intensities of these data points over eight equally whensecondarystripesemergefromtheinteractionsbetween
populatedtimebins(10embryosperbin).DatahavebeennormalizedbyI , Gt and Hb and between Gt and Kr (T ), the positional error
max 4
themaximumintensityreachedoverallembryos,positions,andbinsduringn.c. reducesfurthertolessthanoneinternucleardistancealsoin
14. (C) Developmental progression of the absolute value of the slope at the
the 10–40% EL and 80–90% EL regions. The subsequent
crossingoftheKr(yellow)andKni(green)boundaries,asinB.(D)Summaryof
the time dependences of the intensities at the anterior (solid) and posterior collectivedynamicsofthegapgenenetworkleadtoaneven
(dashed)boundaries(inflectionpoints)forallgapgenes(greenandyellowlines largerreductionofpositionalerror,whicheventuallyreachesa
correspondtothedarkcirclesinB;forallstripesanteriorandposteriorintensities minimumofhalfaninternucleardistanceintheentire10–90%
arenearlyidenticalandthusoverlap).(E)Summaryofthetimedependencesof EL region around 41–45min (T ). Reproducibility eventually
theslopesattheanterior(plain)andposterior(dashed)boundaryofallgapgene 6
deteriorates during the last 10min of n.c. 14, just before
borders(greenandyellowlinescorrespondtodarkcirclesinC).
gastrulationoccurs(T –T ).
7 8
Therefore, as for the reproducibility of the individual
markersabove,alsoin thecaseof simultaneousdecodingof
believe that rigorous experimental quantification is a neces- the four gap genes, we find that the precision achieved in
saryfirststepinthisdirection. position inference in the 40–45-min time window is half a
Second,thevalueofs isonaverageapproximatelyhalf nucleardistancealongtheentireAPaxis.Hence,ratherthan
x/L
theinternucleardistanceinn.c.14(i.e.,4mmor0.85%EL,see favoring a particular row of cells, the gap genes potentially
Supplementary Figure 6B). Hence, at this level of reproduci- providethesamepositionalerrortoallthecellsalongtheAP
bility,by15minbeforegastrulation,nucleilocatedonthegap axis15minbeforegastrulation.Thisremarkableconstancyof
gene boundaries have already access to a measure of their bothprofilereproducibilityanddecodingprecisionatthetime
positionwithan errorsmaller than halfthe distanceto their of simultaneous peak gap gene expression suggests that the
8 MolecularSystemsBiology2013 &2013EMBOandMacmillanPublishersLimited
Dynamicsandreproducibilityingeneticnetworks
JODubuisetal
0.03 T1 T5 G0
σ^x 0.02
, L g
σx/ 0.01
0 0
0.03 T2 T6 G0
σ^x 0.02
σ, x/L 0.01 g
0 0
0.03 T3 T7 G0
σ^x
, L 0.02
σx/ g
0.01
0 0
0.03 T4 T8 G0
σ^x 0.02
σ, x/L g
0.01
0 0
x/L x/L
Figure7 Developmentalprogressionofgapgeneexpressionprofilereproducibility.Positiondependenceofthereproducibilityofthemarkers,computedasthes.d.of
theirpositionsacrossembryoss foreighttimewindowscovering90%ofn.c.14(T ¼10–25min,T ¼26–29min,T ¼30–33min,T ¼34–36min,T ¼37–40min,
x/L 1 2 3 4 5
T6¼41–45min,T7¼46–50min,andT8¼51–55min)areshownasbluecircles.Thepositionalerrors^xobtainedbysimultaneouslydecodingallfourgapgenes(four-
dimensionalextensionofSupplementaryFigure7)isshowninblackfor100APpositions.Forreference,themeangapgeneprofilesareshowninthebackground,color
codedasabove.ProfileshavebeenscaledsuchthatthemaximumlevelofgeneexpressionoftheirmeanovertheeighttimewindowsisG.Theinternucleardistance
0
andhalf-internucleardistancesareshownasdottedanddashedlines,respectively.
cells’ positional identities emerge collectively from the covariancematrixacrossallfourgapgenesatanypositionin
network(Manuetal,2009a,b;Jaeger,2011;Lander,2011). the embryo. These results make our experimental method
suitable to study the limits of a nucleus’ ability to read out
transcriptionfactorconcentrations(Tkaciketal,2008,2009),
and it enables us to measure the precision with which
Discussion
individual nuclei can infer their position based on the
Ourresultsshowthatwhenhandledproperly,immunofluor- simultaneous measurement of multiple input transcription
escent techniques are suitable for making gene expression factorconcentrations(Dubuisetal,2011;Dubuis,2012).
