Improving an Immunoassay Response to Related Polychlorinated

Anal. Chem. 2006, 78, 7240-7247

Improving an Immunoassay Response to Related Polychlorinated Biphenyl Analytes by Mixing Antibodies Thomas R. Glass,*,† Naoya Ohmura,*,‡ Keiichi Morita,§ Kazuhiro Sasaki,‡ Hiroshi Saiki,§,| Yoko Takagi,⊥ Chiwa Kataoka,⊥ and Akikazu Ando#

Sapidyne Instruments Inc., 967 East ParkCenter Boulevard #445, Boise, Idaho 83706, Department of Bioscience, Central Research Institute of Electric Power Industry, 1646 Abiko, Abiko City, Chiba, Japan 270-1194, School of Bionics, Tokyo University of Technology, 1404-1 Katakura, Hachiouji, Tokyo, Japan, 192-0982, Research Center of Bionics, National Institute of Advanced Industrial, Science and Technology, 1404-1 Katakura, Hachiouji, Tokyo, Japan, 192-0982, Biotechnology Research Laboratory, Research & Development Division, Kyoto Electronics Manufacturing Co., Ltd., 68 Ninodan-cho, Shinden, Kisshouin Minami-ku, Kyoto, Japan 601-8317, and Graduate School of Science and Technology, Laboratory of Molecular Cell Biology, Chiba University, Matsudo 648 Matsudo, Chiba Japan 271-8510

Immunoassays for detection of a class of closely related antigens, e.g., PCBs, have often been too specific (responding strongly to some members of the class and missing others) and no general method for adjusting the response has been described. In this paper, the difference in the response of a model immunoassay to different Kanechlors (Japanese commercial mixtures of PCBs, analogous to Aroclors in the United States) is reduced from 20- or 50-fold (depending on which antibody is used) to 3-fold when the antibodies are mixed at the proper ratio. A mathematical model based on competitive binding of two antibodies for up to four antigens has been developed and used to describe the assay performance and to predict optimum mix ratios for the antibodies used. The model (based on separate measurement of each antibody’s effective Kd for each Kanechlor) provides an excellent fit to the measured mixed antibody assay response. The model is also successful in identifying cases where mixing monoclonal antibodies will not improve the response. It is thought the method described will have applicability in a variety of cases where the analytical goal is semiquantitative screening based on the total quantity of an unknown mixture of related compounds. One of the great beauties of an immunoassay is its exquisite specificity. The ability of an antibody to recognize a specific molecule present in a complex mixture was noted by Yalow and Berson in their pioneering immunoassay1 and has been well known and widely celebrated by immunoassay practitioners ever since. At the same time, it is also recognized that antibodies are * To whom correspondence should be addressed. Tel: +81-471-82-8211. Fax: +81-471-83-3347. E-mail; [email protected]. † Sapidyne Instruments Inc. ‡ Central Research Institute of Electric Power Industry. § Tokyo University of Technology. | National Institute of Advanced Industrial, Science and Technology. ⊥ Kyoto Electronics Manufacturing Co., Ltd. # Chiba University. (1) Yalow, R. S.; Berson, S. A. J. Clin. Invest. 1960, 39, 1157-1175.

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not absolutely specific and do exhibit cross reactivity to other molecules. Cross reactivity profiles, i.e., the extent to which an immunoassay developed for one analyte will respond to some other molecule, are commonly measured and published as part of the description of the assay.2-4 In most cases, cross reactivity is regarded as undesirable and minimizing it is a common goal. However, in the case of environmental immunoassay there are several cases where the specificity of immunoassay is a hurdle to its adoption. In the case of polychlorinated biphenyls (PCBs) environmental regulations specify total weight of PCBs, resulting in a situation where the ideal assay response is total PCB irrespective of the mix of individual congeners that are present in a particular sample. Similar situations exist for other analytes such as dioxins, estrogen-like compounds, and β-lactam antibiotics. In each case, a test is required that can detect any of a class of compounds. In some cases, alternative tests based on cellular receptors specific to a class of compounds such as β-lactam antibiotics5,6 or estrogen-like compounds7 have been developed to work around the overly specific response of antibodies. In both of these cases, the assay response is not the same for the entire family of compounds, but use of a receptor is intended to provide a response similar to biologic efficacy. No appropriate receptor has been identified for PCBs, and even if one were identified, it seems unlikely it would respond equally to all PCBs, as needed to meet legal targets. Another approach to the problem has been the development of “generic” antibodies with relatively broad cross reactivity to targeted compounds.8-10 This approach can involve screening of (2) Chin, T. E.; Wong, R. B.; Pont, J. L.; Karu, A. J. Agric. Food Chem. 2002, 50, 3380-3398. (3) Darwish, I. A.; Blake, D. A. Anal. Chem. 2001, 73, 1889-1895. (4) Chiu, Y. W.; Carlson, R. E.; Marcus, K. L.; Karu, A. E. Anal. Chem. 1995, 67, 3829-3839. (5) Gustavsson, E.; Sternesjo, A. J. AOAC Int. 2004, 87, 614-620. (6) Anderson, K. L.; Lyman, R. L.; Moats, W. A.; Hansen, A. P.; Rushing, J. E. J. AOAC Int. 2002, 85, 546-550. (7) Korner, W.; Hanf, V.; Schuller, W.; Kempter, C.; Metzger, J.; Hagenmaier, H. Sci. Total Environ. 1999, 225, 33-48. (8) Kolar, V.; Deng, A.; Franek, M. Food Agric. Immunol. 2002, 14, 91-105. 10.1021/ac0605187 CCC: $33.50

