195
6 Quantum Chemical Approaches in Modeling the Structure of DNA …
was optimized at the PCM/M052X/6-31G(d) level. Although the absence of the
sugar-phosphate backbone does not allow detailed comparison of computation results with experimental data on G-quadruplex DNA, the developed model was able
to reproduce the different location of K
+
and Na
+
ions within the G-quadruplexes.
A similar inter-quartet distance was obtained for Na
+
(3.35 Å) and K
+
(3.36 Å), in
agreement with NMR measurements. As expected, independently of the type of
cation, the two 9-Me-G involved in the electronic transition adopt the structure of
a 9-Me-G
+
cation and a 9-Me-G
−
anion. The position of all the ions changes with
respect to that found in the ground state minimum. The metal ions lose the symmetric arrangement with respect to the G-quadruplex axis; they move farther from the
9-Me-G
+
cation and get closer to the 9-Me-G
−
anion.
As to the cation-free octets, we have determined the structures and energies of
guanine quartets and octets in water by DFT calculations using M06-2X functional
and 6-31G(d, p) basic set [96]. Guanine quartets in vacuum were found to have not
only the Hoogsteen or bifurcated, but also mixed system of hydrogen bonds; in water the latter two forms are transformed into the classic Hoogsteen-type structure, as
it has been mentioned above. Four stable configurations of G-octets with D 4 , C 4 and
S 4 symmetry formed by the pairs of guanine quartets with Hoogsteen, bifurcated or
mixed system of H-bonds were identified. In contrast to G-quartets, the most stable
structure of G-octet in aqueous medium was shown to be S 4 -symmetric assembly
consisting of the pair of mixed Hoogsteen-bifurcated type G-quartets.
Protonation of guanine quartets and a two-plane guanine quartet stack was
studied [117]. For G-quartets, the optimized geometries were obtained at the
B3LYP/LACVP** level of theory. Relative energies were obtained by performing single point calculations at the B3LYP/6-311 + G(2df, p) level for G 4 and B3LYP/6-311 + G(d, p) level for G-octet. The singly protonated G 4 complex prefers
protonation at the Watson–Crick face of the O6 moiety. However, all multi-protonated G 4 complexes were found to favour protonation at the Hoogsteen face of the
O6 base centres. The proton affinities were also calculated for the addition of one,
two, three and four protons to the central oxygens of G 4 and compared with those
of monomeric guanine and other biochemically appropriate bases. These results
suggest that guanine quartet unit might reasonably readily accept two protons. For
the singly to quadruply protonated octets, the added protons prefer to distribute
over both planes with maximally two per plane. Furthermore, unlike the (G 4 -nH
+
)
complexes (n > 2), protonation at the Watson–Crick faces of the O6 moieties was
found to be preferred for all protonation states. In addition, (2G 4 -nH
+
) complexes
(n = 1–4) were also obtained in which inter-plane hydrogen bonds were formed, effectively enabling the protons to “sit between” the planes.
Thus QM methods, primarily DFT calculations, have been successfully used to
study guanine quartets and octets and their interactions. It should be remembered
however that while the conventional DFT is much superior to MM force fields and
can accurately calculate H-bonding in G-quartets and guanine-cation interactions,
most DFT functionals do not account for π-π-stacking and therefore cannot correctly describe the interactions between different G-quartets [68]. In order to accurately calculate stacking interactions, one can alternatively employ e.g. the MP2
6 Quantum Chemical Approaches in Modeling the Structure of DNA …
was optimized at the PCM/M052X/6-31G(d) level. Although the absence of the
sugar-phosphate backbone does not allow detailed comparison of computation results with experimental data on G-quadruplex DNA, the developed model was able
to reproduce the different location of K
+
and Na
+
ions within the G-quadruplexes.
A similar inter-quartet distance was obtained for Na
+
(3.35 Å) and K
+
(3.36 Å), in
agreement with NMR measurements. As expected, independently of the type of
cation, the two 9-Me-G involved in the electronic transition adopt the structure of
a 9-Me-G
+
cation and a 9-Me-G
−
anion. The position of all the ions changes with
respect to that found in the ground state minimum. The metal ions lose the symmetric arrangement with respect to the G-quadruplex axis; they move farther from the
9-Me-G
+
cation and get closer to the 9-Me-G
−
anion.
As to the cation-free octets, we have determined the structures and energies of
guanine quartets and octets in water by DFT calculations using M06-2X functional
and 6-31G(d, p) basic set [96]. Guanine quartets in vacuum were found to have not
only the Hoogsteen or bifurcated, but also mixed system of hydrogen bonds; in water the latter two forms are transformed into the classic Hoogsteen-type structure, as
it has been mentioned above. Four stable configurations of G-octets with D 4 , C 4 and
S 4 symmetry formed by the pairs of guanine quartets with Hoogsteen, bifurcated or
mixed system of H-bonds were identified. In contrast to G-quartets, the most stable
structure of G-octet in aqueous medium was shown to be S 4 -symmetric assembly
consisting of the pair of mixed Hoogsteen-bifurcated type G-quartets.
Protonation of guanine quartets and a two-plane guanine quartet stack was
studied [117]. For G-quartets, the optimized geometries were obtained at the
B3LYP/LACVP** level of theory. Relative energies were obtained by performing single point calculations at the B3LYP/6-311 + G(2df, p) level for G 4 and B3LYP/6-311 + G(d, p) level for G-octet. The singly protonated G 4 complex prefers
protonation at the Watson–Crick face of the O6 moiety. However, all multi-protonated G 4 complexes were found to favour protonation at the Hoogsteen face of the
O6 base centres. The proton affinities were also calculated for the addition of one,
two, three and four protons to the central oxygens of G 4 and compared with those
of monomeric guanine and other biochemically appropriate bases. These results
suggest that guanine quartet unit might reasonably readily accept two protons. For
the singly to quadruply protonated octets, the added protons prefer to distribute
over both planes with maximally two per plane. Furthermore, unlike the (G 4 -nH
+
)
complexes (n > 2), protonation at the Watson–Crick faces of the O6 moieties was
found to be preferred for all protonation states. In addition, (2G 4 -nH
+
) complexes
(n = 1–4) were also obtained in which inter-plane hydrogen bonds were formed, effectively enabling the protons to “sit between” the planes.
Thus QM methods, primarily DFT calculations, have been successfully used to
study guanine quartets and octets and their interactions. It should be remembered
however that while the conventional DFT is much superior to MM force fields and
can accurately calculate H-bonding in G-quartets and guanine-cation interactions,
most DFT functionals do not account for π-π-stacking and therefore cannot correctly describe the interactions between different G-quartets [68]. In order to accurately calculate stacking interactions, one can alternatively employ e.g. the MP2