Guanine tetrads interacting with metal ions. An AIM topological analysis of the electronic density

The interaction of guanine tetrads with various alkaline, alkaline earth and transition metal ions has been studied by means of an AIM topological analysis of the electronic density based on density functional calculations.

The interaction between metal ion and ligand has been characterized in terms of the Laplacian of the electronic density, the Hamiltonian kinetic energy density and the Lagrangian kinetic energy density.

The influence of the metal ion–ligand interaction on tetrad hydrogen bonding is also discussed.


Guanine tetrads (or quartets) represent an unusual, yet important assembly of nucleic acid bases.

They have been investigated by fiber X-ray crystallography about 40 years ago, even though they have been discovered much earlier.1

Now they are an active area of research again because they are important building blocks of DNA and RNA tetraplex structures.2–4

Tetraplex forming sequence motifs occur in telomeres at the ends of linear chromosomes.

The proposed function of telomeres is maintenance of the structural integrity of the genome and insurance of complete replication at the chromosome termini.

Similar sequence motifs do also occur in regulatory regions of oncogenes.

Tetrads also play a role in supra-molecular chemistry, for example, guanosine analogs perform a self-assembly in columnar aggregates in the presence of cations.5

Metal cations are indeed well known to be necessary for the formation of tetraplexes structures.

They induce a stabilization following the order K+ > Rb+ > NH4+ > Na+ > Cs+ > Li+ for the monovalent ones, and Sr2+ > Ba2+ > Ca2+ > Mg2+ for the divalent ones.1

Considering the ionic radii of these ions, it appears that a radius of approximately 1.2 Å is optimal.1

This led to the idea that the stabilization is due to an optimal ratio of the cation size and the size of the cavity formed by the four guanines in the tetrad.

The experimental studies on tetraplexes that followed have confirmed that the metals were very close to the axis, ions with large radii like K+ are located int the cavity between two quartets, whereas ions with smaller radii like Na+ may be located also in the central cavity of a single tetrad.

For the cation selectivity of tetrads also solvation energies seem to have to be taken into account.6

Guanine tetrads have also been investigated by quantum chemical studies.

In order to assess the stability of such biomolecular complexes, Hartree–Fock,7,8 and then DFT calculations showed that the bases can be linked in a Hoogsteen (Fig. 1b) pairing or by bifurcated H-bonds between N1-H, N2-H and O6 (Fig. 1a).7,9,10

However, the energy difference between the two conformations is very small and thus the relative energy depends on the quantum chemical method adopted.

Calculations have also been undertaken in our group9,11 or in others8 for metallated tetrads, in the centre of the cavity or next to it.

Such a bifurcated structure has not been found when cations are located in the central cavity formed by the tetrad.8

From these facts it has been concluded that the metal ions change the hydrogen bond pattern in guanine tetrads.

Meanwhile, quantum chemical calculations have been extended to sandwich type complexes formed by two guanine tetrads and a cation12 and to several other tetrads reviewed in .ref. 3

Tetrads have been investigated by different techniques, e.g. NMR spectroscopy, molecular dynamics and quantum chemistry, but the nature of the metal ion–ligand bonding seems controversial.

On the basis of molecular dynamics calculations, Ross and Hardin viewed the interaction as covalent13 while Gu and Lesczcynski imagined an electrostatic bonding analysing the electrostatic potential of quantum calculations.7

Here we analyse the guanine tetrad metal ligand interaction by means of the Atoms In Molecules (AIM) method.

The AIM theory has proved itself a valuable tool to conceptually define what is an atom, and above all what is a bond in a quantum calculation of a structure of a molecule.14

The AIM theory has been applied to such systems as Van der Waals complexes or hydrogen bonded complexes15 and more recently to characterize interactions between metal ions and ligands.16

In the field of nucleic acids, the AIM formalism has been used for nucleosides,17 nucleic base pairing18 and guanine tetrads,19 and the interaction of a magnesium ion with a base pair has also been studied.20

The reader is addressed to ref. 14 for proper definition of bonding, bond paths, critical points on the basis of electronic density, its gradient and Laplacian, and to ref. 17 for a short summary of how it is employed in hydrogen bonding analysis.

