Synthesis, antimicrobial evaluation and QSAR studies of p-coumaric acid derivatives

2.1 General procedure for the synthesis of amides/anilides of p-coumaric acid

The solution of corresponding amine/aniline (0.1 mol) in ether (50 mL) was added dropwise to a solution of p-coumaric acid chloride (0.1 mol) in ether (50 mL) maintained at 0–10 °C temperature. The solution was stirred for 30 min and the precipitated amide was separated by filtration. The crude amide was recrystallized with alcohol. In case of anilides, the precipitated crude anilide was treated with 5% hydrochloric acid, 4% sodium carbonate and water to remove residual aniline and the resultant anilide was recrystallized with alcohol.

2.2 General procedure for the synthesis of esters of p-coumaric acid (1, 11, 17–22, 25–26)

For the preparation of p-coumaric acid chloride, thionyl chloride (0.3 mol) was added gradually to p-coumaric acid (0.25 mol) in a round bottom flask. After addition of thionyl chloride, the mixture was stirred for 4 h and heated to 80 °C for 30 min in a water bath. The excess of thionyl chloride was removed by distillation. A solution of 8-hydroxy quinoline (0.05 mol) in ether (50 mL) was added to a solution of p-coumaric acid (0.05 mol) in ether (50 mL). The mixture was heated on a water bath until no further evolution of hydrogen chloride was observed and completion of reaction was checked by single spot TLC. The mixture was cooled to room temperature and evaporation of solvent yielded the crude product which was purified by recrystallization with alcohol.

2.3 General procedure for the synthesis of esters of p-coumaric acid (10, 23 and 24)

A mixture of p-coumaric acid (0.08 mol) and appropriate alcohol (0.74 mol) was heated under reflux in the presence of sulphuric acid till the completion of reaction which was checked by single spot TLC. Then, the reaction mixture was poured in 200 mL ice cold water, neutralized with sodium bicarbonate solution followed by extraction of ester with ether (50 mL). The ether layer was separated, which on evaporation yielded the ester derivatives of p-coumaric acid.

2.4 In vitro antimicrobial activity

The antimicrobial activity of the synthesized compounds was tested against Gram-positive bacteria: Staphylococcus aureus MTCC 2901, Bacillus subtilis MTCC 2063, Gram negative bacterium: Escherichia coli MTCC 1652 and fungal strains: Candida albicans MTCC 227 and Aspergillus niger MTCC 8189 using the tube dilution method (Cappucino and Sherman, 1999). Dilutions of test (50–1.56 μg/mL) and standard compounds were prepared in double strength nutrient broth—I.P. (bacteria) or Sabouraud dextrose broth I.P. (fungi) (Pharmacopoeia of India, 2007). The samples were incubated at 37 °C for 24 h (bacteria), at 25 °C for 7 d (A. niger), and at 37 °C for 48 h (C. albicans), and the results were recorded in terms of minimum inhibitory concentration (MIC).

2.5 QSAR Studies

The structures of p-coumaric acid derivatives were first pre-optimized with the Molecular Mechanics Force Field (MM⁺) procedure included in Hyperchem 6.0, 1993 and the resulting geometries were further refined by means of the semiempirical method PM3 (Parametric Method-3). We chose a gradient norm limit of 0.01 kcal/Å for the geometry optimization. The lowest energy structure was used for each molecule to calculate physicochemical properties using TSAR 3.3 software for Windows (TSAR 3D Version 3.3, 2000). Further, the regression analysis was performed using the SPSS software package (SPSS for Windows, 1999).

3.1 Chemistry

p-Coumaric acid derivatives (1–36) were synthesized as outlined in Scheme 1. The physicochemical properties of the synthesized compounds are presented in Table 1. The structures of all the newly synthesized compounds were confirmed by the IR, ¹H NMR and elemental analyses which were in full agreement with their structures.

