University of Groningen Coupled adhesion of bacteria to surfaces Skogvold, Rebecca van der Westen

University of Groningen

Coupled adhesion of bacteria to surfaces

Skogvold, Rebecca van der Westen

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Skogvold, R. V. D. W. (2018). Coupled adhesion of bacteria to surfaces. Rijksuniversiteit Groningen.

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C H A P T E R

2

Quantification of the Viscoelasticity of the

Bond of Biotic and Abiotic Particles

Adhering to Solid-Liquid Interfaces using

a Window-equipped Quartz Crystal

Microbalance with Dissipation

This chapter is published with permission from Elsevier:

Rebecca van der Westen, Henny C. van der Mei, Hans De Raedt, Adam L. J. Olsson, Henk J. Busscher and Prashant K. Sharma

ABSTRACT

The quartzͲcrystalͲmicrobalanceͲwithͲdissipation (QCMͲD) has become a powerful tool for studying the bond viscoelasticity of biotic and abiotic colloidal particles adhering to substratum surfaces. A windowͲequipped QCMͲD allows highͲthroughput analysis of the average bond viscoelasticity,measuringover106_{particlessimultaneouslyinonesingleexperiment.Othertechniques} requirelaboriousanalysesofindividualparticles.Inthisprotocol,thequantitativederivationofthe springͲconstantanddragͲcoefficientofthebondbetweenadheringcolloidalparticlesandsubstratum surfacesusingQCMͲDisexplainedforbacteriaandsilicaparticles,usingtheparticleͲmassderivedfor validation.Bondviscoelasticityiscalculatedusingacoupledresonatormodel,payingspecialattention totheprotocolformathematicalfittingneededtoobtainreliablequantitativeoutput.Knowledgeof the viscoelasticity of the bond between colloidal particles and substratum surfaces facilitates developmentofnewstrategiestodetachadheringparticlesfromorretainthemonasurface.

 INTRODUCTION

Controlovertheadhesionofbiotic(suchasbacteria)andabioticcolloidalparticles(suchas silica, polystyrene or latex particles) is a key concern in engineering and medicine. In particular, adhesionofbacteriatosurfacescanformahazardtohumanhealth,1_{whileadhesioncontrolofabiotic}

particlesisessentialinareassuchassensinganddatastorage.2,3_{Thebondbetweenacolloidalparticle}

andasubstratumsurfaceisseldomrigidandmostlycomprisesanelasticandviscouscomponent.4,5_

Theviscoelasticityofabondisnotonlydeterminantforparticleadhesion,butalsoforthemechanism of particle detachment.6,7_{ For bacteria, the viscoelastic properties of their bond with a substratum}

surface often allow adhering bacteria to remain adhering under shear conditions through gradual elongationofthebond.8_

 Severalexperimentaltechniqueshavebeendevelopedtostudytheadhesivebondbetween adhering colloidal particles and a substratum surface, such as the use of atomic force microscopy (AFM)9–11_{andopticalormagnetictweezers.}12_{Inthesetechniques,asinglecolloidalparticleisforced}

tocontactasubstratumsurfaceafterwhichitispulledoffandtheforcerequiredtobreakthebondis takenastheadhesiveforce.ElasticityandviscosityofthebondcanbemeasuredusingAFMbypressing aparticleonasubstratumsurfaceunderaconstant,appliedforceandmeasuringdeformationorby measuring the force resulting from an applied, constant deformation of the particle. Using this approach,Luetal.13_{describedthebondcomponentsofbacterialcellsurfacesasaspring,representing}

theelasticcomponentasrecognizedinthestandardsolidmodel,placedinaserieswithacombination ofaspringandadashpotinparallel.Inordertoensurethatsuchmodelingonlycomprisesthebond betweenanadheringparticleandasubstratumsurfaceandnotthebulkofaparticleasintraditional Hertz, JohnsonͲKendallͲRoberts or DerjaguinͲMullerͲToropov models, Chen et al.14_{ suggested to}

considerthebondbetweenanadheringparticleandasubstratumsurfaceasacylindricalvolumethat deforms under conditions of constant volume to provide a method allowing to confine traditional analysistothebonditself.AnalysisoftheBrownianmotioninducednanoscopicvibrationsexhibited bybiotic15_andabiotic7,16_{colloidalparticlesoffersacompletelydifferentwaytoobtaintheelasticityof}

thebond,withsmallervibrationalamplitudesbeingindicativeofhigherelasticity.15_{Apartfromthe}

assumptions involved in each of the aboveͲmentioned techniques,they all possess the common limitationthatadheringparticlesmustbestudiedoneͲbyͲoneonanindividualbasis,whichmakesit hardtoobtainstatisticallyreliable,quantitativedata.

