450
I. I. Baskin and N. I. Zhokhova
13.4.2 The Issue of Molecular Alignment
All methods of molecular alignment useful for building traditional lattice-based
3D-QSAR models can also be applied in the framework of the CMF approach.
Meanwhile, thanks to the integrability of continuous functions describing molecular
fields, the latter approach offers additional possibilities.
Molecular alignment exactly corresponds to the “curve registration” procedure,
which is the first necessary step in any functional data analysis [30]. In the case of
biological activity caused by protein–ligand interactions, mutual orientation of different ligands inside binding sites defines their “natural alignment”. Such alignment
can be checked by means of independent physical experiments (X-ray diffraction,
NMR, etc.), and hence its explicit consideration is equivalent to the inclusion of
“external domain knowledge”, which is always preferred in machine learning [4].
Therefore, the choice of the strategy for molecular alignment should be governed by
the necessity to mimic mutual orientation of molecules in the underlying physical
processes. It should however be pointed out that this does not mean that the “natural
alignment” should always provide the strongest 3D-QSAR models.
In the case when the exact information concerning the structure of binding pockets of biological macromolecules is not available, the CMF approach provides a
consistent criterion for the pairwise alignment of molecules i and j: maximization
of the kernel K( M i , M j ). Indeed, its form appears to be closely related to the function
used in the SEAL program for aligning molecules [45]. So, the CMF approach offers the possibility to use the same function both for aligning molecules and building
structure–activity models. This could lead to more close integration of molecular
alignment into the process of chemical data analysis. Moreover, the CMF approach
provides an additional criterion for the multiple alignment of molecules—the “compressibility” of molecular fields, which can be assessed using unsupervised dimensionality reduction approaches, such as the kernel (functional) principal component
analysis. Both criteria can also be applied to choose molecular conformations for
tackling the problem of molecular flexibility.
The issue of alignment-free approaches deserves special attention. Sometimes
the necessity to perform alignment of molecules in several grid-based 3D-QSAR
methods, such as CoMFA and CoMSIA, is considered as limitation of such approaches, which should be avoided [55]. This has led to the development of alignment-free approaches, such as those based on autocorrelation vectors [56], molecular moments (CoMMA) [57], 3D WHIM [58], EVA [55], GRIND [59], FLAP [60],
VolSurf [61] descriptors, etc. The CMF approach provides a new kind of solutions
based on the use of 3D-rotation invariant kernels [62, 63] in the frame of the concept of invariant pattern recognition [64]. The feasibility of this approach results
from the ability to apply the required integral transforms to continuous functions
describing molecular fields.
I. I. Baskin and N. I. Zhokhova
13.4.2 The Issue of Molecular Alignment
All methods of molecular alignment useful for building traditional lattice-based
3D-QSAR models can also be applied in the framework of the CMF approach.
Meanwhile, thanks to the integrability of continuous functions describing molecular
fields, the latter approach offers additional possibilities.
Molecular alignment exactly corresponds to the “curve registration” procedure,
which is the first necessary step in any functional data analysis [30]. In the case of
biological activity caused by protein–ligand interactions, mutual orientation of different ligands inside binding sites defines their “natural alignment”. Such alignment
can be checked by means of independent physical experiments (X-ray diffraction,
NMR, etc.), and hence its explicit consideration is equivalent to the inclusion of
“external domain knowledge”, which is always preferred in machine learning [4].
Therefore, the choice of the strategy for molecular alignment should be governed by
the necessity to mimic mutual orientation of molecules in the underlying physical
processes. It should however be pointed out that this does not mean that the “natural
alignment” should always provide the strongest 3D-QSAR models.
In the case when the exact information concerning the structure of binding pockets of biological macromolecules is not available, the CMF approach provides a
consistent criterion for the pairwise alignment of molecules i and j: maximization
of the kernel K( M i , M j ). Indeed, its form appears to be closely related to the function
used in the SEAL program for aligning molecules [45]. So, the CMF approach offers the possibility to use the same function both for aligning molecules and building
structure–activity models. This could lead to more close integration of molecular
alignment into the process of chemical data analysis. Moreover, the CMF approach
provides an additional criterion for the multiple alignment of molecules—the “compressibility” of molecular fields, which can be assessed using unsupervised dimensionality reduction approaches, such as the kernel (functional) principal component
analysis. Both criteria can also be applied to choose molecular conformations for
tackling the problem of molecular flexibility.
The issue of alignment-free approaches deserves special attention. Sometimes
the necessity to perform alignment of molecules in several grid-based 3D-QSAR
methods, such as CoMFA and CoMSIA, is considered as limitation of such approaches, which should be avoided [55]. This has led to the development of alignment-free approaches, such as those based on autocorrelation vectors [56], molecular moments (CoMMA) [57], 3D WHIM [58], EVA [55], GRIND [59], FLAP [60],
VolSurf [61] descriptors, etc. The CMF approach provides a new kind of solutions
based on the use of 3D-rotation invariant kernels [62, 63] in the frame of the concept of invariant pattern recognition [64]. The feasibility of this approach results
from the ability to apply the required integral transforms to continuous functions
describing molecular fields.