ORIGINAL RESEARCH
Hansch analysis for the prediction of antimycobacterial activityof ofloxacin derivatives
Vikramjeet Judge • Rakesh Narang •
Deepika Sharma • Balasubramanian Narasimhan •
Pradeep Kumar
Received: 26 February 2010 / Accepted: 26 July 2010 / Published online: 14 August 2010
� Springer Science+Business Media, LLC 2010
Abstract The present study was attempted to predict the
antimycobacterial activity of ofloxacin derivatives. The
QSAR results indicated the importance of electronic prop-
erties of molecules viz. energy of the lowest unoccupied
molecular orbital (LUMO), total energy (Te), dipole moment
(l) and the topological parameter, third order shape index
Kappa (j3) in describing the antimycobacterial activity of
ofloxacin derivatives. The validity of developed models has
been supported by significant statistical parameters.
Keywords QSAR � Ofloxacin derivatives �Antimycobacterial � LUMO
Introduction
Tuberculosis (TB) an infectious disease caused by different
species of Mycobacteria represents a major public health
and socioeconomic problem in most of the developing
countries (Tripathi et al., 2006). Approximately, one-third
of world’s population is infected with TB bacillus, Myco-
bacterium tuberculosis, with more than 8 million people
contracting the disease and two million people dying of it
each year (Aparna et al., 2006). A peculiar aspect of its
pathogenicity comes from the fact that it can remain qui-
escent and become active decades later. One of the most
significant risk factor for developing tuberculosis is human
immunodeficiency virus (HIV) infection (Dye et al., 2002).
Quantitative structure–property–activity relationships
(QSPR, QSAR) are certainly not a new field in chemistry. In
fact, correlations between molecular properties and many
kinds of molecular descriptors have been sought for many
years. Usually, molecular descriptors are chosen in an
empirical way, according to their ability to give good results
in statistical models (Agraval et al., 2000). Modern rational
drug design widely relies on building extensive QSAR
models which represent a substantial part of current in silico
research (Francisco et al., 2007). QSAR can thus be utilized
to optimize both the activity profile of a molecule and its
chemical synthesis (Todeschini and Consonni, 2000).
Fluoroquinolones exhibit potent in vitro and in vivo
antimycobacterial activities (Shandil et al., 2007). There is
a significant effort to include fluoroquinolones as new front-
line agents (ofloxacin and moxifloxacin) and second line
agents (ciprofloxacin) to combat tuberculosis (TB) (Neu-
remberger et al., 2004). There is also a considerable effort
to discover and develop newer fluoroquinolones and some
of them might have value in the treatment of TB (Anquetin
et al., 2006; Janin, 2007).
The literature reports reveal that Hansch analysis has
been widely applied for the prediction of antitubercular
activities (Singh et al., 2010; Sharma et al., 2009; Nara-
simhan et al., 2006). In view of above and as a part of our
research work devoted to rational drug design (Narasimhan
et al., 2003, 2004, 2007a, b, c; Kumar et al., 2007, 2008;
Ohlan et al., 2007; Minu et al., 2008; Sharma et al., 2008)
we are hereby reporting the QSAR studies on antimyco-
bacterial activity of ofloxacin derivatives reported by Di-
nakaran et al. (2008) (Table 1).
