3. FOOD ChEMISTRy & bIOTEChNOLOGy 3.1. Lectures

Chem. Listy, 102, s265–s1311 (2008) Food Chemistry & Biotechnology
Table III
Antibacterial screening summary
Compound log 1/cMIC log 1/cMIC exp. predict.
Residuals
1 4.602 4.636 –0.034
2 4.637 4.636 0.001
3 4.609 4.518 0.091
4 4.328 4.373 –0.045
5 4.278 4.213 0.065
6 4.314 4.235 0.079
7 3.981 3.993 –0.012
8 3.704 3.732 –0.028
9 4.627 4.607 0.020
10 4.659 4.591 0.068
11 4.333 4.433 –0.100
12 4.352 4.372 –0.020
Ampicillin 4.446 – –
Gentamicin 5.787 – –
erent structural features of the molecules. Selection of a set of
appropriate descriptors from a large number of them requires
a method, which is able to discriminate between the parameters.
Pearson’s correlation matrix has been performed on all
descriptors by using nCSS Statistical Software. The analysis
of the matrix revealed 8 descriptors for the development of
MLR model (Table II).
Mathematical models were formed by a stepwise addition
of terms. A delition process was then employed where
each variable in the model was held out in turn and using the
remaining parameters models were generated. Each descriptor
was chosen as input for the software package of nCSS
and then the stepwise addition method implemented in the
software was used for choosing the descriptors contributing
to the antibacterial activity of benzimidazole derivatives.
The partition coefficient (log P) tends to correlate with
antibacterial activity exclusively and the best monoparametric
model was found to be the following:
log 1/c MIC = 0.518 log P + 2.391 (1)
n = 12; r = 0.932; s = 0.085; F = 66.43
Addition of HE as an additional parameter to log P,
increased the correlation coefficient from 0.932 to 0.951
(Eq.(2)).
log 1/c MIC = 0.415 log P + 0.031 HE + 2.940 (2)
n = 12; r = 0.951; s = 0.010; F = 42.21
It should be noted that the addition of other parameters
to log P and HE does not significantly improved the correlation
coefficients. However, if quadratic values of descriptors
were included in the stepwise multiple regression procedure,
the best correlation was found as depicted in Eq.(3).
For the testing the validity of the predictive power
of selected MLR model (3) the leave-one-out technique
s759
log 1/c MIC = –0.201 log P 2 + 1.930 logP–
0.001 HE2 + 0.014 HE + 0.082
n = 12; r = 0.967; s = 0.008; F = 25.41
(LOO technique) was used. The developed model was validated
by the calculation of following statistical parameters:
predicted residual sum of squares (PRESS), total sum of squa-
res deviation (SSY), cross-validated correlation coefficient
(r2 CV ), and adjusted correlation coefficient (r2 adj ) (Table IV).
Table IV
Cross-validation parameters
Eq.(2)
PRESS 0.151
SSY 0.942
PRESS/SSY 0.160
r 2 CV 0.840
r 2 adj 0.900
PRESS is an important cross-validation parameter as it
is a good approximation of the real predictive error of the
models. Its value being less than SSY points out that the
model predicts better than chance and can be considered statistically
significant. Thus, in view of this, model 3 is statistically
significant. Further, to be a reasonable QSAR model,
PRESS/SSY ratio should be lesser than 0.4. The data presented
in Table IV indicate that for the developed model this
ratio is 0.160. The high value of r 2 CV and r2 adj
are the essential
criteria for qualifying the QSAR model 3 as the best one.
To confirm the predictive power of a model the inhibitory
activitiy of 12 molecules included in the study was calculated
by the model 3. The data presented in Table III show that the
observed and the estimated activities are very close to each
other. It indicates the good predictability of the established
model 3. Fig. 1. shows the plots of linear regression predicted
versus experimental values of the antibacterial activity of
benzimidazoles investigated. To investigate the existence of a
systemic error in developing the QSAR models, the residuals
Fig. 1. Plots of predicted versus experimentally observed inhibitory
activity against Pseudomonas aeruginosa
(2)