Quantitative structure activity relationships studies of non-steroidal anti-inflammatory drugs: A review

1.1 Non-steroidal anti-inflammatory drugs (NSAID’s)

The term NSAIDs stands for non-steroidal anti-inflammatory drugs. Originally NSAIDs were obtained from plants, which contained salicylates. First synthetic NSAID, aspirin was obtained in 1893. Prostaglandin endoperoxide synthase, commonly called cyclooxygenase, is the key enzyme required for the conversion of arachidonic acid to prostaglandins. It was established in 1972 that the mode of NSAIDs action was associated with cyclooxygenase inhibition. The enzyme COX exists as two isoforms viz, COX-1 and COX-2. The COX-1, a constitutive enzyme, primarily expressed in gastrointestinal (GI) tract, is responsible for the biosynthesis of prostaglandins (PGs) required for the cytoprotection and platelet aggregation. Hence, any disturbance in its routine function for long time leads to gastrointestinal ulceration, bleeding and perforation. In contrast, the COX-2, an inducible enzyme, produced during injury by the proinflammatory cytokines, viz. tumor necrosis factor-a (TNFa), interleukines, mitogens and endotoxins, plays a major role in the biosynthesis of PGs required by inflammatory cells such as monocytes and macrophages to cause pain, inflammation and fever (Marco and Raymond, 2002). The NSAIDs are the most commonly used drugs worldwide today for the treatment of inflammation, pain and fever. NSAIDs form the second largest segment of global pain management market, with sales of USD 5.4 billion. As a class, NSAIDs represent one of the most widely used prescription and over the counter (OTC) drugs. Most of the NSAIDs contain the free carboxylic group (Del Favero, 1999; Qandil, 2012; Zhiyun et al., 2015).

The NSAIDs can be sub-classified on the basis of chemical structure as follows:

• Salicylates-aspirin

• Anilides-paracetamol

• Aryl and heteroaryl acetic acids-indomethacin

• Propionic acid (Profens)-ibuprofen

• Anthranilates/fenamates-mefenamic acid

• Aryl ketones-nabumetone

• Oxicams/enol acids-piroxicam

• Phenylpyrazolones

• Selective COX-2 inhibitors-celecoxib, rofecoxib

NSAIDs structurally constitute of an acidic moiety (carboxylic acid or enols) attached to a planar, aromatic group. This can be represented as given below (see Fig. 1):

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Figure 1 General structure of NSAIDs.

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Due to above structural features, the NSAIDs are characterized by the following properties:

• Most of the NSAIDs are strong organic acids with pK as in the 3–5 range and are carboxylic acids. The acidic group is essential for COX inhibitory activity.

• The NSAIDs differ in their lipophilicities based on the lipophilic character of their aryl groups and additional lipophilic moieties and substituents.

• The acidic group in these compounds serves a major binding group (ionic binding) with plasma proteins. Thus all NSAIDs are highly bound by plasma proteins.

• The acidic group also serves as a major site of metabolism by conjugation. Thus a major pathway of clearance for many NSAIDs is glucuronidation (Dhingra et al., 2015; Smith et al., 2000).

1.2 Quantitative Structure Activity Relationships (QSAR)

Quantitative structure–activity relationship (QSR) (sometimes QSPR: quantitative structure property relationship) is the process by which a chemical structure is quantitatively correlated with a well-defined process, such as biological activity or chemical reactivity. It is based on the fact that biological activity of a compound is a function of its physicochemical parameters, i.e., its physical properties, such as molecular weight, solubility, surface tension, and partition coefficient, and chemical properties such as dissociation or ionization, electron density, and rate of hydrolysis (Verma et al., 2010; Hansch et al., 1962). The quantitative approach depends upon expression of a structure by numerical values and then relating these values (i.e. physicochemical parameters) to the corresponding changes in the biological activity by using statistical methods. The QSAR is an important tool to study role of various physicochemical properties of a drug in providing necessary biological activity.

2.1 2D-QSAR studies of substituted pyrazolone derivatives as anti-inflammatory agents

All the 2D descriptors (thermodynamic, spatial, electronic and topological parameters) were calculated for QSAR analysis using Vlife MDS software (V-Life Sciences). Thermodynamic parameters describe free energy change during drug receptor complex formation. Spatial parameters are the quantified steric features of drug molecules required for its complimentary fit with receptor. Electronic parameters describe weak non-covalent bonding between drug molecules and receptor. For QSAR analysis regression was performed using IC50 values as dependent variables and calculated parameters as independent variables (Chimetnti et al., 2006) (see Fig. 2).

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Figure 2 Substituted pyrazolone derivatives.

