Topological Charge Indices Research Articles

Generation of dark hollow beam by focusing a sine-Gaussian beam using a cylindrical lens and a focusing lens

Based on the generalized Huygens–Fresnel diffraction integral, a closed-form propagation equation related to sine-Gaussian beams through a cylindrical lens and a focusing lens is derived and illustrated with numerical methods . It is found that a sine-Gaussian beam through such a system may be converted into a dark hollow beam (DHB) with topological charge index one and its bright enclosure is approximately an elongated ellipse with very high ellipticity . Moreover, the parameter values at which the DHBs have perfect intensity patterns are designed. The optimal relative orientation between the dislocation line of the input sine-Gaussian beam and the axial orientation of the cylindrical lens is specified. And the ellipticity of the elliptical DHBs is mainly defined by the focal length of the cylindrical lens and the Fresnel number of the optical system. • Convert sine-Gaussian beams into elliptic dark hollow beams with high ellipticity. • Design an optical system consisting of a cylindrical lens and a focusing lens. • Optimize the designing system parameters.

Topological dynamics of optical singularities in speckle-fields induced by photorefractive scattering in a LiNbO3 : Fe crystal

A natural singular dynamics of elliptically polarised speckle-fields induced by the 'optical damage' effect in a photorefractive crystal of lithium niobate by a passing beam of a helium — neon laser is studied by the developed methods of singular optics. For the polarisation singularities (C points), a new class of chain reactions, namely, singular chain reactions are discovered and studied. It is shown that they obey the topological charge and sum Poincare index conservation laws. In addition, they exist for all the time of crystal irradiation. They consist of a series of interlocking chains, where singularity pairs arising in a chain annihilate with singularities from neighbouring independently created chains. Less often singular 'loop' reactions are observed where arising pairsof singularities annihilate after reversible transformations in within the boundaries of a single speckle. The type of a singular reaction is determined by a topology and dynamics of the speckles, in which the reactions are developing.

A Quantitative Structure-Activity Relationship and Molecular Modeling Study on a Series of Biaryl Imidazole Derivatives Acting as H+/K+-ATPase Inhibitors

The H+/K+-ATPase or proton pump is a magnesium-dependant enzyme which causes the exchange of a proton against a potassium ion through a membrane. Over activity of this enzyme causes hyperacidity by producing more of hydrochloric acid inside the stomach. This enzyme, therefore, has been found to be a good target for designing compounds to treat hyperacidity. A quantitative structure-activity relationship (QSAR) study has been made on a novel series of biaryl imidazole derivatives acting as H+/K+-ATPase inhibitors. The H+/K+-ATPase inhibition activity of these compounds is found to be significantly correlated with global topological charge indices (GTCIs) and the total polar surface area (TPSA) of the molecules, indicating the involvement of strong electronic interaction between the molecule and the receptor. Based on the correlations obtained, some new H+/K+-ATPase inhibitors are predicted. The docking studies of these predicted compounds exhibit that these compounds will have even better interaction with the receptor than those already marketed. Thus, they can prove more potent drugs for the treatment of hyperacidity.

A Quantitative Structure-Activity Relationship and Molecular Modeling Study on a Series of Heteroaryl- and Heterocyclyl-Substituted Imidazo[1,2-a]Pyridine Derivatives Acting as Acid Pump Antagonists

A quantitative structure-activity relationship (QSAR) and molecular docking study has been performed on a series of heteroaryl- and heterocyclyl-substituted imidazo[1,2-a]pyridine derivatives acting as acid pump antagonists in order to have a better understanding of the mechanism of H+/K+-ATPase inhibition. The QSAR study shows a significant correlation of activity with Global Topological Charge Indices (GTCI) of the compounds and the hydrophobic constant π of some substituents, indicating that the charge transfer within the molecule and the hydrophobic property of some substituents will be the controlling factor of the activity of these compounds and that there can be dispersion interaction between the molecules and the receptor, where some substituents may have hydrophobic interaction, too. Based on this correlation some new compounds with higher potency have been predicted and their docking study has been performed to see if they can have better interaction with the receptor. The ADME properties of these predicted compounds have also been reported that follow Lipinski's rule of five.

