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Association constants of monoclonal antibodies for hapten: heterogeneity of frequency distribution and possible relationship with hapten molecular weight
JOURNALOF IMMUNOLOGICAL METHOOS ELSEVIER
Journal of ImmunologicalMethods 172 (1994) 219-225
Association constants of monoclonal antibodies for hapten: heterogeneity of frequency distribution and possible relationship with hapten molecular weight O. Chappey
,.a, M . D e b r a y
b, E . N i e l a, J . M . S c h e r r m a n n
a,c
a INSERM U26 (Dr. J.M. Bourre), H~pital Fernand Widal, 200 rue du Faubourg Saint Denis, 75475 Paris cedex 10, France b Laboratoire de Bio-Math&natiques, Facultg de Pharmacie, Par~ I~, 4 avenue de l'Observatoire, 75006 Paris, France c Laboratoire de Pharmacie Clinique et de Pharmacocingtique, Facultg de Pharmacie, Paris I~, 4 Avenue de l'Observatoire, 75006 Paris, France
Received 8 November 1993; revised received 10 January 1994; accepted 24 February 1994
Abstract
Using published data, we have investigated the relationship of the association constant (Ka) of 265 MAbs for haptens with molecular weights ranging from 111 to 1202 Da. The study indicates that: (1) differences of a factor 103-105 are frequently found between the lowest and the highest value of K a for the same hapten; (2) the relationship between log K a and the hapten molecular weight of either the native drug or the molecular entity used for the K a determination is described by a hyperbolic function; (3) beyond a critical molecular weight of approximately 300-325 Da, the log K a reaches a plateau at a maximal value near 10-12 M-1. Key words." Monoclonal antiboby; Affinity; Association constant; Hapten
1. Introduction
Over the last decade, monoclonal antibodies (MAbs) have b e e n successfully used in many aspects of biological research. In therapeutic drug monitoring, MAbs are used for the assay of small
MAbs, monoclonal antibodies; PAbs, polyclonal antibodies; Ka, association constant; mol. wt., molecular weight. * Corresponding author. Tel: (1) 40-05-43-43; Fax (1) 40-3440-64.
Abbreviations:
haptens with the basic advantage of a potentially better specificity than polyclonal antibodies (PAbs) and lower cross-reactivity with metabolites or drug analogues (Quesniaux et al., 1987). However, the association constant (Ka) of MAbs to haptens is often lower than the average value obtained with PAbs by an order of 1 or 2 log (Chappey et al., 1992). Since the limit of detection of an immunoassay is particularly dependent on the K a value, the limit of detection of hapten immunoassays using MAbs is often poor compared to that of PAbs, and this can restrict the
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O. Chappey et al. /Journal of Immunological Methods 172 (1994) 219-225
220
Table 1 Description of MAbs used in the study Molecule
Mol. wt.
IgG type
Method
Log K a evaluation K a constant
Authors
5.28/5.30 8.01/8.1/8.08/8.21/8.15/7.73 7.68/8.12/7.94 8.49/7.75 8.75/8.27/8.49/8.88 8.0/7.6/7.85/6.20/5.7 8.48/7.41 9.74/9.70/9.91/8 7.49 9.85/9.72/9.73/8.66/9.92/10.2 9.99/9.83/9.97/10.67/9.93/9.6 10.7/10.7 6.70 5.49/10.27/10.37/10.42 5.49 9.11/8.18/8.4/8.48/8.54/8.62 8.6 11.04/9.96
Harrison et al., 1986 Bjercke et al., 1986
Maleic acid Nicotine
112 162
1 2
Weir Miiller
Amino-4 quinoline Cotinine Acyclovir Propanolol a-Linolenic acid Oxaprotiline Morphine hemisuccinate
163 176 225 259 280 298 301
1,2 2 1,2 1,2 1,2 2 1
Cheng and Prussof Miiller Scatchard Scatchard Hogg Scatchard Scatchard
1 2 2 1,2 1 2 1,2,3
Scatchard Scatchard Scatchard Scatchard Scatchard Scatchard Scatchard
1,2,3
Scatchard
Desipramine
301
17t~-OH progesterone llt~-OH progesterone hemisuccinate
330 430
10.48/9/10.3/8.95/8.9/8/9.3 9.7/9.3/9.3/8.9/10.3/7.9/10/10 10/8.3/8.3/8/10.48/9.3/9.3/9