measurements with high accuracy and precision. Under These analyses of the gap gene dynamics and of the
conditionsthatcarefullycontrolsourcesofexperimentalerror, temporal evolution of the profile variability during n.c.
itispossibletosimultaneously measuretheexpressionlevel 14suggestthatthesystemusesa‘relay-type’strategytorefine
dynamics of up to four genes and quantify the variances the knowledge that nuclei have about their position from
and covariances of these genes at an unprecedented level of fertilizationtogastrulation:reproducibilityinherentintheBcd
precision.Wehaveillustratedthisbydocumenting,forthefirst gradientistransferredtothegapgenesearlyinn.c.14,reduced
time,thesimultaneousexpressiondynamicsofthefourmajor twofold within the gap gene network, and subsequently
gap genes Hb, Kr, Gt, and Kni during n.c. 14 with minute relayedtothepair-rulegeneslaterinn.c.14.AttheBcdlevel,
precision, and by quantifying the origin of the positional thephysicalmechanismsthatestablishthematernalgradient
accuracyinthesehighlyreproducibleprofiles. already allow nuclei to achieve position decoding up to one
A methodical analysis of the different sources of experi- internucleardistance.Thisreproducibilityincreasesfurtherto
mentalerrorshowsthat20%ofthetotalvariabilityofourgene ahalf-internucleardistanceatthepeakofgapgeneexpression,
expression profiles is due to measurement errors that are 15minbeforegastrulation.
inherent to our protocols. This leaves 80% of the observed Explicitregulatorymechanisms,bywhichreproducibilityof
embryo-to-embryo variability as potentially biologically gapgeneexpressioncouldbeincreasedovertime,havebeen
meaningfulfluctuations.Moreover,thefactthatthefourgap proposed(Lacallietal,1988;Manuetal,2009a,b;Gurskyetal,
genes are simultaneously stained allows us to calculate the 2011)andcannowbesubjectedtoaquantitativetestusingour
&2013EMBOandMacmillanPublishersLimited MolecularSystemsBiology2013 9
Dynamicsandreproducibilityingeneticnetworks
JODubuisetal
of several morphogens in living embryos. Such methods,
whichrelyon liveimagingof embryosexpressingmolecular
fusionsoffluorescentproteins,areknowntobeperturbedby
0.02
photobleaching and the folding and maturation times of the
fluorescent proteins (Tsien, 1998; Ulbrich and Isacoff,
2007; Drocco et al, 2011; Little et al, 2011; Ludwig et al,
2011). Therefore, the method presented here will serve as a
L benchmark to assess the validity of those future versions of
x/
σ transgenicfliesexpressingfluorescentproteins.Italsoserves
0.01
as a methodological framework for analyzing the various
sources of experimental error induced by these live imaging
methods.
The approach put forward here relies on an in-depth
understandingofthedifferentsourcesthatcontributetoerror
0 inexperimentalmeasurements.Assuch,itshouldbeapplic-
15 25 35 45 55 abletothequantitativeanalysisofanysmallgeneregulatory
Time (min) network. Knowing the magnitude of the contribution
Figure 8 Temporal evolution of gap gene expression profile reproducibility. of various sources of experimental error to the observed
Timedependencesoftheaverage reproducibilityosx/L4ofthemarkersin variability in gene expression facilitates the detection of the
Figure7(80dorsalprofilesweresortedaccordingtoageandthendividedinto originsofthesesystematicerrorsandultimatelytostrategies
eightbinsof10profiles).Foreachtimebin,theaverageands.d.acrosstheblue
thatleadtotheirreduction.Suchanapproachprovidestighter
markersisshownasafunctionoftime.Thetimedependenceofthepositional
error s^ is shown as a black line. For comparison, the maximum positional bounds on the measured mean expression levels and
x
reproducibilityofBcdprofiles15mininton.c.14(averagebetween10–60%EL) is essential when using variances and cross-correlations
(Gregoretal,2007a)isshownwithavioletsquare,andtheaveragepositional forfurtheranalysis.
reproducibilityofthepair-rulegenesrnt,eve,andprd45mininton.c.14isshown
withamagentasquare(Dubuisetal,2011;Dubuis,2012).Forreference,the
internucleardistanceandthehalf-internucleardistanceareshownindottedand Materials and methods
dashedlines,respectively.
