Quantifying High-Affinity Binding of Hydrophobic Ligands by

Article pubs.acs.org/ac

Quantifying High-Affinity Binding of Hydrophobic Ligands by Isothermal Titration Calorimetry Georg Krainer,†,‡,§,∥ Jana Broecker,†,‡ Carolyn Vargas,†,‡ Jörg Fanghan̈ el,⊥ and Sandro Keller*,‡ ‡

Molecular Biophysics, University of Kaiserslautern, Erwin-Schrödinger-Strasse 13, 67663 Kaiserslautern, Germany Leibniz Institute of Molecular Pharmacology, Robert-Rössle-Strasse 10, 13125 Berlin, Germany ∥ Institut für Chemie und Biochemie, Freie Universität Berlin, Takustrasse 3, 14195 Berlin, Germany ⊥ Global Drug DiscoveryInnovation Center China, Bayer Healthcare Co. Ltd., 17F Bayer Center, No. 27, Dong San Huan North Road, Chaoyang District, 100025 Beijing, China §

ABSTRACT: A fast and reliable quantification of the binding thermodynamics of hydrophobic high-affinity ligands employing a new calorimetric competition experiment is described. Although isothermal titration calorimetry is the method of choice for a quantitative characterization of intermolecular interactions in solution, a reliable determination of a dissociation constant (KD) is typically limited to the range 100 μM > KD > 1 nM. Interactions displaying higher or lower KD values can be assessed indirectly, provided that a suitable competing ligand is available whose KD falls within the directly accessible affinity window. This established displacement assay, however, requires the high-affinity ligand to be soluble at high concentrations in aqueous buffer and, consequently, poses serious problems in the study of protein binding involving small-molecule ligands dissolved in organic solventsa familiar case in many drug-discovery projects relying on compound libraries. The calorimetric competition assay introduced here overcomes this limitation, thus allowing for a detailed thermodynamic description of high-affinity receptor−ligand interactions involving poorly water-soluble compounds. Based on a single titration of receptor into a dilute mixture of the two competing ligands, this competition assay provides accurate and precise values for the dissociation constants and binding enthalpies of both high- and moderate-affinity ligands. We discuss the theoretical background underlying the approach, demonstrate its practical application to metal ion chelation and high-affinity protein−inhibitor interactions, and explore its potential and limitations with the aid of simulations and statistical analyses.

A

solution without the need for any labels.17 Moreover, it is the only method that directly yields the binding enthalpy, ΔH, which is increasingly recognized as a valuable parameter in guiding the drug-discovery process by complementing structure−activity relationships with thermodynamic information.18 One of the major limitations of ITC in many of the above applications is that a meaningful determination of KD values by conventional titrations is typically restricted to an affinity window of about 100 μM > KD > 1 nM.1 Within these limits, analyte and titrant concentrations in the micro- to millimolar range usually lead to sigmoidal or hyperbolic binding isotherms, from which reliable estimates of KD and ΔH can be derived.19 By contrast, very strong, low-KD or very weak, high-KD interactions are not amenable to precise quantification of affinity based on such titrations. High-affinity interactions give rise to binding isotherms resembling step functions, thus impeding reliable KD determination, whereas low-affinity

reliable quantification of the binding affinity between two or more interacting molecules is a task of paramount importance for the judicious modification of ligands in many fields of contemporary chemistry, including supramolecular chemistry, chemical biology, and medicinal chemistry. Isothermal titration calorimetry (ITC) has become the gold standard for label-free affinity measurements and the comprehensive thermodynamic characterization of interactions in solution.1,2 The method is based on the detection of a nearly universal signal, that is, the heat released or consumed upon titration of an analyte with (sub)microliter aliquots of a titrant. Thus, it has found widespread application across many different research fields, particularly in the quantification of host−guest and supramolecular assemblies,3,4 as well as biomolecular interactions involving proteins,5 peptides,6 nucleic acids,7 carbohydrates,8 lipids,9 detergents,10 metal ions,11 and other compounds (for a recent review, see ref 12). Further examples include, among others, food chemistry,13 materials science,14 nanotechnology,15 and drug discovery.16 In the latter area, highsensitivity ITC is emerging as an important and unique tool for improving the drug-optimization process by providing the dissociation constant, KD, of a protein−inhibitor complex in © 2012 American Chemical Society