Freier et al., 1986 Bjercke et al., 1986 Quinn et al., 1983 Chorev-Wang et al., 1986 Buffi~re et al., 1989 Chouchane et al., 1988 Sawada et al., 1988 No published data Glasel et al., 1983 Liu et al., 1987 Bowles et al., 1988 Sawada et al., 1987 Wright et al., 1987 Schramm et al., 1987 Fantl et al., 1982
9.84 6/3-OH progesterone Fluorescein
334
1,2 1,2 1 1 2 1 1,2
Voss Voss Scatchard Miiller Scatchard Miiller Friguet
Deoxycortisol Colchicine
346 339
Methotrexate
454
Digitoxin
712
1,2,3
Scatchard
Digoxin
781
1,2
1,2
Cyclosporine 2-Phenyloxazolone Paraquat
1202 188 186
Scatchard Scatchard Scatchard Friguet
10/9.3/8.3/9.6/9.9/9.48/8.48 8.95/9.3 10.23/7/8.76/7.86/7.7 7.3/7.45/7/6.74 10.30 9.2 9.18 6.51 8.45/9.2/9.6/8.6/9.23/9.14 8.85/9.85/9.23/8.85/8.48/9.78 7.78/7.65/7.36/7.2/7.15/8.92 8.52/6.79/7.6/5.54/5 9.72/9.76/9.71/9.95/10.04/10.4 9.85/9.3/8.9 9.08
9/9.63/9.77/9.7/8.77/8.51/7.68
8.48 9.06/9.06/9.12/9.16/9.17/9.28 9.28/9.35/9.43/9.46/9,46/9.64 8.25/8.46/8.65/8.85/8.89/8.92 Nisnoff and Pressman 8.96/7.94/8.02/6.32 9.84/9.62/9.48/9.72 Nisnoff and Pressman 8.11/9.28/9.23/11.48/9.04/9.79 9.36/10.65/11.41/10.66/10.99 11.41/10.85/12.23/9.2 9.48/8 Steward and Petty 8.55/7.98/7.55/7.22/6.86/7.63 Farr 11.7 Miiller 7 Scatchard 10.15 5.43 Scatchard Scatchard 7.68
Fantl et al., 1982 Kranz et al., 1982 Kranz et al., 1983 Hosoda et al., 1986 No published data Rouan et al., 1989 Kato et al., 1984 Cot et al., 1987
Collignon et al., 1988 Collignon et al., 1984 Wahyono et al., 1990 Brizgys et al., 1989 Kyurkchiev et al., 1990
Mudgett-Hunter et al., 1982 Mudgett-Hunter et al., 1985
Zalcberg et al., 1983 Pincus et al., 1984 Quesniaux et al., 1987 Kartinen et al., 1983 Wright et al., 1987 Bowles et al., 1988 Bowles et al., 1990
(table continued on next page)
O. Chappey et al. /Journal of Immunological Methods 172 (1994) 219-225
221
Table 1 (continued) Molecule
Mol. wt.
IgG type
Method
Log K a evaluation K a constant
Authors
Nortriptyline Soman Haloperidol
263 182 376
Alprenolol Histamine Phosphorylcholine
249 111 219
1 1 1 1 1,2 1 2
Scatchard Scatchard Scatchard Saturation Scatchard Friguet
Marullo et al., 1985 Brimfield et al., 1985 Juszczak et al., 1987 Bolger et al., 1985 Chamat et al., 1984 Guesdon et al., 1986 Rodwell et al., 1983
Leu-5 enkephalin Imipramine Clonazepam Spiroperidol
566 280 316 395
2 1 1 1,2,3
Scatchard Scatchard Scatchard Scatchard
7.16 5.77/5.57/5.08/4.72 8.59 8.4/7.95/6.84/6.56 7.39/6.82/6.63/6.28 2.43 5.34/5.54/5.38/5.51/5.11/5.64 5.0/5.26/4.4 8.9 7.62 6.64
Doxorubicine Gentamicine Albuterol Testosterone
544 460 239 288
1 2 1 2
Scatchard Scatchard Scatchard Abraham
8.07/7.73/7.82/7.9/7.24/7.43/7.81
Herion et al., 1986 Ronayne et al., 1990 De Bias et al., 1985 Luedtke et al., 1988
7.1/7.6/7.49/7.74/8.55/9/9.7/8.8 8.82/9.1/8.36/9.52/8.35/8.92/8.08 8.55/8.74/8/8.54 8.03 10.09 9.01 10.32/10.27
Balsari et al., 1988 Place et al., 1983 Adam et al., 1990 Kohen et al., 1982
use of MAbs. This paper focuses on the question of why MAbs to haptens do not have a better limit of detection in immunoassays. We have reviewed the published data for MAbs to haptens and investigated the relationship between the K a of such MAbs and the molecular weight of the hapten.
two examined the distribution of log K a of MAbs versus either the molecular weight of the native compound or the molecular entity used for the K a determination, i.e. the native compound or the native compound plus its linkage arm. For the third investigation, the highest published K a values of the same MAb for a hapten were correlated with the molecular weight used for the K a determination.
2. Materials and methods
2.1. Selection criteria for MAbs to haptens
2.3. Mathematical analysis
265 MAbs against small haptens with molecular weights lower than or equal to 1202 Da were selected for the study (Table 1). MAbs of IgG class and isotype 1, 2 or 3 were exclusively selected and Fab fragments to haptens were excluded. The methodology for measuring the K a of the MAbs either by saturation or by competition techniques is given in Table 1.
