Journal of Immunological Methods, 131 (1990) 213-222 Elsevier
213
JIM 05643
Evaluation of dissociation constants of antigen-antibody complexes by ELISA B.B. Kim 1, E.B. Dikova 2, U. Sheller 3, M.M. Dikov 3, E.M. Gavrilova 1 and A.M. Egorov 1 z Chemistry Department, Lomonosov Moscow University, Moscow, U.S.S.R., 2 Bach Institute of Biochemistry, U.S.S.R. Academy of Sciences, Moscow, U.S.S.R., and 3 All- Union Cardiology Research Center, U.S. S.R. Academy of Medical Sciences, Moscow, U.S.S.R. (Received 9 February 1989, revised received 5 January 1990, accepted 20 April 1990)
In this communication some of the advantages and constraints in the use of ELISA (enzyme-linked immunosorbent assay) procedures to evaluate antigen-antibody dissociation constants (Kd) are discussed and experimental conditions under which the effective K d is close to the true value are proposed. Interactions between horseradish peroxidase (POD), human myoglobin and insulin with mono- and polyclonal antibodies (McAb and PcAb) were used to demonstrate that ELISA can be used to determine the average Kd, characterizing the interaction between antigens and PcAb. The K d values obtained by ELISA were similar to those determined by luminescent immuno-cofactor analysis (LICA). Key words: Antigen-antibody complex; Dissociation constant; ELISA; Monoclonal antibody; Polyclonal antiserum
Introduction
immunosorbent assay (ELISA) (Friguet et al., 1985; Stevens et al., 1987; Schots et al., 1988). In this paper we discuss constraints for its application to the determination of K d values for antigen-monoclonal antibody (McAb) complexes and provide protocols for applying ELISA to defining the average K d characterizing antigen interactions with polyclonal antibodies (PcAb). We also describe a modified method based on quantifying the unbound antigen by ELISA.
Modern immunobiotechnology would benefit from simple and reliable methods for the determination of the dissociation constants (K d) of antigen-antibody complexes. The K d value is essential not only for fundamental studies but also for applied fields such as the investigation of the molecular mechanisms underlying immune responses and the quality control of immunoreagents. A simple and convenient method for the determination of K d values is the enzyme-linked
Materials and methods
Correspondence to: B.B. Kim, Chemistry Department, Lomonosov Moscow University, 119899, Moscow, U.S.S.R. Abbreviations: ELISA, enzyme-linked immunosorbent assay; FPLC, fast protein liquid chromatography; e1~, extinction of 1 mg/ml solution; Ka, dissociation constant; McAb, monoclonal antibody; OPD, o-phenylenediamine; PBS, phosphatebuffered saline; PBST, PBS supplemented with 0.5 % Triton X-100; PcAb, polyclonal antibodies; POD, horseradish peroxidase.
The following reagents were used: POD, RZ = 3.0 (NPO Biolar, U.S.S.R.), alkaline phosphatase (1350 U/mg, FMD, G.D.R.), insulin (VNIIKGP, U.S.S.R.), o-phenylenediamine (Koch-Light, U.K.), p-nitrophenyl phosphate, sodium salt (Sigma, U.S.A.), 6 kDa polyethylene glycol (Serva, F.R.G.), Triton X-100, glutaraldehyde (Ferax, W. Berlin), hydrogen peroxide and other inorganic
0022-1759/90/$03.50 © 1990 Elsevier Science Publishers B.V. (Biomedical Division)
214
reagents (Reakhim Products, U.S.S.R.), bovine and human blood sera (ZMP, U.S.S.R.). Anti-insulin guinea pig antiserum and rabbit antiserum against mouse IgG and against guinea pig IgG were obtained as described by Sorokina et al. (1985). Mouse McAb against insulin and POD were kindly provided by Dr. T.V. Cherednikova (Bach Institute of Biochemistry) and monoclonal antibodies against human myoglobin by Dr. E. Yuoronen (Tartu State University). Serum 7-globulin fractions were obtained by double precipitation with 10% polyethylene glycol followed by dialysis. The antibodies used to prepare POD conjugates were additionally purified by ion exchange chromatography on a Mono Q H R 5 / 5 column (Pharmacia LKB Biotechnology, Sweden). 