Received: September 4, 2012 Accepted: November 6, 2012 Published: November 6, 2012 10715

dx.doi.org/10.1021/ac3025575 | Anal. Chem. 2012, 84, 10715−10722

Analytical Chemistry

Article

Figure 1. Experimental setups and inhibitor structures. (a) In the established displacement assay,20,21 a high-affinity ligand of interest (red) is titrated into a calorimeter cell containing a receptor (violet) prebound to a moderate-affinity ligand (green) of known KD. (b) In the new competition assay, receptor is titrated into a mixture of competing high- and moderate-affinity ligands. (c) Sulfonamide inhibitors of carbonic anhydrase II used in this study (see section Ultratight Protein−Inhibitor Interactions).

interactions result in flat, rather featureless binding isotherms from which neither KD nor ΔH can be derived with confidence. To circumvent these problems and extend the experimental window to high-affinity interactions, Sigurskjold20 introduced the displacement method depicted in Figure 1a. Here, binding of a high-affinity ligand of interest is measured indirectly by competition with a second ligand whose KD falls within the directly accessible range. The assay requires two separate titrations, namely, a conventional experiment using the directly measurable moderate-affinity ligand as well as a competition experiment in which the high-affinity ligand is titrated into a solution containing the analyte prebound to the moderateaffinity ligand. Consequently, the apparent affinity of the highaffinity ligand is lowered because it has to displace the moderate-affinity ligand. With the thermodynamic parameters of the moderate-affinity ligand and the linkage equations of the competitive binding model in hand, the thermodynamic profile of the high-affinity ligand can be obtained. Now a routine protocol,21 the displacement assay has been used, for instance, to quantify the binding of metal ions22 and nucleotide inhibitors17 to protein targets. Freire and co-workers23 exploited this approach to measure a KD value as low as 3.9 pM for a small-molecule inhibitor of HIV-1 protease. However, the displacement method is seriously limited in its application to hydrophobic compounds because it requires the high-affinity ligand of interest to be soluble at high concentrations, typically >100 μM. This is particularly unfortunate because hydrophobic contacts oftentimes make an indispensable contribution to ultra-high-affinity interactions,24,25 which comes at the price of decreased solubility in aqueous solutions. When the enhanced potency of, for instance, a high-affinity drug is compared with that of a less avidly binding lead compound, this loss in solubility need not be a disadvantage for the final application, since higher affinity translates into lower dosage requirements and enhanced specificity, thus improving drug efficacy and reducing side effects as well as resistance issues. Nevertheless, poor water solubility is a serious problem during the initial stages of development when potential drugs are characterized with respect to their in vitro binding properties. Though organic cosolvents like dimethyl sulfoxide (DMSO) may be used to

enhance solubility, many proteins will lose their native structures, functions, and binding properties at the cosolvent concentrations required to maintain ligand solubility.26,27 A second, albeit less serious, disadvantage of the displacement assay is that it necessitates two titrations to characterize one high-affinity inhibitor.20,21 Herein, we establish and validate a new ITC competition strategy that overcomes these limitations, thus allowing for a complete thermodynamic profiling of high-affinity receptor− ligand interactions involving poorly soluble compounds in a single experiment.

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EXPERIMENTAL SECTION Materials. All chemicals were purchased in highest available purities. CaCl2·2H2O, DMSO, ethylene glycol bis(β-aminoethyl ether)-N,N,N′,N′-tetraacetic acid (EGTA), NaH 2 PO 4 , Na2HPO4, and tris(hydroxymethyl)aminomethane (Tris) were obtained from Carl Roth (Karlsruhe, Germany). NaCl was from J. T. Baker (Griesheim, Germany), and N-(2hydroxyethyl)ethylenediamine-N,N′,N″-triacetic acid (HEDTA) was from Fluka (Buchs, Switzerland). Carbonic anhydrase II (CAII, 29.0 kDa) from bovine erythrocytes and its inhibitors ethoxzolamide (6-ethoxy-1,3-benzothiazole-2-sulfonamide, ETZ) and furosemide (FRM) were purchased from Sigma−Aldrich (Munich, Germany). Sample Preparation. CaCl 2 , EGTA, and HEDTA solutions were prepared from 10 mM stock solutions in 20 mM Tris buffer, pH 8.5. Lyophilized CAII was dissolved in 50 mM phosphate buffer containing 50 mM NaCl, pH 7.0, at a concentration of ∼11.5 mg·mL−1, gently vortexed, and centrifuged at 5000 g for 20 min. The final protein concentration in the supernatant was typically ∼400 μM, as determined spectrophotometrically with a molar extinction coefficient ε280 nm = 55 100 M−1·cm−1.28 This stock solution was stored at 4 °C and, prior to ITC experiments, was diluted to the desired final protein concentration and supplemented with 0.5% (v/v) DMSO. Stock solutions of 20 mM ETZ or FRM were prepared in DMSO and diluted with buffer to the desired ligand concentrations and a final DMSO concentration of 0.5% (v/v). Pipetting steps with DMSO were performed 10716



