a quantitative structure-activity relationship study of antimicrobial ...

Vol. 8 | No.2 |255 -265 | April - June | 2015 ISSN: 0974-1496 | e-ISSN: 0976-0083 | CODEN: RJCABP http://www.rasayanjournal.com http://www.rasayanjournal.co.in

A QUANTITATIVE STRUCTURE-ACTIVITY RELATIONSHIP STUDY OF ANTIMICROBIAL ACTIVITY OF 1-ARYL / ALKYL-4-AMINO / DIMETHYLAMINO / PYRROLIDINO / MORPHOLINO PYRIDINIUM BROMIDE

1

Arumugam Yasodha1, Ayarivan Puratchikody2,*, Balasubramanian Narasimhan3 and Appavoo Umamaheswari2

Department of Pharmaceutical Chemistry, PGP College of Pharmaceutical Science and Research Institute, Namakkal-637207, Tamilnadu, India. 2 Drug Discovery and Development Research Group, Department of Pharmaceutical Technology, Anna University Chennai, BIT Campus, Tiruchirappalli-620024, Tamilnadu, India. 3 Faculty of Pharmaceutical Sciences, Maharshi Dayanand University, Rohtak-124001, Haryana, India. *E-mail: [email protected] ABSTRACT A Quantitative structure-activity relationship (QSAR) of a sixty pyridinium bromides was done using the Hansch and Fujita models. This study offers a clear understanding of the structural parameters that could be used to explain the antimicrobial activity of all the synthesized pyridinium derivatives. Various molecular descriptors were used in this QSAR study, among them surface area (SA) provided valuable guidelines for new structural designs and further improvement of the antimicrobial activity. Keywords: Pyridinium bromide, antimicrobial, MIC, molecular descriptors, QSAR ©2015 RASĀYAN. All rights reserved

INTRODUCTION Many of the major infectious diseases had perhaps the greatest impact on human history in the past 4,000 years1. Innumerous antibiotics are available to treat various kinds of infectious diseases. But, the arbitrary and incorrect use of antibiotics increases the resistance to antibiotics in patients. The widespread emergence of antibiotic resistance, particularly multidrug resistance (MDR), among bacterial pathogens has become one of the most serious challenges in clinical therapy. Despite this increasing problem of antibiotic resistance, the number of different antibiotics available is dwindling and there are only a handful of new antibiotics in the drug development pipeline. Therefore, there is an urgent need for new antibacterial drugs preferably with new modes of action to potentially avoid MDR 2. The antimicrobial potential of pyridinium salts is well established in the literature 3-5. The literature reports revealed that the pyridinium salts and its derivatives possess wide spectrum of biological activities like antimicrobial6, anticancer7, antiinflammatory8, antiviral 9 and antiAChE 10. Quantitative structureactivity relationship (QSAR) models are highly effective in describing the structural basis of biological activity. The success of QSAR approach can be explained by the insight offered into the structural determination of chemical properties and the possibility to estimate the properties of new chemical compounds 11. Keeping this observation in mind and in continuation of our previously reported work 12-13 on the synthesis and antimicrobial evaluation of 4-amino / dimethylamino / pyrrolidino / morpholino -1- aryl / alkylpyridinium bromide, we herein report the QSAR studies of 1-aryl / alkyl-4-amino / dimethylamino / pyrrolidino / morpholino pyridinium bromides (Compounds 1-60).

