Quantifying High-Affinity Binding of Hydrophobic Ligands byIsothermal Titration CalorimetryGeorg Krainer,†,‡,§,∥ Jana Broecker,†,‡ Carolyn Vargas,†,‡ Jorg Fanghanel,⊥ and Sandro Keller*,‡
‡Molecular Biophysics, University of Kaiserslautern, Erwin-Schrodinger-Strasse 13, 67663 Kaiserslautern, Germany§Leibniz Institute of Molecular Pharmacology, Robert-Rossle-Strasse 10, 13125 Berlin, Germany∥Institut fur Chemie und Biochemie, Freie Universitat Berlin, Takustrasse 3, 14195 Berlin, Germany⊥Global Drug DiscoveryInnovation Center China, Bayer Healthcare Co. Ltd., 17F Bayer Center, No. 27, Dong San Huan NorthRoad, Chaoyang District, 100025 Beijing, China
ABSTRACT: A fast and reliable quantification of the bindingthermodynamics of hydrophobic high-affinity ligands employ-ing a new calorimetric competition experiment is described.Although isothermal titration calorimetry is the method ofchoice for a quantitative characterization of intermolecularinteractions in solution, a reliable determination of adissociation constant (KD) is typically limited to the range100 μM > KD > 1 nM. Interactions displaying higher or lowerKD values can be assessed indirectly, provided that a suitablecompeting ligand is available whose KD falls within the directlyaccessible affinity window. This established displacement assay,however, requires the high-affinity ligand to be soluble at high concentrations in aqueous buffer and, consequently, poses seriousproblems in the study of protein binding involving small-molecule ligands dissolved in organic solventsa familiar case in manydrug-discovery projects relying on compound libraries. The calorimetric competition assay introduced here overcomes thislimitation, thus allowing for a detailed thermodynamic description of high-affinity receptor−ligand interactions involving poorlywater-soluble compounds. Based on a single titration of receptor into a dilute mixture of the two competing ligands, thiscompetition assay provides accurate and precise values for the dissociation constants and binding enthalpies of both high- andmoderate-affinity ligands. We discuss the theoretical background underlying the approach, demonstrate its practical application tometal ion chelation and high-affinity protein−inhibitor interactions, and explore its potential and limitations with the aid ofsimulations and statistical analyses.
A reliable quantification of the binding affinity between twoor more interacting molecules is a task of paramount
importance for the judicious modification of ligands in manyfields of contemporary chemistry, including supramolecularchemistry, chemical biology, and medicinal chemistry. Iso-thermal titration calorimetry (ITC) has become the goldstandard for label-free affinity measurements and thecomprehensive thermodynamic characterization of interactionsin solution.1,2 The method is based on the detection of a nearlyuniversal signal, that is, the heat released or consumed upontitration of an analyte with (sub)microliter aliquots of a titrant.Thus, it has found widespread application across many differentresearch fields, particularly in the quantification of host−guestand supramolecular assemblies,3,4 as well as biomolecularinteractions involving proteins,5 peptides,6 nucleic acids,7
carbohydrates,8 lipids,9 detergents,10 metal ions,11 and othercompounds (for a recent review, see ref 12). Further examplesinclude, among others, food chemistry,13 materials science,14
nanotechnology,15 and drug discovery.16 In the latter area, high-sensitivity ITC is emerging as an important and unique tool forimproving the drug-optimization process by providing thedissociation constant, KD, of a protein−inhibitor complex in
solution without the need for any labels.17 Moreover, it is theonly method that directly yields the binding enthalpy, ΔH,which is increasingly recognized as a valuable parameter inguiding the drug-discovery process by complementingstructure−activity relationships with thermodynamic informa-tion.18
One of the major limitations of ITC in many of the aboveapplications is that a meaningful determination of KD values byconventional titrations is typically restricted to an affinitywindow of about 100 μM > KD > 1 nM.1 Within these limits,analyte and titrant concentrations in the micro- to millimolarrange 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-KDinteractions are not amenable to precise quantification ofaffinity based on such titrations. High-affinity interactions giverise to binding isotherms resembling step functions, thusimpeding reliable KD determination, whereas low-affinity
Received: September 4, 2012Accepted: November 6, 2012Published: November 6, 2012
