Kinetics of antibody binding to solid-phase-immobilised antigen

Journal of Immunological Methods, 101 (1987) 63-71

63

Elsevier JIM04395

Kinetics of antibody binding to solid-phase-immobilised antigen Effect of diffusion rate limitation and steric interaction H~kan Nygren 1, Maria Werthen i and M a n n e Stenberg 2 1 Department of Histology, University of G6teborg, Gfteborg, and 2 Research Laboratory of Electronics, Chalmers University of Technology, G6teborg, Sweden

(Received 20 January 1987, revised received 2 March 1987, accepted 6 March 1987)

The binding of monoclonal antibodies to surface-immobilised antigen was studied. Antibodies against dinitrophenyl-benzene and O6-ethyl-2'-deoxyguanosine with a known affinity for the antigen were used. The amount of bound antibodies was measured by ellipsometry with an accuracy of _+0.15 pmol/cm 2, and a sensitivity of 0.11 pmol/cm 2. The binding rate of the initial antibody binding could become diffusion rate limited, and the binding rate at surface concentrations above 1 pmol/cm 2 was affected by steric interaction between bound antibodies. Bound antibodies did not dissociate when rinsed with saline for up to 20 h, but dissociated in the presence of antigen (0.1 mM). The dissociation rate did not follow any identifiable rate constant. The results are discussed in relation to theoretical models of the kinetics of antigen-antibody reactions at solid-liquid interfaces. Key words: Antibody affinity; Kinetics; Immunoassay; Monoclonal antibody; Solid phase

Introduction Antigen-antibody reactions in a homogeneous liquid phase is a well studied process and the kinetics of the reaction has been described by several authors (for review, see Karush, 1978). In recent years, immunoassays based on liquid-phase reactions have to a large extent been replaced by methods based on antigen-antibody reactions with one of the reactants immobilised on a solid phase. The interpretation of results of solid-phase assays is based on the assumption that the kinetics of the antigen-antibody reaction at a solid phase is equal to the reaction in solution. Measurements of antibody binding to solidCorrespondence to: H. Nygren, Department of Histology. University of GiSteborg, P.O.B. 33031, S-400 33 G~Steborg, Sweden.

phase immobilised antigen have revealed that the kinetics of the reaction differ from the kinetics of the corresponding liquid phase reaction in several respects. The initial forward reaction often becomes diffusion rate limited at plane surfaces (Stenberg et al., 1982; Nygren and Stenberg, 1985) due to the high surface concentration of immobilised antigen together with the slow diffusion of antibodies (Stenberg et al., 1985). The initial diffusion rate-limited binding is followed by a reaction rate-limited association with an unexpectedly low association rate constant (Nygren et al., 1986). The dissociation rate of bound antibody is slower at an interphase than in a solution (Nygren et al., 1985) and the binding of antibody reaches a concentration-dependent saturation level that is not caused by a dynamic equilibrium (Nygren and Stenberg, 1985). The present study was undertaken in order to

0022-1759/87/$03.50 © 1987 Elsevier Science Publishers B.V. (Biomedical Division)

64 further elucidate the mechanisms behind the kinetics of antigen-antibody reactions at a solid-liquid interphase.

Materials and methods

Antigen and antibodies Monoclonal antibodies directed against dinitrophenyl-benzene (DNP antibodies, Mab 41, 47, 49, 51, 53 and 57) were a generous gift from Prof. M. Steward, London. A high affinity monoclonal antibody (ER-6) directed against O6-ethyl 2'-deoxyguanosine (O6-EtdGuO) was a gift from Prof. M. Rajewsky and Dr. J. Adamkiewicz, University of Essen, F.R.G. The characteristics of the antibodies used have been described previously by the suppliers (Rajewsky et al., 1980; Stanley et al., 1983). The equilibrium constants of the antibodies used, measured in solution, are shown in Table I. The DNP was coupled to bovine serum albumin (BSA, Sigma) by mixing dinitrobenzene sulphonic acid and bovine serum albumin in carbonate:bicarbonate buffer (0.1 M pH 9.5). After 24 h, free DNP was removed by dialysis against phosphate-buffered saline (PBS, 0.05 M phosphate pH 7.2). The substitution grade was determined by light absorbance at 280 and 405 nm and an epitope density of 33 determinants/ protein molecule was used for the experiments. The O6-ethylguanosine (O6-EtGuO) was used coupled to keyhole limpet haemocyanin at an epitope density of 80 determinants/protein molecule. The O6-EtGuO preparation was supplied by Prof. M. Rajewsky.

