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.

Chemical Structure-Biological Activity Models for Pharmacophores’ 3D-Interactions

“…As a consequence, neuro-self-organization is correspondingly advanced by the reduction of the archetypal precursor of epileptic seizures to cusp synergetics [ 65 ]. Lastly, but not least, the catastrophe approach enters chemistry through the need to unitarily characterize chemical bonding through elementary processes, leading to the so-called bonding evolution theory; it also triggered the reformulation of the electronic localization functions [ 66 , 67 ]. Catastrophe theory was nevertheless successfully grounded on Hilbert space modeling with the aid of density matrix and non-linear evolution-specific tools including non-commutative (quantum open) systems [ 68 ].…”

Determining Chemical Reactivity Driving Biological Activity from SMILES Transformations: The Bonding Mechanism of Anti-HIV Pyrimidines

“…Note that the Euclidean distance itself employs the square of the correlations factors, i.e. , a higher order statistical framework, which nevertheless may be further enriched with other statistical outputs and factors, although all directly or indirectly depend on the correlation factor [155].…”

Structure and function relationships of proteins based on polar profile: a review.

“…It requires strategies where it is possible to identify minimal regularities. Within the group of Supervised learning algorithms there are some that focus on relating chemical structure to biological activity, evaluating only one physico-chemical property and obtaining the best results in the identification of the main action or function of a protein, these algorithms are called Quantitative structure-activity relationship models (QSAR models) (Putz et al, 2011). The more than 80 QSAR algorithms known (Qureshi et al, 2014) use physico-chemical metrics involving the linear representation and/or the 3D structure of the protein and evaluate one or more properties simultaneously.…”