In silico -based identification of new anti-pfdhfr drug candidates via 1,3,5-triazine derivatives

Abstract

Quantitative structure-activity relationship study was used to investigate the relationship between anti-pfdhfr activity and structure of twenty-eight 1,3,5-triazine derivatives. We performed benchmark studies on the molecular geometry, electron properties of 1,3,5-triazine using semi-empirical(PM3), density functional theory and post Hartree-Fock methods. Followed by a QSAR study using multiple linear regression (MLR) and artificial neural networks (ANN). The QSAR models developed allow identify/describe the relationship between the biological activity of the molecules and their molecular descriptors (topological, physicochemical, electronic...). A further external set of compounds was used for validation where a high correlation between experimental and predicted anti-pfdhfr activity values is noticed. This QSAR study provides useful information for developing novel pfdhfr inhibitors. The set’s ADME properties and drug similarities, as well as newly produced compounds and reference ligand, were investigated. These findings would be extremely useful in guiding optimization for the development of new anti-pfdhfr drug candidates.

Keywords

1 3 5-triazine pfdhfr QSAR MLR ANN drug-like

1 Introduction

One of the big killers of diseases in the worldwide burden is malaria [1], that is a parasitic infection spread by Plasmodium falciparum. An infected mosquito of the species Anopheles bites humans and transmits the parasite [2]. In 2018, estimates suggested by the World Health Organization (WHO) recorded 228 million cases of malaria worldwide, with 213 million cases accounting for 93% of the global burden. Nigeria is still the world’s worst-affected country, accounting for 25% of worldwide morbidity and 24% of global death [3], possibly as a result of rising resistance to present anti-Plasmodium falciparum DHFR medications, there is a need to create innovative anti-pfdhfragents. An integrated strategy for combating malaria must include prevention, vector control, and treatment using potent pfdhfrs [4]. Among the latter, which arouse growing interest among chemists are the derivatives of 1,3,5-triazines (Fig. 1) [5] are precursors for treating malaria. As a result, anti-pfdhfr activity will be a focus of our computation investigation, as will compounds derived from 1,3,5-triazine [6] that may inhibit the bifunctional pfdhfr (Plasmodium falciparum dihydrofolatereductase) enzyme’s function.

Fig. 1

Structures of 1,3,5-triazine with atom numbering.

The in-silico prediction of anti-pfdhfr activity has been highlighted as a critical stage in the development of drugs with targeted biological activity. The computer-aided drug discovery (CADD) has proven to be a beneficial method for discovering prospective lead compounds and assisting in the development of new medications for a number of ailments [7]. In medicinal chemistry, computational analyses based on structure-based approaches, such as QSAR (Quantitative Structure Activity Relationship) method and ADME (Absorption, Distribution, Metabolism, and Excretion) proprieties are now commonly employed to assist speed up the drug design process [8 –13].

QSAR has developed into a well-established area in computational drug design and drug profile exploration [14]. It’s defined as a method of identifying significant correlations between a set of structures and functions by building computational or mathematical models utilizing chemometric approaches [15]. Additionally, the drug-likeness and ADME prediction is a useful tool for selecting drug-like compounds. There are a few important considerations to remember when it comes to improving oral bioavailability in medication development. It uses to enhance data from in silico docking experiments or to prioritize hits from high-throughput screening initiatives [16].

The implementation of these three studies was the subject of this current research. The first section focuses on the development of the best QSAR models using the statically approach Multiple Linear Regression (MLR) and Artificial Neural Networks (ANN), on a set of different molecular characteristics of pfdhfr inhibitors. It would reveal fresh knowledge that might be used to design new pfdhfr inhibitors with increased potency.

A predictive QSAR model was constructed to be utilized for lead optimization and testing of novel compounds, and an in-silico evaluation of drug-likeness features was examined, which gives useful information about the activity of substances in the body that are expected to serve asinhibitors.

2 Materials and methods

2.1 Computational details

Initial calculations were optimized using HyperChem 8.03 software [17]. The geometry of 1,3,5-triazine and its derivatives; were pre-optimized using the MM+force-field (rms = 0,01 Kcal/) in molecular mechanics [18]. The PM3 approach was used to completely re-optimize geometry [19].

In the next step, a parallel study has been made using Gaussian 09 program package, at various computational levels, HF/6-31++G(d,p), HF/6-311++G(d,p), B3LYP/6-31++G(d,p) and B3LYP/6-311++G(d,p) [20].

After that, the different properties of 1,3,5-triazine derivatives were calculated by using MarvinSketch 17.13.0 [21] software, ACD/Chemsketch12.0 [22] and HyperChem software(version 8.0.6) [17]. By means of these software, twenty descriptors are computed and reduced using the stepwise strategy in XLSTAT software [23] to build several QSAR models, just five descriptors of the best QSAR model have been reported in the present work.

2.2 Dataset selection

All in-vitro IC₅₀ (μM) anti-pfDHFR activity data of twenty-eight molecules having similar structures were selected from a series of 1,3,5-triazine-based derivatives expeditiously synthesized and biologically evaluated by Gravestock et al. [5]. The negative logarithm (pIC₅₀ = –log₁₀ (IC₅₀)) was used to convert all of the experimental activity IC₅₀ values for the purpose of providing numerically greater data values, listed in Table 2, after then, it was employed as the dependent variable in the creation of the QSAR models.

2.3 QSAR modeling studies

In an attempt to determine the role of structural features of compounds, which appears to have an effect on anti-pfdhfr activity, a QSAR models were generated. The field of quantitative structure-activity relationships deals with the development of a predictive models correlating biologicalactivity (pIC₅₀) with the physicochemical properties. Once these are available, by using statistical methods, It is possible to establish this predictive MLR-QSAR and ANN-QSAR models for a series of biologically active molecules which have shown inhibitory activity against the pfdhfr enzyme [24].