Preparation of Fab fragments Fab fragments were prepared by digestion of Mab 49 (IgG1) with papain in 0.1 M phosphate buffer pH 7.0, with 0.01 M cysteine and 0.02 M EDTA for 16 h at 37°C. The fragments were isolated by gel filtration on a Sephacryl S-200 column as described previously (Nygren, 1982). Fc fragments were removed by affinity chromatography on a Sephadex column with immobilised protein A (Pharmacia Fine Chemicals, Uppsala, Sweden).

TABLE I AFFINITY OF MONOCLONALANTIBODIES AGAINST DNP AND O6-EtdGuO MEASURED IN SOLUTION a Monoclonalantibody 41 47 49 51 53 57 ER-6

Equilibrium constant 4.3 x 106 0.9 X 10 6 4.1 X 10 7 1.1 x 107 1.6 x 107 0.35 X 10 6 2.0 × 101°

a Data from Rajewskyet al. (1980) and Stanleyet al. (1983).

Experiments Methylised silicon wafers were used as substrate (Nygren et al., 1986). The antigen was adsorbed to the surface by immersion of the silicon wafers into antigen-containing PBS (10 /~g protein/ml) overnight. The wafers were then rinsed in water, blown dry and placed in a humidified chamber. Drops of PBS with different antibody content were placed on the wafers for various periods of time. The dissociation of bound antibodies was measured by rinsing for differing time periods in PBS with or without antigen in the solution. In some experiments the rinsing solution was vigorously stirred with a plastic cylinder rotating at 1500 rpm over the silicon plates which were immobilised in a layer of paraffin. The reactions were stopped by rapid rinsing with PBS followed by a short rinse in distilled water and drying in an air current. Control incubations of antibodies on wafers coated with BSA without hapten was performed in every experiment. The amount of antibody bound to the control plates was subtracted from the values obtained by incubation on the hapten-coated wafers. All of the values subsequently presented are adjusted with respect to any background seen in controls.

Ellipsometry The measurement of thin organic films by ellipsometry is based on a physical characteristic of reflected polarized light. When light linearly polarized in a plane impinges on a reflecting surface, the reflected light is elliptically polarised. The shape and the orientation of the ellipse de-

65

pend on the angle of incidence and the optical constants of the surface material. If a thin transparent film covers the surface, the parameters of the ellipse are altered and the magnitude of the changes are well within the realm of direct measurement. The wafers were examined in a comparison ellipsometer (SagaX 125, SagaX, G6teborg, Sweden) and the amount of bound antigen and bound antibody was determined as described previously (Stenberg and Nygren, 1983). The variation of the results of triplicate samples were the same as triplicate readings of one sample. Thus, the variation of the measurement is the main source of uncertainty. All of the values presented have an uncertainty of _+0.15 pmol/cm 2. The theorethical considerations behind the analysis of data have been described previously (Nygren et al. 1986). The equation used for calculation of diffusion limitation is the solution of Fick's law of diffusion for plane surfaces: S = (2/v~-) C 0 ~ 7

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Negatioe staining The antigen-antibody complexes were examined in the electron microscope after negative staining with uranyl acetate. Sample-supporting grids were made by silicon etching of oxidised silicon wafers as described previously (Stenberg et al., 1987). The resulting quartz membrane was made hydrophobic by incubation in vaporized hexamethyldisilazane (Dow Corning). The grids were immersed in DNP-BSA (10 ffg/ml) for 30 min, rinsed in PBS and placed in a moist chamber. Drops of freshly diluted antibody solutions were placed on the grids and were allowed to react for various periods of time. The reaction was stopped by rinsing with saline followed by 2% uranyl acetate. The excess of uranyl acetate was blotted off with a filter paper and the grids were dried in air.

