Topological Charge Indices Research Articles

Propagation of integral and fractional perfect vortex beams in a gradient-index medium.

The analytical expressions for the complex amplitude of integral and fractional perfect vortex (PV) beams propagating in a gradient-index (GRIN) medium are derived. The intensity and phase distributions, propagation trajectories, Poynting vectors, and the effects of topological charge and refractive index at the medium axis on the intensity of both beams in the medium are numerically investigated. It is shown that both beams propagate periodically in the GRIN medium with alternating spot focusing and reconstruction. Unlike the integral PV beam, the fractional PV beam has a dark line in intensity profiles and a line edge dislocation in phase distributions along the positive x-axis. These properties persist during the beam propagation in the GRIN medium. Moreover, the topological charge and the refractive index at the medium axis have little effect on the intensity of the PV beam propagating in the GRIN medium. The results presented in this paper may be useful for the application of integral and fractional PV beams in optical guiding and optical communications.

Exploring Quantitative Structure-Activity Relationships (QSARs) for Urea-Based Dual FAAH and sEH Inhibitors

Several urea-based compounds have been reported as dual inhibitors of Fatty acid amide hydrolase (FAAH) and Soluble epoxide hydrolase (sEH) enzymes which have potential as anti-inflammatory and antinociceptive agents. QSAR studies were performed on the urea analogs to identify the molecular descriptors influencing the FAAH and sEH inhibitory activity using Small Dataset Modeler tool. Molecular descriptors (1D &2D) were computed using PaDEL-Descriptor software. A set of forty-eight compounds was used in the present study. Statistically significant models were derived for both the enzymes [pIC50 (sEH): R2 = 0.797, Q2 = 0.762 and Q2F1 =0.747; pIC50 (FAAH): R2 = 0.642, Q2 = 0.521 and Q2F1 =0.566]. The results of QSAR on the sEH enzyme revealed the contribution of topological charge indices, ionization potential, and the number of nitrogen atoms (naaN) for defining the potency. Polarizability showed a major influence on FAAH inhibition. The predictive ability of the QSAR models was established based on the dual inhibitory potential of some newly designed molecules.

Simple, efficient and reliable characterization of Laguerre-Gaussian beams with non-zero radial indices in diffraction from an amplitude parabolic-line linear grating.

In this work, we report the characterization of a Laguerre-Gaussian (LG) beam with given values of topological charge (TC) and radial index in a simple, efficient, and robust experimental diffraction scheme. The beam diffracts from an amplitude parabolic-line linear grating and the resulting diffraction patterns at zero- and first-order reveals the values of the TC, l, and radial index p of the incident LG beam using a simple analysis. The zero-order diffraction pattern consists of p + 1 concentric intensity rings and the first-order diffraction pattern contains an (l + p + 1) by (p + 1) two-dimensional array of intensity spots. The experimental scheme is robust since it is not sensitive to the relative locations of the impinging beam axis and the grating center, and is efficient since most of the energy of the output beam is in the diffraction order of interest for LG beam characterization. The measurement is also simple since the intensity spots of the array are placed exactly over straight and parallel lines. Both experimental and simulation results are presented and are consistent with each other.

2D-QSAR modeling and two-fold classification of 1,2,4-triazole derivatives for antitubercular potency against the dormant stage of Mycobacterium tuberculosis.

The dormant or latent form of Mycobacterium tuberculosis (MTB) is not killed by the conventional antitubercular drugs. The treatment of latent TB is essential to reduce the period of treatment as well as incidences of drug resistance. In this background, we have made an attempt to develop the quantitative structure-activity relationship models (QSAR: regression and classification based) against the dormant form of MTB and later used the developed classifier models (linear discriminant analysis (LDA) and random forest (RF)) for the two-fold classifications. The logic of applying this concept of two-fold classification for the MTB modeling is to increase the confidence of correct classification. The 2D-QSAR modeling suggested the contribution of burden eigen, edge adjacency, van der Waals (vdW) surface area, topological charge, and pharmacophoric indices in predicting the antitubercular activity against the dormant MTB. The prediction qualities of the training and test sets were found to be moderate and good, according to the mean absolute error (MAE)-based criteria's. The LDA and RF models unveiled the importance of burden eigen, edge adjacency, Geary autocorrelation, and drug-like indices as discriminating features to differentiate the antitubercular compounds into higher and lower active groups. The LDA model showed the classification accuracies of 85.14% and 87.10% for the training and test sets, while the RF model exhibited the accuracies of 100.00% and 80.65% for both the sets. The descriptors selected in the final models are only two-dimensional (2D), which are easy to compute and does not require computationally expensive steps of structure conversion, optimization, and energy minimization mandatorily needed before the computation of 3D descriptors. These models could be used for identifying and selection of higher active compounds against the dormant form of the MTB.