interactions result in flat, rather featureless binding isothermsfrom which neither KD nor ΔH can be derived with confidence.To circumvent these problems and extend the experimental
window to high-affinity interactions, Sigurskjold20 introducedthe displacement method depicted in Figure 1a. Here, bindingof a high-affinity ligand of interest is measured indirectly bycompetition with a second ligand whose KD falls within thedirectly accessible range. The assay requires two separatetitrations, namely, a conventional experiment using the directlymeasurable moderate-affinity ligand as well as a competitionexperiment in which the high-affinity ligand is titrated into asolution containing the analyte prebound to the moderate-affinity ligand. Consequently, the apparent affinity of the high-affinity ligand is lowered because it has to displace themoderate-affinity ligand. With the thermodynamic parametersof the moderate-affinity ligand and the linkage equations of thecompetitive binding model in hand, the thermodynamic profileof the high-affinity ligand can be obtained. Now a routineprotocol,21 the displacement assay has been used, for instance,to quantify the binding of metal ions22 and nucleotideinhibitors17 to protein targets. Freire and co-workers23
exploited this approach to measure a KD value as low as3.9 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 thehigh-affinity ligand of interest to be soluble at highconcentrations, typically >100 μM. This is particularlyunfortunate because hydrophobic contacts oftentimes makean indispensable contribution to ultra-high-affinity interac-tions,24,25 which comes at the price of decreased solubility inaqueous solutions. When the enhanced potency of, for instance,a high-affinity drug is compared with that of a less avidlybinding lead compound, this loss in solubility need not be adisadvantage for the final application, since higher affinitytranslates into lower dosage requirements and enhancedspecificity, thus improving drug efficacy and reducing sideeffects as well as resistance issues. Nevertheless, poor watersolubility is a serious problem during the initial stages ofdevelopment when potential drugs are characterized withrespect to their in vitro binding properties. Though organiccosolvents like dimethyl sulfoxide (DMSO) may be used to
enhance solubility, many proteins will lose their nativestructures, functions, and binding properties at the cosolventconcentrations required to maintain ligand solubility.26,27 Asecond, albeit less serious, disadvantage of the displacementassay is that it necessitates two titrations to characterize onehigh-affinity inhibitor.20,21
Herein, we establish and validate a new ITC competitionstrategy that overcomes these limitations, thus allowing for acomplete thermodynamic profiling of high-affinity receptor−ligand interactions involving poorly soluble compounds in asingle experiment.
■ EXPERIMENTAL SECTION
Materials. All chemicals were purchased in highest availablepurities. CaCl2·2H2O, DMSO, ethylene glycol bis(β-aminoethylether)-N,N,N′,N′-tetraacetic acid (EGTA), NaH2PO4,Na2HPO4, and tris(hydroxymethyl)aminomethane (Tris)were obtained from Carl Roth (Karlsruhe, Germany). NaClwas from J. T. Baker (Griesheim, Germany), and N-(2-hydroxyethyl)ethylenediamine-N ,N′ ,N″-triacetic acid(HEDTA) was from Fluka (Buchs, Switzerland). Carbonicanhydrase II (CAII, 29.0 kDa) from bovine erythrocytes and itsinhibitors ethoxzolamide (6-ethoxy-1,3-benzothiazole-2-sulfo-namide, ETZ) and furosemide (FRM) were purchased fromSigma−Aldrich (Munich, Germany).
Sample Preparation. CaCl2, EGTA, and HEDTAsolutions were prepared from 10 mM stock solutions in20 mM Tris buffer, pH 8.5. Lyophilized CAII was dissolved in50 mM phosphate buffer containing 50 mM NaCl, pH 7.0, at aconcentration of ∼11.5 mg·mL−1, gently vortexed, andcentrifuged at 5000 g for 20 min. The final proteinconcentration in the supernatant was typically ∼400 μM, asdetermined spectrophotometrically with a molar extinctioncoefficient ε280 nm = 55 100 M−1·cm−1.28 This stock solutionwas stored at 4 °C and, prior to ITC experiments, was dilutedto the desired final protein concentration and supplementedwith 0.5% (v/v) DMSO. Stock solutions of 20 mM ETZ orFRM were prepared in DMSO and diluted with buffer to thedesired ligand concentrations and a final DMSO concentrationof 0.5% (v/v). Pipetting steps with DMSO were performed
Figure 1. Experimental setups and inhibitor structures. (a) In the established displacement assay,20,21 a high-affinity ligand of interest (red) is titratedinto 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 thisstudy (see section Ultratight Protein−Inhibitor Interactions).
