Jaurnal of Immunological Methods, 151 (1992)47-fi6

47

© 1992ElsevierSciencePublishersB.V. All rightsreserved 0022-1759/92/$05.0¢;

JIM06287

Studies of the 'hook' effect in the one-step

sandwich immunoassay S. Amarasiri F e r n a n d o i and G e o r g e S. Wilson Department of Chemistry, Unicersityof Kansas, Lawrence, KS 66045, USA

(Received5 August1991,revisedreceived6 January 1992,accepted 14January 1992)

The one-ste,p sandwich immunoassay is increasingly replacing the traditional two-step immunoassay due to obvious advantages such as assay speed. However, the one-step sandwich immunoassay suffers from the 'hook' effect irrespective of the analyte characteristics. The 'hook' effect is dependent primarily on the ana!yte concentration. Three different model analytes, human growth hormone (hGH), the dimeric form of hGH (D-hGH, having a discrete nt:mber of repeating epitopes) and ferritin (multiple epitopes) having different immunological properttes have been employed in studies of the one-step sandwich immunoassay. The characteristics of each of the model analytes offer new insights into general guidelines for assay procedures. These guidelines permit rapid optimization of assay conditions for an immueoassay without a priori knowledge of the immunological eharaeteristies of the antibody or antigen. Both experimental and theoretical data show several instances where high capacity solid-phase antibodies can effectively shift the 'hook' to relatively higher analyte concentrations. The effect of the concentration of labeled antibody on assay response was examined theoretically. Key words: One-step sandwichimmunoassay;Antibody;Capture antibody;Labeledantibody;Capaeily;'Hook"effect

Introduction There are two types of two-site immunometric assay modes known as one-step and two-step. One-step sandwich immunoassays are currently enjoying an increase in popularity in clinical laboCorrespondence to: G.S.Wilson,Department of Chemisny, Universityof Kansas, Lawrence, KS 66045,USA. 1Present address: Department of Pilarmat:eulicalChemistr/, Universityof Kansas, Lawrence, KS 66045, USA. Abbreviations.. hGH, biosynthetichuman growthhormone; I~l-hGH, tzSt-labeledbiosynthetichuman growth hormone; D-hGH, human growth hormone dimer; GHC 101 and GHC 072, anti-human growth hormone monoclonal antibodies; 0CI054 and FEF021,anli-ferritiEimonoclonalantibodies.

ratories due to their speed. However, the practical advantages of these assays are limited by the high dose 'hook' effect, i.e., a decrease in assay response at high analyte concentration leading to a multi-valued dose-response curve. The 'hook' effect cart be avoided using a conventional twostep sandwich immunoassay pioneered by Miles and Hales (1968). However, for some analytes such as ferritin, which possesses multiple coltopes, the 'hook' effect complicates even the two-step mode (Ryall et al., 1982; Perera and Worwood, 1984). The one-step sandwich immunoassay is increasingly preferred to the traditional two-step mode. The most significant feature in the per-

formanee of these two assays is the mode of addition of the reagents (Sevier et al., 1981). The one-step immunoassay is carried out by simultaneous mixing of the solid-phase (capture) antibody, analyte, and the signal producing labeled antibody, followed by separation of the solidphase for signal measurements. In contrast, in the two-step assay mode the analyte is first permitted to bind only with the immobilized antibody. After this reaction is completed, the excess analyte is washed away. The immobilized capture antibody-antigen complex is then incubated with the excess labeled antibody at the second step. If all of the steps in the formation of the ~sandwich' consisting of the immobilized capture antibody, the analyte, and labeled antibody were reversible then the order or sequence of reagent addition would make no difference. However, this is nnt uniformly the case thus making a detailed understanding of non-reversible behavior essential. The generally accepted cause of the 'hook' effect in one-step immunometric assays involving monoclonal antibodies is an excess of analyte which prevents simultaneous binding of solidphase and liquid-phase monoclonal antibodies. This is assumed to be a reaction which reaches equilibrium. The three reactants - analyte, solidphase antibody, and liquid-phase antibody - react simultaneously. If any one of the reactants is present in insufficient or excess amounts, :he equilibrium may shift in either direction causing significant deviation of the response from the expected behavior. The 'hook' effect in the onestep immunoassay is primarily a concentration effect, although the characteristics of the antibodies and their epitopes also play a significant role in producing the 'hook'. The biphasic nature of the response is extremely critical when the assay is applied to the determination of analytes which may exist at very high levels. In some pathological situations, for example, tumors can secrete much higher levels of peptide markers than those normally found. Accordingly it is possible to obtain, sometimes without warning, curve distortion. Such a potential analytical problem has been reported for the determination of prostate-specific antigen (PSA) in serum which is a marker for adenoearcinoma of the prostate (Alfthan and Stenman, 1988;

Vaidya et al., 1988; Boder et al., 1989; Myrtle, 1989; Wolf et al., 1989). All these reports suggest that this artifact can be prevented by employing the two-step assay procedure (Vaidya et al., 1988; Wolf et al., 1989). However, the two-step assay demonstrates a 'honk" effect identical to that observed in the one-step assay for PSA (Alfthan and Stenman, 1988). This report also showed that 9% of the serum PSA (30 kDa) in one "hook' sample is present as a 16 kDa PSA fragment. This brief report showed a 'hook" effect in both twu-site assay modes. The cause was attributed to an affinity difference between the 16 kDa fragment and PSA. Boder et al. (1989) did not see the 'hook' effect with the two-step assay mode, suggesting that the Alfthan and Stenman observation resulted from an increased incubation time. Recent reports describe low results for lutropin (LH) and fonitropin (FSH) in a one-step immunoassay which was developed for both hormones using two monoelonal antibodies (Dahlmann et al., 1990). This report also indicates that the modified two-step procedure should overcome this artifact. However, no supporting data are presented. Similarly, Gershagen et al. (1986) developed a monoelonal antibody based one-step immunoradiometric assay with no practical limitations (i.e., the dose-response curve does not 'hook' at very high concentrations of the analyte). It was suggested that the absence of a ~hook' could be attributed to coupling of the antibody to high capacity polyaerylamide beads. A time resolved immunofluorometric assay for hCG has been performed to determine the effect of the concentration of the labeled antibody in a one-step assay. In this assay, the increase in the labeled antibody concentration proportionately increases the assay's tolerance to the 'book' effect (Khosravi, 1990). Also, the two-step modification did not exhibit the 'hook' effect for the hCG assay (Khosravi et al., 1987). It is clear that inadequate concentrations of labeled antibody also appear to be one of the causes of the 'hook' effect in one-step assays. Sandwich enzyme immunoassays for hCG have been developed using monoelonal antibodies (Gupta et al., 1985). Different enzyme tags have been utilized to design a one-step assay procedure. The 'hook' effect for the one-step assay is