PYRIDINIUM BROMIDES

Arumugam Yasodha et. al

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EXPERIMENTAL Test Compounds The in vitro antimicrobial activity of 60 pyridinium bromides was used to develop QSAR models. The minimum inhibitory concentration (MIC) assays of the newly synthesized compounds (1-60) were conducted against a Gram positive bacteria Staphylococcus aureus, Streptococcus mutants, Gram negative bacteria Escherichia coli, Klebesilla pneumonia and fungi Rhizopus arrhizus, Aspergillus niger by the two fold serial dilution technique 14. Ciprofloxacin and Fluconazole were used as standards for antibacterial and antifungal activities respectively. Biological activity data determined as MIC values were first transformed into pMIC values (i.e. –log MIC) and used as dependent variable in QSAR study (Table- 1). QSAR studies The main aim of the present work was to develop a quantitative model for prediction of the pMIC values for different pyridinium bromides. In the present work, the pMIC of 60 pyridinium bromides synthesized 12-13 were subjected to multi linear regression (MLR) analysis with their physicochemical properties. The standard drugs ciprofloxacin and fluconazole were not included in model generation because of dissimilarity in structure with the synthesized compounds. The best MLR model was used to predict the pMIC values based on which, 16 outliers were removed from the model set and a final set of 44 compounds were selected for MLR and their data is listed in Table- 1. In multivariate statistics, it is common to define three types of outliers 15. 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. 2. X outliers. Briefly, a substance is an X outlier if the molecular descriptors for this substance 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 the light of the above guidelines, 16 pyridinium bromides were considered as outliers because their response values (pMIC) were outside the range in comparison to the other compounds included in the present study. One of the main problems in developing MLR models is choosing the proper inputs (descriptors) for them. There are two different methods of feature selection techniques: objective and subjective methods. The former method selects the relation between the descriptors themselves, whereas the latter method defines the relation between the descriptors and the dependent variable i.e., pMIC value. Pearson Correlation Analysis In this study, Pearson correlation analysis was employed as an objective feature selection method to classify the descriptors. This technique was adopted for choosing a suitable set of generated descriptors for developing a multiple linear regression model. The best generated MLR model was used to prepare a calibration model, which predicts the pMIC of pyridinium bromides and illustrates the extension of the linear characteristics of the antimicrobial activity of these compounds. Descriptor Generation The next step in developing this model is generation of the numerical description of the molecular structures. The numerical descriptors are responsible for encoding important features of the structure of the molecules. It was categorized as hydrophobic, geometric, electronic and topological characters. Descriptors were calculated for each compound in the data set, using the software Dragon Version 5.0 (Dragon, Talete SRL, Milano, Italy) and Hyperchem Version 6.0 (Hyperchem, Gaineswille, Florida, USA). Since there were large number of descriptors for each compound, Pearson’s correlation matrix was used as qualitative model in order to select the suitable descriptors for MLR analysis. The values of descriptors selected for MLR model are presented in Table- 2.

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Regression Analysis The stepwise multiple linear regression procedure was used for model generation. The stepwise addition method implemented in the SPSS software package Version 10.05 (SPSS Inc, Bangalore, India) was used for choosing the descriptors contributing to the pMIC value. As a first step, a correlation matrix was performed for all descriptors with pMIC. The nine descriptors, molar refractivity (MR), balban index (J), shape (α), wiener topological index (W), total energy (Te), nuclear energy (NE), surface area (SA), energy of lowest unoccupied molecular orbital (LUMO) and energy of highest occupied molecular orbital (HOMO) which have shown maximum correlation with pMIC values. Hence all those nine descriptors were chosen for further evaluation. The predictive powers of the equations were validated by the leave one out (LOO) cross validation method 16. Each compound is left out of the model derivation and predicted in turn. An indication of the performance is obtained from the cross-validated r2 method which is defined as q2 = 1 - ∑(Ypredicted Yactual)2 / ∑(Yactual - Ymean)2 where, Ypredicted, Yactual and Ymean are predicted, actual and mean values of target property (pMIC), respectively. ∑(Ypredicted - Yactual)2 is the predictive residual error sum of squares. Table-1: Antimicrobial activity of pyridinium bromides (1-60) in µmol/mL Compd. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

pMICsa 1.03 1.74 1.70 1.35 0.77 1.32 0.93 1.24 1.57 1.90 2.24 1.07 1.39 1.71 2.03 1.37 1.77 1.73 1.39 1.11 1.36 1.29 1.90 2.24 2.54 2.87 1.39 1.73 2.05 2.39 1.41

PYRIDINIUM BROMIDES

pMICsm 1.03 2.04 1.70 1.35 1.37 1.32 0.93 1.54 1.87 2.21 2.52 1.37 1.70 2.02 2.35 1.37 2.08 1.73 1.39 1.41 1.67 1.59 1.29 1.62 1.94 2.28 1.70 2.03 2.37 2.67 1.41

