Models for Antitubercular Activity of 5′-O-[(N-Acyl)sulfamoyl]adenosines

The relationship between topological indices and antitubercular activity of 5′-O-[(N-Acyl)sulfamoyl]adenosines has been investigated. A data set consisting of 31 analogues of 5′-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 – a novel highly discriminating, non-correlating pendenticity based topochemical descriptor – was also conceptualized and successfully utilized for the development of a model for antitubercular activity of 5′-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%

Markovian nature, completeness, regularity and correlation properties of Generalized Poisson-Kac processes

We analyze some basic issues associated with Generalized Poisson-Kac (GPK) stochastic processes, starting from the extended notion of the Markovian condition. The extended Markovian nature of GPK processes is established, and the implications of this property derived: the associated adjoint formalism for GPK processes is developed essentially in an analogous way as for the Fokker-Planck operator associated with Langevin equations driven by Wiener processes. Subsequently, the regularity of trajectories is addressed: the occurrence of fractality in the realizations of GPK is a long-term emergent property, and its implication in thermodynamics is discussed. The concept of completeness in the stochastic description of GPK is also introduced. Finally, some observations on the role of correlation properties of noise sources and their influence on the dynamic properties of transport phenomena are addressed, using a Wiener model for comparison

Structural Differentiation of Graphs Using Hosoya-Based Indices

In this paper, we introduce the Hosoya-Spectral indices and the Hosoya information content of a graph. The first measure combines structural information captured by partial Hosoya polynomials and graph spectra. The latter is a graph entropy measure which is based on blocks consisting of vertices with the same partial Hosoya polynomial. We evaluate the discrimination power of these quantities by interpreting numerical results

A Large Scale Analysis of Information-Theoretic Network Complexity Measures Using Chemical Structures

This paper aims to investigate information-theoretic network complexity measures which have already been intensely used in mathematical- and medicinal chemistry including drug design. Numerous such measures have been developed so far but many of them lack a meaningful interpretation, e.g., we want to examine which kind of structural information they detect. Therefore, our main contribution is to shed light on the relatedness between some selected information measures for graphs by performing a large scale analysis using chemical networks. Starting from several sets containing real and synthetic chemical structures represented by graphs, we study the relatedness between a classical (partition-based) complexity measure called the topological information content of a graph and some others inferred by a different paradigm leading to partition-independent measures. Moreover, we evaluate the uniqueness of network complexity measures numerically. Generally, a high uniqueness is an important and desirable property when designing novel topological descriptors having the potential to be applied to large chemical databases

Primjene teorije grafova: topologijski modeli za predvi|anje CDK-1 inhibicijske aktivnosti aloizina

Relationship between the topological indices and cyclin-dependent kinase-1 (CDK-1/cyclin B) inhibitory activity of 6-phenyl[5H]pyrrolo[2,3-b]pyrazines (aloisines) was investigated. Three topological indices – the Wiener Index, a distance-based topological descriptor, the Zagreb group parameter, an adjacency based topological descriptor, and the eccentric connectivity index, an adjacency-cum-distance based topological descriptor were used in the study. A data set comprising 51 analogues of aloisine was selected for the present study. Values of the Wiener index, the Zagreb group parameter and the eccentric connectivity index for each of the 51 analogues included in the data set were computed using an in-house computer program. Resultant data was analyzed and suitable models were developed after identification of active ranges. A biological activity was then assigned to each compound using these models, which was then compared with the reported CDK-1 inhibitory activity. Accuracy of prediction using these models was found to vary from a minimum of ≈82 % to a maximum of 84 %. .Istraživan je odnos izmđ|u topologijskih indeksa i CDK-1 inhibicijske aktivnosti 5-fenil[5H]pirolo[2,3-b]- pirazina (aloizina). Upotrebljena su tri topologijska indeksa: Wienerov indeks, zagrebački indeks i ekscentrični indeks povezanosti, koji su izračunani za 51 aloizin. Dobiveni modeli predviđaju inhibijsku aktivnosti aloizina s točnošću od 82–84 %

Topological Anisotropy of Stone-Wales Waves in Graphenic Fragments

Stone-Wales operators interchange four adjacent hexagons with two pentagon-heptagon 5|7 pairs that, graphically, may be iteratively propagated in the graphene layer, originating a new interesting structural defect called here Stone-Wales wave. By minimization, the Wiener index topological invariant evidences a marked anisotropy of the Stone-Wales defects that, topologically, are in fact preferably generated and propagated along the diagonal of the graphenic fragments, including carbon nanotubes and graphene nanoribbons. This peculiar edge-effect is shown in this paper having a predominant topological origin, leaving to future experimental investigations the task of verifying the occurrence in nature of wave-like defects similar to the ones proposed here. Graph-theoretical tools used in this paper for the generation and the propagation of the Stone-Wales defects waves are applicable to investigate isomeric modifications of chemical structures with various dimensionality like fullerenes, nanotubes, graphenic layers, schwarzites, zeolites

A novel representation of RNA secondary structure based on element-contact graphs