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Fig. 1. The amount of bound antibody (pmol/cm2 _+0.15 p m o l / c m 2 error of measurement) measured by ellipsometry in relation to reaction time. a: Anti-DNP antibodies (O, Mab 49 and i , Mab 57) at 30 # g / m l and (zx, Mab 49 and ©, Mab 57) at 100 /~g/ml. b: Anti-DNP antibodies (zx, Mab 41; A, Mab 47; + , Mab 51; and x , Mab 53) at 30 ffg/ml (lower curves) and 100 /~g/ml (upper curves), c: Anti-O6-EtdGuO antibody Mab ER-6 at three different concentrations (100 ffg/ml, 10 /~g/ml and 5 p.g/ml).

66

electron microscope at an accelerating voltage of 80 kV. Photographs were taken at 50000 × magnification and were further enlarged to 300 000 times for evaluation and quantitative measurements of the number of antibody molecules bound per unit area.

above bodies 47, 51 49, 57 bound

1-1.5 p m o l / c m 2 for all monoclonal anti(Mab). The initial binding rate of Mabs 41, and 53 (Fig. lb) is lower than that of Mabs and ER-6 (Figs. l a and c). The amount of antibody plotted in relation to the maxi-

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Fig. 2. The amount of bound antibody, measured by ellipsometry, in relation to the calculated amount of antibody that could reach the surface by diffusion, a: Mabs 49 (O), 57 (11) and E R - 6 ( × ) . Data from Fig. l a a n d c. b: Mabs 41 (zx), 47(A), 5 1 ( + ) and 5 3 ( × ) . Data from Fig. lb.

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Fig. 3. The amount of bound antibody (error= + 0 . 1 5 p m o l / c m 2) in relation to the logarithm of reaction time. A diffusion rate limited reaction is indicated by a line. a: M a b 49 ([]) a n d 57(11) at 1 0 0 / ~ g / m l . b: Mab 41 (zx), 47 (A), 5 1 ( + ) and 5 3 ( × ) at 100 ~ g / m l . c: M a b ER-6 at 100 t~g/ml.

67

m u m amount of antibody that could reach the surface by diffusion is shown in Figs. 2a and b. As can be seen the initial binding of Mabs 49, 57 and ER-6 is diffusion-rate limited (Fig. 2 a ) while the binding of Mabs 41, 47, 51 and 53 is not strictly limited by diffusion (Fig. 2b). In Fig. 3 the amount of antibody bound is plotted versus the logarithm of time for up to 72 h. For the anti-DNP antibodies (Figs. 3a and b)

the amount of bound antibodies shows a linear relation to log(t) in this time interval, which indicates that the binding of antibodies continues slowly without reaching a certain saturation level. The association rate of Mabs 41, 47, and 51 decreases at an amount of bound antibodies of about 1.5 p m o l / c m 2. A time delay is seen as a plateau in the curve of the time dependence of antibody binding (Figs. lb and 3b). After about -11 -

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Fig. 4. Dissociation of bound antibodies. The amount of bound antibody (_+ 0.15 p m o l / c m 2 ) has been plotted against time of rinsing in buffer with or without antigen, a-d: Dissociation with PBS (D), D N P - l y s i n e ( O , 0.1 m M D N P ) a n d D N P - B S A ( I , 0.1 m M D N P ) . a = M a b 41, b = M a b 47, c = M a b 51, d = M a b 53. e: Dissociation in the presence of DNP-lysine (0.1 m M D N P ) of Mab 49 (O), Mab 57 ( I ) and Mab E R - 6 ( O ) . f = Dissociation of Fab fragment of Mab 49 in PBS (13), PBS with stirring at 1500 r p m (m) and in the presence of DNP-lysine ( O , 0.1 m M D N P ) .