Minimum inhibitory concentration (µmol/mL) pMICkp pMICec pMICrhi pMICan pMICab 1.03 1.63 1.33 1.63 1.18 1.44 2.36 1.74 2.04 1.90 1.70 2.00 1.70 2.00 1.77 1.05 1.65 1.35 1.65 1.35 1.37 1.67 1.07 1.37 1.29 1.62 1.92 1.92 2.24 1.55 0.93 1.24 0.93 1.84 1.01 1.24 1.54 1.84 1.54 1.39 1.57 1.87 2.19 1.87 1.72 1.90 2.21 2.50 2.21 2.05 2.24 2.52 2.82 2.52 2.38 1.98 1.98 1.37 1.98 1.60 2.32 2.32 1.70 2.32 1.93 2.62 2.62 2.02 2.62 2.24 2.94 2.94 2.35 2.94 2.57 1.37 1.97 1.67 1.97 1.52 1.77 2.68 2.08 2.39 2.08 1.73 2.35 2.04 2.35 1.89 1.39 2.31 1.69 1.99 1.62 1.11 1.41 1.71 2.61 1.26 1.36 1.97 2.29 1.97 1.59 1.29 1.59 1.29 1.89 1.44 1.59 1.90 1.59 1.90 1.67 1.92 2.24 1.92 2.24 2.00 2.26 2.54 2.26 2.54 2.32 2.57 2.87 2.57 2.87 2.65 1.39 1.70 2.00 1.70 1.55 1.73 2.03 2.35 2.03 1.88 2.05 2.37 2.65 2.37 2.21 2.39 2.67 2.97 2.67 2.53 1.11 1.71 1.11 1.41 1.41

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pMICaf 1.48 1.89 1.85 1.50 1.22 2.08 1.39 1.69 2.03 2.36 2.67 1.68 2.01 2.32 2.65 1.82 2.24 2.19 1.84 2.16 2.13 1.59 1.74 2.08 2.40 2.72 1.85 2.19 2.51 2.82 1.26

pMICam 1.28 1.89 1.80 1.40 1.27 1.72 1.14 1.49 1.82 2.15 2.48 1.63 1.96 2.27 2.59 1.62 2.13 1.99 1.69 1.56 1.77 1.49 1.69 2.03 2.35 2.67 1.65 1.99 2.31 2.63 1.36


Vol. 8 | No.2 |255 -265 | April - June | 2015 32 2.11 1.80 2.11 2.42 1.50 33 1.77 1.77 1.77 2.07 1.46 34 1.43 1.43 1.43 1.73 1.12 35 1.44 1.14 1.44 2.05 1.44 36 1.70 2.00 1.70 2.00 2.32 37 1.63 1.33 1.94 1.63 1.03 38 1.94 1.94 1.64 1.94 1.64 39 2.26 2.26 1.94 2.26 1.94 40 2.58 2.58 2.30 2.58 2.30 41 2.90 2.90 2.60 2.90 2.60 42 1.45 1.15 2.05 1.75 2.37 43 1.77 1.46 2.39 2.07 2.67 44 2.08 1.78 2.69 2.40 2.99 45 2.70 2.10 3.00 2.70 3.00 46 1.43 1.43 1.43 2.03 2.03 47 2.12 1.82 2.12 2.73 2.44 48 1.78 1.78 1.78 2.40 2.40 49 1.45 1.45 1.45 2.05 2.05 50 1.16 1.16 1.46 1.76 2.67 51 2.03 2.34 2.03 1.72 2.03 52 1.36 1.66 1.66 1.96 1.96 53 1.66 1.36 1.66 1.36 1.96 54 1.98 1.68 1.98 1.68 2.30 55 2.32 2.00 2.32 2.00 2.61 56 2.63 2.34 2.63 2.34 2.93 57 1.47 1.77 2.07 1.77 1.77 58 1.78 2.09 2.40 2.09 2.09 59 2.10 2.42 2.70 2.42 2.42 60 2.43 2.72 3.02 2.72 2.72 S.D. 0.49 0.45 0.52 0.41 0.54 Std. 2.63* 2.93* 3.12* 2.93* 2.66** * ** S.D.: Standard deviation, Std.: Standard, Ciprofloxacin, Fluconazole

