Equilibrium Thermodynamics, Formation, and Dissociation Kinetics of Trivalent Iron and Gallium Complexes of Triazacyclononane-Triphosphinate (TRAP) Chelators: Unraveling the Foundations of Highly Selective Ga-68 Labeling

Abstract

In order to rationalize the influence of Fe^III contamination on labeling with the ⁶⁸Ga eluted from ⁶⁸Ge/⁶⁸Ga-generator, a detailed investigation was carried out on the equilibrium properties, formation and dissociation kinetics of Ga^III- and Fe^III-complexes of 1,4,7-triazacyclononane-1,4,7-tris(methylene[2-carboxyethylphosphinic acid]) (H₆TRAP). The stability and protonation constants of the [Fe(TRAP)]³⁻ complex were determined by pH-potentiometry and spectrophotometry by following the competition reaction between the TRAP ligand and benzhydroxamic acid (0.15 M NaNO₃, 25°C). The formation rates of [Fe(TRAP)] and [Ga(TRAP)] complexes were determined by spectrophotometry and ³¹P-NMR spectroscopy in the pH range 4.5–6.5 in the presence of 5–40 fold H_xTRAP^(x−6) excess (x = 1 and 2, 0.15 M NaNO₃, 25°C). The kinetic inertness of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ was examined by the trans-chelation reactions with 10 to 20-fold excess of H_xHBED^(x−4) ligand by spectrophotometry at 25°C in 0.15 M NaCl (x = 0,1 and 2). The stability constant of [Fe(TRAP)]³⁻ (logK_FeL = 26.7) is very similar to that of [Ga(TRAP)]³⁻ (logK_GaL = 26.2). The rates of ligand exchange reaction of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ with H_xHBED^(x−4) are similar. The reactions take place quite slowly via spontaneous dissociation of [M(TRAP)]³⁻, [M(TRAP)OH]⁴⁻ and [M(TRAP)(OH)₂]⁵⁻ species. Dissociation half-lives (t_1/2) of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ complexes are 1.1 × 10⁵ and 1.4 × 10⁵ h at pH = 7.4 and 25°C. The formation reactions of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ are also slow due to the formation of the unusually stable monoprotonated [^*M(HTRAP)]²⁻ intermediates [^*logK_Ga(HL) = 10.4 and ^*logK_Fe(HL) = 9.9], which are much more stable than the [^*Ga(HNOTA)]⁺ intermediate [^*logK_Ga(HL) = 4.2]. Deprotonation and transformation of the monoprotonated [^*M(HTRAP)]²⁻ intermediates into the final complex occur via OH⁻-assisted reactions. Rate constants (k_OH) characterizing the OH⁻-driven deprotonation and transformation of [^* Ga(HTRAP)]²⁻ and [^*Fe(HTRAP)]²⁻ intermediates are 1.4 × 10⁵ M⁻¹s⁻¹ and 3.4 × 10⁴ M⁻¹s⁻¹, respectively. In conclusion, the equilibrium and kinetic properties of [Fe(TRAP)] and [Ga(TRAP)] complexes are remarkably similar due to the close physico-chemical properties of Fe^III and Ga^III-ions. However, a slightly faster formation of [Ga(TRAP)] over [Fe(TRAP)] provides a rationale for a previously observed, selective complexation of ⁶⁸Ga^III in presence of excess Fe^III.

Introduction

Due to the wealth of obtainable information resulting in a high diagnostic value, medical imaging plays an ever-increasing role in modern personalized healthcare. In this context, radionuclide based imaging modalities which exploit George Hevesy's tracer principle (Levi, 1976) allow for unique functional diagnostics, because they enable monitoring of biological processes without significant interference with the investigated subject owing to minuscule amounts of administered active compound. Although the majority of nuclear imaging procedures (estimated >85%) still are scintigraphic or single photon emission computed tomography (SPECT) scans relying on the gamma-emitter ^99mTc, recent times have seen a strong surge in positron emission tomograpy (PET), following introduction of scanners capable of simultaneous functional and morphological imaging utilizing PET and computed tomography (CT) in 2001 (Beyer et al., 2000). While most PET investigations rely on the positron emitter ¹⁸F (more precisely, on the radiofluorinated glucose derivative [¹⁸F]2-fluoro-2-deoxy-d-glucose), some positron-emitting metal ion radionuclides have also received considerable attention in recent times (Wadas et al., 2010). Among these, ⁶⁸Ga has arguably the highest value for preclinical and translational studies (Notni and Wester, 2018), mainly because it is obtained for a low price per dose from radionuclide generators. These small benchtop devices, which act as cyclotron-independent continuous on-site nuclide sources, contain ⁶⁸Ge adsorbed on an inorganic matrix, such as SnO₂ or TiO₂, while decay of ⁶⁸Ge produces ⁶⁸Ga^III which can be eluted with dilute HCl (Notni, 2012; Rösch, 2013). Notably, such eluate frequently contains small amounts of impurities originating from the sorbent (Simecek et al., 2013), such as Ti^IV but also Fe^III, Cu^II, Zn^II, or Al^III in form of their aqua or chlorido complexes.

⁶⁸Ga-labeling of biomolecules usually requires prior decoration with a suitable multidentate ligand capable of binding the ⁶⁸Ga^III ion into a kinetically inert complex (Wadas et al., 2010) and a plethora of ligands have been proposed for this purpose (Frank and Patrick, 2010; Velikyan, 2011). Against the background of aforementioned metal ion impurities in the generator eluate, an investigation of the radionuclide complexation efficiency of certain macrocycle-based chelators, among them TRAP (Notni et al., 2014) and NOTA (Mariko and Susumu, 1977; Scheme 1) pointed at a markedly different influence of non-Ga^III metal ions present in the ⁶⁸Ga^III solutions used for radiolabeling (Simecek et al., 2013). In particular, TRAP was shown to tolerate much higher concentrations of Zn^II, Cu^II, and Fe^III. Although highly similar structural features of [Fe(H₃TRAP)] and [Ga(H₃TRAP)] point at a close relation of both systems (Notni et al., 2010), it was found that even a threefold stoichiometric excess of Fe^III over TRAP or its mono-conjugable congener NOPO (Simecek et al., 2014) did not result in a significant decrease of ⁶⁸Ga incorporation, whereas labeling of NOTA was almost completely inhibited. Particularly in view of the known similarity of Fe^III and Ga^III, this discrepancy sheds a light on the mechanisms governing the superior ⁶⁸Ga labeling properties of 1,4,7-triazacyclononanes bearing (methylene)phosphinic acid N-substituents (Notni et al., 2011). In order to gain a more detailed understanding, thermodynamics as well as formation and dissociation kinetic studies were performed for Ga^III- and Fe^III-complexes formed with TRAP and NOTA.

Scheme 1.

Structural formula of H₃NOTA, H₆TRAP, H₄HBED and HBha chelates (H₃NOTA: 1,4,7-triazacyclononane-1,4,7-triacetic acid; H₆TRAP: 1,4,7-triazacyclononane-1,4,7-tris(methylene[2-carboxyethylphosphinic acid]); H₄HBED: N, N′-Bis(2-hydroxybenzyl)ethylenediamine-N, N′-diacetic acid; HBha: benzhydroxamic acid).

