193
6 Quantum Chemical Approaches in Modeling the Structure of DNA …
as guanine quartet, and forces stabilizing them include π-π-interactions between the
quartets, thus quantum chemical calculations with G-octets are much more complicated and require more computational resources.
Characterization of the monovalent ion position and hydrogen-bond network
in guanine quartets and octets by DFT calculations of NMR parameters was performed by van Mourik and Dingley [110]. The structures of the guanine quartets
at C 4h and S 4 symmetry (G4 and G4-M
+
systems) were fully optimized using the
B3LYP and B97 [111] functionals employing basis sets ranging from 6-31G(d) to
6-311 + + G(d, p) with NWChem software [112]. At the same time, only constrained
optimization was carried out for more complex G4-M
+
-G4 and G4-M
+
-G4-M
+
systems keeping the quartet-quartet distances fixed. Similar calculations using Gaussian 03 package failed to converge or converged to an alternative structure containing
bifurcated hydrogen bonds, whereas using NWChem both the Hoogsteen H-bonded
structure obtained in crystallographic and NMR studies, as well as the bifurcated
structure could be optimized. It was shown that the presence of a monovalent ion
in the centre of G-quartet led to the contraction of the quartet O6–O6 distance. This
effect was largest for the smallest ion, thus showing that the contraction of the Gquartet facilitates the optimal coordination of the monovalent ion with the O6 atoms
of the guanine bases. In addition, cation localization sites were found for G-octets
with the distances between G-quartet planes ranging from 3.3 to 5.2 Å. The results
for the G 4 -M
+
-G 4 model showed that at quartet–quartet distances observed in the
DNA quadruplex crystal structures, the smaller Na
+
and Li
+
cations have two shallow minima located at 0.55 and 0.95 Å outside the plane of the quartet, respectively.
At the same time, the larger K
+
ion has a minimum centred between successive
G-quartets. At increasing quartet–quartet distances the Na
+
and Li
+
ions converged
to a position coplanar with the G-quartet, whereas the optimal K
+
ion position converged to a location just outside the G-quartet. Apparently at shorter quartet–quartet
distances the sodium and lithium cations are weakly attracted to the second G-quartet and therefore do not favour a coplanar position with the G-quartet. Increasing
the quartet–quartet distance reduces this weak attraction to zero and the Na
+
and Li
+
ions shift to an energetically favoured coplanar position. The attraction of the ion to
both G-quartets at quartet–quartet distances observed in DNA quadruplex structures
may facilitate the transport of the ions through the DNA quadruplex central channel.
The smaller Li
+
and Na
+
ions have rather low energy barriers separating the minima
in the quartet-ion-quartet model that under physiological conditions are most likely
overcome by vibrational and thermodynamic effects. Consequently, their movement through the channel is energetically unimpeded, in contrast to larger K
+
ion
that will not move as freely.
An interesting work [98] that we have already mentioned as the paper where
the mixed G-quartet structure was presented, applied the electrospray ionization
mass spectrometry (ESI-MS) to investigate hydrogen-bonded G-quartets and their
complexes. ESI analysis displayed magic numbers of guanine tetramer adducts with
Na
+
, Li
+
and K
+
, not only for guanine, but also for xanthine bases. The optimized
structures of guanine and xanthine quartets have been determined by B3LYP hybrid
DFT calculations. The optimized structures obtained for each quartet explained the
6 Quantum Chemical Approaches in Modeling the Structure of DNA …
as guanine quartet, and forces stabilizing them include π-π-interactions between the
quartets, thus quantum chemical calculations with G-octets are much more complicated and require more computational resources.
Characterization of the monovalent ion position and hydrogen-bond network
in guanine quartets and octets by DFT calculations of NMR parameters was performed by van Mourik and Dingley [110]. The structures of the guanine quartets
at C 4h and S 4 symmetry (G4 and G4-M
+
systems) were fully optimized using the
B3LYP and B97 [111] functionals employing basis sets ranging from 6-31G(d) to
6-311 + + G(d, p) with NWChem software [112]. At the same time, only constrained
optimization was carried out for more complex G4-M
+
-G4 and G4-M
+
-G4-M
+
systems keeping the quartet-quartet distances fixed. Similar calculations using Gaussian 03 package failed to converge or converged to an alternative structure containing
bifurcated hydrogen bonds, whereas using NWChem both the Hoogsteen H-bonded
structure obtained in crystallographic and NMR studies, as well as the bifurcated
structure could be optimized. It was shown that the presence of a monovalent ion
in the centre of G-quartet led to the contraction of the quartet O6–O6 distance. This
effect was largest for the smallest ion, thus showing that the contraction of the Gquartet facilitates the optimal coordination of the monovalent ion with the O6 atoms
of the guanine bases. In addition, cation localization sites were found for G-octets
with the distances between G-quartet planes ranging from 3.3 to 5.2 Å. The results
for the G 4 -M
+
-G 4 model showed that at quartet–quartet distances observed in the
DNA quadruplex crystal structures, the smaller Na
+
and Li
+
cations have two shallow minima located at 0.55 and 0.95 Å outside the plane of the quartet, respectively.
At the same time, the larger K
+
ion has a minimum centred between successive
G-quartets. At increasing quartet–quartet distances the Na
+
and Li
+
ions converged
to a position coplanar with the G-quartet, whereas the optimal K
+
ion position converged to a location just outside the G-quartet. Apparently at shorter quartet–quartet
distances the sodium and lithium cations are weakly attracted to the second G-quartet and therefore do not favour a coplanar position with the G-quartet. Increasing
the quartet–quartet distance reduces this weak attraction to zero and the Na
+
and Li
+
ions shift to an energetically favoured coplanar position. The attraction of the ion to
both G-quartets at quartet–quartet distances observed in DNA quadruplex structures
may facilitate the transport of the ions through the DNA quadruplex central channel.
The smaller Li
+
and Na
+
ions have rather low energy barriers separating the minima
in the quartet-ion-quartet model that under physiological conditions are most likely
overcome by vibrational and thermodynamic effects. Consequently, their movement through the channel is energetically unimpeded, in contrast to larger K
+
ion
that will not move as freely.
An interesting work [98] that we have already mentioned as the paper where
the mixed G-quartet structure was presented, applied the electrospray ionization
mass spectrometry (ESI-MS) to investigate hydrogen-bonded G-quartets and their
complexes. ESI analysis displayed magic numbers of guanine tetramer adducts with
Na
+
, Li
+
and K
+
, not only for guanine, but also for xanthine bases. The optimized
structures of guanine and xanthine quartets have been determined by B3LYP hybrid
DFT calculations. The optimized structures obtained for each quartet explained the