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

In order to rationalize the influence of FeIII 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 GaIII- and FeIII-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 HxTRAP(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 HxHBED(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− (logKFeL = 26.7) is very similar to that of [Ga(TRAP)]3− (logKGaL = 26.2). The rates of ligand exchange reaction of [Fe(TRAP)]3− and [Ga(TRAP)]3− with HxHBED(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 (t1/2) 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 [*logKGa(HL) = 10.4 and *logKFe(HL) = 9.9], which are much more stable than the [*Ga(HNOTA)]+ intermediate [*logKGa(HL) = 4.2]. Deprotonation and transformation of the monoprotonated [*M(HTRAP)]2− intermediates into the final complex occur via OH−-assisted reactions. Rate constants (kOH) 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 FeIII and GaIII-ions. However, a slightly faster formation of [Ga(TRAP)] over [Fe(TRAP)] provides a rationale for a previously observed, selective complexation of 68GaIII in presence of excess FeIII.


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 99m Tc, 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 18 F (more precisely, on the radiofluorinated glucose derivative [ 18 F]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, 68 Ga 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 onsite nuclide sources, contain 68 Ge adsorbed on an inorganic matrix, such as SnO 2 or TiO 2 , while decay of 68 Ge produces 68 Ga 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. 68 Ga-labeling of biomolecules usually requires prior decoration with a suitable multidentate ligand capable of binding the 68 Ga 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  and NOTA (Mariko and Susumu, 1977; Scheme 1) pointed at a markedly different SCHEME 1 | Structural formula of H 3 NOTA, H 6 TRAP, H 4 HBED and HBha chelates (H 3 NOTA: 1,4,7-triazacyclononane-1,4,7-triacetic acid; H 6 TRAP: 1,4,7-triazacyclononane-1,4,7-tris(methylene[2-carboxyethylphosphinic acid]); H 4 HBED: N, N ′ -Bis(2-hydroxybenzyl)ethylenediamine-N, N ′ -diacetic acid; HBha: benzhydroxamic acid).
influence of non-Ga III metal ions present in the 68 Ga 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(H 3 TRAP)] and [Ga(H 3 TRAP)] 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  did not result in a significant decrease of 68 Ga 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 68 Ga 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.

Materials
The chemicals used for the experiments were of the highest analytical grade. Ga(NO 3 ) 3 and Fe(NO 3 ) 3 were prepared by

Equilibrium Studies
For determining the protonation constants of H 6 TRAP and H 3 NOTA ligands three parallel pH-potentiometric titration were made with 0.2 M NaOH in 0.002 M ligand solutions.
The stability constant of the [Fe(TRAP)] 3− complex has been determined by spectrophotometry, using competition reactions between HTRAP 5− 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 -HTRAP 5− -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 TRAP 6− 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 NaNO 3 or NaCl) in 6 mL samples at 25 • C. Solutions were stirred and continuously purged with N 2 . 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 HNO 3 or HCl solution was titrated with the standardized NaOH solution in the presence of 0.15 M NaNO 3 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 HNO 3 -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) 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.

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: wherein A 0 , 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 31 P-NMR spectroscopy on the signal of the forming Ga(TRAP) complex. 31 P-NMR spectra were recorded by a Bruker DRX 400 spectrometer ( 31 P, 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(NO 3 ) 3 and H 6 TRAP solutions were prepared in H 2 O (a capillary with D 2 O was used for lock).
In all experiments, the concentration of Ga III was 1 mM, while that of the H 6 TRAP was varied between 5 and 30 fold excess in order to maintain pseudo-first-order conditions. Pseudo-firstorder 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 NaNO 3 . 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

Solution Thermodynamics
Protonation equilibria of the TRAP 6− , NOTA 3− and Bha − ligands were studied by pH-potentiometry. The protonation constants (logK H i ) 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.
The protonation schemes of TRAP 6− and NOTA 3− 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 NOTA 3− and TRAP 6− . The sixth proton of the TRAP 6− 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 TRAP 6− and NOTA 3− indicates that logK H 1 value of TRAP 6− is significantly lower than that of NOTA 3− ( Table 1). The lower first protonation constant of TRAP 6− can be attributed to formation of a weaker Hbond between the protonated ring nitrogen and the phosphinate oxygens than that formed between the protonated ring nitrogen and the carboxylate oxygens in HNOTA 2− . Comparison of the protonation constants obtained in 0.15 M NaNO 3 or NaCl, 0.  (Table 1) show that the total basicity of TRAP 6− is significantly lower than that of NOTA 3− because of the lower protonation constant of the ring nitrogen (logK H 1 ) and phosphinate oxygen atoms of the TRAP 6− ligand. Therefore, lower stability constants should be expected for the TRAP 6− complexes than those of NOTA 3− complexes.

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 1 H 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 1 H 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 N 3 O 3 coordination cage of NOTA 3− (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 31 P-NMR spectroscopy following the integral value of the forming Ga(TRAP) complex in the pH range 4-6. UV-absorption as well as 31 P-NMR spectra, recorded after mixing of solutions containing Fe(NO 3 ) 3 or Ga(NO 3 ) 3 with HTRAP 5− as functions of time, are shown in Figures S9, S10. For the reaction mixture of Fe III -HTRAP 5− at pH = 6.0, the absorption band observed between λ = 245-320 nm ( Figure S9 (Figures 3, 4) Baes and Mesmer, 1976). Considering the protonation constants of TRAP 6− ( 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).
Comparison of the k OH rate constants presented in Table 3 shows that the formation rates of [Ga ( 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 x HBED (x−4) , so a pseudofirst order kinetic model can be applied and the rates of reaction Equation (15) can be expressed by Equation (16):  Figure 6. The kinetic data presented in Figure 6 show   (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).
wherein  Table 3. We obtained a very low value with a large error for k 0 ; therefore, the spontaneous  (Brucher and Sherry, 1990). Frontiers in Chemistry | www.frontiersin.org 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).