Molecular Descriptors Guide Manual
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Page Count: 70
- 1Descriptorsofdrugs
- 1.1Molecularconstitutionaldescriptors
- 1.2Topologicaldescriptors
- 1.3Molecularconnectivityindices
- 1.4Kappashapedescriptors
- 1.5Burdendescriptors
- 1.6Basakdescriptors
- 1.7ElectrotopologicalStateIndices
- 1.8Autocorrelationdescriptors
- 1.9Chargedescriptors
- 1.10molecularproperties
- 1.11MOE-typedescriptors
- 1.12Molecularfingerprint
- References:
- 2Descriptorsofproteinsandpeptides
- 3Protein-proteininteractiondescriptors
- 4Protein-ligandinteractiondescriptors
- References:
- Appendix:
Molecular
Molecular
Molecular
Molecular Descriptors
Descriptors
Descriptors
Descriptors Guide
Guide
Guide
Guide
Description of the Molecular Descriptors Appearing in the
PyDPI Software Package
Version1.0
© 2012 China Computational Biology Drug Design Group
Table
Table
Table
Table of
of
of
of Contents
Contents
Contents
Contents
1 Descriptors of drugs
................................................................................................................................
4
1.1 Molecular constitutional descriptors
.............................................................................................
4
1.2 Topological descriptors
.................................................................................................................
6
1.3 Molecular connectivity indices
...................................................................................................
11
1.4 Kappa shape descriptors
.............................................................................................................
13
1.5 Burden descriptors
......................................................................................................................
15
1.6 Basak descriptors
........................................................................................................................
19
1.7 Electrotopological State Indices
.................................................................................................
19
1.8 Autocorrelation descriptors
.........................................................................................................
23
1.8.1 Moreau-Broto autocorrelation descriptors
........................................................................
24
1.8.2 Moran autocorrelation descriptors
....................................................................................
26
1.8.3 Geary autocorrelation descriptors
.....................................................................................
27
1.9 Charge descriptors
......................................................................................................................
28
1.10 molecular properties
.................................................................................................................
30
1.11 MOE-type descriptors
...............................................................................................................
31
1.12 Molecular fingerprint
................................................................................................................
33
1.12.1 Daylight-type fingerprint
................................................................................................
35
1.12.2 MACCS keys and FP4 fingerprint
..................................................................................
35
1.12.3 E-state fingerprint
...........................................................................................................
35
1.12.4 Atom pairs and topological torsions fingerprints
............................................................
35
1.12.5 Morgan fingerprint
..........................................................................................................
36
References:
........................................................................................................................................
37
2 Descriptors of proteins and peptides
.....................................................................................................
39
2.1 Amino acid composition
.............................................................................................................
39
2.2 Dipeptide composition
................................................................................................................
39
2.3 Tripeptide composition
...............................................................................................................
39
2.4 Autocorrelation descriptors
.........................................................................................................
40
2.4.1 Normalized Moreau-Broto autocorrelation descriptors
....................................................
40
2.4.2 Moran autocorrelation
.......................................................................................................
41
2.4.3 Geary autocorrelation Descriptors
....................................................................................
41
2.5 Composition, transition and distribution
....................................................................................
42
2.6 Conjoint Triad Descriptors
.........................................................................................................
44
2.7 Quasi-sequence-order Descriptors
..............................................................................................
46
2.7.1 Sequence-order-coupling numbers
...................................................................................
47
2.7.2 Quasi-sequence-order (QSO) descriptors
.........................................................................
47
2.8 pseudo-amino acid composition (PAAC)
...................................................................................
48
2.9 Amphiphilic pseudo-amino acid composition (APAAC)
...........................................................
50
References:
........................................................................................................................................
53
3 Protein-protein interaction descriptors
..................................................................................................
54
4 Protein-ligand interaction descriptors
...................................................................................................
55
References:
...............................................................................................................................................
56
Appendix:
.................................................................................................................................................
57
1
1
1
1 Descriptors
Descriptors
Descriptors
Descriptors of
of
of
of drugs
drugs
drugs
drugs
A
small or drug molecule could be represented by its chemical structure. In the PyDPI software, we
calculate twelve types of molecular descriptors to represent drug molecules, including constitutional
descriptors, topological descriptors, connectivity indices, Burden descriptors, basak
’
s information
indices, E-state indices, autocorrelation descriptors, charge descriptors, molecular properties, kappa
shape indices, MOE-type descriptors, and molecular fingerprints. These descriptors capture and
magnify distinct aspects of chemical structures.
1.1
1.1
1.1
1.1 Molecular
Molecular
Molecular
Molecular constitutional
constitutional
constitutional
constitutional descriptors
descriptors
descriptors
descriptors
1. M olecular weight (
Weight
)
2. Count of hydrogen atoms (
nhyd
)
3. Count of halogen atoms (
nhal
)
4. Count of hetero atoms (
nhet
)
5. Count of heavy atoms (
nhev
)
6. Count of F atoms (
ncof
)
7. Count of Cl atoms (
ncocl
)
8. Count of Br atoms (
ncobr
)
9. Count of I atoms (
ncoi
)
10. Count of C atoms (
ncarb
)
11. Count of P atoms (
nphos
)
12. Count of S atoms (
nsulph
)
13. Count of O atoms (
noxy
)
14. Count of N atoms (
nnitro
)
15. Number of rings (
nring
)
16. Number of rotatable bonds (
nrot
)
17. Number of H-bond donors (
ndonr
)
18. Number of H-bond acceptors (
naccr
)
19. Number of single bonds (
nsb
)
20. Number of double bonds (
ndb
)
21. Number of triple bonds (
ntb
)
22. Number of aromatic bonds (
naro
)
23. Number of all atoms (
nta
)
24. Average molecular weight (
AWeight
)
25. Molecular path counts of length 1 (
PC1
)
26. Molecular path counts of length 2 (
PC2
)
27. Molecular path counts of length 3 (
PC3
)
28. Molecular path counts of length 4 (
PC4
)
29. Molecular path counts of length 5 (
PC5
)
30. Molecular path counts of length 6 (
PC6
)
Introduction:
Introduction:
Introduction:
Introduction:
(1) The molecular weight (MW) is the sum of molecular weights of the individual atoms , defined
as:
1
A
i
i
MWMW
==
∑
a nd the average molecular weight (AWeight) is given as follows:
AWeight=MW/nAT
where
nAT
is the number of atoms
(2) T he number of hydrogen (
nhyd
), carbon (
ncarb
), nitrogen (
nnitro
), oxygen (
noxy
), phosphorus
(
nphos
), sulfur (
nsulph
), fluorine (
ncof
), chlorine (
ncocl
), bromine (
ncobr
), and iodine (
ncoi
)
atoms are simply the total number of each of these types of atoms in the molecule.
T he number of halogen atoms (
nhal
) is simply the sum of the counts of the halogen atoms; the
number of heavy atoms (
nhev
) and hetero atoms (
nhet
) are defined the similar way.
(3) F rom descriptor 15 to 22, they are simply the number of ring, single bond, double bond,
aromatic bond and H-acceptor, etc, in the molecule.
(4) F rom descriptor 25 to 30, they represent the number of path of length 1-6. T he path of length
n
indicates the shortest distance equal
n
between two atoms in a topological molecular graph.
1.2
1.2
1.2
1.2 Topological
Topological
Topological
Topological descriptors
descriptors
descriptors
descriptors
1. Weiner index (
W
)
2. Average Weiner index (
AW
)
3. Balaban
’
s J index (
J
)
4. Harary number (
T
hara
)
5. Schiultz index (
T
sch
)
6. Graph distance index (
Tigdi
)
7. Platt number (
Platt
)
8. Xu index (
Xu
)
9. Polarity number (
Pol
)
10. Pogliani index (
Dz
)
11. Ipc index (
Ipc
)
12. BertzCT (
BertzCT
)
13. Gutman molecular topological index based on simple vertex degree (
GMTI
)
14. Zagreb index with order 1 (
ZM1
)
15. Zagreb index with order 2 (
ZM2
)
16. Modified Zagreb index with order 1 (
MZM1
)
17. Modified Zagreb index with order 2 (
MZM2
)
18. Quadratic index (
Qindex
)
19. Largest value in the distance matrix (
diametert
)
20. Radius based on topology (
radiust
)
21. Petitjean based on topology (
petitjeant
)
22. The logarithm of the simple topological index by Narumi (
Sito
)
23. Harmonic topological index proposed by Narnumi (
Hato
)
24. Geometric topological index by Narumi (
Geto
)
25. Arithmetic topological index by Narumi (
Arto
)
I
I
I
I ntroduction:
ntroduction:
ntroduction:
ntroduction:
(1) Weiner index (
W
)
()/2
ijWd
=
∑
ijd
is the entries of distance matrix D from H-depleted molecular graph.
(2) Average Weiner index (
AW
)
The average Weiner index is given by
2
(1)
WWA
AA
=
−
w here
A
is the total number of atoms in the molecule, W and
AW
are described in more detail
on pa 497 of the Handbook of Molecular Descriptors
(3) Balaban
’
s J index (
J
)
1/2()
1
ijb
b
BJ
C
σσ
−=
+
∑
w here
iσ
and
jσ
are the vertex distance degree of adjacent atoms, and the sum run over
all the molecular bond b , B is the number of bonds in the molecular graph and C is the number
of rings.
J
are described in more detail on pa 21 of the Handbook of Molecular Descriptors
(4) Harary number (
T
hara
)
11
2
ij
ij
Hd
−=
∑∑
The Harary index is a molecular topological index derived from the reciprocal distance matrix
D
-1
(5) Schiultz index (
T
sch
)
1
[()]
n
i
i
MTIv
==+
∑
AD
AD
AD
AD
It is a topological index derived from the adjacency matrix A
A
A
A, the distance matrix D
D
D
Dand
n
-dimensional column vector
v
v
v
v
constituted by the vertex degree of the
A
atoms.
(6) Graph distance index (
Tigdi
)
The graph distance index is defined as the squared sum of all graph distance counts:
2
1
()
D
k
k
GDIf
==
∑
w here D is the topological diameter,
k
f
is the total number of distances in the graph equal to k.
(7) Platt number (
Platt
)
Platt number is also known as the total edge adjacency index A
E
, it is the sum over all entries of
the edge adjacency matrix:
11
BB
Eij
ij
AE
==
=
∑∑
w here B is the number of edges in molecular graph
(8) Xu index (
Xu
)
It is a topological molecular descriptor based on the adjacency matrix and distance matrix; it is
defined as:
2
1
1
log
A
ii
i
A
ii
i
XuA
δσ
δσ
=
=
=
∑
∑
w here
A
is the number of atoms,
δ
is vertex degree and
σ
is distance degree of all the atoms.
(9) Polarity number (
Pol
)
It is usually assumed that the polarity number accounts for the flexibility of acyclic structure; it
is usually calculated on the distance matrix as the number of pairs of vertices at a topological
distance equal to three. Some other polarity number also been defined based on different rules.
(10) Pogliani index (
Dz
)
1
vA
Z
i
i
i
ZD
L
==
∑
w here
A
is the number of atoms, Z is the number of valence electrons and
L
the principal
quantum number.
(11) Ipc index (
Ipc
)
Ipc index is the information for polynomial coefficients based information theory.
(12) BertzCT (
BertzCT
)
It is the most popular complexity index, taking into account both the variety of kinds of bond
connectivities and atom types. It is defined as:
CPXCPBCPA
III
=+
w here I
CPB
and I
CPA
are the information contents related to the bond connectivity and atom type
diversity
(13) Gutman molecular topological index based on simple vertex degree (
GMTI
)
11
AA
Gijij
ij
Sd δδ
==
=
∑∑
w here
ijij
dδδ
is the topological distance between vertex i and vertex j weighted by the product
of the endpoint vertex degrees.
(14) Zagreb index with order 1 (
ZM1
)
The first Zagreb index (Weighted by vertex degrees) is given by
21
a
a
Mδ
=
∑
w here
a
runs over the
A
atoms of the molecule and
δ
is the vertex degree.
(15) Zagreb index with order 2 (
ZM2
)
2()
ijb
b
Mδδ
=
∑
w here b runs over all the bonds in the molecule
The Zagreb indices are described on pg 509 of Handbook of Molecular Descriptors
(16) Modified Zagreb index with order 1 (
MZM1
)
(17) Modified Zagreb index with order 2 (
MZM2
)
(18) Quadratic index (
Qindex
)
2(2)2
2
g
g
ggF
Q
−+=
∑
Quadratic index also called normalized quadratic index, where
g
are the different vertex degree
values and
g
F
is the vertex degree count.
(19) Largest value in the distance matrix (
diametert
)
max()
iiDη
=
max()
ijij
dη
=
iη
called atom eccentricity is the maximum distance from the
ith
vertex to the other vertices.
(20) Radius based on topology (
radiust
)
min()
iiRη
=
(21) Petitjean based on topology (
petitjeant
)
2
DR
I
R
−=
(22) The logarithm of the simple topological index by Narumi (
Sito
)
1
A
i
i
Sδ
==
∏
w here
A
is the number of atoms,
Sito
is a molecular descriptor related to molecular branching
proposed as the product of the vertex degrees.
