DOI: 10.1002/chem.201403043

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& Imaging

Mechanistic Studies of Gd3 + -Based MRI Contrast Agents for Zn2 + Detection: Towards Rational Design** Clia S. Bonnet,*[a] Fabien Caill,[a, b] Agns Pallier,[a] Jean-FranÅois Morfin,[a] Stphane Petoud,[a] Franck Suzenet,[b] and va Tth*[a] Abstract: A series of novel pyridine-based Gd3 + complexes have been prepared and studied as potential MRI contrast agents for Zn2 + detection. By independent assessment of

Introduction Magnetic resonance imaging (MRI) has long been devoted to obtain anatomical and functional images. Recently, molecular imaging has emerged as a new field that seeks information at the molecular level by visualizing the expression or function of bioactive molecules. It allows early diagnosis because biochemical or physiological changes caused by a disease will appear prior to morphological changes. Molecular imaging always requires an imaging probe specific to the molecular event to be detected. Gd3 + -based MRI contrast agents (CAs) are particularly well-adapted to the design of responsive probes. In order to obtain an MRI response specific to a physiological parameter, the relaxivity of the probe has to be selectively modified by the parameter that we want to assess. The design of responsive CAs is typically based on changes in one or more factors that control relaxivity, that is, the number and the exchange rate of water molecules directly coordinated to Gd3 + , or the rotational correlation time of the complex.[1, 2] Several physiological parameters can be interesting to detect by MRI, including pH,[3] O2,[4] enzymes,[5] endogenous anions,[6] and cations[7] . Zinc is the second most abundant transition metal in humans, with 2–4 g of zinc distributed throughout the body.[8] It exists exclusively as a divalent ion (Zn2 + ) and is mostly bound to proteins that play a central role in controlling gene transcription and metalloenzyme function.[9] The concentration [a] Dr. C. S. Bonnet, Dr. F. Caill, A. Pallier, Dr. J.-F. Morfin, Prof. Dr. S. Petoud, Dr. . Tth Centre de Biophysique Molculaire, CNRS Rue Charles Sadron, 45071 Orlans (France) E-mail: [email protected] [email protected] [b] Dr. F. Caill, Dr. F. Suzenet Institut de Chimie Organique et Analytique UMR 7311 CNRS, Universit d’Orlans Rue de Chartres, 45067 Orlans (France) [**] MRI = magnetic resonance imaging Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201403043. Chem. Eur. J. 2014, 20, 10959 – 10969

molecular parameters affecting relaxivity, we could interpret the relaxivity changes observed upon Zn2 + binding in terms of variations of the rotational motion.

of Zn2 + is tightly regulated by cells. The total cellular zinc concentration is in the range of a few hundred micromolar (with a few picomoles present as the free ion).[10] In extracellular media, the average free zinc concentration is several orders of magnitude higher, and it was reported to be 8 mm in human plasma.[11] The zinc level can reach 10–20 mm in vesicles of b cells of the pancreas, and around 2.5 mm in the prostate. Disturbances of these quantities have been related to diabetes and prostate cancer.[12] The brain also contains a high concentration of zinc, reaching 300 mm in vesicles of certain types of glutamatergic neuronal cells.[13] Exposure to uncontrolled concentration of Zn2 + can lead to excitotoxic neuronal death.[14] Moreover, long-term disturbances in Zn2 + homeostasis have also been implicated in neurodegenerative diseases such as Alzheimer’s disease. Indeed, Zn2 + can reach up to 1 mm concentration in amyloid plaques and is implicated in the aggregation of the amyloid-b peptide.[15] Therefore, monitoring Zn2 + in vivo is an important goal in biomedical research to achieve proper understanding of its biological role, and to provide earlier diagnosis for specific pathologies. Inherent difficulties in the design of cation-responsive probes involve the following: i) the selectivity of the probe regarding other physiological cations; ii) the affinity of the probe, which must be relevant to the physiological range in order to avoid disturbances of biological processes.[16] Most zinc imaging probes used so far are fluorescent sensors, limited to cellular studies by low tissue penetration of light.[17] Few Zn2 + -responsive MRI CAs have been reported previously. They are all based on 1,4,7,10-tetraazacyclododecane1,4,7,10-tetraacetic acid (DOTA) or diethylenetriaminepentaacetic acid (DTPA) derivatives for Gd3 + complexation, to which a specific Zn2 + complexing unit has been appended. When the Zn2 + complexing unit is an iminodiacetate moiety, the relaxivity modulation has been related to a change in the hydration number (q) of Gd3 + .[18, 19] Meade et al. studied how changes in q and the relaxivity are influenced by the nature of the Zn2 + recognition site and its distance from the Gd3 + -complexing unit.[20] For iminodiacetate functions, their limited selectivity towards Zn2 + over Cu2 + can be a concern. Nagano et al. func-

