197
6 Quantum Chemical Approaches in Modeling the Structure of DNA …
the circulene stacking complexes with G-quartet by DFT method [107]. We have
proposed a G-octet as a simple and convenient model to study quadruplex-ligand
binding, quite adequate at least in the case of neutral ligands that do not interact
with phosphate DNA backbone [96].
“Pure” QM methods have some intrinsic limitations, including e.g. insufficient
sampling of conformational space and difficulties with modeling the systems evolving in time. These problems can be successfully overcome by MD approaches. In
the studies of large biomacromolecules QM and MM methods are sometimes combined into a single relatively fast QM/MM approach where only a functionally important part of the system is modelled with QM, whereas the most of the molecule
is modelled using MM [121]. Application of combined quantum and molecular
mechanical methods focuses on predicting activation barriers and the structures of
stationary points for organic and biomolecular reactions. Characterization of the
factors that stabilize transition structures in solution and in active sites of biomolecules provides a basis for design and optimization of catalysts and drugs [122, 123].
Combined QM and MM methods were applied to investigate the nature of stacking interactions in triple stacks of guanine quartets which is a central part of the
human telomeric DNA and a drug target [124]. In this fundamental theoretical work
Clay and Gould studied in detail the differences in the human telomeric structures,
including the structural changes observed upon changing the potassium to sodium
cation. The QM calculations were carried out at the DFT B3LYP and HF levels of
theory using the 3–21G* and 6–31G** basis sets. The molecular dynamics simulations were carried out using the AMBER8 suite of programs with the Cornell force
field [125, 126]. It was concluded that the sodium filled guanine core may appear to
be energetically more stable than for the potassium case from the QM calculations,
but the partial QM optimization indicated that the guanine core is not stable and the
MD simulations showed that even with the DNA structure present, the core does
not remain stable. This could be due to the fact that the structure was based on the
potassium form and not the sodium one which has a different strand pattern and the
bases are a mixture of syn and anti conformations rather than just anti.
Another work that employed the combined QM/MM method studied the interaction of preclinical 9-aminoacridine anticancer derivatives with a human telomeric
quadruplex [127]. The mixed pseudo-bond ab initio QM/MM approach was used
along with a molecular docking and MD simulations of G4-ligand complexes. For
the QM/MM calculations, the DNA-ligand system resulting from the docking study
was first partitioned into a QM subsystem and an MM subsystem. The reaction system used a smaller QM subsystem consisting of the ligand and bases within 3.5 Å,
whereas the rest of the system (the MM subsystem) was treated using the AMBER
force field, together with a low memory convergence algorithm. The boundary problem between the QM and MM subsystems was treated using the pseudo-bond approach. With this quadruplex-substrate QM/MM system, an iterative optimization
procedure was applied, using B3LYP/3-21G* QM/MM calculations, leading to an
optimized structure for the reactants. The convergence criterion used was set to obtain an energy gradient below 10
-4
, using the twin-range cut-off method for nonbonded interactions, with a long-range cut-off of 14 Å and a short-range cut-off of
6 Quantum Chemical Approaches in Modeling the Structure of DNA …
the circulene stacking complexes with G-quartet by DFT method [107]. We have
proposed a G-octet as a simple and convenient model to study quadruplex-ligand
binding, quite adequate at least in the case of neutral ligands that do not interact
with phosphate DNA backbone [96].
“Pure” QM methods have some intrinsic limitations, including e.g. insufficient
sampling of conformational space and difficulties with modeling the systems evolving in time. These problems can be successfully overcome by MD approaches. In
the studies of large biomacromolecules QM and MM methods are sometimes combined into a single relatively fast QM/MM approach where only a functionally important part of the system is modelled with QM, whereas the most of the molecule
is modelled using MM [121]. Application of combined quantum and molecular
mechanical methods focuses on predicting activation barriers and the structures of
stationary points for organic and biomolecular reactions. Characterization of the
factors that stabilize transition structures in solution and in active sites of biomolecules provides a basis for design and optimization of catalysts and drugs [122, 123].
Combined QM and MM methods were applied to investigate the nature of stacking interactions in triple stacks of guanine quartets which is a central part of the
human telomeric DNA and a drug target [124]. In this fundamental theoretical work
Clay and Gould studied in detail the differences in the human telomeric structures,
including the structural changes observed upon changing the potassium to sodium
cation. The QM calculations were carried out at the DFT B3LYP and HF levels of
theory using the 3–21G* and 6–31G** basis sets. The molecular dynamics simulations were carried out using the AMBER8 suite of programs with the Cornell force
field [125, 126]. It was concluded that the sodium filled guanine core may appear to
be energetically more stable than for the potassium case from the QM calculations,
but the partial QM optimization indicated that the guanine core is not stable and the
MD simulations showed that even with the DNA structure present, the core does
not remain stable. This could be due to the fact that the structure was based on the
potassium form and not the sodium one which has a different strand pattern and the
bases are a mixture of syn and anti conformations rather than just anti.
Another work that employed the combined QM/MM method studied the interaction of preclinical 9-aminoacridine anticancer derivatives with a human telomeric
quadruplex [127]. The mixed pseudo-bond ab initio QM/MM approach was used
along with a molecular docking and MD simulations of G4-ligand complexes. For
the QM/MM calculations, the DNA-ligand system resulting from the docking study
was first partitioned into a QM subsystem and an MM subsystem. The reaction system used a smaller QM subsystem consisting of the ligand and bases within 3.5 Å,
whereas the rest of the system (the MM subsystem) was treated using the AMBER
force field, together with a low memory convergence algorithm. The boundary problem between the QM and MM subsystems was treated using the pseudo-bond approach. With this quadruplex-substrate QM/MM system, an iterative optimization
procedure was applied, using B3LYP/3-21G* QM/MM calculations, leading to an
optimized structure for the reactants. The convergence criterion used was set to obtain an energy gradient below 10
-4
, using the twin-range cut-off method for nonbonded interactions, with a long-range cut-off of 14 Å and a short-range cut-off of