Determination of intrinsic affinity constants of monoclonal antibodies against carcinoembryonic antigen

Molecular Immunl;~logy, Vol. 24, No. 6, pp. 569-516, Printed in Great Hntain.

1987

0161-5890187 $3.00 +O.OO Pergamon Journals Ltd

DETERMINATION OF INTRINSIC AFFINITY CONSTANTS OF MONOCLONAL ANTIBODIES AGAINST CARCINOEMBRYONIC ANTIGEN .&a LARssoN,*t

RAHUL GHOSH* and STEN HAMMARSTR~M~

*University of Stockholm, Department of Immunology, S-106 91, Stockholm, Sweden; and IUniversity of Urn&, Department of Immunology, S-901 85 Umea, Sweden (First received received 6 Augusf 1986; accepted in revised.form 7 November 1986) Abstract-A 2-phase method is described for the determination of the intrinsic affinity constants (K-values) for the interaction between monoclonal antibodies (MAbs) against carcinoembryonic antigen (CEA) and CEA. The Mabs were coupled covalently to CNBr-activated paper discs. MAb coupled discs and a 2-fold dilution series of 12jI-CEA were incubated at 2O’C until equilibrium was reached. Nonlinear curve-fitting was used for estimation of K-values and different calculation models were thereby tested. The K-values for 12 different anti-CEA MAbs were determined to be 0.3-52 x IO6 Mm’, which is IL2 orders of magnitude lower than the values obtained in a previous study with some of these MAbs using the ammonium sulphate method to separate free from bound antigen. The K-values obtained by the paper disc method are probably better estimates of the intrinsic association constant than those obtained previously. There are two main reasons for this: (1) free and bound antigen are separated from each other under physiological conditions and (2) the opportunity for multipoint interaction between MAb and CEA is minimized when the MAb is coupled to a rigid carrier substance. Thus, even when the MAb reacts with 22 epitopes in CEA, as seems to be the case with several of our anti-CEA MAbs, the intrinsic K-value should be obtained. The fundamental validity of 2-phase assays, sometimes questioned in the literature, is demonstrated.

INTRODUCTION Measurements

of affinity

clonal antibodies cinoembryonic

(MAbs) antigen

constants

between

and proteins have

mono-

such as car-

been performed

several different methods. Generally,

affinity constants are needed in order to select MAbs suitable for sensitive detection of the antigen. The MAbs were coupled covalently to CNBr-activated paper discs. We believe that the use of a rigid carrier substance like paper minimizes divalent or oligovalent binding of MAb to CEA molecules. A further advantage of this technique is that the Ab-Ag binding takes place under physiological conditions at all times. Problems related to precipitation of immune complexes are also avoided.

with

l-phase binding

assays have been employed in which immune complexes are separated from free antigen by precipitation with e.g. ammonium sulphate (Hedin et al., 1982; Haskell et al., 1983), polyethylene glycol (Van Heyningen et d., 1983) or anti-immunoglobulins (Jacobson et al.., 1982). Biotin-labelling of antibodies and precipitation of immune complexes with avidin has also been used (Wagener et al., 1983). Several MAbs against CEA appear to react with at least two identical or cross-reactive epitopes on the same antigen (Ag) molecule (Hedin et al., 1982; Wagener et al., 11983). This finding complicates determination of affinity constants by methods in which both Ag and antibody (Ab) react in solution, since immune comple.Kes of various sizes are formed. Under these circumstances the shape of the binding curve, and consequently the affinity constant, is also dependent on the concns of the reacting molecules (Jacobsen et al., 1982). K-values calculated from such measurements must therefore be regarded as apparent rather than intrinsic. The aim of the present study was to measure the intrinsic affinities of anti-CEA MAbs. Knowledge of tAuthor

to whom! correspondence

should

MATERIALS AND METHODS

Antigens CEA and non-specific cross-reacting antigen, mol. wt 95,000 (NCA-95) were purified from liver metastases of cola-rectal cancer as described previously (Hammarstriim et al., 1978). Two batches of CEA (CEA preparations 45 and 55) and one batch of NCA-95 were used in this study. MAbs Twelve monoclonal mouse anti-CEA antibodies (I-9, I-27, I-38S1, I-46, I-47, H-2, 11-6, 11-7, II-IO, 11-12, 11-16, 11-17) were studied. The MAbs were from mice immunized with highly-purified CEA from liver metastases of cola-rectal (I-series + MAb 11-2) or lung adenocarcinoma (II-6 to 11-17). Briefly, 4-10 x lo6 hybridoma cells in 0.3 ml DMEM were injected intraperitoneally into Pristane-primed

be addressed. 569

570

kE

LAWSON Et a!