Modelling of log K a versus molecular weight was performed using different functions. The best fit to the data was obtained using the following hyperbolic model:
2.2. Relationship between log K a and hapten molecular weight Three relationships between log K a and hapten molecular weight were investigated. The first
log K a = A ( M - M o ) / M +
(3450 - 2M0)
where A is the maximum value of log K a (when M ~ o0), Ms0 is the molecular weight corresponding to the half-maximum value of log K a and M 0 is the molecular weight at and after which log K a becomes positive. A, 3/50 and M 0 were estimated by the least squares method, using a nonlinear regression program (MK Model, Oxford, UK).
O. Chappey et al. /Journal of Immunological Methods 172 (1994) 219-225
222 a 13.0
versus the molecular weight of the native compound cut the x axis at - 7 3 Da and the y axis at log K a = 5 and then increased to a plateau at log K a = 10.4.
i
10.4
!
"/.8 5.2
•
~°
!
i•
4. Discussion 2.6 0.0
I
0
250
500
750
1000
1250
Native compound
13.0
~
1o.4
.A'i
, s
,
, I
.
.
~
5.2 2.6 0.0
iOi
0
~
250
~
50o
I
750
10O0
1250
Molecular weight of the entity used for the Ka determination Fig. 1. Distribution of K a values for MAbs versus the molecular weight of the native compound (a) or the molecular entity used in the K a determination (b). The average hyperbolic relationship between the highest log K a values and the molecular weight of the haptens used for the K a measurement is indicated by the dashed line in b. Hyperbolic relationships were fitted using the least squares method.
3. Results Plots of log K a versus the molecular weight of either the native compound (Fig. la), or the molecular entity used in the Ka determination (Fig. lb), were fitted by hyperbolic relationships. Extrapolation of log g a versus molecular weight of the molecular entity used in the K a determination cut the x axis near the zero value (M 0 = 46 Da) and rose very abruptly to a plateau at log K a = 10.4. Using the highest values of log g a , extrapolation of the curve cut the x axis at M 0 = 71 D a and increased very rapidly to a plateau at log K a = 12.6 (Fig. lb). Extrapolation of log K~
As shown in Fig. 1, it appears that for low molecular weight compounds, K a values are lower than with high molecular weight compounds. Even if a large number of MAbs to low molecular weight compounds (100-200 Da) are produced, g a values around 101°-1011 M -1 are never observed. In contrast, with higher molecular weight compounds, K a values increase and reach a plateau never exceeding 1012 M - 1 . That is why we have investigated a possible relationship between the hapten molecular weight versus log g aA previous study had demonstrated a relationship between the molecular weight and the size of chemical structure (Voss et al., 1976). Moreover, as the linkage arm may influence the affinity of antibodies for haptens, relationships were studied between the molecular weight of either the native compound versus log K a or the molecular entity used for the K a determination versus log K a. In order to establish such relationships, it was first necessary to draw the average curve for each distribution using the same hyperbolic mathematical model which was found to give the best fit. Surprisingly, the two hyperbolic curves were superimposable beyond 325 D a and reached a plateau with a m e a n g a value of 10.4. For molecular weights below 325 Da, the solid line crossed the x axis with a positive value near the origin. This value is imprecise because of the lack of MAbs reacting with haptens having molecular weights below 100 Da. Acetaldehyde (mol. wt. 44 Da) is the smallest compound described which has been able to elicit MAbs. Therefore, MAbs to acetaldehyde were produced in the form of poly-L-lysine acetaldehyde adducts (Israel et al., 1986) and it was found that after extrapolation the y axis was intercepted at log K a = 5 and the x axis with a negative value. In this case, it may theoretically be possible to obtain MAbs with a g a in the range of 105-106 M -1 for a native
O. Chappey et al. /Journal of lmmunological Methods 172 (1994) 219-225
compound having a tool. wt. around 50 Da. However, this is never observed and is probably not practical. In fact, the wide heterogeneity of K a values for the same molecular weight compound precludes finding the maximal K a plateau value. Differences of a factor of 103-105 are often found between the lowest and highest value of K a for the same hapten. The curves suggest that the linkage arm has no influence beyond the critical mol. wt. of 325 Da and using only the highest K a values (Fig. lb), a plateau for log K a = 12.6 was found. This theoretical limit of K a to haptens appears to be in accordance with experimental K a values. The relationship between haptenic molecular weight and log K a raises the question of what is the minimal hapten molecular weight needed to completly fill the paratope area, assuming that the probability of raising anti-hapten MAbs with high K