Direct calibration ELISA: a rapid method for the simplified determination of association constants of unlabeled biological molecules

JOURNAL OF IMMUHDlOGICAL METHODS ELSEVIER

Journal of Immunological

Methods 188

(1995)197-208

Direct calibration ELISA: a rapid method for the simplified determination of association constants of unlabeled biological molecules Hendrik Fuchs, Georg Orberger ‘, Rudolf Tauber, Reinhard Gel3ner

*

Institutjiir Klinische Chemie und Biochemie, Virchow-Klinikum der Humboldt-Vniversitiit zu Berlin, Augustenburger Platz I. D-13353 Berlin, Germany Received

13 March 1995; revised 14 June 1995; accepted 27 July 1995

Abstract We present a novel method for the rapid determination of association constants. The method is based on the direct calibration of an enzyme-linked immunosorbent assay (dcELISA) and does not require any external calibration. It combines kinetic and equilibrium binding experiments and can be performed on a single microtiter plate. The absorbance data are evaluated by several linearized plots without the need for sophisticated computations. The dcELISA has been used to analyze the binding of a monoclonal antibody, OKT9, to its cognate antigen, the human transferrin receptor, and yielded an association constant of K, = 2.2 X lo9 l/mol and a complex formation rate constant of k, = 2.7 X lop4 SC’. A 26% larger association constant was obtained with a radioimmunoassay (RIA)-based Scatchard analysis using ‘251-labeled 0KT9. By quantifying the binding of the same iodinated antibody with the dcELISA we were able to verify that the iodination modifies the binding properties of the antibody. The dcELISA thus appears to be superior to all methods requiring covalent modifications. In principle, the direct calibration method can also be combined with all other solid phase assays. It should thus expand their scope in quantifying the binding properties of biologically important molecules. Keywords: ELISA; Radioimmunoassay; Macromolecular interaction

Equilibrium

association

constant;

Dissociation

constant;

Complex

formation

rate constant;

1. Introduction The Abbreviations: hTfR, human transferrin receptor; dcELISA, direct calibration enzyme-linked immunosorbent assay; RIA, radioimmunoassay; PBS, phosphate-buffered saline (1.50 mM NaCl, 10 mM sodium phosphate, pH 7.5); PBST, PBS containing 0.05% (v/v) Tween 20; HRP, horseradish peroxidase. * Corresponding author. Tel.: +49-30-450-69006; Fax: +4930-450-69900; e-mail: [email protected]. ’ Present address: Department of Neurobiology, Swiss Federal Institute of Technology (ETH), HSnggerbe.rg, CH-8093 Ziirich, Switzerland. 0022.1759/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0022.1759(95)00202-2

characterization

of

molecular

interactions

such as antigen-antibody and receptor-ligand binding is an important goal of biomedical research. For the exact quantitation of these interactions the determination of kinetic and equilibrium binding constants is essential. Solid phase assays have gained increasing importance for this application due to their reliability and ease of handling. In contrast to the commonly used radioimmunoassay (RIA) and

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fluorescence transfer assay, the enzyme-linked immunosorbent assay (ELISA) solely depends on the availability of suitable antibodies while the ligand remains unlabeled. However, the determination of binding constants by ELISA requires either the use of competition assays (Friguet et al., 1985; Hoylaerts et al., 1990) or an independent quantitation of the bound l&and. Such a calibration can be achieved (i> by quantitation of unbound ligand and subsequent calculation of bound ligand by subtracting the unbound ligand from the initial input (Kim et al., 19901, (ii) by direct ligand labeling with either biotin (Jackson et al., 1982) or an enzyme (Schots et al., 1988) or (iii) by an external calibration such as ellipsometry (Nygren and Stenberg, 198.5). In contrast to all these methods requiring independent measurements, we have developed a simple procedure for the absolute quantitation of unlabeled ligand that can be performed on a single microtiter plate. The new direct calibration ELISA (dcELISA) utilizes several linearized plots that permit a simple and accurate determination of the association constant. Here we present the theoretical background and the complete mathematical derivation of the new method as well as its application to the quantitative analysis of the binding properties of a typical mouse monoclonal antibody (OKT9) to its cognate antigen, the human transferrin receptor (CD71). This antibody was originally raised against surface antigens of human leukemic cells (Reinherz et al., 1980) and was later shown to bind to the transferrin receptor (Sutherland et al., 1981). It belongs to the IgGl subclass and has a K light chain (Kung et al., 1980). In order to validate the dcELISA, we have compared the results to those obtained by a classical radioimmunoassay performed with the same antigen and ‘251-labeled 0KT9. We show that the direct calibration method is in general applicable to all solid phase binding assays and, if combined with an ELISA, may be superior to a standard RIA, since ligand labeling is not required.

