Much emphasis has been focused on the stability of GdL complexes and its relationship to toxicity. The thermodynamic stability of a complex simply describes the concentrations of all species present in solution at equilibrium as given by the following equations:
One can see by inspection of equation 1 that the Gibbs free energy of this equilibrium process will have a large favorable entropy term due to release of seven of the eight inner-sphere water molecules from the Gd3+
. This entropy contribution is referred to as the “chelate effect”. Also, we have seen that the metal ion-ligand interaction must have a large electrostatic component that contributes an additional favorable enthalpy term so the overall free energy change becomes quite favorable. As a general rule of thumb, the Gd3+
aqua ion forms the most stable complexes with ligands having the most basic donor atoms. Some thermodynamic data (8
) for the four ligands shown in are summarized in .
Ligand protonation constants (L) and thermodynamic stability constants (GdL).
These data illustrate some common themes. First, the two most basic atoms in ligands such as these are always amines (represented by the first two protonation constants, log K1 and log K2
) and, second, linear amines are typically less basic than macrocyclic amines. This is clearly evident in that the macrocyclic-derived ligand, DOTA, has the most basic nitrogen (highest log K1
), followed by DTPA, followed by the bis-amide of DTPA (DTPA-BMA), and the tetra-amide of DOTA (DOTA-(gly)4
). This trend also shows that amine groups with amide-containing side-chains (DTPA-BMA and DOTA-(gly)4
) are considerably less basic than amine groups with acetate side-chains (DTPA and DOTA). These apparently small differences in log K1
and log K2
values, however, have a significant impact on the thermodynamic stabilities of the resulting GdL complexes. Unlike the relatively small variations in the log K1
and log K2
values for the ligands, the log Kst
values for the complexes vary by over 10 orders of magnitude (). Linear correlations between the sum of ligand protonation constants (Σ log K1-n
) and thermodynamic stabilities (log Kst
) have been noted many times over the years (12
) and the four ligands described here follow that trend nicely. Of course, certain assumptions must be made about how many protonations constants to include in the term Σ log K1-n
for each ligand (see footnote to ) but the general theorem that ligands having more basic donor atoms form the most stable complexes certainly holds true. Given the low value of log Kst
, one would then be tempted to conclude that this system would not be stable enough for in vivo
applications. However, as we shall see from data presented below, this is not the case. In fact, the later system is extraordinarily kinetically inert toward dissociation and it is this chemical feature that plays a critical role in reducing in vivo
The stability constant is widely used to compare contrast agents because it reduces comparisons to a single convenient number. From , it is clear that these different ligands have different basicity and thus different affinities for the proton. The equilibrium described by equation 1 is valid under conditions when the ligand is entirely deprotonated but, at physiological pH values, the ligand will be partially protonated so one can argue that a better way to compare ML stabilities is to use conditional stability constants, defined by equations 3 and 4.
The calculated conditional constants (log Keff) at pH 7.4 are also given in . Because DOTA is such a basic ligand, there is strong competition for protons at pH 7.4 and log Keff is 7 orders of magnitude lower for GdDOTA at pH 7.4 than the thermodynamic stability constant. Consequently, GdDTPA has a more favorable binding constant than does GdDOTA at pH 7.4. For less basic ligands like GdDTPA-BMA and DOTA-(gly)4, the conditional constant is closer to the thermodynamic stability constant because there is less competition by available protons at pH 7.4. Another consequence of equation 3 is that as the pH is lowered, the concentration of protons is increased and the equilibrium in equation 3 is pushed to the left. Thus for GdDTPA, log Keff is 18.4 at pH 7.4 while at pH 4, log Keff = 11.2. Stronger acid conditions clearly results in lower complex stability.
In biological media, there are additional competitors besides the proton. For instance endogenous ions like zinc, copper, and iron form very stable complexes with these ligands. At the same time, gadolinium has a high affinity for phosphate, citrate, and carbonate ions and will bind to proteins like serum albumin. In a widely cited paper, Cacheris et al.
) built a model taking into account a range of equilibrium constants and argued that GdDTPA-BMA had a high LD50
(low acute toxicity) because the DTPA-BMA ligand had a high selectivity for Gd3+
compared to other endogenous ions like Zn2+
. Cacheris et al. (9
) proposed a “selectivity factor” that takes into account the stability constants of the Ca2+
, and Cu2+
complexes as well as the pH. On the basis of their calculations, GdDTPA-BMA is expected to release half as much of its Gd3+ in vivo
as compared with GdDTPA (9
). However animal experiments have consistently demonstrated that more Gd3+
is retained in bone and other organs when the animals are given GdDTPA-BMA than when GdDTPA is administered (13
). Clearly there are additional factors to consider besides thermodynamic stability. Models like the “selectivity factor” are based on the assumption that the system is either at thermodynamic equilibrium or will eventually reach thermodynamic equilibrium – likely a poor assumption in most cases where agents are cleared from the body relatively quickly. Clearly, the kinetics of metal dissociation or metal exchange is much more important in determining long term toxicity. Animal studies and increasingly the experience with NSF patients support the notion that kinetic inertness is the most critical factor.
An informative comparision is GdDTPA versus
the macrocyclic complex, GdHP-DO3A (aka
gadoteridol or Prohance). At pH 7.4, the conditional stability constant is slightly higher for GdDTPA (log Keff
= 18.4 vs 17.2 for GdHP-DO3A) but the rate of acid assisted Gd3+
dissociation is 20× faster for GdDTPA (12
). This appears to correlate with a small but measurable amount of Gd3+
deposited in the bone of mice 14 days after GdDTPA administration, but no detectable Gd3+
after GdHP-DO3A administration (16
). In a very recent paper, Sieber, et al. measured Gd3+
deposited in the skin of rats after 4 weeks of daily high dose (2.5 mmol/kg) administration of Gd-based contrast agents (14
). In that study, gadoteridol was not used but rather gadobutrol (Gadovist), a similar macrocyclic complex with slightly lower stability but greater kinetic inertness (17
) than gadoteridol was used. Predictably, there was significantly less Gd3+
in the skin or femur of rats that received gadobutrol compared to those that received GdDTPA. These examples point to the importance of kinetic inertness as a predictor of Gd3+
loss. Indeed, there appears to be a much lower incidence of NSF among patients who received GdHP-DO3A (18
), likely reflecting its kinetic inertness.