Combination of isothermal titration calorimetry and time-resolved luminescence for high affinity antibody–ligand interaction thermodynamics and kinetics

Methods 56 (2012) 145–153

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Combination of isothermal titration calorimetry and time-resolved luminescence for high affinity antibody–ligand interaction thermodynamics and kinetics Tolulope A. Aweda, Claude F. Meares ⇑ Chemistry Department, University of California, Davis, CA 95616, USA

a r t i c l e

i n f o

Article history: Available online 20 September 2011 Keywords: ITC Thermodynamics Kinetics Binding Antibody Ligand

a b s t r a c t For experiments using synthetic ligands as probes for biological experiments, it is useful to determine the specificity and affinity of the ligands for their receptors. As ligands with higher affinities are developed (KA > 108 M1; KD < 10–8 M), a new challenge arises: to measure these values accurately. Isothermal titration calorimetry measures heat produced or consumed during ligand binding, and also provides the equilibrium binding constant. However, as normally practiced, its range is limited. Displacement titration, where a competing weaker ligand is used to lower the apparent affinity of the stronger ligand, can be used to determine the binding affinity as well as the complete thermodynamic data for ligand–antibody complexes with very high affinity. These equilibrium data have been combined with kinetic measurements to yield the rate constants as well. We describe this methodology, using as an example antibody 2D12.5, which captures yttrium S-2-(4-aminobenzyl)-1, 4, 7, 10-tetraazacyclododecanetetraacetate. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction In developing synthetic probes for molecular imaging and therapy, an important objective is to characterize the binding of probes to their intended receptors. Both binding rates and equilibria must fall into ranges suitable for the desired application; this is true even for the current ‘‘infinite affinity’’ systems where a stable cross-link is formed after the ligand binds to its engineered receptor. Isothermal titration calorimetry, ITC has long been used to characterize equilibrium binding phenomena. Generally used in homogeneous solution, ITC involves the detection of heat produced or absorbed when one interaction partner (e.g., an antibody) binds to another (e.g., a ligand). The experiment usually involves adding small aliquots of one component to a solution containing the other, and measuring the resulting small increments of heat that must be inserted or extracted to keep the sample cell at the same temperature as the reference cell. The only requirement is that the magnitude of the enthalpy change (heat) is large enough to measure quantitatively; for typical binding reactions, this is not a problem. ITC’s biological applications have spanned the range from drug development to membrane interactions [1]. Unlike some other Abbreviations: 2D12.5, monoclonal antibody that specifically binds DOTA-metal chelates; ABD(Co), cobalt(II) S-2-(4-aminobenzyl)-1, 4, 7, 10-tetraazacyclododecanetetraacetate; ABD(Y), yttrium S-2-(4-aminobenzyl)-1, 4, 7, 10-tetraazacyclododecanetetraacetate; DOTA, 1, 4, 7, 10-tetraazacyclododecanetetraacetate; DTPA, diethylenetriaminepentaacetic acid; ITC, isothermal titration calorimetry; SPR, surface plasmon resonance. ⇑ Corresponding author. Fax: +1 530 752 8938. E-mail address: [email protected] (C.F. Meares). 1046-2023/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.ymeth.2011.09.011

experimental approaches, ITC is label-free and does not require chemical modification [2–4] or immobilization [5–7] of either binding partner. There is also no requirement that either partner be a macromolecule. However, additional techniques are usually employed in the determination of rates of the association and dissociation reactions, as explained below. Because it is based on this simple physical principle, ITC is applicable to numerous cases where a detectable heat change is produced. These have included protein–protein [8,9], protein–lipid [10–12], protein–small molecule [13,14], and protein/small molecule–DNA binding [15–17], as well as protein–carbohydrate binding [18,19]. ITC has been used to determine the equilibrium constant, reaction stoichiometry, and changes in enthalpy, entropy and Gibbs free energy involved in biological binding events [12]. However, measurement of high affinity interactions presents special challenges. As detailed below, the ITC experiment is carried out by adding small quantities of a standard solution of ligand to a solution of antibody. In order to extract the equilibrium constant, a nonlinear least squares fit of the calorimetric titration curve is carried out. Experimental conditions must be chosen such that the antibody does not become 100% saturated with ligand at the point where exactly one mole of ligand has been added per mole of binding site, or else there will be no curvature to fit. This depends on the relation between solute concentrations and the equilibrium constant, as explained below. This is usually not a problem for moderate affinities (KA < 108 M1), but is for higher ones. For systems such as nucleic acids, the strength of binding can be adjusted by changing the ionic strength of the medium, bringing the equilibrium constant into a convenient range [20]. Other instances have

