Molecular Descriptors Guide Manual
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Molecular Descriptors Guide
Description of the Molecular Descriptors Appearing in the
PyDPI Software Package
Version1.0
©2012 China Computational Biology Drug Design Group
Table of 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 Descriptors of 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 Molecular constitutional descriptors
1. Molecular 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:
(1)
The molecular weight (MW) is the sum of molecular weights of the individual atoms, defined
as:
A
MW = ∑ MWi
i =1
and the average molecular weight (AWeight) is given as follows:
AWeight=MW/nAT
where nAT is the number of atoms
(2)
The 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.
The 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)
From 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)
From descriptor 25 to 30, they represent the number of path of length 1-6. The path of length n
indicates the shortest distance equal n between two atoms in a topological molecular graph.
1.2 Topological descriptors
1. Weiner index (W)
2. Average Weiner index (AW)
3. Balaban’s J index (J)
4. Harary number (Thara)
5. Schiultz index (Tsch)
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)
Introduction:
(1)
Weiner index (W)
W = (∑ d ij ) / 2
dij is the entries of distance matrix D from H-depleted molecular graph.
(2)
Average Weiner index (AW)
The average Weiner index is given by
WA =
2W
A( A − 1)
where 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)
J=
where
σi
and
σj
B
−1/2
(
σ
σ
)
∑ i jb
C +1 b
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 (Thara)
H=
1
dij−1
∑∑
2 i j
The Harary index is a molecular topological index derived from the reciprocal distance matrix
D-1
(5)
Schiultz index (Tsch)
n
MTI = ∑ [( A + D)v ]i
i =1
It is a topological index derived from the adjacency matrix A, the distance matrix D and
n-dimensional column vector 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:
D
GDI = ∑ ( k f ) 2
k =1
where D is the topological diameter, kf 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 AE, it is the sum over all entries of
the edge adjacency matrix:
B
B
AE = ∑ ∑ Eij
i =1 j =1
where 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:
A
∑δ σ
2
i
∑δ σ
i
i
Xu =
A log
i =1
A
i
i =1
where 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)
Ziv
D =∑
i =1 Li
A
Z
where 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:
I CPX = I CPB + I CPA
where ICPB and ICPA are the information contents related to the bond connectivity and atom type
diversity
(13)
Gutman molecular topological index based on simple vertex
A
degree (GMTI)
A
SG = ∑∑ δ iδ j d ij
i =1 j =1
where δ iδ j d ij 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
M 1 = ∑ δ a2
a
where a runs over the A atoms of the molecule and δ is the vertex degree.
(15)
Zagreb index with order 2 (ZM2)
M 2 = ∑ (δ iδ j )b
b
where 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)
∑
Q=
g
(g 2 − 2g ) g F + 2
2
Quadratic index also called normalized quadratic index, where g are the different vertex degree
values and gF is the vertex degree count.
(19)
Largest value in the distance matrix (diametert)
D = max i (ηi )
ηi = max j (dij )
ηi called atom eccentricity is the maximum distance from the ith vertex to the other vertices.
(20)
Radius based on topology (radiust)
R = min i (ηi )
(21)
Petitjean based on topology (petitjeant)
I2 =
(22)
D−R
R
The logarithm of the simple topological index by Narumi (Sito)
A
S = ∏ δi
i =1
where 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)
H=
A
A
∑1/ δ
i
i =1
(24)
Geometric topological index by Narumi (Geto)
1/ A
⎛ A ⎞
G = ⎜ ∏δi ⎟
⎝ i =1 ⎠
(25)
Arithmetic topological index by Narumi (Arto)
A
∑δ
A=
i =1
A
i
1.3 Molecular connectivity indices
1. Valence molecular connectivity Chi index for path order 0 (0χv)
2. Valence molecular connectivity Chi index for path order 1(1χv)
3. Valence molecular connectivity Chi index for path order 2(3χv)
4. Valence molecular connectivity Chi index for path order 3(4χv)
5. Valence molecular connectivity Chi index for path order 4(5χv)
6. Valence molecular connectivity Chi index for path order 5(6χv)
7. Valence molecular connectivity Chi index for path order 6(7χv)
