Competitively selected protein ligands pay their increase in specificity by a decrease in affinity

Abstract

Protein–ligand interactions characterise and govern the current state and fate of a living cell. The specificity of proteins is mainly determined by the relative affinities to each potential ligand. To investigate the consequences and potentials of ligands with increased specificity in comparison with ligands optimised solely for affinity, it was necessary to identify ligands that are optimised towards specificity instead of a barely optimised affinity to a given target. In the presented example, a modified phage display screening procedure yielded specific ligands for the LckSH3 domain. We found that increased specificity of one of the hereby obtained ligands for LckSH3 is achieved at the cost of a slightly reduced affinity to LckSH3 and a drastically reduced affinity to other SH3 domains. A surface plasmon resonance experiment simulating in vivo-like realistic competitive binding conditions exerted enhanced binding behaviour of the specific ligand under these binding conditions. The experimental data, together with a mathematical model describing the complex experimental situation, and theoretical considerations lead to the conclusion that increased specificity is achieved at the cost of reduced affinity, but after all, it pays if the ligand is applied under realistic, i.e. competitive, conditions.

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Introduction

The specificity of proteins is determined by their relative affinities to each potential ligand. Regulatory networks within a living cell are based on transient interactions between proteins. Thus, the availability of each potential ligand and the specificities of each protein determine the extent to which each protein is complexed to a certain ligand. As an important consequence of this, not only does the absolute affinity of a certain protein–ligand pair govern the concentration of its complex, but the affinity in relation to other available potential ligands, and the absolute concentrations of both protein and ligands contribute as much.

Highly specific ligands are especially difficult to achieve when the protein target is extremely homologous to other proteins that are not to be targeted by their respective ligand. A special challenge in this respect are SH3 domains of the Src-type tyrosine kinase family, which show considerable sequence homology to each other and moreover, exert very similar ligand binding properties. Src-type tyrosine kinase are divided into two groups (group A: Fyn, Fgr, Src, Yrk and Yes; group B: Blk, Hck, Lck and Lyn).^1,2 SH3 domains of kinases within one group show extremely strong homologies.

The principle ligand binding site of SH3 domains was, and still is, heavily investigated. The core motif recognized by the majority of SH3 domains is of the consensus sequence xPxxP and adopts a PPII helix conformation. Due to the pseudosymmetric character of the PPII helix, proline-rich peptides can bind to SH3 domains in two orientations, termed class I and class II. Flanking residues, which provide additional contact sites, are reported to provide most of the recognition specificity of SH3 domains.^3–7 Ligands of Src-type tyrosine kinase SH3 domains with class I orientation are of the consensus sequence +pxPpxP (+ = basic residue, mostly arginine; P = invariant proline, p = proline preferred), while the consensus sequence of class II orientation is xPpxPp+. Both xP-dipeptide parts form contacts with hydrophobic pockets. Often, a basic residue common at position P₋₃ (anchor position) forms contacts with a highly conserved acidic residue within the SH3 compass pocket and determines the binding orientation of the ligand. More details on SH3 ligand recognition are summarised in reviews, for example by Musacchio.⁸

In the past, a number of studies were carried out to enhance the affinity and selectivity of SH3 domain directed ligands. Advancements were achieved by replacing sequences flanking the PxxP motif with natural or non-natural moieties,^9–11 and by using N-substituted glycines, or peptoides, which function as ideal proline mimetics.¹² Recently, a potent non-protein ligand for the Fyn SH3 domain was identified via a combinatorial library strategy using a peptoid as starting point.¹³ In all these studies, increased specificity was achieved only after additional artificial modifications have been introduced to the peptide ligand.

Even though lots of artificial ligands for SH3 domains were identified by standard phage display screening approaches¹⁴ in the past (e.g. at least partially summarised by the iSPOT web tool),¹⁵ less effort to increase specificity is documented by these studies.

