QSAR studies of antimicrobial activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines using topological descriptors

Vikas Verma; Kuldeep Singh; Devinder Kumar; Balasubramanian Narasimhan

doi:10.1016/j.arabjc.2012.11.021

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Original article

10 (

1_suppl

); S747-S756

doi:

10.1016/j.arabjc.2012.11.021

QSAR studies of antimicrobial activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines using topological descriptors

Vikas Verma^{^a}, Kuldeep Singh^{^a}, Devinder Kumar^{^a,⁎}, Balasubramanian Narasimhan^{^b,⁎}

a Department of Chemistry, Guru Jambheshwar University of Science & Technology, Hisar 125001, Haryana, India

b Faculty of Pharmaceutical Sciences, M D University, Rohtak 124001, Haryana, India

⁎Corresponding authors. Mobile: +91 9416588307 (D. Kumar), +91 9416649342 (B. Narasimhan); fax: +91 1662 276240. dk_ic@yahoo.com (Devinder Kumar), naru2000us@yahoo.com (Balasubramanian Narasimhan)

Received: 2012-8-25, Accepted: 2012-11-12, Published: 2012-02-01

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

The antimicrobial activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines was correlated with their physicochemical parameters using Hansch analysis for first time. The QSAR models were developed by both linear and multiple linear regression and the developed models were cross validated by the “leave one out” technique. The QSAR studies indicated that the antibacterial activity of synthesized compounds was governed by topological parameters, Balaban index (J), Kier's second order molecular index (κα₂) and third order molecular connectivity index (³χ) and the antifungal activity was governed by valance first order molecular connectivity index (¹χ^v). The practical applicability of developed models was explored by the design of new compounds based on the information derived from the developed equations.

Keywords

Naphthoxazine

Antimicrobial

QSAR

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1 Introduction

QSAR (Quantitative Structure–Activity Relationship) correlates biological activity data with the physicochemical and/or structural properties of a group of compounds. It has been frequently used to predict biological activities of new compounds and to design compounds with desired properties (Chiu and So, 2004). The basic assumption in quantitative structure–activity/property relationship (QSAR/QSPR) studies is that the molecular structures possess relations with their activities/properties. Thus, if we have methods to describe effectively the molecular structures, we can build a mathematical model to predict the activities/properties for unknown compounds. Since the 1960s, enormous efforts have been made by various investigators to develop quantitative parameters. During this period, Hansch and co-workers made important breakthroughs for biological QSAR with electronic, stereo, and hydrophobic parameters to be known as the extra thermodynamic approach (Xu et al., 2002).

The application, which goes by the name of molecular topology (or connectivity), is still young, its origin dating from the 1970s, when Kier and Hall (1973), and other researchers started using “indices” based on the graph theory to study some physicochemical properties of organic compounds, like heat of formation and boiling temperature. They found that those properties can be expressed as linear combinations of a few such indices. The application of molecular topology to the pharmaceutical research was only a matter of time, the pioneering work being done in the mid-1980s and at the beginning of the 1990s (Galvez et al., 1991). Whatever the field, the interest on molecular topology is clear: Predicting with confidence some specific activity of a molecule saves time and money (Amigo et al., 2009).

The topological indices (TIs) are widely used as molecular descriptors in quantitative structure–activity/property relationships. They have the following advantages over the other molecular descriptors:

They are mathematically well defined.
They can be quickly and easily computed for all real or hypothetical structures represented as molecular graph.

A large number of reports have been published involving the correlation of biological activities with the structure of the molecules (Singh et al., 2010; Sharma et al., 2009). In view of above and in continuation of our work, related to correlation of biological activities with the structure of the molecule using Hansch analysis (Narasimhan et al., 2006; Judge et al., 2010), we hereby report QSAR studies of 1,3-disubstituted-1H-naphtho[1,2-e][1,3] oxazines synthesized in our recent study (Verma et al., 2012). To the best of our knowledge, this is the first report on the correlation of molecular descriptors with the antimicrobial activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines.

2 Results and discussion

The molecular structures of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines with their respective antimicrobial activities (pMIC) are presented in Tables 1 and 2 respectively. The present study was designed to develop quantitative models to predict the correlation between the structural descriptors of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazine with their antibacterial activity against Staphylococcus aureus, Bacillus subtilis and Escherichia coli and the antifungal activity against Candida albicans and Aspergillus niger (Table 2) by the linear free energy relationship model (LFER) described by Hansch and Fujita (1964). The different topological descriptors (independent variables) like Kier's molecular connectivity (ⁿχ, ⁿχ^v) and shape (χ_n_, κα_n) topological indices, Randic topological index (R), Balaban topological index (J) and Wiener topological index (W) calculated for the 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines are presented in Table 3.

Table 1 Molecular structures of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines used in QSAR studies.