2.3.1 Statistical analysis and model validation

To predict the QSAR models, multiple linear regression (MLR) analysis of molecular descriptors was carried out in the present work using the stepwise strategy in XLSTATsoftware [23]. The MLR method was compared to the artificial neural network (ANN) method, which is another reliable and predictive QSAR model that is ideally suited for treating non-linear correlations between descriptors and activity [24 –26]. All the ANN analyses were carried out using JMP 8.0.2.software[27].

Two basic methodologies are used to undertake external and internal validation of models [28]: internal validation utilizing the training set molecules, and external using the test set molecules by partitioning the entire data set into training and test sets; at 80% and 20%, respectively, utilizing the so-called ‘Balanced Subset Method’ (BSM) [29].

Apart from the use of fitness of several parameters, the statistical qualitative analysis of the QSAR model was validated by using the leave-one-out cross validation method (LOOCV) [30, 31]. The best model was chosen in this study using the determination coefficient (R²) and adjusted determination coefficients ( $R_{adj}^{2}$ ), Fisher’s value(F-value) should have high values and p-value (including the critical probability: p-value<0.0001 for descriptors and for the model), predicted residual sum of squares (PRESS) and standard deviation of error of prediction (SDEP), root-mean-squar-error of prediction of training set (RMSE_c)and if the following conditions are satisfied, determination coefficient $(R_{test}^{2})$ of external validation, cross validated determination coefficient $(Q_{cv}^{2})$ , root-mean-squar-error of prediction (RMSE_P) low mean squared error (MSE), and Y-randomization statistical parameters ( $R_{(Rand)}^{2}, Q_{(Rand)}^{2}$ and ${cR}_{p}^{2}$ ).

2.3.2 Applicability domain approach

Another pivotal issue is the definition of a locale in the compound space containing the structural, physicochemical, or natural properties data s where upon the training set of the created model is through the applicability domain (AD) and for which it is applicable to make predictions for new compounds [32, 33]. Even the most comprehensive, significant and validated models cannot reliably predict properties for all existing compounds.

Therefore, the AD of the models must be defined and only predictions for molecules falling in the training set in this domain can be considered acceptable. The method of leverage value hi for each compound i has a calculated of the QSAR model was represented (Fig. 7) $h_{i} = x_{i}^{T} (X^{T} X)^{- 1} x_{i} (i = 1, 2, 3, \dots . ., n)$ , where x_i is the query compound’s descriptor row-vector while X is the n*(k-1) matrix of k descriptor values of model for n training set compounds, and the superscript T is the matrix/transpose vector’s [34]. And there exists a warning leverage value (h*), in general, the critical value of the leverage h* = 3*(k + 1)/N, [35] where N denotes the number of compounds in the training series and k is the number of descriptors in the model. The compound’s strong influence on the model was indicated by a leverage (h) greater than h* [36].

A warning should be presented when hi > h* for a test set compound, suggesting that the prediction is the result of significant model extrapolation and should not be trusted [36].

2.4 Drug likeness parameter and lipophilicity indices

A drug’s physicochemical properties of chemical compounds of series have a substantial impact on its in vivo pharmacokinetic characteristics under research with PFDHFR enzyme. The detailed analysis of drug likeness characteristics and lipophilicity indices were carried out by applying the different rules, by Lipinski’s rules [37, 38], veber’s rules [39], lipophilicity indices [40, 41], and Golden Triangle tool [42].

3 Results and discussion

3.1 Validation method

3.1.1 Equilibrium geometries of 1,3,5-triazine

The main geometrical parameters of the optimal equilibrium geometry to be employed are the most efficient theoretical strategy for the larger of 1,3,5-triazine (Fig. 1) of interest in the current study perhaps selected by comparison with experimental results.

Our investigations started by performing benchmark studies on 1,3,5-triazine using different theoretical methods (PM3, Ab-initio, DFT) in order to select the most reliable predictive method comparatively to experiment and with reduced computational cost.

Table 1 lists the main geometrical parameters of the optimized equilibrium geometry of 1,3,5-triazine are in accordance with the numbering scheme given in (Fig. 1). Table 1 lists also the corresponding experimental geometrical parameters that have been obtained by X-ray diffraction, which revealed that the molecule had D3h symmetry [43]. Since 1,3,5-triazine are planar, the calculated dihedral angle values are either 0° or 180°.

Table 1
Bond lengths (in Å) and valence angles (in degree, °) of 1,3,5-triazine. Experimental data for 1,3,5-triazine are collected from Ref. [44]

Parameters EXP PM3 Ab initio/HF DFT/B3LYP

6-31G++(d,p) 6-311G++(d,p) 6-31G++(d,p) 6-311G++(d,p)

Bond length (Angstrom)

N1-C2 1.338 1.357 1.318 1.317 1.337 1.334

N1-C6 1.338 1.357 1.318 1.317 1.337 1.334

C2-N3 1.338 1.357 1.318 1.317 1.337 1.334

C2-H7 1.084 1.098 1.074 1.075 1.087 1.086

N3-C4 1.338 1.357 1.318 1.317 1.337 1.334

C4-N5 1.338 1.357 1.318 1.317 1.337 1.334

C4-H8 1.084 1.098 1.074 1.075 1.087 1.086

N5-C6 1.338 1.357 1.318 1.317 1.337 1.334

C6-H9 1.084 1.098 1.074 1.075 1.087 1.086

Valence angle (°)

