1. INTRODUCTION:

Because of their involvement in important biological and industrial processes, phenolic antioxidants are of great interest. Chemical toxicity testing on these species is typically a time-consuming, costly, and technically difficult process.^1-2. for these reasons, QSAR methods could be used as an alternative solution to explain chemical toxicity.³ Because they are a much cheaper and faster alternative to medium throughput in vitro and low throughput in vivo assays, which are typically used later in the discovery cascade.⁴

Quantitative structure activity relationship (QSAR) studies can help you find bioactive molecules in a more rational way.⁵ The ability to estimate the properties of new chemicals is the QSAR method's main success.⁶

The QSAR method makes use of powerful computers, molecular graphics, and sophisticated software. Attempts were made to broaden the quantitative understanding of the relationship between intrinsic, physical, chemical, biological, or molecular properties.⁷

2. MATERIAL AND METHODS:

A QSAR model was reported for studying the antioxidant activity of a series of phenols using Dragon version descriptors. 5.3⁸ and hyper hem 7.5 software⁹. Software in addition to empirical descriptor from previous studies (logP)¹⁰.

Other variable selection methods have been found to be inferior to the genetic algorithm (GA)¹¹. Thus, variable selection was performed on the training set by maximizing the variance explained by cross-validation by omitting an observation in Todeschini's version of Moby Digs¹². Ordinary least squares regression and genetic algorithm selection of explanatory variable subsets (Genetic Algorithm-Variable Subset Selection, or GA-VSS)¹³

The crossover and mutation processes of the genetic algorithm in the MobyDigs software are controlled by a parameter T ranging from 0 to 1. The genetic algorithm's parameters were set as follows: Pop = 100 for the model population; T = 0.5 to balance the roles of the two processes of crossover and mutation.

The use of the GA-VSS method resulted in several good models for predicting pcic50 based on various sets of molecular descriptors. The best model was created by combining the R2u (R autocorrelation of lag 2/ unweighted) and logP functions.

Data sources:

Toxicity¹³

Population growth inhibition data. pCIC₅₀ =-log (CIC₅₀) and CIC50 is the concentration in mmol/L, reducing the growth to 50% of the control after 96 h of exposure) for Tetrahymena preforms were secured from the literature.

Definition CIC50 ¹⁴

The concentration required to produce 50% inhibition of a biological activity (for example, an enzyme reaction, cell growth, reproduction, etc.).In simpler terms, it measures how much of a particular substance or molecule is needed to inhibit some biological process by 50%. IC50 is commonly used as a measure of drug-receptor binding affinity.

R2u (R autocorrelation of lag 2/unweighted), GETAWAY descriptors¹⁵:

Getaway (Geometry, Topology, and Atom-Weights Assembly) descriptors are derived from the Molecular Influence Matrix (MIM), that is, a matrix representation of molecules denoted by H and defined as the following [Consonni, Todeschini et al., 2002a, 2002b]:

(1)

Where M denotes the molecular matrix composed of the centered Cartesian coordinates x, y, and z of the molecule atoms (including hydrogens) in a given conformation. Atomic coordinates are assumed to be calculated with respect to the geometrical center of the molecule to obtain translational invariance. The molecular influence is a symmetric AxA matrix, where A represents the number of atoms, and shows rotational invariance with respect to the molecule coordinates, thus resulting independent of molecule-alignment rules. The R indices are defined in the same way as the H indices, by using the off-diagonal elements of the influence/distance matrix R instead of the elements of the matrix H:

(2)

Where hi and hj are the leverages of the atoms i and j, and rij is their geometric distance, The diagonal elements of the matrix R are zero, while each off-diagonal element i–j, resembling the single terms in the summation of the gravitational indices, is calculated by the ratio of the geometric mean of the corresponding ith and jth diagonal elements of the matrix H over the interatomic distance rij provided by the geometry matrix G.

The square-root product of the leverages of two atoms is divided by their interatomic distance. According to the basic idea that interaction between atoms in the molecule decreases as their distance increases, it appears to make less significant contributions from pairs of atoms far apart. Obviously, the largest values of the matrix elements derive from the most external atoms (i.e., those with high leverages) and simultaneously from those next to each other in the molecular space (i.e., those having small interatomic distances).

(3)

Where u is an atomic weighting scheme and d (dij; k) is a Dirac delta function, equal to 1 when the topological distance dij between atoms i and j is equal to k and zero otherwise. D is the molecule's topological diameter; that is, the maximum topological distance in the molecule.

Logp (partition coefficients (n-octanol—water) (P_ow) ¹⁰.

Octanol/water partition coefficients P are experimental values found in the lo databank (Sangster Research Laboratories, Montreal, Canada).

