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: naru2000us@yahoo.com

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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