C2-N1-C6 113 118.433 114.536 114.475 114.245 114.278

N1-C2-N3 127 121.567 125.463 125.524 125.755 125.723

C2-N3-C4 113 118.433 114.536 114.475 114.242 114.275

N3-C4-N5 127 121.567 125.463 125.524 125.756 125.723

C4-N5-C6 113 118.433 114.536 114.475 114.245 114.278

N1-C6-N5 127 121.567 125.463 125.524 125.753 125.721

C2-N1-C6 113 118.433 114.536 114.475 114.245 114.278

Parameters	EXP	PM3	Ab initio/HF	DFT/B3LYP
Bond length (Angstrom)
N1-C2	1.338	1.357	1.318	1.317	1.337	1.334
N1-C6	1.338	1.357	1.318	1.317	1.337	1.334
C2-N3	1.338	1.357	1.318	1.317	1.337	1.334
C2-H7	1.084	1.098	1.074	1.075	1.087	1.086
N3-C4	1.338	1.357	1.318	1.317	1.337	1.334
C4-N5	1.338	1.357	1.318	1.317	1.337	1.334
C4-H8	1.084	1.098	1.074	1.075	1.087	1.086
N5-C6	1.338	1.357	1.318	1.317	1.337	1.334
C6-H9	1.084	1.098	1.074	1.075	1.087	1.086
Valence angle (°)
C2-N1-C6	113	118.433	114.536	114.475	114.245	114.278
N1-C2-N3	127	121.567	125.463	125.524	125.755	125.723
C2-N3-C4	113	118.433	114.536	114.475	114.242	114.275
N3-C4-N5	127	121.567	125.463	125.524	125.756	125.723
C4-N5-C6	113	118.433	114.536	114.475	114.245	114.278
N1-C6-N5	127	121.567	125.463	125.524	125.753	125.721
C2-N1-C6	113	118.433	114.536	114.475	114.245	114.278

Table 2

Optimized structures of the molecules under study [5]

N°	Structures	pIC₅₀ (obs)	N°	Structures	pIC₅₀ (obs)
1		4.303	15^*		5.131
2		5.005	16		5.176
3		4.781	17*		5.338
4		4.954	18		5.100
5		5.075	19		5.176
6^*		4.947	20*		5.105
7		5.148	21		5.344
8		5.172	22		5.345
9		5.364	23		4.965
10		6.004	24		5.412
11		5.338	25		4.910
12^*		5.100	26		5.143
13		5.176	27		5.567
14^*		4.349	28		5.866

(^*): Test set compounds. pIC₅₀ = -log ₁₀ (IC₅₀).

From the obtained values (Table 1), we can also find that the appropriate method to compute the spectroscopic parameters of the 1,3,5-triazine is the density functional theory (DFT with B3LYP/6-31++G(d,p)) which will be used to compute the quantum properties of our series of the 1,3,5-triazine derivatives.

3.1.2 3D molecular electrostatic potential surface maps (3D MESP) of 1,3,5-triazine

The electrostatic potential that is created by a molecule’s electron charge density in space expands in the entire space (nuclei considered as point charges). MESP entails comprehending a variety of physical and chemical phenomena, for instance molecular reactivity, molecular recognition, intermolecular contacts, substituent effects, electrophilic reactions, and reagent-induced interactions, such as those between a drug and its cellular receptor [45]. Figure 2 shows the 3D molecular electrostatic potential surface maps (3DMESP) of 1,3,5-triazine.

Fig. 2

3D MESP of 1,3,5-triazine. The results are color-coded, from red (most negative) to blue (most positive).

As can be seen in Fig. 2, due to its strong electronegativity, 1,3,5-triazine exhibits negative electrostatic potentials (red zone) surrounding the nitrogen atoms (N1, N3, and N5). Additionally, we can observe positive electrostatic potentials (the blue zone) everywhere around the hydrogen and carbon atoms, which explain why these atomic sites are exposed to nucleophilic attack. Carbon atoms attached hydrogen atoms have the most positive charge per atom of hydrogen (dark blue).

In sum, 1,3,5-triazine derivatives exhibit a number of properties that may help us better understand the electrostatic interactions that may occur between the 1,3,5-triazine derivatives under study and reagents or enzyme active sites.

3.2 Quantitative structure-activity relationship studies

3.2.1 Multiple linear regression (MLR)

In the present study we tried to develop the statistical correlation of the best QSAR model that was derived from multi linear regression model generation (MLR).

That the physicochemical descriptors, NRB (number of rotatable bond on the molecule), E_HOMO (energy of highest occupied molecular orbital), E_LUMO (energy of lowest unoccupied molecular orbital), n (refractive index) and µ (dipolar moment) of the series of twenty-eight of 1,3,5-triazine derivatives were used as independent variables and were correlated with anti-pfdhfr activity (pIC₅₀). Additional validation was performed on a data set consisting of 1,3,5-triazine derivatives was randomly divided into two subsets; 23 training and 5 test sets. The values of the descriptors used in MLR analysis are presented in Tables 3. Pearson’s correlation matrix has been performed on alldescriptors.

Table 3
Chemical descriptors used in the regression analysis. They correspond to number of rotatable bond on the molecule (NRB (eV)), energy of highest occupied molecular orbital (E_HOMO (eV)), energy of lowest unoccupied molecular orbital (E_LUMO (eV)), refractive index (n) anddipolar moment (µ (D))