1.80 1.77 1.43 1.44 2.00 1.03 1.94 2.26 2.58 2.90 2.05 2.39 2.69 3.00 1.73 2.12 2.09 1.75 1.76 1.72 1.36 1.96 2.3s0 2.61 2.93 1.77 2.09 2.42 2.72 0.45 2.64**

2.11 1.84 1.50 1.52 1.85 1.63 1.86 2.18 2.51 2.83 1.60 1.92 2.24 2.63 1.58 2.20 1.94 1.60 1.39 2.03 1.66 1.51 1.83 2.16 2.48 1.77 2.09 2.41 2.72 0.42

1.65 1.62 1.28 1.44 2.16 1.03 1.79 2.10 2.44 2.75 2.21 2.53 2.84 3.00 1.88 2.28 2.24 1.90 2.22 1.88 1.66 1.96 2.30 2.61 2.93 1.77 2.09 2.42 2.72 0.46

1.96 1.77 1.43 1.49 1.96 1.43 1.84 2.15 2.49 2.80 1.80 2.12 2.44 2.75 1.68 2.23 2.04 1.70 1.66 1.98 1.66 1.66 1.99 2.31 2.63 1.77 2.09 2.41 2.72 0.42

RESULTS AND DISCUSSION In our previous study,12-13 we had reported the in vitro antimicrobial activity of synthesized compounds 160. The structural requirements essential for enhancing the antimicrobial activity of these compounds were found and summarized as follows:

Z

N+

CH2

Br-

Amino

Increasing activity against E.Coli

Dimethyl amino / Pyrrolidino

Increasing activity against Gram + ve bacteria

Pyrrolidino

Increasing activity against fungi

Morpholino / Pyrrolidino

Increasing activity against K.pneumonia

Hexyl

Increasing activity against Gram + ve bacteria

Bromohexyl

Increasing activity against Gram -ve bacteria and fungi

R

Fig.-1: Structural requirements derived from in vitro antimicrobial studies of 1-60

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In order to identify the substituent effect on the antimicrobial activity, QSAR study was undertaken, using linear free energy relationship (LFER) model described by Hansch and Fujita 17. Biological activity data in pMIC values (i.e. –log MIC) are used as dependent variable in QSAR study. The values of selected molecular descriptors used in the QSAR study are presented in Table- 2. Pearson Correlation Matrix Developing a general model requires a diverse set of data, and, thereby a large number of descriptors have to be considered. Descriptors are numerical values that encode different 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. We have performed Pearson correlation matrix by using SPSS on all descriptors calculated for each molecule. The analysis of the matrix revealed nine descriptors for the development of MLR model. It is noteworthy that the four descriptors (R, W, Ne and SA) appearing in the MLR model showed high variance in the Pearson correlation matrix (Table- 3). The highest interrelationship was observed with randic index (R) and nuclear energy (NE, r = 0.991). The interrelationship among these parameters were found to be very poor, r = 0.028, -0.059 and -0.39 between (TE and HOMO), (NE and HOMO) and (R and HOMO), respectively. Therefore, the Pearson correlation matrix confirms the selection of these descriptors using MLR technique. The structural effects on variations in antimicrobial activity of the synthesized pyridinium bromides in terms of pMICab were examined by regression analysis with molecular parameters shown in Table- 2. Mutiple Regression Analysis Previous studies reported in the field of QSAR studies18-23, indicated that the multi-target QSAR (mtQSAR) models are better than one-target QSAR (ot-QSAR) models in describing the antimicrobial activity. Hence, in the present study, we have developed mt-QSAR models to describe the antimicrobial activity of synthesized pyridinium bromide derivatives. According to the ot-QSAR models, there should be use of six different equations with different errors for the prediction of activity for a new compound against six microbial species. However, very recently, the interest has been increased in the development of mt- QSAR models. In opposition to ot-QSAR, the mtQSAR model is a single equation that considers the nature of molecular descriptors which are common and essential for describing the antibacterial and antifungal activity 24-27. In the present study, we attempted to develop three different types of mt-QSAR models viz. the mt-QSAR model for describing antibacterial activity of synthesized compounds against S. aureus, S. mutants, E. coli and K. pneumonia, the mt-QSAR model for describing antifungal activity against R. arrhizus and A. niger as well as a common mt-QSAR model for describing the antimicrobial (overall antibacterial and antifungal) activity of synthesized pyridinium bromide derivatives by calculating their average antibacterial activity (pMICab), antifungal activity (pMICaf) and antimicrobial activity values (pMICam) which are presented in Table- 1. Table-2: Value of selected descriptors of synthesized pyridinium bromides Compd. No 1 2 3 4 6 7 8 9 10