with solvent-equilibrated Hamilton syringes (Bonaduz, Switzer-land).Isothermal Titration Calorimetry. High-sensitivity ITC
experiments were carried out at 25 °C. Ca2+ chelation titrationswere performed on a VP-ITC (GE Healthcare, Uppsala,Sweden) with an injection volume of 4 μL, a time spacing of360 s between injections, a stirrer speed of 310 rpm, a filterperiod of 2 s, and a reference power of 75−126 μJ·s−1. Thereference cell contained degassed buffer, and all samples weregently vacuum-degassed before experiments. CAII bindingexperiments were performed on an iTC200 (GE Healthcare)with an injection volume of 1 μL, a time spacing of 240 s, astirrer speed of 1000 rpm, a filter period of 5 s, and a referencepower of 4.2 μJ·s−1. Automated baseline assignment and peakintegration were accomplished by use of NITPIC.29 Estimationof best-fit parameter values by nonlinear least-squares fitting(NLSF) and calculation of 95% confidence intervals wereperformed in an Excel (Microsoft, Redmond, WA) spreadsheetusing the Solver add-in (Frontline Systems, Incline Village,NV) as described30 and with the public-domain softwareSEDPHAT.31
Simulations. For the simulation of binding isotherms, weassumed the same titration scheme (i.e., concentrations,injection volumes, etc.) as for the CAII titrations and employedthe experimentally determined best-fit values for this system asdefaults for the thermodynamic parameters. Ideal, noise-freeisotherms were then generated by systematically changing thesevalues, with KD values ranging from 0.1 to 10 times theirrespective default values and ΔH values varying by±10 kJ·mol−1. Noise of realistic magnitude was introduced byadding, to each data point in these isotherms, the residualbetween the experimentally measured heat of reaction and thecorresponding value calculated for the best-fit case. Theresulting simulated, noisy data sets were analyzed likeexperimental binding isotherms to extract best-fit values and95% confidence intervals by use of the equations and theapproach outlined in the next section.
■ THEORYBinding Model. Similar to existing competition titra-
tions,20,22,32 the binding model for the new assay is based ona ternary equilibrium with two ligands, A and B, competing forthe same binding site of a protein P:
+ + + +J Kooo J KoooA PB A P B PA BK
K
D,B
D,A
(1)
The two equilibria are described by
≡K[A][P]
[PA]D,A(2)
≡K[B][P]
[PB]D,B(3)
where KD,A and KD,B are the dissociation constants of the PAand PB complexes, respectively. [A], [B], [P], [PA], and [PB]are the equilibrium concentrations of free ligands A and B, freeprotein P, and protein−ligand complexes PA and PB,respectively. Mass conservation gives the total concentrationsof A, B, and P after the ith injection as
= +n [A] [A] [PA]i i iA 0, (4)
= +n [B] [B] [PB]i i iB 0, (5)
= + +[P] [P] [PA] [PB]i i i i0, (6)
The adjustable parameters nA and nB correct for uncertainties inthe ligand concentrations, whereas the protein concentration isassumed to be known accurately. Combination of eqs 2−5yields
=+
n
K[PA]
[A] [P]
[P]ii i
i
A 0,
D,A (7)
=+
n
K[PB]
[B] [P]
[P]ii i
i
B 0,
D,B (8)
and insertion of eqs 7 and 8 into eq 6 gives
= ++
++
n
K
n
K[P] [P]
[A] [P]
[P]
[B] [P]
[P]i ii i
i
i i
i0,
A 0,
D,A
B 0,
D,B (9)
Rearrangement yields a cubic equation of the form
+ + + =p q r[P] [P] [P] 0i i i3 2
(10)
with the coefficients
= + + + −p K K n n[A] [B] [P]i i iD,A D,B A 0, B 0, 0, (11)
= − + −
+
q K n K n
K K
( [A] [P] ) ( [B] [P] )i i i iD,B A 0, 0, D,A B 0, 0,
D,A D,B (12)
= −r K K [P] iD,A D,B 0, (13)
The only physically meaningful root of eq 10 is
θ= − + −p
p q[P]3
23
3 cos3i
2
(14)
where
θ =− + −
−
p pq r
p qarccos
2 9 27
2 ( 3 )
3
2 3(15)
It is then possible to calculate [PA]i and [PB]i from eqs 7 and8, respectively. The normalized heats of reaction, Qi, observedin an ITC competition experiment are related to theequilibrium concentrations of complexes PA and PB beforeand after the ith injection according to
= Δ − −Δ
+ Δ − −Δ
Δ+
−
−
⎛⎝⎜
⎧⎨⎩⎛⎝⎜
⎞⎠⎟⎫⎬⎭
⎧⎨⎩⎛⎝⎜
⎞⎠⎟⎫⎬⎭
⎞⎠⎟
Q HV
V
HV
VV
nQ
[PA] [PA] 1
[PB] [PB] 1
i i ii
i ii
i
A 1
B 1 d
(16)
where ΔHL denotes the molar binding enthalpy of ligand L (Aor 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) accountsfor sample expulsion from the sample cell into the calorimetri-cally inert access tube, and the term {[PL]i − [PL]i−1(1 − ΔVi/V)} reflects the increase in the concentrations of PA and PBupon each injection. Together with eqs 7, 8, and 14, eq 16constitutes the fit function for analyzing the competitivebinding of two ligands A and B to a protein P as measured by
ITC, with KD,A, KD,B, ΔHA, ΔHB, nA, nB, and Qd being theadjustable 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) werecalculated by constraining the parameter of interest sequentiallyto several values close to but different from its best-fit valuewhile allowing the other parameters to float. Then, confidenceintervals at a desired probability, P, were obtained from thepoints 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
= +−
− −⎡⎣⎢
⎤⎦⎥
MN M
F P M N MSSR SSR 1 (1 /100; ; )th bf
(17)
Here, F is the upper (1 − P/100) quantile of Fisher’s Fdistribution, with M being the number of adjustable parametersand N the number of data points included in the fit.
