J. CHEM. SOC. FARADAY TRANS., 1994, 90(4), 587-590 Kinetic Model for Serum Albumin Adsorption :Experimental Verification Roger Kurrat, Jeremy J. Ramsdent" and Jiri E. Prenosil Department of Chemical Engineering, ETH-Zentrum, 8092Zurich, Switzerland When human serum albumin is adsorbed at a hydrated metal oxide surface, the amounts which can be desorbed by replacing the protein solution with pure solvent steadily decrease. A quantitative kinetic model involving two modes of adsorption, reversible and irreversible, is inferred, and tested by allowing the adsorption and desorption to take place on the surface of planar optical waveguides, and determining the surface coverage from the shift in the mode indices of guided waves due to the adsorption. The method allows the surface coverage to be determined to a precision of ca.1 ng cm-2 every 15-30 s. Excellent agreement with the model was obtained. Protein adsorption has captured the attention of researchers for many years, partly because of its essential technical and medical importance, and partly because of its many baming aspects.',2 There has been no shortage of plausible theoreti- cal models pr~posed,~,~ but many of them predict adsorption kinetics which differ slightly from one model to another, and to test them measurements of high precision are needed. Up until now, the experimental results have only been in qualit- ative agreement with model prediction^.^ A novel approach to this problem is to exploit the well known phase shift which occurs upon total internal reflexion at the boundary between two dielectrics of differing refractive indices (the same phenomenon which is the basis of the tech- niques of ellipsometry4 and reflectometry').In the case of a guided wave propagating in a thin optical waveguide, only discrete modes exist, whose eigenvalues N can be calculated from the opto-geometrical parameters of the For a four-layer waveguide, comprising support S, high refractive index film F, adsorbed adlayer A and cover medium C, the mode equation linking the refractive indices n,, n,, n, and n,, and thicknesses d, and d, -arctan[ (:)2pJ( -)I nf--NZ (z)2pJ(-arctan[ -)]nf--N2 ( 1) where p = 0 and 1 for the transverse electric (TE, containing the field components E,, H, and HJ) and transverse mag- netic (TM, containing the components H,, Ex and E,) modes, respectively, and m = 0, 1, ..., the mode number.The mea- surement of N for any one mode can be used to determine one unknown parameter. A layer of adsorbed protein mol- ecules is characterized by two parameters, its thickness d, and its refractive index n,; measurement of N for two modes allows both nA and d, to be determined by simultaneously solving eqn. (1). ~~ ~~ t Also at : Department of Biophysical Chemistry, Biozentrum, 4056 Basel, Switzerland. 1The z axis is perpendicular to the waveguide which lies in the x, y plane. The TE waves are so called because only the electric field has a transverse component. The adsorbed mass M per unit area of surface is, for a uniform adlayer of thickness d, and concentration within the layer C, 'O,' ' M = (CA -cb)d, (2) where cb is the bulk concentration, and is related to the frac- tional surface coverage, 8, by 8 = Ma/m (3) where a is the area occupied per molecule and m the mass of a single molecule. The refractive index of a protein solution depends linearly upon its concentration according to' nA = n, + cAdn/dc (4) where n, is the refractive index of the pure solvent, and the coeflicient dn/dc depends on the polarizability of the protein and has a quasi-universal value of 0.182 cm3 g-'.lo Combin-ing eqn. (2)-(4), and taking cA % cb ,yields 9= -kIdA m dn/dc (5) The mode indices N can be very conveniently determined if the waveguide incorporates a diffraction grating (period = A).Then, light from an external beam of wavelength I will be coupled into the waveguide provided its angle of incidence a onto the grating satisfies the conditiong*' N = nair sin a + lA/A (6) where nair is the refractive index of the external medium and 1 the diffraction order. Measurement of the angles at which the incoupled power is at a maximum (a series of discrete peaks are observed) allows N to be determined for all possible modes in the waveguide. Experimental Planar optical waveguides of TiSiO,, with a thickness of d, z 180 nm and refractive index nF z 1.8, with an incorpor- ated grating coupler (A = 416.15 nm) were obtained from AS1 AG, Zurich, Switzerland.These are monomode wave- guides which only allow the zeroth TE and TM modes to pro- pagate. They were pre-treated in