2. Materials and methods 2.1. Materials Tween 20 and bovine serum albumin were purchased from Sigma (St. Louis, MO, USA), protein

Methods 188 119951 197-208

A-Sepharose CL-4B was from Pharmacia (Uppsala, Sweden) and fetal calf serum from Gibco BRL (Paisley, Scotland). Iodo-Gen was obtained from Pierce (Rockford, IL, USA), all other compounds were from Merck (Darmstadt, Germany). 2.2. Purifzcation and I251 labeling of the monoclonal antibody 0KT9

Monoclonal antibodies produced by the hybridoma cell line 0KT9 (ATCC, Rockville, MD, USA) were purified by protein A-Sepharose CL-4B affinity chromatography according to the manufacturer. Purified antibodies were iodinated using the Iodo-Gen method described by Fraker and Speck (1978). Non-incorporated ‘251- was removed by gel filtration on PDlO columns (Pharmacia). 2.3. PuriJication of the transferrin

receptor

Human transferrin receptor (hTfR) was prepared from placenta according to the method of Turkewitz et al. (1988) including the modifications described recently (Orberger et al., 1992). hTfR was eluted from Fe3+-transferrin-Sepharose under non-denaturing conditions with 2 M KCl, 10 mM CHAPS in 50 mM Hepes, pH 7.5. 2.4. Solid phase binding assays Three variations of solid phase binding assays were used to analyze the binding of the monoclonal antibody 0KT9 to immobilized hTfR: (i) binding of unlabeled 0KT9 and subsequent ELISA-derived quantitation, (ii) binding of “‘1-0KT9 and RIA analysis, and (iii) binding of ‘2SI-OKT9 as in (ii), but followed by quantitation as in (i). In general, all solid phase assays were performed in modular 96well microtiter plates at room temperature. Sample volumes were 100 ~1 per well if not specified otherwise. Wash procedures between any two successive incubation steps included three wash steps with 250 ~1 PBST, followed by a 5 min incubation with 150 ~1 PBST and again three 250 ~1 PBST wash steps. The microtiter plates were continuously agitated during all incubation steps in a Varishaker

H. Fuchs et al./Journal

Incubator at medium Great Britain).

speed

(Dynatech,

of Immunological Methods 188 (19951 197-208

Guernsey,

2.4.1. Immobilization of hTfR to the polystyrene surfuce of microtiter plates Different amounts of hTfR and different types of Nunc-immuno modules (Nunc, Wiesbaden, Germany) were used depending on the assay performed. For those with unlabeled antibody, 50 ng hTfR per well were incubated in MaxiSorp U16 modules; for those with ‘251-labeled antibody, either 10 ng/well (saturation curves) or 100 ng/well (all other assays) were incubated in MaxiSorp C8 BreakApart modules. Coating was performed in 100 ~1 PBS for 1.5 h. To prevent non-specific binding, the plastic surface was blocked for 30 min with 200 ~1 PBS containing 3% bovine serum albumin and 10% fetal calf serum. 2.4.2. Binding of unlabeled 0KT9 and chromogenic quantijkation Binding of OKT9 to immobilized hTfR was performed with 10 ng of the purified antibody in all kinetic studies. For saturation binding experiments, an incubation time of 3.5 h was used. Bound 0KT9 was quantitated with an HRP-conjugated monoclonal rat antibody against the mouse K light chain (Dianova, Hamburg, Germany) by incubating 5 ng/well of this secondary antibody for 30 min in blocking buffer containing 0.05% (v/v) Tween 20. The substrate used for the peroxidase-catalyzed reaction was a 0.02% (v/v) solution of 3,3’,5,5’-tetramethylbenzidine in a 40 mM potassium citrate buffer, pH 3.95, containing 0.01% H,O, (Gallati and Pracht, 1985). The enzyme reaction was stopped by adding 50 ~1 of 2 M sulfuric acid. Absorbance was measured at 450 nm in a multi-channel photometer (MR 7000, Dynatech, Denkendorf, Germany) and was corrected both for light scattering effects by subtracting the absorbance at 490 nm and for sample background by subtracting the blank absorbance.

199

apart. The activity of individual wells was determined in a gamma-counter (Berthold LB 2111, Bad Wildbad, Germany) and corrected for background. 2.4.4. Quantitation of bound ‘251-OKT9 with HRPconjugated secondary antibody In order to compare the dcELISA method directly to the RIA method, radiometrically analyzed wells ‘251-OKT9 were reassembled in a micontaining crotiter module rack and processed according to the ELISA protocol as described above. In order to avoid drying of the bound proteins, the total processing time of any well in the gamma-counter was limited to a maximum of 10 min. 2.5. Transfer assay ‘251-OKT9 (25 ng/well) or unlabeled OKT9 (10 ng/well) was incubated with immobilized hTfR for a defined incubation period (between 10 and 70 min). Subsequently, the solution was transferred from the first well to the next, identically coated well and again incubated for exactly the same time. The transfer procedure was repeated between two and seven times depending on the length of the incubation period used. The experiment was designed such that unnecessary wait cycles were avoided and so that the final chromogenic enzyme reaction could be performed simultaneously in all wells. 2.6. Protein determination Protein concentrations were determined as duplicates on microtiter plates using the Pierce BCA protein assay (no. 23225, Pierce, Rockford, IL, USA) and a multi-channel photometer (MR 7000, Dynatech). Molar concentrations were calculated using a molecular mass of 150 kDa for mouse IgG (OKT9) and of 95 kDa for the hTfR monomer.