a will be optimal in this case. Fluorescein (tool. w t . = 334 Da) and penta-alanine (mol. wt. = 373 Da) were proposed as compounds with a sufficient binding area for an optimal interaction with the antibody combining site and the corresponding MAbs had high K a values (10 l° M -1) (Voss et al., 1976). Moreover, MudgettHunter et al. (1985) showed that digoxin (mol. wt. 781 Da) completely filled the complementaritydetermining regions (CDR) of MAbs to digoxin, even if the interaction sites between the paratope of MAbs to digoxin and digoxin were restricted to only some areas of the digoxin molecule, as demonstrated later by Whayono et al. (1990) and Kyurchkiev et al. (1990). X ray crystallographic studies have shown that the CDR of the variable heavy and light chains form an irregular shaped cavity or pocket, and the area of this combining site is about 7 nm 2 (Amit et al., 1986.) Moreover, MAbs to 2-phenyloxazolone (mol. wt. 162 Da) possess an interacting area of about 4 nm 2 with a K a never exceeding 105 M-1 (Alzari et al., 1990). These studies indicate that the molecular weight of a hapten which is required for MAbs to bind with high affinity is intermediate between that for histamine and digoxin groups. Haptens such as fluorescein and pentalanine, i.e., in the range 334-374 Da, result in high K a values. In contrast, if the molecular weight of the hapten is
223
under 300 Da the probability of raising MAbs with high affinity is greatly reduced. As well documented by Morel et al. (1990), the small size of haptens precludes the emergence of high affinity antibodies. High affinity MAbs to small size hapten can be raised only against derivatives including the hapten plus a chemical entity resembling an immunogenic conjugate. With these chemical modifications, the antibody binding site encompasses the hapten residue and includes the chemical linker. If the arm linkage is not long enough some amino-acid residues on the protein carrier are also included in the epitope recognized. This strategy results in affinity enhancement by a factor of 105-106 as has been shown for histamine (Morel et al., 1990). In conclusion, an analysis of the relationship between the association constant of 265 MAbs and the molecular weight of haptens suggests that for low molecular weight haptens (tool. wt. < 300-325 Da), the influence of the linkage arm is crucial and that MAbs with high K a can only be produced when using a chemical entity resembling an immunogenic conjugate.
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O. Chappey et al. /Journal of lmmunological Methods 172 (1994) 219-225 Kato, Y., Paterson, A. and Langone, J.J. (1984) Monoclonal antibodies to the chemotherapeutic agent methotrexate: production, properties and comparison with polyclonal antibodies. J. Immunol. Methods 67, 321-336. Kohen, F., Lichter, S., Eshhar, Z. and Linder, H.R. (1982) Preparation of monoclonal antibodies able to discriminate between testosterone and 5 /3-dihydrotestosterone. Steroids 39, 453-459. Kranz, D.M. and Voss, E.W. (1983) Idiotypic analysis of monoclonal anti-fluorescyl antibodies: localization and characterization of idiotypic determinants. Mol. Immunol. 20, 1301-1312. Kranz, D.M., Herron, J.N. and Voss, E.W. (1982) Mechanisms of ligand binding by monoclonal anti-fluorescyl antibodies. J. Biol. Chem. 257, 6987-6995. Kyrukchiev, S.D., Tyutyullkova, S.N. and Kehayov, I.R. (1990) Selection of monoclonal anti-digoxin antibodies with appropriate binding characteristics for immunodiagnostic purposes. Methods Find. Exp. Clin. Pharmacol. 12, 265274. Liu, D., Purssell, R. and Levy, J.G. (1987) Production and characterization of high affinity monoclonal antibodies to cyclic anti-depressant molecules. Clin. Toxicol. 25, 527538. Luedtke, R.R., Korner, M., Neve, K.A. and Molinoff, P.B. (1988). Monoclonal antibodies with high affinity for spiroperidol. J. Neurochem. 50, 1253-1262. Marullo, S., Hoebeke, J., Guillet, J.G. and Strosberg, A.D. (1985) Structural analysis of the epitope recognized by a monoclonal antibody directed against tricyclic antidepressants. J. Immunol. 135, 471-477. Morel, A., Darmon, M. and Delaage, M. (1990) Recognition of imidazole and histamine derivatives by monoclonal antibodies. Mol. Immunol. 27, 995-1000. Mudgett-Hunter, M., Margolies, M.N., Ju, A. and Haber, E. (1982) High-affinity monoclonal antibodies to the cardiac glycoside, digoxin. J. Immunol. 129, 1165-1172. Mudgett-Hunter, M.M., Anderson, W., Haber, E. and Margolies, M.N. (1985) Binding and structural diversity among high-affinity monoclonal anti-digoxin antibodies. Mol. Immunol. 22, 477-488. Pincus, S.H., Watson, W.A., Harris, S., Ewing, L.P., Stoks, C.J. and Rollin, D.E. (1984) Phenotypic and genotypic characterization of monoclonal anti-digoxin antibodies. Life Sci. 35, 433-440. Place, J.B., Thompson, S.G., Clements, H.M., Ott, R.A. and Jensen, F.C. (1983) Gentamicin substrate-labeled fluorescent immunoassay containing monoclonal antibody. Antimicrob. Agents Chemother. 24, 246-251.