Quantitative structure-activity relationship study on the MMP-13 inhibitory activity of fused pyrimidine derivatives possessing a 1,2,4-Triazol-3-yl group as a ZBG

QSAR study has been carried out on the MMP-13 inhibitory activity of fused pyrimidine derivatives possessing a1,2,4-triazol-3-yl group as a ZBG in 0D- to 2D-Dragon descriptors. The derived QSAR models have revealed that the number of Sulfur atoms (descriptor nS), Balaban mean square distance index (descriptor MSD), molecular electrotopological variation (descriptor DELS), structural information content index of neighborhood symmetry of 2nd and 3rd order (descriptors SIC2 and SIC3), average valence connectivity index chi-4 (descriptor X4Av) in addition to 1st order Galvez topological charge index (descriptor JGI1) and global topological charge index (descriptor JGT) played a pivotal role in rationalization of MMP-13 inhibition activity of titled compounds. Atomic properties such as mass and volume in terms of atomic properties weighted descriptors MATS5m and MATS3v, and certain atom centred fragments such as CH2RX (descriptor C-006), X--CX--X (descriptor C-044), H attached to heteroatom (descriptor H-050) and H attached to C0(sp3) with 1X attached to next C (descriptor H-052) are also predominant to explain MMP-13 inhibition actions of fused pyrimidines. PLS analysis has also corroborated the dominance 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 was within the applicability domain of the proposed model and were evaluated correctly.

Computational techniques in designing a series of 1,3,4-trisubstituted pyrazoles as unique hepatitis C virus entry inhibitors

In this study, we developed a QSAR model for studying the antiviral activity of 1,3,4-trisubstituted pyrazoles derivatives on hepatitis C virus infected in human HuH-7 cell lines. We employed random analysis to split the data sets. Statistically robust model was generated with R2, Q2 and R2pred values of 0.777, 0.731 and 0.774 respectively. The reliability of this model was confirmed by acceptable validation parameters, and this model also fulfilled the Golbraikh and Tropsha standard model conditions. Through the evaluation of selected molecular descriptors we observed that, topological charge index of order 4 (GGI4), mean topological charge index of order 1 (JGI1), octanol water partition coefficient (XlogP), 3D topological distance based autocorrelation lag5/weighted by polarizabilities (TDB5p) and total molecular surface area (FPSA-2) are the molecular properties determining biological activities of the study compounds, which shed light on the vital features that aid in the design of unique potent hepatitis C virus entry inhibitors using computer-aided drug design tools.

Superposition of shifted Laguerre–Gaussian beams

In this research, the superposition of shifted Laguerre–Gaussian (LG) beams and their intensity distribution are studied in cylindrical coordinates. By complex transverse shifting of conventional LG beams, the symmetry of intensity structure is lost and deformed to the crescent. Increasing the amount of beam pure imaginary shift causes the beam is focused on a smaller crescent. The obtained results from applying changes on the real transverse shift, topological charge, and radial index parameters of superposed LG beams depict the possibility of these beams to apply in optical trapping. As the radial index increases, in addition to the radial variation of the intensity distribution, the position and shape of the crescents are changed. Besides, analytical formulate for the angular spectrum of the superposed beams is derived and the relation of their orbital angular momentum (OAM) obtained. It is observed, by increasing the OAM, the radius of intensity distribution is increased. By the combination of these difference adjustable parameters, the localized intensity distribution has been prepared, which could be used for the production of controllable optical traps. The obtained experimental results confirm the simulation results.

