New Polynomial-Based Molecular Descriptors with Low Degeneracy

In this paper, we introduce a novel graph polynomial called the ‘information polynomial’ of a graph. This graph polynomial can be derived by using a probability distribution of the vertex set. By using the zeros of the obtained polynomial, we additionally define some novel spectral descriptors. Compared with those based on computing the ordinary characteristic polynomial of a graph, we perform a numerical study using real chemical databases. We obtain that the novel descriptors do have a high discrimination power

The conformation-independent QSPR approach for predicting the oxidation rate constant of water micropollutants

In advanced water treatment processes, the degradation efficiency of contaminants depends on the reactivity of the hydroxyl radical toward a target micropollutant. The present study predicts the hydroxyl radical rate constant in water (kOH) for 118 emerging micropollutants, by means of quantitative structure-property relationships (QSPR). The conformation-independent QSPR approach is employed, together with a large number of 15,251 molecular descriptors derived with the PaDEL, Epi Suite, and Mold2 freewares. The best multivariable linear regression (MLR) models are found with the replacement method variable subset selection technique. The proposed five-descriptor model has the following statistics for the training set: R2 train = 0:88, RMStrain = 0.21, while for the test set is R2 test = 0:87, RMStest = 0.11. This QSPR serves as a rational guide for predicting oxidation processes of micropollutants.Instituto de Investigaciones Fisicoquímicas Teóricas y AplicadasFacultad de Ciencias Agrarias y Forestale

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

Interrelationship of Major Topological Indices Evidenced by Clustering

This study examines the mutual relatedness of 318 major topological indices (TIs) for three sets of molecules: (i) a set of 139 hydrocarbons, (ii) a diverse set of 1029 compounds and (iii) a diverse set of 2887 compounds. The TIs included in this study are those that have been frequently used in the characterization of structure and QSAR/ QSPR studies. After variable reduction based on the elimination of TIs for which all values were zero and those that were completely correlated with another TI, a variable clustering technique was used to cluster the TIs which resulted in 16, 37 and 56 clusters, respectively, for the three data sets mentioned above. Analysis of the correspondence among the clusters derived from the three groups of chemicals has been carried out in an effort to understand the dimensionality of the structure spaces derived for the three different sets of chemicals and the structural aspects characterized by the various TIs

Novel topological descriptors for analyzing biological networks

<p>Abstract</p> <p>Background</p> <p>Topological descriptors, other graph measures, and in a broader sense, graph-theoretical methods, have been proven as powerful tools to perform biological network analysis. However, the majority of the developed descriptors and graph-theoretical methods does not have the ability to take vertex- and edge-labels into account, e.g., atom- and bond-types when considering molecular graphs. Indeed, this feature is important to characterize biological networks more meaningfully instead of only considering pure topological information.</p> <p>Results</p> <p>In this paper, we put the emphasis on analyzing a special type of biological networks, namely bio-chemical structures. First, we derive entropic measures to calculate the information content of vertex- and edge-labeled graphs and investigate some useful properties thereof. Second, we apply the mentioned measures combined with other well-known descriptors to supervised machine learning methods for predicting Ames mutagenicity. Moreover, we investigate the influence of our topological descriptors - measures for only unlabeled vs. measures for labeled graphs - on the prediction performance of the underlying graph classification problem.</p> <p>Conclusions</p> <p>Our study demonstrates that the application of entropic measures to molecules representing graphs is useful to characterize such structures meaningfully. For instance, we have found that if one extends the measures for determining the structural information content of unlabeled graphs to labeled graphs, the uniqueness of the resulting indices is higher. Because measures to structurally characterize labeled graphs are clearly underrepresented so far, the further development of such methods might be valuable and fruitful for solving problems within biological network analysis.</p