Protein-Surface lnteractions in the Presence of Polyethylene Oxide

ll. Effeci of Protein Size

S- I , JEON' AND J- D. , \NDf (ADE

D.pa netus.l Bionsineetin:< urd Matenah srl.ne co!?t.lU Rlalobn$ at tnE4aes, C.llel:c ..lEngikeeing,t,rtqsil!- .d Uluh, sull Ldke cn!. Utdh 81 I I 2

Receile! Oclober 16. 1989: accepted Augu$ 21. 1990

Polyethylene oxide ( PEO) sufacs €xhibit lo* protein adsoDtion. PEO sudace-proiein intenclionsd€ exanined lheorelicall! as a funciion ofsudace densil-v and chain lcnslh ofPEO and vanalion in lheste of the protein (asuncd ro b. a sphere). Rcccnt stndies susgest thal the PEo suriace nay havc asmdl hydfophobic character. we sludy lhc efled of sudace d€nsiry of PEO lnd protcin sizc and deduceihc PEO surfae density condilions for optnnal protein .esislance For snall prolcins (,4 - 20 A). ,should be snall l -10 A), shile for lree prcteins 1n -' 60 80 A), D should be laryer (- 15 A). wheen is the piotein ndius and , is rhe arerage distancc bcl$ccn end-atrached PEO chairs. Thee resullsevolve lron the ladc-ofs berwen steic rpulsion and thc assum€d wak hydrophobic intd&lion bclwende IEO layer and rhc proiein. The longen clain lcneth ofPEO ar optinun surlace densily appcaNbes! lor protein rcsklance. As a numbe. ofrsumprions and esdnal.s are invohed in the modcl, rheresllls can bc rak€n only as qualiBlilc 1rcnds at dris rine. The ftnds should be hclDful in rhe desisDa . . \ d l r d r i o ' u , . ' r l 4 ! . . e , \ L n n p o r e i o d J \ J r p r u n .

lI

I

INTRODUCTION

Polyethylene oxide (PEO) surlhces arebecoming recognized as exhibiting stronglyreduced protein adsortlion ( l-5). Thc pro_tcin-resistant charactct of PEO is gcncrallyrccognized as a steric slabilization effccl (69 ) . Besides this stcnc exclusion characler, wemust consider the van der Waals attractionbetwccn PEO and protein, although t}le vander waals altmction force is generally muchsmaller tllan the steric repulsion force (9).Recent studies ( l0 13) suggest that PEO sur-fhces have a h,vdrophobic character (11),which may induce a weak hydrophobic inter-action between PEO and protein whcn an as_sumed h)drophobic palch on ihe prolein isoriented to PEO. Hcr€ we assume a hydro_

'On teave lrcr lhc Departnenr ol Chemislry, Kan-

sreung Nalonal Uni!enil,\,, Kangreung. Kan8wondo 210-

phobic charactcr to PEO and include this as-sumed h,vdrophobic inleraction in the analysis.

Al l ol lhe forces ( .rer ic. ran der \ \ aJs. andhydrophobic) are considercd as functions ofihe s;e ofthe protein (prolein is assumed tooe a \phere) rnd 'urface denc,r) Jnd ch"rnlenstl of PEO.

MODELINC

We usea model similaf lo ihat in our pfe-vious paper (9) excepi that the protein has al in c .phcncal \hdpe. Our model ing prdurcis shown in Fig. L Wc assumc that thc PEOsufla(e (an bc rcpre\cnlcd r\ r llal plal( lb's impl i . r iL) , c \cn shen Ih( \pher iLdl pro lcrnapproaches and aft-ccts the PEO suri-ace. The\- ! r iab les are pro le in s i /e t radrus ofspher i id lprotein, R) and the surface densit] and charnlergrh o lPl O. rbe d isrance D bet$een rhe re-minally attached PEO chains, and the degleeof polymerization. fl, respectively. Only the' 'bru.h ca.e i . considered l6) . meaning lhar

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! r n J ' . r p d o ' i ' ' b ' e " " oLwtut al.rndd @t kk.4tu tn4. !

160 ]EON ^ND ANDRADE

FIG. L Our model piclure lbr bminally artached PEOchains 10 a solid subsmte wilh a 6ni1e sizc of sDherl@ltiotein in saier solven1. R, d, and D ae rhe rddius ofsph{ic.l prct€in, the distanc bctsccn the ilal PEO sun:Eand a prctein, and the distana berw€cn the teminallyatrached PEOchains, respectively.

the distance, is less than the Flory radius, R!

