Ligand-Substitution Mode Capillary Electrophoretic Reactor

Aug 21, 2009 - Ligand-Substitution Mode Capillary Electrophoretic Reactor: Extending Capillary Electrophoretic Reactor toward Measurement of Slow ...
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Anal. Chem. 2009, 81, 7849–7854

Ligand-Substitution Mode Capillary Electrophoretic Reactor: Extending Capillary Electrophoretic Reactor toward Measurement of Slow Dissociation Kinetics with a Half-Life of Hours Nobuhiko Iki,* Mariko Takahashi, Toru Takahashi, and Hitoshi Hoshino Laboratory of Environmental Analytical Chemistry, Graduate School of Environmental Studies, Tohoku University, 6-6-07 Aramaki-Aoba, Aoba-ku, Sendai 980-8579, Japan A method employing capillary electrophoresis (CE) was developed to determine the rate constant of the very slow spontaneous dissociation of a complex species. The method uses a CE reactor (CER) to electrophoretically separate components from a complex zone and, thus, spontaneously dissociate a complex. The dissociation is accelerated by ligand substitution (LS) involving a competing ligand added to the electrophoretic buffer. The LSCER method is validated using the dissociation of a Ti(IV)-catechin complex and EDTA as a competing ligand. There is good agreement between the spontaneous dissociation rate constant (kd ) (1.64 ( 0.63) × 10-4 s-1) and the rate constant obtained by a conventional batchwise LS reaction (kd ) (1.43 ( 0.04) × 10-4 s-1). Furthermore, the usefulness of the method is demonstrated using a Ti(IV)-tiron complex, for which kd ) (0.51 ( 0.43) × 10-4 s-1, corresponding to a half-life (t1/2) of 3.8 h. Notably, a single run of LS-CER for the Ti(IV) complex is completed within 40 min, implying that LS-CER requires a considerably shorter measurement time (roughly equal to t1/2) than conventional CER. LS-CER can be widely applied to determine the spontaneous dissociation rates of inorganic diagnostic and therapeutic reagents as well as of biomolecular complexes. Kinetics of the spontaneous dissociation of complex species frequently plays a decisive role in biological systems. For instance, dynamic behavior of the formation and dissociation of biomolecular complexes between antigens and antibodies,1-5 deoxyribonucleic acid (DNA) and proteins,6,7 and enzymes and substrates8,9 is of key importance to the regulation of biological functions. In chelation therapy for hemochromatosis, the sequestrating reagents used for free Fe(III) ions are required to form kinetically * To whom correspondence should be addressed. E-mail: iki@orgsynth. che.tohoku.ac.jp. (1) Ruan, Q.; Tetin, S. Y. Anal. Biochem. 2008, 374, 182–195. (2) Pohanka, M.; Pavlis, O.; Skladal, P. Sensors 2007, 7, 341–353. (3) Katakura, Y.; Zhuang, G.; Nakatani, T.; Furuta, T.; Omasa, T.; Kishimoto, M.; Suga, K.; Shioya, S. J. Mol. Catal. B 2004, 28, 191–200. (4) Dornmair, K.; Schneider, C. K.; Malotka, J.; Dechant, G.; Wiendl, H.; Hohlfeld, R. J. Neuroimmunol. 2004, 152, 168–175. (5) Scheuermann, J.; Viti, F.; Neri, D. J. Immunol. Methods 2003, 276, 129– 134. 10.1021/ac901296j CCC: $40.75  2009 American Chemical Society Published on Web 08/21/2009

