Kinetic analysis of interactions between bispecific monoclonal antibodies and immobilized antigens using a resonant mirror biosensor

Journal of Immunological Methods 280 (2003) 183 – 202 www.elsevier.com/locate/jim

Protocol

Kinetic analysis of interactions between bispecific monoclonal antibodies and immobilized antigens using a resonant mirror biosensor Dmitriy A. Dmitriev a,*, Yulia S. Massino b, Olga L. Segal b a b

Department of Chemistry, Division of Chemical Enzymology, Moscow State University, Moscow, Russian Federation Institute of Higher Nervous Activity and Neurophysiology, Russian Academy of Sciences, Moscow, Russian Federation Received 20 May 2003; accepted 4 July 2003

Abstract A resonant mirror biosensor (IAsys) protocol is described for the comparative kinetic analysis of the ability of monoclonal antibodies (Mabs) and bispecific antibodies (Babs) to bind immobilized antigens. The protocol has been optimized and validated using the panel of affinity-purified antibodies, including two parental Mabs, one specific to human immunoglobulin G (hIgG) and another specific to horseradish peroxidase (HRP), and a Bab derived thereof by cell fusion (anti-hIgG/HRP Bab). The real-time kinetic analysis of antigen – antibody interactions using this protocol allows to demonstrate the differences in the avidity of bivalently binding Mabs and monovalent Babs. As shown in our previous study [J. Immunol. Methods 261 (2002) 103], the observed equilibrium association constants (Kass) determined by IAsys using this protocol yield figures almost overlapping with those obtained by solid-phase radioimmunoassay (RIA). The described protocol is suited for the investigation of the effects of valency on the binding properties of antibodies. It also may be applied for the selection of Mabs and Babs with desired features, for different fields of application. D 2003 Elsevier B.V. All rights reserved. Keywords: Resonant mirror biosensor; IAsys; Kinetic constants; Bivalent interaction; Bispecific antibodies

Abbreviations: Babs, bispecific monoclonal antibodies; CMD, carboxymethylated dextran; EDC, N-ethyl-NV-(3-dimethylaminopropyl)carbodiimide hydrochloride; F(ab), antibody fragment produced by proteolysis; hIgG, human immunoglobulin G; HRP, horseradish peroxidase; Kass, observed equilibrium association constant; kass, observed association rate constant; kdiss, observed dissociation rate constant; kon, observed rate constant; Mabs, monoclonal antibodies; NHS, N-hydroxysuccinimide; PBS/T, 0.025 M sodium phosphate buffer (pH 7.4) with 0.15 M sodium chloride and 0.5 ml/l Tween 20. * Corresponding author. Institute of Higher Nervous Activity and Neurophysiology, Russian Academy of Sciences, ul. Butlerova 5a, Moscow 117485, Russia. Tel.: +7-95-140-7620; fax: +7-95-9528940. E-mail addresses: [email protected], [email protected] (D.A. Dmitriev). 0022-1759/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-1759(03)00271-0

1. Type of research With the widespread use of monoclonal antibodies (Mabs) in solid-phase immunoassays, immunohistochemistry and cell targeting has come a need for improved understanding of the mechanisms governing antigen –antibody interactions on the surface of a solid phase, and for methods to evaluate binding parameters of Mabs reacting with immobilized antigens (Crothers and Metzger, 1972; Mason and Williams, 1980; Dower et al., 1984; Karulin and Dzantiev, 1990; Kaufman and Jain, 1992). In the studies devoted to these subjects, it has become common to distinguish between the intrin-

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sic affinity of monovalent binding to solid-phase antigen (true affinity) and the avidity (functional affinity) (Kaufman and Jain, 1992; Mattes, 1995, 1997). True affinity is a basic measure of the binding interaction between two molecules. It refers to the interaction between an epitope and the binding site on one arm of a multivalent antibody (bivalent in case of human immunoglobulin G [IgG]). Avidity refers to the interaction of the antibody with the antigen as a whole, and is the final result of a true affinity, antibody valence, antigen density on a solid phase and steric and statistical factors (Kaufman and Jain, 1992). Obviously, bivalent attachment of IgG molecule to antigens immobilized on a solid phase leads to a larger avidity for the surface than monovalent attachment. Attempts to calculate the augmentation in avidity due to increased valence (frequently termed an ‘‘enhancement factor’’) have been made before, using ELISA, radioimmunological and fluorescent methods (Crothers and Metzger, 1972; Mason and Williams, 1980; Dower et al., 1984; Kaufman and Jain, 1992; Lamarre and Talbot, 1995; Roubey et al., 1995; Davis et al., 1998) and, in recent years, using a biosensor technology (Horenstein et al., 1994; Roggenbuck et al., 1994; George et al., 1995; Gill et al., 1996; Nice et al., 1996; Hall and Winzor, 1997; Muller et al., 1998a). The development of optical biosensor technology has allowed biomolecular interactions to be studied in real time and without the labeling of interacting species. This method seems to be of particular importance in the study of the binding of antibodies to their antigens, as it permits rapid determination not only of association and dissociation equilibrium constants, but also the dissociation and association rate constants (Karlsson et al., 1991; George et al., 1995; Nice et al., 1996). The common approach for the analysis of the effect of bivalence upon equilibrium and kinetic constants was the comparison of antibody fragment produced by proteolysis (F(ab)) and IgG of identical origin. In this experimental model, F(ab) has been used to measure the intrinsic affinity of monovalent binding to immobilized antigen (Mason and Williams, 1980; Dower et al., 1984; Karulin and Dzantiev, 1990; Roggenbuck et al., 1994; George et al., 1995; Nice et al., 1996). However, this approach seems to have some disadvantages. Thus, the differences in the size of IgG molecules and F(ab) fragments may obscure the direct analysis of the effect of bivalence

in biosensor method (Muller et al., 1998a). Besides, as shown in some studies, the Fc region, which is absent in F(ab) fragments, may influence the antibody-binding characteristics in solid-phase system (McCloskey et al., 1997). The alternative approach to measure the intrinsic affinity of Mab binding to solid-phase antigen may be the use of a monovalent antibody keeping the structure of whole-molecule IgG. As shown in our previous studies (Dmitriev et al., 2001, 2002), biologically produced bispecific antibodies (Babs), which are the products of IgG chain recombination in hybrid hybridomas (tetradomas) (Milstein and Cuello, 1983), can be used as such probes. On the one hand, a Bab produced by cell fusion retains the structure of native IgG molecule, being composed of two half-molecules of parental antibodies (Milstein and Cuello, 1983). On the other hand, a Bab molecule bears two different antigenbinding sites and, consequently, is monovalent as regards each of these antigens. Moreover, Babs’ binding sites usually retain the intrinsic affinity of corresponding parental Mabs, as shown in equilibrium-binding experiments in solution (Allard et al., 1992; Smirnova et al., 1997). Babs are considered to be the ideal bioconjugates, which can specifically glue any two different molecules together without the need for chemical conjugation (Cao and Suresh, 1998). They may be used in solid-phase immunoassays and immunochemistry in place of traditional covalently linked enzyme –Mab conjugates and in cell targeting (for review, see Self and Cook, 1996; Cao and Suresh, 1998). The elaboration of experimental protocols for real-time kinetic analysis of Babs binding to immobilized antigens, compared with native antibodies, besides presenting several advantages for the study of antigen –antibody interactions, may enable the selection of appropriate Babs for different fields of application. In the present work, we describe a resonant mirror biosensor (IAsys) protocol for the comparative quantitative analysis of the ability of Mabs and Babs to bind immobilized antigens. This protocol has been optimized and validated using two different Mabs, one specific to human IgG (hIgG) and another specific to horseradish peroxidase (HRP), and a Bab, derived thereof by cell fusion, as described elsewhere (Dmitriev et al., 2002). Moreover, as shown in our previous study (Dmitriev et al., 2002), the affinity constants,

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determined by IAsys with the help of this protocol, yielded figures almost overlapping with those obtained by solid-phase radioimmunoassay (RIA). The protocol allows to investigate the effect of valency on binding properties of antibodies.