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Full Paper are not replaced by physiological anions.[25] Therefore, this chelate seemed interesting for the development of Zn2 + -responsive probes based on a change of the hydration number, ideally from 0 to 2, thus leading to an important relaxivity increase upon Zn2 + binding. The Zn2 + complexing unit was derived from DPA by either appending additional carboxylate functions to the pyridines (L1, “modified DPA pocket”; see Scheme 1) or by replacing a pyridine unit by a carboxylate function (L2 and L3, “AMPA pocket”). Both DPA Scheme 1. Chemical structures and schematic representations of the ligands discussed in this work. and AMPA show good affinity for Zn2 + , (Kd  25 nm)[26] that should be relevant for physiologtionalized a DTPA derivative with N,N-bis(2-pyridyl-methyl)ethyical applications.[12] Finally, the linker is either a simple ethyl lene diamine (BPEN, a ligand presenting a good affinity and sechain (L1) or an alkyl chain of variable length with an amide lectivity for Zn2 + , Scheme 1) and further replaced a pyridylfunction (L2 and L3). Importantly, we carried out a systematic methyl group with an acetate moiety.[21] This modification restudy to assess all the parameters controlling the relaxivity of sulted in a Gd3 + complex with a turn-off relaxivity response to these Gd3 + complexes in the presence and in the absence of 2+ 2+ Zn , and the authors postulated that Zn binding restrained Zn2 + . By determining the maximum number of parameters 3+ the access of the water molecule to Gd . De Len-Rodriguez through independent techniques, our objective was to provide a complete and reliable picture of what governs the relaxivity et al. functionalized a DOTA with two BPEN units and showed changes upon Zn2 + binding. These data will also serve in the a turn-on response to Zn2 + in the presence of HSA (human [22] serum albumin). Only a small relaxivity increase is observed future as a basis for the design of more efficient MRI Zn2 + 2+ upon Zn binding, a result that was hypothesized to be sensors. caused by variation of the water exchange rate. This ternary complex can then bind HSA, and the change in the rotational correlation time is responsible for the important turn-on relaxResults and Discussion ivity response. This probe was used to detect Zn2 + release Synthesis of ligands from b cells of the pancreas during glucose-stimulated insulin secretion.[23] This first example demonstrates the feasibility of H5L1 was synthesized in 6 steps through a convergent procein vivo Zn2 + detection and the potential of MRI Zn2 + sensors. dure (Scheme 2). Reaction of N-Boc-ethylenediamine with two In order to gain deeper insight into the biological role of zinc, equivalents of bromopyridine derivative 1 in the presence of it would be important to develop a toolbox of in vivo imaging probes adapted to a broad range of Zn2 + concentrations. The rational design of Zn2 + -responsive MRI contrast agents has to start with a complete understanding of the parameters affecting their relaxivity, and up-to-date comprehensive studies of such Zn2 + -activated systems are scarce. Herein, we report the synthesis and a complete and detailed potentiometric and relaxometric study of a series of complexes integrating 1) a pyridine unit with aminocarboxylate moieties for Gd3 + complexation, 2) a modified bis(pyridinylmethyl)amine unit (DPA) for Zn2 + recognition, and 3) linkers of different lengths and natures (Scheme 1). The pyridine-based unit has proven previously to form bishydrated Gd3 + Scheme 2. Synthesis of protonated ligand H5L1. Reagents and conditions: (i) N-Boc-ethylcomplexes of relatively high thermodynamic stability enediamine, K2CO3, KI, CH3CN, reflux; (ii) TFA, CH2Cl2, reflux; (iii) BrCH2CO2Me, K2CO3, and kinetic inertness.[24] Moreover, these two water CH3CN, reflux; (iv) HN(CH2CO2Me)2, K2CO3, CH3CN, reflux; (v) 3, K2CO3, KI, CH3CN, reflux; molecules in the first coordination sphere of Gd3 + (vi) LiOH, THF/H2O (1:1 v/v), r.t. Chem. Eur. J. 2014, 20, 10959 – 10969

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Full Paper potassium carbonate and potassium iodide afforded compound 2. The protecting Boc group was cleaved under acidic conditions and the resulting amine was monoalkylated with methyl bromoacetate to give 3 with an overall yield of 66 %. In parallel, monoalkylation of 2,6-di(bromomethyl)pyridine 4 with dimethyl iminodiacetate afforded compound 5. Reaction between compounds 3 and 5 followed by final saponification afforded protonated ligand H5L1 with an overall yield of 33 % from compound 4. H4L2 (n = 1) and H4L3 (n = 3) were synthesized in 9 steps through a convergent procedure (Scheme 3). Acylation of NBoc-ethylenediamine (n = 1) and N-Boc-butylenediamine (n = 3) with chloroacetyl chloride afforded chloro derivatives 6 a and 6 b and subsequent monoalkylation with glycine ethyl ester gave compounds 7 a and 7 b, respectively. Following the procedure developed for compound 5 (Scheme 2), derivative 8 was obtained by monoalkylation of 4 with diethyl iminodiacetate and subsequent N-alkylation with compounds 7 a and 7 b afforded derivatives 9 a and 9 b, respectively. Cleavage of the Boc protecting group under acidic conditions was followed by reductive amination of the resulting amine in presence of 2pyridine carboxaldehyde and sodium cyanoborohydride. Owing to difficulties of purification, the resulting intermediate was not isolated but directly treated with ethyl bromoacetate to give compounds 10 a and 10 b. Final saponification afforded protonated ligands H4L2 and H4L3 with overall yields of 14 % from 7 a and 20 % from 7 b, respectively. Protonation constants of the ligands and stability of the complexes Potentiometric studies on one compound of each family, namely L1 and L3, have been performed in order to determine the species present in solution and their stability constants.

First, the protonation constants of L1 and L3 were assessed, as defined in equation 1. Ki ¼

½Hi L ½Hi1 ½H

ð1Þ

L1 and L3 display six and five protonation constants, respectively (Table 1).

Table 1. Protonation constants measured in KCl (0.1 m) at 298 K. Log KH

L1

L3

Py[a]

EDAMPDA[b]

Log KH1 Log KH2 Log KH3 Log KH4 Log KH5 Log KH6

8.85(6) 8.28(5) 4.78(8) 3.97(7) 3.01(6) 2.8(1)

8.80(3) 7.93(4) 5.55(7) 3.50(9) 2.4(1) –

8.95 7.85 3.38 2.48 – –

8.84 5.63 3.02 2.34 – –

[a] From ref. [25]. [b] From ref. [27].

The first three constants correspond to the protonation of amine nitrogen atoms, and the others to carboxylate functions and/or the pyridine units of the AMPA or “modified DPA” pockets. Even if the exact attribution of the protonation sequence is rather difficult based solely on these data, general trends can be deduced from comparison to literature data of structurally analogous ligands. For L3, the first two protonation constants are very close to those of the parent Py compound,[25] showing that the replacement of the carboxylate by an amide function does not have a strong effect on the basicity of the nitrogen atoms. Concerning L1, the second protonation constant (8.28) is slightly higher than that of L3 (7.93) owing to the removal of the electron-withdrawing amide function. The third protonation constant of L3 is very close to log KH2 of EDAMPDA (N,N’-bis(pyridylmethyl)ethylenediamine-N,N’-diacetate, Scheme 1),[27] and can be attributed to the tertiary amine of the AMPA moiety. For L1, log KH3 (4.78) is significantly lower, which is in line with previous data showing that the replacement of a carboxylate by a pyridinecarboxylate unit leads to decreased basicity of tertiary amines.[28] Complex stability and protonation constants, log KML and log KMLH (equations 2 and 3) have been determined for Gd3 + , Zn2 + , Ca2 + , and Cu2 + (Figure 1 and S1 in the Supporting Information). K Mm L ¼