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The generated QSAR model was selected on the basis of various statistical parameters such as squared correlation co-efficient (r²) which is relative measure of quality of fit. Fischer’s value (F test) which represents F-ratio between the variance of calculated and observed activity, standard error (r²_se) representing absolute measure of quality of fit, and cross validated square correlation co-efficient (q²), standard error of cross-validated square correlation co-efficient (q²_se), predicted squared regression (pred_r²) and standard error of predicted squared regression (pred_r²se) to estimate the predictive potential of the models respectively.

The best QSAR equation is discussed in Eq. (1). The model consist of training set size = 4; test set size = 6

This descriptor signifies a retention index (second order) derived directly from gradient retention times. SdsNcount: This descriptor defines the total number of nitrogen connected with one single and one double bond. The model fulfills the selection criteria’s such as correlation coefficient r² > 0.8 (0.9566) for anti-inflammatory activity with low standard error of squared correlation coefficient r²_se < 0.3 (0.0043) show the relative good fitness of the model and F value > 11 times than tabulated F value show the 99% statistical significance of the regression model. The validation criteria for selection of the model are cross validated squared correlation coefficient q² > 0.8 (0.8873) for training set and pred_r² > 0.40 (0.5228) for test set. This model fulfills all validation criteria with low standard error of cross validated squared correlation coefficient q²_se < 0.3 (0.0095) and standard error of pred_r²se < 0.3 (0.1554), which show accuracy of the statistical calculation. The cross correlation limit is 0.5 which show inter-pair correlations among the selected descriptors are very low. Two descriptors as chi2 and SdsNcount contribute positively to model (Oswal et al., 2012; Bertoša et al., 2012; Hammouti et al., 2014; Zhu et al., 2013).

2.2 QSAR studies of substituted isoxazole derivatives

To develop the best QSAR model, one parameter at a time, was correlated with the anti-inflammatory activity expressed as logarithm of per cent inhibition of edema (Halami et al., 2015). The best QSAR model for 10 compounds was obtained when the anti-inflammatory activity of 3-(4′-methoxyphenyl)-5-substituted phenylisoxazoles was correlated with the parameter accpt HB, which is indicated in Eq. (2) (see Fig. 3)

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Figure 3 Substituted isoxazole derivatives.

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where, accpt HB = acceptable hydrogen bonds of a molecule.

The negative sign associated with the term, accpt HB, indicated that lower the value of accpt HB, higher would be the anti-inflammatory activity of compounds. For the accpt HB to be low, the compounds should have few electron donating groups, which results in a decrease in hydrogen bond formation and an increase in the anti-inflammatory activity of 3-(4′-methoxyphenyl)-5-substituted phenylisoxazoles.

The QSAR models were developed using 5 compounds in the training set by correlating their anti-inflammatory activity with acceptable hydrogen bonds. The best QSAR model for the training set is indicated in Eq. (3).

The correlation coefficient, r² = 0.9135, proved good internal predictivity of the best QSAR model (Asirvatham and Mahajan, 2015; Haroutounian et al., 2014; Kim et al., 2000).

2.3 3D QSAR studies of substituted benzamides as nonacidic anti-inflammatory agents by kNN MFA approach

A series of N-(4,6 dimethyl-2-pyridinyl) benzamides as non acidic anti-inflammatory drugs was subjected to a 3D-quantitative structure activity relationship using kNN MFA approach (Ajmani et al., 2006) (see Fig. 4).

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Figure 4 Substituted benzamide derivatives.

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The kNN methodology relies on a simple distance learning approach whereby an unknown member is classified according to the majority of its k-nearest neighbors in the training set. The nearness is measured by an appropriate distance metric (e.g., a molecular similarity measure calculated using field interactions of molecular structures). This method employs the kNN classification principle combined with the stepwise variable selection procedure for optimization of (i) the number of nearest neighbors (k) used to estimate the activity of each compound and optimization of (ii) selection of variable from the original pool of all molecular descriptors (steric and electrostatic fields at the lattice points) that are used to calculate similarities between compounds (i.e. distances in n-var – dimensional descriptor space).

2.4 Quantitative structure – activity relationships for benzothiazine class

A large number of structural descriptors were performed by using different inhouse programs and QSAR Properties program from HyperChem 5.1 package (total or polar/non-polar molecular surface and volume, hydration energy, log P, refractivity, polarizability). The other descriptor classes were following: constitutional (including total number of atoms, bonds, independent rings, flexible bonds, rigid bonds, heteroatoms, non-polar atoms, positive/negative ionization atoms, H-donor and H-acceptor atoms), topological, molecular walk, BCUT (descriptors derived from Burden matrix), Galvez (topological charge indices), 2D autocorrelation (autocorrelation descriptors, derived from topological descriptors), charge, aromaticity indices, RDF (radial distribution function descriptors), 3D-MoRSE, WHIM, Getaway, functional groups, atom-centered fragments, empirical, and molecular property descriptors (ClogP, water solubility, logWsol, etc.). In the attempt to find statistically significant mathematical models (QSAR equations) in the thiazine anti-inflammatory compounds class, an exhaustive determination of structural descriptors from various classes was performed. The best results were obtained in the case of BCUT and RDF descriptors for monolinear regression, the correlation coefficients being statistically significant for many descriptors from these two classes (Eq. (4)), especially for the second class, where r was higher than 0.7 in many cases (see Fig. 5).

