Noise and crosstalk in two quorum-sensing inputs of Vibrio fischeri

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Title:
Noise and crosstalk in two quorum-sensing inputs of Vibrio fischeri
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BMC Systems Biology
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Pérez, Pablo D.
Weiss, Joel T.
Hagen, Stephen J.
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Background: One of the puzzles in bacterial quorum sensing is understanding how an organism integrates the information gained from multiple input signals. The marine bacterium Vibrio fischeri regulates its bioluminescence through a quorum sensing mechanism that receives input from three pheromone signals, including two acyl homoserine lactone (HSL) signals. While the role of the 3 oxo-C6 homoserine lactone (3OC6HSL) signal in activating the lux genes has been extensively studied and modeled, the role of the C8 homoserine lactone (C8HSL) is less obvious, as it can either activate luminescence or block its activation. It remains unclear how crosstalk between C8HSL and 3OC6HSL affects the information that the bacterium obtains through quorum sensing. Results: We have used microfluidic methods to measure the response of individual V.fischeri cells to combinations of C8HSL and 3OC6HSL. By measuring the fluorescence of individual V.fischeri cells containing a chromosomal gfpreporter for the lux genes, we study how combinations of exogenous HSLs affect both the population average and the cell-to-cell variability of lux activation levels. At the level of a population average, the crosstalk between the C8HSL and 3OC6HSL inputs is well-described by a competitive inhibition model. At the level of individual cells, the heterogeneity in the lux response depends only on the average degree of activation, so that the noise in the output is not reduced by the presence of the second HSL signal. Overall we find that the mutual information between the signal inputs and the lux output is less than one bit. A nonlinear correlation between fluorescence and bioluminescence outputs from lux leads to different noise properties for these reporters. Conclusions: The lux genes in V.fischeri do not appear to distinguish between the two HSL inputs, and even with two signal inputs the regulation of lux is extremely noisy. Hence the role of crosstalk from the C8HSL input may not be to improve sensing precision, but rather to suppress the sensitivity of the switch for as long as possible during colony growth.
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BMC Systems Biology 2011 5:153

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RESEARCHARTICLE OpenAccessNoiseandcrosstalkintwoquorum-sensing inputsof VibriofischeriPabloDPrez,JoelTWeissandStephenJHagen*AbstractBackground: Oneofthepuzzlesinbacterialquorumsensingisunderstandinghowanorganismintegratesthe informationgainedfrommultipleinputsignals.Themarinebacterium Vibriofischeri regulatesitsbioluminescence throughaquorumsensingmechanismthatreceivesinputfromthreepheromonesignals,includingtwoacyl homoserinelactone(HSL)signals.Whiletheroleofthe3-oxo-C6homoserinelactone(3OC6HSL)signalin activatingthe lux geneshasbeenextensivelystudiedandmodeled,theroleoftheC8homoserinelactone(C8HSL) islessobvious,asitcaneitheractivateluminescenceorblockitsactivation.Itremainsunclearhowcrosstalk betweenC8HSLand3OC6HSLaffectstheinformationthatthebacteriumobtainsthroughquorumsensing. Results: Wehaveusedmicrofluidicmethodstomeasuretheresponseofindividual V.fischeri cellstocombinations ofC8HSLand3OC6HSL.Bymeasuringthefluorescenceofindividual V.fischeri cellscontainingachromosomal gfp reporterforthe lux genes,westudyhowcombinationsofexogenousHSLsaffectboththepopulationaverageand thecell-to-cellvariabilityof lux activationlevels.Atthelevelofapopulationaverage,thecrosstalkbetweenthe C8HSLand3OC6HSLinputsiswell-describedbyacompetitiveinhibitionmodel.Atthelevelofindividualcells,the heterogeneityinthe lux responsedependsonlyontheaveragedegreeofactivation,sothatthenoiseinthe outputisnotreducedbythepresenceofthesecondHSLsignal.Overallwefindthatthemutualinformation betweenthesignalinputsandthe lux outputislessthanonebit.Anonlinearcorrelationbetweenfluorescence andbioluminescenceoutputsfrom lux leadstodifferentnoisepropertiesforthesereporters. Conclusions: The lux genesin V.fischeri donotappeartodistinguishbetweenthetwoHSLinputs,andevenwith twosignalinputstheregulationof lux isextremelynoisy.HencetheroleofcrosstalkfromtheC8HSLinputmay notbetoimprovesensingprecision,butrathertosuppressthesensitivityoftheswitchforaslongaspossible duringcolonygrowth.BackgroundQuorumsensingisamechanismofbacterialgeneregulationthatisbasedonthereleaseanddetectionofdiffusiblechemicalsignals.Itis classicallydescribedasa population-sensingscheme:thebacteriareleaseapheromone(autoinducer)intotheirenvironment,andthe accumulationofthisautoinducerisanindicatorofa highpopulationdensity,triggeringchangesinphenotype.Howeverithasbecomeincreasinglyapparentthat bacterialquorumsensing(QS)behaviorsareoftenmore complexthansimplepopulation-counting[1-4].Many QSregulatorynetworksempl oymultiplereceptorsthat receivesignalsfromdifferentautoinducers,forming interactingdetectorsthatmayactsequentiallyorin paralleltoregulatedownstreamgenes.Thedesignprinciplesofthesemulti-inputsystemsremainmysterious: OneoftheinterestingpuzzlesinthestudyofQSisto understandwhatbenefitorinformationanorganism cangainfromcombiningmultipleautoinducerinputs, andhowinformationfromdifferentinputsisprocessed togenerateausefuloutput[5,6]. Hereweinvestigatethisquestionfortwoautoinducer inputsin Vibriofischeri ,a g -proteobacteriumthatuses QStoregulatebioluminescenceaswellasotherbehaviorsthatareimportanttocolonizationofitssymbiotic hostanimal.Thesetwoautoinducersexhibitacompetitiveorantagonisticinteractioninregulatingthe lux operonthatcontrolsbioluminescence.Weusemicrofluidicandsingle-cellmethodstoobservehowcombinationsofthetwoautoinducersignalsaffectthebulkor *Correspondence:sjhagen@ufl.edu DepartmentofPhysics,UniversityofFlorida,GainesvilleFL32611-8440,USAPrez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 2011Prezetal;licenseeBioMedCentralLtd.ThisisanOpenAccessarticledistributedunderthetermsoftheCreativeCommons AttributionLicense(http://creativecommons.org/licenses/by/2.0),whichpermitsunrestricteduse,distribution,andreproductionin anymedium,providedtheoriginalworkisproperlycited.

