Kinetics of formation and dissociation of lanthanide(III) complexes with the 13-membered macrocyclic ligand TRITA

Article abstract of DOI:10.1039/b418991d

The tetraazamacrocyclic ligand TRITA^4- is intermediate in size between the widely studied and medically used 12-membered DOTA^4- and the 14-membered TETA^4-. The kinetic inertness of GdTRITA^- was characterized by the rates of exchange reactions with Zn²⁺ and Eu³⁺. In the Zn²⁺ exchange, a second order [H⁺] dependence was found for the pseudo-first-order rate constant (k₀ = (4.2 ± 0.5) × 10^-7 s^-1; k′ = (3.5 ± 0.3) × 10^-1 M^-1S^-1, k″ = (1.4 ±0.4) × 10³ M^-2s^-1)- In the Eu³⁺ exchange, at pH <5 the rate decreases with increasing concentration of the exchanging ion, which can be accounted for by the transitional formation of dinuclear GdTRITAEu²⁺ species. At physiological pH, the kinetic inertness of GdTRITA^- is considerably lower than that of GdDOTA^- (t_1/2 = 444 h (25°C) vs. 3.8 × 10⁵ h (37°C), respectively). However, GdTRITA ^- is still kinetically more inert than GdDTPA^2-, the most commonly used MRI contrast agent (t_1/2 = 127 h). The formation reactions of LnTRITA^- complexes (Ln = Ce, Gd and Yb) proceed via the rapid formation of a diprotonated intermediate and its subsequent deprotonation and rearrangement in a slow, OH^- catalyzed process. The stability of the LnH₂TRITA* intermediates (log K_LnH2L* = 3.1-3.9) is lower than that of the DOTA-analogues. The rate constants of the OH^- catalyzed step increase with decreasing lanthanide ion size, and are about twice as high as for DOTA-complexes. The Royal Society of Chemistry 2005.

Full text of DOI:10.1039/b418991d

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F U L L P A P E R
Kinetics of formation and dissociation of lanthanide(III) complexes
with the 13-membered macrocyclic ligand TRITA4−
a
b
a
a
´
Edina Balogh, Raphae¨l Tripier, Robert Ruloff and Eva To´th*
a Laboratoire de Chimie Inorganique et Bioinorganique, Ecole Polytechnique Fe´de´rale de
Lausanne, ISIC, BCH, CH-1015, Lausanne, Switzerland. E-mail: eva.jakabtoth@epfl.ch;
Fax: 41 21 693 9875; Tel: 41 21 693 9878
b Universite´ de Bretagne Occidentale, UMR-CNRS 6521, 6 av. Le Gorgeu, CS 93837, 29238,
Brest Cedex 3, France
Received 20th December 2004, Accepted 27th January 2005
First published as an Advance Article on the web 10th February 2005
The tetraazamacrocyclic ligand TRITA4− is intermediate in size between the widely studied and medically used
12-membered DOTA4− and the 14-membered TETA4−. The kinetic inertness of GdTRITA− was characterized by the
rates of exchange reactions with Zn2+ and Eu3+. In the Zn2+ exchange, a second order [H+] dependence was found for
the pseudo-first-order rate constant (k0 = (4.2 0.5) × 10−7 s−1; kꢀ = (3.5 0.3) × 10−1 M−1s−1, kꢀꢀ = (1.4 0.4) ×
103 M−2s−1). In the Eu3+ exchange, at pH <5 the rate decreases with increasing concentration of the exchanging ion,
which can be accounted for by the transitional formation of dinuclear GdTRITAEu2+ species. At physiological pH,
the kinetic inertness of GdTRITA− is considerably lower than that of GdDOTA− (t1/2 = 444 h (25 ◦C) vs. 3.8 × 105 h
(37 ◦C), respectively). However, GdTRITA− is still kinetically more inert than GdDTPA2−, the most commonly used
MRI contrast agent (t1/2 = 127 h). The formation reactions of LnTRITA− complexes (Ln = Ce, Gd and Yb) proceed
via the rapid formation of a diprotonated intermediate and its subsequent deprotonation and rearrangement in a
slow, OH− catalyzed process. The stability of the LnH2TRITA* intermediates (log KLnH2L∗ = 3.1–3.9) is lower than
that of the DOTA-analogues. The rate constants of the OH− catalyzed step increase with decreasing lanthanide ion
size, and are about twice as high as for DOTA-complexes.
GdIII complexes by inducing steric compression around the
Introduction
water binding site, a concept that proved to be valid for both
In the last two decades there has been a growing interest in
linear DTPA-type, and macrocyclic DOTA-type chelates. Steric
the synthesis and complexation properties of functionalized
crowding is induced by elongation of the amine backbone of the
macrocyclic ligands. This has been motivated by both the
ligand, or by replacing a carboxylate arm with a propionate.4,5
peculiar chemical properties and the successful biomedical
The water exchange on the GdIII complex of the 13-membered
application of these chelating agents. The most important and
macrocyclic TRITA4− is 65 times faster as compared to the
widely studied representative of the group is H4DOTA (1,4,7,10-
12-membered DOTA4−, which makes GdTRITA− a potential
tetraazacyclododecane-1,4,7,10-tetraacetic acid) which forms
synthon for the development of high relaxivity, macromolecular
lanthanide complexes of exceptionally high thermodynamic
MRI contrast agents (Scheme 1).
stability. Kinetically, LnDOTA− complexes are very slow to form
and to dissociate, as compared to linear poly(amino carboxylate)
ligands like EDTA4− or DTPA5− (EDTA4− = ethylenediamine-
tetraacetate; DTPA5− = diethylenetriamine-pentaacetate). High
thermodynamic stability and kinetic inertness are both in-
dispensable for safe medical application of metal chelates.
