Kinetics of exchange processes in the adsorption of proteins on solid surfaces.

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Kinetics of exchange processes in the adsorption of proteins on solid surfaces.

V. Ball, P. Huetz, A. Elaissari, P. Cazenave, J. Voegel, P. Schaaf

To cite this version:

V. Ball, P. Huetz, A. Elaissari, P. Cazenave, J. Voegel, et al.. Kinetics of exchange processes in the adsorption of proteins on solid surfaces.. Proceedings of the National Academy of Sciences of the United States of America , National Academy of Sciences, 1994, 91 (15), pp.7330-7334.

�10.1073/pnas.91.15.7330�. �hal-02090851�

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Proc. Natl.Acad. Sci. USA Vol. 91, pp. 7330-7334, July1994 Biophysics

Kinetics of exchange processes in the adsorption ofproteins on solid surfaces

(homomolecular exchange)

V. BALLt, P. HUETZt, A. ELAISSARIt, J.-P. CAZENAVE§, J.-C. VOEGELt, AND P. SCHAAF¶II**

tCentredeRecherchesOdontologiques, Institut National delaSant6etdela RechercheMedicale, ContratJeuneFormetion 92-041, Place del'H6pital-67000 Strasbourg, France;tUnitMmixteCentre Nationalde laRechercheScientifique-Biom6rieux, EcoleNormaleSup6rieuredeLyon 46,Aile d'Italie-69364 Lyon Cedex07, France; CentreR6gional de TransfusionSanguine,Institut Nationalde laSanteetdelaRechercheMedicale, Unit6 311 10,rueSpielmann-67085 Strasbourg Cedex, France;lInstitutCharlesSadron,Centre National de la RechercheScientifique-UniversittLouis Pasteur 6,rueBoussingault-67083 StrassbourgCedex, France; andIlEcoleEurop6enne desHautesEtudesdesIndustriesChimiquesdeStrasbourg (UnitedeRechercheAssocie6 405-Centre National de la RechercheScientifique) 1, rue BlaisePascal,BP296F-67008 Strasbourg, Cedex,France

CommunicatedbyHowardReiss,April 11, 1994(received forreviewMarch3, 1994)

ABSTRACT Thehomogeneousexchange process whereby IgG molecules adsorbed onto latex particlesare replaced by IgGmolecules from the bulk solutionwasstudiedbymeansof ts radiolabeling.Theexchange mechanismwasInvestigatedon surfacessaturatedwith eitherlabeled orunlabeledproteins in the presence of a solution of theopposite species in twosetsof independentexperiments.Afterrinsingof the surfaceby pure buffer followed by supplementary IgG adsorption, the exchange process.followedakinetic lawof first order with respect to theIgG molecules from the bulksolution,andthe apparent exchange rate constant was(2.3 ± 0.4) x 10-5cmhr'1.

One ofthemaindifferencesbetweenadsorptionprocessesof

"small" moleculesandof macromoleculesonsolidsurfaces isthatmacromoleculescanreach thesurfacebytwodifferent mechanisms (1): by direct adsorption or by a progressive exchange reaction. Inthefirstcasethemolecules reachthe adsorption surface directly onfree available space. Incon- trast, forthe exchangemechanismthe molecules reach the surfacebyprogressiveremoval ofalready-adsorbedmacro- molecules. This occurs in particular when the surface is saturatedwithpreadsorbed molecules. This second process has never been observed in theadsorptionof small molecules onsurfaces.

Thephysical origin ofthissecondadsorptionprocesslies in the fact that macromolecules interact with a surface throughseveral links. Theselinksalongthe macromolecule change withtime,even if the moleculeis in anequilibrium configuration.Interactions between macromoleculeandsur- facemustthus beconsideredas adynamicand not astatic process. Moreover, macromolecules are not rigid bodies.

Thus,ifsuchamoleculeentersintothevicinity ofasurface alreadycoveredbyadsorbedmacromolecules,itcanchange its conformation anddiffuse into theadsorbed layer. Once partof the backbone of the diffusing molecule reachesthe adsorption surface, it interacts with it. Thisinteractioncan then be followed by sequential, segmental, reptation-like adsorptionof themolecule, incompetitionwith thedynamic process of the formationand annihilation of links of previ- ouslyadsorbed macromolecules. Finally, thediffusingmol- eculesprogressively replace those already adsorbed onthe surface, completingtheexchange process.