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averageoutputoftheQSnetwork,aswellasthecell-tocellvariabilityintheactivationof lux .Weaskwhether differentcombinationsofsignalinputsthatproducethe sameaverageresponseacrossapopulationalsoproduce thesameresponsefromindividual V.fischeri ,andthereforewhetherthe lux systemgainsadditionalinformation fromthepresenceofanadditionalsignal. Bioluminescencein Vibriofischeri isgeneratedbythe lux operon luxICDABEG ,whichencodesthebacterial luciferaseaswellasenzymesforproductionoftheluciferasesubstrate[7].ItisregulatedbythreeQSchannels [8](Figure1).MostwellknownistheLuxI/Rmechanism.LuxIisthesynthaseoftheautoinducer N -3-oxohexanoylLhomoserinelacton e(3OC6HSL),which interactswithitscognatereceptorLuxRtoformatranscriptionalactivatorforthe lux operon.Threshholdconcentrations(nM)of3OC6HSLinduce V.fischeri bioluminescence. ThesecondQSsystemin V.fischeri istheAinS/Rsystem(Figure1).ItusesthesynthaseAinStoproducethe signal N -octanoylL -homoserinelactone(C8HSL). C8HSLinteractswithitscognatereceptorkinaseAinR toinitiateaphosphorelays ignalingcascade(involving LuxU,LuxO,andasmallRNA)thatinterruptsnegative regulationofLitR,anactivatorofLuxR.Inadditionto regulatingluminescenceviaLuxR,AinS/Ralsoregulates anumberofotherbehaviors,suchasmotilityandacetateutilization[9],thatareimportanttosuccessfulcolonizationofthesymbiotichost[10,11]. ThethirdQSsystemin V.fischeri differsfromthefirst andsecondbecauseitdoesnotemployanacylhomoserinelactone(HSL)autoinducer.Insteadtheautoinducerisafuranosylboratediester(AI2)thatissynthesized byLuxSanddetectedbyLuxPandLuQ.Thesignal feedsintothesamephosphorelaychannelthatdetects theC8HSLautoinduceroftheAinS/Rsystem.AI2influencesluminescence(andpresumablyalsonoiseinluminescence)viaitsdownstreameffectonLuxRexpression. HowevertheAI2inputmakesarelativelysmallcontributiontoluminescenceregulationandcolonization[12], especiallyincomparisontotheHSLautoinducers C8HSLand3OC6HSL.Mutantsdeficientinproduction AinS LuxS C8 HSL AI-2 LuxI LuxR qrr1 (sRNA) AinR LuxP LuxR luxICDABEG litR LitR luxR 54 LuxO Hfq LuxOP 3OC6 HSL IM LuxQ LuxU OM K2 K1 luxICDABEG luxR LuxR LuxR LuxR 3OC6 HSL C8 HSL AB Figure1 SchematicofQSregulationof V.fischeri bioluminescenceandcompetitivemodel .( A )QSregulationofbioluminescencein V. fischeri usesthreeautoinducerchannels[8].Theautoinducer3OC6HSLissynthesizedbyLuxIandbindstoLuxRtoformatranscriptional activatorforthebioluminescencegenes luxCDABEG .Twomoreautoinducers(C8HSLandAI2)drivethephosphorelaythatregulatesproduction ofLuxRaswellasothercolonizationbehaviors.( B )Asimplifiedmodelconsidersonlycompetitiveinteractionbetween3OC6HSLandC8HSL,as proposedbyKuo etal.[13]andLupp etal.[11].ThereceptorLuxRbindstheautoinducersC8HSLand3OC6HSLtoformmultimericcomplexes (ofdegree m and n respectively)whichactivate lux transcription.Inourfitweomit lux activationbytheC8HSLcomplexofLuxR. Prez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page2of14

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oftheHSLautoinducersproduceonlyverylow,basal luminescenceifany[13,14].Therefore,althoughAI2 maybeimportantininterspeciescommunication[2],we havenotincludeditinthisstudy. Interestingly,thesecondautoinducer,C8HSL,also actsonluminescencethroughanadditionalroute, whereitbypassesthephosphorelayandinteracts directlywithLuxRtoactivate lux expression(Figure1). Therefore,whileQScontrolof V.fischeri luminescence primarilyoccursthroughtheC8HSLand3OC6HSL autoinducers,theeffectofthetwoHSLsisnotsimply additive.ThetworoutesofC8HSLactionleadtoa complexcrosstalkbetweentheAinS/RandLuxI/Rsystems.Generally,ina V.fischeri culturelacking 3OC6HSL,theadditionofC8HSLinducesbioluminescence.Bycontrast,inthepresenceof3OC6HSL,the additionofC8HSLsuppressesbioluminescence.FurthermoreC8HSLappearstoinfluenceluminescencelargely throughdirectinteractionwiththe lux operon,rather thanthroughthephosphorelaychannel[13,15].These findingssuggestedacompetitiveinhibitionmodel [11,13]inwhichC8HSLmodulatesthebioluminescence bycompetingforthe3OC6HSLreceptorLuxR(Figure 1):bothC8HSLand3OC6HSLarecapableofbinding tothereceptorLuxRandactivatingtranscriptionofthe lux genes[16],buttheC8HSL-LuxRcomplexisaless effectiveactivatorthanthe3OC6HSL-LuxRcomplex. ThesensitivityofLuxR(asanactivatorofthe lux genes)toC8HSL vs .3OC6HSLisreadilytunable throughsingle-residuemutations[17],indicatingthat crosstalkcouldbeminimizedifitimpairedoptimalregulationofbioluminescence.Infact,interactionbetween AinS/RandLuxI/Rnotonlyexistsbutisstrain-dependent,astheluminescenceof V.fischeri mutantslacking theC8HSLsynthase( ainS mutants)behavesdifferently forstrainsderivedfromdifferentsymbiotichostanimals. Whilethe ainS mutationsuppressedtheluminescence ofastrainextractedfromthesquidhost Euprymnascolopes [11],the ainS mutationacceleratedtheinduction ofluminescenceinastraingatheredfromthefishhost Monocentrisjaponicus [13].Furthermore,genomicanalysisof V.fischeri strainsderivedfromsquid versus fish hostsshowedthatwhilemostgenesarehighlyconserved,luminescenceactivationandtheregulatorytargetsoftheLuxI/LuxRsystemexhibitsignificant divergencebetweenstrains[18,19]. ThestrengthofthecrosstalkbetweenC8HSLand 3OC6HSL,andthetuningofthisinteractioninstrains thatoccupydifferentsymbioticenvironments,suggests thatitisnotincidentalbutratherthatitprovidesan adaptivebenefit.Weshouldaskhowasystemoftwo HSLs,workinginoppositiontoeachother,improves theregulationofbiolumi nescence.Forexample,Kuo et al.notedthatsynthesisofC8HSLwilldelaythe inductionofluminescenceearlyingrowth,conserving theenergyresourcesoftheorganism[13].Luppand Ruby[10],notingthatC8HSLregulatescolonization factorsinadditiontoluminescence,suggestedthat AinS/RandLuxI/Ractsequentiallysothatthemaximuminductionofluminescenceoccursafterhostcolonizationisinitiated.Itisstillpuzzlinghoweverthat AinS/RshouldexhibitsuchstrongcrosstalkwithLuxI/R inregulatingbioluminescence,sincethesameaverage delayinluminescencecouldpresumablybeachieved throughahigheractivationthresholdfor3OC6HSL. Herewehaveinvestigatedhowcombinationsof C8HSLand3OC6HSLsignalsaffecttheresponseofthe lux operonattheindividualcelllevel.Ourrecentstudy ofthebioluminescentemissionfromindividual V. fischeri foundthattheresponseofindividualcellsto definedconcentrationsofexogenous3OC6HSL(alone) wasextremelyheterogeneousintheoverallmagnitude ofluminescentemissionandinthetimescalefor responsetotheHSLsignal[20].AlthoughtheLuxI/R systemexertsgoodcontroloftheaveragebioluminescenceofa V.fischeri population,itprovidesonlyweak controlofindividualcellbehavior.Thereforeweask whetherthepresenceoftwosignals,C8HSLand 3OC6HSL,providesanadditionaldimensionofcontrol attheindividualcelllevel, i.e .whethercombinationsof HSLselicitalessnoisyan dmorepreciseresponsein individualcellsandthereforewhetherthesecondHSL signalimprovesthesensingprecisionoftheQSsystem. Althoughwemeasuredindividualcellbioluminescence directlyinourpreviousstudy,hereweuseafluorescent reportingstrain(JB10)of V.fischeri ,containingachromosomal gfp reporterof lux operonactivation.Wefirst showthattheactivationofJB10 GFP fluorescencein thepresenceofC8HSLan d3OC6HSLisdescribed quantitativelybythecompe titiveinhibitionmodelof Figure1.Theempiricalparametersfromthemodel definetheaverageresponseandprovidethebasisfor microfluidicsinglecellstudies,inwhichweapplycombinationsofC8HSLand3OC6HSLautoinducersand measurethecell-to-cellvariationinthe lux response. Fro mtheobserveddistributionswecandetermine whethercombinationsofHSLinputsimprovetheprecisionofindividualcellresponse.Combiningthesingle cellobservationswiththeparametrizedmodelwecan alsoestimatethethroughputofinformationfromthe HSLsignalinputstotheoverall lux output.ResultsModelingtheluxresponseHereourgoalistoconstructamathematicalrepresentationoftheinteractionbetweenHSLsignalsbyfitting bulk(well-plate)datatothecompetitive-bindingmodel showninFigure1(see Methods ).TheHSL-inducedPrez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page3of14