METHOD

The nonretarded van der Waals inlemctionfree energies (divided by kZ) between the flatPEO surface and spberical protein across watcrmedia, and between the solid substmte andspherical protein across the lerminally attached PEO media, are given as ( 14)

D ^ A l R , Rk r ' 6 k r \ A - , t + 2 R

+h;h) ru

.1thv, (ni - nl)(n) ni)B\5 (n1 + nlttz@3 + ni)t l '1

I

I \ l + n l l / ' + v 3 + n j ) 1 / ' 1 1

, 1 p , ( € r - q X € , € r )4 ( € 1 + € 3 ) ( € r + € 3 )

where ,4 is t}te Hamaker constant betweenbodies I and 2 across a medium 3 (water orPEO in water); R is the radius of sphericalprotein; dis ihe distance belween the flat PEO

renqt alc oaatu tdulirckbt \

t2l

surface and spherical proteint l' js Planck'sconstanq ye is the main electronic absorptionfrequency (3 X l0 '5sec 1);r , ,nr,andn3are

th€ refractive indices ( 15, 16) of phases 1, 2,and 3, respectively, which are determined bythe same method as in our previous paper (9):and er, €2, and q are the static dielectric con-stants ( 15, 16) of phases l, 2, and 3, respec-rively, which are also determined by the samemelhod ds ir our previous paper (9).

The steric rcpulsion free energy of termi-nally attached PEO chains under the eflect ofspherical protein is calculated as the steric re-pulsion fre€ energy per unit surface area. whichis treated as in our previous paper (9), Inul-tiplied by rR'? for simplicity, where R is theradius ofthe spherical protein. The kr and tr,values used for PEO are 0.007 and 0.02, re-spectively. which were developed in our prc-vious paper (9).

The existence of hydrophobic attractiveforces are generally recognized, and such forcesmay be l0 to 100 times stronger than the vander Waals forces ( 17 2l ). The hydrophobiccharacter ofPEO in water has been discussed(10 l3 ); the nearly linear increases in proteinadsorption on PEO surfaces with tempemtulehave been discussed in terms ofthe increasinghydrophobic jnteraction between PEO andprctein ( 13 ) , perhaps due to an increasing hy-drophobicity of PEOwitb temperature, i.e..It.r l/ lo, whe.e 1/ is the relative hydrophobiciryof PEO, I is the syslem temperature, and to isthe reference tempemture ('C). The thicknessofadsorbed PEO appears to increase linearlywlth t€mperature (11),4/La ' t t / to,$,herel, is the thickness of PEO and ao is the thick-ness at the refercnce tempemture. We estimatea relationship between hydrophobicity andthickness of PEO from the Unear relationshipb€tweer the experimenlal data and tempem-ture ( I I, l3). i.e.,1/ - L98l,/la. The scalingtheory relation betweer , and a for a brushmodel is a ,:. D 2/r. A decrease in Dinduc€san increase in volume fraction of PEO (6),dptro cc , a/r, wh€re .rr Lo is the votume fmc,tion of PEO. Thus we can relate an increase

PROTEIN SURFACE INTERACIIONS, Ii l 6 l

in volume fraciion of PEO to the increasedhydrophobicity of PEO from the above con-cepts: 11 - 1.98[dpEol(dpEo)o]'/:, where(dpEo)o is the reference volume fiaction ofPEO ("reference" wil be defined in the nextsection ) . As tlle hydrophobicity of PEO is increased, the hydrophobic interaclion betweenthe PEO surface and protein is also increased.Thc hydrophobic intemction free energy (4 ){divided by tZ) was determined by Pashleyel ai. ( I 8 ) for the case of dihexadecyldimeth-ylammonium acetate (DHDAA) monolayers.For the case ofa sphere ofmdius n nearaflatsurface ( l7),

EH

KT1.90JR. ' i r i r l

where d is tlre distance between a sphere andflat surface. The hydrophobic interaction bc-tween the PEO surface and an assumed un;form hydrophobic surface on the protcjn istreated as 1, 27., etc., ofthe hydrophobic inlcradion (given by Eq. [ 3 ] ) between DHDAAmonolayer surfaces. ln this manner we canvery roughly incorporate the effect of possiblehydrophobic interactions between PEO andprotein in the overall analysis.

The , valuc derived from an adsorptione)iperiment (ll) (for PEO with molecularmass 1900) is 17 A, which wc choose as theexperimental value. Each dillerenl degrcc ofhydrophobjc intemclion betwccn the PEOsurface and hydrophobic patch on the proteinis combined with the steric repulsion at variouslayer thicknesses of PEO for ditrerent , andN values. These calculations were also per-formed as a function of proiein size. "Opti-mum", and N values for each different pro-tein size were thus obtained.