Gadolinium(III) poly(amino carboxylates) are routinely used
today to enhance contrast in Magnetic Resonance Imaging
(MRI). Among the commercialized GdIII chelates, Gd(DOTA)−
Scheme 1
has by far the highest thermodynamic and kinetic stability. The
same features also allow for successful application of DOTA-
type complexes of the b-emitter 90Y in cancer treatment. The
conjugation of 90YDOTA− to monoclonal antibodies or to
other receptor targeting moieties (e.g. somatostatin-analogues)
presents a huge potential in selective internal radiotherapy.1–3
The efficiency of a GdIII chelate as an MRI contrast agent
is given by its proton relaxivity. Proton relaxivity is influenced
by several molecular parameters, involving the rotation of the
complex, the electron spin relaxation of the metal center, and
the exchange rate between coordinated and bulk water. The
development of highly efficient contrast agents requires parallel
optimization of all these parameters. The water exchange on
currently used GdIII complexes is too slow. Consequently, when
such chelates are attached to macromolecules with the objective
of optimizing rotation, the relaxivity gain is limited by the
non-optimal water exchange rate. Recently we have shown
that the water exchange can be considerably accelerated on
Non-toxicity is primordial for in vivo application of GdIII
(or other metal) complexes as MRI contrast agents. In the
recent years it has become evident that competitive equilibria
based on plasma models cannot solely explain the in vivo
behavior of GdIII complexes. The excretion of low molecular
weight GdIII chelates from the body is very rapid (t1/2 = 1.6 h for
Gd(DTPA)2−), whereas the dissociation and transmetallation of
the GdIII complexes is relatively slow. Therefore, the system is
far from equilibrium, and kinetic factors must be considered.6
On administration of the contrast agent into the body fluids,
the GdIII chelate is surrounded by various endogenous metal
ions and ligands. The kinetic stability of the GdIII complex
depends on exchange reactions that take place in plasma.
The most important is probably the displacement of Gd3+
by the endogenous metals Zn2+ and Cu2+.7 This can occur
via the direct attack of the endogenous metal on GdL, or
via the proton-assisted dissociation of the complex, followed
1 0 5 8
D a l t o n T r a n s . , 2 0 0 5 , 1 0 5 8 – 1 0 6 5
T h i s j o u r n a l i s
T h e R o y a l S o c i e t y o f C h e m i s t r y 2 0 0 5
©

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by the fast recombination of the ligand with the scavenging
metal ion. Ligand exchange reactions between GdL and ligands
present in the blood plasma are usually considered to be of
low probability. The dissociation kinetics of macrocyclic and
linear lanthanide chelates differ substantially, the rigidity of
macrocycles leading to considerably slower dissociation.8,9 For
the linear Gd(DTPA)2−, which is probably the most widely used
MRI contrast agent, a kinetic model has been established to
describe the fate of the complex in body fluids.10 The excretion
and the dissociation of Gd(DTPA)2− were regarded as parallel
first-order processes, and by using the kinetic data obtained in
vitro for exchange reactions with Cu2+ and Zn2+, the amount of
the complex dissociated in body fluids was estimated at any time
after intravenous administration.
(log KGdL = 19.17, log KGdHL = 3.2),16 but not for EuTRITA−.
However, we can assume very similar complex stability for
the two neighbouring lanthanides. The stability of ZnTRITA2−
(log KZnL = 19.42, log KZnHL = 4.07, log KZnH2L = 2.60) is
also comparable to that of GdTRITA−. Consequently, in the
presence of 10–60 fold excess of the exchanging Eu3+ or Zn2+, the
exchange reactions (1) are quantitative or close to quantitative.
In the presence of metal ion excess, the reaction is of pseudo-
first-order and the exchange rate is directly proportional to the
total concentration of the Gd3+ complex at a given time, [GdL]t:
(2)
The formation kinetics of lanthanide complexes is also
remarkably different with linear or macrocyclic ligands. Macro-
cyclic ligands tend to form complexes much more slowly.6,11 This
slow formation led to significant discrepancies in complex sta-
bility constants e.g. for LnDOTA− chelates. From the practical
point of view, slow formation kinetics can be a drawback when
macrocyclic ligands are used to complex radioactive lanthanides
where kobs is a pseudo-first-order rate constant. The rates of
the metal exchange reactions have been determined for varying
concentrations of the exchanging metal ion (5–30 mM; cGdTRITA
=
0.5 mM) and for different pH values (4.1–5.2). Figs. 1 and 2 show
the pseudo-first-order rate constants, kobs, for the reactions with
Zn2+ and Eu3+, respectively.
(
153Sm, 90Y) in radiopharmaceutical applications.
