Topochemical models for prediction of cyclin-dependent kinase 2 inhibitory activity of indole-2-ones

On Entropy Measures and Eccentricity-Based Descriptors of Polyamidoamine (PAMAM) Dendrimers

Topological indices (TIs) assign a numeric value to a graph or a molecular structure. Due to their ability to predict the physiochemical properties of a molecular graph, several TIs have been introduced and studied, mainly based on degree and distance. For a vertex $v$ , the maximum distance of $v$ from any other vertex in a graph $G$ is called the eccentricity of $v$ , which is denoted by $\sigma \left(v\right)$ , in $G$ . The eccentricity of vertices gained special attention among the distance-based or degree-distance based TIs. An important TI in the class of eccentricity-dependent TIs is an eccentricity-entropy index. Furthermore, other eccentricity-dependent TIs such as eccentric-connectivity index, total-eccentricity index, and the first Zagreb index have also been extensively studied. On the other hand, dendrimers came out as unique polymeric macromolecules because of extensively branched three-dimensional architectural characteristics. This structure design prepares for various unique properties of dendrimers, including monodispersity, multivalency, uniform size, globular shape, water solubility with hydrophobic internal cavities, and a high degree of branching. These properties make them attractive candidates for different applications. PAMAM (polyamidoamine) dendrimers are promising polymers that can be successfully used in various biomedical applications. The PAMAM dendrimers having different structures such as a primary amine as the end group or porphyrin core have been studied through graph-theoretic parameters. This paper studies these two types of PAMAM dendrimers through eccentricity-dependent parameters. In particular, we establish formulae of eccentricity entropy for two types of PAMAM dendrimers. Moreover, we also derive analytic formulae of some other significant TIs from the class of eccentricity-dependent TIs. Furthermore, we apply graphical tools to demonstrate the trends of the values in the obtained results.

Some Eccentricity-Based Topological Indices and Polynomials of Poly(EThyleneAmidoAmine) (PETAA) Dendrimers

Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical properties. In this article, eccentric connectivity, total eccentricity connectivity, augmented eccentric connectivity, first Zagreb eccentricity, modified eccentric connectivity, second Zagreb eccentricity, and the edge version of eccentric connectivity indices, are computed for the molecular graph of a PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, the explicit representations of the polynomials associated with some of these indices are also computed.

On eccentricity-based topological descriptors of water-soluble dendrimers

Previous studies show that certain physical and chemical properties of chemical compounds are closely related with their molecular structure. As a theoretical basis, it provides a new way of thinking by analyzing the molecular structure of the compounds to understand their physical and chemical properties. The molecular topological indices are numerical invariants of a molecular graph and are useful to predict their bioactivity. Among these topological indices, the eccentric-connectivity index has a prominent place, because of its high degree of predictability of pharmaceutical properties. In this article, we compute the closed formulae of eccentric-connectivity-based indices and its corresponding polynomial for water-soluble perylenediimides-cored polyglycerol dendrimers. Furthermore, the edge version of eccentric-connectivity index for a new class of dendrimers is determined. The conclusions we obtained in this article illustrate the promising application prospects in the field of bioinformatics and nanomaterial engineering.

Construction Algorithm for Zero Divisor Graphs of Finite Commutative Rings and Their Vertex-Based Eccentric Topological Indices

Chemical graph theory is a branch of mathematical chemistry which deals with the non-trivial applications of graph theory to solve molecular problems. Graphs containing finite commutative rings also have wide applications in robotics, information and communication theory, elliptic curve cryptography, physics, and statistics. In this paper we discuss eccentric topological indices of zero divisor graphs of commutative rings Z p 1 p 2 × Z q , where p 1 , p 2 , and q are primes. To enhance the importance of these indices a construction algorithm is also devised for zero divisor graphs of commutative rings Z p 1 p 2 × Z q .

On Eccentricity-Based Topological Indices Study of a Class of Porphyrin-Cored Dendrimers

It is revealed from the previous studies that there is a strong relation between the chemical characteristic of a chemical compound and its molecular structure. Topological indices defined on the molecular structure of biomolecules can help to gain a better understanding of their physical features and biological activities. Eccentricity connectivity indices are distance-based molecular structure descriptors that have been used for the mathematical modeling of biological activities of diverse nature. As the porphyrin has photofunctional properties, such as a large absorption cross-section, fluorescence emission, and photosensitizing properties, due to these properties, porphyrin dendrimers can be used as photofunctional nanodevices. In this paper, we compute the exact formulae of different versions of eccentric connectivity index and their corresponding polynomials for a class of porphyrin-cored dendrimers. The results obtained can be used in computer-aided molecular design methods applied to pharmaceutical engineering.