1 ml of the dialyzed 7-globulin fraction was loaded onto the column, equilibrated with 0.02 M phosphate buffer, p H 6.3. The proteincontaining fractions of the eluate from the first buffer were harvested and the remaining proteins were removed from the column using 1.5 M NaC1. McAb were isolated from ascites by affinity chromatography on protein A-Sepharose (Pharmacia LKB Biotechnology, Sweden), 1 ml of ascites was mixed with an equal volume of buffer containing 0.75 M glycine and 3.0 M NaC1 (pH 8.9). The mixture was passed through a column with 1 ml of carrier and antibody was eluted with citrate buffer (40 mM, p H 3.2). Fractions containing antibody were immediately neutralized by 1 M potassium phosphate buffer (pH 7.2) and dialyzed rigorously against PBS. The purity of the antibody preparations was assessed by determination of the ratio of absorbance at 278 and at 251 nm; this was 2.5-3 for antibodies and 1.0-1.5 for other serum or ascitic fluid proteins (Tijssen, 1985). The PODantibody conjugate was prepared as described by Wilson and Nakane (1978) with minor modifications. Immunoglobulin-alkaline phosphatase conjugates were obtained using glutaraldehyde (Tijssen, 1985) and additionally purified by gel filtration on a TSK-4000 SW column (Pharmacia LKB Biotechnology, Sweden). Human myoglobin was obtained as described by Yermolin et al. (1986). Concentrations of alkaline phosphatase, immunoglobulins, POD, and myoglobin were measured spectrophotometrically using the following extinction values: e278= 6.5 × 104 M -1 • cm -1,
a% = 13 m l / m g • cm -1 (Tijssen, 1985), e403 1.02 X 105 M 1. cm-1 (Frew et al., 1984), e578= 1.41 X 1 0 4 M - 1 . c m - 1 (Stone et al., 1982), respectively. The solutions of insulin were prepared according to a gravimetric standard. Optical measurements were made on a D U 8B spectrophotometer (Beckman, U.S.A.). The data were processed using an IBM PC AT computer. An FPLC system (Pharmacia LKB Biotechnology, Sweden) was used for all chromatography. An ELISA procedure was used to quantify antibodies. Microtiter plates (Nunc, 96F, Denmark) were coated at 37 ° C for 1.5 h (200/xl/well) with 1 0 / ~ g / m l antigen solution in PBS. The plate wells were washed with PBST before dispensing aliquots (150 /d) of both the standard antibody solution and the test samples. After incubation at 37 ° C (0.5 h) and washing, the bound antibodies were detected by adding the antibodies specific for mouse or rabbit IgG, coupled with POD or alkaline phosphatase. The microplate was incubated at 37 ° for 1.5 h and washed with PBST. The enzyme activity of the bound conjugate was then measured: 0.1 ml aliquots of substrate mixture for POD (ABTS, 3.25 mM; citric acid, 39.8 mM; disodium hydrogen phosphate, 60 mM; pH 4.5) or alkaline phosphatase (4 mM p-nitrophenyl phosphate in 1 M diethanolamine buffer, 0.5 mM MgC12, p H 9.8) were pipetted into the wells. After incubation at room temperature for 0.5 h, the absorbance at 405 nm was measured using a Vmax plate analyzer (Molecular Devices, U.S.A.). The K~ values were determined by the method of Friguet et al. (1985). Insulin at various concentrations (5 × 10-8-10 -1° M) was mixed with a constant amount of PcAb or McAb in PBST. The antibody concentration used was derived from a preliminary ELISA calibration (see results section Figs. 1 and 4). After an overnight incubation at 4 ° C 150 /zl aliquots of each mixture were transferred into the wells of a microtitre plate previously coated with insulin and incubated for 20 rain at 37 o C. The concentration of free antibody was then measured by an indirect ELISA as described above. In the case of POD interactions with McAb, the following modifications were used; the concentration of antibody binding sites was 2.5 x 10 -~° M, and the incubation time in the wells of microtiter plates was reduced to 10 min. E278
215 When the K d values of the antibody-myoglobin complexes were determined, the unbound antigen was assayed by ELISA. Myoglobin solution (5 × 1 0 - 9 - 5 × 10 -7 M) in PBST (100 /xl) was incubated with an equal volume of antibody solution (10 -9 M for both McAb and PcAb) overnight. Then 150 #1 aliquots of each mixture were transferred into the wells coated with sheep antimyoglobin antibodies (200 #l/well at 3 / ~ g / m l in PBS for 2 h at 37 ° C). After 15 min incubation at 3 7 ° C and washing with PBST, the bound myoglobin was detected by adding goat antimyoglobin IgG coupled with POD and measuring the POD activity retained in each well as described above. The K d was obtained by plotting the experimental data using the Sips coordinates. To study the kinetics of McAb binding to coated insulin, antibody solutions of differing concentrations (7.7 × 10 -9 M, 4.7 × 10 -9 M, 1.5 × 10 -9 M, 6.2 × 10-10 M, 3.1 × 10-10 M in PBST) were added at certain time intervals over 2 h into microplate wells coated with insulin (10/~g/ml solution in PBS, 100 /~l/well). After washing, the bound immunoglobulins were assayed by ELISA.