8. Valence molecular connectivity Chi index for path order 7 (8χv)
9. Valence molecular connectivity Chi index for path order 8(9χv)
10. Valence molecular connectivity Chi index for path order 9(10χv)
11. Valence molecular connectivity Chi index for path order 10(11χv)
12. Valence molecular connectivity Chi index for three cluster (3χvc)
13. Valence molecular connectivity Chi index for four cluster (4χvc)
14. Valence molecular connectivity Chi index for path/cluster (4χvpc)
15. Valence molecular connectivity Chi index for cycles of 3 (3χvCH)
16. Valence molecular connectivity Chi index for cycles of 4 (4χvCH)
17. Valence molecular connectivity Chi index for cycles of 5 (5χvCH)
18. Valence molecular connectivity Chi index for cycles of 6 (6χvCH)
19. Simple molecular connectivity Chi indices for path order 0 (0χ)
20. Simple molecular connectivity Chi indices for path order 1 (1χ)
21. Simple molecular connectivity Chi indices for path order 2 (2χ)
22. Simple molecular connectivity Chi indices for path order 3 (3χp)
23. Simple molecular connectivity Chi indices for path order 4 (4χp)
24. Simple molecular connectivity Chi indices for path order 5 (5χp)
25. Simple molecular connectivity Chi indices for path order 6 (6χp)
26. Simple molecular connectivity Chi indices for path order 7 (7χp)
27. Simple molecular connectivity Chi indices for path order 8 (8χp)
28. Simple molecular connectivity Chi indices for path order 9 (9χp)
29. Simple molecular connectivity Chi indices for path order 10 (10χp)
30. Simple molecular connectivity Chi indices for three cluster (3χc)
31. Simple molecular connectivity Chi indices for four cluster (4χc)
32. Simple molecular connectivity Chi indices for path/cluster (4χpc)
33. Simple molecular connectivity Chi indices for cycles of 3 (3χCH)
34. Simple molecular connectivity Chi indices for cycles of 4 (4χCH)
35. Simple molecular connectivity Chi indices for cycles of 5 (5χCH)
36. Simple molecular connectivity Chi indices for cycles of 6 (6χCH)
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 (dchi1)
41. the difference between chi2v and chi2 (dchi0)
42. the difference between chi3v and chi3 (dchi3)
43. the difference between chi4v and chi4 (dchi4)
44. the difference between chiv3c and chiv4pc (knotpv)
Introduction:
1.
Simple molecular connectivity index (No.19~36)
The general formula for the molecular connectivity indices (mχt) is as follows:
k
m
χq =
n
∑ (∏ δ
k =1
a
) −k 1/ 2
a =1
where 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
of
graph
and in
the
case
the
path
sub-graphs equals the mth order path count mP. 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.
For the first three path indices (0χ, 1χ, 2χ), the calculation type, p, is often omitted from the variable
name in the software.
2. Valence molecular connectivity indices (No.1~18)
The valence connectivity indices (mχvt) 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: δv=Zv-h=σ+π+n-h. Where Zv 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.
The valence connectivity indices are described on page 86 of the Handbook of Molecular
Descriptors. The connectivity indices are described in detail in the literature.
3. The remains connectivity indices are simple combination of the above simple connectivity indices
and valence connectivity indices.
1.4 Kappa shape descriptors
1. Kappa alpha index for 1 bonded fragment (1κα)
2. Kappa alpha index for 2 bonded fragment (2κα)
3. Kappa alpha index for 3 bonded fragment (3κα)
4. Kier molecular flexibility index (phi)
5. Molecular shape Kappa index for 1 bonded fragment (1κ)
6. Molecular shape Kappa index for 2 bonded fragment (1κ)
7. Molecular shape Kappa index for 3 bonded fragment (1κ)
Introduction:
(1)
Kappa alpha index
The first order kappa shape index (1κ) is given by
1
k = 2 1Pmax 1Pmin / ( 1Pi ) 2 = A( A − 1) 2 / ( 1Pi ) 2
where Pi=# 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 (2κ) is given by
2
k = 2 2 Pmax 2 Pmin / ( 2 Pi ) 2 = ( A − 1)( A − 2) 2 / ( 2 Pi ) 2
The kappa shape indices are described on pg 248 of the Handbook of Molecular Descriptors.
The first order kappa alpha shape index (1κα) is given by
( A + a)( A + a − 1)2
ka =
( 1P + a ) 2
1
where
a = 1−
rx
rx ( sp3 )
where rx is the covalent radius of the atom being evaluated and rx ( sp3 ) is the covalent radius of a
carbon sp3 atom (0.77Å).
