Characterizing Activity Landscapes Using an
Information-Theoretic Approach
Veer Shanmugasundaram & Gerry Maggiora
Computer-Aided Drug Discovery
Pharmacia Corporation, Kalamazoo, MI
What are Activity Landscapes?
•
Activity landscapes are abstract
surfaces drawn on chemistry
space containing compounds
where the height represents
biological activity.
•
Gentle rising hills of activity
represent smooth landscape
where small structural changes
produce gradual changes in
activity.
•
Rough activity landscapes are
characterized by cliffs where
small changes in structure lead
to large changes in activity.
Smooth Landscape - Flint Hills, Kansas
Rough Landscape - Bryce Canyon, Utah
Why do we need to characterize them?
Smooth Landscape
•
What should be the minimum
size of a representative
dissimilarity subset of the
corporate collection? Is it assay
dependent?
•
Develop “stopping-rules” to
assess “have we screened
enough?”
•
Comparing activity landscapes
of different biological targets.
Activity
r2
o
t
p
i
cr
s
e
D
Descriptor 1
Rough Landscape
Activity
r2
o
t
crip
s
e
D
Descriptor 1
Shannon’s Theory of Communication
Transmission of Messages
‘Perfect’
Mapping
‘A’
•
•
•
•
•
‘Noisy’
Mapping
‘B’
•
•
•
•
•
‘A’
•
•
•
•
•
‘Equivocal’
Mapping
‘B’
•
•
•
•
•
‘A’
•
•
•
•
•
‘B’
•
•
•
•
•
‘Mixed’
Mapping
‘A’
•
•
•
•
•
‘B’
•
•
•
•
•
Shannon’s Theory of Communication
Receiver
b1 b2 b3 b4
Sender
a1
a2
Na2b2
a3
.
.
Na
.
.
a4
. . . Nb . . .
•
•
•
•
∑∑ N
ab
a
=N
b
Probabilities or frequencies with which messages are sent.
How each sent message is received.
Probabilities or frequencies with which messages are received.
How each received message was sent.
Shannon’s Theory of Communication
Receiver
b1 b2 b3 b4
Sender
a1
a2
.
.
pa
.
.
pa2b2
a3
∑p
ab
b
a4
. . . pb . . .
∑p
∑∑p
ab
a
=1
b
ab
a
Shannon’s entropy
H ( X ) = −∑ p x log2 px
x
H ( A) = − ∑ pa log2 pa
a
Sender’s entropy
H (B ) = − ∑ pb log 2 pb
b
Receiver’s entropy
H ( AB) = −∑ ∑ pab log2 pab
a
b
Joint entropy
Structural Similarity
Structure - Activity Mapping
Similarity in Activity
b1 b2 b3 b4
a1
a2
.
.
pa
.
.
pa2b2
a3
∑p
ab
b
a4
. . . pb . . .
∑p
∑∑p
ab
a
=1
b
ab
a
•
•
Structural similarity - Tanimoto similarity (Sij) or inter-compound
distances in chemistry space.
Activity similarity can be defined such that compounds that have similar
IC50 or % inhibition values have a high similarity in activity.
Structure - Activity Similarity Map
HIGH
Poor information content
Smooth Landscapes
Similarity in Activity
“Multiple pharmacophores”
or “promiscuous compounds”
Rugged Landscapes
LOW
HIGH
Structural Similarity
Structure - Activity Similarity Map
Rough Activity Landscape
Rugged Regions in
Similarity Map
Activity
r2
o
t
p
cri
s
e
D
Similarity in Activity
HIGH
LOW
Descriptor 1
HIGH
Structural Similarity
Information theoretic measure
HIGH
Similarity in Activity
Similarity in Activity
HIGH
LOW
HIGH
Structural Similarity
LOW
HIGH
Structural Similarity
Kullback-Leibler information theoretic measure could be used as a
global index to characterize the topographic character of activity
landscape and to compare the similarities between two different
structure-activity maps.
Kullback-Leibler Index
p( x )
D (p||q ) = ∑ p( x )log
q( x )
x∈ X
0log
•
•
•
0
=0
q
p log
p
=∞
0
Kullback-Leiber index is always non-negative.
Index is zero, if and only if p=q
Not a true “distance” - not symmetric and does not satisfy the triangle
inequality.
Biological Assay 1
Biological Assay 2
Biological Assay 3
180 cpds
16110 comparisons
465 ( SM ≥ 0.85 )
582 cpds
169071 comparisons
6569 ( SM ≥ 0.85 )
190 cpds
17955 comparisons
9508 ( SM ≥ 0.85 )
2000
100
1600
SM
80
SM
SM
1500
1200
1000
800
500
400
60
40
20
0
0
0
0.85 0.87 0.88 0.9 0.91 0.93 0.94 0.96 0.97 0.99
300
0.85 0.87 0.88 0.9 0.91 0.93 0.94 0.96 0.97 0.99
0.85 0.87 0.88 0.9 0.91 0.93 0.94 0.96 0.97 0.99
6000
SA
4000
SA
SA
3000
200
4000
2000
100
2000
1000
0
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1
0.1
0.2 0.3 0.4 0.5
0.6 0.7
0.8 0.9
1
Biological Assay 1
300
100
80
SM
SA
200
60
40
100
20
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.85 0.87 0.88 0.9 0.91 0.93 0.94 0.96 0.97 0.99
0.09
0.06
0.85 0.87 0.88 0.9 0.91 0.93 0.94 0.96 0.97 0.99
SM
0.1
0
0.6
0.03
SA
1
Biological Assay 1
0.06
3.00E-02
0.03
Similarity Map of an Idealized Rough Landscape
0.1
0.97
0.94
0.91
0.88
0.85
1
0
0.1
Similarity Map of an Idealized Smooth Landscape
Similarity Map of Assay 1
0.09
0.06
0.03
0.1
0
0.85 0.87 0.88 0.9 0.91 0.93 0.94 0.96 0.97 0.99
SM
0.6
0.00E+00
0.97
6.00E-02
0.94
0.09
0.91
9.00E-02
0.88
0.12
0.85
1.20E-01
SA
Biological Assay 1
Biological Assay 2
180 cpds
16110 comparisons
465 ( SM ≥ 0.85 )
582 cpds
169071 comparisons
6569 ( SM ≥ 0.85 )
0.09
0.3
0.06
0.2
Biological Assay 3
190 cpds
17955 comparisons
9508 ( SM ≥ 0.85 )
0.06
0.03
DISTANCES TO
IDEALIZED
LANDSCAPES
ASSAY 1
ASSAY 2
ASSAY 3
SMOOTH
9.59
9.39
9.57
ROUGH
10.68
12.96
10.36
0.97
0.94
0.91
0
0.88
0.1
0.85
0.97
0.94
0.91
0
0.88
1
0.1
0.97
0.94
0.91
0.88
0.85
0
0.85
0.1
0.03
0.1
Summary
• Activity landscapes tend to have smooth and rugged
regions.
• Kullback-Leibler information-theoretic index can be used
to measure the similarity of a given activity landscape to
smooth and rough landscapes.
• If activity landscapes are like Bryce Canyon, we need to
sample chemistry space more thoroughly to identify
important peaks of activity.