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(b) Personal computer working on Windows environment (Windows 95, 98, 2000, NT). (c) IAsys software (Version 1.03) (Affinity Sensors). (d) FASTfit software (Version 1.01) (Affinity Sensors). 3.2. Certified materials for IAsys analysis

2. Time required 2.1. Full kinetic analysis of the interaction between monoclonal antibodies and immobilized antigen

Carboxymethylated dextran (CMD) cuvettes (six sample cells) (Affinity Sensors); product code: FCD0101. 3.3. Chemicals and reagents

For routine analyses of the binding of one species of antibodies (Mab or Bab) on a previously prepared sensor surface, 6 h will suffice. Considering also ligand immobilization, testing regeneration conditions and data analysis, 9 –10 h will be required. Correspondingly, the comparison of the binding of the bivalent (the parental Mab) and monovalent (Bab) versions of the same antibody to immobilized antigen will require about 18– 20 h.

N-Ethyl-NV-(3-dimethylaminopropyl)carbodiimide hydrochloride (EDC) (Sigma, USA), N-hydroxysuccinimide (NHS) (Fluka, Germany), ethanolamine (Sigma), Tween 20 (Sigma), HRP (Calbiochem, USA; Rz> 3.0). The purified human IgG1 (hIgG1) has been provided by T.N. Batalova (Institute of Epidemiology, Moscow). 3.4. Solutions for surface regeneration

2.2. Immobilization of the antigen on the sensor cuvette surface and testing regeneration conditions (a) Covalent immobilization: 50 min. (b) Testing regeneration conditions: 60 min. 2.3. Kinetic analysis of an antibody – antigen interaction

The most common regenerating agents are: acids (10 – 100 mM HCl, 10 –50 mM H3PO4), bases (10 mM NaOH, 100 mM NaHCO3), salts (1 M NaCl) and 20% ethanol. The regeneration procedures corresponding to the assays described in the present protocol may, in principle, be carried out using 50 mM HCl. 3.5. Monoclonal antibodies

(a) Equilibration of cuvette: 3– 9 min. (b) Antibody additions (association + dissociation + regeneration): 13 min. 2.4. Data analysis (Fisons Applied Sensor Technology Fit [FASTFit] software) One hundred and twenty minutes.

3. Materials 3.1. Special equipment (a) The protocol has been optimized on IAsys manual system biosensor (Affinity Sensors, Cambridge, UK).

3.5.1. Antibody production Hybridoma cell lines are used as the sources of Mabs. Babs are produced by the cells of hybrid hybridomas (tetradomas), resulting from the fusion of two parental hybridomas. Antibodies may be purified from the ascetic fluid by affinity chromatography. Cell fusion procedures for the production of hybridomas and tetradomas accepted in our laboratory, antibody purification procedures and methods for testing antibody activity have been described elsewhere (Massino et al., 1992, 1994, 1997; Smirnova et al., 1997; Nikulina et al., 2000; Dmitriev et al., 2001, 2002). The concentrations of purified antibodies in solutions are determined by spectrophotometry, assuming that A280 nm1 cm = 14.0 corresponds to 10 mg/ ml of purified antibodies (Fasman, 1976).

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3.5.2. Criteria of antibody validity for the analysis of avidity effects The biosensor protocol that we present here is suited both for the screening of antibodies (in order to select the best candidates) and for the analysis of the avidity effects. In the latter case, we recommend to prove, in the preliminary experiments, that the parental Mabs and Babs, derived thereof, really have identical affinity constants with respect to soluble antigens. It seems important, because the formation of Babs with altered affinity of antigen-binding sites due to the ‘‘incorrect’’ association of H and L chains is considered to be a rare (Milstein and Cuello, 1984), but yet possible event (Somasundaram et al., 1993). Obviously, the ‘‘abnormal’’ Babs with altered antigenbinding sites are not suitable to measure the intrinsic affinity of monovalent binding to immobilized antigen. The RIA protocols for equilibrium-binding experiments in solution have been described in a number of works (Allard et al., 1992; Smirnova et al., 1997). The binding of immobilized Mabs and Babs with soluble antigens may be compared using ELISA methods (Allard et al., 1992; Smirnova et al., 1997) or biosensor technology (IAsys Cuvette System Methods Guide, 1993). Besides, it should be taken into account, that Babs molecule structure is completely identical to the native immunoglobulin when both ‘‘halves’’ of Babs belong to the same IgG subclass (the parental Mabs are of one IgG subclass). In this case, Babs not only comprise antigen-binding sites identical to parental Mabs, but also have the same structure of the constant part as the parental Mabs. It should be also emphasized that, for the quantitative analysis of antigen– antibody interactions, it is desirable to use affinity purified preparations of Mabs and Babs in binding assays.

neity-binding valence (Kaufman and Jain, 1992). Under such assumptions, antigen– antibody interaction is described in conventional mass action terms. That is:

Kass ¼

½B ; ð½Ab0  ½BÞð½Ag0  ½BÞ

ð1Þ

where terms are: Kass—the observed equilibrium association constant (M 1), [Ab]0—total concentration of antibody (M), [B]—total concentration of bound antibody (equivalent to total concentration of formed antibody– antigen complex) (M), [Ag]0—total concentration of antigen (M). 3.6.2. The model of bivalent binding of Mabs with antigens immobilized on the surface of a solid phase In reality, IgG antibodies may exist in a mixture of monovalently and bivalently bound states on the surface of a solid phase. In this case, the solid-phase methods measure the avidity of Mabs in the given experimental conditions rather than the intrinsic affinity of individual antigen-binding site for antigenic epitope. The proposed model of bivalent binding in heterogeneous systems summarizes previous theoretical elaborations on this subject (Dower et al., 1984; Kaufman and Jain, 1992). A schematic of the bivalent interaction is presented in Fig. 1.

3.6. The theoretical basis of the analysis of the binding of antibodies with immobilized antigens 3.6.1. Equilibrium-binding analysis of antibody binding with solid-phase antigen The IgG antibody is bivalent, capable of binding two antigenic sites under favourable conditions. However, commonly used forms of the analysis of binding data in solid-phase immunoassays model antigen – antibody interaction as a homogeneous, equilibrium, single-step process, exhibiting homoge-

Fig. 1. Schematic of bivalent antibody binding. The bivalent monoclonal antibody in solution [Ab] reversibly binds to a vacant antigenic epitopes at surface concentration [Ag]s (subscript ‘‘s’’ denotes surface concentration and a lack of subscript denotes bulk concentration) to form a monovalently bound complex. The monovalently bound antibody at surface concentration [AbAg]s may then reversibly combine with a vacant antigenic epitopes within arm’s reach of the antibody to form a bivalently bound complex at surface concentration [AbAg2]s (Kaufman and Jain, 1992).

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The process of monovalent binding is characterized by the equilibrium constant of the intrinsic affinity (K1):

K1 ¼

k1 ½AbAgs ¼ ; ðM1 Þ; k1 2½Ab½Ags

ð2Þ

where terms are: [Ab]—the concentration of free antibody (M); ([Ab]=[Ab]0  [B]); k1—association rate constant between the binding site on one antibody arm and antigen (M 1 s 1); k 1—dissociation rate constant between antibody and antigen reactive sites (s 1); [Ag]s—surface concentration of vacant antigenic epitopes; subscript ‘‘s’’ denotes surface concentration and a lack of subscript denotes bulk concentration; [AbAg] s—surface concentration of monovalently bound antibody. The conversion of monovalent to bivalent antibody binding is characterized by the equilibrium constant (K2):

K2 ¼

2½AbAg2 s k2 ¼ ; ðcm2 =molÞ; k2 ½Ags ½AbAgs

ð3Þ

where terms are: k2—association rate constant of conversion from monovalent to bivalently bound antibody (cm2 mol 1 s 1); k 2—dissociation rate constant between bivalently and monovalently bound antibody (s 1); [AbAg2]s—surface concentration of bivalently bound antibody; for other terms, see notes to Eq. (2). The statistical factors of two are introduced due to the fact that, in the first step, IgG (Mabs) can bind at either of its arms but dissociate from only one, while in the second the converse is true. For Babs the second stage is not possible and the statistical factor in this case is equal one. The observed equilibrium association constant, Kass (assuming the model of Eq. (1)) for a given set of experimental conditions is given by:

Kass ¼

½AbAg2 s þ ½AbAgs kass ¼ kdiss ½Ab½Ags

¼ K1 ð2 þ K2 ½Ags Þ; ðM1 Þ;

ð4Þ

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where terms are: kass—the observed kinetic association constant (M 1 s 1); kdiss—the observed kinetic dissociation constant (s 1); for other terms, see notes to Eqs. (1) – (3). Therefore, in the presence of bivalent binding, Kass is not a constant physical value, but depends on the experimental conditions (surface concentration of vacant antigen). The intrinsic affinity of the monovalent interaction (K1) in solid-phase experiments may be measured with the help of monovalent derivatives of antibodies (i.e., F(ab) fragments or their analogues—Babs). 3.6.3. Theoretically expected variations of the observed equilibrium association constant (Kass) depending on the presence or absence of bivalent binding If, for some reasons, a bivalent binding of Mabs is impossible (only monovalent binding occurs) (K2 = 0, Eq. (4)), then Kass for parental Mabs will be equal to 2K1. As Babs molecule carries only one binding site for each antigen, Kass for Babs will be equal to K1. If a bivalent binding of Mabs is taking place, then Kass, as follows from Eq. (4), will be higher than 2K1 (KassH2K1). 3.6.4. The ratio of bivalently and monovalently bound antibodies The described model of bivalent binding may be applied in order to determine the percentage of bivalently and monovalently bound parental Mabs on the surface of a solid phase. From Eq. (3), this ratio may be given by:

½AbAg2 s K2 ½Ags : ¼ ½AbAgs 2

ð5Þ

The value K2[Ag]s is often termed in literature as the ‘‘enhancement factor’’ (Kaufman and Jain, 1992). As can be seen from Eq. (5), this factor is equal to the double ratio of bivalently and monovalently bound antibodies. The ratio of bivalently and monovalently bound Mabs may be obtained from Eq. (4), when the values of Kass for Babs (K1) and Kass for parental Mabs are known.

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3.6.5. Theoretically expected variations of the kinetic parameters depending on the absence or presence of bivalent binding The above-mentioned equations also allow to compare the kinetic parameters of the interaction of parental Mabs and Babs with immobilized antigens. From Eq. (2), the observed association rate constant (kass) for Babs is equal to k1. Usually, it is assumed that kass for parental Mabs is independent of the valence of binding (Karulin and Dzantiev, 1990) and is equal to 2k1. The observed dissociation kinetic constant (kdiss) for Babs is equal to k 1 (Eq. (2)). kdiss for parental Mabs may be obtained from Eq. (4):

kdiss ¼

k1 ; ðs1 Þ: K2 ½Ags =2 þ 1

ð6Þ

Consequently, the rate of dissociation of parental Mabs, which are able to bind bivalently, is significantly lower than the dissociation rate of Babs. If the bivalent binding is not possible, for some reason (K2 = 0), then Babs and Mabs will show identical dissociation rates. 3.6.6. Determination of the observed association and dissociation rate constants and observed equilibrium constant using a resonant mirror biosensor (IAsys) 3.6.6.1. Association rate constant. The rate of formation of antigen– antibody complex (B) is given by the equation: d½B ¼ kass ½Ab½Ag  kdiss ½B; dt

ð7Þ

where [Ag] is the concentration of free antigen; for other terms, see notes to Eqs. (1), (2) and (4). In the cuvette of biosensor IAsys, [Ab] can be considered constant as it is added in large excess, and efficient stirring of the cuvette ensures that the [Ab] remains constant throughout the cuvette. The solution of this equation results in the following pseudo-first order equation (George et al., 1995): ½B ¼ ½Bl ð1  ekon t Þ;

ð8Þ

where [B]l is the equilibrium concentration of antigen – antibody complex for the given concentration of antibody ([Ab]). [B]l is given by: ½Bl ¼

½Ab½Ag0 ; ½Ab þ Kdiss

ð9Þ

where Kdiss (observed dissociation equilibrium constant, M) is given by: Kdiss = kdiss/kass. Therefore, kon (the observed rate constant, s 1) is given by: kon ¼ kass ½Ab þ kdiss :

ð10Þ

In the IAsys, the amount of [B] is measured directly as the response (R) in arc seconds. The [B]l can be termed the extent (E) of the reaction. Thus, the association of the antibody with the immobilized antigen can be described by the following pseudofirst order equation: R ¼ R0 þ Eð1  ekon t Þ;

ð11Þ

where R0 is the response at t = 0. This parameter is intentionally introduced in this equation for correction of possible shift of the response due to the changes of the buffer after the addition of the analyte solution. FASTfit program, specifically designed for biomolecular interaction analysis using the IAsys biosensor, can be used to fit the association curves, obtained with different antibody concentrations, to this pseudo-first order equation, in order to calculate kon, E and R0. As can be seen from Eq. (10), a plot of kon against [Ab] should give a straight line with slope of kass and y-axis intercept of kdiss. 3.6.6.2. Dissociation rate constant. While the kdiss can, in theory, be derived from a plot of kon against [Ab], in practice the errors are, in most cases, too large to allow this. However, in case of a dissociation of the antigen– antibody complex, the reaction can be described by the equation: d½B ¼ kdiss ½B: dt

ð12Þ

This equation makes the assumption that the reaction is occurring in a sufficiently large volume that no rebinding of the free antibodies occurs. By the solu-

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tion of this expression, the following first order equation can be obtained for the dissociation: ½B ¼ ½B0 ekdiss t ;

ð13Þ

where [B]0 is the concentration of antigen –antibody complex at t = 0. In the IAsys, this equation is given by: kdiss t ; R ¼ Rdiss 0 e

ð14Þ

where R0diss is the response at t = 0. FASTfit can be used to fit the data to this equation. A useful way of interpreting dissociation data is to calculate the half-life (t1/2) of the immunological complex: t1=2 ¼

ln2 : kdiss

ð15Þ

3.6.6.3. Equilibrium constants. The association and dissociation equilibrium constants (Kass and Kdiss) are related to the rate constants by the following equation: Kass ¼

1 kass ¼ : Kdiss kdiss

ð16Þ

4. Detailed procedure 4.1. IAsys preparation and maintenance The configuration of the biosensor has been described in detail in a number of works (Buckle et al., 1993; Cush et al., 1993; Davies et al., 1994; George et al., 1995) and in the instrumentation manual (IAsys Cuvette System User’s Guide, 1993). In typical ELISA or other binding assays, the system is usually allowed to reach equilibrium by use of a long incubation time, typically of several hours. The binding analysis performed on IAsys does not have to reach equilibrium. The system allows the biospecific reactions to be watched as they happen, so revealing the dynamics as well as the strength of binding. Analysis

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is carried out rapidly and conveniently, using small amounts of material without the need for labels. IAsys achieves this by using an evanescent field to measure minute changes in refractive index and thickness at the surface of an optical biosensor, the resonant mirror. IAsys manual system biosensor uses a cuvette system, in which the individual micro-cuvette, containing a reaction chamber with a working volume of 50– 200 Al (the well of the cuvette), can be placed into the sensing chamber. The reaction chamber is vibrostirred using a stirrer, which is installed into the sensing chamber. The stirrer vibrates vertically with a frequency of 126 Hz at amplitude selected by the user. The maximum displacement is 0.5 mm, which is equivalent to 100 units of device. The sensing chamber is thermally controlled by the circulating water bath. Samples and buffers are added directly to the cuvette using a pipette, and evacuated by means of a tube attached to a peristaltic pump. The cuvette can be removed and stored for some days at 4 jC before reuse. System preparation and routine maintenance will not be described in detail since they are presented in the instrumentation manual (IAsys Cuvette System User’ Guide, 1993). These procedures are almost entirely automated and computer-controlled through interactive IAsys software in an icon-based windows environment. We would like to pay the special attention to the washing procedures between the addition of different solutions, because these routine procedures may be the sources of serious artifacts. In IAsys, washing may be performed by addition of 200 Al of washing solution (e.g., PBS/T) followed by its removing with the help of a peristaltic pump. To our experience, this action should be repeated three times, to be sure that the former solution is completely evacuated. It is connected with the existence of cuvette dead volume, not allowing the complete evacuation of the contents at once. (a) The first step is to allow the micro-cuvette to equilibrate with buffer, until the reading (the baseline) stabilizes. Place the new CMD cuvette in the instrument. Wash three times with PBS/T (0.025 M sodium phosphate buffer (pH 7.4) containing 0.15 M sodium chloride and 0.5 ml/l Tween 20). For washing, use every time 200 Al of PBS/T. Leave for 10 min in the third portion of PBS/T buffer to allow the baseline to stabilize. Begin data acquisition and gather 5 min of

