Quantum chemical descriptors in the QSAR studies of compounds active in maxima electroshock seizure test

1 Introduction

Quantitative structure-activity relationship study (QSARs) seeks to change drug development process from trial and error format, chemical intuition and experience into a form that can be mathematically computed. It establishes a relationship (a model) between quantifiable molecular properties and biological activity of molecules (Arthur et al., 2016). This model can be used to screen compounds for the studied properties and optimize existing molecules to improve their activity. It is an approach that manages resources and speeds up the process of new molecule development(Arthur et al., 2016). Quantum chemical (QC) calculations are attractive sources for molecular properties. It gives reliable information on all electronic and geometric properties of molecules and their interactions (Choudhary and Sharma, 2014). Many authors had reported the application of quantum descriptors in QSAR/QSPR studies (Olariu et al., 2013; Stachowicz et al., 2014).

Epileptic convulsion occurs as a result of an imbalance between excitatory and inhibitory neurotransmission in the central nervous systems (Ghidini et al., 2006). It is affecting about 1% of the world population and about 30% of those affected do not respond to marketed antiepileptic drugs (AEDs) (Ghidini et al., 2006). As a result of this and many unwanted side effect, the search for a more potent and cheaper anticonvulsant is a continuous endeavor (Stafstrom, 2006). Some 2-amino-N-benzylacetamides were reported to be effective in maximal electroshock seizure (MES) test (King, 2011) which is one of the animal models used in evaluating the anticonvulsant activity of molecules. The objective of the study is to conduct QSAR analysis on these compounds and use the model obtained to screen other known or hypothetical compounds with unknown activities.

2 Materials and methods

3 Result and discussion

3.1

3.1 Dataset structure

72 training set and 18 test set compounds were reported by the dataset division technique used in the study. The test compounds are marked with the letter a superscript in Table 1. Descriptive statistics performed on the two set showed that showed that the test set maximum was less than the training set maximum; the test set minimum was greater than the training set minimum (Table 2). In addition, other parameters reported in the table were similar for both sets. This indicated that the KS algorithm method used study successfully obtain the test set data within the activity range of the training set. Dissimilarity analysis depicted in Fig. 1. showed that the test set compounds descriptor spaces were within the training set descriptors space.

Table 2 Training and test set data descriptive statistics.

Parameters	Training	Test
Mean	4.109	3.907
Standard Deviation	0.464	0.374
Sample Variance	0.215	0.140
Range	2.281	1.764
Minimum	2.728	3.169
Maximum	5.009	4.933

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Fig. 1

Diversity analysis of database compounds.

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3.2

3.2 QSAR model and quality

The model reported in the study is presented below:

(6)

$$\text{pED}50=2.889(+/-0.171)+0.006(+/-0.078){\text{d}}_{\text{x}}+0.179(+/-0.173)\mathrm{\Delta }\mathrm{\epsilon }+0.107(+/-0.121)\mathrm{\Omega }+1.002(+/-0.093){\mathrm{\Phi }}^2+0.427(+/-0.161){\mathrm{\beta }}^2-1.044(+/-0.126){\text{T}}^{\text{E}}-0.801(+/-0.098)\text{QH}+1.785(+/-0.127)\text{QN}$$ The model was obtained from 72 training set compounds and it contained 8 descriptors, therefore, it passed the Topliss ratio test and obeyed the QSAR semi-empirical rule of thumb (Damme and Bultinck, 2007). The model was used to predict the activity values for both training and test reported in Table 1. The plot of SDR against the experimental activity value (Fig. 2) showed that the residuals were evenly distributed around the line SDR = 0, indicating the absence of systematic error in the model (Arthur et al., 2016).

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Fig. 2

Distribution of residual around line SDR equal zero.

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The plot of predicted versus experimental activity by the model (Fig. 3) showed that a linear relationship existed between the two variable and the model had good internal prediction ability. The multi-co-linearity analysis result the highest VIF value for descriptors in the model was 5.097, indicating the model was acceptable and void of the multi-co-linearity problem (Beheshti et al., 2016) (Table 3).

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Fig. 3

Predicted versus experimental activity value.

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Table 3 Descriptors correlation matrix, variance inflation factor and standardized regression coefficient.

	dx	Δ∊	Ω	Ф2	β2	TE	QH	QN	VIF
dx	1								1.3066
Δ∊	0.1069	1							5.0971
Ω	0.0484	−0.753	1						3.9656
Ф2	0.0979	−0.579	0.4437	1					1.9536
β2	−0.148	−0.774	0.7170	0.5734	1				3.3930
TE	−0.281	−0.623	0.6297	0.3902	0.6728	1			3.0683
QH	−0.010	0.0712	0.2013	0.1379	0.0181	0.3597	1		1.7048
QN	−0.072	−0.234	−0.109	0.2134	−0.003	0.1134	−0.128	1	1.4756

3.4

3.4 Model applicability domain

The warning leverage for the model h^∗ was 0.375. Therefore, the AD of the model is defined by a square area bounded by 0 < h < 0.375 and −3 < SDR < 3 as presented pictorially by the models Williams plot (Fig. 4). All the dataset compounds were within the AD of the model. Therefore the dataset was void of outliers.

