Quantitation of reversible binding by particle counting: Hapten ...

Proc. Nail. Acad. Sci. USA Vol. 89, pp. 4703-4707, May 1992 Immunology

Quantitation of reversible binding by particle counting: Hapten-antibody interaction as a model system (equilibrium binding constants/ligand-receptor interactions/carboxylate-modified polystyrene spheres/low-angle light scattering)

Y. K. SYKULEV*t, D. A. SHERMANt, R. J. COHEN§, AND H. N. EISEN*t *Center for Cancer Research and Departments of tBiology and *Physics, Massachusetts Institute of Technology, and §Harvard-MIT Division of Health Sciences and Technology, Cambridge, MA 02139

Contributed by H. N. Eisen, February 10, 1992

ABSTRACT With a view toward developing a general method for measuring intrinsic equilibrium constants for the reversible interactions between two ligands, we used an antibody-hapten model system [2,4-dinitrophenyl (DNP) hapten and anti-DNP antibody] to explore an approach based on particle counting of uniform polystyrene spheres to which the hapten is coupled covalently. This approach was made possible by an optical pulse particle size analyzer that accurately counts individual sphere clusters and quantitates with high precision specific aggregation of spheres crosslinked by antibody. The reduction in crosslinking that results from competition for antibody binding sites between a soluble DNP ligand and immobilized DNP groups on the spheres provides the basis for measuring the intrinsic equilibrium constant for the soluble ligand-antibody interaction. The binding constants measured in this way for several DNP ligands and an anti-DNP antibody (2A1) agreed with the values obtained by conventional methods. The range of intrinsic equilibrium constants that can be determined by particle counting is likely to be exceptionally wide and a value as low as 103 liters/mol has been measured. And since all soluble antigens, regardless of their mass, acquire the same ability to scatter light as a result of their immobilization on the much larger uniform spheres (0.36 pmm), the approach described here should be applicable to virtually any molecularly dispersed antigen and its monoclonal antibody.

low molecular weight 2,4-dinitrophenyl (DNP) ligands and a monoclonal anti-DNP antibody. Our results demonstrate the feasibility of this approach and suggest that, with suitable modifications, it should be applicable to any molecularly dispersed antigen and its monoclonal antibody and, perhaps, to other interacting ligand-receptor systems as well.

MATERIALS AND METHODS Spheres. Uniform carboxylate-modified polystyrene spheres 0.36 ± 0.01 jum in diameter were supplied (lot 10-31-10) by Interfacial Dynamic (Portland, OR). Chemicals. N6-tert-Butyloxycarbonyl-L-lysine (t-boclysine) and t-boc-lysine O-t-butyl ester (t-boc-lysine-t-bu) were from Bachem Bioscience. All other chemicals were analytical or higher grade and were supplied by Sigma or Fluka. Antibody Purification. Monoclonal antibody 2A1 (IgGl) against the DNP group was affinity purified from ascites or culture supernatants. The antibody was adsorbed on DNPlysine covalently attached to Affi-Gel (Bio-Rad) and was eluted with DNP-glycine (10 mM in 100 ,M sodium bicarbonate). The hapten was removed by dialysis against phosphate-buffered saline (PBS; pH 7.6) followed by ionexchange chromatography on Dowex 1-X8 (Cl form) (BioRad). The purity of antibody preparations was checked by SDS/PAGE. Protein concentrations was determined by micro BCA assay (Pierce). Covalent Attachment of DNP-Lysine to CarboxylateModified Spheres. Spheres (3 x 1011) in 200 Al of water were dispersed in 1.3 ml of 50 mM 2-(N-morpholino)ethanesulfonic acid (Mes) buffer containing 0.05% Triton X-100 (pH 5.5) (MesTX100). A freshly prepared solution of 1-ethyl-3-(3dimethylaminopropyl)carbodiimide (2-4 mg/ml in MesTX100) was introduced to bring the final vol to 2 ml, and 100 Ag of 1-hydroxybenzotriazole in 10 1. of dimethylformamide was immediately added. After gentle agitation for 10-15 min at room temperature (220C-250C), the reaction mixture was added to 2 ml of MesTX100 containing 660 nmol of DNP-lysine (10-fold molar excess of DNP-lysine over the number of carboxyl groups on the spheres) and gentle agitation was continued for 2 hr. To vary the density of DNP groups on the spheres, the reaction was also carried out with mixtures of DNP-lysine and t-boc-lysine, maintaining the same total concentration of the lysine derivatives (165 AM) and varying the proportion of DNP-lysine from 5% to 50%o of the total. For most experiments, we used spheres that were prepared with a mixture of 20% DNP-lysine and 80%o t-boclysine. The number of DNP groups per sphere was estimated from the difference between concentration of DNP-lysine in the reaction mixture before and after coupling to the spheres.

