QSAR studies applied to the prediction of antigen–antibody interaction kinetics as measured by BIACORE

Laurence Choulier1, Karl Andersson2, Markku D. Hämäläinen2, Marc H.V. van Regenmortel1, Magnus Malmqvist2 and Danièle Altschuh1,3

1 UMR7100-CNRS, ESBS, Bld Sébastien Brandt, 67400 Illkirch Cedex, France and 2 Biacore AB, Rapsgatan 7, SE754 50 Uppsala, Sweden


    Abstract
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
 References
 
The objective of this work was to investigate the potential of the quantitative structure–activity relationships (QSAR) approach for predictive modulation of molecular interaction kinetics. A multivariate QSAR approach involving modifications in peptide sequence and buffer composition was recently used in an attempt to predict the kinetics of peptide–antibody interactions as measured by BIACORE. Quantitative buffer–kinetics relationships (QBKR) and quantitative sequence–kinetics relationships (QSKR) models were developed. Their predictive capacity was investigated in this study by comparing predicted and observed kinetic dissociation parameters (kd) for new antigenic peptides, or in new buffers. The range of experimentally measured kd variations was small (300-fold), limiting the practical value of the approach for this particular interaction. However, the models were validated from a statistical point of view. In QSKR, the leave-one-out cross validation gave Q2 = 0.71 for 24 peptides (all but one outlier), compared to 0.81 for 17 training peptides. A more precise model (Q2 = 0.92) could be developed when removing sets of peptides sharing distinctive structural features, suggesting that different peptides use slightly different binding modes. All models share the most important factor and are informative for structure–kinetics relationships. In QBKR, the measured effect on kd of individual additives in the buffers was consistent with the effect predicted from multivariate buffers. Our results open new perspectives for the predictive optimization of interaction kinetics, with important implications in pharmacology and biotechnology.

Keywords: interaction kinetics/mathematical models/multivariate analysis/prediction of kinetic parameters/QSAR


    Introduction
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
 References
 
The quantitative structure–activity relationship (QSAR) approach (Hansch and Klein, 1991Go) has been widely used in pharmacology in attempts to optimize drug compounds (reviewed in Kubinyi, 1997aGo,bGo; Grover et al., 2000aGo,bGo). The principle of the QSAR approach is to establish mathematical models that relate variations of factors with variations in responses. The factors are structural or physico-chemical properties of the compounds, described using quantitative molecular descriptors. Responses are various quantifiable biological activities. In practice, biological activity has to be measured for a significant number of modified molecules, in order to develop a QSAR model. Once a mathematical model has been established, the molecular properties of the compound can in principle be predictively modified in order to reach a desired biological activity. The models also help to explain the molecular basis of activity.

The relationship between molecular properties and activity is complex because many different factors, which sometimes act in a cooperative or antagonistic manner, may influence activity. Furthermore, difficulties may be encountered for producing large numbers of modified molecules, and for accounting correctly for their structural or physico-chemical properties using molecular descriptors. In the case of larger molecules such as peptides or proteins, these properties can only be partially described, so that the choice of positions to modify and of descriptors, are crucial for the success of the method. These complexities partly explain why QSAR approaches have seldom been applied to peptides and proteins, although some examples have been published (Hellberg et al., 1991Go; Norinder et al., 1997Go; Damborsky, 1998Go; Bucht et al., 1999Go; Lee et al., 2000Go).

A number of tools have been developed that should help analyzing the activity of peptides and proteins. Modified molecules can easily be produced by peptide synthesis or mutagenesis. Molecular descriptors have been refined and statistical methods both for experimental design and data evaluation have been improved (Hellberg et al., 1987Go, 1991Go; Collantes and Dunn, 1995Go; Andersson et al., 1998Go; Sandberg et al., 1998Go). In multivariate statistical techniques, the experiment is designed in such a way that a maximum of information can be extracted from a minimum number of measurements, by varying several factors simultaneously. Various mathematical analysis procedures can be used to resolve which factors are correlated with the measured activities. Softwares are now available that allow the statistical design of complex experiments and their mathematical interpretation (see for example the internet site of the QSAR and Modelling Society: http://www.ndsu.nodak.edu/qsar_soc/).