Frc. 2. (a) van de. waals anncrion frcc cnelgy (dnidedbykl) EdiLs ofsphend protein prcfles for four dille@L./ valu€s at .usrant surlae deisn) (D = lr A). (b) vandc. w@ls auraction frft enerey (divided by tl)-Rdiusofsphoical protein proliles for four difrcrcn! surlace den-srly valEs fi conslant di$ance berween rhc PEO surfaeand a prcleii (d = 20 A). (c) van der waals a1lr&Lionftee enerEy (dilidcd bt i7) radius of sphe.ical proreinprofles for four ditrcrcnl surlae demity vlues al co.stanl

the PEO su hce and protein at constant ex-perimentally oblainable surface densitl' (,: 17 A). As thc spherical protein approachesthe PEO suface, the effec1 of the size of theprotejn becomes greater. Similar behavior re-sults al conslant distance, d, with the variarionofsurface density (Figs.2b and c). As tlle sur-thce densjty incredses, the el]ect ofprotein sizeinoeases and the t€ndency js greater at smallerr/ values. We choose d = 3 A as the least dis-tance beiween the PEO suface and a proteinunder the condition ofno adsorption betweenthem [d : 3 A is almost same as thc PEOmonomer size (2.78 A)1. If the atiraclion isgreatcr than the repulsion at this disrance, at-

h!4d ll.iltut tu tf,ltIc s,tu. !

RESULTS AND DISCUSSTON

The van dcr Waals attmction free energy(divided by kZ) between the flat PEO sudaceand a spherical protein is obtained as a func-tion oflhe radius (J?) ofprotcin ( Fig. 2). Fig-ure 2a shows the effecl ofdjstance (d) between

162 IEON AND ANDRADI

lraction is aasumed, ard t}le reverse situationis assumed for the reverse case (repulsion).

To cxamire the etrect of van der Waals at,traction toward steric repulsion, these lwo frccenergies are combined as a function of PEOlayer thickness at d - 3 A ancl shown in Fig.3 atN= 120 and, : 17 A for R = 20 and40 A, respectively. ln this figure, the van derWaals atlraction between the solid subslrateand a protein across the terminally attachedPEO medium is also added, but it does rotplay a significanl rolc. The addition of anyvan der Waals attraction to the steric repulsionenergy changes the curve only slightly, wjlhno significanl change in attraclion or repul-sion. Therefore, van dcr Waals attraclion be-tween the PEO surfac€ and prolein is Deglectedin our further consid€rations.

As mentioned above, the hydrophobic in-teraction between hydrophobic species ismuch stronger than the van der Waals attmc-tion. Ii we asrrr?? that the PEO surface andthe hydrophobic patch on the protein have the

same hydrophobicity as DHDAA, and thesphcrical protein approaches with its hydro-phobic surface oriented loward the PEO sur-facc, the hydrophobic jnteraction ftee energy(divided by kZ) between the llat PEO surfaceand spherical prolein is calculated by Eq. [ 3 ] .The results are shown in Fig. 4 for four dif-ferent .l values as a ftrnction ofthe sphericalprotein size. The same trend is obtained as forthe van der Waals attmction case, and only d: 3 A is chosen for our fufher consideraiion.

We can obtajn the basic hydrcphobic in-teraction licc energy (divided by tZ) at 11 = 3A for each d:ffercnt R value of prorcin. Weassume the PEO protein interaction to besome small percentage of the DHDAA pro-tein interaction and compare witl tie slericrepulsion free energy at different surface den-sily and chain lcngth as a function of PEOlayer thickness. Because tle va.iation of sur-face density atfects the volDme fraction ofPEOand tlus i1s possible hydrophobicily, the ex-perimentally oblainable suface density, l)= 1 7 A, js chosen as a rcference at equilibriumchain lenSth lin this case, the volume fractionof PEO at equilibrium chain length, (dpEo)o= 0.141.Ifthe protein contitrues its approachto the PEO surfacc without adsorption. thethickness ofthe PEO layer decreases. the vol-ume fraction of PEO incredses, the hydropho-bicity of PEO increases, and the hydrcphobicintemction between the flat PEO sDrface anda spherical prolein increases. One, two, andthree percenl hydrophobicity is considcred andthe hydrophobic interaction free cnergies arecalculated for these three assumed hydropho-bicity values of PEO. The combined steric ft-pulsion aDd hydrophobic jnteraction freeenergics (divided bykl) are given inFigs.4b,c, and d for two ditrerenl protein sizes, assum-ing l,2, and 3% hydrophobjcity ofDHDAAfor PEO (N = 120, , = 17 A), respecrively,as a function of the PEO layer tlickness. Forcomparisonl the pure steric repulsion frce en-ersy (divided by kI) is siven in Fig. 4a.