Comp.	R	Comp.	R	Comp.	R
1		18		22
10	C3H7	19	C4H9	23	C2H5
11		20		24	CH3
17	-	21		25
26

Comp.	R	R1	R2	R3	R4	R5	R6	R7
32	–	–	–	H	Cl	H	H	H
33	–	–	–	H	H	H	H	H
36	–	–	–	CH3	H	CH3	H	H
2	C6H13	–	–	–	–	–	–	–
4		–	–	–	–	–	–	–
5		–	–	–	–	–	–	–
8	–	C2H4OH	C2H4OH	–	–	–	–	–
16	–	C4H9	C4H9	–	–	–	–	–
29	–	C6H5	C6H5	–	–	–	–	–
30	–	–	–	–	–	–	–	–
34	–	–	–	–	–	–	–	–
35	–	CH3	CH3	–	–	–	–	–

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Scheme 1 Scheme for the synthesis of p-coumaric acid derivatives.

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Compound 12. IR (ATR) cm⁻¹: 3620 (O—H str., phenol), 1708 (C⚌O str., 2⁰ amide), 3098 (C—H str., aromatic), 1539 (C⚌C skeletal str., phenyl), 1643 (C⚌C str., alkene), 753 (C—Cl str., C₆H₃Cl); ¹H NMR (DMSO-d₆, δ ppm): 6.17–7.29 (m, 7H, ArH), 7.38 {d, ¹H, CH (C₃), acryl}, 6.29 {d, ¹H, CH (C₂), acryl}, 7.72 (s, 1H, NH of amide); Anal. Calculated for C₁₅H₁₁Cl₂NO₂: C, 58.46; H, 3.60; N, 4.55; Found: 58.49; H, 3.64; N, 4.50.

Compound 14. IR (ATR) cm⁻¹: 1213 and 1411 (C—O str., and O—H in plane bending, phenol), 1691 (C⚌O str., 2⁰ amide), 3082 (C—H str., aromatic), 1507 (C⚌C skeletal str., phenyl), 1627 (C⚌C str., alkene), 1310 (NO₂ sym. str., Ar—NO₂), 2835 (CH₃ str., Ar—CH₃); ¹H NMR (DMSO-d₆, δ ppm): 6.68–7.87 (m, 7H, ArH), 7.44 {d, 1H, CH (C₃), acryl}, 6.97 {d, 1H, CH (C₂), acryl}, 8.09 (s, 1H, NH of amide), 2.38 (s, 3H, aromatic CH₃); Anal. Calculated for C₁₆H₁₄N₂O₄: C, 64.42; H, 4.73; N, 9.39; Found: C, 64.43; H, 4.78; N, 9.34.

Compound 17. IR (ATR) cm⁻¹: 3612 (O—H str., phenol), 1742 (C⚌O str., ester), 3056 (C—H str., aromatic), 1544 (C⚌C skeletal str., phenyl), 1638 (C⚌C str., alkene), 1399 (ring str., quinoline), 752 (C—H out of plane bending, quinoline), 1637 (C⚌N str., quinoline) ¹H NMR (DMSO-d₆, δ ppm): 7.52–8.03 (m, 10H, ArH), 7.98 {d, 1H, CH (C₃), acryl}, 7.28 {d, 1H, CH (C₂), acryl}; Anal. Calculated for C₁₈H₁₃NO₃: C, 74.22; N, 4.81, H, 4.50; Found: C, 74.25; N, 4.77, H, 4.52.

Compound 22. IR (ATR) cm⁻¹: 3622 (O—H str., phenol), 1728 (C⚌O str., ester), 2917 (C—H str., alkane), 3025 (C—H str., aromatic), 1535 (C⚌C skeletal str., phenyl), 1627 (C⚌C str., alkene); ¹H NMR (DMSO-d₆, δ ppm): 6.98–7.76 (m, 9H, ArH), 7.98 {d, 1H, CH (C₃), acryl}, 6.45 {d, 1H, CH (C₂), acryl}, 5.69 (s, 2H, benzyl); Anal. Calculated for C₁₆H₁₄O₃: C, 75.57; H, 5.55; Found: C, 75.52; H, 5.58.

Compound 25. IR (ATR) cm⁻¹: 1214 and 1464 (C—O str., and O—H in plane bending, phenol), 1740 (C⚌O str., ester), 3038 (C—H str., aromatic), 1545 (C⚌C skeletal str., phenyl), 1628 (C⚌C str., alkene), 1338 (NO₂ sym. str., Ar—NO₂); ¹H NMR (DMSO-d₆, δ ppm): 6.93–8.12 (m, 8H, ArH), 7.45 {d, 1H, CH (C₃), acryl}, 6.86 {d, 1H, CH (C₂), acryl}; Anal. Calculated for C₁₅H₁₁NO₅: C, 63.16; H, 3.89; N, 4.91; Found: C, 63.19; H, 3.90; N, 4.88.

