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Analytical Biochemistry 342 (2005) 300–311

ANALYTICAL

BIOCHEMISTRY

SPOT synthesis: Reliability of array-based measurementof peptide binding affinity

Armin A. Weiser a,1, Michal Or-Guil b,1, Victor Tapia b, Astrid Leichsenring c,Johannes Schuchhardt d, Cornelius Frommel a, Rudolf Volkmer-Engert c,*

a Institute of Biochemistry, Charite, Universitatsmedizin Berlin, Monbijoustr. 2, 10117 Berlin, Germanyb Institute of Theoretical Biology, Humboldt University, Invalidenstrasse 43, 10115 Berlin, Germany

c Institute of Medical Immunology, Charite, Universitatsmedizin Berlin, Hessische Str. 3-4, 10115 Berlin, Germanyd MicroDiscovery GmbH, Marienburger Str. 1, 10405 Berlin, Germany

Received 23 February 2005Available online 23 May 2005

Abstract

Peptide arrays prepared by the SPOT synthesis technology have emerged as a proteomic tool to study molecular recognition andidentify biologically active peptides. However, it was previously not clear how accurately signal intensities obtained by probing pep-tide arrays for protein binding really reflect the dissociation constants of the protein–peptide complexes. Using the monoclonal anti-body CB4-1 as a model system, we systematically compared dissociation constants of antibody–peptide complexes with signalintensities obtained using the SPOT technology. By analyzing a set of peptides possessing different affinities to the antibody, wedetermined the strengths of the SPOT screening method. The accuracy of the measured results was improved by taking regionaltrends in the membrane surface into account. A model based on the mass action law compares well with the experimental results.Interestingly, the applied concentrations of the binding partners do not directly correspond to the effective concentrations in theassay. We show that the SPOT technology is an accurate method for assigning the spots�measured signal intensities to three differentbinding affinity classes. The dissociation constants of the intermediate region were found to be between pKdis = 5 and pKdis = 7.Altering the experimental parameters causes a directed change of this region.� 2005 Elsevier Inc. All rights reserved.

Keywords: SPOT technology; Synthetic peptide arrays; Binding affinity; Dissociation constant; Effective concentration; Mass action law;Competition

As demonstrated by DNA microarray experiments(‘‘DNA chips’’), the array format is a robust, reliable,and now well-established method for large-scale analysisof gene expression, allowing a global view of a living cellor organism�s transcriptome based on a single experi-ment [1,2]. However, it became obvious that the infor-mation obtained from DNA chips is not sufficient forunderstanding life in general. Gene expression levelsdo not closely correlate with the abundance of func-

0003-2697/$ - see front matter � 2005 Elsevier Inc. All rights reserved.

doi:10.1016/j.ab.2005.04.033

* Corresponding author. Fax: +49 30 450 524942.E-mail address: rve@charite.de (R. Volkmer-Engert).

1 These two authors have contributed equally.

tional protein molecules—the principal components inorganizing and mediating cellular physiological func-tions via protein–protein networks [3]. One of the pri-mary goals in functional genomics is to understandhow such networks support cell physiology. Ideally,we would like to draw a map displaying all protein inter-actions in the cell and then trace functional pathwaysalong lines connecting the proteins. Recent interactionanalyses produce an intricate picture and interpretationof the data is still inadequate [4–7]. We have to considerthat the wiring between all components of the intricatenetwork is dynamic. Protein complex formation is influ-enced by all the parameters that determine association

Array-based measurement of peptides / A.A. Weiser et al. / Anal. Biochem. 342 (2005) 300–311 301

and dissociation of all the functional components.Therefore, more or less quantitative readout for map-ping protein–protein interaction in a high-throughputmanner is of general interest.

Synthetic peptide arrays offer the benefit of studyingasymmetric protein–protein interactions: a domain ofpartner A acts as a receptor for a linear peptide in part-ner B. In fact, a fairly large set of cellular protein inter-actions are mediated by families of relatively smallprotein interaction domains (PID),2 such as SH2, SH3,GYF, WW, or PDZ, which act as receptors accommo-dating short peptides in their binding pockets. TheSPOT technology is an ideal tool for preparing syntheticpeptide arrays, because it is an easy-to-use, robust, andinexpensive method. Furthermore, the technique andmany of its applications have been reviewed extensively[8–10]. Recently, we successfully applied SPOT technol-ogy to studying the interaction network of PIDs [11–14].Landgraf et al. [12] describes how we were able to dem-onstrate for the first time that measured spot signalintensities provide an approximation of the affinities ofthe several thousand interactions analyzed simulta-neously on a peptide array. In principle, signal intensi-ties can be used to distinguish between severalinteractions, with different affinities, mediated by thesame protein. We first showed this for peptide–antibodyinteractions [15,16]. Here, we focus in more detail on thecorrelation between spot signal intensities measured inthe array format and dissociation constants determinedfor the appropriate interactions. The question we wantto address is the quantitative reliability of the SPOTtechnique. First, we investigated the reproducibility ofsignals measured on cellulose membrane-bound peptidearrays prepared by the SPOT technology. Second, weassessed the correlation between the measured signalsand the known dissociation constants. Third, we investi-gated the accuracy with which measured signals can beused to classify peptides into binding affinity classes. Fi-nally, we discuss the experimental requirements neededto obtain reliable binding affinity class predictions. Tostudy the quantitative aspects of the SPOT technologywe chose the interaction of the anti-p24 (HIV-1) humanmonoclonal antibody (mAb) CB4-1 [17,18] with 38 well-known peptides as a model system. The recognition pro-file of mAb CB4-1 is a well-established experimental sys-tem that has already been used to evaluate a variety ofstructurally different types of peptide arrays preparedby the SPOT technology. This includes scans of overlap-

