Physicochemical properties and structural features of chemical compounds control their biological activities [1] . For example, the ability of a molecule to cross cell membranes or dissolve in fatty tissues is closely related to its lipophilicity [2] . Likewise, ability of a molecule to form stable complexes and/or react with biological molecules is directed by its electronic distribution [3] . Quantum mechanical descriptors (QMD) such as the energy of the highest occupied molecular orbital ε_HOMO, the energy of the lowest unoccupied molecular orbital ε_LUMO, electronegativity (χ), hardness (η), softness (S), electrophilicity index (ω) have been used in the elucidation of the chemical reactivity [4] [5]. QMD can be divided into two kinds: global descriptors which describe whole molecule such as electrophilic index and dipole moment and local descriptors which describe parts of molecule such as Mullikan atomic charge and Fukui function [6]. Density functional theory (DFT) beside semi empirical PM3 method has been used fairly successful in elucidation of molecular properties and chemical reactivity [7]. In the present study, we report a detailed quantum mechanical study of electronic dispositions of five aminopyrimidoisoquinolinequinones (APIQs) [8] which cluster together when a larger data set of congeneric 27 APIQs was subjected regression clustering as previously reported by our group [9]. Both semi empirical PM3 method and DFT methods were used to calculate several global and local QMDs for these compounds in attempt to rationalize and explain the variability of biological response as a consequence of electronic environment.

Software:

Gaussian 5.0.8 was used to draw/optimize of structures and for DFT calculation of Fukui functions basis set 3 - 21 G and B3LYP method [10]. Arguslab 4 and Molecular Operation Environment (MOE) 2008 softwares were used to calculate Mullikan charge and global descriptors [11]. Statistical analysis was performed using Microsoft Excel 2010 program.

Data set:

The biological activity used in the present study is the anticancer activities of compounds 5, 17, 18, 19 and 23 which are extracted from a larger data set through a reported clustering procedure [9]. We maintain the original numbering as appeared in the previous paper. The cancer cell line used is human gastric adenocarcenoma (AGS) cell line. Biological response is expressed as the inhibitory concentration of 50% of the subjects IC₅₀. The structures and biological activities of the APIQ’s are shown in Table 1.

Figure 1 shows the optimized chemical structures of molecules.

Global electronic descriptors

Table 2 contains the most significant global electronic descriptors of the five APIQs under study. Table 3 shows the correlation matrix between these descriptors including the response.

The correlation matrix between the global electronic descriptors and biological activity, demonstrates that the global dipole moment gives the highest correlation. The QSAR equation can be written as the following:

IC 5 0 = 0.3255   dipo + 1.9086 (1)

n = 5, R² = 0.88, s = 4.9, F = 23.8

It is clear from the data in Table 3 that dipole moment explains up to 88% the variability of the response while electrophilicity index explains up to 86%. These two descriptors are collinear (property spaces overlap to the extent of 72%). The unexplained variability by them combined amount to 16%. This could be attributed to communal effect of the rest of descriptors on variability.

It should be noted that there is a high collinearity between GAP and the electrophilicity index. Molecule 23 has the highest GAP (0.525) with the highest ω (1.731254) whereas molecule 18 has the lowest GAP (0.038) with the lowest ω (0.083993).Thus GAP explains the same variability as ω. GAP is pictorially rendered in Figure 2 to get a feel of the cause of partitioning of this particular set of molecules in one and the same cluster.

Local electronic descriptors

The local environment may be considered by looking at certain atoms around the molecule. We considered N-5, C-6 and C-8 in addition to the nitrogen atom of phenylamino side group at C-8.

Using the PM3 semi-empirical method, the value of Mullikan charge MC remain the same for all these atoms except for C-6 (Table 4), where a significant linear correlation was discerned (R² = 0.6) with the logarithm of the IC₅₀ as depicted in Figure 3.

This shows that this carbon is active in spite of its full valence through its presence in the aromatic ring system in addition to its bonding to methyl group. The reason for this is not far-fetched; The presence of a methyl group adjacent

to the nitrogen of the pyridine part of the chromophore may cause a Chichibabin-type tautomerism to occur in the following manner [12] :

This tautomerism imparts a chemical reactivity which traces the variability of the biological activity to the extent of 60%. Moreover, there an additional element to add to the reactivity which the generation of an enamine scaffold in situ [13]. This opens a whole perspective of chemical reactivity which might even suggest alkylation aspect of the mechanism of action of this particular group of APIQs.