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involved a change in temperature or pH to obtain a measurable value for the association constant [21,22]. These tactics often come with their own limitations, such as aggregation of biomolecules. The system in focus here is not advantageously affected by changes in ionic strength, pH, or temperature; the usual approach to ITC would not be successful [23] without the following alternative. For high affinity interactions, the displacement titration method involves artificially lowering the apparent affinity of the strong ligand by adding a weaker ligand (in an appropriately chosen concentration) as a competitor [24–26]. This actually requires three separate titrations: (i) direct titration of the stronger ligand into the macromolecule, which affords a good measure of its binding enthalpy but not the equilibrium constant; (ii) a separate titration of the weak ligand into the macromolecule to determine both its equilibrium constant and binding enthalpy; (iii) a final titration of the stronger ligand into a solution of the macromolecule–weak ligand complex. Successful displacement titration requires that the binding equilibrium constant, KA of the weak ligand be at least 10 weaker than the strong ligand and that the difference between their binding enthalpies be large (the measured heat is related to the difference between those of the strong and weak ligands), but it offers a number of positive features [25]. It is relatively fast (<5 h to obtain a complete data set), generally has no need to modify solvent conditions or temperature to obtain a good result, and allows protein integrity to be preserved [27]. This article uses the ligands, ABD(Y), ABD(Co) and the macromolecule, antibody 2D12.5 system to model an ITC displacement experiment [28]. Drawing on a combination of protein engineering and synthetic chemistry, engineered antibodies and complementary small molecules have been developed as potential covalentcapture systems for radioimmunotherapy or imaging [29], and have been validated in animal models [30]. The ITC displacement method is used to determine the binding equilibrium constant for complex formation between the strong ligand, yttrium S-2-(4aminobenzyl)-1, 4, 7, 10-tetraazacyclododecanetetraacetate, abbreviated ABD(Y), and the anti-ABD(Y) monoclonal antibody 2D12.5, while making use of a weak ligand, ABD(Co). The ITC displacement experiment provides a reliable measure of the equilibrium constant, but not of the kinetics of ligand binding and dissociation. While there are well-developed methods to study enzyme kinetics by ITC [31], rates of simple binding events are difficult to quantify. We were unable to obtain satisfactory results from surface plasmon resonance experiments, which have worked well in other cases [32]. Instead, we chose a kinetic displacement experiment that depends on a change in light emission when the DOTA(Tb) ligand binds to antibody 2D12.5 as ABD(Y) dissociates from the antibody in homogeneous solution (see Scheme 1). To a solution of the ABD(Y)–antibody 2D12.5 complex at equilibrium, we quickly add a large excess of DOTA(Tb), a competing ligand that becomes luminescent when it binds to antibody 2D12.5 [33]. As

2D12.5 mAb

kon, ABD(Y) koff, ABD(Y)

xs DOTA(Tb) k = koff, ABD(Y) 2D12.5-DOTA(Tb)

2D12.5-ABD(Y) Ó Copyright Ó 2010 American Chemical Society. 2010

ABD(Y)

Scheme 1. Competition experiment to measure koff by forming the luminescent DOTA(Tb) complex with antibody 2D12.5. First the antibody was saturated with ABD(Y), then it was mixed with a large excess of DOTA(Tb). From Ref. [28],

ABD(Y) dissociates from the antibody, its place is taken quickly and quantitatively by DOTA(Tb). The rate-limiting step for this kinetic process is dissociation of ABD(Y) from the antibody, so measuring the resulting luminescence of DOTA(Tb) as a function of time reveals the rate of dissociation of ABD(Y) as explained in more detail below. Combining the measured rate constant for this dissociation and the thermodynamic data from ITC permits calculation of the ligand–antibody association rate constant, completing the desired set of results. 2. Experimental procedures 2.1. Planning considerations Appropriate concentrations of reactants must be chosen to produce a measurable heat change upon mixing. The ITC instrument used in this work, MicroCal VP-ITC, has a sensitivity of 0.1 lcal, so each small injection should cause a heat change averaging 3– 5 lcal. It is also important to choose the appropriate relative concentration of ligand (sample in syringe) to the concentration of macromolecule (sample in cell). For a 1:1 stoichiometry ratio (such as in the system described here, where n = 1), titrating a ligand concentration that is 10–20 higher than that of the macromolecule should ensure a complete binding isotherm. Commonly, the macromolecule concentration is chosen to be 10–50 lM, while the ligand is about 15 times higher, such that the final molar ratio of ligand to macromolecule at the end of the titration is 2–3. An estimate of the macromolecule concentration, M, can be made from the arbitrary constant, c, if one has a rough estimate of the binding affinity, KA. It is recommended that the parameter, c = KA [M], should be greater than 1 but less than 1000 in order to produce binding isotherms that yield accurate KA values [34]. Considering the limits of 1 < c < 1000, measuring the equilibrium constant for high affinity interactions (KA > 108 M1) would require low concentrations of macromolecule, which may lead to heat changes that fall below the calorimeter detection threshold. Using higher concentrations could produce squared-off titration curves, for which only the enthalpy of reaction can be accurately measured. Fortunately, a weaker ligand can be used competitively to lower the apparent affinity of the stronger ligand. For this competitive experiment, the weaker ligand must be present in a concentration high enough to appropriately reduce the apparent affinity of the stronger ligand. Also, the affinity of the weaker ligand should be lower by a factor of 10 or more, with a difference of at least 2– 3 kcal/mol in binding enthalpy. This will ensure an accurately measurable heat change when the stronger ligand binds the macromolecule while displacing the weaker ligand. 2.2. Instrumentation 2.2.1. Isothermal titration calorimetry A VP-ITC calorimeter (MicroCal Inc., Northampton, MA) can be used at different operating temperatures (2–80 °C). Similar instruments are available from other suppliers. The VP-ITC calorimeter consists of a reference cell and a sample cell. The reference cell was usually filled with 18 MX cm water and maintained at the same temperature as the sample cell. A feedback system within the ITC instrument maintains a constant temperature difference between the sample cell and reference cell; this difference was usually maintained close to zero. A spinning syringe was used to deliver aliquots of the ligand into the sample cell and continuously mix the resulting solution. The reaction under study here produced heat during the titration, so it was exothermic. Other reactions the reader might wish