Comp.	Structure	Comp.	Structure
3a		7e
3b		7f
3c		7g
3d		7h
3e		7i
7a		7j
7b		7k
7c		7l
7d

Table 2 In vitro antimicrobial activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines.

Comp.	pMIC_sa	pMIC_bs	pMIC_ec	pMIC_ca	pMIC_an
3a	1.43	2.03	2.33	1.73	1.43
3b	1.46	2.07	1.46	1.76	1.46
3c	1.50^a	2.10^a	2.10	1.80	1.50
3d	1.51	1.81	2.11^a	1.81	1.51
3e	2.07^a	1.77	1.47	1.77	1.47
7a	1.77	1.77	2.37	1.77	1.47
7b	1.75	1.45^a	2.05	1.75	1.45
7c	1.78	1.78	1.78	1.78	1.48
7d	1.77	1.77^a	2.37	1.77	1.47
7e	1.75	2.05	2.35	1.75	1.45
7f	1.52	1.82	1.52^a	1.82	1.52
7g	1.45	1.75	2.35	1.75	1.45
7h	1.78	1.78	2.08	1.78	1.48
7i	1.80	1.80	1.80	1.80	1.50
7j	1.49	1.79	0.88^a	1.79	1.49
7k	1.47	2.07	2.07	1.77	1.47
7l	1.83^a	1.83	1.83	1.83	1.53
S.D.^b	0.19	0.17	0.42	0.03	0.03
Std.	2.61^c	2.61^c	2.61^c	2.64^d	2.64^d

a Outliers.

b Standard deviation.

c Ciprofloxacin.

d Fluconazole.

Table 3 Value of topological descriptors used in the QSAR study.

	⁰χ	⁰χ^v	¹χ	¹χ^v	²χ	²χ^v	³χ	³χ^v	κα₁	κα₂	κα₃	R	J	W
3a	17.35	14.17	12.90	8.78	11.31	6.41	1.22	0.58	15.43	6.48	2.77	12.90	1.24	1513.00
3b	19.09	16.02	13.69	9.60	12.56	7.41	1.79	0.91	17.28	6.96	3.18	13.69	1.23	1895.00
3c	20.50	16.83	14.76	9.82	12.90	7.14	1.62	0.71	19.08	8.08	3.58	14.76	1.22	2359.00
3d	19.09	16.41	13.69	9.79	12.56	7.64	1.79	0.97	17.82	7.29	3.37	13.69	1.23	1895.00
3e	19.09	14.77	13.69	8.98	12.56	6.70	1.79	0.70	17.15	6.88	3.14	13.69	1.23	1895.00
7a	18.92	15.50	13.83	9.30	12.11	6.78	1.42	0.64	17.24	7.27	3.17	13.83	1.22	1922.00
7b	18.22	15.09	13.29	9.19	11.94	6.91	1.51	0.74	16.35	6.72	2.97	13.29	1.23	1704.00
7c	19.79	15.36	14.20	9.28	12.84	6.85	1.72	0.69	17.80	7.28	3.25	14.20	1.21	2142.00
7d	18.22	15.29	13.29	9.29	11.94	7.03	1.51	0.78	16.62	6.88	3.06	13.29	1.23	1704.00
7e	18.22	14.47	13.29	8.88	11.94	6.55	1.51	0.64	16.29	6.68	2.94	13.29	1.23	1704.00
7f	18.22	16.09	13.29	9.69	11.94	7.49	1.51	0.91	16.80	6.99	3.12	13.29	1.23	1704.00
7g	18.22	15.09	13.29	9.19	11.94	6.91	1.51	0.74	16.35	6.72	2.97	13.29	1.24	1692.00
7h	19.79	16.42	14.22	9.71	12.73	7.28	1.71	0.81	18.18	7.51	3.37	14.22	1.22	2126.00
7i	20.66	16.28	14.60	9.69	13.46	7.35	2.01	0.85	18.74	7.52	3.46	14.60	1.21	2359.00
7j	19.09	16.21	13.69	9.70	12.56	7.53	1.79	0.94	17.55	7.13	3.27	13.69	1.23	1895.00
7k	19.09	15.39	13.69	9.29	12.56	7.05	1.79	0.81	17.22	6.92	3.16	13.69	1.23	1895.00
7l	19.09	17.02	13.69	10.10	12.56	7.99	1.79	1.08	17.73	7.24	3.33	13.69	1.23	1895.00

Preliminary analysis was carried out in terms of correlation analysis. A correlation matrix constructed for antifungal activity against A. niger is presented in Table 4. The correlations of different molecular descriptors with antimicrobial activity are presented in Table 5. In general, good colinearity (r > 0.5) was observed between most of the parameters. The high interrelationship was observed between topological parameters, Randic index (R) and first order molecular connectivity index (¹χ) (r = 1.000) and a low interrelationship was observed between topological parameters, Balaban index (J) and valance second order molecular connectivity index (²χ^v) (r = 0.026).