Such processes have beenobservedforsyntheticpolymers (2) as well as for proteins (3, 4) by means of radioactive labeling techniques. NevertHeless, and in spite of a great number ofinvestigations, little is known about adsorption processesof macromolecules (5). Let us rapidly summarize

themainresults that have beenestablished.(i) Theaffinityof proteins for a given surface usually increases with their molecularweight. High molecular weight proteins usually exchange preferentially with lower molecular weight ad- sorbedproteins(6,7). (ii) Thehigherthehydrophobicity of thesurface is, thelargeris theadsorbedquantity (8, 9). (iii) These amounts are maximal for pH values close to the isoelectric point ofthe protein-coatedsurface (10, 11). (iv) For synthetic homopolymersof the same chemical nature, theaffinityfor a surface increases with the molecularweight (12). (v) It has been shownexperimentallythatforhomopoly- mersofthe same nature and the samemolecular weight, the exchange process canbe modeledbyafirst-order chemical reaction with respect to both the bulk molecules and the adsorbedpolymers (2). Thisresulthasbeenexplained theo- retically by De Gennes (13). However, it has never been extendedtoothersituations-forexample,amixture oftwo differentmolecularweight polymers ofthesamenature. For proteins, on the other hand, the order of the exchange reactionhas neverbeen determined for anysituation,despite the importance of this mechanism in the adsorption of proteinsontobiosurfaces.

Itis the goal of this article to present initial experimental resultsdevoted to thisproblem. We will not onlydetermine theorder of the exchange process but alsogive an evaluation ofthe exchange rate constant. The experiments were performed forasystemwhere humanIgG molecules inthebulk were in contact with human IgG molecules adsorbed on polystyrene latex particles. This type ofproteinhas been chosen mainly forits importance in biological andpharma- ceutical fields-for example, inimmunologicaltests.

MATERIALSAND METHODS

Adsorbents and Adsorbates. Adsorption was onto mono- disperse polystyrene latexparticles preparedunderemulsi- fier-freeconditions (14)using potassium persulfate as initiator. Latexparticle size was measuredbytransmission elec- tron microscopy with Hitachi Ha 12A equipment. From sizing of about 100 particles at the Centre deMicroscopie Appliqude alaBiologie (University Claude Bernard, Lyon, France), a number-average diameter (D.) of 790 nm was calculated withapolydispersityindexof1.001.Thespecific areawasdeducedtobe 7.3m2 gel. Thesurface charge of the particles originates from the initiator residues (-OSO3) anchored at the water/polymer interface. After the latex particleswerecleanedby ionic exchange in mixed-bed resins (Duolite),theamountof covalently bound surface groups was determinedby followingtheconductivityupontitration with

**Towhomreprintrequestsshould be addressedat:Institut Charles Sadron6,rueBoussingault, 67083 Strasbourg, Cedex, France.

7330 Thepublicationcostsof this articleweredefrayedinpartbypagecharge payment.This articlemusttherefore beherebymarked "advertisement"

in accordance with 18 U.S.C. §1734solelytoindicatethis fact.

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Proc. Natl.Acad. Sci. USA91 (1994) 7331 0.02 M NaOH; thededuced surfacechargedensitywas-0.68

.C.cm-2.The dry weight content of theparticles in the initial suspension (pH 7.9) was 9.1%. No flocculation occurred when the latex particles were suspended in the Tris/HCl buffer used throughout this study (50 mM Tris, pH 7.35/1 mM NaCl/1 mMNaN3).

The proteins employed were polyclonal IgG (weight- average molecular weight -150,000) isolated from human serum of about 1000 donors. Theseproteins were provided by the Centre Regional deTransfusion Sanguine (Strasbourg, France). They were characterized by SDS/PAGE with Coomassie blue staining; purity wasjudged to be at least 95%.

The IgG molecules were radiolabeled according to the method of McFarlane (15), in whichiodine monochlorideis the iodinating agent. The amountofNaIwas chosensothat about 1 out of 3,000 IgG molecules was labeled. Allprotein solutions were then stored in concentrated form [-20 x 10-2% (wt/wt)] at -200C. Before use, they were quickly thawed and diluted to their final concentrations inTris/HCl buffer. The radioactivities of the labeled solutions were determined byycounting (Minimaxiy,United Technologies, Packard). From comparison of the radioactivity with the absorbance at 280 nm[E = 1.38cm2mg-1(16)] as measured by a spectrophotometer (Beckman, model 34), the specific activity was determined.

