Direct kinetic assay of interactions between small peptides and immobilized antibodies using a surface plasmon resonance biosensor

Ž. Journal of Immunological Methods 259 2002 217–230 www.elsevier.comrlocaterjim Protocol Direct kinetic assay of interactions between small peptides and immobilized antibodies using a surface plasmon resonance biosensor Paula Gomesa, David Andreub,) a() Centro de InÕestigac¸ao em Quımica CIQUP , R. Campo Alegre, 687, P-4169-007 Oporto, Portugal ˜´ bDepartment of Organic Chemistry, UniÕersity of Barcelona, Martı i Franques 1, E-08028 Barcelona, Spain ´` Received 10 July 2001; accepted 9 August 2001 Abstract Ž. A surface plasmon resonance SPR protocol is described for the direct kinetic analysis of small antigenic peptides Ž. Ž . interacting with immobilized monoclonal antibodies mAb . High peptide concentrations up to 2.5 mM and medium mAb Ž 2 . Ž surface densities about 1.5 ngrmm are needed to ensure measurable binding levels, and fast buffer flow rates 60 . mlrmin are required to minimize diffusion-controlled kinetics. Good reproducibility levels in the kinetic constants are Ž. obtained under these analysis conditions standard deviations below 10% of the mean values . Application of this protocol to determine the antigenic ranking of viral peptides shows an excellent agreement between SPR and previous competition Ž. enzyme-linked immunosorbent assays ELISA on the same peptiderantibody systems. q2002 Elsevier Science B.V. All rights reserved. Keywords: Antigen–antibody interactions; Real-time biospecific interaction analysis kinetics; Surface plasmon resonance analysis of small analytes AbbreÕiations: C , analyte concentration; EDC, N-ethyl-NX- A dimethylaminopropylcarbodiimide; ELISA, enzyme-linked immunosorbent assay; Fab, antigen-binding fragment of an antibody; FMDV, foot-and-mouth disease virus; HEPES, N-2-hydroxyethyl- piperazine-NX-2-ethanesulfonic acid; IC , 50% inhibition concen- 50 Žy1y1. tration; k, association rate constant M s ; K, association aA Žy1. thermodynamic constant M ; k, dissociation rate constant d Žy1.Ž. s;K, dissociation thermodynamic constant M ; k, appar- Ds Žy1. ent rate constant s ; mAb, monoclonal antibody; NHS, N-hy- droxysuccinimide; PBS, phosphate buffer saline; R, SPR response Ž. Ž. at time tRU ; R, equilibrium response RU ; RI, bulk refraceq Ž. Ž. tive index RU ; R, maximum response RU ; R, total SPR max tot Ž. response RU ; RU, resonance units; SDS, sodium dodecylsulfate; SPR, surface plasmon resonance; t, run start time. on )Corresponding author. Tel.rfax: q34-93-402-1260. Ž. E-mail address: [email protected] D. Andreu . 1. Type of research Ž The use of SPR biosensors Fagerstam et al., ¨ 1992; Malmqvist and Karlsson, 1997; Homola et al., . 1999 for interaction analysis has made it possible to obtain affinity and kinetic data for a large Ž number of antigen–antibody Brigham-Burke et al., 1992; VanCott et al., 1994; Oddie et al., 1997; . England et al., 1997; Houshmand et al., 1999 , Ž. protein–protein Wu et al., 1995 , protein–peptide Ž.Ž Lessard et al., 1996 and protein–DNA Cheskis . and Freedman, 1996 systems. Other relevant appli- Ž cations are epitope mapping Dubs et al., 1992; . Saunal and Van Regenmortel, 1995 or selective 0022-1759r02r$ - see front matter q2002 Elsevier Science B.V. All rights reserved. Ž. PII: S0022-1759 01 00503-8 () P. Gomes, D. AndreurJournal of Immunological Methods 259 2002 217–230218 concentration analysis of bioactive molecules in Ž. complex samples Richalet-Secordel et al., 1997 . ´ The majority of the direct single-step SPR analyses Ž reported in the literature Altschuh et al., 1992; Wu et al., 1995; Lessard et al., 1996; Brigham-Burke et al., 1992; Lemmon et al., 1994; Tamamura et al., . 