■ RESULTS AND DISCUSSION
Rationale. The titration scheme underlying the newcompetition assay is depicted in Figure 1b. Accordingly, amixture of the high-affinity ligand of interest and a second,moderate-affinity ligand, whose binding characteristics need notbe known a priori, is titrated with a binding partner for whichthe two ligands compete. This setup may appear counter-intuitive since, in contrast with the established displacementassay, no net displacement occurs during the titration.Nevertheless, it leads to an effective competitive situationwhen the high-affinity ligand is almost completely bound, sothat its free concentration is exceeded many times by that of the
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 into0.4 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 and1.0 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 globalfit (blue lines; note that local fits to individual data sets are visually indistinguishable). Best-fit parameter values and associated confidence intervalsare given in Table 1.
Table 1. Best-Fit Values and 95% Confidence Intervals for Ca2+−EGTA/HEDTA Interactionsa
direct nab −81.4 116 −43.7(−81.6 to −81.2) (100 to 122) (−43.8 to −43.6)
displacementc 0.74 −81.2 119 −43.8(0.65 to 0.84) (−81.4 to −81.1) (106 to 134) (−44.0 to −43.7)
new competition 0.96 −81.2 147 −44.7(0.87 to 1.07) (−81.4 to −81.0) (134 to 161) (−44.9 to −44.5)
globald 0.83 −81.2 129 −44.1(0.72 to 0.96) (−81.4 to −81.0) (113 to 146) (−44.9 to −44.3)
aAs obtained by direct (Figure 2a,b), displacement (Figure 2c), and new competition (Figure 2d) titrations. 95% confidence intervals are given inparentheses. bNot applicable. cSimultaneous fit of displacement and direct titrations (Figure 2a−c). dGlobal fit of all four titrations (Figure 1a−d).
moderate-affinity ligand (for a detailed example, see sectionUltratight 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 modelsystem, we set out to demonstrate that a single titration of amixture of competing ligands indeed allows for a simultaneousquantification of both ligands and that the results are bothaccurate and precise. Obviously, solubility is not an issue forthis model system, thus making possible a direct comparison ofthe new competition assay with the established displacementassay, which requires high ligand solubility. The experimentaldata and fit results obtained from a complete set of titrationsare 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 isoutside the affinity window accessible to direct ITC titrations(Figure 2a). With the help of the binding data obtained for themoderate-affinity chelator HEDTA (Figure 2b), the thermody-namics of the Ca2+−EGTA interaction could be extracted byuse of a displacement titration (Figure 2c). The newcompetition method produced a binding isotherm character-ized by three plateaus separated by two well-resolvedtransitions (Figure 2d), which offers an efficient quantificationof all thermodynamic parameters in a single experiment. Thefirst and second plateaus represent the binding enthalpies ofEGTA and HEDTA, respectively, while the third plateau stemsfrom vanishingly small heats of dilution. The slope of the firsttransition reflects the binding strength of the high-affinityligand EGTA relative to that of the moderate-affinity ligandHEDTA, whereas the slope of the second transition dependsonly 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 areKD = 0.96 nM and ΔH = −81.2 kJ·mol−1 for EGTA, as well asKD = 147 nM and ΔH = −44.7 kJ·mol−1 for HEDTA. Thesevalues are in good agreement with those determined from theother titration protocols (Table 1), thus enabling a global fit toall data sets (Figure 2) to yield a consistent picture of thethermodynamics of the competitive chelation of Ca2+ by EGTAand HEDTA. In comparing dissociation constants, one shouldkeep in mind that differences of 20−30% as found in thepresent case are well within the expected and acceptable range.This becomes more obvious on converting dissociationconstants to Gibbs free energies of binding, ΔG° = RT ln KD,for which the displacement and new competition assays yieldvalues of, respectively, −52.1 and −51.5 kJ·mol−1 for EGTA aswell as −39.5 and −39.0 kJ·mol−1 for HEDTA. Thus, for bothligands, the differences between the two assays in terms ofGibbs free energy changes amount to only ∼0.5 kJ·mol−1.Moreover, the 95% confidence intervals for the newcompetition assay are about as narrow as those for theestablished displacement method (Table 1), indicating that allvalues are precise, that is, well-defined by the fit to theexperimental data set considered. The concentration correctionfactors, n, were found to fall in a narrow range between 0.97and 1.00, as expected for a well-defined system in which bothreceptor and ligand concentrations are known accurately.Ultratight Protein−Inhibitor Interactions. After estab-