V. Judge � R. Narang
Department of Pharmaceutical Sciences, Guru Jambheswar
University of Science and Technology, Hisar 125001, India
D. Sharma
University Institute of Pharmaceutical Sciences,
Panjab University, Chandigarh 160014, India
B. Narasimhan (&) � P. Kumar
Faculty of Pharmaceutical Sciences, Maharshi Dayanand
University, Rohtak 124001, India
e-mail: [email protected]
123
Med Chem Res (2011) 20:826–837
DOI 10.1007/s00044-010-9400-8
MEDICINALCHEMISTRYRESEARCH
Table 1 Antimycobacterial activity of ofloxacin derivatives
N
O
R O
OH
O
F
R1
N N
C l
N N
C l
O
C N N
O
O
C N N
O
N NCH 2
O
O
N NCH2
O
O
N NH 3 C
C 6 H 5
N NH 3 C
C 6 H 5
N NC
O
O
O
Med Chem Res (2011) 20:826–837 827
123
Table 1 continued
N NC
O
O
O
N NC
O
N
O CH3
F
F
N NC
O
N
O CH3
F
F
S N
S N
O N
O N
N
H O
C l
N
H O
C l
NN
NH
O
Cl
NN
NH
O
Cl
N
O
O
N
O
O
828 Med Chem Res (2011) 20:826–837
123
Experimental
The aim of the present work was to develop quantitative
models for the prediction of antimycobacterial activity of
ofloxacin derivatives. In the present work, the antimy-
cobacterial activity of 31 ofloxacin derivatives was sub-
jected to MLR analysis with their physicochemical
properties against Mycobacterium tuberculosis (mtb) and
Mycobacterium smegmatis (mc2) and 23 ofloxacin
derivatives against multidrug-resistant Mycobacterium
tuberculosis (mdrtb). The best MLR model was used to
predict the antitubercular activity of the ofloxacin deriv-
atives against different strains of Mycobacterium. Based
upon these predicted activities 6 and 7 outliers were
removed from dataset for Mycobacterium smegmatis
(mc2) and multidrug-resistant Mycobacterium tuberculo-
sis (mdrtb) to get a final dataset of 25 and 16 com-
pounds, respectively, which were then selected for
multiple linear regression (MLR). In multivariate statis-
tics, it is common to define three types of outliers
(Furusjo et al., 2006).
1. X/Y relation outliers are substances for which the
relationship between the descriptors (X variables) and
the dependent variables (Y variables) is not the same as
in the (rest of the) training data.
Table 1 continued
N
O
O
N
CO NHC(CH3)3
N
CO NHC(CH3)3
N
NN
HO O C
N
NN
H O O C
N
NN
HOO C
N
H3CO
H3CO
N
H3CO
H3CO
* Outliers
Med Chem Res (2011) 20:826–837 829
123
2. X outliers are substances the molecular descriptors of
which do not lie in the same range as the (rest of the)
training data.
3. Y outliers are only defined for training or test samples.
They are substances for which the reference value of
response is invalid.
In light of the above guidelines, some ofloxacin derivatives
were considered as outliers because their response values
(antimycobacterial activity) were outside the range in com-
parison to the other compounds included in the present study.
Descriptor generation and regression analysis
The next step in developing a model is generation of the
numerical descriptors of the molecular structures. The
numerical descriptors responsible for encoding structural
features of the molecules can be categorized as hydrophobic,
geometric, electronic and topological characters. The dif-
ferent molecular descriptors (independent variables) i.e. log
of octanol–water partition coefficient (log P), molar refrac-
tivity (MR), Kier’s molecular connectivity (0v, 0vv, 1v, 1vv,2v, 2vv) and shape (j1, j2, j3, ja1, ja2, ja3) topological
indices, Randic topological index (R), Balaban topological
index (J), Wiener topological index (W), total energy (Te),
energies of the highest occupied molecular orbital (HOMO)
and the lowest unoccupied molecular orbital (LUMO) and
dipole moment (l) (Hansch et al., 1973; Kier and Hall, 1976;
Randic, 1975, 1993; Balaban, 1982; Wiener, 1947) were
calculated for each compound in the dataset, using the
software TSAR 3.3 (TSAR 3D Version 3.3, 2000). Since,
there were a large number of descriptors for each compound,
we used Pearson’s correlation matrix as a qualitative model,
in order to select the suitable descriptors for MLR analysis.
The stepwise multiple linear regression procedure was used
for model generation. The stepwise addition method
implemented in the SPSS software package (SPSS for
windows, Version 10.05 1999) was used for choosing the
descriptors contributing to the antimycobacterial activity.
Calculation of statistical parameters
The selected models were validated by the calculation of
following statistical parameters (Mandloi et al., 2005;
Pinheiro et al., 2004): probable error of the coefficient of
correlation (PE), least square error (LSE), Friedman’s lack
of fit measure (LOF), standard error of prediction (SEP)
and quality value (Q). These parameters were calculated
from the following equations.
PE ¼ 2 1� r2� �
=3p
n
where r is the correlation coefficient and n is the number of
compounds used.
LSE ¼ R Yobs � Ycalcð Þ2
where Yobs and Ycalc are the observed and calculated values.
