Comparison of the results obtained by ELISA and surface plasmon resonance for the determination of antibody affinity

Journal of Immunological Methods 352 (2010) 13–22

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Journal of Immunological Methods j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j i m

Research paper

Comparison of the results obtained by ELISA and surface plasmon resonance for the determination of antibody affinity Laurence Heinrich a,⁎, Nathalie Tissot a, Daniel Jean Hartmann a, Richard Cohen a,b a Université de Lyon, Université Lyon 1, ISPB, UPSP 2007-03-135 Réparation Tissulaire Interactions Biologiques et Biomatériaux (RTI2B), 8 Avenue Rockefeller F-69373 Lyon Cedex 08, France b Hôpitaux de Lyon, Hôpital Edouard Herriot, Fédération de Biochimie, 69437 Lyon Cedex 03, France

a r t i c l e

i n f o

Article history: Received 30 April 2009 Received in revised form 22 September 2009 Accepted 8 October 2009 Available online 23 October 2009 Keywords: Fibronectin–antibody interaction Surface plasmon resonance Enzyme linked immunosorbent assay Dissociation rate constant Association rate constant Equilibrium dissociation constant

a b s t r a c t The aim of this study was to compare the affinity values obtained for a monoclonal antibody/ antigen complex using two different techniques, surface plasmon resonance (SPR) and an enzyme linked immunosorbent assay (ELISA) approach recently described by Bobrovnik S.A. and by Stevens F.J. These two techniques can be used in particular to determine the equilibrium dissociation constant, KD, of the complex in solution or on a surface. Bobrovnik's method gives two KD values that differ by a factor of 100, demonstrating that two populations of complexes are present in solution. In an initial step, one protein binds relatively weakly to the other (high KD) and this is followed by a conformational change in the most flexible portion of the antigen, which increases the affinity (low KD). Only the higher of the two KD values can be detected when complex formation in solution is investigated using SPR, because the interaction measured concerns the fibronectin/antibody complexes of lowest affinity. In contrast, when measuring association at the sensor surface, SPR gives an average result between the two KD values because complexes corresponding to both affinities can form in this situation. The constants that characterise the kinetics of the fibronectin–antibody interaction obtained by SPR and ELISA are therefore different, because the methods do not allow the same phenomena to be observed. However they are consistent and complementary. © 2009 Elsevier B.V. All rights reserved.

1. Introduction The biological activity of an antibody for its antigen is related to its affinity. Certain tests such as ELISA (enzyme linked immunosorbent assay) require antibodies of relatively high affinity so that the complex formed will resist the incubation and washing steps (Van Regenmortel et al., 1998). Other techniques, such as affinity chromatography require antibody–antigen complexes of lower affinity, so that the molecule of interest can be recovered easily (Van Regenmortel and Azimzadeh, 2000). It is therefore important to characterise the strength of the interaction between antibodies and their antigen, i.e. to evaluate their

⁎ Corresponding author. Tel.: +33 4 78 78 56 75; fax: +33 4 78 77 28 19. E-mail address: [email protected] (L. Heinrich). 0022-1759/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jim.2009.10.002

equilibrium dissociation constant KD, as well as the parameters that characterise the kinetics of the reaction (the association rate constant ka and the dissociation rate constant kd). These values can be obtained, for example, with methods that use labelled molecules such as ELISA or an optical method, surface plasmon resonance (SPR), which allows the antibody–antigen reaction to be followed in real time without labelling. This method is available on several models of Biacore® apparatus (GE Healthcare, Uppsala, Sweden). The ELISA technique is relatively simple and fast, and presents the advantage of using small quantities of reagents (antibody and antigen). In the original method, the antigen– antibody interaction was investigated while one of the two protagonists was immobilised on a solid phase. However, such adsorption can denature the molecule, and the equilibrium dissociation constant measured in this case will be a relative