shifted to higher concentrations of hCG as the amount of anti-alpha-hCG antibody-HRP conjugate is increased. However, the assay response for the two-step modification shows no 'hook' effect. According to this report, at high analyte concentrations, solid-phase antibodies interact monogamously with the analyte which is much less stable than bigamous binding. Therefore analyte molecules may be released from the solidphase during the washing steps. Various practical aspects of sandwich immunoassays are summarized in this report (Gupta et al., 1985). Comitti et al. (1987) developed a monoelonal based, one-step sandwich enzyme immunoassay for insulin. This work suggests that the one-step immunometric assay gives enhanced sensitivity over the two-step modification for the insulin system and can be performed without a 'hook" effect in a mode which results in an 'enhancement' effect, as described by Moyle et al. (1983). Another study (Rogier ct al., 1989) shows the importance of optimizing the amount of solid- or liquid-phase antibody in order to avoid the 'hook" effect in the two-step sandwich immunoassay. Methodological problems with respect to sensitivity, precision and the 'hook' effect in one-step commercial immunoassays for ferritin have been evaluated (Revenant et al., 1982; Ng et al., 1983; Anido, 1984). The latter group estimated the maximum limits for the determination of ferritin and emphasized the importance of the sample dilution in order to avoid the possibility of misdiagnosis. Garcia-Webb et al. (1986) have also observed a high dose 'hook' effect in the measurement of somatotropin. Hoffman et al. (1984) have reported a novel method called 'kinetic hook screening' which is capable of monitoring the 'hook' effect in two-site immunometric assays. This technique has been designed to eliminate interference by reducing the incubation time resulting in immunometric assays of higher sensitivity. Achieving these attractive advantages, however, requires special instrumentation (Parsons et al., 1983). Practitioners of immunoassays are well aware of the importance of advocating better characterized methodologies in diagnosis (Gosling, 1990). Surprisingly, as these assays become increasingly popular in clinical laboratories, more pitfalls re-

lated to these assay methods are discovered. These incidences are reported often ( e e l and Escares, 1991, Vermes et al., 1991; Wolf and Brem, 1991). To be useful as an analytical technique, ambiguous immunoassay results for test samples should be minimized or eliminated. Examination of the literature reveals that by changing the mode of assay performance ambiguous results can be eliminated. This approach, however, may not necessarily be appropriate for all analytes, as suggested by Alfthan and Stenman (1988) and there have been no reports concerning detailed investigations of the 'hook' effect. Here we prcsent a careful evaluation of the 'hook' effect in the one-step sandwich immunoassay. Three model systems have been employed: human growth hormone (hGH, 22 kDa), non-covalent dimer of human growth hormone (D-hGH, 44 kDa) and ferritin (450 kDa). For all these systems well-characterized monoclonal antibodies are available. In the hGH system, two monoclonal antibodies were selected which bind two distant but different epitopes. These studies were extended with D-hGH as the simplest case of an analyte having two sets of repeating epitopes. The influence of repeating epitopes was further examined using ferritin. All the experimental data are supported by theoretical models. It is not possible to generalize from these three examples, but the objective is to develop a systematic approach to the characterization of an immunological system.

Experimental section Materials The antigens, hGH and purified dimeric hGH, were donated by Eli Lilly (Indianapolis, IN). The following reagents were donated by Hybritech (San Diego, CA): monoclonal antibodies for hGH-GHC 072 and G H C 101; anti-ferritin antibodies, FEF021 and QCI054 (F(ab')2). The 1?5IFEF021 and t~SI-GHC 101 (approximately 10 #.Ci/ml) were prepared in the radioiodination laboratory by Hybritech. Chemical immobilization of G H C 072, G H C 101, FEF021 and QCI054 on plastic beads was carried oat at Hybritech.

Human spleen ferritin (hs-fcrrltin) was purchased from Scripps Laboratories (San Diego, CA). "Maxisorp' ( l l × 70 ram) and Immunostar (12 × 75 mm) polystyrene tubes were purchased from Thomas Scientific (Swedesboro, N J). Bovine serum albumin (BSA, Cohn fraction V) and polystyrene tubes (12 × 75 ram) (for assays with plastic beads) were purchased from Fisher Scientific Co. (St. Louis, MO).

Reagents The sample buffer used throughout all experiments was phosphate-buffered saline (PBS), pH 7.4, 20 mM, containing 0.15 M sodium chloride with 5.0% BSA added. The washing buffer was the same except that 0.05% BSA was added. The stock solution of the coating buffer was 1.0 M carbonate buffer, pH = 9.6. All other reagents were reagent grade and all solutions were prepared weekly in water obtained from a Barnstead Nanopure II system and stored at 4°C.

Apparatus A computer controlled gamma counter (Compugamma 1882-003, Pharmacia LKB Bioteeh., Gaithersburg, MD) was used for all radioactivity measurements.

Methods ~one-step sandwich immunoassay Chemically immobilized antibodies. Each plastic bead (5/16 inch) was removed from the container and the residual drops were blotted without allowing the beads to dry. One plastic bead was introduced into each tube. G H C 072 immobilized plastic beads were supplied in the dry state and were used directly. Different amounts of the analyte (hGH, D-hGH or ferritin) and 100 ~1 of lZSl-labeled liquid-phase antibody were then added and diluted to 200 ~1. Reagents were mixed and then incubated for 4 h at room temperature. After incubation of the beads, 1.0 ml of washing buffer was dispensed into each tube and liquid was aspirated. All plastic beads were washed five times, aspirating the liquid after each washing step. After carefully removing all of the washing buffer, each bead was counted in the gamma counter. Assays for both analytes were performed with shaking to ensure mixing. All measurements were made in triplicate. Any devi-

ations from this procedure are specified in the appropriate figure captions. The one-step sandwich immunoassay for hGH was performed at 37°C. Assays for hs-ferritin were carried out at room temperature. Physically adsorbed antibodies. Antibodies (FEF021 or QC1054) were physically adsorbed on the polystyrene surface of plastic tubes by directly adding 200 ,~1 of antibody in carbonate buffer (0.01 M, pH = 9.6) followed by incubation for 3 h at room temperature. The antibody concentrations are reported in the appropriate figure captions. After coating with antibodies, all tubes were blocked for non-specific binding by incubation with 300 ,u.I of sample buffer for 1 h at room temperature followed by five washings with 250 /~1 of washing buffer. After washing, variable amounts of hs-ferritin and a fixed amount of 1251-1abeled antibody were added and diluted to 200 #1. Tubes were incubated for three hours. These tubes were washed as before, then counted in the gamma counter. All steps were carried out at 37°C. Measurements were made in triplicate.