LOF ¼ LSE= 1� C þ d � p=nð Þf g2
where LSE is the least square error; C is the number of
descriptors ?1; p is the number of independent parameters;
n is the number of compounds used; d is the smoothing
parameter which controls the bias in the scoring factor
between equations with different number of terms and was
kept as 1.0.
SEP ¼ pLSE=n
The quality value, Q is given by, Q = r/Se, where Q is the
quality value; r is the correlation coefficient and Se is the
standard error. The predictive ability of MLR models was
also quantified in terms of q2, which is defined as
q2 ¼ 1� RðYobs � YcalcÞ2=RðYobs � YmeanÞ2n o
The low value of PE, LSE, LOF and SEP and high value of
Q and q2 are the essential criteria for qualifying the model
as the best one.
Variation inflation factor (Kumar et al., 2006) is
employed to determine the multicollinearity between the
physicochemical parameters. The VIF value is calculated as
VIF ¼ 1=1� r2
where, r2 is the squared multiple correlation coefficient of one
parameter’s effect on the remaining parameters. VIF values
greater than 5 indicate the presence of unacceptably large
multicollinearity between the parameters in the correlation.
Results and discussion
The chemical structures of ofloxacin derivatives with their
respective antimycobacterial activities (MIC in lM con-
verted to pMIC) reported by Dinakaran et al. (2008) are
presented in Table 1. The present study was designed to
develop quantitative models to predict the correlation
between the structural descriptors (Table 2) of ofloxacin
derivatives with their antimycobacterial activity against
Mycobacterium tuberculosis (mtb), Mycobacterium
smegmatis (mc2) and multidrug-resistant Mycobacterium
tuberculosis (mdrtb) (Table 1) by MLR analysis.
QSAR studies of ofloxacin derivatives against
Mycobacterium smegmatis (mc2)
In the present study compounds 2, 3, 7, 10, 21 and 31 were
removed as outliers as their presence resulted in very low
correlation (r = 0.315, Eq. 1) with LUMO, whereas their
removal improved the r value significantly (r = 0.704,
830 Med Chem Res (2011) 20:826–837
123
Eq. 2) during linear regression analysis. As there was no
difference in the activity (Table 1) as well as the molecular
descriptor range (Table 2) of these outliers (2, 3, 7, 10, 21
and 31) when compared to the other ofloxacin derivatives
indicated the fact that these outliers belong to the category
of Y outliers (substances for which the reference value of
response is invalid) (Furusjo et al., 2006).
pMICmc2 ¼ �0:713LUMO � 1:534
n ¼ 31; r ¼ 0:315; q2 ¼ 0:026; s ¼ 0:699;F ¼ 3:20
ð1ÞpMICmc2 ¼ �1:187 LUMO� 2:209
n ¼ 25; r ¼ 0:704; q2 ¼ 0:473; s ¼ 0:398;F ¼ 22:59
ð2Þ
Here and thereafter, n is the number of data points, r is the
correlation coefficient, s is the standard error of the
estimate, F is the Fischer ratio, q2 is the cross validated r2
obtained by leave one out method.
Further, correlation analysis was performed on all the
selected parameters to find out colinearity among them and
is presented in Table 3. In general, the parameters showed
low colinearity with the energy of lowest unoccupied
molecular orbital (LUMO) i.e. \ 0.4, so multiple linear
models were developed by stepwise addition of different
parameters with LUMO.
The correlation of antimycobacterial activity of ofloxa-
cin derivatives against different M. tuberculosis strains
with their molecular descriptors are presented in Table 4.