<p>Abstract</p> <p>Background</p> <p>Depending on their specific structures, noncoding RNAs (ncRNAs) play important roles in many biological processes. Interest in developing new topological indices based on RNA graphs has been revived in recent years, as such indices can be used to compare, identify and classify RNAs. Although the topological indices presented before characterize the main topological features of RNA secondary structures, information on RNA structural details is ignored to some degree. Therefore, it is necessity to identify topological features with low degeneracy based on complete and fine-grained RNA graphical representations.</p> <p>Results</p> <p>In this study, we present a complete and fine scheme for RNA graph representation as a new basis for constructing RNA topological indices. We propose a combination of three vertex-weighted element-contact graphs (ECGs) to describe the RNA element details and their adjacent patterns in RNA secondary structure. Both the stem and loop topologies are encoded completely in the ECGs. The relationship among the three typical topological index families defined by their ECGs and RNA secondary structures was investigated from a dataset of 6,305 ncRNAs. The applicability of topological indices is illustrated by three application case studies. Based on the applied small dataset, we find that the topological indices can distinguish true pre-miRNAs from pseudo pre-miRNAs with about 96% accuracy, and can cluster known types of ncRNAs with about 98% accuracy, respectively.</p> <p>Conclusion</p> <p>The results indicate that the topological indices can characterize the details of RNA structures and may have a potential role in identifying and classifying ncRNAs. Moreover, these indices may lead to a new approach for discovering novel ncRNAs. However, further research is needed to fully resolve the challenging problem of predicting and classifying noncoding RNAs.</p

Primjene teorije grafova: topologijski modeli za predvi|anje CDK-1 inhibicijske aktivnosti aloizina

Relationship between the topological indices and cyclin-dependent kinase-1 (CDK-1/cyclin B) inhibitory activity of 6-phenyl[5H]pyrrolo[2,3-b]pyrazines (aloisines) was investigated. Three topological indices – the Wiener Index, a distance-based topological descriptor, the Zagreb group parameter, an adjacency based topological descriptor, and the eccentric connectivity index, an adjacency-cum-distance based topological descriptor were used in the study. A data set comprising 51 analogues of aloisine was selected for the present study. Values of the Wiener index, the Zagreb group parameter and the eccentric connectivity index for each of the 51 analogues included in the data set were computed using an in-house computer program. Resultant data was analyzed and suitable models were developed after identification of active ranges. A biological activity was then assigned to each compound using these models, which was then compared with the reported CDK-1 inhibitory activity. Accuracy of prediction using these models was found to vary from a minimum of ≈82 % to a maximum of 84 %. .Istraživan je odnos izmđ|u topologijskih indeksa i CDK-1 inhibicijske aktivnosti 5-fenil[5H]pirolo[2,3-b]- pirazina (aloizina). Upotrebljena su tri topologijska indeksa: Wienerov indeks, zagrebački indeks i ekscentrični indeks povezanosti, koji su izračunani za 51 aloizin. Dobiveni modeli predviđaju inhibijsku aktivnosti aloizina s točnošću od 82–84 %

Entropy bounds for hierarchical molecular networks

In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of non-hierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entropy of a single hierarchical graph, we see that the derived bounds can also be used for characterizing graph classes. Our contribution is an important extension to previous results about the entropy of non-hierarchical networks because for practical applications hierarchical networks are playing an important role in chemistry and biology. In addition to the derivation of the entropy bounds, we provide a numerical analysis for two special graph classes, rooted trees and generalized trees, and demonstrate hereby not only the computational feasibility of our method but also learn about its characteristics and interpretability with respect to data analysis

Characterization of protein-interaction networks in tumors

<p>Abstract</p> <p>Background</p> <p>Analyzing differential-gene-expression data in the context of protein-interaction networks (PINs) yields information on the functional cellular status. PINs can be formally represented as graphs, and approximating PINs as undirected graphs allows the network properties to be characterized using well-established graph measures.</p> <p>This paper outlines features of PINs derived from 29 studies on differential gene expression in cancer. For each study the number of differentially regulated genes was determined and used as a basis for PIN construction utilizing the Online Predicted Human Interaction Database.</p> <p>Results</p> <p>Graph measures calculated for the largest subgraph of a PIN for a given differential-gene-expression data set comprised properties reflecting the size, distribution, biological relevance, density, modularity, and cycles. The values of a distinct set of graph measures, namely <it>Closeness Centrality</it>, <it>Graph Diameter</it>, <it>Index of Aggregation</it>, <it>Assortative Mixing Coefficient</it>, <it>Connectivity</it>, <it>Sum of the Wiener Number</it>, <it>modified Vertex Distance Number</it>, and <it>Eigenvalues </it>differed clearly between PINs derived on the basis of differential gene expression data sets characterizing malignant tissue and PINs derived on the basis of randomly selected protein lists.</p> <p>Conclusion</p> <p>Cancer PINs representing differentially regulated genes are larger than those of randomly selected protein lists, indicating functional dependencies among protein lists that can be identified on the basis of transcriptomics experiments. However, the prevalence of hub proteins was not increased in the presence of cancer. Interpretation of such graphs in the context of robustness may yield novel therapies based on synthetic lethality that are more effective than focusing on single-action drugs for cancer treatment.</p