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value rather than the “true” value. Friguet and his co-workers have shown, by comparison with immunoprecipitation and fluorescence, how it is possible to obtain the “true” equilibrium dissociation constant of the complex in solution using an indirect ELISA method (Friguet et al., 1985). Furthermore, this method can be applied to unpurified antibodies and enables KD values as low as 10− 9 M to be measured. However, Bobrovnik subsequently showed that it is possible, by plotting a well chosen graph, to obtain more precise and detailed information on the affinity constants (Bobrovnik, 2003). This method will be referred as “Bobrovnik's method” and can be used to detect the coexistence of several populations of complexes in solution. Recently, Stevens and Bobrovnik (Stevens and Bobrovnik, 2007) showed that a simple non-linear fit of the same data to an appropriate formula gives even much better results. This method will be referred as “Stevens's method”. Larvor and his co-workers have highlighted how indirect ELISA can generate additional information about the kinetics and, more specifically, the dissociation rate constant kd of an antibody–antigen complex in solution (Larvor et al., 1994). This method presents all the advantages of conventional ELISA techniques that are mentioned above and can also be applied to protein–protein or protein– nucleic acid interactions. One of its advantages is that the assay is carried out in solution. Its disadvantages are as follows: this method cannot be applied when affinity is very high (KD =10− 10 to 10− 11 M) and it is impossible to measure the dissociation rate constant reliably if it is greater than 5.10− 3 s− 1. Biacore® instruments can be used to analyse the interaction between two molecules: they can be used to demonstrate the existence of an interaction and to quantify this interaction by measuring the equilibrium dissociation constant and the association and dissociation rate constants of the complex formed. The advantage of this technique is that it is carried out in real time and requires no radioactive or fluorescent labelling. The Biacore® technique is based on surface plasmon resonance (SPR). SPR is an optical phenomenon that occurs when polarised light is reflected by a surface coated with a fine layer of metal (gold or silver). Under certain conditions (of wavelength, polarisation and angle of incidence) the free electrons at the surface of the metal of the sensor chip absorb the incident photons during the SPR phenomenon. This phenomenon corresponds to an interaction between the free electrons of the metal and the evanescent wave that penetrates a short distance (a few hundred nanometres) into the medium in the vicinity of the unlit surface of the interface. Under SPR conditions, a dip in the intensity of the reflected light is observed in a well-defined direction. Any change in the refractive index in the vicinity of the surface, caused by a difference in mass when an analyte binds to a previously immobilised ligand, alters the angular direction of the absorption peak (Cullen et al., 1987; Liedberg et al., 1983). SPR can therefore be used to measure a change in refractive index, which is directly related to changes in concentration in the vicinity of the interface. The aim of our study was to compare the affinity values obtained for an antigen and its specific monoclonal antibody, using SPR on a Biacore® system and an ELISA technique for which a new approach of calculation was recently described by Stevens and Bobrovnik. To our knowledge, such a comparison has never been done before. As we dispose of a monoclonal antibody directed against human fibronectin, fibronectin was the model we chose as an example of a multifunctional high molecular weight glycoprotein present at the cell surface and in

pericellular and intercellular matrix, basement membranes, as well as in a large variety of body fluids (Hynes, 1990; White et al., 2008). 2. Materials and methods 2.1. Proteins used in both the ELISA and the SPR techniques 2.1.1. Antibody The monoclonal antibody used (ref FNB8, Novotec, Lyon, France) is a mouse anti-human fibronectin antibody. It was under the form of culture supernatant in RPMI culture medium containing 10% calf serum and was not purified. 2.1.2. Antigen The antigen used was fibronectin purified from human plasma (Merck, Germany), dissolved in PBS pH 7.3, with a molecular weight of 440 kDa. 2.2. ELISA test 2.2.1. Determination of the equilibrium dissociation constant, KD, in solution The KD was determined using the method described by Friguet (Friguet et al., 1985). On the first day, the wells of a 96well plate (Falcon®, ref 353912, VWR, France) were coated with fibronectin in PBS pH 7.2 (ref 75511, Biomérieux). To achieve this, 200 µL of 4 different initial concentrations of fibronectin (4.5, 9, 18 and 36 nM) were incubated at 4 °C overnight. In addition, 7 mixtures of fibronectin and anti-fibronectin antibody were prepared in PBS–BSA pH 7.2 containing 0.45 mM BSA (ref 700-010, I.D. bio, France). The concentration of murine monoclonal antibody was constant (5.7 nM) while the fibronectin concentration ranged from 8.9 nM to 570 nM. The positive control was antibody alone, at a concentration of 5.7 nM. The antigen–antibody reaction was left to proceed overnight at 4 °C. On the second day, the 96-well plate was emptied then washed 5 times with PBS–Tween® (0.1% v/v Tween® 20, ref P7949, Sigma Aldrich, France). 100 µl of each of the 8 samples that had been left to react overnight were dispensed into the fibronectin-coated wells. After incubation at room temperature for 1 h on a plate-shaker, the wells were emptied and washed, then 100 µl of 8 nM peroxidase-labelled anti-mouse IgG secondary antibody (ref 75031, Biorad, France) dissolved in PBS–BSA, were added to each well. After a final incubation of 1.5 h at room temperature on a plate-shaker, the plate was emptied and washed, and then 200 µl of OPD (orthophenylenediamine dihydrochloride, ref P9187-50SET, Sigma Aldrich) were added to each well. The reaction was left to develop in the dark for 30 min. The absorbance, which is proportional to the concentration of free anti-fibronectin antibody in each well, was measured at 450 nm. The results for each series of wells were analysed first using the method described by Friguet et al. This method provides a KD value for the complex in solution (Appendix A). The data were then analysed as described in a subsequent study by Bobrovnik (Bobrovnik, 2003), which develops the study by Friguet et al. It shows that the KD value can be derived from at least 9 equations, which are equivalent in theory but are not necessarily equivalent in practice. Firstly, the difference can