lishing the feasibility, accuracy, and precision of the assay for asimple model system, we sought to demonstrate its applicabilityto high-affinity protein−inhibitor interactions that have thus farevaded such scrutiny. To this end, we studied thethermodynamics of CAII binding to its high- and moderate-
affinity sulfonamide inhibitors ETZ and FRM, respectively (seeFigure 1c for structures). The ubiquitous, monomeric zincmetalloenzyme 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 ofthat, CAII is a popular model for biophysical and physical−organic investigations into protein−inhibitor interactions.35
ETZ is a hydrophobic sulfonamide derivative effective in thetreatment of glaucoma and is one of the strongest known CAIIinhibitors with a KD < 1 nM.36,37 Besides its clinical use, ETZ isalso employed at micromolar concentrations as a pharmaco-logical tool for blocking CAII catalytic activity in cell-basedassays.38,39 The KD value of ETZ is too low for direct bindingassays and is also inaccessible to ITC displacement experimentsbecause ETZ, like many other pharmacologically relevant smallmolecules, is only sparingly soluble in aqueous solution(∼160 μM).40
As exemplified in Figure 3 and Table 2, the new competitionmethod easily copes with ETZ concentrations as low as 20 μM,which is in the concentration range typically used for cell-biological experiments38,39 and far below the solubility limit. Asin the above example of high-affinity ion chelation, a biphasicbinding isotherm observed for CAII−inhibitor interactions(Figure 3a) allows an analysis based on the competitive bindingmodel described by eq 16. The best-fit values for thethermodynamic 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 isonly slightly higher than that obtained previously36,37 from a
Figure 3. Competitive binding of ETZ and FRM to CAII in 50 mMphosphate, 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 μMFRM. (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 givenin Table 2. (b) Speciation curves depicting the unbound fractions, f, ofCAII (black), ETZ (red), and FRM (blue) in the calorimeter cellversus R. (Top) Linear/linear scale; (bottom) logarithmic/linear scale.
probe-based fluorescence quenching assay under somewhatdifferent conditions (∼0.2 nM, for which data were not shownand error margins were not reported), while the KD value forFRM as well as the ΔH values for both inhibitors agreeexcellently with those from direct ITC titrations (Table 2).Furthermore, all of these values are precise, as demonstrated bytheir tight 95% confidence intervals (Table 2). The goodreproducibility of the assay at the experimental level wasdemonstrated by performing 10 independent experiments,yielding average best-fit KD values of 0.41 nM (standarddeviation 0.06 nM) for the high-affinity inhibitor ETZ and299 nM (standard deviation 34 nM) for the moderate-affinityinhibitor FRM. In contrast with the model system discussed inthe preceding section, the concentration correction factors, n,for both CAII inhibitors used here were found to amount toonly 0.90−0.95, indicating that the effective inhibitorconcentrations were 5−10% lower than the nominal valuescalculated from the dry masses weighed during samplepreparation. While such discrepancies are rather commonwhen small quantities of hygroscopic powders of unknownwater and salt content are being handled, they do not interferewith the new competition assay because they are fully absorbedby the adjustable n values without affecting the thermodynamicparameters of interest.On the basis of the above parameter values, speciation curves
depicting the fractions of unbound CAII, ETZ, and FRM in thecalorimeter cell (Figure 3b) were calculated to shed more lighton the competing binding equilibria during the course of atitration. Initially, addition of CAII to a mixture of ETZ andFRM leads almost exclusively to the formation of CAII−ETZcomplex and a rapid decrease in the concentration of free ETZ.However, as the latter drops below ∼1% of the totalconcentration, the large excess of the weaker inhibitor FRMenables it to compete noticeably with ETZ for binding to CAII,resulting in a buildup of CAII−FRM complex and aconcomitant slowdown in the further disappearance ofremaining free ETZ.Simulations. To explore the potential and limitations of the
