MODELING ANTIBACTERIAL ACTIVITY OF 4THIOZOLIDONE DERIVATIVES
HTML Full TextReceived on 12 February, 2014; received in revised form, 23 April, 2014; accepted, 13 June, 2014; published 01 August, 2014
MODELING ANTIBACTERIAL ACTIVITY OF 4THIOZOLIDONE DERIVATIVES
K. Anita*^{1}, V.K. Agrawal ^{2}, B. Shaik ^{2}, S. Sharma ^{1}
Department of Chemistry, Career College ^{1}, Bhopal, Madhya Pradesh, India
Department of Applied Science, National Institute of Technical Teachers Training and Research ^{2}, Shamla Hills, Bhopal462002, Madhya Pradesh, India
ABSTRACT: In the present work, efforts have been made to model the antibacterial activity of 4thiazolidone derivatives against pathogenic bacteria P. aeruginosa by using QSAR (quantitative structureactivity relationship) methodology. Multivariate analysis gave excellent model which was tested using cross validation using leave one out method. The cross validation method was applied to the data set in order to prove the predictive power of statistically significant QSAR models, which help to explore some expectedly potent compounds. The best model predicting the antibacterial activity indicated that the 2D autocorrelation, 3D and WHIM parameters such as MATS8p, RDF070u, RDF035e, Mor30v (3D) and E1u (WHIM Parameter) are very effective in describing the antibacterial activities of these compounds. The study revealed that E1u, MATS8p, RDF035e and RDF070u contribute positively whereas contribution of Mor30v contributes negatively to the antibacterial activity. The compounds with improved antibacterial potential can be successfully designed with selected quantitative structure activity relationship model.
Keywords: 
Antibacterial activity, 4 thiazolidone, Multivariate analysis, Cross validation
INTRODUCTION: Heterocyclic compounds like thiazolidones, are very good antibacterial drugs. Thiazolidones and their derivatives are known to have antimicrobial, antiviral, antitumor, antihypertensive and antiinflammatory properties ^{12}. However, Searching of more potent and efficient antibacterial agents is one of the major tasks of clinical practice due to the antibiotic resistant strains. Quantitative structure activity relationship (QSAR) analysis has been found to be a good tool for prediction of biological activity of novel compounds including antibacterial and antiviral agents ^{37}.
Computer technologies based on model development provide good insight for modification of molecular structures to get new organic molecules giving useful properties (including antibacterial activity). The present work is focused on the modeling of antibacterial activity of 4thiazolidone derivatives.
MATERIALS AND METHODS: QSAR has been widely used for years to provide a quantitative correlation between chemical structure and biological activity ^{8}. Agrawal and coworkers have used many physicochemical and topological parameters to predict the antibacterial activity of many compounds ^{912}.
In the present study, 25 thiazolidone derivatives have been considered having biological activity in terms of its log values. The compounds are taken from the literature ^{13}.
Dragon 6 software is used for the calculation of descriptors. The structural details of the compounds used in the present study are given in Table 1. The clinical isolates of the pathogenic bacteria P. aeruginosa has been used as the test microorganisms.