Materials and methods

Materials

The chemicals used for the experiments were of the highest analytical grade. Ga(NO₃)₃ and Fe(NO₃)₃ were prepared by dissolving Ga₂O₃ (99.9%, Fluka) and Fe₂O₃ (99.9% Fluka) in 6M HNO₃ and evaporating of the excess acid. The solid Ga(NO₃)₃ and Fe(NO₃)₃ were dissolved in 0.1 M HNO₃ solution. The concentration of the Ga(NO₃)₃ and Fe(NO₃)₃ solutions were determined by complexometry with the use of standardized Na₂H₂EDTA in excess. The excess of the Na₂H₂EDTA was measured with standardized ZnCl₂ solution and xylenol orange as indicator. The H⁺ concentration of the Ga(NO₃)₃ and Fe(NO₃)₃ solutions was determined by pH potentiometric titration in the presence of Na₂H₂EDTA excess. The concentration of the H₆TRAP, H₄HBED, benzohydroxamic acid (HBha) and H₃NOTA (provided by Prof. Petr Hermann, Department of Inorganic Chemistry, Faculty of Science, Charles University, Prague, Czech Republic) was determined by pH-potentiometric titration in the presence and absence of a large (40-fold) excess of CaCl₂. All the measurements were made at constant ionic strength maintained by 0.15 M NaNO₃ or NaCl at 25°C.

Equilibrium studies

For determining the protonation constants of H₆TRAP and H₃NOTA ligands three parallel pH-potentiometric titration were made with 0.2 M NaOH in 0.002 M ligand solutions.

Stability constant of [Fe(Bha)]²⁺ complex was determined by spectrophotometry, studying the Fe^III-HBha systems at the absorption band of Fe^III-complex over the wavelength range of 400–800 nm in two sets of experiments. Individual samples were prepared in the first series in which the concentrations of Fe^III and HBha was constant 0.2 and 2.0 mM, while that of the H⁺ was varied between 0.04 and 1.0 mM (eight samples, Figure S1). The H⁺ concentration in the samples was adjusted by addition of calculated amounts of 2.0 M HNO₃. The ionic strength was constant in the samples with [H⁺] < 0.15 M ([H⁺]+[Na⁺] = 0.15 M). Samples were kept at 25°C for a week. Absorbance values were determined at 11 wavelengths (400, 415, 430, 445, 460, 475, 490, 505, 520, 535, and 550 nm). In the second set, spectrophotometric titrations were done with samples containing HBha ligand in 2.0 mM concentration, whereas the concentration of Fe^III was varied between 0.1–0.3 mM (Figures S2–S4). The pH of the samples was adjusted using concentrated NaOH and HNO₃ solutions in the pH range 1.7–11.0 (0.15 M NaNO₃ and 25°C). For calculation of the equilibrium constants, the best fit of the absorbance–pH data was obtained by assuming formation of [Fe(Bha)]²⁺, [Fe(Bha)₂]⁺, [Fe(Bha)₃], and [Fe(Bha)₂(OH)₂]⁻ species (Figure S5). The molar absorptivity of [Fe(Bha)]²⁺, [Fe(Bha)₂]⁺, [Fe(Bha)₃] and [Fe(Bha)₂(OH)₂]⁻ species were also determined at the same 11 wavelengths in these experiments (Figure S6).

The stability constant of the [Fe(TRAP)]³⁻ complex has been determined by spectrophotometry, using competition reactions between HTRAP⁵⁻ and Bha⁻ for Fe^III at pH = 10.0. Concentration of [Fe(TRAP)]³⁻ was 0.2 mM, while that of HBha was varied between 0.0 and 1.5 mM (6 samples). The samples were kept at 25°C for 2 weeks. Absorbance values of the Fe^III-HTRAP⁵⁻-Bha⁻ systems were determined at 11 wavelengths (400, 415, 430, 445, 460, 475, 490, 505, 520, 535, and 550 nm). The molar absorptivities of [Fe(TRAP)]³⁻ and [Fe(TRAP)OH]⁴⁻ in equilibrium solutions were determined by recording the absorption spectra of 0.1, 0.2, and 0.3 mM solution of [Fe(TRAP)]³⁻ in the pH range 6.0–12.0. The molar absorptivity of [Fe(Bha)₂(OH)₂]⁻ species was determined in the separate experiments. Absorbance and pH values were determined in the samples after equilibration (the time needed to reach the equilibria was determined by spectrophotometry). Spectrophotometric measurements were done using 1.0 cm cells with a Cary 1E spectrophotometer at 25°C. Protonation constants of the Fe^III complex formed with TRAP⁶⁻ were determined by direct pH-potentiometric titration at 1:1 metal to ligand ratios (both concentrations were 0.002 M). For calculation of the logK_MHiL values, the mL base–pH data used were measured in the pH range 1.7 −12.0.

For pH measurements and titrations, a Metrohm 785 DMP Titrino titration workstation and a Metrohm-6.0233.100 combined electrode were used. Equilibrium measurements were carried out at a constant ionic strength (0.15 M NaNO₃ or NaCl) in 6 mL samples at 25°C. Solutions were stirred and continuously purged with N₂. Titrations were performed in a pH range of 1.7–12.0. KH-phthalate (pH = 4.005) and borax (pH = 9.177) buffers were used to calibrate the pH meter. For calculation of [H⁺] from measured pH values, the method proposed by Irving et al. was used (Irving et al., 1967). A 0.01 M HNO₃ or HCl solution was titrated with the standardized NaOH solution in the presence of 0.15 M NaNO₃ or NaCl. Differences between the measured (pH_read) and calculated pH (–log[H⁺]) values were used to obtain the equilibrium H⁺ concentration from the pH values, measured in the titration experiments. For equilibrium calculations, the stoichiometric water ionic product (pK_w) is also needed to calculate [H⁺] values in basic conditions. The V_NaOH–pH_read data pairs of the HNO₃–NaOH or HCl–NaOH titration obtained in the pH range 10.5–12.0 have been used to calculate the pK_w value (pK_w = 13.84). For calculation of the equilibrium constants, the program PSEQUAD (Zekany and Nagypal, 1985) was used. The standard deviation (SD) of the equilibrium parameters calculated by the program PSEQUAD is defined by Equation (1)

$$\text{SD}=\sqrt{\frac{{\displaystyle {\sum }_{\text{j}=1}^{\text{j}=N}{\text{res}}_{\text{j}}^{\text{2}}}}{\text{N}-\text{m}}}\times \sqrt{{[{({\text{J}}^{\text{T}}·\text{J})}^{-\text{1}}]}_{\text{ii}}}$$ (1)

where res, N, m, J and J^T are the residual, number of fitted data, number of refined parameters, Jacobian matrix and the transpose of Jacobian matrix, respectively.

Kinetic studies

Formation kinetics of [Fe(TRAP)] and [Ga(TRAP)]

Formation rates of [Fe(TRAP)] were studied by spectrophotometry at 260 nm in the pH range of about 4.5–6.5. Kinetic studies were carried out with Cary 1E and Cary 100 Bio spectrophotometers, using cell holders thermostated to 25°C. The pre-thermostated solutions were mixed in tandem cells (l = 0.874 cm). Formation of Fe^III complexes were studied in the presence of a 5- to 40-fold ligand excess in order to maintain pseudo-first-order conditions ([Fe^III] = 0.1 mM). Pseudo-first-order rate constants (k = k_obs) were calculated by fitting the absorbance values to the equation:

$${\text{A}}_{\text{t}}=({\text{A}}_{\text{0}}-{\text{A}}_{\text{e}}){\text{e}}^{(-\text{kt})}{+\text{A}}_{\text{e}}$$ (2)

wherein A₀, A_e, and A_t are the absorbance values at the start (t = 0 s), at equilibrium and at the time t of the reaction, respectively. Formation of [Ga(TRAP)]³⁻ was monitored by ³¹P-NMR spectroscopy on the signal of the forming Ga(TRAP) complex. ³¹P-NMR spectra were recorded by a Bruker DRX 400 spectrometer (³¹P, 161.97 MHz, 9.4 T) equipped with Bruker VT-1000 thermocontroller, using a 5 mm broad band probe. Kinetic experiments were performed at a constant temperature of 25.0°C. The formation rates were studied in the pH range of about 4.5–6.3. For these experiments, Ga(NO₃)₃ and H₆TRAP solutions were prepared in H₂O (a capillary with D₂O was used for lock). In all experiments, the concentration of Ga^III was 1 mM, while that of the H₆TRAP was varied between 5 and 30 fold excess in order to maintain pseudo-first-order conditions. Pseudo-first-order rate constants (k = k_obs) were calculated by fitting the integral signal values to the Equation (2). The ionic strength of the solutions was kept constant at 0.15 M with NaNO₃. To keep the pH values constant, N-methylpiperazine (pH range of 4.1–5.2) and piperazine (pH range of 4.7–6.6) buffers (0.01 M) were used.