stable complexes without releasing bound Fe(III).10 Kinetic stability is an important prerequisite for inorganic diagnostic reagents, which consist of a functional nucleus and ligand and are used in magnetic resonance imaging (MRI),11-13 single-photon emission computed tomography (SPECT),14,15 and positron emission tomography (PET).16-18 Kinetic stability is also a limiting factor for radiotherapeutic reagents.19,20 Therefore, it is crucial to understand the relationship between the kinetic stability and the ligand structure in designing kinetically more stable complexes. In contrast to formation kinetics, it is difficult to determine the dissociation rate constant of complex species because the measurement requires a rapid decrease in the concentration of at least one of the components. Such a situation has only been realized in a rather indirect fashion using chemical masking or immobilization of a component. For example, when measuring the dissociation rate of a metal complex, researchers often employ ligand substitution (LS) and use a competing ligand to mask the (6) Brady, K. L.; Ponnampalam, S. N.; Bumbulis, M. J.; Setzer, D. R. J. Biol. Chem. 2005, 280, 26743–26750. (7) Suzuki, T.; McKenzie, M.; Ott, E.; Ilkun, O.; Horvath, M. P. Biochemistry 2006, 45, 8628–8638. (8) Kiss, A. L.; Pallo, A.; Naray-Szabo, G.; Harmat, V.; Polgar, L. J. Struct. Biol. 2008, 162, 312–323. (9) Evdokimov, A. A.; Sclavi, B.; Zinoviev, V. V.; Malygin, E. G.; Hattman, S.; Buckle, M. J. Biol. Chem. 2007, 282, 26067–26076. (10) Merkofer, M.; Domazou, A.; Nauser, T.; Koppenol, W. H. Eur. J. Inorg. Chem. 2006, 671–675. (11) Marc, P.; Idee, J.-M.; Medina, C.; Robic, C.; Sabatou, M.; Corot, C. Biometals 2008, 21, 469–490. (12) Bombieri, G.; Artali, R. J. Alloys Cmpd. 2002, 344, 9–16. (13) Sarka, L.; Burai, L.; Brucher, E. Chem.sEur. J. 2000, 6, 719–724. (14) Munoz, M. G.; Domenech, R. G.; Alvarez, J. G.; Frigols, J. M. Int. J. Appl. Radiat. Isot. 1983, 34, 1505–1508. (15) Vitor, R. F.; Alves, S.; Corriea, J. D. G.; Paulo, A.; Santos, I. J. Organomet. Chem. 2004, 689, 4764–6774. (16) Green, M. A.; Mathias, C. J.; Willis, L. R.; Handa, R. K.; Lacy, J. L.; Miller, M. A.; Hutchins, G. D. Nucl. Med. Biol. 2007, 34, 247–255. (17) Boswell, C. A.; Regino, C. A. S.; Baidoo, K. E.; Wong, K. J.; Milenic, D. E.; Kelley, J. A.; Lai, C. C.; Brechbiel, M. W. Bioorg. Med. Chem. 2009, 17, 548–552. (18) Sun, X.; Wuest, M.; Kovacs, Z.; Sherry, A. D.; Motekaitis, R.; Wang, Z.; Martell, A. E.; Welch, M. J.; Anderson, C. J. J. Biol. Inorg. Chem. 2003, 8, 217–225. (19) Benoist, E.; Charbonnel-Jobic, G.; Courseille, C.; Gestin, J.-F.; Parrain, J.L.; Chatal, J.-F.; Quintard, J.-P. New J. Chem. 1998, 22, 615–619. (20) Welch, M. J. Abstracts of Papers, 229th ACS National Meeting, San Diego, CA, March 13-17, 2005; American Chemical Society: Washington, DC, 2005.