By default, a phage display screen includes the following steps. A phage-displayed peptide library is added to an immobilized SH3 target molecule. The different peptide ligands of the library show diverse binding properties to the chosen target, e.g. a certain SH3 domain. The library includes variants, which have no significant affinity to the target at all, as well as variants that show more or less affinity to the target SH3, but principally also to other SH3 domains, which are more or less related to the chosen target. Only a few variants of the library would show significant binding properties to the target SH3 molecule, regardless of their specificity. Conventional selection procedures include washing steps to eliminate the non- or less binding variants from the target SH3. At the end, those variants of the library that are still bound to the target molecule after the washing procedure, due to tight but not necessarily due to specific binding, are eluted and become a part of the sublibrary that is amplified to be used in the next selection round. Not surprisingly, artificial SH3 ligands from conventional phage display studies mostly show very modest specificities and sometimes even higher affinities to other SH3 domains as to the target SH3 used as bait during the screening. Exemplarily, we have recently identified peptidePD1 by a standard phage display approach for binding very tightly to the LckSH3 domain.¹⁶ Further investigation revealed that PD1 binds even more tightly to the SH3 domain of Hck¹⁷ and could be used to successfully shield HckSH3 against HIV-1 Nef binding.¹⁸

In principle, increased specificity during the screening of a phage-displayed peptide library can be obtained by negative selection against molecules that are not supposed to be bound by the ligand to be identified. Such a counterselection can be achieved either by subtractive panning methods or by including the non-target molecules as competitors, for example during distinct washing steps of the procedure. Such examples are reported, for example, the selection of peptideinhibitors for enzymes,^19,20 for cytokine antagonists,²¹ for antibody design,^22,23 or others.^24,25

The objective of the present work was to quantitatively compare the properties of unspecific and specific ligands for LckSH3 that were obtained from the same phage-displayed peptide library without and with a counterselection step for other SH3 domains, respectively. To do this, it was necessary to use the earlier described selection procedure¹⁶ and introduce a negative selection step (counterselection) for the relatively unrelated SH3 domains of Abl and Pi3k, but also for the highly related SH3 domains of Hck, Lyn and Src. Based on a quantitative characterisation of unspecific and specific ligands for LckSH3, we will discuss the consequences of increased specificity under competitive conditions, as it is the case in a living cell.

Experimental

Expression and purification of SH3 domains

Expression and purification of GST-tagged SH3 domains were carried out as described previously.¹⁶

Competitive phage display selection

A commercially available peptide library kit (PhD.-12 Peptide Library Kit, New England Biolabs, Inc., Beverly, MA) was used as described¹⁶ with immobilised GST-tagged LckSH3 as the selection target. Other than given in the standard procedure, the phages were competitively washed in the presence of a mixture of GST-tagged SH3 domains in equal shares, which were added to the washing buffer (step 9 of the panning procedure) at an overall concentration of 1, 10, 100 and 1000 nM in rounds two, three, four and five, respectively. The competitor mixture included equimolar concentrations of the GST-tagged SH3 domains from Hck, Src, Abl and PI3K. Progress of affinity selection after each round was tracked by monitoring the phage titer as well as by using an anti-phage ELISA detection system, which is described in detail elsewhere.¹⁶

Peptide synthesis

Peptides with unmodified N- and C-termini were synthesized commercially by JPT Peptide Technologies GmbH (Berlin, Germany) with a free, unmodified N-terminus, to resemble more closely the peptides in their phage-displayed form. Please note that this resulted for PD1’s binding to LckSH3 in a more than ten-fold increased affinity than previously reported.¹⁶

Determination of dissociation constants (K_d) by surface plasmon resonance analysis (SPR)

The dissociation constants for each complex between the different SH3 domains from Hck, Lyn, Src, PI3K and peptidePD1 or cLck1 were measured using a BIAcore X (Biacore AB, Sweden). Each SH3 domain was immobilized on a CM5 carboxymethyldextran biosensor chip (Biacore) viaamine coupling. Immobilizations of the different SH3 domains (in 10 mM sodium acetate, pH 4.5) were performed at 25 °C at a flow rate of 5 μl min⁻¹ in HBS-EP running buffer (10 mM Hepes, pH 7.4, 150 mM NaCl, 3 mM EDTA, and 0.005% P20 surfactant). In each case a second channel on the same chip was treated only with the sodium acetate buffer as a negative control. The binding curves of peptidePD1 or cLck1 at various concentrations to the different SH3 domains were determined at 25 °C with a flow rate of 5 μl min⁻¹. The K_d values were calculated using the Biacore Analysis Software (Bioevaluation) by fitting the mean maximum response values from the binding curves to a simple 1 : 1 ligand receptor binding model.