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with solvent-equilibrated Hamilton syringes (Bonaduz, Switzerland). Isothermal Titration Calorimetry. High-sensitivity ITC experiments were carried out at 25 °C. Ca2+ chelation titrations were performed on a VP-ITC (GE Healthcare, Uppsala, Sweden) with an injection volume of 4 μL, a time spacing of 360 s between injections, a stirrer speed of 310 rpm, a filter period of 2 s, and a reference power of 75−126 μJ·s−1. The reference cell contained degassed buffer, and all samples were gently vacuum-degassed before experiments. CAII binding experiments were performed on an iTC200 (GE Healthcare) with an injection volume of 1 μL, a time spacing of 240 s, a stirrer speed of 1000 rpm, a filter period of 5 s, and a reference power of 4.2 μJ·s−1. Automated baseline assignment and peak integration were accomplished by use of NITPIC.29 Estimation of best-fit parameter values by nonlinear least-squares fitting (NLSF) and calculation of 95% confidence intervals were performed in an Excel (Microsoft, Redmond, WA) spreadsheet using the Solver add-in (Frontline Systems, Incline Village, NV) as described30 and with the public-domain software SEDPHAT.31 Simulations. For the simulation of binding isotherms, we assumed the same titration scheme (i.e., concentrations, injection volumes, etc.) as for the CAII titrations and employed the experimentally determined best-fit values for this system as defaults for the thermodynamic parameters. Ideal, noise-free isotherms were then generated by systematically changing these values, with KD values ranging from 0.1 to 10 times their respective default values and ΔH values varying by ±10 kJ·mol−1. Noise of realistic magnitude was introduced by adding, to each data point in these isotherms, the residual between the experimentally measured heat of reaction and the corresponding value calculated for the best-fit case. The resulting simulated, noisy data sets were analyzed like experimental binding isotherms to extract best-fit values and 95% confidence intervals by use of the equations and the approach outlined in the next section.

KD,B ≡

[B][P] [PB]

KD,A + [P]i

(7)

nB[B]0, i [P]i KD,B + [P]i

[P]0, i = [P]i +

(8)

nA [A]0, i [P]i KD,A + [P]i

+

nB[B]0, i [P]i KD,B + [P]i

(9)

Rearrangement yields a cubic equation of the form [P]i 3 + p[P]i 2 + q[P]i + r = 0

(10)

with the coefficients p = KD,A + KD,B + nA [A]0, i + nB[B]0, i − [P]0, i

(11)

q = KD,B(nA [A]0, i − [P]0, i ) + KD,A(nB[B]0, i − [P]0, i ) + KD,AKD,B

(12)

r = −KD,AKD,B[P]0, i

(13)

The only physically meaningful root of eq 10 is [P]i = −

p 2 2 θ + p − 3q cos 3 3 3

(14)

where θ = arccos

−2p3 + 9pq − 27r 2 (p2 − 3q)3

(15)

It is then possible to calculate [PA]i and [PB]i from eqs 7 and 8, respectively. The normalized heats of reaction, Qi, observed in an ITC competition experiment are related to the equilibrium concentrations of complexes PA and PB before and after the ith injection according to

(1)

