Introducing catastrophe-QSAR. Application on modeling molecular mechanisms of pyridinone derivative-type HIV non-nucleoside reverse transcriptase inhibitors

Abstract

The classical method of quantitative structure-activity relationships (QSAR) is enriched using non-linear models, as Thom's polynomials allow either uni- or bi-variate structural parameters. In this context, catastrophe QSAR algorithms are applied to the anti-HIV-1 activity of pyridinone derivatives. This requires calculation of the so-called relative statistical power and of its minimum principle in various QSAR models. A new index, known as a statistical relative power, is constructed as an Euclidian measure for the combined ratio of the Pearson correlation to algebraic correlation, with normalized t-Student and the Fisher tests. First and second order inter-model paths are considered for mono-variate catastrophes, whereas for bi-variate catastrophes the direct minimum path is provided, allowing the QSAR models to be tested for predictive purposes. At this stage, the max-to-min hierarchies of the tested models allow the interaction mechanism to be identified using structural parameter succession and the typical catastrophes involved. Minimized differences between these catastrophe models in the common structurally influential domains that span both the trial and tested compounds identify the "optimal molecular structural domains" and the molecules with the best output with respect to the modeled activity, which in this case is human immunodeficiency virus type 1 HIV-1 inhibition. The best molecules are characterized by hydrophobic interactions with the HIV-1 p66 subunit protein, and they concur with those identified in other 3D-QSAR analyses. Moreover, the importance of aromatic ring stacking interactions for increasing the binding affinity of the inhibitor-reverse transcriptase ligand-substrate complex is highlighted.

Keywords: HIV-1 inhibitory activity; QSAR structural domains; Thom’s catastrophe polynomials; minimum statistical paths; statistical factors.

Figure 1

Gaussian (G) and non-Gaussian (NG) screening of the observed activities of the working molecules in Table 4 grouped into trial and test congener series.

Figure 2

3D-representations of the QSAR and catastrophe activities for the tested models of Table 11 in the range of the structural indicators (Log P, Pol, H) as abstracted from Table 4.

Figure 3

Determination of the structural domains of pyridinone-derivative type non-nucleoside reverse transcriptase inhibitors in the same range of structural descriptors by employing the principles of hydrophobicity, minimum polarizability, binding energy, and the minimum difference between the polynomial activity models of Figure 2; the hydrophobic pocket was identified in the p66 subunit of HIV-1-rt of specific transferase R221239 [48,49].