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baseline data. All measurements are performed at 25 jC. The stirring rate is set to 65. The data are collected using IAsys software. The resonant angle is sampled every 1 s. 4.2. The immobilization of the antigen on the sample cell surface by covalent amine coupling and testing of regeneration conditions The CMD cuvette provides a readymade hydrophilic matrix containing carboxymethyl groups that are suitable for amine coupling chemistries. The dextrans’ carboxymethyl groups are converted to active NHS-esters. Subsequently, the primary amino groups of a protein displace NHS, resulting in the formation of peptide bonds between the protein and the matrix. Moreover, the dextran matrix, being threedimensional, allows for higher ligand loading than would a planar surface. For more details, see the instrumentation manual (IAsys Cuvette System Methods Guide, 1993). When the reading has stabilized to F 3 arc seconds/min, the next stage is to activate the CMD hydrogel on the micro-cuvette with EDC/NHS mixture, so that ligand can be immobilized onto it. (a) Prepare the activating mixture by mixing 400 Al of 0.1 M NHS in distilled water and 400 Al of 0.4 M EDC in distilled water (NHS and EDC solutions must be prepared immediately before use). (b) Remove PBS/T and wash three times with 200 Al portions of EDC/NHS mixture. Leave for 8 min in the third portion of EDC/NHS to activate the gel. The display will show a change in refractive index, which should stabilize at a higher value (Fig. 2). Wash three times with 200 Al portions of PBS/T buffer to remove unreacted EDC/NHS mixture; moreover, leave in the third portion of PBS/T for 2 min (to allow the microcuvettes to re-equilibrate with buffer). Subsequently, all washing procedures (using PBS/T or other solutions) should be performed by the same manner (unless stated otherwise). At the next stage, the ligand (the antigen, following this protocol) should be immobilized on CMD hydrogel on the surface of the micro-cuvette, following the recommendations of the IAsys Cuvette System Methods Guide (1993). The immobilization conditions should be optimized with regards to the pH of the coupling buffer. The optimum pH will be approxi-

Fig. 2. Immobilization of antigen to the sensing surface. This figure shows the typical profile obtained following immobilization of the antigen to the carboxymethylated-dextran cuvette. The alteration in resonant angle (response) is shown on the y-axis, with the time of the reaction on the x-axis. Points (1) – (4) indicate addition of: (1) EDC/NHS, (2) antigen in immobilization buffer, (3) 1 M ethanolamine pH 8.5 and (4) 10 mM HCl. The final antigen surface is ready at point (5). The sudden alteration in the response are due to the bulk shift seen when altering buffer.

mately related to the pI of the ligand. Check list for optimization of immobilization via EDC/NHS is given in IAsys Cuvette System Methods Guide (1993). The ionic strength should be as low as possible but the buffer concentration should be sufficient to control the pH of the ligand solution. Typically, this will be so with buffers of 25 mM or less (IAsys Cuvette System Methods Guide, 1993). The optimization of the concentration of the biomolecule on the CMD matrix also is an essential part of the coupling procedure. Concentration of the ligand should be enough to give reliable response but low enough that mass transport limitations and rebinding of analyte are taking place. The surface concentration of ligand depends on the concentration of ligand in immobilization buffer during coupling procedure and contact time. Typical conditions that are used: 25 –50 Ag/ml of ligand in immobilization buffer; contact time about 15 min (IAsys Cuvette System Methods Guide, 1993; George et al., 1995). (c) Wash three times with immobilization buffer (10 mM sodium acetate buffer (pH 5.5) in our case), re-equilibrate for 2 min in the third portion of the buffer. Add 200 Al of ligand solution (25 Ag/ml of antigen in immobilization buffer) for 15 min. Wash three times with PBS/T, leave in the third portion of PBS/T for 2 min.

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(d) Add 200 Al of 1 M ethanolamine hydrochloride (pH 8.5) for 2 min to block unreacted activated carboxyl groups. Wash three times with PBS/T, leave in the third portion of PBS/T for 2 min. (e) Perform four successive washings: (1) with 10 mM HCl, (2) with PBS/T, (3) again with 10 mM HCl and (4) with PBS/T. Every washing should be performed three times. Leave for 2 min after each washing. The cuvette is washed twice with 10 mM HCl before use to remove any non-covalently bound protein. These procedures suggest that epitopes recognized by antibodies under study are not destroyed by 10 mM HCl. (f) Save the experimental curve of immobilization in separate file using IAsys software. The amount of immobilized antigen is measured by subtracting the initial (‘‘empty’’ cuvette) from the final baseline level (PBS/T) using IAsys software. Using the guidelines supplied by the manufacturer (IAsys Cuvette System Methods Guide, 1993), 200 arc seconds correspond to immobilization of approximately 1 ng/mm2 antigen surface density. (g) Test the stability of the immobilized antigen to regeneration conditions. This is done by repeated cycles of antigen –antibody interaction: a constant concentration of the antibody is added (e.g., 500 nM, that corresponds to the middle of the concentration range required) followed by 2 min treatment with a regeneration solution. Depending on the interaction being studied and the ligand of interest, different regeneration solutions are used, for example: low pH (HCl, glycine HCl), high pH (carbonate, hydroxide). The most common regenerating agents are mentioned in Section 3.4 (in our experiments, 50 mM HCl has been used). Past experience (affinity purification of ligand) and the analysis of literature (start with ‘‘IAsys Cuvette System Methods Guide, 1993’’) may help to select the optimal regeneration conditions. As a rule, regeneration conditions are similar to those used in affinity chromatography purification of ligand. If unsure, start with the mildest conditions to preserve ligand activity. A suitable regenerating agent provides full recovery of the baseline level at the end of each cycle while preserving antigen activity (checked by the constancy of analyte binding level in repeated cycles). The details of these procedures are indicated below in Section 4.3.

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The prepared antigen-coupled cuvette may be used to analyze the binding of the corresponding parental Mab (specific to the immobilized antigen) and its monovalent derivative (Bab). 4.3. Binding kinetics analysis IAsys Cuvette System Methods Guide (1993) gives the detailed list of important considerations in obtaining good kinetic and affinity measurements from the IAsys range of optical biosensor. Here, we touch upon the most important moments related to the use of the present protocol. 

A suitable range of antibody concentrations should be analyzed. For antigen – antibody interactions for which an approximate affinity constant is known, it is recommended to use a range of antibody concentrations in the micro-cuvette from 0.1 to 10 times the Kd value. Usually, the responses produced by these antibody concentrations during the first 5 min of association do not exceed 80 arc seconds. At these values, the experimental data usually fit well to pseudo-first order binding kinetics (Eq. (11)).  In general, buffer conditions for analyte binding depend on the particular experiment and binding partners. For the study of antigen – antibody interactions in IAsys, it seems reasonable to use PBS/T, which is widely used in immunochemical methods (ELISA, RIA). Moreover, the association and dissociation should be analyzed in the same buffer. This buffer also is used for the preparation of antibody dilutions. Matching buffers will eliminate steps in signal on sample addition. It should be also emphasized that a suitable range of concentrations should be diluted into the cuvette. Addition of samples by dilution into the cuvette (usually 1 in 10) avoids disturbance of the baseline. (a) Dock the sensor cuvette containing the immobilized antigen. (b) Prepare the antibody solutions to be added into the given micro-cuvette. Fifteen or 20 different concentrations of the antibody under investigation, e.g., a dilution series ranging from 5000 to 10 nM in PBS/T, will suffice. The regeneration solution should also be prepared.