Dissociation kinetics of Fe(TRAP) and Ga(TRAP)

The rates of the ligand exchange reactions of Fe(TRAP) and Ga(TRAP) with H_xHBED^x−4 (x = 0,1 and 2) ligand were studied by following the formation of [Fe(HBED)]⁻ and [Ga(HBED)]⁻ complexes by spectrophotometry at 470 nm and 290 nm, respectively. All experiments were performed in the presence of 10- and 20-fold excess of H_xHBED^x−4 (x = 1 and 2) in order to maintain pseudo-first order kinetic conditions ([Fe(TRAP)] = [Ga(TRAP)] = 0.2 mM). The pseudo-first-order rate constants (k = k_d) were calculated by fitting the absorbance values to the Equation (2). Kinetic studies were performed with Cary 1E and Cary 100 Bio spectrophotometers, using cell holders thermostated to 25°C. The pre-thermostated solutions were mixed in tandem cells (l = 0.874 cm). The ionic strength of the solutions was kept constant at 0.15 M with NaCl. The ligand exchange reactions were followed at 25°C in the pH range 9.0–14.0. The OH⁻ concentration at pH > 12 was adjusted by addition of calculated amounts of 4.0 M NaOH solution. Buffers were not used to keep the pH constant due to the high buffer capacity of the H_xHBED^x−4 (x = 1 and 2) excess at pH < 12. Calculation of the kinetic parameters was performed with the Micromath Scientist computer program (version 2.0, Salt Lake City, UT, USA).

Results and discussion

Solution thermodynamics

Protonation equilibria of the TRAP⁶⁻, NOTA³⁻ and Bha⁻ ligands were studied by pH-potentiometry. The protonation constants (log$K_{\text{i}}^{\text{H}}$) of ligands defined by Equation (3) are listed in Table 1 (standard deviations are shown in parentheses). The charges of ligands and complexes will be indicated when it is necessary.

Table 1.

Protonation constants of TRAP⁶⁻, NOTA³⁻, and Bha⁻ ligands (25°C).

	I	log$K_1^{\text{H}}$	log$K_2^{\text{H}}$	log$K_3^{\text{H}}$	log$K_4^{\text{H}}$	log$K_5^{\text{H}}$	log$K_6^{\text{H}}$	Σlog$K_{\text{i}}^{\text{Hf}}$
TRAP6−	0.15 M NaNO3	11.60(2)	5.39(2)	4.42(2)	4.19(3)	3.46(3)	1.60(2)	18.59 g
	0.15 M NaCla	11.74	5.46	4.80	4.16	3.49	1.50	18.70 g
	0.1 M Me4NCl b	11.48	5.44	4.84	4.23	3.45	1.66	18.58 g
NOTA3−	0.15 M NaNO3	11.94(2)	5.71(3)	3.14(3)	1.60(2)	–	–	22.39
	0.15 M NaCla	12.16	5.75	3.18	1.90	–	–	22.99
	0.1 M KClc	11.98	5.65	3.18	–	–	–	–
	0.1 M Me4NCld	13.17	5.74	3.22	1.96	–	–	24.09
Bha−	0.15 M NaNO3	8.53(3)	–	–	–	–	–	–
	0.2 M KCle	8.69	–	–	–	–	–	–

^aRef. (Baranyai et al., 2015);

^bRef. (Notni et al., 2010);

^cRef. (Clarke and Martell, 1991);

^dRef. (Drahos et al., 2011);

^eRef. (Farkas et al., 1998);

^fTotal ligand basicity (Σlog$k_i^H$) characterizes the sum of basicity of donor atoms;

^gThe protonation constants of the acetate pendants (log$k_3^H$, log$k_4^H$ and log$k_5^H$) of TRAP⁶⁻ were not considered in the calculation of Σlog$k_i^H$ values.

$${\text{K}}_{\text{i}}^{\text{H}}=\frac{[{\text{H}}_{\text{i}}\text{L}]}{[{\text{H}}_{\text{i}-\text{1}}\text{L}][{\text{H}}^{+}]}\text{ i}=\text{0},\text{1},\text{2}\dots \text{6}$$ (3)

The protonation schemes of TRAP⁶⁻ and NOTA³⁻ ligands were well characterized by both spectroscopic and potentiometric methods (Bevilacqua et al., 1987; Geraldes et al., 1991; Notni et al., 2010). These studies reveal that the first and second protonations occur at two ring nitrogen atoms, whereas the third, fourth and fifth protonations occur at the carboxylate groups of NOTA³⁻ and TRAP⁶⁻. The sixth proton of the TRAP⁶⁻ ligand binds on the phosphinate oxygen atom. Interestingly, not all phosphinate groups are protonated, even under very acidic conditions (pH < 1), which is why they are still able to coordinate to metal ions. A comparison of protonation constants of TRAP⁶⁻ and NOTA³⁻ indicates that log$K_1^{\text{H}}$ value of TRAP⁶⁻ is significantly lower than that of NOTA³⁻ (Table 1). The lower first protonation constant of TRAP⁶⁻ can be attributed to formation of a weaker H-bond between the protonated ring nitrogen and the phosphinate oxygens than that formed between the protonated ring nitrogen and the carboxylate oxygens in HNOTA²⁻. Comparison of the protonation constants obtained in 0.15 M NaNO₃ or NaCl, 0.1 M KCl and 0.1 M Me₄NCl solutions indicates that the log$K_{\text{i}}^{\text{H}}$ values of TRAP⁶⁻ are independent of the ionic strength, whereas the log$K_1^{\text{H}}$ value of NOTA³⁻ is significantly lower in the presence of K⁺ and Na⁺ ions, which can be attributed to formation of [K(NOTA)]²⁻ and [Na(NOTA)]²⁻ complexes. Total basicity of ligands (Σlog$K_{\text{i}}^{\text{H}}$, Table 1) generally correlates with the stability constants (K_ML) of their metal complexes. (For the calculation of Σlog$K_{\text{i}}^{\text{H}}$ value of TRAP⁶⁻, the log$K_{\text{i}}^{\text{H}}$ values of the carboxylate groups were not considered because they do not participate in the coordination of metal ions). The Σlog$K_{\text{i}}^{\text{H}}$ values (Table 1) show that the total basicity of TRAP⁶⁻ is significantly lower than that of NOTA³⁻ because of the lower protonation constant of the ring nitrogen (log$K_1^{\text{H}}$) and phosphinate oxygen atoms of the TRAP⁶⁻ ligand. Therefore, lower stability constants should be expected for the TRAP⁶⁻ complexes than those of NOTA³⁻ complexes.

Stability and protonation constants of TRAP⁶⁻ and NOTA³⁻ complexes formed with Fe^III were determined by pH-potentiometry and UV/Vis spectrophotometry. The stability and protonation constants of the metal complexes formed with the TRAP⁶⁻ and NOTA³⁻ ligands listed in Table 2 are defined by Equations (4–6):

Table 2.

Stability and protonation constants (logK) of Fe^III and Ga^III-complexes formed with TRAP⁶⁻, NOTA³⁻, and Bha⁻ ligand (25°C).