(23) Harmonic topological index proposed by Narumi (
Hato
)
1
1/
A
i
i
AH
δ
=
=
∑
(24) Geometric topological index by Narumi (
Geto
)
1/
1
AA
i
i
Gδ
=
⎛⎞
=
⎜⎟
⎝⎠
∏
(25) Arithmetic topological index by Narumi (
Arto
)
1
A
i
iA
A
δ
==
∑
1.3
1.3
1.3
1.3 Molecular
Molecular
Molecular
Molecular connectivity
connectivity
connectivity
connectivity indices
indices
indices
indices
1. Valence molecular connectivity Chi index for path order 0 (
0
χ
v
)
2. Valence molecular connectivity Chi index for path order 1(
1
χ
v
)
3. Valence molecular connectivity Chi index for path order 2(
3
χ
v
)
4. Valence molecular connectivity Chi index for path order 3(
4
χ
v
)
5. Valence molecular connectivity Chi index for path order 4(
5
χ
v
)
6. Valence molecular connectivity Chi index for path order 5(
6
χ
v
)
7. Valence molecular connectivity Chi index for path order 6(
7
χ
v
)
8. Valence molecular connectivity Chi index for path order 7 (
8
χ
v
)
9. Valence molecular connectivity Chi index for path order 8(
9
χ
v
)
10. Valence molecular connectivity Chi index for path order 9(
10
χ
v
)
11. Valence molecular connectivity Chi index for path order 10(
11
χ
v
)
12. Valence molecular connectivity Chi index for three cluster (
3
χ
v
c
)
13. Valence molecular connectivity Chi index for four cluster (
4
χ
v
c
)
14. Valence molecular connectivity Chi index for path/cluster (
4
χ
v
pc
)
15. Valence molecular connectivity Chi index for cycles of 3 (
3
χ
v
CH
)
16. Valence molecular connectivity Chi index for cycles of 4 (
4
χ
v
CH
)
17. Valence molecular connectivity Chi index for cycles of 5 (
5
χ
v
CH
)
18. Valence molecular connectivity Chi index for cycles of 6 (
6
χ
v
CH
)
19. Simple molecular connectivity Chi indices for path order 0 (
0
χ
)
20. Simple molecular connectivity Chi indices for path order 1 (
1
χ
)
21. Simple molecular connectivity Chi indices for path order 2 (
2
χ
)
22. Simple molecular connectivity Chi indices for path order 3 (
3
χ
p
)
23. Simple molecular connectivity Chi indices for path order 4 (
4
χ
p
)
24. Simple molecular connectivity Chi indices for path order 5 (
5
χ
p
)
25. Simple molecular connectivity Chi indices for path order 6 (
6
χ
p
)
26. Simple molecular connectivity Chi indices for path order 7 (
7
χ
p
)
27. Simple molecular connectivity Chi indices for path order 8 (
8
χ
p
)
28. Simple molecular connectivity Chi indices for path order 9 (
9
χ
p
)
29. Simple molecular connectivity Chi indices for path order 10 (
10
χ
p
)
30. Simple molecular connectivity Chi indices for three cluster (
3
χ
c
)
31. Simple molecular connectivity Chi indices for four cluster (
4
χ
c
)
32. Simple molecular connectivity Chi indices for path/cluster (
4
χ
pc
)
33. Simple molecular connectivity Chi indices for cycles of 3 (
3
χ
CH
)
34. Simple molecular connectivity Chi indices for cycles of 4 (
4
χ
CH
)
35. Simple molecular connectivity Chi indices for cycles of 5 (
5
χ
CH
)
36. Simple molecular connectivity Chi indices for cycles of 6 (
6
χ
CH
)
37. mean chi1 (Randic) connectivity index (
mChi1
)
38. the difference between chi3c and chi4pc (
knotp
)
39. the difference between chi0v and chi0 (
dchi0
)
40. the difference between chi1v and chi1 (
dchi 1
)
41. the difference between chi2v and chi2 (
dchi0
)
42. the difference between chi3v and chi3 (
dchi 3
)
43. the difference between chi4v and chi4 (
dchi 4
)
44. the difference between chiv3c and chiv4pc (
knotpv
)
Introduction:
Introduction:
Introduction:
Introduction:
1. S imple molecular connectivity index (No.19~36)
T he general formula for the molecular connectivity indices (
m
χ
t
) is as follows:
1/2
1
1
()
nk
m
qak
k
a
χδ
−
=
==
∑
∏
w here
k
runs over all of the
mth
order sub - graphs constituted by
n
atoms;
K
is the total number of
mth
order sub - graphs present in the molecular graph and in the case of the path
sub - graphs equals the
mth
order path count
m
P
. The product is over the simple vertex degrees of all
the vertices involved in each sub - graph. The subscript “
q
” for the connectivity indices refers to the
type of molecular sub - graph and
ch
for chain or ring,
pc
for path-cluster,
c
for cluster, and
p
for path .
F or the first three path indices (
0
χ ,
1
χ ,
2
χ
), the calculation type,
p
, is often omitted from the variable
name in the software.
2.
V
alence molecular connectivity indices (No.1~18)
T he valence connectivity indices (
m
χ
v
t
) are calculated in the same fashion as the simple connectivity
indices except that the vertex degree are replaced by the valence vertex degree, and the valence
degree is given by:
δ
v
=
Z
v
-
h
=
σ
+
π
+
n
-
h
. Where
Z
v
is the number of valence electrons,
π
is the number
of electrons in
pi
orbital and
n
is the number of electrons in lone-pair orbitals.
T he valence connectivity indices are described on page 86 of the Handbook of Molecular
Descriptors. T he connectivity indices are described in detail in the literature.
3. T he remains connectivity indices are simple combination of the above simple connectivity indices
and valence connectivity indices.
1.4
1.4
1.4
1.4 Kappa
Kappa
Kappa
Kappa shape
shape
shape
shape descriptors
descriptors
descriptors
descriptors
1. Kappa alpha index for 1 bonded fragment (
1
κ
α
)
2. Kappa alpha index for 2 bonded fragment (
2
κ
α
)
3. Kappa alpha index for 3 bonded fragment (
3
κ
α
)
4. Kier molecular flexibility index (
phi
)
5. Molecular shape Kappa index for 1 bonded fragment (
1
κ
)
6. Molecular shape Kappa index for 2 bonded fragment (
1
κ
)
7. Molecular shape Kappa index for 3 bonded fragment (
1
κ
)
I
I
I
I ntroduction:
ntroduction:
ntroduction:
ntroduction:
(1) Kappa alpha index
The first order kappa shape index (
1
κ
) is given by
11112212
maxmin
2/()(1)/()
iikPPPAAP
==−
w here
P
i
=# of paths of bond length
i
in the hydrogen suppressed molecule and
A
is the number
of non hydrogen atoms in the molecule.
The second order kappa shape index (
2
κ
) is given by
22222222
maxmin
2/()(1)(2)/()
ii
kPPPAAP
==−−
The kappa shape indices are described on pg 248 of the Handbook of Molecular Descriptors .
The first order kappa alpha shape index (
1
κ
α
) is given by
2
1
12
()(1)
()
a
AaAa
k
Pa
++−
=
+
w here
3()
1
x
xsp
ra
r
=−
w here
r
x
is the covalent radius of the atom being evaluated and
3()
xsp
r
is the covalent radius of a
carbon
sp
3
atom (0.77 Å ).
The second order kappa alpha shape index (
2
κ
α
) is given by
2
2
22
(1)(2)
()
a
AaAa
k
Pa
+−+−
=
+
The third order kappa alpha shape index (
3
κ
α
) is given by
2
3
32
(1)(3)
()
a
AaAa
k
Pa
+−+−
=
+
if
A
is odd
2
3
32
(3)(2)
()
a
AaAa
k
Pa
+−+−
=
+
if
A
is even
The kappa shape indices are described on page 250 of the Handbook of Molecular Descriptors.
The kappa flexibility index (
phi
) is given by
12
aa
kkphi
A
=
The kappa flexibility index is described on page 178 of the Handbook of Molecular Descriptors.
1.5
1.5
1.5
1.5 Burden
Burden
Burden
Burden descriptors
descriptors
descriptors
descriptors
1. Highest eigenvaluen.1 of Burden matrix/weighted by atomic masses (
bcutm1
)
2. Highest eigenvaluen.2 of Burden matrix/weighted by atomic masses (
bcutm2
)
3. Highest eigenvaluen.3 of Burden matrix/weighted by atomic masses (
bcutm 3
)
4. Highest eigenvaluen.4 of Burden matrix/weighted by atomic masses (
bcutm 4
)
5. Highest eigenvaluen.5 of Burden matrix/weighted by atomic masses (
bcutm 5
)
6. Highest eigenvaluen.6 of Burden matrix/weighted by atomic masses (
bcutm 6
)
7. Highest eigenvaluen.7 of Burden matrix/weighted by atomic masses (
bcutm7
)
8. Highest eigenvaluen.8 of Burden matrix/weighted by atomic masses (
bcutm8
)
9. Lowest eigenvaluen.1 of Burden matrix/weighted by atomic masses (
bcutm1
)
10. Lowest eigenvaluen.2 of Burden matrix/weighted by atomic masses (
bcutm2
)
11. Lowest eigenvaluen.3 of Burden matrix/weighted by atomic masses (
bcutm3
)
12. Lowest eigenvaluen.4 of Burden matrix/weighted by atomic masses (
bcutm4
)
13. Lowest eigenvaluen.5 of Burden matrix/weighted by atomic masses (
bcutm5
)
14. Lowest eigenvaluen.6 of Burden matrix/weighted by atomic masses (
bcutm6
)
15. Lowest eigenvaluen.7 of Burden matrix/weighted by atomic masses (
bcutm7
)
16. Lowest eigenvaluen.8 of Burden matrix/weighted by atomic masses (
bcutm8
)
17. Highest eigenvaluen.1 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv1
)
18. Highest eigenvaluen.2 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv2
)
19. Highest eigenvaluen.3 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv3
)
20. Highest eigenvaluen.4 of Burden matrix/weighted by atomic vander Waals volumes(
bcutv4
)
21. Highest eigenvaluen.5 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv5
)
22. Highest eigenvaluen.6 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv6
)
23. Highest eigenvaluen.7 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv7
)
24. Highest eigenvaluen.8 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv8
)
25. Lowest eigenvaluen.1of Burden matrix/weighted by atomic vander Waals volumes (
bcutv1
)
26. Lowest eigenvaluen.2 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv2
)
27. Lowest eigenvaluen.3 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv3
)
28. Lowest eigenvaluen.4 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv4
)
29. Lowest eigenvaluen.5 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv5
)
30. Lowest eigenvaluen.6 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv6
)
31. Lowest eigenvaluen.7of Burden matrix/weighted by atomic vander Waals volumes (
bcutv7
)
32. Lowest eigenvaluen.8 of Burden matrix/weighted by atomic vander Waals volumes (
bcutv8
)
33. Highest eigenvaluen.1 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute1
)
34. Highest eigenvaluen.2 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute2
)
35. Highest eigenvaluen.3 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute3
)
36. Highest eigenvaluen.4 of Burden matrix/weighted by atomic Sandersonel ectronegativities (
bcute4
)
37. Highest eigenvaluen.5 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute5
)
38. Highest eigenvaluen.6 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute6
)
39. Highest eigenvaluen.7of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute7
)
40. Highest eigenvaluen.8 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute8
)
41. Lowest eigenvaluen.1 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute1
)
42. Lowes teigenvaluen.2 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute2
)
43. Lowest eigenvaluen.3 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute3
)
44. Lowest eigenvaluen.4 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute4
)
45. Lowest eigenvaluen.5 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute5
)
46. Lowest eigenvaluen.6 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute6
)
47. Lowesteigenvaluen.7 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute7
)
48. Lowest eigenvaluen.8 of Burden matrix/weighted by atomic Sanderson electronegativities (
bcute8
)
49. Highest eigenvaluen.1 of Burden matrix/weighted by atomic polarizabilities (
bcutp1
)
50. Highest eigenvaluen.2 of Burden matrix/weighted by atomic polarizabilities (
bcutp2
)
51. Highesteigenvaluen.3 of Burden matrix/weighted by atomic polarizabilities (
bcutp3
)
52. Highest eigenvaluen.4 of Burden matrix/weighted by atomic polarizabilities (
bcutp4
)
53. Highest eigenvaluen.5 of Burden matrix/weighted by atomic polarizabilities (
bcutp5
)
54. Highesteigenvaluen.6 of Burden matrix/weighted by atomic polarizabilities (
bcutp6
)
55. Highesteigenvaluen.7 of Burden matrix/weighted by atomic polarizabilities (
bcutp7
)
56. Highest eigenvaluen.8 of Burden matrix/weighted by atomic polarizabilities (
bcutp8
)
57. Lowes teigenvaluen.1 of Burden matrix/weighted by atomic polarizabilities (
bcutp1
)
58. Lowest eigenvaluen.2 of Burden matrix/weighted by atomic polarizabilities (
bcutp2
)
59. Lowest eigenvaluen.3 of Burden matrix/weighted by atomic polarizabilities (
bcutp3
)
60. Lowest eigenvaluen.4 of Burden matrix/weighted by atomic polarizabilities (
bcutp4
)
61. Lowest eigenvaluen.5 of Burden matrix/weighted by atomic polarizabilities (
bcutp5
)
62. Lowest eigenvaluen.6 of Burden matrix/weighted by atomic polarizabilities (
bcutp6
)
63. Lowest eigenvaluen.7of Burden matrix/weighted by atomic polarizabilities (
bcutp7
)
64. Lowest eigenvaluen.8 of Burden matrix/weighted by atomic polarizabilities (
bcutp8
)
Introduction:
Introduction:
Introduction:
Introduction:
The Burden eigenvalue descriptors are determined by solving the following general eigenvalue
equation:
B
B
B
B.V
V
V
V=V
V
V
V.
e
e
e
e
where B
B
B
Bis a real connectivity matrix to be defined, V
V
V
Vis a matrix of eigenvectors, and
e
e
e
e
is a diagonal
matrix of eigenvalues. The rules defining B
B
B
Bare as follows:
a. Hydrogen atoms are included.
b. The diagonal elements of B
B
B
B,
B
ii
, are either given by the carbon normalized atomic mass, vander
Waals volume, Sanderson electronegativity, and polarizability of atom
i
.
c. The element of B
B
B
Bconnecting atoms
i
and
j
,
B
ij
, is equal to the square root of the bond order
between atoms
i
and
j
.
d. All other elements of B
B
B
B(corresponding non bonded atom pairs) are set to 0.001.