3. Results 2.4.3. Binding of ‘Z51-labeled 0KT9 Corresponding to the binding studies with unlabeled antibody, a constant amount of 25 ng ‘2510KT9 was used for kinetic experiments and a constant binding time of 3.5 h for equilibrium studies. After the last washing step, modules were broken

The objective of this work was to develop a rapid method permitting a direct calibration of the ELISA and thereby the calculation of equilibrium association constants. For the following analysis we named the immobilized molecule (in this case hTfR) recep-

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Methods I88 (19951197-208

rium conditions for each transfer binding step, the absorbance decays exponentially with the number of transfers (n> (see Appendix A): A,=A,.F”-’

2 3 transfer number

1

4

Fig. 1. Schematic representation of the underlying principal for the direct calibration (dcELISA). An initial amount of dissolved ligand was allowed to bind for a defined time period to the immobilized receptor on a microtiter plate. Subsequently, the solution containing the unbound ligand was transferred to the next, identically coated well and incubated there for the same time. Upon repeated transfer from one receptor-coated well to the next, the ligand ultimately became completely bound. Thus, the sum of all concentration related signals corresponded to the initial amount of ligand.

A, is the absorbance of the first well and F is defined as the transfer factor F = (1 + K, . R,)- ’ . Experimentally, 1nF can be determined as the slope of a semi-logarithmic plot of In A, over the transfer number n. We found that our data comply precisely with this equation as indicated by the excellent correlation coefficients of all transfer plots. Thus, a limited number of transfers is sufficient to determine F at high accuracy. The desired calibration factor c can be expressed as a function of the initial amount of ligand (L,), the absorbance of the first well (A,), and F by combining Eqs. 2 and 3: cxrn= Lll c A, n=l

tar (R) and its soluble binding partner (in this case the monoclonal antibody OKT9) Eigand (L). 3.1. Theoretical

deriuation

of the dcELISA

Within one series of ELISA experiments and within the linear range, the absorbance (A) produced by the enzymatically released chromophore is related by a constant but unknown calibration factor (c) to the amount of bound ligand (RL): RL,=c.A, Our rationale for determining the calibration factor is the assumption, that a defined amount of ligand (L,, e.g. an antibody) must ultimately become completely bound to an immobilized receptor (R,, e.g. an antigen) upon repeated transfer of the ligand solution from one receptor-coated well to the next (transfer assay, Fig. 1). The sum of all absorbance readings must then be related to the initial amount of ligand (L,) by the unknown calibration factor c: co 3c L,= zRL,=c. c A, n=l

n=l

In order to solve the sum of this equation, A, has to be expressed as a function of n. Assuming equilib-

(3)

x1 L, c A, .F”-’ fl=l

=2.(1-F)

(4)

’

The initial amount of immobilized receptor (R,) can be determined by a saturation curve according to: Ro=RLLn-rZ=c.ALQ+l: K, is finally calculated from F and R, rearranged version of the definition of F:

(5) using

a

1-F

K,=

2

F-R, Since equilibrium conditions were assumed for the described method, each serial binding step needs to be equilibrated before the next transfer can be performed. In order to shorten the time required for a the question, of complete assay, we addressed whether it would be possible to use finite binding times and to extrapolate to equilibrium conditions. Assuming the approximations detailed in Appendix B, first order kinetics with a complex formation rate constant k, can be derived for the binding reaction: A, = A,+=( 1 - eekc“)

(7)

The rate constant k, can be determined from this equation as the negative slope of a semi-logarithmic plot of ln( A, _ T-- A,) over t. Again, the experimental data correlate perfectly with the described kinet-

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Methods I88 (1995) 197-208

0°7 time (mm)

I

0

30

I

I

I

I

60

so

120

150

time (mm)

Fig. 2. Kinetic analysis using ELISA data obtained with unlabeled 0KT9. Unlabeled 0KT9 (10 ng) was incubated for various times with hTfR immobilized on a microtiter plate. Bound OKT9 was quantified using HRP-conjugated anti-mouse Ig K chain antibodies and a chromogenic enzyme reaction. A: plot of absorbance vs. time. Maximum binding corresponds to A, _ r = 0.450. The data points represent the mean of duplicate experiments and have an average deviation of 4.3%. B: plot of ln( A, _ x - A,) vs. time. A linear regression according to Eq. 7 leads to k, = 2.7 X 10e4 s- ’ (R* = 0.9921.

its and verify our approximations. Based on Rq. 7, we derived a time-dependent expression for F (see Appendix B for details): F,=F+((R,.K,)-‘ f

1))’

.e-‘c.’