As the hydrophobicity ofPEO increases, rheattractioD increases and no overall repulsion

i

nc . 3. ( a) Stenc repulsion and conbined steic repul-sion and var de. w&ls at@tlon fre eneryis {dividedby tI) PEO layer rhicknc$ prohles for,R = 20 A at N= 120 and t = 17 A. (b) Sieric rcpulsion a.d codbiftdslenc .epDhlon and van der Waals aftncrion fN cnersies(divide.d bykl) PEO laye. uliclles p.onles for 1l : ,14A a t I = 120 and D: l r A .

rorad d cdLid tu tfllrJa( suIt!. !

1 6 3PROTEIN'SURFACE INTERACTIONS' II

I

**,*xm**';r'l*mmmffigiffioccurs, regatdLess ot the size ot pforein -FoJlarger prcteins. the attmction between thc Pl:u

surface and protein occurs preclomrnantlv ln

an early srage ot approach asthe hJdropno

hrcit! of PEO iDcrerses The elpenmenully

obtainable PEO sudace with D = i7 A,has a

Drope(y of protern resistance ( Il ) we teel

that the assumpbotr that the hldrophobrcrr)

ofPEO is l% ofthat ofa DHDAA monolaler

is morc prohable than lhe higher ascumed hy-

dfophobici l ) f iguIe' . lhe l% hldrophobrcr l)"

assumplion is coDsidered for theremarnoer oI

the PaPer.' lo obsene lhe el lef l ol \ur lace { lensrr) or

the rcDUlsioD and arl'aflroD pallefn het$eer

lhe Pio surface and a proLern is inlcreslrng

fhe rariatron of qurface dens't) al con\Lanr

chain lengrh ret lect ' lbc equi l ibr ium laler

lhic lness ol PLO and Induce\ di l l -erenr valu€'

ol Layer lhic lDe\s ol PEo ac lhe prolern aP

proaches. Thc calculaled free energv plo$ as

a functioR of laler thrckness of PEO f-not

sho$n herel show that rhe efi-ect ot surtace

deosrr) r : \eD (omplei fhe la)er Ihrcknes'

of PEO is a funclion of volume lmclron. oI

PEO, aoalthe plol offtee energ) as a tunfiron

of \olume fractron of PEO (instead or layer

thicknes5)shows the laristion ot surface den_

ir \ . $tuch i5 \ery ' imple dnd meanjngful Tbc

combrned lrce eDergie\ as a funclion ol-\olum<

iraoron of PFo ar conqanl chain lenglb ( V- 120 ) for \ ar iou\ , values 3re sr len ' t r I rg

5 for R - )0.40.60 and 80 A respccb\er\ '

it'. plo oi,t' lo$ sudace densrr) I high n

lalueJ staff the curve at low volume li'ac11on

ol Pl O (d,p, u I and lhc repulsion again\r al-

rtucLion increa\e. a5 lbc cbain hds been com-

D.ess€d (as the protein approaches wilhoui

aA.orpr ion r ' A' lhe prolein conl inuet lo ap

oroach $i lhour adqorpl ion. lhe prolern res's-

r :rnL propen) detelops at an) volume lraf l ron

of PEO. as sletu telulsion dL\ek)ps more rap'

hvrat ol.abi,l ont latola? &i'<re \

rE:t:as6j'

164 JEON ,\ND ,\NDR^DE

Frc. 5. (a) Conbined stenc Epulsion and hrdrcphobic inleracrion free endgy (divided by t?) rolumefncrion of PEO proliles for vdous D values ar consladt ndius of sphe.icat protejn (n = 20 Al and N= 120. {b) Combined stedc Epulsion ald hrdrophobic intericlion fte€ encryy (diided by tl)-rolumeAa.dor of PEO proliles for rdious , valu6 at conslant F = 40 ,i and N = I 20. ( c ) Conbin€d stcncrepulsion and hydroDnobic inleraclion Iift eftrsy (divided by i?)-volunc fmclion ofpEo Drcil€s for\a . our D \a l re \ r ' con i .a i l n oO 4roJ \ t ' 0 ,d , ,ombrneJ \ t , , F ru \ io i 1dd h ;d 'ophohrinte@tion li€e enercy (dividcd by &?-) voluDe ftactior of PEO Droiles for vdious D varues al constdrR = 80A and rr'= 120.

