Quantitative Structure–Activity Relationship (QSAR) Studies of Some Glutamine Analogues for Possible Anticancer Activity

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B Elidrissia^1*, A Ousaa¹, MA Ajana¹, T Lakhlifi¹ and M Bouachrine²

¹MCNS Laboratory, Faculty of Science, University Moulay Ismail, Meknes, Morocco
²High school of technology, University Moulay Ismail, Meknes, Morocco

*Corresponding author: B Elidrissia, MCNS Laboratory, Faculty of Science, University Moulay Ismail, Meknes, Morocco, Tel: +212 607662438; E-mail:

Received: July 21, 2017; Accepted: September 24, 2017 ; Published: May 30 2018

Citation: Elidrissia B, Ousaa A, Ajana MA, Lakhlifi T, Bouachrine M (2018) Quantitative Structure–Activity Relationship (QSAR) Studies of Some Glutamine Analogues for Possible Anticancer Activity Int J Sci Res Environ Sci Toxicol 3(2):1-12.

Abstract Top

A Quantitative Structure–Activity Relationship (QSAR) study was performed to predict an anticancer activity in tumor cells of thirtysix 5-N-substituted-2-(substituted benzenesulphonyl) glutamine compounds using the electronic and topologic descriptors computed respectively, with ACD/ChemSketch and Gaussian 03W programs. The structures of all 36 compounds were optimized using the hybrid Density Functional Theory (DFT) at the B3LYP/6-31G(d) level of theory. In both approaches, 30 compounds were assigned as the training set and the rest as the test set. These compounds were analyzed by the Principal Components Analysis (PCA) method, a descendant Multiple Linear Regression (MLR), Multiple Nonlinear Regression (MNLR) analyses and an Artificial Neural Network (ANN). The robustness of the obtained models was assessed by leave-manyout cross-validation, and external validation through a test set.

This study shows that the ANN has served marginally better to predict antitumor activity when compared with the results given by predictions made with MLR and MNLR.

Keywords: DFT; QSAR; Tumor cells; Artificial Neural Network; Cross Validation;

Introduction

Cancer remains one of the main causes of death in the world, and as a result there is a pressing need for the development of novel and effective treatments. Despite major breakthroughs in many areas of modern medicine over the past 100 years, the successful treatment of cancer remains a significant challenge at the start of the 21st century. It is very difficult to know and detect novel agents that selectively kill tumor cells or inhibit their proliferation without being toxic [1]. The Cancer has been described as nitrogen trap. Glutamine (GLN) a non essential amino acid, plays a key role in tumor cell growth by supplying its amide nitrogen atoms in the biosyntheses of other amino acids, purine, pyrimidine bases, amino sugars and coenzymes [30, 8] via a family comprised of 16 amido transferases [17] with diversified mechanisms. Thus, different structures of glutamines were synthesized and may supposedly show antitumor activities by GLN [23].In this study, we have modeled the antitumor activity (Inhibition of Tumor (IT)) of 36 new 5-N-substituted- 2-(substituted benzenesulphonyl) glutamines with different substitutions (Table 1), using several statistical tools, Principal Components Analysis (PCA), Multiple Linear Regression (MLR), Multiple Nonlinear Regression (MNLR) and Artificial Neural Network (ANN) calculations [25, 33]. The Quantitative Structure– Activity Relationship (QSAR) method focuses on the motto that the activities of chemical compounds are determined by their molecular structures. Based on accurate experimental data of only some of the chemicals in one group, the biological activity of chemicals in the whole group can be predicted using the suitable models [12], including compounds that have not yet been experimentally synthesized [16, 15, 11, 26 and 27].

The objectives of the current work are to develop predictive QSAR models and to identify the chemical structural features important among our studied molecules for the antitumor cells activity. Thus, a number of quantum chemical methods and calculations have been performed in order to study the molecular structure and antitumor activity [36].

To find the quantitative relationship between molecular structure and antitumor activity for the data taken by K. Srikanth et al. [24], the researcher used the MLR, MNLR and ANN, then they calculated the electronic descriptors by the Gaussian 03 to generate QSAR sets. The MLR was utilized to select the structural features of the molecules relevant to the antitumor activity and to construct the linear model; this last model was used to select descriptors as input parameters for the ANN, which was constructed as the nonlinear model. Both models were validated by an internal validation methods including cross-validation to characterize robustness and an external validation to estimate the predictive power of the models. Finally, the ultimate objective was to establish reliable QSAR models to inhibition of tumor weight prediction of 5-N-substituted-2-(substituted benzenesulphonyl) glutamines.

Material and Methods

Experimental Data

The experimental values of antitumor activities of 36 new 5-N-substituted-2-(substituted benzenesulphonyl) glutamines were taken from the literature treated by Srikanth et al. [24]. For the tumor growth inhibition, an antitumor activity was assessed on the basis of the percentage inhibition of tumor (%IT). The biological activity (IT) data was calibrated to their logarithmic values (log IT).The compounds and their corresponding biological activity Log(IT) values are shown in Figure 1 and Table 1.