 ThequartzͲcrystalͲmicrobalanceͲwithͲdissipation(QCMͲD) effectively avoids this “oneͲbyͲ one”drawback,andhasbeenappliedtoanalyzetheviscoelasticityofthebondbetweenbioticand abioticparticlesadheringtosolidͲliquidinterfacesoverlargenumbersofadheringparticles,typically intheorderof1010_perm2_{ofasensorsurface,approximatelyequivalentto10}6_{particlesonthesensor}

surface.NanometerͲscale shear oscillations of the sensor cause deformation of the bonds with an adheringparticle,withanopposingforcearisingfromthesurroundingliquid.TheQCMͲDregistersthe shiftinresonancefrequencyofthesensor(ȴf)duetoparticleadhesionaswellastheenergylossto the surrounding liquid (change in “dissipation”(ȴD)). Moreover, for studies involving colloidal particles,itisadvantageoustouseaQCMͲDequippedwithawindowchamber,allowingsimultaneous microscopicregistrationofthenumberofparticlesadheringtothesensorsurface.

 Traditionally,QCMͲDhasbeenmostlyusedtodetermineadsorptionofmolecularmasstoa sensor surface, assuming the adsorbed mass directly couples to the sensor surface. According to Sauerbrey’s relation,17_{ an adsorbed coupled mass increases the effective sensor mass, yielding a}

reductioninthesensorresonancefrequency,orinQCMͲtermsanegative(resonance)frequencyshift. Since the penetration depth for the shear wave in QCMͲD is less than 250 nm (at 5 MHz), this representsthemaximumthicknessofadsorbedfilmsthatcanbereliablymeasured.Thesensitivityof the mass detection in QCM is in the nanogram range. Particles however, do not necessarily massͲ coupletothesensorsurface,butinsteadmayadhereascoupledresonators.18–21_{Thesensorresonates} atdifferentfixedfrequencies.A5MHzsensorresonatesnotonlyat5MHzbutalsoatitsovertones (15,25upto65MHz).Providednottouchingeachother,allcolloidalparticlesadheringtothesensor surfaceactasindividual,coupledresonators(Figure1a)withanimpactontheresonancefrequency shift(ȴf)measured.Energydissipationchange(ȴD)ismaximalwhentheparticleresonancefrequency (fp)matchesthesensorresonancefrequency(fs).Thedevelopmentofthecoupledresonatormodel hasgreatlywidenedthepossibilitiesofQCMͲD,whichwerepreviouslyconfinedtomolecularmass adsorption.Itisinterestingtonotethatwhereasbondviscoelasticitiesofindividualparticlesofthe same kind often show large variations,8,15,22_{ QCMͲD identifies a wellͲdefined zeroͲvalue in sensor}

frequency (fZC), see Figure 1b).  Zero crossing frequencies are only observed when the adhering colloidalparticlesoscillateatfrequencieswithinthewindowofthesensorresonancefrequencyand itsobservableovertones,whichrangefrom5MHzto65MHz(seeFigure1b).Positivefrequencyshifts observedintheliterature,couldnotbeexplainedpriortotheintroductionofthecoupledresonator model.4,5,19_                Figure1.Schematicdiagramofthecoupledresonatormodel. a)Colloidalparticlewithmass,mpadheringtoasensorsurfacethroughaviscoelasticbondcomprised ofaspringwithspringconstant(k),anddashpotwithadragcoefficient(ʇ),yieldingaparticleresonance frequencyfp.Inthecurrentscheme,springanddashpotareplacedinparallel,i.e.asintheKelvinͲVoigt modelofviscoelasticresponse. b)Theoreticalshiftsinthesensorresonancefrequency(ȴfs)anddissipationchanges(ȴD)forparticles

adhering with different adhesive bond stiffnesses to a QCMͲD sensor, as explained in the coupled resonatormodel,asafunctionoftheQCMͲDresonancefrequencyfs.Particleresonancefrequencyfp

increaseswithadhesivebondstiffness,andthefrequencyofzeroͲcrossing(fs=fp)canonlybeobserved

withinwhatisreferredtoas‘thewindowofobservableQCMͲDfrequencies’,includingitsresonance frequencyandovertones,indicatedbythedashedrectangles.Theasymptoticshiftfromanegativeto apositiveȴfoccurswhenfpequalsfsandisaccompaniedbyamaximuminȴD.

     

ʇ

k

m







a

b

2

Inthecoupledresonatormodel,thefrequencyshiftsanddissipationchangesderivedfromthe QCMͲDcanberelatedinaKelvinͲVoigtmodeltotheviscoelasticityofthebondaccordingto   οˆ ൅ ୧୼ୈ୤౩ ଶ ൌ  ୤ూ୫౦ ஠୞౧ ή  ୮൤ ன౩య൫ன౦మିஓమ൯ିன౩ன౦ర ሺன౩మିன౦మሻమାன౩మஓమ ൅ ‹ ன౩రஓ ሺன౩మିன౦మሻమାன౩మஓమ൨ [1] 

where ȴf (Hz)istheshift inQCMͲDresonance frequency,ȴDis thechangeindissipation,fFisthe

fundamentalresonancefrequencyofthesensor(5MHz),fsistheQCMͲDsensorsurfaceresonance

frequency,mpistheparticlemass(kg),ʘsisthesensorresonanceangularfrequency(ʘs=2ʋfs),ʘpis

theparticleresonanceangularfrequency(ʘp=2ʋfp),ZqistheacousticimpedanceofanATͲcutquartz

crystal(8.8x106_kgmͲ2_sͲ1_),N

pisthenumberofadheringparticlesperunitsensorarea(m2),ɶequals

ʇ/mpwithʇbeingthedragcoefficient(seeFigure1a),indicativeoftheviscouscomponentofthebond.

