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
3
Elastic and Viscous Bond Components in
the Adhesion of Colloidal Particles and
Fibrillated Streptococci to QCM-D Crystal
Surfaces with Different Hydrophobicities
using Kelvin-Voigt and Maxwell models
This chapter is published with permission from Royal Society of Chemistry:
Rebecca van der Westen, Prashant K. Sharma, Hans De Raedt, IJsbrand Vermue, Henny C. van der Mei and Henk J. Busscher1
ABSTRACT
QuartzͲcrystalͲmicrobalance with dissipation (QCMͲD) can measure molecular mass adsorptionaswellasregisteradhesionofcolloidalparticles.However,analysisofQCMͲDoutputto quantitativelyanalyzeadhesionof(bio)colloidstoobtainviscoelasticbondpropertiesisstillsubjectof debate. Here, we analyze the QCMͲD output to analyze the bond between two hydrophilic streptococcal strains with 91Ͳnm long and without fibrillar surface appendages and micronͲsized hydrophobic polystyrene particles on QCMͲD crystal surfaces with different hydrophobicities, comparingtheKelvinͲVoigtandMaxwellmodel.APoissondistributionwasimplementedinorderto determine possible virtues of including polydispersity when fitting model parameters to the data. QualityofthefitsdidnotindicatewhethertheKelvinͲVoigtorMaxwellmodelispreferentialandonly polydispersityinspringͲconstantsimprovedthefitforpolystyreneparticles.KelvinͲVoigtandMaxwell modelsbothyieldedhigherspringͲconstantsforthebaldstreptococcusthanforthefibrillatedone.In both models, the drag coefficients increased for the bald streptococcus with the ratio of electronͲ donatingoverelectronͲacceptingparametersofthecrystalsurface,whileforthefibrillatedstrainthe drag coefficient was similar on all crystal surfaces. Combined with the propensity of fibrillated streptococci to bind to the sensor crystal as a coupledͲresonator above the crystal surface, this suggeststhatdragexperiencedbyresonatorͲcoupled,hydrophilicparticlesismoreinfluencedbythe viscosity of the bulk water than by interfacial water adjacent to the crystal surface. Hydrophilic particlesthatlackasurfacetetheraremassͲcoupledjustabovethecrystalsurfaceandaccordingly probeadragduethethinlayerofinterfacialwaterthatisdifferentlystructuredonhydrophobicand hydrophilicsurfaces.HydrophobicparticleswithoutasurfacetetherarealsomassͲcoupled,buttheir dragcoefficientdecreaseswhentheratioofelectronͲdonatingoverelectronͲacceptingparameters increases,suggestingthathydrophobicparticlesexperiencelessdragbystructuredwateradjacentto asurface.
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INTRODUCTION
The bond between colloidal particles adhering to a substratum surface is often considered rigid,butinrealityconsistsofanelasticandaviscouscomponent,whichisespeciallythecasewhen workingwithbioͲcolloids,likebacteria.1Bacteriacanbindtosurfacesthroughavarietyofdifferent surfaceappendagessuchasfibrilsandfimbriaeofvariouslengths,2addingtotheviscoelasticityofthe bond.TheviscoelasticnatureofthebacteriumͲsubstratumbondcanbedescribedbycombinationsof alinearlyresponding3,4springandadashpot,inwhichthespringrepresentstheelasticityofthetether and the dashpot represents the viscous drag. Spring and dashpot can either be placed in parallel (KelvinͲVoigtmodel,seeFigure1a)orinseries(Maxwellmodel,seeFigure1b).Thedashpotslows downtheresponsespeed,generallyreferredtoasdamping.5Viscoelasticityofbacterialbindinghas beendescribedasameanstoallowbacteriamoretimetoreactinanappropriatewaytocatastrophic events,suchasremovalforcesorchemicalattack.5,6 Theresponsekineticsofadheringbacteriatoanappliedstressdiffersconsiderablywhenthe dashpotisplacedinparallelwiththespring(Figure1a),dampinganyspringresponseorwhenboth elementsareplacedinseries(Figure1b),allowinganimmediatespringresponsefollowedbyadelayed responseduetothedashpot.7Theviscoelasticresponseofadheringsinglebacteriaunderstresshas been studied using Atomic Force Microscopy (AFM) and modeled to a one component Maxwell element.1,8,9Bacterialinhabitantsinabiofilmadheretoasubstratumsurfaceandtoeachotherand their stress response to low load compression10,11 has been modeled using a series of Maxwell elementsinparallel.AnalysisofBrownianmotioninducednanoscopicvibrationsofsinglebacteria12 andabiotic particles13,14adheringtosubstratumsurfacescanalsoyieldspringconstants ofbinding tethers,butsimilartoAFMandopticaltweezerͲanalyses15yieldsdatathatareaccompaniedbylarge standarddeviations.Thissuggestsapolydispersityofthebindingtethercharacteristics.Atthesame time,theviscoelasticresponseofadheringbacteriaorabioticparticlesobtainedemployingaQuartz CrystalMicrobalancewithDissipation(QCMͲD)hasbeenfittedwithaphenomenologicalKelvinͲVoigt16 orMaxwellmodel.4
The aim of this study is to compare the use of KelvinͲVoigt or Maxwell coupled resonator models in the analysis of the QCMͲD response to adhesion of a fibrillated and nonͲfibrillated streptococcalstrain.Abioticpolystyreneparticleshavebeenincludedforcomparison,whileQCMͲD crystalsurfaceshavebeenappliedpossessingdifferenthydrophobicitiestodeterminewhethereither ofthetwomodelswouldbebetterapplicableforparticlesadheringonahydrophobicorhydrophilic surface. In addition, possible advantages of extending either phenomenological model with a polydispersityindexareexplored.