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free metal ion.21 Surface plasmon resonance (SPR)22 and quartzcrystal microbalance (QCM)23 are useful in separating a component from a biomolecular complex to observe the dissociation kinetics, a process that sometimes suffers from artifacts caused by mass transfer, nonspecific binding, or the non-native stability of the complex at the solid-liquid interface.24 In contrast to these methods, we recently reported a direct method using a homogeneous solution and a capillary electrophoresis reactor (CER),25 in which components are steadily removed from a complex zone by electrophoresis to realize a steep decrease in the concentrations of components. Since the peak height of a complex at separation time tm obeys a first-order decay function exp(-kdtm), a set of CER runs for different values of tm should enable us to obtain the dissociation rate constant kd. Thus, CER was applied to Al(III) and Ga(III) complexes of the tridentate ligand 2,2′-dihydroxyazobenzene5,5′-disulfonate (DHABS), and the dissociation rate constants were estimated to be kd ) 4.9 × 10-4 and 3.7 × 10-3 s-1, respectively. Because CER does not use a competing ligand or immobilization of a component, it is a more straightforward method. More recently, we have shown that CER can be applicable to estimation of dissociation of ssDNA-binding protein-ssDNA complexes to estimate the kd values ranging from 3.99 × 10-4 to 1.50 × 10-3 s-1 depending upon the chain length (20-31 mer).26 The time range that CER can handle corresponds to the separation time window of capillary electrophoresis (CE). In the case of Al(III)- and Ga(III)-DHABS complexes, the half-lives are t1/2 ) 24 and 3 min, respectively; both values are comparable to the time required for a typical CE run. To extend CER toward the measurement of rapid dissociation, microchip (µ)CE employing a miniaturized separation channel was used to realize µ-CER.27 The dissociation rate constant for a Ce(III) complex with 8-amino-2-[(2-amino-5-methylphenoxyl)methyl]6-methoxyquinoline-N,N,N′,N′-tetraacetate (Quin 2) was estimated to be kd ) 6.0 × 10-3 s-1. More recently, the spontaneous dissociation rate of a La(III) complex with O,O′-bis(2-aminophenyl)ethyleneglycol-N,N,N′,N′-tetraacetate (BAPTA) was measured to be as large as kd ) 8.5 × 10-2 s-1, corresponding to a t1/2 of only 8.9 s.28 In contrast, the measurement of slow dissociation kinetics with t1/2 values of several hours using CER is not feasible in practice. First, to determine kd, several CER runs for different tm values are necessary, meaning that the measurement process would have to be carried out over several days. Second, during such a long CE separation, the peak height of the remaining complex will be affected by fluctuations in the electrophoretic mobility, electroosmotic mobility, and (21) Margerum, D. W.; Cayley, G. R.; Weatherburn, D. C.; Pagenkopf, G. K. In Coordination Chemistry, ASC Monograph 174; Martell, A. E., Ed.; ACS: Washigton, D. C., 1978; Vol. 2, pp 1-220. (22) Hahnefeld, C.; Drewianka, S.; Herberg, F. W. Methods in Molecular Medicine, 94 Molecular Diagnosis of Infectious Diseases, 2nd ed.; Humana Press Inc.: Totowa, NJ, 2004; pp 299-320. (23) Mori, T.; Okahata, Y. Trends Glycosci. Glycotechnol. 2005, 17, 71–83. (24) DiGiacomo, R. A.; Xie, L.; Cullen, C.; Indelicato, S. R. Anal. Biochem. 2004, 327, 165–175. (25) Iki, N.; Hoshino, H.; Yotsuyanagi, T. Anal. Chem. 2000, 72, 4812–4820. (26) Takahashi, T.; Ohtsuka, K.; Tomiya, Y.; Iki, N.; Hoshino, H. Electrophoresis, accepted; doi: 10.1002/elps.200900110. (27) Takahashi, T.; Ohtsuka, K.; Iki, N.; Hoshino, H. Analyst 2005, 130, 1337– 1339. (28) Ohtsuka K.; Master Thesis, Tohoku University, 2007.

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dissociation reaction rate itself, and by adsorption of the complex and/or component species. This would lead to poor reproducibility. Note that conventional techniques such as SPR also require considerable time and have poor reproducibility for similar reasons. To reduce the CER operation time to a reasonable value (several tens of minutes), we developed a new CER mode, the LS-CER, by introducing a substitution reaction in a capillary to accelerate the slow dissociation. Kinetically stable Ti(IV) complexes with catechin (H4L, Figure 1) and tiron (H2R2-) were tested as specimens because one of the isotopes of titanium, 45 Ti, is a candidate for a positron emissive nucleus in PET,29,30 for which it is highly desirable to develop a methodology for estimating the dissociation rate constant of the Ti(IV)-ligand complex. EXPERIMENTAL SECTION Reagents and Solutions. Ti(IV) solution was prepared by digestion of TiO2 (Wako Pure Chemical Industries, Osaka) in a heated mixture of concd H2SO4 and (NH4)2SO4 and then diluted with dil H2SO4 solution to make a 0.01 M solution (pH ∼1). The concentration was determined accurately by accepted chelate titrimetry with EDTA.31 Disodium salt of 1,2-dihydroxybenzene-3,5-disulfonic acid (tiron) was purchased from Dojindo Laboratory (Kumamoto) and dissolved in doubly distilled water to make a 0.01 M stock solution. (+)-Catechin hydrate was purchased from Sigma (St. Louis, MO) and dissolved in doubly distilled water before use. Disodium salt of EDTA was purchased from Dojindo Laboratory and dissolved in doubly distilled water to make a 0.01 M solution. The concentration was determined accurately by titrimetry with a standard Zn(II) solution.31 Catechol was purchased from Tokyo Chemical Industry Co., Ltd. (Tokyo) and dissolved in doubly distilled water before use. Thiacalix[4]arene-p-tetrasulfonate (TCAS) was prepared as reported elsewhere32 and stored as a 0.01 M aq solution. Sodium salt of anthraquinone-2-sulfonate (AS) was purchased from Nacalai Tesque, Inc. (Kyoto) and stored and used as a 5.0 mM solution. 2-[4-(2-Hydroxyethyl)-1-piperazinyl]ethane sulfonic acid (HEPES) was purchased from Dojindo Laboratory. An appropriate amount of HEPES was dissolved in distilled water, and then, the pH of the solution was adjusted to 7.40 with NaOH solution and diluted to 0.5 M (H4L, Figure 1). Phosphate buffer was prepared by dissolving an appropriate amount of NaH2PO4 (Wako Pure Chemical Industries, Ltd.) in distilled water and then by adjusting the solution to a pH of 7.4 and diluting it to 0.5 M. For coating of the capillary, 3-methacryloxypropyltrimethoxysilane (Shin-Etsu Chemical Co., Ltd., Tokyo), acryl amide, (NH4)2S2O8 (Wako Pure Chemical Industries, Ltd.), and N,N,N′,N′-tetramethylethylenediamine (TEMED; Tokyo Chemical Industry Co., Ltd.) were used without further purification. The electrophoretic buffer was prepared by mixing appropriate amounts of solutions of phosphate buffer and a competing ligand (EDTA or catechol) and diluting to 20 mM phosphate (pH 7.40). (29) Vavere, A. L.; Welch, M. J. J. Nucl. Med. 2005, 46, 683–690. (30) Vavere, A. L.; Laforest, R. M.; Welch, J. Nucl. Med. Biol. 2005, 32, 117– 122. (31) Ueno, K.; Titrimetry; Nankodo: Tokyo, 1989. (32) Iki, N.; Horiuchi, T.; Oka, H.; Koyama, K.; Morohashi, N.; Kabuto, C.; Miyano, S. J. Chem. Soc., Perkin Trans. 2 2001, 2219–2225.