T.A. Aweda, C.F. Meares / Methods 56 (2012) 145–153

to study could be endothermic, absorbing heat; the calorimeter can measure either kind. In the following text, the language used refers to exothermic processes. Heat evolved during the binding reaction in the sample cell caused a temperature difference between the two cells, which was corrected by the instrument’s feedback system. The power required (lcal/s) to maintain a constant temperature difference was plotted vs. time, giving a peak after each injection; the area under each peak was proportional to the heat produced after each injection. As more ligand was successively titrated into the sample, the amount of unbound macromolecule in the cell decreased as did the magnitude of the heat signal peaks. As saturation of the binding sites on the macromolecule was approached, only background heat due to dilution or other mechanical noise was produced. Subtracting this background data from the main experimental results minimized the effects of such noise. A vacuum pump supplied by the manufacturer was used to degas samples before the experiment, requiring about 10–20 min with stirring. 2.2.2. ITC set-up for running an experiment Set the sample cell at a temperature one or two degrees below the calorimeter running temperature (29 °C for 30 °C and 36 °C for 37 °C) to reduce equilibration time of the cell. If dirty, the sample cell (1.45 mL in volume) and syringe (280 lL) should be thoroughly cleaned with detergent (such as 5% Contrad-70 or Decon 90) and rinsed with about 0.5 L of 18 MX cm water. It is advisable to rinse the cell with the sample buffer before use. After all washes and rinses have been performed using the vacuum pump, the cell is ready for sample application. The sample cell can now be filled carefully with the macromolecule solution, using a 2.5 mL longneedle plastic or glass syringe. To prevent entrance of air bubbles into the sample cell, about 2–3 mL of the macromolecule solution should be prepared and used to fill the cell. For multiple injections, set the calorimeter running parameters to include temperature (30 °C or 37 °C), number of injections (45 or 46), reference power (10 lcal/s), and initial delay (180 s). Set the injection volume such that the first injection (2.5 lL) can be ignored due to mechanical disturbances and the rest to 6 lL. There should be a 210 s time delay between each injection, a noise filter time constant of 2 s, and the equilibrium mode should be set to fast. All thermodynamic data can be analyzed with MicroCal software, Origin 7.0, which performs nonlinear least squares curve fitting. 2.2.3. Fluorescence microplate reader Kinetic measurements involving small ligand molecules and the antibody were measured indirectly using a FluostarÒ fluorescence microplate reader (BMG Lab Technologies). Time-resolved luminescence measurements, from a terbium-DOTA chelate that binds competitively to the antibody, used 280 nm excitation and 550 nm emission filters, each with ±10 nm bandpass. Two hundred measurements of each sample well were carried out every 15 s, with a 40 ls delay after each excitation pulse before the emission signal was registered. 2.3. Materials 2.3.1. ITC (i) Metal–ligand preparation: ABD, aminobenzyl-DOTA (Macrocyclics), rare earth salts of yttrium chloride and cobalt nitrate (Sigma–Aldrich). DTPA and EDTA (Acros Organics). Carrier-free 57CoCl2 solution in 0.05 M HCl. Triethylamine and plastic backed thin layer silica (TLC) plates (EMD Chemicals). DEAE-cellulose (Fisher Scientific). (ii) Macromolecule: parental 2D12.5 monoclonal antibody [35].

147

(iii) DEAE-column elution buffer: ammonium acetate (concentrations ranging from 0.1 M to 1 M). (iv) Calorimetry experimental buffer: 0.1 M sodium phosphate, pH 7.0 (no NaCl added). All buffers were made using 18 MX cm water and thoroughly degassed for all experiments. 2.3.2. Fluorescence (i) Metal–ligand preparation: DOTA (Macrocyclics), rare earth salts of yttrium chloride and terbium chloride (Sigma– Aldrich). (ii) Experimental buffer: 50 mM Tris–HCl pH 7.4, 150 mM NaCl. (iii) Black round-bottomed microtitre plates (Greiner Bio-One). 2.4. Ligand and antibody preparation When preparing samples for ITC binding affinity measurements, the solubility and stability of the ligand and macromolecule must be considered. Preferably, buffers used in ITC experiments are of low ionic strength. The buffer for the ligand and macromolecule must be the same; its composition must be identical in terms of concentration, pH, ionic strength, surfactants, solubility-improving reagents or other additives. Differences in the samples other than ligand vs. macromolecule can lead to interfering heat effects from buffer mixing. To ensure a buffer match, the macromolecule used here was dialyzed in a filtered solution of the buffer at neutral pH, while the ligand was thoroughly desalted and dissolved in the same buffer. To avoid large heats of dilution that may mask the heat of binding, several buffers should be titrated with just the ligand and the data examined. For the reactants discussed below, the best matching buffer was 0.1 M sodium phosphate, pH 7.0, with no other added salt. Tris–HCl, pH 7.4, or HEPES, pH 7.5, did not produce conveniently low heats of dilution, possibly due to their heat of ionization [36]. 2.4.1. Metallation of chelates Stock solutions of ABD and DOTA were prepared and their concentrations accurately measured using Co-57 metal binding assay [37]. Two hundred micromolar stock solutions of YCl3 and Co(NO3)2 were prepared in metal-free 0.05 M HCl. Incubate 80 mM ABD (0.048 mmol in 600 lL) with 1.5 equivalent (120 mM) of YCl3 or Co(NO3)2 at 37 °C for 2 h in 0.5 M triethylammonium acetate, pH 6.0. In another vial, incubate 80 mM DOTA (0.048 mmol in 600 lL) with 1.5 equivalent TbCl3 under the same conditions. Using Co-57 competitive metal-binding assay, the percent saturation of the chelates was determined [37]. The unreacted excess metal was scavenged with DTPA (0.2 M, 300 lL) after a satisfactory degree of saturation (at least 90%) was achieved. 2.4.2. Purification of metal chelates for ITC Each metal chelate in a low-ionic-strength solution was added and bound to a DEAE-cellulose anion-exchange column in the acetate form. The metal chelate was eluted using a gradient from 0.1 M to 1 M ammonium acetate, and the ABD(M) product detected by absorbance at 286 nm. Each eluted sample was lyophilized four or five times (about four days, redissolving the sample in water daily) to get rid of the volatile ammonium acetate. The dry, desalted metal chelate was dissolved in 0.1 M sodium phosphate buffer, pH 7.0. The concentration of the ABD(Y) or ABD(Co) was measured by absorbance at 286 nm, using e286 = 1430 M–1 cm–1. 2.4.3. Protein preparation Parental 2D12.5 monoclonal antibody (whole IgG, 50 lM) was dialyzed into the same 0.1 M sodium phosphate buffer, pH 7.0 as the chelates and filtered through a 0.22 lm disc. The concentration