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bioluminescenceof V.fischeri strainJB10observedinthe well-plateassayisverysimilartothatobservedinwild typestrains[11,13,15]:C8HSLweaklyactivatesthebioluminescenceintheabsenceof3OC6HSL,whileit repressesbioluminescenceinthepresenceof3OC6HSL. 3OC6HSLconsistentlyactivatesbioluminescence.Figure 2showstheGFPfluorescenceofJB10asafunctionof HSLinputs.Sincethe gfp reporterisinsertedintothe lux operonofJB10,weexpecttheGFPfluorescenceto correlateclosely withbioluminescen ceoverthefull rangeofC8HSLand3OC6HSLinputs.Inprinciplewe thenhavethechoiceoffittingthemodeltoeitherthe luminescence L orthefluorescence F ,asfluorescence andluminescencereportersarebothregardedasreliable measuresofgeneexpression[21].HoweverFigure3 showsthatthecorrelationbetweenthefluorescenceand luminescenceofJB10isstrongbutitisnotlinear:at t = 10hrs,whenthebioluminescenceresponsespansa dynamicrangeof~3-4decades,thefluorescencespans only~20-fold.Infact,theempiricalrelationship betweenfluorescence F ([3OC6HSL],[C8HSL])and luminescence L ([3OC6HSL],[C8HSL])isnearertoa powerlaw L1/2 ( F F0 ) (1) Here a isaproportionalityconstantand F0describesabaselinefluores cencethatispresenteven atthelowestactivationlevelswheretheluminescence isundetectable(L 0).Asthebaseline F0growswith thepopulationdensity(F igure3)weinterpretitas eitherabaselineexpressionof lux -occurringindependentofHSLactivation[14]-orautofluorescence ofthecells. ThepowerlawinEqn.(1)suggeststhattheluminescenceintensityisaffectedbytheassociationequilibrium ofLuxAandLuxB,whichformthebacterialluciferaseheterodimer[7]:Inasimpledimerassociationmodel,the concentrationofenzymaticallyactiveluciferase( L ) shouldscaleastheproductoftheLuxAandLuxBconcentrations.Wealsoexpectthat luxA luxB ,and gfp shouldall beexpressedatsimilarlevelsastheyareallunderthecontrolofthesamepromoter.Therefore L shouldcorrelate withthesquareoftheGFPconcentration( F-F0),leading toEqn.(1).Fromthisperspectivefluorescence F (relative toitsbackground F0)ispreferableto L asareporterof lux activationandshouldgiveabetterfittoaphysicalmodel. Thereforewebasedouranalysisonthefluorescence F data.Howeverthemodelalsofits L1/2withvirtuallythe sameparametersasitfits F (Table1). FittingthecompetitiveinhibitionmodeltoGFP fluorescencedataatarangeofopticaldensitiesearly ingrowth(OD=0.05-0.15cm-1)givesaverysatisfactoryfitwithminimalspreadintheparametervalues (Figure2andTable1).Averagingthefitparameters obtainedfor F dataovertheODrangeproducesthe surface F ([3OC6HSL],[C8HSL])showninFigure2. Usingthismodelsurfacewecanpredictthe(average) lux responseunderanyHSLconditionandidentify HSLcombinationsofinterestforsingle-cellstudies. B C A D Figure2 Dataandfitfor lux activationofJB10strainbytwo autoinducers .Thefigureshowsthepopulation-average(bulk measurement)responseofcombinationsofexogenousC8HSLand 3OC6HSLautoinducers,asmeasuredbyGFPfluorescenceofstrain JB10.( A )DataatOD=0.15cm-1,( B )fittocompetitiveinhibition model,( C )residualfromfit,and( D )Dataandfitsectionedat constant[3OC6HSL]. Prez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page4of14

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MicrofluidicstudiesofindividualcellsByloading V.fischeri cellsintoathree-channelmicrofluidicdevice(Figure4)onafluorescencemicroscope wecanobservesimultaneouslythreegroupsofcellssubjecttodifferentcombinationsofHSLinputsandcharacterizetheheterogeneityoftheirGFPresponse.The contourmapofFigure4showstheHSLcombinations usedinfoursuchexperiments.Twoexperiments exploretheheterogeneityalongcontoursofnear-constant lux activationwhiletwoexperimentsusesignal combinationsthatcrosscontourlines. Experiment#1appliedthreedifferentC8HSLconcentrations-alongwith100nM3OC6HSL-tothethree devicechannelsattime t =0.Initiallyallcellsexhibita weakfluorescencewithanar rowdistribution.Inthe absenceofC8HSL,theresponseevolvesover~3-5hrs togiveabroadanddistinctlynon-Gaussiandistribution thatextendsoveranorderofmagnitudeinGFPfluorescence,withaminorityofcellsbecomingfarbrighter thantheaverage.Bycontrast,whenC8HSLwaspresent at500nMor1000nM,theaveragecellfluorescence increasedslightlyovertime,butthedistributionstill remainednarrowerthanintheabsenceofC8HSL.Since thehighC8HSLconditions( i.e .C8HSL=1000nMand 3OC6HSL=100nM)inducedvirtuallyno lux response inourbulkexperiments,weinterprettheweakresponse asthebaselineautofluorescence F0ofEqn.(1).Figure5 showsthatC8HSLdoesnotsimplyreducetheaverage fluorescence,butratherreshapesthedistributionby suppressingthedevelopmen tofthehighlyheterogeneous(noisy)activatedresponse. Experiments#2and#3examinedwhetherdifferent combinationsofC8HSLand3OC6HSLthatinducethe sameaverageresponsealsoelicitthesamedegreeof heterogeneity.Theselected HSLconditionsfor#2and #3(Figure6)followtwocontoursinFigure4correspondingtoroughly25%and60%offullactivation, respectively.Althoughthevariance s2inGFPexpressionincreasesrelativetothemean athigheractivation levels,wefindthatdifferentcombinationsofHSLsthat producesimilaroverallaveragefluorescence F alsoproducesimilardistributions.Thatis,foragivendegreeof activation,thedistributionofindividualcellresponses doesnotappearsensitivetotheparticularcombination ofHSLsignalsthatinducedthatresponse.Wealsofind thatthe lux responsedevelopsonthesametimescale inallthreechannels,regardlessoftherelativeproportionsof3OC6HSLandC8HSL.Thisisconsistentwith priorfindingsthatC8HSLsignalingthroughtheAinR/S routeisnotessentialforluminescence[22].C8HSLacts onthesametimescaleas3OC6HSLasitprimarilyregulatesluminescencethroughadirectassociationwith LuxR.MutualinformationbetweeninputsandoutputThecellfluorescencehistogramscanbeexpressedas probabilitydistributions P ( F |([C8HSL],[3OC6HSL])) 012 0 Fluorescence (105cts) 012 000.050.10.15 O D 01234 F0(104cts) Fluorescence (105cts) 200 400Luminescence 1/2 0.5 1 1.5 2Luminescence (10 5 cts) OD = 0.10 OD = 0.10 F0 BC A Figure3 CorrelationbetweenluminescenceandGFPfluorescenceofJB10strain .( A )Correlationbetweenbioluminescence L andGFP fluorescence F oftheJB10strain,asobservedinabulk(well-plate)experiment.Datawerecollectedat OD =0.10inthepresenceofexogenous C8HSLand3OC6HSLspanningarangeofconcentrationsfromzeroto~1000nM.( B )Samedataplottedas L1/2vs F,showingtheapproximate powerlawofEqn.(1).( C )TheHSL-independentintercept F0inEqn.(1)growsinproportiontoopticaldensityduringearlygrowth. Table1Parametervaluesforthecompetitiveinhibition modelFitk1(nM) m k2(nM) n 13981.10.4163151.350.05 24621.20.21796(= m ) 33850.80.2118111.60.06ParametervaluesforthecompetitivemodelwereobtainedbyfittingEqn.(6) totheGFPexpressiondata(Figure2),forabulkcultureof Vibriofischeri strain JB10atdensityOD=0.05-0.15cm-1.Thefirstrowcontainsparameters obtainedbyfittingtheGFPfluorescencedata( F )withthefour-parameter modeldescribedinthetext.Thesecondrowcontainsparametersobtainedby fittingthefluorescencedataundertheconstraintthat m = n .Thethirdrow containsfitparametersobtainedwhenthefour-parametermodelisfittothe luminescencedata(actually L1/2)ratherthantothefluorescence F .(SeeEqn. (1)).Prez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page5of14