BACKGROUNDONQCMͲDANALYSIS
QCMͲDiswidelyusedinmolecularadsorption.Pertheconventionalmassloadingtheory,17 the adsorbed mass couples directly to the sensor surface (an ATͲcut quartz crystal) increasing its effectivemass,reducingitsresonancefrequencyandleadingtonegativeshiftsinresonancefrequency (ȴf).Massloadingismostlyobservedwhenmolecularlayersadheringtothesensorsurfacearethinner than250nm.Theviscoelasticpropertiesofthebondbetweenanadheringmassandasubstratum surfaceintheQCMͲDcancausedissipation(ȴD).Incontrasttomolecularadsorption,colloidalparticles adhere to the sensor surface via a tethered, nonͲrigid bond, causing positive frequency shifts, as schematicallyoutlinedinFigure1c.18–20Positivefrequencyshiftscanbeexplained18assumingadhering particles and the QCMͲD crystal sensor act as coupled resonators.16,21,22 The maximal energy dissipationchange(ȴD)occurswhentheparticleresonancefrequency(fp)matchesthecrystalsensor resonance frequency (fs). Moreover, the QCMͲD can identify a zeroͲvalue in sensor resonance frequencyshift(ȴfs)whenparticleandthecrystalsensorresonancefrequenciesmatch,referredtoas thefrequencyofzeroͲcrossing(fZC)(seeFigure1c).Zerocrossingfrequenciescanonlybeobserved whenoccurringwithintherangeofthesensorcrystalresonancefrequencyanditsovertones,usually between5and65MHz(seealsoFigure1c).
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Figure1.a,b)Mechanicalequivalentcircuitrepresentingaparticlewithmass,mptetheredtoa surfaceviaaviscoelasticbondcontainingaspringwithspringconstant(k)andadashpotwithadrag coefficient(ʇ)inparallel(a:KelvinͲVoigtmodel)andinseries(b:Maxwellmodel). c)SchematicpresentationoftheshiftsinresonancefrequencyanddissipationinQCMͲDasafunction
of the crystal resonance frequency in a coupled resonator model according to KelvinͲVoigt. The frequencyofzerocrossingischosenwithintheobservablewindowofthesensorresonancefrequency anditsovertonesatwhichtheresonancefrequenciesofthecrystal(fs)andoftheadheringparticles (theparticleresonancefrequencyfp,takenhereas30Hz)match.Inputparametersforthegeneration ofthisgraphaccordingtoEq1:fF=5MHz,mp=3x10Ͳ16kg,ʘp=2ʋx30Hz,ʘs=2ʋxfs,wherefsisin therangebetween5and65MHz,Zq=8.8x106kgmͲ2sͲ1),Np=1.1x1010mͲ2).Note:ȴȳinFigure1cis relatedtodissipationaccordingtoȴȳ=ȴDxfs/2(seedataanalysissection).
Theelasticandviscouscontributionstothebondcanbeevaluatedbyassumingthebondto beeitherKelvinͲVoigtorMaxwellinnature(Figure1aorb)accordingtoEqs.116or2,4,7respectively
[1] ο݂ οೞ ଶ ൌ ಷே గ ή ݅߱௦݉ ଵ ଵିഘೞమ ഘమା ഘ ം [2]
whereȴDistheshiftindissipation,fFisthefundamentalfrequencyofthecrystal(5MHz),mpisthe inertialmass ofthe particleinkg, ʘpistheresonanceangularfrequencyforthe particle,ʘsisthe sensorangularfrequency,ZqistheacousticimpedanceofanATͲcutquartzcrystal(8.8x106kgmͲ2sͲ1),
Npisthenumberofadheringparticlesperunitarea(mͲ2).Eqs.1and2canbesimplyderivedusingthe basicQCMͲDequationandinsertingthemechanicalanaloguesoftheKelvinͲVoigtorMaxwellelement. SincetheQCMͲDisamechanicalsystem,therulesforaddingmechanicalimpedancesdifferfromthe rulesforaddingimpedancesinelectricity:whenmechanicalelementsoperateinparallel,thetotal impedance is additive, opposite to when they operate in series in which case the inverse total impedanceisthesumoftheinverseimpedanceoftheindividualelements.23
ɶ, ʘp and mp can be derived from Eqs. 1 or 2 for both models without accounting for polydispersity, using a bruteͲforce, iterative procedure, as recently described for the KelvinͲVoigt model24 and that can be analogously applied to the Maxwell model. As ʘ
p = ට ൗ ୮ , the spring constantkcanbedirectlycalculated,whilesinceɶ=ʇ/mpthedragcoefficient,ʇimmediatelyfollows. Althoughtheinertialmassmpdoesnotnecessarilyhavetoequalthegravitationalmassoftheparticles, orderofmagnitudematchinghasbeensuggestedforvalidationofphysicallyrealisticresultsofthe bruteͲforce,iterativeprocedure.24 Inordertoaccountforapossiblepolydispersityininertialmass,springconstantanddragͲforce (mp,kandʇ,respectively)assuggestedbythelargestandarddeviationsinAFM,opticaltweezerͲand vibrationanalysesofcolloidalbondcharacteristics,aPoissondistributioncanbeimplementedinto aboveEqs.accordingto25 [3] whereʄindicatesboththemeanandvarianceofthedistributionwherengoesfrom0toN.Inorder toaccountforpolydispersity,Eqs.1and2transformto4 ο݂ ݅߂ܦ ݂ݏ ʹ ൌ ݂ܨ݉ ߨܼݍ ή ܰ ߱ݏ͵൫߱ʹെߛʹ൯െ߱ݏ߱Ͷ ሺ߱ݏʹെ߱ ʹሻʹ߱ ݏ ʹߛʹ ݅ ߱ݏͶߛ ሺ߱ݏʹെ߱ ʹሻʹ߱ ݏ ʹߛʹ൨
