This work demonstrates that the transport properties of various organic substances in the gas phase, such as viscosity and thermal conductivity coefficients, can be estimated with acceptable accuracy by using 1D-QSPR models, which allow for the prediction of the studied property based solely on the chemical composition of the molecule. Here, we studied the transport properties (viscosity coefficient and thermal conductivity coefficient) of organic compounds for sufficiently representative database including approximately 5,000 carbon-, halogen-, oxygen-, nitrogen-, and sulfur-containing compounds. Using a simplex approach for modeling molecular structure and machine learning methods, such as multiple linear regression (MLR) and random forest (RF), adequate 1D QSPR models for the transport properties of individual substances in the gas phase were developed for the formed databases. Analysis of the influence of certain structural and physicochemical factors on the studied transport properties of organic compounds was carried out. Based on the developed 1D RF QSPR models, a computer expert system for predicting the viscosity coefficients and thermal conductivity of new substances was created.

The aim of this work is to analyze the influence of the structure of organic compounds on their ability to penetrate the blood-brain barrier (BBB) using the values of LogPS (logarithm of the product of permeability and surface area of metabolism, which is a measure of the transfer of compounds from the blood to the brain and reflects the degree of penetration of the substance into the brain without relative binding to proteins). The study of the permeability of BBB is necessary both for the development of new drugs for which the CNS is a biointerference, and for the development of effective ways of treating diseases of the brain.

The analysis of the relative role of polar and non-polar factors of the molecular structure on the penetration of substances through the blood–brain barrier (BBB) was carried out. Such analysis will allow a preliminary approximate assessment of the ability of substances to cross the blood–brain barrier. Using previously developed computer expert systems on the basis of QSAR/QSPR models in the framework of simplex approach, the water solubility logSw (polar factor model), the lipophilicity logP (nonpolar factor model), and the characteristics of penetration through the blood–brain barrier (logBB, logPS, logP0PAMPA–BBB) were calculated for a set of 614 different organic compounds. It was determined whether substances belong to classes BBB+ or BBB– and whether these substances are substrates of P-glycoprotein (P-gl) or not (no-P-gl). Analysis of the distribution of the points of the investigated molecules in the logP vs. logSw coordinates revealed that lipophilicity and water solubility for the compounds with high penetrating ability should be approximately in following ranges: 3logP6; and –5logSw–1. For the data, which are presented in different scales, continuous scale and classification scale, a half-sign correlation coefficient Rss was calculated. Rss equals 0.93, that confirms the consistency of the results of the prognosis of Log BB parameters and classification BBB+/BBB–. The general trends in the classification of the investigated compounds according to the BBB+/BBB– and P-gl/no-P-gl classes were quantitatively estimated. The sign coefficient of association, which equals –0.35, emphasizes the antibatic nature of the relationship between the data of the two classifications.

2D PLS QSPR models for analyzing substance permeability across the blood-brain barrier (BBB) using PAMPA (artificial membrane permeability assay) are developed. Physico-chemical and structural interpretation of the constructed models is performed. It is shown that nitrogen-containing fragments and a significant part of oxygen-containing functional groups negatively affect the permeability of compounds across BBB. At the same time, aromatic fragments and halogens positively affect permeability. It is found that electrostatic factors have the highest effect on BBB permeability.

Quantitative structure–activity relationship (QSAR) study has been conducted on 36 terpene derivatives with anticonvulsant activity in timed pentylenetetrazole (PTZ) infusion test. QSAR models for anticonvulsant activity prediction of hydrazones and esters of some monocyclic/bicyclic terpenoids were developed using simplex representation of molecular structure (SiRMS; informational field [IF]) approach based on the SiRMS and the IF of molecule. Four 2D partial least squares QSAR consensus models were developed with the coefficient of determination for test sets Rtest2>0.62{R}_{\text{test}}^{2}\gt 0.62. Based on the established QSAR models, we found that carvone and verbenone cores possess the most significant contribution to antiseizure action examined on the model of PTZ-induced convulsions at 3 and 24 h after oral administration of terpene derivatives. Moreover, carbonyl and hydroxy group substitution in terpenoid molecules followed by hydrazones and esters formation leads to enhancement and prolongation of antiseizure action due to the contribution of additional molecular fragments. The presented QSAR models might be utilized to predict anticonvulsant effect among terpene derivatives for their oral administration against onset seizures.