68

50 s delay the binding increases, but with a lower association rate than the initial. The time delay of antibody binding is also seen with Mabs 49 and 57 in Figs. la, 2a and 3a at an amount bound of 1.0-1.5 p m o l / c m 2. The binding of ER-6 stops at an amount of bound antibodies of 1.2 p m o l / c m 2 (Figs. lc and 3c). Dissociation The dissociation of bound antibody, after rinsing in different solutions, is shown in Figs. 4a-f. With PBS as rinsing solution the bound antibodies do not dissociate within 20 h dissociation time (Figs. 4 a - d ) . Attempts were made to compare dissociation in PBS with and without stirring and there was no change in dissociation rate when the solution was stirred at 1500 rpm. Fig. 4 f shows the dissociation of bound Fab-fragments prepared from Mab 49. In unstirred PBS no dissociation could be detected. In stirred PBS the bound Fab fragments dissociate initially for up to 1 h, but for longer rinsing times the dissociation rates decreases markedly. In the presence of antigen (Fig. 4 f ) the bound Fab fragments are completely dissociated after 5 h of rinsing. (Detection limits in ellipsometry of bound antibodies and Fab fragments are 0.11 p m o l / c m 2 and 0.44 p m o l / c m 2 respectively.). In Figs. 4a-e dissociation of bound antibody in the presence of antigen is shown for all six anti-DNP antibodies. After 20 h of dissociation 78% of the initial amount of antibody 51 is still bound at the surface. For Mabs 41 and 57 less than 5% of the initial amount of antibody ( < 0.11 p m o l / c m 2) is left at the surface. Antibodies 47, 59 and 53 have dissociation rates which are intermediate to these, with an amount bound of 8%,

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29% and 20% respectively of the initial amount of antibodies at the surface. The dissociation of Mab ER-6 starts at a lower surface density as the association stops at about 1.2 p m o l / c m 2. After 20 h of rinsing in the presence of antigen 35% of the initial amount of antibodies is still bound at the surface. Association vs. concentration The amount of bound antibody in relation to antibody concentration after 24 h of association is shown in Fig. 5. At antibody concentrations of 2.56 x 10 -9 M to 2.30 × 10 -s M all six anti-DNP antibodies have a constant amount of bound antibodies of 0.45-0.67 p m o l / c m 2 at the surface. At an increased antibody concentration the amount of bound antibodies is proportional to the logarithm of antibody concentration in the solution. At antibody concentrations higher than 1.88 × 10 7 M the concentration dependence of the

T A B L E II S U R F A C E C O N C E N T R A T I O N OF B O U N D A N T I B O D I E S M E A S U R E D BY E L L I P S O M E T R Y A N D E L E C T R O N CROSCOPY Monoclonal antibody

Concentration of antibodies ( p,g / m l )

Reaction time (s)

Surface concentration of Mab Ellipsometry Electron micros(pmol/cm:) copy ( p m o l / c m 2 )

Intermolecular distance a (nm)

57 47 57

100 100 30

50 15 50

1.9 0.63 1.0

9 17 16

2.07 0.57 0.70

a Value calculated from the surface concentration measured by electron microscopy.

MI-

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Fig. 6. Electron micrograph of monoclonal antibodies (Mab 57) bound to surface-immobilized DNP-BSA. Negative staining with 2% uranyl acetate, a: Control grid incubated in DNP-BSA (100 ~ g / m l for 2 h). The BSA molecules adsorbs to the surface in pattern of spheric structures ( x 200000). b: Grid incubated with DNP-BSA as in a, followed by incubation with antibodies (100 p,g/ml for 50 s) ( x 200000). The insertion ( x 500000) is a detail showing the structure of bound antibodies (arrows).

bound antibody is lower, but still proportional to the logarithm of antibody concentration and no certain saturation level can be identified.

with the picture seen in the electron microscope (Fig. 6b, insert).

Electron microscopy Antibodies bound to surface immobilised antigen were examined in the electron microsope by negative staining with uranyl acetate (Figs. 6a and b). The adsorbed carrier protein (BSA) forms spheric aggregates at the hydrophobic silicon surface (Fig. 6a). The bound antibodies could be seen as Y-shaped molecules (arrows) with a length of 8 nm, width of 7 nm and thickness of 2 nm (Fig. 6b, insert). The number of bound antibodies was counted and the numbers of antibodies seen in the electron microscope were compared to the optical mass of antibodies measured by ellipsometry (Table II). As can be seen, there is an agreement between these results. The calculated distance between molecules (Table II) is consistent

Discussion

In the present study it has been shown that the initial binding of antibodies to solid-phase immobilised antigen is a reaction that often becomes diffusion rate limited. There was no correlation between the antibody affinity for the antigen and the diffusion rate limitation of the association reaction. Diffusion rate limitations of biospecific reactions at solid surfaces have been shown experimentally for enzyme-substrate reactions (Trurnit, 1954), binding of cholera toxin to ganglioside G M t (Stenberg and Nygren, 1982), protein adsorption (De Feijter, 1978; Wojcieshowskij et al., 1986) and binding of polyclonal antibodies to protein antigen (Stenberg et al., 1982; Nygren and