ሺ݊ǡ ݔሻ ൌ
ߣ
݊݁
െߣ݊Ǩ
3
߂݂ οೞ ଶ = ಷே గ ሼሺͲǡ ݔሻܩሺ߱௦ǡ ݕǡ ߱ǡ ߛሻ ሼሺͳǡ ݔሻܩሺ߱௦ǡ ݕሺͳ ߜሻǡ ߱ǡ ߛሻ ሼሺʹǡ ݔሻܩሺ߱௦ǡ ݕሺͳ ʹߜሻǡ ߱ǡ ߛሻ ڮሼሺܰǡ ݔሻܩሺ߱௦ǡ ݕሺͳ ܰߜሻǡ ߱ǡ ߛሻሽ [4] whereGcorrespondstoఠሺఠೞయ൫ఠమିఊమ൯ିఠೞఠర ೞ మିఠ మሻమାఠ ೞ మఊమ ݅ ఠೞరఊ ሺఠೞమିఠమሻమାఠೞమఊమ൨forinclusionofpolydispersityinthe KelvinͲVoigtmodel(Eq.1)andto݅߱௦݉ ଵ ଵିഘೞమ ഘమା ഘ ം forinclusionintheMaxwellmodel(Eq2).Inorder toaccountforpolydispersityininertialmass,springconstantordragcoefficient,y0ischosentobe equal to either mp, k or ʇ, respectively, after which Eq. 4 can be used for fitting that accounts for polydispersitiesineitherofthethreeaboveparametersmp,korʇ. EXPERIMENTALSECTION BacterialStrains,CultureConditionsandHarvesting͘StreptococcussalivariusHB7andHBC12 wereusedinthisstudy.BothS.salivariusstrainsarehydrophilic,andnegativelycharged,butthetwo strainsdifferintheirpossessionofsurfaceappendagesusedtotetherthemselvestoasubstratum surface.S.salivariusHB7possesseswellͲcharacterized91nmfibrilsandS.salivariusHBC12isdevoid ofsurfaceappendageswithademonstrablelength.26S.salivariusstrainswerepreͲculturedin10mL ofToddHewittBroth(THB,OXOID,Basingstoke,UK)understaticconditions,grownfor24hat37°C. After 24 h, preͲcultures were inoculated into 200 mL of THB and maintained under their above conditionsforanother16h.Bacteriawereharvestedbycentrifugationat5000gfor5minat10°Cand subsequently washed in 100 mL adhesion buffer (50 mM potassium chloride, 2 mM potassium phosphate,1mMcalciumchloride,pH6.8.).Next,bacteriaweresonicatedonice3timesfor10sat 30W(VibraCellModel375;SonicsandMaterialsInc.,Danbury,CT)tomaximizethenumberofsingle bacteriainsuspension.ImportantlyforQCMͲDexperiments,bacteriawerewashedoncemoreafter sonicationtoremoveanyfreemoleculesthatmighthavebeenreleasedduringsonicationtoprevent molecular mass adsorption to the crystal sensor during bacterial adhesion. Finally, bacteria were diluted to a concentration of 3 x 108 bacteria per mL, as determined by counting in a BürkerͲTürk chamber.
AbioticParticles.Polystyreneparticles(BangLaboratoriesInc.Fishers,IN,US),withadiameter
of1ʅmsimilarasstreptococci,wereemployedinthisstudyin ordertocompareabiotic adhesion
versusbioticparticleadhesion.Priortoexperiments,particleswerewashedtwicebycentrifugationin 10mLultrapurewater,anddilutedtoaconcentrationof2x108particlespermLin50mMKCl.
PreparationofQCMͲDSensorSurfaces.14mmdiameter,goldͲcoatedquartzsensorcrystals (Qsense,Gothenburg,Sweden)werecleanedpriortoeachexperimentbyimmersionina3:1:1mixture ofultrapurewater(specificresistance>18Mɏcm),ammonia(NH3)(Merck,Darmstadt,Germany)and hydrogenperoxide(H2O2)(Merck,Darmstadt,Germany)at70°Cfor15min,followedby15minof UV/Ozonetreatment.ForQCMͲDexperiments,goldͲcoatedsensorcrystalswereleftfor24hinawellͲ plate. ForcoatingtheQCMͲDcrystalsensorswithahydrophobicselfͲassembledmonolayer(SAM), crystalswereleftimmersedin0.001Mof1Ͳoctadecanethioldissolvedin100%ethanolfor18hunder mild shaking to obtain a homogenous coating. To obtain hydrophilic crystal sensors, crystals were immersedin0.0001Mof11ͲmercaptoͲ1Ͳundecanol(SigmaͲAldrich,Zwijndrecht,TheNetherlands)in 100%ethanolundertheaboveconditions.
ContactAngleMeasurements.Contactanglesweremeasuredondifferently coated crystal
surfaceswiththreeliquidspossessingdifferentpolarities(water,formamide,andmethyleneiodide), usingahomemadegoniometer.Thecontactangleswererecordedbyafixedcameraabout5safter placingan0.5μLliquiddropletonacrystalsurface.Threedropletsofeachliquidwererandomlyplaced over one crystal surface, employing three different crystals for each measurement. The droplet contours were detected by greyͲvalue thresholding and contact angles were calculated from the digitizedcontoursusinghomeͲmadesoftware.Contactanglesoneachsurfacewereconvertedtoa LifshitzͲVanderWaals(ɶLW)andacidͲbase(ɶAB)surfacefreeenergycomponent,whiletheacidͲbase componentsweresplitupintoanelectronͲdonating(ɶͲ)andanelectronͲaccepting(ɶ+)parameter27 accordingto
[5]
whereɶLWistheLifshitzͲVanderWaalssurfacefreeenergycomponentandɶͲandɶ+aretheelectronͲ donating and electronͲaccepting surface free energy parameters, respectively of the three liquids appliedorthesolidsurfaceconsidered(seesubscripts).Thetotalsurfacefreeenergyisdenotedasɶ, whileɽrepresentsthecontactangles.