The second order kappa alpha shape index (2κα) is given by
2
( A + a − 1)( A + a − 2)2
ka =
( 2 P + a) 2
The third order kappa alpha shape index (3κα) is given by
3
( A + a − 1)( A + a − 3)2
ka =
( 3 P + a)2
( A + a − 3)( A + a − 2)2
ka =
( 3P + a)2
if A is odd
3
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
1
ka 2ka
phi =
A
The kappa flexibility index is described on page 178 of the Handbook of Molecular Descriptors.
1.5 Burden 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:
The Burden eigenvalue descriptors are determined by solving the following general eigenvalue
equation:
V=V
V. e
B.V
where B is a real connectivity matrix to be defined, V is a matrix of eigenvectors, and e is a diagonal
matrix of eigenvalues. The rules defining B are as follows:
a.
Hydrogen atoms are included.
b.
The diagonal elements of B, Bii, are either given by the carbon normalized atomic mass, vander
Waals volume, Sanderson electronegativity, and polarizability of atom i.
c.
The element of B connecting atoms i and j, Bij, is equal to the square root of the bond order
between atoms i and j.
d.
All other elements of 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 Basak 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.
1.77 Electrotopological State 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:
The E-State value for a given non-hydrogen atom i in a molecule is given by its intrinsic state (Ii) plus
the sum of the perturbations on that atom from all the other atoms in the molecule:
A
Sk = I k + ∑ ∆I ki
i =1
where the intrinsic state (Ik) is given by
(2 / N ) 2 δ kv + 1
Ik =
δk
where 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
∆I ki =
(Ii − Ik )
rki 2
where
rki = d ki + 1
dki 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.
SX = ∑ S (t )
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.
1.88 Autocorrelation descriptors
The Broto-Moreau autocorrelation descriptors (ATSdw) are given by
A
A
ATSdw = ∑∑ δ ijωiω j
i =1 j =1
where 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 dij=d, zero otherwise), and wi and wj 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
where 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.
1.88.1 Moreau-Broto autocorrelation 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.
1.88.2 Moran autocorrelation 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.
1.88.3 Geary autocorrelation 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.
1.99 Charge descriptors
1. Most positive charge on H atoms (QHmax)
2. Most positive charge on C atoms (QCmax)
3. Most positive charge on N atoms (QNmax)
4. Most positive charge on O atoms (QOmax)
5. Most negative charge on H atoms (QHmin)
6. Most negative charge on C atoms (QCmin)
7. Most negative charge on N atoms (QNmin)
8. Most negative charge on O atoms (QOmin)
9. Most positive charge in a molecule (Qmax)
10. Most negative charge in a molecule (Qmin)
11. Sum of squares of charges on H atoms (QHSS)
12. Sum of squares of charges on C atoms (QCSS)
13. Sum of squares of charges on N atoms (QNSS)
14. Sum of squares of charges on O atoms (QOSS)
15. Sum of squares of charges on all atoms (QaSS)
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)
Introduction:
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 (Qmax)
The maximum positive charge of the atoms in a molecule:
Qmax = max a (qa+ )
where q+ are net atom positive charges
(2)
Most negative charge in a molecule (Qmin)
The maximum negative charge of the atoms in a molecule:
Qmin = max a ( qa− )
where 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:
Tpc = ∑ a (qa+ )
where 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:
Tnc = ∑ a (qa− )
where q- are net atom negative charges
10 molecular properties
1.
1.10
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:
(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:
n 2 − 1 MW
MR = 2
n +2 ρ
where 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 ak
measuring the lipophilic contributions of atoms in the molecule, each described by its
neighbouring atoms.
LogP = ∑ k ak N k
where Nk 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.
TPSA = ∑ a SAa
qa ≥ 0.2
（4） Unsaturation index (UI)
The unsaturation index (UI) is defined as
UI = log 2 (1 + nDB + nTB + nAB)
where 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
N Hy
1
1
(1 + N Hy ) log 2 (1 + N Hy ) + N c ( log 2 ) +
2
A
A
A
Hy =
log 2 (1 + A)
where NHy is the number of hydrophilic groups (or the total number of hydrogen attached to
oxygen, sulfur and nitrogen atoms), Nc 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).
11 MOE-type descriptors
1.