F, is a time-dependent transfer factor determined experimentally for a certain non-equilibrium binding time. The time-independent transfer factor F represents equilibrium conditions (t + m) and can be extrapolated as the ordinate intercept of a plot of various F, over e-kc.r (F-plot). Thus, for a complete direct calibration analysis the following experiments are required: (i) a variation of the binding time to determine k,, (ii) a series

-31

12345678

12345678 transfer number

0.2

F = 0.706

o.oj_-_-_-0.0

0 2

0.4 0.6 e-&r

I 0 8

10

Fig. 3. Direct calibration of ELISA data obtained with unlabeled OKT9. A: transfer plot. Unlabeled 0KT9 (10 ng) was incubated for the indicated binding time in hTfR-coated wells. Between two and seven transfers were performed as indicated by the number of data points (see also Fig. 11. The logarithm of the absorbance was plotted vs. the transfer number to obtain lnF, as the slope of the corresponding linear regression curves (0.956 < RZ < 0.999). All data points represent the mean of three values with an average deviation of 3.6%. Including the absorbances of the first wells A, and the initial amount of ligand CL,,), six individual c, were calculated according to Eq. 4 and averaged to c = 0.362&0.026 nM. E: F-plot. F, obtained for various binding times in (A) is plotted vs. edkc ’ using k, = 2.7X 10mJ s-’ as determined in Fig. 2. According to Eq. B7 of Appendix B, any linear regression curve must pass through the upper right comer of the plot (F, = 1, e-‘c ’ = 1). Applying this condition, we obtained a linear regression resulting in F = 0.706 as the ordinate intercept (Eq. 8).

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Methods 188 (1995) 197-208

of transfer assays at various binding times to determine F, and c, and (iii> a saturation curve under equilibrium conditions to determine R 0. The time-independent F is obtained by combining the results of (i) and (ii> and the inclusion of the result of (iii> permits calculation of the association constant K,. 3.2. Experimental verification of the dcELISA For the experimental verification of the deduced model, the binding of the well characterized monoclonal antibody 0KT9 to its purified antigen, the human transfenin receptor (CD71), was analyzed with the new dcELISA technique. In an independent experiment, “‘I-labeled 0KT9 was used to determine the association constant by a standard radioimmunoassay and Scatchard analysis (Scatchard, 1949). In addition, the potential influence of antibody iodination on its binding properties was determined by performing the same dcELISA analysis with the iodinated antibody instead of the unmodified antibody. We observed a very low background for both the chromogenic (constant absorbance of 0.015 & 0.003) and the radiometric detection system (< 0.05% of the total ligand activity), possibly due to the use of purified components and optimized blocking conditions. The potential loss of 0KT9 in the ELISA during the incubation with the secondary antibody was quantified by using 1251-labeled OKT9 and was found to be less than 15% (data not shown). Since this signal reduction is roughly proportional to the amount of bound 0KT9, it does not induce a systematic error but simply becomes part of the linear calibration factor c.

Table 1 Experimental

results for the binding of unlabeled

4

0

100

200

300

400

OKT9 total (fmol)

Fig. 4. Saturation curve and determination of K, for the binding of unlabeled OKT9 to hTfR. The dcELISA saturation curve was obtained by incubating 1.2-60 ng unlabeled OKT9 CL,,) for 3.5 h in hTfR-coated microtiter plates. Six independent measurements were averaged for each data point; error bars indicate the respective standard deviations. The resulting saturation absorbance of A Lo-,x = 0.536 was converted to RLL,,,, = 0.194 nM according to Eq. 5 using c as obtained in Fig. 3A. This value corresponds to the molar amount of accessible receptor on the microtiter plate surface CR,,). Using Eq. 6 and F as obtained in Fig. 3B, the association equilibrium constant was calculated to K, = 2.15 X lo9 l/mol.

The complex formation rate constant k, was determined by a binding time variation using a constant amount of purified OKT9 (Fig. 2A). A linearized plot according to Eq. 7 yielded a rate constant of k, = 2.7 X low4 s- ’ (Fig. 2B). Although the applied model disregards the true nature of the binding reaction by assuming simple first order kinetics, the excellent accordance with the experimental data justifies the approximations used to derive the time-dependent direct calibration method. To obtain the time-independent transfer factor F and the calibration factor c, six transfer assays were

and labeled ligand 0KT9

Parameter

dcELISA, unlabeled OKT9

RIA/Scatchard, ‘2’I-labeled 0KT9

dcELISA, ‘2sI-labeled OKT9

Time variations Rate constant k, (s- ’ ) Transfer factor F Calibration factor c (nM)

6 2.69 X 10-j 0.706 0.362 f 0.026

Specific activity (cpm/fmol) K, (l/m00 K, = K; ’ (nM)

2.15 X lo9 0.47

1 2.38 x lo-’ _ _ 21*3 2.71 x IO9 0.37

6 2.32 X lo-’ 0.119 2.04 f 0.35 21 f3 2.96 x lo9 0.34

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To determine the molar amount of antigen available for antibody binding (R,), a saturation curve was performed simultaneously with the transfer as-

t=iBmin

t=lOmin

_

-2-

0

100

200

300

-3-

400

‘251-OKT9 total (fmol)

0

10

5 ‘251-OK19

.