The carbon normalized weights are as follows:
The lowest eigenvalues are the absolute values of the negative eigenvalues. The highest eigenvalues are
the eight largest positive eigenvalues. The Burden eigenvalues descriptors are described on the
Handbook of Molecular Descriptors (Todeschini and Consonni 2000)
1.6
1.6
1.6
1.6 Basak
Basak
Basak
Basak descriptors
descriptors
descriptors
descriptors
(1) The information content with order 0 proposed by Basak (IC0)
(2) The information content with order 1 proposed by Basak(IC1)
(3) the information content with order 2 proposed by Basak(IC2)
(4) The information content with order 3 proposed by Basak(IC3)
(5) The information content with order 4 proposed by Basak(IC4)
(6) The information content with order 5 proposed by Basak(IC5)
(7) The information content with order 6 proposed by Basak(IC6)
(8) The structural information content with order 0 proposed by Basak (SIC0)
(9) The structural information content with order 1 proposed by Basak(SIC1)
(10) The structural information content with order 2 proposed by Basak(SIC2)
(11) The structural information content with order 3 proposed by Basak(SIC3)
(12) The structural information content with order 4 proposed by Basak(SIC4)
(13) The structural information content with order 5 proposed by Basak(SIC5)
(14) The structural information content with order 6 proposed by Basak(SIC6)
(15) The complementary information content with order 0 proposed by Basak(CIC0)
(16) The complementary information content with order 1 proposed by Basak(CIC1)
(17) The complementary information content with order 2 proposed by Basak(CIC2)
(18) The complementary information content with order 3 proposed by Basak(CIC3)
(19) The complementary information content with order 4 proposed by Basak(CIC4)
(20) The complementary information content with order 5 proposed by Basak(CIC5)
(21) The complementary information content with order 6 proposed by Basak(CIC6)
1.
1.
1.
1. 7
7
7
7 Electrotopological
Electrotopological
Electrotopological
Electrotopological State
State
State
State Indices
Indices
Indices
Indices
1. Sum of E-State of atom type: sLi (
S1
)
2. Sum of E-State of atom type: ssBe (
S2
)
3. Sum of E-State of atom type: ssssBe (
S3
)
4. Sum of E-State of atom type: ssBH (
S4
)
5. Sum of E-State of atom type: sssB (
S5
)
6. Sum of E-State of atom type: ssssB (
S6
)
7. Sum of E-State of atom type: sCH3 (
S7
)
8. Sum of E-State of atom type: dCH2 (
S8
)
9. Sum of E-State of atom type: ssCH2 (
S9
)
10. Sum of E-State of atom type: tCH (
S10
)
11. Sum of E-State of atom type: dsCH (
S11
)
12. Sum of E-State of atom type: aaCH (
S12
)
13. Sum of E-State of atom type: sssCH (
S13
)
14. Sum of E-State of atom type: ddC (
S14
)
15. Sum of E-State of atom type: tsC (
S15
)
16. Sum of E-State of atom type: dssC (
S16
)
17. Sum of E-State of atom type: aasC (
S17
)
18. Sum of E-State of atom type: aaaC (
S18
)
19. Sum of E-State of atom type: ssssC (
S19
)
20. Sum of E-State of atom type: sNH3 (
S20
)
21. Sum of E-State of atom type: sNH2 (
S21
)
22. Sum of E-State of atom type: ssNH2 (
S22
)
23. Sum of E-State of atom type: dNH (
S23
)
24. Sum of E-State of atom type: ssNH (
S24
)
25. Sum of E-State of atom type: aaNH (
S25
)
26. Sum of E-State of atom type: tN (
S26
)
27. Sum of E-State of atom type: sssNH (
S27
)
28. Sum of E-State of atom type: dsN (
S28
)
29. Sum of E-State of atom type: aaN (
S29
)
30. Sum of E-State of atom type: sssN (
S30
)
31. Sum of E-State of atom type: ddsN (
S31
)
32. Sum of E-State of atom type: aasN (
S32
)
33. Sum of E-State of atom type: ssssN (
S33
)
34. Sum of E-State of atom type: sOH (
S34
)
35. Sum of E-State of atom type: dO (
S35
)
36. Sum of E-State of atom type: ssO (
S36
)
37. Sum of E-State of atom type: aaO (
S37
)
38. Sum of E-State of atom type: sF (
S38
)
39. Sum of E-State of atom type: sSiH3 (
S39
)
40. Sum of E-State of atom type: ssSiH2 (
S40
)
41. Sum of E-State of atom type: sssSiH (
S41
)
42. Sum of E-State of atom type: ssssSi (
S42
)
43. Sum of E-State of atom type: sPH2 (
S43
)
44. Sum of E-State of atom type: ssPH (
S44
)
45. Sum of E-State of atom type: sssP (
S45
)
46. Sum of E-State of atom type: dsssP (
S46
)
47. Sum of E-State of atom type: sssssP (
S47
)
48. Sum of E-State of atom type: sSH (
S48
)
49. Sum of E-State of atom type: dS (
S49
)
50. Sum of E-State of atom type: ssS (
S50
)
51. Sum of E-State of atom type: aaS (
S51
)
52. Sum of E-State of atom type: dssS (
S52
)
53. Sum of E-State of atom type: ddssS (
S53
)
54. Sum of E-State of atom type: sCl (
S54
)
55. Sum of E-State of atom type: sGeH3 (
S55
)
56. Sum of E-State of atom type: ssGeH2 (
S56
)
57. Sum of E-State of atom type: sssGeH (
S57
)
58. Sum of E-State of atom type: ssssGe (
S58
)
59. Sum of E-State of atom type: sAsH2 (
S59
)
60. Sum of E-State of atom type: ssAsH (
S60
)
61. Sum of E-State of atom type: sssAs (
S61
)
62. Sum of E-State of atom type: sssdAs (
S62
)
63. Sum of E-State of atom type: sssssAs (
S63
)
64. Sum of E-State of atom type: sSeH (
S64
)
65. Sum of E-State of atom type: dSe (
S65
)
66. Sum of E-State of atom type: ssSe (
S66
)
67. Sum of E-State of atom type: aaSe (
S67
)
68. Sum of E-State of atom type: dssSe (
S68
)
69. Sum of E-State of atom type: ddssSe (
S69
)
70. Sum of E-State of atom type: sBr (
S70
)
71. Sum of E-State of atom type: sSnH3 (
S71
)
72. Sum of E-State of atom type: ssSnH2 (
S72
)
73. Sum of E-State of atom type: sssSnH (
S73
)
74. Sum of E-State of atom type: ssssSn (
S74
)
75. Sum of E-State of atom type: sI (
S75
)
76. Sum of E-State of atom type: sPbH3 (
S76
)
77. Sum of E-State of atom type: ssPbH2 (
S77
)
78. Sum of E-State of atom type: sssPbH (
S78
)
79. Sum of E-State of atom type: ssssPb (
S79
)
80-158. maximum of E-State value of specified atom type (
Smax1~Smax79
)
159-237. minimum of E-State value of specified atom type (
Smin1~Smin79
)
Introduction:
Introduction:
Introduction:
Introduction:
The E-State value for a given non-hydrogen atom
i
in a molecule is given by its intrinsic state (
I
i
) plus
the sum of the perturbations on that atom from all the other atoms in the molecule:
1
A
kkki
i
SII
==+∆
∑
w here the intrinsic state (
I
k
) is given by
2(2/)1
v
k
k
k
NI
δ
δ
+=
w here N=principle quantum number (which is equal to the element
’
s period or row in the element
table).
The perturbation of atom
k
due to atom
i
is given by
2
()
ik
ki
ki
III
r
−∆=
w here
1
kiki
rd
=+
d
ki
is the number of bonds that separate atom
k
from atom
i
.
The atom type non hydrogen indices (SX) are obtained by summing the E-State values for all the atoms
of a given type
t
that are present in the molecule.
()
SXSt
=
∑In addition, the symbol present in molecular descriptors,
s
,
d
,
t
and
a
indicate single bond, double bond,
triple bond and aromatic bond, respectively.
1.
1.
1.
1. 8
8
8
8 Autocorrelation
Autocorrelation
Autocorrelation
Autocorrelation descriptors
descriptors
descriptors
descriptors
The Broto-Moreau autocorrelation descriptors (ATSdw) are given by
11
AA
ijij
ij
ATSdw δωω
==
=
∑∑
w here
d
is the considered topological distance (i.e. the lag in the autocorrelation terms), d
ij
is the
Kronecker delta function ( d
ij
=1 if
d
ij
=d, zero otherwise), and
w
i
and
w
j
are the weights (normalized
atomic properties) for atoms
i
and
j
respectively. The normalized atomic mass, van der Waals volume,
electronegativity, or polarizability can be used for the weights.
To
match Dragon, the Broto-Moreau
autocorrelation descriptors are calculated in the Software as follows:
The Moran autocorrelation descriptors (MATSdw) are given by
w here
w
is the average value of the property for the molecule and △is the number of vertex pairs at
distance equal to
d
.
The Geary autocorrelation descriptors are given by
The 2D autocorrelation descriptors are described on page17-19 of the Handbook of Molecular
Descriptors.
1.
1.
1.
1. 8
8
8
8 .1
.1
.1
.1 Moreau-Broto
Moreau-Broto
Moreau-Broto
Moreau-Broto autocorrelation
autocorrelation
autocorrelation
autocorrelation descriptors
descriptors
descriptors
descriptors
1. Broto-Moreau autocorrelation of a topological structure-lag1/weighted by atomic masses (
ATSm1
)
2. Broto-Moreau autocorrelation of a topological structure-lag2/weighted by atomic masses (
ATSm2
)
3. Broto-Moreau autocorrelation of a topological structure-lag3/weighted by atomic masses (
ATSm3
)
4. Broto-Moreau autocorrelation of a topologicalstructure-lag4/weighted by atomic masses (
ATSm4
)
5. Broto-Moreau autocorrelation of a topological structure-lag5/weighted by atomic masses (
ATSm5
)
6. Broto-Moreau autocorrelation of a topological structure-lag6/weighted by atomic masses (
ATSm6
)
7. Broto-Moreau autocorrelation of a topological structure-lag7/weighted by atomic masses (
ATSm7
)
8. Broto-Moreau autocorrelation of a topological structure-lag8/weighted by atomic masses (
ATSm8
)
9. Broto-Moreau autocorrelation of a topological structure-lag1/weighted by atomic van der Waals
volumes (
ATSv1
)
10. Broto-Moreau autocorrelation of a topological structure-lag2/weighted by atomic van der Waals
volumes (
ATSv2
)
11. Broto-Moreau autocorrelation of a topological structure-lag3/weighted by atomic van der Waals
volumes (
ATSv3
)
12. Broto-Moreau autocorrelation of a topological structure-lag4/weighted by atomic van der Waals
volumes (
ATSv4
)
13. Broto-Moreau autocorrelation of a topological structure-lag5/weighted by atomic van der Waals
volumes (
ATSv5
)
14. Broto-Moreau autocorrelation of a topological structure-lag6/weighted by atomi van der Waals
volumes (
ATSv6
)
15. Broto-Moreau autocorrelation of a topological structure-lag7/weighted by atomic van der Waals
volumes (
ATSv7
)
16. Broto-Moreau autocorrelation of a topological structure-lag8/weighted by atomic van der Waals
volumes (
ATSv8
)
17. Broto-Moreau autocorrelation of a topological structure-lag1/weighted by atomic Sanderson
electronegativities (
ATSe1
)
18. Broto-Moreau autocorrelation of a topological structure-lag2/weighted by atomic Sanderson
electronegativities (
ATSe2
)
19. Broto-Moreau autocorrelation of a topological structure-lag3/weighted by atomic Sanderson
electronegativities (
ATSe3
)
20. Broto-Moreau autocorrelation of a topological structure-lag4/weighted by atomic Sanderson
electronegativities (
ATSe4
)
21. Broto-Moreau autocorrelation of a topological structure-lag5/weighted by atomic Sanderson
electronegativities (
ATSe5
)
22. Broto-Moreau autocorrelation of a topological structure-lag6/weighted by atomic Sanderson
electronegativities (
ATSe6
)
23. Broto-Moreau autocorrelation of a topological structure-lag7/weighted by atomic Sanderson
electronegativities (
ATSe7
)
24. Broto-Moreau autocorrelation of a topological structure-lag8/weighted by atomic Sanderson
electronegativities (
ATSe8
)
25. Broto-Moreau autocorrelation of a topological structure-lag1/weighted by atomic polarizabilities
(
ATSp1
)
26. Broto-Moreau autocorrelation of a topological structure-lag2/weighted by atomic polarizabilities
(
ATSp2
)
27. Broto-Moreau autocorrelation of a topological structure-lag3/weighted by atomic polarizabilities
(
ATSp3
)
28. Broto-Moreau autocorrelation of a topological structure-lag4/weighted by atomic polarizabilities
(
ATSp4
)
29. Broto-Moreau autocorrelation of a topological structure-lag5/weighted by atomic polarizabilities
(
ATSp5
)
30. Broto-Moreau autocorrelation of a topological structure-lag6/weighted by atomic polarizabilities
(
ATSp6
)
31. Broto-Moreau autocorrelation of a topological structure-lag7/weighted by atomic polarizabilities
(
ATSp7
)
32. Broto-Moreau autocorrelation of a topological structure-lag8/weightedbyatomic polarizabilities
(
ATSp8
)
1.
1.
1.