Equipment. Capillary electrophoresis equipment model CAPI3200 (Otsuka Electronics, Co., Ltd., Osaka) was used. A bare fused-silica capillary tube (50 µm i.d.; 375 µm o.d.) and FunCap CE/Type S sulfonated tube (50 µm i.d.; 375 µm o.d.) were obtained from GL Sciences Inc. (Tokyo). For electrophoresis of Ti(IV)-tiron complex, a capillary coated with poly(acryl amide)33 was used. The temperature of the system was maintained at 300 K. Spectral measurements were performed using a Hitachi model U-3310 spectrophotometer. The pH was recorded with a TOA IM-40S pH meter. Sample Preparation and Injection to CE. In the preparation of Ti(IV) complexes, HEPES was used in place of phosphate to avoid possible interference caused by complex formation between Ti(IV) and phosphate.34 To a solution containing Ti(IV) ion were added a ligand solution (catechin or tiron), an internal standard solution (IS; AS or TCAS), and HEPES buffer solution (pH 7.4). The mixture was made up to a volume of 50 cm3 and allow to stand for 15 min for complex formation. The final composition of the solution is given in the figure captions. The sample solution was injected into the capillary by hydrodynamic action (height difference ∆h ) 25 mm for 40 s). Procedure for Kinetic Measurements. After injecting the sample solution, an electric field was applied to the capillary for the electrophoresis of the Ti(IV) complex, free ligand, and IS. After obtaining an electropherogram, the peak heights and migration times for the Ti(IV) complex and IS were read. Repetition of electrophoresis with a varying applied voltage gave a set of peak height value vs migration time data from which the dissociation rate at a certain concentration of the competing ligand in an electrophoretic buffer could be determined. After changing the ligand concentration in the buffer, the procedure was repeated. PRINCIPLE For the sake of clarity, we describe the case of the spontaneous dissociation of a 1:1 metal-ligand complex. The discussion should be applicable to the dissociation of molecular and biomolecular complexes with stoichiometries of 1:1, 1:n, and m:n (where m and n are integers). Given a solution of 1:1 metal complex (ML) equilibrated with free metal ion (M) and free ligand (L), the complexation equilibrium is

M + Y f MY

Here, MY does not necessarily have 1:1 stoichiometry, but the rapid formation and the high thermodynamic stability of MY are essential prerequisites to suppress the backward reaction of eq 1. Since the reaction 3 is in competition with the backward reaction of eq 1, the reaction rate of the former should be higher than that of the latter. To fulfill this requirement, a ligand to form MY more stable than ML is used in a large excess relative to L. Excessive use of Y over ML is also desirable because of the pseudo-first-order condition. Under such a condition, however, the ligand Y concomitantly attacks ML, and LS (i.e., displacement) results in the dissociation of ML: kY

ML + Y 98 MY + L

-

d[ML] ) kobs[ML] dt

kobs ) kd + kY[Y]

(6)

Therefore, estimation of a series of kobs values by changing [Y] ought to give both kd and kY values. This is a rather indirect method to obtain kd, but it is the only method to measure kd in homogeneous solution without relying on the immobilization of a component. Compared with the LS method, CER is more straightforward because free M and L are directly removed from the vicinity of ML by electrophoresis. Hence, only dissociation (eq 7) occurs in the zone of ML and the reverse reaction does not take place.