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was measured at A280 (e280 = 194,900 M–1 cm–1) and diluted to the needed concentration in the sodium phosphate buffer for each experimental titration. For short-term storage, the dialyzed stock protein was stored in sterile plastic tubes at 4 °C. 2.5. Calorimetry experiment 2.5.1. Estimation of heat of dilution using a buffer blank experiment It is not only good practice to do a buffer blank experiment; it is advisable to estimate the heat of dilution due to non-specific interactions. Alternatively, this can be done by taking averages of the last injections in the titration. A buffer blank involves titration of the ligand in the syringe into the sample cell, containing everything in the main experiment except the macromolecule. This experiment was performed using the same parameters as in the main experiment. Forty-six injections of 128 lM ABD(Y) from the syringe was titrated into the sample cell containing the sample buffer, using the parameters described above (Section 2.2.2). The same blank experiment was performed using 150 lM ABD(Co). The small heat change obtained was subtracted during analysis of the macromolecule–ligand experimental data. 2.5.2. Macromolecule/ligand binding experiments For a macromolecule that binds to ligands with high affinity (KA > 108 M1), two experiments are needed in addition to the direct titration of the macromolecule with the high affinity ligand [24]. These include direct titration of the macromolecule with a weaker ligand, and titration of a defined mixture of weak ligand and macromolecule with the stronger ligand, resulting in displacement of the weaker ligand from the macromolecule. 2.5.2.1. Direct binding of strong ligand with macromolecule. Direct titration was performed to measure the binding enthalpy of the strong ligand, ABD(Y) to the macromolecule, antibody 2D12.5 but the titration curve did not provide the accurate information needed to compute the true binding equilibrium constant. ABD(Y) (64 lM) was added in 45 injections into 5 lM antibody 2D12.5 (analyte in the cell, 1.45 mL). The volume for each injection was 6 lL and the experiment was carried out at 30 °C. 2.5.2.2. Displacement/competitive binding experiments. The results obtained from the direct binding of the strong ligand, ABD(Y) and antibody 2D12.5 did not give satisfactorily reproducible or accurate results for the equilibrium constant calculation. From equilibrium dialysis experiments, it has been reported that a ligand similar to ABD(Y), binds 2D12.5 with a dissociation constant in the nanomolar range [35], though equilibrium dialysis suffers from some of the same limitations as ITC when high affinities are involved. An alternative ITC displacement method as described by Velazquez-Campoy and Freire [25] was employed to assess the high affinity binding data more accurately. This involves 2 additional sets of experiments: (i) Direct titration of weaker ligand with antibody 2D12.5: ABD(Co) (150 lM, 12 the molar concentration of the antibody) was titrated in 46 injections into the sample cell containing the macromolecule, 12.5 lM antibody 2D12.5 in 0.1 M sodium phosphate (pH 7.0), using the parameters in Section 2.2.2. The volume of each injection was 6 lL and the experiment was carried out at 30 °C and 37 °C. (ii) Competitive binding titration with stronger ligand in the syringe: the sample cell was cleaned out after the first direct titration of the monoclonal antibody 2D12.5 with weaker ligand, ABD(Co) using a copious amount of water. The strong ligand was titrated into a solution containing a known concentration of the macromolecule–weak ligand complex.