N° NBR E_HOMO E_LUMO n μ pIC50 MLR Residues ANN Residues

1 2 –0.209 –0.026 1.63 3.67 4.303 4.304 –0.001 4.853 –0.549

2 2 –0.208 –0.026 1.67 3.22 5.005 5.039 –0.034 5.219 –0.214

3 3 –0.214 –0.034 1.63 2.32 4.781 4.881 –0.100 5.031 –0.250

4 5 –0.229 –0.105 1.72 6.87 4.954 4.915 0.039 5.170 –0.216

5 4 –0.220 –0.045 1.67 5.53 5.075 4.967 0.109 5.270 -0.195

6* 5 –0.210 –0.029 1.61 5.11 4.947 4.455 0.492 4.889 0.058

7 6 –0.213 –0.029 1.65 5.75 5.148 5.244 -0.096 5.319 –0.171

8 6 –0.203 –0.024 1.66 7.37 5.172 4.904 0.268 5.314 –0.142

9 6 –0.212 –0.050 1.67 4.56 5.365 5.476 –0.112 5.472 –0.107

10 6 –0.218 –0.028 1.67 5.49 6.004 5.697 0.307 5.771 0.234

11 7 –0.227 –0.103 1.72 7.22 5.131 5.348 –0.216 5.277 –0.146

12* 6 –0.218 –0.031 1.66 5.08 5.177 5.618 –0.442 5.420 –0.243

13 6 –0.211 –0.029 1.65 5.10 5.338 5.349 –0.011 5.343 –0.005

14* 5 –0.210 –0.028 1.65 5.07 5.100 5.031 0.069 5.314 –0.214

15 7 –0.211 –0.028 1.64 5.59 5.177 5.275 –0.098 5.212 –0.035

16 7 –0.181 –0.010 1.64 7.14 4.349 4.555 –0.206 4.860 –0.511

17* 6 –0.217 –0.032 1.64 5.22 5.207 5.250 –0.043 5.121 0.086

18 7 –0.248 –0.047 1.61 5.19 5.257 5.383 –0.126 5.260 –0.003

19 6 –0.214 –0.032 1.68 5.02 5.886 5.818 0.068 5.826 0.061

20* 5 –0.208 –0.040 1.65 4.69 5.106 4.869 0.237 5.159 –0.053

21 6 –0.210 –0.027 1.65 5.26 5.344 5.314 0.029 5.416 –0.072

22 6 –0.221 –0.033 1.66 5.51 5.345 5.555 –0.211 5.314 0.031

23 6 –0.210 –0.027 1.63 5.12 4.965 5.028 –0.063 4.972 –0.007

24 7 –0.225 –0.100 1.67 4.85 5.412 5.231 0.181 5.320 0.092

25 7 –0.206 –0.025 1.62 5.16 4.910 5.131 –0.221 5.096 –0.186

26 6 –0.209 –0.031 1.61 3.91 5.143 4.812 0.331 5.052 0.090

27 7 –0.212 –0.031 1.64 3.76 5.567 5.741 –0.174 5.437 0.130

28 8 –0.212 –0.030 1.63 5.27 5.867 5.529 0.337 5.596 0.270

N°	NBR	E_HOMO	E_LUMO	n	μ	pIC50	MLR	Residues	ANN	Residues
1	2	–0.209	–0.026	1.63	3.67	4.303	4.304	–0.001	4.853	–0.549
2	2	–0.208	–0.026	1.67	3.22	5.005	5.039	–0.034	5.219	–0.214
3	3	–0.214	–0.034	1.63	2.32	4.781	4.881	–0.100	5.031	–0.250
4	5	–0.229	–0.105	1.72	6.87	4.954	4.915	0.039	5.170	–0.216
5	4	–0.220	–0.045	1.67	5.53	5.075	4.967	0.109	5.270	-0.195
6*	5	–0.210	–0.029	1.61	5.11	4.947	4.455	0.492	4.889	0.058
7	6	–0.213	–0.029	1.65	5.75	5.148	5.244	-0.096	5.319	–0.171
8	6	–0.203	–0.024	1.66	7.37	5.172	4.904	0.268	5.314	–0.142
9	6	–0.212	–0.050	1.67	4.56	5.365	5.476	–0.112	5.472	–0.107
10	6	–0.218	–0.028	1.67	5.49	6.004	5.697	0.307	5.771	0.234
11	7	–0.227	–0.103	1.72	7.22	5.131	5.348	–0.216	5.277	–0.146
12*	6	–0.218	–0.031	1.66	5.08	5.177	5.618	–0.442	5.420	–0.243
13	6	–0.211	–0.029	1.65	5.10	5.338	5.349	–0.011	5.343	–0.005
14*	5	–0.210	–0.028	1.65	5.07	5.100	5.031	0.069	5.314	–0.214
15	7	–0.211	–0.028	1.64	5.59	5.177	5.275	–0.098	5.212	–0.035
16	7	–0.181	–0.010	1.64	7.14	4.349	4.555	–0.206	4.860	–0.511
17*	6	–0.217	–0.032	1.64	5.22	5.207	5.250	–0.043	5.121	0.086
18	7	–0.248	–0.047	1.61	5.19	5.257	5.383	–0.126	5.260	–0.003
19	6	–0.214	–0.032	1.68	5.02	5.886	5.818	0.068	5.826	0.061
20*	5	–0.208	–0.040	1.65	4.69	5.106	4.869	0.237	5.159	–0.053
21	6	–0.210	–0.027	1.65	5.26	5.344	5.314	0.029	5.416	–0.072
22	6	–0.221	–0.033	1.66	5.51	5.345	5.555	–0.211	5.314	0.031
23	6	–0.210	–0.027	1.63	5.12	4.965	5.028	–0.063	4.972	–0.007
24	7	–0.225	–0.100	1.67	4.85	5.412	5.231	0.181	5.320	0.092
25	7	–0.206	–0.025	1.62	5.16	4.910	5.131	–0.221	5.096	–0.186
26	6	–0.209	–0.031	1.61	3.91	5.143	4.812	0.331	5.052	0.090
27	7	–0.212	–0.031	1.64	3.76	5.567	5.741	–0.174	5.437	0.130
28	8	–0.212	–0.030	1.63	5.27	5.867	5.529	0.337	5.596	0.270

Among several MLR equations the best model is expressed by the following relation: $\begin{matrix} pIC 50 = - 24.602 + 0.265 * NRB - 20.841 * E_{HOMO} + 14.892 * E_{LUMO} \\ + 15.464 * n - 0.224 * µ \end{matrix}$ (1)

In Fig. 3, We display the experimental activity versus the predicted activity values to further created MLR model’s prediction ability.

Fig. 3

Correlations of experimental versus predicted pIC₅₀ values using MLR.