A multivariate QSAR approach involving modifications in peptide sequence and buffer composition was recently used in an attempt to predict the kinetics of peptide–antibody interactions (Andersson et al., 2001Go). QSAR models were developed using PLS analysis (reviewed in Geladi and Kowalski, 1986Go; Kubinyi, 1997aGo), which enables correlation of large numbers of factors with responses (in this case kinetic parameters) measured from a limited number of experiments. Robust mathematical models allow the predictive modulation of binding kinetics, with important consequences for optimizing buffer composition in biotechnological applications, or for the design of new biomolecules. The aim of the present study is to evaluate the predictive value of models developed by Andersson et al. (Andersson et al., 2001Go).

The system used for the QSAR analysis is the interaction between recombinant Fab 57P (Chatellier et al., 1996aGo) and peptide antigens, a system characterized in great detail. Fab 57P is directed against the coat protein of tobacco mosaic virus and recognizes peptides corresponding to region 134–151 of the protein sequence. The system was selected because experimental conditions for precise kinetic measurements using surface plasmon resonance biosensors have been defined (Rauffer-Bruyère et al., 1997Go; Choulier et al., 1999Go). Furthermore, the epitope recognized by Fab 57P has been delineated by a combination of approaches including peptide spot synthesis and phage display (Altschuh et al., 1992Go; Choulier et al., 1999Go, 2001Go), facilitating the choice of target positions for antigen modification.

In the QSAR study by Andersson et al. (Andersson et al., 2001Go), the varied factors were either buffer composition or peptide sequence. The buffers were described by their pH and the concentration of five different additives (NaCl, urea, EDTA, KSCN and DMSO). Peptide sequence was described using standard zz scales (Sandberg et al., 1998Go), and a helix-forming tendency scale (Deleage and Roux, 1987Go). The zz1, zz2 and zz3 scales, called principal properties of amino acids, were derived from a statistical analysis of 26 physico-chemical descriptors of natural and non-natural amino acids, and were proposed to be related to hydrophobicity, size and electronic properties, respectively (Sandberg et al., 1998Go). Responses were the kinetic parameters of the Fab–peptide interactions as measured using a BIACORE 3000 instrument (BIACORE AB, Uppsala, Sweden). Mathematical models were developed which relate these kinetic parameters to buffer composition [quantitative buffer–kinetic relationships (QBKR)] or to peptide sequence [quantitative sequence–kinetic relationships (QSKR)].

The statistical parameters of the models suggested that they can be used for predicting kinetic parameters of new peptides in a standard buffer (from the QSKR models), as well as for predicting the influence on kinetics of individual additives in the buffer (from the QBKR models). In the present study, the effective predictive power of the models is assessed by comparing predicted and measured kinetic parameters for the interaction of Fab 57P with (i) eight new double or triple variants of the peptide antigen in a standard HEPES buffered saline (HBS), and (ii) nine of the peptides in buffers containing single additives at various concentrations. In addition, buffer space was extended in order to verify if the linear QBKR models were valid over a wider range of chemical concentrations.


    Materials and methods
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
 References
 
Immobilization on BIACORE sensor chips

To determine kinetic parameters or active Fab concentration, 10–30 RU or more than 300 RU of peptides, respectively, were immobilized on CM5 sensor chips (BIACORE) by the thiol activation chemistry (Löfås and Johnsson, 1990Go; BIAapplications Handbook, BIACORE), as previously described (Chatellier et al., 1996bGo; Choulier et al., 1999Go). For kinetic measurements, a non-specific peptide was immobilized as reference surface.

Determination of the active concentration of Fab 57P

The concentration of the active Fab 57P was determined using a calibration curve as previously described (Choulier et al., 1999Go), on a surface containing a high density of the wild-type peptide. The active concentration of Fab 57P was determined in 20 different buffers (HBS, p1–p19), using the calibration curve established in HBS buffer.