½Mm L ½Mm1 ½M

K Mm LHi ¼

Scheme 3. Synthesis of protonated ligands H4L2 and H4L3. Reagents and conditions: (i) chloroacetyl chloride, iPr2NEt, THF, r.t.; (ii) H2NCH2CO2Et, K2CO3, KI, CH3CN, reflux; (iii) HN(CH2CO2Me)2, K2CO3, CH3CN, reflux; (iv) 7 a or 7 b, K2CO3, KI, CH3CN, reflux; (v) TFA, CH2Cl2, reflux; (vi) 2-Pyridine carboxaldehyde, NaBH3CN, EtOH, r.t.; (vii) BrCH2CO2Et, K2CO3, CH3CN, reflux; (viii) LiOH, THF/H2O (1:1 v/v), r.t. Chem. Eur. J. 2014, 20, 10959 – 10969

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½Mm L ½Mm LHi1 ½H

ð2Þ

ð3Þ

The different species formed and their stability constants are summarized in Table 2. Gd3 + forms only mononuclear complexes. Indeed, potentiometric titrations with an excess of Ln3 + gave  2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

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Figure 1. Potentiometric titration curves of solutions containing L3 (ligand) (2.44 mm) with 0 or 1 equivalent of CaCl2, ZnSO4, CuCl2, or GdCl3 and 2 equivalents of ZnSO4 in H2O, 0.1 m KCl, 298 K.

Table 2. Stability constants of the different complexes measured by potentiometric titration in KCl (0.1 m) at 298 K. Log K

L1

L3

Py[a]

Log KGdL Log KGdLH Log KGdLH2 Log KGdLH3 Log KZnL Log KZnLH Log KZnLH2 Log KZnLH3 Log KZnLH4 Log KZn2L Log KZn2LH Log KCuL Log KCuLH Log KCuLH2 Log KCuLH3 Log KCuLH4 Log KCu2L Log KCu2LH Log KCu2LOH Log KCaL Log KCaLH

17.35(5) 4.04(4) 3.51(3) 2.79(3) 14.13(7) 6.67(6) 3.98(6) 3.07(4) 2.74(7) 6.53(6) 3.60(8) 14.97(8) 6.37(8) 3.93(7) 3.00(9) 2.90(9) 8.11(8) 3.24(8) 7.19(8) 9.17(5) –

15.15(5) 7.69(5) 3.68(3) – 12.7(1) 8.15(5) 3.90(5) – – 8.1(1) – 12.7(1) 7.95(9) 3.90(9) 2.9(1) – – – – 8.05(9) 8.10(5)

18.60 – – – 15.84 3.81 – – – – – 15.69 3.45 – – – – – – 9.43 –

[a] From ref. [24].

similar results to that for the presence of stoichiometric concentrations (before the precipitation of Gd(OH)n species at pH around 7). The absence of dinuclear complexes has also been proven by luminescence data on the EuL2 complex. As previously demonstrated, the pyridine can act as a sensitizer of Ln3 + luminescence.[25] The evolution of time-resolved luminescence spectra in a titration of L2 with Eu3 + by using an excitation wavelength of 267 nm is shown in Figure S3 in the Supporting Information. The luminescence emission arising from Eu3 + increases up to one equivalent of Eu3 + added and then remains constant, confirming the formation of a unique 1:1 Ln/L species. The stability constants of GdL1 and GdL3 are lower than that of the parent pyridine complex. For GdL3, this reflects the fact that an amide is less coordinating than a carboxylate funcChem. Eur. J. 2014, 20, 10959 – 10969

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tion. Concerning GdL1, the stability constant is two orders of magnitude higher than that of GdL3 despite the loss of the amide function, but as shown later, this is explained by the participation of the “modified DPA pocket” in Gd3 + coordination. Both complexes display protonation constants corresponding to the protonation of non-coordinating amines, carboxylates, and/or pyridine nitrogen atoms. Both L1 and L3 form mono- and dinuclear Zn2 + complexes, as expected for ligands with two metal ion binding sites. The stability constants for the mononuclear complexes are relatively high (2–3 orders of magnitude lower than that for ZnPy), and therefore correspond to the complexation of Zn2 + in the “pyridine pocket”. Concerning Zn2L1, the stability constant observed for the complexation of the second Zn2 + is 6.53, one order of magnitude lower than that of ZnDPA (log KZnDPA = 7.6).[29] This is consistent with the electrostatic repulsion between the two Zn2 + cations and the higher basicity of the secondary amine in DPA as compared to that of the tertiary amine in L1.[30] In the case of L3, the stability constant of the dinuclear complex (8.1) is surprisingly higher than that of ZnAMPA (log KZnAMPA = 7.57).[27] This could be explained by charge stabilization involving the ZnAMPA entity (charge + 1) and the “pyridine pocket” complexed with Zn2 + (charge 1) in Zn2L3. Ca2 + forms only mononuclear complexes with L1 and L3 and Cu2 + forms mono- and dinuclear species with L1, whereas surprisingly only mononuclear species are observed for L3. The formation of a dinuclear complex could have been expected as log KCuAMPA is 11.8,[27] but despite titrations with excess Cu2 + , such species could not be observed. The stability constants of mononuclear complexes CuL and CaL are in the same range than those of MPy, so the first M2 + complexation occurs in the “pyridine pocket”. The stability constants follow the order: log KML3 < log KML1 < log KMPy. As expected, the replacement of one carboxylate by an amide function leads to a stability decrease. We can also deduce from those results that an additional complexing function from the “modified DPA pocket” may complete the coordination sphere of M2 + in ML1. The second Cu2 + complexation in Cu2L1 occurs in the “modified DPA pocket” and, as for Zn2L1, log KCu2L1 < log KCuDPA = 9.31.[29] It should be noted that above a pH of ca. 6, Cu2L1 undergoes deprotonation, likely of a coordinated water molecule to form a soluble hydroxocomplex. Indeed, at this pH, there is no other possible site of deprotonation because the tertiary amines are all coordinated to one of the two Cu2 + ions, thus they are not protonated. The hydrolysis constant of the complex (7.19) is lower compared to that of the aqua ion (7.67)[26] implying higher acidity of the water molecule in the complex, as previously observed for other Cu2 + complexes,[31] and complexes formed with other metal ions, such as Ln3 + .[32] For GdL1 and GdL3, we have calculated pGd and Ksel values. pGd (pGd = log [Gd3 + ]free at pH 7.4, cL = 1.105 m and cGd = 1.106 m) reflects the influence of the ligand basicity and the protonation of the complex on the stability; the higher the pGd value, the more stable is the complex. For GdL1, pGd = 15.92, and for GdL3, pGd = 14.52, which are significantly lower than that of GdPy (pGd = 17.44). The selectivity constant, Ksel,

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Full Paper reflects the selectivity of the “pyridine pockets” for Gd3 + over endogenous cations such as Ca2 + , Cu2 + , and Zn2 + .[33] For L1, Ksel = 7.46, and for L3, Ksel = 6.74, which is very similar to Ksel = 7.07 for the parent Py.