.*

15

20

bound (fmol)

Fig. 5. RIA saturation cmve and Scatchard analysis of ““I-labeled 0KT9 binding to hTfR. A: the RIA saturation curve was obtained by incubating various amounts of ‘251-labeled OKT9 in hTfR coated wells for 3.5 h. RIA data were converted into fmol using the specific activity of the labeled antibody (Table I). Six independent measurements were averaged for each data point, the error bars indicating the respective standard deviations. B: Scatchard analysis (Scatchard, 1949). The dissociation equilibrium constant was calculated to K, = 0.37 nM corresponding to K, = 2.71 x IO9 I/mol. Error bars indicate the standard deviation derived from the primary data displayed in A.

12345676

12345678 transfer numbat

1 .O

B

0.6 0.6 li-

.

.

.

0.4 0.2 0.0 LZI 0.0 0.2

done with various incubation periods (Fig. 3). The transfer assays were evaluated according to Eq. 3 by plotting the logarithm of the absorbance over the transfer number for each time variation (transfer plot, Fig. 3A). Six F, were obtained in logarithmic form as the slopes of the linear regression curves. They served in turn for extrapolating F by a secondary plot of F, over eekc.’ according to Eq. 8, using the complex formation rate constant determined in Fig. 2B. F was extrapolated to 0.71 (s = 0.026, R2 = 0.87) (Fig. 3B). The calibration factor c was calculated independently for all six time variations according to Eq. 4 and was averaged to c = 0.362 f 0.026 nM.

.

i==o.119 0.4 0.6 a-kct

0.8

1.0

Fig. 6. Determination of K, by dcELISA performed with ‘*‘Ilabeled 0KT9. A: transfer plot. ‘251-labeled 0KT9 (25 ng) was used for the transfer assay, which was performed essentially as described in Fig. 3. The data points represent the mean of duplicate experiments with an average deviation of 6.6%. The correlation coefficients for the six linear regression curves yielding F, were in the range of 0.886 < R* < 0.966. The average calibration factor was c = 2.04tO.35 nM. E: F-plot. F, obtained for the indicated binding times in A were plotted vs. eWkc ’ using k, = 2.32X 1O-4 SC’ derived by a kinetic analysis performed as described in Fig. 2 (data not shown). The ordinate intercept of the regression curve yielded F = 0.119. R, = 2.5 nM was determined as described in Fig. 4 (data not shown). Using Eq. 6 the association equilibrium constant was calculated to K, = 2.96X lo9 l/mol.

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of Immunological Methods 188 (19951 197-208

says, but with an extended 3.5 h incubation period to ensure equilibrium conditions (Fig. 4). At the saturation limit, the molar amount of accessible antigen R, (hTfR) equals that of the antigen-antibody complex RL L,,+= (Eq. 5). Multiplying the saturation absorbance with the calibration factor c leads to RL L,+Z = 0.194 nM. With F and R,, the association constant K, for the binding of 0KT9 to the hTfR was finally calculated to K, = 2.15 X 1O9 l/mol using Eq. 6. Assuming K, = K; ',one obtains K, = 0.47 nM (Table 1). To validate the results of the dcELISA, the association constant was also determined with a standard radioimmunoassay and a Scatchard analysis using ‘251-labeled monoclonal antibody 0KT9 (Fig. 5A). The specific activity of the purified antibody (140 cpm/ng) was obtained by a standard protein determination. From the slope of the Scatchard plot an association constant of K, = 2.71 X lo9 l/mol was calculated (Fig. 5B). The slightly larger association constant determined with the RIA as compared to that measured with the dcELISA (Table 1) could either indicate a systematic deviation or could be due to an increased binding affinity of the iodinated antibody as compared to the unmodified antibody. In order to discriminate between these two interpretations, we performed a dcELISA procedure with iodinated 0KT9 under exactly the same conditions as in the initial experiment with unmodified antibody (Fig. 6). The resulting association constant of K, = 2.96 X lo9 l/mol is almost identical to that obtained by RIA and Scatchard analysis (Table 1).

4. Discussion The present study describes a new, rapid solid phase assay for the accurate determination of association constants. This method, dcELISA, has been applied to and validated by studying the binding of a monoclonal antibody (OKT9) to its cognate antigen (hTfR). We determined an equilibrium association constant of 2.15 X lo9 l/mol, which is in the typical range for a high affinity monoclonal antibody. However, a 26% larger association constant was observed with the ‘251-labeled ligand 0KT9 in the RIA-based Scatchard analysis (Scatchard, 1949). Since iodination of proteins has previously been shown to modu-