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Fig. 4

Williams plot for the model.

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4 Interpretation of descriptors

Calculated descriptors for each molecule in the dataset are presented in Table 5. X-component of molecular dipole moment (d_x) is the first descriptor in the model and is positively correlated with the activity of the studied compounds. It is an index of molecular polarity that explains the charge distribution in the molecule which an essential factor a molecule requires to bind to a biological receptor molecule (Cartier and Rivail, 1987). The value of dipole moment is a function of the differences in the electronegativity of connected atoms and distance between them. It has been reported that addition of bulky group and increase in the symmetry of a molecular system decrease the dipole moment (Singh, 2013).

Higher dipole moment observed for molecules 1, 2, 3 and others may be attributed to the addition of bulky electron loving groups like 1-fluoro-2-(methoxymethyl)benzene; benzyl(methyl)sulfane est. to the parent2-amino-N-benzylacetamide. On the other hand, reduced dipole moment observed for molecules 86–89 may be due to increase in the symmetry of the parent molecule (Table 5). The observed dipole was proportional activity value.

The energy difference between the ∊HOMO and ∊LUMO termed energy gap (Δ∊) (Parthasarathi et al., 2004) is contained in the model and positively correlated to the activity value. It explains charge transfer interaction within the molecule in which a portion of the molecule with higher HOMO donate electrons to that portion with higher LUMO. This is a reflection of the chemical activity of the molecule (Parthasarathi et al., 2004). Addition of larger substituent to a molecular system induces a decrease in Δ∊ value. Localization of HOMO and LUMO at the same site reduces the reactivity of the molecule (Galeazzi et al., 2002). Lower value of Δ∊ was observed for molecule 1, 2, and others with larger substituent added to the parent and higher value of Δ∊ was observed for molecules 86–89. However, lower activity value observed for molecules 86–89 may be due localization of their HOMO and LUMO at the same sites (Fig. 5).

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Fig. 5

(a) HOMO-LUMO energy diagram of molecule 1, (b) HOMO-LUMO energy diagram of molecule 88.

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Electrophilicity index (Ω): the ratio of one half of the square chemical potential to chemical hardness. It is a measure of energy lowering due to maximal electron flow between a donor and acceptor (Parr et al., 1999). It is used to quantitatively classify a molecule as global electrophile within a relative scale (Parthasarathi et al., 2004). A molecule with higher electrophilicity index will act as an electrophile in a reaction, while, those with lower electrophicity index will act as a nucleophile (Chattaraj et al., 2003). A higher value of (Ω) was observed for molecule 1 and other with larger substituent added to the parent (Table 5). Hence, they have a tendency to act as a nucleophile. Lower value of (Ω) was observed for molecules 86–89. Thus, have a tendency to act as the electrophile in a bimolecular reaction. Interaction of molecule 1 and 88 with γ-aminobutyrate aminotransferase (a known target for anticonvulsant) (Fig. 6), showed that the added substituent contributed to the increased activity value observed in molecule 1.

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Fig. 6

(a).

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Other descriptors in the model include square of molecular ovality (ф²) which is a descriptor quantifying the van der Waals molecular shape of the molecules (Olariu et al., 2013). It is positively correlated to the activity of studied compounds. Higher value ф² was observed for molecule 1 and its counterpart. This was in tandem with the activity values of the compound. Anisotropy of the polarizability of a molecule (β²) is another descriptor in the model obtained as the summation of the diagonal element of the polarizability matrix. It’s related to molar volume, hydrophobicity and characterizes the properties of a molecule to accept electron (Karelson et al., 1996). A higher value of β² was observed for molecule 1 and its counterpart.

Topological electronic index (T^E) was obtained from the charges on all atoms that made up a molecule (karelson et al., 1996) and it's negatively correlated to the activity of studied compounds. The square root of the sum of the square of charges on all hydrogen atoms (QH) is yet another descriptor in the model and it’s negatively correlated with the activity of the studied compounds. The final descriptor in the model is QN i.e. the square root of the sum of the square of charges on all nitrogen atoms in a molecule. It’s positively correlated with the activity of studied compounds. This indicated addition of nitrogen-containing substituent increases the activity values of the studied compounds. A molecule with additional N-atom in their system had a high value of QN e.g. molecule, 11, 18 and 20 (Table 1).

5 Conclusion

Quantum mechanics derived descriptors was used to conduct quantitative structure-activity relationships study on some 2-amino-N-benzylacetamide derivatives. The result showed dx; Δ∊; Ω; Ф2; β²; T^E; QH and QN molecular descriptors to influence the anticonvulsant activity of the studied compounds. These descriptors showed that increasing the bulkiness of the molecule and addition of nitrogen-containing substituent electronegative element in the molecular system enhances the anticonvulsant activity of the studied compounds. The model produced in the study had good performance in term of it validation parameters and can be used to screen compounds for anticonvulsant activity in MES test.