Table 4 Correlation matrix for antifungal activity against A. niger.

	pMICan	⁰χ	⁰χ^v	¹χ	¹χ^v	²χ	²χ^v	³χ	³χ^v	κα₁	κα₂	κα₃	R	J	W
PMICan	1.000	0.521	0.850	0.472	0.867	0.557	0.832	0.548	0.750	0.677	0.649	0.751	0.472	−0.275	0.484
⁰χ		1.000	0.663	0.984	0.585	0.962	0.380	0.749	0.245	0.968	0.887	0.922	0.984	−0.714	0.992
⁰χ^v			1.000	0.632	0.991	0.655	0.890	0.586	0.765	0.809	0.796	0.872	0.632	−0.297	0.630
¹χ				1.000	0.542	0.899	0.289	0.620	0.125	0.953	0.924	0.901	1.000	−0.775	0.997
¹χ^v					1.000	0.600	0.938	0.575	0.832	0.742	0.718	0.815	0.542	−0.226	0.545
²χ						1.000	0.481	0.898	0.401	0.924	0.769	0.887	0.899	−0.594	0.924
²χ^v							1.000	0.609	0.972	0.542	0.454	0.634	0.289	0.026	0.309
³χ								1.000	0.627	0.728	0.483	0.721	0.620	−0.253	0.663
³χ^v									1.000	0.395	0.260	0.492	0.125	0.190	0.155
κα₁										1.000	0.951	0.989	0.953	−0.646	0.955
κα₂											1.000	0.947	0.924	−0.687	0.907
κα₃												1.000	0.901	−0.569	0.901
R													1.000	−0.775	0.997
J														1.000	−0.770
W															1.000

Table 5 Correlation of topological descriptors with antimicrobial activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines.

Mol. descriptor	pMIC_sa	pMIC_bs	pMIC_ec	pMIC_ca	pMIC_an
⁰χ	0.407	−0.385	−0.474	0.521	0.521
⁰χ^v	0.033	−0.376	−0.319	0.850	0.850
¹χ	0.483	−0.421	−0.366	0.472	0.472
¹χ^v	−0.025	−0.352	−0.325	0.867	0.867
²χ	0.301	−0.321	−0.614	0.557	0.557
²χ^v	−0.205	−0.252	−0.418	0.832	0.832
³χ	0.081	−0.193	−0.751	0.548	0.548
³χ^v	−0.306	−0.176	−0.479	0.750	0.750
κ₁	0.438	−0.399	−0.433	0.502	0.502
κ₂	0.572	−0.448	−0.226	0.392	0.392
κ₃	0.432	−0.396	−0.435	0.503	0.503
κα₁	0.347	−0.460	−0.416	0.677	0.677
κα₂	0.435	−0.561	−0.199	0.649	0.649
κα₃	0.275	−0.470	−0.402	0.751	0.751
R	0.483	−0.421	−0.366	0.472	0.472
J	−0.780	0.364	0.126	−0.275	−0.275
W	0.471	−0.399	−0.402	0.484	0.484

The different outliers are identified against different microorganisms, and the models have been developed after removal of the outliers (compound numbers in brackets) i.e. B. subtilis (3c, 7b and 7d), S. aureus (3c, 3e and 7l) and E. coli (3d, 7f and 7j). No outliers were found in case of C. albicans and A. niger and QSAR models were developed using the entire dataset of seventeen compounds in case of these fungal strains. In multivariate statistics, it is common to define three types of outliers (Furusjo et al., 2006).

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.
X outliers are substances whose molecular descriptors do not lie in the same range as the (rest of the) training data.
Y outliers are only defined for training or test samples. They are substances for which the reference value of response is invalid.

As there was not much difference in the activity (Table 2) as well as the molecular descriptor range (Table 3) of these outliers when compared to other 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines it indicated the fact that these outliers belong to the category of Y outliers (Substances for which the reference value of response is invalid).

Correlation matrix (Table 4) indicated the importance of the topological parameter, valance first order molecular connectivity index (¹χ^v) in describing the antifungal activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines against A. niger (Eq. (1)).

QSAR model for antifungal activity against A. niger

(1)

\begin{matrix} {pMIC}_{an} = 0.063^{1} χ^{v} + 0.876 \\ n = 17 r = 0.867 q^{2} = 0.689 s = 0.014 F = 45.28 (p < 0.000004) \end{matrix}

Here and thereafter, n – number of data points, r – correlation coefficient, q² – cross validated r² – obtained by the leave one out method, s – standard error of the estimate and F – Fischer statistics.

As the coefficient of ¹χ^v in Eq. (1) is positive, therefore the antifungal activity against A. niger will increase with an increase in the value of ¹χ^v. This is clearly evident from Table 3 that compound 7l having maximum ¹χ^v value of 10.10 has maximum pMIC_an value (pMIC_an = 1.53, Table 2). Similarly, compound 3a having minimum ¹χ^v value of 8.78 (Table 3), has minimum antifungal activity against A. niger (pMICan = 1.43, Table 2).