1. 8
8
8
8 .2
.2
.2
.2 Moran
Moran
Moran
Moran autocorrelation
autocorrelation
autocorrelation
autocorrelation descriptors
descriptors
descriptors
descriptors
33. Moran autocorrelation-lag1/weighted by atomic masses (
MATSm1
)
34. Moran autocorrelation-lag2/weighted by atomic masses (
MATSm2
)
35. Moran autocorrelation-lag3/weighted by atomic masses (
MATSm3
)
36. Moran autocorrelation-lag4/weighted by atomic masses (
MATSm4
)
37. Moran autocorrelation-lag5/weighted by atomic masses (
MATSm5
)
38. Moran autocorrelation-lag6/weighted by atomic masses (
MATSm6
)
39. Moran autocorrelation-lag7/weighted by atomic masses (
MATSm7
)
40. Moran autocorrelation-lag 8/weighted by atomic masses (
MATSm8
)
41. Moran autocorrelation-lag1/weighted by atomic van der Waals volumes (
MATSv1
)
42. Moran autocorrelation-lag2/weighted by atomic van der Waals volumes (
MATSv2
)
43. Moran autocorrelation-lag3/weighted by atomic van der Waals volumes (
MATSv3
)
44. Moran autocorrelation-lag4/weighted by atomic van der Waals volumes (
MATSv4
)
45. Moran autocorrelation-lag5/weighted by atomic van der Waals volumes (
MATSv5
)
46. Moran autocorrelation-lag6/weighted by atomic van der Waals volumes (
MATSv6
)
47. Moran autocorrelation-lag7/weighted by atomic van der Waals volumes (
MATSv7
)
48. Moran autocorrelation-lag8/weighted by atomic van der Waals volumes (
MATSv8
)
49. Moran autocorrelation-lag1/weighted by atomic Sanderson electronegativities (
MATSe1
)
50. Moran autocorrelation-lag2/weighted by atomic Sanderson electronegativities (
MATSe2
)
51. Moran autocorrelation-lag3/weighted by atomic Sanderson electronegativities (
MATSe3
)
52. Moran autocorrelation-lag4/weighted by atomic Sanderson electronegativities (
MATSe4
)
53. Moran autocorrelation-lag5/weighted by atomic Sanderson electronegativities (
MATSe5
)
54. Moran autocorrelation-lag6/weighted by atomic Sanderson electronegativities (
MATSe6
)
55. Moran autocorrelation-lag7/weighted by atomic Sanderson electronegativities (
MATSe7
)
56. Moran autocorrelation-lag8/weighted by atomic Sanderson electronegativities (
MATSe8
)
57. Moran autocorrelation-lag1/weighted by atomic polarizabilities (
MATSp1
)
58. Moran autocorrelation-lag2/weighted by atomic polarizabilities (
MATSp2
)
59. Moran autocorrelation-lag3/weighted by atomic polarizabilities (
MATSp3
)
60. Moran autocorrelation-lag4/weighted by atomic polarizabilities (
MATSp4
)
61. Moran autocorrelation-lag5/weighted by atomic polarizabilities (
MATSp5
)
62. Moran autocorrelation-lag6/weighted by atomic polarizabilities (
MATSp6
)
63. Moran autocorrelation-lag7/weighted by atomic polarizabilities (
MATSp7
)
64. Moran autocorrelation-lag8/weighted by atomic polarizabilities (
MATSp8
)
1.
1.
1.
1. 8
8
8
8 .3
.3
.3
.3 Geary
Geary
Geary
Geary autocorrelation
autocorrelation
autocorrelation
autocorrelation descriptors
descriptors
descriptors
descriptors
65. Geary autocorrelation-lag1/weighted by atomic masses (
GATSm1
)
66. Geary autocorrelation-lag2/weighted by atomic masses (
GATSm2
)
67. Geary autocorrelation-lag3/weighted by atomic masses (
GATSm3
)
68. Geary autocorrelation-lag4/weighted by atomic masses (
GATSm4
)
69. Geary autocorrelation-lag5/weighted by atomic masses (
GATSm5
)
70. Geary autocorrelation-lag6/weighted by atomic masses (
GATSm6
)
71. Geary autocorrelation-lag7/weighted by atomic masses (
GATSm7
)
72. Geary autocorrelation-lag8/weighted by atomic masses (
GATSm8
)
73. Geary autocorrelation-lag1/weighted by atomic van der Waals volumes (
GATSv1
)
74. Geary autocorrelation-lag2/weighted by atomic van der Waals volumes (
GATSv2
)
75. Geary autocorrelation-lag3/weighted by atomic van der Waals volumes (
GATSv3
)
76. Geary autocorrelation-lag4/weighted by atomic van der Waals volumes (
GATSv4
)
77. Geary autocorrelation-lag5/weighted by atomic van der Waals volumes (
GATSv5
)
78. Geary autocorrelation-lag6/weighted by atomic van der Waals volumes (
GATSv6
)
79. Geary autocorrelation-lag7/weighted by atomic van der Waals volumes (
GATSv7
)
80. Geary autocorrelation-lag8/weighted by atomic van der Waals volumes (
GATSv8
)
81. Geary autocorrelation-lag1/weighted by atomic Sanderson electronegativities (
GATSe1
)
82. Geary autocorrelation-lag2/weighted by atomic Sanderson electronegativities (
GATSe2
)
83. Gearyautocorrelation-lag3/weighted by atomic Sanderson electronegativities (
GATSe3
)
84. Geary autocorrelation-lag4/weighted by atomic Sanderson electronegativities (
GATSe4
)
85. Geary autocorrelation-lag5/weighted by atomic Sanderson electronegativities (
GATSe5
)
86. Geary autocorrelation-lag6/weighted by atomic Sanderson electronegativities (
GATSe6
)
87. Geary autocorrelation-lag7/weighted by atomic Sanderson electronegativities (
GATSe7
)
88. Geary autocorrelation-lag8/weighted by atomic Sanderson electronegativities (
GATSe8
)
89. Geary autocorrelation-lag1/weighted by atomic polarizabilities (
GATSp1
)
90. Geary autocorrelation-lag2/weighted by atomic polarizabilities (
GATSp2
)
91. Geary autocorrelation-lag3/weighted by atomic polarizabilities (
GATSp3
)
92. Geary autocorrelation-lag4/weighted by atomic polarizabilities (
GATSp4
)
93. Geary autocorrelation-lag5/weighted by atomic polarizabilities (
GATSp5
)
94. Geary autocorrelation-lag6/weighted by atomic polarizabilities (
GATSp6
)
95. Geary autocorrelation-lag7/weighted by atomic polarizabilities (
GATSp7
)
96. Geary autocorrelation-lag8/weighted by atomic polarizabilities (
GATSp8
)
1.
1.
1.
1. 9
9
9
9 Charge
Charge
Charge
Charge descriptors
descriptors
descriptors
descriptors
1. Most positive charge on H atoms (
Q
Hmax
)
2. Most positive charge on C atoms (
Q
Cmax
)
3. Most positive charge on N atoms (
Q
Nmax
)
4. Most positive charge on O atoms (
Q
Omax
)
5. Most negative charge on H atoms (
Q
Hmin
)
6. Most negative charge on C atoms (Q
Cmin
)
7. Most negative charge on N atoms (Q
Nmin
)
8. Most negative charge on O atoms (Q
Omin
)
9. Most positive charge in a molecule (
Q
max
)
10. Most negative charge in a molecule (
Q
min
)
11. Sum of squares of charges on H atoms (
Q
HSS
)
12. Sum of squares of charges on C atoms (
Q
CSS
)
13. Sum of squares of charges on N atoms (
Q
NSS
)
14. Sum of squares of charges on O atoms (
Q
OSS
)
15. Sum of squares of charges on all atoms (
Q
aSS
)
16. Mean of positive charges (
Mpc
)
17. Total of positive charges (
Tpc
)
18. Mean of negative charges (
Mnc
)
19. Total of negative charges (
Tnc
)
20. Mean of absolute charges (
Mac
)
21. Total of absolute charges (
Tac
)
22. Relative positive charge (
Rpc
)
23. Relative negative charge (
Rnc
)
24. Submolecular polarity parameter (
SPP
)
25. Local dipole index (
LDI
)
I
I
I
I ntroduction:
ntroduction:
ntroduction:
ntroduction:
These are electronic descriptors defined in terms of atomic charges and used to describe electronic
aspects of the whole molecule and of particular regions, such as atoms, bonds and molecular fragments.
Charge descriptors are calculated by computational chemistry and therefore can be considered among
quantum chemical descriptors.
Electrical charges in the molecule are the driving force of electrostatic interactions, and it is well
known the local electron density or charge plays a fundamental role in many chemical reactions and
physic-chemical properties.
Some most used charge descriptors are displayed here as followed :
(1) Most positive charge in a molecule (
Q
max
)
The maximum positive charge of the atoms in a molecule:
max
max()
aaQq
+=
w here q
+
are net atom positive charges
(2) Most negative charge in a molecule (
Q
min
)
The maximum negative charge of the atoms in a molecule:
min
max()
aaQq
−=
w here q
-
are net atom negative charges
(3) Total of positive charges (
Tpc
)
The sum of all of the positive charges of the atoms in a molecule:
()
aaTpcq
+=
∑w here q
+
are net atom positive charges
(4) Total of negative charges (
Tnc
)
The sum of all of the negative charges of the atoms in a molecule:
()
aaTncq
−=
∑w here q
-
are net atom negative charges
1.
1.
1.
1. 10
10
10
10 molecular
molecular
molecular
molecular properties
properties
properties
properties
1. Molar refractivity (
MREF
)
2. LogP value based on the Crippen method (
logP
)
3. Square of LogP value based on the Crippen method (
logP2
)
4. Topological polarity surface area (
TPSA
)
5. Unsaturation index (
UI
)
6. Hydrophilic index (
Hy
)
Introduction:
Introduction:
Introduction:
Introduction:
(1) Molar refractivity (
MREF
)
Molecular descriptor of a liquid which contains both information about molecular volume and
polarizability, usually defined by the Lorenz-Lorentz equation:
2
2
1
2
nMW
MR
nρ
−=
+
w here MW is the molecular weight,
ρ
is the liquid density, and n the refractive index of the
liquid.
（2）LogP value based on the Crippen method (
logP
)
The Ghose-Crippen contribution method is based on hydrophobic atomic constants
a
k
measuring the lipophilic contributions of atoms in the molecule, each described by its
neighbouring atoms.
kk
kLogPaN
=
∑w here
N
k
is the occurrence of the
kth
atom type
（
3
）
Topological polarity surface area (
TPSA
)
It is the sum of solvent-accessible surface areas of atoms with absolute value of partial charges
greater than or equal to 0.2.
0.2
aa
a
TPSASA
q
=
≥
∑
（4）Unsaturation index (
UI
)
The unsaturation index (
UI
) is defined as
2log(1)
UInDBnTBnAB
=+++
w here nDB=the number of double bonds, nTB=the number of triple bonds and nAB=the
number of aromatic bonds. The unsaturation index is described in the user manual for Dragon .
(5) Hydrophilic index (
Hy
)
The hydrophilic index is given by
22
2
2
11(1)log(1)(log)
log(1)
Hy
HyHyc
NNNN
AAAHy
A
++++
=
+
w here
N
Hy
is the number of hydrophilic groups (or the total number of hydrogen attached to
oxygen, sulfur and nitrogen atoms),
N
c
is the number of carbon atoms, and
A
is the number of
non hydrogen atoms. The hydrophilic index is described in more detail on page 225 of the
Handbook of Molecular Descriptors (Todeschini and Consonni 2000).
1.
1.
1.
1. 11
11
11
11 MOE-type
MOE-type
MOE-type
MOE-type descriptors
descriptors
descriptors
descriptors
1. topological polar surface area based on fragments (
TPSA
)
2. Labute's Approximate Surface Area (
LabuteASA
)
3. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 1
)
4. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 2
)
5. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 3
)
6. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 4
)
7. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 5
)
8. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 6
)
9. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 7
)
10. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 8
)
11. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 9
)
12. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 10
)
13. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA
11
)
14. MOE-type descriptors using SLogP contributions and surface area contributions (
SLOGPVSA 12
)
15. MOE-type descriptors using MR contributions and surface area contributions (
SMRVSA 1
)
16. MOE-type descriptors using MR contributions and surface area contributions (
SMRVSA 2
)
17. MOE-type descriptors using MR contributions and surface area contributions (
SMRVSA 3
)
18. MOE-type descriptors using MR contributions and surface area contributions (
SMRVSA 4
)
19. MOE-type descriptors using MR contributions and surface area contributions (
SMRVSA 5
)
20. MOE-type descriptors using MR contributions and surface area contributions (
SMRVSA 6
)
21. MOE-type descriptors using MR contributions and surface area contributions (
SMRVSA 7
)
22. MOE-type descriptors using MR contributions and surface area contributions (
SMRVSA 8
)
23. MOE-type descriptors using MR contributions and surface area contributions (
SMRVSA 9
)
24. MOE-type descriptors using MR contributions and surface area contributions (
SMRVSA 10
)
25. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 1
)
26. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 2
)
27. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 3
)
28. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 4
)
29. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 5
)
30. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 6
)
31. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 7
)
32. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 8
)
33. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 9
)
34. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 10
)
35. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA
11
)
36. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 12
)
37. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 13
)
38. MOE-type descriptors using partial charges and surface area contributions (
PEOEVSA 14
)
39. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA 1
)
40. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA 2
)
41. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA 3
)
42. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA 4
)
43. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA 5
)
44. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA 6
)
45. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA 7
)
46. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA 8
)
47. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA 9
)
48. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA 10
)
49. MOE-type descriptors using Estate indices and surface area contributions (
EstateVSA
11
)
50. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate 1
)
51. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate 2
)
52. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate 3
)
53. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate 4
)
54. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate 5
)
55. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate 6
)
56. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate 7
)
57. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate 8
)
58. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate 9
)
59. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate 10
)
60. MOE-type descriptors using surface area contributions and Estate indices (
VSAEstate
11
)
1.1
1.1
1.1
1.1 2
2
2
2 Molecular
Molecular
Molecular
Molecular fingerprint
fingerprint
fingerprint
fingerprint
Molecular fingerprints are string representations of chemical structures designed to enhance the
efficiency of chemical database searching and analysis. They can encode the 2D and/or 3D features of
molecules as an array of binary values or counts. Therefore, molecular fingerprints consist of bins, each
bin being a substructure descriptor associated with a specific molecular feature.
Molecular fingerprint s directly encode molecular structure in a series of binary bits that represent
the presence or absence of particular substructures in the molecule . Although it divides the whole
molecule into a large number of fragments, it has the potential to keep overall complexity of drug
molecules. Additionally, it does not need reasonable three-dimensional conformation of drug molecules
and thereby does not lead to error accumulation from the description of molecular structures. T hus by
means of such descriptors, each molecule can be described based on a set of fingerprints of structural
keys, which is represented as a Boolean array.