Crystal structures of lanthanide DOTA complexes and the
non-complexed DOTA4− itself indicate similar configurations of
the complexed and free ligand, with the four carboxylate groups
in syn position with respect to the macrocycle plane.12,13 On
metal complexation the ligand undergoes little reorganization,
i.e. it has a preorganized stucture. Contrary to DOTA4−, the
structurally similar, but larger macrocycle size TETA4− has the
adjacent carboxylate arms in anti configuration.14 Consequently,
complex formation requires a drastic ligand rearrangement in
order to achieve the syn stucture of the complex. It has been
postulated that preorganized ligands like DOTA4− form more
stable and kinetically more inert lanthanide complexes than
ligands without, such as TETA4−.11 With regard to formation
kinetics, LnTETA− complexes seem to show a greater pH and
temperature dependency as compared to DOTA analogues and
the reaction mechanism also appears to be more complex.11
The objective of the present study was to complete the
picture on formation and dissociation kinetics of macrocyclic
lanthanide(III)–DOTA and TETA complexes with data on
the intermediate macrocycle size LnTRITA− chelates. This
contributes not only to the general understanding of kinetic
properties of Ln-poly(amino carboxylates), but, given the
fast water exchange on GdTRITA−, it has also importance
with regard to a potential application of this chelate or its
macromolecular derivatives as an MRI contrast agent. The
dissociation kinetics of GdTRITA− has been described by the
rates of exchange reactions with Zn2+ and Eu3+. For direct
comparison, dissociation of GdTETA− has also been studied.
The formation kinetics has been followed with three Ln3+ ions,
Ce3+, Gd3+ and Yb3+, which allow for investigating the effect of
the lanthanide size on the rate of complex formation.
Fig. 1 Pseudo-first-order rate constants, kobs, as a function of the proton
concentration in the reaction of GdTRITA− with Zn2+. cZn = 0.005 M
(ꢀ); 0.01 M (᭺); 0.02 M (᭛) and 0.03 M (ꢁ) (25 ◦C; 0.1 M KCl).
Results and discussion
Dissociation kinetics of GdTRITA− and GdTETA−
To characterize the kinetic stability of GdTRITA−, we have
studied the following metal exchange reactions between the
complex and Zn2+ or Eu3+ as exchanging metal ions (charges
are omitted for simplicity):
Fig. 2 Pseudo-first-order rate constants, kobs, as a function of the Eu3+
concentration in the reaction of GdTRITA with Eu3+. pH = 4.11 (ꢀ);
4.28 (᭺); 4.58 (᭛), 5.02 (+) and 5.33 (ꢁ) (25 ◦C; 0.1 M KCl).
The variation of the kobs values with pH and with the
concentration of the exchanging metal ion is fundamentally
different for Eu3+ and Zn2+. The rate constants are independent
of [Zn2+], but dependent upon [H+], as was previously found
for exchange reactions between Zn2+ or Cu2+ and macrocyclic
LnIII chelates such as LnNOTA complexes†.17 This means that
the rate determining dissociation of GdTRITA− is followed
by rapid formation of ZnTRITA2−. The dependence of the
(1)
Zn2+ is the endogenously most abundant metal ion, with a
concentration estimated to ∼10−5 M in the plasma, while the
second most abundant metal ion Cu2+, is about 10 times less
concentrated.15 The stability constant is known for GdTRITA−
† H3NOTA = 1,4,7-triazacyclononane-1,4,7-triacetic acid.
D a l t o n T r a n s . , 2 0 0 5 , 1 0 5 8 – 1 0 6 5
1 0 5 9

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Table 1 Dissociation rate constants for some LnIII complexes; 25 ◦C
(Fig. 2). Such a dependence on the exchanging metal concen-
tration appears surprising, however, similar results have been
already reported for metal exchange reactions of different linear
poly(amino carboxylate) complexes. Margerum observed that in
the reaction of Cd(CyDTA) with Pb2+ or Cu2+ the exchanging
metal ion suppresses its own rate of exchange‡.21 He explained
this anomaly by steric requirements of CyDTA4− which prevent
the direct exchange of metal ions. Instead, the exchange rate
is controlled by a hydrogen ion reaction with CdCyDTA2−.
Lead(II) forms a weak complex with the acetate groups of
CdCyDTA2− which blocks the protonation of the complex, thus
the excess Pb2+ or Cu2+ slows down the reaction. More recently,
similar results have been found for the metal exchange between
GdDTPA2− and Eu3+10 or GdEOB–DTPA2− and Y3+.22
ko/s−1
kꢀ/M−1s−1
2.0 × 10−5
kꢀꢀ/M−2s−1
GdDOTA−a 5.0 × 10−10
—
GdTRITA− (4.2 0.5) × 10−7 (3.5 0.3) × 10−1 (1.4 0.4) × 103
EuTETA−b 8.3 × 10−4
1.76
—
—
GdNOTAc 8.3 × 10−6
2.3 × 10−2
a 37 ◦C; Ref. 8 b Ref. 18 c Ref. 17
experimentally obtained rate constants on the proton concen-
tration can be expressed by a second-order function of [H+]:
kobs = k0 + kꢀ [H+] + kꢀꢀ[H+]2
(3)
The rate decrease with increasing Eu3+ concentration in Fig. 2
can therefore be interpreted with the transitional formation
of the dinuclear species, [GdTRITA]Eu2+. In the case of
DTPA5−, such Ln2 dinuclear species were not only assumed
from kinetic studies,23 but experimentally detected by NMR.24
For macrocyclic LnIII complexes, we are not aware of similar
data. Therefore it appeared interesting to directly compare the
behaviour of GdTRITA− to a related, macrocyclic chelate. For
this comparative study we have chosen the GdIII complex of the
14-membered analogue TETA4−.