Проблематика. Каталітична активність ензимів, що є їх найважливішою характеристикою, може суттєво змінюватися під впливом ефекторів, наприклад іонів металів, і є предметом спеціальних досліджень, що важливі для біохімії, біотехнології, медицини та інших галузей науки. Зазвичай активність ензимів за наявності металів оцінюють за зміною швидкості ферментативної реакції. Однак проведення подібних експериментальних досліджень, особливо для нових ензимів, як у випадку з пептидазою Вacillus thuringiensis var. israelensis IMV B-7465, потребує значних ресурсів і розгорнутих кіне­тичних досліджень. Тому доцільним є застосування методів комп’ютерної хімії, базовою задачею якої є пошук залежності “структура–властивість”, для побудови моделі, що матиме змогу з високою вірогідністю оцінити вплив іонів металів на активність пептидази. Мета. Розробка QSAR-моделей для аналізу і прогнозування впливу іонів металів на активність пептидази Вacillus thuringiensis var. israelensis IMV B-7465. Методика реалізації. Вплив іонів металів вивчали, визначаючи протеолітичну активність пептидази після сумісної інкубації впродовж 30 хв у 0,0167 M буферного розчину трис-HCl (рН 7,5, 37 °С). Кінцева концентрація хлоридів металів Li+; Na+; K+; Cs+; Cu2+; Be2+; Mg2+; Ca2+; Sr2+; Ba2+; Zn2+; Cd2+; Hg2+; Cr3+; Mn2+; Co2+; Ni2+ у буферному розчині становила 4 ммоль/дм3. Для пошуку кількісного зв’язку “структура–властивість” використовували довідкові дані про властивості іонів металів та методи тренд-вектора і випадкового лісу. Результати. Дослідження впливу іонів металів на протеолітичну активність пептидази Вacillus thuringiensis var. israelensis IMV B-7465 показало, що деякі іони металів (Li +, Mn2+ і Co2+) активували пептидазу, а інші (Cu2 +, Be2+, Cd2+, Hg2+, Cr3+) інгібували активність ензиму. Нелінійними методами тренд-вектора та випадкового лісу побудовано адекватні статистичні моделі без помилок класифікації та помилок прогнозу класу активності для тестового набору. Обидві моделі показують, що найважливішими характеристиками іонів металів, які мають вплив на активність ензиму, є електронегативність (ENPol), перший потенціал іонізації (IP1), ентропія іонів у водному розчині (S) та енергія спорідненості до електрона (Eae). Висновки. Методи QSAR-аналізу в сукупності з нелінійними методами тренд-вектора та випадкового лісу дають змогу адекватно описати вплив іонів металів на активність пептидази Вacillus thuringiensis var. israelensis IMV B-7465 за рахунок дескрипторів, що відображають певний баланс їхніх електронодонорних і електроноакцепторих властивостей (електронегативність, перший потенціал іонізації, енергія спорідненості до електрона) та ступінь структурованості гідратної оболонки (ентропія сольватації іонів). Обидва статистичних методи дають близькі значення важливості дескрипторів, але тільки метод тренд-вектора дає змогу проаналізувати напрям впливу конкретних характеристик іонів.