(7)

(1)

kf

If ML is detected after an elapsed time tm, the concentration is

where kd and kf are dissociation and formation rate constants, respectively. In this system, the rates of formation and dissociation are balanced, and the concentration of ML is determined by the thermodynamic stability constant (K ) kf/ kd) of ML and concentrations [M] and [L] as given by [ML] ) K[M][L]

(5)

where kobs is the apparent dissociation rate constant given by

kd

ML y\z M + L

(4)

where kY is the second-order substitution reaction rate constant. Therefore, the LS reaction (eq 4) competes with spontaneous dissociation (eq 1) and the observed rate is

ML 98 M + L kd

(3)

[ML]/[ML]0 ) exp(-kdtm)

(8)

where [ML] and [ML]0 are the molarities of ML at the times of detection (tm) and injection (0 s), respectively. In a CE run, the migration time tm is

(2)

In a conventional batchwise experiment for the estimation of kd, a competing ligand Y is added to the solution to mask the formation reaction of ML (i.e., the reverse of eq 1). Y then reacts with free M to form the complex MY: (33) Hjerte`n, S.; Kiessling-Johansson, M. J. Chromatogr. 1991, 550, 811–822. (34) Einaga, H.; Komatsu, Y. J. Inorg. Nucl. Chem. 1981, 43, 2449–2454.

tm ) Ll/{V(µeo + µML)}

(9)

where L and l are the total and effective lengths of the capillary, V is the applied voltage, µeo is the electroosmotic mobility, and µML is the electrophoretic mobility of ML. For several CE runs with changing conditions such as varying µeo25 or V,26,27 the dependence of the residual ratio [ML]/[ML]0 on tm was Analytical Chemistry, Vol. 81, No. 18, September 15, 2009

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obtained to allow estimation of kd via fitting with eq 8. In addition, whole-column imaging27 is very useful because a single CER run gives a set of [ML]/[ML]0 vs. tm data and thus kd. In LS-CER, substitution is introduced to accelerate the apparent dissociation of a very slow reaction with a t1/2 of hours to largely reduce the experimental time to within a usual CE time range (vide infra). When using an electrophoretic buffer containing a competing ligand Y, a substitution reaction (eq 4) occurs. A set of CER runs with a buffer containing certain concentrations of Y gives kobs from [ML]/[ML]0 ) exp(-kobstm)

(10)

As discussed in previous reports,25,26 the peak height instead of peak area is used to estimate the residual ratio [ML]/[ML]0.35 Thus, HML [ML] ) R [ML]0 HIS

(11)

Figure 1. Structures of catechol ligands and a 1:3 complex with a Ti(IV) ion. R represents functional groups.

where HML and HIS are the peak heights of ML and internal standard (IS), respectively, and R is a proportional constant. (For the derivation of eq 11, see the Supporting Information.) IS is employed to compensate for the variance of the injection volume of the sample solution and also zone broadening during electromigration. For this purpose, an inert species with size and charge similar to those of ML is used as the IS. Combining eqs 10 and 11 gives eq 12, which is applied to a set of HML/HIS vs. tm data to estimate kobs. HML ) R-1exp(-kobstm) HIS

(12)

Varying the concentration [Y] in an electrophoretic buffer, a set of kobs vs [Y] data is obtained for the estimation of kd and kY via eq 6. This is the principle of LS-CER. RESULTS AND DISCUSSION LS-CER of Ti(IV)-Catechin Complex. Before applying LSCER for the measurement of slow dissociation, it was validated using a Ti(IV)-catechin complex for which kd had been estimated by batchwise LS with spectrometric monitoring.36 Having a catechol moiety, catechin (H4L) coordinated to the Ti(IV) ion to form a dianionic 1:3 complex [Ti(H2L)3]2- at pH 7.4 (Figure 1). Using spectrophotometric titration, the overall stability constant β3 (eq 13) was determined to be 1047.95 (I ) 0.1), implying high thermodynamic stability.36