L. Heinrich et al. / Journal of Immunological Methods 352 (2010) 13–22

be due to experimental errors while measuring absorbance. Secondly, important discrepancies can arise if the condition CFN ≫Ci, where CFN is the total fibronectin concentration and Ci is the concentration of the complex in the mixtures, is not verified. Bobrovnik showed that, in this case, it was even possible to find KD values that were 10 times higher than the theoretical value. When the condition CFN ≫Ci is difficult to check, the author suggests plotting A0A−A against CFN, where A0 and A are the absorbances measured in the absence of antigen and at the antigen concentration CFN, respectively. According to this work if the curve is convex it very probably means that 2 or several types of complex of different affinity coexist in the mixture. Where there are 2 types of binding sites with different affinity constants, Bobrovnik suggests plotting A CFN against A. This curve has 2 asymptotes, when A approaches 0 and when CFN approaches 0. From these asymptotes, it is possible to determine the values of the equilibrium dissociation constants, KD1 and KD2. It is also possible to calculate A01 and A02, values supposed to be proportional to the concentrations of the antibodies involved in the antigen–antibody complex formation characterized by KD1 and KD2, respectively, (Appendix B). The data were finally analysed using “Stevens's method” (Stevens and Bobrovnik, 2007). They published a simulation where the work hypothesis is a mixture of two different affinity antibodies. They supposed that 80% (A01 = 1.6) of high affinity (KD1 = 1.0 × 10 − 8 M) antibodies were mixed with 20% (A02 = 0.4) of lower affinity antibodies (KD2 = 1.0 × 10− 6 M). The authors calculated the theoretical absorbance A obtained by ELISA according to Bobrovnik's following formula (Bobrovnik, 2000): A = A01

ð1 + 2CFN Ka1 Þ ð1 + 2CFN Ka2 Þ + A02 ð1 + CFN Ka1 Þ2 ð1 + CFN Ka2 Þ2

ð1Þ

where Ka1 = K1 and Ka2 = K1 . D1 D2 They showed that fitting the data (A versus CFN) to this formula is more reliable, especially when there are only a few experimental points, than the resolution of the system of four equations and four unknowns described previously (Bobrovnik, 2003). Moreover this non-linear regression was simpler to achieve. In our present work, the non-linear regression fitting of the data was performed using XLSTAT software. 2.2.2. Determination of the dissociation rate constant This experiment was performed using the method described by Larvor (Larvor et al., 1994). It extends over 2 days. On day one, a 96-well plate was coated by placing 200 µl of 18 nM fibronectin in PBS pH 7.2 in the wells. This provided 11 series of 7 wells, 6 of which were coated with fibronectin and one with PBS (negative control). This 96-well plate was incubated overnight at 4 °C. The samples to be applied to the plate on day 2 must also be prepared on day 1: first of all, an antibody–antigen mixture was diluted in PBS/BSA in stoichiometric proportions and at a concentration at least greater than 10KD. In our case, the concentration chosen for each component was 1 µM. Next, a 1 µM antibody-only solution was always prepared in PBS/ BSA. The various samples were incubated overnight at room temperature. On the second day, the 96-well plate was emptied and washed 5 times with PBS–Tween 20. At time t = 0, the samples prepared the previous day were diluted 1/101 in PBS/ BSA. At various times between 0 and 90 min, 100 µl of mixture

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were placed in 3 fibronectin-coated wells and the negative control well. Similarly, the antibody alone was placed in the remaining 3 wells. After incubation for 4 min at room temperature, the plate was washed 5 times with PBS/Tween. Next, 150 µL of PBS/BSA were placed in each well. At the end of the experiment, the plate was washed again. 100 µL of 8 nM peroxidase-conjugated anti-mouse IgG secondary antibody were added to each well. After a 90-minute incubation and 3 wash steps, OPD was added to the wells for 30min at room temperature and in the dark. The ELISA plate was then read by spectrophotometry at 450 nm. This experiment was performed independently in duplicate. To derive the value of the dissociation rate constant, kd, a −At logarithmic plot of AA∞∞−A against time was produced, where At 0 is the absorbance measured at time t and A∞ is the absorbance measured at the end of the reaction. The slope of the line obtained is −kd. 2.3. SPR 2.3.1. Apparatus The experiments on affinity at the surface of the sensor chip and affinity in solution were performed on a Biacore T100. This apparatus was obtained from GE Healthcare (Uppsala, Sweden). Series S CM5 sensor chips developed by GE Healthcare were used in these experiments. 2.3.2. Reagents All the reagents were supplied by GE Healthcare. The chosen running buffer was HBS-EP (pH 7.4, 10 mM HEPES, 150 mM NaCl, 3 mM EDTA and 0.05% surfactant P20). The “amine coupling kit” containing EDC (1-ethyl-3-(3dimethylaminopropyl)-carbodiimide hydrochloride), NHS (Nhydroxysuccinimide) and 1 M ethanolamine–HCl pH 8.5 was used to immobilise the ligand (Johnsson et al., 1991). 10 mM sodium acetate pH 5 was used as the buffer during immobilisation of rabbit polyclonal antibodies. A 10 mM solution of glycine–HCl pH 1.7 was acceptable for surface regeneration. 2.3.3. Proteins used only for SPR Rabbit polyclonal antibodies at a concentration of 6.6 µM in 0.15 M NaCl were supplied by GE Healthcare. Murine polyclonal antibodies (Scantibodies Laboratory, USA) in PBS (100 mM phosphate, pH 7.4) were also used in the affinity experiments performed in solution. These antibodies do not react with fibronectin. 2.3.3.1. Immobilisation of the antibodies on the sensor chip. Antibodies rather than fibronectin are immobilised on the sensor chip. The orientation of the antigen is not necessarily uniform when immobilised on the surface and furthermore the reaction can be bivalent, which complicates analysis (Myszka, 1999; Karlsson et al., 1995). In order to produce a more homogeneous surface (Myszka, 1999), rabbit anti-mouse immunoglobulin polyclonal antibodies were immobilised on the sensor chip for specific capture of the murine monoclonal antibodies. The rabbit polyclonal antibodies were covalently immobilised on two flow cells of a CM5 sensor chip at 25 °C, using the standard amine coupling procedure recommended by Biacore® (Johnsson et al., 1991). The sensor chip was initially