The reversible binding of antigens by antibodies and by antibody-like receptors on T cells underlies the myriad of phenomena that are triggered by antigen recognition by the immune system. Each of these binary interactions can be characterized quantitatively by an intrinsic equilibrium constant, and it is the differences among these constants that account for the often exquisite specificity of immune reactions. To measure the equilibrium constants, a wide variety of methods have been used, and each is significantly limited by various considerations-e.g., by the narrow range of constants that can be reliably determined, by a requirement for special spectral properties (e.g., fluorescence) of antigen or antibody, or by the necessity to introduce special prosthetic groups into one or the other reactant. With the aim of developing a universal method, applicable to any molecularly dispersed antigen and its monoclonal antibody, we are exploring an approach in which the antigen (or a hapten substitute for it) is immobilized on uniform polystyrene spheres and the spheres are subsequently crosslinked by the corresponding antibody. The crosslinking can be measured with great precision and exquisite sensitivity, detecting as little as one sphere dimer in 104 or 10- monomers, with a single-particle light-scattering instrument, termed an optical pulse particle-size analyzer (1). This particle-counting approach has been examined here with a model system that uses The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. §1734 solely to indicate this fact.

Abbreviations: DNP, 2,4-dinitrophenyl; DNP-lysine, N6-DNP-Llysine; t-boc-lysine, NE-tert-butyloxycarbonyl-L-lysine; t-boc-

lysine-t-bu, NE-t-boc-L-lysine O-tert-butyl ester. 4703

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To remove uncoupled ligand, the DNP-covered spheres were dialyzed exhaustively against 10 mM phosphate buffer, containing 0.05% Triton X-100 and 140 mM NaCl (pH 7.6) (PBSTX100), through Spectra/Por (Spectrum, Los Angeles) dialysis membranes (500,000 molecular weight cut off). Stored at 4TC, the modified spheres are stable for at least 1 year. Evaluation of Cluster-Size Distribution of DNP-Covered Spheres Crosslinked by Anti-DNP Antibody. DNP-covered spheres (120 ,ul) in PBSTX100 with 0.02% NaN3 were added to an equal volume of the same buffer containing 2A1 anti-DNP antibody at various concentrations (5-30 ,ug/ml). In the final reaction mixture, the concentration of spheres was 0.92-2.1 x 108 spheres per ml and MgCl2 was at 5 mM. After incubation at room temperature (220C-250C) in particlefree polystyrene cuvettes for 0.5 hr to several days, the reaction mixtures were diluted in particle-free water to a concentration of =106 spheres per ml and injected into a hydrodynamically focused optical flow cell illuminated by a focused laser beam (514 nm) in the optical pulse particle-size analyzer (1). The injection rate (usually 0.012 ul/min) was adjusted with a precision syringe pump Harvard 22 P (Harvard Apparatus) so that no more than one cluster at a time was illuminated. Since the spheres are uniform, the intensity of the light scattered at small angles ( (n -)Cn b =b n==11 -_ 1 n nCn n=l