Classification models for safe drug molecules

Frequent failure of drug candidates during development stages remains the major deterrent for an early introduction of new drug molecules. The drug toxicity is the major cause of expensive late-stage development failures. An early identification/optimization of the most favorable molecule will naturally save considerable cost, time, human efforts and minimize animal sacrifice. (Quantitative) Structure Activity Relationships [(Q)SARs] represent statistically derived predictive models correlating biological activity (including desirable therapeutic effect and undesirable side effects) of chemicals (drugs/toxicants/environmental pollutants) with molecular descriptors and/or properties. (Q)SAR models which categorize the available data into two or more groups/classes are known as classification models. Numerous techniques of diverse nature are being presently employed for development of classification models. Though there is an increasing use of classification models for prediction of either biological activity or toxicity, the future trend will naturally be towards the development of classification models capable of simultaneous prediction of biological activity, toxicity, and pharmacokinetic parameters so as to accelerate development of bioavailable safe drug molecules.

TOPOCHEMICAL MODELS FOR THE PREDICTION OF LIPOPHILICITY OF 1,3-DISUBSTITUTED PROPAN-2-ONE ANALOGS

In the present study, the relationship between the topochemical indices and log P values of 1,3-disubstituted propan-2-one analogs has been investigated. Three topochemical indices, Wiener's topochemical index — a distance-based topochemical descriptor, molecular connectivity topochemical index — an adjacency-based topochemical descriptor, and eccentric connectivity topochemical index — an adjacency-cum-distance-based topochemical descriptor, were used for the present investigation. The values of the Wiener's topochemical index, molecular connectivity topochemical index, and eccentric connectivity topochemical index were computed for each of the 45 analogs constituting the data set using an in-house computer program. The predicted log P values using leave-one-out (LOO) procedure exhibited a q2 of 0.72, 0.70, and 0.71 with reported log P values for Wiener's topochemical index, molecular connectivity topochemical index, and eccentric connectivity topochemical index, respectively. Separate models were developed using training set and log P of each analog in the independent test set was predicted using these models. The correlation of predicted log P values with the reported values, for independent test set, were in good agreement with those predicted using LOO procedure.

Models for anti-tumor activity of bisphosphonates using refined topochemical descriptors

An in silico approach comprising of decision tree (DT), random forest (RF) and moving average analysis (MAA) was successfully employed for development of models for prediction of anti-tumor activity of bisphosphonates. A dataset consisting of 65 analogues of both nitrogen-containing and non-nitrogen-containing bisphosphonates was selected for the present study. Four refinements of eccentric distance sum topochemical index termed as augmented eccentric distance sum topochemical indices 1-4 [formula: see text] have been proposed so as to significantly augment discriminating power. Proposed topological indices (TIs) along with the exiting TIs (>1,400) were subsequently utilized for development of models for prediction of anti-tumor activity of bisphosphonates. A total of 43 descriptors of diverse nature, from a large pool of molecular descriptors, calculated through E-Dragon software (version 1.0) and an in-house computer program were selected for development of suitable models by employing DT, RF and MAA. DT identified two TIs as most important and classified the analogues of the dataset with an accuracy of 97% in training set and 90.7% in tenfold cross-validated set. Random forest correctly classified the analogues with an accuracy of 89.2%. Four independent models developed through MAA predicted the activity of analogues of the dataset with an accuracy of 87.6% to 89%. The statistical significance of proposed models was assessed through intercorrelation analysis, specificity, sensitivity and Matthew's correlation coefficient. The proposed models offer a vast potential for providing lead structures for development of potent anti-tumor agents for treatment of cancer that has spread to the bone.

Models for prediction of (V)600(E)BRAF and melanoma cells growth inhibitory activities of pyridoimidazolones

Targeted inhibition of activated BRAF mutation has emerged as a most promising and putative therapeutic approach for the anticancer drug development. In the present study, an in-silico approach using decision tree and moving average analysis has been applied to a data set comprising of 43 analogues of pyridoimidazolones for development of models for prediction of both (V)600(E)BRAF and melanoma cells (BRAF WM266.4) growth inhibitory activities. A decision tree was mainly employed for determining the importance of molecular descriptors (n=46). The value of majority of these descriptors for each analogue in the dataset was computed using E-Dragon software (version 1.0). The decision tree learned the information from the input data with an accuracy of 98% and correctly predicted the cross-validated (10-fold) data with accuracy up to 79%. A total of three non-correlating descriptors, identified best by the decision tree analysis, were subsequently utilized for development of suitable models using moving average analysis. These proposed models resulted in the prediction of (V)600(E)BRAF inhibitory activity (IC50) and melanoma cells growth (SRB GI50) inhibitory activity with an overall accuracy of ≥90%. The statistical significance of models/descriptors was assessed through intercorrelation analysis, sensitivity, specificity and Matthew's correlation coefficient.