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activated for 7 min with an EDC/NHS mixture at a flow rate of 5 µL/min. The rabbit anti-mouse polyclonal antibodies were diluted to 30 µg/ml in 10 mM sodium acetate solution, pH 5. These antibodies were injected into both flow cells for 420 s at a flow rate of 20 µL/min. A level of immobilisation of about 10,000 RU (resonance units) was achieved. The remaining active sites on the sensor chip were blocked with 1 M ethanolamine– HCl solution, pH 8.5. Capture of murine monoclonal antibodies by rabbit polyclonal antibodies was performed at 25 °C. A 0.93 µM solution of antibody in running buffer was passed over one of the flow cells of the sensor chip, the other flow cell acting as a reference. This is necessary in order to correct for certain artefacts such as changes in the refractive index of the solution, non-specific binding and baseline drift (Myszka, 1999; Karlsson and Fält, 1997). The flow rate was set at 20 µl/min for 360 s. A 60-second stabilisation period completed the procedure. For experiments on affinity in solution, mixtures containing murine anti-fibronectin monoclonal antibodies and fibronectin were injected onto the sensor chip. A second capture step was therefore necessary, in order to saturate the surface of the sensor chip to prevent binding of free monoclonal antibody onto the surface. This saturation step was performed for both flow cells. This was achieved by passing murine polyclonal antibodies through the cell at a flow rate of 20 µl/min for 720 s followed by a 60-second stabilisation period. In this way, the signal detected on the sensor chip was due solely to the reaction with free fibronectin and not to binding of monoclonal antibody. 2.3.4. Regeneration The same sensor chip can be used for several experiments, on condition that the surface is properly regenerated. This means that the fibronectin and the captured antibodies must be removed from the surface, leaving only active polyclonal anti-mouse antibodies covalently bound to the surface of the sensor chip. A 10 mM glycine–HCl pH 1.7 regeneration solution was adopted in these experiments. It was injected at a flow rate of 30 µl/min for 3 min, followed by a stabilisation period of 1 min. 2.3.5. Affinity at the sensor surface It is possible to capture the murine monoclonal antibodies on the sensor chip (Section 2.3.3) using a programme proposed by Biacore® called “kinetic affinity” and the human fibronectin is then injected. The latter is introduced at a flow rate of 30 µl/min for 700s with a dissociation time of 600s, on the two flow cells of the sensor chip. Various concentrations of fibronectin are used, ranging from 0.32 µM to 2.5 nM. 2.3.5.1. Model used for curve-fitting. Curve-fitting of the experimental data enables the association and dissociation rate constants and the equilibrium dissociation constant to be determined. Of the models proposed by Biacore®, the “1:1 binding” model was the one that gave the best fit (the lowest χ2). It is the simplest model and describes the interaction between an analyte A and a ligand B: A + B⇌AB. The association rate ka (in L/(mol s)) corresponding to the number of complexes formed per second in a molar solution of fibronectin and antibody, is defined by the formula d½AB = ka ½A½B: dt