A
SMARTS list of substructure patterns is first
determined as a predefined dictionary. T here is a one-to-one correspondence between each SMARTS
pattern and bit in the fingerprint. F or each SMARTS pattern, if its corresponding substructure is present
in the given molecule, the corresponding bit in the fingerprint is set to 1; conversely, it is set to 0 if the
substructure is absent in the molecule (see Figure 1). Note that different molecular fingerprint systems
abstract and magnify different aspects of molecular topology.
Figure
Figure
Figure
Figure 1
1
1
1Representation of a molecular substructure fingerprint with a substructure fingerprint
dictionary of given substructure patterns. This molecule is represented in a series of binary bits that
represent the presence or absence of particular substructures in the molecules. This Figure is from Ref.
2 in section 3 and 4.
1.1
1.1
1.1
1.1 2
2
2
2 .1
.1
.1
.1 Daylight-type
Daylight-type
Daylight-type
Daylight-type fingerprint
fingerprint
fingerprint
fingerprint
The Daylight fi ngerprints (DFP) are hashed fi ngerprints encoding each atom type, all Augmented
Atoms and all paths of length 2 – 7 atoms, giving a total string of 1024 bits [Daylight-James, Weininger
et al., 1997 ].
1.1
1.1
1.1
1.1 2
2
2
2 .2
.2
.2
.2 MACCS
MACCS
MACCS
MACCS keys
keys
keys
keys and
and
and
and FP4
FP4
FP4
FP4 fingerprint
fingerprint
fingerprint
fingerprint
The FP4 and MACCS fingerprint s are used to construct the substructure dictionaries, respectively.
T he dictionary of FP4 fingerprint contains 307 mostly common substructure patterns. I t is originally
written in an attempt to represent the classification of organic compounds from the viewpoint of an
organic chemist. The MACCS fingerprint uses a dictionary of MDL keys, which contains a set of 166
mostly common substructure features. These are referred to as the MDL public MACCS keys. Both the
definitions of FP4 and MACCS fingerprints are available from OpenBabel (version 2.3.0,
http://openbabel.org/ , accessed October , 2010 ) . All calculations for these substructure fingerprints are
performed in PyDPI package, developed by our group.
1.1
1.1
1.1
1.1 2
2
2
2 .3
.3
.3
.3 E-state
E-state
E-state
E-state fingerprint
fingerprint
fingerprint
fingerprint
Electrotopological State (E-state) fingerprints represent the presence/absence of 79 E-state
substructures defined Kier and Hall in a molecule. The definition of 79 atom types can be found in
section 1.5.
1.1
1.1
1.1
1.1 2
2
2
2 .4
.4
.4
.4 Atom
Atom
Atom
Atom pairs
pairs
pairs
pairs and
and
and
and topological
topological
topological
topological torsions
torsions
torsions
torsions fingerprints
fingerprints
fingerprints
fingerprints
Atom
Atom
Atom
Atom pairs
pairs
pairs
pairs fingerprint:
fingerprint:
fingerprint:
fingerprint:
A tom pairs are substructure descriptors de fi ned in terms of any pair of atoms and bond types
connecting them. An atom pair is composed of two non-hydrogen atoms and an interatomic separation:
{ }
AP[th atom description][separation][th a tom description]
ij
=
The two considered atoms need not be directly connected and the separation can be the topological
distance between them [Carhart, Smith et al., 1985]; these descriptors are usually called topological
atom pairs being based on the topological representation of the molecules. Atom type is de fi ned by the
element itself, the number of heavy-atom connections and number of p electron pairs on each atom.
Unlike topological torsions, atom pairs are sensitive to long-range correlations between the atoms in
molecules and therefore to small changes in one part of even large molecules. Atom pair descriptors
usually are Boolean variables encoding the presence or absence of a particular atom pair in each
molecule.
Topological
Topological
Topological
Topological torsion
torsion
torsion
torsion fingerprint:
fingerprint:
fingerprint:
fingerprint:
The topological torsion descriptor (TT) is related to the 4-atom linear subfragment descriptor of
Klopman because it is de fi ned as a Boolean variable for the presence/absence of a linear sequence of
four consecutively bonded non-hydrogen atoms
k – i – j – l
, each described by its atom type (TYPE), the
number of
p
electrons (NPI) on each atom, and the number of non-hydrogen atoms (NBR) bonded to it
[Nilakantan, Bauman et al., 1987]. Usually NBR does not include
k – i – j – l
atoms that go to make the
torsion itself; therefore, it is - 1 for k and l atoms and - 2 for the two central atoms
i
and
j
. The torsion
around the
i - j
bond and de fi ned by the four indices
k – i – j – l
is represented by the following TT
descriptor:
The TT descriptor is a topological analogue of the 3D torsion angle, de fi ned by four consecutively
bonded atoms. The topological torsion is a short-range descriptor, that is, it is sensitive only to local
changes in the molecule and is independent of the total number of atoms in the molecule.
The use of atom-centered fragments and related descriptors greatly increases the speci fi c chemical
information concerning different functional groups, but cannot discriminate between different
arrangements of functional groups within a molecule.
1.1
1.1
1.1
1.1 2
2
2
2 .5
.5
.5
.5 Morgan
Morgan
Morgan
Morgan fingerprint
fingerprint
fingerprint
fingerprint
This family of fingerprints, better known as circular fingerprints, is built by applying the Morgan
algorithm to a set of user-supplied atom invariants. When generating Morgan fingerprints, the radius of
the fingerprint need be provided. For detailed information about Morgan fingerprint, please refer to Ref.
[19]. Note the default atom invariants use connectivity information similar to those used for the well
known ECFP family of fingerprints. When comparing the ECFP/FCFP fingerprints and the Morgan
fingerprints generated by the PyDPI, remember that the 4 in ECFP4 corresponds to the diameter of the
atom environments considered, while the Morgan fingerprints take a radius parameter. So the examples
above, with radius=2, are roughly equivalent to ECFP4 and FCFP4.
References:
References:
References:
References:
[1] Aguiara, P.F.d., Bourguignon, B., Khotsa, M.S., Massarta, D.L., and Phan-Than-Luub, R.
D-optimal designs. Chemometrics and Intelligent Laboratory Systems . 1995, 30 , 199-210.
[2] Daylight Chemical Information Systems, Inc. Simplified Molecular Input Line Entry System. 2006,
http://www.daylight.com/smiles/index.html.
[3] Elsevier MDL. MDL QSAR Version 2.2. 2006,
http://www.mdl.com/products/predictive/qsar/index.jsp.
[4] Ghose, A.K., Viswanadhan,V. N., and Wendoloski, J.J. Prediction of Hydrophilic (Lipophilic)
Properties of Small Organic Molecules Using Fragmental Methods: An analysis of ALOG an CLOGP
Methods. J. Phys. Chem. 1998 , 102 , 3762-3772.
[5] Gramatica, P., Corradi, M., and Consonni, V. Model ligand Prediction of Soil Sorption Coefficients
of Non-ionic Organic Pesticides by Molecular Descriptors. Chemosphere 2000 , 41 , 763-777.
[6] Hall, L.H., and Kier, L.B. The Molecular Connectivity Chi Indices and Kappa Shape Indices in
Structure-Property Relations. In Reviews of Computational Chemistry, edited by D. Boyd and K.
Lipkowitz. New York: VCH Publishers, Inc., 1991 , 367-422.
[7] Hall, L.H., and Kier, L.B. Molecular Connectivity Chi Indices for Database Analysis and
Structure-Property Modeling. In Methods for QSAR Modelling, edited by J. Devillers. 1999
[8] Kier,L.B. Inclusion of symmetry as a shape attribute in Kappa index analysis. Quantit. Struct.-Act.
Relat. 1987 , 6 , 8-12.
[9] Kier, L.B., and Hall, L.H. Molecular Connectivity in Chemistry and Drug Research. 1976 , New
York: Academic Press Inc.
[10] Kier, L.B.,and Hall, L.H. Molecular Connectivity in Structure-Activity Analysis. 1986 , New York:
John Wiley and Sons.
[11] Kier,L.B., and Hall, L.H. Molecule Structure Description: The Electrotopological State. 1999 ,
New York: Academic Press.
[12] Martin, T.M., Harten, P., Venkatapathy, R., Das, S., and Young, D.M. A Hierarchical Clustering
Methodology for the Estimation of Toxicity. Toxicology Mechanisms and Methods 2008 , 18 , 251-266.
[13] JAMA : A Java Matrix Package. 2005, http://math.nist.gov/javanumerics/jama/ .
[14] Talete. Dragon Version 5.4. 2006 , http://www.talete.mi.it/dragon_net.htm .
Todeschini, R., and Consonni, V. Handbook of Molecular Descriptors. 2000 , Weinheim, Germany:
Wiley-VCH.
[15] Viswanadhan, V.N., Ghose, A.K., Revankar, G. R., and Robins, R.K. Atomic Physicochemical
Parameters for Three Dimensional Structure Directed Quantitative Structure-Activity Relationships. 4.
Additional Parameters for Hydrophobic and Dispersive Interactions and Their Application for an
Automated Superposition of Certain Naturally Occurring Nucleoside Antibiotics. J. Chem. Inf. Comput.
Sci. 1989 , 29 , 163-172.
[16] Wang, R., Gao, Y., and Lai, L. Calculating partition coefficient by atom-additive method.
Perspectives in Drug Discovery and Design 2000 , 19 , 47-66.
[17] R. E. Carhart, D.H. Smith, R. Venkataraghavan. Atom Pairs as Molecular Features in
Structure-Activity Studies: Definition and Applications. J. Chem. Inf. Comput. Sci . 1985, 265, 64-73.
[18] R. Nilakantan, N. Bauman, J.S. Dixon, R. Venkataraghavan. Topological Torsions: A New
Molecular Descriptor for SAR Applications. Comparison with Other Descriptors. J. Chem. Inf. Comput.
Sci . 1987, 27, 82-85.
[19] David Rogers, Mather Hahn. Extended-Connectivity Fingerprints. J. Chem. Inf. Comput. Sci .
2010, 50, 742-754.
[20] Paul Labute. A widely applicable set of descriptors. Journal of Molecular Graphics and Modeling.
2000, 18, 464-477.
[21]
C. A. James , D. Weininger , J. Delany, Daylight Theory Manual 1997,
http://www
.
daylight
.
com/dayhtml/doc/theory/theory.toc.html .
[22] Burden, F.R. A chemically intuitive molecular index based on the eigenvalues of a modi fi ed
adjacency matrix. Quant. Struct. -Act. Relat., 1997 , 16, 309 – 314
[2 3 ] Basak, S.C. Information theoretic indices of neighborhood complexity and their applications, in
Bibliography Topological Indices and Related Descriptors in QSAR and QSPR (eds J. Devillers and
A.T. Balaban), Gordon and Breach Science Publishers, Amsterdam, The Netherlands, 1999 , pp.
563 – 593.
2
2
2
2 Descriptors
Descriptors
Descriptors
Descriptors of
of
of
of proteins
proteins
proteins
proteins and
and
and
and peptides
peptides
peptides
peptides
A protein or peptide sequence with
N
amino acid residues is expressed as: R
1
, R
2
, R
3
, … , R
N
, where R
i
represents the residue at the
i
-th position in the sequence. The labels
i
and
j
are used to index amino
acid position in a sequence and r, s are used to index the amino acid type. The computed features are
divided into 4 groups according to their known applications described in the literature.
A protein sequence can be divided equally into segments and the methods, described as follows for the
global sequence, can be applied to each segment.
2
2
2
2 .1
.1
.1
.1 Amino
Amino
Amino
Amino acid
acid
acid
acid composition
composition
composition
composition
The amino acid composition is the fraction of each amino acid type within a protein. The fractions of
all 20 natural amino acids are calculated as:
()
rNfr
N
=
r
=1, 2, 3, ..., 20
Where
N
r
is the number of the amino acid type
r
and
N
is the length of the sequence.
2
2
2
2 .2
.2
.2
.2 D
D
D
D ipeptide
ipeptide
ipeptide
ipeptide composition
composition
composition
composition
The dipeptide composition gives 400 features, defined as:
(,)
1
rsNfrs
N
=
−
r
,
s
=1, 2, 3, ..., 20
where
N
rs
is the number of dipeptide represented by amino acid type
r
and
s
.
2.3
2.3
2.3
2.3 Tripeptide
Tripeptide
Tripeptide
Tripeptide composition
composition
composition
composition
The tripeptide composition gives 8000 features, defined as:
(,,)
2
rstNfrst
N
=
−
r
,
s
=1, 2, 3, ..., 20
where
N
rst
is the number of tripeptide represented by amino acid type
r
,
s
and
t
.
2
2
2
2 .
.
.
. 4
4
4
4 Autocorrelation
Autocorrelation
Autocorrelation
Autocorrelation descriptors
descriptors
descriptors
descriptors
Autocorrelation descriptors are defined based on the distribution of amino acid properties along the
sequence. The amino acid properties used here are various types of amino acids index
(http://www.genome.ad.jp/dbget/aaindex.html ) .Three type of autocorrelation descriptors are used here
and are described as following.
All the amino acid indices are centralized and standardized before the calculation, i.e.
r
r
PP
P
σ
−=
Where
P
is the average of the property of the 20 amino acids .
20
1
20
r
r
P
P
==
∑
and
20
2
1
1
()
20
r
r
PPσ
==−
∑
2
2
2
2 .
.
.
. 4
4
4
4 .1
.1
.1
.1 Normalized
Normalized
Normalized
Normalized Moreau-Broto
Moreau-Broto
Moreau-Broto
Moreau-Broto autocorrelation
autocorrelation
autocorrelation
autocorrelation descriptors
descriptors
descriptors
descriptors
Moreau-Broto autocorrelation descriptors application to protein sequences may be defined as:
1()
Nd
iid
i
ACdPP
−
+
==
∑
d
=1, 2, 3, ..., nlag
Where
d
is called the lag of the autocorrelation and
P
i
and
P
i
+
d
are the properties of the amino acids at
position
i
and
i
+
d
, respectively.
nlag
is the maximum value of the lag.