β3 )

[[Ti(H2L)3]2-] [Ti4+][H2L2-]3

(13)

(35) We avoided errors derived from uncertainty in deconvolution of peak area, which is employed in most of recently reported CE techniques for reaction kinetics. See: (a) Newman, C. I. D.; Collins, G. E. Electrophoresis 2008, 29, 44–55. (b) Trapp, O. Chem. Today 2008, 26, 26–28. (c) Trapp, O. Anal. Chem. 2006, 78, 189–198. (36) Takahashi, M. Master Thesis, Tohoku University, 2007.

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Figure 2. Typical electropherograms for dissociation of catechin complex, [Ti(H2L)3]2-, obtained using LS-CER with EDTA as a competing ligand. L: catechin, ML: [Ti(H2L)3]2-, IS: anthraquinone-2sulfonate (AS). Sample: [Ti4+] ) 8.0 × 10-5 M, [catechin] ) 2.4 × 10-4 M, [AS] ) 4.2 × 10-5 M, [HEPES] ) 20 mM (pH 7.4). Electrophoretic buffer: [NaH2PO4] ) 20 mM (pH 7.4), [EDTA] ) 6.0 mM. Detection wavelength: 210 nm. Capillary: FunCap CE/Type S, L ) 43.5, l ) 31.0 cm. Applied voltage is shown in the figure.

In a batchwise LS reaction of [Ti(H2L)3]2- with CyDTA as a competing ligand, the dissociation rate constant was estimated to be kd ) (1.43 ± 0.04) × 10-4 s-1 (t1/2 ) 1.35 h),36 suggesting that measurement of the spontaneous dissociation using CER is time-consuming. In the LS-CER of [Ti(H2L)3]2-, EDTA was used as a competing ligand in the electrophoretic buffer. In addition, AS was used as an IS owing to its similar electrophoretic mobility to [Ti(H2L)3]2-. Figure 2 shows typical electropherograms using 6.0 mM EDTA in the electrophoretic buffer. As is seen, a decrease in the applied voltage increased the migration time of [Ti(H2L)3]2-, IS, and free catechin and also broadened each peak. It should be noted that the peak height of [Ti(H2L)3]2- became smaller than that of IS as the migration time increased, suggesting that

Figure 3. Dependence of peak height ratio HML/HIS of [Ti(H2L)3]2on reaction time obtained using LS-CER with EDTA as a competing ligand. Electrophoretic buffer: [NaH2PO4] ) 20 mM (pH 7.4), [EDTA] ) (a) 5.0, (b) 6.0, (c) 7.0, and (d) 8.0 mM. For sample composition and detection wavelength, see the caption of Figure 2. For the sake of clarity, the HML/HIS ratio was normalized with R-1, and kd values were obtained by fitting of original HML/HIS vs tm data with eq 12. The R-1 and kd/10-4s-1 values were (a) 1.33, 6.22 ( 0.20, (b) 1.43, 7.29 ( 0.34, (c) 1.37, 8.05 ( 0.28, and (d) 1.19, 9.00 ( 0.21. R ) 0.997-0.999.

Figure 4. Relationship between observed dissociation rate constant (kobs) of Ti(IV) complex and concentration of competing ligand [Y] in electrophoretic buffer. (a) [Ti(H2L)3]2-, Y: EDTA, kd/10-4 s-1 ) 1.64 ( 0.63, kY/10-2 M-1s-1 ) 9.17 ( 0.96. (b) [TiR3]8-, Y: catechol, kd/ 10-4 s-1 ) 0.51 ( 0.43, kY/10-2 M-1s-1 ) 2.78 ( 0.72. Fitting with eq 6 was implemented by weighted least-squares regression.