Antibody preparation
new set of data. Already at the level of Bcd, it has been
suggestedthatspatialaveragingamongneighboringnucleiis To allowsimultaneous imaging of proteins encoded byall four gap
genes,wegeneratedpolyclonalantibodiesinmice,rats,andguinea
necessary to achieve the observed precision (Gregor et al,
pigs to His–Trx-tagged full-length Hb, Kni, and Gt fusion proteins
2007a; Erdmann et al, 2009). Similarly, a combination (Kosmanetal,1998).ToimageKrprotein,weuseaRabbitanti-Kr
oftemporalandspatialaveragingmightbeatplayinachieving antibodygeneratedbyChrisRushlow.
the further increase in reproducibility by the gap gene
network. However, such averaging mechanisms have a
blurring effect on sharp gap boundaries, and it will be Antibody staining and confocal microscopy
interesting both theoretically and experimentally to under- Allembryoswerecollectedat251Canddechorionatedin100%bleach
standwhetherabalancecanbefound. for 2min, heat fixed in a saline solution (NaCl,Triton X-100), and
Overall, our approach of setting strict bounds on the vortexedinavialcontaining5mlofheptaneand5mlofmethanolfor
1mintoremovethevitellinemembrane.Theywerethenrinsedand
interpretabilityof gene expressionprofilevariabilitiesallows
stored in methanol at (cid:2)201C. Embryos were then labeled with
ustoquantitativelyrestrictthepossibleeffectofthenetwork fluorescent probes. We used rat anti-Kni, guinea pig anti-Gt, rabbit
ontheultimateprecisionoftheexpressionpatterns.Alreadyat anti-Kr,andmouseanti-Hb.Secondaryantibodieswere,respectively,
theearlieststages,beforethenetworkisevenfullyactivated, conjugated with Alexa-488 (rat), Alexa-568 (rabbit), Alexa-594
(guineapig),andAlexa-647(mouse)fromInvitrogen,GrandIsland,
profilesoftheBcdgradientarereproducibletoanextentthat
NY. To prevent cross-binding between the rat and mouse primary
enablesidentificationofneighboringnucleiwithanerrorbar
antibodies, we first incubated the embryos in guinea pig, rat, and
thatissmallerthananinternuclearspacing.Thesubsequent rabbit primaries, followed by their respective secondaries; subse-
twofoldreductionoftheerrorbarsatthelevelofthegapgenes quentlywereblockedtheembryosinblockingbuffer,afterwhichwe
(presumably through the collective effect of the network) appliedthemouseprimaryandsecondaryantibodies.Embryoswere
mounted in Aqua-Poly/Mount (Polysciences Inc., Warringyon, PA).
ensuresthaterrorbarsfromadjacentnucleinolongeroverlap,
Samples were imaged on a Leica SP5 laser-scanning confocal
decreasing the probability of mis-identification to less than microscopeandimageanalysisroutineswereimplementedinMatlab
B16% overlap in the tails of the distribution. It is unclear, software(MathWorks,Natick,MA).ImagesweretakenwithaLeica
however,atwhichlevelofprecisionnuclearfatespecification (cid:4)20HCPLAPONA0.7oilimmersionobjective,andwithsequential
takes place. Is one s.d. enough? Will B16% still matter? excitationwavelengthsof488,546,594,and633nm.Thebandwidth
ofthedetectionfiltersweresetupasshowninFigure1Atominimize
New types of experiments that can directly monitor fate
fluorophore cross-talk while still allowing good detection in each
specificationareneededinordertotellthedifference. optical channel. For each embryo, three high-resolution images
The cartoon-like reconstruction of the gap gene dynamics (1024(cid:4)1024 pixels, with 12 bits, and at 100Hz) were taken along
should stimulate the development of more straightforward theanterior–posterioraxis(focusedatthemidsagittalplane)at (cid:4)1.7
magnifiedzoomandaveragedtogether.Withthesesettings,thelinear
experimental methods to quantify the time evolution of
pixel dimension corresponds to 0.44±0.01mm. All embryos were
morphogen expression levels.In particular, a majoradvance prepared,andimagesweretaken,underthesameconditions:(i)all
would be to simultaneously record the concentration embryos were heat fixed together, (ii) embryos were stained and
10 MolecularSystemsBiology2013 &2013EMBOandMacmillanPublishersLimited