The QSAR model expressed by Eq. (1) was cross validated by its appreciable q² values (q² = 0.689) obtained by the leave one out (LOO) method. The value of q² greater than 0.5 is the basic requirement for qualifying a QSAR model to be valid one (Golbraikh and Tropsha, 2002). The comparison of observed and predicted antibacterial and antifungal activities is presented in Tables 6 and 7, respectively. Predictive power of the developed QSAR model (Eq. (1)) was evidenced by low residual values as observed and predicted antifungal activity values for A. niger were close to each other (Table 7) The plot of predicted pMIC_an against observed pMIC_an (Fig. 1) also favored the model expressed by Eq. (1). Further, the plot of observed pMIC_an vs residual pMIC_an (Fig. 2) indicated that there was no systemic error in model development as the propagation of residuals was observed on both positive and negative sides (Heravi and Kyani, 2004).

Table 6 Comparison of observed and predicted antibacterial activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines.

Comp.	pMIC_sa			pMIC_bs			pMIC_ec
Comp.	Obs.	Pre.	Res.	Obs.	Pre.	Res.	Obs.	Pre.	Res.
3a	1.43	1.48	−0.05	2.03	2.00	0.03	2.33	2.52	−0.19
3b	1.46	1.56	−0.10	2.07	1.89	0.18	1.46	1.84	−0.38
3c	1.50^a	1.75	−0.25	2.10^a	2.65	−0.55	2.10	2.04	0.06
3d	1.51	1.56	−0.05	1.81	1.81	0.00	2.11^a	1.84	0.27
3e	2.07^a	1.56	0.51	1.77	1.91	−0.14	1.47	1.84	−0.37
7a	1.77	1.77	0.00	1.77	1.82	−0.05	2.37	2.28	0.09
7b	1.75	1.60	0.15	1.45^a	2.79	−1.34	2.05	2.18	−0.13
7c	1.78	1.87	−0.09	1.78	1.82	−0.04	1.78	1.93	−0.15
7d	1.77	1.60	0.17	1.77^a	2.77	−1.00	2.37	2.18	0.19
7e	1.75	1.60	0.15	2.05	1.95	0.10	2.35	2.18	0.17
7f	1.52	1.60	−0.08	1.82	1.88	−0.06	1.52^a	2.18	−0.66
7g	1.45	1.46	−0.01	1.75	1.94	−0.19	2.35	2.18	0.17
7h	1.78	1.72	0.06	1.78	1.76	0.02	2.08	1.94	0.14
7i	1.80	1.80	0.00	1.80	1.76	0.04	1.80	1.59	0.21
7j	1.49	1.56	−0.07	1.79	1.85	−0.06	0.88^a	1.84	−0.96
7k	1.47	1.56	−0.09	2.07	1.90	0.17	2.07	1.84	0.23
7l	1.83^a	1.56	0.27	1.83	1.83	0.00	1.83	1.84	−0.01

a Outliers.

Table 7 Comparison of observed and predicted antifungal activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines.

Comp.	pMIC_ca			pMIC_an
Comp.	Obs.	Pre.	Res.	Obs.	Pre.	Res.
3a	1.73	1.74	−0.01	1.43	1.44	−0.01
3b	1.76	1.79	−0.03	1.46	1.49	−0.03
3c	1.80	1.80	0.00	1.50	1.50	0.00
3d	1.81	1.80	0.01	1.51	1.50	0.01
3e	1.77	1.75	0.02	1.47	1.45	0.02
7a	1.77	1.77	0.00	1.47	1.47	0.00
7b	1.75	1.76	−0.01	1.45	1.46	−0.01
7c	1.78	1.77	0.01	1.48	1.47	0.01
7d	1.77	1.77	0.00	1.47	1.47	0.00
7e	1.75	1.74	0.01	1.45	1.44	0.01
7f	1.82	1.79	0.03	1.52	1.49	0.03
7g	1.75	1.76	−0.01	1.45	1.46	−0.01
7h	1.78	1.80	−0.02	1.48	1.50	−0.02
7i	1.80	1.79	0.01	1.50	1.49	0.01
7j	1.79	1.80	−0.01	1.49	1.50	−0.01
7k	1.77	1.77	0.00	1.47	1.47	0.00
7l	1.83	1.82	0.01	1.53	1.52	0.01

Plot of predicted pMICan values against observed pMICan values for the model developed by Eq. (1).

Plot of residual pMICan values against observed pMICan values for the model developed by Eq. (1).

In case of C. albicans, the developed QSAR model (Eq. (2)) also indicated the predominance of valence first order molecular connectivity index (¹χ^v) in describing the antifungal activity of synthesized compounds.