Where [A], [B] and [AB] are the concentrations of A, B and the AB complex.The dissociation rate constant kd (in s− 1), corresponding to the portion of the complex that dissociates in 1 s, is given by the formula:− d½AB = kd ½AB. dt Association and dissociation actually occur at the same time. Furthermore, association is equal to dissociation at equilibrium, resulting in an equilibrium dissociation constant kd of KD = ½A½B ½AB = ka : A high KD therefore means that there is low affinity between the analyte and the ligand. By fitting the analytical expressions of the response R(t) (Appendix C) to the R(t) curves in RU obtained in real time by the Biacore® system, it is possible to deduce these various constants, ka, kd and KD, that characterise the binding of the analyte (fibronectin) to the ligand (antibody). 2.3.6. Affinity in solution To perform this type of experiment, several solutions must be prepared containing a mixture of murine anti-fibronectin monoclonal antibodies and fibronectin. The antibody concentration in these solutions differ (from 0.58 µM to 1.0 × 10− 2 pM) while the fibronectin concentration is kept constant (80 nM). These solutions are placed at 4 °C for about 10 h. After this reaction, the lower the initial antibody concentration, the higher the concentration of free fibronectin will be. When these solutions pass over the sensor chip coated with antibody, only this free fibronectin can bind to the surface of the sensor chip. Using a calibration curve determined previously by passing fibronectin solutions of different concentration (between 0.32 µM and 1.0 × 10− 2 pM) through the system, the concentration of free fibronectin in these mixtures can be determined. 2.3.6.1. Data analysis. As stated above, the equilibrium dissoci½A ½B  ation constant was given by the formula: KD = free½ABfree where A is the analyte (fibronectin) and B the ligand (murine monoclonal antibodies). ½A AB½B AB Hence KD = tot ½ABtot where Atot and Btot are the total concentrations of the analyte and the ligand 2

KD :AB¼Atot :Btot −ABðAtot þBtot ÞþAB : Therefore AB2 −ABðAtot þBtot þKD Þ + Atot :Btot ¼ 0. Which represents a second degree equation where the concentration of the AB complex is unknown. This gives: A + Btot + KD AB = tot  2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðAtot + Btot + KD Þ2 −A :B : 4 tot tot

If Afree = Atot − AB, then:

Afree

A B K = tot tot D  2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðAtot þBtot þKD Þ2 −A :B 4 tot tot

This equation can be fitted to the curve representing Afree, i.e. the concentration of free fibronectin plotted against the total concentration of murine monoclonal antibodies Btot. If the total quantity of fibronectin, Atot, is known, the value of KD can therefore be derived. Each type of experiment was performed independently in triplicate.

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3. Results The KD, kd and ka values obtained with the various methods are given in Table 1. 3.1. ELISA tests Fig. 1 illustrates the determination of KD using the method described by Friguet and his co-workers (Friguet et al., 1985). Then, based on “Bobrovnik's theory”, (A0 −A)/A was plotted against CFN (Fig. 2A1). In the experiment performed here, the antibody concentration in the mixture was maintained at 5.7 nM, while the fibronectin concentration ranged from 8.9 nM to 0.57 µM. Therefore at least at the highest concentrations of fibronectin, it is certain that the condition CFN ≫Ci (where Ci is the concentration of the antigen–antibody complex) was fulfilled. This curve is clearly convex, which supports the assumption that a mixture of two antibody–antigen complexes of different affinity is present. In order to deduce these constants it was necessary to plot the curve A CFN against A (Fig. 2A2), and resolve the system of 4 equations and 4 unknowns described in Appendix B. This system was resolved using Matlab software, which enabled the first determination of the absorbance of both antibodies in the absence of antigen, A01 and A02, as well as the equilibrium dissociation constants KD1 and KD2. Then, the second determination of this set of constants was achieved by fitting the data to Eq. (1) according to “Stevens's method”, Fig. 2B. The dissociation rate was given by the method of Larvor, Fig. 3 (Larvor et al., 1994). 3.2. Determination of the affinity at the sensor surface by SPR Biacore®'s “kinetic affinity” programme was used to measure the affinity at the sensor surface. A sensorgram was recorded, representing the difference between the signal detected on flow cells 2 and 1 of the sensor chip, plotted against time (Fig. 4). Running buffer was introduced at time t=0 of the sensorgram.

Table 1 Table outlining the various experimental methods, giving the values of the following constants: equilibrium dissociation constant, KD (mol/L); absorbance A0i, proportional to the concentration of the antibody involved in the complex formation characterized by KDi; dissociation rate constant, kd (s− 1); and association rate constant, ka (L/(mol s)). KD (M) ELISA (1.3 ± 0.6).10− 9 Friguet ELISA KD1 = (2.6 ± 0.9) 10− 9 Bobrovnik A01 = (2.4 ± 0.3) KD2 = (6 ± 3) 10− 7 A02 = (0.18 ± 0.07) KD1 = (1.1 ± 0.5) 10− 9 ELISA Stevens A01 = (2.4 ± 0.3) and KD2 ≥ 10− 7 Bobrovnik A02 = (0.11 ± 0.04) ELISA – Larvor SPR (4.8 ± 0.3) 10− 7 solution SPR (1.5 ± 0.2) 10− 8 surface

kd (s− 1)

ka (L/(mol s))

–

–

(3.6 ± 0.7) 10− 4 – –

–

(1.8 ± 0.4) 10− 4 (1.2± 0.2) 104

Fig. 1. Determination of KD using the ELISA method proposed by Friguet for a plate coated with 18 nM of fibronectin. On the x-axis, x = (A0 − A)/A0 where A0 is the measured absorbance of the sample containing antibody alone and A is the absorbance for a given well. y is proportional to the fraction of bound antibody in solution, divided by the concentration of free fibronectin in solution in the mixture: y =

A0 −A A0



CFN −CAb

 : Fitting the experimental data

A0 −A A0

points to a straight line gives: y = − 6.00 × 108× + 5.66 × 108 where KD is between 1 and 2 nM.