Development and Validation of QSAR Model:

Application of the GA-VSS led to several good models for the prediction of based on different sets of molecular descriptors. The best two models were constructed using the log p and R2u pretreated data, which were divided into the training set and test set based on Kennard-Stone permutation, where 70% of the dataset (60 compounds) is the training set and the remaining 30% (25 compounds) is the test set.

The data is shown in the following table 1.

Table 1: parameter of 85 substituted phenol

MolID	N°	Status	PcicI50	logP	R2u
2,3,6-trimethylphenol	1	Training	0.418	2.67	1.778
2,3-dichlorophenol	2	Training	1.271	3.04	0.803
2,4,6-tribromophenol	3	Training	1.695	3.69	0.762
2,4,6-trichlorophenol	4	Training	1.036	3.17	0.809
2,4-dibromophenol	5	Training	-0.029	2.3	1.663
2,4-dichlorophenol	6	Training	1.128	3.14	0.807
2,4-dimethylphenol	7	Training	0.396	1.65	0.854
2,5-dichlorophenol	8	Training	0.078	1.92	1.601
2,5-dimethylphenol	9	Training	0.789	2.91	1.449
2,6-difluorophenol	10	Training	0.504	2.33	0.838
2-acetylphenol	11	Training	0.64	2.85	1.472
2-allylphenol	12	Training	0.277	2.15	0.851
2-bromo-4-methylphenol	13	Training	0.031	1.61	0.778
2-bromophenol	14	Training	0.176	2.47	1.626
2-chloro-5 -methylphenol	15	Training	0.284	1.76	0.875
2-chlorophenol	16	Training	0.483	1.81	0.851
2-cyanophenol	17	Training	-0.252	1.1	0.802
2-ethylphenol	18	Training	-0.953	0.73	1.359
2-fluorophenol	19	Training	0.803	2.88	1.716
2hydroxy benzaldhyde	20	Training	0.842	2.78	0.822
2-hydroxybenzaldoxime	21	Training	2.573	5.7	1.265
2-hydroxybenzamide	22	Training	0.93	3.42	1.704
2-hydroxybenzylalcohol	23	Training	1.562	3.61	0.792
2-isopropylphenol	24	Training	0.113	2.35	1.678
2-phenylphenol	25	Training	0.957	2.5	0.839
2-tert-butyl-4-methylphenol	26	Training	-0.065	1.7	0.756
3 -chloro-4-fluorophenol	27	Training	0.473	1.93	0.869
3 -methoxyphenol	28	Training	0.085	1.38	0.835
3,4,5,6-tetrabromo-2-methylphenol	29	Training	1.118	2.93	0.815

Table 1: Parameter of 85 substituted phenol (Continued).

MolID	N°	Status	PcicI50	logP	R2u
3,4,5-trimethylpheno	30	Training	-0.819	0.46	1.543
3,4-dimethylphenol	31	Training	-0.093	1.35	1.575
3,5-dichlorophenol	32	Training	1.038	3.14	1.427
3,5-dimethylphenol	33	Training	1.278	3.93	1.612
3-acetylphenol	34	Training	0.702	2.9	1.725
3-chlorophenol	35	Training	0.7	2.78	1.43
3-cyanophenol	36	Training	0.795	3.1	1.458
3-ethylphenol	37	Training	1.203	3.78	1.652
3-fluoropheno	38	Training	0.545	2.39	0.849
3-hydroxybenzaldehyde	39	Training	1.292	3.69	1.964
3-iodophenol	40	Training	0.013	1.81	1.645
3-iso-propylphenol	41	Training	0.206	2.5	1.606
3-methylphenol	42	Training	0.017	1.77	0.873
3-phenylphenol	43	Training	2.033	4.75	1.811
3-tert-butylphenol	44	Training	1.779	3.84	0.751
4-acetamidophenol	45	Training	1.024	3.07	1.021
4-acetylphenol	46	Training	-0.384	0.9	1.342
4-benzyloxyphenol	47	Training	0.854	2.9	0.829
4-bromo-2,6-dimethylpheno	48	Training	-0.143	1.34	1.639
4-bromo-6-chloro-2-methylphenol	49	Training	-0.192	1.97	1.502
4-bromophenol	50	Training	1.355	3.75	1.032
4-butoxyphenol	51	Training	0.635	3.2	1.645
4-chloro-2-methylphenol	52	Training	0.913	3.31	1.691
4-chloro-3 -methylphenol	53	Training	2.092	5.31	1.908
4-chloro-3,5-dimethylpheno	54	Training	1.233	3.98	1.731
4-chloro-3,5-dimethylphenol	55	Training	0.618	2.88	1.37
4-chlorophenol	56	Training	0.478	2.47	1.656
4-cyclopentylphenol	57	Training	0.572	2.47	1.649
4-ethoxyphenol	58	Training	-0.046	1.89	1.551
4-ethylphenol	59	Training	0.084	1.96	1.561
4-fluorophenol	60	Training	2.523	5.18	0.684

Table 1: parameter of 85 substituted phenol (Continued).