1.11
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 (SLOGPVSA1)
4. MOE-type descriptors using SLogP contributions and surface area contributions (SLOGPVSA2)
5. MOE-type descriptors using SLogP contributions and surface area contributions (SLOGPVSA3)
6. MOE-type descriptors using SLogP contributions and surface area contributions (SLOGPVSA4)
7. MOE-type descriptors using SLogP contributions and surface area contributions (SLOGPVSA5)
8. MOE-type descriptors using SLogP contributions and surface area contributions (SLOGPVSA6)
9. MOE-type descriptors using SLogP contributions and surface area contributions (SLOGPVSA7)
10. MOE-type descriptors using SLogP contributions and surface area contributions (SLOGPVSA8)
11. MOE-type descriptors using SLogP contributions and surface area contributions(SLOGPVSA9)
12. MOE-type descriptors using SLogP contributions and surface area contributions(SLOGPVSA10)
13. MOE-type descriptors using SLogP contributions and surface area contributions(SLOGPVSA11)
14. MOE-type descriptors using SLogP contributions and surface area contributions(SLOGPVSA12)
15. MOE-type descriptors using MR contributions and surface area contributions (SMRVSA1)
16. MOE-type descriptors using MR contributions and surface area contributions (SMRVSA2)
17. MOE-type descriptors using MR contributions and surface area contributions (SMRVSA3)
18. MOE-type descriptors using MR contributions and surface area contributions (SMRVSA4)
19. MOE-type descriptors using MR contributions and surface area contributions (SMRVSA5)
20. MOE-type descriptors using MR contributions and surface area contributions (SMRVSA6)
21. MOE-type descriptors using MR contributions and surface area contributions (SMRVSA7)
22. MOE-type descriptors using MR contributions and surface area contributions (SMRVSA8)
23. MOE-type descriptors using MR contributions and surface area contributions (SMRVSA9)
24. MOE-type descriptors using MR contributions and surface area contributions (SMRVSA10)
25. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA1)
26. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA2)
27. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA3)
28. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA4)
29. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA5)
30. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA6)
31. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA7)
32. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA8)
33. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA9)
34. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA10)
35. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA11)
36. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA12)
37. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA13)
38. MOE-type descriptors using partial charges and surface area contributions (PEOEVSA14)
39. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA1)
40. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA2)
41. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA3)
42. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA4)
43. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA5)
44. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA6)
45. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA7)
46. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA8)
47. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA9)
48. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA10)
49. MOE-type descriptors using Estate indices and surface area contributions (EstateVSA11)
50. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate1)
51. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate2)
52. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate3)
53. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate4)
54. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate5)
55. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate6)
56. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate7)
57. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate8)
58. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate9)
59. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate10)
60. MOE-type descriptors using surface area contributions and Estate indices (VSAEstate11)
1.1
1.122 Molecular 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 fingerprints 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. Thus 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. There is a one-to-one correspondence between each SMARTS
pattern and bit in the fingerprint. For 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 1 Representation 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
1.122.1 Daylight-type fingerprint
The Daylight fingerprints (DFP) are hashed fingerprints 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
1.122.2 MACCS keys and FP4 fingerprint
The FP4 and MACCS fingerprints are used to construct the substructure dictionaries, respectively.
The dictionary of FP4 fingerprint contains 307 mostly common substructure patterns. It 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
1.122.3 E-state 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
1.122.4 Atom pairs and topological torsions fingerprints
Atom pairs fingerprint:
Atom pairs are substructure descriptors defined 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 = {[ith atom description][separation][ jth atom description]}
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 defined 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 torsion fingerprint:
The topological torsion descriptor (TT) is related to the 4-atom linear subfragment descriptor of
Klopman because it is defined 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 defined 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, defined 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 specific chemical
information concerning different functional groups, but cannot discriminate between different
arrangements of functional groups within a molecule.
1.1
1.122.5 Morgan 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:
[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 modified
adjacency matrix. Quant. Struct. -Act. Relat., 1997, 16, 309–314
[23] 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 Descriptors of proteins and peptides
A protein or peptide sequence with N amino acid residues is expressed as: R1, R2, R3, …, RN, where Ri
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.
2.1 Amino acid 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:
f (r ) =
Nr
N
r=1, 2, 3, ..., 20
Where Nr is the number of the amino acid type r and N is the length of the sequence.
2.2 Dipeptide composition
The dipeptide composition gives 400 features, defined as:
f (r , s) =
N rs
N −1
r, s=1, 2, 3, ..., 20
where Nrs is the number of dipeptide represented by amino acid type r and s.