hot concentrated Caro's acid for 30 min to remove any organic matter, rinsed exten- sively in doubly distilled water, and equilibrated overnight in buffer solution [lo mmol dm-3 "(2-hydroxyethyl) piperazine-N-ethanesulfonic acid-NaOH (HEPES) at pH 7.341. Human serum albumin (Calbiochem) was of high purity (>99%) and was used as received. A small silicone to voltmeter k-air bubbles \\measuring aperture Fig. 1 Measuring cuvette. The measuring aperture is the grating in the surface of the optical waveguide (‘chip’), onto which the external beam (He-Ne laser, A = 632.8 nm) is incident from below. The ther- mocouple for monitoring the temperature is located at the bottom of the tube for extracting the air bubbles, barely projecting into the cuvette proper.The cuvette has a semicircular cross section of 1.7 mm2, a radius R of 1 mm and is 8 mm long; the length x from the middle of the inlet tube to the middle of the measuring aperture (the grating coupler region) is 3.5 mm. rubber flow-through cuvette was sealed to the surface of the waveguide over the grating region such that the waveguide formed one wall of the cuvette (Fig. 1). Protein solutions of concentration cb were drawn through the cuvette using a peristaltic pump at a rate F of 0.56 mm3 s-‘. A second pump, operating at a quarter of the rate of the first, drew out material before the measuring area; the object of this was to remove any adventitious gas bubbles in the inlet stream which would disturb the guided modes.Temperature was monitored by a thermocouple inserted into this second outlet port. The measurements of a were carried out using an IOS-1 goniometer scanning device (AS1 AG, Zurich), which allows a to be determined with a resolution of 1.25 x rad, and hence N [eqn. (6)] to be determined to an accuracy of +2 x The light source was a linearly polarized He-Ne laser, I, = 632.8 nm, oriented such that the plane of polariza- tion made an angle of 45” with the plane of reflexion; hence the TE and TM modes were excited with equal intensities. The Model Under the experimental conditions used, the Reynolds number is ca.1. Flow is laminar, and since the diffusion coef- ficient of proteins is very small, the Peclet number is large, of the order 1O00, and hence the hydrodynamic boundary layer is about ten times thicker than the diffusion boundary Under these conditions the flux I to the surface is given by an expression of the form DcdS, where 6 is the diffu- sion boundary layer thickness. If every molecule arriving at the surface were immediately and irreversibly adsorbed, dM/dt would be equal to I. However, some of the adsorbed protein may be desorbed by flushing the cuvette with pure buffer solution, although the proportion desorbed tends to decrease as the surface fills up. Therefore, a reversible process must also be taken into account. Let us define rate constants k, and kd for adsorption and desorption, respectively, and in addition a rate constant ki for J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 irreversible adsorption. The adsorbed molecules are divided into two types, reversibly and irreversibly adsorbed, with coverages M, and Mi, respectively, such that M = M, + Mi (7) k, and ki may be a priori and, as will be seen, are a posteriori different from one another. Now we define a layer directly above the surface, in which the concentration of protein is c, (Fig. 2). At first glance, the total net rate of adsorption (i.e. the rate of change of the experimentally measured quantity M) is, according to the scheme of Fig. 2, dM/dt = (k, + ki)cS$ -kd M, (8) where $ denotes the fraction of the surface available for adsorption.Continuity in this layer, i.e. dc$dt = 0, means that I + k, M, = (k, + k&, $ (9) where I is now the net flux to the layer: I = (Cb-c,)D/6 (10) I may be eliminated between eqn. (9) and (10) to give an expression for c, The thickness of the diffusion boundary layer is given by” 6 = (3/2)(D~R/u)”~ (12) In this equation x and R depend on the dimensions of the flow cell and are defined in the legend to Fig. 1, and U is the maximum velocity of the fluid in the cell, given by U = 3F/(2A) (13) where A is the cross-sectional area of the cell. According to the Langmuir model, $ = 1 -8. Since pro- teins being adsorbed at random positions on the surface leave gaps between themselves too small to enable other proteins to be adsorbed (multilayer formation can be excluded because the adsorption always tends to a definite plateau), this expression does not accurately describe protein adsorp- ~~ layer directly above P DA the surface desorptionI,, ladsorption ?sorption~ ,surface I ka Cb -cs Mr kil kd Mi Fig.2 Reaction scheme for serum albumin adsorption. The distance of the layer directly above the surface from the surface is much smaller than 6. Reversibly adsorbed proteins are drawn resting on one of their apices, and irreversibly adsorbed molecules resting on a side. The lower part shows the rate constants. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 0.24 I 1 NI 6 0,xs 0 0 10000 Fig.3 Typical experimental curves showing M us. time, t ( x). The solid line shows eqn. (6) fitted to the experimental data. The calcu- lated curves using the fitted parameters are: M,(t), (----) [from eqn. (16)]; Mi@),(....) [from eqn. (17)]. Conditions were c,, = 82.1 pg m-', F = 0.56 mm' s-', T = 25 f0.5"C. The arrows labelled a and b indicate, respectively, when protein flow began, and when it was replaced by pure buffer flow. tion, as has been verified by recent experiments.'3,'4 Instead, taking the excluded area properly into account,' 5,16 4 = 1 -4e + (qyn)e2 -[176/(3~2) -40/(.,/3)]e3 + o(e4) (14) where 0(04) are terms of order O4.t Results Fig. 3 shows a typical experimental curve (M us. t). After 5800 s adsorption, the protein solution was replaced with pure buffer.In order to fit the curves to eqn. (8), the following procedure was adopted :each parameter was optimized (using the least-squares criterion) in turn, holding the others con- stant. These optima defined a new search direction, in which the procedure was repeated, and so on until the desired M I b r Fig. 4 Sketch of the influence of the four fitting parameters on the shape of simulated M(t)curves Table I Fitted parameters collected from experiments, with condi- tions as in Fig. 1 k,/1OP6 cm s-l kds -I ki/10-6 cm s-l aa 3.5 -t 1.9 130 k60 1.9 f0.8 15+4 a is calculated from the fitting parameter m/a using a molecular weight of HSA = 65000 g mol-'. '* t Dickman et a1." have calculated the fourth-order term. degree of accuracy was attained.The adjustable parameters used in fitting were k,, ki, and the ratios k$ka and m/a. m is a constant and equal to 1.08 x g.18 Each of these parameters has a distinctly perceptible effect on the shape of a simulated kinetic curve (Fig. 4), and a rough optimum could be found by fitting by eye. Typically, each curve com- prised ca. 100 points; for the four adjustable parameters con- ditions for fitting were therefore very stringent. The parameters D and 6 were fixed: D was taken to be 3.261 x cm2 s-', measured for bovine serum albumin,' which is hydrodynamically almost identical to human serum albumin and 6 was calculated from eqn. (12) and (13) using the cell dimensions given in the legend to Fig.1. Several plausible variants on the model depicted in Fig. 2 were examined initially, but had to be rejected because it was imposible to fit them to the data. For example, addition of a parameter describing the conversion of reversibly adsorbed to irreversibly adsorbed protein was found to have a negligi-ble effect on the goodness of fit, and no good fit was possible if the distinct pathway of irreversible adsorption (parameter ki) was replaced by the conversion of M, to Mi on the surface. Furthermore, it was impossible to fit the simple expression for the rate of desorption, kdM, included in eqn. (8), to the data. In order to obtain satisfactory fits, an inverse square root dependence on the free area had to be included,t i.e.(dM/dt)dcsorption = -kd Mr/J4 (15) The complete model is therefore dMr/dt = ka c, 4 -kd Mr/J4 and dMJdt = kit,$ (17) the experimentally measured quantity being M=Mi+M,, with cb D/6 + kd Mr/J$c, = (ka + kiM + D/S The fitted parameters are collected in Table 1. Discussion From these results the following points could be deduced: (1) The significance of a: The hydrodynamically similar bovine serum albumin is a prolate ellipsoid with major and minor axes of 14 and 4 nm, respectively.20 The experimen- tally determined area a of 14 nm2 therefore implies a vertical orientation of human serum albumin at the solid/liquid inter- face. (2) There are separate pathways for reversible and irrevers- ible adsorption. Although the protein is quite symmetrical regarding its shape chemically it is not at all, and different orientations will bring different amino acids into contact with the surface.These will have different energy bar- riers for adsorption. Our choice of just two rate constants for adsorption, ka and ki, implies that the differences have been subsumed into two distinct groups, which also have different rate constants for desorption, kd and 0 respectively.