Figure 1: Chemical structure of 5-N-substituted-2-(substituted benzenesulphonyl) glutamines

Table 1: Experimental antitumor activity values of studied molecules

Compound	R₁	R₂	R₃	R₄	R₅	% Inhibition of Tumor weight (IT)	Log(IT)
1	H	H	H	H	i-Butyl	52.73	1.722
2	H	H	CH₃	H	i-Propyl	50	1.699
3	H	H	CH₃	H	i-Butyl	25	1.398
4	CH₃	H	H	NO₂	H	37.5	1.574
5	CH₃	H	H	NO₂	CH₃	68.75	1.837
6*	CH₃	H	H	NO₂	C₂H₅	25	1.398
7	CH₃	H	H	NO₂	n-C₃H₇	50	1.699
8	CH₃	H	H	NO₂	n-C₄H₉	62.5	1.796
9*	CH₃	H	H	NO₂	i-Propyl	62.5	1.796
10	CH₃	H	H	NO₂	i-Butyl	12	1.079
11	CH₃	H	H	NO₂	C₆H₁₁	33	1.519
12	CH₃	H	H	NO₂	C₆H₅	33	1.519
13	CH₃	H	H	NO₂	C₆H₅CH₂	60.17	1.779
14	CH₃	H	H	NO₂	n-C₅H₁₁	60.83	1.784
15	CH₃	H	H	NO₂	n-C₆H₁₃	67.37	1.828
16*	H	NO₂	CH₃	H	H	49.53	1.695
17	H	NO₂	CH₃	H	CH₃	40.86	1.611
18	H	NO₂	CH₃	H	C₂H₅	27.05	1.432
19	H	NO₂	CH₃	H	n-C₃H₇	26.95	1.431
20	H	NO₂	CH₃	H	n-C₄H₉	41.37	1.617
21	H	NO₂	CH₃	H	n-C₅H₁₁	24.88	1.396
22	H	NO₂	CH₃	H	n-C₆H₁₃	59.45	1.774
23	H	NO₂	CH₃	H	i-Propyl	37.64	1.576
24*	H	NO₂	CH₃	H	i-Butyl	45.95	1.662
25	H	NO₂	CH₃	H	C₆H₁₁	35.33	1.548
26	H	NO₂	CH₃	H	C₆H₅CH₂	22.35	1.349
27*	H	NO₂	CH₃	H	C₆H₅	59.6	1.775
28	H	H	C₂H₅	H	CH₃	90.45	1.956
29	H	H	C₂H₅	H	C₂H₅	38.46	1.585
30	H	H	C₂H₅	H	n-C₃H₇	65.64	1.817
31	H	H	C₂H₅	H	n-C₄H₉	55.64	1.745
32	H	H	C₂H₅	H	n-C₅H₁₁	56.36	1.751
33	H	H	C₂H₅	H	n-C₆H₁₃	65.37	1.815
34	H	H	C₂H₅	H	-CH(CH₃)₂	41.53	1.618
35*	H	H	C₂H₅	H	C₆H₅CH₂	37.5	1.574
36	H	H	C₂H₅	H	C₆H₅	70.76	1.85

Calculation of Molecular Descriptors

Density Functional Theory (DFT) methods were used in this study and were in agreement with their results. The energy of the fundamental state of a polyelectronic system can be expressed through the total electronic density and, as a matter of fact, the electronic density was used to reconsider the wave function for calculating the energy that constitutes the fundamental base of DFT using the B3LYP functional and a 6-31G(d) basis set [29, 9, 5]. The B3LYP, a version of DFT method, uses Becke’s threeparameter functional (B3) and includes a mixture of HF with DFT exchange terms associated with the gradient corrected correlation functional of Lee, Yang and Parr (LYP). The geometry of the studied compounds was determined by optimizing all geometrical variables without any symmetry constraints. The molecular properties which were calculated: Highest Occupied Molecular Orbital Energy E_HOMO(eV), Lowest Unoccupied Molecular Orbital Energy E_LUMO(eV), dipole moment μ(Debye), Total Energy ET(eV), Activation Energy EA(eV), absolute electronegativity χ(eV) and the Total Negative Charges of the molecule TNC [6, 35, 2].

χ was determined by the following equations:

χ = \frac{E_{L U M O} + E_{H O M O}}{2} (1)

On the other hand, ACD/ChemSketch and Chem3D programs [3] are employed to calculate the topological descriptors which are: Molecular Weight MW(cm³), Density D (g/cm³), Partition Coefficient Log P, Bend Energy EB (Kcal/mol), Electronic Energy EE(Kcal/mol), Steric Energy ES(Kcal/mol), Shape Attribute ShA, Shape Coefficient ShC, Mulliken Charges ChM.

Statistical Analysis

The compounds of 5-N-substituted-2-(substituted benzenesulphonyl) glutamines (1 to 36) were studied by statistical methods based on the Principal Component Analysis (PCA) [7] using the software XLSTAT 2015. PCA is an essentially a descriptive statistical method which aims to present in graphic form, the maximum information contained in the data (Table 1). This method is a statistical technique useful for summarizing all the information encoded in the structures of compounds, and it is also very helpful for understanding the distribution of the compounds.