Compound 27. IR (ATR) cm⁻¹: 3649 (O—H str., phenol), 1690 (C⚌O str., 2⁰ amide), 3088 (C—H str., aromatic), 1525 (C⚌C skeletal str., phenyl), 1622 (C⚌C str., alkene), 1351 (NO₂ sym. str., Ar—NO₂); ¹H NMR (DMSO-d₆, δ ppm): 6.95–7.39 (m, 8H, ArH), 7.34 {d, 1H, CH (C₃), acryl}, 6.98 {d, 1H, CH (C₂), acryl}; Anal. Calculated for C₁₅H₁₂N₂O₄: C, 63.38; H, 4.25; N, 9.85; Found: C, 63.42; H, 4.22; N, 9.81.

Compound 28. IR (ATR) cm⁻¹: 3650 (O—H str., phenol), 1693 (C⚌O str., 2⁰ amide), 3058 (C—H str., aromatic), 1544 (C⚌C skeletal str., phenyl), 1647 (C⚌C str., alkene), 690 (C—Cl str., C₆H₅Cl); ¹H NMR (DMSO-d₆, δ ppm): 6.07–7.52 (m, 8H, ArH), 7.50 {d, 1H, CH (C₃), acryl}, 7.10 {d, 1H, CH (C₂), acryl}, 7.62 (s, 1H, NH of amide); Anal. Calculated for C₁₅H₁₂ClNO₂: C, 65.82; H, 4.42; N, 5.12; Found: C, 65.88; H, 4.41; N, 5.15.

Compound 30. IR (ATR) cm⁻¹: 3591 (O—H str., phenol), 1646 (C⚌O str., 2⁰ amide), 3063 (C—H str., aromatic), 1545 (C⚌C skeletal str., phenyl), 1627 (C⚌C str., alkene), 787 (C—H out of plane bending, 1-naphthalene), ¹H NMR (DMSO-d₆, δ ppm): 7.28–7.87 (m, 11H, ArH), 7.62 {d, 1H, CH (C₃), acryl}, 7.46 {d, 1H, CH (C₂), acryl}, 8.02 (s, 1H, NH of amide); Anal. Calculated for C₁₉H₁₅NO₂: C, 78.87; H, 5.23; N, 4.84; Found: C, 78.90; H, 5.22; N, 4.81.

Compound 33. IR (ATR) cm⁻¹: 3643 (O—H str., phenol), 1698 (C⚌O str., 2⁰ amide), 3083 (C—H str., aromatic), 1523 (C⚌C skeletal str., phenyl), 1629 (C⚌C str., alkene); ¹H NMR (DMSO-d₆, δ ppm): 7.03–7.32 (m, 9H, ArH), 7.29 {d, 1H, CH (C₃), acryl}, 7.06 {d, 1H, CH (C₂), acryl}, 9.57 (s, 1H, NH of amide); Anal. Calculated for C₁₅H₁₃NO₂: C, 75.30; H, 5.48; N, 5.85; Found: C, 75.33; H, 5.52; N, 5.80.

Compound 34. IR (ATR) cm⁻¹: 3620 (O—H str., phenol), 1677 (C⚌O str., 2⁰ amide), 3029 (C—H str., aromatic), 1534 (C⚌C skeletal str., phenyl), 1628 (C⚌C str., alkene), 3468 (N—H str., morpholine), 2677 (C—H str., morpholine), 1103 (C—O—C str., morpholine); ¹H NMR (DMSO-d₆, δ ppm): 6.97–8.10 (m, 4H, ArH), 7.92 {d, 1H, CH (C₃), acryl}, 6.94 {d, 1H, CH (C₂), acryl}, 2.82–3.78 (t, 8H, morpholine); Anal. Calculated for C₁₃H₁₅NO₃: C, 66.94; H, 6.48; N, 6.00; Found: C, 66.96; H, 6.52; N, 5.96.