SurfaceRoughnessMeasurementsbyAtomicForceMicroscopy(AFM).Surfaceroughnesses
of the QCMͲD crystal sensors, without coating and with hydrophobic or hydrophilic SAMs were measured using AFM in the contact mode with a silicon nitride cantilever tip (DNP from Bruker,
»» » » » ¼ º « « « « « ¬ ª » » » » ¼ º « « « « ¬ ª » » » » ¼ º « « « « ¬ ª 2 . cos 1 2 . cos 1 2 . cos 1 RGLGH PHWK\OHQHL RGLGH PHWK\OHQHL IRUPDPLGH IRUPDPLGH ZDWHU ZDWHU /: RGLGH PHWK\OHQHL RGLGH PHWK\OHQHL /: RGLGH PHWK\OHQHL IRUPDPLGH IRUPDPLGH /: IRUPDPLGH ZDWHU ZDWHU /: ZDWHU J T J T J T J J J J J J J J J J J J
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Woodbury,NY,USA).Eachcrystalsensorwasimagedatthreerandomlychosenlocationsonthecrystal surfaceandsurfaceplotsweregeneratedinordertoobtainathreeͲdimensionalperspectiveofthe surface,fromwhichthesurfaceroughness(Ra)wascalculated(seeTable1).
QCMͲD. All QCMͲD experiments were carried out at room temperature using a windowͲ
equippedchamber(E1,Qsense,Gothenburg,Sweden).Thewindowchambercontainingthesensor crystalwasmountedunderneathamicroscope(LeicaDM2500M,Rijswijk,TheNetherlands)equipped withaCCDcamera(ModelA101,Baslervisiontechnologies,Ahrensburg,Germany),enablingrealͲtime monitoringofparticulateadhesionontheQCMͲDsensorsurface.Frequencyanddissipationshiftsat 7differentsensorfrequencies(5,15,25,35,45,55and65MHz)wereacquired.Priortoparticulate adhesionintheQCMͲD,bufferwasperfusedthroughthechamberataflowrateof300ʅLminͲ1until asteadybaseline(variationsinȴflessthan2MHzover5Ͳ10min)wasobtained. Followingthis,aparticulatesuspensionwasperfusedthroughthechamberataflowrateof 300ʅLminͲ1for1h.Subsequently,bufferwasperfusedagaintoremovetheparticulatesuspension fromtheQCMͲDchamber,followedbythedeterminationofthenumberofadheringparticlesperunit area.
Data Analysis. The frequency and dissipation shifts were retrieved from the QCMͲD, as
illustratedinFigure2,andconvertedintoȴfandȴȳ,withȴȳ=ȴDxfs/2.Thesevalueswerethenused tofitthedatanonͲlinearlytoEqs.1(KelvinͲVoigtmodel)or2(Maxwellmodel),usingabruteͲforce, iterativealgorithm,writteninPython,toobtainparametersvaluesforthespringconstant(k),dashpot (ʇ),massoftheparticle(mp),andtherootmeansquaredeviation(RMSD)oftheresultingfitvizaviz themeasureddata.24DatapresentedarethoseyieldingthelowestRMSD.Asimilariterativealgorithm wasalsousedtosolveEq.4astheextendedformofEqs.1and2accountingforapolydispersityindex ʄfortheinertialmass,springconstantanddragforce(Eqs.3and4)settingʄto0(nopolydispersity), 2,5or7(highpolydispersity).PolydispersityindicespresentedarethoseyieldingthelowestRMSD. RESULTS
Hydrophobicities of the QCMͲD crystal surfaces were varied by the application of a hydrophobicandhydrophilicSAM,yieldingawidevariationinwatercontactanglerangingfrom17to 90degrees,includingthegoldͲcoatedcrystalwithawatercontactangleof54degrees(seeTable1). Water contact angles are not sufficient to characterize surface hydrophobicity however, since hydrophobicityisdueeithertolowelectronͲdonatingorlowelectronͲacceptingsurfacefreeenergy parameters,ascanbecalculatedfromthecontactangleswiththreeliquids,asalsopresentedinTable 1.WhereasLifshitzͲVanderWaalssurfacefreeenergycomponentsofallthreesurfacesarefairlyhigh, only the hydrophobic SAM demonstrates a zero acidͲbase surface free energy component. The absenceofanacidͲbasesurfacefreeenergycomponentisduetoazeroelectronͲdonatingandelectron
accepting parameter of the hydrophobic SAM, opposite to the goldͲcoated crystal surface and the hydrophilic SAM, possessing both nonͲzero electronͲdonating and electronͲaccepting surface free energy parameters.Accordingly, theratioofelectronͲdonating overelectronͲacceptingparameters varieswidelyacrossthethreesurfaces(seealsoTable1),indicativeofdifferentstructuringofwater molecules adjacent to the surface.28 All crystal surfaces employed were extremely smooth in the nanoscale region, although the hydrophilic SAM layer demonstrated a less rough surface than the hydrophobicone(seealsoTable1).