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Quesniaux, V., Tees, R., Schreier, M.H., Wenger, G. and Van Regenmortel, M.H.V. (1987) Fine specificity and cross-reactivity of antibodies to cyclosporine. Mol. Immunol. 24, 1159-1168. Quinn, R.P., Bye, A., Shand, F., Tadepalli, S. and Gerald, L. (1983) Specificity of various monoclonal antibodies for use with the radioimmunoassay for acyclovir. Abstr. 2nd Int. Acyclovir (ZOVIRAX) Symp., 7 [abstract]. Rodwell, J.D., Gearhart, P.J. and Karush, F. (1983) Affinity analysis of monoclonal anti-phosphorylcholine antibodies. J. Immunol. 130, 313-316. Ronayne, L., Mclnerney, M., Phillips, O.M., Regan, C.M. and Williams, D.C. (1990) A monoclonal anti-imipramine antibody with antidepressant Binding properties similar to the muscarinic receptor. Biochem. Pharmacol. 39, 507-511. Rouan, E.S.K., Otterness, I.G., Cunningham, A.C. and Rhodes, C.T. (1989) Specific, high affinity colchicine binding monoclonal antibodies: development and characterization of the antibodies. Hybridoma 8, 435-448. Sawada, J.I., Terao, T., Itoh, S.I., Maeda, M., Tsuji, A., Hosoda, H. and Nambara, T. (1987) Production and characterization of monocional antibodies to 17/3-hydroxyprogesterone. J. Steroid Biochem. 28, 405-410. Sawada, J.I., Janejai, N., Nagamatsu, K. and Terao, T. (1988) Production and characterization of high-affinity monoclonal antibodies against morphine. Mol. Immunol. 25, 937-943. Schramm, W., Yang, T. and Midgley, A.R. (1987) Monoclonal antibodies used in solid-phase and liquid-phase assays, as exemplified by progesterone assay. Clin. Chem. 33, 13311337. Voss, E.W., Eschenfeldt, W. and Rott, R.T. (1976) Fluorescein: a complete antigenic group. Immunochemistry 13, 447-453. Wahyono, D., Piechaczyk, M., Mourton, C., Bastide, J.M. and Pau, B. (1990) Novel anti-digoxin monoclonal antibodies with different binding specificities for digoxin metabolites and other glycosides. Hybridoma 9, 619-629. Wright, A.F., Green, T.P., Robson, R.T., Niewola, Z., Wyatt, L. and Smith, L. (1987) Specific polyclonal and monoclonal antibody prevents paraquat accumulation into rat lung slices. Biochem. Pharmacol. 36, 1325-1331. Wright, L.L., Feinstein, A., Heap, R.B., Saunders, J.C., Bennett, R.C. and Wang, M.Y. (1982) Progesterone monoclonal antibody blocks pregnancy in mice. Nature 295, 415-417. Zalcberg, J.R., Healey, K., Hurrell, J.G.R. and McKenzie, I.F.C. (1983) Monoclonal antibodies to drugs-digoxin. Int. J. Immunopharmacol. 5, 397-402.
Journal of ImmunologicalMethods 172 (1994) 219-225
Association constants of monoclonal antibodies for hapten: heterogeneity of frequency distribution and possible relationship with hapten molecular weight O. Chappey
,.a, M . D e b r a y
b, E . N i e l a, J . M . S c h e r r m a n n
a,c
a INSERM U26 (Dr. J.M. Bourre), H~pital Fernand Widal, 200 rue du Faubourg Saint Denis, 75475 Paris cedex 10, France b Laboratoire de Bio-Math&natiques, Facultg de Pharmacie, Par~ I~, 4 avenue de l'Observatoire, 75006 Paris, France c Laboratoire de Pharmacie Clinique et de Pharmacocingtique, Facultg de Pharmacie, Paris I~, 4 Avenue de l'Observatoire, 75006 Paris, France
Received 8 November 1993; revised received 10 January 1994; accepted 24 February 1994
Abstract
Using published data, we have investigated the relationship of the association constant (Ka) of 265 MAbs for haptens with molecular weights ranging from 111 to 1202 Da. The study indicates that: (1) differences of a factor 103-105 are frequently found between the lowest and the highest value of K a for the same hapten; (2) the relationship between log K a and the hapten molecular weight of either the native drug or the molecular entity used for the K a determination is described by a hyperbolic function; (3) beyond a critical molecular weight of approximately 300-325 Da, the log K a reaches a plateau at a maximal value near 10-12 M-1. Key words." Monoclonal antiboby; Affinity; Association constant; Hapten
1. Introduction
Over the last decade, monoclonal antibodies (MAbs) have b e e n successfully used in many aspects of biological research. In therapeutic drug monitoring, MAbs are used for the assay of small
MAbs, monoclonal antibodies; PAbs, polyclonal antibodies; Ka, association constant; mol. wt., molecular weight. * Corresponding author. Tel: (1) 40-05-43-43; Fax (1) 40-3440-64.