2 Abbreviations used: AuC, area under curve; BG, background signalintensity; FQ, membrane functionality quotient; Kdis, dissociationconstant; pKdis, negative decadic logarithm of Kdis; mAb, monoclonalantibody; ROC, receiver operator characteristic; CM, cellulose mem-brane; SCM, standard cellulose membrane; SI, signal intensity; PID,protein interaction domain; MALD, matrix-assisted laser descriptionionization.

ping peptides [10], randomly generated peptide libraries[19], transition pathway libraries that reveal evolution-ary connections between different peptides with similaractivities [20], and peptide arrays to elucidate thecross-reactivity of mAb CB4-1 [21].

Materials and methods

Synthesis of the cellulose-membrane-bound peptide arrays

Cellulose-bound peptide arrays were semiautomati-cally prepared according to standard SPOT synthesisprotocols using a SPOT synthesizer (Intavis, Koeln,Germany) as described in detail [22]. The peptides weresynthesized on amino-functionalized cellulose mem-branes of the ester type [10] prepared by modifying a cel-lulose paper (Whatman 50, Whatman, Maidstone, UK)with Fmoc-b-alanine as the first anchor residue. Load-ing of the amino-functionalized cellulose membranewas determined as described [22]. In the second step ofcoupling the next anchor position, a mixture of differentratios of a 0.3 M solution of Fmoc-b-alanine-OPfp anda 0.3 M solution of N-acetyl-b-alanine-OPfp in dimethylsulfoxide was used (100, 50, 25, and 10 Fmoc-b-alanine-OPfp) leading to membranes with a 100, 50, 25, and 10%amino-functionalization quotient (FQ) at the spot posi-tions [16]. The cellulose-bound peptide arrays wereassembled on these membranes by using 0.3 M solutionsof Fmoc-amino acid-OPfp in NMP (in case of Ser andThr the ODNp-esters were used). Side-chain protectionof the used Fmoc-amino acids was as follows: Glu, Asp(OtBu); Ser, Thr, Tyr (tBu); His, Lys, Trp (Boc); Asn,Gln, Cys (Trt); Arg (Pbf). The sequence files for the ar-ray design were generated with the in-house tool Pool1.0 and translated into chemistry files for the automatedsynthesis using the in-house software LISA 1.571. Forsynthesis quality control of the peptide library, a repre-sentative selection of peptides was prepared (spot size0.25 cm2) and cleaved by ammonia vapor in the drystate [22,23]. Subsequently, identity was verified by ma-trix-assisted laser desorption ionization mass spectrome-try (MALDI-MS) (LaserTec BenchTop II, AppliedBiosystems, Foster City, CA, USA) and peptide qualitywas tested by analytical reversed-phase HPLC (Waters600, Waters, Eschborn, Germany) on a C-18 column(Vydac, Hesparia, CA, USA). According to the generalprotocol a standard peptide array (dimension6 cm · 8 cm) was synthesized on cellulose membranescontaining 37 different peptides (Table 1, entries 2–38)with an average of 13 repeats of each peptide and 120times the peptide GATPEDLNQKLAGN (Table 1, en-try 1). The peptides were equally distributed on the ar-ray, resulting in a cellulose membrane that contains607 spots. Such an array was generated on membraneswith four different FQ values (100, 50, 25, and 10%)

Table 1Dissociation constants obtained for mAb CB4-1/peptide complexes

No. Sequence pKdis No. Sequence pKdis

1 GATPEDLNQKLAGNa 9.0 20 RDFDKEWNLIEQNSa 5.72 GATPQDLkTMLb 9.0 21 LELIQDLNQKLQDGFd 5.73 GATPEDLNQKLc 8.2 22 TTMEWFRITDGARIMd 5.74 sATPwDLkTsle 7.7 23 sAGPwDLksslb 5.35 FATPEDLNQKLc 7.7 24 LEMKQDLNQKLQDGFd 5.36 GATPQDLNTMLe 7.3 25 LEMKQDLNQMLQDGFd 5.27 GLKEWGGARITc 7.1 26 DYFDLTQDNIITRRLd 5.08 DATPEDLNAKLe 7.0 27 LEMKQDLNIKLQDGFd 5.09 DATPEDLNARLe 7.0 28 efslkGpllqwrsGa 4.710 GATPQDLkTMle 6.9 29 DYFDLTQDNIITRRNd 4.711 GATPEDLNAKLe 6.8 30 LEMKQDLNPMLQDGFd 4.712 FDKEWGGIRITc 6.8 31 sAGdwwLksslb 4.513 DALYEWGGARIc 6.7 32 saGdwwGksslb 4.414 GLYEWGGARITNTDa 6.7 33 sAGdwDLksslb 4.315 sATPwDLkTMle 6.6 34 saGdwwLksslb 4.216 DALPEWGGARIe 6.2 35 ITDGARIMd 4.017 GATPwDLkTMle 6.1 36 DYFDLTQDNIIERRNd 4.018 sATPwDLksslb 6.0 37 LEMKQDLNIMLQDGFd 4.019 EAWVLEGAMILWKTDc 6.0 38 EAWVLRGAMILWKTDd 3.5

a [21].b [19].c [20].d [15].e BIAcore studies.