This pH-dependence implies the equilibrium formation of the
protonated complex, GdHTRITA, which dissociates faster then
the non-protonated complex:
(4)
The quadratic term in eqn. (3) shows that, in addition to eqn. (4),
the proton-assisted dissociation of the monoprotonated species
has also to be considered:
Fig. 3 shows the pseudo-first-order rate constants obtained
for the exchange reaction between GdTETA− and Eu3+ as a
function of the exchanging metal ion concentration at variable
pH values. At all pHs studied, the kobs values diminish with
increasing [Eu3+], indicating that, similarly to GdTRITA−, the
transitional formation of dinuclear complexes has to be taken
into account. The formation of such GdLEu2+ species becomes
increasingly important with increasing Eu3+ concentration, and
will result in a decrease of the concentration of the monopro-
tonated GdHTRITA or GdHTETA by shifting the protonation
equilibrium in eqn. (4) to the left. Since the protonated complex
contributes actively to the observed dissociation rate, this latter
can decrease with increasing Eu3+ concentration.
(5)
The pseudo-first-order rate constants in Fig. 1 were fitted
to eqn. (3) and the rate constants obtained are shown in
Table 1. Within the tetraazamacrocycles, the kinetic stability
remarkably increases with decreasing macrocycle size from L =
TETA to TRITA and DOTA. In comparison to EuTETA−, the
rate constant k0, characterizing the spontaneous dissociation
of GdTRITA− is three orders of magnitude, while kꢀ, which
describes the proton-assisted dissociation, is one order of mag-
nitude lower. For GdDOTA−, the corresponding rate constants
are again several orders of magnitude lower. The proton-assisted
dissociation of the protonated complex was not detected for
EuTETA− or GdNOTA in studying exchange reactions with
Zn2+ or Cu2+.17,18 In the protonated GdHTRITA complex,
the proton is attached to a carboxylate oxygen, however, the
dissociation of the complex will only occur when the proton is
transferred to a macrocycle nitrogen. This rearrangement of the
complex is probably the rate-controlling step of the dissociation,
as was previously stated for various LnIII macrocyclic chelates.8,17
Although the spontaneous dissociation of these GdIII com-
plexes is very slow, at physiological pH (7.4), important for
biomedical application, it is the k0 value that essentially
determines the overall dissociation rate (for GdTRITA−, the
proton-assisted pathway represents ∼3%). Assuming the validity
of eqn. (3) at pH 7.4, the half-live of the dissociation is
444 h for GdTRITA− vs. 0.23 h for EuTETA−, 23.2 h for
GdNOTA (25 ◦C) and 3.8 × 105 h for GdDOTA− (37 ◦C). This
clearly shows the exceptional kinetic inertness of GdDOTA−,
linked to the perfect size match between the metal ion and
the coordination cage. The coordination cage of the NOTA-
macrocycle is too small for Gd3+, while that of TRITA4− is too
large, which in both cases leads to a considerable decrease of
the kinetic stability of the Gd3+ complexes. It should be noted
that for the spontaneous dissociation of 111InTRITA− in human
serum (37 ◦C), a value of kobs ≈ 4 × 10−8 s−1 was estimated.19 For
Fig. 3 Pseudo-first-order rate constants, kobs, as a function of the Eu3+
concentration in the reaction of GdTETA with Eu3+. pH = 4.51 (ꢀ);
4.70 (᭺); 5.10 (ꢁ), 5.30 (᭛) and 5.55 (+) (25 ◦C; 0.1 M KCl).
Based on considerations on the metal-assisted dissociation of
LnIII poly(amino carboxylates) as previously reported,10,22,23 the
following possible reaction pathways are assumed to describe
the experimental rate data in the exchange of GdTRITA− or
GdTETA− with Eu3+ (Scheme 2): According to this reaction
scheme, the rate of the exchange reaction can be given as in
eqn. (6):
the linear GdDTPA2−, a half-life of t1/2 = 127 h was calculated
◦
(pH = 7.4; cZn = 10−5 M, cCu = 10−6 M; 25 C).20 In addition
to the proton-assisted dissociation, this t1/2 takes into account
the Zn2+ and Cu2+-assisted pathways, which are very efficient in
the case of linear, DTPA-derivative Gd3+ complexes.
2+
2+
Contrary to Zn2+ exchange, in the reaction of GdTRITA−
with Eu3+ the pseudo-first-order rate constants change with
the Eu3+ concentration. Moreover, they show different trends
depending on the pH: at lower pH the kobs values strongly
decrease, while at higher pH they increase with increasing [Eu3+]
(6)
‡ H4CyDTA = trans-diaminocyclohexane-N,N,Nꢀ,Nꢀ-tetraacetic acid.