Abbreviations:
haptens with the basic advantage of a potentially better specificity than polyclonal antibodies (PAbs) and lower cross-reactivity with metabolites or drug analogues (Quesniaux et al., 1987). However, the association constant (Ka) of MAbs to haptens is often lower than the average value obtained with PAbs by an order of 1 or 2 log (Chappey et al., 1992). Since the limit of detection of an immunoassay is particularly dependent on the K a value, the limit of detection of hapten immunoassays using MAbs is often poor compared to that of PAbs, and this can restrict the
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O. Chappey et al. /Journal of Immunological Methods 172 (1994) 219-225
220
Table 1 Description of MAbs used in the study Molecule
Mol. wt.
IgG type
Method
Log K a evaluation K a constant
Authors
5.28/5.30 8.01/8.1/8.08/8.21/8.15/7.73 7.68/8.12/7.94 8.49/7.75 8.75/8.27/8.49/8.88 8.0/7.6/7.85/6.20/5.7 8.48/7.41 9.74/9.70/9.91/8 7.49 9.85/9.72/9.73/8.66/9.92/10.2 9.99/9.83/9.97/10.67/9.93/9.6 10.7/10.7 6.70 5.49/10.27/10.37/10.42 5.49 9.11/8.18/8.4/8.48/8.54/8.62 8.6 11.04/9.96
Harrison et al., 1986 Bjercke et al., 1986
Maleic acid Nicotine
112 162
1 2
Weir Miiller
Amino-4 quinoline Cotinine Acyclovir Propanolol a-Linolenic acid Oxaprotiline Morphine hemisuccinate
163 176 225 259 280 298 301
1,2 2 1,2 1,2 1,2 2 1
Cheng and Prussof Miiller Scatchard Scatchard Hogg Scatchard Scatchard
1 2 2 1,2 1 2 1,2,3
Scatchard Scatchard Scatchard Scatchard Scatchard Scatchard Scatchard
1,2,3
Scatchard
Desipramine
301
17t~-OH progesterone llt~-OH progesterone hemisuccinate
330 430
10.48/9/10.3/8.95/8.9/8/9.3 9.7/9.3/9.3/8.9/10.3/7.9/10/10 10/8.3/8.3/8/10.48/9.3/9.3/9
Freier et al., 1986 Bjercke et al., 1986 Quinn et al., 1983 Chorev-Wang et al., 1986 Buffi~re et al., 1989 Chouchane et al., 1988 Sawada et al., 1988 No published data Glasel et al., 1983 Liu et al., 1987 Bowles et al., 1988 Sawada et al., 1987 Wright et al., 1987 Schramm et al., 1987 Fantl et al., 1982
9.84 6/3-OH progesterone Fluorescein
334
1,2 1,2 1 1 2 1 1,2
Voss Voss Scatchard Miiller Scatchard Miiller Friguet
Deoxycortisol Colchicine
346 339
Methotrexate
454
Digitoxin
712
1,2,3
Scatchard
Digoxin
781
1,2
1,2
Cyclosporine 2-Phenyloxazolone Paraquat
1202 188 186
Scatchard Scatchard Scatchard Friguet
10/9.3/8.3/9.6/9.9/9.48/8.48 8.95/9.3 10.23/7/8.76/7.86/7.7 7.3/7.45/7/6.74 10.30 9.2 9.18 6.51 8.45/9.2/9.6/8.6/9.23/9.14 8.85/9.85/9.23/8.85/8.48/9.78 7.78/7.65/7.36/7.2/7.15/8.92 8.52/6.79/7.6/5.54/5 9.72/9.76/9.71/9.95/10.04/10.4 9.85/9.3/8.9 9.08
9/9.63/9.77/9.7/8.77/8.51/7.68
8.48 9.06/9.06/9.12/9.16/9.17/9.28 9.28/9.35/9.43/9.46/9,46/9.64 8.25/8.46/8.65/8.85/8.89/8.92 Nisnoff and Pressman 8.96/7.94/8.02/6.32 9.84/9.62/9.48/9.72 Nisnoff and Pressman 8.11/9.28/9.23/11.48/9.04/9.79 9.36/10.65/11.41/10.66/10.99 11.41/10.85/12.23/9.2 9.48/8 Steward and Petty 8.55/7.98/7.55/7.22/6.86/7.63 Farr 11.7 Miiller 7 Scatchard 10.15 5.43 Scatchard Scatchard 7.68
Fantl et al., 1982 Kranz et al., 1982 Kranz et al., 1983 Hosoda et al., 1986 No published data Rouan et al., 1989 Kato et al., 1984 Cot et al., 1987
Collignon et al., 1988 Collignon et al., 1984 Wahyono et al., 1990 Brizgys et al., 1989 Kyurkchiev et al., 1990
Mudgett-Hunter et al., 1982 Mudgett-Hunter et al., 1985
Zalcberg et al., 1983 Pincus et al., 1984 Quesniaux et al., 1987 Kartinen et al., 1983 Wright et al., 1987 Bowles et al., 1988 Bowles et al., 1990
(table continued on next page)
O. Chappey et al. /Journal of Immunological Methods 172 (1994) 219-225
221
Table 1 (continued) Molecule
Mol. wt.