Determination of kinetic parameters

Kinetic parameters for the interaction between Fab 57P and peptides were measured using a BIACORE 3000 instrument. Fab 57P was used as an Escherichia coli crude extract, diluted to three concentrations (121.5, 27.9 and 8.5 nM) in each buffer, and was serially injected on the four flow cells at 30 µl/min, for 120 s at 20°C. The sensor surfaces were regenerated by injecting 10 µl of glycine, pH 1.7, at the end of each cycle. The sensorgrams were corrected for signals in the reference flow cell and evaluated with BIAevaluation 3.0 (BIACORE), using a simple 1:1 kinetic model.

Statistical analysis of data

MODDE 5.0 (Umetrics AB, Umea, Sweden: http://www.umetrics.com), a program for the generation and evaluation of statistical experimental designs, was used to derive mathematical models from the designed experiments and to check for the reliability of these models. The mathematical models used in this study for relating sequence or buffer composition to kinetics were developed as previously described (Andersson et al., 2001Go). For all experiments, when replicates were available, data were used separately without calculating mean values. ka values were not analyzed (see Results). For QSKR, kd values were transformed to log kd. For QBKR, kd was not transformed.

Refining the mathematical model

After incorporating the dissociation rate parameters obtained for the interaction between the eight new peptides (from the second set) and Fab 57P in HBS, it became possible to reconsider which terms should be included in the predictive model. Previously (Andersson et al., 2001Go), the peptides were designed for developing linear models describing the relationship between amino acid sequence and kinetic parameters. The eight new peptides make it possible to use non-linear models (second degree polynomial) and investigate interaction terms (dependence between two factors) when developing a model. The inclusion of an interaction term is the mathematical way to describe that two amino acids are dependent of each other, i.e. act cooperatively or antagonistically on kd. However, due to the low number of newly added peptides, the validity of the added non-linear or interaction term must be carefully controlled. Such terms can be correlated to other single terms or non-linear/interaction terms if the values of the factors vary in a similar way for several terms. In such a case only one of these terms may be responsible for the observed effect. In this experiment, special investigations were performed for all terms that had a correlation above 0.4 with the added interaction term [see section `Quantitative sequence kinetics relationship in HBS (QSKR)'].

Evaluation of predictions

The success of predictions was evaluated by comparing the SD of the residuals (RSD) of set1 with those of set2 (Hellberg et al., 1987Go). The RSD was calculated as follows:

where x is the difference between observed and predicted kd for each measurement.


    Results
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
 References
 
Experimental design

In the study of Andersson et al. (Andersson et al., 2001Go), a BIACORE 3000 instrument was used to measure kinetic parameters for the interaction of Fab 57P with various peptides in several buffers in order to develop QSAR models that were used for predictions. In this study, different experiments were designed in order to validate the models. Altogether, 26 peptides and 47 buffers were used. It was not possible to analyze all peptides in all buffers because of the considerable amount of data to be collected and treated. Table IGo summarizes the experimental design, by indicating which peptides have been analyzed in which buffers, together with the purpose of each of the six experiments: two in the study by Andersson et al. (Andersson et al., 2001Go) and four in the present study.


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Table I. Summary of experiments performed by Andersson et al. (Andersson et al., 2001Go) and in this study
 
The 18 peptides (12 triple and double mutants, five single mutants and the wild-type) used in the previous study are called set1 peptides, or training peptides. The eight peptides synthesized in order to verify predictions are called set2 peptides. Peptides are designated by the amino acid type present at the three positions that were varied in the antigen (positions 142, 145 and 146). For example, the wild-type peptide containing S142, E145 and S146, is called SES. Buffers are numbered p1–p46 (Table IIGo). Buffers p1–p19 correspond to the previously described multivariate buffers (Andersson et al., 2001Go). Multivaried buffers p20–p29 were designed to extend buffer space. The term `buffer space' describes the range of buffer compositions that are covered by the statistical design of multivaried buffers. Buffers p30–p46 contain only one chemical additive at various concentrations. The six experiments in Table IGo are briefly described below.


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Table II. Composition of buffers
 
Experiment 1. The QSKR models, relating association or dissociation rate parameters to peptide sequence, were developed by analyzing the kinetics of Fab 57P with the wild-type and 17 variants of the peptide antigen (set1 peptides), in the standard HBS. All peptides bound to the Fab except one (MGS). The models were used to predict kinetic parameters for the eight set2 peptides (see `Experiment 3').