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(c) Equilibrate sensor cuvette for 3 –9 min in 180 Al of PBS/T buffer. (d) Add 20 Al of antibody solution to 180 Al of PBS/T followed by association in PBS/T buffer. In general, the association time of 5 min is adequate. (e) Remove antibody solution. Wash the cuvette three times in 200 Al portions of PBS/T buffer, and leave for 5 min in the third portion of PBS/T for dissociation. (f ) Regenerate the immobilized antigen by washing the cuvette three times in 200 Al portions of regenerating solution (in our experiments, 50 mM HCl has been used). Leave for 2 min in the third portion. Wash three times in PBS/T for re-use. (g) Plan out the experiment. It should be taken into account, that for analysis of Bab’s interaction with the immobilized antigen, compared with native antibody (the parental Mab specific to CMDcuvette coupled antigen), each antibody (Mab and Bab) should be analyzed at least at five different concentrations (each corresponding to antigen – antibody binding cycle as described in (c) – (f)). It is recommended to select a range of antibody concentrations, which produce the responses not exceeding 80 arc seconds during the first 5 min of association. The following approach may be used to select the optimal range of antibody concentrations. Start with maximal antibody concentration (i.e., 5000 nm). If this concentration produces the response exceeding 80 arc seconds during the first 5 min of antigen – antibody interaction, analyze 10-fold lower antibody concentration (500 nM). If this concentration also gives the same effect, take the next 10-fold dilution (50 nM), until the response not exceeding 80 arc seconds (during 5 min contact time) will be obtained. This dilution will show the upper limit of the optimal range of antibody concentrations for real-time kinetic analysis. All measurements are run at least in duplicate. (h) Save the experimental data of association and dissociation in separate file using IAsys software. 4.4. Data processing and analysis Data is analyzed using the FASTfit program (Fisons Applied Sensor Technology, UK), specifically designed for biomolecular interaction analysis using

the IAsys optical biosensor. It performs the detailed mathematical analysis of the association and dissociation curves obtained in IAsys. The FASTfit program allows the user to select areas of the graph (analysis regions) covering the baseline, association and dissociation of the reaction. In addition, the user identifies the start points of both the association and dissociation phases of the reactions. The instrumentation manual (IAsys Cuvette System FASTfit Guide, 1993) gives the detailed information on how to use FASTfit software to determine the kinetic parameters of interaction from data obtained using IAsys. (a) Open FASTfit program and open the fail with experimental data for the antibody under investigation. (b) Specify antibody concentration for each region you are going to analyze (baseline, association and dissociation). (c) Select the piece of the baseline corresponding to 1 min preceding the association phase. (d) Identify the start of the association phase (the moment of the addition of the antibody sample). The association analysis region is selected such that the first point is 5 s after the addition of the antibody sample (the start point of the association). This allows time both for efficient mixing to occur and for any bulk shift, caused by a change in buffer, to be finished. The end of the association analysis region is selected at the end of the 5 min of data. (e) Identify the start of the dissociation phase (the moment of the addition of the buffer). The dissociation analysis region is selected such that the first point is 10 s after the last wash in PBS/T (the start point of the dissociation). This allows time both for nonspecific dissociation to occur and for any bulk shift, caused by a change in buffer, to be finished. The dissociation analysis may be finished after 5 min of data. (f ) Fit the experimental data for each antibody concentration to Eqs. (11) and (14), using the menu commands ‘‘single phase association’’ and ‘‘single phase dissociation to baseline’’, respectively. In the latter case, the data is extrapolated to the baseline determined from the baseline section of the curve. Estimate the errors using the menu command ‘‘matrix inversion’’. Determine kon and

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dissociation rate constant (kdiss) for each concentration of antibody. Determine average dissociation rate constant (kdiss). (g) Make the plot of kon against antibody concentration (Eq. (10)). In making the plot use the kon values, which have been calculated from the association curves showing good fitting to Eq. (11) (Fig. 3a). Determine association rate constant (kass) for antibodies. (h) Determine the association and dissociation equilibrium constants (Kass and Kdiss) from Eq. (16). ( i ) Obtain the kinetic and equilibrium constants for all examined antibodies, as described in items (a) – (h). Compare the association equilibrium constants and dissociation rate constants of parental Mabs and Babs derived thereof. Compare the experimentally obtained differences between

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binding parameters of Babs and Mabs with theoretical predictions of bivalent binding model (see Section 3.6) and make the conclusions about the mode of parental Mabs interaction (monovalent or bivalent) with the immobilized antigen.

5. Results In this section, examples of the expected results will be presented for each one of the main stages of the analysis protocol. 5.1. Antigen covalent immobilization A standard antigen covalent immobilization monitored by IAsys is depicted in Fig. 2. In a first stage

Fig. 3. Curve fitting analysis of association. This figure shows a typical analysis of the association data. (a) FASTfit is used to analyse the data obtained over 5 min of the association of 7 nM of Mabs (anti-hIgG) with immobilized antigen (hIgG1), fitting it to the association Eq. (11). The top graph shows the raw data (thin broken line) and the curve of the best fit (thick fluent line), demonstrating the closeness of the fit (v2 = 0.24). The calculated value for kon in this experiment is (1.98 F 0.09) 10 3 s 1 and that for E (the extent of the reaction) 73 F 2 arc seconds. R0 (response for t = 0) is equal  0.8 F 0.1 arc seconds. The errors for the curve fitting are shown in the bottom graph, showing that the deviations of the data from the fitted curve (calculated from Eq. (11)) do not exceed 1.5 arc seconds. (b) FASTfit is used to analyse the data obtained over 5 min of the association of 1031 nM of anti-hIgG/HRP Babs with hIgG1, fitting it to the association Eq. (11). The top graph shows the raw data (thin broken line) and the curve of best fit (thick fluent line), demonstrating the discrepancy of the fit (v2 = 36.07). The calculated value for kon in this experiment is (8.44 F 0.29) 10 3 s 1 and that for E (the extent of the reaction) 260 F 3 arc seconds. R0 (response for t = 0) is equal 39.3 F 2.7 arc seconds. The errors for the curve fitting are shown in the bottom graph, showing significant deviations of the data from the fitted curve (calculated from Eq. (11)).

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(1), the EDC/NHS activating mixture is added with the consequent increase in the biosensor signal due to a change in the bulk refractive index. The antigen solution is then added and the binding event (2) can be followed in real time. The remaining active carboxylNHS esters are blocked with ethanolamine hydrochloride (3), causing a significant change in the bulk refractive index. The cuvette is washed twice with 10 mM HCl (4) before use to remove any noncovalently bound protein. The biospecific antigen surface is then ready to be used (5). By the analysis of the profiles of the sensograms obtained following immobilization of antigens (HRP and IgG1 in our experiments), the alteration of the resonant angle (the response) is measured. Using the IAsys software, these responses (5500 arc seconds for hIgG1 and 1700 arc seconds for HRP) correspond to immobilization of (17 F 1) 10 14 mol/mm 2 of hIgG1 and (21 F 2) 10 14 mol/mm2 of HRP (see Section 4.2(f)). 5.2. The kinetics of the binding of parental Mabs and Babs to immobilized antigens Fig. 4a and b shows typical profiles seen following binding of bivalent and monovalent versions of the same antibody (Mabs and Babs) to antigens immobilized on the surface of biosensor. The presented sensograms correspond to equal concentrations of Mabs and Babs. The analyzed panel of affinity purified antibodies included two parental Mabs (i.e., antihIgG and anti-HRP) and a Bab, derived thereof by cell fusion (i.e., anti-hIgG/HRP). Visual inspection of the sensograms shows more rapid association of both parental bivalent Mabs with corresponding antigens if compared with Babs. At the dissociation phase, the presented sensograms illustrate two essentially different situations, which are possible in such kind of experiments: (a) a much more rapid loss of Babs is observed (Fig. 4a); (b) no significant difference in the dissociation of parental Mabs and Babs is observed (Fig. 4b). 5.3. Data processing and evaluation The sensograms are transformed in order to eliminate baseline, dissociation and regeneration regions and to normalize the time and response axes. Fig. 5

