Дота макроциклическая полость в металлических радиофармацевтиках

Background

The hypothetical concept of ‘macrocyclic cavity’ is largely employed as useful model to interpret the affinity of metal ions for the macrocyclic chelating ligand 2,2′,2′′,2′′′-(1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrayl)tetraacetic acid (H₄DOTA). It Is hypothesized that a close matching between the size of the macrocyclic cavity and that of the metallic ion is a key parameter to ensure the high-yield formation of stable coordination metal-DOTA complex. This approach has become popular in the design of radiopharmaceuticals containing radiometals and H₄DOTA as chelating group.

Results

Based on X-ray structural data of metallic complexes formed by the ligand H₄DOTA upon coordination with a variety of metals, an elementary argument based on Euclidean geometry is presented here that questions the existence of the hypothetical ‘macrocyclic cavity’ within the chelator macrocycle. The geometrical analysis was applied to the complex formed by a Ga³⁺ ion coordinated to H₄DOTA as model compound.

Conclusions

Application of Euclidean geometry to calculate bond angles in the coordination complex of the ligand H₄DOTA with the Ga⁺³ ion, supposed to incorporate a hypothetical ‘macrocyclic cavity’, revealed that this conceptual entity has no physical reality and, therefore, cannot be considered a meaningful description of a stable structural arrangement for metallic radiopharmaceuticals.

The notion of ‘macrocyclic cavity’ has become popular after Pedersen’s discovery of crown ethers in 1967 and has been used as a key theoretical hypothesis to explain the strong affinity of this class of macrocyclic ligands for alkali metal ions (Pedersen 1967). Since the outer electron distribution of an alkali metal ion always overlaps that of the noble gas that precedes it in the periodic table, the inherent inertness of this closed-shell electronic configuration prevents the formation of strong covalent bonds between the ligand and the cation. Therefore, to account for the high selectivity of crown ethers for alkali metal ions the model of ‘macrocyclic cavity’ was introduced. It has been argued that a stable coordination complex between the alkali metal cation and the crown ether can be formed when there exists an appropriate match between the size of the ion and the cavity size of the crown ether (Liou and Brodbelt 1992). In this example, the size of the cation is simply interpreted as its volume calculated from the value of its ionic radius, whereas the size of the macrocyclic cavity is conventionally determined by considering the bond distances of the main atoms surrounding the cavity and drawing its boundaries, as measured from X-ray diffraction data (Henrick et al. 1984; Henrick et al. 2007; Comba 1999; McNeil et al. 2022).

After its introduction in radiopharmaceutical chemistry, the macrocyclic ligand 2,2′,2″,2‴-(1,4,7,10-tetraazacyclododecane-1,4,7,10-tetrayl)tetraacetic acid (H₄DOTA) has been popularized as a kind of ‘universal’ polymetallic chelating agent (Stasiuk and Long 2013; Baranyai et al. 2020) able to form stable complexes with a multitude of metallic cations. This hypothetical universal coordination affinity of the DOTA ligand towards radiometals was initially rationalized by considering quantities such as the thermodynamic stability constant, the macrocyclic effect, and the strength of the metal-nitrogen bonds. However, the idea that a cationic radiometal binds H₄DOTA based on size fit with the interior of a hypothetical cavity associated with the macrocyclic ring has progressively gained widespread acceptance and, as a result, is often applied to the design of metallic radiopharmaceuticals particularly with the new emerging rare-earth radiometals (Stasiuk and Long 2013; Baranyai et al. 2020; Hancock 1992; Hancock and Martell 1989). Still, it is reasonable to ask whether this cavity really exists. When forming a metallic complex with H₄DOTA, do cationic radiometals truly enter this sort of virtual hole lurking within the macrocyclic ligand the same way alkali metal ions are trapped within crown ethers?

Although in the past years, various authors (Hancock 1992; Hancock and Martell 1989) had questioned the concept of size-match selectivity between the dimensions of the macrocyclic cavity and the radius of the metallic ion, in the radiopharmaceutical literature this intuitive and easy to understand model continues to be extensively utilized despite the lack of a scientifically rigorous analysis of its structural nature and real existence.

The concept of ‘macrocyclic ligand’ is closely related to that of ‘chelating ligand’ (Hancock and Martell 1989). Both types of ligands bind a metallic center with multiple coordinating atoms linked together by chemical bonds to form a polydentate ligand. In contrast, a monodentate ligand binds the metal atom through only one coordinating atom. When the chain of coordinating atoms in a polydentate ligand forms a closed loop, this gives rise to a ‘macrocyclic ligand’. It is exactly the size of this internal ring that inspired the concept of ‘macrocyclic cavity’.