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forthecellfluorescence F ,giventheHSLinputs.The findingthatthesedistributionsareafunctionofthe overall lux activation F ([C8HSL],[3OC6HSL]),rather thandependingontheC8HSLand3OC6HSLlevels separately(Figures6and7),stronglysuggeststhatthe additional(C8HSL)inputdoesnotinducearesponse fromthe lux genesoftheindividualcellthat3OC6HSL alonecouldnotextract.Inthissensethe lux system doesnotgainadditionalinformationbyemployingtwo HSLautoinducers.(ThiswouldnotbetrueofotherregulatorytargetsofthephosphorelaycontrolledbyAinS/R andLuxS/P/Q,whichisnot regulatedby3OC6HSL.) Wecanquantifytheinformationthatisgainedbycalculatingthemutualinformation,whichmeasurestheregulatoryprecision,orthenumberofpractically distinguishableinput/outputstates,ofthisregulatory system.Onemaythinkofmutualinformationasmeasuringtheamountbywhichtheuncertaintyinthe (GFP)outputisreducedbyknowledgeoftheHSL inputs(andviceversa)[23-25].Mutualinformationhas beenilluminatinginrecentstudiesofinformation throughputinothersingle-cellchemicalsensingsystems suchasthemultiple-autoinducerQSschemeof V.harveyi [25]andthechemotaxisof Dictyosteliumdiscoideum [26]. Calculatingthemutualinformationbetweenthecell s environment,asdefinedbytheHSLinputs,andthe lux outputrequiresamathematicalmodelfor P ( F ).For higheractivationl evelswefoundthat P ( F )istoobroad tobesatisfactorilyrepresen tedasaGaussian,although itisreasonablywell-describedbyagammadistribution [27]: p ( F ) dF = dFF( v 1 )exp F / b / ( v ) bv (2) Thegammadistributiondependsontwoindependent parameters, and b ,thatdependonthevariance s2and mean ofthedistribution.Thedimensionlessparameter = 2/ s2completelydeterminestheshapeof P ( F ).TheFanofactor b = s2/ doesnotaffecttheshape ofthedistribution,butitscalesthehorizontalaxisand normalizationaccordingtotheunitsofmeasurementof F ( e.g .proteincopynumber,GFPfluorescencecounts, etc.).Eqn.(2)isanappealingmodelfor P ( F )becauseit arisesnaturallyinanintrinsicnoisemodel,where mRNAsfromonegenearesynthesizedinaPoissonprocess,witheachmRNAleadingtoaburstofprotein expression[27,28].Thereforewemodeledtheobserved heterogeneity P ( F )asagammadistributionthathasthe samerelationshipbetweentheratio s / andtheaverage activationlevelasweobservedinourexperiments. Forthiscalculationwealsodefinetwonewcoordinates, X and Y ,torepresenttheprogressofthetwo LuxR-HSLbindingequilibria: L = 10 mm 20xw = 400 mh = 10-15 mPDMSFlow [3OC6HSL] (nM)[C8HSL] (nM) 0 200 400 600 800 1000 3 10 30 100 300 1000 #1 #2 #3 #4 0 400 300 200 100-2.5 2.5 2 -2 1.5 -1.5 -0.50.50 1 -1Separation ri j ( m)Correlation Cij[C8HSL] = 0 nM [3OC6HSL] = 200 nM0 8 0 6 0 4 0 2 0 A B Ccoverslipobjective Figure4 MicrofluidicmeasurementsofGFPfluorescence .( A ) Schematicofmicrofluidicdeviceformeasuring lux expressionin individual V.fischeri .GrowthmediumcontainingexogenousHSL flowsthroughthreeparallelrectangularchannelsthatarecastinto thelowersurfaceofaPDMSblock.Livecellsinchannelsadhereto theglasswindow(coverslip)thatsealsthechannelsfrombeneath, andareobservedinaninvertedmicroscope.Theshallowratioof channelheighttowidth( h/w ~0.02-0.04)ensuresauniformflow velocityprofileacrossthewidthandlengthofeachchannel.( B ) Contourmapof lux activation F versusHSLinput.Thewhitecircles showHSLcombinationsappliedtothecellsduringthemicrofluidic experimentsdescribedinthetext.Thecontourlabelsshowthe activationfractionabovethebaselevel, i.e.( F-F0)/max( F-F0),as derivedfromthebulkmeasurementsandcompetitiveinhibition model.( C )Histogramcomparingthecorrelation Cij(Eqn.(7))in gfp expressionofapairofcells( i,j )tothephysicalseparation rij= ( xij 2+ yij 2)betweenthosecells.Thecolorofeachbinindicatesthe numberofcellpairs( i,j )whosephysicalseparationandbrightness correlationfallwithinthatbin.Pairsofnear-neighborcellsarenot morecorrelatedintheir lux activationthanpairsofdistantcells. Prez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page6of14

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X= [ 30C6 ]n/ [ 30C6 ]n+k2 n Y= [ C8 ]m/ [ C8 ]m+k1 m (See Methods ). X and Y arebothconfinedtotheinterval0 1.Whenplottedintermsofthesecoordinates, theresponsesurface F (X,Y)generatedbythecompetitivemodelhasacurvedshape(Figure7)thathighlights theasymmetryinthe lux responseto Y ( i.e .to[C8 HSL])versus X ([3OC6HSL]):thesensitivityto Y dependsonthevalueof X Themodelsfor F ( X,Y)andP ( F )togetherprovidean accuratemathematicalrepresentationofourbulkand single-celldata,fromwhichwecancalculatethemutual information I ( F ;( X,Y))betweentheinputcombination ( X,Y )andtheoutput F .Thecalculation,describedin Methods ,leadstoaverymodest I ( F ;( X,Y)) 0.53bits. Bycontrast,asimplenoiseless ON / OFF switchwould transmitpreciselyonebit.Therefore,whiletheLuxI/ LuxRsystemprovidesprecisecontroloftheaverage lux responseofapopulationoverarangeofHSLinputconcentrations,thatresponseactivatessograduallywith respecttotheinputlevels,andwithsuchaheterogeneousoutput,thattheindividualcellcannotbesaidto exhibitacleanswitchingbetweenthe OFF and ON statesofits lux response.DiscussionThefunctionaladvantagesofmulti-inputquorumsensing(QS)systemsarenotgenerallyunderstood,even thoughmanysucharchitecturesareknown[5,6]. Becauseourpreviousstudyof V.fischeri bioluminescenceshowedanextremelynoisyresponseto3OC6HSL alone,weinvestigatedwhetherthepresenceofthe C8HSLsignalinadditionto3OC6HSLaffectsthenoise performanceoftheLuxI/Rsystem.Toaccomplishthis wefirstconstructedadata-basedmodelforcompetitive inhibitionof3OC6HSLbyC8HSLandusedthismodel todrawacontourmapof lux activationbythetwo 0 0.5 1 0 0.5 0 0.5 0 0.5 0 50 1000 0.5 lux activation (GFP) 0 nM 500 nM 1000 nM C8HSL t = 0.7 hrst = 2.1 hrst = 3.1 hrs t = 4.1 hrst = 4.5 hrsA BCD E lux activation (GFP)100 25102050 t = 0.7 hrs t = 2.1 hrs t = 3.1 hrs t = 4.1 hrs 00 0 00 5050 505050 100 100 100100 100 t = 4.5 hrs FG HIJ Histograms in lux activation Percentiles in lux activation Figure5 Temporalresponseofthe lux activationhistogram .( A )-( E )ProgressionoftheGFPexpressionhistogramforindividualcellsinthe microfluidicchamber,asmeasuredforthethreesignalcombinationsindicatedasExperiment#1( i.e.100nM3OC6HSLandvariableC8HSL)in Figure4B;( F)-(J )Percentilesin gfp fluorescenceofindividualcellsunderdifferentHSLconditions.Eachcurveshowsthecumulativeareaunder thecorrespondinghistograminpanels( A )-(E )(andwiththesamecolorscheme).IntheabsenceofC8HSLthedistributionbroadens(and increasesinmeanvalue)over3-4hrs,whilethepresenceofC8HSLsuppressesthisresponse. Prez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page7of14