QSAR rationales for the dipeptidyl peptidase-4 (DPP-4) inhibitors: The imidazolopyrimidine amides

The DPP4 inhibition activity of imidazolopyrimidine amides has been quantitatively analyzed in terms of chemometric descriptors. The statistically validated QSAR models provided rationales to explain the inhibition activity of these congeners. The descriptors identified through CP-MLR analysis have highlighted the role of mean electrotopological state (Ms), number of double bonds in molecular structure (nDB), 2D Petitijean shape index (PJI2), Moran autocorrelation of lag-2/weighted by atomic polarizabilities (MATS2p), Moran autocorrelation of lag-6 and lowest eigenvalue n.5 of Burden matrix /weighted by atomic Sanderson electronegativities (MATS6e and BELe5), lowest eigenvalue n.3 and highest eigenvalue n.1 of Burden matrix/weighted by atomic van der Waals volumes (BELv3 and BEHv1). In addition to these 2nd order mean Galvez topological charge index (JGI2), number of ring tertiary C(sp3) (nCrHR) and R--CR--X type structural fragments (C-028) have also shown prevalence to model the inhibitory activity. From statistically validated models, positive contribution of descriptors Ms, PJI2, JGI2, MATS2p, BELe5, BELv3 and BEHv1 suggested that higher values of these are conducive in improving the DPP4 inhibition activity. On the other hand, negative contribution of descriptors nDB, C-028, nCrHR and MATS6e advocated that absence of number of double bonds (nDB), R--CR--X type structural fragment (C-028), number of ring tertiary C(sp3) (nCrHR) and lower value of descriptor MATS6e would be advantageous. PLS analysis has confirmed the dominance of the CP‐MLR identified descriptors and applicability domain analysis revealed the acceptable predictability of suggested models. All the compounds are within the applicability domain of the proposed models and were evaluated correctly.

In Silico Prediction of O⁶-Methylguanine-DNA Methyltransferase Inhibitory Potency of Base Analogs with QSAR and Machine Learning Methods.

O6-methylguanine-DNA methyltransferase (MGMT), a unique DNA repair enzyme, can confer resistance to DNA anticancer alkylating agents that modify the O6-position of guanine. Thus, inhibition of MGMT activity in tumors has a great interest for cancer researchers because it can significantly improve the anticancer efficacy of such alkylating agents. In this study, we performed a quantitative structure activity relationship (QSAR) and classification study based on a total of 134 base analogs related to their ED50 values (50% inhibitory concentration) against MGMT. Molecular information of all compounds were described by quantum chemical descriptors and Dragon descriptors. Genetic algorithm (GA) and multiple linear regression (MLR) analysis were combined to develop QSAR models. Classification models were generated by seven machine-learning methods based on six types of molecular fingerprints. Performances of all developed models were assessed by internal and external validation techniques. The best QSAR model was obtained with Q2Loo = 0.83, R2 = 0.87, Q2ext = 0.67, and R2ext = 0.69 based on 84 compounds. The results from QSAR studies indicated topological charge indices, polarizability, ionization potential (IP), and number of primary aromatic amines are main contributors for MGMT inhibition of base analogs. For classification studies, the accuracies of 10-fold cross-validation ranged from 0.750 to 0.885 for top ten models. The range of accuracy for the external test set ranged from 0.800 to 0.880 except for PubChem-Tree model, suggesting a satisfactory predictive ability. Three models (Ext-SVM, Ext-Tree and Graph-RF) showed high and reliable predictive accuracy for both training and external test sets. In addition, several representative substructures for characterizing MGMT inhibitors were identified by information gain and substructure frequency analysis method. Our studies might be useful for further study to design and rapidly identify potential MGMT inhibitors.