302 Array-based measurement of peptides / A.A. Weiser et al. / Anal. Biochem. 342 (2005) 300–311

leading to the standard cellulose membranes SCM-100,SCM-50, SCM-25, and SCM-10. The membraneSCM-50 was prepared three times and each replicawas incubated with a different antibody concentration.A membrane with the same FQ and the same peptidesas SCM-50 was prepared but with about the three- tofourfold number of each peptide resulting in the mem-brane CM2090-50 with 2090 spots. Furthermore, the cel-lulose membrane CM6000-50 (FQ = 50%) was preparedusing six different peptides from Table 1 (entries: 1, 6,14, 20, 26, 36) but with each peptide equally distributedas 1000 reiterations on the array (size: 18 · 24.4 cm).The peptides cover the affinity spectrum from pKdis = 9to pKdis = 3.5.

Binding studies on cellulose-membrane-bound peptides

All incubation and washing steps were usually carriedout under gentle shaking. After washing the membranewith ethanol once (10 min) and three times for 10 minwith Tween–Tris-buffered saline (T-TBS, 50 mMTris(hydroxymethyl)aminomethane, 137 mM NaCl,2.7 mM KCl, adjusted to pH 8 with HCl/0.05% Tween20), the membrane-bound peptide arrays were blocked(3 h) with blocking buffer, i.e., blocking reagent (CRB,Northwich, UK) diluted 1:10 in T-TBS containing 5%(w/v) sucrose, and then washed with T-TBS(1 · 10 min). Subsequently, the peptide arrays wereincubated with the anti-p24 (HIV-1) monoclonal anti-body CB4-1 (mouse IgG2a/k) [17,18] at different con-

centrations in T-TBS blocking buffer for 16 h at 4 �C.The following concentrations of mAb CB4-1 were used:0.1, 1, and 10 lg/ml. The concentration of 1 lg/ml wasused with the membranes SCM-10, SCM-25, SCM-50,and SCM-100. After washing three times for 10 minwith T-TBS, the second anti-mouse IgG peroxidase-la-beled antibody (Sigma, Deisenhofen, Germany) wasadded at a final concentration of 1 lg/ml in T-TBSblocking buffer for 2 h, followed by washing three timeswith T-TBS. Analysis and quantification of peptide-bound mAb CB4-1 was carried out using a chemilumi-nescence substrate and a Lumi-Imager (Roche Diagnos-tics, Basel, Switzerland). All steps were carried out atroom temperature, unless stated otherwise.

Measurement of spot signal intensities

Analysis and quantification of spot signal intensitieswere executed with the software Genespotter (MicroDis-covery GmbH, Berlin, Germany). Genespotter has afully automatic grid finding routine resulting in repro-ducible signal intensities. The spot signal is calculatedfrom a circular region around the spot center detectedon the image. The background signal for each spot isdetermined with a safety margin to this circular region.

Standard solid-phase peptide synthesis

Soluble peptides were synthesized (50 l mol scale) asamides on a multiple synthesizer AMS 422 (Abimed,

Fig. 1. Binding of the anti-p24 (HIV-1) monoclonal IgG antibodyCB4-1 to cellulose-bound peptides. Shown is the membrane SCM-10(6 · 8 cm) with 607 generated spots representing 38 peptides (Table 1)all known to interact with mAb CB4-1 but possessing differentaffinities to the antibody.

Array-based measurement of peptides / A.A. Weiser et al. / Anal. Biochem. 342 (2005) 300–311 303

Langenfeld, Germany) according to the standard Fmocmachine protocol using TentaGel S RAM resin (RappPolymere, Tubingen, Germany) and PyBOP activation.All peptides were analyzed by reversed-phase HPLCon a Vydac C18 column using a linear gradient of5–60% acetonitrile/water (0.05% trifluoroacetic acid)for 20 min at 1.2 ml/min flow rate (detection at214 nm) and by MALDI-MS using a-cyano-4-hy-droxy-cinnamic acid as matrix and purified to >95%purity by preparative HPLC on a Vydac C18 column,if necessary.