	TRAP6−		NOTA3−		Bha−
	FeIII	GaIII	FeIII	GaIII	FeIII
I	0.15 M NaNO3	0.1 M Me4NCla	0.1 M KClb	0.1 M Me4NClc	0.15 M NaNO3	0.2 M KCld
ML	26.73(8)	26.24	28.3	29.60	10.80(2)	11.08
MHL	5.07(2)	5.18	–	0.9	–	–
MH2L	4.34(2)	4.55	–	–	–	–
MH3L	3.20(2)	3.77	–	–	–	–
MH4L	–	0.7	–	–	–	–
M(L)OH	9.76(2)	9.84	9.12(4)e	9.83	–	–
ML2	–	–	–	–	9.03(2)	10.12
ML3	–	–	–	–	7.41(3)	7.60
logβFeL2(OH)2	–	–	–	–	6.68(5)	–

^aRef. (Notni et al., 2010);

^bRef. (Clarke and Martell, 1991);

^cRef. (Simecek et al., 2012);

^dRef. (Farkas et al., 1998);

^eIn this work (0.15 M NaNO₃, 25°C).

$$\begin{array}{l}{\text{M}}^{\text{III}}+\text{L}\rightleftharpoons \text{ML}\\ {\text{K}}_{\text{ML}}=\frac{[\text{ML}]}{[\text{M}][\text{L}]}\end{array}$$ (4)

$$\begin{array}{l}{\text{MH}}_{\text{i}-\text{1}}\text{L}+{\text{H}}^{+}\rightleftharpoons {\text{MH}}_{\text{i}}\text{L}\\ {\text{K}}_{{\text{MH}}_{\text{i}}\text{L}}=\frac{[{\text{MH}}_{\text{i}}\text{L}]}{[{\text{MH}}_{\text{i}-\text{1}}\text{L}][{\text{H}}^{+}]}\end{array}$$ (5)

$$\begin{array}{l}\text{M}(\text{L})\text{OH}+{\text{H}}^{+}\rightleftharpoons \text{ML}\\ {\text{K}}_{\text{M}(\text{L})\text{OH}}=\frac{[\text{ML}]}{[\text{M}(\text{L})\text{OH}][{\text{H}}^{+}]}\end{array}$$ (6)

wherein i = 1, 2, or 3. Since the [Fe(TRAP)]³⁻ and [Fe(NOTA)] complexes are highly stable, formation of Fe^III complexes was practically completed at about pH < 2.0. Therefore, from the data obtained by pH-potentiometric titrations performed at 1:1 metal to ligand concentration ratio, only the protonation constants of the [Fe(TRAP)]³⁻ and [Fe(NOTA)] complexes could be calculated. In order to determine the logK_FeL value, we studied the competition reactions between HTRAP⁵⁻ and Bha⁻ for Fe^III [Equation (7)] by spectrophotometry in the wavelength range 400–800 nm. To calculate the stability constant of [Fe(TRAP)]³⁻, the equilibrium constants characterizing the species formed in the Fe^III-HBha system have been determined from the data obtained by pH-potentiometric and spectrophotometric measurements (experimental detail and calculation procedures used for the characterization of Fe^III-HBha system are summarized in the Supplementary information).

$$\begin{array}{l}{\left[\text{Fe}(\text{TRAP}){(\text{OH})}_{\text{x}}\right]}^{(-\text{3}-\text{x})}{\text{+Bha}}^{-}\rightleftharpoons {\left[\text{Fe}{(\text{Bha})}_{\text{2}}{(\text{OH})}_{\text{2}}\right]}^{-}\\ {\text{+HTRAP}}^{\text{5}-}\end{array}$$ (7)

wherein x = 0 and 1. The pH of the samples was 10.0, when [Fe(TRAP)]³⁻, [Fe(TRAP)OH]⁴⁻ and [Fe(Bha)₂(OH)₂]⁻ were formed. Some characteristic absorption spectra of Fe^III-HTRAP⁵⁻Bha⁻ systems are shown in Figure 1.

Figure 1.

Absorption spectra of Fe^III–HTRAP⁵⁻-Bha⁻ equilibrium systems. Open symbols and solid lines represent experimental and calculated absorbance values, respectively. ([Fe(TRAP)(OH)_x^(−3−x)] = 0.2 mM, [HBha] = 0.0 mM (black). $0.25$ mM (blue), $0.5$ mM (purple), $0.75$ mM (green), $1.0$ mM (brown), and $1.5$ mM (red), x = 0 and 1, pH = 10.0, 0.15 M NaNO₃, 25°C).

The stability and protonation constants of [Fe(TRAP)]³⁻ complex have been calculated by the combination of the pH-potentiometric data obtained by the titration of [Fe(TRAP)]³⁻ complex with NaOH solution in the pH range 1.7–12.0 (Figure S7) with the spectrophotometric data acquired at pH = 10.0 in Fe^III-HTRAP⁵⁻–Bha⁻ system (Figure 1). For calculation of the logK_FeL value, protonation constants of Bha⁻ (Table 1), the stability constant (Table 2) and the molar absorptivity of the [Fe(Bha)₂(OH)₂]⁻ complex were used. Stability and protonation constants obtained for [Fe(TRAP)]³⁻ are shown in Table 2.

Comparison of stability constants in Table 2 reveals that the logK_ML values of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ complexes are essentially equal and 2–3 logK unit smaller than those of the corresponding NOTA³⁻ complexes. The higher stability constant of [Fe(NOTA)] and [Ga(NOTA)] complexes can be attributed to higher total basicity of NOTA³⁻. The stability constant of [Fe(NOTA)] is about one logK unit lower than that of [Ga(NOTA)], which corresponds to a lower log$K_1^{\text{H}}$ value of NOTA³⁻ obtained in 0.1 M KCl solution. The triazacyclononane macrocyclic ligands with carboxylate or phosphinate pendant arms show similar affinity to Fe^III and Ga^III, which is readily explained by the facts that Ga³⁺ and Fe³⁺ have similar ionic radii (0.62 Å and 0.65 Å, respectively), and share the same charge and preferred coordination number (CN = 6).

The species distribution diagram of the Fe^III-TRAP⁶⁻ system (Figure 2) shows that the Fe^III complex is fully formed even at pH < 2 in the form of a tri-protonated [Fe(H₃L)] species. Upon rising the pH from 2.0 to 7.0, stepwise deprotonation results in consecutive formation of [Fe(H₂L)]⁻ and [Fe(HL)]²⁻. Since the protonation constants characterizing the formation of the [Fe(HL)]²⁻, [Fe(H₂L)]⁻ and [Fe(H₃L)] species are very similar to the log$K_3^{\text{H}}$, log$K_4^{\text{H}}$ and log$K_5^{\text{H}}$ values of the free TRAP⁶⁻ ligand, [Fe(TRAP)]³⁻ is protonated on the non-coordinating carboxylate pendant arms. According to the known solid state structures of [Fe(H₃TRAP)], the coordination environment of Fe^III is characterized by the trigonal antiprismatic structure formed by the parallel ring-N₃ and phosphinate-O₃ planes, whereas the carboxylate groups are protonated and non-coordinated (the solid state structure of [Ga(H₃TRAP)] complex is very similar to that of [Fe(H₃TRAP)]) (Notni et al., 2010). The [Fe(TRAP)]³⁻ complex predominates in the pH range 6.0–9.0. The pH-potentiometric titration data, obtained at pH > 8 for [Fe(TRAP)]³⁻, indicate a base-consuming process, which can be attributed to substitution of one of the phosphinate oxygens with a OH⁻ ion in the coordination sphere of Fe^III upon formation of the [Fe(TRAP)OH]⁴⁻ species [Equation (6)]. Similar processes were also identified for [Ga(TRAP)]³⁻, [Fe(NOTA)] (Figure S8 and Table 2) and [Ga(NOTA)] complexes (Notni et al., 2010; Simecek et al., 2012).

Figure 2.

Species distribution of Fe^III – TRAP⁶⁻ system ([Fe^III] = [TRAP⁶⁻] = 0.2 mM, 0.15 M NaNO₃, 25°C).