1 0 6 0
D a l t o n T r a n s . , 2 0 0 5 , 1 0 5 8 – 1 0 6 5

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kGdHL = (2.3 0.5) × 10−4 s−1, kH
= 0.055 0.021 s−1M−1
and kGdLEu = (8.2 1.5) × 10−5 s−G1 dfHoLr GdTETA−. k0 could be
determined only with a large error, since at pHs of this study it
represents a small contribution in the numerator of eqn. (10).
However, k0 values for both GdTRITA− and GdTETA− are in
the same order of magnitude as those reported in Table 1.
Formation kinetics of LnTRITA− complexes
The kinetics of formation of LnTRITA− complexes has been
studied for three lanthanide ions, Ce, Gd and Yb, representing
the early, middle and late lanthanides, respectively. In the pH
range studied, the formation is slow enough to be followed by
classical UV-Vis spectrophotometry. For CeTRITA−, we fol-
lowed the change in the absorbance of the complex, while for Gd-
and YbTRITA− the formation was studied in weakly buffered
solutions by monitoring the pH decrease with bromocresol green
as a dye. In the presence of Ln3+ excess, the complex formation
is a pseudo-first-order process and its rate can be expressed as
in eqn. (11):
Scheme 2
In eqn. (6), the first term refers to the spontaneous, the second
and third terms to the proton-assisted dissociation of the
complex, while the last contribution describes the metal-assisted
dissociation. The equilibrium constants for the protonated and
the dinuclear species are given by eqns. (7) and (8):
(7)
(11)
(8)
where [TRITA]0 is the total concentration of the free ligand
and kobs is the pseudo-first-order rate constant. The formation
reactions were investigated at different pHs with varying concen-
tration of the lanthanide ions. For all systems and at each pH, the
kobs values show a saturation curve against Ln3+ concentration
(Fig. 4). Such saturation kinetics can be ascribed to the rapid
formation of an intermediate that rearranges to the product in
The total concentration of the complex can be expressed as:
[GdL]t = [GdL] + [GdHL] + [GdLEu]
(9)
Thus for the pseudo-first-order rate constant one derives:23
(10)
with k0 = kGdL, k1 = kGdHL × KHGdL, k2 = kH
× KH
GdHL
GdL
and k3 = kGdLM × KGdLM. The protonation constants for
GdTRITA− and GdTETA− have been previously determined
by pH-potentiometry (logKH
= 3.2 and 4.5, respectively).16
GdL
The pseudo-first-order rate constants in Figs. 2 and 3 were fitted
to eqn. (10) by fixing logKH
to the above values, and the
GdL
rate constants k0, k1, k2 and k3, as well as the stability constant
of the dinuclear complex, KGdLEu were calculated. All constants
obtained are listed and compared to those for GdDTPA2− in
Table 2.
In some of the exchange reactions of LnIII DTPA- or DTPA-
derivative complexes with different metal ions (M = Ln3+,
Cu2+ or Zn2+), the proton assisted dissociation of the dinuclear
complex LnLM had also to be taken into account in order
to describe the experimental reaction rates.10,23 This reaction
pathway, usually characterized by a rate constant k4, does not
seem to be operative in our case (a value of k4 = 40 M−2s−1 was
reported for the GdDTPA–Eu3+ exchange10). In fact, including
this reaction route in the analysis, the fit of the data did not
improve for the GdTRITA−/GdTETA− + Eu3+ systems, and
small negative k4 values were obtained with large errors.
By using the rate constants presented in Table 2, one can
derive the individual rate constants for each reaction pathway
of Scheme 2: kGdHL = (1.3
0.2) × 10−4 s−1, kH
= 2.6
GdHL
0.6 s−1M−1; kGdLEu = (2.1 0.5) × 10−6 s−1 for GdTRITA− and
Table 2 Rate constants obtained for the exchange reaction of GdL
complexes with Eu3+; 25 ◦C
TRITA
TETA
DTPA10
k0/s−1
≤6 × 10−7
(1.3 0.5) × 10−4
10.8 2.1
—
Fig. 4 Pseudo-first-order rate constants, kobs, as a function of the Ln3+
concentration in the formation reaction of LnTRITA complexes. Yb:
pH = 4.45 (᭜); 4.65 (᭹); 4.87 (ꢁ), 5.00 (ꢂ); Gd: pH = 4.49 (ꢁ); 4.66
(᭹); 4.89 (ꢂ), 5.08 (᭜); Ce: pH = 4.40 (᭜); 4.70 (᭹); 5.00 (ꢂ), 5.80 (ꢁ)
(25 ◦C: 1.0 M KCl). The solid lines represent the simultaneous fit of the
data at all pHs to eqn. (18).