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Table1Watercontactangles,surfacefreeenergycomponentsandparameterstogetherwithsurface roughnessesofQCMͲDcrystalsurfaceswithahydrophobicorhydrophilicSAMcoating.Datarepresent averageswithstandarddeviationsoverthreedropletsonthreedifferentcrystals. Crystalwith hydrophobicSAM GoldͲcoatedcrystal Crystalwith hydrophilicSAM CONTACTANGLES(degrees) Water 90±7 54±3 17±5 Formamide 27±7 17±1 0±0 Methyleneiodide 48±10 37±4 38±8 SURFACEFREEENERGYCOMPONENTSANDPARAMETERS(10Ͳ3JmͲ2) ɶ 35±6 55±2 58±0 ɶLW 35±6 41±2 40±4 ɶAB 0±0 13±0 17±7 ɶͲ 0±0 15±2 49±3 ɶ+ 11±5 3±1 2±1 ɶͲ/ɶ+ 0±0 5±2 25±2 SURFACEROUGHNESSBYAFM(nm) Ra 3.0±0.4 3.4±0.3 1.7±0.1
Table2presentsthenumberofbacteriaandpolystyreneparticlesthatadheredtothecrystal surfacesafter1hofperfusingtheQCMͲDchamberwithaparticlesuspension.Numberswereallinthe order of 1010 mͲ2, representing a surface coverage of around 1Ͳ10%, sufficiently low to avoid interactionsbetweenadheringparticlesduringcrystaloscillation.Thefibrillatedstreptococcalstrain S.salivariusHB7adheredinsimilarnumberstoallthreecrystalsurfaces.Thebaldstrain,S.salivarius HBC12,adheredequallywelltothecrystalsurfacesasdidS.salivariusHB7,withtheexceptionofthe hydrophilicSAMcoatedcrystaltowhichitadheredintwoͲfoldlowernumbersthantotheothercrystal surfaces.Polystyreneparticlesadheredinsimilarnumbertoallcrystalsurfaces,comparablewiththe numberinwhichthebaldstreptococcalstrainadheredtothehydrophiliccrystalsurface. Table2Thenumberofadheringstreptococciandpolystyreneparticlesperunitarea(NpmͲ2)oncrystal surfaceswithdifferenthydrophobicities.Datarepresentsaverageswithstandarddeviationsoverthree separateexperiments,withseparatelygrownbacterialculturesanddifferentlypreparedsuspension. Biocolloidsandcolloids Crystalsurface Np(x1010mͲ2) S.salivariusHB7 HydrophobicSAM 4.1±0.6 GoldͲcoatedcrystal 3.5±0.4 HydrophilicSAM 4.2±1.3 S.salivariusHBC12 HydrophobicSAM 3.8±1.4 GoldͲcoatedcrystal 3.4±0.4 HydrophilicSAM 2.0±0.7 Polystyreneparticles HydrophobicSAM 1.8±0.7 GoldͲcoatedcrystal 1.0±0.2 Hydrophilic 2.0±0.3 AnexampleoftherawQCMͲDdataasafunctionoftimeispresentedinFigure2forS.salivarius HB7adheringtoahydrophobicSAMcoatedcrystal.Frequencyaswellasdissipationshiftsvaryover timeandwiththeovertonefrequency.DatasuchaspresentedinFigure2andTable2,wereinserted inphenomenologicalKelvinͲVoigtandMaxwellmodels,withandwithoutaccountingforpolydispersity intheforthcomingpartsoftheResultssection.
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Figure2.Exampleofthechangesinfrequencya),anddissipationb)asafunctionoftimeduring adhesionofS.salivariusHB7onhydrophobicSAM.f1tof13(apanel)andD1toD13(bpanel) correspondtothedifferentovertonesfrequenciesrangingfrom5to65MHz.Notedatapointsmay beoverlapping. Figures3,4and5showexamplesofthebestfitsofKelvinͲVoigtandMaxwellparametersfor
S. salivarius HB7, S. salivarius HBC12 and polystyrene particles under the experimental conditions
specified,respectively,whileTables3and4summarizetheresultingparametersafterfittingtheQCMͲ DoutputforstreptococcalandpolystyreneparticleadhesiontotheKelvinͲVoigtorMaxwellmodel, respectively.
Figure 3. Examples of the QCMͲD responses, ȴf and ȴȳ for adhesion of S. salivarius HB7 to a
hydrophobic SAMͲcoated crystal surface as a function of the sensor frequency in absence of a polydispersityindexfora)theKelvinͲVoigtmodelandb)theMaxwellmodel. Ͳ20 Ͳ15 Ͳ10 Ͳ5 0 5 10 15 20 0 20 40 60 80 100 120 ȴ f(Hz ) Time(min) f1 f3 f5 f7 f9 f11 f13 a
Buffer Bacteria Rinsing Endofexperiment
b 0 20 40 60 80 100 0 20 40 60 80 100 120 D (x1 0 6) Time(min) D1 D3 D5 D7 D9 D11 D13 Buffer Bacteria Rinsing Endofexperiment
Figure 4. Examples of the QCMͲD responses, ȴf and ȴȳ for adhesion of S. salivarius HBC12 to a
hydrophobic SAMͲcoated crystal surface as a function of the sensor frequency in absence of a polydispersityindexfora)KelvinͲVoigtmodelandb)fortheMaxwellmodel. Figure5.ExamplesoftheQCMͲDresponses,ȴfandȴȳforadhesionofpolystyrenetoahydrophobic SAMcrystalsurfaceasafunctionofthesensorfrequencyfora)theKelvinͲVoigtmodelinabsenceof apolydispersityindexandb)theMaxwellmodelinpresenceofapolydispersityindex. FitsforS.salivariusHB7(Figure3)consistentlyshowafrequencyofzerocrossing(between5 and15MHz)inlinewithDybwadcoupledresonatormodel,whereasS.salivariusHBC12(Figure4)and abioticpolystyreneparticles(Figure5)donotdemonstratefrequenciesofzerocrossing,indicatingthe twoparticlesbehavemorelikeanadsorbedmassratherthancouplingasaresonatortotheQCMͲD crystal.ThequalityofthefitscanbejudgedfromtheRMSDvaluesinTables3and4.Onaverage,RMSD valuesobtainedusingtheKelvinͲVoigtmodel(43±13Hz)aresimilarasobtainedfromtheMaxwell model(44±11Hz).Theparticlemassesobtainedforthebioticandabioticparticlesrangebetween1 x10Ͳ16kgand12x10Ͳ16kgintheKelvinͲVoigtmodel,whereasintheMaxwellmodelparticlemasses between1x10Ͳ16kgand20x10Ͳ16kgareobtained.Therewithallmassesobtainedarewithinthesame orderofmagnitudeascanbecalculatedforbacteria(yielding5x10Ͳ16kg)frompublishedbacterial
dimensions and densities or calculated from the dimension of the polystyrene particles and their density(yielding5.5x10Ͳ16kg).29ForS.salivariusHBC12,bothmodelsyieldanidentical,smallmassof 2x10Ͳ16kgonaverage,whilealsoforpolystyreneparticlesbothmodelsyieldasimilarmassthatis comparable with the gravitational mass of polystyrene particles. Interestingly, while both of these particlesadheredmoreinlinewithmassadsorptiontheory,particlemassesforS.salivariusHB7that adheredmorelikeacoupledresonatordifferconsiderablyasobtainedfromtheKelvinͲVoigt(6x10Ͳ16 kg;seeTable3)versustheMaxwellmodel(20x10Ͳ16kg;seeTable4).
