Nonspecific Adhesion of Phospholipid Bilayer Membranes in

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Chapter 6

Nonspecific Adhesion of Phospholipid Bilayer Membranes in Solutions of Plasma Proteins Measurement of Free-Energy Potentials and Theoretical Concepts 1

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Proteins at Interfaces Downloaded from pubs.acs.org by UNIV OF TEXAS AT EL PASO on 10/28/18. For personal use only.

E. Evans , D. Needham , and J . Janzen

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Departments of Pathology and Physics, University of British Columbia, Vancouver, British Columbia V6T 1W5, Canada Department of Pathology, University of British Columbia, Vancouver, British Columbia V6T 1W5, Canada 2

Recent experimental advances have made quantitation of weak membrane adhesion possible in concentrated solutions of macromolecules. We report direct measure­ ments of the free energy potential for adhesion of phospholipid bilayers in solutions of two plasma proteins (fibrinogen and albumin) over a wide range of volume fraction (0-0.1). The results are consistent with a thermodynamic model for adhesion based on depletion of macromolecules from the contact zone. Aggregation of c e l l s and other membrane bound capsules i n solutions of large macromolecules i s generally separated i n t o two catagories: s p e c i f i c and non-specific. S p e c i f i c adhesion involves l d e n t i f i a o i e binding reactions between suspended macromolecules and receptor molecules located on the surfaces. Such processes are basic elements of c e l l agglutination ana removal of aDerrant organisms and foreign bodies i n a l i v i n g animal. On the other hand, non-specific adhesion cannot be a t t r i b u t e d to binding of macromolecules a t s p e c i f i c s i t e s on the capsule surfaces. Well known - ana always present even i n the absence of macromolecules are the c l a s s i c c o l l o i d forces that act oetween continuous media, i . e . van der Waals a t t r a c t i o n , e l e c t r i c douDle layer repulsion, other s t r u c t u r a l and solvation forces (1-2). In general, these c o l l o i d a l forces simply superpose on i n t e r a c t i o n s peculiar to the suspended molecules. For b i o l o g i c a l c e l l s with s i g n i f i c a n t s u p e r f i c i a l carbohyarate structures, only e l e c t r i c douole layer (repulsive) i n t e r a c t i o n i s important; van der Waals a t t r a c t i o n and the shorter range - hydration repulsion can be neglected. However for synthetic membranes with small molecular head groups at the water i n t e r f a c e s , a t t r a c t i o n as well as repulsion i s present between surfaces. Even with marked differences of surface composition and topography, c e l l s and synthetic membrane capsules often e x h i b i t s i m i l a r aggregation behavior i n solutions o f large macromolecules, e.g. red blood c e l l s and phospholipid b i l a y e r v e s i c l e s i n solutions of dextran polymers (3_) or i n solutions o f plasma proteins (e.g. fibrinogen and macroglobulins, 4). No s p e c i f i c receptors or binding s i t e s for these macromolecules have 1

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0097-6156/87/0343-0088$06.00/0 © 1987 American Chemical Society

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EVANS ET AL.