RESULTS Characterization of DNP-Covered Spheres. The particlecounting method described here depends on the stable dispersion of hapten-modified spheres as monomers in the absence of crosslinking antibody molecules. A critical factor is the high density of carboxylate groups on the surface of the spheres, resulting in repulsive electrostatic forces that minimize nonspecific aggregation. When DNP-lysine or t-boclysine was covalently coupled to the spheres, each sphere NO2

C (CH3)3 0

C(CH3)3

JN02

co

co

NH

NH

NH

(CH2)4

NH -CH-COO 1

E

where .I'nCCnY/Xn=Cn is the mean cluster size (h). Inhibition of Specific Aggregation of DNP-Covered Spheres by Soluble Ligand and Determination of Equilibrium Constant. DNP-covered spheres were diluted in PBSTX100 with 0.02% NaN3 to a concentration of 1.8-2.4 x 108 spheres per ml and were mixed with an equal volume of a solution of anti-DNP antibody containing increasing amounts of a competing ligand, whose intrinsic affinity for the antibody was to be determined. The final concentration of antibody was 10 ,ug/ml in all samples. After the samples were incubated in particle-free cuvettes for 2-5 days at room temperature (22°C-25°C), the parameter b was determined as described above and the dependence of b on the concentration of free competing ligand (H) was plotted. The best fit of experimental points (b, H) to the theoretical curve described by the following equation b = bmax/(1 + KH)2 + bo,

intrinsic equilibrium binding constant for the reaction beantibody and the competing ligand. Sample Preparation for Analysis. All solutions were filtered through a 0.22-jm filter (Millipore) and were stored in particle-free flasks. Before use, the antibody stock solution (500S,ug/ml) was centrifuged for 30 min at about 16,000 x g to remove aggregates and dust particles. Pipette tips were rinsed with optically pure water just before use. Fluorescence Quenching. The equilibrium constant for the binding of DNP-lysine to the anti-DNP antibody 2A1 was determined by fluorescence quenching as described (4). Ultrafiltration. Antibody 2A1 (6.3 nmol; 940 Ag) in PBS (pH 7.6) was mixed with 18 nmol of DNP-glycine in a final vol of 2 ml. After 1 hr at room temperature (22°C-25°C), the reaction mixture was placed in the upper chamber of a Centricon tube (Amicon) equipped with an 11,000 MWCO membrane filter and centrifuged at 2800 x g for 15-20 min at 22°C. The concentration of unbound ligand was determined from the absorbance (Ej6J~Am = 15,890) of the filtrate. The quantity of bound ligand was taken as the difference between the total amount of ligand in the reaction mixture and the amount of free ligand. tween

[21

was used to determine the values for b0, a measure of colloidal (nonspecific) aggregation of the spheres; b,,m, the average number of crosslinks per sphere in the absence of competing ligand (H = 0), corrected for bo; and K, the

(CH 2)4 NH -CH-COO

(CIH2)4 NH- CH-COOC(CH3)3

Sphere Sphere Sphere E-N-DNP-L-Iysine s-N-t-Boc-L-lysine e-N-t-boc-L-lysine-t-bu

carboxyl group that reacted was replaced by a carboxyl group of the coupled ligand (shown below). The density of negatively charged surface groups thereby remained unchanged and resulted in an essentially monomerized population of DNP-covered spheres-e.g., 99.5% monomers (ii = 1.013). According to the manufacturer, carboxyl groups are spaced 18 A apart on the spheres (333 A2 per carboxyl group), corresponding to 10i groups per sphere. To determine how many of these groups were covalently substituted in the reaction with DNP-lysine the spheres underwent reaction under precisely the same conditions with t-boc-lysine-t-bu, and after the spheres were washed free of unreacted reagent, the amount of lysine in 6 M HCl hydrolysates was measured. The results showed that virtually all carboxyl groups were substituted. This meant that the spacing between the attached DNP groups was also =18 A, on average, which is considerably shorter than the average distance between two binding sites of an antibody molecule (60-90 A; see refs. 5-7). Moreover, in our initial preparations the reaction was carried out with DNP-lysine at 10-fold molar excess over sphere carboxyl groups. Under these conditions, the carbodiimide reaction is expected to couple some a-carboxyl and a-amino groups of DNP-lysine to form short DNP-lysyl oligomers