Alsospringconstantskobtainedfrombothmodelsdifferordersofmagnitudeforthethree different particle types involved (compare Tables 3 and 4). In the KelvinͲVoigt model, the hydrophobicityofthecrystalsurfaceshowsnosystematictrendwiththespringconstantobtained,but in the Maxwell model the spring constants of S. salivarius HB7 and polystyrene particles were consistentlysmalleronthehydrophiliccrystalsurface.
Unlike the spring constants, but alike the particle masses obtained, both models yielded comparable results for the drag coefficients of massͲadsorbing S. salivarius HBC12 and abiotic polystyreneparticles.ThedragcoefficientsincreasedtowardstothehydrophilicSAMcoatedcrystals forthehydrophilicS.salivariusHBC12,whileoppositelyadecreasewasobservedforthehydrophobic polystyreneparticles.ForS.salivariusHB7demonstratingcoupledresonatorcharacteristics,thedrag coefficients obtained are comparable for both models and hardly vary among the different crystal surfaces.
Inclusionofpolydispersityinmass,springconstantordragͲforceforeitherbacterialstrainsdid notincrease thequalityofthefitinKelvinͲVoigt norinMaxwellmodels. However,forpolystyrene particlesintheMaxwellmodelinclusionofpolydispersityinspringconstantyieldedabetterfitthan could be obtained in the absence of polydispersity or including polydispersity in mass or drag coefficient.
Table3Springconstantsk,dragcoefficientsʇmassesmpandRMSDvaluesobtainedintheKelvinͲ VoigtcoupledͲresonatormodel,forboththefibrillated(S.salivariusHB7)andnonͲfibrillated(S. salivariusHBC12)streptococcalstrainsaswellasforabioticpolystyreneparticles.ʄindicatesthe rangeofpolydispersitytoobtainbestfit. Bacterialstrains mp (10Ͳ16kg) k (kgsͲ2) ʇ (10Ͳ9kgsͲ1) ʄ RMSD (Hz) S.salivariusHB7onhydrophobicSAM 6 0.35 10 0 41 S.salivariusHB7ongoldͲcoatedcrystal 6 0.22 9 0 20 S.salivariusHB7onhydrophilicSAM 5 0.24 5 0 84 S.salivariusHBC12onhydrophobicSAM 1 0.00 19 0 42 S.salivariusHBC12ongoldͲcoatedcrystal 3 0.06 5 0 22 S.salivariusHBC12onhydrophilicSAM 1 0.45 46 0 22 Polystyreneparticles onhydrophobicSAM 12 0.00 61 0 39 ongoldͲcoatedcrystal 5 0.00 113 0 64 onhydrophilicSAM 8 0.00 16 0 55
3
Table4Springconstantsk,dragcoefficientsʇmassesmpandRMSDvaluesobtainedintheMaxwell coupledͲresonatormodel,forboththefibrillated(S.salivariusHB7)andnonͲfibrillated(S.salivarius HBC12) streptococcal strains as well as abiotic polystyrene particles. ʄ indicates the range of polydispersitytoobtainbestfit. Bacterialstrains mp (10Ͳ16kg) k (kgsͲ2) ʇ (10Ͳ9kgsͲ1) ʄ RMSD (Hz) S.salivariusHB7onhydrophobicSAM 20 9.75 13 0 48 S.salivariusHB7ongoldͲcoatedcrystal 20 15.0 9 0 25 S.salivariusHB7onhydrophilicSAM 20 2.10 13 0 80 S.salivariusHBC12onhydrophobicSAM 0 15.0 21 0 44 S.salivariusHBC12ongoldͲcoatedcrystal 5 15.0 5 0 23 S.salivariusHBC12onhydrophilicSAM 1 15.0 45 0 26 Polystyreneparticles onhydrophobicSAM 10 554 79 2* 41 ongoldͲcoatedcrystal 5 241 141 2* 58 onhydrophilicSAM 4 50.2 71 2* 51 *indicatespolydispersityink
DISCUSSION
KelvinͲVoigt and Maxwell models are both versatile instruments to model and explain the viscoelastic behavior of materials,3 including biofilms.5 This study compares the use of coupled resonatorapproachesbasedonphenomenologicalKelvinͲVoigtorMaxwellmodelsandthepossible role of polydispersity in the analysis of the QCMͲD response to adhesion of a fibrillated and nonͲ fibrillated streptococcal strain and abiotic polystyrene particles to QCMͲD crystal surfaces having different hydrophobicities. The hydrophobicity of a goldͲcoated QCMͲD crystal was varied by applicationofahydrophobicorhydrophilicSAM,thatdifferednotonlyinwatercontactangle,but moreover in the ratio between electronͲdonating and electronͲaccepting surface free energy parameters.Allcrystalsurfaceswereextremelysmoothinthenanometerrange(Table1),although thehydrophilicSAMwasslightlysmootherthanthetwohydrophobiccrystalsurfacesNevertheless,it is generally considered unlikely that such small nanoscopic differences in Ra will affect bacterial
adhesion.30
QCMͲD responses ȴf and ȴȳ to the adhesion of biotic fibrillated streptococci and abiotic polystyrene particles could be fitted equally well using the KelvinͲVoigt or Maxwell model and comparisonofRMSDvaluesdidnotyieldanindicationastowhichmodelmightbepreferentiallyused intheanalysisofQCMͲDresponsesfromamathematicalperspective.Calculationsofbacterialand polystyrene particle masses validate both phenomenological models within wide ranges, but it is uncertaintowhichextenttheQCMͲDyieldsactualgravitationalorinertialmassesandhowthetwo relate.16Chindametal.3markedtheKelvinͲVoigtmodelasmoreaccuratethantheMaxwellmodel basedoncomparisonwiththeYoung’smoduliobtainedwithitsrealvalue,butsuch“real”valuesfor the bacterial properties are impossible to obtain. Comparison of the spring constants of bacterial bondstosubstratumsurfaceswithindependentlyobtainedliteraturedataisalsodifficult,notinthe least since QCMͲD operates at a forced, high frequency in the MHz range, whereas for instance bacterialvibrationspectroscopyexploresspringconstantsundernaturally,Brownianmotioninduced, lowfrequencyvibrations.Bacterialvibrationspectroscopyindicatedthatthefibrillatedstreptococcal strain, S. salivarius HB7, had higher vibrational amplitudes than its bald mutant strain S. salivarius HBC12,correspondingwithspringconstantsofaround2and3x10Ͳ5NmͲ1,respectively,12whichis5 ordersofmagnitudedifferentthanfoundhere.AlsospringconstantsobtainedbymeansofAFMfor whole cells, thus not specifically of the bond itself,31,3 were orders of magnitude different than obtainedhere.