The ‘macrocyclic chelate effect’ refers to the increase in thermodynamic stabilization of the metal complex when n monodentate ligands are replaced by a macrocyclic ligand containing the same n coordinating atoms connected in a ring (Hancock 1992; Hancock and Martell 1989). It is considered essentially an entropic effect generated by the decrease of free energy of the reaction of complex formation between the metal and the macrocycle brought about by the concomitant decrease of the entropy of reaction according to the equation ΔG° = ΔH° – TΔS° (where ΔG° is the change of standard free energy, ΔH° is the change in standard enthalpy, T is the absolute temperature and ΔS° is the change in standard entropy). Since the enthalpic term ΔH° is associated with the formation of new chemical bonds, its impact is considered negligible because the metal forms the same type of bond with a coordinating atom whatever it belongs to a monodentate or macrocyclic chelating ligand. Therefore, it is the entropic term that apparently governs the stabilization of the macrocyclic complex and a decrease in entropy leads to the favorable decrease of free energy. Among the entropic effects that are commonly held responsible for the decrease in entropy the close matching between the size of the metal ion and that of the hypothetical macrocyclic cavity is also included. As discussed below, the notion of macrocyclic cavity is not rigorously defined and, moreover, it is not even necessary to explain the experimental facts. Instead, it will be argued that it is precisely the metal electronic properties that determine the observed chemical behavior (Hancock 1992; Hancock and Martell 1989) and that the entropic factor associated with the model of the hypothetical macrocyclic cavity is largely redundant.

The simple geometrical model illustrated below has been used to analyze and question the concept of ‘macrocyclic cavity’.

Figure 1 shows an idealized drawing of the chemical structure of the H₄DOTA ligand (Stasiuk and Long 2013) and the position of the hypothetical spherical cavity at the center of the plane defined by the four coordinating nitrogen atoms. The circle marked in red is generated by the intersection of this plane with the surface of the spherical cavity along the equatorial line.

Idealized drawing of the structure of the H₄DOTA ligand and of the location of the hypothetical ‘macrocyclic cavity’ assumed to be of spherical shape (not shown) and positioned at the center of the N4 plane. The red line is the circumference generated by the intersection of the sphere with the N4 plane

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To better illustrate this model, it is convenient to imagine that the DOTA macrocycle is coordinated to a Ga³⁺ ion as exemplified by a large number of Ga-DOTA complexes and ⁶⁸ Ga-DOTA radiopharmaceuticals (Viola et al. 2006; Davey and Paterson 2022). In Fig. 2, the green ball represents a Ga⁺³ ion placed in the center of the plane defined by the four nitrogen atoms of the H₄DOTA ligand, R is the radius of the hypothetical spherical cavity, and L is the Ga–N bond distance (Pyykkö and Atsumi 2009).

Idealized drawing of the coordination of a Ga³⁺ ion inside the hypothetical spherical cavity (not shown) located at the center of the plane defined by the four coordinated nitrogen atoms. L is the Ga–N bond distance, R is the radius of the cavity, and the red circle is the circumference generated by the intersection of the spherical hole with the N4 plane

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Pictorial representation of the location of the Ga³⁺ ion relative to the N4 plane in a generic Ga(DOTA) complex as determined by X-ray crystal data (Viola et al. 2006)

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The lesson that can be drawn from these observations is that electronic factors are always predominant in determining the structure of a metal complex and, in turn, of metallic radiopharmaceuticals. More precisely, it is the electronic configuration of the metal ion and the energy distribution and symmetry of molecular orbitals that shape the structure of a coordination compound. Electronic factors (i.e., enthalpic) govern the formation of chemical bonds and establish their characteristic lengths that are almost completely independent of steric (i.e., entropic) factors. Ultimately, electronic factors dictate the spatial arrangement of the ligands around the metallic center, thus controlling the final geometry of a metal complex. In short, it is the ligand that adapts to the metal and not the reverse. These considerations raise many questions about the real existence of a hypothetical cavity inside the DOTA macrocyclic ligand and question the widespread habit of designing the structure of a metallic radiopharmaceutical based on the matching between the size of the ion and the dimensions of the elusive cavity.

H₄DOTA:

Authors and Affiliations

1. Department of Chemical and Pharmaceutical Sciences, University of Ferrara, Via L. Borsari, 46, 44121, Ferrara, Italy

Contributions

AD provided the scientific design of the present work, wrote all sections, and created all figures.

Corresponding author

Correspondence to
Adriano Duatti.

Ethics approval and consent to participate

Consent for publication

Competing interests

The author declares that he has no competing interests.

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