1996; Chao et al., 1996; England et al., 1997 involve analytes weighing above 5 kDa. Since the SPR response is directly related to changes in mass on the sensing surface, there is an experimental limitation for direct SPR detection of small analytes, which led to a golden rule in SPR: immobilize the smaller binding partner. A clear example of this rule can be found, for instance, in antigen–antibody interaction studies where antigens are immobilized on the sensor surface and the larger antibodies are used as analytes Ž. Altschuh et al., 1992; Zeder-Lutz et al., 1997 . When this rule is not suitable for the purposes in view, alternative SPR approaches are employed, such Ž as multistep sandwich Cheskis and Freedman, 1996; Huyer et al., 1995; Shen et al., 1996; Lookene et al., .Ž 1996 or indirect competitive Lasonder et al., 1994, 1996; Karlsson, 1994; Zeder-Lutz et al., 1995; Nieba . et al., 1996 analysis. However, in antigen–antibody interaction studies, the general rule is that a high Ž number of potential antigens e.g., peptides with key . residue substitutions are to be screened against a small set of specific antibodies. Thus, antibody immobilization has clear practical benefits over peptide immobilization. Comparison between different peptide antigens is meaningful only if they are analyzed Ž under exactly the same conditions e.g., all injected . over the same antibody surface . Moreover, large Ž. analytes e.g., antibodies are more prone to generate steric hindrance and mass-transport artifacts that affect true kinetic data. The protocol that we present here is suited for Ž. direct single-step surface plasmon resonance SPR analysis of small ligand–large receptor interactions, Ž where small peptides are used as analytes injected . in the buffer continuous flow and monoclonal anti- Ž. bodies mAb are immobilized on the SPR sensor chip surface. The protocol has been optimized and validated using foot-and-mouth disease virus Ž. FMDV peptides and anti-FMDV neutralizing mAb as the binding partners, as described elsewhere Ž. Gomes et al., 2000a,b, 2001a . 2. Time required 2.1. Full kinetic analysis of a peptide–antibody interaction For routine analyses on a previously prepared sensor surface, 2–3 h will suffice. Considering also ligand immobilization and instrument maintenance procedures, 4–5 h will be required. 2.2. Immobilization of the antibody on the sensor chip surface Ž. 1 Preconcentration assays: 60 min Ž. 2 Covalent immobilization: 30 min Ž. 3 Testing regeneration conditions: 30 min 2.3. Binding kinetics assays Ž. Ž . 1 Blank injections two runs : 20 min Ž. Ž . 2 Analyte injections sampleqregeneration : 20 min () 2.4. Data analysis BIAeÕaluation software : 60 min 2.5. Maintenance Ž. Ž 1 Priming the system once a day or each time a . sensor chip is changed : 10 min Ž. Ž 2ADesorbBonce a week: washing the system . in harsh conditions : 30 min Ž. Ž . 3 Sanitizing the system once a month : 40 min Ž. Ž 4 Normalizing the signal once a week or when . buffer is changed : 40 min 3. Materials 3.1. Special equipment v The protocol has been optimized on a BIAcore 1000 SPR biosensor v Personal computer working on a Windows envi- Ž. ronment Windows ’95, ’98, 2000 or NT v BIACORE control 3.1 software v BIAevaluation 3.0 software v Ž. BIAsimulation software optional () P. Gomes, D. AndreurJournal of Immunological Methods 259 2002 217–230 219 3.2. Certified materials for SPR assays Certified materials for running SPR assays on the BIAcoreebiosensors are commercially available Ž. Biosensor, Uppsala, Sweden : v Ž CM5 sensor chips, certified grade code BR- . 1000-12, package of three chips —carboxymethylated dextran matrix, with aG4000 RU binding capacity for a 40-kDa protein standard and with user-defined binding specificity. v Ž HBS-EP running buffer code BR-1001-88, 6= .Ž 200 ml —10 mM HEPES N-2-hydroxyethylpipe- X. razine-N-2-ethanesulfonic acid with 0.15 M NaCl, 3.4 mM EDTA and 0.005% surfactant P20 at pH 7.4. v Ž Amine coupling kit code BR-1000-50, for 50 .XŽ immobilizations —750 mg N-ethyl-N- 3-dimethyl- .