Models for antitubercular activity of 5â-O-[(N-Acyl)sulfamoyl]adenosines

The relationship between topological indices and antitubercular activity of 5â-O-[(N-Acyl)sulfamoyl]adenosines has been investigated. A data set consisting of 31 analogues of 5â-O-[(N-Acyl)sulfamoyl]adenosines was selected for the present study. The values of numerous topostructural and topochemical indices for each of 31 differently substituted analogues of the data set were computed using an in-house computer program. Resulting data was analyzed and suitable models were developed through decision tree, random forest and moving average analysis (MAA). The goodness of the models was assessed by calculating overall accuracy of prediction, sensitivity, specificity and Mathews correlation coefficient. Pendentic eccentricity index â a novel highly discriminating, non-correlating pendenticity based topochemical descriptor â was also conceptualized and successfully utilized for the development of a model for antitubercular activity of 5â-O-[(N-Acyl)sulfamoyl]adenosines. The proposed index exhibited not only high sensitivity towards both the presence as well as relative position(s) of pendent/heteroatom(s) but also led to significant reduction in degeneracy. Random forest correctly classified the analogues into active and inactive with an accuracy of 67.74%. A decision tree was also employed for determining the importance of molecular descriptors. The decision tree learned the information from the input data with an accuracy of 100% and correctly predicted the cross-validated (10 fold) data with accuracy up to 77.4%. Statistical significance of proposed models was also investigated using intercorrelation analysis. Accuracy of prediction of proposed MAA models ranged from 90.4 to 91.6%.

Validation of topochemical models for the prediction of permeability through the blood-brain barrier

Recently published topochemical models for permeability through the blood-brain barrier were validated and cross-validated in the present study. Five models based on three topochemical indices, Wiener's topochemical index - a distance-based topochemical descriptor, molecular connectivity topochemical index - an adjacency-based topochemical descriptor and eccentric connectivity topochemical index - an adjacency-cum-distance based topochemical descriptor, for permeability of structurally and chemically diverse molecules through blood-brain barrier were used in the present investigation. A data set comprising 62 structurally and chemically diverse compounds was selected. This data set was divided into two sets of 31 compounds each - one to serve as the validation set and other as the cross-validation set. The values of all the three-topochemical indices in the original as well as in the normalized form for each of the 31 compounds of the validation set were computed using an in-house computer program. Resultant data was analyzed and each compound was assigned a permeability characteristic using topochemical models, which was then compared with the reported permeability through the blood-brain barrier. Accuracy of prediction of these models was calculated. The same procedure was similarly followed for the cross-validation set. Studies revealed accuracy of prediction of the order of 70-80% during validation. Surprisingly, very high predictability of the order of 77-91% was observed during cross-validation. High predictability observed during validation as well as cross-validation authenticates topochemical models for prediction of permeability through the blood-brain barrier.

Topochemical Models for Prediction of Telomerase Inhibitory Activity of Flavonoids

In the present study, the relationship between the topochemical indices and telomerase inhibitory activity of flavonoids has been investigated. Three topochemical indices, Wiener's topochemical index (a distance-based topochemical descriptor), molecular connectivity topochemical index (an adjacency-based topochemical descriptor) and superadjacency topochemical index (an adjacency cum distance-based topochemical descriptor) were used for the present investigation. The values of the Wiener's topochemical index, molecular connectivity topochemical index and superadjacency topochemical index for each of the 30 analogues comprising the data set were computed using an in-house computer program. Resultant data was analysed and suitable models were developed after identification of the active ranges. Subsequently, a biological activity was assigned to each analogue involved in the data set using these models, which was then compared with the reported telomerase inhibitory activity. Statistical significance of proposed models was investigated using intercorrelation analysis. Accuracy of prediction using proposed models was found to vary from 80% to 83%.

