Kappa Shape Index Research Articles

How the Spacer Influences the Stability of 2D Perovskites?

Two-dimensionallead halide perovskites (2D HPs) represent as an emerging class of materials given their tunable optoelectronic properties and long-term stability in perovskite solar cells. However, the ever-growing field of optoelectronic devices using 2D HPs requires fundamental understanding of the influence of the spacer on the physiochemical properties and stability of perovskites as well as establish which cation properties are closely related to suppress the halogen ion mobility. This study focuses on investigating the influence of organic spacers with intrinsic properties (e.g., rigidity and flexibility, special groups) and variations of material dimensions on the stability of halogen ions and inorganic frameworks in 2D HPs. It is found that the perovskite structure composed of rigidity molecules owns better stability of halogen ion and inorganic framework than that of flexible molecules. The stability of ions exhibits a negative correlation with the dimensions of perovskite. More importantly, a simple descriptor for measuring the stability of halogen ions in 2D HPs is constructed. By causal discovery algorithms with more physical and chemical significance, the Kappa shape index, number of rotatable bonds, and aromatic carbocycles in organic spacers are identified as causal and important features for the stability of halogen ions in 2D HPs.

Linear quantitative structure-ecotoxicity relationship modeling of a series of symmetrical triazine derivatives based on physicochemical parameters

The present study reports the Quantitative Structure-Ecotoxicity Relationship (QSER) analysis of a series of 21 1,3,5-triazine derivatives based on multiple-linear regression (MLR) method. The ecotoxicity data were estimated by using in silico approach and included the following parameters: acute algae toxicity (AAT), acute daphnia toxicity (ADT), Daphnia Magna LC50 48h/EPA (DMepa) and Daphnia Magna LC50 48h/DEMETRA (DMdemetra). The ecotoxicity data were correlated with molecular descriptors selected by using the stepwise selection method. The considered molecular descriptors are lipophilicity descriptors (CrippenLogP, ALogp2), Autocorrelation Descriptor Mass (ATSm1, ATSm2, ATSm3, ATSm4), Autocorrelation Descriptor Charge (ATSc2), minimum E-states for (strong) hydrogen bond acceptors (minHBa), maximum E-states for (strong) hydrogen bond acceptors (maxHBa), second kappa shape index (Kier2), maximum atom-type E-State: ?:N:? (maxaaN), sum of path lengths starting from nitrogens (WTPT-5) and McGowan characteristic volume (McGowan_Volume). The modeling resulted in four statistically valid MLR models. The models were validated by the internal and external validation approaches. The external validation confirmed high predictive ability of the established MLRs.

Prediction of Antagonistic Activity of <i>β</i>-Carboline and Its Derivatives Using Topological Descriptors

Prediction of antagonistic activity of β-carboline and its thirteen derivatives has been made using topological descriptors viz, connectivity index, and kappa shape index of different orders. For evaluation of values of descriptor, molecular modeling and geometry optimization of all the compounds were carried out with CAChe Pro software by opting semiempirical PM3 method using MOPAC 2002. For prediction of activity multiple linear regression analysis (MLR) was performed. MLR analysis has been made by Project Leader Software associated with CAChe by using the above descriptors as independent variables and biological activity as dependent variables. We were performed leave-one-out methods and the result reflected a direct relationship between biological activity and connectivity index of zero order, while indirect relationship with connectivity index of second order and thus connectivity index is a reliable descriptor to predict the biological activity of β-carboline and its various derivatives.

Classification of High‐Activity Tiagabine Analogs by Binary QSAR Modeling

Classification of High‐Activity Tiagabine Analogs by Binary QSAR Modeling

ChemInform Abstract: Neural Network Based Quantitative Structural Property Relations (QSPRs) for Predicting Boiling Points of Aliphatic Hydrocarbons.

Quantitative structural property relations (QSPRs) for boiling points of aliphatic hydrocarbons were derived using a back-propagation neural network and a modified Fuzzy ARTMAP architecture. With the back-propagation model, the selected molecular descriptors were capable of distinguishing between diastereomers. The QSPRs were obtained from four valance molecular connectivity indices (1χv,2χv,3χv,4χv), a second-order Kappa shape index (2κ), dipole moment, and molecular weight. The inclusion of dipole moment proved to be particularly useful for distinguishing between cis and trans isomers. A back-propagation 7−4−1 architecture predicted boiling points for the test, validation, and overall data sets of alkanes with average absolute errors of 0.37% (1.65 K), 0.42% (1.73 K), and 0.37% (1.54 K), respectively. The error for the test and overall data sets decreased to 0.19% (0.81 K) and 0.31% (1.30 K), respectively, using the modified Fuzzy ARTMAP network. A back-propagation alkene model, with a 7−10−1 architectu...