Herewith it becomes impossible to conclude which phenomenological model is mathematicallyorbycomparisonwithotherindependentmethodspreferable.Suchaconclusionat thesametimemaybelessimportantthanthequestionwhetherapplicationofeithermodelyieldsthe sameordifferentinsightsinthephysicoͲchemistryofthebondunderlyingthephenomenonstudied.
Both KelvinͲVoigt as well as Maxwell analyses, bacterial vibration spectroscopy and AFM of the streptococcalbondspointtoastifferbindingofthebaldstrainS.salivariusHBC12thanofthefibrillated S.salivariusHB7.12InneitherQCMͲDmodels,didinclusionofpolydispersityyieldabetterqualityof thefitforstreptococcaladhesion.Forpolystyreneparticlesonlyaminorpolydispersity(ʄ=2)inspring constantwasinferred.ThissuggeststhatpolydispersityplayslessofaroleintheanalysisofQCMͲD responsestoparticleadhesionthanproposedbefore.16
In both the KelvinͲVoigt and in the Maxwell analysis, the drag coefficient increases for the hydrophilicS.salivariusHBC12goingfromthehydrophobictothehydrophiliccrystalsurfaces,despite beingnumericallydifferentinbothanalyses.Thesehydrophilic,bioticparticleshavenoorveryshort surfaceappendagesandconcurrently,theQCMͲDresponsesuggeststhattheseparticlesbehaveon thecrystalsurfaceasanadsorbedmassandmaythusbemoresusceptibletothepropertiesofthe crystalsurfaceandtheresultingwaterstructuringundertheinfluenceofthesurface,asindicatedby the high ratio of electronͲdonating over electronͲaccepting parameters on the hydrophilic SAMͲ coating. Oppositely for hydrophobic polystyrene particles in both models, the drag coefficient decreases when the ratio of electronͲdonating over electronͲaccepting parameters increases, suggesting that hydrophobic particles experience less drag by structured water on a surface than hydrophilicones.ThefactthatthedragcoefficientofS.salivariusHB7isquitesimilaronhydrophilic and hydrophobic crystal surfaces combined with its propensity to bind to the sensor crystal as a coupled resonator, suggests that the drag coefficient of resonator coupled particles is much more influencedbytheviscosityofthebulkwater,i.e.farabovethecrystalsurfacethanbythestructured wateradjacenttothecrystal(noteitsfibrilsare91nmlong).
Separatingtheparticletypesinvolvedinthisstudyintomassadsorbingandresonatorcoupling ones,revealsaninterestingdifferencebetweentheKelvinͲVoigtandtheMaxwellmodel.Whereasfor
S. salivarius HBC12 and polystyrene particles, particle masses derived are nearly the same in both
models,S.salivariusHB7hasafourfoldhighermassintheMaxwellmodelthanintheKelvinͲVoigt model.Pendingtheuncertaintyregardingthepropermass(gravitationalorinertial)derivedinQCMͲ Dandits“real”value,andthepossibleimpactonthespringconstantsanddragcoefficientsderived, Johannsmann4suggestedtousetheratioனஞ ୩ortan(ɷ)asa“lossiness”parametertobederivedfrom QCMͲDanalyses,thatissolelybasedontheratiobetweenthedragcoefficientsandspringconstants ofthebond.