Between points A and B, murine anti-fibronectin monoclonal antibodies were injected into flow cell 2. These molecules bound to the primary antibody, increasing the signal on the sensorgram. At point B, injection of antibody was replaced by flushing with running buffer. Between points C and D, fibronectin was introduced into both flow cells. It bound to the anti-fibronectin antibodies of flow cell 2. The signal on the sensorgram therefore increased again. At D, a flush step followed the injection of fibronectin. The regeneration phase took place between E and F, and the anti-fibronectin antibody/fibronectin complexes dissociated from the rabbit polyclonal antibodies. The signal on the sensorgram returned to the baseline level obtained at time t=0. It is the signal between points C and E, i.e. the phases of association and dissociation of fibronectin on the anti-fibronectin antibodies that is subjected to curve-fitting to obtain the association and dissociation rate constants. To obtain a more robust fit, the ‘kinetic affinity’ programme requires several sensorgrams using different concentrations of the analyte, i.e. fibronectin (Fig. 5). The signal detected on the sensor chip, in RU, intensified as the concentration of the fibronectin solution increased. The mean values and standard deviations of the constants were calculated after curve-fitting. 3.3. Determination of the affinity in solution by SPR The sensorgrams obtained to determine the affinity in solution resemble those in Fig. 4A. The only difference is an extra step where murine polyclonal antibodies are injected, between points B and C, to saturate the surface. The calibration curve was obtained from the sensorgrams by plotting the quantity of bound fibronectin (the difference between the signal, in RU, at points E and C) against the fibronectin concentration in solution. The response, shown in grey, was between 16 and 130 RU (Fig. 6A). The black triangles on the same figure represent the signal obtained for the samples, i.e. the portion of fibronectin that remained free after reacting with the antibodies in solution in the mixture.

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Fig. 2. ELISA for a 96-well plate coated with 18 nM fibronectin. A0 and A are the absorbances measured in the absence of fibronectin and for a given concentration of fibronectin, CFN, respectively. A) “Bobrovnik's method”. A1) The graph of (A0 − A)/A versus CFN is a convex curve, which means that at least 2 populations of complex of different affinity are present. A2) The graph of A CFN versus A and the equations for asymptotes 1 and 2 (A CFN = − 3.49 × 10− 9 A + 9.75 × 10− 9 and A CFN = − 9.40 × 10− 7 A + 2.15 × 10− 7 respectively) result in a system of 4 equations and 4 unknowns, which can be used in particular to determine KD1 and KD2. B) “Stevens's method”. Measured absorbance A versus fibronectin concentration CFN fitted to Eq. (1) by nonlinear regression.

On injection of the samples, this fibronectin binds to the antifibronectin antibodies captured on the sensor chip. The responses obtained were between 51.3 and 72.5 RU. The corresponding fibronectin concentrations calculated from the calibration curve ranged from 45 nM to 86 nM. These values are represented on Fig. 6B by black squares, plotted against

the initial concentration of monoclonal antibody in the sample, which ranged from 0.58 µM to 1.0 × 10− 2 pM. These values, representing the concentration of free fibronectin, plotted against antibody concentration, are curve-fitted to give the equilibrium dissociation constant KD. 4. Discussion

Fig. 3. Determination of kd, using Larvor's ELISA method. x-axis: the −At dissociation time, in s. y-axis: logarithmic plot of AA∞∞−A where At is the 0 absorbance at time t, and A∞ is the absorbance at the end of the experiment, for t = 90 min. The slope of the straight line is −kd.

In this study, the association rate constant ka was determined for the fibronectin/monoclonal antibody complex only when the latter was anchored to a surface. The dissociation rate constant kd and the equilibrium dissociation constant KD were calculated for the same complex forming on a surface or in solution. The results obtained here for the ka were between those measured by Pellequer (3× 105 and 0.05 × 105 L/(mol s)) using a Biacore instrument on a different antibody–antigen complex (Pellequer and Van Regenmortel, 1993). The kd values found for the formation of the complex in solution by ELISA (Larvor's method) and on a surface by SPR are of the same order of magnitude and correspond to those cited in the literature for different antibody–antigen complexes (Larvor et al., 1994; Malmborg et al., 1996).