Experimental Procedure. All the experiments were performed in 2-ml Eppendorf tubes. The initial suspension of latex particles was diluted in filtered and deaeratedTris/HCl buffer, with a dilution factor of =15. The precise dilution factor for each individual experiment was determined pre- cisely by weighing. All ^the experiments were performed at room temperature, 23 ±10C.

Direct adsorption experiments. Prior to exchange experiments, the direct adsorption conditions must be determined.

First, the absence of particle aggregation in the presence of proteins was verified by optical microscopy. Further, to avoid direct adsorption during the exchange process, saturated surfaces should be used and thus plateau adsorption conditions, in particular both characteristic adsorption times and the bulk protein concentration necessary for saturation, had to be evaluated.

Adsorption kinetics were first assessed: 1 ml of diluted latex particles was mixed with1ml of a labeled IgG solution of known concentration [2.3x 10-2%(wt/wt)]in an Eppen- dorf tube. After a given adsorption time t, under gentle rotation of 8-10 rpm (Agitest 34050, Bioblock Scientific,

Illkirch, France), the tube was centrifuged at 8000x g for 12 min and the mean activity was determined from three pre- cisely weighed 200-,ul samples of supernatant solution. The activity difference before and after the adsorption process allows the determination of the amount of adsorbed protein as a function of time. Great care was taken to avoid the presence of latex particles in the supernatant after centrifugation. Turbidimetric control (turbidimeter model 800, En- gineered Systems & Designs, Newark, DE) showed a loss of

<0.02% of the particles during this step. All experiments were duplicated. Fig. 1 shows a typical kinetic curve; equilibrium seems to be reached within <2 hr and the final bulk concentration at equilibrium is (0.45 ± 0.05)x 10-2% (wt/

wt).

To determine the adsorption isotherm, the same kind of experiments as just described were performed, but varying the bulk concentration of the labeled proteins (cG*)instead of the adsorption time t, which was held constant at 3 hr.

Again, each experiment was duplicated and Fig. 2 represents the evolution of the quantity of adsorbed proteins as a function of cw*. From this, one can conclude that the adsorption plateau of the isotherm at 0.54 Lg-cm-2is reached for a bulk concentration of the order of 2 x 10-2%(wt/wt).

U

C) 0

%-.

0.4

0.8

0.2

0.1

0.0

... ...I...I... I...

0 0 @ 8

T

1 2 ( 4 6 6

Time (hour.)

FIG.1. Adsorption kineticsoflabeledIgG, with an initialprotein concentration(in the Eppendorftube)cgcj*of(1.5 +0.05)x 10-2%

(wt/wt), performed at 23 ± 10C. Each experimental point was duplicated. The final protein bulk concentration in the tube was

found to be (0.45 ±0.05) x 10-2%(wt/wt).

Moreover, the reproducibility of these experiments can be evaluated to be of theorder of5%.

Exchange experiments. Two types ofexchange experiments wereperformed. (Set I)Kineticexperiments in which the surface oftheparticles was firstsaturatedwithunlabeled IgG molecules,followedbyexchangewithlabeledones. The bulk concentrationoflabeledproteins (cfo*) was chosen so that its relative variationwas <15% over the whole experimental time. For each concentration, six Eppendorftubes containing latex particles coated with unlabeled proteins were prepared. The amount ofadsorbed labeled molecules was then determinedafter adifferent reaction time for each tube (in the 1- to 5-hrtimeinterval).This set ofexperiments wascomplementedbyadditionalmeasurementsat a constant reaction time of 4 hr. (Set II) Exchange experiments at a constant reaction time twithlabeled IgGmoleculesadsorbed on the particle surface, but in contact with solutions of unlabeledproteins atvarying bulkconcentrations cI .

For all these experiments, IgG molecules were first adsorbed onto the latex particles for 3 hr at an initial bulk concentration of(3.5 ± 0.3) x 10-2% (wt/wt). Thiscorre- sponds to adsorption plateau conditions. This step was performed as described in the "directadsorption" section.

After 3hrofcontactbetweentheparticles and theproteins, followed by centrifugation, the unadsorbed IgG molecules were removed, avoiding any particle loss. To do this, the latex particles were separated from the solution by centrifugation, and aportion (1.2/2 ml) of the liquid wasremoved;

great care wastaken that all latex particles remained inthe tubes. A turbidimetric control on the eliminated liquid showed thattheloss ofparticlesduring this step was<0.5%.