© 2006 American Chemical Society Published on Web 09/14/2006

antibodies produced against one member of the family of target compounds10 or production of specially designed analogues (often based on a fragment of one of the target compounds) intended to present key features present in multiple members of the class.8,9 In this paper, we describe an immunoassay for PCBs in which we broaden the assay reactivity by including two antibodies with complementary cross reactivities. We also describe in detail the models we developed and employed to predict assay response curves for mixed antibodies and to predict optimum antibody mix ratios. We are aware of other work describing use of mixed antibodies to increase the working range of an immunoassay11,12 but believe this is the first description of controlled mixing of antibodies to create a generic immunoassay able to respond to a class of analytes. MATERIALS AND METHODS Safety Considerations. At least some PCB congeners (notably the “dioxin-like” coplanar congeners) present a significant health threat, and prudence dictates treating all PCBs as dangerous. All personnel handling PCB-containing samples were provided with nitrile gloves and all PCB-contaminated glassware and solutions (including wash buffers) were collected and turned over to a (Japanese) government approved contractor for disposal. Concentrated stocks of PCBs were kept in a locked box to limit access to trained personnel. Antibodies and Chemicals. Monoclonal anti-PCB (Catalog No. RDI-PCBabm-35) was purchased from Research Diagnostics Inc. (Flanders, NJ). Monoclonal anti-PCB clone PCB-K2A-1 was graciously supplied by Kyoto Electric Manufacturing (Kyoto Japan), and clone Sk3A11 was graciously supplied by Kazuhiro Sasaki of CRIEPI (Abiko, Japan). A detailed description of clone Sk3A11 can be found in Japanese Patent Application 2005-357433. A patent application for clone PCB-K2A-1 is currently being prepared. Commercial mixtures of PCBs (Kanechlor or KC 300, 400, 500, and 600 with numbers 1021-19103, 1021-19104, 102119105, and 1021-19106, respectively) came from GL Sciences (Tokyo, Japan). Dimethyl sulfoxide (DMSO; Catalog No. 34603615) came from Dojindo (Kumamoto Japan). Bovine serum albumin (BSA; Catalog No. A-9647) came from Sigma Aldrich (St. Louis, MO) Cy-5 labeled F(ab′)2 fragment goat anti-mouse IgG (H&L) was purchased from Jackson ImmunoResearch (West Grove PA). Phosphate-buffered saline (PBS; consisting of 137 mM NaCl, 3 mM KCl, 20 mM Na2HPO4, 1.5 mM KH2PO4, pH 7.4) was produced in-house. PBSB consisted of PBS supplemented with 1 g/L BSA. PBSBD consisted of PBSB supplemented with 2% (v/v) DMSO. Antigen Immobilization. One to five milliliters of NHSactivated Sepharose for fast flow (Amersham Biosciences, 17-090601) was placed in a column, and the 2-propanol it was supplied in was allowed to drain. The particles were then suspended in 1030 mL of cold 0.1 mM HCl and allowed to drain. This process was repeated a minimum of three times with 0.1 mM HCl and then repeated a minimum of three times with cold PBS. After the (9) Franek, M.; Diblikova, I.; Cernoch, I.; Vass, M.; Hruska, K. Anal. Chem. 2006, 78, 1559-1567. (10) Wei, R. D.; Chu, F. S. Anal. Biochem. 1987, 160, 399-408. (11) Ohmura, N.; Tsukidate, Y.; Shinozaki, H.; Lackie, S. J.; Saiki, H. Anal. Chem. 2003, 75, 104-110. (12) Kramer, P. M.; Kremmer, E.; Forster, S.; Goodrow, M. H. J. Agric. Food Chem. 2004, 52, 6394-6401.