The elastic component of the bond follows from ʘp equaling with ට ൗ _୮ . Note that the coupled

resonatormodelasdescribedinEq.1assumescompletecouplingofadheringparticleswiththesensor surface,includingtorsionandsheardeformationofthesensorsurfaceduetoparticleoscillation.23_

Moreover,itisassumedthatthespringanddashpotareindependentfromthefrequencyaccording to the coupled resonance model, which means that the frequency should not be causing any perturbationsoftheadhesivebond.Stillitshouldbenotedthatbondstiffnessesdeterminedusingthe QCMͲDmaybeinfluencedbytheexperimentalconditionofhavingbeendeterminedintheMHzrange. Inthisprotocolpaper,weexplaintheusetheQCMͲDanddataanalysistoobtainelasticities (thespringconstant,k)andviscosities(thedragcoefficient,ʇ)ofthebondofbioticandabioticparticles adhering to sensor surfaces, as calculated with the coupled resonator model. Knowledge of the elasticityandviscosityofthebondthroughwhichcolloidalparticlesadheretosubstratumsurfaceswill assist in a better understanding of the mechanisms of particle adhesion and in developing new strategiestodetachadheringparticlesfromorretainingthemonasurface.         

MATERIALSANDPREPARATORYPROCEDURESAPPLIED Reagentsused  x 1Ͳoctadecanothiol(SigmaͲAldrich,Zwijndrecht,TheNetherlands) x 11ͲmercaptoͲ1Ͳundecanol(SigmaͲAldrich,Zwijndrecht,TheNetherlands) x Ammonia(NH3)(Merck,Darmstadt,Germany) x Calciumchloride(CaCl2)(Merck,Darmstadt,Germany) x Ethanol100%(VWRChemicals,FontenayͲSousͲBois,France) x Hydrogenperoxide(H2O2)(Merck,Darmstadt,Germany) x Ultrapurewater(>18Mɏcm) x Potassiumchloride(KCl)(SigmaͲAldrich,Zwijndrecht,TheNetherlands) x Potassiumphosphate(KH2PO4)(Merck,Darmstadt,Germany) x Sodiumdodecylsulphate(SDS)2%(w/v)(Merck,Darmstadt,Germany) x Silicaparticles(radius0.5ʅm)(Bangslaboratories,Inc.,Fischer,IN,USA) x ToddHewittbroth(THB)(Oxoid,Basingstoke,UK)  Mainequipmentused x Centrifuge(JͲlite,JLA16.250FixedAngleRotor,BeckmanCoulter,CA,USA) x Sonicatorbath(TranssonicTP640,ElmaGmbH&CoSingen,Germany) x Sonicator(VibraCellmodel375:Sonicaandmaterials,DanburyCT,USA) x UV/Ozone(BioforceNanosciences,SloughBerkshire,UnitedKingdom)

x Quartz Crystal Microbalance with Dissipation Monitoring (QCMͲD) E1 system (QͲSense AB, Stockholm,Sweden)

x CCDcamera(ModelA101,Baslervisiontechnologies,Ahrensburg,Germany)

x Metallurgicalmicroscopewith20xobjective(LeicaDM2500M,Rijkswijk,TheNetherlands) x PeristalticPump(Ismatec,Wertheim,Germany)

x QCMcrystalswithsiliconoxideandgoldcoatings(QͲSenseAB,Stockholm,Sweden)

 NOTE Most QCMͲD systems operate at a fixed driving power to bring the crystal into resonance.Currentlytheimpactofdrivingpowerontheoscillatorybehaviorofparticlesadheringto aQCMͲDcrystalsurfaceisnotknown.