Table 3. Stability constants of the different complexes formed with L4 and various cations measured by potentiometric titration in KCl (0.1 m) at 298 K. Log K

Gd3 +

Zn2 +

Cu2 +

Ca2 +

Log KML4

14.2(1)

15.1(1)

16.1(1)

7.23(4)

Study of LnL1 The longitudinal proton relaxivity of GdL1 is 2.85 mm1 s1 at 20 MHz, 298 K (0.1 m HEPES, pH 6.7). This low value is indicative of a purely outer-sphere relaxation mechanism with no water molecule present in the first coordination sphere of Gd3 + (q = 0). This was confirmed by luminescence lifetime measurements on the corresponding EuL1 complex. Indeed, owing to different quenching efficiencies of the OH and OD oscillators, the measurement of the Eu3 + luminescence lifetimes of the excited state of the complex in H2O and D2O allows an estimation of q. For EuL1, the lifetimes are 1.05  0.03 ms and 1.9  0.2 ms in H2O and D2O solutions, respectively, leading to a q value of 0.1.[34] This means that carboxylate functions and nitrogen atoms from the “modified DPA pocket” fully complete the coordination of the metal ion. This is consistent with the relatively high stability constant obtained from potentiometric titrations. Upon Zn2 + addition, an ca. 40 % relaxivity increase is observed with the addition of up to 0.5 equivalent of Zn2 + , followed by an increase of more than 400 % to reach a relaxivity of ca. 15 mm1 s1 at 1.5 equivalents of Zn2 + (see Figure S4 in the Supporting Information). This high relaxivity, close to that of the aqua ion [Gd(H2O)8]3 + , suggests Gd3 + decomplexation upon Zn2 + addition. The modulation of the luminescence intensity of EuL1 upon Zn2 + addition, with excitation at 266 nm, (see Figure S5 in the Supporting Information) was also studied. The changes mirror the relaxivity results: a small intensity decrease occurs until 0.5 equiv of Zn2 + are added, followed by a dramatic decrease until nearly full extinction of Eu3 + luminescence, indicating Ln3 + decomplexation. To double check this result, 17O NMR transverse relaxation rates and chemical shifts were measured on GdL1 in the presence of two equivalents of Zn2 + . The results are identical to those of the aqua ion (Gd(H2O)83 + )[35] (see Figures S6 and S7 in the Supporting Information), thus unambiguously confirming decomplexation of Gd3 + upon Zn2 + addition. This result was not predictable solely on the basis of the stability and selectivity constants determined by potentiometry. Indeed, Zn2 + complexation by LnL1 modifies the coordination sphere of Ln3 + . Therefore we synthesized ligand L4 (Scheme 1) that models the coordination sphere of Gd3 + in GdL1 in the presence of Zn2 + . The synthesis is described in the Supporting Information and potentiometric titrations were performed to compare the stability of GdL4 and ZnL4. The protonation constants of L4 were determined to be 8.67(3), 8.14(4), 2.94(3), 2.00(8), the first two corresponding to the protonation of amine nitrogen atoms, and the others to carboxylate functions. The potentiometric titrations of L4 with various cations are presented in the Supporting Information (Figure S2) and the corresponding stability constants are described in Table 3. Chem. Eur. J. 2014, 20, 10959 – 10969

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ZnL4 is one order of magnitude more stable than GdL4, explaining the decomplexation observed in GdL1 upon Zn2 + addition. As expected, for Ca2 + and Gd3 + , which have high coordination numbers (typically 6–8 for Ca2 + and 8–9 for Gd3 + ), the stability constants follow the order: log KML4 < log KML3 < log KML1 < log KMPy. Thus the removal of one coordinating function has a dramatic effect on the stability of the complex. In contrast, for Zn2 + (with a typical coordination number of 4), the removal of the carboxylate function hardly affects the stability (L4 has a sufficient number of coordinating functions). The stability constants follow then the order: log KZnL3 < log KZnL1 < log KZnL4 < log KZnPy.

Modulation of longitudinal proton relaxivity of GdL2 and GdL3 with zinc The relaxivities of GdL2 and GdL3 are 11.72 and 10.70 mm1 s1 at 20 MHz and 298 K (0.1 m HEPES, pH 7.4). These high values suggest that the complexes are bishydrated in the absence of zinc and no remote carboxylate function intervenes in the coordination sphere of Gd3 + . Because addition of more than two equivalents of Zn2 + to GdL2 and GdL3 did not result in any Gd3 + release, we performed a full relaxometric titration of these complexes with Zn2 + (Figure 2). The addition of Zn2 + to a GdL3 solution resulted in a relaxivity increase of ca. 20 % up to 0.5 equivalents of Zn2 + , then a subsequent decrease up to 1 equivalent of Zn2 + . This suggests the formation of a 2:1 GdL3/Zn species endowed with a higher relaxivity, and subsequently of a 1:1 GdL3/Zn species, with a lower relaxivity (about the same as GdL3). A similar trend is observed for GdL2 except that the maximum relaxivity is higher and is reached upon 0.66 equivalents

Figure 2. 1H relaxivity measurements in the presence of [GdL2] = 1 mm (diamonds), or [GdL3] = 0.5 mm (squares) in water, pH 7.4 (HEPES 0.1 m) in the presence of Zn2 + at 20 MHz and 298 K.

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Full Paper of Zn2 + added. This means that the maximum corresponds to a species of higher molecularity, probably resulting from aggregation. In the presence of zinc, aggregation was indeed evidenced by concentration-dependent relaxivity measurements (0.5–5 mm, see Figures S10 and S11 in the Supporting Information). In the absence of Zn2 + , the relaxivity remains constant over the whole range of concentration explored, whereas in the presence of 0.66 equivalents of Zn2 + , it increases up to 3 mm. In contrast, for GdL3, no variation of relaxivity in the presence of 0.5 equivalents of Zn2 + is observed over the range of concentration 0.5 to 13 mm (see Figure S12 in the Supporting Information). This result was quite unexpected as the two complexes differ only by the length of their respective linker (only the shorter linker leads to aggregation).