Table 5 Lossiness tan(ɷ) obtained for both the fibrillated (S. salivarius HB7) and nonͲfibrillated (S. salivariusHBC12)streptococcalstrainsaswellasforabioticpolystyreneparticlesintheKelvinͲVoigt andMaxwellmodel. Bacterialstrains tan(ɷ) KelvinͲVoigt tan(ɷ) Maxwell S.salivariusHB7onhydrophobicSAM 0.14 0.01 S.salivariusHB7ongoldͲcoatedcrystal 0.21 0.00 S.salivariusHB7onhydrophilicSAM 0.11 0.03 S.salivariusHBC12onhydrophobicSAM ग़1 0.01 S.salivariusHBC12ongoldͲcoatedcrystal 0.41 0.00 S.salivariusHBC12onhydrophilicSAM 0.51 0.01 Polystyreneparticles onhydrophobicSAM ग़1 0.00 ongoldͲcoatedcrystal ग़1 0.00 onhydrophilicSAM ग़1 0.00 Asummaryofthe“lossiness”valuesinTable5forbothmodelsyieldsthegeneralconclusion that the Maxwell model yields predominantly elastic bond characteristics with minimal damping contributions.ThiscanbeexplainedbythefactthatintheKelvinͲVoigtmodelthespringinparallel withthedashpotaidsinparticlemovement(Figure6a),whereasintheMaxwellmodelthespringand dashpotactcompletelyindependentofeachotherandthedashpotisnotforcedtoparticipateinits response to the oscillations of the crystal by the spring (Figure 6b). Possibly this explains why the
KelvinͲVoigtmodelhasbeenjudgedpreferentialabovetheMaxwellmodelinexplainingthethermoͲ mechanicalresponseofmetalsunderelasticcyclicloading.3Thismayputlargeremphasisontheelastic response in the Maxwell model compared with the KelvinͲVoigt model as suggested by the small “lossiness”valuesfortheMaxwellmodelinTable5.However,thefactthatfluidispresentallaround theadheringparticlesandthebonditselfishydrated,indicatesanecessarydampingcontributionto thebond,orlossiness,whichtheKelvinͲVoigtmodelallowsforincontrasttotheMaxwellmodel(see Table 5). This realization may also explain why S. salivarius HB7 has a fourfold higher mass in the MaxwellmodelthanintheKelvinͲVoigtmodel,asthedashpotdoesnotbecomeactivatedbythespring to make the particle resonate in tune with the crystal through the bulk liquid. However, also two Maxwellelementsplacedinparallel,asoftenemployedtomodeltheviscoelasticresponseofbiofilms,5 withone being predominantlyelastic andtheother mainlyviscouswouldin essenceresemblethe KelvinͲVoigtelementandgivethesameresponse.Forbiofilms,itappearstrivialthattheirviscoelastic response comprises too many independent processes for capturing in one KelvinͲVoigt or Maxwell element,butitcannotberuledoutthatalsotheQCMͲDresponsetosingleparticleadhesioncomprises multipleMaxwellelementsthatmightpairwiseresembletheKelvinͲVoigtelement.Unfortunately,the useofmultipleelementsinanalogywith theanalysisofstressrelaxationof biofilmsforfittingthe QCMͲD response of adhering bacteria, is mathematically impossible due to the limited number of frequenciesthatcanbeobservedinQCMͲD. Figure6.SchematicpresentationofthestrainofabondintheKelvinͲVoigt(a)versustheMaxwellͲ model(b)asafunctionoftime7duringapplicationofaconstantstress,asexperiencedbyadhering (bio)colloidalparticlesexposedtofluidshear. a)Thedashpotinparallelwiththespring,dampensthespringresponse.Thestretchingcontinuestoa plateaulevel.b)Springanddashpotinseriesactindependently.Thespringimmediatelystretchesto aconstantstrain,butthedashpotcontinuestostretchwithoutbeinglimitedtillultimatelythebond breaks. ɸ1 ɸ2
ɸ
1ɸ
2b
ɸ
t
ɸ
1a
ɸ
t
ɸ1 ɸ2CONCLUSION
In conclusion, we demonstrated a new way to quantitatively analyze QCMͲD responses of (bio)colloid adhesion to hydrophobic and hydrophilic crystal surfaces to obtain viscoelastic bond properties. The use of a phenomenological KelvinͲVoigt or Maxwell model in a coupledͲresonator approachesyieldedgoodfitstotheQCMͲDdata.Onlyinclusionofpolydispersityinspringconstant onlyimprovedthequalityofthefitsintheMaxwellmodelforhydrophobicpolystyreneparticles.In theKelvinͲVoigtandMaxwellmodel,thedragcoefficientincreasedforthebaldstreptococcuswiththe ratioofelectronͲdonatingoverelectronͲacceptingparametersofthecrystalsurface,likelybecauseit coupledclosertothecrystalsurfaceandmorelikeanadsorbedmassthanthefibrillatedstrain.Forthe fibrillatedstrain,thedragcoefficientwassimilaronallcrystalsurfaces.Thusthedragexperiencedby resonatorͲcoupled,hydrophilicparticlesismoreinfluencedbytheviscosityofthebulkwaterthanby the structured water adjacent to the crystal surface that is probed by particles coupled without a tether,positioningtheparticlejustabovethethininterfaciallayerofstructuredwateronasurface.
KelvinͲVoigt and Maxwell models both have their virtues in analyzing the phenomenon of bacterialorparticleadhesionwhenitcomestofittingofcoupledresonatormodelstoQCMͲDdata. Apartfromtheaboveconclusionsthatcouldbedrawnonbasisofbothmodels,theMaxwellmodelin generalemphasizedtheelasticresponsemorethantheKelvinͲVoigtmodel.Placedinserieswitha dashpot,theelasticresponseintheMaxwellmodelactsindependentlyofdamping.IntheKelvinͲVoigt model,thespringisplacedinparallelwiththedashpotandcontinuouslyopposedinitsresponseby thedashpot.Exposedtofluidshear,thisimpliesthatintheMaxwellmodel,thebondelongatestill rupture,whichisunrealisticandmaymaketheKelvinͲVoigtmodelpreferential. ACKNOWLEDGEMENTS WethankDr.PhilippKühnfromtheDepartmentofBiomedicalEngineering,Groningen,for performingtheAFMmeasurementsonQCMͲDcrystals. FUNDING ThisstudywasentirelyfundedbyUMCG,Groningen,TheNetherlands. COMPETINGINTEREST
The authors declare no potential conflicts of interest with respect to authorship and/or publication of this article. HJB is also director of a consulting company SASA BV. Opinions and assertionscontainedhereinarethoseoftheauthorsandarenotconstruedasnecessarilyrepresenting viewsofthefundingorganizationortheirrespectiveemployer(s).
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