Maximal and minimal entry in the principal eigenvector for the distance matrix of a graph

AbstractLet G=(V,E) be a simple, connected and undirected graph with vertex set V(G) and edge set E(G). Also let D(G) be the distance matrix of a graph G (Janežič et al., 2007) [13]. Here we obtain Nordhaus–Gaddum-type result for the spectral radius of distance matrix of a graph.A sharp upper bound on the maximal entry in the principal eigenvector of an adjacency matrix and signless Laplacian matrix of a simple, connected and undirected graph are investigated in Das (2009) [4] and Papendieck and Recht (2000) [15]. Generally, an upper bound on the maximal entry in the principal eigenvector of a symmetric nonnegative matrix with zero diagonal entries and without zero diagonal entries are investigated in Zhao and Hong (2002) [21] and Das (2009) [4], respectively. In this paper, we obtain an upper bound on minimal entry in the principal eigenvector for the distance matrix of a graph and characterize extremal graphs. Moreover, we present the lower and upper bounds on maximal entry in the principal eigenvector for the distance matrix of a graph and characterize extremal graphs

Graph Energies of Egocentric Networks and Their Correlation with Vertex Centrality Measures

Graph energy is the energy of the matrix representation of the graph, where the energy of a matrix is the sum of singular values of the matrix. Depending on the definition of a matrix, one can contemplate graph energy, Randi\'c energy, Laplacian energy, distance energy, and many others. Although theoretical properties of various graph energies have been investigated in the past in the areas of mathematics, chemistry, physics, or graph theory, these explorations have been limited to relatively small graphs representing chemical compounds or theoretical graph classes with strictly defined properties. In this paper we investigate the usefulness of the concept of graph energy in the context of large, complex networks. We show that when graph energies are applied to local egocentric networks, the values of these energies correlate strongly with vertex centrality measures. In particular, for some generative network models graph energies tend to correlate strongly with the betweenness and the eigencentrality of vertices. As the exact computation of these centrality measures is expensive and requires global processing of a network, our research opens the possibility of devising efficient algorithms for the estimation of these centrality measures based only on local information

Búsqueda racional de nuevos fármacos antichagásicos inhibidores de la cruzipaína

En el presente trabajo de tesis se propone descubrir nuevos agentes terapéuticos aplicables en la farmacoterapia de la Enfermedad de Chagas, mediante Cribado Virtual (CV) (también conocido como screening o tamizado virtual) de grandes bases de datos de compuestos químicos. La diversidad química de las bases de datos utilizadas permitirá encontrar prototipos activos novedosos (nuevos líderes). Se han desarrollado, desde el ligando, modelos computacionales capaces de establecer qué características estructurales fundamentales debe reunir un compuesto químico para poseer actividad inhibitoria sobre la cruzipaína (Cz). La Cz es la principal cisteín proteasa del Trypanosoma cruzi (T. cruzi), involucrada en diversas etapas relacionadas con el ciclo de vida del parásito lo cual la convierte en un interesante blanco terapéutico para el desarrollo de nuevos fármacos antichagásico. Aplicamos el conocimiento teórico generado en la búsqueda racional, mediante CV, de nuevos agentes terapéuticos contra la enfermedad de Chagas, contrastando cada estructura química de la base de datos con los modelos generados, para determinar qué compuestos de la base de datos cumplen con los requisitos estructurales definidos por el modelo. Por último a fin de validar de manera experimental las predicciones de los modelos teóricos adquirimos aquellas estructuras señaladas como más promisorias por los modelos desarrollados y evaluamos experimentalmente sus efectos sobre Cz y su capacidad de inhibir el crecimiento de epimastigotes de T. cruzi. 6 compuestos demostraron un efecto inhibitorio sobre Cz dependiente de la concentración y efectos antiproliferativos en T. cruzi. Se estudiaron posteriormente los efectos sobre amastigotes de tres de ellos, y finalmente se avanzó a ensayos preclínicos (modelo murino de infección aguda) con 2 candidatos obteniéndose resultados positivos los cuales permiten ilustrar el potencial de la estrategia propuesta. Este trabajo integra con éxito la búsqueda racional de fármacos asistida por computadora con la biología molecular, celular y ensayos pre-clínicos, lo cual confirma la utilidad de CV para desarrollar el reposicionamiento de fármacos basados en el conocimiento orientado a enfermedades olvidadas.Facultad de Ciencias Exacta

Development and use of databases for ligand-protein interaction studies

This project applies structure-activity relationship (SAR), structure-based and database mining approaches to study ligand-protein interactions. To support these studies, we have developed a relational database system called EDinburgh University Ligand Selection System (EDULISS 2.0) which stores the structure-data files of +5.5 million commercially available small molecules (+4.0 million are recognised as unique) and over 1,500 various calculated molecular properties (descriptors) for each compound. A user-friendly web-based interface for EDULISS 2.0 has been established and is available at http://eduliss.bch.ed.ac.uk/. We have utilised PubChem bioassay data from an NMR based screen assay for a human FKBP12 protein (PubChem AID: 608). A prediction model using a Logistic Regression approach was constructed to relate the assay result with a series of molecular descriptors. The model reveals 38 descriptors which are found to be good predictors. These are mainly 3D-based descriptors, however, the presence of some predictive functional groups is also found to give a positive contribution to the binding interaction. The application of a neural network technique called Self Organising Maps (SOMs) succeeded in visualising the similarity of the PubChem compounds based on the 38 descriptors and clustering the 36 % of active compounds (16 out of 44) in a cluster and discriminating them from 95 % of inactive compounds. We have developed a molecular descriptor called the Atomic Characteristic Distance (ACD) to profile the distribution of specified atom types in a compound. ACD has been implemented as a pharmacophore searching tool within EDULISS 2.0. A structure-based screen succeeded in finding inhibitors for pyruvate kinase and the ligand-protein complexes have been successfully crystallised. This study also discusses the interaction of metal-binding sites in metalloproteins. We developed a database system and web-based interface to store and apply geometrical information of these metal sites. The programme is called MEtal Sites in Proteins at Edinburgh UniverSity (MESPEUS; http://eduliss.bch.ed.ac.uk/MESPEUS/). MESPEUS is an exceptionally versatile tool for the collation and abstraction of data on a wide range of structural questions. As an example we carried out a survey using this database indicating that the most common protein types which contain Mg-OATP-phosphate site are transferases and the most common pattern is linkage through the β- and γ-phosphate groups