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Stenberg, 1985). The mechanisms behind the diffusion rate limitation of biospecific reactions has been described theoretically (Stenberg et al., 1986). The binding of the anti-DNP antibodies showed a sudden rate decrease at a surface concentration of 1.0-1.5 pmol/cm 2 and then continued at a rate that was linear with the logarithm of time, without reaching an identified saturation level. An amount of bound antibody of 1.5 pmol/cm 2, is equal to a molecule density of 9 × 10 ]1 IgG molecules/cm2. At this antibody density the average distance between the molecules is about 10 nm which corresponds to the molecular diameter of IgG. The time delay of antibody binding could indicate that further binding needs a reorganization of the antibodies at the surface, which would also explain the slow rate of binding at surface concentrations above 1 pmol/cm 2. In a previous study (Nygren et al., 1986), the slow non-diffusion rate-limited binding of antibodies was interpreted as a reaction with an identified forward rate constant. The rate constant was surprisingly low and did not relate to the antibody affinity. Similar calculations of the forward rate constant of the data presented in Figs. 3a and b give values that correspond to those presented previously. It seems reasonable to conclude that the rate of antibody binding above a critical surface concentration of bound antibodies is limited by a reorganization of the layer of bound antibodies. The binding of the high affinity antibody ER-6 was shown to cease at a surface concentration of 1.2 pmol/cm 2 after the initial diffusion rate limited reaction. The saturation level of the binding of Mab ER-6 could be theoretically explained in alternative ways, (i) saturation of the binding sites according to a simple Langmuir isotherm (Langmuir, 1918) (ii) steric blocking of available antigen by bound antibodies (Nygren et al., 1986) or (iii) equilibrium according to the law of mass action. Considering the fact that the epitope density of the O6-Et-Guo was higher than that of the DNP it is not likely that cessation of binding is due to saturation of sites. More probably, the bound antibodies block further binding. The difference compared to the anti-DNP antibodies which continue to bind slowly at higher surface concentrations could be a lack of reorganisation of the layer

of bound ER-6, either due to its higher affinity or due to the higher epitope density. An equilibrium is the least probable alternative since we cannot measure any dissociation of bound antibodies in the absence of antigen in solution. The increased binding strength of antibodies due to their bivalence and the slow diffusion of dissociated antibodies have been suggested as a possible mechanism behind the stability of antigen-antibody complexes at a surface (Berzowsky and Berkower, 1984). We here show that stirring of the rinsing buffer increases the dissociation rate of Fab fragments in PBS, indicating that the diffusion of dissociated ligand may limit the dissociation rate. The finding that antibodies dissociated only in the presence of antigen could be interpreted in two ways, either as blocking of a reassociation or as an induced dissociation of bound antibodies. The dissociation of antibodies in the presence of antigen did not follow a simple and identifiable rate constant and it is not possible to interpret the data from the dissociation experiments as a result of a local equilibrium at the surface. It should be noted that the dissociation of bound antibodies in our experiments is qualitatively similar to the dissociation of adsorbed proteins which has been shown not to proceed spontaneously in buffer, but proceed rapidly as an exchange reaction with other proteins (Bosco and Brash, 1981; Vroman et al., 1980). The relationship between the amount of bound antibodies to the logarithm of the concentration of antibodies could be interpreted as a result of a dynamic equilibrium with a K d at the antibodyconcentration that gives a binding half of the maximum. The experimental data could then be plotted as a Scatchard plot (Nygren et al., 1986). However, the amount of bound antibodies continues to increase during 72 h reaction time and the reaction could then not be at equilibrium after 24 h. We also conclude from the results of the present study that antibody binding at levels above 1 pmol/cm 2 is influenced by steric interactions to a degree where this interaction rather than the intrinsic antibody binding rate is rate determining. Furthermore, in the experimental data shown in Fig. 5, no correlation could be found between the concentration dependence of binding and anti-

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body affinity measured in solution. Thus it could be concluded that the relation between amount of bound antibody and antibody concentration that is demonstrated in the present study and in a previous study (Nygren et al., 1986) is not merely a reflection of the binding strength of the antibodies. In conclusion we have found that the formalism used to describe the kinetics of the antigen-antibody reaction in solution is not satisfactory for the description of the corresponding reaction at a solid phase.