Experiment 2. The QBKR models for each peptide, relating kinetic parameters to buffer composition, were developed by analyzing the different peptide–Fab binding kinetics in 19 multivaried buffers (p1–p19, Table IIGo), which differ by their pH values and by the concentration of different additives (NaCl, urea, EDTA, KSCN and DMSO). The QBKR models obtained for each peptide predict the influence on kinetic parameters of the chemicals added individually in the buffer (see `Experiment 6').

Experiment 3. QSKR models were evaluated by comparing predicted and experimental kinetic parameters in HBS, for eight new double and triple mutants of the peptide antigen (set2 peptides). Seven set1 peptides were also included, to verify the consistency of kinetic measurements over the 10 months that separated the experiments.

Experiment 4. The eight set2 and seven set1 peptides were analyzed in buffers p1–p19 to, respectively, derive QBKR models for the set2 peptides, and validate QBKR models previously developed for set1 peptides.

Experiment 5. The three set2 and six set1 peptides were tested in new buffers designed to extend buffer space. Buffers p20–p29 are identical to buffers p17–p19, except for the level of one of the additives, which is outside the range of buffers p17–p19 (Table IIGo). The aim of these experiments was to increase the effect of chemicals on off-rates in order to validate the models obtained with buffers p1–p19. This extended design also supports non-linear models, whose properties could now be investigated.

Experiment 6. The QBKR models for each peptide were deduced from experiments in multivaried buffers, i.e. buffers in which several chemical additives are present simultaneously. In order to verify the predicted effects, three set2 and six set1 peptides were tested in buffers p30–p46 (Table IIGo) which contained only one additive (NaCl, DMSO, EDTA, urea, KSCN) at different concentrations (five for NaCl and three for the others).

QSKR in HBS

The range of kinetic parameters obtained with the 18 set1 and eight set2 peptides in HBS (Table IGo, experiments 1 and 3) is represented in Figure 1Go, where peptides are classified according to increasing mean ka (Figure 1AGo) or mean log kd (Figure 1BGo) values. Figure 1AGo shows that ka variations are small, ranging from 2.7x105 M-1 s-1 for peptide ERS to 11.3x105 M-1 s-1 for peptide SAS, which corresponds to a 4-fold variation. The variation of ka in replicate experiments was large compared to the variation between different peptides. Furthermore, six out of the eight set2 peptides, indicated in bold on the x-axis, have similar ka parameters. Therefore, association data were not further evaluated. Variations in kd were larger, ranging from 0.4x10-3 (log kd = –3.4) for the wild-type peptide SES to 60x10-3 s-1 (log kd = –1.2) for peptide FGR, corresponding to a 147-fold variation. The kd values measured for the set2 peptides span the entire kd range, and when expressed in log kd, tend to be more regularly distributed than ka values. Dissociation data are evaluated below.



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Fig. 1. Range of kinetic association (A) and dissociation (B) parameters measured for set1 and set2 peptides, classified according to increasing mean value. The bars indicate the lowest and highest values measured for each peptide. Set2 peptides are indicated in bold.

 
The mathematical model developed by Andersson et al. (Andersson et al., 2001Go) for relating kd to peptide sequence in the standard HBS buffer (called HBSmod1), suggested that the log of the dissociation rate was related to the helix-forming tendency (HFT) at position 145, and to the electronic properties (zz3) at position 146.

Is HBSmod1 confirmed by the new data? In a first step, we have combined all kinetic data for set1 peptides, i.e. those obtained by Andersson et al. (Andersson et al., 2001Go) (experiment 1) and those obtained in the present study (experiment 3, set1 peptides). The statistical parameters of the model applied to this set of data (Table IIIGo, HBSmod1a) were slightly improved (Q2 = 0.81; R2 = 0.83) compared to the statistical parameters obtained previously (Q2 = 0.73; R2 = 0.78) (Andersson et al., 2001Go), thus confirming the model when using set1 peptides, and demonstrating the reproducibility of kinetic parameter measurements over a significant time interval (10 months). The error over replicate experiments ranged from 0.1 to 6.2%.