The Multiple Linear Regression (MLR) statistical technique was used to study the relation between one dependent variable and several independent variables. It is a mathematic technique that minimizes differences between actual and predicted values. The statistical qualities of the MLR equation were judged by parameters such as the R² value (coefficient of determination), the F value (Fischer statistics) and the RMSE value (Root Mean Squared Error). The MLR was generated using the software XLSTAT 2015, to predict the antitumor activity (IT) and was manipulated to select the descriptors used as the input parameters in the Multiple Non Linear Regression (MNLR) and Artificial Neural Network (ANN) [34].

Nonlinear models were then developed by submitting the selected descriptors from MLR to a three-layer, fully connected, feed forward ANN. The number of input neurons was as equal as that of the descriptors in the linear model. The number of hidden neurons was optimized by a trial and error procedure on the training process. One output neuron was used to represent the experimental % inhibition of tumor weight Log (IT). To avoid overtraining, one tenth of the data from the training set was randomly selected as a separate validation set to monitor the training process that is during the training of the network the performance was monitored by predicting the values for the systems in the validation set. When the results for the validation set ceased to improve, the training was stopped [13].

In order to check the reliability and the stability of QSAR model elaborated by MLR, MNLR and ANN methods, both the internal and external validations were conducted. The goodness of the fitting was firstly characterized by the coefficient of determination (R²) between calculated and experimental values for the molecules of the training set. The formula is given by equation:

R^{2} = 1 - \frac{\sum_{i = 1}^{n} {(y_{i} - y_{i}^{'})}^{2}}{\sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2}} (2)

Where

y_{i}, y_{i}^{'}

and are the observed, calculated and mean values of the activity, respectively.

Validation of Model

Cross-validation is one of the most popular methods of estimating the robustness of a model. Based on this technique, a number of modified data sets are created by deleting in each case one or a small group of molecules, these procedures are named respectively “leave-one-out” and “leave-some-out” [4, 28,14]. In this work, the internal predictive capability of the model was evaluated by the leave-many-out cross-validation (Q²), following the mathematic form:

Q^{2} = 1 - \frac{\sum_{i = 1}^{training set} {(y_{i} - y_{i}^{'})}^{2}}{\sum_{i = 1}^{training set} {(y_{i} - \bar{y})}^{2}} (3)

The reliability and robustness of the models were further validated by using the external test set composed of data not used to develop the prediction models. The external

R_{t e s t}^{2}

for the test set is determined with the following equation:

R^{2} = 1 - \frac{\sum_{i = 1}^{test set} {(x_{i} - x_{i}^{'})}^{2}}{\sum_{i = 1}^{test set} {(x_{i} - {\bar{y}}_{t r})}^{2}} (4)

where x_i, x’_i, and are the observed value, the calculated value in the test set and the mean value of the activity in the training set, respectively.

QSAR model is successful if it satisfies the following criteria:

R^{2} > 0.6; Q^{2} a n d R_{t e s t}^{2} > 0.5

.

To further refine the predictive ability of the developed QSAR models, another group of metrics was used: the r_m² metrics. They determine the proximity between the observed and predicted activities, was introduced by Roy and Ojha [21, 31]. They are calculated based on the correlation between the observed and predicted response data. Presently two different indicators are calculated for both the training (internal validation) and the test (external validation) sets:

{\bar{r}}_{m}^{2}

and

Δ r_{m}^{2}

For an acceptable QSAR model,

{\bar{r}}_{m}^{2}

should be > 0.5,

Δ r_{m}^{2}

and should be < 0.2.

Y-Randomization Test

The models were also evaluated against chance correlation by Y-randomization [10]. Property values were randomized within the training set by much iteration. From each new randomized data set, a new model QSAR was computed again, with performances expected to have lower Q2 and R2 values than those the original models. Finally, the average values of the Q2 and R2 were calculated to check that the original model was strongly more performant than the randomized ones.

Results and Discussion

This study was carried out for a series of 36 compounds of 5-N-substituted-2- (substituted benzenesulphonyl) glutamines, in order to determine a quantitative relationship between the structural information and the antitumor activity (IT) of these glutamines compounds.

The set of sixteen descriptors encoding the 36 compounds of 5-N-substituted-2-(substituted benzenesulphonyl) glutamines, electronic, energetic and topologic parameters are submitted to PCA analysis [13]. The first three principal axes are sufficient to describe the information provided by the data matrix. Indeed, the percentages of variance are 30.36%, 20.95% and 15.95% for the axes F1, F2 and F3, respectively. The total information was estimated to a percentage of 67.26%. The principal component analysis (PCA) [32] was conducted to identify the link between the different variables. Bold values are different from 0 at a significance level of p= 0.05.

The Pearson correlation coefficients were summarized in the following Table 3. The obtained matrix provides information on the negative or positive correlation between variables.

A strong correlation is observed between MW and ShA (r = 0.995), high a negative correlation is between MW and Et (r = -0.965), and a high correlation is observed between ShA and Et (r = -0,945).