k1/M−1s−1
k2/M−2s−1
k3/M−1s−1
KGdLEu
0.21 0.04
(4.1 1.0) × 103
(3.7 1.1) × 10−4
180 44
0.58
(2.6 1.5) × 103
9.7 × 104
(4.7 1.3) × 10−3 4.9 × 10−4
57 20
20
2.0
log KH
3.2
4.5
GdL
D a l t o n T r a n s . , 2 0 0 5 , 1 0 5 8 – 1 0 6 5
1 0 6 1

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Table 3 Protonation constants of H4TRITA
log K1
log K2
log K3
log K4
H4TRITA 0.1 M TMACl (this work)
H4TRITA 0.1 M KCl (this work)
H4TRITA 0.1 M KCl16
11.03(0.04)
10.91(0.08)
11.79
9.47(0.02)
9.48(0.08)
9.20
4.62(0.07)
4.52(0.13)
4.00
3.74(0.07)
4.06(0.09)
2.57
H4DOTA 0.1 M KCl16
11.14
9.69
4.85
3.95
a slow, rate controlling process. Similar formation behaviour
has been reported for a series of macrocyclic chelates, such
as CaDOTA2−,25 LnDOTA− and LnDOTA-derivatives,8,26–28 or
LnNOTA complexes.17
The dependence of the kobs values on the metal ion concentra-
tion is given by eqn. (12):
(cCe = 2.5 × 10−3M; cTRITA = 5 × 10−4M; pH 4.40; V = 10.0 ml),
one observes an immediate pH drop to 4.36 (within ∼30 s),
which is followed by a slow decrease of the pH to an equilibrium
value of 4.25 (measured after ∼1 day). The exact amount of
protons released in each of the two steps could be determined
from an independent titration of a solution of the same N-
methylpiperazine concentration with 0.1 M HCl, by measuring
the amount of HCl necessary for a pH decrease corresponding
to that observed above (0.054 ml and a further 1.080 ml 0.1 M
HCl had to be added to reach pH 4.36 and 4.25, respectively).
The amount of protons released in the first 30 s which leads
to the intermediate is half of that liberated in the slow step
(formation of the complex from the intermediate). According to
the protonation constants, at the starting pH (4.40), the ligand is
in H2.98TRITA form. Therefore this experiment proves that the
intermediate is the diprotonated GdH2TRITA* complex.
The conditional equilibrium constant of the intermediate,
K*, as given in eqn. (12) can be related to the thermodynamic
stability constant, KLnH2TRITA∗, defined in eqn. (13):
(12)
where K* is the equilibrium constant (conditional stability
constant) characterizing the formation of the intermediate and
k is the rate constant of the deprotonation and rearrangement
of the intermediate to the product.
We propose that the intermediate is the diprotonated species,
LnH2TRITA*. This is supported on one hand by previous
data on the formation of Ln3+–DOTA analogues, for which the
presence of diprotonated intermediates has been experimentally
proved.8,26 In the formation of CeDOTA−, the intermediate
could be directly detected by UV-Vis spectroscopy. At pH <
8, the intermediate was found to be diprotonated, while above
this pH it was monoprotonated, however, they both had the
same spectrum, thus the same structure.29 For CeTRITA−, the
isosbestic point in the UV-Vis spectrum does not overlap with
the spectrum of the aqua ion, thus points to the formation
of an intermediate (Fig. 5). The protonation constants of
TRITA4− and DOTA4− are similar (Table 3). The formation
of the diprotonated intermediates is a consequence of the large
difference between the first two and the third-fourth protonation
constants of the ligands. The LnH2TRITA* intermediate is likely
to be similar in structure to LnH2DOTA*, where the two protons
are attached to the ring nitrogens and the lanthanide ion has not
yet entered the coordination cage.
(13)
If we assume that the rate determining step of the formation
reaction is the proton release from the intermediate and the
rearrangement of the complex, the rate of this first-order process
can be expressed as in eqn. (14):
(14)
The total ligand concentration is given by eqn. (15)
[TRITA]0 = [LnH2TRITA*] + [TRITA]free
(15)
where [TRITA]free is the total concentration of the non-
complexed ligand.
[TRITA]free = [H4TRITA] + [H3TRITA−] +
[H2TRITA2−] + [HTRITA3−] + [TRITA4−]
(16)
The concentration of the fully deprotonated and the mono-
protonated ligand is practically zero at the pH of the complex
formation study. Using the protonation constants one obtains:
(17)
From eqns. (13), (14) and (17), one derives eqn. (18), with K* =
K
LnH2TRITA∗/aH.
Fig. 5 UV-Vis spectra recorded at different t times after mixing Ce3+
and TRITA (solid lines) at pH = 4.30 (0.02 M N-methylpiperazine;
cCe = cTRITA = 2 × 10−4 M; 0.1 M KCl, 25 ◦C); t = 10, 20, 30, 60, 90 and
150 min (from bottom to top). The dotted line shows the spectrum of
Ce3+ aq.
(18)
The pseudo-first-order rate constants at the various pHs and
metal concentrations (Fig. 4) were simultaneously fitted to
eqn. (18), and the rate constants k and the stability constant
of the intermediate, KLnH2TRITA∗, were calculated for each of the
three lanthanides. (By fitting the kobs rate constants separately
for each pH, the KLnH2TRITA∗ values did not show any tendency
with pH).