To get a more accurate picture of the above mentioned argument, we used DFT method to calculate the following Fukui functions: forward Fukui function f⁺, backward Fukui function f⁻and neutral Fukui function f⁰ for nucleophilic, electrophilic and radical attacks respectively. These functions are calculated as follows [14] :

For nucleophilic attack:

f + = q a ( N e l + 1 ) − q a ( N e l ) (2)

For electrophilic attack:

f − = q a ( N e l ) − q a ( N e l − 1 ) (3)

For radical attack:

f 0 = q a ( N e l + 1 ) − q a ( N e l − 1 ) / 2 (4)

In these equations q_a is the atomic charge (evaluated from Mullikan population analysis) at the jth atomic site in the neutral (N), anionic (N + 1) or cationic (N − 1) chemical species. We calculated Fukui function for our 5 APIQs and the results are summarized in Table 5.

We correlated Fukui functions for atoms N-5, C-6, C-8 and N-atom of 8-phenylamino side group each with the response. The outcomes (as R²) of these correlations are summarized in Figure 4.

Upon examining the value of R² summarized in Figure 4, the following remarks could be made:

· N-5: it is apparent that this atom is prone to nucleophilic attack, i.e., it is an electron deficient atom or an electrophilic site. This is to be expected as tuatomer b generated by Chichibabin-type tautomerism (Figure 5) contains a secondary amino group with a free lone pair of electron which could easily

be protonated to enhance nucleophilic attack as already indicated in Figure 5.

· C-6: also exhibits similar behavior because of the presence of electrophilic N-5 atom which withdraws electron density from it. Reviewing the value of Fukui functions for the five APIQs shows that compound 5 in which there is no methyl group at C-6 has the highest f⁺ value indicative that this position is open to nucleophilic attack to a degree of forming a full-fledge covalent bond, moreover, it is well-known that isoquinoline nucleus undergoes nucleophilic aromatic substitution at position 1 in pyridine ring which correspond to C-6 in isoquinoline [15] . While the other four compounds, owing to the covalent bond to the methyl group, might enter into an electrostatic interaction with electron rich center in the receptor. Thus we can say that the enamine in tautomer b (Figure 5) is complimentary with an electrophilic pocket in the receptor.

· C-8: Upon concentrating on C-8 and we notice the R² values for f⁺ and f⁰ = 0.98 and 0.9 respectively. This is easily justifiable by noting that this atom is a part of α,β-unsaturated carbonyl system and may constitute a Michael acceptor [16], Figure 6, which represents an electron deficient site. The same electron deficient site is attractive for free radicals which give justification of the high value of f⁰.

· N-phenyl group: As for the N atom of 8-phenylamino group the R² value of f⁻ and f⁺ of 0.9 and 0.67 respectively may indicate a protonation equilibrium as such (Figure 7):

The variability in chemical reactivity for present set of APIQ (five molecules) has been studied using global and local descriptors. Dipole moment, as a global descriptor, demonstrated a high correlation with the biological activity. The Mullikan charge for C-6, as a local descriptor, showed that this carbon atom is active in spite of its full valence through its presence in an aromatic ring system in addition to its bonding to a methyl group as presence of methyl group adjacent to the nitrogen of the pyridine part of the chromophore may cause a Chichibabin-type rearrangement. The correlation between IC₅₀ and Fukui functions for atoms N-5, C-6, C-8 and N-atom of 8-phenylamino side group is consistent with variation in chemical behavior for each atom.

The authors declare no conflicts of interest regarding the publication of this paper.

Sultan, M.Q.S., El-Faki, M.O. and Mohammed, I.O.K. (2023) Detailed Quantum Mechanical QSAR Analysis of Certain Aminopyrimidoisoquinolinequinones with Anticancer Activity. Computational Chemistry, 11, 24-35. https://doi.org/10.4236/cc.2023.111002