Once developed, the model must be interpreted by analyzing all the statistical parameters. In the model obtained in Equation (1), we note that N RB, E_LUMO and n with positive coefficients suggest that biological activity increases with the increase in the values of these descriptors. On the other hand, the negative coefficients of E_HOMO and μ suggest the opposite. There after, the molecular descriptors and the values of calculated activities of MLR and ANN are reported in Table 3.

From the observed and predicted biological activity data of the molecules given in Table 3, we can notice that there is a strong similarity between the observed and predicted pIC50 values. This can be explained by the low values of the residuals. This means that the QSAR models developed via the MLR and ANN techniques have a strong predictive capacity of the biological activity of the studied molecules according to the selected molecular descriptors (NBR E_HOMO, E_LUMO, n, μ).

In order to detect the absence of the multi-collinearity for the selected descriptors the variance inflation factors (VIF) were calculated [46]. All five descriptors in the MLR-QSAR model have VIF values less than 5 (VIF = 1.716, 1.800, 3.023, 2.572, and 1.855, for N RB, E_HOMO, E_LUMO, n and μ respectively), indicating that the multi-collinearity is not present in the MLR model, which is the unique explanation for this condition.

Moreover, the predictive power of the equation of the model is confirmed by metrics of Golbraikh and Tropsha’s criteria are listed in Table 4. The MLR model having R² > 0.6 for both training and test sets will only be considered for validation [47]. Equation (1) exhibited high values of R² and $R_{adj}^{2}$ , these are essential criteria are confirmed a strong association between the observed activities (pIC50) and the predicted activities (pIC50_Pred), Our results for these two indices are 0.811 and 0.756, respectively, as shown in Table 4. The small PRESS (0.717) and SDEP (0.176) values indicate the model predictability and lack of over fitting. Value of F-value (14.635) (Table 4) of MLR model with p-value less than 0.0001 show that the model is statistically significant [48].

Table 4

MLR statistics of predicted model

Parameter Parameter	MLR	Threshold
R ²	0.811	>0.6
$R_{adj}^{2}$	0.756	>0.6
RMSE_c	0.195	A low value
PRESS	0.717	A low value
SDEP	0.176	A low value
F-value	14.635	A high value
$R_{test}^{2}$	0.628	>0.6
$Q_{cv}^{2}$	578	>0.5
RMSE_p	0.258	A low value
MSE	0.011	A low value

This is on the other hand confirmed by metrics for external validation that has also used Golbraikh and Tropsha’s criteria to judge the predicted model from a calculation the larger $R_{test}^{2} (0 . 628)$ for the test set, $Q_{cv}^{2} (0.578)$ , RMSE_p (0.258) and MSE (0.011)values indicate good predictive ability of the MLR model [49].

Furthermore, the robustness of the MLR model was ensuring by applying the Y-randomization test. Mostly, the Y-randomization test is used to test the stability of the predictive power of statistical models. Therefore, in the present study, this test was used to check the stability of the statistically modeled structure-activity relationship. This is to eliminate the probability of generating a QSAR model at random. We performed many Y vector random shuffles. After 100 random tests we have obtained small average values of 0.217 for $R_{(Rand)}^{2}$ and –0.573 for $Q_{(Rand)}^{2}$ , also the smaller ${cR}_{p}^{2}$ (0.706 > 0.5) values indicate good predictive ability of the model and demonstrate its high robustness[50].

3.2.1.1. QSAR model’s applicability domain. A William’s plot is used to show the AD of models (Fig. 4). According to the “three-sigma rule” [51], the AD is established using Excel 2013 software [52], in this plot inside a square region within the standard deviation x (in this study, x = 3). Outliers are molecules with standardized residuals three times higher than the modes standard deviation.

Fig. 4

MLR model’s applicability domain plot. The vertical dashed line represents the warning leverage (h* = 0.782), whereas the horizontal lines denote±3.

All substances in the dataset fall within the applicability range of the suggested MLR model, as can be seen by carefully examining Fig. 4. The leverage values of the inhibitors are all less than the warning h* value (0.782), and none of them exhibit standardized residuals that are more than the threshold. As a consequence, the model exhibits the best statistical parameters and strong predictive capabilities, and it can be used in this AD with a high level of confidence.

3.2.2 Artificial neural networks (ANN)

The existence of a non-linear relationship between pIC₅₀ and the five selected descriptors by the MLR model as inputs was studied in the second stage. The number of hidden layers was determined using the value 2n+1, where n denotes the number of input layers, which plays an important role in establishing the optimum ANN architecture [53].

For pIC₅₀ data, the architecture of the chosen ANN model was 5-3-1, with 5 descriptors in the first layer, three neurons in the hidden layer, and one neuron in the output layer after optimization. In this work, the intermediate (hidden) layer is made up of three neurons that form a deep internal pattern that identifies the strongest correlations between expected and experimental data. The output layer is made up of one neuron that returns the value of pIC₅₀ (Fig. 5).

Fig. 5

Architecture of ANN.

The Gauss Newton method was then used to train the ANN [54]. The experimental and predicted pIC50 using ANN are found to be highly correlated. This is indicated in Fig. 6 with 0.987 and 0.841 value of R² and $Q_{cv}^{2}$ , respectively. We are also obtained 0.968 a high value of R²_test and a low value of MSE (–0.073) for the external validation.

Fig. 6

Correlations of experimental versus predicted pIC50 values using ANN.

Fig. 7

Compound 10.

We could infer that the ANN model with (5-3-1) architecture is capable of establishing a suitable link between the five descriptors and anti-pfdhfr activity based on both training and test set outcomes (Fig. 5).

A simple comparison of the values of the statistics parameters of ANN model in Table 5 with those obtained using the MLR method confirms that ANN outperforms MLR, demonstrating the existence of a non-linear relationship between the pIC₅₀ and the five selected descriptors of the investigated compounds.