BALB/c mice. Animals were observed daily for abdominal swelling. After approx. 14 days the mice were sacrificed and the ascites fluid was collected (McKearn, 1980). The IgG fraction was purified by DEAE Affi-gel blue (Bio-Rad Laboratories, Richmond, California) chromatography (Bruck et al., 1982). The specificities and binding properties of the MAbs have been described by Hedin er al. (1982, 1986). All antibodies were IgGl, kappa. Table I summarizes some of their characteristics. IgG isolated from ascites was used in the analysis of Ab affinities. Preparation

ofMAb-coupled

discs

In a typical experiment, 4OOpg of purified IgG in 0.1 A4 NaHCO, was coupled to approx. 400 mg of cyanogen bromide activated paper discs (N - 40; Pharmacia, Uppsala, Sweden) at 4’ C for 18 hr with slight stirring. After washing, remaining CNBrgroups were inactivated by incubating the discs with I M ethanolamine. Control discs containing bovine serum albumin (BSA) instead of MAb were prepared in the same way. Direct binding experiments

with ‘lsI-CEA

Iodination of proteins was done with Iodo-gen” (Pearce, Rockford, Illinois) as a solid phase oxidizing agent as described by Fraker and Speck (1978). 3.7-22 MBq of NalZ51 (Radiochemical Centre, Amersham, Bucks, U.K.) was used per mg of CEA. In the direct binding experiments, discs were incubated with 130 ~1 of serial 2-fold dilutions of ‘*‘ICEA in 0.067 M phosphate buffer, pH 7.2, containing 0.15 M NaCl (PBS) and 1% BSA. The highest “‘1-CEA concns used in the experiments were 0.2-0.8 g/l. An identical dilution series was set up with control discs coupled with BSA. All samples were set up in duplicates. After approx. 18 hr of incubation at room temp, with slight stirring, a sample of the supernatant (90 ~1) was transferred to empty tubes. The paper discs were taken out with a pair of tweezers and were pressed between filter papers to minimize the fluid content. Samples of

Table

MAb

I.

Epitope

reactivities

Specificity group

I-47

7

CEA

Reduction

_ -

(+) (+) _ _ _ _

_

+ + + +

ef al., 1982, 1986.

CEA

or

Sephar-

I$ data

of 12 anti-CEA

Reactivity in ELISA against NCA-I60 NCA-95 NCA-55

+ + + + +

111

radio-

In each experiment the radioactivity of the BSAcoupled control discs was evaluated first. In control discs radioactivity was approximately proportional to the radioactivity in the supernatants, in most experiments amounting to 34% of the radioactivity in 90 ~1 of the supernatants. The finding that there was a constant fraction of radioactivity in the control discs indicates that they contain approximately the same amount of fluid and that there is little nonspecific binding. Values for “51-CEA in supernatants and discs were transformed logarithmically and were thereafter used for construction of a straight line. The correlation coefficient (r) was 0.991-0.999. This line was used for calculating the amount of CEA in the fluid contained within the Ab-coupled discs together with possibly unspecifically-bound antigen. The ratio

+ + + + + + +

unlabelled

for

A small sample of ‘251-labelled CEA (2 pg) was applied on a column containing excess amounts of MAb conjugated to Sepharose 4B (Pharmacia, Uppsala, Sweden; 1 ml bed vol, 1.5-3.0mg MAb). The fraction of radioactivity that passed through the column by passage of two bed vols of PBS was regarded as the fraction of radioactivity lacking CEA-binding ability.

+

II-III

with

Binding of labelled CEA to MAb-conjugated ose 4B

+

I-38Sl I-46

experiments

measured

A constant amount of “‘ICEA (75 ~1, l&20 nM CEA) was added to a series of tubes each containing one MAb-coupled disc. Seventy-five microlitres of a dilution series of unlabelled CEA or NCA-95 was then added and the tubes were incubated for 18 hr at 20°C with slight stirring. As controls, four MAbcoupled discs and four BSA-coupled discs were incubated with buffer instead of unlabelled antigen. A 100 ~1 aliquot of the supernatant and the paper disc dried between filter papers were then counted.