final PBS wash, the particles were distributed into microcentrifuge tubes (∼0.5 mL of Sepharose gel/tube) and 200 µg of the coating protein (designated S-3, a chlorophenol derivative described previously13) was added. The particles were rotated to maintain them in suspension (Labquake Shaker, Lab Industries Inc., Berkeley, CA) for 2 h at room temperature, after which 30 µL of concentrated ethanolamine was added to each tube to cap any remaining NHS esters and reduce nonspecific binding. Particles were rotated for a minimum of 1 h before use and were kept refrigerated for up to several weeks. Immunoassay System. Immunoassays were performed on a KinExA 3000 instrument supplied by Sapidyne Instruments Inc. (Boise, ID). The theory and operation of this instrument have been described previously by us11,14,15 and others.16-18 Briefly, antigencoupled solid phase (described above) is captured in a small flow cell held at the focus of a fluorometer. Samples, PCB mixtures in the present case, are mixed with a PCB-specific antibody and flowed through the solid phase. Anti-PCB antibody that binds PCB in the sample solution cannot bind to the antigen on the solid phase and passes through the flow cell. A small fraction of the antibody that is not bound in solution is captured on the solid phase. The captured detection antibody is fluorescently labeled using a fluorescently labeled antispecies antibody, and binding signals are measured as fluorescent accumulation on the solid phase. A zero PCB sample gives the highest response, and very high concentrations of PCB cause total inhibition of the specific binding signal. Affinity Measurement. The binding affinity (or its inverse, the Kd) was measured on the KinExA 3000 following the procedures described elsewhere.16,18,19 Briefly, equilibrated antibody/ antigen solutions of known antigen concentration are measured as described above. The unoccupied fraction of antibody at equilibrium is fit with a theory15 having fit parameters of the Kd, the active antibody concentration, the uninhibited signal level, and the NSB. Sample Timing. Except where noted otherwise below, all KinExA experiments were initiated with a flow of 30 s of PBSB followed by a flow of primary antibody (one or more clones) mixed with specified PCBs in PBSBD for 180 s. This was followed by an additional 30 s of PBSB and then a labeling step consisting of 2 nM Cy-5 F(ab′)2 fragment goat anti-mouse IgG flowed for 180 s. The flow rate was 0.25 mL/min for all sample and label flows. Finally, a two-step wash was used consisting of an additional 30 s of PBSB at 0.25 mL/min followed by 90 s of PBSB at 1.5 mL/ min. Signal levels were recorded as the difference between the end point (at the end of the final wash) and the baseline (at the beginning of the initial PBSB). (13) Ohmura, N.; Glass, T. R.; Sasaki, K.; Joh, T.; Taemi, Y.; Yokobori, N. Bunseki Kagaku 2006, 55, 1-7. (14) Glass, T. R.; Saiki, H.; Blake, D. A.; Blake, R. C., II.; Lackie, S. J.; Ohmura, N. Anal. Chem. 2004, 76, 767-772. (15) Ohmura, N.; Lackie, S. J.; Saiki, H. Anal. Chem. 2001, 73, 3392-3399. (16) Darling, R. J.; Brault, P. A. Assay Drug Dev. Technol. 2004, 2, 647-657. (17) Blake, R. C., 2nd; Pavlov, A. R.; Blake, D. A. Anal. Biochem. 1999, 272, 123-134. (18) Blake, D. A.; Chakrabarti, P.; Khosraviani, M.; Hatcher, F. M.; Westhoff, C. M.; Goebel, P.; Wylie, D. E.; Blake, R. C., 2nd. J. Biol. Chem. 1996, 271, 27677-27685. (19) Glass, T. R.; Ohmura, N.; Saiki, H.; Sawadaishi, K.; Kataoka, C.; Takagi, Y.; Ohiwa, T. Anal. Chim. Acta 2004, 517, 161-168.

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RESULTS AND DISCUSSION Modeling. Simple Competition, Analytic Solution. Overall, our intent was to work with mixtures of antibodies and with mixtures of antigens. This leads to fairly complicated systems of equations requiring numerical solutions; however, one of the simpler cases (a mixture of two antibodies reacting with a single antigen) can be represented analytically. Consider a system of generalized reactants where A is the solution concentration of one binding partner, B is the solution concentration of the other partner, Ap is the solution concentration of competing partner to A, AB is the concentration of the AB complex, ApB is the concentration of the ApB complex, TA is total A, both in complex and in free form, TAp is total Ap, both in complex and in free form, TB is total B, both in complex and in free form, K is the equilibrium affinity of the AB interaction ()1/Kd), and Kp is the equilibrium affinity of the ApB interaction. From the definition of affinity, the fundamental equations to be satisfied are

physical (e.g., negative concentrations) and that the following equation is applicable cases where K is greater than Kp

K[A][B] ) [AB]

(1)

Kp[Ap][B] ) [ApB]

(2)