Ž. aminopropyl carbodiimide EDC , 115 mg N-hydro- Ž. xysuccinimide NHS , 10.5 ml ethanolamine hydrochloride. v Ž BIAmaintenance kit code BR-1002-22, for 6 .Ž. months normal usage —solutions of sucrose 65 ml , Ž. Ž. Ž. glycerol 30 ml , SDS 90 ml , glycine 90 ml , Ž. diazolidinyl urea with surfactant P20 60 ml , sodium Ž. hypochlorite 10 ml . v Ž BIAnormalizing solution code BR-1003-22, 90 . ml —for normalization of BIACORE probe signal. 3.3. Solutions for surface regeneration The regeneration procedures corresponding to the assays described in the present protocol may, in principle, be carried out using either 50 mM HCl or 10 mM NaOH. The most common regenerating agents are: v Ž. acids 10–100 mM HCl, H PO 34 v Ž. bases 10–100 mM NaOH v Ž. salts 1–5 mM NaCl v Ž. detergents 0.5% SDS v Ž denaturants 8 M urea, 6 M guanidine hydro- . chloride 3.4. Monoclonal antibodies Purified mAbs in PBS can be used as stock solutions for subsequent dilution in the immobilization buffer. Generally, mAb stock solutions corre- Ž.Ž. spond to ca. 20 mg antibody rml PBS and are diluted to ca. 5 mgrml in the chosen immobilization buffer. 3.5. Immobilization buffers Preconcentration assays are performed in order to establish which is the best immobilization buffer. Electrostatic preconcentration is best achieved at low ionic strength. A 10-mM sodium acetate buffer with pHs5.5 is generally adequate for mAb amine coupling immobilization on a CM5 sensor chip. The most common immobilization buffers for sensor chip CM5 are: v Ž. 10 mM sodium formate pHs3.0–4.5 v Ž. 10 mM sodium acetate pHs4.0–5.5 v Ž. 5 mM sodium maleate pHs5.5–6.0 3.6. Peptides Peptide 2.5 mM stock solutions in water or 100 mM acetic acid can be prepared for 1000-fold and subsequent serial dilutions in the SPR running buffer Ž. HBS . Thus, peptide solutions injected on the biosensor typically range from 2500 to 20 nM in HBS. 4. Detailed procedure 4.1. Preparing the system System preparation and routine maintenance will not be described in detail since they are presented in the instrumentation manuals. These procedures are almost entirely automated and computer-controlled through interactive software in an icon-based windows environment. Ž. i Dock the new sensor chip, replace the HBS running buffer bottle by a fresh one and prime the system. Ž. ii Normalize the probe signal according to the manufacturer’s instructions. 4.2. Preconcentration assays Ž. iii Prepare different mAb solutions to test for the best immobilizing conditions. Different mAb concen- Ž. trations e.g., 5, 10 and 50 mgrml and immobiliza- Ž tion buffers e.g., 10 mM formate, pH 4.5; 10 mM () P. Gomes, D. AndreurJournal of Immunological Methods 259 2002 217–230220 . acetate, pH 5.0; 10 mM acetate, pH 5.5 should be considered. Ž. iv Select one out of the four independent CM5 sensor chip flow cells and set the running buffer flow rate to 5 mlrmin. Ž. v Inject sequentially 25 ml of each one of the Ž.Ž different mAb solutions prepared in iii 5-min in- .Ž. jections , with short 1-min pulses of a 1-M ethanol- Ž. amine hydrochloride solution pHs8.5 between each injection. Ž. vi Examine carefully which combination of mAb concentrationrimmobilization buffer pH is most suitable for efficient ligand electrostatic preconcentration on the sensor chip surface. This corresponds to the lowest ligand concentration and to the highest pH giving maximum response. Immobilization conditions leading to extremely high mAb attachment Ž. rates steep ascent should be avoided. 