Structural study of the complexes formed with L3 Before a complete determination of the microscopic parameters influencing the relaxivity, we studied by NMR spectroscopy the structure and the dynamics of the diamagnetic LuL3 complex in D2O at pD = 7.1, in the absence and in the presence of Zn2 + (see Figure S8 in the Supporting Information). The proton spectrum of LuL3 consists of 24 signals, which points to a C1 symmetry of the complex. It also indicates the presence of a single major species in solution. The complete assignments of the proton and carbon signals of L3 and LuL3 (see Figure S24 and Tables S1 and S2 in the Supporting Information) were based upon 2D homonuclear TOCSY, NOESY, and heteronuclear HSQC and HMBC experiments. The comparison of the 1 H and 13C chemical shifts in the ligand and in the complex shows major differences for the “pyridine pocket”. More importantly, the signals owing to the CH2 protons of the acetate pendant arms and the amide (H14, H15, H17, H24, and H26, see Figure 3) show AB spin patterns, which indicates a coordination of these arms to Lu3 + , and a slow interconversion between D and L optical isomers arising from the different ori-

entation of the pendant arms. It should be noted that no AB spin pattern is observed for H6 and H7, and no significant difference in the chemical shifts of the 1H or 13C nuclei between the free ligand and the complex. These data provide further indication that the carboxylate function from the “AMPA pocket” is not coordinated to the metal ion. Addition of 0.5 equivalents of Zn2 + to LuL3 results in a very broad spectrum at room temperature, suggesting the presence of a dynamic equilibrium in solution between the Zn2 + free complex and bound form(s). A temperature decrease to 278 K results in a slightly better resolved spectrum, confirming the presence of several species in solution, but the spectrum is still too broad for a complete assignment of the proton signals. The addition of a further 0.5 equivalents of Zn2 + (1 equivalent in total) results in a sharpening of the spectrum. In this case, two sets of signals are observed showing the presence of two species in slow exchange in solution (see Figure S9 in the Supporting Information). The complete assignment of the signals was performed on a 700 MHz spectrometer in order to obtain better resolution (see Tables S1 and S2 in the Supporting Information). For both species, AB spin patterns are observed for H6 and H7 additionally to those already observed for LuL3. These patterns mean that Zn2 + is complexed in the “AMPA pocket” in both species. The chemical shifts of the two sets of signals are very close, pointing to similar structures. Therefore, we can deduce that either we have two conformations of the LnL3 around the Zn2 + ion, or a mixture of a monomer LuL3Zn and a dimer (LuL3)2Zn complex. In the first case, it is unlikely that this conformation equilibrium will be slow on the NMR time scale, so the two species could be attributed to the monomer and dimer complexes in the proportions of ca. 80 %– 20 %. To summarize the NMR results, the “AMPA pocket” does not coordinate the Ln3 + in the absence of Zn2 + , and both mono- and dimeric species can be formed depending on the GdL3:Zn2 + ratio.

Determination of the macroscopic parameters influencing relaxivity

Figure 3. Partial 1H NMR spectrum of LuL3, 2.62 mm in D2O, pD = 7.06 at 25 8C and 500 MHz. Chem. Eur. J. 2014, 20, 10959 – 10969

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To characterize the parameters governing proton relaxivity of the complexes, nuclear magnetic relaxation dispersion (NMRD) profiles of GdL2 and GdL3 were recorded at three different temperatures in the absence or in the presence of Zn2 + (Figure 4 and S16–22 in the Supporting Information). The relaxivity is determined by at least 8 parameters: (1) the number of water molecules directly coordinated to Gd3 + , q; (2) their water exchange rate, kex ; (3) the rotational correlation time of the Gd3 + complex, tR ; (4) the GdH effective mean distance, rH, of the coordinated water molecules; (5) the collision diameter, aGdH, between the proton of diffusing H2O and Gd3 + ; (6) the relative diffusion coefficient, D, of the water molecule and the complex; (7) the longitudinal electronic relaxation time, T1e ; (8) the transverse electronic relaxation time, T2e. Therefore, to explain the relaxivity changes, the determination of the maximum number of parameters by complementary techniques is essential. 10964

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Full Paper Determination of the self-diffusion coefficient, DT The self-diffusion coefficients of L2, L3, and their Lu3 + complexes were measured in the absence and in the presence of Zn2 + in D2O at 298 K by 1H pulsed-gradient spin-echo (PGSE) NMR spectroscopy (Table 4).

Table 4. Self-diffusion coefficients measured by NMR in D2O at 11.7 T and 298 K. DT/109 m2 s1

L

L2 L3

0.32(1) 0.32(1) 0.35(1) 0.34(1)

LuL

LuL + 0.5 equiv Zn2 +

LuL + 1 equiv Zn2 +

0.29(1) 0.31(1)

0.31(1) 0.34(1)

As expected, the translational self-diffusion coefficients of the ligands and the corresponding complexes are similar. When 1 equivalent of Zn2 + is added, we know from the structural NMR study that we have mainly the LuLZn complex (80 %), so within a reasonable error, the self-diffusion coefficient can be attributed to this species. Indeed, DTLuLZn is very close to DTLuL excluding any important conformational change upon Zn2 + coordination. When 0.5 equivalents of Zn2 + is added, the NMR data (see above) indicate a dynamic equilibrium between the Zn2 + -free and Zn2 + -bound complexes. This average diffusion coefficient measured under these conditions is ca. 10 % smaller than that of the monomers DTLuL or DTLuLZn, implying the formation of a slowly diffusing species, corresponding to the dimer (LuL)2Zn also identified in the structural NMR study. The translational self-diffusion coefficient is an important parameter defining the outer-sphere relaxivity, but it can also be related to the rotational correlation time (equation 4), through the rotational diffusion coefficient with the assumption that the translational and rotational microviscosity factors are equal.[36, 37]

Figure 4. Temperature dependence of reduced 17O transverse relaxation rates (A) and reduced chemical shifts (B) of GdL3 at 11.7 T. 1H NMRD profiles (C) at 298 K of aqueous solutions containing [GdL3] = 1.88 mm (HEPES 0.1 m, pH 7.4) in the presence of 0 (squares), 0.66 (circles) and 2 (diamonds) equivalents of Zn2 + . The lines represent the least-squares fit of the data points using the Solomon—Bloembergen–Morgan theory.

