Aiming to assess the role of individual molecular structures in the molecular mechanism of ligand-receptor interaction correlation analysis, the recent Spectral-SAR approach is employed to introduce the Quantum-SAR (QuaSAR) "wave" and "conversion factor" in terms of difference between inter-endpoint inter-molecular activities for a given set of compounds; this may account for inter-conversion (metabolization) of molecular (concentration) effects while indicating the structural (quantum) based influential/detrimental role on bio-/eco-effect in a causal manner rather than by simple inspection of measured values; the introduced QuaSAR method is then illustrated for a study of the activity of a series of flavonoids on breast cancer resistance protein.

In the context of quantitative structure–activity relationship (QSAR) studies the traditional statistical indices, i.e. simple correlation factor, standard error of estimates, as well as t-Student and Fisher's tests are challenged against the algebraic spectral description of the multi-linear models. While the new correlation approach is built on the algebraic (Euclidian) norms and on the associate correlation factor, the validation and predictive features are assured throughout so-called "ergodic" least action principle across the investigated models. The reliability of the present proposed spectral respecting statistical QSAR analysis is evaluated on modeling the aliphatic amines' ecotoxicity by means of hydrophobicity, polarizability, and total energy structural parameters resulting in better prediction of molecular hierarchy of observed bioactivity being susceptible to such general behavior.

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.

Combined experimental and quantitative structure inter-activity relationship (QSIAR) computation methods were advanced in order to establish the structural and mechanistic influences that steroids and triterpenes, either as newly synthesized or naturally isolated products, have on human HT1080 mammalian cancer cells. The main Hansch structural indicators such as hydrophobicity (LogP), polarizability (POL) and total energy (Etot) were considered and both the structure-projected as well as globally computed correlations were reported; while the inter-activity correlation of the global activity with those projected on structural information was revealed as equal to the direct structural-activity one for the trial sets of compounds, the prediction for the testing set of molecules reported even superior performances respecting those characteristic for the calibration set, validating therefore the present QSInAR models; accordingly, it follows that the LogP carries the most part of the cytotoxic signal, while POL has little influence on inhibiting tumor growth—A complementary behavior with their earlier known influence on genotoxic carcinogenesis. Regarding the newly hemisynthetic compounds it was found that stigmasta-4,22-dien-3-one is not adapted for cell membrane diffusion; it is recommended that aminocinnamyl chlorohydrate be further modified in order to acquire better steric influence, while aminocinnamyl-2,3,4,6-O-tétraacétyl-α-D-glucopyranoside was identified as being inhibited in the tumor cell by other molecular mechanisms–here not revealed–although it has a moderate-high anti-cancer structurally predicted activity.

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