TABLE 1: STRUCTURES OF COMPOUNDS USED IN THE PRESENT STUDY
The calculated descriptors from Dragon software are reported in Table 2. Useful descriptors were selected by variable selection procedure and multiple regression analysis was performed using NCSS software ^{14}. The models obtained were subjected to cross validation by leave one out procedure ^{15}. The parameters which have been calculated for modeling are:
TABLE 2: CALCULATED VALUES OF PARAMETERS ALONG WITH THEIR BIOLOGICAL ACTIVITY
Mol ID  MATS8p  RDF070u  RDF035e  Mor30v  E1u  log BA 
m1  0.097  16.86  14.2  0.18  0.566  0.813 
m2  0.288  14.634  14.879  0.213  0.542  0.708 
m3  0.021  28.143  25.506  0.49  0.521  0.763 
m4  0.013  9.569  17.282  0.157  0.57  0.813 
m5  0.016  17.013  16.407  0.237  0.574  0.839 
m6  0.141  11.937  13.932  0.34  0.525  0.724 
m7  0.038  16.967  20.018  0.251  0.437  0.699 
m8  0.158  32.736  25.099  0.406  0.456  0.699 
m9  0.059  26.361  23.32  0.186  0.431  0.740 
m10  0.134  26.763  28.588  0.363  0.456  0.740 
m11  0.065  18.737  30.301  0.389  0.444  0.708 
m12  0.133  12.862  30.674  0.303  0.466  0.740 
m13  0.002  12.07  13.825  0.313  0.584  0.785 
m14  0.094  11.004  16.343  0.346  0.538  0.740 
m15  0.122  13.397  12.736  0.201  0.553  0.740 
m16  0.014  16.025  15.293  0.41  0.512  0.695 
m17  0.147  15.227  12.574  0.363  0.543  0.716 
m18  0.056  16.62  22.987  0.254  0.562  0.814 
m19  0.03  13.573  13.474  0.277  0.538  0.723 
m20  0.013  47.857  39.12  0.666  0.439  0.741 
m21  0.007  52.755  40.874  0.572  0.441  0.786 
m22  0.146  21.902  19.19  0.374  0.538  0.763 
m23  0.157  15.774  22.249  0.449  0.546  0.724 
m24  0.072  2.142  8.353  0.033  0.515  0.732 
m25  0.052  18.879  28.528  0.521  0.642  0.845 
 E1u: 1st component accessibility directional WHIM index / unweighted ^{1620}. WHIM descriptors are based on the statistical indices calculated on the projections of atoms along principal axes. They are built in such a way as to capture relevant molecular 3D information regarding the molecular size, shape, symmetry and atom distribution with respect to invariant reference frames. The algorithm consists of performing a Principal Components Analysis on the centered Cartesian coordinates of a molecule by using a weighted covariance matrix obtained from different weighing schemes for the atoms.
The following weighting schemes are used for computing the weighted covariance matrix, S^{w}:
 Unweighted (u), that is the weight w_{i}= 1 for each i.
 Atomic masses (w_{i }= m_{i} )
 Atomic van der waals volumes (w_{i }= v_{i})
 Atomic Sanderson electronegativities (w_{i }= e_{i})
 Atomic polarizabilities (w_{i }= p_{i})
 Atomic electro topological states (w_{i }= s_{i})
 MATS8p: Moran autocorrelation of lag 8 weighted by polarizability ^{2122}. Moran Autocorrelation Descriptors is labeled as MATS. The symbol for each of the autocorrelation descriptors is followed by two indices d and w where d stands for the lag and w stands for the weight. The lag is defined as the topological distance d between pairs of atoms. The topological distance between a pair of atoms (i, j) is given in the ij^{th}entry in the Topological Level Matrix. The lag can have any value from the set {0, 1, 2, 3, 4, 5, 6, 7, 8}.The weight can be m (relative atomic mass), p (polarizability), e (Sanderson electronegativity) and v (Van der Waals volume). Relative mass is defined as the ratio of atomic mass of an atom to that of carbon. Similarly, the other three weights p, e and v are scaled by the corresponding values for Carbon.
Let n be the number of atoms in the molecule. For any chosen value for lag d and any chosen weight w, we compute the Autocorrelation Descriptors using the following formulae.
Where, w_{i} and w_{j} are the weights of the atoms i and j, , and δ_{ij} is Kronecker delta, that is, δ_{ij} =1 if the ij^{th} entry in the Topological Level Matrix is = d, and δ_{ij} = 0 otherwise.