⎛ ⎧ ⎛ ΔVi ⎞⎫ ⎟⎬ Q i = ⎜ΔHA ⎨[PA]i − [PA]i − 1 ⎜1 − ⎝ V ⎠⎭ ⎩ ⎝ ⎧ ⎛ ΔVi ⎞⎫⎞ V ⎟⎬⎟ + ΔHB⎨[PB]i − [PB]i − 1 ⎜1 − + Qd ⎝ V ⎠⎭⎠ Δni ⎩

(2)

(16)

where ΔHL denotes the molar binding enthalpy of ligand L (A or B), ΔVi is the injection volume, V is the sample cell volume, Δni is the molar amount of titrant added during the injection, and Qd is the heat of dilution. The term (1 − ΔVi/V) accounts for sample expulsion from the sample cell into the calorimetrically inert access tube, and the term {[PL]i − [PL]i−1(1 − ΔVi/ V)} reflects the increase in the concentrations of PA and PB upon each injection. Together with eqs 7, 8, and 14, eq 16 constitutes the fit function for analyzing the competitive binding of two ligands A and B to a protein P as measured by

(3)

where KD,A and KD,B are the dissociation constants of the PA and PB complexes, respectively. [A], [B], [P], [PA], and [PB] are the equilibrium concentrations of free ligands A and B, free protein P, and protein−ligand complexes PA and PB, respectively. Mass conservation gives the total concentrations of A, B, and P after the ith injection as nA [A]0, i = [A]i + [PA]i

nA [A]0, i [P]i

and insertion of eqs 7 and 8 into eq 6 gives

The two equilibria are described by [A][P] [PA]

(6)

[PB]i =

KD,A

KD,A ≡

[P]0, i = [P]i + [PA]i + [PB]i

[PA]i =

■

KD,B

(5)

The adjustable parameters nA and nB correct for uncertainties in the ligand concentrations, whereas the protein concentration is assumed to be known accurately. Combination of eqs 2−5 yields

THEORY Binding Model. Similar to existing competition titrations,20,22,32 the binding model for the new assay is based on a ternary equilibrium with two ligands, A and B, competing for the same binding site of a protein P: A + PB JoooK A + P + B JoooK PA + B

nB[B]0, i = [B]i + [PB]i

(4) 10717



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Figure 2. Competitive chelation of Ca2+ by EGTA and HEDTA in 20 mM Tris, pH 8.5, 25 °C. (a) High-affinity titration: 5.0 mM EGTA into 0.4 mM CaCl2. (b) Moderate-affinity titration: 5.0 mM HEDTA into 0.4 mM CaCl2. (c) Displacement assay: 5.0 mM EGTA into 0.4 mM CaCl2 and 1.0 mM HEDTA. (d) New competition assay: 5.0 mM CaCl2 into 0.4 mM EGTA and 0.4 mM HEDTA. (Upper panels) Differential heating power, Δp, versus time, t. (Lower panels) Integrated and normalized heats of reaction, Q, versus molar ratio, R, for experimental data (red circles) and global fit (blue lines; note that local fits to individual data sets are visually indistinguishable). Best-fit parameter values and associated confidence intervals are given in Table 1.

Table 1. Best-Fit Values and 95% Confidence Intervals for Ca2+−EGTA/HEDTA Interactionsa EGTA ITC method direct displacementc new competition globald

KD (nM) b

na

0.74 (0.65 to 0.84) 0.96 (0.87 to 1.07) 0.83 (0.72 to 0.96)

HEDTA −1

ΔH (kJ·mol )

KD (nM)

ΔH (kJ·mol−1)

−81.4 (−81.6 to −81.2) −81.2 (−81.4 to −81.1) −81.2 (−81.4 to −81.0) −81.2 (−81.4 to −81.0)

116 (100 to 122) 119 (106 to 134) 147 (134 to 161) 129 (113 to 146)

−43.7 (−43.8 to −43.6) −43.8 (−44.0 to −43.7) −44.7 (−44.9 to −44.5) −44.1 (−44.9 to −44.3)

a

As obtained by direct (Figure 2a,b), displacement (Figure 2c), and new competition (Figure 2d) titrations. 95% confidence intervals are given in parentheses. bNot applicable. cSimultaneous fit of displacement and direct titrations (Figure 2a−c). dGlobal fit of all four titrations (Figure 1a−d).