Table 5

ANN and MLR statistics of predicted models

Parameter	ANN	MLR
R ²	0.987	0.811
$R_{test}^{2}$	0.986	0.628
$Q_{cv}^{2}$	0.841	0.578
MSE	0.073	0.011

Thus, therefore, our QSAR models can be successfully applied to predict the anti-PFDHFR activity of this class of molecules.

3.3 Design of novel pfdhfr inhibitors

Using the foregoing results as a guide, we made appropriate substitutions and then proceeded to calculate their activities using the proposed model Equation (1). As a result, the proposed model will help us to speed up the time when it comes to synthesizing and assessing the anti-pfdhfr activity of 1,3,5-triazine derivatives.

According to the preceding discussions, our MLR model might be used to calculate pIC₅₀pred of various 1,3,5-triazine derivatives as shown in Table 6 and could contribute to the development of new anti-pfdhfr druglike. If we create a new compound with higher values than existing compounds, we may be able to create more active compounds than those now in use. In this manner, we performed structural alteration using compounds with the greatest pIC₅₀ values as a template comp.10 (Fig. 7).

Table 6
Values of descriptors and pIC50 for the new designed compounds (derivatives of comp.10) of the Fig. 7

N° Comp NBR E _HOMO E _LUMO n μ pIC₅₀ pred

C1 7 –0.215 –0.033 1.70 5.99 6.251

C2 7 –0.201 –0.008 1.70 6.18 6.291

C3 7 –0.218 –0.029 1.75 5.35 7.191

C4 7 –0.202 –0.008 1.72 3.73 7.097

C5 7 –0.226 –0.046 1.76 4.91 7.385

C6 7 –0.199 –0.017 1.75 2.85 7.574

Comp. 10 (Ref) 6 –0.218 –0.028 1.67 5.49 6.004

N°	NBR	E _HOMO	E _LUMO	n	μ	pIC₅₀ pred
C1	7	–0.215	–0.033	1.70	5.99	6.251
C2	7	–0.201	–0.008	1.70	6.18	6.291
C3	7	–0.218	–0.029	1.75	5.35	7.191
C4	7	–0.202	–0.008	1.72	3.73	7.097
C5	7	–0.226	–0.046	1.76	4.91	7.385
C6	7	–0.199	–0.017	1.75	2.85	7.574
Comp. 10 (Ref)	6	–0.218	–0.028	1.67	5.49	6.004

Table 6 lists the structures of the designed compounds, as well as their parameter values computed using the same procedures and the pIC₅₀ values predicted by the MLR model.

3.4 Drug likeness screening of 1,3,5-triazine derivatives

Chemicals’ drug-likeness is a qualitative feature [55], beneficial for early-stage drug development. From the standpoint of this concept, it would be ideal to encode the equilibrium between a compound’s molecular characteristics that effects its pharmacokinetics and eventually optimizes their absorption, distribution, metabolism and excretion (ADME) in the human body like a medicine.

At present, we should evaluate the oral bioavailability of the twenty-eight 1,3,5-triazine derivatives under study. Continuous, the quickest strategy for appreciating the drug-likeness of a set is to apply “rules”, they have been applied. As first, the most commonly Lipinski’s rules are used [37, 38].

Continuous, our parameters determined that good absorption or permeation is more likely to occur when: the molecular weight (MW < 500da), number of hydrogen bond donors (HBDs < 5) (counting the sum of all NH and OH groups), to estimate hydrophobicity of molecules used the partition coefficient octanol/water (Log p < 5), and the number of hydrogen bond acceptors (HBA < 10) are all within a certain range (counting all N and O atoms). In this rule of five-score, there are a total of four violations of Lipinski’s rules.

Veber et al. identified the other two descriptors. [39]: number of rotatable bonds (NBR < 10) and topological polar surface area (PSA < 140 Å²). The TPSA is an important measure for predicting molecular transport properties, especially in the areas of blood-brain barrier (BBB) penetration and intestinal absorption [56, 57]. It is well known that molecules with a TPSA of 140 Å² have a great ability to penetrate in an environment that is hydrophobic, like biological membranes. However, this could explain their quick penetration in hydrophilic settings, for instance, the core of transporter proteins [58]. The TPSA values were discovered to be in the range of (74,8 Å²–127,17Å²); these chemicals may be able to penetrate the BBB, resulting in increased bioavailability. TPSA was used to compute the percentage of absorption ((% ABS) in accordance with the equation the equation % ABS = 109±0.345×TPSA [59]. All of the compounds had a high % ABS, ranging from 65.126 to 83.194 %, implying that the permeability of their cellular plasmatic membrane is good.

The results obtained are shown in Table 7, they were calculated using HyperChem 8.0.8 (for MW, Log p and N_H) and MarvinSketch 6.2.1 software (for HBD, HBA, NBRand TPSA). As can be seen there, The Lipinski and Veber criteria are satisfied by all substances, indicating that their theoretical oral bioavailability is optimal. The association between appropriate aqueous solubility and intestinal permeability, as well as these physicochemical molecular properties that represent the first steps in oral bioavailability.

Table 7
Drug-likeness parameters and Lipophilicityindices of 1,3,5-triazine derivatives

N° Lipinski’s rules Veber’s rules Lipophilicity indices

MW≤500 Da Log p≤5 HBD≤5 HBA≤10 Lipin-ski score NBR≤10 TPSA≤140 Å² Veber score % ABS LE LLE pIC₅₀ N_H