The electronic parameter LUMO was found to be an
important parameter in explaining the antimycobacterial
activity against mc2 (r = -0.704; Table 4). Further, the
addition of topological parameter j3 to LUMO demon-
strated the improvement in r value from 0.704 (Eq. 2) to
Table 2 Values of selected molecular descriptors used in MLR analysis
Comp. log P MR 1v j2 j3 ja2 ja3 Te LUMO Dipole
1 4.732 147.194 18.829 12.313 5.694 10.387 4.630 -6971.990 -0.747 6.446
2 4.685 154.518 20.168 13.388 6.117 11.193 4.919 -7802.270 -1.326 11.873
3 0.755 110.328 15.363 9.568 4.290 7.925 3.410 -6117.730 -0.810 5.425
4 0.708 117.653 16.701 10.637 4.707 8.729 3.697 -6947.980 -1.474 10.174
5 1.701 123.723 16.902 10.285 4.707 8.681 3.834 -6557.480 -0.753 7.398
6 1.655 131.048 18.240 11.350 5.134 9.482 4.129 -7387.820 -1.301 10.667
7 2.437 117.776 15.363 9.568 4.290 7.987 3.442 -5789.230 -0.735 7.600
8 2.391 125.101 16.701 10.637 4.707 8.790 3.729 -6619.480 -1.391 11.091
9 1.161 127.966 17.829 11.111 5.025 9.298 4.048 -7006.000 -0.810 5.536
10 1.115 135.291 19.168 12.179 5.451 10.101 4.343 -7836.180 -1.454 10.248
11 2.688 139.725 19.578 12.416 5.552 10.430 4.492 -8102.750 -0.856 6.905
12 2.642 147.050 20.917 13.485 5.977 11.233 4.787 -8933.010 -1.524 11.588
13 0.888 92.692 11.986 7.197 3.122 6.296 2.648 -4784.970 -0.834 6.283
14 0.842 100.017 13.324 8.263 3.550 7.100 2.945 -5615.220 -1.500 10.126
15 1.272 95.354 12.774 7.680 3.545 6.574 2.936 -5222.370 -0.854 6.392
16 1.226 102.679 14.112 8.741 3.972 7.375 3.232 -6052.660 -1.354 10.830
17 2.373 120.475 15.692 9.465 4.390 8.089 3.632 -6249.790 -0.834 6.243
18 2.326 127.799 17.030 10.526 4.816 8.889 3.927 -7080.070 -1.410 10.441
19 1.528 128.891 17.240 10.194 4.507 8.633 3.686 -6790.740 -0.774 5.262
20 1.482 136.216 18.578 11.250 4.925 9.430 3.976 -7620.990 -1.454 8.837
21 1.503 99.341 13.900 7.848 3.457 6.763 2.886 -5670.910 -0.785 6.626
22 1.457 106.666 15.239 8.897 3.882 7.557 3.184 -6501.230 -1.285 11.354
23 0.720 104.042 14.328 8.094 3.479 6.991 2.913 -5892.000 -0.558 6.321
24 2.499 131.718 16.975 10.526 5.158 8.791 4.160 -6549.500 -0.794 5.257
25 2.453 139.042 18.313 11.589 5.574 9.591 4.443 -7379.890 -1.216 12.216
26 0.949 103.802 14.757 8.652 3.866 7.265 3.129 -6028.090 -0.999 2.950
27 0.902 111.127 16.095 9.708 4.292 8.061 3.426 -6858.340 -1.607 7.085
28 0.165 108.503 15.184 8.897 3.882 7.493 3.152 -6249.160 -0.849 1.634
29 2.041 118.292 15.833 9.806 4.283 8.210 3.447 -6209.350 -0.761 5.645
30 1.995 125.616 17.171 10.873 4.710 9.013 3.744 -7039.640 -1.356 9.770
31 0.590 93.494 12.380 7.438 3.338 6.327 2.740 -4966.550 -0.812 7.324
Med Chem Res (2011) 20:826–837 831
123
0.753 (Eq. 3). The electronic parameter LUMO which
denotes the energy of the lowest unoccupied molecular
orbital directly relates to the electron affinity and charac-
terizes the susceptibility of the molecule toward an attack
by nucleophiles (Van de Waterbeend et al., 1998).
pMICmc2 ¼ �1:262 LUMO � 0:197 j3 � 1:399
n ¼ 25; r ¼ 0:753; q2 ¼ 0:473; s ¼ 0:378;F ¼ 22:59
ð3Þ
A negative correlation of antimycobacterial activity with
LUMO in linear as well as in multiple linear regression
models indicated that the magnitude of antimycobacterial
activity of ofloxacin derivatives is inversely proportional to
LUMO values. This was evidenced by the fact that the
compounds which have the minimum LUMO values
compared to other compounds (Table 2), have maximum
antimycobacterial activity (Table 1). The developed MLR
model (Eq. 3) was used to predict the antimycobacterial
activity of ofloxacin derivatives and the values of observed,
predicted and residual pMICmc2 are presented in Table 5,
which indicated the predictability of the Eq. 3. The plot of
the observed pMICmc2 and the predicted pMICmc2
showed that the activity values are close to each other
(Fig. 1).