Formation kinetics of Fe(TRAP) and Ga(TRAP) complexes

The formation reactions between NOTA and various metals, such as lanthanide(III) ions (Ln^III) but also Ga^III, are typically slow at pH around 2.0–5.0 (Brucher and Sherry, 1990; Morfin and Toth, 2011). Since formation of Ln^III and Ga^III complexes of open-chain ligands is generally fast, the slow formation kinetics of the NOTA complexes can be attributed to the rigidity of the triaza-cyclononane macrocycle. Incorporation of Ln^III- and Ga^III-ions into the preformed coordination cage of NOTA is slow because of formation of stable mono-protonated [^*Ln(HNOTA)]⁺ and [^*Ga(HNOTA)]⁺ intermediates, which has been confirmed earlier by spectrophotometry measurements (Brucher and Sherry, 1990) and ¹H NMR spectroscopy(Morfin and Toth, 2011). Stability constants of such intermediates have furthermore been determined from kinetic data obtained by spectrophotometry (Brucher and Sherry, 1990) and ¹H NMR spectroscopy (Morfin and Toth, 2011). In the intermediate, the proton is most likely attached to a macrocyclic nitrogen, and the electrostatic repulsion between the proton and a Ln^III- or Ga^III-ion can inhibit fast entrance of the metal ion into the coordination cage. Formation rates of the [Ln(NOTA)] and [Ga(NOTA)] complexes are directly proportional to the OH⁻ concentration, meaning that a rate-determining OH⁻ assisted deprotonation and rearrangement of the monoprotonated intermediate is followed by entrance of the Ln^III- or Ga^III-ion into the N₃O₃ coordination cage of NOTA³⁻(Brucher and Sherry, 1990; Morfin and Toth, 2011).

In the present work, formation kinetics of M(TRAP) complexes (M^III = Fe^III and Ga^III) have been studied by spectrophotometry on the absorption band of the forming Fe(TRAP) (λ = 260 nm) and by ³¹P-NMR spectroscopy following the integral value of the forming Ga(TRAP) complex in the pH range 4–6. UV-absorption as well as ³¹P-NMR spectra, recorded after mixing of solutions containing Fe(NO₃)₃ or Ga(NO₃)₃ with HTRAP⁵⁻ as functions of time, are shown in Figures S9, S10. For the reaction mixture of Fe^III-HTRAP⁵⁻ at pH = 6.0, the absorption band observed between λ = 245–320 nm (Figure S9) can be explained by the formation of the intermediate. The absorbance values in the λ = 250–280 nm range increase with time, allowing for the conclusion that the intermediate is transformed into the final [Fe(TRAP)]³⁻ in-cage complex. Formation of the intermediate in Ga^III-TRAP reactions mixtures was previously proven by ³¹P- and ⁷¹ Ga-NMR spectroscopy (Notni et al., 2010). Based on the similarity of TRAP and NOTA, it can be assumed that protonation of the ring nitrogen below pH = 10.0 initially hampers the formation of in-cage TRAP complexes while the three carboxylate and three phosphinate oxygen atoms of HTRAP⁵⁻ can be coordinated to the metal ions to form a mono-protonated [^*M(HTRAP)]²⁻ intermediate, in which the Fe^III and Ga^III -ion is situated outside of the coordination cage. To complete the complex formation, the proton has to be removed from the ring nitrogen via a OH⁻-assisted reaction, followed by the rearrangement of the intermediate to the final [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ complexes (Scheme 2).

Scheme 2.

Formation mechanism of [M(TRAP)]³⁻ complexes.

The formation rates of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ have been studied under pseudo-first-order conditions in the presence of high excess of H_xTRAP^(x−6) ([Fe^III] = 1.0 × 10⁻⁴ M; [TRAP]_t = 0.5–4.0 × 10⁻³ M; [Ga^III] = 1.0 × 10⁻³ M; [H_xTRAP]_t = 5.0–30 × 10⁻³ M, x = 1 and 2). Under such conditions the rate of formation reactions can be expressed by Equation (8).

$$\frac{\text{d}{[\text{ML}]}_{\text{t}}}{\text{dt}}={\text{k}}_{\text{obs}}{[{\text{M}}^{\text{III}}]}_{\text{t}}$$ (8)

wherein [ML]_t is the concentration of the [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ complexes, [M^III]_t is the total concentration of species containing the Fe^III and Ga^III ions not bound to the H_xTRAP^(x−6) ligand, and k_obs is a pseudo-first-order rate constant. As expected, the k_obs vs. [H_xTRAP]_t curves (Figures 3, 4) are saturation curves indicating the formation of the [^*M(HTRAP)]²⁻ intermediates characterized by the stability constant defined by Equation (9).

Figure 3.

k_obs pseudo-first order rate constants for the formation reaction of [Fe(TRAP)]³⁻ as function of [H_xTRAP]_t ([Fe^III] = 0.1 mM, pH = 4.5 (), 5.0 (), 5.5 (), and 6.0 (), x = 1 and 2, 0.15 M NaNO₃ and 25°C).

Figure 4.

k_obs pseudo-first order rate constants for the formation reaction of [Ga(TRAP)]³⁻ as a function of [H_xTRAP]_t ([Ga^III] = 1 mM, pH = 4.6 (), 5.0 (), 5.6 (), and 6.0 (), x = 1 and 2, 0.15 M NaNO₃ and 25°C).

$$\ast {\text{K}}_{\text{M}(\text{HL})}=\frac{{[}^{\ast }\text{M}(\text{HTRAP})]}{[{\text{M}}^{\text{III}}][\text{HTRAP}]}$$ (9)

The rate-determining step of the reactions is the deprotonation and rearrangement of the [^*M(HTRAP)]²⁻ intermediates followed by the entrance of the metal ion into the coordination cage of the TRAP⁶⁻ ligand:

$$\begin{array}{l}\frac{\text{d}{[\text{ML}]}_{\text{t}}}{\text{dt}}={\text{k}}_{\text{obs}}{\left[{\text{M}}^{\text{III}}\right]}_t={\text{k}}_{\text{f}}{[}^{\ast }\text{M}(\text{HTRAP})]\\ ={\text{k}}_{\text{f}}{}^{\ast }{\text{K}}_{\text{M}(\text{HTRAP})}[{\text{M}}^{\text{III}}][\text{HTRAP}]\end{array}$$ (10)

wherein [^*M(HTRAP)] is the concentration of [^*M(HTRAP)]²⁻ intermediate and k_f is the rate constant characterizing the deprotonation and rearrangement of the intermediate to the [M(TRAP)]³⁻ complex. In the pH range studied, the concentration of the non-complexed ligand ([TRAP]_free) can be expressed by Equation (11) using the protonation constants of TRAP⁶⁻ ligand (Table 1).

$$\begin{array}{l}{\left[\text{TRAP}\right]}_{\text{free}}=\left[\text{HTRAP}\right](\text{1+}{K}_{\text{2}}^{\text{H}}\left[{\text{H}}^{+}\right]+K_{\text{2}}^{\text{H}}{K}_{\text{3}}^{\text{H}}{\left[{\text{H}}^{+}\right]}^2+\dots \\ \text{ +}{K}_{\text{2}}^{\text{H}}{K}_{\text{3}}^{\text{H}}{K}_{\text{4}}^{\text{H}}{K}_{\text{5}}^{\text{H}}{K}_{\text{6}}^{\text{H}}{\left[{\text{H}}^{+}\right]}^5)=(\text{1+}{\alpha }_{\text{H}})[\text{HTRAP}]\end{array}$$ (11)

where α_H = $K_2^{\text{H}}$[H⁺]+$K_2^{\text{H}}$$K_3^{\text{H}}$[H⁺]²+…+$K_2^{\text{H}}$$K_3^{\text{H}}$$K_4^{\text{H}}$$K_5^{\text{H}}$$K_6^{\text{H}}$[H⁺]⁵. Under the conditions used in our experiments (pH = 4.0–6.0), hydrolysis of Fe^III and Ga^III may occur by formation of [M(OH)]²⁺, [M(OH)₂]⁺ and M(OH)₃ species, i.e., OH⁻ ions may compete with H_xTRAP^(x−6) for formation of [^*M(HTRAP)]²⁻ intermediate. Considering the hydrolysis of Fe^III and Ga^III, the total metal ion concentration can be expressed by Equation (12).