Nonspecific Adhesion of Phospholipid Bilayer Membranes

been demonstrated to e x i s t on red c e i l or v e s i c l e surfaces; nence, the aggregation i s l a b e l l e d "non-specific". Likewise, no adequate explanation and mechanisrn(s) have oeen established to provide an understanding of non-specific adhesion between natural or syntnetic membranes due to suspended macromolecules. With recent experimental advances, i t i s now possible to quantitate adhesion energies, t e s t r e v e r s i b i l i t y , and c r i t i c a l l y evaluate disparate theories for non-specific adhesion i n concentrated solutions of macromolecules. Here, we present d i r e c t measurements of the free energy p o t e n t i a l for adhesion of phospholipid b i l a y e r membranes i n solutions of two plasma proteins (fibrinogen and aloumin) over a wide range of volume f r a c t i o n (0-0.1). The r e s u l t s are consistent with a thermodynamic theory for non-specific adhesion based on depletion of macromolecules from the contact zone. Experimental Methods and Materials Solutions of fibrinogen (Imco, Stockholm) or albumin (Calbiochem, San Diego) were formed with 130 mM sodium chloride buffered to pH 7.4 by 20 mM sodium phosphate to give 150 mM PBS. P r o t e i n concentrations were determined from o p t i c a l density at 280 nm (33) and were made-up to give f i n a l concentrations i n the range of 0-iUg% (wt:wt). D-phenylalanyl-L-prolyl-L-arginine chloromethylketone (Calbiochem) was added to the fibrinogen solutions for s t a b i l i z a t i o n . [Note: i t was d i f f i c u l t to produce stable s o l u t i o n s with fibrinogen at high concentration (>6% wt:wt) even with the i n h i b i t o r present.j V e s i c l e s were produced by rehydration of an anhydrous l i p i d ( i - s t e a r o y l - 2 o l e o y l phosphatidylcholine SOPC, Avanti Biochem., Alabama). Although few i n number, some v e s i c l e s i n the f i n a l aqueous suspension were of s u f f i c i e n t s i z e (10~^cm or greater i n diameter) to be used i n micromechanical adhesion t e s t s . The v e s i c l e s were formed i n non-ionic (sucrose or other small sugars) buffers. Hence when resuspended i n iso-osmotic s a l t s o l u t i o n s , the small difference i n index of r e f r a c t i o n between the i n t e r i o r and e x t e r i o r of the v e s i c l e greatly enhanced the o p t i c a l image as shown i n Figure 1. Because of the extremely low s o l u b i l i t y of phospholipids i n aqueous media and the osmotic strength of the solutes trapped i n s i d e the v e s i c l e s , v e s i c l e s deform as l i q u i d - f i l l e d bags with nearly constant surface area and volume (5-6); thus, s p h e r i c a l v e s i c l e s are r i g i d and undeformaole. When v e s i c l e s are s l i g h t l y deflated by osmotic increases i n the external s o l u t i o n , the bending s t i f f n e s s i s so small that the capsule becomes completely f l a c c i d and deformable (7). Thus, f l a c c i d non-spherical v e s i c l e s e a s i l y form adhesive contacts with n e g l i g i b l e resistance to deformation u n t i l the surfaces become pressurized i n t o s p h e r i c a l segments. We have taken advantage of these deformability properties to e s t a b l i s h a s e n s i t i v e method for measurement of adhesion energy between b i l a y e r surfaces ( 6 ^ 8-10). Two s p h e r i c a l v e s i c l e s are selected and transferred from tne i n i t i a l suspension i n a cnamoer on the microscope stage to an adjacent chamber which contains a s l i g h t l y more concentrated buffer (0.15M PBS) plus macromolecules. There, the v e s i c l e s r a p i d l y d e f l a t e to new equilibrium volumes. One v e s i c l e i s aspirated by a small

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Figure 1. Video micrographs of an adhesion t e s t , (a) Vesicles i n p o s i t i o n for contact, (u) Adhesion - equilibrium c o n t r o l l e d by tne suction pressure. (Pipet c a l i b r e ~1 χ l u t e i n ; v e s i c l e diameters ~ 2 χ lu-^cm).

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Nonspecific Adhesion of Phospholipid Bilayer Membranes 91

EVANS ET AL.