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Figure 5 Substituted benzothiazine derivatives.

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A better model was obtained by using two descriptors from these classes, which are not intercorrelated, the correlation coefficient being >0.8 (Eq. (5)).

Even if the correlation coefficient is statistically significant, no predictive power (low q²) could be obtained for these QSARs.

The following conclusions can be drawn from QSAR study that the attempt to obtain QSARs in the anti-inflammatory benzothiazine class conduct to statistically significant equations, but without predictive power for designing new non-steroidal anti-inflammatory benzothiazine compounds (Amzoiu et al., 2010; Bakavoli et al., 2007; Hădărugă, 2011; Gupta and Kumar Satuluri, 2008).

2.5 QSAR studies of novel (E)-3-(4-methanesulfonylphenyl)-2-(aryl) acrylic acids as dual inhibitors of cyclooxygenases and lipoxygenases

Quantitative Structure Activity Relationships (QSAR) are widely used in the drug design process whenever detailed structural information on the ligand–receptor interactions is not experimentally available (Hansch and Fujita, 1964). The mathematical QSAR equations can be computed with the help of a large number of statistical models, such as multi linear regression, partial least squares (PLS). For this study, many descriptors were calculated by the EDRAGON programs for all the compounds. To select the set of descriptors that are most relevant to the IC50 of these agents, the MLR models were built and the QSAR equations with stepwise selection and elimination of variables were established by MLR method (see Fig. 6).

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Figure 6 (E)-3-(4-methanesulfonylphenyl)-2-(aryl) acrylic acids.

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By using a stepwise multiple linear regression method, two QSAR equations were obtained as follows for each part. In the QSAR equations,

• q² is the LOO cross-validated coefficient, which was obtained by a multiple linear regression.

• y_i is the actual activity, $\overline{y}$ is the average actual activity.

• ${\widehat{y}}_i$ is the predicted activity of compound i computed by the new regression equation.

Large F, small S, very small p-value, as well as R² and q² values close to one indicate a good QSAR model. In general, the regression model is significant at p-value < 0.001 using the F statistics, so the below QSAR models are all significant.

In equation that belongs to COX2 (Eq. (6)), the E3v and E1s belong to the descriptors of WHIM descriptors. The WHIM descriptors appeared in this model indicating the relevant feature of electro-topological state factors that might be considered in compounds with COX receptor bindings. The appearance of E3v descriptor in this equation also considers, indirectly, the vdw volume weighted properties. E1s descriptor in this equation considers electro-topological state weighted. In equation that belongs to 5-LOX (Eq. (7)), H1e is the GETAWAY descriptors. The GETAWAY descriptors (Geometric Topology and Atom Weights Assembly) are related to the influence of the atoms in the determination of the molecular form, and to the distance between them. And Hnar is narumi harmonic topological index, topological descriptors, that most related about the structure of compounds. The results obtained from QSAR equations emphasize that mass, volume and topological properties are so important in COX 2 and 5-LOX potency (Alireza and Asghar, 2010; Pontiki et al., 2011; Pommery et al., 2004; Tan et al., 2011; Yu et al., 2010; Reddanna et al., 2012).

2.6 QSAR study on 3-substituted indole derivatives as anti-inflammatory agents

QSAR studies have been performed on a series of 3-substituted indole derivatives with a hope to design compounds with better anti-inflammatory activity and lesser side effects. A training set of 30 3-substituted indole derivatives exhibiting potent anti-inflammatory activity was taken from the reported work of Rani et al. (2004). Various physicochemical parameters were calculated and good predictive QSAR models were generated for anti-inflammatory activity using stepwise multiple regression analysis. Statistically significant models were obtained that gave r-value (correlation coefficient) as <0.80 which depicts a good correlation between anti-inflammatory activity with physicochemical properties, connectivity and conformation of molecule. The indicator variables such as presence of aromatic ring and lipophilic groups play an important role in anti-inflammatory activity. Cross validation was performed using the leave one-out method. The results obtained along with validated models bring important structural insight in designing novel 3-substituted indole derivatives as anti-inflammatory agents (see Fig. 7).

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Figure 7 General structure of substituted indoles.

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Biological activity data and various physicochemical parameters were taken as dependent and independent variables; respectively and correlations were established using sequential multiple regression analysis. Among the many correlations generated, two best quadratic and triparametric models were selected on the basis of statistical significance. The best models obtained are given below along with their statistical measures.