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signals.Wethenusedmicrof luidicdevicestocontrol thechemicalenvironmentwhilewemeasuredtheheterogeneityof lux responseamongindividualcells.The microfluidicflowchamberallowsforextendedobservationofindividualcellsasw ellasprecisedefinitionof theexogenousHSLlevels,eliminatingthepossibilityof QScircuitautoactivation. V.fischeri luminescenceisamodelsysteminquorum regulation,andaccordinglyithasbeenthesubjectof mathematicalstudiesofbothdeterministicandstochasticQSbehavior[29-36].Moststudieshaveemphasized dynamicsandsteadystatesofthe lux systemand 3OC6HSLalone,withoutconsideringtheroleofAinS/ R.OneexceptionistheworkofKuttlerandHense[34], whopresentedadetaileddynamicalmodelforthecombined ain and lux signalingpathwayasoutlinedby Lupp etal .[11]andothers.Theresultingsystemof ordinarydifferentialequationsdisplaysavarietyofpossiblestationarystatesanddynamics,althoughtheseoutcomesdependonsomepoorly-knownmicroscopic parametersthatcharacterizetransport,productionand degradationoftheHSLs,syn thaseproduction,andthe kineticsofHSL-LuxRcomple xformation.Interestingly however,thoseauthorsfoundthattheexperimentallyobserveddifferencesintheeffectofthe ainS mutation insquid-derived[11]versusfish-derived[13]strainsof V.fischeri couldarisefromrelativelyminordifferencesin parametersdescribingtheC8HSLand3OC6HSLcompetitionforLuxR.Specifically,therelativeaffinityofthe C8HSL-LuxR vs.3OC6HSL-LuxRcomplexforthe lux box,andtherelativestrengthof lux activationby C8HSL-LuxR vs .3OC6HSL-LuxR,candetermine whetheran ainS mutantwillbedark(asin[11])or showacceleratedluminescenceresponse(asin[13]). Theseparametersinfluencedynamicaleffectssuchas theroleof ainS intheautoactivationoftheLuxIsystem. Becauseautoactivationisnotpossibleinthemicrofluidicchamber,andbecauseC8HSLprimarilyaffectsbioluminescencethroughitsdirectinteractionwithLuxR, wesetasidemanyofthesedynamicalcomplexitiesin modelingourpopulation-averageddataontheeffectof differentHSLcombinations.Insteadweusedthefourparametercompetitiveinhibitionmodel(Figure1) describedin Methods .Themodelprovidesasatisfactory fittoexperimentaldatacollectedonthefluorescent reportingstrain(JB10),althoughthesamemodelwill notdescribethebioluminescenceasaccurately(seeEqn. (1)).Fromthefitparameterswecalculatedthefluorescenceresponsesurface F ((C8HSL),(3OC6HSL)),which weusedasthebasisformicrofluidicstudiesoftheheterogeneityin lux activationinthepre senceofmultiple autoinducers.Westudiedtheheterogeneityinthe lux responsealongcontours(ofconstantfluorescence F )or alongslices(ofvarying F )inthe[C8HSL],[3OC6HSL] 0 0.5 1 0 0.5 1 0 1 2 3 105 Y X Fluorescence (model) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 R e l a tiv e A c tiv a ti o nCoefficient of variation A B Figure7 Responsesurface F ( X,Y)andthecoefficientof variation .( A )The(population-average)responsesurface F( X,Y) generatedbythecompetitivemodelwiththechangeofvariable, Eqn.(8).( B )Themeasuredcoefficientofvariation CV = s / in lux activationofindividualcellsdeclinesathigheractivationlevels. Relativeactivationisdefinedas( F-min ( F))/( max ( F) -min ( F)).The dashedlineshowsalinearfit,usedtoparameterize CV inthe calculationofthemutualinformation I ( F; ( X,Y )). GFP fluorescence 0 50 100 150 0 0.05 0.1 0 nM C8HSL 200 nM 3OC6HSL 0 50 100 150 0 0.05 0.1 20 nM C8HSL 500 nM 3OC6HSL 0 50 100 150 0 0.05 0.1 100 nM C8HSL 800 nM 3OC6HSL 0 20 40 60 0 0.05 0.1 300 nM C8HSL 500 nM 3OC6HSL 0 20 40 60 0 0.05 0.1 1000 nM C8HSL 1000 nM 3OC6HSL 0 20 40 60 0 0.05 0.1 0 nM C8HSL 50 nM 3OC6HSL GFP fluorescence BAC DEF Figure6 Cell-to-cellheterogeneityatfixedaverageactivation Cellfluorescencebrightnessdistributionsmeasuredforexperiments #2and#3inFigure4B.( A )-(C )Distributionscollectedfortwo-HSL combinationsthatgenerated~25%offull lux activation(Experiment #2)and( D )-(F)distributionscollectedforcombinationsthat generated~60%offull lux activation(Experiment#3).Thedashed curvesshowmaximumlikelihoodfitstoagammadistribution.Each histogramisderivedfromroughly200individualcells. Prez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page8of14

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plane.Ingeneraltheheterogeneityvarieswiththeaveragedegreeof lux expression,withthecoefficientofvariation( s / )trendingdownwardasactivationincreases (Figure7).Thevarianceinindividualcellresponses appearsmuchlesssensitivetotheparticularcombinationofC8HSLand3OC6HSLinputsthantotheoverall degreeofactivation.Therelativeproportionsof 3OC6HSLandC8HSLdonotappeartoinfluencethe timescalefordevelopmentofthe lux response.These findingsarefullyconsistentwiththecompetitiveinhibitionmodel,ifthenoiseinLuxI/Riscontrolledbyalow copynumberoftheHSLreceptorLuxR[35]. Oneofthepuzzlesinourpreviousstudyofbioluminescencewasthatthenoiseinthe3OC6HSLresponse wasquitelarge i.e .CV= s / 1,especiallyasaGFPreporterstudyfoundsignificantlylowernoiselevels,CV ~0.15-0.4in V.harveyi QS[37].Hereitisinteresting theempiricalEqn.(1)predictsdifferentnoiselevelsfor luminescence vs .fluorescencereportersof lux .If F =FF0istheleveloffluorescenceactivationabovethreshhold,thenEqn.(1)predicts L / L 2 F / F ,sothatthe coefficientofvariation(CV= s / )shouldberoughly twiceaslargefortheluminescenceasforthefluorescence.Thereforetheheterogeneityseeninthesingle cellfluorescence,whichischaracterizedbyCV 0.40.6,isfullyconsistentwithoursinglecellbioluminescencedata.Neverthelesstheregulationof lux still appearsnoisierin V.fischeri thanin V.harveyi [37,38]. TheantagonisticinteractionbetweenHSLsignalsin V.fischeri isanintriguingcontrasttotheadditivesignalingfoundin V.harveyi bioluminescence,amodelsystemforQSregulationthatlackstheLuxI/LuxR mechanism.In V.harveyi threedistinctautoinducersare detectedbythreemembrane-boundhistidinekinases thatfeedintothesamephosphotransferaseLuxU.LuxU controlsaphosphorelaycascadethatregulatesthesingle outputLuxRVH(unrelatedto V.fischeri LuxR).Thefact thatthecircuitmergesinputsfrombothanHSLanda furanosylboratediester(AI2)autoinducersuggeststhat itsensesbothintra-speciesandinterspeciesQSsignals, possiblyfunctioningasacoincidencedetectorforthe inputsignals[39].Thiscouldincreasethesystem sresistancetocrosstalkfromotherbacterialQSsignalsor preventitfromrespondingincertainhabitats.Moreover theautoinducerresponseisadditiveandsymmetricin thesensethatallthreereceptorscontributepositively andinparalleltotheoutput,withtwohavingequal kinaseactivities,sothattheoutputrespondsinthe samewaytoactivationofeachreceptor[5,25,37].Those authorssuggestedthatequalsensitivitytoeachautoinducerbenefitstheorganismbyprovidingagraded, sequentialactivationofbioluminescenceduringgrowth. Lupp etal .proposedasimilar,sequentialinterpretation[11]fortheroleofC8HSLand3OC6HSLin V. fischeri .TheysuggestedthatC8HSLactsfirsttostimulateluminescenceatintermediatecelldensities(asin cultures),activatingluxRexpressionthroughtheAinS/R routeandalsointeractingdirectlywithLuxR.Athigher celldensities(aslaterduringcolonization) luxR remains activatedbyC8HSLbut3OC6HSLaccumulatestosufficientconcentrationstointeractwithLuxRandactivate lux.Itwouldindeedberemarkableifboth V.fischeri and V.harveyi usedmultipleautoinducerstoachievesequentialactivationof lux ,yetonly V.fischeri didsobyusing antagonisticsignalinputs. Alternatively,Kuo etal .suggestedthatthesuppressing roleofC8HSLservedadifferentfunction,conserving theenergyresourcesoftheorganismbydelayingthe inductionofluminescenceearlyin V.fischeri growth [13].Onepuzzlehoweveri sthatthesamedelayedoutcomecouldpresumablybeachievedbysettingahigher thresholdforinductionby3OC6HSL,makingthesecondsignalunnecessary. Wecannotfullyinterpretbio luminescenceregulation in V.fischeri withoutconsideringitssymbioticcontext, asthefullQSnetworkthatregulatesbothbioluminescenceandhostcolonizationreceivesinputfrommany environmentalfactors[22,40].Howeverwecanstillask whichpropertiesofthe V.fischeri LuxI/LuxRsystem couldmakeanantagonisticinteractionbetween 3OC6HSLandC8HSLadvantageous.Weusedour experimentalandmodelingr esultstoquantifythesignal-transmissionproperty ofthetwo-HSLsystem.We calculatedthemutualinformationbetween lux output andthesignalinputs[23-25]bymodelingthepopulation-averaged lux activation F ( X,Y )withthecompetitive inhibitionmodel(where X and Y arescaledvariables correspondingtotherelativesaturationofLuxRby 3OC6HSLandC8HSLrespectively),andthenmodeling thenoisein F byagammadistributionthatcapturesthe coefficientofvariationobservedinoursingle-cell experiments(Figure7and Methods ).Intheabsenceof any otherinformationaboutsignalinputsi.e .using thesimplestassumptionthatallinputcombinations( X, Y )areequallylikely apriori-thecalculationleadstoa surprisinglylowestimateforthemutualinformation, I ( Z ,( X,Y)) 0.53bits.Evenwithitstwosignalinputs, theoutput F ( X,Y)oftheLuxI/LuxRsystemtransmits lessinformationaboutitsinputsthanwouldasimple ON/OFFswitch.Bycontrast,Mehta etal .estimated ~1.2-1.7bitsofmutualinformationbetweentheoutput andtwoinputs(AI1andAI2)ofthephosphorelaysystemin V.harveyi QS.Thenoisyperformance(CV~0.5) andgradualswitchingofLuxI/Rsignificantlydegrades itssensingcapability,incomparisontothe V.harveyi circuit. Thereforewefindnoindicationthatthesecond (C8HSL)autoinducerenhancestheprecisionofsignalPrez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page9of14