assay, we simulated a set of binding isotherms in which the KDand ΔH values of both ligands were systematically varied.Figure 4 exemplarily demonstrates changes in the shape ofideal, noise-free binding isotherms (left panels) and effects onthe precision in the determination from noisy data sets of theparameter of prime interest, that is, the KD value of the high-affinity ligand (right panels). A useful measure of precision isthe width of the confidence interval at the desired level ofconfidence (here 95%), which for KD values may be expressedas the ratio, FKD
95%, of its upper bound to its lower bound.19
When all other values and experimental settings are keptconstant, a decrease in the high-affinity KD results in a steeperslope of the first transition and reduced precision (Figure 4a).In the example under consideration, the width of the 95%
confidence interval is FKD
95% < 3 for KD values down to
∼100 pM, demonstrating excellent precision in this affinityrange. Interactions with higher affinities could not be quantifiedprecisely under such conditions but become tractable uponusing a more avidly binding moderate-affinity ligand. This isbecause reducing the KD of the latter flattens the first andsharpens the second transition, thus pushing the lower limit fordetermination of high-affinity KD values (Figure 4b).Specifically, a 10-fold decrease in the moderate-affinity KD
enables a roughly 10-fold enhancement in the detection limit ofthe high-affinity KD. In all of the above simulations, an increasein the high-affinity KD or a decrease in the low-affinity KD isalways beneficial, but more pronounced changes wouldeventually also result in reduced precision, namely, when thefirst transition becomes too flat. In the present case, a furtherincrease in the high-affinity KD is irrelevant because suchmoderate affinities could be measured directly withoutcompeting ligand. Another quantity of interest is the differencein ΔH between the two ligands. Obviously, increasing thisdifference causes a clearer separation of the first and secondplateaus and an improvement in the precision of the fit (Figure4c,d). Here, an additional 10 kJ·mol−1 extends the detectionlimit by somewhat more than 1 order of magnitude. Similarly, asharper separation of the two plateaus and a concomitantenhancement in precision can be brought about by raising theconcentration of the competing moderate-affinity ligand such asto shift the second transition to higher protein concentrations(Figure 4e). In doing so, however, one has to make sure thatthe final protein concentration in the sample cell is high enoughto fully capture the second transition, unless the bindingparameters for the moderate-affinity ligand are extracted froman additional, direct titration experiment. As in the establisheddisplacement assay, the best-fit values thus determined maythen be fixed in the analysis of the actual competitionexperiment; alternatively, both experiments can be fittedglobally to properly account for uncertainties inherent in thebest-fit values of the moderate-affinity ligand.31
Three rules of thumb for a successful application of the assayemerge from such simulations: First, the KD values of thecompeting ligands must differ by a factor of at least ∼10 but nomore than ∼10 000. Theoretically, there is no lower limit onthe high-affinity KD value as long as a suitable competing ligandis available and slow off-rates do not become limiting. Second,the ΔH values should be as different as possible. Under theconditions assumed here, a difference of ∼10 kJ·mol−1 maysuffice; in general, this value depends on several factors,including the sensitivity and baseline stability of the calorimeteras well as the injection volumes and concentrations used. Third,the concentration of the competing moderate-affinity ligandshould be chosen such as to yield a clear separation of the twotransitions, which typically is the case for an approximately 2-
Table 2. Best-Fit Values and 95% Confidence Intervals for CAII−ETZ/FRM Interactionsa
fold molar excess of the moderate-affinity ligand over the high-affinity ligand.