Further, a graph was plotted between observed
pMICmc2 and residual pMICmc2 to check the systemic
error in the model development. The progression of
residual values on both sides of zero indicated that there
was no systemic error in the developed model (Jalali-He-
ravi and Kyani, 2004) (Fig. 2).
The validity of the models was also supported by the
low LSE, LOF, PE and the high Q values (Table 6). The
low colinearity (VIF \ 5) among different parameters used
in the development of MLR models was also supported by
their low VIF values (Table 6). Similarly, combinations of
the LUMO with other parameters like MR, 1v, j2, and
R also led to the increase in r value. The respective models
for MLR analysis described by these parameters are pre-
sented in Table 7 and their statistical parameters are pre-
sented in Table 6.
QSAR studies of ofloxacin derivatives against
Mycobacterium tuberculosis (mtb)
The entire dataset of 31 ofloxacin derivatives was subjected
to linear regression analysis to find out the correla-
tion between their antimycobacterial activity and
Table 3 Correlation matrix of antimycobacterial activity of ofloxacin derivatives against Mycobacterium smegmatis (mc2)
pMIC mc2 log P MR 1v j2 j3 ja2 ja3 R Te LUMO l
pMIC mc2 1.000
log P -0.320 1.000
MR -0.209 0.745 1.0001v -0.129 0.606 0.963 1.000
j2 -0.098 0.668 0.963 0.983 1.000
j3 -0.149 0.719 0.969 0.959 0.980 1.000
ja2 -0.112 0.688 0.969 0.983 0.998 0.978 1.000
ja3 -0.170 0.745 0.974 0.954 0.973 0.997 0.976 1.000
R -0.129 0.606 0.963 1.000 0.983 0.959 0.983 0.954 1.000
Te -0.059 -0.461 -0.867 -0.959 -0.936 -0.888 -0.932 -0.877 -0.959 1.000
LUMO -0.704 0.100 -0.075 -0.183 -0.226 -0.163 -0.195 -0.122 -0.183 0.368 1.000
l 0.634 0.220 0.244 0.269 0.333 0.311 0.322 0.294 0.269 -0.384 -0.725 1.000
Table 4 Correlation of antimycobacterial activity of ofloxacin
derivatives with molecular descriptors
Descriptor pMICmc2 pMICmtb pMICmdrtb
log P -0.320 -0.329 -0.008
MR -0.209 -0.272 0.5270v -0.058 -0.142 0.5960vv -0.178 -0.241 0.5371v -0.129 -0.188 0.6051vv -0.210 -0.277 0.553
j1 -0.042 -0.156 0.569
j2 -0.098 -0.253 0.530
j3 -0.149 -0.289 0.483
ja1 -0.044 -0.157 0.567
ja2 -0.112 -0.264 0.525
ja3 -0.170 -0.304 0.472
R -0.129 -0.188 0.605
B 0.430 0.270 -0.554
W -0.126 -0.254 0.577
Te -0.059 0.056 -0.647
LUMO -0.704 -0.460 -0.263
HOMO -0.323 -0.256 -0.250
l 0.634 0.110 0.113
832 Med Chem Res (2011) 20:826–837
123
physicochemical parameters. As in case of Mycobacterium
smegmatis (mc2), the linear regression analysis demon-
strated the importance of energy of the lowest unoccupied
molecular orbital (LUMO) in describing the antimyco-
bacterial activity (Eq. 4).
pMICmtb ¼ �0:685 LUMO� 1:075
n ¼ 31; r ¼ 0:460; q2 ¼ 0:092; s ¼ 0:432;F ¼ 7:764
ð4Þ
The low r value and very low interrelationship observed
between LUMO and different other physicochemical
parameters stimulated us to go for the development of
multiple linear regression (MLR) models to get better
regression coefficient. The maximum increase in r value
was observed on combination of LUMO with topological
parameter j3 with r value 0.650 (Eq. 5) as compared to
r value of Eq. 4 i.e. 0.460.