Theoretical aspects Various methods for the evaluation of equilibrium constants of antigen-antibody interactions and based on assaying one of the reactants have been discussed by Berson (1959), Fazekas de St. Groth (1981), Steward (1981), Steward et al. (1983), Friguet et al. (1985), and Yagisawa et al. (1986). In general, the component to be quantified is eliminated from the reaction mixture which leads to dissociation of the antigen-antibody complex in solution and the establishment of a new equilibrium. Therefore, an error proportional to the degree of the equilibrium shift is introduced. The Friguet method (Friguet et al., 1985) is based on detection of free antibodies in the reaction mixture by an indirect ELISA procedure after the system reaches equilibrium. In this case, the key assumption is that the interaction between unbound antibody and the immobilized antigen does not differ significantly from the equilibrium in solution. The experimentally determined effective constant of the antigen-antibody interaction is
evidently a function of the antigen-antibody interaction equilibrium constants in solution and on the solid phase. Considering this question in greater detail: (1) The interactions o f M c A b with antigen in solution and on solid phase
An adsorbed antigen molecule can take various spatial arrangements which determine the accessibility of the antigenic determinants. In this case, the model of ligand interaction with a number of independent binding sites (Varfolomeev et al., 1985) can be used: IAb+Ag ~ B
(1)
[Ab+Ag* ,~ B~* (i) i=l.., n, where Ab is the antibody, Ag is the antigen in solution, Ag* is the i type of the antigen adsorbed on solid phase, B is the antigen-antibody complex in solution, B~* is the i type of the antigen-antibody complex on the solid phase, n is the number of binding sites. In this system, equation (1) describes antigenantibody interactions in solution, while equations 2 . . . n describe those on the solid phase. From the analysis of the above system, the following equation can be derived to determine the K d (for details see appendix 1): A0
(
n
)
Ao _ A = I + K d \ 1+ i=l ~_ Ki*Ag~. i J Ago 1 '
(I)
where A 0 is the absorbance of antibodies measured in solution by ELISA in the absence of antigen. A is the absorbance in the presence of antigen, Ago*i is the initial concentration of the coated i type binding site (antigen), Ag o is the initial concentration of antigen in solution, K~* is the association constant of the i type antigen-antibody complex formed on solid support, K d is the dissociation constant of antigen-antibody complex in solution. It follows from equation (I) that the straight line (the slope equals the effective Ko, K ' : n
K ' = K d 1+ X" /..., K*A~* i ,~o,~/ i=l
/
216
This is obtained by plotting the experimental results using the coordinates A o / ( A o - A ) versus 1 / A g 0. Then: A° K' 1 Ao - A =1+ Ag o .