micropipet and held with s u f f i c i e n t suction pressure to form a r i g i d s p h e r i c a l segment outside of the pipet, i . e . the "test'* surface for adhesion. The otner v e s i c l e i s aspirated by a second pipet with a low l e v e l of suction pressure controlled to regulate the adhesion process. The second v e s i c l e i s then maneuvered i n t o close proximity of the t e s t v e s i c l e surface (Figure l a ) and the adhesion process i s allowed to proceed i n discrete (equilibrium) steps by reduction of the suction pressure (Figure l b ) . This experimental procedure y i e l d s the tension i n the adherent v e s i c l e b i l a y e r as a function of the extent of coverage of the t e s t v e s i c l e surface, both for the forward process of adhesion and the reverse process of separation. In the tests to be reported here, the adhesion processes were r e v e r s i b l e as shown i n Figure 2. Because of the macroscopic dimensions observable i n these experiments, i t i s not possible to determine the i n t e r o n a y e r forces d i r e c t l y ; however, cumulation o f forces i n t o an i n t e g r a l over distance i s measurable. This i n t e g r a l i s the negative worK or free energy reduction per unit area ( i . e . adhesion energy) f o r assembly of the b i l a y e r s from i n f i n i t e separation to staple contact (where the force between the surfaces i s zero).

Ύ = ~ Ja

n

' dz

(1)

00

Mechanical equilibrium i s established when small reductions i n free energy due to formation of adhesive contact j u s t balance small increases i n mechanical work of deformation of the v e s i c l e (8,11). This v a r i a t i o n a l statement leads to a d i r e c t r e l a t i o n between the free energy p o t e n t i a l f o r adhesion and the suction pressure applied to tne adherent v e s i c l e ,

pT^- = f (geom)

( 2 )

When the product of suction pressure Ρ and pipet radius Rp i s converted to b i l a y e r tension for the adherent v e s i c l e , t h i s equation takes the form of the Young equation where the geometric function i s ( l - c o s 0 ) and θ i s the included angle between the b i l a y e r surfaces. Based on constraints that the v e s i c l e area and volume remain fixed throughout deformation and the mecnanical requirement that the b i l a y e r surface exterior t o the pipet i s a surface of constant mean curvature, the contact angle can be derived from measurements of e i t h e r the diameter or polar length of the adhesion zone (cap on the r i g i d v e s i c l e , 8,11). I f adhesion i s uniform over the contact zone, then a s i n g l e curve i s predicted f o r the r e l a t i o n s h i p Detween pipet suction pressure and the f r a c t i o n a l extent of coverage of the t e s t v e s i c l e as shown i n Figure 2 ( x = polar length of the adhesion zone divided by the diameter of the spherical t e s t surface). To a i d i n selection of an appropriate model for the adhesion process, we c a r r i e d out two a d d i t i o n a l sets of experiments. The f i r s t set involved the following sequence of v e s i c l e adhesion-separation: an adherent v e s i c l e pair was assembled i n the s a l t buffer without macromolecules; adhesive contact was c

c

0

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PROTEINS AT INTERFACES

maintained by van der Waals a t t r a c t i o n (6,10). The adherent v e s i c l e p a i r was transferred i n a few seconds to an adjacent chamber (with care so as not to disrupt tne contact) that contained s a l t buffer with high concentration of macromolecules (5g&, wt:wt). The adhesion energy was then measured oy separation of the contact i n the f i n a l s o l u t i o n . S i m i l a r l y , an adherent v e s i c l e p a i r was assembled i n the s o l u t i o n with macromolecules and transferred to the pure s a l t buffer without d i s r u p t i o n of the contact; the adhesion energy was again measured by separation i n the f i n a l s o l u t i o n . The r a t i o n a l e behind these t e s t s was the expectation tnat macromolecules ( v i a the f i r s t procedure) would l i k e l y be prevented from entering the gap or be trapped i n the gap (via the second procedure) oecause of k i n e t i c r e s t r i c t i o n s . Tnus i f the macromolecules formed cross-bridges, the adhesion energies would be determined by the composition of tne i n i t i a l s o l u t i o n i n which adhesion was established. However, the r e s u l t s were exactly opposite, i . e . the adhesion energies at separation were i d e n t i c a l to values determined for r e v e r s i b l e assembly and separation i n solutions of composition equivalent to that of tne f i n a l s o l u t i o n . Estimates of molecular dimensions (50S χ 450Â for fibrinogen, 12; 38Â χ 150Â for albumin, 13) and values measured for SOPC b i l a y e r separation i n pure s a l t solutions (26Â from x-ray d i f f r a c t i o n and composition data provided by Dr. P. Rand, Brock U n i v e r s i t y ) , i n d i c a t e that no appreciable concentration of macromolecules could be present i n the gap a f t e r v e s i c l e s were f i r s t assembled i n pure s a l t buffer and then transferred i n t o the solution with macromolecules unless macromolecules r a p i d l y diffused into the t h i n gap. Likewise, a f t e r v e s i c l e s were f i r s t assembled i n the s o l u t i o n with macromolecules and then transferred to the pure s a l t b u f f e r , macromolecules would be trapped i n the gap unless these molecules r a p i d l y d i f f u s e d out of the gap into the s a l t buffer. This k i n e t i c "escape" would be u n l i k e l y i f s p e c i f i c cross-bridges existed. 1