MolID	N°	Status	Pcic50	logP	R2u
4-heptyloxyphenol	61	Test	2.05	4.08	0.727
4-hexyloxyphenol	62	Test	1.403	3.25	0.783
4-hromo-2,6-dichlorophenol	63	Test	0.009	2.34	1.644
4-hydroxybenzamide	64	Test	0.346	2.64	1.356
4-hydroxybenzophenone	65	Test	-0.242	1.28	0.888
4-hydroxybenzylcyanide	66	Test	1.094	3.09	0.989
4-hydroxyphenethylalcohol	67	Test	1.297	4.1	1.842
4-hydroxypropiophenone	68	Test	-0.145	1.58	1.623
4-iodophenol	69	Test	0.122	2.23	1.622
4-iso-propylphenol	70	Test	-0.381	1.39	1.565
4-methoxyphenol	71	Test	0.229	2.5	1.621
4-methylphenol	72	Test	0.609	3.05	1.645
4-phenoxyphenol	73	Test	-0.062	1.98	1.496
4-phenylphenol	74	Test	1.351	3.23	0.962
4-propylphenol	75	Test	0.73	3.3	1.701
4-sec-butylphenol	76	Test	1.277	3.87	1.38
4-tert-butylphenol	77	Test	0.681	2.59	0.836
4-tert-octylphenol	78	Test	1.203	3.78	1.629
4-tert-pentylphenol	79	Test	1.648	4.22	1.788
a-3-trifluoro-p-cresol	80	Test	-0.78	0.33	0.875
ethyl-3-hydroxybenzoate	81	Test	-0.828	0.67	1.492
ethyl-4-hydroxybenzoate	82	Test	0.056	2.03	1.63
methyl-3-hydroxybenzoate	83	Test	0.473	3.05	1.678
methyl-4-hydroxybenzoate	84	Test	1.355	3.75	0.963
pentachlorophenol	85	Test	0.98	3.58	1.734

The formula used to calculate the cross-validated:

A multiple linear regression analysis method was used to generate QSAR models employing Quick Stat software. To check the predictive power of the models, cross validation was done by the leave one out procedure. The following statistical parameters were considered to compare the generated QSAR models: R ², Q2, standard deviation (S), F–test and internal predictive power by cross validated coefficient (Q2)¹⁶.

Determination coefficient (R²)¹⁷.

R² The coefficient of determination (R ²) indicates the quality of fit and is calculated as:

(4)

Where yi and are, respectively, the measured and averaged (over the entire data set) values of the dependent variable for the ideal model, the sum of squared residuals being 0, the value of R² is 1. As the value of R² deviates from 1, the fitting quality of the model deteriorates. The square root, or R2, is the multiple correlation coefficient (R). Correlation coefficient (r2) which is relative measure of quality of fit¹⁸.

Adjusted determination coefficient (Adjusted R²)¹⁹

(5)

n refers to the number of observation and k number of descriptors

If one goes on increasing the number of descriptors in a model for a fixed number of observations, R² values will always increase, but this will lead to a decrease in the degree of freedom and low statistical reliability. Therefore, a high value of R² is not necessarily an indication of a good statistical model that fits well the available data²⁰.

Ratio (The Fisher-Snedécor Coefficient)²¹.

The F statistic, calculated from R2 and the number of data points, determines the statistical significance of the regression equation at specified degrees of freedom (df)

F-ratio test is the most well-known statistical tests, this is defined as:

(6)

Standard deviation (s)²².

Values of R² and adj R² attest the good fitting performances of the model which, moreover, is very highly significant (great value of the Fisher parameter F).¹⁸

(7)

It is an indicator of dispersion. It provides information on how the distribution of data is performed around the average. The closer its value is to 0, the better the adjustment and the more reliable the prediction will be.

The Predicted residual sum of squares (PRESS)²³

The PRESS (predicted residual sum of squares) statistic appears to be the most important parameter for a good estimate of the real predictive error of the models. Its small value indicates that the model predicts better than chance and can be considered statistically significant. It is calculated by the following equation:

(8)

eii^thresidual

hii i^thdiagonal element of (9)

Standard deviation error in calculation defined as²⁴

(10)

Standard deviation error of prediction (SDEP²³

(11)

Cross-validated R² (R²cv) (or Q²)²⁵

(12)

A value Q2 > 0.5 is generally regarded as a good result and Q2 > 0.9 as excellent²⁶

External validation coefficient ²⁷

(13)

Here, n_ext refers to the number of test set compounds.

(14)

Where the sum runs over the test set objects (ext n).