late the binding properties either by decreasing the affinity (Hugues et al., 1982; Mattera et al., 1982) or by increasing it (Hofmann et al., 1988), we assume that the covalent modification is responsible for the increased affinity. This interpretation gains further support from the slightly larger association constant determined for the same ‘25I-labeled antibody using the dcELISA method (Table 1). Since the latter experiment was performed essentially as the dcELISA with unlabeled antibody, the observed difference cannot be simply attributed to a systematic variation between the two methods. It must rather be interpreted as a small but measurable effect of the chemical modification introduced by the labeling procedure. The dcELISA is thus a valuable tool for studying the binding properties of biological macromolecules without the risk of introducing systematic deviations by covalent isotopic labeling. Such effects may have been previously overseen since different methods are only rarely applied to the same biological system. In this respect, the dcELISA appears also to be superior to other non-radioactive methods that rely on covalent modifications of the ligand molecule such as biotinylation (Jackson et al., 1982), fluorochrome attachment (Friguet et al., 1985) or enzyme-crosslinking (Schots et al., 1988). To our knowledge, only a small number of ELISA-based methods have been published for equilibrium binding studies using unmodified ligand molecules. Among these are the quantitation of unbound ligand by a second, standard ELISA (Kim et al., 1990) and direct complex quantitation by ellipsometry (Nygren and Stenberg, 1985). While the first method is less accurate, especially at low ratios of bound to free ligand, ellipsometry has proven to be a very powerful method, but requires expensive, specialized equipment not available to all laboratories. An indirect ELISA calibration has been achieved by Friguet et al. (1985) by competing the immobilized receptor with various amounts of soluble receptor. Although some intrinsic problems of this assay have been solved by later analytical modifications (Stevens, 1987), the association constants determined by this method depend heavily on the amount of immobilized receptor (Hetherington, 1990). This problem cannot be solved easily, since the experimental deviations vary unpredictably between different systems

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(Seligman, 1994). Thus, the dcELISA appears to be a useful alternative to the hitherto published non-radioactive solid phase assays. Although a dcELISA experiment is easily designed and can be performed on a single microtiter plate, some precautions should be considered during the planning step. Due to the implied approximations, the initial amount of ligand (La) must be small in relation to the immobilized binding partner CR,). Otherwise a rather constant and not an exponentially decreasing signal is observed for the initial steps of the transfer assay. Since the linearity between bound ligand and final signal is essential for the assay, we advise the use of high affinity monoclonal antibodies for the secondary detection system. The evaluation of the F-plot is greatly facilitated by the fact that any linear regression curve must pass through the point (F, = 1, emkc.’ = I>, as derived in Appendix B (Eq. B7). In principle, one transfer assay would thus be sufficient to determine F. However, using several F, facilitates the extrapolation and makes it possible to verify the accuracy of the experiment. A close examination of Figs. 3 and 6 reveals that F, determined at extremely short binding periods are co-linear with those obtained using longer incubation times. This suggests that the time dependent direct calibration is accurate enough to perform the experiment far from equilibrium conditions. However, the required extrapolation of the F-plot becomes less accurate for a steeper slope of the regression line. Since the slope depends solely on R, and K, (Eq. 8) we propose to choose R, > 0.1 X K; ’ which will result in F > 0.09 and thus in a reasonable accuracy for the calculation of K,. According to the manufacturer, the maximum amount of protein that can be immobilized to a standard microtiter plate (R,) is in the range of 100 ng to 450 ng per well. Due to the given limitations of the F-plot, the binding of a 100 kDa ligand molecule can thus only be analyzed if K, > 10’ l/mol. In order to expand the scope of the dcELISA towards studying weaker molecular interactions, the number of immobilized receptors has to be significantly increased, possibly by coupling the receptor molecules to latex beads. In the dcELISA, the total amount of binding sites CR,) is indirectly determined by a saturation curve (Eq. 5). Thus the number of bindings sites per receptor molecule can easily be calculated whenever

205

the molar amount of immobilized receptor has been quantified independently. In contrast, the impact of multiple binding sites of the ligand (e.g. of the antibody) is more difficult to assess. Due to the fixed distance and orientation of surface immobilized antigens, divalent antibodies will only rarely match the conditions required for a simultaneous binding to two epitopes. Experimentally, such a binding mode would be equivalent to a second binding site with an increased affinity and should thus produce a non-linear curve in the Scatchard analysis (Schreier and Schimmel, 1974). As is obvious from Fig. 5B, we do not find any systematic deviation and conclude that the binding of divalent antibodies can thus be studied at sufficient accuracy. The dcELISA permits analysis of the interaction between any two molecules whenever one of them can be immobilized on a microtiter plate and enzyme-labeled high affinity antibodies exist for the other one. It is thus not limited to protein-protein interactions, but can also be used to determine association constants for the binding of proteins to other biological macromolecules such as nucleic acids or carbohydrates. In the case of small ligand molecules, a reciprocal assay is recommended, i.e. the small molecule is immobilized and defined as recepfoor, while the presumably large binding partner is defined as the ligand and is quantified with specific antibodies. Even partially purified ligand molecules could be employed as long as their initial amount can be determined accurately. The sensitivity of the assay could be significantly enhanced by using a fluorogenic or luminogenic rather than the chromogenic detection system. Such a modification should also permit analysis of the binding of ligand molecules to immobilized crude cellular extracts or even to the surface of living cells. In its most general form, the direct calibration method is not restricted to the use of antibodies but can be combined with any kind of solid phase binding assay requiring signal calibration. In summary, the dcELISA is superior to all methods that rely on covalent labeling techniques and are thereby prone to possible alterations of the binding properties. In contrast to all previously published true solid phase ELISAs, the dcELISA does not require any external calibration and can be performed without any specialized laboratory equip-

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ment. It should thus greatly facilitate the routine determination of equilibrium association constants for biologically important molecular interactions.