linked at their N termini to the spheres. The resulting close packing of DNP groups suggested that many anti-DNP antibodies might not crosslink these spheres to one another but instead might bind to spheres "monogamously" (8)-i.e., with both sites of an antibody molecule linked to neighboring DNP groups of the same sphere. To minimize this possibility, the spheres used in this study were prepared by reacting them with a mixture of 20% DNP-lysine and 80% t-boc-lysine. We estimate that this mixture resulted in spheres having 1-3 x 104 DNP groups per sphere, corresponding to an average distance between randomly distributed DNP groups of 40-60 A. Given this distance, monogamous antibody binding still could not be ruled out but was probably minimal. Crosslinking of DNP-Covered Spheres by Anti-DNP Antibody Is Reversible. In previous studies of the specific crosslinking of bovine serum albumin (BSA)-covered spheres by anti-BSA antibodies, it appeared that once the spheres were crosslinked, they were irreversibly joined to one another (2). However, as shown in Fig. 1, the system reported here is reversible. The mean cluster size of DNP-covered spheres increased progressively with time in the presence of anti-DNP antibody 2A1. But, when an excess of free DNPlysine was added (1 mM), it competed with immobilized DNP groups on the spheres and caused the spheres to dissociate (Fig. 1). Prolonged (2-5 days) incubation of the spheres with antibody molecules in the absence of the inhibiting ligand brought the mean cluster size, ni, to a value (the equilibrium value) that did not change further with time, except for a very small and slow increase due to nonspecific (colloidal) aggregation. In control experiments, DNP-covered spheres were incubated with an isotype-matched irrelevant monoclonal antibody (1B2, IgGl), and no specific aggregation of the spheres was detected. Linear Dependence of Bond Parameter b on Antibody Concentration. We evaluated the dependence of bond parameter b on antibody 2A1 concentration at a fixed concentration of DNP-covered spheres in the absence of free DNP-lysine. Since the binding of antibody to the spheres is reversible, and only a very small fraction of binding sites on the spheres are bound by antibodies it follows that (9)

AO, = 2 Ko (NCO) Aoo,

[3]

A= K1KO (NCO)2 A00,

[4]

and

where AO1 is the concentration of antibody molecules bound to one sphere, A02 is the concentration of antibody molecules that crosslink two spheres, A00 is the concentration of free antibody molecules (both sites unoccupied), C0 is the concentration of spheres in the reaction mixture, N is the number 8

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e-N-D P-L-Iysine

of accessible DNP groups per sphere, Ko is the equilibrium constant for the binding of an immobilized DNP group to an antibody molecule. having two free sites, and K1 is the equilibrium constant for binding an immobilized DNP group to an antibody molecule that has one free site and the other site bound to a DNP group on another sphere. Because of mutual electrostatic repulsion of the spheres and because of steric hindrance, K1 is smaller than KO. The total concentration of anti-DNP antibody (AT) in the reaction mixture is [51

AT = A00 + AO1 + A02.

The concentration of specific crosslinks in the reaction mixture equals A02, and A02

[6]

bCo.

=

AO1 and A02 can be determined from Eqs. 3-6 in terms of the parameter b, the concentration of DNP epitopes on the spheres (NCO), and the equilibrium constants Ko and K1: A00 = b/[NKo) (NK1) Co]

[71

AO, = 2b/[NK1]

t8]

AT = b{1/[NKO) (NK1) CO]

+

2/[NK1]

+

[9]

CO}.

