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...

Machine learning (ML) algorithms are gaining importance in the processing of chemical information and modeling of chemical reactivity problems. In this work, we have developed a perturbation-theory and machine learning (PTML) model combining perturbation theory (PT) and ML algorithms for predicting the yield of a given reaction. For this purpose, we have selected Parham cyclization, which is a general and powerful tool for the synthesis of heterocyclic and carbocyclic compounds. This reaction has both structural (substitution pattern on the substrate, internal electrophile, ring size, etc.) and operational variables (organolithium reagent, solvent, temperature, time, etc.), so predicting the effect of changes on substrate design (internal elelctrophile, halide, etc.) or reaction conditions on the yield is an important task that could help to optimize the reaction design. The PTML model developed uses PT operators to account for perturbations under experimental conditions and/or structural variables of all the molecules involved in a query reaction, compared to a reaction of reference. Thus, a dataset of >100 reactions has been collected for different substrates and internal electrophiles, under different reaction conditions, with a wide range of yields (0-98%). The best PTML model found using General Linear Regression (GLR) has R = 0.88 in training and R = 0.83 in external validation series for 10 000 pairs of query and reference reactions. The PTML model has a final R = 0.95 for all reactions using multiple reactions of reference. We also report a comparative study of linear versus nonlinear PTML models based on artificial neural network (ANN) algorithms. PTML-ANN models (LNN, MLP, RBF) with R ≈ 0.1-0.8 do not outperform the first PMTL model. This result confirms the validity of the linearity of the model. Next, we carried out an experimental and theoretical study of nonreported Parham reactions to illustrate the practical use of the PTML model. A 500 000-point simulation and a Hammett analysis of the reactivity space of Parham reactions are also reported.

Predicting the activity of new chemical compounds over pathogenic microorganisms with different metabolic reaction networks (MRN s ) is an important goal due to the different susceptibility to antibiotics. The ChEMBL database contains >160 000 outcomes of preclinical assays of antimicrobial activity for 55 931 compounds with >365 parameters of activity (MIC, IC50, etc.) and >90 bacteria strains of >25 bacterial species. In addition, the Leong and Barabàsi data set includes >40 MRNs of microorganisms. However, there are no models able to predict antibacterial activity for multiple assays considering both drug and MRN structures at the same time. In this work, we combined perturbation theory, machine learning, and information fusion techniques to develop the first PTMLIF model. The best linear model found presented values of specificity = 90.31/90.40 and sensitivity = 88.14/88.07 in training/validation series. We carried out a comparison to nonlinear artificial neural network (ANN) techniques and previous models from the literature. Next, we illustrated the practical use of the model with an experimental case of study. We reported for the first time the isolation and characterization of terpenes from the plant Cissus incisa. The antibacterial activity of the terpenes was experimentally determined. The more active compounds were phytol and α-amyrin, with MIC = 100 μg/mL for Vancomycin-resistant Enterococcus faecium and Acinetobacter baumannii resistant to carbapenems. These compounds are already known from other sources. However, they have been isolated and evaluated for the first time here against several strains of multidrug-resistant bacteria including World Health Organization (WHO) priority pathogens. Last, we used the model to predict the activity of these compounds versus other microorganisms with different MRNs in order to find other potential targets.

The competition between C À H activation and Heck reactions has been studied on 2-alkenylsubstituted o-iodobenzylpyrroles. The reaction can be switched from the alkene to the pyrrole nucleus by choosing the adequate catalytic system, regardless of the nature of the substituent on the alkene, obtaining excellent yields of pyrroloA C H T

The Parham cyclization-intermolecular α-amidoalkylation sequence results in the facile enantioselective synthesis of 12b-substituted isoindoloisoquinolines (ee up to 95%) using BINOL-derived Brønsted acids. α-Amidoalkylation of indole occurs through the formation of a chiral conjugate base/bicyclic quaternary N-acyliminium ion pair.