SPR assay to determine empiric equilibrium response (R_eq/emp) values in the presence of competing SH3 domains

For measuring the equilibrium response (R_eq/emp) under competitive conditions, all analyte solutions were preincubated with a mixture of GST-tagged SH3 domains from Hck, Lyn, Src and PI3K at concentrations of 40 μM each in HBS. R_eq/emp was measured for injections of different concentrations of the investigated preincubated analytes (peptidePD1: 5, 15, 45, 60, 75, 90, 120, 150, 250 and 350 μM; peptidecLck1: 15, 30, 60, 90, 150 and 250 μM) in HBS buffer over a sensor chip with immobilized LckSH3 domain at a flow rate of 5 μl min⁻¹ for 180 s. The binding curve of a HBS buffer injection without peptideanalyte and of HBS buffer supplemented with the competitor SH3 domain mixture was subtracted from each analyte binding curve (‘double referencing’).²⁶ For the calculation of R_eq/emp, steady-state values between 90 and 170 s of each binding curve were averaged.

Theoretical model of the competitive SPRassay

To describe the behaviour of the LckSH3-specific ligand cLck1 in comparison with the high affinity and low specificity ligand PD1 identified previously,¹⁶ a quantitative theoretical approach was established, which models the theoretical equilibrium response (R_eq/theo) of a SPR experiment. R_eq/theo therefore mirrors the expected RU signal when the current conditions are applied long enough to reach equilibrium in the experimental system. When the analyte (peptidecLck1 or PD1) is injected in different concentrations (P_k) over the ligand surface (immobilized LckSH3 domain; LckSH3), then R_eq/theo resembles the amount of occupied binding places. R_eq/theo depends on the maximal feasible signal in response units (R_max), the dissociation constant of the analyte ligand complex (K_dSH3_LckP_k) and the free analyte concentration ([P_kfree])²⁷).R_max : R_max is the maximal feasible signal in response units (RU). The theoretical R_max/theo can be calculated by multiplying the RU value, which corresponds to the total amount of bound LckSH3 (R_SH3Lck), by the amount of analyte binding places per ligand (valency V) and by the molecular weight (MW) relation between ligand LckSH3 and analyte P_k. With an R_SH3Lck = 300 RU, MW_SH3Lck = 7018 Da, V_SH3Lck = 1, MW_PD1 = 1347.7 and MW_cLck1 = 1365.6 Da. R_max/theo for PD1 or cLck1 binding follows to be 57.6 RU or 58.4 RU, respectively. We saw that R_max/theo differed from the maximal experimentally measured signals at saturation, which were around 35 and 38 RU for PD1 and cLck1. Thus, we determined the empirical R_max/emp from fitted SPR data, which were generated to determine the K_d values of the respective LckSH3 peptide complexes (above) by non-linear regression, which was 35.3 RU for PD1 and 37 RU for peptidecLck1, respectively. The differences between R_max/theo and R_max/emp can easily be explained by the fact that due to damage during the immobilisation procedure or due to sterical hindrances, not every immobilized ligand molecule is able to bind to an analytepeptide. In the case of the hereby used LckSH3 the valency had to be multiplied by an accessibility (correction) factor of ∼0.6, which means that around 60% of all LckSH3 molecules are undamaged and attached to the sensor chip in such way that their peptide binding pockets are accessible for the analytepeptides.

K _dSH3_LckP_k: the used dissociation constants K_dSH3_LckP_k were determined by SPR as described above, and were 3.6 × 10⁻⁶ M for the complex of LckSH3 with peptidePD1 and 6.5 × 10⁻⁵ M for its complex with peptidecLck1.

P_kfree: whereas values for the parameters R_max and K_d are easily accessible, values for P_kfree are not. Under the competitive conditions of our study, the analyte concentration equals the free peptide concentration [P_kfree] of the preincubation mixture. Preincubation means that the peptideanalytes were mixed with the competitor SH3 domains from Hck, Lyn, Src and PI3K at definite concentrations before they are allowed to encounter the immobilized LckSH3 domain. Thus, n = 4 competing SH3 domains (HckSH3, LynSH3, SrcSH3, PI3KSH3) bind to peptide P_k (PD1 or cLck1) and form complexes [SH3_iP_k]. Only those peptide molecules, which are not bound by a competing SH3 domain, are free for binding to the immobilized LckSH3 and contribute to the SPR signal. Known preincubation parameters are the total concentrations of the peptideanalyte [P_ktot] and the competitor SH3 domains [SH3_itot], as well as the corresponding dissociation constants K_dSH3_iP_k, which we determined by SPR (Table 1). With the following equations the distribution of concentrations of all components in the reaction vial can be described:

[P_kfree] = [P_ktot] − ([SH3₁P_k] + [SH3₂P_k] + [SH3₃P_k] + [SH3₄P_k]) (2a)

[SH3_ifree] = [SH3_itot] − [SH3_iP_k], i = 1,…,4 (2b)

[SH3_iP_k] × K_dSH3_iP_k = [SH3_ifree] × [P_kfree], i = 1,…,4 (2c)

Herein, SH3₁ = SH3_Hck, SH3₂ = SH3_Lyn, SH3₂ = SH3_Src, SH3₂ = SH3_P13K.