Quantitative Prediction of Thiazole Derivatives as Potent Xanthine Oxidase Inhibitors

AbstractIn humans, xanthine oxidase (XO) is a critical rate‐limiting enzyme in biosynthesis of uric acid. Moreover, XO is the most promising target to control uric acid levels and the treat of hyperuricemia and gout. However, XO inhibitors can effectively treat gout through the inhibition of urate synthesis, and by impairing the conversion of hypoxanthine and xanthine to uric acid. In this paper, four different quantitative structure‐activity relationship (QSAR) models of 80 thiazole derivatives were constructed to comprehend chemical‐biological interactions and predict their bioactivities using GA‐MLR (Genetic Algorithm‐Multiple Linear Regression), HQSAR (Hologram Quantitative Structure Activity Relationship), Topomer CoMFA (Comparative Molecular Field Analysis) and CoMSIA (Comparative Molecular Similarity Indices Analysis) methods. Furthermore, R2 and Q2 of the obtained GA‐MLR, HQSAR, Topomer CoMFA and CoMSIA models are 0.956 and 0.911, 0.932 and 0.876, 0.946 and 0.917, 0.964 and 0.877, respectively. In addition, the external predictive values of the GA‐MLR, HQSAR, Topomer CoMFA and CoMSIA models are 0.963, 0.936, 0.973 and 0.934, respectively. Therefore, all QSAR models exhibited good prediction performances, which can be used to quantitatively evaluate bioactivity and screen new XO inhibitors. Moreover, topological charge index, atomic electronegativity and polarizability, atomic van der Waals volumes and hydrophobic van der Waals surface area are very relevant to bioactivity of thiazole derivatives.

Towards the design of 3-aminopyrazole pharmacophore of pyrazolopyridine derivatives as novel antioxidants

Free radicals and oxidants can cause oxidative damage to physiologically important biomolecules that subsequently leads to the development of a wide range of chronic and degenerative diseases such as aging, cancer, cardiovascular and neurodegenerative diseases. Antioxidants have been shown to be instrumental in counteracting the deleterious effects of these reactive oxygen species. Herein, a series of 20 pyrazolopyridine derivatives with antioxidant activity were utilized for constructing a quantitative structure–activity relationship model as to unravel the origins of the antioxidant activity. Quantum chemical and molecular descriptors were used to quantitate the physicochemical properties of investigated compounds. Significant descriptors as identified by stepwise regression analysis consisted of Mor11m, Mor25v, JGI5, H8p, GATS5p, and GVWAI-50. Statistical parameters suggested that the constructed quantitative structure–activity relationship models were robust with Q 2 = 0.9370 and root mean square error = 4.7414 as evaluated via leave-one-out cross-validation. The mechanistic basis of the antioxidant activity as deduced from significant descriptors was rationalized. Particularly, compounds with the highest antioxidant activity required compounds to have the highest mean topological charge index of order 5 (JGI5) and Geary autocorrelation–lag 5/weighted by atomic polarizabilities (GATS5p) but necessitated low 3D-MoRSE-signal 25/weighted by atomic van der Waals volumes (Mor25v). Such properties are well corroborated by the 3-aminopyrazole pharmacophore from investigated compounds. Molecular insights unraveled herein is anticipated to be useful as guidelines for further rational design of novel pyrazole analogs with potent antioxidant activity.

Long-Chain 4-Aminoquinolines as Quorum Sensing Inhibitors in Serratia marcescens and Pseudomonas aeruginosa.

Antibiotic resistance has become a serious global threat to public health; therefore, improved strategies and structurally novel antimicrobials are urgently needed to combat infectious diseases. Here we report a new type of highly potent 4-aminoquinoline derivatives as quorum sensing inhibitors in Serratia marcescens and Pseudomonas aeruginosa, exhibiting weak bactericidal activities (minimum inhibitory concentration (MIC) > 400 μM). Through detailed structure-activity study, we have identified 7-Cl and 7-CF3 substituted N-dodecylamino-4-aminoquinolines (5 and 10) as biofilm formation inhibitors with 50% biofilm inhibition at 69 μM and 63 μM in S. marcescens and P. aeruginosa, respectively. These two compounds, 5 and 10, are the first quinoline derivatives with anti-biofilm formation activity reported in S. marcescens. Quantitative structure-activity relationship (QSAR) analysis identified structural descriptors such as Wiener indices, hyper-distance-path index (HDPI), mean topological charge (MTC), topological charge index (TCI), and log D(o/w)exp as the most influential in biofilm inhibition in this bacterial species. Derivative 10 is one of the most potent quinoline type inhibitors of pyocyanin production described so far (IC50 = 2.5 μM). While we have demonstrated that 5 and 10 act as Pseudomonas quinolone system (PQS) antagonists, the mechanism of inhibition of S. marcescens biofilm formation with these compounds remains open since signaling similar to P. aeruginosa PQS system has not yet been described in Serratia and activity of these compounds on acylhomoserine lactone (AHL) signaling has not been detected. Our data show that 7-Cl and 7-CF3 substituted N-dodecylamino-4-aminoquinolines present the promising scaffolds for developing antivirulence and anti-biofilm formation agents against multidrug-resistant bacterial species.