IgG type
Method
Log K a evaluation K a constant
Authors
Nortriptyline Soman Haloperidol
263 182 376
Alprenolol Histamine Phosphorylcholine
249 111 219
1 1 1 1 1,2 1 2
Scatchard Scatchard Scatchard Saturation Scatchard Friguet
Marullo et al., 1985 Brimfield et al., 1985 Juszczak et al., 1987 Bolger et al., 1985 Chamat et al., 1984 Guesdon et al., 1986 Rodwell et al., 1983
Leu-5 enkephalin Imipramine Clonazepam Spiroperidol
566 280 316 395
2 1 1 1,2,3
Scatchard Scatchard Scatchard Scatchard
7.16 5.77/5.57/5.08/4.72 8.59 8.4/7.95/6.84/6.56 7.39/6.82/6.63/6.28 2.43 5.34/5.54/5.38/5.51/5.11/5.64 5.0/5.26/4.4 8.9 7.62 6.64
Doxorubicine Gentamicine Albuterol Testosterone
544 460 239 288
1 2 1 2
Scatchard Scatchard Scatchard Abraham
8.07/7.73/7.82/7.9/7.24/7.43/7.81
Herion et al., 1986 Ronayne et al., 1990 De Bias et al., 1985 Luedtke et al., 1988
7.1/7.6/7.49/7.74/8.55/9/9.7/8.8 8.82/9.1/8.36/9.52/8.35/8.92/8.08 8.55/8.74/8/8.54 8.03 10.09 9.01 10.32/10.27
Balsari et al., 1988 Place et al., 1983 Adam et al., 1990 Kohen et al., 1982
use of MAbs. This paper focuses on the question of why MAbs to haptens do not have a better limit of detection in immunoassays. We have reviewed the published data for MAbs to haptens and investigated the relationship between the K a of such MAbs and the molecular weight of the hapten.
two examined the distribution of log K a of MAbs versus either the molecular weight of the native compound or the molecular entity used for the K a determination, i.e. the native compound or the native compound plus its linkage arm. For the third investigation, the highest published K a values of the same MAb for a hapten were correlated with the molecular weight used for the K a determination.
2. Materials and methods
2.1. Selection criteria for MAbs to haptens
2.3. Mathematical analysis
265 MAbs against small haptens with molecular weights lower than or equal to 1202 Da were selected for the study (Table 1). MAbs of IgG class and isotype 1, 2 or 3 were exclusively selected and Fab fragments to haptens were excluded. The methodology for measuring the K a of the MAbs either by saturation or by competition techniques is given in Table 1.
Modelling of log K a versus molecular weight was performed using different functions. The best fit to the data was obtained using the following hyperbolic model:
2.2. Relationship between log K a and hapten molecular weight Three relationships between log K a and hapten molecular weight were investigated. The first
log K a = A ( M - M o ) / M +
(3450 - 2M0)
where A is the maximum value of log K a (when M ~ o0), Ms0 is the molecular weight corresponding to the half-maximum value of log K a and M 0 is the molecular weight at and after which log K a becomes positive. A, 3/50 and M 0 were estimated by the least squares method, using a nonlinear regression program (MK Model, Oxford, UK).
O. Chappey et al. /Journal of Immunological Methods 172 (1994) 219-225
222 a 13.0
versus the molecular weight of the native compound cut the x axis at - 7 3 Da and the y axis at log K a = 5 and then increased to a plateau at log K a = 10.4.
i
10.4
!
"/.8 5.2
•
~°
!
i•
4. Discussion 2.6 0.0
I
0
250
500
750
1000
1250
Native compound
13.0
~
1o.4
.A'i
, s
,
, I
.
.
~
5.2 2.6 0.0
iOi
0
~
250
~
50o
I
750
10O0
1250
Molecular weight of the entity used for the Ka determination Fig. 1. Distribution of K a values for MAbs versus the molecular weight of the native compound (a) or the molecular entity used in the K a determination (b). The average hyperbolic relationship between the highest log K a values and the molecular weight of the haptens used for the K a measurement is indicated by the dashed line in b. Hyperbolic relationships were fitted using the least squares method.