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Fig. 4. Description of the reactions taking place at the surface of the Biacore® sensor chip during a “kinetic affinity” experiment. Flow cell 1 acts as a reference surface. At point A: on flow cell 2, murine anti-human fibronectin monoclonal antibodies are introduced onto the sensor chip coated with rabbit anti-mouse polyclonal antibodies. At point B: on flow cell 2, the antibodies introduced previously are bound to the sensor chip. A flushing phase starts on flow cells 1 and 2. At point C: human fibronectin is injected into both flow cells. At point D: fibronectin injection is stopped, a flushing phase is started in both flow cells. At point E: the regeneration phase is started in both flow cells. At point F: regeneration is complete. Running buffer is injected into both flow cells. A) Sensorgram or difference in the signal (in RU) between flow cells 2 and 1 detected by the Biacore® versus time. B) Diagram showing the reactions at the surface of the sensor chip: the black Ys represent rabbit anti-mouse polyclonal antibodies. The grey Ys represent murine anti-fibronectin monoclonal antibodies. The ovals symbolise fibronectin molecules.

Friguet's ELISA method was used to determine an equilibrium dissociation constant, KD, for the formation of the antibody–fibronectin complex in solution. However, the use of a more recent method proposed by Bobrovnik revealed the presence of 2 dissociation constants at equilibrium for the same complex, which differed by 2 orders of magnitude. This theory showed also that the mean concentration of antibody involved in the formation of high affinity complex is one order of magnitude higher than the second one. The latest method, suggested by Stevens, also allowed to determine A01 and A02 values which are close to those obtained previously by “Bobrovnik's method” (Table 1). The resulting values for KD1 are very similar whatever the method used. On the other side, using “Stevens's method” to analyse our experimental data does not allow to determine very precisely KD2. Indeed if it is possible to assert that KD2 ≥ 10− 7 M, the correlation

coefficient resulting from the fit is not sufficiently discriminating to arbitrate between the higher values. A possible explanation is that Eq. (1) involved in the fit contains two terms depending on the fibronectin concentration (CFN) but also on A01, Ka1 (=1/KD1) and A02, Ka2 (=1/KD2) respectively. For KD2 ≥ 10− 7 M, in our experimental conditions (CFN ≤ 5.67 × 10− 7 M), the second term of Eq. (1) varies weakly with CFN compared to the first term and thus does not allow a more precise estimation of KD2. Theoretically, increasing CFN would also increase the variation of this term but unfortunately experimental absorbance values obtained would not be different from blank. The subsequent signal becomes therefore unusable. The existence of two equilibrium dissociation constants could potentially be explained by previous studies such as those conducted by Colman's group on the influenza virus

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L. Heinrich et al. / Journal of Immunological Methods 352 (2010) 13–22

Fig. 5. Affinity measurement on the sensor surface using Biacore®: curve-fitting (in black) of the experimental data (in grey) corresponding to phases of association and dissociation of fibronectin at various concentrations on the monoclonal antibody anchored to the sensor chip. Starting from the bottom, the fibronectin concentrations are: 2.5 nM, 5.0 nM, 10 nM, 20 nM, 40 nM, 80 nM, 160 nM, and 320 nM. These curves can be used to determine ka, kd and KD.

and an antibody (Colman et al., 1987), by Sheriff's group on lysozyme and its monoclonal antibody (Sheriff et al., 1987) or by Raman on cytochrome C and a monoclonal antibody (Raman et al., 1992). These showed that, on formation of the

complex, conformational change in the 3-dimensional structure could occur, particularly on the antigen when the epitope was a flexible portion of the structure. As described by Friguet (Friguet et al., 1989), one can imagine that in some cases association is a 2-step rather than a 1-step process: the antibody initially binds rapidly to the antigen with a relatively low affinity (in our case a KD of about 0.1 µM). Then a second step, involving a conformational change of the complex, appears to take place. It appears to result in a more stable complex and higher interaction energy between the antibody and the antigen (in our study, a KD of about 1 nM). When the affinity of the complex in solution was measured using the Biacore® technique, a single KD value was obtained, corresponding to the higher of the 2 values found by Bobrovnik's method. Indeed, using this technique, KD was determined from the concentration of free fibronectin in solution which then bound to the surface. However, the antibody–antigen complexes with the lowest affinity will release their fibronectin first during the relatively short contact time between the solution and the sensor chip. The affinity determined for the formation of the complex on the surface of the Biacore sensor chip lies between the 2 values calculated using Bobrovnik's method for the formation of complexes in solution. This could be explained by the fact that conformational rearrangement of the complex can be observed at the surface (leading to a relatively low KD) or cannot be observed at the surface (leading to a higher KD). 5. Conclusion

Fig. 6. A) Affinity in solution by SPR. A) Calculation of the concentration of fibronectin CFN remaining free in solution. Grey circles: calibration curve for fibronectin bound to the monoclonal antibodies. Black triangles: response in RU and calculation of the concentration of fibronectin, CFN, remaining free after reacting in solution with the monoclonal antibodies for about 10 h at 4 °C. B) The free fibronectin concentration is calculated (CFN calculated (mol/L)) from the calibration curve plotted against the antibody concentration in the solution, CAb (mol/L). The KD can be calculated after curve-fitting.