Results and discussion

As the simplest ease, an analyte, hGH, having two different epitopes was chosen to illustrate the characteristics of the one-step sandwich immunoassay. The fundamental reaction resulting from the reaction of the analyte, P, with solidand liquid-phase antibodies in a one-step sandwich immunoassay can be represented by the following equation: P~/b+ Qt(,) +Q~J)~-~Q*PQI{,b+ PQR~)+ PQ~II

(1)

where Q~ and Q~ represent the capture and labeled monoelonal antibodies, respectively. Symbols s and l specify the phase of each reactant: solid-phase or liquid-phase, respectively. The concentration of Ql is defined as the total number of moles of immunologically active Qi immobilized on the surface divided by the solution volume. The analyte, P, interacts with Qi and Q~' to form the sandwich complex, Q~PQt which generates the binding response for this assay. PQI (solid-phase) and PQ* (liquid-phase) are the

51

o o

01

Xo

X1 Anolyte

X2

concentration Fig. L A hypothetical standard curve for the monoclonal based one-step sandwich immunoassay represented by an analyte havingtwo different epitopes. Analyleconcentration range is Xa-X 2. Curve A represents a non-hooked calibration curve. Curve B exhibits the 'hook' effect and the response is maximumat analyte concentration XI.

only other forms of bound analyte except the sandwich complex. Curve A in Fig. 1 is the resulting hypothetical standard curve. This curve can be regarded as the normal curve for the immunoassay. Xo, X I and X 2 correspond to various analyte concentrations as shown in Fig. 1. When the assay is optimized, the capture and the labeled antibodies are in excess with respect to the analyte concentration so that the calibration curve is expected to be linear at low analyte concentrations. At higher analyte concentrations either the amount of solid-phase antibody or the labeled antibody could be inadequate leading to saturation and a plateau response. If a large excess of capture antibody is used for the reaction, then curve A is asymptotic at infinite dose because only the amount of labeled antibody is insufficient. In practice, contrary to the hypothetical curve A, a 'hooked' dose-response curve is observed if the assay is performed in a wider analyte concentration range as shown in curve B (Fig. 1). According to curve B, as the analyte concentration increases, a biphasic calibration curve is ob-

served if either the capacity of the solid-phase is exceeded or the labeled antibody concentration is inadequate. Generally, the ascending response of the calibration curve results from the labeled antibody reacting in excess with the analyte (i,e., concentrations X 0 and Xt). The descending response begins and continues when the analyte is in excess (curve B, concentration range X r X 2 ) . X~ is the analyte concentration at which the maximum response is demonstrated in the doseresponse curve. Generally the practical assay curve is generated in the linear response range. However, samples may contain an analyte concentration of perhaps X z and it is necessary to distinguish this case from that where the analyte concentration falls between X . and X I. To detect the presence of the high dose 'hook' effect a sample is analyzed at the highest concentration and is then diluted to verify that the same original sample concentration is obtained. In contrast, the 'hook' effect in the competitive binding assay occurs at low analyte concentrations. Therefore, the 'hook" can he seen in the standard curve even before the sample is analyzed. A conceptual account of the 'hook' effect related to the competitive binding assay is documented (Fernando et al., 1992). As an extension of the characteristics of the analytes, the behavior of the dimeric form of P (D-hGH, symbolized as H) in a one-step sandwich immunoassay can be evaluated. H has a total of four epitopes for the interaction with antibodies Qi and Q~ q~ or q,*. In this reaction, a significant amount of labeled antibody. Q* (i.e., about 93%) is complexed to form soluble species such as PQ~t> and PQ.,* Pt~)which are washed away at the separation step, Thus, only 7% of the original concentration of Q~ is available to generate the response. Approximately 4% of the added analyte contributes to the solid-phase complex formation, resulting in a lower signal. A greater proportion of the analyte (i.e., about 40%) either in the form of PQIt~) or PQ~P~ remains uncomplexed with the labeled antibody, resulting in a lower response. Accordingly, it is predicted that if the labeled antibody is not in excess with respect to either the capacity of the solid-phase or the analyte concentration, solution complexes will predominate, resulting in a "hook'. Ttle effect o f eapacio' of solid-phase antibody Inodel 2 Theoretical values for model 2 show similar effects to those just dr:tailed in model 1. A high capacity solid-phase antibody would eliminate the 'hook" effect for model 2 (results not shown). The effect o f labeled antibody concentration model 1 The performance of one-step sandwich immunoassays can be controlled by selecting appropriate concentrations of labeled antibody. A study of model 1 is sufficient to explain the effect of the labeled antibody concentration. This model is detailed for three different concentrations of the solid-phase antibodies selected from Fig. 2, 0.5 nM (low), 5 nM (moderate), and 20 nM (high) (curves A, D and F respectively). As can be seen for the low solid-phase concentration 1,0.5 nM), if the concentration of the labeled antibody is raised while keeping both the solid-phase and analyte concentration range the same, resulting computer simulated data show that the "hook' shifts to higher analyte concentrations (Fig. 5). Curve F in Fig. 5 is analogous to

80

F,G 60

0

2 4 6 Anolyte c o n c e n t r a t i o n

e (n M)

10

Fig. 5. Theoretical curves; effecl of the labeled antibody concentralion (q~) on the "hook' effect in one-step sandwich immunoassay for model |. Theoretical parameters: K I = ] n M -t, K=~ = 1 n M - I , ql =0.5 nM, q~ ( n M ) = 50 (A), 10 (B), 5 (C), 2.5 (D), 1.25 (El, 0.5 (F), 50 pM (G), 5 pM (HI. Analyte concentration range is 0.!- 10 nM.

curve A from Fig. 2. Curve F shows the 'hook' effect even though equal amounts of labeled (q~) and capture antibodies (ql) are employed. The dose-response curve is linear up to about 0.6 nM. The 'hook' occurs when the analyte concentration (p) is greater than ql or q*. It will be noted that in order to avoid the "hook' not only the solid-phase capacity and the concentration of the labeled antibody have to be considered but also analyte concentration range. The sensitivity, however, decreases and the sharpness of the 'hook' diminishes from curve E to curve C. Curve C was generated using ten-fold less labeled antibody (q~) than the capacity (q~) while the values for curves D and E are 5 and 2.5, respectively. Extremely high concentrations of labeled antibody suppress the 'hook' (curves A and B), but at the same time significantly reduce the formation of the signal generating complex. Moreover such high concentrations of radiolabeled antibody may not be achievable practically. This situation can be encountered when performing ELISAs because the capacity of the solid-phase is very limited. The ql/q2* ratios for curves A and B are