PYRIDINIUM BROMIDES

R 6.84 7.24 8.15 7.24 6.22 4.83 4.83 5.33 5.83

J 2.29 2.30 2.32 2.30 4.08 3.96 3.96 3.89 3.82

W 329.00 404.00 586.00 404.00 278.00 127.00 127.00 174.00 232.00

Te -2481.63 -2821.23 -3312.46 -2637.51 -2739.09 -1941.77 -1970.48 -2126.31 -2282.15

Ne 11820.40 13031.80 15763.10 13210.90 11299.00 7609.49 8033.06 9220.74 10416.90

259

SA LUMO HOMO µ 253.56 0.10 -7.96 2.68 274.78 -0.31 -8.05 2.51 283.46 -1.24 -8.32 5.21 275.60 0.08 -7.94 2.93 260.45 -0.65 -7.59 5.29 206.88 0.32 -7.98 2.64 214.89 0.34 -7.96 2.80 237.27 0.35 -7.96 2.85 258.67 0.34 -7.96 2.83


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5.33 5.83 6.33 6.83 7.75 8.15 9.06 8.15 7.13 5.74 5.74 5.86 6.74 7.24 7.74 8.92 9.24 10.15 8.29 6.90 7.40 7.90 8.40 9.42 9.81 10.72 8.79 7.40 7.40 7.90 8.40 7.90 8.40 8.90 9.40

3.89 3.82 3.75 3.68 2.31 2.32 2.34 2.32 4.19 4.13 4.13 3.93 3.99 3.91 3.84 1.69 1.84 1.83 2.35 2.38 2.33 2.28 2.23 1.67 1.67 1.67 2.33 2.34 2.34 2.30 2.26 2.30 2.26 2.21 2.17

174.00 232.00 302.00 385.00 489.00 586.00 816.00 586.00 420.00 215.00 215.00 226.00 358.00 450.00 557.00 682.00 735.00 999.00 593.00 328.00 413.00 513.00 629.00 798.00 932.00 1242.00 698.00 400.00 400.00 496.00 608.00 496.00 608.00 737.00 884.00

-2310.07 -2465.92 -2621.50 -2777.60 -2792.25 -3131.84 -3622.72 -2948.12 -3049.74 -2252.39 -2281.09 -2465.43 -2776.54 -2930.94 -3088.22 -3076.26 -3415.47 -3906.82 -3333.97 -2536.41 -2904.70 -3059.93 -3216.39 -3396.52 -3736.11 -4227.34 -3654.19 -2856.63 -2885.33 -3041.19 -3197.02 -3224.93 -3380.19 -3536.04 -3692.48

9040.01 10236.60 10862.60 12689.90 14899.20 16198.90 18672.10 16381.40 14225.70 10301.10 10776.30 10369.30 13173.90 13931.00 15788.40 17591.30 18828.20 22438.30 17487.40 12753.80 14423.50 15396.60 17145.90 19661.20 20868.60 24052.10 19211.70 14555.80 15089.90 16334.00 17733.20 16136.50 17092.60 18500.90 20361.60

LR mt-QSAR model for antibacterial activity pMICab = 0.006 SA - 0.018 n = 44 r = 0.689 q2 = 0.427

236.40 257.70 298.63 301.50 293.60 314.38 328.38 314.36 300.47 246.87 254.60 257.59 297.19 316.33 340.95 317.41 349.39 336.77 313.23 272.81 300.93 333.99 345.93 329.06 349.26 356.51 321.88 280.31 288.59 311.81 333.34 309.65 344.96 367.16 376.42

0.20 0.24 0.32 0.28 0.12 -0.29 -1.26 0.11 -0.58 0.37 0.39 0.21 0.29 -1.55 0.33 0.13 -0.42 -1.23 0.21 0.37 0.26 -0.05 0.33 0.02 -0.36 -1.34 0.07 0.20 0.23 0.24 0.24 0.09 -0.23 -0.20 0.18