pMICmtb ¼ �0:915 LUMO � 0:285 j3 � 0:0282
n ¼ 31; r ¼ 0:650; q2 ¼ 0:283; s ¼ 0:376;F ¼ 10:226
ð5Þ
Similarly, the combination of LUMO with other physico-
chemical parameters like j2, ja2 and ja3 led to the
increase in r values and the respective models are presented
in Table 7. The coefficient of LUMO in linear regression
model as well as multiple linear regression model is neg-
ative which implies that a decrease in LUMO value will
increase the antimycobacterial activity which is evidenced
by the low LUMO values of compounds 4, 20, 22 and 27
and their high antimycobacterial activity values i.e. 0.100,
Table 5 Comparisons of observed versus predicted antimycobacterial activity of ofloxacin derivatives using best MLR models
Comp. pMICmc2 pMICmtb pMICmdrtb
Obs. Pre. Res. Obs. Pre. Res. Obs. Pre. Res.
1 -1.660 -1.575 -0.085 -0.760 -0.970 0.210 – – –
2 – – – -0.420 -0.560 0.140 -0.420 -0.194 -0.226
3 – – – -0.850 -0.511 -0.339 – – –
4 -0.510 -0.463 -0.047 0.100 -0.022 0.122 -0.200 -0.363 0.163
5 -1.410 -1.373 -0.037 -0.810 -0.682 -0.128 – – –
6 -0.170 -0.766 0.596 -0.470 -0.303 -0.167 – – –
7 – – – -1.160 -0.580 -0.580 – – –
8 -0.810 -0.568 -0.242 -0.510 -0.098 -0.412 -0.510 -0.466 -0.044
9 -1.690 -1.365 -0.325 -1.090 -0.721 -0.369 – – –
10 – – – -0.450 -0.253 -0.197 -0.150 -0.146 -0.004
11 -1.640 -1.410 -0.230 -1.040 -0.829 -0.211 – – –
12 -0.100 -0.651 0.551 -0.710 -0.340 -0.370 – – –
13 -0.630 -0.960 0.330 -0.330 -0.156 -0.174 -0.930 -0.802 -0.128
14 -0.280 -0.203 -0.077 -0.280 0.332 -0.612 -0.280 -0.690 0.410
15 -0.620 -1.018 0.398 -0.620 -0.258 -0.362 -0.920 -0.697 -0.223
16 -0.270 -0.470 0.200 -0.270 0.078 -0.348 -0.570 -0.600 0.030
17 -1.420 -1.209 -0.211 -0.820 -0.517 -0.303 – – –
18 -0.780 -0.566 -0.214 -0.180 -0.112 -0.068 -0.480 -0.337 -0.143
19 -1.690 -1.308 -0.382 -0.180 -0.606 0.426 0.120 -0.283 0.403
20 -0.140 -0.532 0.392 0.470 -0.103 0.573 – – –
21 – – – 0.330 -0.297 0.627 – – –
22 -0.540 -0.540 0.000 0.680 0.040 0.640 – – –
23 -1.050 -1.379 0.329 -0.570 -0.511 -0.059 -0.570 -0.530 -0.040
24 -1.700 -1.410 -0.290 -0.500 -0.773 0.273 -0.500 -0.342 -0.158
25 -0.460 -0.960 0.500 -0.160 -0.506 0.346 -0.160 -0.306 0.146
26 -1.470 -0.898 -0.572 0.040 -0.217 0.257 – – –
27 -0.820 -0.214 -0.606 0.720 0.218 0.502 – – –
28 -0.720 -1.090 0.370 0.060 -0.359 0.419 -0.250 -0.328 0.078
29 -1.140 -1.280 0.140 -0.240 -0.554 0.314 -0.540 -0.435 -0.105
30 -1.100 -0.613 -0.487 -0.190 -0.131 -0.059 -0.490 -0.331 -0.159
31 – – – -0.330 -0.238 -0.092 – – –
Med Chem Res (2011) 20:826–837 833
123
0.470, 0.680 and 0.720, respectively. The plot of the
observed pMICmtb versus the predicted pMICmtb (Fig. 3)
and the observed pMICmtb versus the residual pMICmtb
(Fig. 4) depicts the predictability of developed MLR model
(Eq. 5).