Determination of the hydration number, q Eu3 + and Tb3 + luminescence lifetimes were measured in the absence and in the presence of Zn2 + (0.5 and 2 equivalents) in order to assess the hydration state of the Ln3 + ion in the various complexes (see Table S3 in the Supporting Information). The calculated number of water molecules is always close to 2, independent of the presence or absence of Zn2 + . Thus, the coordination sphere of Ln3 + is independent of the presence of Zn2 + . This is consistent with the NMR results and the relaxivity values. Chem. Eur. J. 2014, 20, 10959 – 10969

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tR ¼

2 a2 9 DT

ð4Þ

a being the radius of the species. Because the radii of the various species are not known, and average self-diffusion coefficients are measured, we cannot extract exact rotational correlation times from these experimental data. Nevertheless, the diffusion coefficients qualitatively show the following tendency: tR increases up to 0.5 equivalents of Zn2 + added, and then it decreases, which nicely reflects the relaxivity changes observed upon Zn2 + addition. Determination of the water exchange rate, kex and analysis of the NMRD profiles Variable-temperature 17O NMR measurements can give access to various microscopic parameters of the complex, including the number of water molecules directly coordinated to Gd3 + ,

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Full Paper Table 5. Parameters obtained from the simultaneous fitting of the transverse 17O NMR relaxation rates and chemical shifts as a function of temperature at 11.7 T, and of the NMRD profiles at 298 K, 310 K, and 323 K.

Zn2 + [equiv]

0

GdL2 0.66

2

0

GdL3 0.5

2

6 1 k298 es [10 s ] ¼ 6 DH [kJ mol1] DS ¼6 [J mol1 K1] [a,b] t298 RO [ps] ER [kJ mol1] A/h [106 rad s1]

4.2(1) 37.7(8) 8.6(5) 170(4) 26.1(2) 3.6(1)

4.3(1) 36.9(8) 6.0(4) 256(6) 35.3(2) 3.6(1)

4.2(1) 38.3(8) 10.5(8) 220(6) 25.6(2) 3.6(1)

3.3(1) 47.3(8) 39(2) 147(5) 16.8(2) 3.6(1)

3.2(1) 46.4(8) 36(2) 210(8) 18.8(2) 3.6(1)

3.2(1) 47.8(8) 40(3) 121(6) 13.9(2) 3.6(1)

GdPy[a] 0

GdDTPA[b] 0

9.3 50.4 58 92 20.2 3.7

3.3 51.6 53.0 58[c] 17.3 3.8

[a] From [24]. [b] From ref. [26]. [c] t298 RH

q, and its exchange rate with the bulk, kex. The experimental values of the reduced 17O chemical shifts measured on GdL3, which are directly proportional to q, confirmed the bishydrated character of the complex in the absence of Zn2 + . The reduced 17 O transverse relaxation rates (1/T2r) can give access to the water exchange rate. For GdL2 and GdL3 in the absence of Zn2 + , the 17O-reduced transverse relaxation rates first increase (up to ca. 310 K), then decrease with increasing temperature, thus indicating that the complexes are in the slow kinetic region at low temperatures and in the fast exchange region at higher temperatures (Figure 4 and Figure S13 in the Supporting Information). In the slow kinetic region, 1/T2r is directly determined by the exchange rate constant, kex, whereas in the fast exchange region, it is determined by the transverse relaxation rate of the coordinated water oxygen, 1/T2m, which is in turn influenced by the water exchange rate, kex, the longitudinal electronic relaxation rate, 1/T1e, and the scalar coupling constant, A/ h. In our case, the slow kinetic region is well-defined and enables a reliable determination of kex. 17 O transverse relaxation rates were also measured in the presence of 0.6 and 2 equivalents of Zn2 + (see Figures S14 and S15 in the Supporting Information). Within experimental error, they are similar to those obtained in the absence of Zn2 + . This result proves that the water exchange rate, kex, is independent of the Zn2 + concentration. The transverse and longitudinal 17O relaxation rates, and the NMRD profiles, were simultaneously analyzed with Solomon– Bloembergen–Morgan (SBM) theory to yield the microscopic parameters characterizing water exchange and rotation (see the Supporting Information for equations). Indeed, if we are not interested in detailed information about the electron spin relaxation and if we restrict the analysis of the NMRD data to medium and high magnetic fields, the SBM approach gives reliable information on dynamic processes like water exchange and rotational correlation times for small complexes.[38, 39] Therefore we decided to include only relaxivity values above 6 MHz for the fitting process. In the analysis of the data, several parameters have been fixed to common values. Among these, rGdO has been fixed to 2.5 , based on available crystal structures and electron nuclear double resonance (ENDOR) results,[40] and the quadrupolar coupling constant, c(1+h2/3)1/2, has been set to the value for pure water, 7.58 MHz.[41] The diffusion coefficients, DT, were meaChem. Eur. J. 2014, 20, 10959 – 10969

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sured by NMR in D2O, and the value in H2O was scaled with the viscosity ratio h(D2O)/h(H2O) = 1.23 according to the T Stokes–Einstein formula. The diffusion coefficients, D298 GdH = D + DH2O were fixed, and the corresponding activation energies EDGdH were fitted. The Gd–water proton distance was fixed to rGdH = 3.1 , and the closest approach between the Gd3 + ion and the outer-sphere protons to aGdH = 3.6 . The empirical constant describing the outer-sphere contribution to the 17O chemical shift, Cos, was fixed to 0 for GdL2 and fitted to 0.18 for GdL3 (see Table 4 in the Supporting Information) to account for the larger chemical shifts obtained. A hydration number of q = 2 was considered in all cases, and the following parameters have been adjusted: the water exchange rate, k 298 ex , the activation enthalpy for water exchange, DH ¼6 , the scalar coupling constant, A/h, the rotational correlation time, t298 R , and its activation energy, ER, and the parameters describing electron spin relaxation, the mean square of the zero-field splitting, D2, the correlation time for the modulation of the zero-field splitting, t298 V , while its activation energy, EV, has been fixed to 1 kJ mol1. The parameters resulting from the best fit are presented in Table 5 and S4 in the Supporting Information. The fit yielded the values of kex of 4.2  106 s1 for GdL2 and 3.2  106 s1 for GdL3. By comparison with the parent pyridine compound, and derivatives of this family, our complexes are expected to undergo dissociative water exchange.[24, 42] In the case of dissociative exchange for all DTPA- and DOTA-derivatives, it was generally observed that the replacement of one negatively charged carboxylate in the complex with a neutral amide decreases the exchange rate to about one third.[43] The same rule is observed here if we compare the water exchange rate of GdPy (9.3  106 s1) with those of GdL2 and GdL3. For both GdL2 and GdL3, the rotational correlation time in the absence of Zn2 + is higher than that of the parent compound GdPy, which is consistent with the size of the complexes. In the presence of less than 1 equivalent of Zn2 + , tR increases for both complexes then decreases when more than 1 equivalent of Zn2 + is added. This is in accordance with the qualitative results obtained from the diffusion-coefficient measurements. These results clearly demonstrate that only the rotational correlation times are responsible for the relaxivity changes observed.