Exploring QSARs for Binding Affinity of Azoles with CYP2B and CYP3A Enzymes Using GFA and G/PLS Techniques

Eighteen azole compounds, including some commercial fungicides, reported by Daisuke Itokawa et al. have been subjected to quantitative structure-activity relationship (QSAR) analysis for their binding affinity with cytochrome enzymes CYP3A and CYP2B. The analyses were performed using electronic (Charge, FCharge, Apol, Dipole, HOMO, LUMO, and Sr), spatial (Radius of gyration, Jurs descriptors, Shadow indices, Area, PMI-mag, Density, Vm), different topological parameters (E-state index, kappa shape index, molecular connectivity index, subgraph cont, information content indices), and thermodynamic (Alog P, Alog P98, Molref) descriptors calculated using CERIUS2 version 10 software. Genetic function approximation and genetic partial least squares were used as chemometric tools for modeling. The derived binding affinity models are of high statistical quality (leave-one-out Q(2) ranging from 0.946 to 0.977). The selectivity models also satisfy the statistical significance (Q(2) ranging from 0.680 to 0.761). The models indicate that the binding affinity of these compounds is related to topological, steric, electronic, and spatial properties of the molecules. The spline-based genetic models indicate optimum range of different parameters. The models have also been validated by leave-25%-out cross-validation.

QSTR with Extended Topochemical Atom (ETA) Indices 8.a QSAR for the inhibition of substituted phenols on germination rate of Cucumis sativus using chemometric tools

AbstractQuantitative structure‐toxicity relationship (QSTR) study has proved to be a valuable approach in ecotoxicity estimations of acute and chronic toxicity to various organisms, and in fate estimations of physical/chemical properties, degradation, and bioconcentration. In this background, we have modeled the inhibition of 41 substituted phenols on germination rate of Cucumis sativus with extended topochemical atom (ETA) indices using different chemometric tools and compared the ETA relations with non‐ETA models derived from different topological indices (Wiener W, Balaban J, Hosoya Z, Zagreb, molecular connectivity indices, E‐state indices and kappa shape indices) and physicochemical parameters (AlogP98, MolRef, H_bond_acceptor, H_bond_donor, MW, logKow and Elumo). Different statistical tools used in this communication are stepwise regression analysis, multiple linear regression with factor analysis as the preprocessing step for variable selection (FA‐MLR), multiple linear regression with genetic function approximation (GFA‐MLR), partial least squares regression with factor analysis as the preprocessing step for variable selection (FA‐PLS), genetic partial least squares (G/PLS) and principal component regression analysis (PCRA). The results show that the best statistical quality along with prediction statistics with ETA descriptors is found in case of GFA‐MLR equation. In case of non‐ETA descriptors, the best equation is obtained from PCRA considering both equation statistics and predictive ability. When combined descriptors were considered, FA‐PLS gave the best equation. The best ETA equation (GFA‐MLR) has better leave‐one‐out Q2 value than the best non‐ETA equation (PCRA). The results suggest that the ETA descriptors are sufficiently rich in chemical information to encode the structural features contributing significantly to the comparative inhibition activity of substituted phenols on germination rate of Cucumis sativus.

QSTR with extended topochemical atom (ETA) indices. VI. Acute toxicity of benzene derivatives to tadpoles (Rana japonica)