The composition of the LnH2TRITA* intermediates has also
been evidenced by monitoring the pH decrease, thus the quantity
of the protons released in the first rapid, and the second slow
step of the formation reaction.8,17 On mixing slightly buffered
solutions (0.025 M N-methylpiperazine) of Ce3+ and TRITA
The stability constants of the LnH2TRITA* intermediates,
presented in Table 4, are comparable to those obtained for
1 0 6 2
D a l t o n T r a n s . , 2 0 0 5 , 1 0 5 8 – 1 0 6 5

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Table 4 Rate constants, kOH, characterizing the formation of a selection
of LnL complexes, stability constants of the reaction intermediates, log
K
LnH2L∗, and of the complexes, log KLnL
Complex
kOH /M−1s−1
log KLnH2L∗
log KLnL
e
CeTRITA−
GdTRITA−
YbTRITA−
CeDOTA−
EuDOTA−
YbDOTA−
CeDO3ABb
CeDO3AMEb
CeDO2A+b
CeNOTAc
(6.9 0.3) × 106
(2.6 0.1) × 107
(5.0 0.2) × 107
3.5 × 106a
3.11 0.05
3.89 0.05
3.73 0.04
4.5a
4.4
4.3
19.17
21.6f
23.7f
24.0f
17.8
18.8
11.3
1.1 × 107a
4.1 × 107a
2.1 × 106
2.4
3.1
6.7 × 106
2.8 × 105
1.98
6.3 × 107
3.2d
a Ref 8; b Ref 28; c Ref 17; d log KLnHL∗
;
e log KLnL = 17.02 for LaTRITA−,
Fig. 6 Correlation between the stability constant of the formation
intermediate, log KLnHxL∗, and the stability constant of the final complex,
log KLnL for various macrocyclic lanthanide(III) complexes reported in
the literature. 1. CeDO2A+;28 2. CeDOTAGl3+*;30 3. CeNOTA;17 4.
EuDOTAGl3+¶;30 5. CeDO3AB*;28 6. YbDO3AB;28 7. EuDO3AB;28 8.
YbDO3AMe;28 9. CeDO3AMe;28 10. CeDOTA−;8 11. EuDOTA−;8 12.
YbDOTA−.8 For CeTRITA−, we used the log K value of LaTRITA−.16
The solid line represents a linear fit to the data points only to show the
tendency (R2 = 0.78).
Ref 16; f Ref 31
NOTA- or DO3AME§-intermediates, but lower than the sta-
bility constants of the LnH2DOTA* analogues. A correlation
between the stability constant of the formation intermediate
and the thermodynamic complex stability constant of the final
product has already been observed for different Ln3+ cyclen-
derivatives.28 LnH2DOTA* intermediates were found to be
the most stable among all macrocyclic complexes, while the
intermediate stability is progressively reduced for macrocycles
that possess three or two carboxylates (DO3A- and DO2A-
derivatives). This was rationalized by the coordination of four
carboxylates in the DOTA-intermediates, compared to only
three or two coordinated carboxylates for the DO3A- and
DO2A-derivatives. Moreover, even within the DO3A- or DO2A-
derivatives, the intermediate stability could be related to the
complex stability. Indeed, by plotting the log KLnHxL∗ stability
constant of the intermediate versus the log K stability constant
of the complex, the data for the various systems reported in
the literature seem to show a linear tendency, though with
large scattering (Fig. 6). The LnH2TRITA* intermediates also
fit into this picture. As the Ln3+ complexes are less stable for
TRITA4− than for DOTA4−, the stability of the intermediates
is also decreased by about one order of magnitude, even if in
both cases all four carboxylates are likely coordinated to the
metal in the intermediate stage. On the other hand, the three
different lanthanides studied do not show any trend with respect
to the intermediate stability, as it was also observed for cyclen
derivatives studied so far.
Fig. 7 Formation rates of LnTRITA− complexes vs. the inverse H+
concentration for Ln = Ce (ꢁ), Gd (᭹) and Yb (ꢂ). 0.1 M KCl, 25 ◦C.
of the monoprotonated intermediate.28 Since the TRITA4−
ligand is close in structure to these cyclen derivatives, the
same considerations are likely to apply for the formation of
LnTRITA− complexes as well.
The rate constants, k, characterizing the formation of the
product from the intermediate are inversely proportional to the
proton concentration (eqn. (19); Fig. 7).
For LnTRITA− formation, the kOH rate constants increase
with decreasing lanthanide size (Table 4). This is not surprising,
since the OH− catalyzed deprotonation is faster for a late lan-
thanide with a greater charge density which leads to a stronger
electrostatic repulsion between the metal ion and the proton.
This tendency of the kOH values in the lanthanide series seems
to be general, as it has been reported for all cyclen deriva-
tives with acetate pendant arms, however, not for LnNOTA
complexes.9,17,28 Interestingly, in the formation reaction of
CeTETA− a second-order [OH−] dependence was found for the k
constants, indicating the contribution a di-hydroxide ion assisted
pathway.11 This was explained with the hydroxide catalyzed
rearrangement of the non-pre-organized TETA ligand.
(19)
Similar rate laws have been obtained for Ln3+ complexes of all
cyclen derivatives or NOTA.8,17,28 The kOH values determined are
presented and compared to different cyclen derivative complexes
in Table 4.