The samebuffervolumevwas thenadded to theEppendorf tube andthelatexsuspensionwasredispersed. Afterfurther

.1-1 N

N.- Co

0.6

0.6 0.4

0.9

0.2

0.1 0.0

0 2 9 4 ⁵

C *IG⁽ ^{1 0}2% (Wf/W) )

FIG.2. Adsorptionisothermof labeledIgGat(23 ± 1)0Cafter3

hrofadsorption.

8so

0

Biophysics: Baffetal.

l

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Proc.Nadl.Acad. Sci. USA 91(1994) centrifugation and redispersion, a control with an optical

microscope showed that the particle redispersion wassatis- factory (no aggregates were present in the solution). The removal-dilution-redispersion-centrifugation step was re-

peatedfour times (five times for the^pure desorption experiments,whencWg- 0)and ledtoadilution ratio of30-40(75

for the^puredesorptionexperiments)for the protein solution remainingfrom thedirect adsorption step.

After the last removaWdilution-redispersion-centrifuga-

tionstep(onaverage2 hrafterthebeginning ofthefirst step),

a volume v of protein solution ^was added to replace the buffer.Theproteinconcentrationpresentin the bulk solution

wasthencoo (orcWg*). ^The^particles ^were^thenredispersed and this^wastaken^astimet ⁼ 0for the exchange reaction.

This reaction was allowed to take place under a gentle rotation of 8-10rpm. Afteratime t, thesolution wasagain

centrifugedand theactivity of thesupernatantwasmeasured.

For the experiments ofsetI, the difference between the activity ofthe supernatant after the exchange stepandthe initial activity of thesolution correspondstothefixedamount of labeled proteins during the exchange step. In setII, the activity ofthe supernatantwasfound tobe verysmall. Care

mustbe takentoaccountfor the activity duetoany-labeled proteins remainingin thesolution fromtheinitialadsorption

step. Hence, we proceeded as follows: after the direct adsorption step with the labeled proteins, the adsorbed

amountrF- wasdeterminedasdescribed above. Unlabeled IgG molecules were added ^to the solution (after the four removal-dilution-redispersion-centrifugation steps)toallow for the exchange. Atthe end of the exchangestepandbefore centrifugation, the activityof thesolution(composedby both the latex particles and the exchanging protein solution) was

measured.Thesolutionwasthencentrifuged and theactivity of thesupernatantdetermined. Thedifferencebetweenthese

twoquantities correspondstotheamountof labeledproteins

r* that remained on the surface of the particles, and the difference betweenr-* ^(value of direct adsorption at the plateau) andr* representstheamountArF*(wheresubscript

"r99means "'released") ofproteins thatwere releasedfrom thesurface during theexchange step. This methodrequires the determination of three activities, which leads to more scatter in these experimental results compared with those from experimental setI.

For all the exchange processes taking place in these experiments, therelative variationsof the bulk proteincon-

centrationand thesurfaceconcentrationof adsorbed proteins

were small (<15%). Consequently, we assumed these con-

centrationstoremainconstantfor theanalysis of thekinetic laws.

RESULTS AND DISCUSSION

Wefirst performedexperimentsetI.Fig. 3 shows thetypical evolution ofAl'F0*, theprotein amountthat adsorbs onthe surface of the particles during the exchange step, as a

functionof the reaction time t. Two characteristic periods

appear onthe graph: (i)arapidprocess taking place during approximatively thefirst2hr(for the experimental conditions under study) followed by (ii) a slower and quasilinear in-

creasewith time (of slopeSe, ^{the symbol}"e" beingusedfor

"exchange")of theamountof labeled proteins that adsorbon

the surface. Independent experiments ^were made for 10 different bulk concentrations. The values ofSe ^were ^deter-

mined fromthekineticcurvesby alinear least-squares fitting procedure; the linear correlation coefficients were in the

range 0.93-0.98. A linear dependence ofSe with bulkcon-

centrationcWo*wasobserved (Fig. 4). During the exchange

process, the relative variations of cG*were <15%. More-

over,theexperimentswererealizedwith IgG*bulkconcen-

trations thatwere close toor within theadsorption plateau

U11

el

0.20

0.16

0.12

0.08

0 1 2 3 4 5 6

Time (hours)

FIG. 3. Examples of kinetic experiments according to set I.