Background. The catalytic activity of enzymes, which is their most important characteristic, can change significantly under the influence of effectors, for example, metal ions, and is the subject of special studies that are important for biochemistry, biotechnology, medicine, and other branches of science. Usually, the activity of enzymes in the presence of metals is assessed by the change in the rate of the enzymatic reaction. However, conducting such experimental studies, especially for new enzymes, as in the case of peptidase Bacillus thuringiensis var. israelensis IMV B-7465, requires significant resources and extensive kinetic studies. Therefore, it is advisable to use the methods of computational chemistry, the basic task of which is to search for the structure–property relationship, to build a model that can assess the effect of metal ions on peptidase activity with a high degree of probability. Objective. We are aimed to develop QSAR models for analysis and prediction of the effect of metal ions on the activity of peptidase Bacillus thuringiensis var. israelensis IMV B-7465. Methods. The effect of metal ions was studied by determining the proteolytic activity of peptidase after co-incubation for 30 min in 0.0167 M Tris-HCl buffer solution (pH 7.5, 37 °C). The final concentration of metal chlorides Li+; Na+; K+; Cs+; Cu2+; Be2+; Mg2+; Ca2+; Sr2+; Ba2+; Zn2+; Cd2+; Hg2+; Cr3+; Mn2+; Co2+; Ni2+ in the buffer solution was 4 mmol/dm3. To search for the quantitative structure–property relationship, we used the reference data on the properties of metal ions, as well as trend vector and random forest methods. Results. A study of the effect of metal ions on the proteolytic activity of peptidase Bacillus thuringiensis var. israelensis IMV B-7465 showed that some metal ions (Li+, Mn2+ и Co2+) activated peptidase, while others (Cu2+, Be2+, Cd2+, Hg2+, Cr3) inhibited the enzyme activity. Adequate statistical models without classification errors and activity class prediction errors for the test set were constructed by nonlinear trend vector and random forest methods. Both models show that the most important characteristics of metal ions affecting enzyme activity are electronegativity (ENPol), the first ionization potential (IP1), the entropy of ions in aqueous solution (S), and the electron affinity energy (Eae). Conclusions. QSAR analysis methods in combination with nonlinear trend vector and random forest methods allow adequately describing the effect of metal ions on the peptidase Bacillus thuringiensis var. israelensis IMV B-7465 activity due to descriptors reflecting a certain balance of their electron-donating and electron-accepting properties (electronegativity, the first ionization potential, the electron affinity energy) and thermodynamic properties in aqueous solution (entropy of solvation). Both statistical methods give similar values of the importance of descriptors, but only the trend vector method allows us to analyze the direction of influence of specific characteristics of ions.

Nano-QSPR modeling often requires considering variety of factors, if neglected, may lead to erroneous result of the study. Frequently, the data turned out to be inaccurate, incomplete, or fragmentary. Obviously, the quality of experimental data directly depends on many factors: laboratory equipment, organization of internal regulations, skills of researchers, and so on. As a result of violations of algorithms and protocols of initial data streams processing – there are errors and distortions of data, that is why performing a solid multistep data-curation process is crucial for such procedures. Data curation procedure was performed and approximately 60% was rejected (due to various errors, incomplete or absent records for physicochemical parameters or conditions of performed experiment), followed up by using zeta-potential value dataset for 37 various sizes nanoparticles of 14 metal oxides for calculation of 1D SiRMS descriptors as well as «liquid drop» model cross-descriptors. An efficient consensus model was built (R2 = 0.88, R2test = 0.81). Predictive power (R2 = 0.84) of the model was tested using an external set of 5 nano-oxides and the possibility of satisfactory zeta-potential prediction was shown. Prediction of zeta-potential value within domain applicability of obtained QSPR model confirmed using a Williams plot. The interpretation of the final model was carried out and it was found that the contribution of descriptors was distributed between individual descriptors and cross-descriptors by 46% and 54% respectively. The contribution 1D SiRMS descriptors was 59%, the second group – 41% (liquid drop model descriptors – 29%, descriptors characterizing the metal atom – 12%). It was found that the most influential parameters are the characteristics that reflect the nature of the oxides. The parameters of electrostatic interactions have the highest contribution.