Surface plasmon resonance measurements

The affinity of peptides in solution to the mAb CB4-1was measured with regard to Kdis by monitoring adsorp-tion-dependent surface plasmon oscillations using theBIACOREX system (Biacore, Uppsala, Sweden). Boththe mAb CB4-1 and the anti-GST monoclonal antibody(control antibody) were immobilized on a dextran-coated gold surface in separate flow cells of a CM5sensor chip (Biacore AB) using the amine coupling pro-cedure (5 ll/min; activation with 1:1 EDC/NHS, 7 min;immobilization with 50 lg/ml antibody, 5- to 75-ll mul-tiple injections; deactivation of excess groups with 1 Methanol amine-HCl, pH 8.5, 7 min). The amount ofcovalently coupled antibodies corresponded to a signalincrease of approximately 5000 resonance units (RU)for both antibodies (flow cell 1: control antibody; flowcell 2: mAb CB4-1). All binding experiments were per-formed at 20 �C with a flow rate of 15 ll/min (injectionvolume 10 ll). Peptides were used at various concentra-tions between 20 pM and 200 mM in HBS (10 mMHepes with 0.15 M NaCl, 3.4 mM EDTA, and 0.005%surfactant P20, pH 7.4). Complete regeneration was ob-tained after dissociation without regeneration buffer inmost cases. Different regeneration procedures (BIAco-reX manual) were required in some cases. Transforma-tion of data and analysis were performed with theBIA-evaluation software, version 3.0. The control sen-sorgram (flow cell 1) was subtracted from the sensor-grams obtained with flow cell 2. The steady statevalues of the binding equilibrium were plotted versusthe different peptide concentrations and fitted usingthe implemented steady state evaluation, resulting inthe Kdis for each model peptide (Table 1).

Results and discussion

Spot signal intensities: reproducibility and improvements

Performing a binding experiment with a cellulose-membrane-bound peptide array (see Materials andmethods) results in measurable spot signal intensitiessignifying peptide–protein interactions (Fig. 1). Stan-

dard deviation of the SIs measured for several peptidereplicas on one membrane varies in the range from 8to 22%. We assume that inhomogeneity of the modifiedcellulose membrane is largely responsible for this varia-tion, since the synthesis quality of all peptides used inthe binding experiment is well established [15,16,19–21]. The membrane-related inhomogeneity of measuredSIs was confirmed by analyzing their spatial distribution(Fig. 2). For this purpose, we determined the mean val-ues of the replica SIs for each peptide on the membraneCM6000-50 and calculated the relation of each single SIto its mean value, thus determining regional trends. Thisrevealed that peptides with similar mean signal intensi-ties tend to have similar regional trends and peptideswith different mean signal intensities have different re-gional trends (Figs. 2B and D). Here, regional trends de-note the trends of spots in different local parts of themembrane. Furthermore, signal intensity fluctuationsof the background correlate with those of weak binders(Figs. 2C and D). After analyzing several membranes itbecame obvious that regional trends are intrinsic charac-teristics of individual membranes. This presents anopportunity to correct measured SIs and thus reducestandard deviation. A minimum of two references are

Fig. 2. (A) Neighborhood of a spot (gray). The size of the neighborhood N indicates that it consists of N · N spots. The black spots representreference spots. (B–D) Mapping of the membrane CM6000-50 (18 cm · 24.4 cm) containing 6000 spots (67 rows · 90 columns). Light areas denoterelatively high and dark areas low signal intensity values. (B) Relative signals of the high-affinity reference peptide (about 1000 data points,pKdis = 9), (C) background (6000 data points), (D) a weak-binding peptide (about 1000 data points, pKdis = 4). Note that maxima and minima ofmapping (B) have different locations compared to (C and D). The scale gives the relation between the local and the global mean signal.

304 Array-based measurement of peptides / A.A. Weiser et al. / Anal. Biochem. 342 (2005) 300–311

necessary—one peptide with high-affinity and one withlow-affinity to the binding partner. The algorithm forimproving measured SIs involves the following fivesteps: first, calculating the mean SI values of all high-ð �H globalÞ and low-affinity references ð�LglobalÞ; second,defining a neighborhood i for each spot with N spotsaround it (Fig. 2A); third, calculating the mean SI valuesof the high- ð �H local;iÞ and low-affinity references ð�Llocal;iÞwithin each neighborhood i; fourth, calculating the vari-ables a and b with the equations �Lglobal ¼ ai � �Llocal;i þ biand �H global ¼ ai � �H local;i þ bi; fifth, the improved signalintensity for each spot in its neighborhood i (SIimproved)can then be calculated from the measured signal intensi-ties (SImeasured).

SIimproved ¼ ai � SImeasured þ bi. ð1ÞThe standard deviation of the SIimproved values for

replicas of the same peptide will be smaller than thatof SImeasured. As an alternative to a low-affinity referencepeptide, the background signals of each spot can also beused as references. The resulting standard deviations areshown for the SCM-50 membrane in Fig. 3A (stars). Theefficiency of improvement is influenced by the neighbor-hood size N and the percentage of reference peptidesregularly distributed on the membrane. To determineoptimal parameters, standard deviations of SIimproved

were calculated for the CM6000-50 membrane usingbackground signals as the low-affinity reference andconsidering different neighborhood sizes N and differentpercentages of high-affinity reference peptide replicas(Fig. 3B). As expected, increasing the number of high-affinity reference peptides improves the efficiency ofthe method and reduces the optimal neighborhood sizeN (Fig. 3B). The results suggest that good adjustmentfor regional trends can be achieved when around 4%of the spots on a membrane are high-affinity referencepeptides and by using a neighborhood with N · N spots,when N is between 10 and 20.

In practice, there are often no replicas available on amembrane or no high-affinity peptide is known before-hand. In such cases, SIimproved can be calculated by usingonly the background signal around each spot accordingto

SIimproved ¼ SImeasured ��Lglobal;i

�Llocal;i. ð2Þ

The improvements achieved by applying Eqs. (1) and(2) are compared in Fig. 3C. Note that the decrease instandard deviation is smaller when using Eq. (2), espe-cially for peptides with high signal intensities.