Generally, the complex formed in the sample cell from the first weak ligand–macromolecule titration is not used in the second titration, due to uncertainty in its final concentration. ABD(Y) (150 lM) was titrated in 46 injections into the sample cell containing a mixture of 100 lM ABD(Co) and 16.1 lM antibody 2D12.5 in 0.1 M sodium phosphate (pH 7.0) using the parameters in Section 2.2.2. The volume of each injection was 6 lL and the experiment was performed in duplicate or triplicate, at each temperature of interest. 2.6. Determination of the dissociation rate constant by kinetic displacement The monoclonal antibody 2D12.5 has strong affinity for DOTA complexes of lanthanides [33]. The lanthanide, Tb, exhibits easily observable luminescence when DOTA(Tb) binds in the antibody site, and its long (millisecond) lifetime makes it easy to detect [33,38–40]. The UV excitation at 280 nm of an unbound DOTA(Tb) complex in solution results in minimal luminescence, while DOTA(Tb) bound to antibody 2D12.5 luminesces brightly due to energy transfer from the aromatic side chains of the antibody to the bound DOTA(Tb), emitting easily detectable green Tb luminescence at 545 nm [33]. A kinetic displacement method was used to measure the dissociation rate of the ligand, ABD(Y) from its binding site on antibody 2D12.5. The principle is straightforward: an equilibrium solution of the ligand ABD(Y)–macromolecule 2D12.5 complex is perturbed by rapid addition of a large excess of the competitive ligand DOTA(Tb), as outlined in Scheme 1. As the nonemissive ABD(Y) dissociates from 2D12.5, it is quickly replaced by DOTA(Tb) to form an emissive product. Conditions are chosen and validated such that the dissociation of ABD(Y) is the rate-limiting step of the process; measurement of the rate of increase of luminescence from bound DOTA(Tb) reveals the rate of dissociation of ABD(Y). 2.6.1. 2D12.5–DOTA(Tb) method development Solutions of antibody 2D12.5 were prepared to final concentrations of 1, 5 and 10 lM, and DOTA(Tb) to final concentrations ranging from 5 lM to 1 mM in 50 lL or 100 lL of TBS (50 mM Tris buffered saline, 150 mM NaCl) buffer, pH 7.4. Sample solutions were prepared in round-bottomed black polystyrene 96-well microplates. A BMG FluostarÒ fluorometer was used to scan each well using the following instrument parameters: 100–200 scans, 10 flashes per scan, 40 ls delay, and 1.536 ms integration with the detector gain set to the brightest sample. The excitation and emission wavelengths for each sample were at 280 ± 10 nm and 550 ± 10 nm respectively. 2.6.2. Observations from 2D12.5–DOTA(Tb) method development The optimal 2D12.5 and DOTA(Tb) concentrations used in the main experiment were obtained first. In order to minimize noise interference from the background fluorescence of the 2D12.5 antibody only or DOTA(Tb) only, the concentration of the antibody should be in the low micromolar while DOTA(Tb) should be in the high micromolar range. Also, the concentration range of DOTA(Tb) should be in excess (20 ABD(Y) was chosen) to out compete the ABD(Y) efficiently. Using DOTA(Tb) and antibody 2D12.5 at 1 mM and 5 lM final concentrations respectively, satisfied all these conditions. Using 10 lM 2D12.5 with more than 1 mM DOTA(Tb) produced higher background noise. Table 1 shows the response from the binding of antibody 2D12.5 to DOTA(Tb). 2.6.3. Determining the off-rate of ABD(Y) from antibody 2D12.5 Antibody 2D12.5 (10 lM) was incubated with 100 lM ABD(Y) in TBS buffer, pH 7.4, overnight to achieve equilibrium association.

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T.A. Aweda, C.F. Meares / Methods 56 (2012) 145–153 Table 1 Response from the binding of antibody 2D12.5 to DOTA(Tb) using black round-bottomed 96-well microplates on the BMG Fluostar. DOTA(Tb) + 2D12.5 fluorescence

Ratio of 2D12.5–DOTA(Tb)/DOTA(Tb) response

DOTA (Tb) concn

10 lM 2D12.5

5 lM 2D12.5

1 lM 2D12.5

DOTA (Tb) response

10 lM 2D12.5/Tb

5 lM 2D12.5/Tb

1 lM 2D12.5/Tb

1 mM 500 lM 200 lM 100 lM 50 lM 25 lM 10 lM 5 lM 0 lM

57,008 52,900 54,582 53,662 52,315 50,191 45,465 24,917 4117

28,750 34,466 36,933 35,332 25,031 30,929 29,201 26,376 4516

12,369 11,819 14,835 12,125 11,690 14,674 13,364 8976 4965

5042 3076 1678 1147 446 390 197 169

11 17 33 47 117 129 231 148

6 11 22 31 56 79 148 156

2 4 9 11 26 38 68 53

To ensure that each ABD(Y) dissociating from the 2D12.5 antibody binding pocket could be immediately replaced by DOTA(Tb), the DOTA(Tb) ligand should be added in large excess at the beginning of the luminescence experiment. The fluorometer was equipped with an auto-injecting syringe so the addition could be performed quickly. The fluorometer was set to autoinject 50 lL of 2 mM DOTA(Tb) into a well containing 50 lL of 10 lM 2D12.5 + ABD(Y) in TBS, pH 7.4. Using 5 sets of controls: 2D12.5, 2D12.5 + ABD(Y), 2D12.5 + DOTA(Tb), DOTA(Tb) only, and TBS buffer only, the experiment was performed in 96-well black round bottom microplates at 30 °C and 37 °C. In all the wells, the total volume was kept at 100 lL while, the final concentration of antibody 2D12.5 was 5 lM in the appropriate wells. The samples were excited at 280 nm and the time-resolved luminescence was detected at 550 ± 10 nm using a 40 ls delay, with 200 scans every 15 s. For data analysis, each reading was blanked with the TBS buffer and DOTA(Tb)-only readings. Increasing concentrations of DOTA(Tb) (2 mM and 4 mM final concentrations) were also evaluated to assure that sufficient excess of the DOTA(Tb) complex had been used to make the results independent of DOTA(Tb) concentration (i.e. to assure that dissociation of ABD(Y) from 2D12.5 was indeed the rate-limiting step). The experiments were carried out in triplicate to improve precision. As a control, a non-specific mouse IgG was used and analyzed the same way as the 2D12.5 antibody.