3.2 In-vitro antimicrobial activity

Biological activity data determined as MIC values in μg/mL were first transformed into pMIC values (i.e. −log MIC in μM/mL) for the purpose of QSAR study. The synthesized p-coumaric acid derivatives were evaluated for their in vitro antibacterial activity against S. aureus, B. subtilis, E. coli and antifungal activity against C. albicans and A. niger by the tube dilution method. From the recorded pMIC values (Table 2), it was observed that compounds 17 and 30 were found to be most active against S. aureus having pMIC_sa value 1.67 μM/mL. Compound 31 was found to be most potent against B. subtilis having pMIC_bs value 2.01 μM/mL. Compounds 6 and 29 were found to be most active against E. coli, having pMIC_ec values 1.71 and 1.70 μM/mL respectively. In case of antifungal activity against C. albicans and A. niger, compound 17 was found to be most active antifungal agent having pMIC_ca and pMIC_an values 1.67 and 1.97 μM/mL, respectively.

In general, the results of MBC/MFC studies revealed that the synthesized compounds were bacteriostatic and fungistatic in action as their MFC and MBC values were 3-fold higher than their MIC values (a drug is considered to be bacteriostatic/fungistatic when its MFC and MBC values are 3-fold higher than its MIC value) (Rodriguez-Arguelles et al., 2005).

3.3 Structure–activity relationship

From the antimicrobial activity results of the synthesized p-coumaric acid derivatives, the following structure–activity relationship can be withdrawn:

• In case of antibacterial activity of synthesized p-coumaric acid derivatives against S. aureus, esters and amides having bulky aromatic groups increased the antibacterial potential as evidenced by high antibacterial activity of compounds 17 and 30 (synthesized using 8-hydroxy quinoline and naphthylamine respectively).

• Results of antibacterial screening of synthesized p-coumaric acid derivatives against B. subtilis indicated that anilides having electron withdrawing substituents on phenyl nucleus were found to be the most potent antibacterial agents as evidenced by the highest antibacterial activity of compound 31 (having 2-chloro-4-nitro substituents) against B. subtilis. Role of electron withdrawing groups in improving antimicrobial activity is similar to the results of Sharma et al. (2004).

• In case of antibacterial activity of p-coumaric acid derivatives against E. coli, anilides having electron withdrawing substituents on phenyl nucleus (6) and amides having bulky aromatic substituents (29, having diphenyl) were found to be the most potent antibacterial agents. The high antibacterial activity of compounds having bulky aromatic substituents is in accordance with the results of Mahiwal et al. (2012).

• Results of antifungal activity of p-coumaric acid derivatives against C. albicans and A. niger indicated that ester derivative synthesized using 8-hydroxy quinoline (17) was found to be the most potent one. The high antifungal activity of 8-hydroxy quinoline ester is supported by findings of Sarova et al. (2011).

• From the above mentioned antimicrobial activity results, it can be concluded that different structural requirements are necessary for different p-coumaric acid derivatives to become active against different microbial targets. This is in accordance with the results obtained by Sortino et al. (2007).

The above mentioned findings are summarized in Fig. 1.

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Figure 1 SAR of antimicrobial activity of synthesized p-coumaric acid derivatives.

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3.4 QSAR Studies

In order to identify the substituent effect on the antimicrobial activity, quantitative structure–activity relationship (QSAR) study was undertaken, using the linear free energy relationship model (LFER) (Hansch and Fujita, 1964). Biological activities in pMIC values are used as dependent variable in the QSAR study. The different molecular descriptors (independent variables) selected for the present study are listed in Table 3. The values of selected molecular descriptors used in the QSAR study are presented in Table 4.

Our earlier studies (Kumar et al., 2012b; Judge et al., 2012a,b; Narang et al., 2012a,b) indicated that the multi-target QSAR (mt-QSAR) models are better than one-target QSAR (ot-QSAR) models in describing the antimicrobial activity. So, in the present study we have developed multi-target QSAR models to describe the antimicrobial activity of synthesized p-coumaric acid derivatives.

According to the ot-QSAR models, one should use five different equations with different errors to predict the activity of a new compound against five microbial species. However, very recently the interest has been increased in the development of multi-target QSAR (mt-QSAR) models. As opposed to ot-QSAR, the mt-QSAR model is a single equation that considers the nature of molecular descriptors which are common and essential for describing the antibacterial and antifungal activities (Gonzalez-Diaz et al., 2007, 2008; Cruz-Monteagudo et al., 2007; Gonzalez-Diaz and Prado-Prado, 2008).