100 and 20. Very low concentrations of labeled antibody (curves G and H) give high sensitivity but a sharp 'hook'. The ratio, q t / q ~ for curves G and H arc 10 and 100 respectively. Fig. 6 shows the theoreueal curves when the concentration of solid-phase antibody is increased to moderate levels (5 nM). The 'hook" becomes broader as the concentration of labeled antibody decreases (Fig. 6, curves A - D ) . To generate these curves a ten-fold higher capacity of the solid-phase antibody than that of Fig. 5 was assumed. Curve F is analogous to curve D from Fig. 2 which shows a 'hook' effect. The solid-phase capacity (ql) is ten-fold higher than the liquidphase antibody (q~). The sensitivity for each of the curves A - E is lowered compared to curve F. Curves A and B result from ten-fold and two-fold higher q~ than q= while curve C is generated using equal concentrations of ql and q~. Curves D, E and G require 4-. 10- and 100-fold excess of q= over q~. For curves D - G ql > q~, however, there is a "hook' effect. A similar result is also shown in Fig. 5. However, the shapes of the response profiles are somewhat different from those of Fig. 6 and this difference can be at-

20 G,H 15

F E

-.~,la

D

c

2 4 6 a 10 Anolyte c o n c e n t r o t i o n (n M) Fig. 6. Theoretical curvc~: effect of the labeled antibody concentration (q~) on the 'hook' effect in one-step sandwich immunoassay for model I. Theoretical parameters: Kt= I nM I Kz = I nM t, q i = 5 nM, q~ (nM)= 50 (A), 10 (B), 5 (C), 2.5 (D), 1.25(E), 0.5 (F), 50 pM (G). Anaiyt¢ concentration range P, 0.1-10 nM.

O

80 A

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B,C,D

60

40

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.........

~ .........

~ .........

~ .........

~ ........

'1'0

Anolyte concentration (nM) Fig. 7. Theoretical curves: effect of the labeled antibody concentration (q~) tm the 'hot~k' effect in tree-step sandwich immunoassay for model I. Theoretical parameters: K I - l nM ~,Kz-lnM I. ql=20nM, q~(nM)=5O(A),lO(B),5 (CI. 2,5 (13). 1.25(El. Analyte concentration range is D.I-1O riM. tributed to the capacity, qL. These theoretical values also suggest that some of the assays have sufficient sensitivity to permit measurements in the low analyte concentration range thus avoiding the 'hook" effect (Fig. 6, curves E - G ) . As Fig. 7 shows, extremely high capacity solidphases provide dose-response curves without any 'hook' effect. A similar result is shown in Fig. 2 (curves F and G). Consequently, those assays with variable amounts of liquid-phase antibody show no "hook' (curves A - E , Fig. 7). The apparent absence of the 'hook' depends on the solid-phase capacity (qi). All of the curves were generated when ql exceeded the analyte concentrations (p) and which can effectively capture almost all the analyte (P). Thus, fewer molecules of labeled antibody (Q~) are consumed to form soluble complexes which will result in asymptotic behavior for the response. Examination of simulated results in Figs. 5, 6 and 7 shows significantly different response profiles even for a well defined model (model 1). The value of ql used to generate the curves in Fig. 7 is 4-fold and 40-fold higher than for the curves generated in Figs. 5 and 6, respectively. Comparison of these curves in

58 cach figure reveal the magnitude of the change in the shape of the dose-response curve. As the theoretical study shows, excess concentrations of any of the reagents (qn, q~ and p) should control the effective species formation. Across all concentrations of the solid-phase, there is an upper limit in the improvement in sensitivity that can be obtained by restricting the concentration of labeled antibody in the assay. It seems reasonable therefore to conclude that the 'hook' effect can be effectively avoided within a broader analyte concentration range if extremely high capacity solid phases are employed which cause almost all analytes to react with the capture antibody and leavcs fewer analyte molecules in the liquid-phase. The above conclusion further suggests that the minimization or elimination of soluble complex formation is a general requirement in o r d e r to circumvent the 'hook" effect. According to theoretical studies on model 1 the following general guidelines can be adopted: (1) the 'hook' appears when p > ql, q*; (2) no 'hook' appears when qt > P (ifq~ > q~) or q~ > p (if q~ > q l ) .

Experimental results for analytes hGH and D-hGH Experimentally the assays for h G H and D - b G H were tested over a broad analyte concentration range in order to observe how the developed theory could be useful in practical assays. T h e objective criteria for these two assay systems are similar to those of model I. The experiments for h G H and D - h G H were performed in parallel for comparison. These data are collectively illustrated in Figs. 8, 9 and 10 in low, moderate and high concentration ranges, respectively, h G H is discussed in a single assay mode where G H C 072 is the solid-phase antibody and O H C ll)l is the liquid-phase antibody ( G H C 0 7 2 / h G H / G H C 101 system). Assay protocols for D - h G H are appropriately discussed in two different assay modes: G H C 1 0 1 / D - h G H / G H C 101 and G H C 0 7 2 / D h G H / G H C 101 systems.

An analyte with two differeat epitopes /assay for hGH GHC 072 / h G H / GHC 101 system. As equation 1 shows the analyte, h G H , can be assayed with two different monoclonal antibodies. The

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B~// /

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/~A7 /~

0.b . . . . . . . . .

JB

b,'4 . . . . . . . .

iJ.~. . . . . . . .

Analyte concentration (nM)

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Fig. 8. Dose-response curves glr hGH and D-hGH in one-step sandwich immunoassay: low analyte ¢oncentralion range. Analyles: hGlt (t~), D-hGI-I (z~); labeled antibody: GHC 10l; n251-GHC 101 concentration: 0.59 nM (t~), 0,8 (,a) nM; solidphase antibodies (chemically aUached to plastic beads): G]tC 072 (m). GHC 101 t t,). Experimental dose-response curves (dashed line): curve A', bGH (~), curve B', D-hGH (A). Theoretical curves: curve A, hGH (•); curve B, D-hGH (~ ]. Theorelical parameters: curve A (model I). K t = 0.013 nM - t, K z = l nM-t, q t = 10 riM, q~ = 0.6 nM; curve B (model 2b], K; ~ 0.32 nM- i. qt - 5 nM, q~ = 0.8 nM. Analyte concentration (p) range is 311pM-l.2 nM.

effect of the analyte concentration on the response was studied and each set of data was fitted to a theoretical curve. Fig. 8 shows the experimental data and the relevant theoretical curves for the low concentration range of h G H . According to these data the response varies linearly with b G H concentration in this analyte range which is normally encountered in such an experiment. Curve A represents the theoretical binding curve using model I in which the antibody is permitted to interact both mono- and bivalently with h G H . Model 1 broadly agrees with the experimental data up to 0.4 nM of h G H . T h e experimentally determined affinities of G H C 072 and G H C 101 are 1.1 nM ~ and 3.8 n M -n (Sportsman et al., 1989). T h e affinity and the concentration of the solid-phase antibody have not been directly estimated experimentally following attachment to the plastic surface. T h e r e -

59 fore the solid-phase antibody concentration was assumed to be 10 nM (q=). T h e affinity for the capture antibody is about 77-fold lower than the c,~p6rimental value. T h e difference in affinity may be attributed to the modification of G H C 072 in the immobilization process. T h e affinity value for the liquid-phase antibody only differs by four-fold compared to the experimental value. If the assay in Fig. 8 is reproduced at high analytc concentrations either the amount of capture o r labeled antibody or both is certainly inadequate. Surprisingly, it was revealed that G H C 072 and G H C 101 are known to have synergistic interactions with h G H which could enhance the assay response in solution. A detailed examination of the synergistic interactions in solution is documented elsewhere ( F e r n a n d o et al., 1992).