Although eq 12 may appear formidably complicated, it can be defined as a function of the primary physical variables (K, Kp, etc.) and readily handled computationally. In the case where Kp is greater than K, one of the other roots yields the physical solution; however, it may be procedurally simpler to define an if statement to swap the affected variables (K, Kp, TA, TAp) and then use eq 12. Expressions for the other equilibrium concentrations (A, B, Ap, AB) can be readily found by substituting eq 12 into algebraic rearrangements of eqs 1-5. The result is analytic solutions for the case of two binding species competing for a single binding partner. A, Ap, and B are arbitrary so the solution can readily be applied to the case of two antibodies competing for a single antigen species or for two distinct antigens competing for a single antibody. Equivalent Kd. In accordance with our overall goal of developing an immunoassay for detecting PCBs in transformer oil in Japan, Kanechlor mixtures rather than individual congeners were used in this work. As described previously,21 the PCBs added to transformer oil in Japan were Kanechlor mixtures. The goal of our effort is to mix complementary antibodies together to reduce the difference in response that a single antibody shows for the different Kanechlor mixtures. We also wished to develop a theoretical model to help us understand our results and guide our experiments. The obvious model to use is one based on the antibody Kd; however, a Kd can only be defined for a single welldefined binding interaction. In the case of Kanechlor mixtures, the net response is that of 70 or more individual congeners22 competing for a single antibody. In principle, a model based on Kd’s for each individual congener could be constructed, but the measurement of 144 Kd’s (the total number of distinct congeners in all four Kanechlor mixtures) for each antibody is daunting. We decided to explore an alternate model based on an equivalent Kd. We knew we would be using the antibodies at the lowest possible concentration, as this leads to the best sensitivity,15 so as a starting point we made the simplifying assumption that the antibody concentration would be below the Kd for all PCBs present in the sample. In this case, the

From conservation of mass

[TA] ) [A] + [AB]

(3)

[TAp] ) [Ap] + [ApB]

(4)

[TB] ) [B] + [AB] + [ApB]

(5)

Solving eq 3 for A, eq 4 for Ap, and eq 5 for B and substituting back into eqs 1 and 2 gives

K([TA] - [AB])([TB] - [AB] - [ApB]) ) [AB] (6) Kp([TAp] - [ApB])([TB] - [AB] - [ApB]) ) [ApB]

(7)

Solving eq 7 for AB and substituting into eq 6 gives (after algebraic manipulation and collection of terms)

([ApB])3 + C1([ApB])2 + C2 [ApB] + C3 ) 0

(8)

where

C1 ) {-(KKp[TB] - Kp - 2Kp2[TAp] - Kp2[TB] + KKp[TAp] + K - K[TA]Kp)}/{[Kp(K - Kp)]} (9)

C2 ) [TAp]

(-Kp[TAp] - 2Kp[TB] - 1 + K[TB] - K[TA]) (K - Kp) (10)

C3 ) Kp([TAp])2

[TB] (K - Kp)

(11)

Solutions to cubic equations of the form of eq 8 can be looked up in standard tables,20 yielding three roots. Examination of the roots for realistic values of the reactants shows that two roots are not (20) Spiegel, M. R. Mathematical Handbook of Formulas and Tables; McGrawHill Book Co.: New York, 1968.

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(21) Glass, T. R.; Ohmura, N.; Taemi, Y.; Joh, T. Environ. Sci. Technol. 2005, 39, 5005-5009. (22) Masuzaki, Y.; Matusmura, T.; Morita, M.; Ito, H. Japan Society for Environmental Chemistry, 12th Symposium on Environmental Chemistry 2003; pp 686-687.

complex formed is negligible in comparison to the total PCB concentration and eqs 3 and 4 above reduce to

[TA] ) [A]

(13)

[TAp] ) [Ap]

(14)

This assumption results in the following simple expression for the fraction of B (the antibody) free at equilibrium

Bfrac )

[B] 1 ) [TB] [TAp] [TA] + +1 Kpd Kd

(

)

(15)

Note that in the simpler case of a single antigen (TAp equals zero)

Bfrac )

1 [TA] +1 Kd

(

)

(16)

The goal is to reach an equivalent Kd that can be used with the sum of the antigens to give results equivalent to eq 15. If TAeq is equal to the sum of the individual antigens then the variables x1 and x2 can be defined as

x1 )

[TAp] [TAeq]

(17)

x2 )

[TA] [TAeq]

(18)

[

1 x1 x2 [TAeq] + +1 Kpd Kd

) ]

(

1

(

x2 x1 + Kpd Kd

)

(20)

1 xi

∑K i

K2[A2][B] ) [A2B]

(23)

K3[A3][B] ) [A3B]

(24)

K4[A4][B] ) [A4B]

(25)

K5[A1][B2] ) [A1B2]

(26)

K6[A2][B2] ) [A2B2]

(27)

K7[A3][B2] ) [A3B2]

(28)

K8[A4][B2] ) [A4B2]

(29)

[TA1] ) [A1] + [A1B] + [A1B2]

(30)

[TA2] ) [A2] + [A2B] + [A2B2]

(31)

[TA3] ) [A3] + [A3B] + [A3B2]

(32)

[TA4] ) [A4] + [A4B] + [A4B2]

(33)

[TB] ) [B] + [A1B] + [A2B] + [A3B] + [A4B] (34) [TB2] ) [B2] + [A1B2] + [A2B2] + [A3B2] + [A4B2] (35)