Using the law of mass action and conservation of mass, the total concentration of the ligands and macromolecule can be defined with Eqs. (5)–(7)

½WT ¼ ½W þ ½MW

ð5Þ

½ST ¼ ½S þ ½MS

ð6Þ

½MT ¼ ½M þ ½MS þ ½MW

ð7Þ

Solving Eqs. (3) and (4) for [W] and [S] respectively, with substitution into Eqs. (5) and (6) gives Eqs. (8) and (9) below.

½M½WT 1=K W þ ½M ½M½ST ½MS ¼ 1=K S þ ½M

½MW ¼

Time (min) 0

80

120

160

µcal/sec

-0.1

-0.2

-0.3 0

M þ W MW

ð1Þ

M þ S MS

ð2Þ

Then, the equilibrium binding constant for the weak and strong ligand can be described by Eqs. (3) and (4) respectively, where S does not interact with W nor is it possible to form a MWS complex.

ð3Þ ð4Þ

kcal/mole of injectant

A complete mathematical solution to the displacement titration method has been performed by Sigurskjold [26] and Zhang and Zhang [41] where Eqs. (1) and (2) describe the binding reactions of a weak ligand W and a strong ligand S that can bind to the same site on macromolecule M with 1:1 stoichiometry.

½MW ½M½W ½MS KS ¼ ½M½S

40

0.0

3.1. Data analysis

KW ¼

ð9Þ

Substituting Eqs. (3)–(5) into Eqs. (7) gives a set of Eqs. that allows us to show the relationship between the heat change for the

3. Results Isothermal titration calorimetry can directly measure a complete set of thermodynamic binding data. Although the practical range for accurate measurement of dissociation constants is approximately between 10–8 M and 10–4 M for most commercial ITC instruments, the displacement method has extended this to 10–12 M [24,25,41] and even to 10–3 M [41].

ð8Þ

-5 -10 -15 -20 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Molar Ratio Fig. 1. Standard calorimetric titrations of wild-type 2D12.5 monoclonal antibody (5 lM) with the chelate ABD(Y) (64 lM) (direct titration) at 30 °C in 0.1 M sodium phosphate, pH 7.0. The upper vertical axis represents the raw differential power in lcal/s between the reference and sample cells, while the lower vertical axis represents the normalized kcal/mol of injected ABD chelate.

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T.A. Aweda, C.F. Meares / Methods 56 (2012) 145–153

a

Time (min) 0

40

80

120

b

160

Time (min) 0

40

80

120

160

0.0

0.0

-0.1

-0.3

-0.2

0

0

-2

-2

-4 -6

-4

-8 -10

-6 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

-12 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Molar Ratio

Molar Ratio

Ó Copyright Ó 2010 American Chemical Society 2010

-0.2

-0.1

Fig. 2. Calorimetric titrations of parental 2D12.5 monoclonal antibody (12.5 lM for ABD(Co) or 16.1 lM for competitive titration) with a) the chelate ABD(Y) (150 lM) in the presence of ABD(Co) (100 lM) (competitive titration), b) chelate ABD(Co) (150 lM). The upper vertical axis represents the raw differential power in lcal/s between the reference and sample cells, while the lower vertical axis represents the normalized kcal/mol of injected ABD chelate. The experiments were performed at 30 °C in 0.1 M sodium phosphate, pH 7.0. From Ref. [28],

a 0.1

Time (min) 0

40

80

120

160

b

Time (min) 0

40

80

120

160

0.0 0.0

-0.1

-0.1

-0.3

-0.2

-0.4 -0.3 0

0 -2

-2

-4

-4

-6 -8

-6

-10

-8

-12 0.0

0.5

1.0

1.5

Molar Ratio

2.0

2.5

3.0

-14

0.0

0.5

1.0

1.5

2.0

Molar Ratio

2.5

3.0

3.5

Ó Copyright Ó 2010 American Chemical Society 2010

-0.2

Fig. 3. Calorimetric titrations of parental 2D12.5 monoclonal antibody (15.6 lM for ABD(Co) or 12.4 lM for competitive titration) with a) the chelate ABD(Y) (150 lM) in the presence of ABD(Co) (100 lM) (competitive titration), b) chelate ABD(Co) (150 lM). The upper vertical axis represents the raw differential power in lcal/s between the reference and sample cells, while the lower vertical axis represents the normalized kcal/mol of injected ABD chelate. The experiments were performed at 37 °C in 0.1 M sodium phosphate, pH 7.0. From Ref. [28],