-8.09 -8.06 -8.40 -8.02 -7.86 -7.95 -7.40 -7.84 -7.50 -7.89 -7.86 -8.02 -7.96 -6.58 -7.92 -7.84 -7.68 -8.33 -7.98 -7.86 -7.96 -7.04 -7.91 -8.10 -8.15 -8.37 -8.24 -8.09 -8.04 -8.05 -8.06 -8.18 -7.31 -7.28 -8.12

2.37 2.85 5.86 2.87 2.88 2.62 13.00 3.19 5.94 2.88 2.99 2.59 3.23 20.09 3.24 2.77 3.34 7.27 3.65 2.73 2.64 4.38 2.61 3.38 3.03 4.14 2.51 3.46 3.65 4.10 4.11 2.47 2.93 2.68 3.29

(1) s = 0.270

F = 37.92

Here and thereafter, n = number of data points; r = correlation coefficient; r2 = squared correlation; q2 = cross validated r2 obtained by leave one out (LOO) method; s = standard error of estimate; F = Fischer’s statistics Coefficient of SA in Eq. (1) is positive which indicates that antibacterial activity of the synthesized compounds is positively correlated to surface area i.e. antibacterial activity of synthesized compounds will increase with an increase in value of SA and vice versa. This is evidenced by antibacterial activity data of synthesized compounds (Table- 1) and their SA values (Table- 2) i.e. compounds 59 and 60 having highest SA values of 367.16 and 376.42 respectively are having highest antibacterial activity (pMIC = 2.10 and 2.43 µmol/ml respectively), whereas compound 7 was least active (pMIC = 0.93 µmol/ml) with minimum SA value (206.88). In order to improve the value of correlation coefficient (r), we coupled SA with Balaban index (J) which resulted in an improved QSAR model (Eq. 2) having improvement in r and q2 values.

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MLR mt-QSAR model for antibacterial activity pMICab = 0.236 J + 0.009 SA – 1.663 s = 0.219 n = 44 r = 0.813 q2 = 0.602

(2) F = 40.18

The QSAR model expressed by Eq. (2) was cross validated by its high q2 value (q2=0.602) obtained by leave one out (LOO) method. It is learnt that the value of q2 greater than 0.5 is the criteria for a QSAR model to be considered valid 28. Correlations between the observed and predicted antibacterial values (Table- 4) confirm the validity of mt-QSAR model for antibacterial activity (Eq.2). LR mt-QSAR model for antifungal activity pMICaf = 0.005 SA + 0.385 n = 44 r = 0.536 q2 = 0.228

(3) s = 0.356

F = 17.01

As in case of antibacterial activity, coefficient of SA in Eq. (3) is positive which indicates that antifungal activity of the synthesized compounds is positively correlated to surface area (SA) i.e. that antifungal and antimicrobial activity of synthesized pyridinium bromides will increase with an increase in value of SA (Table- 1 and 2). The validity and predictability of the QSAR model for antifungal activity i.e. Eq. (3) is cross validated by q2 value (q2 = 0.228) obtained by leave one out (LOO) method. The value of q2 less than 0.5 indicated that the developed model is not valid. It was recommended that estimation of the true predictive power of a model is the only way to predict the biological activities of compounds accurately 28. Correlations between the observed and predicted antifungal values (Table- 4) confirm the validity of mt-QSAR model for antifungal activity (Eq.-3). MLR mt-QSAR model for antifungal activity pMICaf = 0.320 J + 0.010 SA – 1.914 n = 44 r = 0.757 q2 = 0.516 s = 0.278

(4) F = 27.56

In search of a better QSAR model, we have coupled surface area (SA) with Balaban index (J) which led to best QSAR model for explaining antibacterial activity of the synthesized compounds (Eq.4) having improved r and q2 values. LR mt-QSAR model for antimicrobal activity pMICam = 0.006 SA + 0.114 n = 44 r = 0.669 q2 = 0.398 s = 0.274