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~

t

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20

S 10 15 Analyte c o n c e n t r a t i o n

20 (nM)

~4Q B 20 o

......~,~ .......i66 .......146 .......i~6 .......i ~

Analyte c o n c e n t r a t i o n

(nM)

Fig. 10. Dose-response curves for hGH and D-hGH in one-step sandwich immunoassay: high analyte concentration range. Analytes: hGH (D), D-hGH (z~, o); labeled antibody: GHC 101; 12SI-GHC 101 concentration: 0,56 nM (D), 0.8 nM (t,, o); solid-phase antibodies (chemically attached to plastic beads): GHC 072 (a). GHC t01 (z~, o), Theoretical curves: curve A; hGH (D); curve B, D-hGH (A); curve C, D-hGH (). Theoretical parameters: curve A (model l), Kj = 0.015 nM - =, K2 = 0.1 nM - = q I = 0.3/¢M, q~ = 0.56 aM; cur~¢ B (model 2h], Ki =0.2 nM -t, q1=25 riM, q~ = 0.8 aM; curt =C (model 2a), K==0.02 nM J, K2=0.015 nM -I, q~-40 nM, q~ = 0.8 nM. Analyte concentralion (p) range ~ I nM0.25/*M.

A

60

80-

25

,~i~. 9. Dose-response curves for hGH and D-hGH in one-step sandwlch immunnassay: moderale analyt¢ concentration range. Atlalytes: hGH (D), D-hGH (zx, ~>);labeled antibody: GHC ]0l; I251-GHC 101 concentration: 0.59 nM (D), 0.8 nM (z,, o); solid-phas~ antibodies (chemically altacbed to plastic beads): GHC 072 (c:, ),GHC t0[ (,2,). Experimental curves (dashed lines): curve B', D-hGH (zx); curve C', D-hGH (o). Theoretical curves: curve A, hGH (o); curve B, D-hGH (A); curve C. D-hGH ().Theoretical parameters: curve A (model 1), KI=0.1 nM i, K2=0.2 nM-t, q l = 5 0 nM, q~=0.56 nM; curve B (model 2h), K 1= 0.l nM ~. q~ = 39 nM. q~ = 0.8 nM. Curve C (model 2a), K==20 /~M i K2=30 /~M-=, q= = 10 nM, q~' = 0.8 aM. Analyte concentration (p) range is 1.4-22 aM.

T h e developed dose-response d a t a and the theoretical curves over moderate and high analyte concentration ranges are shown in Figs. 9 and 10. T h e ana[yte concentration is the only experimental condition changed from Fig. 8. T h e response progressively increases with increasing h G H concentrations asymptotically approaching an upper limit (Fig. 9). Fig. 10 shows a decrease in response at high a~lalyte concentration as more soluble complexes ar~ formed. Theoretical curves have been drawn similar to curve A in Fig. 8. T h e s e theoretical carves have been obtained assuming the bivalency of both the capture and the labeled antibody (i.e., model 1). T h e parameters of Fig. 8 had to be changed considerably to fit the data for curve A in Figs. 9 and 10 (details given in figure captions). T h e deviation of the theory and experiments may be explained indirectly by showing that the h G H molecule forms a series of

complexes when it coexists with GHC 101 and GHC 072 monoelonal antibodies (Fernando et al., 1992). However, it should be noted that the above experimental prediction has been obtained assuming the antibodies are in solution. These deviations are inferred to be the result of concomitant interactions of both antibodies with the antigen, forming higher molecular weight linear and circular complexes. In a related study, Ehrlich e t a l . (1983) were able to demonstrate a similar solid-phase enhancement for hCG.

An analyte hatting two repeatblg epitopes/assay for D-hGH D-hGH is a well characterized analyte (Becker et al., 1987). It can provide a model antigen having two known repeating epitupes. The selection of the solid- or liquid-phase antibody will determine the binding characteristics of D-hGH in a one-step sandwich immunoassay. As discussed in model 2b, a single antibody (GHC 101 or GHC 072) can be used to design a one-step sandwich immunoassay for D-hGH. GHC IOI/D-hGH/GHC 101 system. This assay system is compatible with model 2b and has some similarities with the hGH system discussed previously in which only two epitopes are accessible for reaction with the capture and the labeled antibodies. As detailed in this model, complexes of D-hGH with capture antibody are similar to hGH. but different soluble complexes can be formed for D-hGH. The experimental data for GHC 1 0 1 / D - h G H / G H C 101 system are plotted concurrently with hGH data (Figs. 8-10). Curve B represents the simulated dose-response carves generated using model 2b. The dose-response curves over the low and moderate D-hGH concentration ranges are sigmoidal in nature as opposed to the analogous data for hGH (curve B' in Figs. 9 and 10). Theory and experimental data do not agree as well at low analyte concentrations. The sigmnidal binding behavior of D-hGH may be caused by the fact that the labeled GHC 101 can effectively mask both epitopes of D-hGH while the analyte is in solution. Thus, the analyte is not permitted to react with the solid-phase resulting in a lower response. Furthermore the nature of the solution-phase complexes of D-hGH and GItC 101 can be described using cross reac-

tivity studies of the competitive binding assay. As described in the companion paper (Fernando et al., 1992) the competitive binding assay fur hGH with GHC 101 shows an inhibition curve which is normally expected. However, if the above assay is performed with D-hGH instead of unlabeled hGH a low dose 'hook" appears (data not shown). In both experiments the labeled antigen was ~zsIhGH. The appearance of a low dose 'hook' in a competitive binding assay with a single antibody further suggests that GHC 101 can effectively interact with multiple epitopes of D-hGH to form multicomponent stable complexes. Moreover according to model 2b both epitopes are assumed to have similar affinities. However, when the dimeric molecule is formed or after D-hGH reacts with a single antibody, the possible distortions of the epitopes in D-hGH may also cause a deviation of the experimental data from the theoretical model. All of the above reasons account for the divergence of the experimental data from theory as well as from the hGH system. As predicted previously, this assay exhibits a high dose 'hook' effect. The 'hooked" dose-response curve is shown in Fig. 10. At higher analyte concentrations, a lower response is observed owing to the formation of soluble liquid-phase complexes and the consumption of labeled antibody. The possible liquid-phase complexes are described in model 2b.