Fig. 4. Sensograms for the interaction of parental monoclonal antibodies and bispecific antibodies with antigens immobilized onto the biosensor surface. The antigen-coupled cuvette is equilibrated in PBS/T buffer. Then, antibody samples are added to the cuvette containing immobilized antigen (1) and allowed to bind for 5 min, to follow the association of the antibodies. The antibodies are then removed from the reaction chamber and PBS/T is added (2). The dissociation follows for 5 min after the addition of the buffer. For other details, see Section 4.3. (a) Binding of anti-HRP Mabs and anti-hIgG/HRP Babs to immobilized HRP (antibody concentration is 490 nM). (b) Binding of anti-hIgG Mabs and anti-hIgG/HRP Babs to immobilized hIgG1 (antibody concentration is 34 nM).

illustrates typical picture resulting from the superposition of several transformed sensograms (only association regions are presented) depicting the binding of antibodies with antigen at five different concentrations. As can be seen, the rate of association increases with the antibody concentration. The iterative curve fitting program FASTfit is used to fit the raw association curves to the pseu-

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the data presented in Fig. 3b, it should be also paid attention, that the value of E (the extent of the reaction, corresponding to the equilibrium concentration of antigen –antibody complex for the given concentration of antibody) is significantly lower the expected value for the given surface concentrations of immobilized antigen (i.e., hIgG1). Thus, extrapolation of data, obtained by immobilization of hIgG1 (see Section 5.1) to binding experiments, allows to suggest that the binding of anti-hIgG/HRP Babs with all immobilized hIgG1 molecules at high anti-

Fig. 5. Concentration dependence of antibody association with antigen immobilized onto the biosensor surface. Various concentrations of the antibody (anti-hIgG/HRP) are added to the cuvette containing immobilized antigen (HRP). These data are obtained as described in Section 4.3 and are used to calculate the kon for each antibody concentration, with the help of the iterative curve fitting procedure, according to Eq. (11). The bottom graph corresponds to the concentration of anti-hIgG/HRP Babs equal to 80 nM, the top graph—to the concentration equal to 490 nM.

do-first order equation describing the binding of a single molecular species to its ligand (Eq. (11)). From our experience, the data fit Eq. (11) well and consistently at a range of antibody concentrations, which produce the responses not exceeding 80 arc seconds during the time of analysis (5 min). As has been shown in previous studies (O’Shannessy et al., 1993), the optimal concentrations in the microcuvette span the estimated Kdiss of the reaction. The effect of antibody concentrations on the analysis is illustrated in Fig. 3, at the examples of the binding of anti-hIgG Mabs (Fig. 3a) and anti-hIgG/HRP Babs (Fig. 3b) with immobilized hIgG1. Fig. 3a corresponds to the data obtained at one of the optimal antibody concentrations (7 nM). The top graph shows the raw data and the curve of the best fit, the bottom graph shows the errors of the curve fitting. As can be seen from these graphs, there are no major or systematic deviations of the data from the fitted curve: typically, the errors are within 1.5 arc seconds. However, at the higher concentrations of antibody (>10Kdiss) and with long periods of analysis (>5 min), the data show more significant deviations from Eq. (11), resulting in the increase of the value of the error (Fig. 3b). In consideration of

Fig. 6. Plot of kon against antibody concentration for parental monoclonal antibodies and bispecific antibodies. The value of kon for each concentration is calculated using Eq. (11). The slopes of the lines are then used to give the kass of the molecules (from Eq. (10)). (a) The plot of kon vs. antibody concentration for the binding of antiHRP parental Mabs and Babs to immobilized HRP. (5—5) AntiHRP Mabs; (n—n) anti-hIgG/HRP Babs. (b) The plot of kon vs. antibody concentration for the binding of anti-hIgG parental Mabs and Babs to immobilized human IgG1. (o—o) Anti-hIgG Mabs; (.—.) anti-hIgG/HRP Babs.

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Fig. 7. The method of the drawing of the plot of kon against antibody concentration. The value of kon for each antibody concentration (for the binding of anti-hIgG/HRP Babs with immobilized hIgG1) is calculated using Eq. (11). The values of kon obtained at high antibody concentrations (>10Kdiss) are found to be lower than predicted by the other data points (dotted line). Such non-linear data are omitted from further analysis. To construct the final linear plot of kon against antibody concentration (solid line), we use five points corresponding to the lowest antibody concentrations.

body concentrations should produce the response approximately equal to 5500 arc seconds. In reality, the maximal response for the binding of anti-hIgG/ HRP Babs with immobilized hIgG1 (corresponds to E value) at high antibody concentration does not exceed 300 arc seconds (Fig. 3b). The further increase of antibody concentration does not result in the significant rise of the extent of reaction (data not shown). This implies that only 5% of hIgG1 molecules immobilized to the sensing surface are capable of being recognized by antibodies. The immobilization of HRP also results in the significant loss of antigenic activity, approximately to the same degree as it is observed with hIgG1 (data not shown). This may be because some of the epitopes recognized by antibodies are destroyed. Alternatively, some of antigen molecules may be buried in the hydrogel and are not accessible to antibodies. According to other studies (George et al., 1995), the partial destruction (or concealment) of epitopes is a usual phenomenon in biosensor analysis. The curves obtained after the iterative curve fitting procedure of the raw association data are used to calculate the kon and to establish the plots of kon

against antibody concentration, as shown in Fig. 6. The slopes of the plots ‘‘kon vs. antibody concentration’’ are then used to give the kass of the molecules (from Eq. (10)). The values of kon obtained at high antibody concentrations (>10Kdiss) are sometimes found to be lower than predicted by the other data points (Fig. 7). If necessary, such non-linear data are omitted from further analysis. For all antibody species, the final plot gives a straight line allowing accurate calculation of the kass of the antibodies. The values of kdiss are determined from the data using iterative curve fitting to Eq. (14). This equation extrapolates the dissociation to baseline, and gives consistent results so long as the baseline of the data is linear at the time of the experiment (Fig. 8). To

Fig. 8. Curve fitting analysis of dissociation. This figure shows a typical analysis of the dissociation data. FASTfit is used to analyse the data obtained over 5 min of the dissociation of antigen – antibody complexes, fitting it to Eq. (14) (the interaction of 488 nM of antihIgG/HRP Babs with immobilized HRP is analyzed). The top graph shows the raw data (thin broken line) and the curve of best fit (thick fluent line), demonstrating the closeness of the fit (v2 = 0.23). The calculated value for kdiss in this experiment is (8.7 F 0.1) 10 4 s 1 and that for Rdiss (response for t = 0) is equal 58.9 F 0.1 arc seconds. 0 The errors for the curve fitting are shown in the bottom graph, showing that the deviations of the data from the fitted curve (calculated from Eq. (14)) do not exceed 1.5 arc seconds.

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Table 1 Equilibrium and kinetic binding parameters for the interaction of antibodies with antigens immobilized on a solid phase obtained by biosensor Antibody

Anti-HRP Anti-hIgG/HRP Anti-hIgG Anti-hIgG/HRP

Immobilized antigen HRP HRP hIgG1 hIgG1

Biosensor, IAsys kass, M 1 c 1

kdiss, c 1 4

(1.9 F 0.1) 10 (8.0 F 1.0) 103 (1.5 F 0.2) 105 (6.8 F 0.5) 104

calculate kdiss, we usually select the analysis region covering the first 5 min of dissociation, the baseline not to be significantly changed during this time. The comparison of experimentally obtained binding parameters of Mabs and Babs allows to estimate the influence of valency on the binding properties of antibodies. This may be illustrated using the data presented in Table 1. For example, in case of antiHRP antibodies, the significant difference in kdiss for Babs and Mabs is observed: kdiss is 21 times higher for Babs. It may be calculated (using Eq. (15)) that t1/ 2 for the dissociation of anti-HRP Mabs and antiHRP arm of Babs constitutes 5 h and 14 min, respectively. Consequently, as shown in Table 1, Kass for anti-HRP Mabs, determined from Eq. (16), is 50fold higher that for Babs. As follows from the theoretical model (Sections 3.6.3 and 3.6.5), the obtained differences in the values of kdiss and Kass for Babs and Mabs are consistent with the proposition of bivalent binding of anti-HRP Mabs with antigen (HRP) coupled to biosensor surface. It can be calculated from Eqs. (4) and (5) that about 96% of anti-HRP Mabs on the surface of biosensor are bound bivalently to immobilized antigen. On the contrary, the values of kdiss for anti-hIgG Mabs and anti-hIgG arm of Babs are shown to be very close (Table 1), suggesting the absence of bivalent binding of antiIgG Mabs with antigen coupled to biosensor surface (see Section 3.6.5). The ratio of Kass for Mabs and Babs is equal to 2.3, in this case. Evidently, this ratio is very close to the theoretical value of 2, expected for the situation when Mabs are not able to bind bivalently to immobilized antigen, and the constant gain is due only to the statistical factor (see Section 3.6.3). Theoretically, the ratio of kass for Mabs and Babs should be equal 2 (see Section 3.6.5). As can be seen, the deviation of experimental ratio of kass values