In light of above, we have attempted to develop three different mt-QSAR models viz. mt-QSAR model for describing antibacterial activity of synthesized compounds against S. aureus, B. subtilis and E. coli, mt-QSAR model for describing antifungal activity against C. albicans and A. niger as well as a common mt-QSAR model for describing the antimicrobial (overall antibacterial and antifungal) activity.

In order to develop mt-QSAR models, initially we calculated the average antibacterial, antifungal and antimicrobial activities of p-coumaric acid derivatives which are presented in Table 2.

During the regression analysis studies compounds 1, 17, 30 and 32 were designated as outliers and were not involved in the data set for QSAR model generation. In multivariate statistics, 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.

2. X outliers are substances whose molecular descriptors 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.

As there was no difference in the activity (Table 2) as well as the molecular descriptor range (Table 4) of these outliers when compared to the other p-coumaric acid derivatives, these outliers belong to the category of Y outliers (substances for which the reference value of response is invalid) (Furusjo et al., 2006).

Preliminary analysis was carried out in terms of correlation analysis. A correlation matrix constructed for antibacterial activity of the synthesized compounds is presented in Table 5. In general, high collinearity (r > 0.5) was observed between different parameters. The high interrelationship was observed between topological parameters, Wiener index and first order molecular connectivity index (¹χ) (r = 0.987) and low interrelationship was observed between electronic parameter, energy of the highest occupied molecular orbital (HOMO) and topological parameter, first order molecular connectivity index (¹χ) (r = −0.023). Correlation of calculated molecular descriptors with antibacterial, antifungal and antimicrobial activities is presented in Table 5.

The structural effects on variations in antibacterial activity of the synthesized p-coumaric acid derivatives in terms of pMIC_ab (−log MIC_ab) were examined by regression analysis with molecular parameters. For 32 p-coumaric acid derivatives, Eq. (1) was derived as that of the best quality using the topological parameter, first order molecular connectivity index (¹χ, r = 0.753, Table 4).

3.4.1

3.4.1 LR mt-QSAR model for antibacterial activity

(1)

$${\text{pMIC}}_{\text{ab}}={0.0819}^1\chi +0.569$$ $$n=32r=0.753q^2=0.508s=0.096F=39.25$$

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

Coefficient of ¹χ in Eq. (1) is positive which indicates that antibacterial activity of synthesized compounds is positively correlated to first order molecular connectivity index (¹χ) i.e. antibacterial activity of synthesized compounds will increase with increase in the value of ¹χ and vice versa. This is evidenced by antibacterial activity data of synthesized compounds (Table 2) and their ¹χ values (Table 3) i.e. compounds 6, 17 and 29 having high ¹χ values of 10.45, 10.72 and 11.74 are having high antibacterial activity (pMIC_ab = 1.61, 1.67 and 1.60 μM/mL ,respectively).

The molecular connectivity index, an adjacency based topological index proposed by Randic is denoted by χ and is defined as sum of over all the edges (ij) as per following $$\chi ={\displaystyle \sum _{i=1}^n}{(V_i{V}_j)}^{-1/2}$$ where V_i and V_j are the degrees of adjacent vertices i and j and n is the number of vertices in a hydrogen suppressed molecular structure (Lather and Madan, 2005). The topological index, χ signifies the degree of branching, connectivity of atoms and unsaturation in the molecule which accounts for variation in activity.

The QSAR model expressed by Eq. (1) was cross validated by its high q² value (q² = 0.508) 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). As the observed and predicted antibacterial activity values are close to each other (Table 7), the mt-QSAR model for antibacterial activity (Eq. (1)) is a valid one. The plot of predicted pMIC_ab against observed pMIC_ab (Fig. 2) also favours the developed QSAR model expressed by Eq. (2). Further, the plot of observed pMIC_ab vs. residual pMIC_ab (Fig. 3) indicated that there was no systemic error in model development as the propagation of error was observed on both sides of zero (Kumar et al., 2007).

Table 6 Correlation of antibacterial (pMIC_ab), antifungal (pMIC_af) and antimicrobial (pMIC_am) activities of synthesized p-coumaric acid derivatives with calculated molecular descriptors.