An analyte having two repeating epitopes/assay for D-hGH GHC 072/D-hGH/GHC 101. This assay design for D-hGH deviates from the previous system by employing GHC 072 as the capture antibody and the experimental and the theoretical results are plotted together with other systems (Figs. 9 and 10). The theoretical model 2a supports this assay design and the theoretical curve is denoted as C. At low concentrations of D-hGH, the response is very poor and the experimental data are not shown in Fig. 8. As the D-hGH concentration is increased, a sigmoidal dose-response curve is obtained (curve C', Fig. 9). The response gradually increases and eventually generates a 'hook' as shown in Fig. 10. The disagreement between the theory and the experimental data over the moderate analyte concentration

range is illustrated in Fig. 9. The apparent deviation can again be attributed to the formation of soluble complexes. However, soluble complexes may not explain all of the observed behavior. This led us to explore other factors contributing to the poor response (Fig. 8) and sigmoidal nature of the curves (Fig. 9). As noted in model 2a, two GHC 10i molecules can interact with D-hGH in solution or when the analyte is reacted with GHC 072 antibody. But D-hGH is only permitted to react with two GHC 101 molecules when both are in solution in the previous assay mode. Thus, it is possible to assume that the analyte should be able to bind the capture antibody (GHC 072) even after multiple epitope interactions of the analyte with the labeled antibody (GHC 101) have occurred. However, the same assay for DhGH in the two-step mode reveals that the analyte dissociates from the solid support if multiple epitope interactions of the bound analyte and liquid-phase antibody occur (Fernando and Wilson, 1992). Therefore it is reasonable to conclude that the capture antibody is prohibited from interacting with D-hGH if the analyte reacts multiply with the liquid-phase antibody. Most probably a conformational change of the D-hGH occurs after multiple epitope interactions with the analyte and the labeled antibody. The theoretical and experimental studies on hGH and D-hGH indicate that all the analytes exhibit a high dose 'hook' effect. Moreover, the selection of the solid- and liquid-phase antibody contributes to the specificity of the one-step assay mode.

An analyte having multiple epitopes /assay for ferr#in As described in model 2, an individual antibody, (FEF021) or two different antibodies, (FEF021 and QCI054) were selected to design a one-step sandwich immunoassay for ferritin. To examine the practical implications of the capacity of the solid-phase antibody, antibodies chemically immobilized on plastic beads (c-FEF021 or eQCI054) or physically adsorbed on plastic tubes (p-FEF021 or p-OCt054) were employed. All assays for ferritin were performed with FEF021 as the liquid-phase antibody. Most immunoassays employ physically ad-

sorbed capture antibodies, typically bound to polystyrene tubes. Plastic bends have also been used in these experiments to provide a higher surface area than the plastic tubes. As shown by Cantarero et al. (1980) one can estimate the surface saturation capacity for an antibody when it is physically adsorbed. As an example, the surface saturation capacity of bovine lgG is approximately 250 ng/em 2. This discussion can be extended using model I to envisage the possibility predicting the 'hook' effect in advance (i.e., before the assay is applied to real samples). Protein concentrations on a plastic surface can be 160-320 ng/cm ~. For tht: purposes of the model assume the antibody concentration is 161) ng/cm z (c I) and the tolal volume used for the reaction is 0.2 ml (v). T,me liquid volume, 0.2 ml, corresponds approximately to 1.55 cmz surface area. Therefore the theoretical total solid-phase antibody concentration is 7.75 nM. However, it is practically impossible to obtain 100% surface coverage. If only 50% of the total antibody is immunoreact:ve and covers the plastic surface then the capture antibody concentration should be 4 nM (q i). I:or the sake of simplicity it is assumed that the binding constants of the solid- and liquid-phase antihodies are equal and the labeled antibody concentration is assumed to be 0.5 nM (q~). Thus, it can be predicted that the test samples exceeding an analyte concentration of 2.5 nM would give a lower result due to the 'hook" effect in model 1. The immobilization process may promote chemical modification of the capture antibody which can also lead to changes in its immunological characteristics (Olson et al., 1989). The alterations in reactivity fl~r covalently immobilized antibodies can bt compensated by increasing the coneentrat'on of the solid-phase antibody (i.e., use of higher surface area). Physically adsorbed antibodies are expected to have similar or greater aflinities than the chemically immobilized antibodies. As indicated previously, the ferritin system will be used to illustrate several points: capacity effects of different solid-phases and the comparison of theory and experiment for a onestep sandwich immunoassay where the analytc has multiple epitopes. However, as a practical matter, the capacity effect of the capture anti-

02 body can only be demonstrated by studying the dose-response curves in different concentration domains of the analyte while maintaining the concentration of the liquid-phase labeled antibody constant. Therefore the overall performances of these assays were studied at low, moderate and high ferritin concentrations. Four assay moc.ies for ferritin were investigated: c,pFEFO21/hs-ferritin/FEF021 and c,p-QCI 054/hs-ferritin/FEF021 in which c and p denote chemically immobilized and physically adsorbed surfaces respectively.

~°° 1

A

,:~

° ~

o

2

c,p.FEF021 / hs-ferritin / FEF021 and c,p.QC1054 / hs-ferritin / FEF021 systems Experimental results presented in this section .~upport the prediction that high capacity solidphase matrices shift the 'hook' maximum of the dose-response curve to higher analyte concentrations. Figs. 11, 12 and 13 show the experimental data and the theoretical curves for all of these assays. Simulated dose-response curves for models 2a and 2b are shown in each figure. Computer simulated curves are represented as curve A (cFEF021), curve B (c-QCi054). curve C (p-QCI054) and curve D (p-FEF021), in each figure. The theoretical curves and the experimental data for all four assays over the low analyte concentration range are shown in Fig. 11. As seen in this figure, systems with chemically immobilized antibodies (denoted as c-FEF021 and eQCI054) demonstrate no 'hook' effect. However, systems with physically adsorbed antibodies (symbolized as p-FEF021 and p-QCi054) do show 'hooked' dose-response curves. This difference in behavior is attributed to the difference in capacity. As Figs. 11 and 12 show, all ferritin systems have a linear response up to 500 pM of analyte concentration as expected. Over a moderate analyte concentration range the assay response becomes asymptotic for the c-FEF021 system while c-QC1054 and p-QCI054 systems show a 'hook" effect (Fig. 12). The data for p-FEF021 system show a "hook' in Fig. 11 and therefore this system was not studied over the moderate and higher analyte concentration ranges. All one-step sandwich immunoassay systems for ferritin demonstrate a 'hook' at high analyte concentrations (Fig. 13). It can he seen that the e-FEF021 and