Model-I

Model-II

Comparison of Model-I and Model-II reveals that the former shows better correlation (r = 0.905) between descriptors and biological activity than latter one (r = 0.847). The bootstrapping r² (r² bs = 0.86) results reflect the significance of the Model-I as compared to Model-II. The cross validation (q²) values reflect predictive power of the Model-I. Low standard error of estimation (<0.4) suggests a high degree of confidence in the analysis. Moreover, the descriptors used to construct the model are not correlated with each other as suggested by their correlation matrix values; respectively. However, the model manifests moderate predictive potential as indicated by cross-validated correlation coefficient values (Bhadoriya et al., 2014; Chaitanya et al., 2010; Narute et al., 2013; Singh and Verma, 2014).

2.7 QSAR of 1-phenyl-[2H]-tetrahydrotriazin-3-one analogs

QSAR of sixty 1-phenyl-[2H]-tetrahydrotriazin-3-one analogs were examined for their inhibitory potency IC50 on 5-LOX, in a broken cell (see Fig. 8).

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Figure 8 General structure of 1-phenyl-[2H]-tetrahydrotriazin-3-one analogues.

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The parameters p-3′, p-5′, p-5 are for the lipophilic effects of 3′-, 5-′ and 5-substituents, respectively. Ssm is the sum of Hammett sm values for the 3′- and 5-′phenyl or a-pyridyl substituents, Ssp is the sum of Hammett sp values for the 3-′ and a-pyridyl substituents, and MR-2 and MR-4 are the molar refractivities (MR) of 2- and 4-substituents respectively. I-4OR and I-thiourea are indicator variables for 4-OR substituents and for thiourea analogs, respectively. As we can see from the equation, potency is increased by lipophilic substituents at the 3′-, 5′- and 5-positions, and with 3′- and 5′-substituents that withdraw electrons. On the contrary it is decreased with 3′-substituents on the pyridyl ring, which donates electrons. The size of 2′-substituents affects the potency. It decreases as the size increases. Thiourea analogs compared to the corresponding carbonyl analogs, are more potent (Khadikar et al., 2003; Gonzalez-Diaz et al., 2007; Hansch and Fujita, 1964; Kim et al., 1996; Niu et al., 2012).

2.8 QSAR studies of 6-aminopyrimidin-4-one derivatives as anti-inflammatory agent

Around eighteen 6-aminopyrimidin-4-one derivatives were synthesized and subjected for QSAR study using modified version of Allinger MM2 force field in Chem3D ultra structural descriptors. The models for anti-inflammatory agents were constructed based on the training set and the generated models were then validated: internally using the leave one out technique (LOO) and externally by predicting the activities of the test set. Molecular structures were generated with ChemDraw Ultra 6.0 and optimized in CS Chem3D Ultra (Cambridge soft), first by molecular mechanics (MM2) and reoptimized via the Austin model 1 (AM1) method using the closed-shell (restricted) wave function of MOPAC module until the root mean square (RMS) gradient value becomes smaller than 0.0001 kcal/mol Å (see Fig. 9).

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Figure 9 General structure of 6-aminopyrimidin-4-one derivatives.

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In QSAR studies, all physicochemical parameters of each compound from the series were calculated and subjected to stepwise, multiple and sequential regression analysis with respect to biological activity. Correlation of each parameter was generated with biological activity. The number of developed models was high. So further analysis was based on statistically significant parameters namely correlation coefficient (R), its square (R²), variance ratio (F), cross validation method (Q²), standard deviation based on predicted residual sum of squares (SPRESS) and standard deviation of error of prediction (SDEP).

Model 1

Model 2

Two best models are selected from series, out of which Model 2 was selected as the best. Because, this model has better statistically significant value, minimum standard deviation, low variance and statistically significant F-value. The Model 2 was tested for eighteen compounds as a test set, showed overall significant level greater than 99.9 as it exceeded the tabulated F value. The equation was validated by leave one out cross validation method and bootstrapping method as an internal validation, which gives statistically significant value. Q² was found greater than 0.5. From the results, it has been concluded that the bulkier aromatic substituents increases lipophilicity. The presence of electron withdrawing group in the compound results an enhanced anti-inflammatory activity (Hanna, 2012; Sharma et al., 2004; Shinde et al., 2014; Zhang et al., 2014).