 RDF035e: Radial Distribution Function035 /weighted by Sanderson electronegativity
 RDF070u: Radial Distribution Function  070 / unweighted ^{23}. The radial distribution function (RDF) descriptors are based on the distance distribution in the molecule. The radial distribution function of an ensemble of n atoms can be interpreted as the probability distribution of finding an atom in a spherical volume of radius R. A typical RDF descriptor is denoted by RDFsw where s and w take the values 10 ≤ s ≤ 155 in units of 5 and, and it is defined as follows:
Where, f is a scaling factor, r_{ij} is the Euclidean distance between the atoms i and j, w_{i} and w_{j } are the weights of the atoms i and j respectively, n is the total number of atoms, β is the smoothing parameter which defines the probability distribution of the individual interatomic distance. β can be interpreted as the temperature factor that defines the movement of the atoms.
 Mor30v: 3DMoRSE descriptors Weighted by van der Waals volume ^{2426}. 3D MoRSE descriptors (3D Molecule Representation of Structures based on Electron diffraction) are derived from Infrared spectra simulation using a generalized scattering function (Soltzberg and Wilkins, 1977). A typical MoRSE descriptor is denoted by M orsw where s and w take the values 1≤ s ≤ 32 and, where, u is unweighted, m is weighted by mass, v is weighted by van der Waals volume, e is weighted by electronegativity and p is weighted by polarizability
The MoRSE descriptor is defined as follows:
Where, r_{ij} is the Euclidean distance between the atoms i and j, and w_{i} and w_{j}are the weights of the atoms i and j respectively.
RESULTS AND DISCUSSION: The parameters calculated have been summarized in Table 2 which includes MATS8p, RDF070u, RDF035e, Mor30v and E1u. A correlation matrix has been obtained which shows correlation among the selected parameters and activity and is reported in Table 3. This table reveals that E1u is the only parameter which may be useful in oneparametric modeling. However, the combination of different parameters may result better models. The data was subjected to regression analysis and many statistically significant models have been obtained which are summarized in Table 4.
TABLE 3: CORRELATION MATRIX
log BA  MATS8p  RDF070u  RDF035e  Mor30v  E1u  
log BA  1.0000  
MATS8p  0.3085  1.0000  
RDF070u  0.0356  0.0472  1.0000  
RDF035e  0.1031  0.0549  0.8166  1.0000  
Mor30v  0.0298  0.1026  0.7266  0.7264  1.0000  
E1u  0.5859  0.1806  0.5405  0.5336  0.2090  1.0000 
TABLE 4: REGRESSION PARAMETERS AND QUALITY OF CORRELATIONS
Model No.  Parameters used  Ai= (1………5)  B  Se  R^{2}  R^{2}_{A}  Fratio  Q=R/Se 
1  E1u  0.4621(±0.1333)  0.5125  0.0490  0.3432  0.3147  12.020  11.9558 
2  E1uMATS8p  0.4323(±0.1340)0.0898(±0.0728)  0.5309  0.0485  0.3857  0.3298  6.906  12.8051 
3  E1uRDF070u  0.6743(±0.1387)0.0020(±0.0007)  0.3643  0.0429  0.5185  0.4748  11.847  16.7848 
4  E1uRDF035e  0.7068(±0.1281)0.0031(±0.0009)  0.3212  0.0399  0.5849  0.5471  15.497  19.1676 
5  E1uMATS8p
RDF035e 
0.6759(±0.1279)0.0793(±0.0588)
0.0030(±0.0008) 
0.3410  0.0391  0.6179  0.5633  11.320  20.1040 
6  E1uMor30v
RDF070u 
0.7771(±0.1321)0.1573(±0.0643)
0.0037(±0.0009) 
0.3297  0.0388  0.6253  0.5718  11.682  20.3804 
7  E1uMor30v
RDF035e 
0.8288(±0.1072)0.1942(±0.0524)
0.0059(±0.0010) 
0.2633  0.0317  0.7488  0.7129  20.869  27.2975 
8  E1uMor30v
RDF035e RDF070u 
0.9343(±0.0969)0.2595(±0.0492)
0.0047(±0.0010) 0.0022(±0.0007) 
0.2132  0.0268  0.8292  0.7951  24.276  33.9778 
9  E1uMATS8p
Mor30v RDF035e RDF070u 
0.9059(±0.0772)0.1161(±0.0324)
0.2826(±0.0395) 0.0048(±0.0008) 0.0023(±0.0006) 
0.2342  0.0213  0.8981  0.8713  33.488  44.4921 
Here some statistically significant models having R^{2} more than 0.7 have been discussed.