$$\begin{array}{l}{\left[{\text{M}}^{\text{III}}\right]}_{\text{t}}=\left[{}^{*}\text{M}\left(\text{HTRAP}\right)\right]+\left[\text{M}(\text{OH})\right]+\left[\text{M}{(\text{OH})}_2\right]+\left[\text{M}{(\text{OH})}_3\right]\\ +\left[{\text{M}}^{\text{III}}\right]\end{array}$$ (12)

By taking into account the stability constant of the [^*M(HTRAP)]²⁻ intermediate [Equation (9)] and the equilibrium constants characterizing the hydrolysis of Fe^III and Ga^III (β_x = [M(OH)_x][H⁺]^x/[M^III], x = 1, 2, and 3), the total metal ion concentration can be expressed as follows:

$${\left[{\text{M}}^{\text{III}}\right]}_{\text{t}}=\left[{\text{M}}^{\text{III}}\right]\left(1+\frac{{}^{*}\text{K}{}_{\text{M}(\text{HTRAP})}{\left[\text{TRAP}\right]}_{\text{free}}}{\text{1+}{\alpha }_{\text{H}}}+\frac{{\beta }_{\text{1}}^{\text{OH}}}{[{\text{H}}^{+}]}+\frac{{\beta }_{\text{2}}^{\text{OH}}}{{[{\text{H}}^{+}]}^{\text{2}}}+\frac{{\beta }_{\text{3}}^{\text{OH}}}{{[{\text{H}}^{+}]}^{\text{3}}}\right)=\left[{\text{M}}^{\text{III}}\right]\left(1+\frac{{}^{*}\text{K}{}_{\text{M}(\text{HTRAP})}{\left[\text{TRAP}\right]}_{\text{free}}}{\text{1+}{\alpha }_{\text{H}}}+{\alpha }_{\text{OH}}\right)$$ (13)

wherein α_OH = ${\beta }_1^{\text{OH}}$/[H⁺] +${\beta }_2^{\text{OH}}$/[H⁺]²+ ${\beta }_3^{\text{OH}}$/[H⁺]³ (log${\beta }_1^{\text{OH}}$ = −2.19; log${\beta }_2^{\text{OH}}$ = −5.67 and log${\beta }_3^{\text{OH}}$ = −12.0 for Fe^III and log${\beta }_1^{\text{OH}}$ = −2.97; log${\beta }_2^{\text{OH}}$ = −5.92 and log${\beta }_3^{\text{OH}}$ = −8.2 for Ga^III ion; Baes and Mesmer, 1976). Considering the protonation constants of TRAP⁶⁻ (Table 1), the stability constant of the [^*M(HTRAP)]²⁻ intermediate [Equation (9)], the total concentration of the M^III ion [Equation (13)], the concentration of the non-complexed TRAP_free ligand [Equation (11) and Equation (10)], the pseudo-first order rate constant can be expressed by Equation (14).

$$k_{\text{obs}}=\frac{\frac{k_{\text{f}}{}^{*}K{}_{\text{M}(\text{HTRAP})}{[TRAP]}_{\text{free}}}{\text{1+}{\alpha }_H}}{1+\frac{{}^{*}K{}_{\text{M}(\text{HTRAP})}{[TRAP]}_{\text{free}}}{\text{1+}{\alpha }_{\text{H}}}+{\alpha }_{\text{OH}}}$$ (14)

The pseudo-first-order rate constants determined at various pH and [TRAP]_t values (Figures 3, 4) were fitted to Equation (14) and the stability constant of the [^*M(HTRAP)]²⁻ intermediates [^*K_M(HL)] and the k_f rate constants were calculated.

The stability constants of the [^*Fe(HTRAP)]²⁻ and [^*Ga(HTRAP)]²⁻ intermediates [log^*K_M(HL)] are 9.9 ± 0.1 and 10.4 ± 0.1, respectively. The log^*K_M(HL) values of the [^*Fe(HTRAP)]²⁻ and [^*Ga(HTRAP)]²⁻ intermediates are significantly higher than those of the mono-protonated [^*Ga(HNOTA)]⁺ (log^*K_Ga(HL) = 4.2), (Morfin and Toth, 2011) [^*Ce(HNOTA)]⁺ (log^*K_Ce(HL) = 3.2), (Brucher and Sherry, 1990) [^*Gd(HNOTA)]⁺ (log^*K_Gd(HL) = 3.6) (Brucher and Sherry, 1990) and [^*Er(HNOTA)]⁺ (log^*K_Er(HL) = 3.8) (Brucher and Sherry, 1990) intermediates. In the [^*Fe(HTRAP)]²⁻ and [^*Ga(HTRAP)]²⁻ intermediates, Fe^III and Ga^III are presumably coordinated by three carboxylate and three phosphinate oxygen donor atoms, whereas the metal ions in [^*M(HNOTA)]⁺ intermediates are coordinated by three carboxylate oxygen donor atoms, resulting in lower log^*K_M(HL) values.

The calculated k_f rate constants obtained for formation of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ complexes are shown in Figure 5 as functions of [OH⁻]. Kinetic data in Figure 5 show that the k_f values increase monotonously with increasing OH⁻ concentration, while interception of linear extrapolations at the origin indicates that under our experimental conditions, deprotonation and transformation of the [^*M(HTRAP)]²⁻ intermediate to the final [M(TRAP)]³⁻ complex predominantly occurs by an OH⁻-catalyzed pathway. The k_OH rate constants calculated from the slopes of the straight lines in Figure 5 are shown in Table 3.

Figure 5.

Formation rate constants (k_f) for [$\text{Ga}\left(\text{TRAP}\right){]}^{3-}$ and [$\text{Fe}\left(\text{TRAP}\right){]}^{3-}$ as a function of [OH⁻].

Table 3.

Rate constants characterizing the formation (k_OH) and dissociation (^M(L)OHk_OH, ^M(L)(OH)2k_OH) of [Fe(TRAP)]³⁻, [Ga(TRAP)]³⁻, [Ga(NOTA)], and [Ln(NOTA)] complexes (25°C).

	Formation kinetics	Dissociation kinetics
	kOH /M−1s−1	M(L)OHkOH/s−1	M(L)(OH)2kOH/s−1	logKM(L)(OH)2	kd/s−1 at pH = 7.4	t1/2/h at pH = 7.4
[Fe(TRAP)]3−	(3.37 ± 0.02) × 104	(4 ± 1) × 10−7	(5.2 ± 0.4) × 10−4	13.4 (1)	1.8 × 10−9	1.1 × 105
[Ga(TRAP)]3−	(1.47 ± 0.02) × 105	(4.3 ± 0.5) × 10−7	(3.8 ± 0.2) × 10−6	10.9 (1)	1.4 × 10−9	1.4 × 105
[Ga(NOTA)]a	1.14 × 105	–	–	–	–	–
[Ce(NOTA)]b	6.3 × 107	–	–	–	–	–
[Gd(NOTA)]b	7.1 × 107	–	–	–	–	–
[Er(NOTA)]b	5.5 × 107	–	–	–	–	–

^aRef. (Morfin and Toth, 2011);

^bRef. (Brucher and Sherry, 1990).