QSAR model for antifungal activity against C. albicans

(2)

\begin{matrix} {pMIC}_{ca} = 0.063^{1} χ^{v} + 1.176 \\ n = 17 r = 0.867 q^{2} = 0.688 s = 0.014 F = 45.28 (p < 0.000004) \end{matrix}

The coefficient of ¹χ^v is positive in Eq. (2), which indicates that the antifungal activity will increase with the increase in ¹χ^v of the synthesized compounds, which can be clearly seen from their antifungal activity against C. albicans (Table 2) and their ¹χ^v values (Table 3).

For antibacterial activity against S. aureus, the developed QSAR model (Eq. (3)) depicted the importance of Balaban index (J). In this case, a negative correlation was observed between J and antibacterial activity against S. aureus.

QSAR model for antibacterial activity against S. aureus

(3)

\begin{matrix} pMICsa = - 11.737 J + 16.044 \\ n = 14 r = 0.779 q^{2} = 0.490 s = 0.101 F = 18.59 (p < 0.0008) \end{matrix}

The negative correlation of molecular descriptor (J) with antibacterial activity reveals that a decrease in the value of J (Table 3) will lead to an increase in the antibacterial activity against S. aureus (Table 2).

The model described by Eq. (4) depicted the importance of topological parameter, κα₂, in describing the antibacterial activity against B. subtilis.

QSAR model for antibacterial activity against B. subtilis

(4)

\begin{matrix} {pMIC}_{bs} = - 0.226 κ α_{2} + 3.463 \\ n = 14 r = 0.560 q^{2} = 0.112 s = 0.108 F = 5.49 (p < 0.03) \end{matrix}

The negative correlation of molecular descriptor (κα₂) with antibacterial activity reveals that a decrease in the value of κα₂ (Table 3) will lead to an increase in the antibacterial activity against B. subtilis (Table 2).

The Eq. (5), derived for the antibacterial activity of synthesized compounds against E. coli indicated the importance of the topological parameter, third order molecular connectivity index (³χ) in describing the antibacterial activity against E. coli.

QSAR model for antibacterial activity against E. coli

(5)

\begin{matrix} {pMIC}_{ec} = - 1.179^{3} χ + 3.958 \\ n = 14 r = 0.751 q^{2} = 0.375 s = 0.218 F = 15.54 (p < 0.001) \end{matrix}

The negative correlation of ³χ with antibacterial activity against E. coli reveals that a decrease in value of ³χ (Table 3) will lead to an increase in the antibacterial activity against E. coli (Table 2).

As in case of Eq. (1), the predictive ability of Eqs. 2–5 against respective microorganisms is supported by the low residual activity values (Tables 6 and 7). Further, the high q² value (q² > 0.5) observed also supports the suitability of the QSAR model for antifungal activity against C. albicans (Eq. (2)). In case of the QSAR models derived for S. aureus, B. subtilis and E. coli (Eqs. 3–5 ) the q² value is less than 0.5, which shows that the developed models are invalid one. But one should not forget the recommendations of Golbraikh and Tropsha (2002) who have reported that the only way to estimate the true predictive power of a QSAR model is to test their ability to predict accurately the biological activities of compounds. As the observed and predicted antibacterial activity values are close to each other (Table 6), the QSAR models for S. aureus, B. subtilis and E. coli (Eqs. 3–5 ), are valid ones.

It is important to note a fact here that the different compounds which were removed as outliers against different microorganisms at the beginning of the study showed high residual values (Table 6), which justified their removal as outliers.

Summarizing, the antibacterial activity of synthesized compounds were governed by topological parameters, Balaban index (J), Kier's second order molecular index (κα₂) and third order molecular connectivity index (³χ) and the antifungal activity was governed by valance first order molecular connectivity index (¹χ^v).

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. But it is important to note that the predictability of the QSAR models developed in the present study is highly evidenced by the low residual values. This is in accordance with results suggested by Bajaj et al. (2005), who stated that the reliability of the QSAR model lies in its predictive ability even though the activity data are in the narrow range. Further, recent literature reveals that the QSAR has been applied to describe the relationship between a narrow range of biological activity and physicochemical properties of the molecules (Narasimhan et al., 2007; Sharma et al., 2006; Hatya et al., 2006 ). When biological activity data lie in the narrow range, the presence of minimum standard deviation of the biological activity justifies its use in QSAR studies (Narasimhan et al., 2007; Kumar et al., 2007). The minimum standard deviation (Table 2) observed in the antimicrobial activity data justifies its use in QSAR studies.

3 Application of developed QSAR models

QSAR (Quantitative Structure activity Relationship) correlates biological activity data with the physicochemical and/or structural properties of a group of compounds. It has been frequently used to predict biological activities of new compounds and to design compounds with desired properties.