We compared SI measurements made from two iden-tical membranes prepared with the same peptides, the

Fig. 3. Standard deviation of the signal intensity versus size of the neighborhood and the mean signal intensities, respectively, after applying the noisereduction algorithm. (A) Standard deviations of the signal intensities for each of the 38 different peptides (10–15 spots each) on the SCM-10membrane (Fig. 1) versus their mean values (circles). Gray diamonds denote the standard deviation after application of the noise reduction algorithmusing only background SI values as a reference. Black stars show the effect of the noise reduction algorithm using background SI values and high-affinity peptide repeats (14% of total spots) as references. The standard deviation obtained for the corrected signal intensities depends on the size ofthe chosen local neighborhood (N) and on the number of reference peptides in it. (B) and (C) show the standard deviation of corrected signalintensities for two peptides, one with low and one with high binding affinity, using the background and a high-affinity reference peptide (B) or onlythe background as reference (C). In (B), four cases where the numbers of high-affinity reference peptides are 14, 7, 4, and 2% of the total number ofspots on the membrane are shown. The signals are derived from membrane CM6000-50.

Array-based measurement of peptides / A.A. Weiser et al. / Anal. Biochem. 342 (2005) 300–311 305

same number of spots, the same concentration of anti-body, the same FQ, and the same incubation time. Wefound signal intensity deviations of around a factor of10. Nevertheless, the relations of the signals were fairlyconstant for all peptides, suggesting that, to compareSIs from different membranes, these values should firstbe normalized using

SInorm ¼ SImeasured � SImin

SImax � SImin. ð3Þ

Note that, below, this equation will be used only for bet-ter visualization of the intermediate region (Fig. 4), withSI being the mean signal intensity values for each recur-rent peptide.

Correlation between signal intensities and dissociation

constants

A representative repertoire of 38 peptides was se-lected from a set of over 100 peptides, all known tointeract with mAb CB4-1 (Table 1). All chosen peptidesare well described in the literature and dissociation con-stants (pKdis) for the various peptide/antibody com-plexes span a range of more than five orders ofmagnitude (pKdis = 9 to pKdis = 3.5). As an example,mean values of measured SIs obtained from a SCM-10membrane were used to draw an SI/pKdis scatter plot(Fig. 4A). It demonstrates that the obtained SIs corre-late with given pKdis. To describe the SI/pKdis depen-

½A � � ½P i � ¼ Kdisi � ½AP i�; ð4Þ

Fig. 4. Mean signal intensities versus dissociation constants of all measured peptides. All signal intensities are normalized according to Eq. (3). Thegray region marks all signals that are weaker than the mean background signal. (A)Mean values of the 38 different peptides on the SCM-10 membranewith an antibody concentration of [AT] nM. The solid curve was derived by fitting Eqs. (4)–(7) to the data. The scale of the SI axis is logarithmic. (B–D)Fitting of the results from several experimental setups with all parameters held constant except one: (B) two membranes prepared with a differentnumber of peptide replicas, (C) two membranes loaded with different FQ, (D) two membranes incubated with different antibody concentrations.

306 Array-based measurement of peptides / A.A. Weiser et al. / Anal. Biochem. 342 (2005) 300–311

dency mathematically and elucidate understand whichparameters influence the correlation, we defined a massaction law model. It is based on the assumption that thesystem is in equilibrium and that the mass action law isthe underlying effect. Furthermore, we have to take intoaccount that competition among the peptides for mAbCB4-1 might take place, especially in cases when peptideconcentrations or the number of spots are high com-pared to the antibody concentration.

Since cellulose membranes are porous, the concen-tration of antibody within the fibers may be differentfrom the antibody concentration [AT] in the bulk solu-tion. The inter-fiber spaces could be on the order ofmagnitude of antibody molecules in size. As describedby Minton [24], this could lead to confinement effectsand modified diffusion lengths. Since peptide–antibodyinteractions primarily occur in the inter-fiber spaces, we

define a total effective antibody concentration ½AeffT � for

this space. Furthermore, the surface density of accessi-ble peptides on a spot is not known. It may be influ-enced by positive cooperativeness: cluster formationof several peptide molecules within a spot may decreaseits concentration [25,26]. We define a total effectivepeptide concentration per spot ½P eff

T � and assume thatit is the same for all spots. Unfortunately, it is not pos-sible to determine the parameters ½P eff

T � and ½AeffT � exper-

imentally. We therefore estimate these effectiveparameters by the proposed mass action law model.To formulate the model, we first define Eqs. (4)–(6).Here, ½P eff

i � and [Aeff] denote the concentrations of un-bound peptide within a spot i (i = 1, . . . , n) and un-bound antibody, respectively.

eff eff

Array-based measurement of peptides / A.A. Weiser et al. / Anal. Biochem. 342 (2005) 300–311 307