the dissociation of [Ti(H2L)3]2- occurred over time. In fact, the dependence of the H[Ti(H2L)3]2-/HIS ratio decreased with migration time following a single exponential decay (Figure 3b), implying first-order decay according to eq 12. In addition, dissociation of [Ti(H2L)3]2- can be monitored within a reasonable operation time (ca. 20 min). With increasing concentration of EDTA in the electrophoretic buffer, the decay of H[Ti(H2L)3]2-/HIS as a function of time became pronounced (Figure 3), implying that the dissociation of ML via substitution (eq 4) became more prominent. From the first-order decay curves shown in Figure 3, kobs is linearly dependent on [EDTA] (Figure 4a) in accordance with eq 6, giving kd ) (1.64 ± 0.63) × 10-4 s-1 and kY ) (9.17 ± 0.96) × 10-2 M-1s-1. The kd value estimated with LS-CER was in good agreement with that

estimated by batchwise LS, confirming the validity of the LSCER method. In addition, from a technical point of view, it is interesting to compare the time to acquire all necessary data for estimation of kd of the Ti(IV)-catechin complex, 16.7 h with a conventional batchwise method36 and 4.2 h with the present LS-CER. Thus, LS-CER is considerably less time-consuming than the conventional method. LS-CER of Ti(IV)-Tiron Complex. Tiron (H2R2-) is a disulfonated derivative of catechol and has been used as a spectrophotometric reagent for Ti(IV) and Fe(III).37 Since the thermodynamic stability of a 1:3 complex with Ti(IV), [TiR3]8(log β3 ) 57.6, I ) 0.138), is even higher than that of the catechin complex [Ti(H2L)3]2-, it can be assumed that spontaneous dissociation of [TiR3]8- is slower than that of [Ti(H2L)3]2-. This shows the necessity of a method more effective than CER to perform the measurement of kd in a reasonable experimental time. The reason why the conventional batchwise LS reaction is not applicable to the tiron complex [TiR3]8- is the lack of a suitable ligand to replace the coordinating tiron ligand in [TiR3]8-. For instance, EDTA and CyDTA were unusable because the thermodynamic stabilities of their Ti(IV) complexes are lower than that of [TiR3]8-.39 In contrast, catechol (H2cat) forms a thermodynamically more stable complex, [Ti(cat)3]2-, (log β3 ) 61.6)40 than tiron does, but excessive addition of catechol in a solution of tiron complex [TiR3]8- resulted in a large absorption band due to catechol that overlaps that of [TiR3]8- to hinder spectroscopic monitoring of the dissociation process. In the present LS-CER, however, catechol can be employed as the competing ligand because CE allows detection of [TiR3]8- as a sharp electrophoretic zone rather than a broad absorption band in the spectral observation. TCAS was used as an IS owing to its anionic charges being as high as 5 in the electrophoretic buffer of pH 7.4.41 Typical electropherograms of [TiR3]8- (Figure 5) showed baseline separation from free tiron and IS. Although the electrophoretic buffer absorbed light at the detection wavelength (210 nm) owing to the dissolved catechol, the peak of [TiR3]8- was clearly detected. This implies a merit of the use of CE detection over spectral detection for the substitution reaction. As the applied voltage decreased, the separation time increased and the peak height of [TiR3]8- decreased, suggesting the dissociation of [TiR3]8- occurred. Between the peaks of [TiR3]8- and IS, a small peak was observed, which can be attributed to 1:2 complex species, [TiR2]4-, remaining in the injected sample owing to incomplete equilibration in the formation of [TiR3]8-. It should be noted that the existence of this different complex species in the sample solution did not interfere with the detection of the dissociation of [TiR3]8-. The dependence of the H[TiR3]8-/HIS ratio on the reaction time indicated first-order decay (Figure 6c), from which kobs was estimated. Although the data were scattered, fitting with a first-order decay was possible and showed more distinct decay at a higher (37) Cheng, K. L.; Ueno, K.; Imamura, T. CRC Handbook of Organic Analytical Reagents; CRC Press, Inc.: Boca Raton, FL, 1982. (38) Sillen, L. G.; Martell, A. E. Stability Constants of Metal-Ion Complexes; The Chemical Society: London, 1964. (39) Log β values (I ) 0.1 with NaClO4): [TiO(edta)]2- 17.3; [TiO(cydta)]2- 19.9. Data cited from ref 38. (40) Sommer, L. Collect. Czech. Chem. Commun. 1963, 28, 210–212. (41) Matsumiya, H.; Takahashi, Y.; Iki, N.; Miyano, S. J. Chem. Soc., Perkin Trans. 2 2002, 1166–1172.

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Figure 5. Typical electropherograms for dissociation of tiron complex, [TiR3]8-, obtained using LS-CER with catechol as a competing ligand. L: tiron; ML: [TiR3]8-; IS: TCAS. Sample: [Ti4+] ) 4.0 × 10-5 M, [tiron] ) 1.2 × 10-4 M, [TCAS] ) 2.0 × 10-5 M, [HEPES] ) 20 mM (pH 7.4). Electrophoretic buffer: [NaH2PO4] ) 20 mM (pH 7.4), [catechol] ) 6.5 mM. Detection wavelength: 210 nm. Capillary: poly(acryl amide) coated, L ) 52.5, l ) 40.0 cm. Applied voltage is shown in the figure.

