435
13 Continuous Molecular Fields Approach Applied to Structure-Activity Modeling
site in biological macromolecule and can be viewed as a “negative image” of its
molecular fields) learned by the corresponding one-class model. The feasibility of
this approach in practice has also been demonstrated by us [13, 14].
13.2 Method of Continuous Molecular Fields
3D-QSAR approaches, in which information concerning the spatial structure of
molecules is explicitly taken into account, play very important role in medicinal
chemistry and drug design [15–17]. Most of them are based on the use of the molecular fields reflecting different types of intermolecular interactions in which molecules under study can be involved. Historically the first and still the most popular 3D-QSAR method is CoMFA (Comparative Molecular Field Analysis) [18], in
which electrostatic interactions are approximated by means of the Coulomb law
with point partial charges computed for each atom, whereas steric interactions are
expressed using the Lennard-Jones potentials with standard force field parameters.
Several other types of molecular fields, such as the hydrophobic [19], hydrogen
bond donor and acceptor fields [20], molecular orbital fields [21], E-state fields
[22], fields of atom-based indicator variables [23] are also used in the framework
of the CoMFA method. In the CoMSIA (Comparative Molecular Similarity Indices
Analysis) approach [24] the same types of molecular fields are approximated using
the Gaussian radial basis functions. In the GRID method [25] the values of various
types of molecular fields are computed as interaction energies with certain probe
atom or group of atoms placed at grid nodes.
In all of the above approaches molecular fields are evaluated at node points of
some imaginary grid surrounding the set of aligned molecules. The advantage of using such lattices lies in the possibility to use the values of molecular field potentials
calculated at grid nodes as a vector of descriptors, which can further be fed to some
standard statistical analysis procedure, usually PLS (Partial Least Squares) [26], in
order to build regression QSAR models. Another appealing feature of this approach
is the possibility to visualize the resulting regression coefficients using easily interpretable isosurfaces (usually colored according to the sign of coefficients and the
type of the corresponding molecular field) surrounding the molecules. Nonetheless,
this approach has certain considerable drawbacks. Indeed, it is necessary to: (1)
choose biologically active conformation for each molecule; (2) align in space the
training set of molecules; (3) build a lattice around such set of molecules; (4) choose
molecular fields and compute their potentials at grid points; (5) build regression
QSAR models. The problems associated with each of these stages are well known
and present a challenge for the current stage of the development of the 3D-QSAR
methodology.
The CMF approach addresses the problems caused by the necessity to choose a
grid of points around molecules. It is known that 3D-QSAR models sharply depend
on the spatial orientation and extent of such grid, as well as on the step size (i.e. the
distance between the closest points) in it [16]. Another problem caused by the use
13 Continuous Molecular Fields Approach Applied to Structure-Activity Modeling
site in biological macromolecule and can be viewed as a “negative image” of its
molecular fields) learned by the corresponding one-class model. The feasibility of
this approach in practice has also been demonstrated by us [13, 14].
13.2 Method of Continuous Molecular Fields
3D-QSAR approaches, in which information concerning the spatial structure of
molecules is explicitly taken into account, play very important role in medicinal
chemistry and drug design [15–17]. Most of them are based on the use of the molecular fields reflecting different types of intermolecular interactions in which molecules under study can be involved. Historically the first and still the most popular 3D-QSAR method is CoMFA (Comparative Molecular Field Analysis) [18], in
which electrostatic interactions are approximated by means of the Coulomb law
with point partial charges computed for each atom, whereas steric interactions are
expressed using the Lennard-Jones potentials with standard force field parameters.
Several other types of molecular fields, such as the hydrophobic [19], hydrogen
bond donor and acceptor fields [20], molecular orbital fields [21], E-state fields
[22], fields of atom-based indicator variables [23] are also used in the framework
of the CoMFA method. In the CoMSIA (Comparative Molecular Similarity Indices
Analysis) approach [24] the same types of molecular fields are approximated using
the Gaussian radial basis functions. In the GRID method [25] the values of various
types of molecular fields are computed as interaction energies with certain probe
atom or group of atoms placed at grid nodes.
In all of the above approaches molecular fields are evaluated at node points of
some imaginary grid surrounding the set of aligned molecules. The advantage of using such lattices lies in the possibility to use the values of molecular field potentials
calculated at grid nodes as a vector of descriptors, which can further be fed to some
standard statistical analysis procedure, usually PLS (Partial Least Squares) [26], in
order to build regression QSAR models. Another appealing feature of this approach
is the possibility to visualize the resulting regression coefficients using easily interpretable isosurfaces (usually colored according to the sign of coefficients and the
type of the corresponding molecular field) surrounding the molecules. Nonetheless,
this approach has certain considerable drawbacks. Indeed, it is necessary to: (1)
choose biologically active conformation for each molecule; (2) align in space the
training set of molecules; (3) build a lattice around such set of molecules; (4) choose
molecular fields and compute their potentials at grid points; (5) build regression
QSAR models. The problems associated with each of these stages are well known
and present a challenge for the current stage of the development of the 3D-QSAR
methodology.
The CMF approach addresses the problems caused by the necessity to choose a
grid of points around molecules. It is known that 3D-QSAR models sharply depend
on the spatial orientation and extent of such grid, as well as on the step size (i.e. the
distance between the closest points) in it [16]. Another problem caused by the use