151

T.A. Aweda, C.F. Meares / Methods 56 (2012) 145–153

Table 2 Thermodynamic parameters for the reversible association of aminobenzyl-DOTA chelates to antibody 2D12.5 at 30 °C and 37 °C [28] (standard deviations in parentheses).a Chelate ABD(Co) ABD(Co) ABD(Y) ABD(Y) a

T, °C 30 37 30 37

KA, M1 8.2 7.1 3.3 5.2

DG, kcal/mol 5

(±0.9)  10 (±0.4)  105 (±2.1)  108 (±0.9)  108

8.2 8.3 11.7 12.4

(±0.1) (±0.1) (±0.4) (±0.2)

DH, kcal/mol 12.2 12.4 18.2 20.1

(±0.4) (±4.8) (±0.5) (±1.2)

DS, cal/mol K 13.2 13.3 21.5 24.9

(±1.3) (±4.8) (±2.9) (±4.1)

KD, M 1.2 1.4 3.1 2.0

(±0.1)  106 (±0.1)  106 (±2.0)  109 (±0.4)  109

Data from ITC experiments in Figs. 2 and 3.

macromolecule–weak binder complex, MW and the macromolecule–strong binder complex MS.

½MS2 þ ½MSð½ST  ½MT  1=K app Þ þ ½MT ½ST ¼ 0

ð10Þ

This quadratic equation can be solved to give the apparent concentration of the strong ligand-macromolecule complex formed as given by Eq. (11).

½MS ¼ 1=2ð½MT þ ½ST þ 1=K app Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 1=4ð½MT þ ½ST þ 1=K app Þ2  ½MT ½ST

ð11Þ

Keeping this fact in mind, two different titration approaches were investigated; direct titration of strong binder ABD(Y) and a competitive titration. Although the direct titration of ABD(Y) with antibody 2D12.5 gave a poor fit for the binding affinity, an estimate of the associated enthalpy was obtained: DH = –19.2(±0.4) kcal/mol (Fig. 1). We next turned to the method of Velazquez-Campoy and Freire [25] to measure the equilibrium constant. In this competitive or displacement titration, the apparent affinity of the strong ligand ABD(Y) is artificially lowered by the presence of a weaker ligand ABD(Co) so that a more accurate

where the apparent binding affinity for the strong ligand Kapp can be represented by Eq. (12), which depends on the free weak ligand whose concentration changes as the titration progresses.

K app ¼

KS 1 þ K W ½W

ð12Þ

The heat change DQ produced from the association of the strong ligand with the macromolecule and displacement of the weak ligand can be related to changes in [MW] and [MS] and their associated binding enthalpies as shown in Eq. (13):

DQ ¼ DHS  V T  d½MS þ DHW  V T  d½MW

ð13Þ

where VT is the volume of the sample cell and DHW and DHS are the respective molar enthalpies of the weak and strong ligands. The change in concentration of the weak affinity-macromolecule complex can be obtained from Eqs. (3) and (7) as in Eq. (15).

ð14Þ ð15Þ

Eq. (15) can be substituted into Eq. (14) to obtain:

  K W ½W DQ ¼ DHS  VT  d½MS þ DHW  V T  d½MS 1 þ K W ½W   K W ½W DQ ¼ V T  d½MS DHS  DHW  1 þ K W ½W DQ ¼ V T  d½MS  DHapp

ð16Þ ð17Þ ð18Þ

and,

DHapp ¼ DHS  DHW 

K W ½W 1 þ K W ½W

ð19Þ

Thus, the molar enthalpy of the strong ligand can be defined as:

DHS ¼ DHapp þ DHW 

K W ½W 1 þ K W ½W

ð20Þ

where DHW and KW have been determined from a prior direct titration of the weak ligand W with the macromolecule M. 3.1.1. Thermodynamic Parameters obtained from ITC Previous studies on the binding of ABD(Y) ligand to monoclonal antibody 2D12.5 have suggested that KD should be on the order of 108 M or stronger, indicating a strong binding interaction.

Ó Copyright Ó 2010 American Chemical Society 2010

K W ½W 1 þ K W ½W d½MW d½MS K W ½W ¼  d½S d½S 1 þ K W ½W

½MW ¼ ½MT  ½MS

Fig. 4. Curve fits from the determination of the dissociation rate constant between ABD(Y) and parental 2D12.5 antibody. Upper panel, 30 °C; lower panel 37 °C (note: time scales are different). One, 2 and 4 mM DOTA(Tb) was used to competitively replace the ABD(Y) when it dissociated from the 2D12.5 binding site. Triplicate experiments were done at each DOTA(Tb) concentration, and all the data were combined for the fits and plots. Insets show longer total time courses, which indicate that equilibrium has been reached. From Ref. [28],

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T.A. Aweda, C.F. Meares / Methods 56 (2012) 145–153

Table 3 Kinetic parameters for the dissociation of ABD(Y) ligand from antibody 2D12.5 [28].b Experiment

37 °C koff, s

Avg(SD) b

30 °C 1

7.0 (±0.7)10

Half-life, s 3

97 ± 9

Calc kon, M 6

3.5  10

1

s

1

koff, s1 3

4.0 (±0.3) x10

Half-life, s

Calc kon, M1 s1

161 ± 13

1.3  106

Data from luminescence experiments in Fig 4.