2.9 QSAR studies of novel 3-(aminooxalyl-amino)- and 3-(carbamoyl-propionylamino)-2-phenylamino-benzoic acid derivatives

The objectives of the present work were the QSAR studies of 2-phenylaminobenzoic acids derivatives and their methyl esters as novel anti-inflammatory and analgesic agents. The percentage protection against inflammation and the writhing severity of synthesized compounds as the response for further QSAR analysis was reported. HyperChem 7.5 software was used for the molecular modeling and energy optimization. The molecular mechanics MM+ and semi-empirical algorithm with Hamiltonian Austin Model 1 (AM1) force field at 0.01 RMS gradients were used to optimize the molecules. A large number of theoretical molecular descriptors available in EDRAGON software package were calculated to define the structural property of the molecules needed to perform QSAR analysis. 3D molecular descriptors had been shown to be very useful in QSAR problems in order to perform a rational analysis of different pharmacological activities. DRAGON E-version software allowed 6 subsets of 3D molecular descriptors calculating including: randic molecular profiles, geometrical descriptors, radial distribution function descriptors (Gonzălez et al., 2006), 3D-MoRSE, weighted holistic invariant molecular descriptors (WHIM) and GETAWAY descriptors. Multiple linear regression (MLR) analysis implemented into BuildQSAR software application was used to perform the QSAR studies. The statistical processing of the QSAR models obtaining was carried out by using systematic search algorithm within each descriptors subset firstly. The most significant descriptors from each set were then included into single 3D descriptors set followed by the systematic search procedure in order to confirm that the selected descriptors were the most optimal for describing the biological properties. The statistical significance of the models was determined by examining the correlation coefficients, the standard deviations, and the number of variables, F-test ratio and the residuals analysis. The rule of thumb was applied to select number of descriptors in the models: the number of compounds used for the model generation (n) and the number of parameters under consideration (M) should undergo the ratio n/M ⩾ 5 (see Fig. 10).

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Figure 10 General structure of 3-(aminooxalyl-amino)-and 3-(carbamoyl-propionylamino)-2-phenylamino-benzoic acid derivatives.

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The significant models selected were further undergone validation study by internal leave-one-out (LOO) cross validation method. In the LOO approach, each predicted compound is deleted from the n compounds and its activity is computed. The square of LOO cross-validation coefficient Q² can be considered as a criterion of both predictive ability and robustness of the model as well as its stability. For a reliable model, the square of cross validation coefficient Q² should be ⩾0.5.

The best QSAR models obtained with 3D descriptors for anti-inflammatory activity are given below with the statistical parameters of the regressions:

where n is the number of compounds included in the model, R is the correlation coefficient, s is the standard deviation of the regression, F is the Fisher ratio, p is significance of the variables in the model, Q² is the correlation coefficient of cross-validation, SPRESS is the predicted residual sums of squares standard deviation, and SDEP is the standard deviation error in prediction (O’Boyle et al., 2011; Suleiman et al., 2014).

2.10 Development of pyrimidine derivatives as selective Cox-2 inhibitors

The builder module of the Vlife MDS 3.5 was used to generate molecular models of series of Pyrimidine derivatives. These were then energy minimized using the Merck Molecular Force Field (MMFF) until the root-mean-square (rms) gradient reached value 0.001 kcal mol Å. The physicochemical properties of each compound were specified using various descriptors, which delineate liphophilic, conformational, electronic, spatial, structural, thermodynamic and quantum mechanical information. Twenty compounds from this data set were divided into training and test sets, the former set consisting 80% of the total compounds. A relationship between independent (physicochemical properties) and dependent (biological activity) variables were determined statistically using regression analysis. Linear regression is achieved by fitting a best-fit straight line to the data using the least predictivity and other statistical terms such as the pred r, F squares method. The outcomes of QSAR studies indicate that hydrophilic nature of compounds lead to selective COX-2 inhibition in vitro (Baettie et al., 2003; Bhatia et al., 2012; Bozorov et al., 2015) (see Fig. 11).

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Figure 11 General structure of pyrimidine derivatives.

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QSAR model generated for the in vitro and in vivo COX-2 and COX-1 inhibitory activity is given in Eq. (17)

The activity is dependent on the descriptors kappa2, Ionization potential and QM Dipole Magnitude. The kappa1 descriptor signifies first kappa shape index: (n−1)²/m². The shape descriptor is negatively correlated with the in vivo COX-2 activity. This indicates the increase in hydrogen atoms in the structure will lead to increase in activity. The second parameter that is correlated with the activity is ionization potential. The parameter is negatively correlated with the activity, meaning that ionization potential should be lesser for the compound so that charged interactions would be easily aggravated (Kilaru et al., 2015).

2.11 QSAR of structurally similar 1,3,4-oxadiazole/thiadiazole and 1,2,4-triazole derivatives of biphenyl-4-yloxy acetic acid as anti-inflammatory agents

Twenty-one compounds from series of structurally similar 1,3,4-oxadiazole/thiadiazole and 1,2,4-triazole derivatives of biphenyl-4-yloxy acetic acid as anti-inflammatory agents were selected from literature reported by Kumar et al. (2008). The experimental biological activities, in the form of percentage inhibition of paw volume were converted into logarithmic form and used as dependent variable for development of valid 2D QSAR and 3D QSAR models. Energy minimizations were performed using Merck Molecular Force Field (MMFF) and MMFF charge for the atom followed by considering distance-dependent dielectric constant of 1.0 and convergence criteria (rms gradient) of 0.01 kcal/mol (see Fig. 12).