This result can be generalized to an arbitrary number of antigens giving

Kdeq )

(22)

(19)

Comparing eq 19 to eq 16, it is clear that they will have the same form if

Kdeq )

K1[A1][B] ) [A1B]

which all arise from the definition of affinity for each of the eight possible binding pairs. In addition, the following six equations express conservation of mass

Equation 15 can be rewritten as

Bfrac )

given by eq 15 (results not shown). Since it is always necessary to work with antibody concentrations near or below the Kd to achieve maximum sensitivity15 and since we could be reasonably confident from the shape of the curves that we were below the Kd of all congeners present in significant quantity, we felt optimistic that a model built around the equivalent Kd described above would be adequate for the present purposes. Complex Competition, Numeric Solution. Equation 12 is adequate for modeling the case of a mix of two antibodies reacting with a single Kanechlor mixture (in the case that both antibodies are used at concentrations below the Kd of the individual congeners), but is not suitable for the more interesting case of the two antibodies reacting with a mixture of the various Kanechlors. To model this more general case. a numerical solution was implemented. The basic equations that must be satisfied in the general case are

(21)

di

Rearranging eqs 30-35 and substituting into eqs 22-29 leads to the following eight equations, which must all be satisfied simultaneously at equilibrium.

K1([TA1] - [A1B] - [A1B2]) × ([TB] - [A4B] - [A1B] - [A2B] - [A3B]) ) [A1B] (36) K2([TA2] - [A2B] - [A2B2]) ×

where i is the number of individual congeners, xi is the relative abundance (as a fraction of the total) of the ith congener, and Kdi is the Kd of the ith congener. Mathematical modeling also shows that if the antibody concentration is significantly above the Kd of even a minor (1%) constituent, the resulting response curve is too steep to be adequately fit by a Kd controlled curve of the form

([TB] - [A4B] - [A1B] - [A2B] - [A3B]) ) [A2B] (37) K3([TA3] - [A3B] - [A3B2]) × ([TB] - [A4B] - [A1B] - [A2B] - [A3B]) ) [A3B] (38) K4([TA4] - [A4B] - [A4B2]) × ([TB] - [A4B] - [A1B] - [A2B] - [A3B]) ) [A4B] (39) Analytical Chemistry, Vol. 78, No. 20, October 15, 2006

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K5([TA1] - [A1B] - [A1B2]) × ([TB2] - [A4B2] - [A1B2] - [A2B2] - [A3B2]) ) [A1B2] (40) K6([TA2] - [A2B] - [A2B2]) × ([TB2] - [A4B2] - [A1B2] - [A2B2] - [A3B2]) ) [A2B2] (41) K7([TA3] - [A3B] - [A3B2]) × ([TB2] - [A4B2] - [A1B2] - [A2B2] - [A3B2]) ) [A3B2] (42) K8([TA4] - [A4B] - [A4B2]) × ([TB2] - [A4B2] - [A1B2] - [A2B2] - [A3B2]) ) [A4B2] (43)

This system of eight equations was solved numerically, subject to the additional constraint that all concentrations be greater than or equal to zero. Signal Level from Antibody Mixtures. The signal level on the KinExA system is proportional to the concentration of free antibody (not bound to antigen) present in solution; however, the constant of proportionality varies from antibody to antibody. There are at least two reasons for this; the first is that because the contact time is short, the antibody captured on the solid phase is proportional to the on rate of the antibody-solid-phase reaction. Thus, antibodies with a faster on rate (for the solid-phase material) will give a larger signal. The second reason is variation in labeling efficiency. In the present case, labeling is accomplished with a Cy-5-labeled anti-mouse antibody that is flowed through the flow cell after the primary antibody(s) has (have) been captured, and the binding of the anti-mouse is expected to differ for each primary mouse antibody. To calculate signal levels from mixtures of antibodies, it is necessary to correctly account for the difference in signal level from a given concentration of free antibody. As described below, the difference in response between the antibodies was measured and used to calculate factors of difference. These factors were used to scale the relative response from each antibody in equations of the form

MixSig% )

[freeAb1] + F [freeAb2] [totalAb1] + F [totalAb2]

(44)

where F is measured ratio of signal response of Ab2 over Ab1. EXPERIMENTAL SECTION Antibody Response to Kanechlor Mixtures. We began by measuring the response curves of each of three antibodies for each of four Kanechlor mixtures. In every case, the primary antibody concentration was 250 pM and Kanechlor concentrations were varied across a range from fully saturating (signal level near zero) to zero Kanechlor. Figure 1 shows the results, which are also summarized in Table 1. As shown in Table 1, clone PCB-K2A-1 (Figure 1A) shows the best overall response to the four Kanechlor mixtures with the equivalent Kd varying from 0.5 (KC 300) to 1.4 ppb (KC 600). The other two clones show much larger variations in response; however, they also exhibit comple7244 Analytical Chemistry, Vol. 78, No. 20, October 15, 2006