We review the development and application of the Simplex approach for the solution of various QSAR/QSPR problems. The general concept of the simplex method and its varieties are described. The advantages of utilizing this methodology, especially for the interpretation of QSAR/QSPR models, are presented in comparison to other fragmentary methods of molecular structure representation. The utility of SiRMS is demonstrated not only in the standard QSAR/QSPR applications, but also for mixtures, polymers, materials, and other complex systems. In addition to many different types of biological activity (antiviral, antimicrobial, antitumor, psychotropic, analgesic, etc.), toxicity and bioavailability, the review examines the simulation of important properties, such as water solubility, lipophilicity, as well as luminescence, and thermodynamic properties (melting and boiling temperatures, critical parameters, etc.). This review focuses on the stereochemical description of molecules within the simplex approach and details the possibilities of universal molecular stereo-analysis and stereochemical configuration description, along with stereo-isomerization mechanism and molecular fragment “topography” identification.

A series of adamantane derivatives (rimantadine and amantadine) incorporating amino-acid residues are investigated by simplex representation of molecular structure (SiRMS) approach in order to found correlation between chemical structures of investigated compounds and obtained data for antiviral activity and cytotoxicity. The obtained data from QSAR analysis show that adamantane derivatives containing amino acids with short aliphatic non-polar residues in the lateral chain will have good antiviral activity against the tested virus A/H3N2, strain Hong Kong/68 with low cytotoxicity. QSAR experiments and in vitro data also show good correlation and reveal that modified adamantine derivatives including guanidated in the lateral chain amino acid and ?-amino acids as substituents show low to none activity.

In the present study, adequate quantitative structure-activity relationship (QSAR) models were developed to analyze the water solubility of some ammonium hexafluorosilicates. All models were developed using structural descriptors calculated by the SiRMS method based on the simplex representation of the molecular structure and Dragon descriptors. Log P, equalized electronegativity, molecular refraction, and molecular weight were used as integral descriptors in addition to 2D structural descriptors. All QSAR models were obtained using the partial least squares (PLS) method. Model M1 examined the influence of various physicochemical and structural factors on the water solubility of the studied compounds. The interpretation results are consistent with the qualitative data of previous experimental works. It was possible to detail the features of the hydrogen bonds effect on the water solubility for investigated compounds The non-trivial nature of the effect of the hydrogen bond was also shown. QSPR model M2 could predict the solubility of new compounds of the studied type with satisfactory accuracy.

In recent years, a high carioprophylactic efficacy of ammonium hexafluorosilicates with biologically active cations has been discovered (АHBC). In the case of using AHBC, there is a potential possibility of enhancing the anticaries effect of the fluorine-containing anion as a result of the contribution of the effects of cations, for example, anti-inflammatory effects. The purpose of the work is a virtual analysis of the biological activity and lipophilicity of pyridine derivatives containing pharmacophores associated with anti-inflammatory activity (AIA), as possible candidates for the synthesis of AHBC as anticaries agents. Objects of research are the commercially available pyridine derivatives (PubChem database) containing pharmacophore groups – residues of acetic, propionic, phenylacetic acids, the presence of which is associated with the manifestation of AIA. Assessment of the potential biological activity of the compounds was carried out using the program. PASS 2017 Professional. The lipophilicity values of logP pyridines were calculated using software packages ALOGPS, KowWin, model QSPR. It has been established that in the series of acetic acid derivatives the highest probability of the presence of AIA (Ра) is expected for isomeric pyridine acetic acids: there is a relative increase in the values of Pa in the series of 2-, 3-, 4-isomers (Ра = 0,454, 0,506, 0,537 respectively). The introduction of the second substituent into the pyridine ring (fluorine, bromine, chlorine atoms, CF3 group) is accompanied by a decrease in the values Ра. In the rows of 2-, 3-, 4-substituted derivatives of phenylacetic and propionic acids, an increase in the likelihood of AIA manifestation is also recorded; the introduction of substituents in the propionic acid residue (fluorine atoms, НО-, H2N-groups) leads to lower values Ра. For all studied derivatives, there was no significant probability of manifestation of hepatotoxicity and nephrotoxicity (Ра < 0,5), the calculated lipophilicity values of the compounds are in the range of -2,65‒2,26. Thus, all the studied pyridine derivatives correspond to Lipinsky's «rule 5» and can be classified as low toxic «drug-like» compounds. Despite the presence of pharmacophores in the pyridines, the presence of which is associated with AIA, for almost all structures the probability of the appearance of this type of activity is small (Ра ≤ 0,5). In our opinion, compounds with phenylacetic and propionic acids fragments are interesting as objects of further experimental research as the models for elucidating the influence of the position of the pharmacophore group in the structure of the pyridine ring on the value of the CPE and AIA of the corresponding AHBC.

