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I. I. Baskin and N. I. Zhokhova
structures. Different types of molecular fields can be used for this purpose, including electrostatic, steric, hydrophobic, hydrogen bond donor and acceptor fields, etc.
This way to describe chemical structures corresponds well to the physical nature of
the molecules, which interact with the environment through molecular fields. The
suggested approach is an alternative to traditional methods of representing chemical structures in SAR/QSAR/QSPR (Structure-Activity Relationships/Quantitative
Structure-Activity Relationships/Quantitative Structure-Property Relationships)
studies by means of fixed-sized vectors of descriptors derived from topological
molecular graphs, as well as interaction energies with certain probes calculated at
specific points in space (e.g., at the nodes of a hypothetic lattice).
So far, the direct use of continuous molecular fields in their functional form in
statistical analysis was not possible because standard data analysis procedures can
only work with finite and fixed number of features (molecular descriptors). Only
recently, thanks to the development of the statistical learning theory [5] and the
methodology of using kernels [6] in machine learning instead of fixed-sized feature
vectors, it has become possible to process data of any form and complexity.
The essence of the Continuous Molecular Fields (CMF) approach consists in performing
statistical analysis of functional molecular data by means of joint application of kernel
machine learning methods and special kernels which compare molecules by computing
overlap integrals of their molecular fields. [7, 8]
The principal novelty of our approach is the ability to conduct a statistical analysis
of chemical data represented in the form of continuous molecular fields, i.e. an
infinite number of attributes organized in a functional form. In this case, statistical
model is not a function relating the values of some properties of chemical compounds with the values of several molecular descriptors, like in the case of traditional SAR/QSAR/QSPR models, but a functional relating the properties of chemical
compounds with functions describing spatial distribution of molecular fields. As a
result, the resulting models are characterized by continuous fields of model coefficients, which can be visualized in the same manner as molecular fields themselves
to provide intuitive interpretation of the models and a deep insight into the nature of
the corresponding chemical phenomenon. The principal advantage of this approach
follows from a natural, accurate and comprehensive representation of molecules by
means of continuous molecular fields.
In combination with kernel based machine learning methods, such as the Support Vector Machines (SVM) [9], the Kernel Ridge Regression (KRR) [10], the
Gaussian Processes (GP) [11], etc., continuous molecular fields can be used to provide the quantitative prediction of various properties of chemical compounds. The
feasibility of this was demonstrated by us earlier [7, 8]. In conjunction with kernelbased methods of one-class classification (novelty detection), such as the One-Class
Support Vector Machines (1-SVM) [12], the use of continuous molecular fields
allows one to set up a ligand-based virtual screening procedure for searching huge
databases of available chemical compounds and retrieving from them potentially
biological active compounds (hits), molecular fields of which are similar to the
“idealized configuration” (which reflects the structure of the corresponding binding
I. I. Baskin and N. I. Zhokhova
structures. Different types of molecular fields can be used for this purpose, including electrostatic, steric, hydrophobic, hydrogen bond donor and acceptor fields, etc.
This way to describe chemical structures corresponds well to the physical nature of
the molecules, which interact with the environment through molecular fields. The
suggested approach is an alternative to traditional methods of representing chemical structures in SAR/QSAR/QSPR (Structure-Activity Relationships/Quantitative
Structure-Activity Relationships/Quantitative Structure-Property Relationships)
studies by means of fixed-sized vectors of descriptors derived from topological
molecular graphs, as well as interaction energies with certain probes calculated at
specific points in space (e.g., at the nodes of a hypothetic lattice).
So far, the direct use of continuous molecular fields in their functional form in
statistical analysis was not possible because standard data analysis procedures can
only work with finite and fixed number of features (molecular descriptors). Only
recently, thanks to the development of the statistical learning theory [5] and the
methodology of using kernels [6] in machine learning instead of fixed-sized feature
vectors, it has become possible to process data of any form and complexity.
The essence of the Continuous Molecular Fields (CMF) approach consists in performing
statistical analysis of functional molecular data by means of joint application of kernel
machine learning methods and special kernels which compare molecules by computing
overlap integrals of their molecular fields. [7, 8]
The principal novelty of our approach is the ability to conduct a statistical analysis
of chemical data represented in the form of continuous molecular fields, i.e. an
infinite number of attributes organized in a functional form. In this case, statistical
model is not a function relating the values of some properties of chemical compounds with the values of several molecular descriptors, like in the case of traditional SAR/QSAR/QSPR models, but a functional relating the properties of chemical
compounds with functions describing spatial distribution of molecular fields. As a
result, the resulting models are characterized by continuous fields of model coefficients, which can be visualized in the same manner as molecular fields themselves
to provide intuitive interpretation of the models and a deep insight into the nature of
the corresponding chemical phenomenon. The principal advantage of this approach
follows from a natural, accurate and comprehensive representation of molecules by
means of continuous molecular fields.
In combination with kernel based machine learning methods, such as the Support Vector Machines (SVM) [9], the Kernel Ridge Regression (KRR) [10], the
Gaussian Processes (GP) [11], etc., continuous molecular fields can be used to provide the quantitative prediction of various properties of chemical compounds. The
feasibility of this was demonstrated by us earlier [7, 8]. In conjunction with kernelbased methods of one-class classification (novelty detection), such as the One-Class
Support Vector Machines (1-SVM) [12], the use of continuous molecular fields
allows one to set up a ligand-based virtual screening procedure for searching huge
databases of available chemical compounds and retrieving from them potentially
biological active compounds (hits), molecular fields of which are similar to the
“idealized configuration” (which reflects the structure of the corresponding binding