+ II

Data from Hedin

Competition NCA -95

and cross-reactivity patterns study

I-9 1-27 II-2 II-6 II-12

II-7 II-IO II-16 II-17

supernatants and discs were activity in a gammacounter.

_ _ _ _

MAbs native BGPI

used in the

Epitope

+

_

E

_

_ _ _ _

A C C G F

_ _

D D

_ _ -

G H H A

_ _ _

Determination

of intrinsic affinity constants

of specifically-bound/unspecifically-contained CEA was, on average, 7.58 at the lower and 1.41 at the higher end of the binding curves. The concns of CEA bound to the Ab-coupled discs could be calculated in two ways from each experiment. Firstly, :as F,, - Fobs, where Fref is the concn of free CEA in tubes with control discs and Fobs is the free CEA concn in tubes with MAb-coupled discs compared at the same total CEA concn. Secondly, the bound CEA concn per 90 p 1 of fluid was calculated from the radioactivity in the MAb-coupled discs, corrected as described above for the amount that is contained unspecifically in the paper discs. The latter values were used for curve-fitting. The methods for data transformation, the aim of which is a linear relationship between variables, namely Scatchard’s plot, Woolf’s plot or the double reciprocal plot., are most often used for assessment of equilibrium data in immunology. We, instead, estimated the parameters from the binding curves directly by nonlinear curve-fitting. The reason for this is the easier application of weighted regression and less bias due to those deviations from the ideal binding curve Ithat are often seen at low Ag concns. Deviations from the binding curves that are modest may be very prominent when data are transformed to e.g. Scatchard’s plot. Nonlinear curve-fitting has previously been advocated also by others for evaluation of macromolecule-ligand interactions (Cooke and McIntosh, 1986; Maes, 1984; Munson and Rodbard, 1980). The curve-fitting program ELSNLR, written in BASIC for Hewlett-Packard 85, generously provided by Dr Carl C. Peck, Bethesda, Maryland, was used. Shortly, the user provides the program with his own structural and variance (weighting) models at start. The program works iteratively by minimizing an objective function, that is twice the negative log likelihood of the data, with Marquardt’s algorithm. The most prominent feature of ELSNLR is that it finds the parameters of the variance model at the same time as the parameters describing the shape of the curve. This curve-fitting method is referred to as extended least-squares nonlinear regression (Peck et al., 1984). In this study we used the empirical power model VAR (Y)=a,YJ

(1)

for description of the variance of the curve (Y =f(F, P, . P, I), where F is the free CEA concn and P,... P, are the parameters of the structural model (see below), whereas a, and J are parameters of the variance model. This variance model has been used previously by Finney (1976, 1978). The structural models described below were based on the direct binding plot which is a rearrangement of the law of mass action, but it can also be derived by modification of the Langmuir adsorption isoterm. B=AKFJ(I+KF),

(2)

571

where B is the concn of bound Ag, K is the affinity constant and A refers to the average concn of available Ab combining sites on the discs divided into the vol of fluid with which it equilibrates. Three variants of direct curve-fitting models were used. In model 1 the curve-fitting was done with the uncorrected values of free CEA concns (Fobs). A single parameter, VAR( Y) = a,,, was used as the variance model, which makes ELSNLR equivalent to unweighted least-squares regression. In model 2 the free CEA concn was corrected in order to compensate for the fraction of radioactivity present on antigenically inactive molecules, defined as the fraction lacking ability to bind to the respective MAb conjugated to Sepharose: F = Fuha- P(F,,, + B),

(3)

where F is the corrected free CEA concn and p the fraction of radioactivity on antigenically inactive molecules. After this correction, curve-fitting was done with equation (2) as the structural model and equation (1) as the variance model. J was assigned a constant value of 1.5 or in one case 1.0, whereas a,, remained as a parameter. In model 3 uncorrected values were used for free CEA concns. Instead, the correction of equation (3) was inserted into equation (2) which gives the quadratic equation: pB2 + B(P&,,

- Fobs- l/K - PA ) + AF,,,(l

-p)

= 0.

(4a)

With substitutions g =pF,,,

- Fobs- 1/K -pA

h = AF,,,(l we can write equation B =(-g

-P)

and

(4b) (k)

(4a) as (4d)

- &=%/(2~).