ITC, with KD,A, KD,B, ΔHA, ΔHB, nA, nB, and Qd being the adjustable parameters. Statistical Analysis. Statistical analysis according to Johnson33 was done as outlined previously.19,30 In brief, projection maps of the sum of squared residuals (SSR) were calculated by constraining the parameter of interest sequentially to several values close to but different from its best-fit value while allowing the other parameters to float. Then, confidence intervals at a desired probability, P, were obtained from the points of intersection of the SSR projection with SSR threshold (th) values (SSRth) calculated from the best-fit (bf) SSR (SSRbf) on the basis of Fisher’s F distribution as

Here, F is the upper (1 − P/100) quantile of Fisher’s F distribution, with M being the number of adjustable parameters and N the number of data points included in the fit.

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RESULTS AND DISCUSSION

Rationale. The titration scheme underlying the new competition assay is depicted in Figure 1b. Accordingly, a mixture of the high-affinity ligand of interest and a second, moderate-affinity ligand, whose binding characteristics need not be known a priori, is titrated with a binding partner for which the two ligands compete. This setup may appear counterintuitive since, in contrast with the established displacement assay, no net displacement occurs during the titration. Nevertheless, it leads to an effective competitive situation when the high-affinity ligand is almost completely bound, so that its free concentration is exceeded many times by that of the

⎡ ⎤ M F(1 − P /100; M ; N − M )⎥ SSR th = SSR bf ⎢1 + ⎣ ⎦ N−M (17) 10718



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affinity sulfonamide inhibitors ETZ and FRM, respectively (see Figure 1c for structures). The ubiquitous, monomeric zinc metalloenzyme CAII catalyzes the reversible hydration of CO2 to HCO3− and represents a therapeutic target for the treatment of glaucoma, osteoporosis, and other pathologies.34 On top of that, CAII is a popular model for biophysical and physical− organic investigations into protein−inhibitor interactions.35 ETZ is a hydrophobic sulfonamide derivative effective in the treatment of glaucoma and is one of the strongest known CAII inhibitors with a KD < 1 nM.36,37 Besides its clinical use, ETZ is also employed at micromolar concentrations as a pharmacological tool for blocking CAII catalytic activity in cell-based assays.38,39 The KD value of ETZ is too low for direct binding assays and is also inaccessible to ITC displacement experiments because ETZ, like many other pharmacologically relevant small molecules, is only sparingly soluble in aqueous solution (∼160 μM).40

moderate-affinity ligand (for a detailed example, see section Ultratight Protein−Inhibitor Interactions and Figure 3b below). High-Affinity Metal Ion Chelation. Using Ca2+ chelation by EGTA and HEDTA as a well-characterized and cheap model system, we set out to demonstrate that a single titration of a mixture of competing ligands indeed allows for a simultaneous quantification of both ligands and that the results are both accurate and precise. Obviously, solubility is not an issue for this model system, thus making possible a direct comparison of the new competition assay with the established displacement assay, which requires high ligand solubility. The experimental data and fit results obtained from a complete set of titrations are summarized in Figure 2 and Table 1, respectively. At pH 8.5, EGTA chelates Ca2+ with an affinity in the subnanomolar range, which in the concentration regime used is outside the affinity window accessible to direct ITC titrations (Figure 2a). With the help of the binding data obtained for the moderate-affinity chelator HEDTA (Figure 2b), the thermodynamics of the Ca2+−EGTA interaction could be extracted by use of a displacement titration (Figure 2c). The new competition method produced a binding isotherm characterized by three plateaus separated by two well-resolved transitions (Figure 2d), which offers an efficient quantification of all thermodynamic parameters in a single experiment. The first and second plateaus represent the binding enthalpies of EGTA and HEDTA, respectively, while the third plateau stems from vanishingly small heats of dilution. The slope of the first transition reflects the binding strength of the high-affinity ligand EGTA relative to that of the moderate-affinity ligand HEDTA, whereas the slope of the second transition depends only on the absolute binding strength of HEDTA. The best-fit values for the thermodynamic parameters derived on the basis of eq 16 from the competition assay are KD = 0.96 nM and ΔH = −81.2 kJ·mol−1 for EGTA, as well as KD = 147 nM and ΔH = −44.7 kJ·mol−1 for HEDTA. These values are in good agreement with those determined from the other titration protocols (Table 1), thus enabling a global fit to all data sets (Figure 2) to yield a consistent picture of the thermodynamics of the competitive chelation of Ca2+ by EGTA and HEDTA. In comparing dissociation constants, one should keep in mind that differences of 20−30% as found in the present case are well within the expected and acceptable range. This becomes more obvious on converting dissociation constants to Gibbs free energies of binding, ΔG° = RT ln KD, for which the displacement and new competition assays yield values of, respectively, −52.1 and −51.5 kJ·mol−1 for EGTA as well as −39.5 and −39.0 kJ·mol−1 for HEDTA. Thus, for both ligands, the differences between the two assays in terms of Gibbs free energy changes amount to only ∼0.5 kJ·mol−1. Moreover, the 95% confidence intervals for the new competition assay are about as narrow as those for the established displacement method (Table 1), indicating that all values are precise, that is, well-defined by the fit to the experimental data set considered. The concentration correction factors, n, were found to fall in a narrow range between 0.97 and 1.00, as expected for a well-defined system in which both receptor and ligand concentrations are known accurately. Ultratight Protein−Inhibitor Interactions. After establishing the feasibility, accuracy, and precision of the assay for a simple model system, we sought to demonstrate its applicability to high-affinity protein−inhibitor interactions that have thus far evaded such scrutiny. To this end, we studied the thermodynamics of CAII binding to its high- and moderate-