½P effT � ¼ ½P eff

i � þ ½AP i�; ð5Þ

½AeffT � ¼ ½Aeff � þ

Xni¼1

½AP i�. ð6Þ

Eq. (4) simply states the mass action law for one sin-gle spot, Eq. (5) sums the unbound and bound fractionsof the peptide population in spot i, and Eq. (6) sums theconcentration of free antibody with the sum of all com-plexes to the given total antibody concentration. Thisdescribes a nonlinear system of 2n + 1 equations withthe 2n + 1 variables ½P eff

i �, [APi], and [Aeff] and theparameters ½Aeff

T � and ½P effT �. Furthermore, it is reasonable

to assume that the concentration of the antibody–pep-tide complex [APi] within a spot is proportional to itsmeasured signal intensity and to introduce the back-ground signal as an additive factor. Thus, we addition-ally define Eq. (7) with the proportionality factor aand the background parameter b:

SIi ¼ f ðpKdisiÞ ¼ a � ½AP i� þ b. ð7Þ

Eqs. (4)–(7) are used to fit the free parameters ½AeffT �,

½P effT �, and b to the measured experimental data using

the functions ‘‘nls’’ and ‘‘nls.lm’’ from the R languageenvironment [27]. We exclude parameter a from the fit-ting procedure to avoid redundancies and due to the factthat a differs from membrane to membrane. Instead, itwas estimated by the formula a ¼ SImax

½P 0T� , where ½P 0

T� de-notes the sweeping start parameter of the fitting processfor ½P eff

T �.To evaluate the relevance of the model, we specifi-

cally varied several experimental parameters: the num-ber of spots on a membrane, the FQ, and the antibodyconcentration. The fitting process was accomplishedfor each binding experiment. The correlation coefficientsbetween the mean values of the measured SI and the fit-ted SI were found to be between 0.83 and 0.91. Table 2summarizes all fitting results and the experimental con-ditions used. Figs. 4B–D show the best fits to the ob-tained experimental data after normalization with Eq.(3).

First, we observed that the effective peptide concen-tration increases with decreasing FQ. Increasing themembrane FQ from 10 to 100% resulted in a decrease

Table 2Several fitted and experimental parameters for different experimental setups

No. Membrane Spots FQ (%) [AT] (nM) a

1 SCM-10 607 10 6.3 5.2e2 SCM-25 607 25 6.3 6.6e3 SCM-50 607 50 0.63 8.7e4 SCM-50 607 50 6.3 7.4e5 SCM-50 607 50 63 6.9e6 SCM-100 607 100 6.3 1.0e7 CM2090-50 2090 50 6.3 9.8e

of the fitted total effective peptide concentration from280 to 42 pM. This result is supported by the fact thatabsolute measured SIs decrease with increasing FQ also(data not shown). The decrease of effective accessiblepeptide concentration with increasing FQ can be ex-plained by a clustering effect [25,26], suggesting thatmuch lower FQs than those used here could also yieldgood results.

Second, the fitted total effective antibody concentra-tion ½Aeff

T � does not increase with the same order of mag-nitude as the concentration [AT] originally applied in thebulk solution. While [AT] increases by a factor of 100,½Aeff

T � increases only by a factor of approximately 4. Mostlikely, the total effective concentration of the antibodysaturates within the membrane and one consequence isa nonlinear correlation between the total effective con-centration within the spots and the concentration ofthe antibody in solution.

Third, several competition effects were observed. Twomembranes with identical antibody concentration andFQ and the same peptides, but with a different numberof spots, i.e., different reiteration of the peptides (seeMaterials and methods), show very different signalbehavior. This can be understood if one considers thatmany spots with high-affinity bind many antibody mole-cules, thus depleting the solution of free antibodies. Few-er antibody molecules are then available for binding topeptides with lower affinity, so they will have lower SIscompared to when there are only a few high-affinity spotsand therefore less competition for antibody (Fig. 4B).

Furthermore, competition for antibodies may alsopossibly explain an effect described by Kramer et al.[16]: signal intensities either increase or decrease withthe FQ of the membrane, depending on the peptideinvestigated. In a simulation of this experiment applyingEqs. (4)–(7), we compared two model results where onlythe peptide concentration was varied: ½P eff

T � ¼ 100 nMand ½P eff

T � ¼ 400 nM, both with ½AeffT � ¼ 10 lM and seven

peptides (pKdis = 9 up to pKdis = 3) each replicated 15times. The results shown in Fig. 5 illustrate that peptideswith high binding affinity show decreasing signal inten-sities for decreasing ½P eff

T � (and hence increasing FQ),while the converse applies to peptides with low bindingaffinity.

b ½P effT � ðpMÞ ½Aeff

T � ðnMÞ Correlation

+13 2100 280 180 0.88+13 3100 140 190 0.86+13 1400 130 70 0.89+13 2800 90 190 0.86+13 2500 100 260 0.85+14 2400 40 190 0.83+12 300 100 100 0.91

Fig. 6. (A) Signal intensity versus dissociation constant for eachsingle spot. The class borders obtained by maximizing the contin-gency coefficient R (Eq. (12)) for classification into three affinityclasses are shown as dashed lines. The gray region marks all signalsthat are weaker than the mean background signal. The SI axis haslogarithmic scale. (B) ROC curve generated for classification ofpeptides on the SCM-25 membrane with [AT] = 6.3 nM in twobinding affinity classes. The area under the curve (AuC value) is 0.97,indicating that signal intensity obtained as the output of the SPOTtechnology is an excellent quantity for the discrimination betweenhigh- and low-affinity binders.