This explicit form was used for curve-fitting with the same mode of weighting as in model 2. The value of p was not estimated as a parameter of the curve. Instead, it was estimated from the immunosorbent column experiments and inserted as a constant. The binding data were also analyzed with Sips’ model (1948): B = A(&F)“/[l where K, is the average geneity index.

+ (K,F)“] affinity

(9

and a the hetero-

RESULTS The concns of bound CEA were calculated in two different ways for each experiment: As Frer- Fobs and as the amount of CEA in the Ab-coupled discs corrected for the amount of CEA in the control discs at comparable free CEA concns. At low CEA concns the two methods of assessment were equally good and gave consistent results. However, at high CEA

&E

,572

LARSON et al.

concns (when Fobs is close to F,,) the bound CEA values calculated with the second method most often gave more reliable results with lower scatter and better fit to the binding model. By passage through an immunosorbent column containing an excess of the respective MAb coupled to Sepharose the fraction of radioactivity unable to bind was determined and found to be in the range 2@-45%. This fraction varied with the batch of labelling (the degree of iodination) and, to some extent, from one MAb to another. In the beginning several structural and variance models were tested for calculation of the binding data. For example, one could usually obtain an excellent fit to Sips’ equation with our data also, without any correction for antigenically inactive CEA. However, we did not accept Sips’ equation as a main alternative for calculation. The average affinity of Sips’ equation is derived for the case of heterogeneous binding sites on a solid phase interacting with a homogeneous solute. To our knowledge, the parameters K, and a can not be interpreted when, instead, the ligand is heterogeneous. In seven experiments, using equation (4) as the structural model, the average of the variance parameter J in equation (1) was 1.59 (range 1.10-2.09). In the final calculations of all experiments except one we have used J = 1.5 as a constant. Fixed J values makes ELSNLR equivalent to nonlinear regression with weights l/a, YJ. To first estimate the value of J from a large body of data and then use it as a constant, agrees with the recommendations of Finncy (1978). One experiment was evidently too heavily weighted with J = 1.5. For this experiment the value .I = I was used instead. It is better to use conservative values of J than high values. Excessive weighting may result in erroneous outcomes because it amplifies the influence of the low Ag concn area where some deviation from the ideal curve was suspected in some experiments. Testing different models with these data also showed that there was a better fit to the variance model VAR( Y) = a, Y’ [equation (I)] than the model VAR( Y) = a,F’, both with maximum likelihood values and with low standard errors (S.E.) of the parameters as criteria of a good fit. One experiment (MAb 38S1) is used in Fig. 1 to illustate the three models of curve-fitting described in Materials

and Methods.

Figure

CONC

Y

0

200

400

CONC

Y

0

I

200

CONC

FREE

600

FREE

CEA

CEAfnM)

800

CORRECTED

I

400

600

FREE

CEA

1000

800

1200 tnM)

1

I

1000

1200

(MA)

Fig. 1. Bound vs free CEA concns in one paper disc experiment for det~~ination of the intrinsic affinity constant of MAb I-38Sl. In (B) the free CEA concn was corrected for the fraction that was unable to bind to the MAb conjugated to Sepharose, whereas this correction was not done in (A) or (C). In (A) curve-fitting was performed with method I (see Materials and Methods), in (B) with method 2 and in (C) with method 3.

l(A) shows the bind-

ing data caiculated according to model 1 with unweighted nonlinear regression, and no correction for the fraction of CEA molecules that was antigenically inactive. Figure l(B) shows the curve-fitting with model 2, where a correction was done for the fraction of “‘ICEA that could not bind to the respective MAb conjugated to Sepharose. This correction reduces the free CEA concns for every point, while the bound CEA concns are unchanged. Hence, the initial slope of the curve increases while the plateau level is essentially unchanged. Consequently, a higher value

of the affinity constant is obtained with model 2. In model 3, correction of the free CEA concn was included in the structural model [equation (4)] resulting in the curve shown in Fig. I(C). The shape of this curve does not differ much from that obtained with model 1. In Table 2 the affinity constants for a series of I2 anti-CEA MAbs calculated with the three different methods are given. Naturally, the affinity constants became higher when they were calculated according to models 2 and 3 than according to model I. The

Determination

Table 2. Affinity constants, Model I-9 1-27 l-38% I-46 I-47 II-2 II-6 II-7 II-IO II-12 II-16 II-17d

5.48 15.0 2.87 0.62 37.0 1.00 0.76 8.77 0.22 0.68 1.19 0.51

x x x x x x x x x x x x

affinity

573

constants

K-values (M-‘), of 12 different anti-CEA paper disc solid phase assay I’

K -_.