Figure 3. Competitive binding of ETZ and FRM to CAII in 50 mM phosphate, 50 mM NaCl, and 0.5% (v/v) DMSO, pH 7.0, 25 °C. (a) New competition assay: 400 μM CAII into 20 μM ETZ and 40 μM FRM. (Top) Differential heating power, Δp, versus time, t; (bottom) integrated and normalized heats of reaction, Q, versus molar CAII/ ETZ ratio, R, for experimental data (red circles) and fit (blue line). Best-fit parameter values and associated confidence intervals are given in Table 2. (b) Speciation curves depicting the unbound fractions, f, of CAII (black), ETZ (red), and FRM (blue) in the calorimeter cell versus R. (Top) Linear/linear scale; (bottom) logarithmic/linear scale.

As exemplified in Figure 3 and Table 2, the new competition method easily copes with ETZ concentrations as low as 20 μM, which is in the concentration range typically used for cellbiological experiments38,39 and far below the solubility limit. As in the above example of high-affinity ion chelation, a biphasic binding isotherm observed for CAII−inhibitor interactions (Figure 3a) allows an analysis based on the competitive binding model described by eq 16. The best-fit values for the thermodynamic parameters are KD = 0.46 nM and ΔH = −50.9 kJ·mol−1 for ETZ, as well as KD = 361 nM and ΔH = −30.9 kJ·mol−1 for FRM. The KD value determined for ETZ is only slightly higher than that obtained previously36,37 from a 10719



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Table 2. Best-Fit Values and 95% Confidence Intervals for CAII−ETZ/FRM Interactionsa ETZ ITC method direct new competition a

FRM

KD (nM)

ΔH (kJ·mol−1)

KD (nM)

ΔH (kJ·mol−1)

nab

−50.8 (−51.3 to −50.3) −50.9 (−51.4 to −50.4)

322 (281 to 370) 361 (312 to 417)

−31.1 (−31.5 to −30.6) −30.9 (−31.5 to −30.3)

0.46 (0.31 to 0.66)

As obtained by direct (not shown) and new competition (Figure 3a) titrations. 95% confidence intervals are given in parentheses. bNot applicable.