The QSPR methodology is very promising for the creation of new materials, including materials based on inorganic compounds. However, the majority of QSPR descriptor systems are applicable only for organic molecules. In this work the 1D - QSPR descriptor system is proposed for analysis of the properties of various inorganic compounds. These descriptors are easily accessible, as they describe the most fundamental atom properties. The combinatorial schemes for computing these descriptors provide for their wide variety. The effectiveness of the proposed approach has been demonstrated to study the refractive indices and melting points of various inorganic compounds - components of potential optical film-forming materials. The developed QSPR models are suitable for the evaluative virtual screening of inorganic compounds; the mean relative error of prediction is 6 - 15%. The interpretation of the developed models reflects the nature of interatomic interactions in compounds with ionic structure.

In the present study, quantitative structure-activity relationship (QSAR) models were developed to predict analgesic activity of some mono-/bicyclic terpenoids and their esters with neurotransmitter amino acids. All the models were developed using structural descriptors calculated by SiRMS approach based on the simplex representation of the molecular structure. Log P, molecular refraction, electronegativity, and molecular mass were used as integral descriptors additionally to calculated 2D simplex descriptors. Predictive QSAR models were obtained using the partial least squares (PLS) method. The analysis of structural factors influence on the manifestation of analgesic activity for studied compounds was carried out in the following pharmacological tests: capsaicin, formalin, allylisothiocyanate, and “hot plate” tests. We found that the most significant contribution to analgesic action in all pharmacological tests exhibited molecular fragments representing menthol and borneol residues. Also, we may conclude that –OH group substitution in terpenoid molecules for GABA or glycine residues leads to enhancement of analgesic effect due to the presence of additional highly reactive C=O and N–H groups playing the role of H-bond donors/acceptors.

A series of 60 nitrobenzonitrile analogues of the anti-viral agent MDL-860 were synthesized (50 of which are new) and evaluated for their activity against three types of enteroviruses (coxsackievirus B1, coxsackievirus B3 and poliovirus 1). Among them, six diaryl ethers (20e, 27e, 28e, 29e, 33e and 35e) demonstrated high in vitro activity (SI > 50) towards at least one of the tested viruses and very low cytotoxicity against human cells. Compound 27e possesses the broadest spectrum of activity towards all tested viruses in the same way as MDL-860 does. The most active derivatives (27e, 29e and 35e) against coxsackievirus B1 were tested in vivo in newborn mice experimentally infected with 20 MLD50 of coxsackievirus B1. Compound 29e showed promising in vivo activity (protection index 26% and 4 days lengthening of mean survival time). QSAR analysis of the substituent effects on the in vitro cytotoxicity (CC50) and anti-viral activity of the nitrobenzonitrile derivatives was carried out and adequate QSAR models for the anti-viral activity of the compounds against poliovirus 1 and coxsackievirus B1 were constructed.