Descriptor	pMICab	pMICaf	pMICam
Cos E	−0.355	−0.168	−0.341
log P	0.365	0.291	0.399
MR	0.722	0.551	0.780
0χ	0.737	0.626	0.822
0χv	0.675	0.573	0.753
1χ	0.753	0.569	0.811
1χv	0.621	0.522	0.690
2χ	0.715	0.592	0.791
2χv	0.557	0.557	0.656
3χ	0.495	0.589	0.621
3χv	0.358	0.536	0.495
κ1	0.721	0.636	0.815
κ2	0.590	0.460	0.641
κ3	0.253	0.243	0.294
κα1	0.688	0.633	0.788
κα2	0.474	0.388	0.523
κα3	0.137	0.163	0.172
R	0.753	0.569	0.811
J	−0.471	−0.186	−0.437
W	0.752	0.600	0.823
Te	−0.732	−0.630	−0.820
Ele. E	−0.695	−0.654	−0.801
Nu. E	0.681	0.649	0.789
SA	0.599	0.539	0.681
IP	−0.084	0.239	0.035
LUMO	−0.381	−0.358	−0.439
HOMO	0.084	−0.239	−0.035
μ	0.440	0.310	0.465

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Figure 2 Plot of observed pMIC_ab against predicted pMIC_ab obtained by Eq. (1).

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Figure 3 Plot of observed pMIC_ab against residual pMIC_ab obtained by Eq. (1).

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Results of correlation of calculated molecular descriptors with antifungal activity of synthesized compounds (Table 5) indicated that electronic parameter, electronic energy (Ee) was the most dominating descriptor for antifungal activity of synthesized compounds. So, QSAR model for antifungal activity of synthesized p-coumaric acid derivatives was developed by using the electronic parameter, electronic energy (Ee) (r = 0.654, Table 5, Eq. (2)).

3.4.3

3.4.3 LR mt-QSAR model for antimicrobial activity

(3)

$${\text{pMIC}}_{\text{am}}=0.000312W+1.016$$ $$n=32r=0.823q^2=0.635s=0.065F=62.98$$

As in case of antibacterial activity, coefficient of W in Eq. (3) is positive which indicates that antimicrobial activity of synthesized compounds is positively correlated to Wiener index (W) i.e. antimicrobial activity of synthesized compounds will increase with increase in the value of W. This is evidenced by the antimicrobial activity data of synthesized compounds (Table 2) and their W values (Table 3).

The Wiener index W = W(G) of G is defined as the half sum of the elements of the distance matrix. $$W=W(\text{G})=1/2{\displaystyle \sum _{i=1\text{,}j=1}}(\text{D})\mathit{ij}$$ where (Dij) is the ijth element of the distance matrix which denotes the shortest graph–theoretical distance between sites i and j of G (Wiener, 1947).

The QSAR models expressed by Eq. (3) were cross validated by its high q² values (q² = 0.635) 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). As the observed and predicted antimicrobial activity values are close to each other (Table 6), the mt-QSAR model for antimicrobial activity (Eq. (3)) is a valid one. The plot of predicted pMIC_am against observed pMIC_am (Fig. 4) also favours the developed model expressed by Eq. (3). Further, the plot of observed pMIC_am vs. residual pMIC_am (Fig. 5) indicated that there was no systemic error in model development as the propagation of error was observed on both sides of zero (Kumar et al., 2007). Further, high residual values (Table 6) observed in case of outliers also justified their removal before the development of QSAR models.

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Figure 4 Plot of observed pMIC_am against predicted pMIC_am obtained by Eq. (3).

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Figure 5 Plot of observed pMIC_am against residual pMIC_am obtained by Eq. (3).

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It was observed from mt-QSAR models (Eqs. (1)–(3)) that the antibacterial, antifungal and overall antimicrobial activities of synthesized p-coumaric acid derivatives were governed by the topological parameters, Wiener index (W) and first order molecular connectivity index (¹χ) as well as electronic parameter, electronic energy (Ee).

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. who stated that the reliability of the QSAR model lies in its predictive ability even though the activity data are in the narrow range (Bajaj et al., 2005). 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). The minimum standard deviation (Table 2) observed in the antimicrobial activity data justifies its use in QSAR studies.