t

idb tha hydtophobic aurudion. Th"- pre-dominance of repulsion over athaction atlower volume fractions of PEO is better forprotein resistance. The existence of rcpulsionat lower volume fraction of PEO mcalls thatthe repulsion occurs as soon as the protein ap-proaches the PEO surface. We can obtain theoptimum surface deNity, which starts the re-pulsion at lowest volume fraclion ofPEO, foreach dilierent R value. Bur the dilterence betwee[ the surface densities is small. Thus theapproximate optimum surface density for dif-ferent R valucs becomes, : 9 ll A for R= 20 A, 11,15 A for 40 A, and 13-17 A for60 and 80 A (Figs. 5a, b, c, and d, respec-tively). Frcm thjs result, a relat ell high sur-face densit! o[ PEO i: best to resist small pro-tein$ a lowef surface density of PEO is betterJbt laryer ones: and the hiehest surface de sity(Ior etumple, D : 5 or 7 i) nq) ot be efrirtireJot uotein resistance.

To investigate the effect of chain length ofPEO on protein resistanc€, the combined free

ttuut af.dldd 4d ht4q. sdor, y

1

energies as a function of volume fraction ofPEO at constant surface density (, = l0 A)and conslant size of protein (R = 20 A) forthree different N values are calculated andglven in Fig. 6. For these three diFerent Nval-ues, the attraction has the same magnitudebecause ofthe same surface density. For PEOvrilh longer chain length, the repulsion sta(s

P ,

!

FIG. 6. Combined $encrcpulsionand hydrophobic in-tencnon freeeneryy(dilided by lI) volnne lacrion ofPEO prciit$ for thrce difcrcnt /f values at constant R

IIIIrI

II

I

PROTEIN SURFACE INTERACTIONS. N 1 6 5

at the lower volume fraction of PEO after thecompression of PEO begins- From Fig. 6, weknow that the magnitude of repulsion is thegreatest for the longesl chain length of PEo.PEO wilh the longesl chain lenglh (highesl Nvalue), al the optimum.\urface density, is bestlbr protein rcsistancE. ln ihe attachment ofionger-chain PEO molecules to substrate, tlledecrease in suface density occun naturally(22 24);i.e., ihe smaller chain lenstl resultsin higher surface densjty of attached PEO, al-though it is dimcult to have a very higb surfacedensity ftom the end attachment of a hig!-molecular-weiglrt PEO. The optimum condi-tion for protein resistancc is to produce PEOsurfaces with the longesl chain length whilemaintaining the above-mentioned , values foreach different size ofprolein.

CONCLUSION

This study is based on the assumption ofPEO chains, terminally attached to a solidsubstrate in water, interacting with a linitespherical protein. Steric repulsion is comparedwith van der Waals attraclion. showing thalthe van der Waals attraction has lilde ellecl,We tlen considered hydrophobic interactionbetween the flat PEO surfac€ and sphericdlprotein under lhe'r$rnprid, tlat PEO has alow hydrophobicity and that the protein hasa hydrophobic sudace. The more realistic caseofa sma[, hydrophobic "patch" on ihe proteinremains to be studied.

As the PEO chains are compressed, the sur-face densjty ofPEO is incresed gadually; thusthe "hydrcphobicity" of the PEO layer increascs. This concepl is applied to seek an op-timum surface densily for each different sizeof protein. The study of the effec1 of chainlenglh of PEO on protein rcsislance suggeststhat the longest chain length of PEO is best,assuming constant suface density. The vari-ation in chain length ofPEO induces a va.i-ation in PEO surface density. So tlle optimumcondition of PEO for protein resistance is toobtain the PEO surface with longer chain

lenglh, rnaintaining the "optimal" D valuesfor eacb difi'erent protein size range.

It is hoped and expected that these predictions may be experimentally tested in the rearfuture. For the time being, those investigatonapplying PEO surfaces to minimize proteinadsorption or to enhance biocompatibilitshould be awarc that their results may be sen-sitive to the details of their PEO sufaces, thatis, surface density and chain length, and to thedetalled protein composition and nature oftltesolutlon.

ACl<NOWLEDCMENIS

S I Jco. acknowledees panial suppon Eom the KoreaSciencc and Eryineerilg Foundalion (KOSEF). Thn workhs been pafiially support€d by a ganr lion Ciba CeigyPhamaceuricals (HoBhah. Engladd) to the Cenler lorBiopolymes aL lnte aces ( CBl l. Unilesily of Utah. wethank C. G. Golarder, K. Caldwell, J. Kopecck. and K.Pelmk for slinulaling disu$ions wc thank ProfcserP. G. dc Gcnncs for srinulalins onr inrer€sl in Rlingapp.oaches ro inten.rci.l phenonena.

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1.