The normalized Moreau-Broto autocorrelation descriptors are defined as:
()()
ACdATSd
Nd
=
−
d
=1, 2, 3, ...,
nlag
Figure
Figure
Figure
Figure 2
2
2
2An illustrated example in the AAIndex database
2
2
2
2 .
.
.
. 4
4
4
4 .2
.2
.2
.2 Moran
Moran
Moran
Moran autocorrelation
autocorrelation
autocorrelation
autocorrelation
Moran autocorrelation descriptors application to protein sequence may be defined as:
1
2
1
1
()()
()
1
()
Nd
iid
i
N
i
i
PPPP
NdId
PPN
−
+
=
=
−−
−=
−
∑
∑
d
=1, 2, 3, ..., 30.
Where
d
and
P
i
and
P
i
+
d
are defined in the same way as in 2.2.1, and is the average of the considered
property
P
along the sequence, i.e.,
1
N
i
i
P
P
N
==
∑
Where
d
,
P
,
P
i
and
P
i
+
d
,
nlag
have the same meaning as in the above.
2
2
2
2 .
.
.
. 4
4
4
4 .3
.3
.3
.3 Geary
Geary
Geary
Geary autocorrelation
autocorrelation
autocorrelation
autocorrelation Descriptors
Descriptors
Descriptors
Descriptors
Geary autocorrelation descriptors application to protein sequence may be defined as:
2
1
2
1
1
()2()
()
1
()
1
Nd
iid
i
N
i
i
PPNdCd
PPN
−
+
=
=
−−=
−−
∑
∑
d
=1, 2, 3, ..., 30.
Where
d
,
P
,
P
i
and
P
i
+
d
,
nlag
have the same meaning as in the above.
The amino acid indices used in these autocorrelation descriptors can be specified in file
“ input-param.dat ” from “ input-aaindexdb.dat ” .
For each amino acid index, there will be 3 ×
nlag
autocorrelation descriptors.
2
2
2
2 .
.
.
. 5
5
5
5 Composition,
Composition,
Composition,
Composition, transition
transition
transition
transition and
and
and
and distribution
distribution
distribution
distribution
These descriptors are developed by Dubchak, et.al.
Figure
Figure
Figure
Figure 3
3
3
3The sequence of a hypothetic protein indicating the construction of composition, transition
and distribution descriptors of a protein. Sequence index indicates the position of an amino acid in the
sequence. The index for each type of amino acids in the sequence ( ‘ 1
’
‘ 2
’
or ‘ 3 ’ ) indicates the position
of the first, second, third, ... of that type of amino acid. 1/2 transition indicates the position of ‘ 12
’
or
‘ 21
’
pairs in the sequence (1/3 and 2/3 are defined in the same way.). This figure is from Ref. 2 in
section 3 and 4.
Step1.
Step1.
Step1.
Step1. Sequence
Sequence
Sequence
Sequence encoding
encoding
encoding
encoding
The amino acids are divided in three classes according to its attribute and each amino acid is encoded
by one of the indices 1, 2, 3 according to which class it belonged. The attributes used here include
hydrophobicity, normalized van der Waals volume polarity, and polarizability, as in the references. The
corresponding division is in the table 1 .
Table
Table
Table
Table 1
1
1
1Amino acid attributes and the division of the amino acids into three groups for each attribute
Group
Group
Group
Group 1
1
1
1 Group
Group
Group
Group 2
2
2
2 Group
Group
Group
Group 3
3
3
3
hydrophobicity
Polar
R,K,E,D,Q,N
Neutral
G, A, S,T,P,H,Y
Hydrophobicity
C,L,V,I,M,F,W
normalized van
der Waals
volume
0-2.78
G,A,S,T,P,D
2.95-4.0
N,V,E,Q,I,L
4.03-8.08
M,H,K,F,R,Y ,W
polarity
4.9-6.2
L,I,F,W,C,M,V,Y
8.0-9.2
P,A,T,G,S
10.4-13.0
H,Q,R,K,N,E,D
polarizability
0-1.08
G,A,S,D,T
0.128-0.186
C,P,N,V,E,Q,I,L
0.219-0.409
K,M,H,F,R,Y ,W
charge
Positive
K,R
Neutral
A,N,C,Q,G,H,I,L,M,F,P,S,T,W,Y,
V
Negative
D,E
secondary
structure
Helix
E,A,L,M,Q,K,R,H
Strand
V,I,Y,C,W,F,T
Coil
G,N,P,S,D
solvent
accessibility
Buried
A,L,F,C,G,I,V,W
Exposed
R,K,Q,E,N,D
Intermediate
M,S P,T,H,Y
For example, for a given sequence “ MTEITAAMVKELRESTGAGA ” , it will be encoded as
“ 32132223311311222222 ” according to its hydrophobicity division.
Step
Step
Step
Step 2:
2:
2:
2: Composition,
Composition,
Composition,
Composition, Transition
Transition
Transition
Transition and
and
and
and Distribution
Distribution
Distribution
Distribution descriptors
descriptors
descriptors
descriptors
Three descriptors, “ Composition (C) ” , “ Transition (T) ” , and “ Distribution (D) ” were calculated for a
given attribute as follows:
Composition:
Composition:
Composition:
Composition: It is the global percent for each encoded class in the sequence. In the above example
using h ydrophobicity division, the numbers for encoded classes “ 1 ” , “ 2 ” , “ 3 ” are 5, 10, 5 respectively,
so the compositions for them are 5/20=25%, 10/20=10%, and 5/20=25% respectively, where 20 is the
length of the protein sequence. Composition can be defined as:
r
r
nC
n
=
r=
1, 2, 3
Where
n
r
is the number of
r
in the encoded sequence and
N
is the length of the sequence.
Transition:
Transition:
Transition:
Transition: A transition from class 1 to 2 is the percent frequency with which 1 is followed by 2 or 2 is
followed by 1 in the encoded sequence. Transition descriptor can be calculated as:
1
rssr
rs
nn
T
N
+=
−
rs
="12", "13", "23"
Where
n
rs
,
n
sr
is the numbers of dipeptide encoded as “
rs
” and “
sr
” respectively in the sequence and
N
is the length of the sequence.
Distribution:
Distribution:
Distribution:
Distribution: The “ distribution ” descriptor describes the distribution of each attribute in the sequence.
There are five “ distribution ” descriptors for each attribute and they are the position percents in the
whole sequence for the first residue, 25% residues, 50% residues, 75% residues and 100% residues ,
respectively, for a specified encoded class. For example, there are10 residues encoded as “ 2 ” in the
above example, the positions for the first residue “ 2 ” , the 2th residue “ 2 ” (25%*10=2), the 5th
“ 2 ” residue (50%*10=5), the 7th “ 2 ” (75%*10=7) and the10th residue “ 2 ” (100%*10) in the
encoded sequence are 2, 5, 15, 17, 20 respectively, so the distribution descriptors for “ 2 ” are: 10.0
(2/20*100), 25.0 (5/20*100), 75.0 (15/20*100), 85.0 (17/20*100) , 100.0 (20/20*100), respectively.
2.6
2.6
2.6
2.6 Conjoint
Conjoint
Conjoint
Conjoint Triad
Triad
Triad
Triad Descriptors
Descriptors
Descriptors
Descriptors
Conjoint triad descriptors are proposed by J.W. Shen et.al. These conjoint triad features abstracts the
features of protein pairs based on the classification of amino acids. In this approach, each protein
sequence is represented by a vector space consisting of features of amino acids.
To
reduce the
dimensions of vector space, the 20 amino acids were clustered into several classes according to their
dipoles and volumes of the side chains. The conjoint triad features are calculated as follows:
Step
Step
Step
Step 1:
1:
1:
1: classification
classification
classification
classification of
of
of
of amino
amino
amino
amino acids
acids
acids
acids
Electrostatic and hydrophobic interactions dominate protein-protein interactions. These two kinds of
interactions may be reflected by the dipoles and volumes of the side chains of amino acids, respectively.
Accordingly, these two parameters were calculated, respectively, by using the density-functional theory
method B3LYP/6-31G and molecular modeling approach. Based on the dipoles and volumes of the side
chains, the 20 amino acids could be clustered into seven classes (See Table 2). Amino acids within the
same class likely involve synonymous mutations because of their similar characteristics.
Table
Table
Table
Table 2 Classification of amino acids based on dipoles and volumes of the side chains
a
Dipole scale (Debye): -, Dipole<1.0; +, 1.0<Dipole<2.0; ++, 2.0<Dipole<3.0; +++, Dipole>3.0; +'+'+', Dipole>3.0
with opposite orientation.
b
Volume scale ( Å
3
): -, Volume<50; +, Volume> 50.
c
Cys is separated from class 3 because
of its ability to form disulfide bonds. This table is from Ref. 13.
Step
Step
Step
Step 2:
2:
2:
2: Conjoint
Conjoint
Conjoint
Conjoint triad
triad
triad
triad calculation
calculation
calculation
calculation
The conjoint triad descriptors considered the properties of one amino acid and its vicinal amino acids
and regarded any three continuous amino acids as a unit. Thus, the triads can be differentiated
according to the classes of amino acids, i.e., triads composed by three amino acids belonging to the
same classes, such as ART and VKS, could be treated identically.
To
conveniently represent a protein,
we first use a binary space ( V
V
V
V,F
F
F
F) to represent a protein sequence. Here, V
V
V
Vis the vector space of the
sequence features, and each feature
v
i
represents a sort of triad type; F
F
F
Fis the frequency vector
corresponding to V
V
V
V, and the value of the
i
th dimension of F
F
F
F(
f
i
) is the frequency of type
v
i
appearing in
the protein sequence. For the amino acids that have been catalogued into seven classes, the size of V
V
V
V
should be 7
×
7
×
7; thus
i
= 1,2, ..., 343. The detailed description for ( V
V
V
V,F
F
F
F) is illustrated in Figure 3.
Clearly, each protein correlates to the length (number of amino acids) of protein. In general, a long
protein would have a large value of
f
i
, which complicates the comparison between two heterogeneous
proteins. Thus, we defined a new parameter,
d
i
, by normalizing
f
i
with the following equation.
123343123343
(min{,,,...,})/max{,,,...,}
ii
dfffffffff
=−
The numerical value of
d
i
of each protein ranges from 0 to 1, which thereby enables the comparison
between proteins. Accordingly, we obtain another vector space (designated D
D
D
D) consisting of
d
i
to
represent protein
Figure
Figure
Figure
Figure 3
3
3
3Schematic diagram for constructing the vector space
(V,
F) of protein sequence. V is the vector space of the
sequence features; each feature (v
i
) represents a triad composed of three consecutive amino acids; F is the frequency
vector corresponding to
V,
and the value of the
i
th dimension of F(f
i
) is the frequency that v
v
v
v
i
i
i
i
triad appeared in the
protein sequence. This figure is from Ref. 13.
2
2
2
2 .
.
.
. 7
7
7
7 Quasi-sequence-order
Quasi-sequence-order
Quasi-sequence-order
Quasi-sequence-order Descriptors
Descriptors
Descriptors
Descriptors
The quasi-sequence-order descriptors are proposed by K.C. Chou, et.al. They are derived from the
distance matrix between the 20 amino acids.
2
2
2
2 .
.
.
. 7.
7.
7.
7. 1
1
1
1 Sequence-order-coupling
Sequence-order-coupling
Sequence-order-coupling
Sequence-order-coupling numbers
numbers
numbers
numbers
The dth-rank sequence-order-coupling number is defined as:
2
,
1
()
Nd
diid
i
dτ
−
+
==
∑
d
=1, 2, 3, ... ,
maxlag
Where
d
i
,
i+d
is the distance between the two amino acids at position
i
and
i+d
.
Note:
Note:
Note:
Note:
m axlag
is the maximum lag and the length of the protein must be not less than
maxlag
.
2
2
2
2 .
.
.
. 7
7
7
7 .2
.2
.2
.2 Quasi-sequence-order
Quasi-sequence-order
Quasi-sequence-order
Quasi-sequence-order (QSO)
(QSO)
(QSO)
(QSO) descriptors
descriptors
descriptors
descriptors
For each amino acid type, a quasi-sequence-order descriptor can be defined as :
20
11
r
r
maxlag
rd
rd
fX
fw τ
==
=
+∑∑
r
=1, 2, 3, ... , 20
Where
f
r
is the normalized occurrence for amino acid type
i
and
w
is a weighting factor (
w
=0.1). These
are the first 20 quasi-sequence-order descriptors. The other 30 quasi-sequence-order are defined as:
20
20
11
d
r
maxlag
rd
rd
wX
fw
τ
τ
−
==
=
+∑∑
d
=21, 22, 23, ... , 20+
maxlag
In addition to Schneider-Wrede physicochemical distance matrix used by Chou et al, another
chemical distance matrix by Grantham is also used here.
Figure
Figure
Figure
Figure 4
4
4
4A schematic drawing to show (a) the 1st-rank, (b) the 2nd-rank, and (3) the 3rd-rank
sequence-order-coupling mode along a protein sequence. (a) Reflects the coupling mode between all
the most contiguous residues, (b) that between all the 2nd most contiguous residues, and (c) that
between all the 3rd most contiguous residues. This figure is from Ref. 4.
2
2
2
2 .
.
.
. 8
8
8
8 pseudo-amino
pseudo-amino
pseudo-amino
pseudo-amino acid
acid
acid
acid composition
composition
composition
composition (PAAC)
(PAAC)
(PAAC)
(PAAC)
This groups of descriptors are proposed by Kuo-chen Chou. PAAC descriptors
(http://www.csbio.sjtu.edu.cn/bioinf/PseAAC/type1.htm ) are also called the type 1 pseudo-amino acid
composition. Let
1
()
oHi
,
2
()
oHi
, ()
oMi
(
i
=1,2,3, ..., 20) be the original hydrophobicity values, the
original hydrophilicity values and the original side chain masses of the 20 natural amino acids,
respectively. They are converted to following qualities by a standard conversion:
20
11
1
1
2020
2
11
11
1()()
20()
1[()()]
20
20
oo
i
oo
ii
HiHi
Hi
HiHi
=
==
−
=
−
∑
∑∑
2
()
oHi
and
()
oMi
are normalized as
2
()
Hi
and
()
Mi
in the same way.
