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

2260 R. P. Verma, C. Hansch / Bioorg. Med. Chem. 15 (2007) 2223–2268
Table 44. Biological, physicochemical, and structural parameters used to derive QSAR equation 48 for the inhibition of MMP-14 by
pyrimidinetrione derivatives (XXXVI)
No. X log1/IC50 (Eq. 48) ClogP B1X I
Obsd. Pred. D
1 4-F 7.64 8.21 0.57 3.11 3.35 1
2 3-F 7.22 7.48 0.26 3.11 3.35 0
3 2-F 7.80 7.38 0.42 2.91 3.35 0
4 4-Cl 7.74 7.45 0.29 3.68 3.80 1
5 3-Cl 6.92 6.72 0.20 3.68 3.80 0
6 2-Cl 6.29 6.60 0.31 3.45 3.80 0
7 4-CH3 7.64 7.27 0.37 3.47 3.52 0
8 3-CH3 7.30 7.27 0.03 3.47 3.52 0
9 2-CH3 7.15 7.27 0.12 3.47 3.52 0
10 4-Br 7.72 7.18 0.54 3.83 3.95 1
11 4-CF3 6.82 7.09 0.27 3.85 3.99 1
12 4-C(CH3) 3 5.17 5.41 0.24 4.79 4.60 0
13
14
4-C6H5 7.44 7.52 0.08 4.86 3.71 0
a
4-OCH3 6.66 7.37 0.71 2.89 3.35 0
15 4-SO2CH3 5.06 5.00 0.06 1.33 4.03 0
16 4-CN 6.70 6.54 0.16 2.40 3.60 0
17 4-CONH2 6.21 6.31 0.10 1.48 3.50 0
18
19
4-CONHCH3 6.19 6.32 0.13 1.69 3.54 0
a
4-CON(CH3) 2 5.03 6.06 1.03 1.43 3.60 0
a Not included in the derivation of QSAR 48.
log 1=IC50 ¼ 0:50ð 0:20ÞClogP
2:33ð 0:61ÞB1X þ 0:73ð 0:42ÞI
þ 13:73ð 2:10Þ; ð48Þ
n =17, r 2 = 0.877, s = 0.333, q 2 = 0.752, Q = 2.811,
F = 30.897. Clog P versus B1 X: r = 0.384.
B1X is the sterimol parameter for X-substituents, which
is the measure of minimum width and suggests a negative
effect on the inhibition. The indicator variable I
takes the value of 1 for the presence of halogen at
X-4. The positive coefficient of I indicates that the
presence of halogen at X-4 position will improve the
activity.
10.2.3. Validation of QSAR. The real utility of a QSAR
model is in its ability to accurately predict the modeled
property for new compounds. Thus, the validation of
QSAR models is absolutely essential for its successful
application and interpretation. A comparison of the statistics
of QSAR (1)–(48) obtained from multi-regression
analyses (MRA) has been shown in Table 45. All the
QSARs are found to be statistically significant. The following
approaches have been used for the validation of
QSAR (1)–(48):
• Fraction of the variance. It is important to note that a
QSAR model must have to explain a sufficiently high
fraction of the variance for any data set. The fraction
of the variance of an MRA model is expressed by r 2
(measure of the goodness of fit between model-predicted
and experimental values). It is believed that
the closer the value of r 2 to unity, the better the
QSAR model. The values of r 2 for QSAR models
(1)–(48) are found from 0.827 to 0.973 (Table 45).
The high values of r 2 confirmed that the high fraction
of the variance (82.7–97.3%) has been explained by
these QSAR models. According to the literature,
the predictive QSAR model must have
r 2 > 0.60. 109,143
• Cross-validation test. The cross-validated correlation
coefficient (q 2 ) was obtained by using the leave-oneout
procedure. 106 The values of q 2 for QSAR models
(1)–(48) are 0.718–0.941 (Table 45). The high values
of q 2 validate these QSAR models. In the literature,
it must be greater than 0.50. 109,143
• Standard deviation (s). s is the standard deviation
about the regression line. This is a measure of how
well the function derived by the QSAR analysis
predicts the observed biological activity. The smaller
the value of s the better is the QSAR. The values of
s for QSAR models (1)–(48) are 0.046–0.548
(Table 45).
• Quality factor or quality ratio (Q). Chance correlation,
due to the excessive number of parameter
(which increases also the r and s values), is
detected by the examination of Q value (quality
factor or quality ratio). 107 The values of Q for
QSAR models (1)–(48) are 1.690–21.435 (Table
45).
• Fischer statistics (F). Fischer statistic (F) is a value
derived from F-test indicating the probability of a
true relationship, or the significance level of the
MLR model. The F-value is the ratio between
explained and unexplained variance for a given number
of degree of freedom. The larger the F-value the
greater the probability that the QSAR equation is significant.
The F-values for the QSAR models (1)–(48)
are 21.974–216.222 (Table 45).
• All the QSAR models also fulfill the thumb rule condition,
that is (number of data points)/(number of
descriptors) P4.
10.2.4. Overview. An analysis of our QSAR results on
the inhibition of various compound series against