The second set of experiments involved an attempt to quantitate tne number of macromolecules captured i n the gap between the adherent surfaces. Mdnerent v e s i c l e s were assembled in a s o l u t i o n that contained f l u o r e s c e n t l y l a b e l l e d macromolecules then transferred to an adjacent chamber that contained the same concentration of the macromolecuie but without fluorescent l a b e l . Since the v e s i c l e s did not separate, i t was expected that the fluorescent macromolecules trapped i n tne adhesion zone would De detectaole over a long time period u n t i l diminished by exchange d i f f u s i o n with the e x t e r i o r s o l u t i o n . Tests with both fluorescently l a b e l l e d fibrinogen and albumin were performed. The r e s u l t s were negative; we could not detect any fluorescence i n the contact zone except at the exceptional l o c a t i o n where there was obvious invagination formed by l i q u i d trapped during the adhesion process. Trapped l i q u i d regions were not formed when the v e s i c l e s were assemoled c a r e f u l l y i n slow-discrete steps; the contact zone appeared uniform i n o p t i c a l thickness. Based on molecular dimensions as estimates of the minimum gap thickness, fluorescence should have e a s i l y been detected with our photometric system for gap concentrations equivalent to 10% of the bulk concentration. The t e s t c l e a r l y showed that there was a s i g n i f i c a n t reduction of molecules i n the gap i n comparison to the bulk concentration.

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Free Energy P o t e n t i a l s for L i p i d B i l a y e r Adnesion Adhesion t e s t s were c a r r i e d out on 5-10 v e s i c l e p a i r s at s p e c i f i c concentrations of e i t h e r fiûrinogen or albumin i n the range of 0-10g% (wt:wt); the r e s u l t s are p l o t t e d i n Figure 3. Since the v e s i c l e surfaces were uncharged at pH 7.4, there was a threshold l e v e l of adhesion energy caused by van der Waals a t t r a c t i o n between the SOPC b i l a y e r s (6,10) at zero concentration. Based on protein density, the concentration range represented volume f r a c t i o n s from 0-0.1. Even for these f a i r l y concentrated s o l u t i o n s , the free energy p o t e n t i a l for adhesion increased progressively with concentration and showed no tendency t o plateau or saturate. This behavior has also been observed for b i l a y e r adhesion i n solutions of dextran polymers (9,14; although the l e v e l s of adhesion energy were s i g n i f i c a n t l y greater i n dextran solutions at comparable volume f r a c t i o n s . The e f f e c t of surface composition and molecular topography was tested by measuring the free energy p o t e n t i a l for adhesion of a red blood c e l l to a sphered l i p i d b i l a y e r i n concentrated fibrinogen s o l u t i o n s ( s i m i l a r experiments were c a r r i e d out at low concentrations previously, 15). Because of the s t e r i c separation maintained by tne s u p e r f i c i a l carbohydrate structures on the red c e i l memorane, there was no perceptable l e v e l o f van der Waals a t t r a c t i o n i n pure s a l t ouffer. In 5g% fibrinogen, the l e v e l of free energy p o t e n t i a l for red c e l l - v e s i c l e adhesion was equal to the free energy p o t e n t i a l i n excess of the van der Waals threshold observed for o i l a y e r - b i l a y e r adhesion i n 5g% fibrinogen. Also, the slope of adnesion energy versus fibrinogen concentration derived from Figure 3 i s s i m i l a r t o the rate o f increase found f o r red c e l l - r e d c e i l adhesion i n fibrinogen solutions (4_). These r e s u l t s demonstrate the non-specific character of the adhesion process, i . e . no recognizable dependence on surface composition. 1

