Biomedical Engineering Reference
In-Depth Information
activity similarity of data set compounds are compared in a pairwise manner, and
activity similarity is defined for a pair of compounds
i
and
j
as follows:
P
i
−
P
j
sim
act
(
i
,
j
)
=
1
−
(16.1)
P
max
−
P
min
In this equation,
P
i
and
P
j
are experimental potency values of compounds
i
and
j
,
respectively, and
P
max
−
P
min
is the difference between the maximum and minimum
potency occurring in the compound data set. Hence, for each possible compound
pair, a normalized potency difference is obtained as well as a calculated pairwise
similarity value, typically Tanimoto similarity based on molecular fingerprints, one
of the standard similarity assessments in chemoinformatics [6]. Albeit not formally
integrated in an equation, the combined evaluation of molecular and activity similarity
underlying SAS maps represents the essence of an SAR analysis function.
16.2.2 SAR Index
The SAR index (SARI) [9] consists of separately calculated continuity and dis-
continuity scores. The “raw” continuity score is derived as the potency weighted
mean of pairwise compound dissimilarity within a data set
A
. This continuity score
highly weights structurally diverse compounds with high potency and small potency
differences:
weight(
i
,
j
)
·
j
)
1
1
+
sim(
i
,
1
1
+
sim(
i
,
j
)
{
(
i
,
j
)
∈
A
|
i
=
j
}
cont
raw
(
A
)
=
weighted mean
{
=
weight(
i
,
j
)
(
i
,
j
)
∈
A
|
i
=
j
}
{
(
i
,
j
)
∈
A
|
i
=
j
}
P
i
·
P
j
+
P
i
−
P
j
weight(
i
,
j
)
=
(16.2)
1
P
stands for potency and sim(
i
,
j
) for the similarity of compounds
i
and
j
(also
calculated as Tanimoto fingerprint similarity).
In addition, the raw discontinuity score is derived as the average pairwise potency
difference between compounds multiplied by pairwise similarity:
disc
raw
(
A
)
=
mean
(
|
P
i
−
P
j
|·
sim(
i
,
j
))
(16.3)
(
i
,
j
)
∈
A
|
sim(
i
,
j
)
>
T
,
|
P
i
−
P
j
|
>
1
This discontinuity score emphasizes structurally similar compounds with large
potency differences. Because the discontinuity score should account for the pres-
ence of activity cliffs, only pairs of similar compounds (above a predefined similarity
threshold
T
) with at least one order of magnitude difference in potency are taken into
account for dissimilarity score calculation.