Analysis of projections according to the planes F1–F2 and F1- F3 (51.31% and 46.31% of the total variance respectively) of the studied molecules (Fig. 2) shows that the molecules are dispersed in two regions: region 1 contains compounds having a values of total energy Et between -49709,561 (eV) and -45559,132 (eV), region 2 contains compounds having a values of total energy Et between -45211,746 (eV) and -38920,188 (eV).

Table 2: Values of the calculated parameters obtained by DFT/B3LYP 6-31G* optimization of the studied compounds

N°	Log (IT)	MW	D	LogP	E_b	ChM	Es	Ee	ShA	ShC	E_t	E_HOMO	E_LUMO	m	χ	TNC	E_a
1	1,722	342,41	1,253	0,733	13,343	0,131	118,836	-31761	21,043	1,00	-39990,72	-6,621	-3,195	7,688	-4,908	-9,910	2,763
2	1,699	342,41	1,253	1,003	13,352	0,133	81,472	-31303	21,043	0,85	-39990,88	-6,637	-3,305	8,023	-4,971	-9,805	2,205
3	1,398	356,44	1,231	1,221	13,547	0,132	89,597	-55577	22,041	0,85	-41061,16	-6,553	-2,441	6,856	-4,497	-10,526	4,327
4	1,574	345,33	1,501	-0,597	13,445	0,151	124,324	-31824	21,043	0,83	-42347,69	-6,594	-3,292	7,613	-4,943	-9,125	4,038
5	1,837	359,35	1,428	-0,361	13,446	0,148	237,583	-33793	22,041	1,00	-43418,03	-6,574	-3,214	7,885	-4,894	-9,418	3,641
6	1,398	373,38	1,392	-0,023	13,446	0,132	240,852	-35745	23,040	0,87	-43418,03	-6,574	-3,214	7,885	-4,894	-9,418	3,632
7	1,699	387,41	1,361	0,463	13,446	0,125	243,938	-37609	24,038	1,00	-45559,13	-6,561	-3,153	8,162	-4,857	-10,342	3,627
8	1,796	401,43	1,333	0,880	13,446	0,125	246,975	-39468	25,037	0,85	-46629,64	-6,557	-3,137	8,215	-4,847	-10,790	3,620
9	1,796	387,41	1,359	0,295	13,727	0,135	237,493	-38022	24,038	0,85	-45559,20	-6,535	-2,853	8,055	-4,694	-10,375	3,138
10	1,079	401,43	1,332	0,513	13,717	0,134	243,411	-40586	25,037	0,85	-46629,58	-6,522	-2,685	8,206	-4,603	-10,989	4,237
11	1,519	427,47	1,390	1,187	13,924	0,128	242,563	-43662	27,034	0,85	-48738,06	-6,528	-2,720	7,399	-4,624	-11,186	4,086
12	1,519	421,42	1,452	1,302	13,445	0,199	249,208	-41243	27,034	0,87	-48639,08	-6,425	-3,630	7,482	-5,027	-10,095	2,779
13	1,779	435,45	1,394	1,372	13,446	0,198	241,799	-44337	28,033	1,00	-49709,56	-6,521	-2,985	7,825	-4,753	-9,735	2,235
14	1,784	415,46	1,307	1,298	13,687	0,127	244,960	-41310	26,035	1,00	-47700,16	-6,522	-2,873	8,439	-4,697	-11,076	4,063
15	1,828	429,49	1,285	1,715	13,884	0,118	242,747	-43102	27,034	0,88	-48770,67	-6,521	-2,872	8,430	-4,697	-11,687	4,056
16	1,695	345,33	1,501	-0,597	13,445	0,148	108,939	-31556	21,043	0,83	-42347,62	-6,871	-2,875	8,074	-4,873	-9,111	4,025
17	1,611	359,35	1,428	-0,361	13,446	0,119	112,573	-33511	22,041	1,00	-43418,07	-6,842	-2,905	7,832	-4,873	-9,390	3,584
18	1,432	373,38	1,392	-0,023	13,446	0,147	115,783	-35441	23,040	0,85	-44488,66	-6,789	-2,860	7,610	-4,824	-9,869	3,588
19	1,431	387,41	1,361	0,463	13,446	0,124	118,840	-37291	24,038	1,00	-45559,18	-6,755	-2,830	7,622	-4,792	-10,323	3,587
20	1,617	401,43	1,333	0,880	13,446	0,122	121,877	-39133	25,037	0,87	-46629,69	-6,737	-2,815	7,851	-4,776	-10,770	3,583
21	1,396	415,46	1,307	1,298	13,446	0,125	124,904	-40938	26,035	1,00	-47700,21	-6,726	-2,806	7,404	-4,766	-11,219	3,581
22	1,774	429,49	1,285	1,715	13,446	0,123	127,929	-42741	27,034	0,88	-48770,72	-6,718	-2,800	7,592	-4,759	-11,493	3,580
23	1,576	387,41	1,359	0,295	13,727	0,170	125,653	32749	24,038	0,85	-45559,13	-6,662	-2,597	9,093	-4,630	-10,361	5,547
24	1,662	401,43	1,332	0,513	13,924	0,133	119,540	34963	25,037	0,85	-46629,51	-6,622	-2,510	8,816	-4,566	-10,973	4,855
25	1,548	427,47	1,390	1,187	13,924	0,132	137,258	38586	27,034	0,87	-48737,89	-6,568	-2,518	9,352	-4,543	-11,196	5,527
26	1,349	435,45	1,394	1,372	13,446	0,198	116,706	37256	28,033	1,00	-49709,30	-6,727	-2,954	7,714	-4,840	-10,027	3,355
27	1,775	421,42	1,452	1,302	13,445	0,200	120,216	35363	27,034	0,87	-48639,18	-6,780	-2,942	7,562	-4,861	-10,073	3,668
28	1,956	328,38	1,281	0,763	13,276	0,114	92,524	24667	20,045	0,85	-38920,18	-6,775	-2,892	6,000	-4,833	-9,405	3,405
29	1,585	342,41	1,255	1,102	13,276	0,148	95,753	26366	21,043	1,00	-39990,78	-6,726	-2,848	6,040	-4,787	-9,886	3,413
30	1,817	356,44	1,231	1,588	13,276	0,123	98,816	27990	22,041	0,87	-41061,30	-6,692	-2,818	5,839	-4,755	-10,339	3,412
31	1,745	370,46	1,211	2,005	13,276	0,127	101,852	29614	23,040	1,00	-42131,81	-6,674	-2,804	5,943	-4,739	-10,624	3,408
32	1,751	384,49	1,192	2,422	13,276	0,124	104,880	31205	24,038	0,88	-43202,32	-6,662	-2,795	5,928	-4,729	-11,235	3,407
33	1,815	398,52	1,176	2,840	13,276	0,121	107,905	32800	25,037	1,00	-44272,83	-6,655	-2,789	6,160	-4,722	-11,684	3,406
34	1,618	356,44	1,230	1,420	13,557	0,144	92,273	28274	22,041	1,00	-41061,36	-7,172	-2,857	6,204	-5,014	-10,371	3,384
35	1,574	404,48	1,275	2,496	13,401	0,199	96,369	33194	26,035	0,88	-45211,74	-6,586	-2,854	6,211	-4,720	-10,412	3,284
36	1,850	390,45	1,324	2,427	13,276	0,200	100,248	31175	25,037	1,00	-44141,30	-6,716	-2,869	5,375	-4,793	-10,089	3,649