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Theoretical Implications and Methods of Analysis Two diverse views of non-specific adhesion processes form the bases for contemporary theories introduced to r a t i o n a l i z e observations of c o l l o i d a l s t a b i l i t y and f i o c c u l a t i o n i n s o l u t i o n s of macromolecules (see 16-18 for general reviews). The f i r s t view i s based on adsorption and cross-bridging of the macromolecules between surfaces. Theories derived from t h i s concept i n d i c a t e a strong i n i t i a l dependence on concentration of macromolecules; there i s a rapid r i s e i n surface adsorption for i n f i n i t e s i m a l volume f r a c t i o n s (32) followed by a plateau with gradual attenuation o f surface-surface a t t r a c t i o n because o f excluded volume e f f e c t s i n the gap at l a r g e r volume f r a c t i o n s (19-20). The i n t e r a c t i o n of the macromolecule with the surface i s assumed t o be a snort range a t t r a c t i o n proportional to area of d i r e c t contact. The second - completely disparate - view of non-specific adhesion i s based on the concept that there i s an exclusion or depletion of macromolecules i n the v i c i n i t y of the surface, i . e . no adsorption to the surfaces. Here, theory shows that a t t r a c t i o n i s caused by i n t e r a c t i o n of the (depleted) concentration p r o f i l e s associated with each surface whicn leads to a depreciated macrornolecuiar concentration a t the center of the gap. The concentration

93

PROTEINS AT INTERFACES

0^ 0

1 20

1 40

l/(P-R ) P

L_ 60

(cm/dyn)

Figure 2. F r a c t i o n a l area x of tne r i g i d v e s i c l e covereo oy the adherent v e s i c l e versus the r e c i p r o c a l of suction pressure Ρ m u l t i p l i e d by pipet radius K . Triangles ( Δ ) - contact formation; open c i r c l e s (ϋ) - separation; s o l i d curve prediction from mecnanical analysis for a uniform value of adhesion energy. c

p

0.06 • Fibrinogen Δ Albumin 0.04

{HI (erg/cm ) 2

*ι 0.02

I* I

0.00Ο

2

4

I 6

I

ί-

8

10

12

g % (w/w) 2

Figure 3. Adhesion energy (erg/cm ) for SuPC o i i a y e r s i n ϋ.15 M s a l t (PBS) plus either albumin or fibrinogen.

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95 Nonspecific Adhesion of Phospholipid Bilayer Membranes