Kass, M 1 5

(4.0 F 0.1) 10 (8.3 F 0.1) 10 4 (2.7 F 0.1) 10 4 (3.0 F 0.1) 10 4

(4.8 F 0.1) 108 (9.6 F 1.1) 106 (5.5 F 0.5) 108 (2.3 F 0.1) 108

for Babs and Mabs from theoretical ratio (2) does not exceed the scatter common for the method. It should be emphasized that these estimations are based on the assumption that Babs and parental Mabs have identical intrinsic affinities of their binding sites. Earlier, we have shown that both parental Mabs (i.e., antiHRP and anti-hIgG) and their derivative Babs (i.e., anti-hIgG/HRP), used to obtain the data presented in Table 1, have identical affinity constants with respect to soluble antigens (Smirnova et al., 1997). Besides, both parental Mabs are of IgG1 subclass, therefore, Babs derived thereof have the same structure of their Fc region as the bivalent antibodies. Consequently, these antibodies are valid for avidity study described here. It should be noted that the visual inspection of sensograms obtained for Mabs and Babs (Fig. 4), and the mathematical analysis of binding curves, lead to the qualitatively common conclusions about the differences in antigen-binding properties of the examined antibodies.

6. Discussion 6.1. Trouble-shooting 6.1.1. Data do not fit to the expected kinetic model Generally, antigen – antibody interactions display pseudo-first order kinetics on the biosensor. However, in some cases, the deviations from the pseudo-first order kinetics are observed. Usually, this is considered to be one of the most difficult problems to solve in biosensor analysis (Gomes and Andreu, 2002). These deviations can arise from several factors. 6.1.1.1. Ligand heterogeneity. Partial inactivation (alteration) of some of the ligand molecules, due to

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random immobilization procedures, is resulting in ligand heterogeneity. Usually, the proteins are coupled to the hydrogel via e amino groups of lysine residues. However, in case of lysine rich proteins, the coupling in this way may lead to some heterogeneity in the immobilized antigen (George et al., 1995; O’Shannessy and Winsor, 1996). In addition, if the molecule is linked to CMD via lysine residues present in or close to the epitope recognized by the antibody, it will probably disrupt the interaction. If coupling with standard EDC/ NHS chemistry is problematic, there is recommended to use alternate chemistries, for example linking thiol or carbohydrate groups on the molecule to the carboxymethyl groups on the hydrogel (O’Shannessy and Winsor, 1996), or oriented methodologies such as streptavidin – biotin. 6.1.1.2. Steric effects. Careful studies on the kinetics of complex formation on the IAsys biosensor show that the non-monophasic nature of the interactions most frequently seems to represent steric effects in the antigen –hydrogel matrix at relatively high ligand concentrations (Edwards et al., 1995). Usually, these deviations of the experimental data from the pseudofirst order Eq. (11) (Fig. 3b) are observed at high antibody concentrations (>10Kdiss) and with long periods of analysis in biosensor systems (O’Shannessy et al., 1993; George et al., 1995; Edwards et al., 1995). Steric effects may be reduced by coupling the antigen onto a planar surface (such as amino-silane) or by reducing the amount of ligand immobilized (Edwards et al., 1995). 6.1.1.3. Non-specific binding. Non-specific binding may produce the significant effect on the data at higher concentrations of antibodies. This can be checked with relevant controls. These include: binding antibodies to non-specific cuvette (having an alternative ligand immobilized, which does not specifically bind antibodies), preabsorbtion of antibodies with excess antigen before binding to immobilized ligand. 6.1.1.4. Intrinsic binding mechanisms. In some cases, the sources of deviation may be connected with complex binding mechanisms (e.g., involving conformational changes, positive or negative co-operative binding) (IAsys Cuvette System Methods Guide, 1993; Gomes and Andreu, 2002). When these effects

are present, the more complex fitting models have to be used (Gill et al., 1996; Edwards et al., 1998; Muller et al., 1998a). 6.1.1.5. A contribution from mass transport. Limitations in mass transport theoretically also should be taken in account (Schuck and Minton, 1996). However, the IAsys system relies on a stirrer to ensure efficient mixture of the cuvette contents, ensuring equal distribution of the fluid phase antibody. Mass transport influence can be detected by testing the effect of different stirrer amplitude on analyte initial binding rates (curve slopes at the initial stage of the association step). Another problem is the decrease in observed kass at high antibody concentration (Fig. 7). This phenomenon possibly represents saturation of the antigenic epitopes at high antibody concentrations (Pellequer and Van Regenmortel, 1993). It may be recommended to omit such non-linear data from further analysis. 6.1.2. The observed dissociation rate is very low Some antibodies may show very low values ( < 10 4) of the observed dissociation rate constants (kdiss). In particular, this situation may be expected in the case of bivalent antigen – antibody interaction. Sometimes, antigen – antibody binding in solid-phase systems even is considered to be irreversible, for practical purposes (for review, see Mattes, 1997). In this situation, the decrease in response during the standard measurement time (5 min) will be too small ( < 2%) to allow the reliable detection. In this case, the dissociation phase should be followed for at least 20 min. 6.2. Alternative procedures 6.2.1. The intrinsic affinity of monovalent binding may be measured using monovalent antibody fragments The distinctive feature of our experimental model from a number of previous studies on antigen – antibody interaction (Mason and Williams, 1980; Dower et al., 1984; Karulin and Dzantiev, 1990; Roggenbuck et al., 1994; George et al., 1995; Nice et al., 1996) using a variety of methods is the application not of F(ab) fragments but of tetradoma produced Babs for the evaluation of the enhancement effect due to biva-

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lent binding. Apparently, the use of whole-molecule Babs, retaining the structure of native antibodies, to measure the intrinsic affinity, may provide more correct estimation of the mechanisms of antigen –antibody interactions in heterogeneous systems, if compared with the models using monovalent antibody fragments. However, if teradoma produced Babs are not available, F(ab)s may be used to measure the intrinsic affinity of monovalent binding. The modern analogues of F(ab)s, the single-chain Fv antibody fragments, also may be applied for this purpose (Coloma and Morrison, 1997; Pluckthun and Pack, 1997; Muller et al., 1998b; Todorovska et al., 2001). In general, the biosensor protocol described here is suitable for the comparisons of monovalent antibody fragments and IgG molecules of identical origin, with respect of their interaction with immobilized antigens. However, the difference in the molecular weight of IgG and F(ab) (Mr = 160,000 and 50,000, respectively) may somewhat complicate the comparison of binding curves obtained in biosensor method, because in this method the response is proportional to the mass of analyte. On the contrary, Mabs and Babs derived thereof have identical molecular weights. Obviously, this factor simplifies the comparative real-time kinetic analysis of monovalent and bivalent probes, allowing the direct comparison of obtained sensograms. It should be also noted that the strength of monovalent binding of bivalent antibody with a soluble antigen might be easily measured in equilibrium binding experiments in solution. However, the absolute values of equilibrium association constants measured in solution are not valid for solid-phase experiments due to the possible conformational alterations of immobilized proteins (Djavadi-Ohaniance and Friguet, 1991). 6.2.2. Alternative theoretical models to evaluate the avidity effects Several theoretical models have been suggested to calculate the influence of bivalent binding of IgG antibody in solid-phase systems. As shown in our work, the simple model of bivalent binding, based on the earlier studies (Dower et al., 1984; Kaufman and Jain, 1992), is valid for the analysis of antibody binding parameters in the biosensor system (Hall et al., 1997), allowing to discriminate between monovalent and bivalent modes of binding. In some studies, the attempts have been made to apply more compli-

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cated models for these purposes (Edwards et al., 1998). Thus, Muller et al. (1998a) have described the mathematical computer model of bivalent binding specially adapted for the conditions of biosensor systems. In this model, the influence of bivalent binding on the sensor signal is quantitated as a function of ligand density, analyte concentration and binding site distance.