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responseinthe V.fischeri LuxI/Rsystem.Howeverthe poorinformationthroughputofthissystemdoessuggest adifferentperspectiveontheidea[13]thatC8HSLconservesenergyresourcesbydelayinginductionof lux at lowpopulationdensities.Atthepopulation-average level,thesamedelayinactivationcouldbeachievedby raisingtheactivationthresholdforthe3OC6HSLsignal. Howeveratthesinglecelllevel,thepresenceofany 3OC6HSLinducesahighlyh eterogeneousresponse, withsomecellsluminescingmuchmorebrightlythan average.Thus,evenifthethresholdissetveryhigh,a fewcellswillwasteenergybyemittinglightduringearly growth.Onebenefitofproducingasmallconcentration ofC8HSListhatitcollapsesthebioluminescencedistribution,suppressingthemostactiveemittersandconservingmetabolicenergy.Simultaneoussynthesisof C8HSLand3OC6HSLmayther eforereduceluminescentoutputbyvirtuallyallcells,atleastuntil3OC6HSL attainshighconcentration.Inthissensethecrosstalk fromtheC8HSLsignaldoesnotimprovetheenvironment-sensingprecisionofLuxI/Ratsteadystate,butit maytendtocompensateforthenoisyperformanceof theLuxI/Rswitchbysuppressingtheswitchforaslong aspossibleduringgrowthandcolonization.Itwouldbe intriguingtoseeifdynamicalmodelsthataccurately capturethenoiseinthecircuitandthetemporalaccumulationofHSLcancharacterizethisbehavior quantitatively.ConclusionsAlthoughmultiple-inputquorum-sensingsystemsare widespreadinthemicrobialworld,themechanismsby whichtheycombineandprocessinformationfromparallelsignalinputsareingeneralpoorlyunderstood.One oftheintriguingpropertiesofthe V.fischeri QSnetwork isthatitemploystwoautoinducersignalsthatcanact competitivelyorantagonist icallyinregulatingthe lux genes.Inordertounderstandthepossibleadvantagesof thiscompetitiveinteractionwehavestudiedthe responseofindividual V.fischeri tocombinationsofHSL signals.Thepopulation-averaged,steadystateactivation of lux bythetwoHSLsignalsisreadilydescribedbya quantitative,competitive inhibitionmodel.Ourmeasurementsof lux activationinindividualcellsshowa noisyresponse,withtheLuxI/Rcircuitconveyingless thanonebitofmutualinformationbetweenitsHSLsignalinputsandits lux output.Furtherthedataprovide noindicationthateitherthedynamicsofthe lux responseortheheterogeneityinthatresponsearesensitivetodifferentcombinationsofsignalsthatgenerate thesamepopulation-averagedoutput.Inthissensethe secondHSLsignalinputappearstoprovidelittleifany additionalinformationtothe lux system.Thesefindings mayinsteadsuggestadynamicalroleinwhichthe productionofC8HSLsignalprovidesanenergetic advantagebysuppressingsensitivityoftheluminescence switchduringthegrowthofapopulation.MethodsFluorescenceandluminescenceresponseofbulkcultureV.fischeri mutantJB10isaderivativeoftheES114strain inwhichachromosomal gfp reporterisinsertedinto the lux operonbyalleleexchange,producing luxI-gfpluxCDABEG [40].WepreparedJB10fromaglycerol stockandgrewthecellstoexponentialphaseindefined artificialseawatermedi um[41]towhichwasadded 0.3%casaminoacids.Cellswerethendilutedand regrowntoOD~0.1-0.3infreshmedium,washedthree times,andthenrediluted100intoa96-wellassayplate containingfreshmedium.Theindividualwellswerepreloadedwithan118arrayofconcentrationsofthetwo HSLautoinducers N -3-oxohexanoylL -homoserinelactone(3OC6HSL,Sigma#K3007)and Noctanoyl-L homoserinelactone(C8HS L,CaymanChemicalCo. #10011199).ThewellplatewasthenincubatedinaBiotekSynergy2platereaderat25C,givingagrowthrate 1.10.1hr-1.Opticaldensitywasmeasuredat600nm, andGFPfluorescencewasmeasuredusinga485/20nm excitationfilteranda528/20nmemissionfilter.The opticaldensity,luminescenceandGFPfluorescence valuesforeachwellwererecordedatregularintervals duringexponentialgrowth(Figure2).Datacollected earlyingrowth( t <12hrs)showedasensitivedependenceontheexogenouslevelsofbothHSLs,indicating thatendogenousHSLdidnotaccumulatesignificantly duringthisinterval.CompetitiveinhibitionmodelforbulkresponseInordertogenerateamathematicalrepresentationof the lux response,asafunctionofthe3OC6HSLand C8HSLsignals,wefittheJB10well-platedata(fluorescence vs HSLconcentrations)tothecompetitiveinhibitionmodelofFigure1[11,13].Inthismodel lux is regulatedprimarilythroughcompetitionbetween C8HSLand3OC6HSLtoformLuxRcomplexesthatact astranscriptionalactivatorsforthe lux genes.The actionofC8HSLonLuxRsynthesisthroughAinRand thephosphorelayisnotconsidered.Weassumethat 3OC6HSLandC8HSLdiffusefreelyacrossthecell envelopeandformmultimericcomplexeswithLuxR. Weallowanarbitrarydegreeofmultimerizationbutwe donotconsiderheterocomplexes( i.e .involvingboth C8HSLand3OC6HSL).Althoughitissimpletoinclude theweakactivationof lux byC8HSL-LuxR,whichisevidentinthebioluminescencedataatlow3OC6HSLconcentrations,thisactivationisscarcelyvisibleintheGFP fluorescencedatathatisthetargetofourmodeling. ThereforeweomittedthismechanismfromourmodelPrez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page10of14