 

Preparatoryproceduresapplied Preparationofbacterialsuspensions.Twodayspriortotheactualadhesionexperiment,makeapreͲ cultureofthebacterialstrain,selectasinglecolonyfromanagarplateandinoculateinto10mlTHB, andincubateat37°C.Twentyfourhourslater,pourthe10mlsolutionofTHBandbacteriaintoa200 mlsolutionofTHB,andgrowat37°Cfor16h,afterwhichharvestingofthebacteriacanbegin.  Harvestthebacteriabycentrifuging(5minat5000g)andbywashingthesuspensionin100 mlbuffer(50mMpotassiumchloride,2mMpotassiumphosphateand1mMcalciumchloride,pH6.8) twotimes,followedbysonicating10mlofbacterialsuspensionthreetimesfor10sat30W,while cooling in an ice bath. Sonication is particularly needed for streptococci as they grow in chains, consideringsinglebacteriaarepreferredformostexperiments.Afterwards,thebacterialsuspension iscentrifuged,andwashedonelasttimein100mlbufferbeforebeingdilutedinthebuffertoafinal concentrationof3x108_{bacteriaperml.} CrucialstepBywashingthebacteriaaftersonication,itisensuredthatfreemoleculesthat mighthavebeenreleasedduringthesonicationareremovedfromthesuspension.Freemolecules yielddirectmasscouplingwhenadsorbingtoaquartzcrystal,givingrisetonegativefrequencyshifts duringparticulateQCMͲDmeasurements,therebyseverelycomplicatingdataanalysis.  Preparationofsilicaparticlesuspensions.Silicaparticleswitharadiusof0.5ʅmwerewashedtwiceby centrifugationin10mlofultrapurewater,anddilutedtoafinalconcentrationof2x108_{particlesper} ml.Forthesilicaparticleadhesionexperiment,asuspensionin50mMKCl,pH6.8wasprepared.  SetͲupoftheQCMͲD.ColloidalparticleadhesionisstudiedunderflowusingaQͲsenseE1window chamber.Foropticalmonitoring,aCCDcameraisconnectedtothemicroscopeinordertofacilitate realͲtimemonitoringofparticleadhesionandtheirenumeration(seeFigure2).TheQCMͲDwindow chamberisdiscͲshaped(diameter14mm)encompassingavolumeofapproximately100ʅlcombined withaninletandoutletarea.Fluidflowisestablishedusingaperistalticpumpandcanbeswitched frombuffertoacolloidalparticlesuspensionbyinsertingtheattachedtubingsintoacontainerwith thedesiredfluid.      

  Figure2.SchematicsoftheQCMͲDsetͲup.ThesetͲupconsistsofaninletandanoutletwheretubings canbeattachedtoleadingdifferentfluidsthroughaperistalticpumpthroughthewindowchamber intoawastecontainer.Inthewindowchamber,aquartzcrystalsensorisplacedbetweenapairof electrodesandbyapplyinganACvoltageovertheelectrodes,thecrystalisbroughttooscillationatits acousticresonancefrequencyfs.Whenthisvoltageisturnedoff,theoscillationdecaysexponentially fromwhichthedissipationcanbedetermined.  METHODSACCORDINGTOPROTOCOL QCMͲDmeasurementprocedure 1.Cleanthequartzcrystalsbasedonsupplier’sinstructions.Goldcoatedcrystalsaregenerallycleaned byimmersionina3:1:1mixtureofultrapurewater,NH3(28%)andH2O2(30%)at70°Cfor10min.Silica

coatedcrystalsmustbecleanedbysubmergingtheminto2%(w/v)sodiumdodecylsulphate(SDS)for 15mininasonicatingbath,followedbysubmersioninultrapurewateralsoinasonicatingbathfor15 min.Asafinalstep,independentofapossiblesurfacecoatingofthecrystals,itisessentialtoremove molecularcontaminantsfromthecrystalsurfacebyputtingtheminanUV/ozoneenvironmentfor15 min.

 Crucial step H2O2 should not be added until the temperature of ultrapure water and NH3

reaches70°CasthereactionbetweenNH3andH2O2requiredforpropercleaningofthequartzcrystals

islesseffectiveatlowertemperature.



2. Freshly cleaned goldͲcoated quartz crystals are hydrophilic by nature, but can simply be made hydrophobicbyleavingthecleanedgoldcrystalsovernightinambientair.Thecrystalmayrequirea further coating to adjust its surface composition and associated physicoͲchemical properties. SelfͲ assembled monolayers (SAMs) for instance, can be applied rendering the gold coated crystals hydrophobicbysubmersingthefreshlycleanedcrystalsintoasolutionof0.001M1Ͳoctadecanethiol orhydrophilicbysubmersingthemintoasolutionof0.001M11ͲmercaptoͲ1Ͳundecanoldissolvedin 100%ethanolfor18h.

 Crucial step During the coating process, it is important in order to obtain a homogeneous coatingonthecrystals,thatthecrystalsareleftinthesolutionforthefull18h,sincethealkylchains needtimetoalignthemselvestogiveahomogeneouscoatingonthesurface.Itisadvisabletoperform somesortofcharacterizationofthecrystalsurfaceinordertoruleoutthatpossibledeviatingresults are due to aberrant properties of the crystal surface. Water contact angle measurements usually suffice to this end, but when more chemical confirmation of the crystals surface composition is required, XͲray Photoelectron Spectroscopy may be considered, amongst other surface chemical analysistechniques.