MAb

of intrinsic

Model 2

rel S.E.b

IO* 106 10’ 106 106 106 lo6 IO6 I06 106 106 106

MAbs determined

0.165 0.125 0.177 0.123 0.237 0.135 0.144 0.240 0.258 0.200 0.265 0.319

K 15.7 19.2 5.0s 1.60 54.0 2.14 1.44 17.0 0.31 1.03 1.58 0.76

x x x x x x x x x x x x

Model

K

ret S.E. 106 IO6 106 106 106 lob 106 10” IOC” IO” 10” IO”

0.169 0.102 0.101 0.114 0.253 0.099 0.136 0.249 0.180’ 0.138 0.231 0.195

15.4 19.2 5.03 1.64 52.0 2.00 1.38 16.5 0.31 1.02 1.59 0.76

were calculated according to the three different curve-fitting Materials and Methods. bRelative S.E. of K. ‘Weighting approximately proportional to l/bound CEA eoncn. dBound CEA values calculated as F,, - Fobr used for curve-fitting. sK-values

difference was 1.28-2.87 times. Using model 2 or 3 for calculation, the intrinsic affinity constants between our MAbs and CEA were found to be 0.3-52 x 10hM-‘. The affinity constants given in Table 2 were all obtained with the same preparation of CEA from cola-rectal carcinoma. The ratios between the S.E. of K and the K-value itself (rel SE.) were on average lower in models 2 and 3 than in model 1, although this was not true for every experiment. This fact indicates that the correction introduced in models 2 and 3 for the fraction of radioactivity on antigenically inactive molecules enhances the fit to the data. The 12 MAbs included in this study reacted with at least seven different epitopes (Hedin et al., 1986). With this low degree of replication at the level of epitopes no relationship at all could be found between the affinity constants and the specificity of the MAbs. One of the MAbs, I-47, cross-reacts with NCA-95 (Hedin et al., 1982, 1986). To determine whether this MAb binds with similar affinity to CEA and NCA-95 a competition experiment was performed. As can be seen in Fig. 2, NCA-95 is an even more efficient

10 CONC

100 INHlBlTOR

1000

10000

(nmf

Fig. 2. Inhibition of ‘zSI-CEA binding to MAb 1-47 coupled paper discs by unlabelled CEA or NCA-95. B, is the binding of *25i-CEA in the absence of any inhibitor, B the binding in the presence of inhibitor. (0) CEA, (V) NCA-95.

x x x x x x x x x x x x

by a

3

ret S.E. 106 lo6 10” IO6 106 10” IO’ IO6 lOti 106 IO” IO”

models

0.176 0.103 0.104 0.112 0.253 0.100 0.135 0.259 0.184’ 0.139 0.225 0.200 described

in

competitor than CEA. A 2.9 higher concn of CEA than NCA-95 was needed to accomplish 50% inhibition of “‘1-CEA binding to MAb I-47 coupled discs. Provided that only trace amounts of labelled CEA are used, the ratio between the concns of the inhibitors at the 50% level also reflects the ratio between their K-values with the most efficient inhibitor, namely NCA-95, having the higher affinity constant. However, the criteria of what are trace amounts of the labelled substance (Berzofsky and Schechter, 1981) seems not to be fulfilled in our experiment, so the KNCA.PS/KcEAratio should be somewhat higher than 2.9 for MAb I-47 [Underwood, 1985; equation (l)]. One MAb (H-16), previously found not to cross-react with NCA-95, was used similarly in one control experiment. Inhibition was then achieved with unlabelled CEA (two different preparations) but not at all with NCA-95 (data not shown). There was no significant difference in the inhibiting power between the two CEA preparations. DISCUSSION