An adequate QSAR model based on the simplex representation of the molecular structure was built in order to optimize the search for new anti-influenza agents. Structural interpretation of the model allowed us to identify molecular fragments that determine the activity of compounds against human influenza viruses. Further virtual screening and targeted synthesis allowed us to select a group of potentially effective compounds, three of which, derivatives of piperidine and isoindoline, turned out to be the most promising.

QSAR analysis of the structural infl uence of 3-substituted 1,2-dihydro-3Н-1,4-benzodiazepine derivatives on the thermodynamic characteristics (ΔН0, ΔS0 and ΔG0) of their complexation with compounds was the main problem of QSAR analysis in this study. For small sets a new approach was developed for constructing statistical models and estimating their predictive ability. The developed special procedure for the generation of ensembles of QSAR models made it possible to construct adequate «structure – thermodynamic parameters» models for an «extremely small» set (6 compounds). 2D-PLS QSAR models were developed using the structural descriptors calculated by Dragon program and the descriptors calculated by the method based on the simplex representation of the molecular structure. The consensus models with quite good statistical characteristics (R2 > 0.95 for work set, R2 test > 0.78 for test set) were obtained for thermodynamic charact eristics complexation of investigated compounds. The prognosis of the thermodynamic parameters of binding of the related compounds with R = H, iso-C4H9, sec.-C4H9 to the CBDR was carried out using the simplex descriptors and Dragon descriptors. The increa se in the corresponding alkyl substituent from ethyl to isomeric butyl does not signifi cantly affect the interaction of ligands with the CBDR. It is assumed that the amount of Hydrogen atoms bounding to the Carbon atom adjacent to the carbonyl group has a certain infl uence on the thermodynamic characteristics of ligands interaction with CBDR; this may be due to the hyperconjugation effect. Exner’s method has revealed that the mechanism of interaction of the methyl-substituted compound with the CBDR differs from the mechanism of interaction with the CBDR of other investigated compounds.

A poor applicability of classic 2D descriptors for representation of metal oxide nanoparticles is briefly discussed. The combination of 1D descriptors with previously calculated size-dependent descriptors is utilized to represent the structural features of nanoparticles in QSAR modeling. For this purpose, descriptors based on the fundamental characteristics of atoms (nuclear charge, oxidation level, electronegativity, ionic radius, ionic refraction etc.) were combined with those derived from structural formula (doublets –A2, AB, …; triplets – A3, A2B, ABC, … etc.) and “liquid drop model” derived size-dependent parameters. Nano-QSAR models are developed for cytotoxicity of metal oxide nanoparticles against E. coli and HaCaT cells. Two developed nano-QSAR models are discussed in terms of cluster analysis.

In this chapter we describe different structural, physicochemical and stereochemical approaches towards interpretation of QSAR models based on simplex representation of molecular structure (SiRMS). These techniques are feasible due to the flexible nature of SiRMS, which may encode not only structural and physicochemical features of molecules, but also stereochemical ones (to represent molecules with different types of chirality). The developed approaches to structural and physicochemical interpretation do not depend on used machine learning methods that makes it possible to easily interpret traditional "black box" models like Support Vector Machine and Random Forest. We demonstrated an applicability of the developed interpretation approaches in a number of case studies including classical Hammett and Free-Wilson analysis, as well as several data sets with various physical and biological end-points. A good correspondence of the interpretation results with classical Hammett and Free-Wilson approaches supports validity of the proposed approaches. The analysis of different data sets with different end-points showed three possible scenarios of QSAR models' interpretation depending on the mechanisms of action for studied compounds that brings us to a conclusion that despite all models are interpretable, not all end-points are. The stereochemical interpretation was applied to the classical Cramer's set of steroids and to the data set that includes compounds with mixed central and axial chirality. In both cases we demonstrated the substantial contribution of the chiral descriptors in 2.XD QSAR models and revealed certain stereochemical features, which have the biggest contributions to investigated properties. As SiRMS represents an attractive framework for developing predictive and interpretable models, we developed several open-source software tools to make it available for the community. They are discussed at the end of the chapter.