0

1000

2000

3000

hs-fer'ritin concentrotion (pM) Fig. I 1. Effect of/.')w hs-ferritin concentrations on the 'hook' effect in one-step sandwich immunoassay for chemicallyand physically immobilized antibodies, Solid-phase antibodies (physicallyadsorbed (p) to plastictubes): FEF021(t~), QCIC54 (zx); solid-phase antibodies (ebon~ieaiiy attached (c) plastic beads): QCI054to), FEF021 (*~; labeled antibody: FEF021; 'z~I-FEF02I concentration: 0.375nM On, o. zx),0.5 nM t*}. Concentrations of the coating solutions for physically adsorbed antibodies, FEF02I and QCI054 are (50/xg/ml) and t9 p.g/ml) respectively.Theoreticalcurves:curve A, e-FEF02I (*); curve B, e-QCI054(o); curve C, p-QCI054 ( tx ); curve D, p-FEF02] (~). Theoretical parameters: curve A (model 2b), K I =5 nM-I, ql=g nM, q~' =0.5 nM; curve B (model 2a), Kl=0"2 riM-t, K2"7 nM-l, ql =8 nM, q* =0.375 nM; curve C (model 2a), Ki = 2 nM - I, K: z g nM 7 q I = 1.7 nM, q~ =0.375 nM; curve D (model 2b), K t - l l nM -I, ql=2 nM, q~' = 0.375 nM. Analyte concentralion (p) range is 4.0 pM-3.0 riM. c-QCI054 systems do exhibit significantly broader 'hooks' than those encountered for the D-hGH system (Fig. 10). Curve A in Figs. 11-13 represents a general view of the theoretical binding response for model 2b in which FEF021 is used as both the solid- and liquid-phase antibodies. It will be noted that the theoretical curves do not correlate well with the experimental data. Moreover, the two sets of data deviate substantially especially at low and high ferritin concentrations. The experimentally determined affinity constant for FEF021 antibody in solution is 56 n M - ~. The comparison of hGH, D-hGH and ferritin systems would be appropriate to explain the apparent deviation between the theoretical and experimen-

63 tal data. As ferritin has many repeating epitopes, this molecule can exhibit multiple binding with the labeled antibody, Q~ without affecting its immunological activity. In contrast, h G H and Dh G H can accommodate only one and two labeled antibody molecules while the analyte is on the solid-phase. In both theoretical models Q * PQI is

~,~ so

assumed to be the response generating complex.

~-~ i [

However, the response generating species of arialyte, ferritin can be associated with more than a single Q ~ antibody. T h e r e f o r e the overall binding response is magnified for the ferrltin assay. The same principle is applicable to other ferritin assay systems, T h e second reason for the deviation between the theoretical and experimental data of the c-FEF021 system is a difference in the affinities of the solid- and liquid-phase antibodies. Model 2b assumes that the affinities of capture

t~6A

t00-~

l

g0

:. o: .........

4b . . . . . . . . .

~ ........

hs-ferritin concentretlon (nM)

'~io

Fig. 13. Effect of high hs-ferritin concentrations on the ~hook" effect in one-step sandwich immunoassay for chemically immobilized antibodies; solid-phase antibodies (chemically immobilized (c) to the plastic bead): c-QCI054 (o), c-FEF021 (*), labeled antibody: FEF021; I~I-FEF0"2I concentration: 0.5 nM. Theoretical curves: cuwe A, c-FEFO2I (*); Curve n, c-QCI054 to). Tbeo~ticzl parameters: curve A (model 2b), K t ~ 7 nM- i, ql - 31}nM, q~ = 0.S nM; curve B (model 2a), Kt =0.l nM i, K2 = 7 nM-t. ql = 8 nM, q~' = U.5 nM. Analyre concentration (p) range is 0.22-120 nM,

60

4O

........

~ .........

6

.........

hs-ferritin concentration (nM)

t~

Fig, 12. Effect of moderate hs-ferritin concentrations on the 'hook' effect in one-step sandwich immunoassay for chemically and physically immobilized antibodies. Solid-phase anh-

body(physicallyadsorbedplastic tubes):p-OC1054(c~,coated with S /:g/ml solution); solid-phaseantibodies (chcmlcally attached to plasticbeads): QC1054(o), FEF02I (*);, labeled antibody:FEF021:t~I-FEF021 concentration:0.5 nM. Theoreticalcu~'es: curve A, e-FEF021 (*); cu~e B, c-QCIO54(o); curve (2, p-QCI0J4 (Q). Theoretical parameters: curve A (model 2b), K 1= I nM -I, qt = 30 nM, q~ = 0.5 nM; curve B (model 2a), K I = 0.1 nM i. K2 = 7 nM- 1 ql = 8 nM, q[ = 0.5 nM; curve C (model 2a), K I = 1 nM - i, K2 = 8 nM - t, q I = 1.6 nM, q~ = 1}.5nM. Analyte concentration range is 20 pM-12 nM.

and labeled antibodies are the same in establishing curve A. Although the same antibody is used for both the solid- and liquid-phase, in the experimental procedure, the capture antibody is chemically modified so that the affinity of this antibody may be lower, Increasing the value of Kj is not sufficient to yield a good curve fit especially at low analyte concentrations. As a result, the experimental data is shifted from the theoretical curves. Curves A in Figs. 12 and 13 show similar deviations from the experimental data. Again the lower theoretical values of curve A in Fig. 13 can only be explained by taking multiple binding of the ferritin into account. Comparison of the experimental and theoretical parameters would be helpful to describe the differing capacities o f the c-FEF021 and pFEF021 assay designs. As noted from Fig. 11, these are similar, the exception being the capacity of the solid phase. T h e e-FEF021 assay system employed about 1.5-fold higher concentration of the labeled antibody than the p - F E F 0 2 I assay

system. The concentration difference of the labeled antibody is not great and therefore the appropriate assay responses can be qualitatively compared. The p-FEF021 assay system does not give a response at moderate and higher analyte concentrations because tile solid-phase capacity is not high enough. The binding parameter used to generate the theoretical curves A and D can be adopted to estimate the difference in capacity. Curve D assumes 2.5-fold higher affinity (K~) and approximately four-fold less capacity of capture antibody (ql) than curve A. This shows that the higher affinity cannot compensate for lower capacity. This is also supported by theoretical curve D. To elaborate the above discussion the studies of the e-QCI054 and p-QCI054 systems can be illustrated. Theoretical curves for c-QCI054 and p-QCI054 are denoted B and C, respectively. It is clear that there is an obvious lack of fit between the theory and the experimental data for the QCI054 systems especially at lower and higher analyte concentrations (curves B and C). Experimentally, both systems have been studied under similar experimental conditions. As Figs. 11 and 12 show, the p-QCI054 assay system cannot be applied to an analytical sample without yielding aberrant results whereas the c-QCI054 system shows no 'hook' at least up to 3500 pM of ferritin. The dose-response curves for the e-QCI054 systems over the moderate and higher analytical concentrations are 'hooked' curves (Figs. 12 and 13). It will be noted that the c-FEF021 assay system can be effectively used up to 15 nM without ambiguous results. The obvious difference between e-FEF021 and c-QC1054 systems cannot be directly attributed only to differences in the capacity of the capture antibody. However, it can be inferred that the assays with high capacity capture antibodies postpone th.¢. 'hooked' nature of the standard curve attributed to the nature of the interactions of the analyte. Moreover, as Fig. 11 shows, it will be noted that all assay systems have similar response profiles over the linear range of ferritin. Therefore it is quite clear for all ferritin assay systems that the multiple epitope interactions of the analyte increase the sensitivity of the assay and lower the linear response range. According to the results with the c-FEF021 and