3.MountthecleanedorcoatedcrystalintheQCMͲD.

Crucial step After mounting of the crystal, it is crucial that the window chamber is not tightenedtoostrongly,sincecrystalsmaybreakduetotheexcessivepressure.



4. Switch on the QCMͲD and controlling software. Adjust the setting to the desired temperature. Throughoutthisprotocol,wehavedoneallourmeasurementsat21°C.  5.Closethewindowchamberandobtainthecrystal’sresonancefrequenciesanddissipationvaluesat thefundamentalfrequencyandobservableovertonesinordertoensurethatthecrystalisingood condition.  CrucialstepThedissipationvalueatthecrystalsfundamentalfrequencyshouldbearound40 x 10Ͳ6_{ or less (oral communication with application specialist, QͲSense, Biolin Scientific AB Västra}

Frölunda,Sweden).Ifthedissipationvaluedeviatesmorethan5x10Ͳ6_{fromthis“normal”value,its} causeshouldfirstbedeterminedbeforecontinuingtheexperiment.Sometimesithelpstoloosenor tightenthescrewsthatholdthecrystalinthewindowchamberinordertoregain“normal”values.In othercasesitmayhelptotaketheentirewindowchamberapartandremountthecrystal.Ifnothing helps,thecrystalhastobereplaced. 

6.ConnectthetubingstotheQCMͲDchamberandstarttheperistalticpumptointroduceaflow(300 ʅl/min)ofbufferthroughtheQCMͲDwindowchamber.

Crucial step It is crucial to ensure that filling of the system is done free of air bubbles. Air bubblescanbepreventedbytiltingthewindowchamberduringfillingwithbuffer,therebyallowing thebuffertoslowlyrunintothechamberanddisplaceallair.Incaseairbubblesareformed,theycan oftenberemovedbyincreasingthespeedofthefluidflowtoforcethebubblesoutofthesystem.Itis alsopossibletodeͲaeratethebuffersbysonicationpriortousingthemintheexperiment.Airbubbles canspecificallyarisewhenworkingwithcrystalscoatedwithahydrophobiccoating.  7.Findresonancefrequenciesanddissipationvaluesofthesensorcrystalinbufferbylettingthebuffer flow through the system until the frequency is stabilized, typically requiring approximately 5 min. Stabilityisacceptedwhenthedriftinfrequencyshiftsforallobservableovertonesislessthan2Hzper 10min. CrucialstepItisadvisedtosetupalogͲjournalofcrystalresonancefrequenciesanddissipation valuesinbufferaswellasinairtodefine“normal”valuesinbothmediaforthespecificusemade. Afterfillingthechamberwithbuffer,dissipationvaluesusuallyincrease,butthisincreaseshouldnever bemorethantenͲfold(oralcommunicationwithapplicationspecialist,QͲSense,BiolinScientificAB Västra Frölunda, Sweden). Aberrant resonance frequencies and dissipation values after filling the chamberwithbuffercanbeduetothepresenceofminorairbubblesinthechamber.

 

8. Introduce the suspension containing either biotic or abiotic particles, typically at particle concentrations of around 108_{particles per ml. Particle adhesion proceeds at a speed that mainly}

dependsontheirsedimentationinsuspensionandisusuallyfasterforparticleswithahigherspecific density.Asurfacedensityof1010_{particlesadheringperm}2_{shouldbeaimedfor,yieldingasurface}

coverageformicronͲsizedcolloidalparticlesthatpreventsthemfromtouchingeachother.Particle adhesionshouldbemonitoredusingthemicroscopemountedCCDcamera.Followingtheappropriate adhesiontime,thenumberofadheringparticlesmustbedeterminedusingimageanalysissoftware, whichcanbeeasilywrittenusingtheMatlabplatform.Appropriateprogramsforbiologicalanalysis canalsobedownloadedforfreefromtheinternet,suchasImageJ,CellProfilerandFiji.24_  CrucialstepInordertocountthenumberofadheringcolloidalparticlesproperlyusingthe CCDcamera,itisimportantthatbufferisrunningthroughthesysteminordertoremoveanynonͲ adhering particles from the chamber and prevent them from intervening with the enumeration of adhering ones. Alternatively for kinetic analysis of particle adhesion during flow with a particle suspension,imageanalysissoftwarethatfiltersoutparticlesthatchangepositionalongwiththefluid flowshouldbeuse.25_