Table 1 SPR derived dissociation constants (K_d) of PD1 and cLck1 (given to the left) with the SH3 domains indicated in the line above

Peptide	K d value/μM
	LckSH3	HckSH3	LynSH3	SrcSH3	PI3KSH3
PD1	3.6	0.13	0.73	56	112
cLck1	6.5	8.6	27	150	800

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By combining eqns (2c) and (2b), applying eqn (2a), rewriting and factoring out of [SH3_iP_k] the following nonlinear system of equations and (2a) give the concentrations of the complexes [SH3_iP_k] and of the free peptide concentration [P_kfree], which is necessary to calculate R_eq/theo:

This nonlinear system of equations has no unambiguous analytical solution. Using sequential quadratic programming (SQP), non-negative solutions [P_kfree] ≥ 0 for the nonlinear system of equations, which are the only relevant solutions for our model, were obtained. SQP is a generalization of Newton’s method for nonlinear optimization problems.^28,29 Using a script, which conforms to the assumptions above, the concentrations of complexes [SH3_iP_k] and the concentration for [P_kfree] can be gained automatically depending on the applied total concentrations of competitor SH3 protein [SH3_itot] and peptide [P_ktot]. Once the free peptide concentrations in the preincubation mixture are known for the different peptide input concentrations, R_eq/theo can be calculated according to eqn (1).

Additionally, we calculated for every [P_ktot] the resulting complex concentration [SH3_LckP_k] by using the law of mass action.

After replacing the free LckSH3 concentration ([SH3_Lckfree]) by the term [SH3_Lcktot] − [SH3_LckP_k], eqn (4) can be solved for the different [SH3_LckP_k] values. On this, the theoretical LckSH3 concentration in the flow cell was assessed for [SH3_Lcktot]. It is known that for an average protein ligand on sensor chip CM5 a SPR response of 1000 RU corresponds approximately to a surface concentration of 1 ng mm⁻². If the thickness of the dextran matrix is taken to be 100 nm, this is equivalent to a volume concentration in the dextran matrix of 10 mg ml⁻¹ (Biacore Sensor Surface Handbook). In our experiments the total concentration of bound LckSH3 corresponded to 300 RU, which is equivalent to 3 mg ml⁻¹. Taking the volume of the dextran matrix into account (thickness of the dextran matrix × length and width of the flow cell = 100 nm × 2.1 mm × 0.5 mm = 1.05 × 10⁻⁴ mm³) 0.315 ng LckSH3 is bound. As the 0.315 ng LckSH3 (MW of 7018 Da) which equals 4.5 × 10⁻¹⁴ mol are distributed in the volume (2.1 mm × 0.5 mm 2 × 0.05 mm) of the flow cell which is 5.25 × 10⁻⁸ l, the theoretical LckSH3 concentration corresponds approximately to 860 nM. As we know from the R_max/emp to R_max/theo comparison only around 60% of the immobilized LckSH3 are able to bind the analytepeptide. Thus, the relevant [SH3_Lcktot] value reduces to approximately 520 nM.

Results

Screening of a randomised 12-mer peptide library for LckSH3 ligands by competitive selection with SH3 domain mixtures

A standard biopanning procedure was carried out using immobilized GST-tagged LckSH3 domain to a commercially available randomized peptide library that contains more than 10⁹ different 12-mer peptides. The only modification of the standard procedure to achieve a counterselection-type procedure consisted of adding recombinantly expressed and purified GST-tagged SH3 domains, which the ligands should not bind to, into the washing buffer. As described in more detail in the methods section, increasing concentrations of the respective competing SH3 domain mixtures were added to the washing solution in rounds two to five of the phage display screening procedure. The sequences of the phage-displayed peptides obtained after five rounds of selection against GST-tagged LckSH3 with the competing GST-tagged SH3 domains from Hck, Src, Pi3k and Abl present in the washing buffer are shown in Fig. 1. All but one phage variant (cLck5) contained the core PxxP binding motif.