Three variable model: When Mor30v and RDFo35e is added with Elu a three parametric model is resulted with R^{2 }= 0.7488. The adjusted R^{2}_{A} (0.7129) for this model also shows significant improvement. The model is as below:
log BA =0.8288(±0.1072) E1u0.1942(±0.0524) Mor30v+0.0059(±0.0010) RDF035e+0.2633
N=25, R^{2 }= 0.7488, R^{2}_{A}= 0.7129, Se = 0.0317, F=20.869, Q = 27.2975
Addition of RDF070u to above model yielded a four parametric model with better statistics. The R^{2 }value changes from 0.7488 to 0.8292 and R^{2}_{A} change from 0.7129 to 0.7951. Change in adjusted R^{2 }clearly indicates that the added parameter has its fair share in the model. The model is as below:
Four variable model: log BA =0.9343(±0.0969) E1u0.2595(±0.0492) Mor30v+0.0047(±0.0010) RDF035e+0.0022(±0.0007) RDF070u+ 0.2132
N=25, R^{2 }= 0.8292, R^{2}_{A}= 0.7951, Se= 0.0268, F=24.276, Q = 33.9778
Further improvement was observed when E1u, MATS8p,Mor30v, RDF035e and RDF070u have been taken together resulting into a fiveparametric model (model 9, Table 4). The values of R^{2} and R^{2}_{A} have come out to be 0.8981 and 0.8713 and the Q value ^{2728} has come out to be 44.4921. The model is as under:
Five variable model: log BA =0.9059(±0.0772) E1u+0.1161(±0.0324) MATS8p0.2826(±0.0395) Mor30v+0.0048(±0.0008) RDF035e+0.0023(±0.0006) RDF070u+ 0.2342
N=25, R^{2 }= 0.8981, R^{2}_{A}= 0.8713, Se= 0.0213, F=33.488, Q = 44.4921
No higher order model is permitted as Rule of Thumb restricts that (No of compounds are 25 hence maximum permitted no of parameters is 5.) Therefore, the five parametric model is the best model for modeling the antibacterial activity (log BA) of compounds used in the present study. Further confirmation is obtained by plotting observed activity against estimated activity and such a comparison is demonstrated in figure 1. The predictive power of the model comes out to be 0.8981. The biological activity (log BA) of all the compounds have been estimated using model 9 (Table 5). The estimated log BA values are in good agreement with the observed values showing that the proposed model is best suited for estimating log BA values of present set of compounds.
To validate the model cross validation parameters have been calculated and they are reported in Table 6. We know that PRESS is a good estimate of the real predictive power of the model. If this value is smaller than SSY, the model predicts better than chance and can be considered statistically significant. Table 6 shows that all the proposed models are better than chance and are statistically significant. The ratio PRESS ⁄ SSY can be used to calculate the approximate confidence interval of the prediction of new compounds. If this ratio should be smaller than 0.4 the model is reasonably good. In the proposed model, this ratio is smaller than 0.4 and therefore, the model9 has excellent predictive power.