Table 3: Correlation matrix (Pearson (n)) between different obtained descriptors

	Log (IT)	MW	D	LogP	Eb	ChM	Es	Ee	ShA	ShC	Et	E_HOMO	E_LUMO	µ	χ	TNC	Ea
Log (IT)	1
MW	-0,143	1
D	-0,214	0,160	1
LogP	0,244	0,402	-0,683	1
Eb	-0,252	0,463	0,261	-0,206	1
Char.	-0,087	0,300	0,386	0,166	-0,124	1
Es	-0,039	0,442	0,356	-0,210	0,435	-0,009	1
Ee	0,210	-0,044	-0,313	0,453	-0,166	0,282	-0,558	1
ShA	-0,128	0,995	0,150	0,450	0,416	0,374	0,408	0,002	1
ShC	0,112	0,037	-0,229	0,248	-0,334	0,065	-0,038	0,106	0,055	1
Et	0,189	-0,965	-0,381	-0,162	-0,528	-0,302	-0,519	0,167	-0,949	0,019	1
E_HOMO	-0,049	0,371	0,102	0,057	0,300	0,050	0,643	-0,353	0,363	-0,219	-0,366	1
E_LUMO	-0,151	0,165	-0,334	0,225	0,409	-0,243	-0,335	0,330	0,144	-0,095	-0,096	-0,194	1
µ	-0,237	0,340	0,537	-0,560	0,686	-0,091	0,474	-0,412	0,281	-0,268	-0,503	0,338	-0,014	1
χ	-0,170	0,357	-0,264	0,245	0,552	-0,205	0,028	0,124	0,333	-0,209	-0,290	0,355	0,848	0,169	1
TNC	0,013	-0,614	0,516	-0,618	-0,408	0,336	-0,134	-0,071	-0,582	-0,003	0,477	-0,229	-0,498	-0,059	-0,598	1
Ea	-0,240	0,158	0,183	-0,209	0,640	-0,169	-0,010	0,210	0,115	-0,317	-0,213	0,049	0,619	0,426	0,616	-0,296	1

Figure 2 Cartesian diagram showing the separation between the two regions and the dispersal of different molecules by groups

Multiple Linear Regressions (MLR)

To establish quantitative relationships between the inhibition of tumor weight log(IT) and selected descriptors, our array data were subjected to a multiple linear regression. Only variables whose coefficients are significant were retained.

Modeling the inhibition of tumor cells log(IT) value of all training compounds (5-N-substituted 2-(substituted benzenesulphonyl) glutamines) led to the best value corresponding to the linear combination of the following descriptors: Partition Coefficient logP, Mulliken charges ChM, steric energy Es, dipole moment μ , absolute electronegativity χ, total negative charges of the molecule TNC, activation energy Ea.