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Table III. Summary of factors, statistical parameters and predictive ability of the QSKR models
 
In a second step, all data for set1 and set2 peptides in HBS (Table IGo, experiments 1 and 3) were combined. The statistical parameters of the model applied to this set of data were not as good (Q2 = 0.57; R2 = 0.59) (Table IIIGo, HBSmod1b). A plot of observed versus predicted log k d values (Figure 2AGo) indicates that experimentally measured parameters deviate most from the predictions for peptide GAK. When data for peptide GAK were removed, the statistical parameters of the model were Q2 = 0.71, R2 = 0.72 (Table IIIGo, HBSmod1c), indicating that seven of the eight new peptides do not contradict the model.



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Fig. 2. Predicted versus observed log kd for set1 (diamonds) and set2 (squares) peptides. The ideal correlation is indicated by a straight line. Set2 peptides are identified by name. (A) HBSmod1a; (B) HBSmod3a.

 
The RSD for set2 peptides predicted from HBSmod1a is 0.76, and drops to 0.37 when peptide GAK is removed (Table IIIGo, HBSmod1a). The RSD for the training and predicted sets are therefore not too different (0.28 and 0.37, respectively) indicating that the predictions with HBSmod1 were successful from a statistical point of view.

Can the model be refined? A series of independent evaluations were conducted using all peptides, in an attempt to refine the mathematical model by adding new terms. A refined model with predictive power of Q2 = 0.61, R2 = 0.66 was developed. One new single term and one new interaction term were found to be significant. For computational reasons, one non-significant term had to be included to be able to form the interaction term. The refined model was called HBSmod2 (Table IIIGo).

The interaction term 145HFT*142zz3 was included after verifying the absence of strong correlations with other interaction terms and single terms. The interaction term 145zz1*146zz3 was also a candidate for the new model. It was not correlated to other terms but did not contribute much to the predictions. Since it was on the borderline of being significant it was not included in the model. The model was tested by reordering the results randomly 10 times. None of the reordered sets of data gave an interpretable model. In addition, a plot of predicted versus model error for the different models (data not shown) indicates that predictions are better than those obtained from random data or from unrelated models.

Although HBSmod2 describes all peptides reasonably well, its statistical parameters are not as good as those of HBSmod1, suggesting some underlying complexity in the relationship between molecular properties and kinetics.

Evaluation of a subset of peptides. It has been emphasized that QSAR models may be valid only for a set of closely related compounds (Van der Graaf et al., 1999Go). Therefore, the presence of a subset of molecules that behave differently from others may blur out a possible relationship. Examination of the predicted versus observed log kd values (Figure 2AGo) indicates that six peptides with a similar predicted activity (log kd = –3), vary significantly for their measured kd values (log kd = –2.4 to –3.4). Sets of five out of the six peptides (SES, NES, SEA, SAS, AES, EES) share common features not present in other peptides, which could be responsible for a particular binding mode. The common features are (i) three additional residues at their N-terminus (except SES), (ii) the wild-type residue Ser at position 146 (except SEA), and (iii) the wild-type residue E at position 145 (except SAS).

Peptides of sequence XES, XXS and 19mers were sequentially removed from set1 or set1 + set2 for data evaluation to search for a better model. Removing either 19mers or XXS peptides yielded models with excellent statistical parameters, involving HFT at positions 142 and 145. HFT at position 146 could be included, but did not contribute much to the model, and was slightly correlated to HFT145 for the smallest data sets. The highest Q2 value of 0.92 is reached when removing the five XXS peptides from set1 (Table IIIGo, HBSmod3a). The observed versus predicted log kd values are plotted in Figure 2BGo for set1 and set2 peptides. The RSD values calculated for set1 peptides and set2 peptides were 0.15 and 0.46, respectively, indicating that HBSmod3 is unable to predict the eight set2 peptides, possibly because of the presence of S146 in five of them. Among the three set2 peptides that do not have S146, EGK is reasonably well predicted (residual = 0.26, average over three independent experiments), but AEL and GAK were not well predicted. Applying HBSmod3 to set1 + set2, from which all XXS peptides are removed, yielded a Q2 value of only 0.42 (Table IIIGo, HBSmod3b). When removing also peptide GAK, Q2 = 0.81 (Table IIIGo, HBSmod3c).