The purpose of this study was to determine the intrinsic affinity constants for the interaction between a series of anti-CEA Mabs and CEA. We chose a 2-phase assay with the MAb coupled covalently to paper discs and the protein antigen in solution since it has obvious technical advantages. However, in the literature there seems to be uncertainty of the validity of aIIinity constants determined by 2-phase assays (Berzofsky and Berkower, 1984; DeLisi, 1981). These concerns are justified when divalent molecules in solution bind to surface receptors on living cells, where the receptors can move in the plasma membrane to form patches or caps, that can be seen as a correspondence in two dimensions to precipitation in three dimensions. However, when the macromolecule is anchored to a rigid carrier substance like paper such “patching effects” can be excluded. Divalent binding can only occur at rare places where two antibody molecules are positioned and directed to fit

574

Am

LARSS~N

the distance and the angles between the epitopes on the antigen molecule. However, special antigens may have two identical epitopes positioned at the same side of the molecule with the possibility of directing themselves to fit the 2 combining sites of one IgG molecule. In such a situation the binding to both epitopes is favoured very much and it can probably not be distinguished from l-site binding either in 2-phase or in l-phase affinity assays, without the use of fragments of one of the participating reagents. Whether some of the epitopes in CEA that seem to occur at least twice have such properties is not known. There have also been concerns about the effect of high local concns of the binding macromolecules on surfaces, even when the Ag is monovalent (Berzofsky and Berkower, 1984; DeLisi, 1981). The affinity constant (K-value) is the ratio between the association rate constant and the dissociation rate constant. Exceedingly complicated reasoning about the association rate and dissociation rate constants in the 2-phase situation resulted in the false conclusion that the affinity constant measured at a surface can be 4 or 5 orders of magnitude higher than when the macromolecules are dispersed (DeLisi, 198 1). This analysis of association and dissociation rates was reassessed for a spherical cell situation with the correct conclusion that equilibrium is not affected by the fact that the macromolecules arc fixed to a surface (DeLisi and Wiegel, 1981). That the equilibrium is unaffected by restricting the Ab to a small vol can easily be understood by using equation (2) for calculation of data from equilibrium dialysis. The concn of Ab combining sites, A, is first interpreted as the concn of combining sites in the compartment where the Ab is enclosed. This is the way such experiments are usually regarded. The vol containing the low mol. wt Ag in equilibrium with the Ab exceeds the Ab compartment with a factor L. The average Ab combining sites concn in the Agcontaining vol is then A/L. Similarly, the average concn of bound antigen, B, becomes B/L, resulting in unchanged parameters of equation (2). This reasoning is valid also when other methods are used to restrict the antibodies to a limited vol. Only electrostatic forces may, in special cases, cause a change in the equilibrium because of increased macromolecules concn An obvious advantage with the solid phase assay is that separation of Ab-bound from free Ag is achieved automatically, which permits physiological conditions throughout. When a hapten like dinitrophenol is used as a model system for affinity assays there is reasonably good agreement between equilibrium dialysis and the ammonium sulphate precipitation method (Stupp rf ul., 1969). However with protein antigens the situation is different in several respects. Their secondary and tertiary structure is often sensitive to unphysiological conditions. Their solubility often changes by high concns of solutes.

et

al.

which can be seen as a total or partial salting-out of the antigen. A small hapten stays relatively protected in its combining site, while a protein antigen like CEA, with a mol. wt of - 180,000 protrudes enormously from the Ab molecule. This may cause strain in the immune complex at the moment of precipitation. All these factors may change the equilibrium in an unpredictable way when agents like ammonium sulphate or polyethylene glycol are used for separation of immune complexes from free antigen. Haskell er al. (1983) studied the affinity constants of MAbs against CEA by first incubating the two reactants under physiological or hypotonic conditions and then precipitating the immune complexes with ammonium sulphate. Two MAbs out of four clearly had higher affinity when incubated in the hypotonic buffer. The influence of the stronglyhypertonic ammonium sulphate in the second step was not elucidated by this study. Precipitation with anti-immunoglobulins reduces the difficulties described above. but other problems arise with the introduction of a second cquilibrium. The affinity constants of MAbs against CEA assayed with our paper disc method were in the range 0.3-52 x 10’ M ‘, whereas previous studies of MAbs against CEA using precipitation methods resulted in affinity constants of lox-5 x IO” M ’ (Haskell rc ~11.. 1983; Hedin et ul., 1982; Wagener et al.. 1983). IgG from one sheep and one monkey anti-CEA serum has also been studied with the disc assay. Their average affinities were both around 5 x 1OhM ’ when evaluated with Sips’ model. These results are within the range of affinity constants of our MAbs. Both Ab preparations were heterogeneous, and the monkey Ab preparation in particular, was highly heterogeneous. Table 3 shows the affinity constants for three anti-CEA MAbs determined with the new disc method and with the ammonium precipitation method used in a previous study (Hedin et (II., 1982). The disc method gave values which were I-2 orders of magnitude lower. Lower values with the disc method were expected for two of the MAbs, since they react with two or more cross-reactive epitopes on the same CEA molecule. This situation, where both Ab and Ag are at least divalcnt will, in l-phase assays, result in enhanced K-values. that we prefer to call cqpurmt affinity constants (Jacobsen rf ul., 1982). Our experiments, where conditions were used to minimize diTable 3. Afinity constanta of m~noclonal anti-CEA antibode determined by the paper disc solid phase method and an ammomum sulphate preclpltation method. respectively Affimty constant MAb