structure-toxicity relationship (QSTR) studies have proved to be a valuable approach in research on the toxicity of organic chemicals for ranking chemical substances with respect to their potential hazardous effects on living systems. With this background, we have modeled here the acute lethal toxicity of 51 benzene derivatives with recently introduced extended topochemical atom (ETA) indices [Roy and Ghosh, Internet Electron J Mol Des 2:599-620 (2003)]. We also compared the ETA relations with non-ETA models derived from different topological indices (Wiener W, Balaban J, flexibility index, Hosoya Z, Zagreb, molecular connectivity indices, E-state indices and kappa shape indices) and physicochemical parameters (AlogP98, MolRef,H_bond_donor and H_bond_acceptor). Genetic function approximation (GFA) and factor analysis (FA) were used as the data-preprocessing steps for the development of final multiple linear regression (MLR) equations. Principal-component regression analysis (PCRA) was also used to extract the total information from the ETA/non-ETA/combined matrices. All the models developed were cross-validated using leave-one-out (LOO) and leave-many-out techniques. The summary of the statistics of the best models is as follows: (1) FA-MLR: ETA model- Q 2 (LOO)=0.852, R 2=0.894; non-ETA model- Q 2=0.782, R 2=0.835; ETA + non-ETA model-Q 2 =0.815, R 2=0.859. (2) GFA-MLR: ETA model-Q 2 =0.847, R 2=0.915; non-ETA model-Q 2 =0.863, R 2=0.898; ETA + non-ETA model-Q 2 =0.859, R 2=0.893. 3. PCRA: ETA model-Q 2 =0.864, R 2=0.901; non-ETA model- Q 2=0.866, R 2=0.922; ETA + non-ETA model-Q 2=0.846, R 2=0.890. The statistical quality of the ETA models is comparable to that of non-ETA models. Again, use of non-ETA descriptors in addition to ETA descriptors does not increase the statistical acceptance of the relations significantly. The predictive potential of these models was better than that of the previously reported models using physicochemical parameters [Huang et al., Chemosphere 53:963-970 (2003)]. The relations from ETA descriptors suggest a parabolic dependence of the toxicity on molecular size. Furthermore, the toxicity increases with functionality contribution of chloro substituent and decreases with those of methoxy, hydroxy, carboxy and amino groups. This study suggests that ETA parameters are sufficiently rich in chemical information to encode the structural features that contribute significantly to the acute toxicity of benzene derivatives to Rana japonica.

In silico ADME modelling: prediction models for blood–brain barrier permeation using a systematic variable selection method

Quantitative Structure–Property Relationship models (QSPR) based on in vivo blood–brain permeation data (logBB) of 88 diverse compounds, 324 descriptors and a systematic variable selection method, namely ‘Variable Selection and Modeling method based on the prediction (VSMP)’, are reported. Of all the models developed using VSMP, the best three-descriptors model is based on Atomic type E-state index (SsssN), AlogP98 and Van der Waal’s surface area ( r = 0.8425, q = 0.8239, F = 68.49 and SE = 0.4165); the best four-descriptors model is based on Kappa shape index of order 1, Atomic type E-state index (SsssN), Atomic level based AI topological descriptor (AIssssC) and AlogP98 ( r = 0.8638, q = 0.8472, F = 60.982 and SE = 0.3919). The performance of the models on three test sets taken from the literature is illustrated and compared with the results from other reported computational approaches. Test set III constitutes 91 compounds from the literature with known qualitative BBB indication and is used for virtual screening studies. The success rate of the reported models is 82% in the case of BBB+ compounds and a similar success rate is observed with BBB− compounds. Finally, as the models reported herein are based on computed properties, they appear as a valuable tool in virtual screening, where selection and prioritization of candidates is required.

Towards the chemometric dissection of peptide – HLA-A*0201 binding affinity: comparison of local and global QSAR models

The affinities of 177 nonameric peptides binding to the HLA-A*0201 molecule were measured using a FACS-based MHC stabilisation assay and analysed using chemometrics. Their structures were described by global and local descriptors, QSAR models were derived by genetic algorithm, stepwise regression and PLS. The global molecular descriptors included molecular connectivity chi indices, kappa shape indices, E-state indices, molecular properties like molecular weight and log P, and three-dimensional descriptors like polarizability, surface area and volume. The local descriptors were of two types. The first used a binary string to indicate the presence of each amino acid type at each position of the peptide. The second was also position-dependent but used five z-scales to describe the main physicochemical properties of the amino acids forming the peptides. The models were developed using a representative training set of 131 peptides and validated using an independent test set of 46 peptides. It was found that the global descriptors could not explain the variance in the training set nor predict the affinities of the test set accurately. Both types of local descriptors gave QSAR models with better explained variance and predictive ability. The results suggest that, in their interactions with the MHC molecule, the peptide acts as a complicated ensemble of multiple amino acids mutually potentiating each other.