3. Results Plots of log K a versus the molecular weight of either the native compound (Fig. la), or the molecular entity used in the Ka determination (Fig. lb), were fitted by hyperbolic relationships. Extrapolation of log g a versus molecular weight of the molecular entity used in the K a determination cut the x axis near the zero value (M 0 = 46 Da) and rose very abruptly to a plateau at log K a = 10.4. Using the highest values of log g a , extrapolation of the curve cut the x axis at M 0 = 71 D a and increased very rapidly to a plateau at log K a = 12.6 (Fig. lb). Extrapolation of log K~
As shown in Fig. 1, it appears that for low molecular weight compounds, K a values are lower than with high molecular weight compounds. Even if a large number of MAbs to low molecular weight compounds (100-200 Da) are produced, g a values around 101°-1011 M -1 are never observed. In contrast, with higher molecular weight compounds, K a values increase and reach a plateau never exceeding 1012 M - 1 . That is why we have investigated a possible relationship between the hapten molecular weight versus log g aA previous study had demonstrated a relationship between the molecular weight and the size of chemical structure (Voss et al., 1976). Moreover, as the linkage arm may influence the affinity of antibodies for haptens, relationships were studied between the molecular weight of either the native compound versus log K a or the molecular entity used for the K a determination versus log K a. In order to establish such relationships, it was first necessary to draw the average curve for each distribution using the same hyperbolic mathematical model which was found to give the best fit. Surprisingly, the two hyperbolic curves were superimposable beyond 325 D a and reached a plateau with a m e a n g a value of 10.4. For molecular weights below 325 Da, the solid line crossed the x axis with a positive value near the origin. This value is imprecise because of the lack of MAbs reacting with haptens having molecular weights below 100 Da. Acetaldehyde (mol. wt. 44 Da) is the smallest compound described which has been able to elicit MAbs. Therefore, MAbs to acetaldehyde were produced in the form of poly-L-lysine acetaldehyde adducts (Israel et al., 1986) and it was found that after extrapolation the y axis was intercepted at log K a = 5 and the x axis with a negative value. In this case, it may theoretically be possible to obtain MAbs with a g a in the range of 105-106 M -1 for a native
O. Chappey et al. /Journal of lmmunological Methods 172 (1994) 219-225
compound having a tool. wt. around 50 Da. However, this is never observed and is probably not practical. In fact, the wide heterogeneity of K a values for the same molecular weight compound precludes finding the maximal K a plateau value. Differences of a factor of 103-105 are often found between the lowest and highest value of K a for the same hapten. The curves suggest that the linkage arm has no influence beyond the critical mol. wt. of 325 Da and using only the highest K a values (Fig. lb), a plateau for log K a = 12.6 was found. This theoretical limit of K a to haptens appears to be in accordance with experimental K a values. The relationship between haptenic molecular weight and log K a raises the question of what is the minimal hapten molecular weight needed to completly fill the paratope area, assuming that the probability of raising anti-hapten MAbs with high K a will be optimal in this case. Fluorescein (tool. w t . = 334 Da) and penta-alanine (mol. wt. = 373 Da) were proposed as compounds with a sufficient binding area for an optimal interaction with the antibody combining site and the corresponding MAbs had high K a values (10 l° M -1) (Voss et al., 1976). Moreover, MudgettHunter et al. (1985) showed that digoxin (mol. wt. 781 Da) completely filled the complementaritydetermining regions (CDR) of MAbs to digoxin, even if the interaction sites between the paratope of MAbs to digoxin and digoxin were restricted to only some areas of the digoxin molecule, as demonstrated later by Whayono et al. (1990) and Kyurchkiev et al. (1990). X ray crystallographic studies have shown that the CDR of the variable heavy and light chains form an irregular shaped cavity or pocket, and the area of this combining site is about 7 nm 2 (Amit et al., 1986.) Moreover, MAbs to 2-phenyloxazolone (mol. wt. 162 Da) possess an interacting area of about 4 nm 2 with a K a never exceeding 105 M-1 (Alzari et al., 1990). These studies indicate that the molecular weight of a hapten which is required for MAbs to bind with high affinity is intermediate between that for histamine and digoxin groups. Haptens such as fluorescein and pentalanine, i.e., in the range 334-374 Da, result in high K a values. In contrast, if the molecular weight of the hapten is
223
under 300 Da the probability of raising MAbs with high affinity is greatly reduced. As well documented by Morel et al. (1990), the small size of haptens precludes the emergence of high affinity antibodies. High affinity MAbs to small size hapten can be raised only against derivatives including the hapten plus a chemical entity resembling an immunogenic conjugate. With these chemical modifications, the antibody binding site encompasses the hapten residue and includes the chemical linker. If the arm linkage is not long enough some amino-acid residues on the protein carrier are also included in the epitope recognized. This strategy results in affinity enhancement by a factor of 105-106 as has been shown for histamine (Morel et al., 1990). In conclusion, an analysis of the relationship between the association constant of 265 MAbs and the molecular weight of haptens suggests that for low molecular weight haptens (tool. wt. < 300-325 Da), the influence of the linkage arm is crucial and that MAbs with high K a can only be produced when using a chemical entity resembling an immunogenic conjugate.
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