ArIp*, surface concentration of labeledIgGfor various bulk con-

centrations cwoG: ^v, (1.22 0.05) ^x 10-2%; o, (1.97 0.05) x

10-2%;*, (3.60 0.10) x 10-2%. Straight lines correspond to least-squares fits inthe interval 2-5 hr.

domain. Due to the large amount of unlabeled adsorbed proteins,the surface concentrationof the latter isassumedto beconstant. Consequently the lineardependence ofSe with

cG*indicates that theprocessunderstudycanbe modeled byachemical reaction of order 1for theIgG* molecules in the bulk. Thus, the amount of exchanged proteins A1'Wc*

varies as

d(Al'IgG*)/dt kef(rlgj,To)C ^-*, [1]

wheref("4Tr ) is an unknown function of the amount of adsorbed protein rIwG,TOt (considered as constant over the experimental periodbetween 2 and 5 hr), and isthekinetic

constantfor the exchange. The value ofkCf(I'WG,Tot) ^can be deduced from Fig. 4, yielding (2.3 ± 0.4) x 10- cm-hr-1.

To prove that the adsorption process described in the experimentsofsetIisindeed duetoanexchangemechanism (andnot tofurther adsorption),it isnecessarytodemonstrate that-correlated to the adsorption process-proteins are

released from the saturatedsurfaceoftheparticles.Thiswas

the aimof the experiments ofsetII lastingoveranexchange period of4hr,with unlabeled proteins in thebulk solution.

The direct preadsorption was performed with labeled proteins.Fig.5representstheamount ZLr' ofmoleculesreleased from the particles during the exchange mechanism as a

function of the bulk concentration cG measured at the beginning of the experiment. The experimental data were

plottedagainsttheinitial andnotthe finalbulkconcentration of proteins (as we have done above). Indeed, the final concentration could not be evaluated because the proteins

t .

vu

C) _m

0.012

0.008

0.004

0.000

0 1 2 3 4

C~g_CIg_G X102% (W/W)

FIG. 4. Slopes (Se)fromFig. 3 (andthe sevenexperiments not presented), plotted againstfinal bulkconcentration cwo*. Straight line corresponds to a least-squares fit with a linear correlation coefficientof 0.95. A Student'stestshowedthat theinterceptwith they axiswasstatistically indistinguishablefrom zero.