Quantitative buffer–kinetics relationship

For the QBKR study, interaction kinetics were measured in various buffers, which could have affected the stability as well as activity of Fab 57P. The active concentration of Fab 57P was measured in HBS buffer as well as in buffers p1–p19, using a calibration curve establihed in HBS (Choulier et al., 1999Go). The measured concentration of active Fab 57P varied in the different buffers, decreasing up to 40% in buffer p16 compared to HBS buffer. Since calculation of ka relies on a precise knowledge of the active concentration of Fab 57P, ka data were not evaluated.

The QBKR models (also called chemical sensitivity fingerprints) developed for the 17 set1 peptides (Table IGo, experiment 2) indicated which additives influenced dissociation for each Fab–peptide interaction (Andersson et al., 2001Go). They are of the form:

(i = 1–18, i.e. for all peptides)

The chemical sensitivity fingerprints were different for the various peptides. The presence of urea, DMSO and NaCl in the buffer influenced binding properties, while change in pH, and the presence of EDTA and KSCN had no effect.

The models were evaluated in three ways: first, by reproducing the QBKR experiments for seven set1 peptides (Table IGo, experiment 4); secondly, by an extension of buffer space (Table IGo, experiment 5; Table IIGo, buffers p20–p29); and thirdly, by analyzing the effect on kinetics of adding only one chemical at a time (Table IGo, experiment 6; Table IIGo, buffers p30–46).

Reproducibility of QBKR models (Experiment 4). Seven of the set1 peptides (VQE, MYT, DYD, GSQ, FGR, QDF and the wild-type SES) were retested in this study in buffers p1–p19. Freshly prepared buffers, newly immobilized peptides and a new preparation of Fab were used, so that experiments are independent of those performed in Andersson et al. (Andersson et al., 2001Go). Sensitivity fingerprints for the seven peptides were similar to those obtained previously (data not shown), indicating that models derived from the kinetic measurements were reliable.

QBKR models for the eight new peptides confirm the influence on kd of urea, DMSO and NaCl in the buffer, and the lack of influence of EDTA and KSCN. It is noteworthy that pH variations in the range 7–7.8 did not influence interaction kinetics, except for peptide THS (Figure 3Go), the only peptide containing a His residue whose pI is 7.59. Furthermore, the QBKR models differed with peptide sequence, as observed previously.



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Fig. 3. Comparison of chemical sensitivity fingerprints for nine peptides, obtained with buffers p1–p19 and p1–p29. y-Axis values represent the change of kd (s-1) (relative to kd in buffers p17–19) due to an increase in additive from the low to the high level.

 
Extension of the buffer space (experiment 5). Buffer space was extended by adding 10 new multivariate buffers (p20–p29) in order to investigate whether the relation between kd and the presence of additives in the buffer is linear over a wider range of concentrations. This extended design also supports non-linear models.

As mathematical models would not be reliable when analyzing data from the 10 p20–p29 buffers alone, the fingerprints compared in Figure 3Go were developed using data from buffers p1–p19, and combined data from buffers p1–p19 and p20–p29. The comparison was possible for nine peptides: the three set2 peptides GDS, THS and GAK and the six set1 peptides VQE, MYT, DYD, GSQ, FGR and QDF (Table IGo). Figure 3Go shows that the sensitivity fingerprints were similar, validating the models and indicating linearity over a wider range of chemical concentrations.

Quadratic terms for each additive were also included to investigate possible non-linear relationships between chemical concentrations and kd. The models could not be improved by including any of these terms, indicating that the relationship between additives and kd is best described by a linear model.

Effect on kd of adding one chemical at a time in the buffers (experiment 6). The addition of chemicals individually in the HBS buffer gave results predicted by the multivariate approach, for the nine peptides tested (three set2 and six set1 peptides), validating the multivariate approach and confirming that the effects of the different chemicals are not correlated as suggested from data in the extended buffer space.