probe-based fluorescence quenching assay under somewhat different conditions (∼0.2 nM, for which data were not shown and error margins were not reported), while the KD value for FRM as well as the ΔH values for both inhibitors agree excellently with those from direct ITC titrations (Table 2). Furthermore, all of these values are precise, as demonstrated by their tight 95% confidence intervals (Table 2). The good reproducibility of the assay at the experimental level was demonstrated by performing 10 independent experiments, yielding average best-fit KD values of 0.41 nM (standard deviation 0.06 nM) for the high-affinity inhibitor ETZ and 299 nM (standard deviation 34 nM) for the moderate-affinity inhibitor FRM. In contrast with the model system discussed in the preceding section, the concentration correction factors, n, for both CAII inhibitors used here were found to amount to only 0.90−0.95, indicating that the effective inhibitor concentrations were 5−10% lower than the nominal values calculated from the dry masses weighed during sample preparation. While such discrepancies are rather common when small quantities of hygroscopic powders of unknown water and salt content are being handled, they do not interfere with the new competition assay because they are fully absorbed by the adjustable n values without affecting the thermodynamic parameters of interest. On the basis of the above parameter values, speciation curves depicting the fractions of unbound CAII, ETZ, and FRM in the calorimeter cell (Figure 3b) were calculated to shed more light on the competing binding equilibria during the course of a titration. Initially, addition of CAII to a mixture of ETZ and FRM leads almost exclusively to the formation of CAII−ETZ complex and a rapid decrease in the concentration of free ETZ. However, as the latter drops below ∼1% of the total concentration, the large excess of the weaker inhibitor FRM enables it to compete noticeably with ETZ for binding to CAII, resulting in a buildup of CAII−FRM complex and a concomitant slowdown in the further disappearance of remaining free ETZ. Simulations. To explore the potential and limitations of the assay, we simulated a set of binding isotherms in which the KD and ΔH values of both ligands were systematically varied. Figure 4 exemplarily demonstrates changes in the shape of ideal, noise-free binding isotherms (left panels) and effects on the precision in the determination from noisy data sets of the parameter of prime interest, that is, the KD value of the highaffinity ligand (right panels). A useful measure of precision is the width of the confidence interval at the desired level of confidence (here 95%), which for KD values may be expressed as the ratio, FKD95%, of its upper bound to its lower bound.19 When all other values and experimental settings are kept constant, a decrease in the high-affinity KD results in a steeper slope of the first transition and reduced precision (Figure 4a). In the example under consideration, the width of the 95%

confidence interval is FKD95% < 3 for KD values down to ∼100 pM, demonstrating excellent precision in this affinity range. Interactions with higher affinities could not be quantified precisely under such conditions but become tractable upon using a more avidly binding moderate-affinity ligand. This is because reducing the KD of the latter flattens the first and sharpens the second transition, thus pushing the lower limit for determination of high-affinity K D values (Figure 4b). Specifically, a 10-fold decrease in the moderate-affinity KD enables a roughly 10-fold enhancement in the detection limit of the high-affinity KD. In all of the above simulations, an increase in the high-affinity KD or a decrease in the low-affinity KD is always beneficial, but more pronounced changes would eventually also result in reduced precision, namely, when the first transition becomes too flat. In the present case, a further increase in the high-affinity KD is irrelevant because such moderate affinities could be measured directly without competing ligand. Another quantity of interest is the difference in ΔH between the two ligands. Obviously, increasing this difference causes a clearer separation of the first and second plateaus and an improvement in the precision of the fit (Figure 4c,d). Here, an additional 10 kJ·mol−1 extends the detection limit by somewhat more than 1 order of magnitude. Similarly, a sharper separation of the two plateaus and a concomitant enhancement in precision can be brought about by raising the concentration of the competing moderate-affinity ligand such as to shift the second transition to higher protein concentrations (Figure 4e). In doing so, however, one has to make sure that the final protein concentration in the sample cell is high enough to fully capture the second transition, unless the binding parameters for the moderate-affinity ligand are extracted from an additional, direct titration experiment. As in the established displacement assay, the best-fit values thus determined may then be fixed in the analysis of the actual competition experiment; alternatively, both experiments can be fitted globally to properly account for uncertainties inherent in the best-fit values of the moderate-affinity ligand.31 Three rules of thumb for a successful application of the assay emerge from such simulations: First, the KD values of the competing ligands must differ by a factor of at least ∼10 but no more than ∼10 000. Theoretically, there is no lower limit on the high-affinity KD value as long as a suitable competing ligand is available and slow off-rates do not become limiting. Second, the ΔH values should be as different as possible. Under the conditions assumed here, a difference of ∼10 kJ·mol−1 may suffice; in general, this value depends on several factors, including the sensitivity and baseline stability of the calorimeter as well as the injection volumes and concentrations used. Third, the concentration of the competing moderate-affinity ligand should be chosen such as to yield a clear separation of the two transitions, which typically is the case for an approximately 210720