Using a similar approach, we perform an analysis of the interaction of the metal ion and the guanine ligand, and its influence on the tetrad structure and hydrogen bonding network, all of this on the basis of the analysis of the AIM topology of the electronic density, as a complementary study of the energetical one,9,11 which only provides global, and not local information on molecular structure.

Computational details

We have investigated complexes consisting of guanine tetrads and the mono- and divalent ions Li+, Na+, K+, Cu+, Be2+, Mg2+, Ca2+ and Zn2+.

Fig. 1 displays the atom numbering and chemical structure of guanine tetrads in the Hoogsteen and two bifurcated conformations (thereafter referred as G4).

For comparison we have also taken into account square planar complexes of these ions with formamide, since this molecule mimics the part of the pyrimidine ring that is relevant for metal ion binding.

The geometries have been optimised at various levels of theory in the present study and in a previous paper.9,11

The B3LYP21/DZVP22//B3LYP/DZVP level has been retained for the analysis of the electronic density, in both C4h (planar) and S4 symmetry group structures, using the Gaussian 98 software.23

For the K+ complex, it has to be noted that the C4h geometry is not a true minimum, the minimum being in a C4 symmetry, with the potassium ion out of the plane formed by the guanine units.

For comparison, square planar complexes of the same metal ions with four formamide molecules have been optimised at the same level of theory.

Coordinates of the optimised structures have been provided (Fig. 2).

The AIM analysis has been performed with the AIM 2000 code,24 with all default options.

Integration of atomic properties over the atomic basins have been performed in natural coordinates, with a tolerance of 10−4 per integration step.

The radius of the beta sphere used for integration of atomic properties (default value 0.5 a.u.) had sometimes to be set to 0.4 a.u., when the bond critical point (BCP) was too close to the nucleus.

Results and discussion

Metal ion–ligand bonding

The topological analysis of metal ion ligand bonding not only requires a study of the density and density Laplacian along the bond path, like in the case of atoms of the second period, but also an investigation of the energetic densities between the metal ion and the ligand atoms.

In this case, it is completed with the Hamiltonian kinetic energy H(r), and Lagrangian kinetic energy G(r).

Fig. 3 shows the molecular graph of a metallated tetrad.

The covalent Lewis bonding scheme between ligand atoms is revealed by the bond paths.

In addition, intermolecular, Hoogsteen type (with only two exceptions, Be2+ and Mg2+, which show a type b bifurcated (Fig. 1c) structure), hydrogen bonding is also characterized, as depicted in .ref. 19

The metal ion–ligand bonding is also characterized by a bond path and a BCP between the metal and each of the four O6 oxygen atoms.

For the Li+ and Be2+ tetrad complexes, a supplementary bond path exists between two O6 ligands (as can be noted in Fig. 4).

This occurs because the electronic density envelope of such small metal ions is overwhelmed by the one of the oxygen atoms.

The metal ion–ligand interaction is the one on which we concentrate in this paragraph.

Fig. 5 shows the metal ion–ligand interaction in detail, with density contours of the function L(r), which is the opposite of the Laplacian (Fig. 5a) and of the Hamiltonian kinetic energy H(r) (Fig. 5b).

A negative L(r) at the BCP is supposed to be typical of a closed shell interaction.

Correlatively, H(r) is positive at the BCP in such a case.14

In the case of interactions involving transition metals, though, the correlation is not confirmed and a further study of G(r)/ρ(r) at the BCP is required to characterize the interaction as electrostatic or covalent.16

In Table 1, the corresponding data are listed.

For alkaline and alkaline earth metal interactions, L(r) = −lap(r) is negative and H(r) is positive (this means for all metals except for Cu+ and Zn2+), while for transition metal interactions (Cu+ and Zn2+), both are negative, which is typical of transition metal ions in general.16

The key factor is thus G(r)/ρ(r), which is greater than unity in all cases.

This leads to the conclusion that the nature of the interaction between the metal ion and ligand is electrostatic16 for all metal ions, including transition metals, according to the analysis of the electronic density.

Influence on tetrad structure

In order to understand how the presence of the metal cation affects the stability of the tetrad, we also analysed the topology of the electronic density of each involved hydrogen bond, comparing it with the same analysis of non-metallated tetrads.19

We also compared our structures with square planar complexes of the same metal ions with four formamide ligands.

The formamide molecule is chemically very similar to the guanine part of the molecule involved in the ligand interaction, but presents less steric strain than the guanine ligand (Fig. 4).