Acknowledgements The present study was supported by grants from the Swedish Medical Research Council Project no. 06235 and from the Research Council of the Swedish Board of Technical Development Project no. 85-3222.

References Berzowsky, I.A. and Berkower, I.J. (1984) Antigen-antibody interaction. In: W.E. Paul (Ed.), Fundamental Immunology (Raven Press, New York) p. 595. Bosco, M.C. and Brash, J.L. (1981) Adsorption of fibrinogen on glass: reversibility aspects. J. Colloid Interface Sci. 82, 217. De Feijter, J.A., Benjamins, 1. and Veer, F.A. (1978) Ellipsometry as a tool to study the adsorption behaviour of synthetic and biopolymers at the air-water interface. Biopolymers 17, 1759. Karush, F., (1978) The affinity of antibody: range, variability and the role of multivalence. In: G.W. Litmann and R.A. Good (Eds.), Immunoglobulins (Plenum, New York) p. 85. Langmuir, I. (1918) The adsorption of gases on plane surfaces of glass, mica and platinum. J. Am. Chem. Soc. 40, 1361. Nygren, H. (1982) Conjugation of horseradish peroxidase to Fab fragments with different homobifunctional and hetero-

bifunctional cross-linking reagents. J. Histochem Cytochem. 30, 407. Nygren, H. and Stenberg, M. (1985) Kinetics of antibody binding to surface immobilized antigen: effect of mass transport on the ELISA. J. Colloid Interface Sci. 107, 560. Nygren, H., Czerkinsky, C. and Stenberg, M. (1985) Dissociation of antibodies bound to surface immobilized antigen. J. Immunol. Methods 85, 87. Nygren, H., Kaartinen, M. and Stenberg, M. (1986) Determination by ellipsometry of the affinity of monoclonal antibodies. J. Immunol. Methods 92, 219. Rajewsky, M., MiJller, R., Adamkiewicz, J. and Drozdiok, W. (1980) Immunological detection and quantification of DNA components structurally modified by alkylating carcinogens. In: B. Pullman, P.O.P. Ts'o and H. Gelboin (Eds.), Carcinogenesis: Fundamental Mechanisms and Environmental Effects (Reidel, F.R.G.) p. 207. Stanley, C., Lew, A.M. and Steward, M. (1983) The measurement of antibody affinity: a comparison of five techniques utilizing a panel of monoclonal anti-DNP antibodies and the effect of high affinity antibody on the measurement of low affinity antibody. J. Immunol. Methods 64, 119. Stenberg, M. and Nygren, H. (1982) A receptor ligand reaction studied by a novel analytical tool - the isoscope ellipsometer. Anal. Biochem. 127, 183. Stenberg, M. and Nygren, H. (1983) The use of the isoscope ellipsometer in the study of adsorbed proteins and biospecific reactions. J. Phys. (Paris), Colloq. 10, 12. Stenberg, M., Elwing, H. and Nygren, H. (1982) Kinetics of reaction zone formation with radial diffusion of ligands over a receptor-coated surface. J. Theor. Biol. 98, 307. Stenberg, M., Stiblert, L. and Nygren, H. (1986) External diffusion in solid-phase immunoassays. J. Theor. Biol. 120, 129. Stenberg, M., Stemme, S. and Nygren, H. (1987) An improved negative staining technique using a thin quartz membrane as sample support. J. Staining Technol., in press. Trurnit, H.J. (1954) Studies on enzyme systems at a solid-liquid interface. I1. The kinetics of adsorption and reaction. Arch. Biochem. 51, 176. Vroman, L., Adams, A.L., Fischer, G.C. and Munoz, P.C. (1980) interaction of high molecular weight kininogen, Factor XII and fibrinogen in plasma at interfaces. Blood 55, 156. Wojcieshowskij, P., Ten Hove, P. and Brash, I.L. (1986) Phenomenology and mechanisms of the transient adsorption of fibrinogen from plasma. J. Colloid Interface Sci. 111,455.