Fig. 5. Signal intensity versus dissociation constant calculated fromEqs. (4)–(7) for two cases which differ only in the peptide concentra-tion. In this theoretical investigation the signal intensities are smallerfor ½P eff

T � ¼ 100 nM than for ½P effT � ¼ 100 nM if peptides have low-

affinity but larger if their binding affinity is high.

308 Array-based measurement of peptides / A.A. Weiser et al. / Anal. Biochem. 342 (2005) 300–311

Detection of high-affinity binders from signal intensity

data

The most important application of the SPOT synthe-sis technique is to detect peptides that have a strongbinding affinity to defined targets. In practice, thereare often no replicate peptides on cellulose membranearrays so one cannot calculate mean values. Therefore,we investigated the confidence of the SPOT synthesistechnique in detecting high-affinity binders for nonre-current spots. First, we had to define classes of high-and low-affinity peptides. As depicted in Fig. 6A, wedefine two borders SI1 and SI2 on the y axis (for the sig-nal intensities) and two borders pK1

dis and pK2dis on the x

axis (for the peptides� affinity). The four borders are freeparameters defining three classes of signal intensities andthree classes of dissociation constants, resulting in ninedisjoint quadrants in the plot. For each of the ninequadrants the number of occurrences of spots can be as-signed for each membrane and is denoted as nij (i,j = 1,2, 3 are the enumerations of the SI classes and the pKdis

classes, respectively).To determine how well the signal intensity class cor-

responds to the actual affinity class of the peptide, wecalculate their mutual information (transinformation).We introduce the following quantities: first, the entro-pies of signal intensity and dissociation constant (Eqs.(8)–(10)) and second, the transinformation of signalintensity and dissociation constant (Eq. (11)):

HðSIÞ ¼ �X3i¼1

P3j¼1nijP3j;k¼1njk

� log 2P3

j¼1nijP3j;k¼1njk

! !; ð8Þ

HðpKdisÞ ¼ �X3i¼1

P3j¼1njiP3j;k¼1njk

� log 2P3

j¼1njiP3j;k¼1njk

! !; ð9Þ

HðSI;pKdisÞ ¼ �X3i¼1

X3j¼1

nijP3k;l¼1nkl

� log 2 nijP3k;l¼1nkl

! !;

ð10Þ

IðSI; pKdisÞ ¼ HðSIÞ þ HðpKdisÞ � HðSI; pKdisÞ. ð11ÞThe value for the transinformation I lies between zeroand infinity. To rank the value of the transinformation,we normalize it and define the contingency coefficient(R) that is bounded by zero and one (Eq. (12)):

Table 3Calculated pKdis and SI borders with their corresponding contingency coefficients (R) and AuC values

No. Membrane FQ (%) [AT] (nM) R SI1 SI2 pK1dis pK2

dis AuC

1 SCM-10 10 6.3 0.92 4500 8900 6.8 7.2 0.972 SCM-25 25 6.3 0.92 3300 7400 5.3 6.8 0.973 SCM-50 50 0.63 0.96 3700 9200 6.8 7.2 0.984 SCM-50 50 6.3 0.90 3700 6500 5.3 6.8 0.965 SCM-50 50 63 0.93 3200 7600 5.3 6.8 0.956 SCM-100 100 6.3 0.83 3200 4800 5.3 6.8 0.90

For calculating the AuC value the SI border of the ROC curve was the mean value of the background signals plus three times its standard deviation(see Fig. 6B).

Array-based measurement of peptides / A.A. Weiser et al. / Anal. Biochem. 342 (2005) 300–311 309

RðSI; pKdisÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� expð�2 � IðSI; pKdisÞÞ

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� expð�2 �minðHðSIÞ;HðpKdisÞÞÞ

p .

ð12ÞNote that, when the classifications SI and pKdis are inde-pendent, then H(SI) + H(pKdis) = H(SI, pKdis) andtherefore R(SI, pKdis) = 0. The larger the value of thecontingency coefficient R, the more informationthe two classifications have in common. We calculatethe R values for a sweep of the parameters pK1

dis,pK2

dis, SI1, and SI2 and determine the borders with the

best R value.This procedure was applied to several cellulose mem-

branes that we examined and the resulting contingencycoefficients lay between 0.83 and 0.96 (Table 3) showinghigh correlation for the distinction of the three definedclasses of peptide binding affinities. SIs larger than SI2

may be associated with a dissociation constant smallerthan pK2

dis and SIs smaller than SI1 may be associatedwith a dissociation constant larger than pK1

dis. The inter-mediate class between the two borders pK1

dis and pK2dis

isolates a small region of dissociation constants (‘‘dy-namic range’’), so that measured signals inside the corre-sponding SI class may be associated with anapproximate dissociation constant. Under the oftenused condition (FQ = 50% and [AT] = 6.3 nM), the dy-namic range of the curve is between pK1

dis ¼ 5.3 andpK2

dis ¼ 6.8.Applying the transinformation to more than the three

classes described above led to singleton classes (data notshown). This suggests that any other attempt to classifythe results of the SPOT technology into more classeswould be meaningless. For instance, it seems to beimpossible to assign a dissociation constant to eachmeasured signal. This is due to the extreme variabilityof the data in the central class and the saturation takingplace far off the dynamic range.