9. The frequency shifts and dissipation changes are retrieved from the QCMͲD at the crystals fundamentalfrequencyanditsovertones,andaresubsequentlyusedinEq.1.Forthepurposeoflater fittingitisadvantageoustoconvertdissipationchanges(ȴD)intoȴȳvalues((ȴDfs)/2),thatisthehalf bandwidthathalfheight(“bandwidth”)oftheresonancecurve.26_{Thesedataarethenusedtofitthe} parametersoccurringinEq.1usingabruteforcefittingprograminFortran90(seeSupplementary Material)toderivevaluesforthespringconstantkthedragcoefficient,ʇ,theparticlemassmp,and thequalityofthefitortheRootMeanSquaredDeviation(RMSD). CrucialstepThenumberofdatapointsthatcanbeobtainedperexperimentisrestrictedby thenumberofovertonesthatcanbeobserved.Withtheinstrumentusedinourstudies,amaximum ofsevendatapointsforȴfandȴȳasafunctionofthecrystalsresonancefrequencycanbeobtainedin eachexperiment.Thisisnotnecessarilyenoughtoreliablycalculatealloutputparameterssincethe iterative numerical procedure can easily get trapped in local minima yielding physically unrealistic results,mostnoticeablyfortheparticlemassandoutputdatashouldbecriticallyevaluatedforbeing physicallyrealistic.Forvalidationoftheoutput,wesuggesttocomparethemassderivedfromthe QCMͲDoutputwiththeparticlemasscalculatedfromitsdimensionsandspecificdensity.  ANALYSISOFBRUTEFORCEFITTINGOFQCMͲDTOACOUPLEDRESONATORMODEL GiventhatonlysevenvaluesofȴfandȴDareavailableandthat,also,thescatterinthedata isfrequentlyconsiderable,itisessentialtodeviseafittingalgorithm,whichisrobusttoavoidphysically unrealisticresults.AbruteforcealgorithmisagenericproblemͲsolvingalgorithminwhichallpossible data points are employed to obtain the best fitting parameters, while checking whether each fit satisfiestheproblem'sstatement.Byimplementingthisbruteforcetechnique,physicallyunrealistic, erroneousoutputispreventedduetosolutionsgettingtrappedinlocalminimaofthefittingalgorithm. The algorithm achieves robustness by defining the lower and upper bound of the three output parametersi.e.mp,kandʇandthenthealgorithmdefinesagridofchoicesforparameters(typically

100x100x100parametercombinations)andsearchestheglobalminimumoftherootͲmeanͲsquared deviationbetweenthedataandthefit.Careshouldbetakenhowever,thatfittedparametersdonot hittheboundariesinstalledandwheneverthisisthecase,boundariesshouldbewidened.

 To demonstrate advantages and disadvantages of using seven data points of, for instance, triplicateexperimentsinseparatebruteforcefitsversustheuseofall21datapointsinonebruteforce fitforthederivationofthespringconstantk,thedragcoefficientʇandtheparticlemassmpfromthe

QCMͲDoutput,wefirstlypresentresultsfromtriplicateexperimentswithseparatebacterialcultures eachcomprisingsevendatapoints.Inthespecificexamplechosen(seeFigures3aͲcandTable1)we aimed to analyze the properties of the bond between a streptococcal bacterium, Streptococcus salivarius HB7 possessing 91 nm long fibrillar surface appendages, and a hydrophobic SAM on the

crystalsensorsurface.ResultsoffittingthethreeparametersoccurringinEq.1tothedatapointsin eachofthethreeexperimentscanbeseeninFigures3aͲc,whileresultingoutputparametersincluding therootmeansquaredeviation(RMSD)valuesdescribingthequalityofthefitsarepresentedinTable 1.Onaverage,physicallyrealisticresultsareobtainedwiththeaverageparticlemass(theonlyoutput parameterthatcanbecomparedwithanexpectedvalueascanbefoundintheliterature)coinciding wellwiththeonebasedonparticledimensionsandspecificdensity(5x10Ͳ16_{kg).Qualitiesofthefit} arevariableacrossthethreeexperimentsthough.Next,all21datapointsweresubjectedtoasingle bruteforceanalysis(seeFigure3dandTable1),yieldingnearlyidenticalresultsforthespringconstant, dragcoefficientandparticlemassasobtainedafteraveragingthethreedatasetscomprisingseven datapoints.Thustherearenooverridingargumentstoeitherusesevendatapointsfrommultiple experimentsinseparatebruteforcefitsversustheuseofalldatacombinedinonebruteforcefit,else thanthatfitting21pointsdirectlyyieldsanRMSDvalue,oppositetoaveragingthreeindividualfits.           Figure3.Comparisonofusingsevendatapointsoftriplicateexperimentsinseparatebruteforcefits (Figs.3aͲc)versustheuseof21datapointsinonebruteforcefit(Fig.3d)forthederivationofthe spring constant k, the drag coefficient ʇ and the particle mass mp from the QCMͲD output for S.

salivariusHB7adheringonahydrophobicSAMonthecrystalsensorsurface.