4.3. mAb immobilization by coÕalent amine coupling Once immobilization conditions are chosen, the mAb can be covalently bound to the sensor chip surface. The amine coupling procedure involves chemical activation of the CM5 surface carboxyl groups and subsequent covalent binding to the mAb primary amino groups. Ž. vii Prepare the activating mixture by mixing 35 ml of 0.05 M NHS in water with 35 ml of 0.2 M Ž EDC in water the NHS and EDC solutions must be kept separately below 0 8C and should be mixed . immediately before usage . Ž. viii Select the flow cell and set the running buffer flow rate to 5 mlrmin. Ž. Ž . ix Inject 35 ml 7 min of the activating mixture Ža response will be observed due to a change in the . refractive index . Ž. Ž x Immobilize the ligand by injecting 35 ml7 . min of the mAb solution chosen in the preconcentration assays, inspecting carefully the slope of the response ascent and the maximum level reached. Ž. xi Block the nonreacted surface active sites by Ž. injecting 35 ml 7 min of 1 M ethanolamine hydrochloride adjusted to pH 8.5. This will also serve to break remaining ligand-surface electrostatic bonds. Ž. xii Measure the amount of immobilized ligand Ž. by subtracting the initial AemptyBflow cell from Ž the final baseline level 1000 resonance units—RU 2. —correspond to a 1-ngrmm ligand surface density . When performing kinetic analyses, the ligand density should be as low as possible, provided signal-to-noise ratios are adequate. Direct detection of small peptide Ž. antigens ca. 1.5 kDa binding to immobilized mAbs Ž. ca. 150 kDa on a Biacore 1000 generally requires immobilization responses of about 1800 RU. Ž. xiii Test the regeneration conditions of the surface: this is done by repeated cycles of analyte Ž injection e.g, 25 ml of a 600-nM solution of the . antigenic peptide specific for the immobilized mAb Ž. followed by a short pulse 1–3 min of a regenerat- Ž ing solution the most common ones are mentioned . in Section 3.3 . A suitable regenerating agent provides full recovery of the baseline level at the end of Ž each cycle while preserving ligand activity checked by the constancy of analyte binding level in repeated . cycles . 4.4. Binding kinetics assays Ž. xiv Dock the sensor chip containing the immobilized mAb, replace the HBS bottle by a new one, prime the system and normalize the probe signal according to the manufacturer’s instructions. Ž. xv Prepare the peptide solutions to be injected. Six or seven different analyte concentrations, e.g., a dilution series ranging from 2500 to 20 nM in HBS, Ž. will suffice. One blank sample buffer only and a Ž. negative control analyte e.g., scrambled peptide should be included in the analyses. The regeneration solution should also be prepared. Ž. xvi Set the running buffer flow rate to 60 mlrmin on the flow cell containing the immobilized Ž ligand for kinetic analyses, buffer flow rates must be higher than 30 mlrmin to avoid diffusion-con- . trolled kinetics . Ž. xvii Program the injection cycle: use the Akinject mode,Bwhich minimizes sample dispersion and provides user-defined dissociation times in running Ž buffer. Needle-cleaning operations Apredip needleB before analyte injection and Aextra clean-upBafter . regeneration should be also included in each cycle to avoid carry-over. Each cycle comprises two main steps: Ž. Ž . aAkinjectB90 ml 1.5 min of sample solution Ž. followed by 4 min 240 s dissociation in running buffer. () P. Gomes, D. AndreurJournal of Immunological Methods 259 2002 217–230 221 Ž. Ž . b inject 60 ml 1 min of the regenerating solution. Ž. xviii Program the peptide binding assays: each peptide should be analyzed at least at six different Ž concentrations each corresponding to one injection Ž.. cycle as described in xvii . Each measurement should be run at least in triplicate and injections should preferably follow a random order. Flush the system whenever a new peptide is to be screened and prime the system once a day. 4.5. Data processing and analysis Data processing is done by means of the BIAE- valuationesoftware