o

~~~~~~fI

^fv

7332 Biophysics: Balletal.

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Proc. Natl. Acad. Sci. USA 91 (1994) 7333

Oi

0

100)

a)

diNr

0.20

0.15

0 0.10

wo A

II 0.05

0.00

0 2 4 6 8

Bulk IgG concentration

( x102% (w/w) )

FIG. 5. O, Releasedamountsof labeledIgG* (Ar,.)from latex particles (saturated withIgG*)versuscWo ataconstantreaction time

of4hr. a, Puredesorption experiments (c o- 0).Solid linewas

calculated from thekinetic law deduced fromFig.4 withk1(FIso,Tot)

=(2.3 + 0.4) x 10-5cm hr-1 anda yintercept of 0.06 pgcm2.m,

Fixed amounts oflabeled IgG* (Afto*) versus cftop at the same

reaction time. Datainclude the values from the 10 kineticsmeasure-

ment(set I) and from 11 additionalmeasurements(see text).

wereunlabeled. However,asinsetItherelative variations inc% should be <15%.A value of about0.06 Ag.cm-2was

measured forArl* when the particleswerebroughtincontact with pure buffer(cG = 0) instead ofan unlabeled protein solution. Thisvaluecorrespondstoalmostpuredesorption, since at the end of the experiment, the concentration of labeledproteinsinthebuffer, which is duetopuredesorp- tion,was<0.2x10-2%(wt/wt).ThevaluesforAr,.increase

as co is increased. The large scatter in the experimental values does not allow us to affirm conclusively a linear dependence of Al'r* ^on cW, but such a dependence is compatiblewiththe observed data.

Ifonecomparestheexchangeprocessesperformedin the experimental setsI and ^II,the amountadsorbed (set I)and the amountreleased (set II)foragiven bulkconcentration should beidenticalwithin theexperimental precision.This is notthe^case,ascanbe observedinFig.⁵(differencebetween

*andO). However, ifone assumes alineardependenceof

Arr*withcG,withslope equaltoitsvalue determined from set I and passing through the value of Arr* at cW = 0

(quantityreleasedbypuredesorption), one recovers agood agreementforsetII(straightline inFig. 5)with theexperimental data ofsetI.

To understand the origin of thedifferences between the adsorbed and released amounts,given by experimental sets I andII,respectively,wereanalyzethedata from the kinetic experiments (set I) by focusingourattentiononthedifference

between the amount AI'r.* adsorbed during the exchange stepand theamountkef(rI G,Tot).cfG*tactuallyattributedto the exchange mechanism. Fig. 6 shows the evolution of Arl'*-ke~f(rlgo,Tot)jcigG*.t^{as a}function ofcG*.Itcanfirst be noticed that these quantities are almost independent of time and thusdepend onlyoncw*.Thisagain showsthatat leasttwomechanismswith different timescalesareinvolved duringthe exchange ^step:theslowexchange^process, characterized by a lineardependence with time and with bulk concentration,andamorerapidprocesswhose contribution isplotted inFig. 6. The curve shows aplateau domain for protein concentrations above (2-2.5) ^x 10-2o (wt/wt)^asfor the directadsorption isotherm (Fig. 2). The observed plateau value inFig.6 is closeto0.125,ugCcm-2.

Due to its resemblance to the adsorption isotherm, we

suggestthat thisrapidprocessis duetoadditionaladsorption.

This adsorption occurs after the four removal-dilution- redispersion-centrifugation steps as soon as the surface

0

0.20

o _-% ^0.15

E-CQ2

_ Wo

,0 0.05

tio

0.00

0 1 2 3 4

CIgG* (x 0 %(w/W) )

FIG. 6. CalculatedvaluesofAF715.-kflrgGTot)c,*,t,forthe different reaction times with theexperimental datafromsetI,versus

CWpo.Symbolso,a,a,*, andvcorrespondtothe reactionat2, 3, 4, 4.5, and 5 hr, respectively. Dashed line shows the amountof labeled molecules thatreplaced the desorbedones(0.06pgcm2;see

Fig. 5). X,Additionalexperimentsperformed accordingtosetIwith only labeled molecules (see text).

coveredwithunlabeledmoleculesisbrought incontactwith the labeledones.

Suchaprocesscannotbeobserved when unlabeledpro-

teinsareintroduced after thesamedilutionsteps,asinsetII.

Onlythe release oflabeledproteinscanbeobservedinthat

case; this included a pure desorption (independent of the

presenceofadditional proteins, seeabove) contribution of 0.06pgcm-2which should alsooccurinsetI. Someof the additionaladsorption afterthe adsorption-rinse-adsorption cyclewould replace this desorbedprotein amount,but the

higher additionaladsorption, with aplateau value of 0.125 gCm-2 as seen in Fig. 6, suggests, ifour assumption is correct,that theplateau value of the isothermisincreased by

asupplementaryamountofabout 0.06 rgcm-2.This^wasin fact observed intwoadditionalexperiments performedasin set I but by adsorbing labeled IgG both during the initial adsorptionperiod and during the adsorption-exchangestep.

Thesetwoadditional experimentswereperformed with Coo*

=(4.0^±0.3)x 10-2%(wt/wt)intheplateau region. The total amountofadsorbed materialwasmeasuredasinsetIIfrom the difference between the activity of the homogeneous solutionandthesupernatantaftercentrifugation. In the first experiment, the measurement wasperformed after 4 hr; a

supplementary adsorbedamountof0.06 Wgcm-2^wasⁱⁿfact found (Fig. 6). In a second kinetic experiment (Fig. 7) we

0-- C)

0

C)

aI

*0 0.7 0.6

0.5 0.4 0.3 0.2 0.1 0.0

0 1 2 3 4 5

Time (Hours)

6

FIG. 7. Kineticsofsupplementary adsorption that takes place after the four removal-dilution-redispersion-centrifugation steps.

LabeledIgG moleculesataninitialconcentration of(3.5 ± 0.1) x

10-2%(wt/wt)werefirst adsorbedontothesurface of theparticles, and after the dilutionsteps,labeledproteinsat(4.0^± 0.3)x 10- (wt/wt)wereadded. Dashedlinecorrespondstothemeanadsorbed value after the firstadsorptionstep:0.54pg-cm2.

. I

8

I^- ^-. ^-

-* ^- ^-

I I . -

Biophysics: Balletal.