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Figure 12 General structure of biphenyl-4-yloxy acetic acid derivatives.

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2D QSAR model

Model 1

The Model 1 suggest that the anti inflammatory activity of structurally similar 1,3,4-oxadiazole/thiadiazole and 1,2,4-triazole derivatives of biphenyl-4-yloxy acetic acid dependent on SssNHE-index, VolumeCount and SulfursCount descriptors. Out of that SssNHE-index descriptors signify electrotopological state indices for number of –NH group connected with 2 single bonds. VolumeCount descriptor signifies volume of compound and SulfursCount descriptor signifies number of sulfur atom in a compound. Both the descriptors that is VolumeCount and SulfursCount are positively contributing toward the biological activity

3D QSAR model

Model 2

The Model-2 describes the optimum structural features for anti-inflammatory activity. The E_281 and E_612 are the electrostatic field energy interaction between methyl probe and compounds at their corresponding spatial grid points of 281 and 612. This model suggest that electrostatic field descriptors E_281 and E_612 with positive coefficient indicate that the less electropositive (electron deficient or electron withdrawing) groups are favorable in this region. The S_27 is the steric descriptor which negatively contributes toward the biological activity. It signifies that substitution of bulkier group in this region around descriptor S_27 with its grid point at 27 is not favorable for the activity.

The QSAR analysis of series of structurally similar 1,3,4-oxadiazole/thiadiazole and 1,2,4-triazole derivatives of biphenyl-4-yloxy acetic acid as anti-inflammatory agents have revealed that substitutions of electro positive group are essential for the activity on the ortho and para position of biphenyl ring and also substitution of electropositive groups on first position of five membered heterocyclic ring increases the biological activity, while substitution of bulky group on para position of biphenyl ring retards the activity of compounds (Mihaela and Valeriu, 2009; Sawant et al., 2013).

2.12 QSAR study of novel NSAID acetaminophen conjugates with amino acid linkers

Best multi-linear regression (BMLC) was initiated which is a stepwise search for the best n-parameter regression equations (where n stands for the number of descriptors used), based on the highest R² (squared correlation coefficient), R²cvOO (squared cross-validation “leave one-out, LOO” coefficient), R²cvMO (squared cross-validation “leave many-out, LMO” coefficient), F (Fisher statistical significance criteria) values, and (s²) is the standard deviation. The QSAR models up to 3 descriptors describing bioactivity of the anti-inflammatory active agents were generated (obeying the rule of 5:1, which is the ratio between the data points and the number of QSAR descriptor models). The established QSAR model is statistically significant. The descriptors are sorted in descending order of the respective values of the Student’s t-criterion, which is a widely accepted measure of statistical significance of individual parameters in multiple linear regressions. The assigned model is statistically significant and the scatters are uniformly distributed, about 0.9 logarithmic units (ranges: observed 0.940–1.853, predicted 0.997–1.814).

The most important descriptor controlling QSAR model is hydrogen-donors charged surface area (MOPAC PC) (HDCA) (Todeschini and Consonni, 2008), which describes the hydrogen-bonding ability of compounds defined by (Eq. (20)),

Relative positive charged surface area (SAMPOS^∗RPCG) (MOPAC PC) (RPCS) is the second most important descriptor controlling the attained QSAR model which is the solvent accessible surface area of the most positive atom $+{\mathit{SA}}_{\text{max}}^{+}$ divided by the relative positive charge (RPCG) and defined by (Eq. (21)).

Difference (positive–negative) in charged surface areas (MOPAC PC) is the third descriptor governing the QSAR model, which can be determined by the difference between partial positive surface area (PPSA) (Eq. (22)) and partial negative surface area (PNSA) (Eq. (23)).

From all the above, it can be concluded that the QSAR model is applicable for both highly potent and mild anti-inflammatory active agents, which suggests that the model may have predictive capacity for more anti-inflammatory hits (Barsoum et al., 2006; Nazeruddin et al., 2014; Panda et al., 2014).