Chemometric Descriptor Based QSAR Rationales for the MMP-13 Inhibition Activity of Non-Zinc-Chelating Compounds

The MMP-13 inhibition activity of non-zinc-chelating compounds has been quantitatively analyzed in terms of chemometric descriptors. The statistically validated quantitative structure-activity relationship (QSAR) models provided rationales to explain the inhibition activity of these compounds. The descriptors, identified through combinatorial protocol in multiple linear regression (CP-MLR) analysis, have highlighted the role of 3-path Kier alpha-modified shape index (S3K), complementary information content index of 1-order neighborhood symmetry (CIC1), eigenvalue sum from mass weighted distance matrix (SEigm), lowest eigenvalue n. 6 of Burden matrix / weighted by atomic van der Waals volumes (BELv6) and by atomic polarizabilities (BELp6), 3-order topological charge index (GGI3) and the functionality, R--CR--R (C-025). From statistically validated models, it appeared that the descriptors S3K, BELv6, BELp6 and SEigm make positive contribution to activity and their higher values are conducive in improving the MMP- 13 inhibition activity of a compound. On the other hand, the descriptors CIC1, GGI3 and C-025 render detrimental effects to activity. Therefore, the absence of functionality, R--CR--R and lower values of descriptors CIC1 and GGI3 would be advantageous. PLS analysis has further corroborated the dominance of the CP-MLR identified descriptors. Applicability domain analysis revealed that the suggested models have acceptable predictability. All the compounds are within the applicability domain of the proposed models and were evaluated correctly.

Methods of studies on quantitative structure–activity relationships for chiral compounds

Chiral compounds are very important in drug development, organic synthesis, materials science, toxicology, or environmental chemistry. Therefore, for creating new drugs, several methods have been suggested in recent years. In several laboratories in the world, some new methods for the derivations of the parameters were constructed and used for studies on quantitative structure–activity/property relationships of chiral molecules. The algorithms reviewed in this paper involve Zargeb group chiral indices, chiral molecular connectivity index, chiral topological charge index, chiral Am index, chiral indices based on the matrixes, chiral indices based on chiral product, conformation‐independent chirality code, conformation‐dependent chirality code, quantitative two‐dimensional chirality degrees of benzenoids, and so on. Copyright © 2012 John Wiley & Sons, Ltd.

Two-mode superposition coherent states with spatial vortex structure for the quantized radiation field

Through superposing M two-mode coherent state a two-mode superposition coherent state with a spatial vortex structure in configuration space is constructed. Such quantum vortex state is an eigenstate of sum of squared two-mode annihilation operators and is always entangled. In the limiting condition of large M the quantum vortex state has a modified Bessel–Gaussian vortex structure with topological charge index n. Experimentally, such two-mode vortex states may be prepared by virtue of a multimode coherent state with currently available technology.

Non-Gaussian state with vortex structure of quantized radiation field

A new kind of quantum non-Gaussian state with vortex structure termed as a modified Bessel–Gaussian vortex state is constructed, and it is an eigenstate of sum of squared annihilation operator a2+b2. The quantum vortex state exhibits a rich variety of nonclassical signatures and is always entangled. The dependence of its statistical properties on state parameters is analyzed, and the non-Gaussianity is investigated in detail. It is found that, for sufficient small values of α, the properties clearly depend on the topological charge index n. Moreover, a scheme for generating such quantized vortex states is proposed.

Study of indole derivative inhibitors of Cytosolic phospholipase A2α based on Quantitative Structure Activity Relationship

Cytosolic phospholipase A2α, one of the three subtypes of Cytosolic phospholipase A2 (α, β and γ), is deemed to play an important role in the arachidonate pathway. Due to the rate-limiting provider for proinflammatory mediators, it is a particularly attractive target for drug development. Studies have revealed that indol derivate compounds can inhibit the activities of Cytosolic phospholipase A2α. However, few papers on the relationship between the molecular structure and the activity of inhibitor were reported. In this study, the Quantitative Structure Activity Relationship (QSAR) of indole derivates has been performed based on the dataset of 49 compounds. By using stepwise multiple linear regression, 5 descriptors were selected from 1777 molecular descriptors, including GGI5 (Topological charge index G5), TIE(dssC) (sum of E-State of atom type dssC: ¦2S(dssC)), RDF115a (the atomic Sanderson ALOGP), RDF100c (the atomic charge), and RDF065p (the atomic polarizability). Subsequently, Partial Least Squares (PLS), Artificial Neural Networks (ANN) and Support Vector Machine (SVM) were adopted to build the QSAR model, respectively. The independent test indicated that the SVM can give the best statistical results. And indole derivative inhibitors activity might be related to global charge transfers, carbon atoms type linked benzyl sulfonamide and molecule geometrical the distance distribution.

Pair coherent state evolutions through parametric frequency conversion and the realization of quantized vortex states

The pair coherent state evolution during a parametric frequency conversion is analyzed. And the wavefunction of the evolving pair coherent state in configuration space is obtained. It is found that the state may become a modified Bessel-Gaussian vortex state with topological charge index q which is a new non-Gaussian state. In coherent state representation such a modified Bessel-Gaussian vortex state is an eigenstate of sum of squared two-mode annihilation operators a2 + b2. The result obtained in this paper provides a new scheme for generating quantized vortex states in experiment with currently available technology.