TABLE 5: OBSERVED AND ESTIMATED BIOLOGICAL ACTIVITY AND RESIDUAL VALUES USING MODEL 9
Compd. No.  Observed biological activity log BA  Estimated biological activity log BA  Residual log BA 
m1  0.813  0.792  0.021 
m2  0.708  0.737  0.029 
m3  0.763  0.753  0.011 
m4  0.813  0.81  0.003 
m5  0.839  0.803  0.035 
m6  0.724  0.725  0 
m7  0.699  0.69  0.009 
m8  0.699  0.71  0.011 
m9  0.74  0.738  0.002 
m10  0.74  0.728  0.012 
m11  0.708  0.708  0 
m12  0.74  0.733  0.008 
m13  0.785  0.769  0.016 
m14  0.74  0.739  0.002 
m15  0.74  0.756  0.016 
m16  0.695  0.694  0.001 
m17  0.716  0.702  0.014 
m18  0.814  0.827  0.013 
m19  0.723  0.743  0.02 
m20  0.741  0.743  0.002 
m21  0.786  0.791  0.005 
m22  0.763  0.775  0.012 
m23  0.724  0.727  0.003 
m24  0.732  0.745  0.013 
m25  0.845  0.855  0.01 
TABLE 6: CROSS VALIDATION PARAMETERS FOR PROPOSED MODELS
Model No.  Parameters used  PRESS  SSY  PRESS/SSY  R^{2}CV  S_{PRESS}  PSE 
1  E1u  0.0312  0.0163  1.9141  0.9141  0.0368  0.0353 
4  E1uRDF035e  0.0197  0.0278  0.7086  0.2914  0.0299  0.0281 
7  E1uMor30v
RDF035e 
0.0119  0.0356  0.3343  0.6657  0.0238  0.0218 
8  E1uMor30v
RDF035e RDF070u 
0.0081  0.0394  0.2056  0.7944  0.0201  0.0180 
9  E1uMATS8p
Mor30v RDF035e RDF070u 
0.0048  0.0427  0.1124  0.8876  0.0159  0.0139 
FIG. 1: CORRELATION BETWEEN OBSERVED AND ESTIMATED BIOLOGICAL ACTIVITY VALUES USING MODEL 9
The developed models are crossvalidated by leaveoneout method. Another crossvalidated parameter related to uncertainty of prediction, the PSE, has also been calculated. The lowest value of PSE for model 9 supports its highest predictive potential (power).
The low value of PSE and S_{PRESS} and high value of R^{2}_{CV} suggest that the fiveparametric model is most appropriate in predicting the log BA values of present set of compounds.
There is no colinearity among the used parameters which has been established by ridge analysis as well as various inflation factors calculated from the model 9 (Table 7, figures 2 and 3).
TABLE 7: RIDGE ANALYSIS FOR FIVE VARIABLE MODEL (MODEL 9)
Independent variables  VIF  T  λ  k  





VIF= Variance inflation factor; T= Tolerance; λ = Eigen value; k= Condition number
FIG. 2: RIDGE TRACE FOR FIVE VARIABLE MODEL (MODEL 9)
FIG. 3: VIF PLOT FOR FIVE VARIABLE MODEL (MODEL 9)
CONCLUSIONS: On the basis of above discussion following conclusions can be drawn.
 E1u along with MATS8p, RDF035e, RDF070u and Mor30v are suitable parameters for modeling the antibacterial activity of present set compounds
 Coefficients for E1u, MATS8p, RDF035e and RDF070u are positive suggesting that higher value of these parameters will favour the biological activity. Negative coefficient of Mor30v suggests that it has retarding effect towards log BA values, hence in future designing of potent compounds its lower value will give better results.
ACKNOWLEDGEMENT: One of the authors (Anita K.) is thankful to UGC for providing financial assistance (F. MS  132/102003/1112/ CRO (2)) to this work.
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How to cite this article:
Anita K, Agrawal VK, Shaik B and Sharma s: Modeling antibacterial activity of 4thiozolidone derivatives. Int J Pharm Sci Res2014; 5(8): 333341.doi: 10.13040/IJPSR.09758232.5(8).333341
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IJPSR
K. Anita*, V.K. Agrawal, B. Shaik, S. Sharma
Department of Chemistry, Career College, Bhopal, Madhya Pradesh, India
anitakamala19@gmail.com
12 February, 2014
23 April, 2014
13 June, 2014
http://dx.doi.org/10.13040/IJPSR.09758232.5(8).333341
01 August, 2014