The most significant QSAR model was obtained, as shown in the following equation:

log(IT) = 2,34+0,45 logP-7,03 ChM+1,57 10^-03 Es+8,08 10^-02 μ-0,66 χ+0,46 TNC+0,15 Ea (5)

For our 30 compounds, the correlation between experimental and calculated log(IT) one based on this model are quite significant (Figure 3) as indicated by statistical values:

N = 30 R² = 0.626 > 0.6

{\bar{r}}_{m}^{2}

= 0.606

Δ r_{m}^{2}

= 0.184 F=5.255 RMSE = 0.134 P < 0.0001

In the above regression equation, N is number of compounds, R is correlation coefficient, F is Fisher’s test, RMSE is root mean square error and P is the significance level. Generally, the higher the correlation coefficient and the lower the standard error, the more reliable is the model. High values of F and P is much smaller than 0.05 indicate the significance of Eq. (5), which reflects the ratio of variance explained by the model and the variance due to the error in the model. Based on Eq. (5), the positive correlation coefficient for logP, Es, μ TNC and Ea indicates that a compound with a larger value for these descriptors would have a larger log(IT) value (increase inhibition of tumor cells), the negative correlation for ChM and χ indicate that a compound with a larger value for these descriptors would have a smaller log(IT) value (decrease inhibition of tumor cells).

The correlations of predicted and observed activities and the residual values are illustrated in Figure 3.

The figure 3 shows a very regular distribution of Log (IT) values depending on the experimental values.

As part of this conclusion, we can say that the inhibition of tumor cells Log(IT) values obtained from MLR are good correlated to that of the observed values.

In this work, variance inflation factors (VIF) was calculated to test if multicollinearities existed among the descriptors which is defined as

V I F = \frac{1}{r^{2}} (6)

Where r is the correlation coefficient of multiple regression between one independent variable and the others. If VIF=1, no self-correlation exists among each variable, when VIF ranges from 1.0 to 5.0, the correlation equation is acceptable; if VIF>10.0, the regression equation is unstable and a recheck is necessary. As can

Figure 3: Graphical representation of calculated and observed activity and the residues values calculated using MLR

be seen from Table 4, the VIF values of the five descriptors are all less than 5 and two descriptors are not more than 10, indicating that there is no multicollinearity among the selected descriptors and the resulting model has good stability.

In order to distinguish the importance of each descriptor on antitumor of glutamines, standard regression coefficients (SR) and t test values of the seven descriptors are also listed in Table 4. As shown in Table 4, the absolute value of SR and t test value of log P are 0.386 and 5.027, respectively, both larger than the other descriptors, which indicates that in this QSAR model, the influence of LogP on antitumor cells is stronger than that of the others.

Table 4: VIF, SR and t test value of descriptors in QSAR model

Descriptor	VIF	SR	t test value
LogP	8,780	0,386	5,027
ChM	2,499	0,206	-4,694
Es	1,789	0,174	3,004
μ	3,177	0,232	1,859
χ	2,496	0,206	-2,159
TNC	8,558	0,382	4,498
Ea	3,051	0,228	2,551

Descriptors Analysis and Interpretation

Based on the Eq.(5), we would attempt to explain mechanisms of the inhibitory tumor activity of the 5-N-substituted 2-(substituted benzenesulphonyl) glutamines, in the following:

** Partition coefficient (LogP) appeared as the most significant positively descriptor for the derived QSAR model. Glutamine compounds with higher lipophilicity are more likely to give better anticancer activity [19].

** Total negative charges TNC has a positive sign in the model, So, glutamine compounds with lower TNC have stronger electrondonating groups on phenyl rang, marginally contributing to the activity [18].

** The dipole moment μ has a positive sign in the model, which suggests that increased activity can be achieved by increasing the polarity of the glutamine derivatives [22].

** The inhibitory tumor activity is varies positively with the activation energy Ea of the substituted glutamines. Activation energy Ea is influencing by the temperature of the system and the energy of repulsion between the reacting centers.

** Steric energy Es has a positive sign in the model, it dependents to the steric effect of substituent groups of glutamines, the bulk or small groups are possibly contributing to the activity.

The descriptors proposed in Eq. (5) by MLR were, therefore, used as the input parameters in the Multiples nonlinear regression (MNLR) and artificial neural network (ANN).

Multiple Nonlinear Regressions (MNLR)

We have used also the technique of nonlinear regression model to improve the predicted activity in a quantitative way. It takes into account several parameters. This is the most common tool for the study of multidimensional data. We have applied to the data matrix constituted obviously from the descriptors proposed by MLR corresponding to the 30 glutamines compounds used in training set.