Figure 4Go illustrates results obtained when varying NaCl concentration from 150 to 700 mM for five peptides. NaCl increased kd for peptides GSQ, FGR and GDS, decreased kd slightly for DYD and had no effect for THS. These measured effects are comparable to effects predicted from QBKR models on a quantitative level as shown in Figure 5Go. Effects predicted from data in multivaried buffers p1–p29 are represented as QBKR histograms, where each bar corresponds to the predicted change of kd due to increase of additive concentration from the lowest to the highest level (i.e. 150–750 mM for NaCl, etc.). The effect from the singly modified buffers (p30–p46) was calculated as the difference in kd measured in buffers with additive concentrations corresponding to these lowest and highest levels (i.e. buffers p34 and p31 for NaCl).



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Fig. 4. Variation of kd as a function of NaCl concentration for five peptides. The kd values for the interaction between Fab 57P and the peptides were measured in HBS buffers containing increasing NaCl concentrations.

 


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Fig. 5. Comparison of predicted (dark gray) and measured (light gray) effects of buffer components for nine peptides. Predicted effects correspond to the chemical sensitivity fingerprints developed from data in buffers p1–p29 (Figure 3Go). Observed effects were deduced from measurements in buffers containing single additives (p30–p46). The value plotted is the difference in kd value between highest and lowest additive concentration (Figure 4Go).

 

    Discussion
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 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
 References
 
Range of kd variations

The kd range varied 147-fold for all multiple peptide variants in HBS, and only 1.5–4-fold (depending on the peptide) in the different buffers. When considering kd values for all peptides in all buffers, the extreme values differed about 300-fold. One peptide (MGS) out of 26 did not show measurable binding to the Fab.

The relatively narrow range of measured kinetic parameters is most likely due to the inherent characteristics of the Fab 57P epitope. Even small changes at four key positions in the epitope decrease binding affinity below detectable level. Accessory positions, which are the ones varied in the present study, are highly tolerant to changes and only marginally influence kinetic parameters (Choulier et al., 2001Go). In this particular system of interaction, it is unlikely that antigen positions can be found whose modification would significantly increase dissociation rates, while retaining measurable binding. With respect to QBKR, other buffer components may be identified that have stronger effects on kinetic parameters. However, they should be compatible with Fab stability.

The slowest dissociation was observed for the wild-type peptide in standard HBS buffer, indicating that a stronger binding affinity cannot be achieved by modifying the particular sequence and buffer factors selected in this study. The chances of success in attempts to improve binding affinity may increase when starting with low affinity interactions, although the validity of QSAR predictions is generally limited to the range of activities covered by the training set.

Biochemical significance of the QSKR models

While the previously published model (HBSmod1) described all peptides but one, the refined model (HBSmod2) could describe all available peptides in a satisfactory manner, although its precision is less (Table III Go,Q2 = 0.61 as compared to 0.81). It is not known whether HBSmod2 better describes the binding event, or if peptide GAK must be considered as an outlier, as commonly found in QSAR studies (Hellberg, 1987, 1991; Van der Graaf et al., 1999Go; Penny and Jolliffe, 1999Go). Model HBSmod3 developed when excluding peptides with sequence XXS, had excellent statistical parameters suggesting that subsets of peptides with different structural characteristics use slightly different binding modes.

Overall, all models are consistent since they have HFT at position 145 in common. They also indicate that residue size and hydrophobicity at positions 142, 145 and 146 have little influence on kd. Helix-forming tendency seems to be the most important factor. An influence on kinetics of peptide conformation can therefore be hypothesized, in agreement with previous observations. Region 141–148, which corresponds to the epitope region, is helical in the crystallographic structure of the protein (Mondragon, 1984Go). Positions essential for binding, which were identified by a mutational analysis of the peptide antigen, are contiguous in space in a helix, suggesting that the peptide adopts a helical conformation when complexed to the Fab (Altschuh et al., 1992Go). The protein and peptide antigens bind to the Fab with similar equilibrium affinity but very different interaction kinetics, suggesting an influence on kinetics of antigen conformational properties (Choulier et al., 1999Go).