2.3 Tripeptide composition
The tripeptide composition gives 8000 features, defined as:
f ( r , s, t ) =
N rst
N −2
r, s=1, 2, 3, ..., 20
where Nrst is the number of tripeptide represented by amino acid type r, s and t.
2.4 Autocorrelation 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.
Pr =
Pr − P
σ
Where P is the average of the property of the 20 amino acids.
20
∑P
r
P=
r =1
and
20
σ=
1 20
( Pr − P )2
∑
20 r =1
2.4.1 Normalized Moreau-Broto autocorrelation descriptors
Moreau-Broto autocorrelation descriptors application to protein sequences may be defined as:
N −d
AC (d ) =
∑ PP
i i+ d
d=1, 2, 3, ..., nlag
i =1
Where d is called the lag of the autocorrelation and Pi and Pi+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:
ATS ( d ) =
AC (d )
N −d
d=1, 2, 3, ..., nlag
Figure 2 An illustrated example in the AAIndex database
2.4.2 Moran autocorrelation
Moran autocorrelation descriptors application to protein sequence may be defined as:
I (d ) =
1
N −d
N −d
∑ ( P − P)( P
i
i+d
− P)
i =1
1
N
d=1, 2, 3, ..., 30.
N
∑ ( P − P)
2
i
i =1
Where d and Pi and Pi+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.,
N
∑P
i
P=
i =1
N
Where d, P , Pi and Pi+d, nlag have the same meaning as in the above.
2.4.3 Geary autocorrelation Descriptors
Geary autocorrelation descriptors application to protein sequence may be defined as:
N −d
1
∑ ( Pi − Pi + d )2
2( N − d ) i =1
C (d ) =
1 N
( Pi − P) 2
∑
N − 1 i =1
d=1, 2, 3, ..., 30.
Where d, P , Pi and Pi+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.
2.5 Composition, transition and distribution
These descriptors are developed by Dubchak, et.al.
Figure 3 The 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. Sequence 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 1 Amino acid attributes and the division of the amino acids into three groups for each attribute
Group 1
Group 2
Group 3
Polar
Neutral
Hydrophobicity
R,K,E,D,Q,N
G, A, S,T,P,H,Y
C,L,V,I,M,F,W
0-2.78
2.95-4.0
4.03-8.08
G,A,S,T,P,D
N,V,E,Q,I,L
M,H,K,F,R,Y,W
4.9-6.2
8.0-9.2
10.4-13.0
L,I,F,W,C,M,V,Y
P,A,T,G,S
H,Q,R,K,N,E,D
0-1.08
0.128-0.186
0.219-0.409
G,A,S,D,T
C,P,N,V,E,Q,I,L
K,M,H,F,R,Y,W
Positive
Neutral
Negative
K,R
A,N,C,Q,G,H,I,L,M,F,P,S,T,W,Y,
D,E
hydrophobicity
normalized van
der
Waals
volume
polarity
polarizability
charge
V
Helix
Strand
Coil
E,A,L,M,Q,K,R,H
V,I,Y,C,W,F,T
G,N,P,S,D
Buried
Exposed
Intermediate
A,L,F,C,G,I,V,W
R,K,Q,E,N,D
M,S P,T,H,Y
secondary
structure
solvent
accessibility
For example, for a given sequence “MTEITAAMVKELRESTGAGA”, it will be encoded as
“32132223311311222222” according to its hydrophobicity division.
Step 2: Composition, Transition and Distribution descriptors
Three descriptors, “Composition (C)”, “Transition (T)”, and “Distribution (D)” were calculated for a
given attribute as follows:
Composition: It is the global percent for each encoded class in the sequence. In the
above example
using hydrophobicity 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:
Cr =
nr
n
r=1, 2, 3
Where nr is the number of r in the encoded sequence and N is the length of the sequence.
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:
Trs =
nrs + nsr
N −1
rs="12", "13", "23"
Where nrs, nsr is the numbers of dipeptide encoded as “rs” and “sr” respectively in the sequence and N
is the length of the sequence.