The equilibrium and kinetic constants that characterise the formation of an antibody–antigen complex were compared using different techniques, Biacore® and ELISA. In particular, the dissociation rate constant kd proved to be similar for the formation of the complex in solution, using Larvor's ELISA method, and on a surface using the SPR technique. Furthermore, the equilibrium dissociation constant(s), KD, were determined for antibody–antigen association on a surface and in solution using SPR. They were also calculated for the formation of the complex in solution by ELISA, using two methods from the same group, the first one described by Bobrovnik and the second one recently published by Stevens and Bobrovnik. To our knowledge,

L. Heinrich et al. / Journal of Immunological Methods 352 (2010) 13–22

this is the first time that such a comparison has been made. The values obtained in the various cases are not necessarily similar but they are consistent and justifiable because the phenomena demonstrated in each approach are not being observed under the same conditions. Our results highlighted the interest of using complementary methods to get access of equilibrium or kinetics constants of a biological reaction. Acknowledgements Our deep thanks go to Cyril Pailler-Mattei and Olivier Roualdes for their help in preparing the figures, Christian Heinrich for the calculations performed with Matlab, Mustapha Moulsma for helpful discussion on nonlinear regression and Christophe Quétard and Madame Le Professeur Sylvie RicardBlum for their advice on the Biacore system. We would also like to thank Anne-Marie Freyria for her careful proofreading of the manuscript. Finally, we are grateful to the company Novotec for providing the monoclonal antibodies. Appendix A. Analysis of the ELISA test using the method described by Friguet The following formula is applied: 1 KD

A0 −A A0

CFN −CAb



 =

A0 −A A0

  where A0 is the absorbance measured for the 1− A0A−A 0

wells that reacted with the sample containing the monoclonal antibody in the absence of antigen, A is the absorbance for a given well, CAb is the total concentration of monoclonal antibody and CFN is the total concentration of antigen in A0 −A A0

  solution. A line y =a x + b is plotted, where y = CFN −CAb A0A−A 0 and x = A0A−A . The slope of this line is therefore equal to −1/KD 0 and the y-axis intercept point is 1/KD. The mean value of KD and its standard deviation are determined using the 4 plots obtained for the 4 fibronectin concentrations coating the 96-well plate. Appendix B. Analysis of the ELISA test described by Bobrovnik System of 4 equations and 4 unknowns, I1, I2, p1 and p2, deduced from the curve A CFN versus A. I1 is the intersection of asymptote 1 with the x-axis and I2 is the intersection of asymptote 2 with the y-axis. p1 and p2 are the slopes of the respective asymptotes 1 and 2 (Fig. 2A2). lim A¼A01 + A02 = I1

CFN→0

lim A:CFN =

CFN →∞

lim CFN→0

A01 A + 02 = I2 Ka1 Ka2

dðA:CFN Þ A01 + A02 =− = p1 dðAÞ A01 Ka1 + A02 Ka2

2 2 dðA:CFN Þ A01 Ka2 + A02 Ka1 =− = p2 CFN→∞ dðAÞ Ka1 Ka2 ðA01 Ka2 + A02 Ka1 Þ

lim

It is possible to calculate Ka1 and Ka2, the equilibrium association constants that characterise the first and second complex, respectively: Ka1 = 1/KD1 and Ka2 = 1/KD2.

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Appendix C. Determination of KD, kd and ka from the response versus time plot obtained on the Biacore® system Association and dissociation occur simultaneously, hence d½AB = ka ½Afree ½Bfree −kd ½AB dt The concentration of free ligand at the surface is given by Bfree ¼Btot AB, hence d½AB dt = ka ½Afree ½Btot AB−kd ½AB where [Afree] is the concentration of analyte in solution. It is maintained at a constant level ([Afree] =C) throughout the association phase, by setting the flow rate on the Biacore®. [AB] is the concentration of the complex formed at the surface, termed R, and measured directly in RU. Initially the concentration Afree is high and the concentration AB is low: the association phase predominates. At the end of the experiment, [Afree] and [Bfree] decrease whereas [AB] increases and the dissociation phase therefore prevails. Btot is the total quantity of ligand on the sensor chip, and corresponds to the maximum quantity of complex that can form, Rmax. This gives therefore: d½R = ka C½Rmax −R−kd ½R dt Which after integration gives RðtÞ = Req −Req ⋅e−kObs ⋅t (C1). Where Kobs = ka ⋅ C + kd and Req is proportional to the concentration of complexes formed at equilibrium Req = CRmax kd . Cþk

a

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