Structural interpretation of the topological index. 2. The molecular connectivity index, the Kappa index, and the atom-type E-State index.

The structural interpretation is extended to the topological indices describing cyclic structures. Three representatives of the topological index, such as the molecular connectivity index, the Kappa index, and the atom-type E-State index, are interpreted by mining out, through projection pursuit combining with a number theory method generating uniformly distributed directions on unit sphere, the structural features hidden in the spaces spanned by the three series of indices individually. Some interesting results, which can hardly be found by individual index, are obtained from the multidimensional spaces by several topological indices. The results support quantitatively the former studies on the topological indices, and some new insights are obtained during the analysis. The combinations of several molecular connectivity indices describe mainly three general categories of molecular structure information, which include degree of branching, size, and degree of cyclicity. The cyclicity can also be coded by the combination of chi cluster and path/cluster indices. The Kappa shape indices encode, in combination, significant information on size, the degree of cyclicity, and the degree of centralization/separation in branching. The size, branch number, and cyclicity information has also been mined out to interpret atom-type E-State indices. The structural feature such as the number of quaternary atoms is searched out to be an important factor. The results indicate that the collinearity might be a serious problem in the applications of the topological indices.

QSTR with Extended Topochemical Atom Indices. 3. Toxicity of Nitrobenzenes to Tetrahymena pyriformis

AbstractThe experimental determination of toxicological properties of commercial chemicals being costly and time consuming process, there is a need to develop mathematical predictive tool to theoretically quantify such properties. In this background, we have modeled toxicity of nitrobenzene derivatives to Tetrahymena pyriformis using extended topochemical atom (ETA) indices recently introduced by us (Roy and Ghosh, 2003). We have also modeled the toxicity data using other topological descriptors (Balaban J, kappa shape indices, connectivity indices, Wiener index) and two physicochemical variables (AlogP98, MolRef) and compared the ETA models with non‐ETA ones. Principal component factor analysis was used as the data‐preprocessing step to reduce the dimensionality of the data matrix and identify the important variables that are devoid of collinearities. Multiple linear regression analyses show that the best non‐ETA model involves 2κ and AlogP98 as predictor variables and the quality of the relation is as follows: n=42, Q2=0.70, R$ {_{{a}}^{2}}$=0.75, R2=0.76, R=0.87, F=61.0 (df 2, 39), s=0.36. On the other hand, the best ETA model has the following quality: n=42, Q2=0.88, R$ {_{{a}}^{2}}$=0.91, R2=0.92, R=0.96, F=101.4 (df 4, 37), s=0.22. The ETA relations showed positive contributions of molecular bulk (size), halogen and additional nitro substitutions in the nitrobenzene ring and negative contributions of the substituents like methyl and hydroxymethyl groups to the toxicity. An attempt to use non‐ETA descriptors along with the ETA ones slightly improves the quality in comparison to the best ETA model. Interestingly, the ETA model developed by us for the nitrobenzene toxicity is comparable to the previously reported models on the same data set (Estrada et al., 2001; Cronin et al., 1998). Thus, it appears that the ETA descriptors have significant potential in QSAR/QSPR/QSTR studies, which warrants extensive evaluation.

E-state modeling of HIV-1 protease inhibitor binding independent of 3D information.

Data for HIV-1 protease inhibitors (in vitro enzyme binding) were used as a training set to develop a QSAR model based on topological descriptors, including two hydrogen E-state indices, along with a molecular connectivity chi and a kappa shape index. A statistically satisfactory four-variable model was obtained for the 32 compounds in the training set, r2 = 0.86, s = 0.60, and q2 = 0.79, without the use of information from 3D geometries or detailed interaction energy calculations. The model was validated through the prediction of 15 compounds in the external test set, yielding a mean absolute error, MAE, = 0.82. Structure interpretation is given for each variable to assist in the design of new compounds. Structure features emphasized in the model include hydrogen bond donating ability, nonpolar groups, skeletal branching, and molecular globularity. On the basis of these statistical criteria, this E-state model may be considered useful for prediction of pIC50 values for new HIV-1 protease inhibitors.

E-state modeling of corticosteroids binding affinity validation of model for small data set.