available from Biosensor. Ex- Ž. perimental curves i.e., sensorgrams corresponding Ž. to the same analyte at different concentrations are simultaneously processed. The software includes several kinetic models and nonlinear least squares methods to optimize parameter values. Simple kinetic models perfectly described by integrated rate equations use analytical integration, while more Ž complex ones e.g., involving mass transport limitations, ligand or analyte heterogeneity, conformational changes, analyte multivalency or ligand coop- . erativity use numerical integration. Ž. xix Open a new BIAevaluation file and, from there, access all the experimental curves corresponding to a given peptide–mAb system analyzed under Ž identical conditions except for varying peptide con- . centration . Also from the same file, open the experimental curves corresponding to the blank run and to the negative-control peptide injections. Ž. Ž . xx Adjust the time scale abscissa so that ts0 Ž. injection start is the same for all curves, and the Ž. baseline level ordinate, before injection start so that it equals 0 RU in all sensorgrams. Ž. xxi Delete the useless parts of the sensorgrams Ž. e.g., the regeneration pulses , after which subtract Ž. the blank run buffer only curve to all the others Žthis will eliminate buffer response and instrumental . drifts or artifacts . Ž. xxii Subtract from each peptide concentration curve the one from the scrambled peptide, to eliminate nonspecific binding. Ž. xxiii Fit the set of binding curves by global curve fitting to those kinetic models compatible with your system. Judge which one gives the best fit and Ž the most reliable parameters a 1:1 Langmuirian behavior—pseudo-first order reaction—should be expected for the interaction between each antigen molecule and each one of the Fabs on the immobi- . lized mAb . The fitting models are based on AblindBmathematical tools and the Abest fitBdepends on the ability of the fitting algorithm to converge for the true minimum and on the number of parameters that can be varied in the model, i.e., the complexity of Ž the model O’Shannessy et al., 1993; Morton et al., . 1995 . Therefore, caution must be taken when judging the Abest fitBfrom a purely mathematical point of view. In general, the best choice is the simplest model of those giving reasonably good fits. Ž. xxiv Once the Abest fitBis chosen, a further detailed evaluation should be performed in order to Ž establish data consistency Schuck and Minton, . 1996 . Different zones of the experimental curves should be used for fitting purposes. Local fittings Ž. each sensorgram separately should be done and compared with globally fitted data. When applicable, Ž analytical integration methods separate fitting of . association and dissociation phases should be tested and compared with numerical integration methods. Ž This means that, for a 1:1 interaction pseudo-first . order kinetics , data should be fitted as follows: Ž. a global fitting to the 1:1 interaction model Ž. numerical integration ; Ž. Ž . b local fitting each concentration separately to Ž the 1:1 interaction model numerical integra- . tion ; Ž. Ž c local fitting, separate krkanalytical intead gration in each one of the separate association . and dissociation phases . If kinetic parameters are consistent throughout all these fits, the kinetic model chosen is most probably correct and interaction data are meaningful. 