QSPR-based estimation of the half-lives for polychlorinated biphenyl congeners

In this study, the depuration half-lives of 62 polychlorinated biphenyl (PCB) congeners in juvenile rainbow trout (Oncorhynchus mykiss) were estimated from their structural features based on QSPR methodology. A genetic algorithm (GA) was applied as a variable subset selection strategy and QSPR models established upon multiple linear regression (MLR), multilayer perceptron neural network (MLP NN) and support vector regression (SVR) procedures. Robustness and predictive stability of the constructed models were evaluated through internal and external validation methods. The high numerical values of and , and low RMSE in the case of the MLP NN model, confirm the supremacy of this model as well as nonlinear dependency of molecular structural features to the PCB congeners half-lives. In the best developed QSPR model the following four descriptors are used; lopping centric index (Lop), mean topological charge index of order 1 (JGI1), Geary autocorrelation lag-8/weighted by atomic Sanderson electronegativities (GATS8e) and highest eigenvalue of Burden matrix/weighted by atomic masses (BEHm3). Analysis of the descriptors involved in these models revealed that 2D molecular structural features, compactness and electronegativities are the main factors contributing to the half-lives of PCBs. The structural information presented in this work can be used for further evaluation of half-lives of PCBs and other similar structural compounds in the environment.

Two-dimensional quantitative structure–activity relationship study on polyphenols as inhibitors of α-glucosidase

Polyphenols and their derivates have been reported to exhibit inhibitory activity against α-glucosidase. The relationship between structure and inhibitory activity of polyphenols was studied by means of multiple linear regression analysis with use of various descriptors derived from the 2D and 3D representations of molecules and physicochemical parameters calculated by DRAGON. The best model for the prediction of inhibitory activity was obtained using combination of topological charge index (JGI2), information index (CIC2) and number of exo-conjugated C atoms (nCconjR). This study revealed that an enhanced inhibitory activity of polyphenols is mainly conditioned by stabilization of molecule due to intramolecular electron and charge delocalization.

Importance of some classes of molecular descriptors on classification of antitumor acridinones using factor analysis

Factor analysis method has been applied to determine the relationships between some classes of structural descriptors series of acridinones drugs differing in chemical structures and their antileukemia activity. Molecular modeling studies were performed with the use of HyperChem and Dragon computer programs, and molecular geometry optimization using MM+ molecular mechanics and semi-empirical AM1 method. Sixteen classes of molecular descriptors include over 1200 descriptors were calculated and taken for factor analysis. Importantly, among the classes of molecular structural descriptors studied, the most significant influence was recognized for descriptors from classes of constitutional descriptors as well as topological charge indices descriptors, and allowed to distribution of individual compounds on the plane determined by two principal components (factors 1 and 2) produced patterns in good agreement with their ability to antitumor activity as well as with their chemical structures.

QSAR Study on 5-Lipoxygenase Activating Protein (FLAP) Inhibitors: The Derivatives of 2,2-Bisaryl-Bicycloheptane

The FLAP inhibitory activity of 2,2-bisaryl-bicycloheptane derivatives has been quantitatively analyzed in terms of Dragon descriptors. The derived QSAR models have provided rationales to explain the FLAP inhibitory activity of 2,2-bisaryl-bicycloheptane derivatives. The presence of quinolinylmethoxy substituent at R2-position in a molecular structure is a crucial feature for the FLAP inhibitory activity. The occurrence of R-CR-X type structural fragment (descriptor C-028) and higher number of sulfur atoms (descriptor nS) in a molecular structure are prevalent to rationalize the FLAP actions of bicycloheptane derivatives. The topological charge indices (descriptors GGI3, 3rd order Galvez topological charge index; and JGI4, 4th order Galvez mean topological charge index), path/walk ratio 2 (Randics molecular shape descriptor PW2) and atomic polarizabilities at lag 2 (descriptor GATS2p, Geary autocorrelation of lag 2 weighted by atomic polarizabilities) are also important to explain the FLAP activity. The PLS analysis has also confirmed the dominance of information content of CP-MLR identified descriptors. Applicability domain analysis revealed that the suggested model matches the high quality parameters with good fitting power and the capability of assessing external data, and all of the compounds were within the applicability domain of the proposed models and were evaluated correctly.