■ CONCLUSIONIn summary, we have established a reliable and efficientapproach for quantifying high-affinity receptor−ligand inter-actions in solution within a single experiment. The assay is bothaccurate and precise and should be widely applicable to theanalysis of poorly soluble ligands, including hydrophobic small-molecule inhibitors of target proteins. We have, for example,exploited this strategy to characterize the binding thermody-namics of a series of hydrophobic high-affinity small-moleculeinhibitors of the kinase domain of Polo-like kinase 1 (Plk1).The approach necessitates that the target protein must besoluble and stable at rather high concentrations, but thisrequirement is usually met when the lead optimization processis supported by structure-based drug discovery and in otherprojects employing X-ray crystallography or NMR.41 In return,the new assay can cope with much lower inhibitorconcentrations, which is of particular advantage when smallmolecules dissolved in DMSO or other organic solvents, as isusually the case with compound libraries, are subjected toprotein-binding studies in aqueous solution. On top ofalleviating solubility issues, titrations of protein into a mixtureof inhibitors are largely insensitive to uncertainties in inhibitorconcentrations and can, in fact, be used to determine them aslong 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 high-affinity derivatives, two scenarios are conceivable: If a completecompetition titration spanning both transitions is performed,the second transition can serve as an internal standard to assessthe overall quality of the experiment and, in particular, confirma competitive binding mode and rule out potential nonspecificinhibitor−inhibitor interactions. Alternatively, a titration maybe stopped after the first transition to increase samplethroughput and reduce protein consumption. Together withthe recent advent of fully automated medium-throughputnanocalorimeters,42 this paves the way for extending secondaryscreening by ITC to high-affinity protein inhibitors. Theapproach presented here thus may enhance the potential ofenthalpy arrays43 as promising tools for the calorimetricscreening of compound libraries, since hundreds of ligandsmay be analyzed in parallel by use of a single syringe filling ofthe same target protein. Besides high-affinity binding,competition titrations can be applied also to the chelation ofmetal ions that are difficult to remove from protein solutions,22
racemic ligand mixtures,44 and calorimetrically silent or low-affinity interactions, which play important roles in fragment-based drug design.45
Figure 4. Influence of parameter values on (left panels) isothermshape and (right panels) precision of high-affinity KD. (a) Change inhigh-affinity KD by factors of 0.1, 0.2, 0.5, 1, 2, 3, 4, 5, or 10 (from blueto 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 by10, 5, 2, 0, −2, −5, or −10 kJ·mol−1 (from blue to red). (d) Change inmoderate-affinity ΔH by −10, −5, −2, 0, 2, 5, or 10 kJ·mol−1 (from
Figure 4. continued
blue to red). (e) Influence of molar ratio of moderate-affinity ligand tohigh-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 ligandand 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 simulatedisotherms; (right) ratio, FKD
Author Contributions†These authors contributed equally to this work.
NotesThe authors declare no competing financial interest.
■ ACKNOWLEDGMENTS
This work was supported by the Stiftung Rheinland-Pfalz furInnovation (Grant 961-386261/969 to S.K.). We thankDr. Peter Schuck (National Institutes of Health, Bethesda,MD), Dr. Christian Stegmann (Bayer Healthcare Co. Ltd.,Berlin), Sebastian Fiedler (University of Kaiserslautern), andElisabeth Fischermeier (FMP Berlin and Helmholtz-ZentrumDresden−Rossendorf) for fruitful discussions and MonikaGeorgi (FMP Berlin) for excellent technical assistance.
■ REFERENCES(1) Wiseman, T.; Williston, S.; Brandts, J. F.; Lin, L.-N. Anal.Biochem. 1989, 179, 131−137.(2) Peters, W. B.; Frasca, V.; Brown, R. K. Comb. Chem. HighThroughput Screening 2009, 12, 772−790.(3) Cooper, A.; Nutley, M. A.; Camilleri, P. Anal. Chem. 1998, 70,5024−5028.(4) Schonbeck, C.; Holm, R.; Westh, P. Anal. Chem. 2012, 84, 2305−2312.(5) Leavitt, S.; Freire, E. Curr. Opin. Struct. Biol. 2001, 11, 560−566.(6) Wafer, L. N.; Streicher, W. W.; McCullum, S. A.; Makhatadze, G.I. Biochemistry 2012, 51 (36), 7189−7201.(7) Khakshoor, O.; Wheeler, S. E.; Houk, K. N.; Kool, E. T. J. Am.Chem. Soc. 2012, 134, 3154−3163.(8) Wang, X.; Matei, E.; Gronenborn, A. M.; Ramstrom, O.; Yan, M.Anal. Chem. 2012, 84, 4248−4252.(9) Keller, S.; Heerklotz, H.; Blume, A. J. Am. Chem. Soc. 2006, 128,1279−1286.(10) Heerklotz, H.; Tsamaloukas, A. D.; Keller, S. Nat. Protoc. 2009,4, 686−697.(11) Majonis, D.; Herrera, I.; Ornatsky, O.; Schulze, M.; Lou, X.;Soleimani, M.; Nitz, M.; Winnik, M. A. Anal. Chem. 2010, 82, 8961−8969.(12) Ghai, R.; Falconer, R. J.; Collins, B. M. J. Mol. Recognit. 2012, 25,32−52.(13) Poncet-Legrand, C.; Gautier, C.; Cheynier, V.; Imberty, A. J.Agric. Food Chem. 2007, 55, 9235−9240.(14) Wadso, L. Cem. Concr. Res. 2010, 40, 1129−1137.(15) Huang, P. J.; Liu, J. Anal. Chem. 2012, 84, 4192−4198.(16) Chaires, J. B. Annu. Rev. Biophys. 2008, 37, 135−151.(17) Velazquez-Campoy, A.; Freire, E. Biophys. Chem. 2005, 115,115−124.(18) Ladbury, J. E.; Klebe, G.; Freire, E. Nat. Rev. Drug Discovery2010, 9, 23−27.(19) Broecker, J.; Vargas, C.; Keller, S. Anal. Biochem. 2011, 418,307−309.(20) Sigurskjold, B. W. Anal. Biochem. 2000, 277, 260−266.(21) Velazquez-Campoy, A.; Freire, E. Nat. Protoc. 2006, 1, 186−191.(22) Nielsen, A. D.; Fuglsang, C. C.; Westh, P. Anal. Biochem. 2003,314, 227−234.(23) Ohtaka, H.; Velazquez-Campoy, A.; Xie, D.; Freire, E. ProteinSci. 2002, 11, 1911−1916.(24) Lipinski, C. A.; Lombardo, F.; Dominy, B. W.; Feeney, P. J. Adv.Drug Delivery Rev. 2001, 46, 3−26.(25) Freire, E. Drug Discov. Today 2008, 13, 869−874.(26) Jackson, M.; Mantsch, H. H. Biochim. Biophys. Acta 1991, 1078,231−235.