Figure 6. Dependence of peak height ratio HML/HIS of [TiR3]8-, normalized with R-1, on reaction time obtained using LS-CER with catechol as a competing ligand. Electrophoretic buffer: [NaH2PO4] ) 20 mM (pH 7.4), [catechol] ) (a) 5.0, (b) 6.0, (c) 6.5, and (d) 7.0 mM. For sample composition and detection wavelength, see the caption of Figure 5. The R-1 and kd/10-4 s-1 values: (a) 1.20, 1.95 ( 0.08, (b) 1.23, 2.42 ( 0.13, (c) 1.17, 2.14 ( 0.05, and (d) 1.19, 2.60 ( 0.18. R ) 0.990-0.999.

concentration of catechol in the electrophoretic buffer (Figure 6). The dependence of kobs on the concentration of catechol further gave dissociation rate constants kd ) (0.51 ± 0.43) × 10-4 s-1 and kY ) (2.78 ± 0.72) × 10-2 M-1 s-1 (Figure 4b). From the kd value, the half-life was estimated to be t1/2 ) 3.8 h, suggesting that normal CER without LS would require an operation time of several hours to obtain a HML/MIS datum for the dissociation of [TiR3]8-. In contrast, the LS-CER measurement to give a HML/MIS ratio was completed within 40 min. Even taking into account the fact that the experiment needs to be run several times (four times in this case) with varying [Y] to obtain the dependence of kobs on

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Analytical Chemistry, Vol. 81, No. 18, September 15, 2009

[Y] (eq 6), introducing the substitution reaction to CER considerably reduces the experimental time. Thus, the usefulness of LS-CER in measuring kd for slow dissociation kinetics has been demonstrated using the tiron complex [TiR3]8-. Besides the analytical significance of LS-CER methodology, it is interesting to note the difference in kinetic stabilities of the two kinds of 1:3 Ti(IV)-catechol complexes; the half-life of tiron complex [TiR3]8- (t1/2 ) 3.8 h) indicates higher kinetic stability than the catechin complex [Ti(H2L)3]2- (t1/2 ) 1.17). In spite of two electron-withdrawing groups, -SO3-, which are attached to the catechol and reduce the basicity of the ligand, thermodynamic stability of [TiR3]8- is higher than that of [Ti(H2L)3]2- as mentioned above. This can be attributed to the sizes of substituents; catechin has much bulkier substituents, the thermal motion of which should lead to destabilization of the Ti(IV)-catechol bond. In contrast, the compact and rigid structure of tiron should lead not only to high thermodynamic stability but also to higher kinetic stability of [TiR3]8- than for [Ti(H2L)3]2-. CONCLUSION Using an inert Ti(IV)-tiron complex, it was demonstrated that LS-CER involving LS in an electrophoretic separation field is highly useful for measuring the dissociation rate of an extremely slow dissociation within a practically acceptable period. The LS-CER methodology was validated by considering kd for catechin complex [Ti(H2L)3]2-, which was estimated using a batchwise LS method. Thus, the CER method was successfully extended toward very slow reaction kinetics. The advantages of the LS-CER method over CER and/or batchwise substitution are summarized as follows. (i) It can be applied to slow dissociation kinetics with a t1/2 of hours to considerably reduce the experimental time. (ii) In principle, it can use a competing ligand Y without MY being more stable than ML because the formation reaction of ML (reverse reaction of eq 1) does not occur owing to electrophoretic separation of the components. (iii) The spectral resolution of Y with ML is not necessary, thus relaxing the prerequisites of the competing ligand. In addition, as a merit of CER over the batchwise method, (iv) the sample solution of ML does not necessarily need to be pure because other components such as complex species of different metal-ligand stoichiometry and metal species are separated and do not interfere with the estimation of remaining [ML]. On the whole, LS-CER is a useful method for estimating the slow rate of spontaneous dissociation, which CER and batchwise methods cannot handle. Thus, it is a powerful tool in the rational design of ligands for diagnostic and therapeutic reagents. ACKNOWLEDGMENT This work was supported by JSPS Grant-in-Aid for Scientific Research (B) 20350070. SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org.

Received for review June 16, 2009. Accepted July 28, 2009. AC901296J