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”,
“2” residue (50%*10=5),
the 2th residue “2”
the 7th “2” (75%*10=7) and
(25%*10=2),
the 5th
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 Conjoint Triad 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 1: classification of amino 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 2 Classification of amino acids based on dipoles and volumes of the side chains
a
Dipole scale (Debye): -, Dipole<1.0; +, 1.03.0; +'+'+', Dipole>3.0
with opposite orientation. b Volume scale (Å3): -, 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 2: Conjoint triad 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,
V, F) to represent a protein sequence. Here, V is the vector space of the
we first use a binary space (V
sequence features, and each feature vi represents a sort of triad type; F is the frequency vector
corresponding to V, and the value of the ith dimension of F (fi) is the frequency of type vi appearing in
the protein sequence. For the amino acids that have been catalogued into seven classes, the size of V
V, F) is illustrated in Figure 3.
should be 7×7×7; thus i = 1,2, ..., 343. The detailed description for (V
Clearly, each protein correlates to the length (number of amino acids) of protein. In general, a long
protein would have a large value of fi, which complicates the comparison between two heterogeneous
proteins. Thus, we defined a new parameter, di, by normalizing
fi with the following equation.
di = ( f i − min{ f1 , f 2 , f 3 ,..., f 343}) / max{ f1 , f 2 , f 3 ,..., f 343}
The numerical value of di of each protein ranges from 0 to 1, which thereby enables the comparison
between proteins. Accordingly, we obtain another vector space (designated D) consisting of di to
represent protein
Figure 3 Schematic diagram for constructing the vector space (V, F) of protein sequence. V is the vector space of the
sequence features; each feature (vi) represents a triad composed of three consecutive amino acids; F is the frequency
vector corresponding to V, and the value of the ith dimension of F(fi) is the frequency that vi triad appeared in the
protein sequence. This figure is from Ref. 13.
2.7 Quasi-sequence-order 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.
2.7.
7.11 Sequence-order-coupling numbers
The dth-rank sequence-order-coupling number is defined as:
N −d
∑ (d
τd =
i ,i + d
)2
d=1, 2, 3, ... , maxlag
i =1
Where di,i+d is the distance between the two amino acids at position i and i+d.
Note: maxlag is the maximum lag and the length of the protein must be not less than maxlag.
2.7.2 Quasi-sequence-order (QSO) descriptors
For each amino acid type, a quasi-sequence-order descriptor can be defined as:
Xr =
fr
r=1, 2, 3, ... , 20
maxlag
20
∑f
r
+w
r =1
∑τ
d
d =1
Where fr 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:
Xr =
wτ d − 20
∑f
r =1
d=21, 22, 23, ... , 20+maxlag
maxlag
20
r
+w
∑τ
d
d =1
In addition to Schneider-Wrede physicochemical distance matrix used by Chou et al,
chemical distance matrix by Grantham is also used here.
another
Figure 4 A 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.
2.8 pseudo-amino acid composition (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 H1o (i ) , H 2o (i ) , M o (i) (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:
H1o (i ) −
H1 (i ) =
1 20 o
∑ H1 (i )
20 i =1
20
∑[ H1o (i) −
i =1
1 20 o 2
∑ H1 (i)]
20 i =1
20
H 2o (i ) and M o (i) are normalized as H 2 (i ) and M (i ) in the same way.
Figure 5
A 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 (aa) reflects the correlation mode
b) that between all the second-most contiguous
between all the most contiguous residues, panel (b
residues, and panel (cc) that between all the third-most contiguous residues. This figure is from Ref. 8.
Then, a correlation function can be defines as:
Θ( Ri , R j ) =
2
2
2
1
⎡⎣ H1 ( Ri ) − H1 ( R j ) ⎤⎦ + ⎡⎣ H 2 ( Ri ) − H 2 ( R j ) ⎤⎦ + ⎡⎣ M ( Ri ) − M ( R j ) ⎤⎦
3
{
}
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:
Θ( Ri , R j ) = ⎡⎣ H1 ( Ri ) − H1 ( R j ) ⎤⎦
2
where H(Ri) is the amino acid property of amino acid Ri after standardization.
For a set of n amino acid properties, it can be defined as: where Hk(Ri) is the kth property in the amino
acid property set for amino acid Ri.
2
1 n
⎡⎣ H k ( Ri ) − H k ( R j ) ⎤⎦
∑
n k =1
Θ( Ri , R j ) =
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:
θ1 =
1 N −1
∑ Θ( Ri , Ri+1 )
N − 1 i =1
θ2 =
1 N −2
∑ Θ( Ri , Ri +2 )
N − 2 i =1
θ3 =
1 N −3
∑ Θ( Ri , Ri +3 )
N − 3 i =1
...
θλ =
1
N −λ
N −λ
∑ Θ( R , R
i
i+λ
)
i =1
λ (
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