Acknowledgements We would like to thank the Deutsche Forschungsgemeinschaft for financial support (Sonderforschungsbereich 312) and Dr. Ute Hofmann for purifying the monoclonal antibody 0KT9.

Appendix A. Time-independent direct calibration The mathematical derivation of the time-independent direct calibration assumes equilibrium conditions for all binding reactions. The association’ constant (K,) for the binding of a ligand (L) to its receptor (R) is defined as: RL K, = R.L

(Al)

If the initial amount of immobilized free receptor (R,) is much larger than that of the soluble ligand, it will remain essentially unchanged upon complex formation (R, = R,) and the amount of free ligand in the nth transfer well (L,) can be approximated by: L,=-~_

RL, R, . K,

RL” . K,

(A21

R,

Upon transferring the free ligand containing natant CL,,) from one well into the next, part ligand will become bound to the receptor second well (RL,, ,> while the rest remains supematant (L, + ,I:

L,=RL,+,

superof the in the in the

(A31

+L,+l

Substituting L n and L n+ 1 by Eq. (A2) and defining the transfer factor -1

F=(l+K;R,)-‘=

(Ad)

leads to: 1 RL “i-1 =RL;

1 +K;R,

RL, = RL, . F”- ’

=RL;F

(‘9 (fw

time

Fig. 7. Schematic binding curve describing the definitions used for the time-dependent dcELISA derivation. A certain part (RL: _ ,) of the initial amount of ligand (L,) becomes bound to the immobilized receptor under equilibrium conditions. This part can be viewed in a simplified kinetic model as a bindable fraction of the initial amount of ligand (Lq= ,, = RL: _ ,). The remaining part is regarded as unbindable (L” = L,, - Lt=,,). At time t, part of the bindable fraction has become bound to the receptor (RLb,). The rest of the bindable fraction (L!) adds up with the unbindable fraction (L”) to the total amount of free ligand at time t (L, = L” +Lb,). The simplified model implies first order kinetics and facilitates the derivation of the time-dependent direct calibration method.

Assuming a constant calibration factor relating RL, and the absorbance A, (IQ. 1, Results section), this equation is equivalent to Eq. 3 in the Results section.

Appendix B. Time-dependent direct calibration The mathematical derivation of the time-dependent direct calibration is based on a simplified kinetic model implying that the binding of a soluble ligand (L) to an immobilized receptor (R) can be approximated by an irreversible reaction of an assumed bind&e fraction of the ligand (Lb), defined as the amount of ligand that becomes complexed by the receptor under equilibrium conditions (Lb,_, = RL, ~ ,). The remaining, unbindable fraction (L”) is constant throughout the reaction and corresponds to the amount of free ligand at equilibrium (L” = L, _ ,>. The Appendix figure (Fig. 7) illustrates the definitions used for this model and permits to compare them to those for an exact description by a reversible reaction. Although our model disregards the dynamic exchange of ligand molecules at equilibrium conditions, it approximates the experimental data quite accurately as shown in Fig. 2. Assuming a large

H. Fuchs et al./Journal

of Immunological Methods 188 (1995) 197-208

excess of immobilized receptor over the ligand (R, > > La), first order kinetics with a complex formation rate constant k, can be formulated for the bindable fraction of the ligand: e-kc-‘=

Lb, = L”,‘, Accordingly, scribed as:

RL”, = RLb,,,

RL”,+%. e-kc”

the complex

w

formation

can

be de-

207

At t = 0 the exponential term of Eq. B6 becomes unity. The expression simplifies and substituting F by Eq. A4 yields: F,_,=F+((R,X,)-‘+1)-I = (R,.K,+

1))’

+((R,.K,))’

+ i)j’

= i (B7)

(1 - eekc”)

(B2)

Due to Eq. 1, this equation is equivalent to Eq. 7 in the Results section. A time-dependent expression can be formulated for the transfer factor F (Eq. A4) using the definitions introduced by the simplified kinetic model (RL, = RLb, and L, = L” + Lb,):

Therefore any regression line has to pass through the point (F, = 1, eekc-l = 1). This simplifies the regression analysis and increases the accuracy of extrapolating F.