5. Results In this section, examples of the expected results will be presented for each one of the main stages of the analysis protocols. () P. Gomes, D. AndreurJournal of Immunological Methods 259 2002 217–230222 Ž. Fig. 1. Example of three successive electrostatic pre-concentration assays. A Injection of a 5 mgrml mAb solution in 10 mM acetate buffer, pH 5.5, leads to an efficient mAb preconcentration on the carboxylmethyl-dextran matrix of the sensor chip and to a satisfactory final Ž. response level. B Injection of a 5 mgrml mAb solution in 10 mM formate buffer, pH 4.5, leads to a slow and inefficient electrostatic Ž. preconcentration of the ligand. C Increasing mAb concentration to 50 mgrml in 10 mM acetate buffer, pH 5.5, leads to a fast preconcentration and to a too high final response. Ž. Fig. 2. Example of a covalent immobilization of antibody on a CM5 sensor chip. 1 The carboxyl groups are reacted with a NHSrEDC Ž. Ž mixture and reactive NHS esters are formed. 2 The antibody solution is injected and coupling reaction through the primary amino groups .Ž. from the antibody lysine residues is allowed to proceed. 3 Remaining reactive NHS ester sites are blocked with ethanolamine Ž.Ž. hydrochloride pH 8.5 . 4 The final antibody surface is ready. () P. Gomes, D. AndreurJournal of Immunological Methods 259 2002 217–230 223 5.1. Preconcentration assays Fig. 1 illustrates the results of three sequential preconcentration assays. Using ca. 1700 RU as a reasonable immobilization level for the direct kinetic assay of small peptide binding to an antibody sur- Ž face, situation A 5 mgrml mAb in 10 mM acetate . buffer, pH 5.5 is clearly the most satisfactory. In B Ž. 5mgrml mAb in 10 mM formate buffer, pH 4.5 , mAb response increases rather slowly and the final Ž mAb level is insufficient. In contrast, situation C 50 . mgrml mAb in 10 mM acetate buffer, pH 5.5 corresponds to a fast mAb uptake by the surface resulting in a too high mAb final density. 5.2. Antibody coÕalent immobilization A standard ligand covalent immobilization monitored by SPR is depicted in Fig. 2. In a first stage Ž. 1 , the EDCrNHS activating mixture is injected with the consequent increase in the SPR signal due to a change in the bulk refractive index. The mAb Ž. solution is then injected and the binding event 2 can be followed in real time. Once the adequate binding level is reached, the remaining active carboxyl-NHS esters are blocked with ethanolamine Ž. hydrochloride 3 , causing a significant change in the bulk refractive index. The biospecific mAb surface is Ž. then ready to be used 4 . 5.3. Binding assays The binding assays consist of sequential peptide injection plus regeneration cycles. Fig. 3A shows the three main stages observed when monitoring the Ž. biospecific interaction in real time: 1 Analyte bind- Ž.Ž. ing to the immobilized ligand association . 2 Bound analyte detaching from the immobilized lig- Ž. Ž. Ž . Fig. 3. A One injection cycle. B Superposition of several binding curves sensorgrams corresponding to distinct injection cycles Ž. different concentrations of the same peptide . () P. Gomes, D. AndreurJournal of Immunological Methods 259 2002 217–230224 Ž.Ž. and dissociation in running buffer . 3 Ligand surface regeneration. Each cycle corresponds to a new sample, so that all blanks, controls, different peptide concentrations Ž and assay repeats are covered. When a full set i.e., . all concentrations of a given peptide of injection cycles is finished, the corresponding sensorgrams can be transformed in order to eliminate irrelevant Ž. regions e.g., regeneration pulses and to normalize the time and response axes. This results in the super- Ž. position of several sensorgrams Fig. 3B , ready to be processed by the curve fitting software. Fig. 4. Illustration of the different stages in the analysis of the interaction between an FMDV peptide and an anti-FMDV neutralizing mAb. Ž. Ž. A Sensorgrams generated by injection of five distinct concentrations of a nonspecific peptide scrambled sequence on an anti-FMDV Ž. mAb surface. B Sensorgrams generated by injection of five distinct concentrations of a specific FMDV peptide on the same anti-FMDV Ž. Ž. mAb surface. C Corrected sensorgrams for the specific FMDV peptide-mAb interactions, obtained by subtraction of curves shown in A Ž.