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Figure 4. continued blue to red). (e) Influence of molar ratio of moderate-affinity ligand to high-affinity ligand: 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, or 3.5 (from blue to red). Default values: 400 μM protein in syringe, 20 μM high-affinity ligand and 40 μM low-affinity ligand in cell, KD = 0.46 nM and ΔH = −50.9 kJ·mol−1 for high-affinity ligand, KD = 361 nM and ΔH = −30.9 kJ·mol−1 for moderate-affinity ligand. (Left) Ideal simulated isotherms; (right) ratio, FKD95%, of upper bound to lower bound of 95% confidence interval for high-affinity KD.

fold molar excess of the moderate-affinity ligand over the highaffinity ligand.

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CONCLUSION In summary, we have established a reliable and efficient approach for quantifying high-affinity receptor−ligand interactions in solution within a single experiment. The assay is both accurate and precise and should be widely applicable to the analysis of poorly soluble ligands, including hydrophobic smallmolecule inhibitors of target proteins. We have, for example, exploited this strategy to characterize the binding thermodynamics of a series of hydrophobic high-affinity small-molecule inhibitors of the kinase domain of Polo-like kinase 1 (Plk1). The approach necessitates that the target protein must be soluble and stable at rather high concentrations, but this requirement is usually met when the lead optimization process is supported by structure-based drug discovery and in other projects employing X-ray crystallography or NMR.41 In return, the new assay can cope with much lower inhibitor concentrations, which is of particular advantage when small molecules dissolved in DMSO or other organic solvents, as is usually the case with compound libraries, are subjected to protein-binding studies in aqueous solution. On top of alleviating solubility issues, titrations of protein into a mixture of inhibitors are largely insensitive to uncertainties in inhibitor concentrations and can, in fact, be used to determine them as long as the protein concentration is known independently. For a typical drug-discovery project in which the same moderate-affinity ligand is used for analyzing an array of highaffinity derivatives, two scenarios are conceivable: If a complete competition titration spanning both transitions is performed, the second transition can serve as an internal standard to assess the overall quality of the experiment and, in particular, confirm a competitive binding mode and rule out potential nonspecific inhibitor−inhibitor interactions. Alternatively, a titration may be stopped after the first transition to increase sample throughput and reduce protein consumption. Together with the recent advent of fully automated medium-throughput nanocalorimeters,42 this paves the way for extending secondary screening by ITC to high-affinity protein inhibitors. The approach presented here thus may enhance the potential of enthalpy arrays43 as promising tools for the calorimetric screening of compound libraries, since hundreds of ligands may be analyzed in parallel by use of a single syringe filling of the same target protein. Besides high-affinity binding, competition titrations can be applied also to the chelation of metal ions that are difficult to remove from protein solutions,22 racemic ligand mixtures,44 and calorimetrically silent or lowaffinity interactions, which play important roles in fragmentbased drug design.45

Figure 4. Influence of parameter values on (left panels) isotherm shape and (right panels) precision of high-affinity KD. (a) Change in high-affinity KD by factors of 0.1, 0.2, 0.5, 1, 2, 3, 4, 5, or 10 (from blue to red). (b) Change in moderate-affinity KD by factors of 10, 5, 2, 1, 0.5, 0.2, or 0.1 (from blue to red). (c) Change in high-affinity ΔH by 10, 5, 2, 0, −2, −5, or −10 kJ·mol−1 (from blue to red). (d) Change in moderate-affinity ΔH by −10, −5, −2, 0, 2, 5, or 10 kJ·mol−1 (from 10721



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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]. Author Contributions †

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by the Stiftung Rheinland-Pfalz für Innovation (Grant 961-386261/969 to S.K.). We thank Dr. Peter Schuck (National Institutes of Health, Bethesda, MD), Dr. Christian Stegmann (Bayer Healthcare Co. Ltd., Berlin), Sebastian Fiedler (University of Kaiserslautern), and Elisabeth Fischermeier (FMP Berlin and Helmholtz-Zentrum Dresden−Rossendorf) for fruitful discussions and Monika Georgi (FMP Berlin) for excellent technical assistance.

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Quantifying High-Affinity Binding of Hydrophobic Ligands by

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