(II)
The advantage of this procedure is that it is not necessary to know precisely the concentration of antibody active sites. There are cases when the latter cannot be measured (e.g., McAb in ascites). If in the step of free antibody quantitation the n . Ago, , / equilibrium is reached, the value 1 + Y'.i=lKi is a maximal possible error in the K d. If " * Ago, * /
213
JIM 05643
Evaluation of dissociation constants of antigen-antibody complexes by ELISA B.B. Kim 1, E.B. Dikova 2, U. Sheller 3, M.M. Dikov 3, E.M. Gavrilova 1 and A.M. Egorov 1 z Chemistry Department, Lomonosov Moscow University, Moscow, U.S.S.R., 2 Bach Institute of Biochemistry, U.S.S.R. Academy of Sciences, Moscow, U.S.S.R., and 3 All- Union Cardiology Research Center, U.S. S.R. Academy of Medical Sciences, Moscow, U.S.S.R. (Received 9 February 1989, revised received 5 January 1990, accepted 20 April 1990)
In this communication some of the advantages and constraints in the use of ELISA (enzyme-linked immunosorbent assay) procedures to evaluate antigen-antibody dissociation constants (Kd) are discussed and experimental conditions under which the effective K d is close to the true value are proposed. Interactions between horseradish peroxidase (POD), human myoglobin and insulin with mono- and polyclonal antibodies (McAb and PcAb) were used to demonstrate that ELISA can be used to determine the average Kd, characterizing the interaction between antigens and PcAb. The K d values obtained by ELISA were similar to those determined by luminescent immuno-cofactor analysis (LICA). Key words: Antigen-antibody complex; Dissociation constant; ELISA; Monoclonal antibody; Polyclonal antiserum
Introduction
immunosorbent assay (ELISA) (Friguet et al., 1985; Stevens et al., 1987; Schots et al., 1988). In this paper we discuss constraints for its application to the determination of K d values for antigen-monoclonal antibody (McAb) complexes and provide protocols for applying ELISA to defining the average K d characterizing antigen interactions with polyclonal antibodies (PcAb). We also describe a modified method based on quantifying the unbound antigen by ELISA.
Modern immunobiotechnology would benefit from simple and reliable methods for the determination of the dissociation constants (K d) of antigen-antibody complexes. The K d value is essential not only for fundamental studies but also for applied fields such as the investigation of the molecular mechanisms underlying immune responses and the quality control of immunoreagents. A simple and convenient method for the determination of K d values is the enzyme-linked
Materials and methods
Correspondence to: B.B. Kim, Chemistry Department, Lomonosov Moscow University, 119899, Moscow, U.S.S.R. Abbreviations: ELISA, enzyme-linked immunosorbent assay; FPLC, fast protein liquid chromatography; e1~, extinction of 1 mg/ml solution; Ka, dissociation constant; McAb, monoclonal antibody; OPD, o-phenylenediamine; PBS, phosphatebuffered saline; PBST, PBS supplemented with 0.5 % Triton X-100; PcAb, polyclonal antibodies; POD, horseradish peroxidase.
The following reagents were used: POD, RZ = 3.0 (NPO Biolar, U.S.S.R.), alkaline phosphatase (1350 U/mg, FMD, G.D.R.), insulin (VNIIKGP, U.S.S.R.), o-phenylenediamine (Koch-Light, U.K.), p-nitrophenyl phosphate, sodium salt (Sigma, U.S.A.), 6 kDa polyethylene glycol (Serva, F.R.G.), Triton X-100, glutaraldehyde (Ferax, W. Berlin), hydrogen peroxide and other inorganic
0022-1759/90/$03.50 © 1990 Elsevier Science Publishers B.V. (Biomedical Division)
214
reagents (Reakhim Products, U.S.S.R.), bovine and human blood sera (ZMP, U.S.S.R.). Anti-insulin guinea pig antiserum and rabbit antiserum against mouse IgG and against guinea pig IgG were obtained as described by Sorokina et al. (1985). Mouse McAb against insulin and POD were kindly provided by Dr. T.V. Cherednikova (Bach Institute of Biochemistry) and monoclonal antibodies against human myoglobin by Dr. E. Yuoronen (Tartu State University). Serum 7-globulin fractions were obtained by double precipitation with 10% polyethylene glycol followed by dialysis. The antibodies used to prepare POD conjugates were additionally purified by ion exchange chromatography on a Mono Q H R 5 / 5 column (Pharmacia LKB Biotechnology, Sweden). 