(27) Tjernberg, A.; Markova, N.; Griffiths, W. J.; Hallen, D. J. Biomol.Screening 2006, 11, 131−137.(28) Nyman, P. O.; Lindskog, S. A. Biochim. Biophys. Acta 1964, 85,141−151.(29) Keller, S.; Vargas, C.; Zhao, H.; Piszczek, G.; Brautigam, C. A.;Schuck, P. Anal. Chem. 2012, 84, 5066−5073.(30) Kemmer, G.; Keller, S. Nat. Protoc. 2010, 5, 267−281.(31) Houtman, J. C.; Brown, P. H.; Bowden, B.; Yamaguchi, H.;Appella, E.; Samelson, L. E.; Schuck, P. Protein Sci. 2007, 16, 30−42.(32) Wang, Z. X. FEBS Lett. 1995, 360, 111−114.(33) Johnson, M. L. Anal. Biochem. 1992, 206, 215−225.(34) Supuran, C. T. Nat. Rev. Drug Discovery 2008, 7, 168−181.(35) Krishnamurthy, V. M.; Kaufman, G. K.; Urbach, A. R.; Gitlin, I.;Gudiksen, K. L.; Weibel, D. B.; Whitesides, G. M. Chem. Rev. 2008,108, 946−1051.(36) Kernohan, J. C. Biochem. J. 1970, 120, 26P.(37) Mocharla, V. P.; Colasson, B.; Lee, L. V.; Roper, S.; Sharpless, K.B.; Wong, C. H.; Kolb, H. C. Angew. Chem., Int. Ed. 2004, 44, 116−120.(38) Stridh, M. H.; Alt, M. D.; Wittmann, S.; Heidtmann, H.;Aggarwal, M.; Riederer, B.; Seidler, U.; Wennemuth, G.; McKenna, R.;Deitmer, J. W.; Becker, H. M. J. Physiol. 2012, 590, 2333−2351.(39) Wang, X. W.; Suzawa, T.; Ohtsuka, H.; Zhao, B.; Miyamoto, Y.;Miyauchi, T.; Nichimura, R.; Inoue, T.; Nakamura, M.; Baba, K.;Kamijo, R. J. Cell. Physiol. 2010, 225, 709−719.(40) Eller, M. G.; Schoenwald, R. D.; Dixson, J. A.; Segarra, T.;Barfknecht, C. F. J. Pharm. Sci. 1985, 74, 155−160.(41) Stegmann, C. M.; Seeliger, D.; Sheldrick, G. M.; de Groot, B. L.;Wahl, M. C. Angew. Chem., Int. Ed. 2009, 48, 5207−5210.(42) Torres, F. E.; Recht, M. I.; Coyle, J. E.; Bruce, R. H.; Williams,G. Curr. Opin. Struct. Biol. 2010, 20, 598−605.(43) Torres, F. E.; Kuhn, P.; De Bruyker, D.; Bell, A. G.; Wolkin, M.V.; Peeters, E.; Williamson, J. R.; Anderson, G. B.; Schmitz, G. P.;Recht, M. I.; Schweizer, S.; Scott, L. G.; Ho, J. H.; Elrod, S. A.; Schultz,P. G.; Lerner, R. A.; Bruce, R. H. Proc. Natl. Acad. Sci. U.S.A. 2004,101, 9517−9522.(44) Fokkens, J.; Klebe, G. Angew. Chem., Int. Ed. 2006, 45, 985−989.(45) Shelke, S. V.; Cutting, B.; Jiang, X.; Koliwer-Brandl, H.; Strasser,D. S.; Schwardt, O.; Kelm, S.; Ernst, B. Angew. Chem., Int. Ed. 2010, 49,5721−5725.