Data for 31 steroids binding to the corticosteroid binding globulin (CBG) were modeled using E-state molecular structure descriptors and a kappa shape index. Both E-state and hydrogen E-state descriptors appear in the model in atom-level and atom-type descriptors. A four-variable model is obtained that is statistically satisfactory: r (2) = 0.81, s = 0.51; r (2)(press) = 0.72; s(press) = 0.62. Structure interpretation is given for each variable in the model. A leave-group-out (LGO) approach to model-validation is presented in which each observation is removed from the data set three times in random groups of 20% of the whole data set. The average of the resulting predicted values constitutes consensus predictions for these data for which r (2)(LOO) = 0.70. These collective results support the claim that the E-state model may be useful for prediction of pK binding values for new compounds.

A Fuzzy ARTMAP-Based Quantitative Structure−Property Relationship (QSPR) for Predicting Physical Properties of Organic Compounds

A modified fuzzy ARTMAP neural-network-based QSPR for predicting normal boiling points, critical temperatures, and critical pressures of organic compounds was developed. Seven or eight molecular descriptors (the sum of atomic numbers; five valence connectivity indices; and the second-order kappa shape index, without or with the dipole moment) were used to describe the topological and electronic features of a heterogeneous set of 1168 organic compounds. Optimal training and testing sets were selected with fuzzy ART. The fuzzy ARTMAP models with eight descriptors as input provided the best predictive and extrapolation capabilities compared to optimal back-propagation models and group contribution methods. The absolute mean errors of predictions for the normal boiling point (1168 compounds), the critical temperature (530 compounds), and the critical pressure (463 compounds) were 2.0 K (0.49%), 1.4 K (0.24%), and 0.02 MPa (0.52%), respectively. A composite model for simultaneously estimating the three propert...

Novel shape descriptors for molecular graphs.

We report on novel graph theoretical indices which are sensitive to the shapes of molecular graphs. In contrast to the Kier's kappa shape indices which were based on a comparison of a molecular graph with graphs representing the extreme shapes, the linear graph and the "star" graph, the new shape indices are obtained by considering for all atoms the number of paths and the number of walks within a graph and then making the quotients of the number of paths and the number of walks the same length. The new shape indices show much higher discrimination among isomers when compared to the kappa shape indices. We report the new shape indices for smaller alkanes and several cyclic structures and illustrate their use in structure-property correlations. The new indices offer regressions of high quality for diverse physicochemical properties of octanes. They also have lead to a novel classification of physicochemical properties of alkanes.

Neural network based quantitative structural property relations (QSPRs) for predicting boiling points of aliphatic hydrocarbons

Quantitative structural property relations (QSPRs) for boiling points of aliphatic hydrocarbons were derived using a back-propagation neural network and a modified Fuzzy ARTMAP architecture. With the back-propagation model, the selected molecular descriptors were capable of distinguishing between diastereomers. The QSPRs were obtained from four valance molecular connectivity indices (1chiv,2chiv,3chiv,4chiv), a second-order Kappa shape index (2kappa), dipole moment, and molecular weight. The inclusion of dipole moment proved to be particularly useful for distinguishing between cis and trans isomers. A back-propagation 7-4-1 architecture predicted boiling points for the test, validation, and overall data sets of alkanes with average absolute errors of 0.37% (1.65 K), 0.42% (1.73 K), and 0.37% (1.54 K), respectively. The error for the test and overall data sets decreased to 0.19% (0.81 K) and 0.31% (1.30 K), respectively, using the modified Fuzzy ARTMAP network. A back-propagation alkene model, with a 7-10-1 architecture, yielded predictions with average absolute errors for the test, validation, and overall data sets of 1.96% (6.79 K), 1.83% (6.45 K), and 1.25% (4.42 K), respectively. Fuzzy ARTMAP reduced the errors for the test and overall data sets to 0.19% (0.73 K) and 0.25% (0.95 K), respectively. The back-propagation composite model for aliphatic hydrocarbons, with a 7-9- architecture, yielded boiling points with average absolute errors for the test, validation, and overall set of 1.74% (6.09 K), 1.25% (4.68 K), and 1.37% (4.85 K), respectively. The error for the test and overall data sets using the Fuzzy ARTMAP composite model decreased to 0.84% (1.15 K) and 0.35% (1.35 K), respectively. Performance of the QSPRs, developed from a simple set of molecular descriptors, displayed accuracy well within the range of expected experimental errors and of better accuracy than other regression analysis and neural network-based boiling points QSPRs previously reported in the literature.