The resulting equation is:

log (IT) = -89,94+0,53 LogP+3,89 ChM+3,63E-03 Es+0,97 μ-39,69 χ+1,34 TNC-0,32 Ea+9,43 10^-3 (LogP)²-36,99 (ChM)²- 4,50 10^-6 (Es)²-6,35 10^-2 x (μ)²-4,06 (χ)²+3,85 x 10^-2 (TNC)²+8,11 10-2 (Ea)² (7)

N = 30 R² = 0.792 > 0.6

{\bar{r}}_{m}^{2}

= 0.698

Δ r_{m}^{2}

= 0.137 RMSE = 0.121

The correlations of predicted and observed activities and the residual values are illustrated in Fig. 4.

Figure 4: Graphical representation of calculated and observed activity and the residues values calculated using MNLR

Figure 5: Graphical representation of calculated and observed activity and the residues values calculated using ANN

Artificial Neural Networks (ANN)

The ANN has become an important and widely used nonlinear modeling technique for QSAR studies, it can be used to generate predictive models of quantitative structure-activity relationships (QSAR) between a set of molecular descriptors obtained from the MLR and observed values of antitumor activity log(IT).

The correlations coefficients and Standard Error of Estimate, obtained with the ANN, show that the selected descriptors by MLR are pertinent and that the model proposed to predict the anticancer activity is relevant.

The correlation between ANN calculated and experimental activities and the residues values are very significant as illustrated in Fig. 5 and as indicated by R and R² values.

The values of predicted activities calculated using ANN and the observed values are given in Table 6.

N = 30 R² = 0.828 > 0.6

{\bar{r}}_{m}^{2}

= 0.658

Δ r_{m}^{2}

= 0.175 RMSE=0.0041

Model validation

In order to check the reliability and the stability of the QSAR model elaborated by the MLR, MNLR and ANN methods, we have used the internal and external validations. The leave-many-out cross-validation of three models, showeding the good robustness of the model. Moreover, predictions realized on the test set were in good agreement with the experimental values.

True predictive power of a QSAR model is to test their ability to predict accurately the anticancer activity of glutamine compounds from an external test set: 6-9-16-24-27-35, (compounds which were not used for the model development).

The comparison of the values of log (IT-test) to log (ITobs) shows that a good prediction has been obtained for the 6 compounds. The main performance parameters of the three models are shown in table 5.

Table 5:- Performance comparison between models obtained by MLR, RNLM and ANN

Table 5: Performance comparison between models obtained by MLR, RNLM and ANN

	Leave many-out cross-validation		test set
	N	Q²	N	R²test
MLR	30	0.636	6	0.662
MNLR	30	0.604	6	0.69
ANN	30	0.76	6	0.821

Applicability Domain

The AD is an important tool for reliable application of QSAR models, while characterization of interpolation space is significant in defining the AD. We have reported that the web application can be easily used for identification of the X-outliers for training set compounds and detection of the test compounds residing outside the applicability chemical domain using the descriptor pool of the training and test sets [37]. The selected four molecular descriptors in this model were used for the calculation of the leverage values:

h_{i} = x_{i} {(X^{T} X)}^{- 1} x_{i}^{T}

, x_i namely row vector of descriptors of compound i, X called Matrix of model deducted from the descriptors of training set and T correspondent to Matrix transposed.

The critical leverage h* is fixed at (3P+1)/N or P and N are respectively the number of descriptors and number of compounds of training set. If h>h*, the prediction of the compound can be considered as unreliable and vice versa. As illustrated in the Williams graph of Figure. 6, excepting thate compounds 6, 9 and 24 are outside (has standardized residual less or more than standard deviation units

\pm 3 σ

), the majority of the molecules in the training and test sets (91.66%) fall within the applicability chemical domain and then the predicted inhibitory activity by the developed QSAR model is reliable

Figure 6: Williams plot for the presented MLR model

Y-randomization

Table 6:- Y-Randomization validation results of the CoMFA and CoMSIA models (Q2 and R2 values after several Y-randomization tests).

In this test, random RML, RNLM and ANN models are generated by randomly shuffling the dependent variable while keeping the independent variables as it is. The new QSAR models are expected to have significantly low R² and Q² values for several trials, which confirm that the developed QSAR models are robust and the results of the RML, RNLM and ANN methods are not due to a chance correlation of the training set.

A comparison of the quality of MLR, MNLR and ANN models shows that the ANN is the best models that indicate the effects of these descriptors on the biological activity of the studied compounds.

Table 6: Y-Randomization validation results of the CoMFA and CoMSIA models (Q² and R² values after several Y-randomization tests)

Iteration	MLR		MNLR		ANN
	Q²	R²	Q²	R²	Q²	R²
1	0.421	0.54	0.435	0.476	0.435	0.44
2	0.347	0.407	0.389	0.39	0.279	0.53
3	0.291	0.301	0.279	0.321	0.299	0.371
4	0.161	0.251	0.198	0.254	0.223	0.451
5	0.369	0.464	0.317	0.592	0.217	0.364