A rationale for the activity profile of arylpiperazinylthioalkyls as 5-HT 1A-serotonin and α 1-adrenergic receptor ligands

The 5-HT 1A and α 1-receptor binding affinities of the arylpiperazinylthioalkyl derivatives have been quantitatively expressed in terms of topological and molecular features. The analysis revealed that a lower value of atomic composition based index (AAC), higher values of structural information content (SIC3) and topological charge index (GGI9) would be beneficial to the 5-HT 1A receptor binding. For the α 1-receptor binding affinity the higher values of topological charge index (GGI9) and atomic Sanderson electronegativities weighted descriptor (GATS3e) and more number of hydrogen atoms attached to sp or sp 3 hybridized carbon atoms in a molecular structure (H-047) would be favorable. The derived significant models may further be used to synthesize new potential and selective compounds.

Modeling of cyclooxygenase-2 and 5-lipooxygenase inhibitory activity of apoptosis-inducing agents potentially useful in prostate cancer chemotherapy: Derivatives of diarylpyrazole

The structure-activity models of the twenty derivatives for COX-2 and ten derivatives of 1,5-diarylpyrazole for 5-LOX inhibitory activity have been investigated using Combinatorial Protocol in Multiple Linear Regression (CP-MLR) with topological descriptors which were calculated from DRAGON software. Among the descriptor classes considered collectively in the study the COX-2 inhibitory activity was, however, correlated with topological (TOPO) and Galvez topological charge indices (GVZ). Modified Burden eigenvalues (BCUT) and 2D autocorrelations (2DAUTO) classes of descriptors have shown correlation to 5-LOX inhibitory activity. The developed models and participating descriptors in them have suggested that the substitutional modification in the diarylpyrazole moiety may have sufficient scope in optimization of prevailing inhibitory activities of these analogues.

QSAR study about ATP-sensitive potassium channel activation of cromakalim analogues using CP-MLR approach

The structure–activity models of the myorelaxant activity of the cromakalim analogues have been investigated with nearly 470 topological descriptors from DRAGON software using Combinatorial Protocol in Multiple Linear Regression (CP-MLR). Among the descriptor classes considered in the study, the binding affinity is correlated with simple functional (FUN), topological (TOPO), atom centered fragments (ACF), empirical (EMP), modified Burden eigenvalues (BCUT), Galvez topological charge indices (GVZ), 2D-autocorrelation (2D-AUTO) and constitutional (CONS) descriptors. The models developed, and the participating descriptors suggest that the substituent groups of 4,6-disubstituted-2,2-dimethylchromans hold scope for further modification in the optimization of activity. The higher path lengths rich in polarizability and lower path length rich in atomic mass in addition to the lower charge indices of the molecule are beneficiary to the activity. The participating descriptors also suggested that certain structural features such as carbon atoms attached to the heteroatom by single or multiple bonding, and lesser or ‘no’ branching in a molecule are helpful to augment the activity.

Improving the local vertex invariants in alkane graphs through a standard molecular orbital approach

In this work, novel topological indices are introduced by the application of algorithms based on molecular orbital theory. Actually, the novel indices are obtained by computing new values of the local vertex invariants (LOVIs) in alkane graphs. The most significant result is the dramatic increase in the predictive capability achieved with the topological charge indices weighted according the new LOVIs’ values in the prediction of four key properties in the set of octane isomers, namely heat of atomization, molar refraction, heat of vaporization and boiling point.

A radial-distribution-function approach for predicting rodent carcinogenicity

Carcinogenic activity has been investigated using the Radial-Distribution-Function (RDF) approach. A discriminant model was developed to predict the carcinogenic and non-carcinogenic activity on a data set of 188 compounds. The percentage of overall classification was 76.4% for the carcinogenic chemicals and 72.5% for the non-carcinogenic chemicals. The predictive power of the model was validated by two tests: a cross-validation by the resubstitution technique and a test set (compounds not used in the development of the model) with 79.3 and 72.5% good classification, respectively. The RDF descriptors were compared with eight other methodologies; Constitutional, Molecular walks counts, Galvez topological charge indices, 2D autocorrelations, Randić molecular profiles, Geometrical, 3D-MORSE, and WHIM, demonstrating that the RDF descriptors are better to the rest of the approaches used.

Quantitative structure–activity relationship studies of vitamin D receptor affinity for analogues of 1α,25-dihydroxyvitamin D 3. 1: WHIM descriptors

The weighted holistic invariant molecular (WHIM) approach has been applied to the study of the VDR affinity of 86 vitamin D analogues. A model able to describe more than 71% of the variance in the experimental activity was developed with the use of the mentioned approach. In contrast, none of three different approaches, including the use of BCUT, Galvez topological charge indices, and 2D autocorrelations descriptors, was able to explain more than 38% of the variance in the mentioned property, even with more variables in the equation.