F,=(l+T)-‘=(l+&)-’

References

(B3)

Substitution of the time-dependent terms L: and RLb, by Eqs. Bl and B2, respectively, leads to an expression of F, as a direct function of t. All remaining concentration terms represent equilibrium conditions (t -+ =):

=

L” + RLb,,,

.eekc”

W)

L” + RLb,,,

Thus, the terms defined for the simplified kinetic model can be substituted by those for equilibrium conditions, i.e. L” by L and RLb,,, by RL: F = L + RL . epkc” _ L f L+RL LfRL

) RL. ePkc” L+RL (B5)

Substituting the first summand according to Eq. A4 and using Eq. A2 to reformulate the second, finally leads to Eq. 8 in the results section: -I

. e-k<.’ =F+((R,.K,)e’+

l)-’

.emkc”

(B6)

Fraker, P.J. and Speck, J.J. (1978) Protein and cell membrane iodinations with a sparingly soluble chloroamide, 1,3,4,6-tetrachloro-3n,6a-diphrenylglycoluril. Biochem. Biophys. Res. Commun. 80, 849. Friguet, B., Chaffotte, A.F., Djavadi-Ohaniance, L. and Goldberg, M.E. (1985) Measurements of the true affinity constant in solution of antigen-antibody complexes by enzyme-linked immunosorbent assay. J. Immunol. Methods 77, 305. Gallati, H. and Pracht, I. (1985) Horseradish peroxidase: kinetic studies and optimization of peroxidase activity determination using the substrates HzO, and 3,3’,5,5’-tetramethylbenzidine. J. Clin. Chem. Clin. Biochem. 23, 453. Hetherington, S. (1990) Solid phase disruption of fluid phase equilibrium in affinity assays with ELISA. J. Immunol. Methods 131, 195. Hofmann, C., Luthy, P., Hutter, R. and Pliska, V. (1988) Binding of the delta endotoxin from Bacillus thuringiensis to brushborder membrane vesicles of the cabbage butterfly (Pieris brassicae). Eur. J. Biochem. 173, 85. Hoylaerts, M.F., Bollen. A. and De Broe, M.E. (1990) The application of enzyme kinetics to the determination of dissociation constants for antigen-antibody interactions in solution. J. Immunol. Methods 126, 253. Hugues, M., Duval, D., Kitabgi, P., Lazdunski, M. and Vincent, J.P. (1982) Preparation of a pure monoiodo derivative of the bee venom neurotoxin apamin and its binding properties to rat brain synaptosomes. J. Biol. Chem. 257, 2762. Jackson, S., Sogn, J.A. and Kindt, T.J. (1982) Microdetermination of rabbit immunoglobulin allotypes by ELISA using specific antibodies conjugated with peroxidase or with biotin. J. Immunol. Methods 48, 299. Kim, B.B.. Dikova, E.B., Sheller, U., Dikov, M.M., Gavrilova, E.M. and Egorov, A.M. (1990) Evaluation of dissociation constants of antigen-antibody complexes by ELISA. J. Immunol. Methods 131, 213. Kung. P.C., Talle, M.A., DeMaria, M.E.. Butler, M.S., Lifter, J. and Goldstein, G. (1980) Strategies for generating monoclonal

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antibodies defining human T-lymphocyte differentiation antigens. Transplant. Proc. 12, 141. Mattera, R., Turyn, D., Femandez, H.N. and Dellacha, J.M. (1982) Structural characterization of iodinated bovine growth hormone. Int. 1. Pept. Protein Res. 19, 172. Nygren, H. and Stenberg, M. (1985) Calibration by ellipsometry of the enzyme-linked immunosorbent assay. J. Immunol. Methods 80, 15. Orberger, G., Geyer, R., Stirm, S. and Tauber, R. (1992) Structure of the N-linked oligosaccharides of the human transfertin receptor. Eur. J. Biochem. 205, 257. Reinherz, E.L., Kung, P.C., Goldstein, G., Levey, R.H. and Schlossman, S.F. (1980) Discrete stages of human intrathymic differentiation: analysis of normal thymocytes and leukemic lymphoblasts of T-cell lineage. Proc. Natl. Acad. Sci. USA 77, 1588. Scatchard, G. (1949) The attraction of proteins for small molecules and ions. Ann. N.Y. Acad. Sci. 51, 660. Schots, A., Van der Leede, B.J., De Jongh, E. and Egberts, E. (1988) A method for the determination of antibody affinity using a direct ELISA. J. Immunol. Methods 109, 225.

Schreier, A.A. and Schimmel, P.R. (1974) Interaction of matganese with fragments, complementary fragment recombinations, and whole molecules of yeast phenylalanine specific transfer RNA. J. Mol. Biol. 86, 601. Seligman, S.J. (1994) Influence of solid-phase antigen in competition enzyme-linked immunosorbent assays (ELISAS) on calculated antigen-antibody dissociation constants. J. Immunol. Methods 168, 101. Stevens, F.J. (1987) Modification of an ELISA-based procedure for affinity determination: correction necessary for use with bivalent antibody. Mol. Immunol. 24, 1055. Sutherland, R., Delia, D., Schneider, C., Newman, R., Kemshead, J. and Greaves, M. (1981) Ubiquitous cell-surface glycoprotein on tumor cells is proliferation-associated receptor for transferrin. Proc. Natl. Acad. Sci. USA 78. 4515. Turkewitz, A.P., Amatruda, J.F., Borhani, D., Harrison, S.C. and Schwartz, A.L. (1988) A high yield purification of the human transferrin receptor and properties of its major extracellular fragment. J. Biol. Chem. 263, 8318.