General Theory for Multiple Input-Output Perturbations in Complex Molecular Systems. 1. Linear QSPR Electronegativity Models in Physical, Organic, and Medicinal Chemistry

Abstract

In general perturbation methods starts with a known exact solution of a problem and add "small" variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor's quantum model, Heisenberg's matrix mechanincs, Feyman diagrams, and Poincare's chaos model or "butterfly effect" in complex systems are examples of perturbation theories. On the other hand, the study of Quantitative Structure-Property Relationships (QSPR) in molecular complex systems is an ideal area for the application of perturbation theory. There are several problems with exact experimental solutions (new chemical reactions, physicochemical properties, drug activity and distribution, metabolic networks, etc.) in public databases like CHEMBL. However, in all these cases, we have an even larger list of related problems without known solutions. We need to know the change in all these properties after a perturbation of initial boundary conditions. It means, when we test large sets of similar, but different, compounds and/or chemical reactions under the slightly different conditions (temperature, time, solvents, enzymes, assays, protein targets, tissues, partition systems, organisms, etc.). However, to the best of our knowledge, there is no QSPR general-purpose perturbation theory to solve this problem. In this work, firstly we review general aspects and applications of both perturbation theory and QSPR models. Secondly, we formulate a general-purpose perturbation theory for multiple-boundary QSPR problems. Last, we develop three new QSPR-Perturbation theory models. The first model classify correctly >100,000 pairs of intra-molecular carbolithiations with 75-95% of Accuracy (Ac), Sensitivity (Sn), and Specificity (Sp). The model predicts probabilities of variations in the yield and enantiomeric excess of reactions due to at least one perturbation in boundary conditions (solvent, temperature, temperature of addition, or time of reaction). The model also account for changes in chemical structure (connectivity structure and/or chirality paterns in substrate, product, electrophile agent, organolithium, and ligand of the asymmetric catalyst). The second model classifies more than 150,000 cases with 85-100% of Ac, Sn, and Sp. The data contains experimental shifts in up to 18 different pharmacological parameters determined in >3000 assays of ADMET (Absorption, Distribution, Metabolism, Elimination, and Toxicity) properties and/or interactions between 31723 drugs and 100 targets (metabolizing enzymes, drug transporters, or organisms). The third model classifies more than 260,000 cases of perturbations in the self-aggregation of drugs and surfactants to form micelles with Ac, Sn, and Sp of 94-95%. The model predicts changes in 8 physicochemical and/or thermodynamics output parameters (critic micelle concentration, aggregation number, degree of ionization, surface area, enthalpy, free energy, entropy, heat capacity) of self-aggregation due to perturba...

Experimental Study and ANN Dual-Time Scale Perturbation Model of Electrokinetic Properties of Microbiota

“…The other type refers to the Box-Jenkins Operators (or perturbation values) ΔV ϕ (t k ), t k representing the time scale t 1 and t 2 , while V ϕ is V q or V f , respectively. In addition, the MA component was used to account for the dispersion of variables (Gonzalez-Diaz et al, 2013). In the present work, the terms < V ϕ (t k )> are the MA of the variable V ϕ (t k ) in one of the original combinatorial experimental conditions with the format of 4 ST × 3 SSA.…”

“…The main feature of PT is to break the sophisticated issue into “perturbation” or “solvable” components. Our group has developed different PT models that start with a known solution to a problem and add corrections considering the variations of various experimental conditions (c j ) (Gonzalez-Diaz et al, 2013). In the context of Cheminformatics, the effect of these deviations has been quantified using Moving Average (MA) operators.…”

Latest advances in molecular topology applications for drug discovery

“…The perturbation methods consist in adding a measured increase to the independent variable and observing how the dependent one varies as a function of that increase [62]. First of all, the molecular descriptors are calculated using a descriptor, D i , of a given hit compound employing different software.…”

Model for Vaccine Design by Prediction of B-Epitopes of IEDB Given Perturbations in Peptide Sequence, In Vivo Process, Experimental Techniques, and Source or Host Organisms

“…Epitopes. Very recently Gonzalez-Diaz et al [58] formulated a general-purpose perturbation theory or model for multipleboundary QSPR/QSAR problems. We adapted here this new theory or modeling method to approach to the peptide prediction problem from the point of view of perturbation theory.…”

“…Perturbation models have been widely used in all branches of science from QM to astronomy and life sciences including chaos or "butterfly effect, " Bohr's atomic theory, Heisenberg's mechanics, Zeeman's and Stark's effects, and other models with applications in like protein spectroscopy and others [53][54][55][56][57]. In a very recent work Gonzalez-Diaz et al [58] formulated a general-purpose perturbation theory or model for multiple-boundary QSPR/QSAR problems. However, there is not report in the immunoinformatics literature of a general QSPR perturbation model for IEDB B-epitopes.…”