Notethatin previousstudiesQCMͲD dataand fittingwerepresentedinsoͲcalledpolarplotsofȴf versus ȴȳ,27_{ we prefer to present both ȴf and ȴȳ versus f as two separate functions, the blue line}

representingȴfandtheredlinerepresentingȴȳasafunctionofthesensorresonancefrequency  c

a

b

c

d

2

Table1.Valuesforthespringconstantk,dragcoefficientʇandmassoftheparticlesmpobtainedusing sevendatapointsoftriplicateexperimentsinseparatebruteforcefits(seealsoFigs.3aͲc)versusthe useof21datapointsinonebruteforcefit(seeFig.3d)inaKelvinͲVoigtmodel.RMSDindicatesthe qualityofthebruteforcefit. S.salivariusHB7 onahydrophobicSAM k(kg/s2_{) Ɍ(10}Ǧ9_kg/s) m_p(10Ǧ16kg) RMSD (Hz) š’‡”‹‡–ͳǡ •‡˜‡†ƒ–ƒ’‘‹–• ͲǤʹͶ ͸ ͷ ʹ͵ š’‡”‹‡–ʹǡ •‡˜‡†ƒ–ƒ’‘‹–• ͲǤͶͺ ͳʹ ͺ ͹ʹ š’‡”‹‡–͵ǡ •‡˜‡†ƒ–ƒ’‘‹–• ͲǤ͵ͷ ͳͳ ͸ ʹͲ ˜‡”ƒ‰‡†‘ˆ‡š’‡”‹‡–ͳǦ ͵ ‘—–’—–’ƒ”ƒ‡–‡”• ͲǤ͵͸άͲǤͳʹ ͳͲά͵ ͸άʹ Ǧ š’‡”‹‡–•ͳǦ͵…‘–ƒ‹‹‰ ʹͳ†ƒ–ƒ’‘‹–• ͲǤ͵͸ ͳͲ ͹ Ͷʹ  TheassumptionunderlyingEq.1thatalladheringparticlescouplecompletelywiththesensor surface to cause torsion and shear deformation is not necessarily true, which reflects in minor deviationsoftheparticlemassderivedfromthetrueparticlemass.23_{Anotherassumptionunderlying}

Eq.1isthatalladheringparticlespossessidenticalsizeandshape.Polydispersityhowever,maygive rise to a distribution in angular particle frequency,20,23_{ that can be accounted for by adding a}

polydispersityparametertoEq.1.Althoughthismayincreasethequalityofthefit,andpossiblyavoid overlysmallspringconstantsasobservedforsilicaparticlesonsilicacrystalsurfacesandbiotinylated crystalsurfaces(seeTable2),fittingoffourparameterstoacomplicatedequationasEq.1withonlya limitednumberofdiscretedatapointbearstheriskofyieldingphysicallyunrealisticvalues.  DURATIONOFEXPERIMENT Inthisestimateofthetimerequiredforexperiments,weneglectthetimetoprepareparticle suspensions, as preparation of biotic particle suspensions usually requires much more time due to culturingthanabioticparticlessuspensions,especiallywhencommerciallypurchased.Onceaparticle suspensionhasbeenprepared,atypicalQCMͲDexperimentasdescribedabove,shouldnottakemore than4htoperform.Bruteforcefittingofthedatacanbedonewithin30minaftermeasurements. 

EXPECTEDRESULTS Allquantitativepropertiesoftheadhesivebondreportedinthissectionhavebeenobtained byfittingk,ʇ,andmp,asoccurringinEq.1totheQCMͲDfrequencyshiftsanddissipationchangesat theobservablefrequenciesusingabruteforcefittingalgorithmandusingalldatapointsavailableina singlefitwithoutaveragingdataobtainedinseparateexperimentsatthesamefrequency.Figure4 depictsthefittoEq.1ofexperimentaldataforabioticsilicaparticlesandsilicaparticlescoatedwith streptavidin,adheringtoasilicasensorcrystalorasilicasensorcoatedwithbiotinylatedpolyethylene glycol(PEG)alkanethiol.Visualinspectionofthegraphsshowsagoodfittothedatapoints.        

Figure4. ȴf and ȴȳ versusfsforabioticsilicaparticlesandsilicaparticles coatedwithstreptavidin,

adheringtoasilicasensorcrystalorasilicasensorcoatedwithabiotinylatedPEGalkanethiol. a)silicaparticlesonasilicacrystal b)silicaparticlesonabiotinylatedPEGalkanethiolcoatedsilicacrystal c)streptavidincoatedsilicaparticlesonbiotinylatedPEGalkanethiolcoatedsilicacrystal.  GoodqualityofthefitisconfirmedbytherelativelylowRMSDvaluesofthefitssummarized in Table 2, with the exception of the fit for the experiments comprising streptavidin coated silica particlesonbiotinylatedPEGalkanethiolcoatedsilicacrystal.Valuesforkandʇreflecttheinfluence ofanadsorbedproteinfilmonthecrystalsurfaceversusabarecrystalsurfaceontheadhesivebond properties(higherdragcoefficient)aswellastheimpactofspecificligandͲreceptorbindingversusnonͲ specificbinding(higherspringconstantsanddragcoefficients).Importantly,althoughvaluesforthe particlemassmpobtainedvaryoverafactorofthree(seealsoTable2),theyareofthesameorderof magnitudeasexpectedfor1μmdiametersilicaparticles(14x10Ͳ16_kg).  