Fig. 1 Amino acid sequences of peptide variants obtained from a PhD-12 peptide library by competitive phage selection against GST-tagged LckSH3 in the presence of a mixture of the GST-tagged SH3 domains from Hck, Src, Abl and PI3K. The number in parentheses denotes how often the respective sequence was found among the independently picked phages at the end of the selection procedure The proline residues belonging to the conserved PxxP motif of SH3 ligands together with the respective preceding residue and the “compass position” P₋₃ are boxed. The relative numbering of the sequence positions in the peptide sequences are according to the commonly used scheme.⁴

Semiquantitative characterization of phage-displayed peptide variants obtained by competitive selection

To obtain a rough impression of the binding properties of the most dominating peptide ligands derived from the competitive selection, we determined the relative binding affinities of the respective phages by anti-phage ELISA (Fig. 2A). The results suggest that cLck1 and cLck2 indeed bind to LckSH3 more tightly than the other SH3 domains assayed. Binding of cLck1 and cLck2 was significantly reduced to both SH3 domains of the B-group Src-type tyrosine kinases (HckSH3, LynSH3) and was even more diminished (cLck2) or virtually completely lost (cLck1) for the SH3 domain of Src, which belongs to the group A Src-type tyrosine kinases. AblSH3 and PI3KSH3 exerted virtually no binding to both peptides. Thus, the binding behaviour of cLck1 and cLck2 resembles the extent of sequence homologies among the assayed SH3 domains illustrated in Fig. 2B.

Fig. 2 A: Relative binding affinities of the phage displayed peptides cLck1 (black bars) and cLck2 (grey bars) to SH3 domains of proteins given below. Relative affinities were estimated using an anti-phage ELISA described in detail elsewhere.¹⁶ Briefly, phage particles, displaying peptide cLck1 (black) or cLck2 (grey), were adsorbed to microplate vials coated with the indicated SH3 domain as a recombinantly expressed and purified GST-tagged protein. After several washing steps retained phages were detected by using a HRP-conjugated anti-M13 antibody and measuring absorption at 450 nm upon addition of HRP substrates. For each phage clone, the mean values and the standard deviations of 10 colorimetric reactions for a set of different SH3 domains are shown. B: Homologies among the SH3 domains used in the study. The illustration was generated with the “Distances”-program (Wisconsin Package, Version 3.10; p-distance, gap penalty = 1) according to the commonly used classification for Src-type tyrosine kinases.⁵ Please note that FynSH3 appears in the phylogenetic tree solely to show a second member (in addition to Src) of the group A Src-type tyrosine kinases. It was not used in any experiment reported in the present work.

Quantitative analysis of various SH3 domain affinities to the competitively selected peptidecLck1 versus the PD1peptide obtained from a standard selection procedure

Dissociation constants between cLck1 and the SH3 domains from Lck, Hck, Lyn, Src and PI3K were determined by surface plasmon resonance (SPR) (Table 1). The obtained values can easily be compared with the dissociation constants of PD1 and the mentioned SH3 domains, as reported previously.¹⁶PD1 binds HckSH3 about 30-fold tighter than the original target LckSH3 (K_dSH3_HckP_PD1 = 0.13 μM, K_dSH3_LckP_PD1 = 3.6 μM). If the specificity of cLck1 for LckSH3 in relation to HckSH3 is expressed as the ratio of the K_d values for its binding to HckSH3 and LckSH3, it becomes obvious that for cLck1 this ratio is 37-fold that of PD1. Therefore, in the presence of HckSH3, cLck1 is much more specific for LckSH3 than PD1. The specificity increase of cLck1 compared to PD1 with respect to other SH3 domains is not that drastic, but still considerable.

Setup of an in vitro model to study competitive binding of PD1 and cLck1 to LckSH3

To study the competitive binding of the peptides PD1 and cLck1 to LckSH3, we designed an in vitroassay that comes as close as possible to the in vivo situation.

This was achieved by surface plasmon resonance (SPR) experiments performed with immobilized LckSH3 on the sensor chip surface. This allowed injection of defined amounts of either cLck1 or PD1 in order to determine the fraction of LckSH3 in complex with either one of the peptides. By injecting either one of the peptides together with increasing concentrations of competing GST-tagged SH3 domains (Src, Abl, PI3K, Hck and Lyn), the fraction of LckSH3, which is in complex with either one of the peptides, can be determined. This in vitro system enabled us to exactly control the concentrations of all proteins and ligands involved to allow comparison of the experimental results (fraction of LckSH3 in complex with cLck1 or PD1) with predicted values obtained from a mathematical simulation model describing complex formation in a mixture consisting of various SH3 domains and either cLck1 or PD1 based on their pairwise affinities (K_d values). The fraction of LckSH3 that is in complex with one of the peptides is simply measured as the increase of response units (RU) upon peptide injection (value after reaching the equilibrium phase, R_eq) divided by the increase of RU that can be reached under saturating conditions (R_max), when 100% of LckSH3 is complexed.