According to Eq. 9 the bond parameter b should depend linearly on antibody concentration. This expectation was confirmed by the data shown in Fig. 2, which plots changes in b values with variations of antibody concentration at a fixed concentration of DNP-covered spheres (1.7 x 108 spheres per ml). Only a very small fraction of antibody in the reaction mixture was bound to the spheres under the conditions used. For example, when the total concentration of anti-DNP antibody was 10 Ag/ml, fewer than one antibody molecule in a million was calculated to crosslink two spheres (Ao2 = 8 pg/ml). The concentration of antibody bound only to one sphere was estimated to be 0.5% of the total (AO1 = 54 ng/ml). Equilibrium Constants for the Binding of Soluble DNP Ligands to the Anti-DNP Antibody. The extent to which the competing ligand reduces the specific crosslinking of spheres serves to measure the intrinsic equilibrium constant for binding of competing ligand to the antibody. We used this effect to measure the equilibrium constant for the binding of DNP-lysine, DNP-glycine, and 2,4-dinitrophenol to antibody 2A1. In a reaction mixture that contains DNP-covered spheres, anti-DNP antibody, and competing DNP ligand, the antibody molecules exist in several states. These are (with the respective antibody concentrations in parentheses) antibody molecules with two free sites (Aoo), with one (Ao0) or two (Ao2)

7

0.3

6

AX

5

IC 4

A

0.2

A

A&

3

n

0.1

2 0

200

400

600

800

1000

1200

time, min

0.0

2.5

FIG. 1. Crosslinking of DNP-covered spheres by monoclonal anti-DNP antibody 2A1 can be reversed by DNP-lysine. Final concentrations of the reactants were 109 spheres per ml and 10 jLg of antibody per ml. Arrow shows time at which DNP-lysine was added (to 1 mM).

7.5

12.5

17.5

Antibody concentration, pg/ml FIG. 2. Crosslinking of DNP-covered spheres is linearly dependent on the concentration of anti-DNP antibody 2A1. Bond parameter b is plotted against antibody concentration.

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sites bound to immobilized DNP groups on spheres, with one (A10) or two (A20) sites bound to soluble competing ligand, and with one site occupied by a soluble competing ligand and the other site bound to an immobilized DNP group on a sphere (All). Thus, the total concentration of antibody in the reaction mixture is AT

=

A00 +

AlO+ A20

+

A01

+

A02

+

All.

[10]

As noted before, under the conditions used only a very small fraction of antibody molecules was bound to the spheres. Hence,

AO,

+ A02 +

All
DNP-glycine > 2,4dinitrophenol) agree with earlier findings with polyclonal rabbit anti-DNP antibodies (11).

DISCUSSION The essence of the particle-counting method described in this paper is that uniform polystyrene spheres, coated covalently with hapten and stably dispersed as monomers, can be specifically crosslinked by antibody molecules. The extent of crosslinking is linearly dependent on the free antibody concentration, and the crosslinking can be specifically reduced by addition of soluble ligands that compete for antibody binding sites with immobilized epitopes on the spheres. Under these circumstances, -the spheres serve as nonperturbative probes with which to monitor the binding of soluble ligands to antibody. As a result, the intrinsic equilibrium constant (or intrinsic affinity) of the antibody for the ligand could be measured without the necessity of separating free from antibody-bound ligand or otherwise disturbing the equilibrium reaction. Because of the sensitivity with which oligomers can be distinguished and counted (e.g., 1 dimer in 104 monomers), very small differences in the extent of crosslinking can be measured with precision, permitting the use of low concentrations of antibody and the measurement of lowaffinity interactions. Indeed, a striking advantage of the particle-counting method is its ability to measure very low-affinity interactions, as low as 1 x 103 liters/mol (Fig. 3, Table 1). This value was determined with only 10 jg of antibody per ml, whereas to determine such a binding constant by equilibrium dialysis, an antibody concentration of -1 mM (=150 mg/ml) would be required. It appears that the only limit to measuring equilibrium constants this low, or lower, is the inherent solubility of the relevant ligands. At the other extreme, there appears to be, in principle, no upper limit to the equilibrium constants that can be measured. Thus the particle-counting method seems to be virtually unlimited in the range of intrinsic equilibrium constants it can measure. Low-affinity interactions are highly significant for many biological processes (12), and the ability to measure them with precision may offer interesting opportunities. Some obvious examples from the immune system are the antibodies made very early in immune responses, before somatic mutations and affinity maturation occur (11, 13). Indeed, it may now be possible to explore the range of intrinsic affinities of antibodies in the repertoire of immunologically naive animals-i.e., before antibody-producing cells have encountered the corresponding antigen. The antibodies involved in autoimmune responses are often also considered to be of low affinity (14), and this method could likewise be used to measure the affinities of such antibodies. A major limitation to the method described here is the long time required for the antibody reaction with spheres to reach equilibrium (2-5 days with the concentrations of antibodies