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Full Paper Affinity and selectivity towards zinc Despite the fact that the affinity of the “AMPA pocket” for Zn2 + in our GdL complexes could not be determined precisely, from the potentiometric data (log KZn2L3) we can estimate a dissociation constant KD (= [Zn2 + ][GdLZn]/[GdLZn2]) at pH 7.4 in the nanomolar range (ca. 10 nm). This affinity is similar to that of the Zn2 + sensor reported by Sherry et al.,[22] and is in the relevant range for physiological applications. In order to assess the selectivity of the “AMPA pocket” for Zn2 + , relaxivity measurements were performed with GdL2 in the presence of Ca2 + , Mg2 + , and Cu2 + (Figure 5). With Ca2 + and Mg2 + , the relaxivity change is negligible, whereas in the presence of less than 1 equivalent of Cu2 + , a small response is observed. As for Zn2 + , the relaxivity first increases and then decreases. Such a response to Cu2 + has been previously observed with another Gd3 + -based MRI Zn2 + sensors,[22] however, it is not problematic as the concentration of Cu2 + in vivo is much smaller than that of Zn2 + .[23]

of Zn2 + . Second, both Gd3 + complexes containing the amide function in the linker show a similar relaxivity response in the presence of Zn2 + , thus proving that the length of the linker does not influence the relaxivity behavior of the complexes. The structural study in the presence and in the absence of Zn2 + showed that the Zn2 + binding site does not coordinate to Gd3 + in the absence of Zn2 + . A thorough evaluation of the microscopic parameters responsible for the relaxivity response has been performed by independently assessing the maximum number of parameters, that is, the hydration number, q, the water exchange rate, kex, and the self-diffusion coefficients of the various species in the presence and in the absence of Zn2 + . It has been demonstrated unambiguously that the variation of the rotational correlation time, tR, is responsible for the relaxivity changes observed. Finally, these compounds show a sufficient selectivity for Zn2 + over physiological cations, proving that the “AMPA pocket” is adapted for Zn2 + detection. The relaxivity changes based on small tR variations as in our case are certainly not sufficient to develop responsive probes. To achieve q variations (ideally from 0 to 2) and still retaining thermodynamic stability for these pyridine-based complexes, all four carboxylate functions should be preserved and the Zn2 + binding unit should be conjugated in a way to allow saturation of the Gd3 + coordination sphere in the absence of Zn2 + .

Experimental Section Synthesis See the Supporting Information.

Liquid sample preparation The ligand concentrations were determined by adding an excess of lanthanide solution to the ligand solution and titrating the metal excess with standardised Na2H2EDTA in urotropine buffer (pH 5.6–5.8) in the presence of Xylenol Orange as an indicator. The concentrations of the metal solutions were determined similarly by complexometric titrations. The concentrations of Gd3 + -containing solutions were also checked both by ICP-MS and BMS measurements when possible.

Figure 5. 1H relaxivity measurements of aqueous solutions containing [GdL2] = 3 mm in HEPES buffer, pH 6.7, in the presence of Zn2 + (diamonds), Cu2 + (triangles), Mg2 + (squares), or Ca2 + (circles) at 20 MHz, 298 K. Inset: relaxivity values in the same conditions and in the presence of 0.66 equivalents of M2 + .

Conclusion

Potentiometric studies

We have conceived, synthesized, and characterized the behavior of a series of novel Gd3 + complexes for Zn2 + sensing. The design of the ligands combines a pyridine scaffold for Gd3 + complexation, a Zn2 + coordinating unit derived from the wellknown DPA to which coordinating carboxylate functions have been added, and a linker. This modular design allows the independent optimization of each part of the molecule. These sensors clearly do not have potential for in vivo applications because the stability of the complexes obtained is too low and the relaxivity response to Zn2 + is very small and non-monotonic. Nevertheless several conclusions can be drawn from these studies to help design better sensors. First, we have demonstrated that an amide function in the linker is required to ensure sufficient stability of the Gd3 + complex in the presence

Carbonate-free 0.1 mol L1 KOH and 0.1 mol L1 HCl were prepared from Fisher Chemicals concentrates. Potentiometric titrations were performed in 0.1 mol L1 aqueous KCl under a nitrogen atmosphere and the temperature was maintained at 25  0.1 8C with a circulating water bath. The pH (pH = log [H + ], concentration in molarity) was measured for each titration with a combined pH glass electrode (Metrohm) filled with 3 m KCl and the titrant addition was automated by use of a 702 SM titrino system (Metrohm). The electrode was calibrated in hydrogen ion concentration by titration of HCl with KOH in 0.1 mol L1 electrolyte solution.[44] A plot of meter reading versus pH allows the determination of the electrode standard potential (E8) and the slope factor (f). Continuous potentiometric titrations with HCl and KOH 0.1 mol L1 were conducted on aqueous solutions containing 5 mL of L1 2.60 mm, L3 2.44 mm, and L4 2.30 mm in KCl 0.1 mol L1, with 2 min waiting between successive points. The titrations of the metal complexes were per-

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Full Paper formed with the same ligand solutions containing 1 or 2 equivalents of metal cation, with 2 min waiting time between 2 points. Experimental data were refined by using the computer program Hyperquad 2008.[45] All equilibrium constants are concentration quotients rather than activities and are defined as:

K mlh ¼

½Mm Ll Hh  ½Mm ½Ll ½Hh

The ionic product of water at 25 8C and 0.1 mol L1 ionic strength is pKw = 13.77.[26] Fixed values were used for pKw, ligand acidity constants, and total concentrations of metal, ligand, and acid. All values and errors (one standard deviation) reported are at least the average of three independent experiments.