1 ml of the dialyzed 7-globulin fraction was loaded onto the column, equilibrated with 0.02 M phosphate buffer, p H 6.3. The proteincontaining fractions of the eluate from the first buffer were harvested and the remaining proteins were removed from the column using 1.5 M NaC1. McAb were isolated from ascites by affinity chromatography on protein A-Sepharose (Pharmacia LKB Biotechnology, Sweden), 1 ml of ascites was mixed with an equal volume of buffer containing 0.75 M glycine and 3.0 M NaC1 (pH 8.9). The mixture was passed through a column with 1 ml of carrier and antibody was eluted with citrate buffer (40 mM, p H 3.2). Fractions containing antibody were immediately neutralized by 1 M potassium phosphate buffer (pH 7.2) and dialyzed rigorously against PBS. The purity of the antibody preparations was assessed by determination of the ratio of absorbance at 278 and at 251 nm; this was 2.5-3 for antibodies and 1.0-1.5 for other serum or ascitic fluid proteins (Tijssen, 1985). The PODantibody conjugate was prepared as described by Wilson and Nakane (1978) with minor modifications. Immunoglobulin-alkaline phosphatase conjugates were obtained using glutaraldehyde (Tijssen, 1985) and additionally purified by gel filtration on a TSK-4000 SW column (Pharmacia LKB Biotechnology, Sweden). Human myoglobin was obtained as described by Yermolin et al. (1986). Concentrations of alkaline phosphatase, immunoglobulins, POD, and myoglobin were measured spectrophotometrically using the following extinction values: e278= 6.5 × 104 M -1 • cm -1,
a% = 13 m l / m g • cm -1 (Tijssen, 1985), e403 1.02 X 105 M 1. cm-1 (Frew et al., 1984), e578= 1.41 X 1 0 4 M - 1 . c m - 1 (Stone et al., 1982), respectively. The solutions of insulin were prepared according to a gravimetric standard. Optical measurements were made on a D U 8B spectrophotometer (Beckman, U.S.A.). The data were processed using an IBM PC AT computer. An FPLC system (Pharmacia LKB Biotechnology, Sweden) was used for all chromatography. An ELISA procedure was used to quantify antibodies. Microtiter plates (Nunc, 96F, Denmark) were coated at 37 ° C for 1.5 h (200/xl/well) with 1 0 / ~ g / m l antigen solution in PBS. The plate wells were washed with PBST before dispensing aliquots (150 /d) of both the standard antibody solution and the test samples. After incubation at 37 ° C (0.5 h) and washing, the bound antibodies were detected by adding the antibodies specific for mouse or rabbit IgG, coupled with POD or alkaline phosphatase. The microplate was incubated at 37 ° for 1.5 h and washed with PBST. The enzyme activity of the bound conjugate was then measured: 0.1 ml aliquots of substrate mixture for POD (ABTS, 3.25 mM; citric acid, 39.8 mM; disodium hydrogen phosphate, 60 mM; pH 4.5) or alkaline phosphatase (4 mM p-nitrophenyl phosphate in 1 M diethanolamine buffer, 0.5 mM MgC12, p H 9.8) were pipetted into the wells. After incubation at room temperature for 0.5 h, the absorbance at 405 nm was measured using a Vmax plate analyzer (Molecular Devices, U.S.A.). The K~ values were determined by the method of Friguet et al. (1985). Insulin at various concentrations (5 × 10-8-10 -1° M) was mixed with a constant amount of PcAb or McAb in PBST. The antibody concentration used was derived from a preliminary ELISA calibration (see results section Figs. 1 and 4). After an overnight incubation at 4 ° C 150 /zl aliquots of each mixture were transferred into the wells of a microtitre plate previously coated with insulin and incubated for 20 rain at 37 o C. The concentration of free antibody was then measured by an indirect ELISA as described above. In the case of POD interactions with McAb, the following modifications were used; the concentration of antibody binding sites was 2.5 x 10 -~° M, and the incubation time in the wells of microtiter plates was reduced to 10 min. E278
215 When the K d values of the antibody-myoglobin complexes were determined, the unbound antigen was assayed by ELISA. Myoglobin solution (5 × 1 0 - 9 - 5 × 10 -7 M) in PBST (100 /xl) was incubated with an equal volume of antibody solution (10 -9 M for both McAb and PcAb) overnight. Then 150 #1 aliquots of each mixture were transferred into the wells coated with sheep antimyoglobin antibodies (200 #l/well at 3 / ~ g / m l in PBS for 2 h at 37 ° C). After 15 min incubation at 3 7 ° C and washing with PBST, the bound myoglobin was detected by adding goat antimyoglobin IgG coupled with POD and measuring the POD activity retained in each well as described above. The K d was obtained by plotting the experimental data using the Sips coordinates. To study the kinetics of McAb binding to coated insulin, antibody solutions of differing concentrations (7.7 × 10 -9 M, 4.7 × 10 -9 M, 1.5 × 10 -9 M, 6.2 × 10-10 M, 3.1 × 10-10 M in PBST) were added at certain time intervals over 2 h into microplate wells coated with insulin (10/~g/ml solution in PBS, 100 /~l/well). After washing, the bound immunoglobulins were assayed by ELISA.