a

b

c

2

Table2.Springconstantsk,dragcoefficientsʇandmassesofabioticandbioticparticles,mp, adheringtovariouscrystalsurfaces,includingtheRMSDindicatingthequalityofthebruteforcefitto theQCMͲDoutput._ k(kg/s2_{) Ɍ(10}Ǧ9_kgsǦ1) m_p(10Ǧ16kg) RMSD(Hz) Abioticparticles:silicaparticles ‹Ž‹…ƒ’ƒ”–‹…Ž‡•Ǧ•‹Ž‹…ƒ …”›•–ƒŽ•—”ˆƒ…‡ Ͳ ͳ͸ ͳ͵ ͳͺ ‹Ž‹…ƒ’ƒ”–‹…Ž‡•Ǧ„‹‘–‹›Žƒ–‡† …”›•–ƒŽ•—”ˆƒ…‡ Ͳ ͳͲʹ Ͷ ͳͺ –”‡’–ƒ˜‹†‹…‘ƒ–‡† ’ƒ”–‹…Ž‡•Ǧ„‹‘–‹›Žƒ–‡† …”›•–ƒŽ•—”ˆƒ…‡ ͲǤͲͺ ʹ͹ͻ ͸ ͹ͺ Bioticparticles:S.salivariusHB7 ƒŠ›†”‘’Š‘„‹…— •—”ˆƒ…‡ ͲǤʹͳ ͳͲ ͹ ͳͻ ƒŠ›†”‘’Š‘„‹… ͲǤ͵ͷ ͳͲ ͸ Ͷʹ ƒŠ›†”‘’Š‹Ž‹… ͲǤʹ͵ ͷ ͷ ͺͻ  Table2alsoillustratestheanticipatedresultsfortheadhesionofS.salivariusHB7adheringto differentcrystalsurfaces.Mostnoticeably,springconstantskofthestreptococcalbondsarehigher thanforabioticsilicaparticleswithlittleinfluenceofthecrystalsurfaceproperties.Thedragcoefficient ʇhowever,isordersofmagnitudesmallerthanforabioticsilicaparticles,indicatingthatlowerfriction lossesduetooscillationsasaresultofthelowerweightanddensityofthebioticparticles.Notethat inallcases,thebacterialmassmpobtainedinthefitmatchesverywellwiththemassexpectedfor bacteria(5x10Ͳ16_kg). Insummary,theproposedprotocolinvolvestheuseofacoupledresonatormodeltoobtain valuesforthespringconstantanddragcoefficientofthebondbetweenadheringbioticandabiotic particlesonQCMͲDcrystalsurfacesaswellastheirmasses.Thesethreeoutputparametersarefitted totheQCMͲDoutputȴfandȴȳasafunctionofthecrystalsresonancefrequencieswithinthewindow ofobservablefrequencies.KnowledgeofthebondpropertiesinparticularadhesiontoasolidͲliquid interfaceallowsbetterunderstandingonhowtoinfluenceparticleadhesionanddetachment.   

FUTUREPROSPECTS

QCMͲD data analysis for particle adhesion is neither trivial nor beyond dispute. Other viscoelastic modelsthan the KelvinͲVoigt modelimplementedinEq.1,such asthe Maxwellmodel (springanddashpotplacedinseries)mightimprovethequalityofthefitandyieldlowerRMSDvalues (D.Johannsmann,privatecommunication).Asmost“oneͲbyͲone”methodstoderiveviscoelasticbond properties indicate large standard deviations over individual particles, inclusion of a polydispersity parameterinEq.1isalsoworthwhiletoattemptinordertoimprovethequalityoffitting.Finally,as molecularadsorptionofbacterialbiͲproductssuchaspolysaccharides,proteinsandDNAishardto avoid,analysesofcombinedmolecularadsorptionandresonatorcouplingbyintroducinganoffsetin frequencyanddissipationinEq.1todifferentiatebetweenmolecularadsorptionandmassͲcoupling mightincreasetheeaseofuseofQCMͲDpreparatorystepsforbacterialadhesionstudies.  ACKNOWLEDGEMENTS ThisworkwassupportedbytheUniversityMedicalCenterGroningen,TheNetherlands.  COMPETINGFINANCIALINTERESTS HJBisalsodirectorofaconsultingcompany,SASABV(GNSchutterlaan4,9797PCThesinge, TheNetherlands).Theauthorsdeclarenopotentialconflictsofinterestwithrespecttoauthorship and/orpublicationofthisarticle.Opinionsandassertionscontainedhereinarethoseoftheauthors andarenotconstruedasnecessarilyrepresentingviewsoftheirrespectiveemployers  Supplementarymaterial ThebruteforcefittingprogramoftheQCMͲDoutputcanbefoundinthesupplementary information.           

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