We ran a series of SPR experiments to obtain a set of empirical R_eq values (R_eq/emp), the averaged signals of each run during the equilibrium phase in the flow cell upon application of either cLck1 or PD1 at various concentrations. Competition was realised by adding the respective peptide solution to mixtures of GST-tagged SH3 domains from Hck, Lyn, Src and PI3K prior to injection. R_eq/emp was measured for different PD1 concentrations between 5 and 350 μM, and cLck1 concentrations between 15 and 250 μM. For clarity, only a small selection of the raw data is depicted in Fig. 3A. Equilibrium was usually reached after 90 s and was measured for 80 s. Thus, each R_eq/emp value was obtained by averaging the response during these 80 s. The R_eq/emp values of all experiments are summarized in Fig. 3B. Due to only moderate R_eq/emp absolute values of about 40 RU reached at saturation (R_max) and well below at lower analyte concentrations, the plots are somewhat scattered.

Fig. 3 SPR analysis of PD1 and cLck1 binding to the LckSH3 domain under competitive conditions. A: sensorgrams from PD1 or cLck1 binding to immobilised LckSH3 in the presence of 40 μM GST-tagged SH3 domains of Hck, Lyn, Src and PI3K, each. For reasons of clarity, only a subset of sensorgrams are shown for the injections of 15 μM, 30 μM and 250 μM of PD1 (grey) and cLck1 (black). To obtain the equilibrium response value (R_eq/emp) shown in Fig. 3B, the time dependent RU values of each SPR experiment were averaged between 90 s and 170 s after injection. B: experimentally determined equilibrium response values (R_eq/emp) for PD1 (□) and cLck1 (■) binding to immobilized LckSH3 compared with theoretically calculated equilibrium response values (R_eq/theo) using eqns (1)–(3) for PD1 (solid line) and cLck1 (dashed line).

Nevertheless, it is obvious, that cLck1 binds to immobilized LckSH3 under competitive conditions even at low concentrations, in contrast to PD1, which shows significant binding in presence of competing SH3 domains only at substantially increased peptide concentrations. The observed R_eq/emp values at low PD1 concentrations resemble very much a lag phase, which is clearly dominated by the strong interaction of PD1 with HckSH3 (K_d = 0.13 μM). This would explain why PD1 concentrations above the concentration of HckSH3 (40 μM) were necessary to yield R_eq/emp values above the background level.

Theoretical model describing the SPRassay

We developed a mathematical model describing the SPRassay with immobilized LckSH3 and injections comprised of competing SH3 domains with different PD1 or cLck1 concentrations. A detailed description of the model and its derivation is given in the methods section. Briefly, the concentrations of cLck1, PD1 and soluble SH3 domains were known. In addition, all pairwise dissociation constants between cLck1 or PD1 and all present SH3 domains were determined and thus known as well (Table 1). The amount of immobilised LckSH3 domain was determined by the RU difference value before and after immobilisation. A fraction of the immobilised LckSH3 was potentially damaged during the immobilisation procedure and thus was not competent for ligand binding. Therefore, a correction factor was determined from the ratio of R_eq/emp obtained under saturating conditions and the maximal R_eq that could theoretically be expected from the amount of immobilised LckSH3 when completely bound to either one of the peptides, and applied to the amount of immobilised LckSH3. According to all pairwise K_d values and the known total peptide and SH3 domain concentrations, the concentrations of free peptide, free SH3 domains, and complexed SH3 domains could be calculated using a sequential quadratic programming procedure. As a consequence, the fraction of immobilized LckSH3 that is complexed to either PD1 or cLck1peptide could be calculated as well, leading to theoretical R_eq values (R_eq/theo).

Table 2a and b present the results from the theoretical model for various concentrations of cLck1 and PD1. Table 2b clearly supports the above mentioned hypothesis that especially HckSH3 is responsible for the low concentration of free PD1 due to formation of large amounts of complexes with PD1. Calculated (R_eq/theo) and empirical values (R_eq/emp) are summarized and compared to each other in Table 3. Importantly, the values in Table 3 demonstrate that at high analyte concentrations, the modelled data for the concentration of the respective LckSH3 peptide complexes (504.3 for cLck1 and 508.9 for PD1) in fact converge very well with the theoretically accessible total LckSH3 concentration [SH3_Lcktot], which was determined to be approximately 520 nM. Finally, Fig. 3B compares the empirical R_eq values (single data points) with the expected, theoretical values (lines).