Ž. from the curves shown in B . D Residual data distribution for the association and dissociation phases, after global curve fitting to the 1:1 Ž.Ž. bimolecular interaction model numerical integration . E Linear correlation between the analyte concentration, C, and the apparent rate Ž .Ž. constant, k, calculated by local curve fitting to the 1:1 bimolecular interaction model analytical integration . F Correlation between fitted s equilibrium response, R, and analyte concentration, C. eq () P. Gomes, D. AndreurJournal of Immunological Methods 259 2002 217–230 225 Table 1 Kinetic and affinity data from the SPR analysis of the peptide–immobilized antibody interaction illustrated in Fig. 4 y1y1y1y1 wxŽ. Ž . Ž . Ž . Curve fitting Peptide nM kMs ksKM adA 4y37 Global – 6.2=10 2.6=10 2.3=10 4y37 Local, simultaneous krk152 6.0=10 2.4=10 2.5=10 ad 4y37 305 5.8=10 2.6=10 2.3=10 4y37 610 5.9=10 2.6=10 2.3=10 4y37 1220 6.1=10 2.7=10 2.3=10 4y37 2440 6.2=10 2.9=10 2.1=10 4y37 Local, separate krk152 6.7=10 2.4=10 2.8=10 ad 4y37 305 6.2=10 2.6=10 2.4=10 4y37 610 5.5=10 2.6=10 2.1=10 4y37 1220 5.8=10 2.8=10 2.1=10 4y37 2440 5.9=10 2.7=10 2.2=107 wx Rvs. peptide plot 2.0=10 eq Three different curve fitting methods were tested in order to evaluate the consistency of the fitted parameters. 5.4. Data processing and eÕaluation Fig. 4 depicts the most important stages in data processing and evaluation. In A, sensorgrams corresponding to a nonspecific peptide injected on a mAb surface are shown. The sensorgrams are square-wave shaped due to a mere refractive index jump, which is confirmed by the fact that no peptide is bound to the mAb at the beginning of the dissociation phase. In B, sensorgrams correspond to a specific interaction between an injected peptide and the immobilized mAb. This same interaction is depicted in C, after being corrected by subtraction of the sensorgrams corre- Ž sponding to the nonspecific peptide analogue shown . in A . Sensorgrams in C were globally fitted to a 1:1 interaction model, with calculated curves totally coincident with the experimental ones and residuals Ž. randomly distributed around zero Fig. 4D , corresponding to a chi-squared lower than 1. The kinetic parameters obtained are shown in Table 1. These sensorgrams were also fitted locally to the same Ž. kinetic model Table 1 . Further local fitting was performed using the sep- Ž. arate krkmodel Table 1 and the locally fitted ad apparent rate constant, k, was plotted against pepsŽ. tide to check the linearity ksk=Cqkexsa d Ž. pected for a 1:1 interaction kinetics Fig. 4E . The locally fitted response at equilibrium, R, was also eq plotted against peptide concentration so that the Ž. affinity constant Kvalues withdrawn from this A plot and calculated by the krkratio could be ad Ž. compared Table 1 . 6. Discussion 6.1. Trouble-shooting 6.1.1. Immobilization is not satisfactory The immobilization level depends on several factors, such as ligand concentration, pH, ionic strength, Ž. activation time EDCrNHS mixture and injection Ž. time ligand . Generally, lower ligand binding levels can be reached by decreasing ligand concentration, pH, activation and contact times or by increasing ionic strength. Conversely, higher concentrations and activation or contact times, as well as lower ionic strength, contribute to increase ligand immobilization levels. 6.1.2. Baseline responses increase oÕer repeated cycles The regeneration step is not efficient and bound analyte is not fully washed off after each binding cycle. Regenerating agents must be tested and a Ž. cocktail approach Andersson et al., 1999a,b may be required. 6.1.3. Binding leÕels decrease oÕer repeated cycles There is loss of ligand activity, either due to ligand inactivation under the analysis conditions em-