Figure
Figure
Figure
Figure 5
5
5
5A schematic drawing to show (a) the first-tier, (b) the second - tier, and (3) the third-tier
sequence order correlation mode along a protein sequence. Panel ( a
a
a
a) reflects the correlation mode
between all the most contiguous residues, panel ( b
b
b
b) that between all the second-most contiguous
residues, and panel ( c
c
c
c) that between all the third-most contiguous residues. This figure is from Ref. 8.
Then, a correlation function can be defines as:
{ }
222
1122
1(,)()()()()()()
3
ijijijij
RRHRHRHRHRMRMR
⎡⎤⎡⎤⎡⎤
Θ=−+−+−
⎣⎦⎣⎦⎣⎦
This correlation function is actually an averaged value for the three amino acid properties:
hydrophobicity value, hydrophilicity value and side chain mass. Therefore we can extend this
definition of correlation function for one amino acid property or for a set of n amino acid properties.
For one amino acid property, the correlation can be defined as:
2
11(,)()()
ijij
RRHRHR
⎡⎤
Θ=−
⎣⎦
where
H
(
R
i
)
is the amino acid property of amino acid
R
i
after standardization.
For a set of n amino acid properties, it can be defined as: where
H
k
(
R
i
) is the
k
th property in the amino
acid property set for amino acid
R
i
.
2
1
1(,)()()
n
ijkikj
k
RRHRHR
n
=
⎡⎤
Θ=−
⎣⎦
∑
where Hk(Ri) is the kth property in the amino acid property set for amino acid Ri.
A set of descriptors called sequence order-correlated factors are defined as:
1
11
1
1
(,)
1
N
ii
i
RRNθ
−
+
==Θ
−
∑
2
22
1
1
(,)
2
N
ii
i
RRNθ
−
+
==Θ
−
∑
3
33
1
1
(,)
3
N
ii
i
RRNθ
−
+
==Θ
−
∑
...
1
1
(,)
N
ii
i
RRN
λ
λλ
θ
λ
−
+
==Θ
−
∑
λ
(<L) is a parameter to be chosen. Let
f
i
is the normalized occurrence frequency of the 20 amino acids
in the protein sequence, a set of 20+
λ
descriptors called the pseudo-amino acid composition for a
protein sequence can be defines as:
20
11
c
rj
rj
fXc
fw
λ
θ
==
=
+∑∑
(1<c<20)
20
20
11
c
rj
rj
wXc
fw
λ
θ
θ
−
==
=
+∑∑
(21<
c
<20+ λ )
where
w
is the weighting factor for the sequence-order effect and is set as
w
=0.05 in PyDPI as
suggested by Chou KC.
Note: the original hydrophobicity values for amino acids in PyDPI are different from the values by
Chou KC. In this updated version, the default values of amino acid properties are the values of Chou
KC. However, in the work of Chou KC, the definition for “ normalized occurrence frequency ” is not
given and in this work we define it as the occurrence frequency of amino acid in the sequence
normalized to 100% and hence our calculated values are not the same as values by them.
2
2
2
2 .
.
.
. 9
9
9
9 A
A
A
A mphiphilic
mphiphilic
mphiphilic
mphiphilic pseudo-amino
pseudo-amino
pseudo-amino
pseudo-amino acid
acid
acid
acid composition
composition
composition
composition (APAAC)
(APAAC)
(APAAC)
(APAAC)
APAAC ( http://www.csbio.sjtu.edu.cn/bioinf/PseAAC/type2.htm ) are also called type 2 pseudo-amino
acid composition. The definitions of these qualities are similar to the above PAAC descriptors. From
H
1
(
i
) and
H
2
(
j
) defined in eq. 16 and eq. 17, the hydrophobicity and hydrophilicity correlation functions
are defined respectively as:
1
,11
()()
ijHHiHj
=
2
,22
()()
ijHHiHj
=
From these qualities, sequence order factors can be defines as:
1
1
1,1
1
1
1
N
ii
i
HNτ
−
+
==
−
∑
1
2
2,1
1
1
1
N
ii
i
HNτ
−
+
==
−
∑
2
1
3,2
1
1
2
N
ii
i
HNτ
−
+
==
−
∑
2
2
4,2
1
1
2
N
ii
i
HNτ
−
+
==
−
∑
...
1
21,
1
1
N
ii
i
HN
λ
λλ
τ
λ
−
−+
==
−
∑
2
2,
1
1
N
ii
i
HN
λ
λλ
τ
λ
−
+
==
−
∑
Figure
Figure
Figure
Figure 6
6
6
6A schematic diagram to show ( a1
a1
a1
a1 /a2
a2
a2
a2 ) the first-rank, ( b1
b1
b1
b1 /b2
b2
b2
b2 ) the second-rank and ( c1
c1
c1
c1 /c2
c2
c2
c2 ) the
third-rank sequence-order-coupling mode along a protein sequence through a
hydrophobicity/hydrophilicity correlation function, where
H
1
i
,
j
and
H
2
i
,
j
are given by Equation (3).
Panel (a1/a2) reflects the coupling mode between all the most contiguous residues, panel (b1/b2) that
between all the second-most contiguous residues and panel (c1/c2) that between all the third-most
contiguous residues. This figure is from Ref. 12.
Then a set of descriptors called “ Amphiphilic pseudo amino acid composition ” (APAAC) are defined
as:
202
11
c
rj
rj
fPc
fw
λ
τ
==
=
+∑∑
1<
c
<20
202
11
u
rj
rj
wPc
fw
λ
τ
τ
==
=
+∑∑
21<
u
<20+2
λ
Where
w
is the weighting factor and is taken as
w
=0.5 in PyDPI as in the work of Chou KC.
References
References
References
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computing structural and physicochemical features of proteins and peptides from amino acid sequence.
Nucleic Acids Research. 2011, 39, 385-390.
[16] Kawashima, S., Ogata, H., and Kanehisa, M.; AAindex: amino acid index database. Nucleic Acids
Res. 1999, 27, 368-369.
[17] Kawashima, S. and Kanehisa, M.; AAindex: amino acid index database. Nucleic Acids Res. 2000,
28, 374.
[18] Kawashima, S., Pokarowski, P., Pokarowska, M., Kolinski, A., Katayama, T., and Kanehisa, M.;
AAindex: amino acid index database, progress report 2008. Nucleic Acids Res. 2008, 36, D202-D205.
[19] Chou, K.-C. , and Shen, H.-B. Cell-PLoc: a package of Web servers for predicting subcellular
localization of proteins in various organisms. Nat. Protocols, 2008, 3, 153-162.
3
3
3
3 Protein-protein
Protein-protein
Protein-protein
Protein-protein interaction
interaction
interaction
interaction descriptors
descriptors
descriptors
descriptors
Let F
F
F
F a
a
a
a={ F
F
F
F a
a
a
a(i),i=1,2, … ,n} and F
F
F
F b
b
b
b={ F
F
F
F b
b
b
b(i),i=1,2, … ,n} are the two descriptor vectors for interaction
protein A and protein B, respectively, then there are 3 methods to construct the descriptor vector F
F
F
Ffor
A and B:
(1)
(1)
(1)
(1) Two vectors F
F
F
Fab and F
F
F
Fba with dimension of 2n are constructed: F
F
F
Fab = ( F
F
F
Fa, F
F
F
Fb ) for interaction
between protein A and protein B and F
F
F
Fba=( F
F
F
Fb, F
F
F
Fa ) for interaction between protein B and protein A.
(2)
(2)
(2)
(2) One vector F
F
F
Fwith dimension of 2n is constructed: F
F
F
F={ F
F
F
Fa(i)+ F
F
F
Fb(i), F
F
F
Fa(i) × F
F
F
Fb(i), i=1,2, … , n}.
(3)
(3)
(3)
(3) One vector F
F
F
Fwith dimension of n
2
is constructed by the tensor product: F
F
F
F={ F
F
F
F(k)= F
F
F
Fa(i) × F
F
F
Fb(j), i=1,
2, … , n, j=1, 2 , … , n, k=(i-1) × n+j}.
4
4
4
4 Protein-ligand
Protein-ligand
Protein-ligand
Protein-ligand interaction
interaction
interaction
interaction descriptors
descriptors
descriptors
descriptors
There are two methods for construction of descriptor vector F
F
F
Ffor protein-ligand interaction from the
protein descriptor vector F
F
F
F
p
p
p
p
( F
p
(i), i=1,n
p
) and ligand descriptor vector F
F
F
F
l
l
l
l
(F
F
F
F
l
(i), i=1,n
l
):
:
:
:
(1)
(1)
(1)
(1) One vector V with dimension of np+nl are constructed: F
F
F
F=( F
F
F
F
p
p
p
p
,F
F
F
F
l
l
l
l
)for interaction between protein P
and ligand L.
(2)
(2)
(2)
(2) One vector V with dimension of n
p
× n
l
is constructed by the tensor product: F
F
F
F={ f (k)= F
F
F
F
p
(i) × F
F
F
F
l
(j),
i=1,2, … , np, j=1,2, … ,n
l
, k=(i-1) × np+j}.
Figure
Figure
Figure
Figure 7
7
7
7The schematic diagram dealing with the drug-target interaction by using the chemogenomics
approach. This interaction can be considered as an event triggered by many factors influencing the
binding between this drug and this protein. Therefore it can be efficiently represented by
simultaneously considering the structure content from this drug and this protein under a common
chemogenomics representation framework. This figure is from Ref. 2.
References:
References:
References:
References:
[1] Cao, D.-S., Liu, S., Xu, Q.-S., Lu, H.-M., Huang, J.-H., Hu, Q.-N. and Liang,
Y.-Z.
Large-scale
prediction of drug-target interactions using protein sequences and drug topological structures. Analytica
Chimica Acta, 2012, 752, 1-10.
[2]
Yu,
H., Chen, J., Xu, X., Li,
Y.,
Zhao, H., Fang,
Y.,
Li, X., Zhou,
W.,
Wang,
W.
and Wang,
Y.
A
Systematic Prediction of Multiple Drug-Target Interactions from Chemical, Genomic, and
Pharmacological Data. PLoS ONE, 2012, 7, e37608.
[3] Cao, D.-S., Liang,
Y.-Z.,
Deng, Zhe, Hu, Q.-N., He Min, Xu, Q.-S., Zhou, G.-H., Zhang, L.-X.,
Deng, Z.-X., Liu Shao. Genome-Scale Screening of Drug-Target Associations Relevant to Ki Using a
Chemogenomics Approach. PLOS ONE, 2013, 8, e57680.
[4] Hiroaki
Y.,
Satoshi N., Hiromu,
T.,
Tomomi, L., Takatsugu, H., Takafumi, H., Teppei, O., Yohsuke,
M., Gozoh, t., Yasushi, O. Analysis of multiple compound-protein interactions reveals novel bioactive
molecules. Mol. Syst. Biol., 2011, 7, 472-483.
[5] J.W. Shen, J. Zhang, X.M. Luo, W.L. Zhu, K.Q. Yu, K.X. Chen, Y.X. Li, H.L. Jiang. Predicting
protein-protein interactions based only on sequences information. Proc. Natl. Acad. Sci. 2007, 104,
4337-4341.
Appendix:
Appendix:
Appendix:
Appendix:
Table
Table
Table
Table S1
S1
S1
S1 List of PyDPI computed features for protein sequences
Feature
Feature
Feature
Feature group
group
group
group Features
Features
Features
Features Number
Number
Number
Number of
of
of
of descriptors
descriptors
descriptors
descriptors
Amino acid composition Amino acid composition 20
Dipeptide composition 400
Tripeptide composition 8000
Autocorrelation Normalized Moreau-Broto
autocorrelation
240
a
Moran autocorrelation 240
a
Geary autocorrelation 240
a
CTD Composition 21
Transition 21
Distribution 105
Con joint Triad Con joint Triad 343
Quasi-sequence order Sequence order coupling number 60
Quasi-sequence order descriptors 100
Pseudo amino acid composition Pseudo amino acid composition 50
b
Amphiphilic pseudo amino acid
composition
50
c
a
The number depends on the choice of the number of properties of amino acid and the choice of the maximum values
of the
lag
. The default is use eight types of properties and
lag
= 30.
b
The number depends on the choice of the number of the set of amino acid properties and the choice of the
lamda
value. The default is use three types of properties proposed by Chou et al and
lamda
= 30.
c
The number depends on the choice of the
lamda
vlaue. The default is that
lamda
= 30.