Table 2 (a) List of all possible SH3 peptide complex concentrations [SH3_iP_cLck1] and the free peptide concentration [P_cLck1free] after virtual preincubation of the peptidecLck1 with the competing SH3 domains from Hck, Lyn, Src and PI3K according to the mathematical simulation model. (b) The respective list for peptidePD1 instead of cLck1 (see heading of Table 2a)

(a)
PcLck1tot/μM	SH3iPcLck1/μM				PcLck1free/μM
	Hck	Lyn	Src	PI3K
5	3.04497	1.02295	0.18807	0.03540	0.70861
15	8.65238	3.23243	0.62313	0.11833	2.37372
30	15.79015	6.88041	1.44184	0.27850	5.60910
45	21.40452	10.73106	2.47635	0.48891	9.89917
60	25.64855	14.51009	3.71765	0.75400	15.36970
75	28.77518	17.98002	5.12568	1.07276	22.04637
90	31.05543	21.00568	6.64055	1.43924	29.85910
120	33.95914	25.66604	9.74976	2.27952	48.34554
150	35.60516	28.82851	12.68690	3.20464	69.67479
250	37.85403	33.95638	20.11275	6.37599	151.70085
350	38.62429	35.97694	24.67247	9.27369	241.452607

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(b)
PPD1tot/μM	SH3iPPD1/μM				PPD1free/μM
	Hck	Lyn	Src	PI3K
Please note that although AblSH3 was used as a competitor during the counterselection step of the selective phage display screening procedure, it was not applied as a competitor in the SPRassay , because the affinity of AblSH3 to both peptides (cLck1 and PD1) was too low to be determined. Thus, we did not add AblSH3 to the competitive SPRassay to avoid any component that was not quantitatively characterized. Concentrations were calculated using the nonlinear system of equations^3 which was solved by sequential quadratic programming. Only non-negative solutions for the concentration of the free peptide in the preincubation are shown ([Pkfree] ≥ 0). The concentration of the competing SH3 domains [SH3i] was 40 μM each, the total concentration of peptidecLck1 [PcLck1tot] was varied between 5 and 350 μM. The dissociation constants of the formed SH3icLck1 complexes (KdSH3iPcLck1) used for the calculation are shown in Table 1.
5	4.15892	0.80984	0.01077	0.00539	0.01508
15	12.03636	2.84778	0.03993	0.01997	0.05596
30	22.31900	7.34150	0.11687	0.05852	0.16410
45	30.11434	14.06783	0.28088	0.14094	0.39601
60	35.24896	22.76776	0.67726	0.34152	0.96450
75	38.14588	31.42330	1.82333	0.93293	2.67457
90	39.29855	36.35912	4.60753	2.44455	7.29025
120	39.77387	38.76836	11.64512	6.81444	22.99821
150	39.87807	39.32491	17.26457	11.00786	42.52460
250	39.95743	39.76210	27.41635	20.85541	122.00871
350	39.97552	39.86294	31.65185	26.18660	212.32308

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Table 3 List of the theoretically calculated and empirically determined equilibrium values (R_eq/theo; R_eq/emp) together with the theoretically calculated complex concentrations of LckSH3 and peptide ([SH3_LckP_k]) at given total peptide concentrations (P_ktot)

Pktot/μM	Pk
	cLck1				PD1
	Req/theo/RU	Req/emp/RU	[SH3LckPcLck1]/nM		Req/theo/RU	Req/emp/RU	[SH3LckPPD1]/nM
Req/theo values were calculated according eqn (1) using the respective Pkfree values from Table 2a and b. The complex concentrations were obtained by solving eqn (4) for [SH3LckPk]. The total concentration of peptidescLck1 and PD1 [PcLck1tot] was varied between 5 and 350 μM. Parameters for KdSH3LckPk were 6.5 μM for cLck1 and 3.6 μM for PD1. [SH3Lcktot] was experimentally estimated to be about 520 nM. Some Req/emp values that were not measured are indicated as not determined (“n.d.”).
5	3.63	n.d.	47.4		0.15	−1.94	1.9
15	9.90	10.13	129.6		0.54	−1.63	7.0
30	17.14	19.28	226.9		1.54	−0.43	19.8
45	22.33	n.d.	299.0		3.50	4.40	45.1
60	26.00	20.31	351.4		7.46	13.23	96.8
75	28.58	n.d.	389.2		15.05	23.15	198.9
90	30.39	29.41	416.3		23.63	24.43	323.1
120	32.62	n.d.	450.4		30.52	29.63	434.1
150	33.84	31.88	469.5		32.55	27.59	469.3
250	35.48	37.88	495.5		34.29	32.92	501.0
350	36.03	n.d.	504.3		34.71	32.76	508.9