QSAR studies of ofloxacin derivatives against
multidrug-resistant Mycobacterium tuberculosis
(mdrtb)
For QSAR studies of ofloxacin derivatives against multi-
drug-resistant Mycobacterium tuberculosis 23 ofloxacin
derivatives were subjected to linear regression analysis out
of 31 compounds reported by Dinakaran et al., Compounds
6, 20, 21, 22, 26, 27 and 31 were removed as outliers as
value of r for antimycobacterial activity (pMICmdrtb) with
total energy (Te) has significantly improved from 0.292
(Eq. 6) to 0.647 (Eq. 7) on their removal.
pMICmdrtb ¼ �0:0002 Te � 1:652
n ¼ 23; r ¼ 0:292; q2 ¼ 0:238; s ¼ 0:638;F ¼ 1:97
ð6Þ
pMICmdrtb ¼ �0:0002 Te � 1:756
n ¼ 16; r ¼ 0:647; q2 ¼ 0:238; s ¼ 0:216;F ¼ 10:089
ð7Þ
Further, during MLR study there was a marginal increase
in r value on addition of dipole moment (l) to total energy
(Te) [r = 0.647 (Eq. 7) to r = 0.689 (Eq. 8)]. The
statistical parameters of the aforementioned models are
shown in Table 6.
pMICmdrtb ¼ �0:00025 Te � 0:024l � 1:829
n ¼ 16; r ¼ 0:689; q2 ¼ 0:109; s ¼ 0:213;F ¼ 5:88
ð8Þ
The monoparametric as well as multiparametric models
revealed the importance of total energy (Te) of ofloxacin
derivatives toward the antimycobacterial activity against
strain mdrtb. The coefficient of Te in monoparametric
model (Eq. 7) as well as in multiparametric models (Eq. 8)
is negative indicating thereby that antimycobacterial
activity of different selected ofloxacin derivatives against
mdrtb is inversely proportional to the magnitude of Te. This
is evidenced by the high observed pMICmdrtb values
-0.150, 0.120 and -0.160 of compounds 10, 19 and 25
Observed pMICmc20.0-.5-1.0-1.5-2.0
Pre
dict
ed p
MIC
mc2
0.0
-.2
-.4
-.6
-.8
-1.0
-1.2
-1.4
-1.6
Fig. 1 Plot of observed pMICmc2 versus predicted pMICmc2 for
MLR model by Eq. 3
Observed pMICmc2
0.0-.5-1.0-1.5-2.0
Res
idua
l pM
ICm
c2
.8
.6
.4
.2
0.0
-.2
-.4
-.6
-.8
Fig. 2 Plot of observed pMICmc2 versus residual pMICmc2 for MLR
model by Eq. 3
Table 6 PE, LSE, LOF, SEP, VIF and Q values calculated for the
derived models for modeling antimycobacterial activity of ofloxacin
derivatives
S. no. Descriptor PE LSE LOF SEP VIF Q
For Mycobacterium smegmatis (mc2)
1 LUMO 0.067 3.634 3.358 0.381 – 1.77
2 LUMO, j3 0.057 2.543 0.587 0.318 2.31 1.99
3 LUMO, MR 0.058 3.139 0.725 0.354 2.29 1.99
4 LUMO, 1v 0.058 3.139 0.725 0.354 2.29 1.99
5 LUMO, j2 0.058 3.179 0.735 0.356 2.29 1.99
6 LUMO, R 0.058 3.139 0.726 0.354 2.29 1.99
For Mycobacterium tuberculosis (mtb)
7 LUMO 0.094 5.410 5.079 0.417 – 1.07
8 LUMO, j3 0.070 3.960 0.929 0.357 1.72 1.73
9 LUMO, j2 0.070 3.991 0.937 0.358 2.82 1.70
10 LUMO, ja2 0.070 3.997 0.938 0.359 2.82 1.70
11 LUMO, ja3 0.069 3.982 0.935 0.358 2.84 1.71
For multidrug-resistant Mycobacterium tuberculosis (mdrtb)
12 Te 0.097 0.651 0.058 0.201 – 3.00
13 Te, l 0.088 0.813 0.180 0.225 1.90 3.24
834 Med Chem Res (2011) 20:826–837
123
having low Te values, respectively (Table 2) as compared
to other ofloxacin derivatives under study.