reduction i n the gap ( r e l a t i v e to the e x t e r i o r bulk solution) gives r i s e to an osmotic e f f e c t that acts to draw the surfaces together (21-22). When equilibrium e x i s t s between the gap and the bulk, s t a b i l i z a t i o n or approach to a plateau l e v e l i s not anticipated for s t r u c t u r e l e s s surfaces (14). The free energy p o t e n t i a l for adhesion increases progressively with concentration even at large volume f r a c t i o n s . Thus, adsorption-based and (non-adsorption) depletion-based concepts predict d i s t i n c t l y d i f f e r e n t adhesion properties: ( i ) an excess versus a reduction i n macromolecular concentration i n the contact zone; ( i i ) a quick r i s e i n free energy p o t e n t i a l for aanesion at i n f i n i t e s i m a l concentrations which should l e v e l - o f f and eventually attenuate versus an adnesion energy that progressively increases with concentration without s t a b l i z a t i o n . Also, i t i s expected that adsorption-based phenomena w i l l depend on cnemical a t t r i b u t e s of the suspended macromolecule and surface whereas (non-adsorption) depletion-based processes w i l l depend only on c o l l i g a t i v e properties of the macromolecules i n aqueous suspension. C l e a r l y , our r e s u l t s for adhesion of l i p i d b i i a y e r s i n fibrinogen and albumin solutions are consistent with the (non-adsorption) depletion type of assembly process. This deduction i s based on ( i ) the n u l l observation that no fluorescently l a b e l l e d material was detected i n the gap between b i i a y e r s , ( i i ) the continuous increase of the free energy p o t e n t i a l with concentration even for f a i r l y large volume f r a c t i o n s , and ( i i i ) the transfer of adherent v e s i c l e p a i r s with subsequent separation which showed that adhesion energy depended only on the composition of the medium e x t e r i o r to the gap but not the gap composition. S i m i l a r r e s u l t s have been obtained for adhesion of l i p i d b i i a y e r s i n solutions of high molecular weight dextran polymers (Figure 4, 14). Hence, we have chosen to c a r e f u l l y examine (non-adsorption) depletion-based theories i n conjunction with these experiments. Theoretical development over the past decade or so has focused on analysis of the configurations and d i s t r i b u t i o n of polymer segments i n the v i c i n i t y of a s o l i d surface or between surfaces to predict the deviation of free energy density from that i n the adjacent bulk region (19-25). Even though these studies are very elegant and i n s i g n t f u l , l i t t l e care has been taken to obtain a s u i t a b l e work p o t e n t i a l , the d i f f e r e n t i a l of which y i e l d s stresses at the surfaces. We w i l l o u t l i n e a simple thermodynamic approach that provides a formalism for d e r i v a t i o n of p h y s i c a l stresses from free energy of mixing and cnam configuration (14); then, we w i l l discuss methods for p r e d i c t i o n of stationary concentration p r o f i l e s which r e s u l t from the proximity of non-adsorbing, impermeable boundaries. Variations i n t o t a l free energy associated with adhesion must include both the gap and e x t e r i o r (bulk) regions,

ôF= 5Fg * ôFg Tnese cnanges are subject to conservation requirements for the t o t a l number of solute molecules and the t o t a l volume of gap and e x t e r i o r regions (whicn implies conservation of s o l v e n t ) ,

PROTEINS AT INTERFACES

0.25-

0.20-

0.1 5 -

(erg/cm ) 2

0.1 0

0.05

0.10

Volume Fraction (0.611 χ w t / v o l ) 2

Figure 4. Adnesion energy (erg/cm ) f o r SUPC b i i a y e r s i n Q.i M s a l t (PBS) plus dextran polymers. Number average polymer indices - Np (numoer of glucose monomers). S o l i d and dasned curves - predictions from mean f i e l d theory with f i r s t and second v i r i a l c o e f f i c i e n t s from osmotic pressure measurements (14).

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Nonspecific Adhesion of Phospholipid Bilayer Membranes 97