The developed equations can be used for the designing of new 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines with improved antimicrobial activity. For example Eq. (1) (for A. niger) and Eq. (2) (for C. albicans) indicated the positive correlation of valance first order molecular connectivity index (¹χ^v) with antifungal activity i.e. if we develop a new compound with high ¹χ^v value than the existing compounds it may give the more active compound than the existing ones. In this way, we have designed compounds A, B, C, and D (Table 8) with high ¹χ^v values than the existing compounds by adding suitable substituents and calculated their activity using Eqs. (1) and (2). From the predicted activity, it has been observed that the designed compounds are more active than the existing compounds in case of A. niger and C. albicans.

Table 8 The proposed novel compounds with improved antimicrobial activity based on the information derived from Eqs. 1–5 .

S. No.	Parameter value	Predicted activity (μM/ml)
For C. albicans and A. niger
A	¹χ^v = 10.60	pMIC_an = 1.54, pMIC_ca = 1.84
B	¹χ^v = 11.35	pMIC_an = 1.59, pMIC_ca = 1.89
C	¹χ^v = 12.35	pMIC_an = 1.65, pMIC_ca = 1.95
D	¹χ^v = 13.35	pMIC_an = 1.65, pMIC_ca = 2.02

For E. coli
E	³χ = 0.88	pMIC_ec = 2.92
F	³χ = 0.61	pMIC_ec = 3.24

For B. subtilis
G	κα₂ = 4.14	pMIC_bs = 2.53
H	κα₂ = 2.68	pMIC_bs = 2.86

For S. aureus
I	J = 1.21	pMIC_sa = 1.84

Similarly the antibacterial activity of oxazines against S. aureus, B. subtilis and E. coli is governed by negative Balaban index (J), Kier's second order alpha shape index (κα₂₎ and third order molecular connectivity index (³χ) respectively and the designed compound on the basis of these parameters are presented in Table 8. It has been observed from the predicted activity that the designed compounds were more active than the existing compounds. It is important to note a fact here that compounds E, F (E. coli) and H (B. subtilis) (Table 8) are not only more active than the existing compounds but also more active than the reference compound ciprofloxacin against B. subtilis and E. coli and have the potential to be selected as lead compounds for the development of novel antimicrobial agents.

4 Conclusion

In conclusion, the QSAR study throws some light for the first time on the correlation of antimicrobial activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines with their topological parameters. The QSAR studies indicated that the antibacterial activity of synthesized compounds were governed by topological parameters, Balaban index (J), Kier's second order molecular index (κα₂) and third order molecular connectivity index (³χ) and the antifungal activity was governed by valance first order molecular connectivity index (¹χ^v). Further, the predictive powers of the equation were validated by determination of cross-validated r² (q²) using the leave one out (LOO) method.

5 Experimental

5.1

5.1 Descriptor Generation and regression analysis

The structures of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines were pre-optimized using MM⁺ molecular mechanics force field and the final geometries of the minimum energy conformation were obtained by a more precise optimization with the semi-empirical AM1 method. Then theoretical molecular descriptors were calculated in the TSAR program. The next step in developing a model was generation of the numerical description of the molecular structures. The different topological descriptors (independent variables) viz. i.e. Kier's molecular connectivity (⁰χ, ⁰χ^v, ¹χ, ¹χ^v, ²χ, ²χ^v) and shape (κ_1, κ_2, κ_3, κα_1, κα_2, κα₃) topological indices, Randic topological index (R), Balaban topological index (J), and Wiener topological index (W), (Hansch and Fujita, 1964; Hansch et al., 1973; Kier and Hall, 1973; Randic, 1975; Balaban, 1982; Wiener, 1947; Randic, 1993 ) were calculated for each compound in the data set, using the software TSAR 3.3 (TSAR 3D Version 3.3, 2000). The various topological descriptors can be calculated as follows. The developed models were cross-validated by the ‘leave one out' (LOO) technique (Kumar et al., 2009).

5.2

5.2 Topological descriptors

All the topological indices used are calculated from the hydrogen suppressed molecular graphs. Though their calculations are exclusively discussed in the literature, we give below the expressions used for their calculations.

5.3

5.3 Wiener index (W) (Wiener, 1947)

Wiener index W = W(G) of G is defined as the half sum of the elements of the distance matrix. $W = W (G) = 1 / 2 \sum_{i = 1} \sum_{j = 1} (D) ij$ where (Dij) is the ijth element of the distance matrix which denotes the shortest graph-theoretical distance between sites i and j of G.