Theoretical aspects Various methods for the evaluation of equilibrium constants of antigen-antibody interactions and based on assaying one of the reactants have been discussed by Berson (1959), Fazekas de St. Groth (1981), Steward (1981), Steward et al. (1983), Friguet et al. (1985), and Yagisawa et al. (1986). In general, the component to be quantified is eliminated from the reaction mixture which leads to dissociation of the antigen-antibody complex in solution and the establishment of a new equilibrium. Therefore, an error proportional to the degree of the equilibrium shift is introduced. The Friguet method (Friguet et al., 1985) is based on detection of free antibodies in the reaction mixture by an indirect ELISA procedure after the system reaches equilibrium. In this case, the key assumption is that the interaction between unbound antibody and the immobilized antigen does not differ significantly from the equilibrium in solution. The experimentally determined effective constant of the antigen-antibody interaction is
evidently a function of the antigen-antibody interaction equilibrium constants in solution and on the solid phase. Considering this question in greater detail: (1) The interactions o f M c A b with antigen in solution and on solid phase
An adsorbed antigen molecule can take various spatial arrangements which determine the accessibility of the antigenic determinants. In this case, the model of ligand interaction with a number of independent binding sites (Varfolomeev et al., 1985) can be used: IAb+Ag ~ B
(1)
[Ab+Ag* ,~ B~* (i) i=l.., n, where Ab is the antibody, Ag is the antigen in solution, Ag* is the i type of the antigen adsorbed on solid phase, B is the antigen-antibody complex in solution, B~* is the i type of the antigen-antibody complex on the solid phase, n is the number of binding sites. In this system, equation (1) describes antigenantibody interactions in solution, while equations 2 . . . n describe those on the solid phase. From the analysis of the above system, the following equation can be derived to determine the K d (for details see appendix 1): A0
(
n
)
Ao _ A = I + K d \ 1+ i=l ~_ Ki*Ag~. i J Ago 1 '
(I)
where A 0 is the absorbance of antibodies measured in solution by ELISA in the absence of antigen. A is the absorbance in the presence of antigen, Ago*i is the initial concentration of the coated i type binding site (antigen), Ag o is the initial concentration of antigen in solution, K~* is the association constant of the i type antigen-antibody complex formed on solid support, K d is the dissociation constant of antigen-antibody complex in solution. It follows from equation (I) that the straight line (the slope equals the effective Ko, K ' : n
K ' = K d 1+ X" /..., K*A~* i ,~o,~/ i=l
/
216
This is obtained by plotting the experimental results using the coordinates A o / ( A o - A ) versus 1 / A g 0. Then: A° K' 1 Ao - A =1+ Ag o .
(II)
The advantage of this procedure is that it is not necessary to know precisely the concentration of antibody active sites. There are cases when the latter cannot be measured (e.g., McAb in ascites). If in the step of free antibody quantitation the n . Ago, , / equilibrium is reached, the value 1 + Y'.i=lKi is a maximal possible error in the K d. If " * Ago, * /