equilibrium constant can be measured for ABD(Y) binding to antibody 2D12.5. These experiments were carried out at 30 °C (Fig. 2) and 37 °C (Fig. 3) and the average results summarized in Table 2. It should be noted that the enthalpy change DH and binding affinity KA for the weak ligand ABD(Co) and strong ligand ABD(Y) differ by at least 6 kcal/mol and a factor of 103 respectively. 3.2. Kinetic data obtained from fluorescence time-resolved experiments The dissociation rate constant, koff at 30 °C and 37 °C was indirectly evaluated by measuring the luminescence of DOTA(Tb) as it bound to the 2D12.5 antibody when ABD(Y) dissociated. The terbium luminescence response at 545 nm for DOTA(Tb) bound to antibody 2D12.5 (33) was monitored as a function of time. As shown in Scheme 1, the rate of association of the excess DOTA(Tb) with 2D12.5 was taken to equal the rate of dissociation of ABD(Y) from the antibody. To assure that dissociation of ABD(Y) was the rate-limiting step in this process, three different concentrations of DOTA(Tb) were used. Similar results were obtained in all cases, and all three sets of triplicate results were fitted to one curve. The koff was obtained from a fit of the following equation that describes the pseudo-first order association kinetics: Y = Ymax(1  ekt), where Y is the terbium luminescence intensity and the pseudo-first-order rate constant for binding DOTA(Tb) is k = koffs1 (the rate constant for ABD(Y) dissociation). The dissociation rate constant was determined from the plot of the fluorescence signal growth of 2D12.5–DOTA(Tb) complex with time (Fig. 4). Attempts to fit the data to more than one rate constant gave inferior results. Having measured koff and kD, we can calculate kon = (koff/KD) M1 s1 (Table 3). In the experimental example given above, our attempts to study the system with surface plasmon resonance failed to give reliable results. Part of the challenge seemed to be the asymmetry in properties of the binding pair: the bivalent antibody binds to surfaceimmobilized ligands more tightly than the biologically relevant monovalent association, and in our hands the small ligand produces too little signal when it binds to surface-immobilized antibody. On the other hand, isothermal calorimetry is suitable for small molecules as well as macromolecules. In ITC experiments, both reactants are in solution (no immobilization necessary) such that binding interactions can be studied in homogenous mixtures, minimizing complications arising from diffusion and heterogeneity. Although the complete binding energetic parameters can be obtained using ITC, measurements of association and dissociation rate constants cannot be directly determined without using other biophysical techniques. Here, a fluorometer has been used to indirectly measure the dissociation rate constant. 4. Discussion The equilibrium thermodynamic properties of ligand–receptor systems such as those involving haptens and antibodies are of fundamental importance to understanding and measuring their functions. Further, the kinetic rate constants for complex formation and dissociation add insights beyond equilibrium properties. In recent years, the technique of Surface Plasmon Resonance (SPR) has assumed a central position in measuring kinetic and thermodynamic

properties of biological systems. Though it involves immobilization of one of the binding partners, SPR has proven to be widely applicable in the study of kinetics of macromolecular interactions, from which thermodynamic parameters may be derived. However, when one or both binding partners possess more than a single binding site, complications arise. In the case discussed here, antibody 2D12.5 is bivalent. Immobilizing the monovalent ligand ABD(Y) on an SPR chip proved problematic in our hands: too high a density of ABD(Y) on the surface led to practically irreversible (bivalent?) binding of the antibody, not relevant to the imaging application we wished to develop, while too low a density led to no detectable binding. Uncertainties in validating monovalent binding discouraged further attempts using whole antibody. Preparation of monovalent Fab fragments of antibody 2D12.5 led to ambiguous results, either showing that the kinetics of association and dissociation were unusually fast or that non-specific binding was interfering with the SPR experiment. Taking the alternative approach of immobilizing the antibody and attempting to observe binding of the small molecule ABD(Y) failed due to lack of sensitivity of our SPR instruments for small-molecule binding. Attaching ABD(Y) to a macromolecule in an attempt to improve sensitivity led to numerous uncertainties. We turned to ITC because it offered the prospect of directly observing at least the equilibrium properties of complex formation in homogeneous solution, independent of molecular size. Having success with the equilibrium measurements encouraged us to develop an optical method to observe the kinetics of dissociation of ligand from antibody in solution. Here we discovered that the kinetics of dissociation were quite fast for a high-affinity system, with a bound half-life of less than two minutes for the complex. The association kinetics therefore must also be unusually fast, as summarized in Table 3. This is plausible, based on the structure of the complex [29].

5. Concluding remarks The displacement or competitive titration method in ITC has shown to be effective for accurately measuring the equilibrium thermodynamics of high affinity interactions. In the usual ITC strategy of direct titration, as the interaction between binding partners gets stronger, the concentration of the macromolecule that can be used to measure equilibrium constants progressively gets lower, until it is outside instrumental range. By forcing the high affinity ligand to compete and displace a lower affinity ligand at the binding site of the macromolecule, the binding affinity is artificially lowered such that a more accurate affinity can be obtained after mathematical analysis [26]. Using the displacement titration method, the range of ITC measurement has been extended to the high affinity picomolar range [27] and even to very low affinity measurements [41]. Combining ITC with time-resolved luminescence has extended the results to include analysis of the kinetic properties of this ligand–receptor system. Acknowledgments This work was supported by NIH research grants CA016861 and CA136639 from the National Cancer Institute.

T.A. Aweda, C.F. Meares / Methods 56 (2012) 145–153

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