196
M. Ilchenko and I. Dubey
method. Nice example is a recent work [118] examining how guanine base stacking
influences the stability of G-quadruplexes. Quartet models were created by first
performing QM geometry optimization of a single G-tetrad at the MP2/6-31(d, p)
level. The optimized tetrad was then used to create models for single-point energy
calculations and structural characterization, which contain two parallel G-tetrads
with a single central K
+
ion. The geometries of stacked tetrads were varied by their
separation and relative rotation. Single-point interaction energy calculations used to
create energy landscapes were performed at the MP2 level using the modified split
valance basis set 6-31G*(0.25). The calculations of stacked G-tetrads revealed large
energy differences of up to 12 kcal/mol between different experimentally observed
geometries at the interface of stacked G-quadruplexes. Energy landscapes were also
computed using an AMBER molecular mechanics description of stacking energy
and were shown to agree quite well with QM calculated landscapes.
Nowadays, old issue of deficient description of stacking interactions in DFT has
been satisfactorily resolved, and many current DFT approaches include quite well
the dispersion energy. The most popular and computationally most effective way
to do so is to add well-calibrated empirical dispersion force-field-like correction
to the DFT electronic structure calculations [47]. New empirical dispersion corrections such as D3 (DFT-D3) can be successfully applied for the study of G-quartet
systems [119].
Gradient optimization of a two-quartet structure (i.e. G-octet) can result in BSSE
error originating from the incompleteness of the basis set of atomic orbitals and
causing an artefactual stabilization of complexes. As has been already mentioned,
this error can be corrected for single-point calculations by employing the standard
counterpoise method [101]. It should be mentioned that empirical dispersion corrections are also able to absorb small BSSE effects [120].
6.3.2.4 QM and QM/MM Modelling of Small Organic Molecules Binding
to G4 DNA
Determining the accurate structures of guanine quartets and their stacks is a key
step in the development of specific G4 ligands using the computer modelling approaches. However, drug design is based on studying the interactions of potential
ligands with their biomolecular targets, in this case quadruplex DNA. Molecular
dynamics is most often employed in these studies. G-quadruplexes for which X-ray
and NMR structures are available are large molecular systems (from 500 to 1000
atoms) that cannot be easily computed with non-empirical QM methods. For this
reason, quadruplex fragments can be used as G4 models to perform quantum chemical studies on ligand binding. Of course, the optimization of ligand structures is
routinely performed by QM calculation methods, usually DFT (often followed by
the manual docking of the optimized ligand onto G4 target and MD simulations of
quadruplex-ligand interaction).
Theoretical calculations applying the “pure” QM method to the studies on quadruplex-ligand binding are quite rare. We have already mentioned a work studying
M. Ilchenko and I. Dubey
method. Nice example is a recent work [118] examining how guanine base stacking
influences the stability of G-quadruplexes. Quartet models were created by first
performing QM geometry optimization of a single G-tetrad at the MP2/6-31(d, p)
level. The optimized tetrad was then used to create models for single-point energy
calculations and structural characterization, which contain two parallel G-tetrads
with a single central K
+
ion. The geometries of stacked tetrads were varied by their
separation and relative rotation. Single-point interaction energy calculations used to
create energy landscapes were performed at the MP2 level using the modified split
valance basis set 6-31G*(0.25). The calculations of stacked G-tetrads revealed large
energy differences of up to 12 kcal/mol between different experimentally observed
geometries at the interface of stacked G-quadruplexes. Energy landscapes were also
computed using an AMBER molecular mechanics description of stacking energy
and were shown to agree quite well with QM calculated landscapes.
Nowadays, old issue of deficient description of stacking interactions in DFT has
been satisfactorily resolved, and many current DFT approaches include quite well
the dispersion energy. The most popular and computationally most effective way
to do so is to add well-calibrated empirical dispersion force-field-like correction
to the DFT electronic structure calculations [47]. New empirical dispersion corrections such as D3 (DFT-D3) can be successfully applied for the study of G-quartet
systems [119].
Gradient optimization of a two-quartet structure (i.e. G-octet) can result in BSSE
error originating from the incompleteness of the basis set of atomic orbitals and
causing an artefactual stabilization of complexes. As has been already mentioned,
this error can be corrected for single-point calculations by employing the standard
counterpoise method [101]. It should be mentioned that empirical dispersion corrections are also able to absorb small BSSE effects [120].
6.3.2.4 QM and QM/MM Modelling of Small Organic Molecules Binding
to G4 DNA
Determining the accurate structures of guanine quartets and their stacks is a key
step in the development of specific G4 ligands using the computer modelling approaches. However, drug design is based on studying the interactions of potential
ligands with their biomolecular targets, in this case quadruplex DNA. Molecular
dynamics is most often employed in these studies. G-quadruplexes for which X-ray
and NMR structures are available are large molecular systems (from 500 to 1000
atoms) that cannot be easily computed with non-empirical QM methods. For this
reason, quadruplex fragments can be used as G4 models to perform quantum chemical studies on ligand binding. Of course, the optimization of ligand structures is
routinely performed by QM calculation methods, usually DFT (often followed by
the manual docking of the optimized ligand onto G4 target and MD simulations of
quadruplex-ligand interaction).
Theoretical calculations applying the “pure” QM method to the studies on quadruplex-ligand binding are quite rare. We have already mentioned a work studying