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andconsideredC8HSLonlyinitsroleasacompetitor forLuxR.Thatis,weassumethattheGFPfluorescence isproportionaltotheconcentrationofthe3OC6HSLLuxRcomplex.Morebiochemicalaccuracycouldbe includedbyintroducingextraparameters,butthesimplermodelappearssufficienttodescribetheJB10data. ThemodelallowsC8HSLand3OC6HSLtoformmultimericcomplexes(ofdegree m and n respectively)with LuxR, mC 8HSL + mLuxR ( C8HSL LuxR )mn 3OC6HSL + nLuxR ( 3OC6HSL LuxR ) n wheretheHillcoefficients n and m arenotassumed tobeintegers.Theseequilibriaarecharacterizedbytwo dissociationconstants, K1and K2: K2 m 1 1= [ LuxR ]m[ C8HSL]m ( C8HSL LuxR )m K2 n 1 2= [ LuxR ]n[ 3OC6HSL]n ( 3OC6HSL LuxR )n K1and K2aredefinedsoastohaveunitsofconcentration,regardlessofthevaluesof m and n .If[LuxR0]is theaveragetotalconcentrationofLuxR,includingcomplexes,then [ LuxR0] = [ LuxR ] + n ( 3OC6HSL LuxR )n + m ( C8HSL LuxR )m (3) AswedonotmeasuretheactualLuxRcopynumber (althoughsee[42]),itisconvenienttoredefinethedissociationconstantsintermsof[LuxR0]andadimensionlessconcentration r : r = [ LuxR ] / [ LuxR0] km 1= rm[ C8HSL]m ( C8HSL LuxR )m [ LuxR0] kn 2= rn[ 3OC6HSL]n ( 3OC6HSL LuxR )n [ LuxR0] (4) Here k1and k2havedimensionsof(autoinducer)concentration.ThenEqn.(3)becomes 1= r + mrm[ C8HSL]m km 1 + nrn[3 OC6HSL]n kn 2 (5) StartingfromtheHSLconcentrationsandaninitial guessfortheparameters( k1,k2,m,n ),wesolveEqn.(5) tofind r .ThenEqn.(4)givestheconcentrations(relativetoLuxR0)ofthetwomultimerspecies.Wecompare themodeltothewell-platedatabyassumingthatthe GFPfluorescence F isalinear,non-saturatingfunction ofthetwomultimerconcentrations: F = F0+ a1 ( C8HSL LuxR )m [ LuxR0] + .. a2 ( 3OC6HSL LuxR )n [ LuxR 0 ] (6) Here F0, a1and a2arepositiveconstants(see Results). Asexplainedabove, a1isevidentinluminescencebutis scarcelydetectableinthefluorescence;setting a1=0 doesnotimpairthefit.Thentheshapeofthe 2D surface F (3OC6HSL,C8HSL)isdeterminedsolelybythe fourparameters k1,k2, n ,andm ,whiletheparameters F0and a2provideaninstrument-dependentoffsetand amplitudethatscalethe 2d model F surfaceontothe measuredvalues.Weestimatethefourmodelparametersthroughanonlinearleastsquaresfitofthefluorescenceresponsesurfaces F (3OC6HSL,C8HSL) measuredatopticaldensities0.05-0.15cm-1toEqn.(6), withthescaleparameters a2and F0determinedbylinearregression.Thisprovidesaparametrizationofthe averageresponse F asafunctionofthetwoHSLinputs (Table1). Thedatadonotrequirethat m and n aredifferent.As Table1indicates,thefityieldssimilarvaluesforthetwo Hillcoefficients( m =1.10.4and n =1.350.05),and infactweobtainaverysimilarfitifweassumethatthe samecoefficientappliesforbothautoinducers( m = n = 1.20.2).Table1alsoshows(asexpectedfromEqn. (1))thatweobtainsimilarparameterswhenwefitEqn. (6)tothesquarerootofthemeasuredluminescence L1/ 2ratherthantotheGFPfluorescence F .MicrofluidicstudiesofindividualcellsTomeasuretheeffectofexogenousHSLsignalson lux expressioninindividualJB10cellsweloadedcellsinto microfluidicperfusionchambersthatsuppliedaflowof mediumcontainingexogenous3OC6HSLandC8HSL. Eachmicrofluidicdeviceconsistedofthreeparalleland unconnectedchannels(Figure4),witheachchannel havingwidth400 m(paralleltotheobservationwindowbutperpendiculartothefluidflow),depth10-15 m(perpendiculartotheobservationwindow),and length(paralleltoobservationwindowandtofluidflow) 10mm.ThedeviceswerefabricatedfromPDMSsiliconeelastomer(Sylgard184,Dow-CorningCorporation) byastandardsoft-lithographicmethodinwhicha PDMSreplicaiscastfromareactiveion-etchedsilicon master[43].Thedevicechannelsweresealedbyaglass coverslipbondedtothePDMS.Inordertopromotecell adhesiontotheinterioroftheglasswindow,wecoated theinteriorofthedevicebyfillingitwithasolutionof polyL -lysine(1mg/ml,MW300000)andincubatingitPrez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page11of14

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for24hoursat5C,priortocellinjection.Thisprovided stableadhesionofthe V.fischeri totheglasswindow. JB10cellsformicrofluidicstudieswerepreparedin exponentialphaseasforthe96-wellassayabove:We grewcellstoexponentialphaseindefinedartificialseawatermediumwithcasaminoacids[41],thenwashed (3)andredilutedthecells,andthenregrewthemto OD(600nm)=0.015-0.03cm-1infreshmedium.Once thecellsandthemicrofluidicdevicewereprepared,we flushedthepolyL -lysinesolutionbypumpingtheJB10 cultureintoallthreeparallelchannelsat1-2ml/hrwith asyringepump.Wethenplacedthedevice(withglass windowfacingdownward)onthestageofaNikon TE2000Umicroscopeandreducedtheflowrateto ~0.02ml/hr.Atthisslowflowratethecellsgradually settleandadheretotheglasswindow.Onceasufficient numberofcellshadadheredtothewindow(requiring 15-30minutes),wesuppliedautoinducerbyconnecting thedeviceinputstosyringepumpsthatdelivered definedmediumcontainingexogenous3OC6HSLand/ orC8HSL.Eachofthethreechannelswassuppliedwith adifferentcombinationofHSLs,flowingatarate~0.02 ml/hrduringfluorescencemeasurements. The0.02ml/hrflowrateofmediumcorrespondsto anaverageflowvelocityof~1mm/swithineachchannel.Boththedevicedesignandexperimentaltesting ensuredthatthisflowwassufficientlyuniformand rapidtowashawayendogenous(nativelyproduced) autoinducerthatmightotherwiseaffectactivationof the lux genes.Firstofall,controlexperimentsinour flowsystemshowedthat-intheabsenceofanyexogenousautoinducer(HSL)gfp expressionfromthe lux reporterstrainwasatitsbaselinelevel(andluminescencewasunobservable).Moreover,thephysical parametersoftheflowsystemmakeithighlyimplausiblethatspatialheterogeneityintheflowcoulddevelop orallowexperimentallyrelevantconcentrationsofHSL toaccumulatenearanyofthecellsunderobservation: First,thedimensionsofthedeviceandtheflowrateof growthmediumleadtofluidflowataverylowReynoldsnumber( Re ~0.03).Atthis Re theflowvelocity profileishighlyuniformacrossthewidthandlength oftheflowchamber,uptowithin~10 mofthe chamberedges[44].Second,theonlysignificantheterogeneityinthisflowvelocityprofileoccursalongthe depthofthechannel( i.e .perpendiculartothewindow),whichis10-15 m.HoweverHSLrequiresonly ~0.1stodiffusethisdistance.Thisissomuchfaster thanotherrelevanttimescalesintheexperimentthat ameaningfulHSLgradientcannotbeestablishedin thisdirection.Third,thechambervolumeandthe1 mm/sflowratetogetherindicatethattheentire volumeofthecellchamberregion(10mmlength)is completelyflushedevery~10seconds.Howeverthe onlycellsoccupyingthechamber(andproducingHSL) arethoseformingasparsesinglelayer(cellsaretypicallyspaced>20 mapart)onthechamberwindow. LiteratureestimatesofHSLproductionratesin V. fischeri indicatethatsuchasparselayerofindividual cells,withinachamberthatisflushedatthisrate, wouldnotbeabletogenerateanendogenousHSL concentrationabove~100pM[20].Thisconcentration isatleasttwoordersofmagnitudesmallerthanthe exogenousHSLconcentratio nsthatweareproviding. Finally,ifthecellsdidgenerateenoughHSLtoaffect localconcentrations,wewouldexpectthatcellsdownstreamwouldingeneralex pressmoreGFPthancells upstream.Moregenerallywewouldexpectthecorrelation CijbetweentheGFPfluorescence Fi,Fjofapairof cells i,j Cij= ( Fi ) Fj / 2 (7) todependontheirspa tialseparations xij, yij,or rij. (Here isthemeancellfluorescenceand s2isthevariancein F .)Weanalyzedourdataforsuchspatialcorrelationsandfoundnone.Forexample,Figure4showsno relationshipbetween Cijand rij:the gfp expressionof twoneighboringcellsisno moresimilarthanthatof twodistantcells.Inshortthedataandthesystem designarguestronglyagainstanyautoactivationof(or localcrosstalkbetween)theindividualcellsunder observation.Characterizingheterogeneityin lux activationThethree-channeldeviceallowedustocollectthefluorescencehistogramofcellsunderthreedifferentHSL signalcombinations,asitevolvedover4-5hours.Once HSLswereintroducedtothedeviceat t= 0,wecollectedphasecontrastandfluorescenceimagepairsfor eachchannel(HSLcombination)atintervalsof20minutes,usinga20/0.50NAphaseobjectiveandaGFP filtercube.ImageswererecordedbyaCoolsnapHQ2 camera(Photometrics)at-30Candcorrectedinsoftwarefordarkcurrentandflat-field. Foreachexperimentalconditionweevaluatedthe fluorescentemissionfrom(ty pically)~200individual cellsbyfirstdeterminingthe physicallocations(pixel coordinates)ofsinglecellsinaphasecontrastimage. WethenusedahomemadeMatlabcodetoevaluatethe fluorescencepercellpixelintheassociatedfluorescence imagebysummingthefluorescenceemission(relative tobackground)ofthecontiguousbrightpixelsassociatedwiththecell spixelcoordinates.Normalizingthe histogramofindividualcellfluorescencevaluesgivesa distribution P ( F |([3OC6HSL],[C8HSL ])),representing theprobabilityofcellfluorescence F giventheHSL inputconcentrations.Prez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page12of14