The applicability domain (AD)^[28-29]is a theoretical region in space is defined by the descriptors of the model and the modeled response for which a given QSRR should make reliable predictions. In this work, the structural AD was verified by the leverage approach. The leverage, hii, 32, is defined as follows:

n (15)

Where xi is the i th compound's descriptor row vector, x T i is its transpose, and X is the model matrix derived from the calibration set descriptor values.The warning leverage, h*, is, generally, fixed at 3(p+1)/n, where n is the total number of samples in the training set and m is the number of descriptors involved in the correlation.

The Williams plot, the plot of the standardized residuals versus the leverage, was exploited to visualize the applicability domain (AD).

The warning leverage (h*) is defined as:

(16)

Where N is the number of training compounds, p is the number of predictor variables. When the h value of a compound is lower than h *, the probability of accordance between predicted and actual values is as high as that for the compounds in the training set. A chemical with i h > * h will reinforce the model if the chemical is in the training set. But such a chemical is in the validation set and its predicted data may be unreliable. However, this chemical may not appear to be an outlier because its residual may be low. Thus, the leverage and the jackknifed residual should be combined for the characterization of the AD.

External validation criteria or “Tropsha’s criteria³⁰

Golbraikh and Tropsha’s criteria proposed a set of parameters for determining the external predictability of a QSAR model. According to Golbraikh and Tropsha, models are considered satisfactory if all of the following conditions are satisfied:

2- R²_ext>0.7

R² Correlation coefficient between the predicted and observed activities

R₀² is a quantity characterizing linear regression with the Y-intercept set to zero and observed versus predicted activities R₀′² slopes k and k′ of regression lines (predicted versus observed activities, and observed versus predicted activities) through the origin.

3. RESULTS AND DISCUSSION:

QSAR Analysis:

The MLR model was built by stepwise regression on training set as follows:

pCIC₅₀ = - 0.602(±0.60192) + 0.661(± 0.66051)

*logP - 0.400(±0.40005) *R2u (15)

S = 0.157 R² = 95.5% R² (adj) = 95.3% F= 604.34 p= 0.000

In the equation, n is the number of compounds, and R² is the multiple correlation coefficient, and S is the standard error, and F is the Fisher inspection value, and P is the prominence rate. A higher correlation coefficient and lower standard error indicate that the model is more reliable. The P value is much smaller than 0.05, which means that the regression equation has statistical significance statistical parameters.

External validation:

The results are shown in the table 2.

Table 2. External validation

ntr	next	Q²	R²	R²_adj
60	25	95.01	95.5	95.34
Q² ext	SDEC	SDEP	SDEPext
95.96	0.153	0.161	0.153

Cross-validation

Fig. 1. Cross-validation vs. experimental Pcic50

The additional external validation according to (Golbraikh and Tropsha 2002) and described previously confirms the validity of the proposed model. The results are as follows

Fig. 2. Plot of experimental vs. predicted values in a regression model

Fig. 3. Plot predicted of vs. experimental values in a regression model

Applicability Domain:

As shown in the Williams plot (Fig. (4).

Fig. 4. The Williams plot, the plot of the standardized residuals vs. leverages

The He Williams plot for the presented MLR model is shown in Fig. 5. From this plot, the leverage values (hi) of any compound in the training and test sets are less than the critical value (h* = 0.15) excepting the compounds (4-fluorophenol and 2-hydroxy benzaldoxime) as outliers. Also, the standardized residuals of all compounds in the training and test sets are less than two standard deviation units (±2σ). Therefore,

As a result, the model displays the best statistical parameters and good prediction properties.

Y-randomization Test

Table 3. Randomization test

Itération	R²%	Q²%
0	95.5	95.01
1	13.3	3.78
2	1.1	0
3	0.7	0
4	2.5	0
5	0.5	0
6	1.5	0
7	0.1	0
8	1.7	0
9	1.7	0
10	2	0

This is a widely used technique to ensure the robustness of a QSAR model. In this test, the dependent-variable vector, Y-vector, is randomly shuffled and a new QSAR model is developed using the original independent-variable matrix.

Results are shown in table 3. Q2 and R2 are both low.

Values obtained after every shuffle indicate that the good results in our original model are not due to a chance correlation of the training set.

General conclusion:

The toxicity of 85 variously substituted phenols, characterized by the concentration of inhibition at 50% of the growth (CIC₅₀) of a population of ciliated protozoa of the Tetrahymena pyriformis family, could be linked to the octanol/water partition coefficient (logkow) and R2u.

Through the determination of suitable statistical parameters, we have observed a high relationship between experimental and predicted activity values, indicating the validation and excellent quality of the derived QSAR model.

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Received on 26.05.2022 Modified on 22.07.2022

Asian J. Research Chem. 2022; 15(6):433-438.

DOI: 10.52711/0974-4150.2022.00076