The use of formamide tetrads allowed us to gain insight into the effect of the metal on the guanine quartet structure: without any metal the cavity (evaluated by the distance of the oxygen atoms from the center) is bigger for the formamide complex than the guanine tetrad cavity.

When a metal ion binds to the tetrad, the cavity narrows, and one can see from Fig. 4 that the size of the cavity depends mostly on the nature of the metal and clearly depends less on the nature of the ligand.

This is remarkable because one could expect that the steric constraints would prevent the guanine tetrads cavities to narrow to the same level as the formamide ones.

One way to interpret this is to consider that the metal–oxygen electrostatic attraction would be the most important driving force on the tetrad structure modification upon metallation.

We shall now look at the effect of the metal presence on the hydrogen bonds.

We can first point out that the structure are almost all of the Hoogsteen type, as the molecular graphs pointed out, except for the structures of C4 symmetry containing Be2+ or Mg2+ ions, which are bifurcated, possessing a weak H1⋯N7 hydrogen bond in addition to the two Hoogsteen bonds.

It has to be pointed out that this bifurcated structure (Fig. 1c) is different (in fact, opposite) to the bifurcated structure encountered in non-metallated tetrads (Fig. 1a).19

In this latter case, the repulsion of the oxygens of the cavity were tending to make the guanines repel each other.

In the present case, on the contrary, the double charged metal ion electrostatically attracts the guanines closer to the center of the cavity.

In the tetrad metal ion complex, the H1⋯O6 hydrogen bond presents a different behaviour from the H2⋯N7 bond.

Firstly it can be seen on Fig. 6a, where the electronic density of the H bond has been plotted against the donor–acceptor distance for all tetrads: the correlation for a 2nd order polynomial is higher for the latter (R = 0.999 for H2⋯N7) than for the former (R = 0.988 for H1⋯O6).

This shows that several phenomena interfere in the geometry of the bond closer to the center (H1⋯O6), whereas for the second (H2⋯N7) there is only an indirect influence of the metal, and its behaviour is thus more predictable.

Secondly, one would expect that the narrowing of the tetrad cavity would decrease the H1⋯O6 distance and enhance the hydrogen bond, but this is not the case.

In fact, at our level of calculation, there is no correlation between the H1⋯O6 hydrogen bond strength (as measured by the density and the density Laplacian at the BCP) and the metal–oxygen distance (Fig. 6).

This can be explained by taking into account the repulsion between the positively charged H1 and the metal.

We have then obtained optimised structures of formamide complexes containing the common Na+ ion, in which the M–O distance had been constrained at a wide range of values.

When this distance was reduced, the hydrogen bond strength was following an evolution far from monotonous.

The H2⋯N7 hydrogen bond is slightly correlated with the M–O distance: as one would expect, the bond strengthens while the cavity narrows, but it is only a very rough trend and some metals do not follow it, in particular the smallest of them.

The explanation may lie in the differences between the S4 and C4 structures and the deformations that the metal ions cause: for Na+, K+ and Ca2+, there is no or very little difference between the two geometries of different symmetry, but as the metal becomes smaller, it favours a tetrahedral coordination, which greatly favours an S4 geometry in which it becomes possible to come closer to an ideal tetrahedron for the first coordination sphere (Fig. 7).

This in turn provokes a proportional deviation of the guanines from the S4 plane.

For such ions as Li+, Cu+, Mg2+ and Zn2+ the deformation is high, while with Be2+ the quartet is very near to dislocation.

As a matter of fact, these ions are not the best suited to favour the formation of quadruplexes.1

This reflects their tendency to dislocate the tetrad structure.


The topological study of the electronic density of the interaction between a metal ion and guanine tetrads thus sheds light on the nature of the bonding between metal ion and ligand.

It also allows one to characterize the influence of this interaction on the structure of the tetrad itself, via its network of hydrogen bonding.

The metal ion–ligand interaction may thus be viewed as electrostatic in nature, and this, in turn, is recognized to be the driving force of sometimes dramatic geometrical rearrangements of guanine tetrads upon metallation.

When forced to stay in a planar conformation (C4h), some metals distort the Hoogsteen hydrogen bond network to a new bifurcated structure.

When allowed to relax in a three dimensional conformation (S4), it may distort until it almost breaks its original hydrogen bond network.