1 231.30 2.18 3 5 4 2 74.80 2 83.194 0.354 2.123 4.303 17

2 271.37 3.21 3 5 4 2 74.80 2 83.194 0.350 1.795 5.005 20

3 279.77 2.21 3 6 4 3 74.80 2 83.194 0.352 2.571 4.781 19

4 407.26 1.52 3 9 4 5 117.94 2 68.311 0.257 3.431 4.954 27

5 380.25 1.74 3 8 4 4 74.80 2 83.194 0.284 3.335 5.075 25

6* 309.80 1.42 3 7 4 5 84.03 2 80.01 0.330 3.526 4.947 21

7 357.84 1.77 3 7 4 6 84.03 2 80.01 0.288 3.378 5.148 25

8 392.29 1.55 3 8 4 6 84.03 2 80.01 0.278 3.622 5.172 26

9 426.73 1.33 3 9 4 6 84.03 2 80.01 0.278 4.034 5.364 27

10 347.80 0.04 3 7 4 6 97.17 2 75.476 0.350 5.964 6.004 24

11 402.84 0.96 3 9 4 5 117.94 2 68.311 0.257 4.171 5.131 28

12* 392.29 1.55 3 8 4 6 84.03 2 80.01 0.279 3.626 5.176 26

13 363.89 2.56 3 7 4 6 84.03 2 80.01 0.299 2.778 5.338 25

14* 349.86 2.45 3 7 4 5 84.03 2 80.01 0.297 2.650 5.100 24

15 387.87 0.78 3 8 4 7 93.26 2 76.825 0.268 4.396 5.176 27

16 400.91 0.82 3 8 4 7 87.27 2 78.892 0.217 3.529 4.349 28

17* 375.83 1.17 3 8 4 6 84.03 2 80.01 0.280 4.037 5.207 26

18 425.84 2.34 3 6 4 7 84.03 2 80.01 0.254 2.916 5.256 29

19 373.90 2.12 3 5 4 6 100.1 2 74.465 0.330 3.766 5.886 25

20* 325.86 1.77 3 6 4 5 100.1 2 74.465 0.340 3.336 5.106 21

21 357.84 1.77 3 7 4 6 84.03 2 80.01 0.299 3.574 5.344 25

22 392.29 1.55 3 8 4 6 84.03 2 80.01 0.288 3.795 5.345 26

23 341.39 1.39 3 7 4 6 84.03 2 80.01 0.278 3.575 4.965 25

24 368.40 1.18 3 8 4 7 127.17 2 65.126 0.281 4.232 5.412 27

25 353.42 1 3 7 4 7 93.26 2 76.825 0.264 3.910 4.910 26

26 323.83 1.87 3 7 4 6 84.03 2 80.01 0.327 3.273 5.143 22

27 371.87 2.22 3 7 4 7 84.03 2 80.01 0.300 3.347 5.567 26

28 385.90 2.62 3 7 4 8 84.03 2 80.01 0.304 3.246 5.866 27

N°	Lipinski’s rules	Veber’s rules	Lipophilicity indices
1	231.30	2.18	3	5	4	2	74.80	2	83.194	0.354	2.123	4.303	17
2	271.37	3.21	3	5	4	2	74.80	2	83.194	0.350	1.795	5.005	20
3	279.77	2.21	3	6	4	3	74.80	2	83.194	0.352	2.571	4.781	19
4	407.26	1.52	3	9	4	5	117.94	2	68.311	0.257	3.431	4.954	27
5	380.25	1.74	3	8	4	4	74.80	2	83.194	0.284	3.335	5.075	25
6*	309.80	1.42	3	7	4	5	84.03	2	80.01	0.330	3.526	4.947	21
7	357.84	1.77	3	7	4	6	84.03	2	80.01	0.288	3.378	5.148	25
8	392.29	1.55	3	8	4	6	84.03	2	80.01	0.278	3.622	5.172	26
9	426.73	1.33	3	9	4	6	84.03	2	80.01	0.278	4.034	5.364	27
10	347.80	0.04	3	7	4	6	97.17	2	75.476	0.350	5.964	6.004	24
11	402.84	0.96	3	9	4	5	117.94	2	68.311	0.257	4.171	5.131	28
12*	392.29	1.55	3	8	4	6	84.03	2	80.01	0.279	3.626	5.176	26
13	363.89	2.56	3	7	4	6	84.03	2	80.01	0.299	2.778	5.338	25
14*	349.86	2.45	3	7	4	5	84.03	2	80.01	0.297	2.650	5.100	24
15	387.87	0.78	3	8	4	7	93.26	2	76.825	0.268	4.396	5.176	27
16	400.91	0.82	3	8	4	7	87.27	2	78.892	0.217	3.529	4.349	28
17*	375.83	1.17	3	8	4	6	84.03	2	80.01	0.280	4.037	5.207	26
18	425.84	2.34	3	6	4	7	84.03	2	80.01	0.254	2.916	5.256	29
19	373.90	2.12	3	5	4	6	100.1	2	74.465	0.330	3.766	5.886	25
20*	325.86	1.77	3	6	4	5	100.1	2	74.465	0.340	3.336	5.106	21
21	357.84	1.77	3	7	4	6	84.03	2	80.01	0.299	3.574	5.344	25
22	392.29	1.55	3	8	4	6	84.03	2	80.01	0.288	3.795	5.345	26
23	341.39	1.39	3	7	4	6	84.03	2	80.01	0.278	3.575	4.965	25
24	368.40	1.18	3	8	4	7	127.17	2	65.126	0.281	4.232	5.412	27
25	353.42	1	3	7	4	7	93.26	2	76.825	0.264	3.910	4.910	26
26	323.83	1.87	3	7	4	6	84.03	2	80.01	0.327	3.273	5.143	22
27	371.87	2.22	3	7	4	7	84.03	2	80.01	0.300	3.347	5.567	26
28	385.90	2.62	3	7	4	8	84.03	2	80.01	0.304	3.246	5.866	27

Therefore, for the series of interest, Table 7 shows that the rule of five is 4 and 2 for Veber’s score. Indeed, to be marginal for further developments the compounds with Rule of five-scores>1 are taken into consideration [60]. Overall, our findings show that most compounds defy Lipinski and Veber rules, indicating that all chemical compounds would have no issues with oral bioavailability.