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Discussion

The main objective of the present study was to investigate the consequences and potentials of ligands with increased specificity in comparison with ligands optimised solely for high affinity. To obtain ligands with increased specificity, we needed to modify the previously described phage display screening procedure that yielded PD1, a peptide that binds to LckSH3, but binds to, for example, HckSH3 even tighter.¹⁶ In order to identify ligands that are optimised towards specificity instead of a purely optimised affinity to LckSH3, a counterselection step was added to the procedure very similar as has been reported, for example, to identify inhibitors of tissue factor-factor VIIa complex.¹⁹ Similar to this approach, we added all proteins to the washing buffer, which the ligand was not supposed to bind to, i.e. the SH3 domains of Abl, Pi3k, Hck, Lyn and Src.

As shown for the LckSH3 ligand selection in the present study, the ligands identified at the end of the described procedure (e.g. cLck1), have decreased affinities compared to ligands obtained from non-competitive approaches (e.g. PD1). At a first glance, this might be surprising. Nothing else, however, could be expected because at least under saturating conditions, any potential ligand with increased affinity to the target (LckSH3) should have been identified already in the non-competitive selection approach due to its increased affinity, if both selections were carried out under identical conditions, except for the counterselection step. Thus, based on the example of LckSH3 ligand selection, our study shows that increased specificity has to be paid for by a decrease in absolute affinity. This may be a theoretical but even though a logic and inevitable general conclusion for in vitro screenings with any library that consists of a finite collection of ligands, as it is the case for a phage displayed peptide library. Indeed, we are not aware of any example in the literature where it was shown that in comparison with a selection for purely optimised affinity of the same library, a selection/counterselection procedure has yielded ligands with increased specificity and increased affinity at the same time.

We were able to show experimentally that cLck1 is much better suited than PD1 to specifically target LckSH3 even though the absolute affinity to LckSH3 was lower than that of PD1. Real quantitative data are derived from a controlled SPRassay , which confirmed the superior potential of cLck1 over PD1. Significant or even drastic differences between PD1 and cLck1 have been detected only at lower peptide concentrations (<100 μM). In the presence of higher peptide concentrations (>100 μM) both, PD1 and cLck1 behave very similar.

In order to understand the basis of the experiment in a fully quantitative manner, we created a mathematical model to describe the situation in the SPR sensor chip cell. The compelling comparison of the experimental data with the theoretical values from the mathematical model (Fig. 3B) supports the idea that under competitive conditions, as it is the case in a living cell, specific ligands are binding to their targets more efficiently than unspecific ones.

If the specificity of a ligand is defined as the ratio of affinities to the desired target and any undesired attractor, any decrease in affinity for the original target may well be outweighed by the larger decrease of affinities to all competing proteins. This exactly is observed in the example of the present report. In comparison with PD1, which was identified in a maximum affinity selection procedure, the competitively selected ligand cLck1 shows a slightly decreased affinity to the desired target LckSH3, but a much more decreased affinity to any attractor SH3 that was added into the washing buffer.

This is a striking result, because it is known from the literature that HckSH3 generally seems to bind to native ligands like HIV-1 Nef³⁰ or Tip from Herpes saimiri virus³¹ with much higher affinities than LckSH3.

As shown in our example, specific ligands can even be obtained for protein modules that share considerable homology to other proteins or protein modules the ligand is supposed not to bind to, e.g. WW, PDZ or Gyf domains.

Interestingly, the sequence of cLck1 is identical to the PD1 sequence in seven out of twelve positions. Recently, we were able to solve the structure of the HckSH3 PD1 complex in solution, which showed novel interaction modes.¹⁷ Further structural studies, for example, the structure determination of the complexes between LckSH3 and other SH3 domains with the peptide ligands PD1 and cLck1 will yield important insights into the structural basis and the essence of specificity.

All together, the experimental and theoretical investigation of the advantages and potentials of specific ligands over unspecific ones, leads to the conclusion that increased specificity is achieved at the cost of reduced affinity, but after all, it pays if the ligand is applied under realistic (competitive) conditions.

Acknowledgements

We thank Dr Heinrich Sticht (University Erlangen-Nuremberg; Germany) for supporting us with the LynSH3 expression vector and Esther Jonas for excellent technical assistance.

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