Generation of self-healing and transverse accelerating optical vortices

Self-healing and transverse accelerating optical vortices are generated via modulating Gaussian beams through subsequent liquid crystal q-plate and polarization Airy mask. We analyze the propagation dynamics of these vortex Airy beams, and find that they possess the features of both optical vortices and Airy beams. Topological charges and characteristics of nondiffraction, self-healing, and transverse acceleration are experimentally verified. In addition, vortex Airy beams with both topological charge and radial index are demonstrated and mode switch among Gaussian, vortex, vector, Airy beams and their combinations can be acquired easily. Our design provides a flexible and highly efficient way to generate unique optical vortices with self-healing and transverse acceleration properties, and facilitates prospective applications in optics and photonics.

Pred-binding: large-scale protein–ligand binding affinity prediction

Drug target interactions (DTIs) are crucial in pharmacology and drug discovery. Presently, experimental determination of compound–protein interactions remains challenging because of funding investment and difficulties of purifying proteins. In this study, we proposed two in silico models based on support vector machine (SVM) and random forest (RF), using 1589 molecular descriptors and 1080 protein descriptors in 9948 ligand–protein pairs to predict DTIs that were quantified by Ki values. The cross-validation coefficient of determination of 0.6079 for SVM and 0.6267 for RF were obtained, respectively. In addition, the two-dimensional (2D) autocorrelation, topological charge indices and three-dimensional (3D)-MoRSE descriptors of compounds, the autocorrelation descriptors and the amphiphilic pseudo-amino acid composition of protein are found most important for Ki predictions. These models provide a new opportunity for the prediction of ligand–receptor interactions that will facilitate the target discovery and toxicity evaluation in drug development.

Fabrication and characterization of high-quality spiral phase plates for optical applications

The discovery that light beams with a helical phase front carry orbital angular momentum (OAM) has enabled applications in many fields ranging from optical manipulation to quantum information processing and, recently, free-space information transfer and communications. Here, a novel three-dimensional fabrication process by electron beam lithography was finely tuned in order to realize high-quality spiral phase plates (SPPs) for the generation of OAM-carrying optical beams. Single- and multi-step SPPs have been realized for the generation of high-order Laguerre–Gaussian beams with different values of topological charge and radial index. The optical response of these optical elements was experimentally investigated and compared with theoretical models.

CP-MLR Directed QSAR Rationales for the 1-aryl Sulfonyl Tryptamines as 5-HT6 Receptor Ligands

A QSAR study has been carried out to rationalize the 5-HT6 receptor binding affinities of the 1-aryl sulfonyl tryptamine derivatives using Dragon descriptors. A higher value of molecular symmetry and topology accounting Randic shape index descriptor PW4 (path/walk 4) would be favorable to improve the binding affinity. Presence of more number of bromine atoms (descriptor nBR) and presence of such structural fragment in which a hydrogen atom attached to sp3 hybridized carbon with no hetero atom rather than one hetero atom attached to next carbon atom (descriptors H-046 and H-052) will be supportive to the activity. The prevalence of atomic properties to explain the binding affinity is evident from the associations of polarizability to the path length 7 of Moran autocorrelation (MATS7p), masses to eigenvalues n.2 and 7 of Burden m atrix (BELm2 and BEHm7), Sanderson electronegativity to highest eigenvalue n.2 Burden matrix (BEHe2) and van der Waals volume to path length 8 of Geary autocorrelation (GATS8v) and charge content in terms of topological and mean topological charge indices (GGI3 and JGI2). The dominance of the information content of the descriptors, emerged in CP-MLR models, has also confirmed by the PLS analysis. The derived QSAR models and descriptors shared in these models revealed that the substituents of tryptamine moiety have sufficient scope for further modification.