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CalculatingthemutualinformationBycombiningmathematicalparametrizationsofboth the lux response, F ([3OC6HSL],[C8HSL])andtheprobabilitydistribution P ( F |([3OC6HSL],[C8HSL])),wecalculatethemutualinformation[23]betweentheHSL signalinputsand lux output.Thesignalconcentrations areinconvenientparametersforthiscalculationbecause onlyaninfiniteconcentrationofautoinducercansaturatetheresponse.Intheiranalysisof V.harveyi QS, Mehta etal .[25]definednewcoordinatesthatdescribe thestateofsaturationoftheautoinducerreceptors.In similarfashionwereplace[3OC6HSL]and[C8HSL] withcoordinates X and Y thatdescribethestateofthe associationequilibriafortheHSL-LuxRcomplexes: X = [ 3OC6HSL]n [ 30 C6HSL]n+ kn 2Y = [ C8HSL]m [ C8HSL]m+ km 1 (8) X =1or Y =1correspondstocompletesaturationof the3OC6HSL-LuxRorC8HSL-LuxRbindingequilibriumrespectively.Withthesecoordinatestheresponse surface F ( X,Y )forthecompetitiveinhibitionmodelhas asimpleshape(Figure7)thatisindependentofthe parameters k1, n k2, m Themutualinformationbetweenacombinationof inputs( X,Y )andtheoutput F isthencalculatedas: I ( F ; ( X Y )) = dFdXdYP ( F ( X Y )) log2P ( F ( X Y )) P ( F ) P ( X Y ) = dFdXdYP ( F | ( X Y )) P ( X Y ) log2P ( F | ( X Y )) P ( F ) (9) Here P ( F )istheprobabilityoffindingoutput F ,inthe absenceofanyknowledgeoftheinput( X,Y). P ( F |( X, Y ))istheprobabilityof F ,giventhecombination( X,Y ). P ( F ,( X,Y ))istheprobabilityofobservingtheparticular combination F ,( X,Y ): P ( F ( X Y )) = P ( F | ( X Y )) P ( X Y ) Theseprobabilitydistributionsarenormalizedasfollows: P ( F )= dXdYP ( F ,( X Y ))= = dXdYP ( F | ( X Y )) P ( X Y ) dFP ( F ) =1 dFP ( F | ( X Y )) =1 dFdXdYP ( F ,( X Y ))=1 dXdYP ( X Y ) =1 ToevaluateEqn.(9)wemodel P ( F ,(X,Y))asthe gammadistributionthathasthesamemeanandvarianceasobservedinthebulkandsingle-cellmeasurementsrespectively.Thecalculationalsorequiresan estimateof P ( X,Y ),thepriorprobabilityofaparticular combination( X,Y). P ( X,Y)isnotsoeasilypredicted. However,giventhat X and Y arebothboundedby0 and1wemadethestraightforwardassumptionthat P ( X,Y)=constant .ThemutualinformationEqn.(9)is thenfoundtobe I 0.53bits.Howeverthisresultis notsensitivetoourassumptionsaboutthepriorprobability:various P ( X,Y)functionsthatwerestrongly bimodalinboth X and Y ,andeithersymmetricor asymmetricin X vs. Y [25],allgavesimilarvaluesof I 0.5bits.ListofAbbreviations C8HSL:C8homoserinelactone, N-octanoylL -homoserinelactone;GFP:green fluorescentprotein;HSL:homoserinelactone;JB10: Vibriofischeri strainJB10; QS:quorumsensing;3OC6HSL:3-oxo-C6homoserinelactone, N -3oxohexanoylhomoserinelactone. Acknowledgements Prof.EricStabbandProf.RahulKulkarniprovidedvaluableadviceandmany suggestionsduringthiswork.Prof.EricStabbalsoprovidedthestrainJB10 usedinthisstudy.Thesiliconmasterforthemicrofluidicdeviceswas designedandfabricatedbyMinjunSon.Theauthorsgratefullyacknowledge fundingsupportfromtheNationalScienceFoundationunderawardDMR0851707andtheNationalInstitutesofHealthNIDCRunderaward 1R21DE018826.Publicationofthisarticlewasfundedinpartbythe UniversityofFloridaOpen-AccessPublishingFund.Thefundingagencies playednoroleintheresearchdesignandactivityorinthepreparationand submissionofthismanuscript. Authors contributions PDP-Acquiredandanalyzeddata;JTW-Acquireddata;SJH-Designedresearch, analyzeddata,anddraftedthemanuscript.Allauthorsreadandapproved thefinalmanuscript. Received:3June2011Accepted:29September2011 Published:29September2011 References1.RedfieldRJ: Isquorumsensingasideeffectofdiffusionsensing? Trends Microbiol 2002, 10(8) :365-370. 2.WatersCM,BasslerBL: Quorumsensing:Cell-to-cellcommunicationin bacteria. AnnuRevCellDevBiol >2005, 21 :319-346. 3.HenseBA,KuttlerC,MuellerJ,RothballerM,HartmannA,KreftJ: OpinionDoesefficiencysensingunifydiffusionandquorumsensing? Nature ReviewsMicrobiology 2007, 5(3) :230-239. 4.DunnAK,StabbEV: Beyondquorumsensing:thecomplexitiesof prokaryoticparliamentaryprocedures. AnalBioanalChem 2007, 387(2) :391-398. 5.NgWL,BasslerBL: Bacterialquorum-sensingnetworkarchitectures. Ann RevGenet 2009, 43 :197-222. 6.GoryachevAB: Designprinciplesofthebacterialquorumsensinggene networks. WileyInterdisciplinaryReviews:SystemsBiologyandMedicine 2009, 1(1) :45-60. 7.MeighenEA: Molecularbiologyofbacterialbioluminescence. Microbiol MolBiolRev 1991, 55(1) :123-142. 8.VisickKL: LayersofsignalinginaBacterium-Hostassociation. JBacteriol 2005, 187(11) :3603-3606. 9.StuderSV,MandelMJ,RubyEG: AinSQuorumSensingRegulatesthe VibriofischeriAcetateSwitch. JBacteriol 2008, 190(17) :5915-5923.Prez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page13of14

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Submit your next manuscript to BioMed Central and take full advantage of: Convenient online submission Thorough peer review No space constraints or color gure charges Immediate publication on acceptance Inclusion in PubMed, CAS, Scopus and Google Scholar Research which is freely available for redistribution Submit your manuscript at www.biomedcentral.com/submit Prez etal BMCSystemsBiology 2011, 5 :153 http://www.biomedcentral.com/1752-0509/5/153 Page14of14