5 ( V

δ(ΰ ·ν *ΰ ·ν=)Ξθ α

α

Β

R

V

B

) = 0

Vg, V B are the volumes of the gap and bulk regions r e s p e c t i v e l y ; Vg, vg are the mean volume f r a c t i o n s of the solute molecules i n the gap and bulk regions. The t o t a l free energy v a r i a t i o n can oe expressed i n terms of four independent v a r i a t i o n s : ( i ) v a r i a t i o n with respect t o s p a t i a l d i s t r i b u t i o n - 0 and configuration of macromolecules i n the gap (where the mean concentration, thickness-Zg, and contact area-Α f o r the gap are held f i x e d ) ; ( i i ) v a r i a t i o n with respect to mean concentration o f macromolecules i n tne gap (where the s p a t i a l d i s t r i b u t i o n , gap thickness and contact area are held constant); ( i i i ) v a r i a t i o n with respect to gap thickness (where s p a t i a l d i s t r i b u t i o n , mean concentration, and contact area are held constant); and f i n a l l y ( i v ) v a r i a t i o n witn respect to contact area (where s p a t i a l d i s t r i b u t i o n , mean concentration, and thickness for the gap are held constant). Symbolically, the t o t a l v a r i a t i o n i s written as, 5F = 5F

«F|



x X

,

\

(14)

c - ( % / 2 ^ )

and the value o f the concentration at the mid-point o f the gap region, „ r * du Z /2 = β - ] — ; Γ172 (15) g

Rod-like shapes w i l l require more c a r e f u l consideration than globular forms oecause r o t a t i o n w i l l be r e s t r i c t e d i n the v i c i n i t y of the surface before t r a n s l a t i o n . The chemical p o t e n t i a l w i l l involve the uniform mixing of r o d - l i k e molecules and solvent i n a gap which depends on the reduction i n entropy caused by s t e r i c elimination of o r i e n t a t i o n a l states. The phenomenoiogical c o e f f i c i e n t 13^ w i l l depend on gap width. Hence at large

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EVANS ET AL.

Nonspecific Adhesion of Phospholipid Bilayer Membranes

separations, the depletion zones w i l l be scaled by the large dimension o f the molecule whereas, at small separations, depletion zones w i l l oe reduced to the scale o f the shorter molecular dimension. Thus, i t i s expected that the osmotic pressure between the bulk region and the gap w i l l increase progressively over the range of separations beginning at a value characterized by the long dimension of the molecule down to a value given by the shorter molecular dimension; for separations smaller than the shorter dimension, the osmotic pressure d i f f e r e n t i a l w i l l remain constant. In a d d i t i o n , most protein macromolecules contain charged residues that a t t r a c t counterions; thus, there w i l l be v a r i a t i o n s i n ion concentrations commensurate with gradients i n protein concentration. As such, the osmotic e f f e c t due to depletion of the protein concentration i n the gap could be enhanced. For fibrinogen and albumin, i t i s expected that fibrinogen w i l l create l a r g e r free energy p o t e n t i a l s for adhesion at common molar concentrations because the range of the i n t e r a c t i o n i s mucn larger for fibrinogen as previously discussed (even though the osmotic pressures of the s o l u t i o n s are inversely proportional to the molecular weights). Obviously, t h i s i s consistent with our measurements because the osmotic a c t i v i t y of albumin i s about three times greater than that o f fibrinogen but adhesion energies are comparable a t the same mass concentrations. For large r i g i d macromolecules, the free energy p o t e n t i a l for adhesion would be approximated by the magnitude o f the osmotic pressure due to the macromolecules i n the e x t e r i o r s o l u t i o n m u l t i p l i e d by a distance determined by the difference between the s i z e scale o f the macromolecule and the strong repulsive b a r r i e r . C l e a r l y , the magnitude of the free energy p o t e n t i a l s measured i n these experiments are consistent with the product of major molecular dimension and the osmotic pressures for fiorinogen and alDumin molecules i n s o l u t i o n . This preliminary c o m p a t i b i l i t y of numbers for two d i f f e r e n t protein macromolecules and a wide range o f concentrations strongly indicates that c a r e f u l development o f a depletion-oased theory w i l l give successful c o r r e l a t i o n s with these theories as for the dextran polymers. I t i s important t o note that s p e c i f i c binding i n t e r a c t i o n s between proteins and the surfaces would greatly modulate t h i s behaviour. Acknowledgment This work was supported i n part by the Medical Research Council of Canada through grant MT 7477 and the U.S. National I n s t i t u t e s of Health through grant HL 26965.

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