5.4

5.4 The first-order connectivity index (¹χ) (Randic, 1993)

The first order connectivity index 1w = 1w(G) of G is defined by Randic as $^{1} χ =^{1} χ (G) = \sum_{i, j} {[d (i) . d (j)]}^{- 0.5}$

5.5

5.5 Balaban index (J) (Balaban, 1982)

The Balaban index J = J(G) of G is defined as $J = M / (μ + 1) \sum_{Bonds} {(di . dj)}^{- 0.5}$ where M is the number of bonds in G, μ is the cyclomatic number of G, and di (i = 1,2,3, N; N is the number of vertices in G) is the distance sum. The cyclomatic number μ = μ(G) of a cyclic graph G is equal to the minimum number of edges necessary to be erased from G in order to transform it into the related acyclic graph. In case of monocyclic graph μ = 1 otherwise it is calculated by means of the following expression $μ = M - N + 1$

5.6

5.6 Kappa shape indices

Another set of very useful topological indices of the second generation is composed by the kappa indices of molecular shape and flexibility (Kier and Hall, 1999). According to Kier, the shape of a molecule may be partitioned into attributes, each describable by the count of bonds of various path lengths. The basis for devising a relative index of shape is given by the relationship of the number of paths of length l in the molecule i, ^lP_i, to some reference values based on molecules with a given number of atoms, n, in which the values of ^lP are maximum and minimum, ^lP_max and ^lP_min. The first order shape attribute, κ₁, is given by the following expression: $κ_{1} = n {(n - 1)}^{2} / {(^{1} P_{i})}^{2}$ The second and third order kappa indices are defined as follows: $κ_{2} = (n - 1) {(n - 2)}^{2} / {(^{2} P_{i})}^{2}$ $κ_{3 i} = (n - 1) {(n - 3)}^{2} / {(^{3} P_{i})}^{2} When n is odd$ $κ_{3 i} = (n - 3) {(n - 2)}^{2} / {(^{3} P_{i})}^{2} When n is even$

In order to account for the variation in size contribution to shape from different atoms the radius of atom X relative to the covalent radius of a carbon sp³ hybrid atom is considered. The specific correction in computing κ₁ is made by modifying the count of atoms, n, with a modifier, a, calculated as: $α_{X} = (rX / r_{csp 3}) - 1$ where α represents a decrement or increment of n for a noncarbon sp³ element X. The modified kappa shape indices are given by: $κ_{α_{1}} = (n + α) {(n + α - 1)}^{2} / {(^{1} P_{i} + α)}^{2}$ $κ_{α_{2}} = (n + α - 1) {(n + α - 2)}^{2} / {(^{1} P_{i} + α)}^{2}$ $κ_{α_{3}} = (n + α - 1) {(n + α - 3)}^{2} / {(^{3} P_{i} + α)}^{2} n is odd$ $κ_{α_{4}} = (n + α - 3) {(n + α - 2)}^{2} / {(^{3} P_{i} + α)}^{2} n is even$

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 LR analysis. The regression analysis was carried out using the SPSS software package (SPSS for windows, Version 10.05, 1999) for choosing the descriptors contributing to the antimicrobial activity.

Acknowledgements

The authors thank University Grants Commission, New Delhi for financial support.

References

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Introduction

Results and discussion

Application of developed QSAR models

Conclusion

Experimental

Descriptor Generation and regression analysis
Topological descriptors
Wiener index (W) (Wiener, 1947)
The first-order connectivity index (1χ) (Randic, 1993)
Balaban index (J) (Balaban, 1982)
Kappa shape indices

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[1] Amigo J.M., Galvez J., Villar V.M., . A review on molecular topology: applying graph theory to drug discovery and design. Naturwissenschaften. 2009;96:749-761.
[Google Scholar]

[2] Bajaj S., Sambi S.S., Madan A.K., . Prediction of anti-inflammatory activity of N-arylanthranilic acids: computational approach using refined Zagreb indices. Croat. Chem. Acta. 2005;78:165-174.
[Google Scholar]

[3] Balaban A.T., . Highly discriminating distance based topological indices. Chem. Phys. Lett.. 1982;89:399-404.
[Google Scholar]

[4] Chiu T.L., So S.S., . Development of neural network QSPR models for Hansch substituent constants. 1. Method and validations. J. Chem. Inf. Comput. Sci.. 2004;44(1):147-153.
[Google Scholar]

[5] Furusjo E., Svenson A., Rahmberg M., Andersson M., . The importance of outlier detection and training set selection for reliable environmental QSAR predictions. Chemosphere. 2006;63:99-108.
[Google Scholar]

[6] Galvez J., Garcia-Domenech R., Bernal J., Garcia-March F., . Drug design based upon molecular topology: application to nonnarcotic analgesics. Anal. Real Acad. Farm.. 1991;57:533-546.
[Google Scholar]

[7] Golbraikh A., Tropsha A., . Beware of q². J. Mol. Graphics Model.. 2002;20:269-276.
[Google Scholar]

[8] Hansch C., Fujita T., . P–σ–π analysis. A method for the correlation of biological activity and chemical structure. J. Am. Chem. Soc.. 1964;86:1616-1626.
[Google Scholar]

[9] Hansch, Leo A., Unger S.H., Kim K.H., Nikaitani D., Lien E.J., . Aromatic substituent constants for structure–activity correlations. J. Med. Chem.. 1973;16:1207-1216.
[Google Scholar]