Topochemical models for anti-HIV activity of 1-alkoxy-5-alkyl-6-(arylthio)uracils

Relationship between topochemical indices and anti-HIV-1 (HTLV-III) inhibitory activity of 1-alkoxy-5-alkyl-6-(arylthio)uracils has been studied. Superadjacency, an adjacency-cum-distance-based, topochemical index and Wiener’s, a distance-based, topochemical index were calculated for a set of 36 1-alkoxy-5-alkyl-6-(arylthio)uracils. Resulting data were analyzed and suitable models were developed after identification of the active ranges. Subsequently, a biological activity was assigned to each of the compounds using these models and compared with the reported anti-HIV-1 activity. High accuracy of prediction was observed using these models. Statistical analysis revealed significance of the proposed models as well as a lack of correlation between the topochemical indices employed for the chosen data set.

Structure–activity relationship study of oxindole-based inhibitors of cyclin-dependent kinases based on least-squares support vector machines

The least-squares support vector machines (LS-SVMs), as an effective modified algorithm of support vector machine, was used to build structure-activity relationship (SAR) models to classify the oxindole-based inhibitors of cyclin-dependent kinases (CDKs) based on their activity. Each compound was depicted by the structural descriptors that encode constitutional, topological, geometrical, electrostatic and quantum-chemical features. The forward-step-wise linear discriminate analysis method was used to search the descriptor space and select the structural descriptors responsible for activity. The linear discriminant analysis (LDA) and nonlinear LS-SVMs method were employed to build classification models, and the best results were obtained by the LS-SVMs method with prediction accuracy of 100% on the test set and 90.91% for CDK1 and CDK2, respectively, as well as that of LDA models 95.45% and 86.36%. This paper provides an effective method to screen CDKs inhibitors.

Prediction of h5-HT2A receptor antagonistic activity of arylindoles: Computational approach using topochemical descriptors

Relationship between the topochemical indices and h5-HT2A receptor antagonistic activity of arylindoles has been investigated. Three topochemical indices, Wiener's topochemical index--a distance-based topochemical descriptor, molecular connectivity topochemical index--an adjacency-based topochemical descriptor and eccentric connectivity topochemical index--an adjacency-cum-distance based topochemical descriptor, were used for the present investigation. A data set comprising 31 differently substituted arylindoles was selected for the present study. The values of the Wiener's topochemical index, molecular connectivity topochemical index and eccentric connectivity topochemical index were computed for all the analogues involved in the data set using an in-house computer program. Resultant data was analyzed and suitable models were developed after identification of the active ranges. Subsequently, a biological activity was assigned to each analogue using these models, which was then compared with the reported h5-HT2A receptor antagonistic activity. Accuracy of prediction was found to vary from a minimum of approximately 81% to a maximum of approximately 84%.

Topochemical models for the prediction of permeability through blood–brain barrier

Relationship between the topochemical indices and permeability of diverse series of compounds through blood-brain barrier has been investigated. Three-topochemical indices, Wiener's topochemical index--a distance-based topochemical descriptor, molecular connectivity topochemical index--an adjacency based topochemical descriptor and eccentric connectivity topochemical index--an adjacency-cum-distance based topochemical descriptor, were used for the present investigation. A data set comprising of 28 compounds with established CNS permeation tendency was selected for present study. The values of all the three-topochemical indices in the original as well as in the normalized form for each of the 28 compounds comprising the data set were computed using an in-house computer program. Resultant data was analyzed and suitable models were developed after identification of the permeable ranges. Subsequently, permeability characteristic was assigned to each compound involved in the data set using these models, which was then compared with the reported permeability through blood-brain barrier. Accuracy of prediction was found to vary from a minimum of 83% to a maximum of approximately 95% using these models.

Topochemical models for the prediction of voltage-gated sodium channel binding activity of hydantoins and related non-hydantoins

The relationship of Wiener's topochemical index-a distance based topochemical index, molecular connectivity topochemical index-an adjacency based topochemical index and eccentric connectivity topochemical index-an adjacency-cum-distance based topochemical index with sodium channel binding activity has been investigated. A dataset comprising 50 hydantoins and related non-hydantoins was selected. The dataset was divided equally into training and test sets. The values of the three topochemical indices for all the compounds present in both the training and test sets were computed using an in-house computer program. The resulting data was analyzed and suitable models were developed after identification of the active ranges in the training set. Subsequently, a biological activity was assigned to each compound involved in the training set using these models, which was then compared with the reported sodium channel binding activity. An accuracy of prediction of the order of >99% was observed using the proposed models. Cross-validation of these models using the test set revealed an exceptionally high accuracy of approximately 95%.