We have also defined ligand efficiency (LE), lipophilic ligand efficiency (LLE) and the golden triangle as LE = 1.4pIC50/NH, and LLE = pIC₅₀–LogP; where NH is the number of heavy atoms [61]. They are described as crucial parameters for drug discovery, furthermore as a means of determining a compound’s potency in relation to its molecular weight. LE is influenced by ligand size, with smaller ligands having higher biological efficiency than bigger ligands on average [62, 63].

Further, we used LLE to facilitate a deeper comprehension of the affinity of structural alterations in the series, with respect to lipophilia. As a rough guide, LLE values have been stranded in the range 5–7 in drug-like space for medicinal compounds [64]. That compounds with high LE and LLE tries to improve a potency interact with biological targets [65]. In the studied series, the change of LE and LLE during optimization (Table 7).

Other characteristics that affect ADME and drug-likeness attributes such as molecular weight (MW) and distribution coefficients (logD) were used to illustrate the simultaneous absorption and clearance of optimal medicines using Warring rules and the Golden Triangle tool [42]. The Golden Triangle is a visualization tool developed from in vitro permeability, in vitro clearance and computational data designed to aid medicinal chemists in achieving metabolically stable, permeable and potent drug candidates [42]. Plotting MWvs. logDon estimated octanol: buffer (pH 7.4) and classifying compounds of a series as permeable and stable (pH 7.4).

A triangular shape known as the “golden triangle” is formed when the design properties are moved into an area with a baseline of log D_7.4 = –2.0 to log D_7.4 = 5.0 at MW = 200 Da and a peak at log D_7.4 = 1.0 to 2.0 and MW = 450 Da, this increases the chance of success in maximizing potency, stability, and permeability. According to the fighting rule, with MW = 414 Da and logD_7.4 _> 1.3 have a 74% chance of 74% chance of becoming highly permeable. Golden triangle’s rules apply to the majority of our substances. These findings should aid in the development of permeability-enhancing chemicals. The metabolic stability and good membrane permeability of compounds found inside the Golden Triangle are more likely to be present than others outside.

According to the Golden Triangle (Fig. 8), the most of compounds under study are located within of it, indicating that these 1,3,5-triazine derivatives have good permeability and clearance [66]. The other compounds are the reverse, consisting of six compounds: 1,3,5,9, 20 and 22.

Fig. 8

Permeability and clearance patterns in vitro for MW and logD.

3.4.1 ADME study of new designed compounds

Table 8 lists the physicochemical parameters of novel designed compounds. All of the proposed compounds’ LogP and HBA values which indicate that they have a fair absorbency and resulting in an increase in the electrostatic interactions of the 1,3,5-triazine derivatives with the amino acid residues in the active sites. They were in great accord with the most important rules of drug similarity e.g. Lipinski, Veber and Lipophilicity indices.

Table 8
Drug-likeness of the new designed compounds and reference compounds

Comp Lipinski’s rules Veber’s rules Lipophilicity indices

MW ≤ Log HBD HBA Lipinski NBR TPSA Veber LE LLE NH

500Da p≤5 ≤5 ≤10 score ≤10 ≤140 Å2 score

C 1 361.83 0.19 3 6 4 7 87.94 2 0.350 6.061 25

C 2 361.83 0.19 3 6 4 7 87.94 2 0.352 6.101 25

C 3 363.86 0.38 3 6 4 7 87.94 2 0.419 6.811 24

C 4 343.45 0.76 3 6 4 7 87.94 2 0.414 6.337 24

C 5 382.84 –0.13 3 7 4 7 87.94 2 0.414 7.515 25

C 6 342.46 0.44 3 6 4 7 87.94 2 0.442 7.134 24

Comp.10 347.80 0.04 3 7 4 6 97.17 2 0.350 5.964 24

Comp	Lipinski’s rules	Veber’s rules	Lipophilicity indices
C 1	361.83	0.19	3	6	4	7	87.94	2	0.350	6.061	25
C 2	361.83	0.19	3	6	4	7	87.94	2	0.352	6.101	25
C 3	363.86	0.38	3	6	4	7	87.94	2	0.419	6.811	24
C 4	343.45	0.76	3	6	4	7	87.94	2	0.414	6.337	24
C 5	382.84	–0.13	3	7	4	7	87.94	2	0.414	7.515	25
C 6	342.46	0.44	3	6	4	7	87.94	2	0.442	7.134	24
Comp.10	347.80	0.04	3	7	4	6	97.17	2	0.350	5.964	24

The number of rotatable bonds 7(NBR < 10), hydrogen bond acceptor 6 or 7 (HBA < 10) and octanol/water partition coefficients (Log p < 5) are used to forecast a compound’s lead-likeness. When compared to the reference compound 10, these compounds showed no discomfort, indicating that they have good drug likeness properties.

4 Conclusion

Starting with a comparison between the spectroscopic parameters of 1,3,5-triazine with different calculation methods showed that the B3LYP/6-31 G++(d,p) approach is sufficiently reliable. Then by studying the benchmarks on the structure and electron density of 1,3,5-triazine, we validated the use of DFT B3LYP/6-31 G++(d,p) to study the drug Likeness Screening and the structure activity-relationship for a series of 1,3,5-triazine derivatives that are known to be inhibitors of pfdhfr. The both methods MLR and ANN were used to create QSAR models. The constructed models showed a strong connection between experimental and anticipated pIC₅₀ values, demonstrating its great predictive capacity. We have also created and proposed some novel compounds that could have a wide range of applications. As a result, this model can be used to predict the inhibitory activity of this class of compounds (1,3,5-triazine derivatives) against PFDHFR. Our work shows the use of multi-parameter optimization desirability score that the series and new compounds obey the Lipinski’s and Viber’s rules, lipophilicity indices and golden triangle rules showed that the majority of these compounds exhibit improved permeation, intestinal permeability, and oral bioavailability, as well as desirable in vitro ADME and safety properties [65].

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