Comparison of the k_OH rate constants presented in Table 3 shows that the formation rates of [Ga(TRAP)]³⁻ and [Ga(NOTA)] complexes in this pathway are similar and about two orders of magnitude lower than those of [Ln(NOTA)] complexes. The results of the labeling experiments with the TRAP and NOTA chelates of ⁶⁸Ga^III at identical conditions (10 nM ligand, pH = 3.3 and 20 °C) shows that the formation rate of [⁶⁸Ga(TRAP)]³⁻ surpasses that of [⁶⁸Ga(NOTA)] (Notni et al., 2010). The faster formation of [⁶⁸Ga(TRAP)]³⁻ can be explained by the higher stability [^*K_Ga(HL)] and consequently the higher concentration of the kinetically active [^*Ga(HTRAP)]²⁻ intermediate that results in the more rapid formation of [⁶⁸Ga(TRAP)]³⁻ in the same labeling condition. On the other hand, the formation rate of [Fe(TRAP)]³⁻ is about 3 times lower than that of Ga(TRAP), which allows to perform selective labeling of TRAP with ⁶⁸Ga^III even in presence of Fe^III contaminations in the eluate.

Kinetic inertness and transchelation reaction of complexes

In order to compare the kinetic inertness, the rates of transchelation reactions of Fe(TRAP) and Ga(TRAP) complexes with H_xHBED^x−4 (x = 0, 1 and 2) ligand were studied because of the high stability of the [Fe(HBED)]⁻ and [Ga(HBED)]⁻ complexes [logK_Fe(HBED) = 39.01, logK_Ga(HBED) = 38.51, 0.1 M KCl, 25°C, (Ma et al., 1994)]. The transchelation reactions were followed by spectrophotometry on the absorption band of the forming [Fe(HBED)]⁻ and [Ga(HBED)]⁻ complexes in the pH ranges 11.0–14.0 and 9.0–12.0, respectively. The absorption spectra of the protonated HHBED³⁻ and H₂HBED²⁻ ligands and [Ga(HBED)]⁻ complex are different, whereas that of the deprotonated HBED⁴⁻ ligand and [Ga(HBED)]⁻ complex are very similar. Therefore, the transchelation reactions of [Ga(TRAP)]³⁻ with HHBED³⁻ and H₂HBED²⁻ could be monitored by spectrophotometry only up to pH = 12.0 (HBED⁴⁻: log$K_1^{\text{H}}$ = 12.57(4), log$K_2^{\text{H}}$ = 11.41(3), log$K_3^{\text{H}}$ = 8.22(5), log$K_4^{\text{H}}$ = 4.73(6) and log$K_5^{\text{H}}$ = 1.45(6), 0.15 M NaCl, 25°C). Some characteristic absorption spectra of [Fe(TRAP)]³⁻-H_xHBED^x−4 and [Ga(TRAP)]³⁻–H_xHBED^x−4 (x = 0, 1 and 2) reacting systems are shown in Figures S11, S12, respectively. The transchelation reactions can be described by Equation (15)

$$\begin{array}{l}{\left[\text{M}(\text{TRAP})\right]}^{\text{3}-}+{\text{H}}_{\text{x}}{\text{HBED}}^{(\text{x}-\text{4})}\rightleftharpoons {\left[\text{M}(\text{HBED})\right]}^{-}\\ +{\text{H}}_{\text{y}}{\text{TRAP}}^{(\text{y}-\text{6})}\text{+}(\text{x}-\text{y}){\text{H}}^{\text{+}}\end{array}$$ (15)

wherein M^III is Fe^III or Ga^III, x = 0, 1 and 2 and y = 0 and 1. The rates of the transchelation reactions have been studied in the presence of 10- and 20-fold excess of H_xHBED^(x−4), so a pseudo-first order kinetic model can be applied and the rates of reaction Equation (15) can be expressed by Equation (16):

$$-\frac{\text{d}{[\text{M}(\text{TRAP})]}_{\text{t}}}{\text{dt}}={\text{k}}_{\text{d}}{[\text{M}(\text{TRAP})]}_{\text{t}}$$ (16)

wherein k_d is a pseudo-first-order rate constant, [M(TRAP)]_t is the total concentration of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ complexes. The pseudo-first-order rate constants (k_d) characterizing the transchelation reactions of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ with H_xHBED^(x−4) at different –log[H⁺] and [OH⁻] values are shown in Figure 6. The kinetic data presented in Figure 6 show that the k_d values are independent of the concentration of H_xHBED^(x−4) and increase with –log[H⁺] and [OH⁻], indicating that the rate-determining step of the transchelation reactions is the dissociation of the [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ complexes, followed by fast reaction of free Fe^III and Ga^III with H_xHBED^(x−4). The k_d values presented in Figure 6 show the similar behavior of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ complexes in their transchelation reactions. The k_d vs. –log[H⁺] and k_d vs. [OH⁻] curves (Figure 6) obtained for [Ga(TRAP)]³⁻ and [Fe(TRAP)]³⁻ reach saturation of the k_d values at [OH⁻] > 0.015 M and [OH⁻] > 1.0 M, respectively. Based on the species distribution of the Ga^III-TRAP⁶⁻ (Notni et al., 2010) and Fe^III-TRAP⁶⁻ (Figure 2) systems, the transchelation reaction of [Ga(TRAP)]³⁻ and [Fe(TRAP)]³⁻ with H_xHBED^(x−4) may occur by the spontaneous dissociation of [M(TRAP)]³⁻ (k₀) and [M(TRAP)OH]⁴⁻ species (^M(L)OHk_OH), whereas the pH-independent dissociation rate (k_d) of [M(TRAP)]³⁻ under more basic conditions corresponds to formation [K_M(L)(OH)2, Equation (17)] and slow dissociation of the bis(hydroxo) [M(TRAP)(OH)₂]⁵⁻ intermediate.

Figure 6.

Pseudo-first-order rate constants (k_d) of the ligand exchange reactions of [$Ga{(TRAP)}^{3-}$] ($\text{A},\text{C}$) and [${\text{Fe(TRAP)}}^{3-}$] ($\text{B},\text{D}$) wih H_xHBED^(x−4) as a function of –log[H⁺] and [OH⁻] (x = 0,1, and 2). Solid lines and symbols represent calculated and experimental k_d pseudo-first-order rate constants, respectively. ([Ga(TRAP)] = [Fe(TRAP)] = 0.2 mM, [H_xHBED] = 2.0 mM (), and 4.0 mM (), 0.15 M NaCl, 25°C).

$$\begin{array}{l}{\left[\text{M}(\text{TRAP}){(\text{OH})}_2\right]}^{\text{5}-}+{\text{H}}^{+}\rightleftharpoons {\left[\text{M}(\text{TRAP})\text{OH}\right]}^{\text{4}-}\\ K_{\text{M}(\text{L}){(\text{OH})}_{\text{2}}}=\frac{[\text{M}(\text{TRAP})\text{OH}]}{[\text{M}(\text{TRAP}){(\text{OH})}_{\text{2}}][{\text{H}}^{+}]}\end{array}$$ (17)

It can be assumed that in the [M(TRAP)(OH)₂]⁵⁻ intermediate, TRAP⁶⁻ is coordinating via four donor atoms, whereas the remaining two coordination sites of Ga^III and Fe^III are occupied by two OH⁻ ions. Hence, a spontaneous dissociation of the [M(TRAP)(OH)₂]⁵⁻ intermediates is more probable, which is reflected by the ^M(L)(OH)2k_OH rate constants. The mechanisms of the transchelation reactions of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ are summarized in Scheme 3.

Scheme 3.

Proposed mechanism of the dissociation of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ complexes (x = 0 and 1).