Figure 1. Response curves for each of three antibodies reacting with each of the four Kanechlor mixtures. Panel A is clone PCB-K2A1, panel B is clone PCB35M, and panel C is clone SK3A11. In all panels, symbols 2, b, 1, and [ represent Kanechlor 300, 400, 500, and 600, respectively. Solid lines are calculated from the best fit Kd for each data set. Kd values for the curves shown, approximately equal to the midpoint for the curves shown, are summarized in Table 1.

mentary variations in that PCB35M is tightest for KC 600 (0.5 ppb Kd) while Sk3A11 is tightest for KC 300 (0.6 ppb Kd). This complementarity lead to the idea that mixing these antibodies together could reduce the overall Kanechlor-dependent response variation. The spread in Kd values defines a response window in the sense that if one of these clones were used to measure an unknown Kanechlor or mixture of Kanechlors, the response would always fall somewhere within the region defined by the outermost of the four individual response curves. Antibody Signal Response. To properly model the system response to mixtures of two antibodies, it was necessary to first measure the KinExA signal levels for each antibody. For these experiments, various concentrations of each antibody (see Figure 2) were flowed over the solid phase in the absence of any PCBs. The results, Figure 2, show that, for equal concentrations of primary antibody, the signal is ∼2.3 times higher for the PCB35M clone than for the Sk3A11 clone. A similar experiment with the PCB35M and PCB-K2A-1 clones showed a ratio of 2.0. Antibody Mixtures. Clones PCB35M and Sk3A11. Working first with the PCB35M and Sk3A11 clones, a mixture was prepared with a concentration ratio of 1 part PCB35M to 2 parts Sk3A11. The final total concentration was 500 pM. In molar terms, the tightest binding antibody used in this study is PCB35M, whose Kd of 0.49 ppb for KC600 (see Table 1) is equivalent to 1.3 nM (the weighted average MW of KC 600 is 381). The combined antibody concentration was kept below this Kd to ensure the equivalent Kd calculation above is valid. Under this condition, we can reasonably hope the models developed above (which are only

Table 1. Estimated Equivalent Kd Values for Each of Three Antibodies to Four Kanechlor Mixturesa antibody clone PCB-K2A-1

PCB35M

SK3A11

kanechlor mixture

Kd

Kd high

Kd low

Kd

Kd high

Kd low

Kd

Kd high

Kd low

KC 300 KC 400 KC 500 KC 600

0.51 0.57 0.56 1.44

0.71 0.70 0.72 1.92

0.36 0.45 0.42 0.96

10.22 3.55 1.44 0.49

12.62 4.31 1.75 1.16

7.97 2.71 0.88 0.00

0.60 1.56 9.60 29.91

0.72 1.83 12.80 37.58

0.41 1.04 4.78 17.63

a

Kd high and Kd low are 95% confidence interval bounds. All values are in units of ppb total Kanechlor.

Figure 2. In the absence of PCB, signal response proportionality to antibody concentration, with each antibody having a unique constant of proportionality. The signal response of clone PCB35M (b) is 2.3 times higher than the signal response of SK3A11 (2).

strictly valid for two antibodies reacting with either a single welldefined antigen (exact model) or up to four well-defined antigens (numeric model)) will apply. Panels A-D in Figure 3 show the response of the mixed antibody to Kanechlor 300, 400, 500, and 600, respectively. The theoretical lines shown in each panel are not fit to the data points but instead are based on the exact competition model and use the Kd values derived from separate measurement of each Kanechlor with each antibody; see Figure 1 and Table 1. Panel E of Figure 3 shows the mixed antibodies’ response to a mixture of equal parts (by weight) of all four Kanechlors, along with a theory line derived from the numeric model described above and using the same Kd values. Panel F replots the data of panels A-E on a single graph. Notice in panel F that the responses to the four individual Kanechlors are considerably closer together than is the case for either the PCB35M (see Figure 1B) or SK3A11 (Figure 1C). The 50% inhibition response range has been reduced from approximately 20- (PCB35M alone) or 50-fold (SK3A11 alone) to ∼2-fold in Figure 3-F. When either antibody alone is exposed to a mixture of Kanechlors, the response to the mixture will fall somewhere within the envelope defined by the reaction to the individual Kanechlors. Our initial naı¨ve expectation was that the same thing would hold for the mixture; however, this is not the case, as is shown by both the measured data points and the theoretical line for the mixed Kanechlors in Figure 3F. To understand this phenomenon, consider how the mixed antibodies respond to Kanechlor 300 present at 10 ppb. At this concentration, the PCB35M clone is seeing approximately a Kd equivalent concentration and should be ∼50% bound up while the SK3A11 clone is seeing a concentration nearly 20 times above its Kd and so should be nearly all bound. The net response then should be in the range of 25% free. On the other hand, if we consider 10 ppb Kanechlor 600, then the

Figure 3. Kanechlor response curves of a 2:1 mix of clones SK3A11 and PCB35M (0.5 nM combined antibody concentration). Panels A-D show the response of the mixed antibodies to individual Kanechlors 300-600, respectively. Panel E shows the response of a mix of equal parts of all four Kanechlors, and panel F replots all data on the a single axis to show the response spread. See text for discussion.