2.13 QSAR analysis of centrally fused 1,5-diaryl pyrazoles for cyclooxygenase inhibition using MOE-Qua-SAR descriptors

Quantitative structure–activity relationship analysis has been carried out on a series of conformationally restricted 1,5-diaryl pyrazoles reported as selective cyclooxygenase-2 (COX-2) inhibitors in order to explore the selectivity requirement for COX-2 inhibition among these congeners. From a series of 15 compounds, 6 QSAR models were derived after ensuring reasonable correlation of COX-2 inhibitory activity with the individual descriptors and minimum intercorrelation among the descriptors used in the derived models. The quality of the models were assessed using the statistical parameters viz., correlation coefficient (r) or coefficient of determination (r²), adjusted r² $(r_A^2)$ , standard error of estimate (s), Fischer F-value, and Student’s t-distribution. While deriving the QSAR models predictor variables with p value greater than 0.05 were eliminated in order to assure statistical reliability. In order to corroborate the self-consistency of the derived models, they were validated using the leave-one-out (LOO) process and the predictability of each model was assessed using cross-validation parameters such as r² or q². Derived QSAR models evinced a satisfactory correlation of COX-2 inhibitory potency with a three-dimensional (3D) spatial descriptor, std_dim3, and a two-dimensional (2D) partial charge descriptor, PEOE_VSA-1. Balaban J, a highly discriminating topological descriptor, was found to play an imperative role in governing both COX-1 inhibitory potency as well as selective inhibition of COX-2 over COX-1. PEOE_VSA-1 denotes the sum of the van der Waals surface areas of the atoms whose partial equalization of orbital electronegativities (PEOE) is in the range [−0.10, −0.05]. Std_dim3, an external 3D descriptor, is a measure of the square root of the third largest eigenvalue of the covariance matrix of atomic coordinates. A standard dimension is equivalent to the standard deviation along the principle component axis. The negative coefficient indicates overall steric hindrance of the ligands toward the COX-2 enzyme. The value a_ns is a function of the number of sulfur atoms. The positive contribution of a_ns indicates a thiochromanone and/or isothiochromanone ring-type fusion of nonbenzene sulfonamide ring with central pyrazole ring for improved COX-2 inhibitory potency. The selective COX-2 inhibition could be influenced by the size, shape, and polarizability of the whole molecules and was discerned by the contribution of molar refractivity (MR), Balaban J descriptors. The possible explanation for the outlying behaviors of compounds is also explained Table 1 (see Fig. 13).

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Figure 13 General structure of centrally fused 1,5-diaryl pyrazoles derivatives.

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In general, the investigations on conformationally restricted 1,5-diaryl pyrazoles revealed a best fusion type of nonsulfonyl aromatic ring with central pyrazole ring for improved COX inhibitory activities. QSAR models derived to explore selective inhibition over COX-1 showed good correlation with topological and physicochemical descriptors. The size, shape, and polarizability of ligands as shown by the MR and Balaban, respectively, were found to influence the selectivity among these congeners. Bulkier, polar substituent will have a better fit into the hydrophilic COX-2 side pocket and improved selectivity (Manivannan and Chaturvedi, 2009; Penning et al., 1997; Prasanna et al., 2004).

2.14 QSAR study on dehydro-abietylamine derivatives

In a series of dehydro-abietylamine derivatives, inhibitors of PLA₂, with anti-inflammatory activity, a systematic QSAR study has been done (see Fig. 14).

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Figure 14 General structure of dehydro-abietylamine derivatives.

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n = 28, r² = 0.78, s = 0.46, F = 43.77.

These quadratic equations are logical, suggesting an ideal lipophilic and size requirement.

The parabolas provided the better fit and indicated that the best anti-inflammatory agents should have log P = 6–8 and MR = 11–13. These data would suggest that the lipophilicity and size requirements for optimal anti-inflammatory activity are different from those required for PLA₂ inhibition (log P = 11–13, MR = 14–16) (Wilkerson et al., 1992).

2.15 Quantitative structure structure–activity relationship for 2-amino-5-selenothiazole derivatives as anti-inflammatory and analgesic agents

The physicochemical properties (descriptors) of the investigated chemical compounds obtained from Hyperchem version 8.1 program at the semi empirical theoretical method using PM3 method. These descriptors include the area, volume, binding energy, heat formation, refractivity, polarizability. Multiregression statistical equation is based on the chemical descriptor data obtained from QSAR investigation, Table 2 (see Fig. 15).

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Figure 15 General structure of 2-amino-5-selenothiazole derivatives.

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Results are expressed as mean standard error. Multiregression analysis (one way ANOVA, Newman–Keuls and Ftest) was used for correlating physicochemical descriptors to the edema inhibition through QSAR and analysis of the pharmacological data. Mann Whitney for average S.E was used for comparing different groups; statistical difference was considered significant at p-value 50.05 (Foroumadi et al., 2015; Sherif and Gouda, 2014).

2.16 QSAR study of 4,5-diarylpyrroles as anti-inflammatory agents

QSAR study has been made for a series of 2-substituted and 2,3-disubstituted 4-(4-fluorophenyl)-5[4-(methylsulphonyl)phenyl]-1Hpyrroles. The derivatives were found to be active in the rat adjuvant arthritis model of inflammation (AA).

where, F is the Swain–Lupton field effect and MR the molecular refractivity.

QSAR studies suggested that the action could be correlated with the molar refractivity and the inductive field effect of the 2-substituent and the lipophilicity of the 3-substituent (Wilkerson et al., 1994, 1995).