QSAR Study of the Inhibitors of the Acetyl-CoA Carboxylase 1 and 2 using Bayesian Regularized Genetic Neural Networks: A Comparative Study

Linear and non-linear quantitative structure-activity relationship (QSAR) models were presented for modeling and predicting anti-diabetic activities of a set of inhibitors of acetyl-CoA carboxylase 1 and 2 (ACC1 and ACC2). Different algorithms were utilized to choose the best variables among large numbers of descriptors and then these selected descriptors were used for non-linear (artificial neural network) and linear (multiple linear regression) modeling. The variable selection methods were consisted of stepwise-multiple linear regression (stepwise-MLR), successive projections algorithm (SPA), genetic algorithm-multiple linear regression (GA-MLR) and Bayesian regularized genetic neural networks (BRGNNs). The prediction abilities of the models were evaluated by Monte Carlo cross validation (MCCV) in variable selection and modeling steps. The results revealed that the best variables for describing the inhibition mechanism of ACC were among topological charge indices, radial distribution function, geometrical, and autocorrelation descriptors. The statistical parameters of R2 and root mean square error (RMSE) indicated that BRGNNs is superior for modeling the inhibitory activity of ACC modulators over the other methods. The sensitivity analysis together with the frequency of the selected molecular descriptors in this work can establish an understanding to the mechanism of ACC inhibitory activity of small molecules.

Support vector machine classification of streptavidin-binding aptamers.

BackgroundSynthesizing and characterizing aptamers with high affinity and specificity have been extensively carried out for analytical and biomedical applications. Few publications can be found that describe structure–activity relationships (SARs) of candidate aptamer sequences.MethodologyThis paper reports pattern recognition with support vector machine (SVM) classification techniques for the identification of streptavidin-binding aptamers as “low” or “high” affinity aptamers. The SVM parameters C and γ were optimized using genetic algorithms. Four descriptors, the topological descriptor PW4 (path/walk 4 - Randic shape index), the connectivity index X3A (average connectivity index chi-3), the topological charge index JGI2 (mean topological charge index of order 2), and the free energy E of the secondary structure, were used to describe the structures of candidate aptamer sequences from SELEX selection (Schütze et al. (2011) PLoS ONE (12):e29604).ConclusionsThe predicted fractions of winning streptavidin-binding aptamers for ten rounds of SELEX conform to the aptamer evolutionary principles of SELEX-based screening. The feasibility of applying pattern recognition based on SVM and genetic algorithms for streptavidin-binding aptamers has been demonstrated.

Gyrator transform of generalized sinh-Gaussian beam and generation of dark hollow light beam with vortex

Starting from the Gyrator trnasform formula, the closed-form filed distribution of generalized sinh-Gaussian beam passing through such a transform system is derived, and the intensity distribution and the corresponding phase distribution associated with the transforming generalized sinh-Gaussian beams are analyzed. Based on the numerical method, the distributions are graphically drawn and it is found that, for appropriate beam parameters and by carefully adjusting the transform angle of Gyrator transform, the dark hollow beam with topological charge index being unity can be realized with sinh-Gaussian beam carrying an edge dislocation. And the influences of the beam parameters and the transform angle on the formation of perfect dark hollow beams are analyzed. However, it is impossible to obtain dark hollow beam with Gyrator transforming cosh-Gaussian beam.

Preparing quantum vortex states with odd Schrödinger cat states through a coupled waveguide system

A scheme is proposed for preparing a quantum vortex state with a coupled waveguide, in which a single-mode odd cat state with weak intensity and a single-mode coherent state are inserted in the input ports, respectively. The analytical wavefunction of the resulting state in the quadrature space is derived, and the vortex structure of the output state is analyzed. It is found that the obtained states, which may carry a vortex with topological charge index one, are entangled and nonclassical, depending only on the scaled propagation time and the weak intensity of the input odd cat state instead of the displacement parameter of the input coherent state. The phase distribution, however, in the quadrature space, depends on the displacement parameter of the input coherent state