(5) F = 33.99

As in case of antibacterial and antifungal activities, coefficient of SA in Eq. (5) is positive which indicates that antimicrobial activity of the synthesized compounds is positively correlated to surface area (SA) i.e. antimicrobial activity of the synthesized compounds will increase with an increase in value of SA. This is evidenced by the antimicrobial activity data of the synthesized compounds (Table- 1) and their J values (Table- 2). In order to improve the value of the correlation coefficient (r), we coupled surface area (SA) with Balaban index (J) which improved the value of r from 0.669 to 0.832 and q2 from 0.398 to 0.640(Eq.6). MLR mt-QSAR model for antimicrobial activity pMICam = 0.267 J + 0.009 SA – 1.749 n = 44 r = 0.832 q2 = 0.640 s = 0.206

(6) F = 46.18

The QSAR models expressed by Eq.(6) were cross validated by its high q2 values (q2 = 0.640) obtained by leave one out (LOO) method. Since the q2 value is greater than 0.5, the QSAR model is considered to be valid28. Correlations between the observed and predicted antimicrobial values are illustrated in Table- 4.

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Further, the plot of observed pMICam against residual pMICam (Fig. 2) indicated that there was no systemic error 29 in model development as the propagation of error was observed on both sides of zero (Fig. 3). It is important to note a fact that the high residual values observed in case of outliers justify their removal before development of QSAR models. It was observed from mt-QSAR models [Eq. (1– 6)] that topological parameter, solvent-accessible surface area (SA) is highly important in describing the antibacterial, antifungal and the overall antimicrobial activities of 1-aryl / alkyl-4-amino / dimethylamino / pyrrolidino / morpholino pyridinium bromide. Generally for QSAR studies, the biological activities of compounds should span 2–3 orders of magnitude. But in the present study, the range of antimicrobial activities of the synthesized compounds is within one order of magnitude. This is in accordance with results suggested by Bajaj et al 30 who stated that the reliability of the QSAR model lies in its predictive ability even though the activity data are in the narrow range. When biological activity data lies in the narrow range, the presence of minimum standard deviation of the biological activity justifies its use in QSAR studies31. The minimum standard deviation (Table- 1) observed in the antimicrobial activity data justifies its use in QSAR studies. Table-3: Correlation matrix for the antimicrobial activity of compounds 1-60

pMICsa R J W Te Ne SA LUMO HOMO µ

pMICsa 1.000

R 0.516 1.000

J -0.244 -0.838 1.000

W 0.512 0.976 -0.759 1.000

TE -0.556 -0.963 0.719 -0.960 1.000

NE 0.546 0.991 -0.798 0.978 -0.972 1.000

SA 0.720 0.899 -0.644 0.868 -0.900 0.900 1.000

LUMO -0.141 -0.494 0.243 -0.548 0.571 -0.476 -0.351 1.000

HOMO 0.094 -0.039 0.149 -0.075 0.028 -0.059 0.155 -0.292 1.000

µ 0.173 0.136 0.114 0.161 -0.197 0.131 0.176 -0.691 0.561 1.000

Table-4: Comparison of observed and predicted antibacterial, antifungal and antimicrobial activities of synthesized pyridinium bromides by mt-QSAR models Compd. No 1 2 3 4 6 7 8 9 10 12 13 14 15 16 17 18 19

PYRIDINIUM BROMIDES

Obs 1.18 1.90 1.77 1.35 1.55 1.01 1.39 1.72 2.05 1.60 1.93 2.24 2.57 1.52 2.08 1.89

pMICab Pre 1.28 1.48 1.57 1.49 1.77 1.23 1.31 1.50 1.69 1.49 1.68 2.05 2.06 1.66 1.86 2.00

Res -0.10 0.42 0.20 -0.14 -0.22 -0.22 0.08 0.22 0.36 0.11 0.25 0.19 0.51 -0.14 0.22 -0.11

1.62

1.86

-0.24

Obs 1.48 1.89 1.85 1.50 2.08 1.39 1.69 2.03 2.36 1.68 2.01 2.32 2.65 1.82 2.24 2.19

pMICaf Pre 1.39 1.61 1.70 1.61 2.05 1.47 1.55 1.75 1.95 1.75 1.94 2.32 2.33 1.80 2.01 2.16

