B. Narasimhan et al. / Bioorg. Med. Chem. Lett. 16 (2006) 3023–3029
3025
Table 2. The in vitro activity of synthesized myristic acid derivatives
The topological parameter, valence molecular connec-
2
tivity indices (0vv and vv) for the esters and amides of
Compound
ꢀlog MIC
M. luteus
myristic acid, has been found to exhibit best correlation
and high statistical significance (p < 0.01). The resulting
best-fit models applying the principle of Parsimony are
reported in Eqs. 1–3 together with statistical parameters
of regression. It is important to note that all these mod-
els were developed by using the entire training set
(n = 20), since no outliers were identified.
S. aureus
E. coli
Training set
M-1
M-2
2.48
2.38
2.65
2.76
2.70
2.78
2.80
2.91
2.93
2.80
2.38
2.59
2.67
2.71
2.86
2.83
2.83
2.83
2.82
2.82
2.48
2.29
2.65
2.76
2.70
2.70
2.89
2.82
2.93
2.73
2.29
2.59
2.61
2.71
2.76
2.75
2.93
2.83
2.75
2.75
2.26
2.38
2.43
2.50
2.52
2.52
2.59
2.61
2.63
2.60
2.38
2.43
2.45
2.50
2.56
2.57
2.57
2.57
2.62
2.62
M-3
M-4
M-5
M-6
The quality of the models is indicated by the following
parameters: r, correlation coefficient; F, Fisher’s statis-
tics; and s, standard error of estimation; r2cv, cross vali-
dated r2 obtained by ‘leave one out’ (LOO) method.
M-7
M-8
M-9
M-10
M-11
M-12
M-13
M-14
M-15
M-16
M-17
M-18
M-19
M-20
QSAR model for antibacterial activity against E. coli
0
ꢀ log MIC ¼ 0:061 vv þ 1:635 n ¼ 20
r ¼ 0:963 F ¼ 232:661 s ¼ 0:027 r2cv ¼ 0:902. ð1Þ
QSAR model for antibacterial activity against S. aureus
2
ꢀ log MIC ¼ 0:217 vv þ 1:375 n ¼ 20
r ¼ 0:978 F ¼ 407:85 s ¼ 0:030 r2cv ¼ 0:931. ð2Þ
QSAR model for antibacterial activity against M. luteus
Test set
M-21
M-22
M-23
M-24
M-25
M-26
M-27
Sa
2.41
2.63
2.58
2.59
2.86
2.56
2.58
3.33
2.61
2.63
2.36
2.29
2.76
2.46
2.67
3.33
2.61
2.34
2.45
2.51
2.46
2.56
2.65
3.33
2
ꢀ log MIC ¼ 0:229 vv þ 1:268 n ¼ 20
r ¼ 0:934 F ¼ 123:968 s ¼ 0:064 r2cv ¼ 0:810. ð3Þ
0
The coefficient of vv in the mono-parametric model in
Eq. 1 is positive, indicating thereby that antibacterial
activity of myristic acid derivatives against E. coli is
a Standard drug—ciprofloxacin.
0
directly proportional to the magnitude of vv. The anti-
bacterial activity increases with an increase in magnitude
0
0
of vv. This is evidenced by the values of vv in Table 3.
topological index (J),25 Wiener topological index (W),26
Total energy (Te),4 energies of highest occupied molecu-
lar orbital (HOMO) and lowest unoccupied molecular
orbital (LUMO),27 dipole moment (l), electronic energy
(ElcE), nuclear energy (NuE), and molecular surface
area (SA).28 The values of these descriptors are present-
ed in Table 3.
The values of vv for compounds M-8, M-9 are 16.04
0
and 16.75, respectively, which are higher than the vv
0
values of other compounds in the training set which
make them the most active compounds against E. coli.
Similarly the compounds M-1, M-2, and M-11 have
the minimum 0vv values of 10.84, 11.80, and 11.47,
respectively, and have minimum activity. Similar trend
was observed in case of S. aureus and M. luteus with va-
In the present work, a training set consisting of 20 mol-
ecules (M-1–M-20) was used for linear regression model
generation and a prediction set consisting of 7 molecules
(M-21–M-27) was used for the evaluation of generated
linear regression model. The reference drug ciprofloxa-
cin was not included in model generation as it belongs
to a different structural series.
2
lence second order molecular connectivity index, vv.
In order to confirm our results we have synthesized a
prediction set consisting of 7 myristic acid derivatives
viz. M-21–M-27, predicted their activities using the
model expressed by Eqs. 1–3, and compared them with
the observed values. We have also applied the same
model to predict the activity of training set. The data
presented in Table 6 show that the observed and the esti-
mated activities are very close to each other evidenced
by low values of residual activity.
First, correlation analysis of various descriptors with
biological activity was performed. The data are pre-
sented in Table 4, which shows that most of the
parameters are highly correlated with antibacterial
activity. A correlation matrix (Table 5) was constructed
to find the interrelationship among the parameters,
which shows that each parameter selected in the study
is highly correlated with the other (r > 0.8) except the
The cross-validation of the models was also done by
LOO technique.29 The high cross-validated correlation
coefficient (r2cv or q2) values obtained for the best
QSAR models indicated their reliability in predicting
the antibacterial activity of myristic acid derivatives.
But one should not forget the recommendations of
Golbraikh et al.,30 who have recently reported that
3
descriptors ionization potential, LUMO, and vv. Any
combination of these descriptors in multiple regression
analysis may result with a model suffering from multi-
colinearity.