[10] Hatya S.A., Aki-Sener E., Tekiner-Gulbas B., Yildiz I., Temiz-Arpaci O., Yalcin I., Altanlar N., . Synthesis, antimicrobial activity and QSARs of new benzoxazine-3-ones. Eur. J. Med. Chem.. 2006;41:1398-1404.
[Google Scholar]

[11] Heravi M.J., Kyani A., . Use of computer-assisted methods for the modeling of the retention time of a variety of volatile organic compounds: a PCA-MLR-ANN approach. J. Chem. Inf. Comput. Sci.. 2004;44:1328-1335.
[Google Scholar]

[12] Judge V., Narang R., Sharma D., Narasimhan B., Kumar P., . Hansch analysis for the prediction of antimycobacterial activity of ofloxacin derivatives. Med. Chem. Res.. 2010;20:826-837.
[Google Scholar]

[13] Kier L.B., Hall L.H., . Molecular Connectivity in Chemistry and Drug Research. New York: Academic Press; 1973. pp. 79–82

[14] Kier L.B., Hall L.H., . Devillers J., Balaban A.T., eds. Topological indices and related descriptors in QSAR and QSPR. Amsterdam: Gordon and Breach Sci. Pub.; 1999. p. :455-489.

[15] Kumar A., Narasimhan B., Kumar D., . Synthesis, antimicrobial and QSAR studies of substituted benzamides. Bioorg. Med. Chem.. 2007;15:4113-4124.
[Google Scholar]

[16] Kumar P., Narasimhan B., Sharma D., Judge V., Narang R., . Hansch analysis of substituted benzoic acid benzylidene/furan-2-yl-methylene hydrazides as antimicrobial agents. Eur. J. Med. Chem.. 2009;44(5):1853-1863.
[Google Scholar]

[17] Narasimhan B., Judge V., Narang R., Ohlan S., Ohlan R., . Quantitative structure–activity relationship studies for prediction of antimicrobial activity of synthesized 2,4-hexadienoic acid derivatives. Bioorg. Med. Chem. Lett.. 2007;17:5836-5845.
[Google Scholar]

[18] Narasimhan B., Kumari M., Jain N., Dhake A.S., Sundaravelan C., . Correlation of antibacterial activity of some N-[5-(2-furanyl)-2-methyl-4-oxo-4H-thieno[2,3-d] pyrimidin-3-yl]carboxamide and 3-substituted-5-(2-furanyl)-2-methyl-3H-thieno[2,3-d] pyrimidin-4-ones with topological indices using Hansch analysis. Bioorg. Med. Chem. Lett.. 2006;16:4951-4958.
[Google Scholar]

[19] Randic M., . On characterization of molecular branching. J. Am. Chem. Soc.. 1975;97:6609-6615.
[Google Scholar]

[20] Randic M., . Comparative regression analysis: regression based on a single descriptor. Croat. Chem. Acta. 1993;66:289-312.
[Google Scholar]

[21] Sharma P., Kumar A., Sharma M., . Synthesis and QSAR studies on 5-(2-(2-methylprop-1-enyl)-1H-benzimidazol-1yl)-4,6-diphenyl-pyrimidin-2-(5H)-thione derivatives as antibacterial. Eur. J. Med. Chem.. 2006;41:833-840.
[Google Scholar]

[22] Sharma S., Sharma B.K., Prabhakar Y.S., . Juglone derivatives as antitubercular agents: a rationale for the activity profile. Eur. J. Med. Chem.. 2009;44(7):2847-2853.
[Google Scholar]

[23] Singh S., Mandal P.K., Singh N., Misra A.K., Singh S., Chaturvedi V., Sinha S., Saxena A.K., . Substituted hydrazine carbothioamide as potent antitubercular agents: synthesis and quantitative structure–activity relationship (QSAR) Bioorg. Med. Chem. Lett.. 2010;20(8):2597-2600.
[Google Scholar]

[24] SPSS for Windows, Version 10.05, 1999. SPSS Inc., Bangalore, India.

[25] TSAR 3D Version 3.3, 2000 Oxford Molecular Limited.

[26] Verma V., Singh K., Kumar D., Klapotke T.M., Stierstorfer J., Narasimhan B., Qazi A.K., Hamid A., Jaglan S., . Synthesis, antimicrobial and anticancer studies of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines. Eur. J. Med. Chem.. 2012;56:195-202.
[Google Scholar]

[27] Wiener H., . Structural determination of paraffin boiling points. J. Am. Chem. Soc.. 1947;69:17-20.
[Google Scholar]

[28] Xu L., Yang J.A., Wu Y.P., . Effective descriptions of molecular structures and the quantitative structure–activity relationship studies. J. Chem. Inf. Comput. Sci.. 2002;42(3):602-606.
[Google Scholar]

QSAR studies of antimicrobial activity of 1,3-disubstituted-1H-naphtho[1,2-e][1,3]oxazines using topological descriptors