Matrix metalloproteinases (MMPs): Chemical–biological functions ...

2238 R. P. Verma, C. Hansch / Bioorg. Med. Chem. 15 (2007) 2223–2268
Table 6. Description about the physicochemical parameters used for the QSAR models listed in Table 5
No. Physicochemical parameter Description
1 logP or ClogP Hydrophobicity of the molecules
2 logPo Optimum value of hydrophobicity for the molecules
3 p Hydrophobicity of the substituents
4 NVE Number of valence electron
5
1 v
v Kier’s first-order valence molecular connectivity index ( 1 v v ) of the substituents/molecules
6 Si Electrotopological state (E-state) indices (Si) of the atom: measure of the availability of p or
lone pair electrons on the atom
7 SN (E-state) indices nitrogen atom: availability of p or lone pair electrons on the nitrogen atom.
8 SS (E-state) indices sulfur atom: availability of p or lone pair electrons on the sulfur atom.
9 r Sigma (electronic parameter)
10 MR Molar refractivity
11 Pol Polarizability
the QSAR are executed with the C-QSAR program. 100
The parameters used in this review have already been
discussed in detail along with their application. 79 Briefly,
ClogP is the calculated partition coefficient in n-octanol/
water and is a measure of hydrophobicity, and p is the
hydrophobic parameter for substituents. Cp is the calculated
hydrophobic parameter of the substituents. r, r + ,
and r are Hammett electronic parameters that apply
to substituent effects on aromatic systems. B1, B5, and
L are Verloop’s sterimol parameters for substituents. 101
B1 is a measure of the minimum width of a substituent,
B5 is an attempt to define maximum width of the whole
substituent, and L is the substituent length.
CMR is the calculated molar refractivity for the whole
molecule. MR is calculated from the Lorentz–Lorenz
equation and is described as follows: [(n 2
1)/
(n 2 + 2)](MW/d), where n is the refractive index, MW
is the molecular weight, and d is the density of the substance.
MR is dependent on volume and polarizability.
It can be used for a substituent or for the whole molecule.
A new polarizability parameter, NVE, was developed,
which is shown to be effective at delineating
various chemico-biological interactions. 85,102–104 NVE
represents the total number of valence electrons and is
calculated by simply summing up the valence electrons
in a molecule, that is, H = 1, C = 4, Si = 4, N = 5,
P = 5, O = 6, S = 6, and halogens = 7. It may also be
represented as: NVE = nr + np + nn, where nr is the
number of electrons in r-orbital, np is the number of
electrons in p-orbitals, and nn is the number of lone pair
electrons. MgVol is the molar volume for the whole
molecule. 105 The indicator variable I is assigned the
value of 1 or 0 for special features with special effects
that cannot be parametrized and has been explained
wherever used.
In QSAR equations, n is the number of data points, r is
the correlation coefficient between observed values of
the dependent and the values calculated from the equation,
r 2 is the square of the correlation coefficient representing
the goodness of fit, q 2 is the cross-validated r 2 (a
measure of the quality of the QSAR model), and s is
the standard deviation. The cross-validated r 2 (q 2 ) is
obtained by using leave-one-out (LOO) procedure as
described by Cramer et al. 106 Q is the quality factor (quality
ratio), where Q = r/s. Chance correlation, due to the
excessive number of parameter (which increases the r
and s values also), can, thus, be detected by the examination
of Q value. F is the Fischer statistics (Fischer ratio),
F = fr 2 /[(1 r 2 )m], where f is the number of degree of
freedom, f = n (m+1), n is the number of data points
and m is the number of variables. The modeling was
taken to be optimal when Q reached a maximum together
with F, even if slightly nonoptional F values have
normally been accepted. A significant decrease in F
with the introduction of one additional variable (with
increasing Q and decreasing s) could mean that the new
descriptor is not as good as expected, that is, its introduction
has endangered the statistical quality of the
combination that nevertheless can again improve with
the ulterior introduction of a more convincing descriptor.
107 Compounds were assigned to be outliers on the
basis of their deviation between observed and calculated
activities from the equation (>2s). 108 Each regression
equation includes 95% confidence limits for each term
in parentheses.
All the new QSARs reported here are derived by us and
were not formulated by the original authors. These
QSARs are found to be statistically significant, which
fulfill the conditions given by Golbraikh and Tropsha 109
as the acceptable models. These models also fulfill the
condition of (number of data points)/(number of
descriptors) P 4. For a list of outliers in each data set,
refer to the corresponding tables.
10.2.2. Results and discussion
10.2.2.1. MMP-1 inhibitors. Inhibition of MMP-1 by
acyclic a-sulfonamide hydroxamates (I). Data obtained
from Levin et al. 110 (Table 7).
O Y
HO
NH
N
S
O
X
I
O
log 1=IC50 ¼ 0:94ð 0:39ÞClogP 1:01ð 0:46ÞI Y
O
þ 4:72ð 0:88Þ; ð1Þ
n = 13, r 2 = 0.849, s = 0.369, q 2 = 0.727, Q = 2.499,
F = 28.113.