Res 0.09 0.28 0.15 -0.11 0.03 -0.08 0.14 0.28 0.41 -0.07 0.07 0.00 0.32 0.02 0.23 0.03

1.84

2.01

-0.17

262

Obs 1.28 1.89 1.80 1.40 1.72 1.14 1.49 1.82 2.15 1.63 1.96 2.27 2.59 1.62 2.13 1.99

pMICam Pre 1.31 1.52 1.61 1.53 1.86 1.31 1.39 1.59 1.77 1.58 1.76 2.14 2.15 1.71 1.91 2.05

Res -0.03 0.37 0.19 -0.13 -0.14 -0.17 0.10 0.23 0.38 0.05 0.20 0.13 0.44 -0.09 0.22 -0.06

1.69

1.91

-0.22


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1.59 1.44 1.67 1.55 1.88 2.21 2.53 1.41 2.11 1.84 1.63 1.92 2.24 1.85 1.58 2.20 1.94 2.03 1.66 1.51 1.83 2.16 1.77 2.09 2.41 2.72

2.17 1.65 1.72 1.70 2.09 2.26 2.47 1.74 2.08 1.96 1.48 2.04 2.14 1.86 1.85 2.04 2.11 1.93 1.54 1.62 1.83 2.03 1.81 2.14 2.34 2.41

-0.58 -0.21 -0.05 -0.15 -0.21 -0.05 0.06 -0.33 0.03 -0.12 0.15 -0.12 0.10 -0.01 -0.27 0.16 -0.17 0.10 0.12 -0.11 0.00 0.13 -0.04 -0.05 0.07 0.31

2.13 1.59 1.74 1.85 2.19 2.51 2.82 1.26 1.65 1.62 1.03 2.53 2.84 2.16 1.88 2.28 2.24 1.88 1.66 1.96 2.30 2.61 1.77 2.09 2.42 2.72

2.49 1.93 2.01 1.97 2.39 2.56 2.78 1.83 2.20 2.07 1.61 2.19 2.30 2.01 1.94 2.15 2.22 2.09 1.67 1.76 1.98 2.18 1.96 2.30 2.51 2.59

-0.36 -0.34 -0.27 -0.12 -0.20 -0.05 0.04 -0.57 -0.55 -0.45 -0.58 0.34 0.54 0.15 -0.06 0.13 0.02 -0.21 -0.01 0.20 0.32 0.43 -0.19 -0.21 -0.09 0.13

1.77 1.49 1.69 1.65 1.99 2.31 2.63 1.36 1.96 1.77 1.43 2.12 2.44 1.96 1.68 2.23 2.04 1.98 1.66 1.66 1.99 2.31 1.77 2.09 2.41 2.72

2.28 1.74 1.82 1.79 2.19 2.36 2.58 1.77 2.12 2.00 1.53 2.09 2.19 1.91 1.88 2.08 2.14 1.99 1.59 1.67 1.88 2.08 1.86 2.19 2.39 2.47

-0.51 -0.25 -0.13 -0.14 -0.20 -0.05 0.05 -0.41 -0.16 -0.23 -0.10 0.03 0.25 0.05 -0.20 0.15 -0.10 -0.01 0.07 -0.01 0.11 0.23 -0.09 -0.10 0.02 0.25

Fig.-2: Plot of predicted pMICam values against observed pMICam values for linear regression developed model

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Fig.-3: Plot of residual pMICam values against observed pMICam values for linear regression developed model

CONCLUSION QSAR were undertaken using the LFER model described by Hansch and Fujita. pMIC values were correlated with different molecular descriptors. Further, the regression analysis was performed using the SPSS software package. The minimum standard deviation observed in the antimicrobial activity data justifies its use in QSAR studies. The antimicrobial activity of the pyridinium bromides (1-60) were predicted by mt-QSAR models and evidenced by the low residual value as well as their high q2 values (q2 > 0.5). The validity of the models has been established by the determination of suitable statistical parameters. The high q2 value supports the validity of the developed QSAR model. The MLR model indicated the importance of topological parameter surface area to antimicrobial activity. The results obtained from the QSAR studies of pyridinium bromides as antimicrobial agents can be expected to instruct the description of protein surface for understanding molecular recognition.

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