measure to assess their usefulness in predicting activities and mathematical–statistical methods are used to do that. However, no structure generation method is
used for this work [14].
In this chapter, we have described in detail a graph theory-based method,
developed recently by our research group [15], for combinatorial generation of
chemical structures from activity-related substructural topological information. This
approach [15] has been found to be useful in generating structures of active antitubercular compounds from activity-related vertices of the molecular graphs representing different other active antitubercular compounds. For developing the present
method [15], we have leveraged primarily a non-isomorphic rooted tree generation
algorithm [16] and a cycle enumeration method [17] to design novel bioactive
compounds in the form of reconstructed molecular graph as outlined earlier [18, 19].
In the proposed integrated method, activity-related vertices are first identified by
using the rule-based method [18, 19] where topological distance-based vertex
indices are used as local molecular descriptors in data sets having the biological
activities of interest. Once the activity-related vertices are identified, a suitable vertex
is taken for structure generation using the distance distribution associated with the
vertex which gives the topological distances of all the vertices in molecular graph
from that vertex (say, the root vertex). A large number of rooted trees are thus
generated de novo [15]. Subsequently, 2D molecular structures containing cycles of
different size are created by joining vertices of the tree graphs. In this way, all the
generated structures contain this activity-related substructure, and therefore, there is
a possibility that some of generated structures may be classified as active.
Furthermore, to get complete 2D structures of the compounds, user-defined
parameters are used to add multiplicity of bonds (e.g. double and triple bonds)
between pairs of vertices and add chemical nature of the atoms (nitrogen, oxygen,
etc.) represented by the vertices. Canonicalization is used to identify unique structures which are further used for screening of potential active compounds.
It may be noted that scaffold hopping [7] is embedded in the method since the
generated structures are different from the starting compound and are expected to
have diverse topological architecture. Also, since both compound generation and
activity prediction are done using the same vertex index (substructural/local descriptor), the method may also be regarded as an attempt to address the inverse
quantitative structure–activity relationship (iQSAR) problem [13] in its integrated
framework. Furthermore, in order to relax the condition for structure generation
from distance distribution as outlined earlier [18, 19] and to make it more flexible,
we have developed an algorithm for generating sub-trees by adding or deleting
vertices from the tree structures generated on the basis of a given distance distribution associated with an activity-related vertex. To our knowledge, this is the first
time that a method [15] has been developed and used for drug discovery through
database searching using rooted tree and sub-tree matching algorithms.
The method has already been used to investigate its usefulness for a series of 41
acid alkyl ester (AAE) derivatives and three known antitubercular drugs [15]. In
this chapter, we have furnished new results obtained for a series of 19 convulsant
and anticonvulsant barbiturates [18], 20 nucleoside analogues (NA) for their
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Md.I. H. Rizvi et al.
used for this work [14].
In this chapter, we have described in detail a graph theory-based method,
developed recently by our research group [15], for combinatorial generation of
chemical structures from activity-related substructural topological information. This
approach [15] has been found to be useful in generating structures of active antitubercular compounds from activity-related vertices of the molecular graphs representing different other active antitubercular compounds. For developing the present
method [15], we have leveraged primarily a non-isomorphic rooted tree generation
algorithm [16] and a cycle enumeration method [17] to design novel bioactive
compounds in the form of reconstructed molecular graph as outlined earlier [18, 19].
In the proposed integrated method, activity-related vertices are first identified by
using the rule-based method [18, 19] where topological distance-based vertex
indices are used as local molecular descriptors in data sets having the biological
activities of interest. Once the activity-related vertices are identified, a suitable vertex
is taken for structure generation using the distance distribution associated with the
vertex which gives the topological distances of all the vertices in molecular graph
from that vertex (say, the root vertex). A large number of rooted trees are thus
generated de novo [15]. Subsequently, 2D molecular structures containing cycles of
different size are created by joining vertices of the tree graphs. In this way, all the
generated structures contain this activity-related substructure, and therefore, there is
a possibility that some of generated structures may be classified as active.
Furthermore, to get complete 2D structures of the compounds, user-defined
parameters are used to add multiplicity of bonds (e.g. double and triple bonds)
between pairs of vertices and add chemical nature of the atoms (nitrogen, oxygen,
etc.) represented by the vertices. Canonicalization is used to identify unique structures which are further used for screening of potential active compounds.
It may be noted that scaffold hopping [7] is embedded in the method since the
generated structures are different from the starting compound and are expected to
have diverse topological architecture. Also, since both compound generation and
activity prediction are done using the same vertex index (substructural/local descriptor), the method may also be regarded as an attempt to address the inverse
quantitative structure–activity relationship (iQSAR) problem [13] in its integrated
framework. Furthermore, in order to relax the condition for structure generation
from distance distribution as outlined earlier [18, 19] and to make it more flexible,
we have developed an algorithm for generating sub-trees by adding or deleting
vertices from the tree structures generated on the basis of a given distance distribution associated with an activity-related vertex. To our knowledge, this is the first
time that a method [15] has been developed and used for drug discovery through
database searching using rooted tree and sub-tree matching algorithms.
The method has already been used to investigate its usefulness for a series of 41
acid alkyl ester (AAE) derivatives and three known antitubercular drugs [15]. In
this chapter, we have furnished new results obtained for a series of 19 convulsant
and anticonvulsant barbiturates [18], 20 nucleoside analogues (NA) for their
74
Md.I. H. Rizvi et al.