Proc. Natl. Acad. Sci. USA 89 (1992)

4707

and spheres used in the present study). To overcome this drawback, the kinetics of aggregation will have to be characterized in order to be able to predict from the rate of aggregation early in the reaction the cluster-size distribution at equilibrium. Because they are bivalent, IgG antibody molecules are well adapted for specific crosslinking of hapten (or antigen)coated spheres. It may prove possible, however, to determine intrinsic equilibrium constants when antibody molecules are attached to one set of spheres (A) and antigens are attached to another set of spheres (B) and to follow the specific crosslinking reaction by measuring the formation of A-B clusters. In that event, the approach described here for measuring equilibrium constants of an antibody-hapten model system might be applicable to receptor-ligand interactions more generally. We are grateful to Profs. G. Benedek and P. Schimmel for critical reviews of the manuscript and thank Drs. R. Taylor for supplying ascites fluid, D. Birmingham and W. Sutherland for 2A1 cells, T. Tsomides for helpful discussions on sphere modification, R. Cook and MIT Biopolymers Laboratory for amino acid analysis, and A. Hicks for secretarial assistance. This work was supported by grants from the Whitaker Health Science Fund, the National Science Foundation (8720308-CHE), and the National Cancer Institute (R35CA42504 and CA14051) of the National Institutes of Health. 1. Bowen, M. S., Broide, M. L. & Cohen, R. J. (1985) J. Colloid. Interface Sci. 105, 605-616. 2. von Schultess, G. K., Benedek, G. B. & DeBlois, R. W. (1980) Macromolecules 13, 939-945. 3. Cohen, R. J. & Benedek, G. B. (1982) J. Phys. Chem. 86,

3696-3714. 4. Eisen, H. N. & McGuigan, J. E. (1971) in Methods in Immunology and Immunochemistry, eds. Williams, C. & Chase, M. (Academic, New York), Vol. 3, pp. 395-411. 5. Werner, T. C., Bunting, J. R. & Cathou, R. E. (1972) Proc. Natl. Acad. Sci. USA 69, 795-799. 6. PoIjak, R. J., Amzel, L. M., Avey, H. P., Chen, B. L., Phizackerley, R. P. & Saul, F. (1973) Proc. Nati. Acad. Sci. USA 70, 3305-3310. 7. Schumaker, V. N., Phillips, M. L. & Hanson, D. C. (1991) Mol. Immunol. 28, 1347-1360. 8. Hornick, C. L. & Karush, F. (1972) Immunochemistry 9, 325-340. 9. Cohen, R. J. (1976) Ph.D. thesis (Massachusetts Institute of Technology, Cambridge). 10. Cosio, F. G., Birmingam, D. J., Sexton, D. J. & Hebert, L. A. (1987) J. Immunol. 138, 2587-2592. 11. Eisen, H. N. & Siskind, G. H. (1964) Biochemistry 3, 9961008. 12. Jencks, W. P. (1986) in Design and Synthesis of Organic Molecules Based on MolecularRecognition, Proceedings of the 18th Solvay Conference on Chemistry, November 1983, Brussels, Belgium, ed. van Binst, G. (Spriger, Berlin), pp. 59-80. 13. Eisen, H. N. (1991) in Molecular Evolution on Rugged Landscapes, SFI Studies in the Science of Complexity, eds. Perelson, A. & Kauffman, S. (Addison-Wesley, Reading, MA), Vol. 9, pp. 75-82. 14. Stollar, B. D. (1991) Mol. Immunol. 28, 1399-1412.