Table
Table
Table
Table S2
S2
S2
S2 List of PyDPI computed descriptors for small molecules
Molecular
Molecular
Molecular
Molecular descriptors
descriptors
descriptors
descriptors
Constitutional
Constitutional
Constitutional
Constitutional descriptors
descriptors
descriptors
descriptors
1
a
Weight Molecular weight
2 nhyd Count of hydrogen atoms
3 nhal Count of halogen atoms
4
a
nhet Count of hetero atoms
5
a
nhev Count of heavy atoms
6 ncof Count of F atoms
7 ncocl Count of Cl atoms
8 ncobr Count of Br atoms
9 ncoi Count of I atoms
10 ncarb Count of C atoms
11 nphos Count of P atoms
12 nsulph Count of S atoms
13 noxy Count of O atoms
14 nnitro Count of N atoms
15
a
nring Number of rings
16
a
nrot Number of rotatable bonds
17
a
ndonr Number of H-bond donors
1 8
a
naccr Number of H-bond acceptors
19 nsb Number of single bonds
20 ndb Number of double bonds
21 ntb Number of triple bonds
22 naro Number of aromatic bonds
23 nta Number of all atoms
24 AWeight Average molecular weight
25-30 PC1
PC2
PC3
PC4
PC5
PC6
Molecular path counts of length 1-6
Topological
Topological
Topological
Topological descriptors
descriptors
descriptors
descriptors
1 W Weiner index
2 AW Average Wiener index
3
a
J Balaban
’
s J index
4 T
hara
Harary number
5 T
sch
Schiultz index
6 Tigdi Graph distance index
7 Platt Platt number
8 Xu Xu index
9 Pol Polarity number
10 Dz Pogliani index
11
a
Ipc
Ipc index
12
a
BertzCT
BertzCT
13 GMTI Gutman molecular topological index based on simple vertex degree
14-15 ZM1
ZM2
Zagreb index with order 1-2
16-17 MZM1
MZM2
Modified Zagreb index with order 1-2
18 Qindex Quadratic index
19 diametert Largest value in the distance matrix
20 radiust radius based on topology
21 petitjeant Petitjean based on topology
22 Sito the logarithm of the simple topological index by Narumi
23 Hato harmonic topological index proposed by Narumi
24 Geto Geometric topological index by Narumi
25 Arto Arithmetic topological index by Narumi
Connectivity
Connectivity
Connectivity
Connectivity descriptors
descriptors
descriptors
descriptors
1-11
a 0
χ
v
1
χ
v
2
χ
v
3
χ
p
v
4
χ
p
v
5
χ
p
v
6
χ
p
v
7
χ
p
v
Valence molecular connectivity Chi index for path order 0-10
8
χ
p
v
9
χ
p
v
10
χ
p
v
12
3
χ
v
c
Valence molecular connectivity Chi index for three cluster
13
4
χ
v
c
Valence molecular connectivity Chi index for four cluster
14
4
χ
v
pc
Valence molecular connectivity Chi index for path/cluster
15-18
3
χ
v
CH
4
χ
v
CH
5
χ
v
CH
6
χ
v
CH
Valence molecular connectivity Chi index for cycles of 3-6
19-29
a 0
χ
1
χ
2
χ
3
χ
p
4
χ
p
5
χ
p
6
χ
p
7
χ
p
8
χ
p
9
χ
p
10
χ
p
Simple molecular connectivity Chi indices for path order 0-10
30
3
χ
c
Simple molecular connectivity Chi indices for three cluster
31
4
χ
c
Simple molecular connectivity Chi indices for four cluster
32
4
χ
pc
Simple molecular connectivity Chi indices for path/cluster
33-36
3
χ
CH
4
χ
CH
5
χ
CH
Simple molecular connectivity Chi indices for cycles of 3-6
6
χ
CH
37 mChi1 mean chi1 (Randic) connectivity index
38 knotp the difference between chi3c and chi4pc
39 dchi0 the difference between chi0v and chi0
40 dchi1 the difference between chi1v and chi1
41 dchi2 the difference between chi2v and chi2
42 dchi3 the difference between chi3v and chi3
43 dchi4 the difference between chi4v and chi4
44 knotpv the difference between chiv3c and chiv4pc
Kappa
Kappa
Kappa
Kappa descriptors
descriptors
descriptors
descriptors
1
1
κ
α
Kappa alpha index for 1 bonded fragment
2
2
κ
α
Kappa alpha index for 2 bonded fragment
3
3
κ
α
Kappa alpha index for 3 bonded fragment
4 phi Kier molecular flexibility index
5
a 1
κ Molecular shape Kappa index for 1 bonded fragment
6
a 2
κ Molecular shape Kappa index for 2 bonded fragment
7
a 3
κ Molecular shape Kappa index for 3 bonded fragment
Burden
Burden
Burden
Burden Descriptors
Descriptors
Descriptors
Descriptors
1-16 bcutm1-16 Burden descriptors based on atomic mass
17-32 bcutv1-16 Burden descriptors based on atomic vloumes
33-48 bcute1-16 Burden descriptors based on atomic electronegativity
49-64 bcutp1-16 Burden descriptors based on polarizability
Basak
Basak
Basak
Basak information
information
information
information descriptors
descriptors
descriptors
descriptors
1 IC0 Information content with order 0 proposed by Basak
2 IC1 Information content with order 1 proposed by Basak
3 IC2 Information content with order 2 proposed by Basak
4 IC3 Information content with order 3 proposed by Basak
5 IC4 Information content with order 4 proposed by Basak
6 IC5 Information content with order 5 proposed by Basak
7 IC6 Information content with order 6 proposed by Basak
8 SIC0 Complementary information content with order 0
proposed by Basak
9 SIC1 Structural information content with order 1 proposed by Basak
10 SIC2 Structural information content with order 2 proposed by Basak
11 SIC3 Structural information content with order 3 proposed by Basak
12 SIC4 Structural information content with order 4 proposed by Basak
13 SIC5 Structural information content with order 5 proposed by Basak
14 SIC6 Structural information content with order 6 proposed by Basak
15 CIC0 Complementary information content with order 0
proposed by Basak
16 CIC1 Complementary information content with order 1 proposed by Basak
17 CIC2 Complementary information content with order 2 proposed by Basak
18 CIC3 Complementary information content with order 3 proposed by Basak
19 CIC4 Complementary information content with order 4 proposed by Basak
20 CIC5 Complementary information content with order 5 proposed by Basak
21 CIC6 Complementary information content with order 6 proposed by Basak
E-state
E-state
E-state
E-state descriptors
descriptors
descriptors
descriptors
1 S(1) Sum of E-State of atom type: sLi
2 S(2) Sum of E-State of atom type: ssBe
3 S(3) Sum of E-State of atom type: ssssBe
4 S(4) Sum of E-State of atom type: ssBH
5 S(5) Sum of E-State of atom type: sssB
6 S(6) Sum of E-State of atom type: ssssB
7 S(7) Sum of E-State of atom type: sCH3
8 S(8) Sum of E-State of atom type: dCH2
9 S(9) Sum of E-State of atom type: ssCH2
10 S(10) Sum of E-State of atom type: tCH
11 S(11) Sum of E-State of atom type: dsCH
12 S(12) Sum of E-State of atom type: aaCH
13 S(13) Sum of E-State of atom type: sssCH
14 S(14) Sum of E-State of atom type: ddC
15 S(15) Sum of E-State of atom type: tsC
16 S(16) Sum of E-State of atom type: dssC
17 S(17) Sum of E-State of atom type: aasC
18 S(18) Sum of E-State of atom type: aaaC
19 S(19) Sum of E-State of atom type: ssssC
20 S(20) Sum of E-State of atom type: sNH3
21 S(21) Sum of E-State of atom type: sNH2
22 S(22) Sum of E-State of atom type: ssNH2
23 S(23) Sum of E-State of atom type: dNH
24 S(24) Sum of E-State of atom type: ssNH
25 S(25) Sum of E-State of atom type: aaNH
26 S(26) Sum of E-State of atom type: tN
27 S(27) Sum of E-State of atom type: sssNH
28 S(28) Sum of E-State of atom type: dsN
29 S(29) Sum of E-State of atom type: aaN
30 S(30) Sum of E-State of atom type: sssN
31 S(31) Sum of E-State of atom type: ddsN
32 S(32) Sum of E-State of atom type: aasN
33 S(33) Sum of E-State of atom type: ssssN
34 S(34) Sum of E-State of atom type: sOH
35 S(35) Sum of E-State of atom type: dO
36 S(36) Sum of E-State of atom type: ssO
37 S(37) Sum of E-State of atom type: aaO
38 S(38) Sum of E-State of atom type: sF
39 S(39) Sum of E-State of atom type: sSiH3
40 S(40) Sum of E-State of atom type: ssSiH2
41 S(41) Sum of E-State of atom type: sssSiH
42 S(42) Sum of E-State of atom type: ssssSi
43 S(43) Sum of E-State of atom type: sPH2
44 S(44) Sum of E-State of atom type: ssPH
45 S(45) Sum of E-State of atom type: sssP
46 S(46) Sum of E-State of atom type: dsssP
47 S(47) Sum of E-State of atom type: sssssP
48 S(48) Sum of E-State of atom type: sSH
49 S(49) Sum of E-State of atom type: dS
50 S(50) Sum of E-State of atom type: ssS
51 S(51) Sum of E-State of atom type: aaS
52 S(52) Sum of E-State of atom type: dssS
53 S(53) Sum of E-State of atom type: ddssS
54 S(54) Sum of E-State of atom type: sCl
55 S(55) Sum of E-State of atom type: sGeH3
56 S(56) Sum of E-State of atom type: ssGeH2
57 S(57) Sum of E-State of atom type: sssGeH
58 S(58) Sum of E-State of atom type: ssssGe
59 S(59) Sum of E-State of atom type: sAsH2
60 S(60) Sum of E-State of atom type: ssAsH
61 S(61) Sum of E-State of atom type: sssAs
62 S(62) Sum of E-State of atom type: sssdAs
63 S(63) Sum of E-State of atom type: sssssAs
64 S(64) Sum of E-State of atom type: sSeH
65 S(65) Sum of E-State of atom type: dSe
66 S(66) Sum of E-State of atom type: ssSe
67 S(67) Sum of E-State of atom type: aaSe
68 S(68) Sum of E-State of atom type: dssSe
69 S(69) Sum of E-State of atom type: ddssSe
70 S(70) Sum of E-State of atom type: sBr
71 S(71) Sum of E-State of atom type: sSnH3
72 S(72) Sum of E-State of atom type: ssSnH2
73 S(73) Sum of E-State of atom type: sssSnH
74 S(74) Sum of E-State of atom type: ssssSn
75 S(75) Sum of E-State of atom type: sI
76 S(76) Sum of E-State of atom type: sPbH3
77 S(77) Sum of E-State of atom type: ssPbH2
78 S(78) Sum of E-State of atom type: sssPbH
79 S(79) Sum of E-State of atom type: ssssPb
80-158 Smax1-Smax79 maxmum of E-State value of specified atom type
159-237 Smin1-Smin79 minimum of E-State value of specified atom type
Autocorrelation
Autocorrelation
Autocorrelation
Autocorrelation descriptors
descriptors
descriptors
descriptors
1-8 ATSm1-ATSm8 Moreau-Broto autocorrelation descriptors based on atom mass
9-16 ATSv1-ATSv8 Moreau-Broto autocorrelation descriptors based on atomic van
der Waals volume
17-24 ATSe1-ATSe8 Moreau-Broto autocorrelation descriptors based on atomic
Sanderson electronegativity
25-32 ATSp1-ATSp8 Moreau-Broto autocorrelation descriptors based on atomic
polarizability
33-40 MATSm1-MATSm8 Moran autocorrelation descriptors based on atom mass
41-48 MATSv1-MATSv8 Moran autocorrelation descriptors based on atomic van der Waals
volume
49-56 MATSe1-MATSe8 Moran autocorrelation descriptors based on atomic Sanderson
electronegativity
57-64 MATSp1-MATSp8 Moran autocorrelation descriptors based on atomic polarizability
65-72 GATSm1-GATSm8 Geary autocorrelation descriptors based on atom mass
73-80 GATSv1-GATSv8 Geary autocorrelation descriptors based on atomic van der Waals
volume
81-88 GATSe1-GATSe8 Geary autocorrelation descriptors based on atomic Sanderson
electronegativity
89-96 GATSp1-GATSp8 Geary autocorrelation descriptors based on atomic polarizability
Charge
Charge
Charge
Charge descriptors
descriptors
descriptors
descriptors
1-4 Q
Hmax
Q
Cmax
Q
Nmax
Q
Omax
Most positive charge on H,C,N,O atoms
5-8 Q
Hmin
Q
Cmin
Q
Nmin
Q
Omin
Most negative charge on H,C,N,O atoms
9-10 Q
max
Q
min
Most positive and negative charge in a molecule
11-15 Q
HSS
Q
CSS
Sum of squares of charges on H,C,N,O and all toms
Q
NSS
Q
OSS
Qass
16-17 Mpc
Tpc
Mean and total of positive charges
18-19 Mnc
Tnc
Mean and total of negative charges
20-21 Mac
Tac
Mean and total of absolute charges
22 Rpc Relative positive charge
23 Rnc Relative negative charge
24 SPP Submolecular polarity parameter
25 LDI Local dipole index
Molecular
Molecular
Molecular
Molecular property
property
property
property descriptors
descriptors
descriptors
descriptors
1
a
MREF Molar refractivity
2
a
logP LogP value based on the Crippen method
3 logP2 Square of LogP value based on the Crippen method
4
a
TPSA Topological polarity surface area
5 UI Unsaturation index
6 Hy Hydrophilic index
MOE-type
MOE-type
MOE-type
MOE-type descriptors
descriptors
descriptors
descriptors
1
a
M TPSA topological polar surface area based on fragments
2
a
LabuteASA Labute's Approximate Surface Area
3-14
a
SLOGPVSA MOE-type descriptors using SLogP contributions and surface area
contributions
15-24
a
SMRVSA MOE-type descriptors using MR contributions and surface area
contributions
25-38
a
PEOEVSA MOE-type descriptors using partial charges and surface area
contributions
39-49
a
EstateVSA MOE-type descriptors using Estate indices and surface area
contributions
50-60
a
VSAEstate MOE-type descriptors using surface area contributions and Estate
indices
Fragment/Fingerprint-based
Fragment/Fingerprint-based
Fragment/Fingerprint-based
Fragment/Fingerprint-based descriptors
descriptors
descriptors
descriptors
1
a
FP2 (Topological fingerprint) A Daylight-like fingerprint based on
hashing molecular subgraphs
2
a
MACCS (MACCS keys)Using the 166 public keys implemented as SMARTS
3 E-state 79 E-state fingerprints or fragments
4 FP4 307 FP4 fingerprints
5
a
Atom Paris Atom Paris fingerprints
6
a
Torsions Topological torsion fingerprints
7
a
Morgan/Circular Fingerprints based on the Morgan algorithm
Note:
a
indicates that these descriptors are from RDkit. In PyDPI, we wrapped most of molecular
descriptors form RDkit. The other descriptors are independently coded by us.