The total energy (Te) calculated by semiempirical
methods can be used as a measure of non-specific inter-
actions of a drug with its target site i.e. the total energies of
the protonated and neutral forms of the molecule can be
considered as a good measure of the strength of hydrogen
bonds (the higher the energy, the stronger the bond) and
can be used to determine the correct localization of the
most favorable hydrogen bond acceptor site (Karelson
et al., 1996). The plot of observed pMICmdrtb versus
predicted pMICmdrtb (Fig. 5) and observed pMICmdrtb
versus residual pMICmdrtb (Fig. 6) depicts the predict-
ability of developed MLR model (Eq. 8).
In the developed QSAR models the cross validated r2
values (q2) are low (q2 \ 0.5). But one should not forget
the recommendations of Golbraikh et al. (Golbraikh and
Table 7 Other statistically significant MLR models derived for antimycobacterial activity of ofloxacin derivatives
S. no. QSAR Model (pMIC=) n r q2 F S
Mycobacterium smegmatis (mc2)
1 -1.221 LUMO - 0.009 MR - 1.145 25 0.751 0.428 14.250 0.378
2 -1.269 LUMO - 0.068 1v - 1.183 25 0.751 0.423 14.241 0.378
3 -1.291 LUMO - 0.095 j2 - 1.362 25 0.751 0.424 14.300 0.377
4 -1.269 LUMO - 0.068 R - 1.183 25 0.751 0.424 14.241 0.378
Mycobacterium tuberculosis (mtb)
5 -0.956 LUMO - 0.138 j2 ? 0.027 31 0.646 0.281 10.06 0.378
6. -0.939 LUMO - 0.171 ja2 ? 0.103 31 0.646 0.284 10.03 0.378
7. -0.892 LUMO - 0.366 ja3 ? 0.048 31 0.648 0.285 10.13 0.377
Observed pMICmtb1.0.50.0-.5-1.0-1.5
Pre
dict
ed p
MIC
mtb
.4
.2
0.0
-.2
-.4
-.6
-.8
-1.0
Fig. 3 Plot of observed pMICmtb versus predicted pMICmtb for
MLR model by Eq. 5
Observed pMICmtb1.0.50.0-.5-1.0-1.5
Res
idua
l pM
ICm
tb
.8
.6
.4
.2
0.0
-.2
-.4
-.6
-.8
Fig. 4 Plot of observed pMICmtb versus residual pMICmtb for MLR
model by Eq. 5
Observed pMICmdrtb.20.0-.2-.4-.6-.8-1.0
Pre
dict
ed p
MIC
mdr
tb
-.1
-.2
-.3
-.4
-.5
-.6
-.7
-.8
-.9
Fig. 5 Plot of observed pMICmdrtb versus predicted pMICmdrtb for
MLR model by Eq. 8
Med Chem Res (2011) 20:826–837 835
123
Tropsha, 2002) who have recently reported that the only
way to estimate the true predictive power of a model is to
test their ability to predict accurately the biological activ-
ities of the compounds. As the observed and the predicted
values are close to each other, the QSAR models are valid
ones. Further, the low PE, LSE, LOF and the high
Q (Table 6) values of the developed models also supports
their validity.
Conclusion
Different versatile MLR models were developed for the
prediction of antimycobacterial activity of ofloxacin
derivatives against different strains of Mycobacterium
tuberculosis. The problem of selecting the appropriate
descriptor as input for MLR model was overcome by
Pearson correlation matrix, which can be used as a tool for
identifying the appropriate descriptors when a large num-
ber of descriptors with different features are available. The
MLR model indicated the importance of electronic
parameters energy of lowest unoccupied molecular orbital
(LUMO), total energy (Te) and dipole moment (l) followed
by the topological parameter, Kier’s third order shape
index (j3), in describing the antimycobacterial activity of
ofloxacin derivatives. The validity of developed models has
been established by low LSE, LOF, PE and high Q values.
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