$ (3) There is no interconversion of reversibly and irrevers- ibly adsorbed forms at the surface. When a particle is desorbed, it will initially attempt to be readsorbed in the t As well as -4, various other powers of 4 were tried but none were satisfactory. $ We intend to correlate these rate constants with the surface chemistry of the protein as soon as the crystallographic coordinates become available.590 0.0006 r I I tn \ NI \ \5 \2--. \ \ \313 \ '. 0 0 6000 Fig. 5 Rate of adsorption (---) and rate of desorption (-) us. time. Both approach zero asymptotically. vicinity of its former adsorption site.21*22 If during its excur- sion into the solution its orientation is randomized, such that irreversible adsorption is also possible, desorption + adsorption would provide a pathway equivalent to the con- version from reversibly to irreversibly adsorbed at the surface (by means of a conformational or orientational change of the adsorbed protein). Good fits could only be obtained by means of separate steps for irreversible and reversible adsorp- tion, implying that the correlation time for rotational motion of the particles is considerably longer than for lateral motion.(4) The rate of desorption is inversely proportional to the square root of the free area available for adsorption, an unex- pected finding. The root free area available for adsorption is proportional to a characteristic linear dimension of the gaps between adsorbed molecules. Hence the protein is desorbed more readily from a crowded interface; the presence of neigh- bours either impedes the formation of hydrogen bonds with the substrate, or else neighbours repel each other electrostati- cally (the isoelectric point of human serum albumin is at about pH 4.5,23and the experiments were carried out at pH 8).Fig.5, showing how the rates of adsorption and desorption vary with time, illustrates a key feature in protein adsorption. As the space available at the surface becomes filled up, the rate of adsorption drops dramatically. Initially, a high pro- portion of the molecules are reversibly adsorbed, but they are slowly replaced by their irreversible congeners, and the rate of desorption drops slowly but inexorably to zero. This is of great significance in establishing a criterion for when to begin regeneration of fouled ultrafiltration membranes and other surfaces contaminated by adsorbed proteins.24 Summary Using planar optical waveguides as substrates for protein adsorption, the opto-geometric parameters of the adsorbed J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 protein layer can be calculated from the mode indices, which can rapidly and accurately be determined from the incoup- ling angle of an external light beam directed onto a diffrac- tion grating incorporated into the planar waveguides. From these opto-geometric parameters, the mass of adsorbed protein per unit area can be calculated to an accuracy of ca. 1 ng cm-2. A complete (packed, ordered) monolayer of human serum albumin would give M = 0.77 pg cm-2. The present method is therefore accurate to about 0.1YOof a monolayer. A simple kinetic model was found to give excellent agree- ment with the measured data. Two states of the adsorbed protein were required, irreversibly and reversibly adsorbed.These states do not interconvert on the surface, but have separate adsorption and desorption pathways, which are believed to correspond to orientations of the molecule distin- guished by the particular amino acids in contact with the surface. The rate of desorption was proportional not only to the mass of reversibly adsorbed protein, but also inversely proportional to the square root of the free area, implying an interesting type of lateral interaction between adsorbed pro- teins, in which neighbours promote their desorption. References 1 F. MacRitchie, Ado. Protein Chem., 1978,32, 283. 2 J. D. Andrade and V. Hladky, Adv. Polym. Sci., 1986,29, 1. 3 I. Lundstrom and H. Elwing, J. Colloid lnterface Sci., 1990, 136, 68.4 R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, North-Holland, Amsterdam, 1977. 5 P. Schaaf, Ph. Dejardin and A. Schmitt, Rev. Phys. Appl., 1985, 20, 631. 6 P. K. 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Rabinowitch, Trans. Faraday SOC.,1937,33, 1225. 22 B. Senger, P. Schaaf, J. C. Voegel, A. Johner, A. Schmitt and J. Talbot, J. Chem. Phys., 1992,97, 3813. 23 P. G. Righetti, G. Tudor and K. Ek, J. Chromatugr., 1981, 220, 115. 24 T. Hediger, Dissertation No. 7933, ETH, Zurich, 1985. Paper 3/05484E;Received 13th September, 1993