Together with the limited influence on kinetics of accessory epitope residues, the possible relationship between peptide conformation and kinetics contributes to make the Fab 57P–peptide interaction a difficult example for QSAR studies. Indeed, peptide conformation is a property more difficult both to control and to quantify, compared to residue size or hydrophobicity. However, the approach was able to highlight the possible influence on kinetics of antigen conformation, in opposition with other properties, and was therefore informative with respect to structure–function relationships.

Value of the predictions

The QSKR study is a first investigation of the possibility to relate kinetic parameters measured by BIACORE to peptide sequence. When excluding peptide GAK, HBSmod1 was successful for predictions from a statistical point of view. HBSmod3, which has a higher precision, may be valid only for sub-groups of peptides, such as 16mers that do not contain S146. Discrimination between the role of additional N-terminal residues (19mers) and the role of Ser at position 146, as well as validation of HBSmod3 through predictions would require the analysis of a number of additional peptides.

The QBKR study confirms previous reports (Andersson et al., 1999aGo,bGo) showing that a mutlivariate approach and mathematical modeling may be used to predict the effect on interaction kinetics of buffer additives. A multivariate approach is particularly valuable for detecting the possible presence of dependence between factors. This would require a large number of experiments in a conventional approach, but requires only a limited number of experiments in the multivariate approach. Although variations in kd were small, prediction for QBKR was correct, both with respect to the effect on kd of individual chemicals in the buffer, and with respect to the absence of interaction between chemicals.

Due to the small range of kd variations achieved, the agreement between observed and predicted kd values limits the practical value of the models in the present antibody system. Fab 57P is not ideally suited for kinetic modulation because the modified accessory positions seem to play a role in influencing peptide conformation, a property difficult to vary in a controlled manner. Other systems may behave differently. For example, an epitope delineation study for the interaction of scFv1F4 (Giovane et al., 1999Go) with peptides derived from the E6 oncoprotein, has shown that both ka and kd can be significantly affected by a number of antigen modifications (Choulier et al., 2002Go). The QSKR approach applied to such systems might prove more successful on both theoretical and practical levels. Alternatively, if further studies would establish that precise QSKR models (as HBSmod3) can only be established for structurally similar, and therefore most likely also functionally similar molecules, successful predictions may be achievable only for a narrow range of kinetic values.


    Conclusions
 Top
 Abstract
 Introduction
 Materials and methods
 Results
 Discussion
 Conclusions
 References
 
The validation of both QSKR and QBRK models despite the small kd variations, emphasizes the high precision of kinetic measurements using BIACORE instruments, and is encouraging for future applications of the approach to other molecular interaction systems with pharmacological or biotechnological applications. In pharmacology, the QSAR approach applied to interaction kinetics may represent a relatively rapid and inexpensive alternative to library screening, once families of potential candidates have been selected from large scale screening. Many authors have suggested the existence of a relationship between receptor-binding affinity or dissociation kinetics and the pharmacodynamic or pharmacokinetic properties of drugs (Martin, 1981Go; Alterman et al., 1998Go; Markgren et al., 1998Go, 2000Go, 2001Go; Hamalainen et al. (2000)).

Our study also demonstrates that molecular descriptors developed for protein sequences can yield consistent QSAR models, which are informative with respect to structure–activity relationships. Sequence changes were limited to the 20 natural amino acids, but could be extended to non-natural amino acids for which physico-chemical property scales have been derived (Sandberg et al., 1998Go). The introduction of non-natural amino acids would facilitate peptide design because of a larger choice of different physico-chemical properties, and would also help to reduce proteolytic sensitivity of active compounds.

QSKR and QBKR studies could be greatly facilitated if the approach used in this study could be standardized (experimental design, data collection, evaluation and handling), and if higher throughput or more automated methods became available.


    Notes
 
3 To whom correspondence should be addressed. E-mail: daniele.altschuh{at}esbs.u-strasbg.fr Back


    Acknowledgments
 
Laurence Choulier was supported by a grant from `La Ligue Nationale contre le Cancer'.


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Received August 7, 2001; revised December 5, 2001; accepted January 3, 2002.