As for the DOTA complexes,28 the inverse proportionality
between the formation rates and the H+ ion concentration can
be explained in terms of the equilibrium deprotonation of the
LnH2L* intermediate, which is followed by the release of a
second proton in a rate-controlling step and the subsequent,
fast rearrangement of the complex. The concentration of the
monoprotonated complex, which will then deprotonate in the
rate determining step, is inversely proportional to the [H+],
which thus accounts for the observed rate law (eqn. (19)). The
validity of a general base catalysis was proved for CeDO3AB
which supports the rate controlling role of the deprotonation
Conclusion
We have described the kinetic stability of GdTRITA− by deter-
mining the rates of exchange reactions with the endogenously
most abundant Zn2+ and with Eu3+ ions. In the first case, the
¶ DOTAGl = 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetylgly-
cine.
§ H3DO3AME = 1-methoxyethyl-4,7,10-tris(carboxymethyl)-1,4,7,10-
* H3DO3AB = 1-butriol-4,7,10-tris(carboxymethyl)-1,4,7,10-tetraaza-
tetraazacyclododecane.
cyclododecane.
D a l t o n T r a n s . , 2 0 0 5 , 1 0 5 8 – 1 0 6 5
1 0 6 3

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rate is independent of the exchanging metal concentration, and
shows a quadratic dependence on [H+]. In contrast to this, the
dissociation of GdTRITA− (and GdTETA−) in the presence of
Eu3+ can be slowed down by the exchanging metal ion, due to a
competition between the formation of dinuclear GdLEu species
and the protonation of the GdL complex, this latter leading
to an efficient pathway for dissociation. The kinetic inertness
of Ln3+ tetraazamacrocyclic complexes gradually decreases by
several orders of magnitude from the 12-membered DOTA to
the 13-membered TRITA and to the 14-membered TETA. The
formation of LnTRITA− complexes is very similar in mechanism
to that of the DOTA analogues (or other cyclen derivatives), but
proceeds about twice as fast as for LnDOTA− complexes.
Given the fast water exchange rate on GdTRITA−, these
results may have implications for the future design of contrast
agents for Magnetic Resonance Imaging. In particular, they
show that with regard to kinetic inertness GdTRITA− is better
than GdDTPA2−, the most commonly used contrast agent.
and Gd(TETA)− was 5 × 10−4 M. 0.02 M N-methylpiperazine
was used as buffer and the ionic strength was 0.1 M KCl. The
pH varied between 4.1–5.3.
The relaxivities, r1, were calculated from the measured 1/T1obs
water protonrelaxationrates according toeqn. (20), where1/T1w
is the relaxation rate of water at the given temperature, and [Gd]
is the Gd3+ concentration in mM.
(20)
The pseudo-first-order rate constants (kobs) were calculated by
fitting the relaxation rate data to eqn. (21),
r1t = (r10 − r1e) exp (−kobst) + r1e
(21)
where r1t, r10 and r1e are the relaxivity values at time t, time zero
and at equilibrium, respectively.
Formation kinetics. The formation rates of Ce(TRITA)−,
Gd(TRITA)− and Yb(TRITA)− were studied at 25 ◦C and 0.1 M
KCl ionic strength by direct spectrophotometry for Ce3+ and by
an indicator method for Gd3+ and Yb3+, on a Perkin-Elmer
Lambda 19 UV-Vis spectrometer. In the indicator method,
bromocresol green was used and the pH was allowed to change
0.05–0.1 unit in slightly buffered solutions. The measurements
were performed in tandem cuvettes (HELLMA, optical path
length 2 × 4.38 mm) in a cuvette holder capable of being
thermostatted. The metal concentrations varied between 2 ×
10−4–2 × 10−3 M, while the concentration of TRITA was 2 ×
10−4 M. N-Methylpiperazine was used as buffer, and its suitable
concentration was determined in each experiment. The pH
varied between 4.1–5.5.
Experimental
H4TRITA was synthesized according to procedures described
in the literature.4,32 H4TETA was purchased from Fluka and
used without further purification. The concentration of TRITA
and TETA solutions was determined by pH-potentiometry, on
the basis of titration curves of the ligands obtained in the
absence and presence of at least 50 fold excess of CaCl2. The
difference in the inflection points between the two titration
curves corresponds to 2 equivalents of the ligand.
Preparation of the stock solutions
The stock solution of GdCl3 and EuCl3 were prepared by
dissolving Gd2O3 and Eu2O3 (Fluka) in a slight excess of
conc. HCl in doubly distilled water. The excess of HCl was
evaporated off. The ZnCl2 and CeCl3 solutions were made from
chloride salts in doubly distilled water. The concentrations were
determined by complexometric titrations with Na2H2EDTA
solution using xylenol orange as an indicator.
The solutions of the GdL complexes were prepared by mixing
equimolar amounts of LnCl3 and the ligand, the pH was
adjusted to about 6.0 by adding 0.1 M HCl or 0.1 M KOH.
Acknowledgements
The authors are very grateful to La´szlo´ Burai for discussions.
We also thank Prof. Henri Handel, Universite´ de Bretagne Oc-
cidentale, for his help in the ligand synthesis. This research was
financially supported by the Swiss National Science Foundation
and the Office for Education and Science (OFES). This work was
carried out in the frame of the EC COST Action D18 and the
European-founded EMIL programme (LSHC-2004–503569).
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