In the data investigated we found that the lowerborder for signal intensities (SI1) never exceeds thebackground signal plus three times its standard devia-tion. To confirm that this value is an objective borderfor distinguishing between the two classes of high- andlow-affinity peptides we applied ROC statistics to themeasured data. Contrary to the above, we need to de-fine only one border pK1

dis as the border distinguishing

between low- and high-binding affinity classes. Fur-thermore, we determine the border for separatinglow and high signal intensities (SI1) with the criteriadescribed above (background signal plus three timesits standard deviation), finally resulting in four quad-rants nij (i,j = 1,2). With these, we calculate true posi-tive (TP) rates and false positive (FP) ratesðTP ¼ n11

n11þn21;FP ¼ n12

n12þn22Þ. Moving the border pK1

dis

over the range of all possible values will change TPand FP. Plotting (TP, FP) points into a diagramand connecting those gives a ROC curve (Fig. 6B).The area under the ROC curve is a measure of thequality of discrimination between the two classes.Random prediction would result in a bisecting ROCline, giving an AuC value of 0.5. The closer theAuC is to 1.0, the better is the classification. TheSI1 border of background signal plus three times itsstandard deviation results in AuC values of up to0.98 for the differently synthesized membranes (Table3), suggesting that signal intensity is an excellent clas-sifier for high- and low-affinity binders. Note that thebest pK1

dis value for the distinction of high and low-af-finity is defined by the experimental setup and willusually not be known by the experimenter. The exam-ple ROC curve for membrane SCM-25 shown in Fig.6B suggests a good pK1

dis value at 6.7: 90% of peptidesclassified as having high affinity in fact belong to theclass of peptides with pKdis < pK1

dis, while only 7%of the peptides in this class were wrongly classifiedas being low-affinity binders ðpKdis > pK1

disÞ. An evenhigher accuracy of classification can be achieved whenmean SI values of replica peptides are used.

Conclusions

We describe a method to reduce the standard devia-tion of signals measured with the SPOT technique. Itis able to approximately halve the standard deviation(Fig. 3A), resulting in improved signal intensities for fur-ther analysis. To make the best use of this method, wesuggest that around 4% of the spots on a membraneshould be homogeneously distributed repeats of a refer-ence peptide possessing high-affinity toward the ligand,if available. This leads to (i) optimal results in the algo-

310 Array-based measurement of peptides / A.A. Weiser et al. / Anal. Biochem. 342 (2005) 300–311

rithm for reducing signal noise due to regional trendsand (ii) optimal conditions for automatic grid position-ing by the software that measures signal intensities. Forexperiments where no strong binding peptides areknown beforehand, the noise reduction algorithm canstill be applied with only background signals as refer-ences. In this case noise reduction is suboptimal (Fig.3A).

We report good agreement between model resultsbased on the mass action law (Fig. 4A). The model takesinto account competition among peptides for free anti-body molecules. It describes several observed effects,such as a shift in the ‘‘dynamic’’ range and hence theborder separating high- and low-affinity classes whenonly the number of peptide replicas on a membrane ischanged (Fig. 4B) and the apparently contradictorybehavior of different peptides� SIs when experiments per-formed with different amino-functionalization (FQ) val-ues are compared. This observation suggests thatcompetition effects do indeed play a role in the usualexperimental setup and that, due to this effect, inter-membrane SI comparisons have to be handled with careeven after normalization of the values (but note that thiseffect does not disrupt the ability to classify peptidesaccording to their affinity when the SIs used were mea-sured on a single membrane). It also suggests that a de-crease in effective peptide concentration, possibly bydramatically decreasing FQ, could help diminish thiseffect.

Fitting of the model to experimental data to estimateexperimental parameters suggests that the effective con-centration of accessible peptides on the cellulose mem-brane decreases for increasing FQ. It is expected thatfor an FQ much smaller than 10% this behavior canbe reversed. Moreover, the fitted parameters suggestthat the effective ligand concentration within the mem-brane fibers increases sublinearly with increased ligandconcentration in the bulk solution.

Classification of peptides into two classes representinghigh and low binding affinities is possible with high pre-dictive power using the measured signal intensities as cri-teria. The SI threshold separating both classes is bestchosen as the mean value of the SIs of the spot back-ground signals plus three times its standard deviation.Re-cently, the method derived here was successfully appliedto characterizing PDZ domain/ligand specificity [13,14].

The SPOT technique also allows differentiation be-tween three classes of dissociation constants: high,low, and intermediate. The most frequently usedexperimental condition (FQ = 50% and [AT] = 6.3 nM)yields an intermediate class whose affinities lie betweenpK1

dis ¼ 5.3 and pK2dis ¼ 6.8. This dynamic range, and

with that the pK1dis border of classification in two clas-

ses, can be shifted by altering the effective concentra-tions of the binding partners. There are twopossibilities for varying the peptide concentration:

changing the FQ or using a differently coated mem-brane, e.g., CAPE, as described [23]. Furthermore,the ligand concentration in the bulk solution can bevaried.

Acknowledgments

This work was in part supported by the DeutscheForschungsgemeinschaft (SFB 618 and SFB 449).M.O.G and V.T. thank the Volkswagen Foundationfor funding. We thank W. Hoehne (Institut fur Bioche-mie, Berlin, Germany) for providing the CB4-1 anti-body. Excellent technical assistance by I. Kretzschmaris gratefully acknowledged. We thank N. Bruni for help-ful criticism and comments.

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