PCB35M clone should be nearly completely bound, while the SK3A11 clone is seeing a concentration somewhat below its Kd and should be less than half bound, leading to a net response somewhat above 25%. However, if we mix 5ppb KC 300 and 5 ppb KC 600, then both antibodies see concentrations well above their individual Kds, and the net response is thus well below 25%. This effect, clearly visible in the mixed antibody response curve of Figure 3E and F, broadens the response range beyond the 2-fold estimate of the previous paragraph. To explore the effect of this, the net response was simulated with various mixtures of Kanechlors, including mixtures at various ratios of two, three, or all four Kanechlors. Ratios considered included equal parts by weight as well as mixtures dominated by one Kanechlor but with minority contributions from one or more others. In all, 65 combinations were simulated and the net window of response is shown in Figure 4A. For completely unknown mixtures of Analytical Chemistry, Vol. 78, No. 20, October 15, 2006

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Figure 4. Panel A, the estimated response envelope for a 2:1 mix of clones SK3A11 and PCB35M. The upper limit of the envelope, shown as a heavy dashed line, is defined by the response to individual Kanechlors (KC 500 below ∼5 ppb and KC 600 above) while the lower limit, also a heavy dashed line, is defined by a mixture of equal parts of KC 300 and KC 600. Panel B shows the predicted response envelope width, expressed as the ratio of the worst case (maximum) concentration for 50% inhibition over the best case (minimum) concentration for 50% inhibition, as a function of the mix ratio of the antibodies; see text for further discussion.

Kanechlors, we expect the mixed antibody response to fall within the window defined by the bold dashed lines in Figure 4A. The dotted lines show the individual response curves that correspond to the limits. The upper limit of the response envelope is defined by the mixed antibody response to pure KC 500 (below ∼5 ppb) or by pure KC 600 (above 5 ppb). The lower limit of the response envelope is defined by a mixture of equal parts of KC 300 and KC 600. It makes intuitive sense that the upper limit will always be defined by the response to a pure Kanechlor since once the weakest Kanechlor at a given concentration is identified, substitution of any other Kanechlor is necessarily stronger. In the present case, the lower limit is defined by a mix of equal parts of two Kanechlors, but this is specific to the antibodies used and changes for other antibody combinations, as seen below. The width of the response envelope shown in Figure 4A varies with the mix ratio of the antibodies, starting from the width of response of one antibody alone, passing through a minimum, and then increasing to the width of the second antibody alone. Figure 4B shows the calculated envelope width, expressed as the ratio of the maximum PCB needed for 50% inhibition over the minimum PCB giving 50% inhibition, as a function of the mix ratio of the antibodies. In Figure 4B, the x axis is the percentage of antibody Sk3A11 present in the antibody mixture with the balance of the mix being antibody PCB35M. When there is zero Sk3A11, e.g., pure PCB35M, the response window for unknown mixtures of Kanechlors is defined by PCB35M’s response to Kanechlor 300 (10.2 ppb gives 50% inhibition) and Kanechlor 600 (0.49 ppb gives 50% inhibition). The goal of using mixed antibodies is to bring these numbers closer together so a convenient figure of merit is the ratio of the larger of these numbers divided by the smaller. 7246 Analytical Chemistry, Vol. 78, No. 20, October 15, 2006

Figure 5. Panel A, response curves of a 2:1 mix of clones PCBK2A-1 and PCB35M (0.5 nM combined antibody concentration) with symbols 2, b, 1, and [ representing Kanechlor 300, 400, 500, and 600, respectively. Panel B shows the predicted response envelope width as a function of the antibody mix ratio. The optimum mix is 82% PCB-K2A-1 and 18% PCB35M.