2.17 3D-QSAR models for chalcones as 5-lipoxygenase antagonists

For the study, all molecular modeling and 3D-QSAR studies were performed on a Silicon Graphics INDY R-4000 work-station employing Molecular Simulation Incorporation (MSI) software (Insight-II, Builder, Search-compare, Discover, and APEX-3D) (see Fig. 16).

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Figure 16 General structure of chalcones.

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Out of 53 3,4-dihydroxy chalcons reported as 5-lipoxy-genase inhibitors by Sogawa et al. (1993) only 51 compounds were considered for analysis because of non-availability of IC50 values for two compounds. Several biophoric models were obtained with different size and arrangement. Among several biophoric models for all 51 compounds, only two models were considered based on the statistical criteria (R² > 0.75, Chance < 0.001, superimposition match > 0.7).

Both these models with three biophoric sites showed very good superimposition as indicated by the high match value > 0.70 with, high squared correlation co-efficient value (r² = 0.88), high reliability (chance value 0.00) and low difference in RMSA and RMSP value (<0.03) (Bruneau et al., 1991; Choudhary et al., 2012; Sivakumar et al., 2007; Nowakowska et al., 2008; Saxena et al., 2002; Tomar et al., 2007).

2.18 QSAR studies on some thiophene analogs as anti-inflammatory agents

The Quantitative Structure Activity Relationship (QSAR) studies of a series of 43 thiophene analogs were carried out. The analogs when subjected to cluster analysis technique led to the formation of four homogeneous groups. The cluster analysis technique grouped the 2-anilino-5-substituted-4-methyl-thiophene-3-carboxylic acid methyl esters as one homogeneous group. The clusters were individually taken up for a Hansch type of QSAR study with 10 molecular descriptors. The QSAR equations generated were cross validated by the leave out one method. The studies gave an insight into the dominant role played by electronic properties such as energy of the lowest unoccupied molecular orbital (E_LUMO) and dipole moment (dipole) in modulating the anti-inflammatory activity (see Fig. 17).

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Figure 17 General structure of thiophene analogs.

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From the QSAR studies, the molecular descriptors such as dipole and E_LUMO proved important in defining the activity of the candidates. A logical reason for the dominance of these two parameters might be the more number of carbonyl groups in the designed series. The oximino analogs and the methyl sulfonyl analogs were dominating the biological activity chart and a close look at them reveal the high E_LUMO and dipole moments for these candidates. Based on these studies we disclose a novel three point pharmacophore for designing better anti-inflammatory agents (Pothen et al., 2010; Pillai et al., 2005; Tetko et al., 2001).

2.19 QSAR study for thiazolyl-N-substituted amides derivatives

Regression analysis was performed to find out whether any correlation exists between anti-inflammatory activity (CPE%, the percentage inhibition of carrageenan mice paw edema in log-form) and several physicochemical parameters (lipophilicity, polarizability, steric, and electronic variables) (see Fig. 18).

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Figure 18 General structure of thiazolyl-N-substituted amides derivatives.

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The assessment of the anti-inflammatory activity is performed in vivo from the initial set of derivatives. A parabolic dependence of activity from clog D 7.4 and a linear dependence from the surface tension (SURF) was found.

n = 16, r² = 0.711, s = 0.107, F = 4.086.

The anti-inflammatory effect in correlation with the examined variables gave poor correlations, with low statistical significance, e.g., with clog P (r² < 0.1) or R M (r² < 0.2) or steric (B 1−X–thesterimol parameter of Verloop r² < 0.1). Indicator parameters, e.g., I 1 (assigning 1 for n = 1) or I 2 (assigning 1 for n = 2) did not contribute significantly to the antiinflammatory activity (Hadjipavlou-Litina et al., 1999; Kouatly et al., 2009; Franklin et al., 2008).

2.20 3D-QSAR of tetrahydroisoindole nucleus as cyclooxygenase-2 inhibitors

A series of molecules has been reported as specific COX-2 inhibitors belonging to the class of tetrahydroisoindole nucleus. A 1,3-diaryl substitution on the central polycyclic ring system and absence of sulfonyl moiety are the two structural features of this chemical series. We report the three-dimensional quantitative structure–activity relationship (3D-QSAR) performed by genetic function approximation (GFA) on this class of compounds. QSAR models were generated using a training set of 20 compounds and the predictive ability of each model was assessed using a set of 7 molecules. The internal and external consistency of the final QSAR model was 0.656 and 0.669 respectively. The results indicate that shape (steric), electronic and spatial (conformational) descriptors govern the COX-2 enzyme inhibition. The descriptors appeared in the final model are compatible with the COX-2 enzyme topology. The observed COX-2 enzyme inhibition activity for 1,3-diaryltetrahydroisoindole derivatives is influenced by descriptors COSV, Dipole-Z, and PMI-Z. The descriptors COSV and Dipole-Z were positively correlated and PMI-Z negatively correlated (Raichurkar and Kulkarni, 2003).