Table 7: Observed, predicted Log(IT) and residue according to different methods

N°	Log(IT)
	Obs.	RML		MNLR		ANN
	Obs.	Pred.	Resid.	Pred.	Resid.	Pred.	Resid.
1	1,722	1,713	0,009	1,709	0,013	1,682	0,040
2	1,699	1,793	-0,094	1,725	-0,026	1,775	-0,076
3	1,398	1,499	-0,101	1,277	0,121	1,443	-0,045
4	1,574	1,546	0,028	1,638	-0,064	1,489	0,085
5	1,837	1,650	0,187	1,718	0,119	1,632	0,205
6*	1,398	1,916	-0,518	1,999	-0,601	1,402	-0,004
7	1,699	1,770	-0,071	1,753	-0,054	1,704	-0,005
8	1,796	1,751	0,045	1,737	0,059	1,686	0,110
9*	1,796	1,403	0,393	1,319	0,477	1,758	0,038
10	1,079	1,360	-0,281	1,250	-0,171	1,317	-0,238
11	1,519	1,539	-0,020	1,565	-0,046	1,443	0,076
12	1,519	1,673	-0,154	1,529	-0,010	1,568	-0,049
13	1,779	1,626	0,153	1,727	0,052	1,745	0,034
14	1,784	1,783	0,001	1,782	0,002	1,745	0,039
15	1,828	1,746	0,082	1,772	0,056	1,750	0,078
16*	1,695	1,542	0,153	1,625	0,070	1,630	0,065
17	1,611	1,646	-0,035	1,638	-0,027	1,583	0,028
18	1,432	1,334	0,098	1,356	0,076	1,297	0,135
19	1,431	1,491	-0,060	1,487	-0,056	1,412	0,019
20	1,617	1,506	0,111	1,481	0,136	1,456	0,161
21	1,396	1,431	-0,035	1,472	-0,076	1,452	-0,056
22	1,774	1,521	0,253	1,590	0,184	1,579	0,195
23	1,576	1,399	0,177	1,517	0,059	1,420	0,156
24*	1,662	1,301	0,361	1,313	0,349	1,595	0,067
25	1,548	1,672	-0,124	1,611	-0,063	1,663	-0,115
26	1,349	1,522	-0,173	1,527	-0,178	1,533	-0,184
27*	1,775	1,509	0,266	1,530	0,245	1,642	0,133
28	1,956	1,949	0,007	1,974	-0,018	1,829	0,127
29	1,585	1,618	-0,033	1,660	-0,075	1,549	0,036
30	1,817	1,774	0,043	1,765	0,052	1,758	0,059
31	1,745	1,812	-0,067	1,843	-0,098	1,847	-0,102
32	1,751	1,736	0,015	1,784	-0,033	1,807	-0,056
33	1,815	1,757	0,058	1,880	-0,065	1,837	-0,022
34	1,618	1,726	-0,108	1,595	0,023	1,682	-0,064
35*	1,574	1,604	-0,030	1,633	-0,059	1,501	0,073
36	1,850	1,759	0,091	1,745	0,105	1,736	0,114

All the results discussed above showed that the presented MLR,MNLR and ANN models could be effectively used to predict the log(IT) of 5-N-substituted-2-(substituted benzenesulphonyl) glutamines compounds with different substitutions, and they were able to establish a satisfactory relationship between the molecular descriptors and the antitumor activity of the studied compounds.

From the values of correlation coefficient of the six compounds (test set), the Cross-Validated coefficient (training set) and other statistical parameters of these methods (MLR, MNLR and ANN), it is clear that the predictive power of our models are equally robust and stable, andit can be efficiently used for estimating the antitumor activity of other some glutamine compounds for which no experimental data are available.

The predicted antitumor activity values of 5-N-substituted- 2-(substituted benzenesulphonyl) glutamines compounds of training set, obtained by different methods are listed in table 76 along with their observed activity.

Table 7:- Observed, predicted Log(IT) and residue according to different methods.

Conclusion

In present work, we have carried out a comparative analysis of % Inhibition of Tumor weight Log(IT) of glutamine compounds by three QSAR approaches, MLR, MNLR and ANN. These approaches have showed good predictive power. Comparison of the qualities of MLR, MNLR and ANN models shown that the ANN has a good predictive ability and strong robustness than the MLR, yields a regression model with improved predictive power, and we have established a relationship between several descriptors and the % Inhibition of Tumor weight Log (IT). The predictive ability and robustness of the obtained models were assessed by cross-validation, and external validation through test set. Thus, the model could be efficiently employed for estimating the antitumor activity and for select the descriptors which have an impact on this biological activity and which are sufficiently rich in chemical, electronic and topological information to encode the structural feature.

The present study shows that molecular descriptors, namely the partition coefficient logP, Mulliken charges ChM, steric energy Es, dipole moment μ, absolute electronegativity χ, total negative charges of the molecule TNC, activation energy Ea, are useful for the prediction of the best % Inhibition of Tumor cells of 5-N-substituted-2-(substituted benzenesulphonyl) glutamines compounds, for which the experimental data are unavailable. The QSAR model is statistically significant, robust and can be used for prediction the activity more accurately, and it may be helpful for a better understanding of the anticancer activity of this class of compounds and useful as guidance to estimate the antitumor cells as biological activity of new glutamine compounds.

Acknowledgment

We are grateful to the “Association Marocaine des Chimistes Théoriciens” (AMCT) for its pertinent help concerning the programs.

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