Paper disc method

I-9 I-27 I-38Sl

I.6 x 10: I.9 x IO’ 0.5 x IO’

(M ‘) Ammonium sulphate method 14 x 10; 33 x IO’ I2 x lo-

Determination

of intrinsic

valent binding, are an attempt to estimate the intrinsic affinity constants. Some of the other factors discussed above may also be responsible for the higher values obtained with the precipitation methods. Even weaknesses of our disc assay may contribute to this discrepancy. Some CEA molecules may be denatured or partially denatured during the radiolabelling procedure (Hedin et al., 1!)86; Wagener et al., 1983). We have tried to minimize damage during labelling by using a solid phase oxidizing agent. Even so, some epitopes may be affected by the labelling procedure. We have determined the fraction of radioactivity on antigenitally active molecules by passage of the labelled product over an excess amount of immunosorbent made up of the respective MAb coupled to Sepharose. Correction was made for this fraction with two related methods (calculation models 2 and 3 in Materials and Methods). Between themselves they gave very similar results, and they resulted in higher affinity values than from calculations without correction for the fraction of non-binding “‘ICEA. Even among the “‘1-CEA molecules that bind to the immunosorbent there may be molecules that are partially denatured and therefore show a decreased binding strength. Consequently, the average affinity of ‘251-labelled CEA may be somewhat lower than that of unlabellecl CEA. These problems are of course not restricted to 2-phase assays. Another technical complication was the variation between experiments in the number of combining sites on the discs available to the Ag in solution. The proportion of specific Ab in the IgG preparation varies from MAb to MAb. Similarly, the purity of the IgG preparation lmay also vary. Moreover, only those combining sites that are directed out from the paper fibres can catch Ag molecules, and there may also be differences between the MAbs regarding the proportion of molecules that couple “correctly” to the discs. For some of these reasons some experiments were of inferior quality and were rejected, most often because of too low Ag-binding capacity, but occasionally also because of too high capacity. New discs were then conjugated with an adjusted amount of MAb per disc. It is of course possible that the disc method gives values which are too low, because chemical coupling of the Ab to the solid phase may change the structure of the antibody in such a way that it now binds Ag less avidly. We consider this possibility unlikely since calculation of heterogeneity indices, a, with Sips’ model from the data. after correction for the fraction of antigenically inactive CEA, gave values which were close to I (mean value 0.96, range 0.79-1.20). If the Ab molecules on .the solid phase, that are involved in binding the Ag, were affected by the coupling procedure one would expect them to be affected to a variable degree and hence give a heterogeneity index clearly lower than I. Since the heterogeneity index is

affinity

constants

515

close to 1 we conclude that the antibodies involved in binding are essentially unchanged. No formal calculation was made of the variation between experiments of the same MAbs. However, comparisons between the “accepted” experiments shown in Table 2 and the experiments rejected because of low technical quality indicated that the measured affinities varied by a factor of 1.5-2 between experiments. This variation is higher than the values of standard errors relative to the K-values given in Table 2, which reflects only the statistical errors within experiments. The performance of this disc assay may be improved by developments in two different areas. Firstly, methods should be sought to standardize the number of Ab combining sites on the discs, preferably by catching the Ab in its Fc part and still avoid the problems with a second equilibrium. Secondly, the protein Ag should be carefully handled at all stages of preparation, storage and radiolabelling to avoid denaturation. Acknowledgemenr-This work was supported from the Swedish Cancer Society.

by a grant

REFERENCES

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