By taking into account all possible pathways (Scheme 3), the dissociation rate of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ can be expressed by Equation (18).

$$\begin{array}{l}-\frac{\text{d}{[\text{ML}]}_{\text{t}}}{\text{dt}}\text{=}{k}_{\text{d}}{\left[\text{ML}\right]}_{\text{t}}=k_{\text{0}}[\text{ML}]{+}^{\text{M}(\text{L})\text{OH}}{k}_{\text{OH}}[\text{M}(\text{L})\text{OH}]\\ {+}^{\text{M}(\text{L}){(\text{OH})}_{\text{2}}}{k}_{\text{OH}}\left[\text{M}(\text{L}){(\text{OH})}_2\right]\end{array}$$ (18)

Considering the total concentrations of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ ([ML]_t = [ML]+[M(L)OH]+[M(L)(OH)₂]) and the protonation constants of [M(L)OH]⁴⁻ [K_M(L)OH, Equation (6), Table 2) and [M(L)(OH)₂]⁵⁻ intermediates (K_M(L)(OH)2, Equation (17)], the k_d pseudo-first-order rate constants presented in Figure 6 can be expressed by Equation (19).

$$k_d=\frac{k_0{K}_{\text{M}(\text{L})\text{OH}}[{\text{H}}^{+}]{+}^{\text{M}(\text{L})\text{OH}}{k}_{\text{OH}}{+}^{M(L){(OH)}_2}{k}_{OH}{(K_{\text{M}(\text{L})\text{OH}}[{\text{H}}^{+}])}^{-1}}{1+{\text{K}}_{\text{M}(\text{L})\text{OH}}[{\text{H}}^{+}]+{(K_{\text{M}(\text{L}){(\text{OH})}_{\text{2}}}[{\text{H}}^{+}])}^{-1}}$$ (19)

wherein k₀, ^M(L)OHk_OH and ^M(L)(OH)2k_OH are the rate constants characterizing the spontaneous dissociation of [M(TRAP)]³⁻, and [M(TRAP)OH]⁴⁻ complexes and [M(TRAP)(OH)₂]⁵⁻ intermediates, whereas K_M(L)(OH)2 is the equilibrium constant characterizing the formation of the bis(hydroxo) [M(TRAP)(OH)₂]⁵⁻ intermediates.

The rate and protonation constants characterizing the transchelation reactions of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ with H_xHBED^(x−4) have been calculated by fitting the k_d values presented in Figure 6 to the Equation (19), and the resulting values are shown in Table 3. We obtained a very low value with a large error for k₀; therefore, the spontaneous dissociation of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ is negligible under our experimental conditions. The ^M(L)OHk_OH rate constants characterizing the spontaneous dissociation of [Fe(TRAP)OH]⁴⁻ and [Ga(TRAP)OH]⁴⁻ complexes are very similar, which indicates that the kinetic inertness of [Fe(TRAP)OH]⁴⁻ and [Ga(TRAP)OH]⁴⁻ are comparable. Interestingly, the K_M(L)(OH)2 protonation constants indicate that the formation of [Fe(TRAP)(OH)₂]⁵⁻ intermediate takes place at significantly higher –log[H⁺] values than that of [Ga(TRAP)(OH)₂]⁵⁻. However, the ^M(L)(OH)2k_OH rate constant of [Fe(TRAP)(OH)₂]⁵⁻ intermediate is about two orders of magnitude higher than that of [Ga(TRAP)(OH)₂]⁵⁻, which indicates the considerably lower kinetic inertness of the [Fe(TRAP)(OH)₂]⁵⁻ intermediate.

In order to compare the kinetic inertness directly, the half-lifes (t_1/2 = ln2/k_d) of the dissociation reactions of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ at pH = 7.4 have been calculated, utilizing the rate and equilibrium constants presented in Table 3. The t_1/2 values of Fe(TRAP) and Ga(TRAP) are 1.1 × 10⁵, and 1.4 × 10⁵ h, respectively, which indicates a similar kinetic inertness of [Fe(TRAP)]³⁻ and [Ga(TRAP)]³⁻ due to comparable ^M(L)OHk_OH rate constants of the [Fe(TRAP)OH]⁴⁻ and [Ga(TRAP)OH]⁴⁻ complexes. On the other hand, reliability of our kinetic data is supported by a good agreement of the dissociation half-life for [Ga(TRAP)]³⁻ at pH = 11 determined in this study (t_1/2 = 86 h) with the literature value of t_1/2 ≈ 60 h (Notni et al., 2010).

Conclusion

Due to the availability of ⁶⁸Ge/⁶⁸Ga generators, recent years have seen an ever-growing interest in the radionuclide ⁶⁸Ga^III for PET examinations. The corresponding radiopharmaceuticals generally contain ⁶⁸Ga^III in form of chelates, for which purpose dedicated bifunctional chelators are usually conjugated to biological targeting vectors. The carrier-free ⁶⁸Ga^III obtained by acidic elution from the generator may contain some metal ions as impurities in trace amounts. These metal ions, like Ti^IV, Fe^III, Cu^II, and Zn^II, may compete with the ⁶⁸Ga^III for the chelator's binding sites. Hence, knowledge of the possible interactions of these ions and Ga^III with chelates are highly important.

In this work, the interaction of Ga^IIII and Fe^III ions with H₆TRAP, a phosphinic acid analog of H₃NOTA, were studied and compared. The stability constants of the [Ga(TRAP)]³⁻ and [Fe(TRAP)]³⁻ complexes were found to be very similar, as are their very low dissociation rates at physiological pH. The dissociation predominantly occurs via spontaneous dissociation of mono-hydroxo [M(TRAP)OH]⁴⁻ complexes and bis(hydroxo) [M(TRAP)(OH)₂]⁵⁻ intermediates. Similarly to the respective NOTA complexes, formation of Ga(TRAP) and Fe(TRAP) is slow and occurs by formation of the monoprotonated [^*M(HTRAP)]²⁻ intermediates. The stability of these intermediates is very high, presumably because both the phosphinate and carboxylate groups of the ligand are coordinated. However, although we observed an extraordinary similarity of the thermodynamic and kinetic properties of the Ga(TRAP) and Fe(TRAP) complexes, there is a small but important difference between the two systems: the formation rate of Ga(TRAP) is approximately three times higher than that of the Fe(TRAP), which has implications for the influence of Fe^III contaminations on ⁶⁸Ga labeling of TRAP.

Apparently, the previously observed selectivity of TRAP for ⁶⁸Ga^III over Fe^III is rooted in a totally different mechanism than the preference of TRAP for Ga^III over Cu^II and Zn^II (Simecek et al., 2013). Because Fe(TRAP) is formed more slowly than Ga(TRAP), formation of ⁶⁸Ga(TRAP) is preferred and even a 3-fold excess of Fe^III over TRAP does not substantially reduce the labeling yield. However, Fe(TRAP) is kinetically inert, and a higher excess of Fe^III ultimately inhibits the ⁶⁸Ga^III incorporation due to an irreversible consumption of all available TRAP. On the other hand, the TRAP complexes of Zn^II and Cu^II are formed much faster but they are not inert (Baranyai et al., 2015). Unlike Fe^III, TRAP-bound Cu^II and particularly Zn^II may therefore be readily displaced by Ga^III (Simecek et al., 2013), driven by a much higher thermodynamic stability of [Ga(TRAP)]³⁻ as compared to [Zn(TRAP)]⁴⁻ and [Cu(TRAP)]⁴⁻ (logK_ML of 26.24, 16.07, and 19.09, respectively) (Notni et al., 2010; Baranyai et al., 2015). Hence, in contrast to Fe^III, even high concentrations of Cu^II and particularly that of Zn^II do not completely inhibit ⁶⁸Ga labeling of TRAP, likewise resulting in a pronounced tolerance of these potential contaminants. We conclude that even a phenomenon of elementary character, namely, the selectivity of TRAP for Ga^III which manifests itself in a tolerance of remarkably high concentrations of different metal ion impurities during ⁶⁸Ga^III labeling, may rely on a variety of driving forces and molecular properties, thus requiring a detailed investigation of mechanistic details for thorough understanding.

Author contributions

AV and AF contributed to the equilibrium and kinetic characterizations; AW performed the ligand synthesis; EB, IT, AM, H-JW, JN, and ZB contributed to the evaluation of the physico-chemical parameters and to the manuscript preparation.

Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The reviewer, FG, and handling Editor declared their shared affiliation.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/fchem.2018.00170/full#supplementary-material