7. Essential literature references 7.1. Original papers Allard, W.J., Moran, C.A., Nagel, E., Collins, G. and Largen, M.T. (1992). Dmitriev, D.A., Massino, Y.S., Segal, O.L., Smirnova, M.B., Kolyaskina, G.I., Pavlova, E.V., Osipov, A.P., Egorov, A.M. and Dmitriev, A.D. (2001). George, A.J.T., French, R.R. and Glennie, M.J. (1995). Milstein, C. and Cuello, A.C. (1983). 7.2. Other sources http://www.affinity-sensors.co.uk. http://www.biochem.northwestern.edu/Keck/ PDF%20documents/IAsys. IAsys Cuvette System FASTfit Guide (1993). Fisons Applied Sensor Technology, Cambridge, England. IAsys Cuvette System Methods Guide (1993). Fisons Applied Sensor Technology, Cambridge, England. IAsys Cuvette System User’s Guide (1993). Fisons Applied Sensor Technology, Cambridge, England.

8. Quick procedure (a) Optimize the coupling buffer pH (with regards to pI of ligand), using the check list presented in the IAsys Cuvette System Methods Guide (1993). (b) Prepare PBS/T, immobilization buffer, 10 mM HCl and solutions for testing regeneration conditions (10, 30 and 100 mM HCl, 20% ethanol, 1 M NaCl and 10 mM NaOH).

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(c) Prepare antigen solutions (25 – 50 Ag/ml in immobilization buffer). (d) Prepare 1 M ethanolamine hydrochloride solution, adjusting the pH to 8.5. (e) Prepare antibody solutions. Fifteen or 20 different concentrations in PBS/T, e.g., a dilution series ranging from 5000 to 10 nM in PBS/T will suffice. (f ) Set the IAsys manual system biosensor ready, according to the manufacturer’s instructions. All measurements are performed at 25 jC. (g) Place the new CMD cuvette in the instrument. Wash with PBS/T buffer three times and leave for 10 min in PBS/T to allow the micro-cuvette to stabilize. (h) Start data collection and obtain a buffer baseline. The stirrer should be set at 65 units of the device. The resonant angle is sampled every 1 s. 8.1. Antigen immobilization and testing of regeneration conditions (a) Prepare the activating mixture by mixing 400 Al of 0.1 M NHS in water with 400 Al of 0.4 M EDC in water (the NHS and EDC solutions must be prepared immediately before use). (b) Remove PBS/T and wash three times with 200 Al portions of EDC/NHS mixture. Leave for 8 min in the last portion of EDC/NHC to activate the gel. Aspirate cuvette, wash with PBS/T three times to remove unreacted EDC/NHC and re-equilibrate for 2 min in the third portion of PBS/T. (c) Wash three times with 200 Al portions of immobilization buffer, re-equilibrate for 2 min in the third portion. Aspirate cuvette and pipette in 200 Al of ligand solution (25 – 50 Ag/ml in the immobilization buffer), leave for 15 min. Wash (three times) with PBS/T buffer to remove unbound ligand, equilibrate for 2 min. (d) Aspirate cuvette, pipette in 200 Al of 1M ethanolamine hydrochloride (pH 8.5) and leave for 2 min. Wash (three times) and equilibrate (for 2 min) with PBS/T. (e) Aspirate cuvette, wash three times with 200 Al portions of 10 mM HCl and leave to equilibrate for 2 min in the third portion. Wash (three times) and re-equilibrate (for 2 min) with PBS/T buffer. Remove PBS/T. Again, wash (three times) and

leave for 2 min with 10 mM HCl. Once more, wash and equilibrate with PBS/T. (f) Save the experimental curve of immobilization in separate file using IAsys software. (g) Test the regeneration conditions of the surface of cuvette: this is done by repeated cycles of antibody addition (e.g., 500 nM in immobilization buffer) followed by 2 min incubation in a regeneration solution. 8.2. Binding kinetics analysis (a) Re-equilibrate the micro-cuvette with 180 Al of PBS/T for 3– 10 min. (b) Add 20 Al of antibody solution to 180 Al of PBS/T in micro-cuvette and leave for 5 min to associate. (c) Aspirate cuvette, wash three times with 200 Al portions of PBS/T and leave for 5 min in the third portion to dissociate. (d) Aspirate cuvette, wash three times with 200 Al portions of regenerating solution and leave to regenerate for 2 min in the third portion. Wash (three times) and re-equilibrate (for 2 min) with PBS/T. (e) Analyze each antibody (Mab and Bab) at least at five different concentration, each corresponding one cycle as described in points (a) – (d). The analyzed concentrations are selected such that the responses do not exceed 80 arc seconds during the first 5 min of association. All measurements are run at least in duplicate. (f) Save the experimental data of association and dissociation in separate file using IAsys software. 8.3. Data processing and analysis (a) Open FASTfit program and open the fail with experimental data for antibody under investigation. (b) Specify antibody concentration for each region you are going to analyze (baseline, association and dissociation). (c) Select at least 1 min of baseline before association of antibody. (d) Identify the start of the association phase. The association analysis region is selected such that the first point is 5 s after the start marker. The end of the association analysis region is selected at the end of the 5 min of data.

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(e) Identify the start of the dissociation phase. The dissociation analysis region is started approximately 10 s after the elimination of the unbound antibodies and PBS/T washing. The end of the dissociation analysis region is selected at the end of the 5 min of data. (f) Fit the experimental data of association to Eq. (11) using the menu command ‘‘single phase association’’. Fit the experimental dissociation curves to Eq. (14), using the menu command ‘‘single phase dissociation to baseline’’. Estimate the errors using the menu command ‘‘matrix inversion’’. Determine the kon and dissociation rate constant (kdiss) for each concentration of antibody. Determine the average dissociation rate constant (kdiss). (g) Make the plot of kon against antibody concentration (Eq. (10)) and determine the association rate constant (kass) for antibodies. (h) Determine association and dissociation equilibrium constants (Kass and Kdiss) from Eq. (16). (i) Calculate kinetic and equilibrium constants for all examined antibodies. Compare association equilibrium constants and dissociation rate constants of parental Mabs and their monovalent derivatives (Babs). Basing on this comparison and the predictions of the theoretical bivalentbinding model (Section 3.6), identify whether Mabs bind to immobilized antigen bivalently or monovalently. References Allard, W.J., Moran, C.A., Nagel, E., Collins, G., Largen, M.T., 1992. Antigen binding properties of highly purified bispecific antibodies. Mol. Immunol. 29, 1219. Buckle, P.E., Davies, R.J., Kinning, T., Yeung, D., Edwards, P.R., Pollard-Knight, D., Lowe, C.R., 1993. The resonant mirror: a novel optical biosensor for direct sensing of biomolecular interactions: Part II. Applications. Biosens. Bioelectron. 8, 355. Cao, Y., Suresh, M.R., 1998. Bispecific antibodies as novel bioconjugates. Bioconjug. Chem. 9, 635. Coloma, M.J., Morrison, S.L., 1997. Design and production of novel tetravalent bispecific antibodies. Nat. Biotechnol. 15, 159. Crothers, D.M., Metzger, H., 1972. The influence of polyvalency on binding properties of antibodies. Immunochemistry 9, 341. Cush, R., Cronin, J.M., Stewart, W.J., Maule, C.H., Molloy, J., Goddard, N.J., 1993. The resonant mirror: a novel optical biosensor for direct sensing of biomolecular interactions: Part I. Principle of operation and associated instrumentation. Biosens. Bioelectron. 8, 347.

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