In the present case, the width of the response window, characterized by this dimensionless ratio varies from ∼21 (10.2/0.49) with 0 Sk3A11 to ∼50 (29.9/0.6) with 100% Sk3A11 and is predicted to pass through a minimum of 2.95 at a mix ratio of 62% SK3A11 and 38% PCB35M. The theoretical width at the 2:1 mix ratio used experimentally (66% SK3A11 and 33% PCB35) is 3.1. Either of these numbers is in general agreement with the measured responses shown in Figure 3 and show that even with the broadening effect of mixed antigens there is still a substantial improvement over using either antibody alone. In this case, the optimum mix ratio (1.8) is close to the relative response ratio (2.3; see Figure 2), which is a reflection of the fact that Kanechlor responses of these antibodies are nearly perfect inverses of each other in terms of Kanechlor response. Clones PCB35M and PCB-K2A-1. In terms of an envelope width as discussed above, clone PCB-K2A-1 already possesses an excellent reactivity profile for the Kanechlors with an envelope width at 50% of 2.8. Even so, PCB-K2A-1’s profile (binding tightest to KC 300 and loosest to KC 600) is in the opposite direction from clone PCB35M’s profile, suggesting that some improvement might be possible by mixing these antibodies together. Based on the signal level experiments described above, initial experiments were performed using two times more PCB-K2A-1 than PCB35M. The results for individual pure Kanechlors are shown in Figure 5A. The theoretical lines shown are again based on equivalent Kd’s measured separately for each antibody reacting with a pure Kanechlor (see Figure 1). Again, the fit of the theory to the mixed antibody measurements is very reasonable. Figure 5B shows the predicted width of the response envelope as a function of percentage of PCB-K2A-1 in the mixture. The 2:1 mix used in panel A corresponds to 66.66% PCB-K2A-1 in panel B. The predicted

Figure 6. Ratio of clones PCB-K2A-1 and PCB35M changed to 9:1 (0.5 nM combined antibody concentration), Individual Kanechlors and a mix of equal parts of all four Kanechlors were again checked. Error bars ((2 standard deviations based on triplicate measurement) are included but in some cases are obscured by the symbols used.

response envelope width at 50% inhibition is 2.8, coincidentally the same as the response envelope width for clone PCB-K2A-1 alone, although the response profile shown in Figure 5A is reversed compared to PCB-K2A-1 alone (Figure 1A). Figure 5B shows a predicted minimum response envelope width of 1.4 for a mixture containing 82% PCB-K2A-1 and 18% PCB35M. After completing the analysis, another experiment was performed with clones PCB35M and PCB-K2A-1 in hopes of demonstrating the narrower response window predicted by Figure 5B. The initial batch of clone PCB-K2A-1 had run out and a new batch was obtained from hybridoma that gave smaller signals (relative to PCB35M) that the first batch. The new signal factor measured (data not shown) was 4.0. With the new signal factor, the predicted optimum mix ratio shifted to 90% PCB-K2A-1 and 10% PCB35M so the new experiments were conducted with 0.45 nM PCB-K2A-1 mixed with 0.05 nM PCB35M. As shown in Figure 6, the resultant data is fit reasonably well by the theoretical lines, though several points for Kanechlor 300 show less inhibition thanexpected. The modest improvement in response envelope width we were hoping for is clear in the theoretical lines in Figures 5 and 6, but somewhat ambiguous with regard to the measured data points. Clones PCB-K2A-1 and Sk3A11. In this case, there is no clear complementarity in the Kanechlor responses of these clones. That is, both clones show their tightest binding for KC 300 and loosest for KC 600. Experiments with mixed antibodies were nevertheless carried out to check the validity of the modeling in this situation. As shown in Figure 7A, the competition model does a reasonable job of fitting the measured data from the mixed antibodies (mixed here at equal concentrations of 250 pM each), with noticeable deviation between the theory and experiment only in the case of KC 600. The reason for this discrepancy is not known; however, if the Kd values of the clones for KC 600 aremoved to the lower limit of the 95% confidence interval of their measurement (see Table 1), the fit is very much improved. Figure 7B shows the predicted width of the response window as a function of percent PCB-K2A-1 clone in the antibody mixture. As expected, addition of Sk3A11 does not narrow the response window and the optimum mixture consists of pure PCB-K2A-1.

Figure 7. Panel A, response curves of a 1:1 mix of clones PCBK2A-1 and SK3A11 (0.5 nM combined antibody concentration) with symbols 2, b, 1, and [ representing Kanechlor 300, 400, 500, and 600, respectively. Panel B shows the predicted response envelope width as a function of the antibody mix ratio. The optimum mix is 100% PCB-K2A-1 and 0% SK3A11.

CONCLUSIONS The combination of judiciously selected antibodies has been shown to result in a narrowing of the overall response window of an immunoassay to an unknown mixture of related antigens. As shown here, antibodies that individually exhibit 20- or 50-fold differences in response between Kanechlor 300 and Kanechlor 600 can be mixed so that the overall difference in response is reduced to 3-fold. A modeling approach is described that can be used to select suitable pairs of monoclonal antibodies, determine optimum mix ratios, and estimate the resulting response window. Although illustrated using commercial mixtures of PCBs (Kanechlors), the concept described is expected to be directly applicable to other important classes of analytes. The work described here has increased the cross reactivity of a PCB immunoassay resulting in an assay system that more closely approximates the ideal case of responding to total PCBs independent of specific congener content. If Kd values are available for undesirable cross-reacting species, the models developed may be straightforwardly extended to estimate the assay susceptibility to these interfering substances as well. ACKNOWLEDGMENT The authors gratefully acknowledge the financial support of Japan’s National Institute of Advanced Industrial Science and Technology. Received for review March 21, 2006. Accepted August 9, 2006. AC0605187

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