Temperature-dependent 17O NMR measurements The transverse 17O relaxation rates (1/T2) and the chemical shifts were measured in aqueous solutions of GdLi (i = 1–3) in the temperature range 280–350 K, on a Bruker Avance 500 (11.7 T, 67.8 MHz) spectrometer. The temperature was calculated according to previous calibration with ethylene glycol and methanol.[46] An acidified water solution (HClO4, pH 3.3) was used as external reference. Transverse relaxation times (T2) were obtained by the Carr– Purcell–Meiboom–Gill spin-echo technique.[47] The technique of the 17 O NMR measurements on Gd3 + complexes has been described elsewhere.[48] The samples were sealed in glass spheres fitted into 10 mm NMR tubes to avoid susceptibility corrections of the chemical shifts.[49] To improve the sensitivity, 17O-enriched water (10 % H217O, CortectNet) was added to the solutions to reach around 1 % enrichment. The concentrations and pH of solutions were as follows: [GdL1] = 9.62 mm, pH 5.8 with 2 equivalents of Zn2 + ; [GdL2] = 2.77 mm, pH 6.60, [Zn2 + ] = 0, 0.6 and 2 equivalents; [GdL3] = 15.2 mm, pH 7.4, [Zn2 + ] = 0, 0.5 equivalents. The 17O NMR data have been treated according to the Solomon–Bloembergen– Morgan theory of paramagnetic relaxation (see the Supporting Information). The least-squares fit of the 17O NMR data were performed using Micromath Scientist version 2.0 (Salt Lake City, UT, USA). The reported errors correspond to two times the standard deviation.

Luminescence measurements Luminescence spectra were recorded on a modified Jobin–Yvon Horiba Fluorolog-322 spectrofluorimeter equipped with a Hamamatsu R928 detector. A solution of L2 at 50 mm in 0.1 m HEPES in H2O at pH 6.7 was prepared and titrated with a Eu3 + solution. A solution of EuL1 at 100 mm in 0.1 m HEPES in H2O at pH 6.7 was prepared, and titrated with Zn2 + . Luminescence spectra were recorded after each addition and upon excitation at 267 nm. Europium and terbium luminescence lifetimes were measured in H2O and D2O by recording the decay of the emission intensity at 616 and 545 nm, respectively, upon excitation at 280 and 396 nm (for Eu), or 280 and 215 nm (Tb). The instrument settings (initial delay, maximum delay, delay increment, and sample window) were adjusted depending on the solutions. Luminescence lifetimes were also determined under excitation at 266 nm provided by a YG 980 Quantel Nd:YAG laser (fourth harmonic) while the signal was detected in the UV/Visible (220–800 nm) with a photomultiplier tube R928P from Hamamatsu. The output signal from the detectors was then fed to a Tektronix TDS 754C 500 MHz bandpass digital oscilloscope. Experimental luminescence decay curves were treated with Origin 7.0 software using exponential fitting models. All the lifetimes were analyzed as monoexponential decays, even at 0.5 equiv of Zn2 + where a mixture of MLZn and (ML)2Zn is present, however, the close environment of Ln3 + is identical in those species. Both techniques give similar results within the experimental errors and three decay curves were collected on each sample, for each technique and reported lifetimes are an average of at least three successful measurements.

Diffusion coefficient measurements

NMR spectroscopy The NMR spectra were recorded on a Bruker Avance 500 (11.7 T) spectrometer, and on a Bruker Avance III HD 700 equipped with a CPTCI cryoprobe. The spectra were recorded in D2O at 2.62 mm (L3), pD = 7.08; 2.45 mm (LuL3), pD = 7.06, and 0.5 and 1 equivalents of Zn2 + in total was added to the latter solution. 1H and 13 C NMR spectra were recorded at 298 K (otherwise stated) on 10 and 220 ppm, respectively. When necessary, a solvent suppression was achieved by using an excitation sculpting sequence. 1H, 13C, TOCSY, NOESY, HSQC, and HMBC spectra were systematically recorded. A mixing time of 70 ms and 300 ms were used for the TOCSY and NOESY experiments, respectively.

Relaxometric measurements Proton NMRD profiles were recorded on a Stelar SMARTracer Fast Field Cycling relaxometer (0.01–10 MHz) and a Bruker WP80 NMR electromagnet adapted to variable field measurements (20– 80 MHz) and controlled by a SMARTracer PC-NMR console. The temperature was monitored by a VTC91 temperature control unit and maintained by a gas flow. The temperature was determined by previous calibration with a Pt resistance temperature probe. Chem. Eur. J. 2014, 20, 10959 – 10969

The longitudinal relaxation rates (1/T1) were determined in water. The least-squares fit of the 1H NMRD data was performed by using MicroMath Scientist version 2.0 (Salt Lake City, UT, USA). The solutions were made in HEPES buffer (0.1 m) at pH 7.4 and at the following concentrations: GdL2: 3 mm, GdL3: 1.88 mm. Zn2 + was added to obtain 0.5 (GdL3), 0.66 (GdL2), and 2 equivalents (GdL2 and GdL3) compared to GdL. The Zn2 + titrations of GdL2 and GdL3, as well as the concentration effects, were performed at 20 MHz, and 298 K.

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The self-diffusion coefficients, DT, were measured by applying the bipolar stimulated spin-echo sequence to protons in the complex in D2O solutions.[50] The proton gyromagnetic ratio is denoted by gI, the strength of the gradient pulse by g, the duration of this gradient by d and the diffusion delay by D. The self-diffusion coefficient DT was calculated by fitting of the theoretical expression of the proton signal intensity I(d,D,g) = I0exp[-(gIgd)2(D-d/3)DT], in which I(d,D,g) and I0 are the intensities in the presence and absence of the gradient pulses, respectively. The values chosen for d and D in these measurements depend on the magnitude of the diffusion coefficient being measured. For quickly diffusing HOD molecules, the values of d and D were 2 and 100 ms, respectively. For the slowly diffusing complex, they were 3 and 200 ms respectively. In the experiments g was increased from 1.8 to 35.3 G cm1.

Acknowledgements We thank Herv Meudal for recording spectra on the Bruker 700 MHz NMR spectrometer. C.S.B. thanks the Agence Nationale de la Recherche (ANR-13-JS07-0007) for financial support.

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