c-QCI054 assay systems the replacement of the capture antibody seems to show no adverse effects on the dose-response curve in the one-step sandwich immunoassay for analytes such as ferritin. Similarly, both assay protocols produce a high dose 'hook' effect in the two-step sandwich immunoassay (Fernando and Wilson, 1992). In contrast, assays with an analyte having a discrete number of epitopes (D-hGH) do not exhibit assay characteristics similar to ferritin. These studies underline the importance of increasing the capacity of the capture antibody to forestall the 'hook' effect. However, it is not possible to arbitrarily increase the capacity of the capture antibody as there are practical limitations. Thus, there should be a very close balance between the capacity of the solid-phase, the concentmtion of the labeled antibody and the analyte COncentration range. The above described assay conditions are very appropriate for clinically significant analyte concentration ranges. However the scope of this report is to evaluate the necessary steps to circumvent aberrant results when such assays are performed on an tlrlknown sample, whose analyte concentration may fall outside the expected range.

Conclusions

Generally, all one-step sandwich immunoassays exhibit the 'hook' effect, irrespective of the characteristics of the analyte. This is the general disadvantage of this assay mode. In a one-step assay, it is apparent that the u:e of excess solidand liquid-phase antibody is necessary to shift the 'honk' to higher analyte concentrations. Theoretical and experimental studies show that tI:c use of high capacity solid-phase antibodies should prevent ;he 'hook' at analytically significant concentrations. in addition, analyte characteristics must be considered since the interactions of the solid- and liquid-phase antibodies with the analyte are multifold. The characteristics of solid- and liquidphase antibodies also play a role in avoiding or minimizing the ambiguous results of the one-step sandwich immunoassay. This assay can be properly designed if two different antibodies are em-

ployed. A n aly tes having mu ltip le e pi t ope s can specifically improve the sensitivity of the assay with c o n c o m itan t lo w er in g of the l i n e a r res pons e range. F o r m a c r o m o l e c u l e s , the assay can use e i t h e r o n e antibody reacting with identical epit o p e s o r two antibodies b i n d i n g with different epitopes. Ho w ev er , assays for analytes having a discrete n u m b e r o f identical o r different e pi t ope s m a y lead to c o n s i d e r a b l e c h a n g e s in the assay r e s p o n s e unless two different antibodies for nmlr e p e a t i n g e p i t o p e s are selected. T h e o n e - s t e p sandwich i m m u n o a s s a y s s h o u l d not be used over analytically significant c o n c e n t r a t i o n r a n g e s if the liquid-phase antibody p e r m i t s m u l t i p l e interact~'ns, especially at low analyte concentrations. However, this effect m a y not be serious in a two-step assay mo d e. T h e effect of analyte concentration on the "hook' effect m a y be m i t i g a t e d with analytes having mu ltip le epitopes. In such an assay m o r e labeled an tib o d y b i n d s to the analyte, the sensitivity o f the assay is improved, a n d the ' h o o k ' shifts to h i g h e r analyte concentrations.

Acknowledgements W e t h a n k R o b e r t O . H u s s a , S u s a n M. H o c h s c h w e n d e r a n d M a r k S a r n o of Hybritech for s u p p l y i n g the a n t i b o d i e s for this project. W e are m o s t grateful to C a r o l i n e Scc,!~ri, N o r a R a n k i n a n d T h u s i t h a J a y a w a r d e n a for t hei r advice in c o m p u t e r p r o g r a m m i n g . T h i s w o r k was s u p p o r t e d in part by a g r a n t from the N a t i o n a l Institutes of H e a l t h , g ran t no. G M 4 0 0 3 8 .

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assays for proslale-spacific antigen [LenerL Clio. Chem, 35, 1262. Cantarero, L.A.. Butler. J.E. and Osborne, J.W. 119891The adsorptive char~leteristics of proleins for polystyrene ;rod their significance in solid-phase immunoassays. Anal. Biochem. 1115,375. ('omitti, R., Raccheni, G.. Gnocchi, P.. Morandi, E, and Galante, Y.M. 11987) A monnebmal-hased, twt~sile enzyme immunoassay of human insulin. J. Immunol. Methods 9g, 25. Dahlmann. N.. Brensing, K.A,, Klingmnller, D. ;Jnd Bidlingmeier, F. (19g01 'Hook-effect' in a patient with a 80nadotropin-secreting tumor [Letter}, Clin. Chem. 36. 168. Ehrlich, P.H, Moyle, W.R. and Moustafa. Z,A. (19831 Further characterization of c~operalive interactions of monoelonal antibodies. J. Immunol. 131. 1906. Fernando, S,A. and Wilson, G.S. 119921 Multiple epitope interactions in the two-step sandwich immunoassay. J. Immunol. Methods 151, 67. Fernando, S.A., Sportsman, J.R. and Wilson. G.S. (19921 Studies of low dose 'hook' effect in homogeneous competitive immunoas.say. J. tmmunok Methods 151.27. Garcia-Webb, P,, Watson, F.E. and Whiteside. N. 119861 High-dose 'hook" effect in measurement of somatolropin by two-site immunoradiometric assay. Ctin. Chem. 32. 2102. Gershagen, S. and Fernlund, P. 119861 lmmunoradiomelric assay of sex-hormone binding globulin with use of two different monochmal antibodies. Clio. Chem. 32, 1311. Gosling, J.P. (1990t A decade of development in immhnoassay methodology. Clin. Chem. 3fi, 1408. Gupla, S.K., Guesdon, J.L., Avrameas, S. and Talwar, G.P. 119851 Solid-phase sandwich enzyme immunoassays of human cborionic gonadotropin using monoclona: antibodies. J. h,.mum.'.. Methods 83, 159. He((man, L.K., Pa'sons, G.H., Allerdt, L.J., Brooks, J.M. and Miles, L.E.M. 11984) Elimination of 'hook-effect' ie, twosite immunoradiometric assays by kinetic rate analysis. Clio. Chem. 30. 1499. Kbosravi, M.J. 119901 Shifting the 'hook effect' in one-step immunometric assays. Clio. Chem. 36, 169. Khosravi, M.J. and Diamandis, E.P. 119871 Immunofluoromere/ of choriog