MDI G
ð Þ ¼
X M
0
j¼1
IRV u j
À Á
ð3Þ
In Eq. 3, IRV stands for inactive range value and is the sum of IRL (inactive range
length) and IRW (inactive range weight) which is in line with the definitions used
for such measures of active ranges. Computation of IRV can be done using Eq. (4)
given below:
IRV ¼ IRL þ IRW
ð
Þ
ð 4Þ
Therefore, by considering a combined effect of MAI and MDI, one can prioritize the
newly generated active compounds and curate some high-ranking compounds for
further studies. Thus, in order to get a measure of combined effect of the vertices
falling in active ranges and inactive ranges (if any) and prioritizing (ranking) the
compounds according to their activities, we propose a measure, Molecular Priority
Score (MPS), for G and it may be computed using Eq. (5):
MPS G
ð Þ ¼ MAI G
ð Þ À MDI G
ð Þ
ð5Þ
Considering MPS value as a measure for prioritization of active compounds, a
compound with higher MPS value will occupy a higher position in the ranking.
Therefore, a compound may be regarded as more active if it gets higher MPS value.
This will then help screen some top-ranking compounds. However, ranking of
active compounds using MPS is not mandatory. One may always wish to consider
all the predicted active compounds for further studies particularly if the number of
highly ranked compounds (in terms of MPS value) is very small. At the same time,
there is no need to prioritize those compounds which are predicted inactive since
the idea is to screen potentially highly active compounds for a given biological
endpoint.
2.5 Combinatorial Structure Generation from Root Vertex
In developing the structure generation method, we have used an algorithm for
generating rooted trees [16] which have been extended to the generation of cyclic
compounds and finally a complete 2D structure of chemical compounds. The
structure generation exercise starts off as generating all possible canonical trees for
any given number of vertices. Subsequently, topological distance restriction on the
generated tree structures is used to filter and keep only those trees having a desired
distance distribution. Further, for the application of relaxed distance criteria for
compound structures having increased or decreased number of vertices
(non-hydrogen atoms), the matching criteria of distance distribution have been
suitably changed to accommodate the addition, deletion and migration of the
80
Md.I. H. Rizvi et al.
ð Þ ¼
X M
0
j¼1
IRV u j
À Á
ð3Þ
In Eq. 3, IRV stands for inactive range value and is the sum of IRL (inactive range
length) and IRW (inactive range weight) which is in line with the definitions used
for such measures of active ranges. Computation of IRV can be done using Eq. (4)
given below:
IRV ¼ IRL þ IRW
ð
Þ
ð 4Þ
Therefore, by considering a combined effect of MAI and MDI, one can prioritize the
newly generated active compounds and curate some high-ranking compounds for
further studies. Thus, in order to get a measure of combined effect of the vertices
falling in active ranges and inactive ranges (if any) and prioritizing (ranking) the
compounds according to their activities, we propose a measure, Molecular Priority
Score (MPS), for G and it may be computed using Eq. (5):
MPS G
ð Þ ¼ MAI G
ð Þ À MDI G
ð Þ
ð5Þ
Considering MPS value as a measure for prioritization of active compounds, a
compound with higher MPS value will occupy a higher position in the ranking.
Therefore, a compound may be regarded as more active if it gets higher MPS value.
This will then help screen some top-ranking compounds. However, ranking of
active compounds using MPS is not mandatory. One may always wish to consider
all the predicted active compounds for further studies particularly if the number of
highly ranked compounds (in terms of MPS value) is very small. At the same time,
there is no need to prioritize those compounds which are predicted inactive since
the idea is to screen potentially highly active compounds for a given biological
endpoint.
2.5 Combinatorial Structure Generation from Root Vertex
In developing the structure generation method, we have used an algorithm for
generating rooted trees [16] which have been extended to the generation of cyclic
compounds and finally a complete 2D structure of chemical compounds. The
structure generation exercise starts off as generating all possible canonical trees for
any given number of vertices. Subsequently, topological distance restriction on the
generated tree structures is used to filter and keep only those trees having a desired
distance distribution. Further, for the application of relaxed distance criteria for
compound structures having increased or decreased number of vertices
(non-hydrogen atoms), the matching criteria of distance distribution have been
suitably changed to accommodate the addition, deletion and migration of the
80
Md.I. H. Rizvi et al.