14 research outputs found

    Graphical Indices and their Applications

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    The biochemical community has been using graphical (topological, chemical) indices in the study of Quantitative Structure-Activity Relationships (QSAR) and Quantitative Structure-Property Relationships (QSPR), as they have been shown to have strong correlations with the chemical properties of certain chemical compounds (i.e. boiling point, surface area, etc.). We examine some of these chemical indices and closely related pure graph theoretical indices: the Randić index, the Wiener index, the degree distance, and the number of subtrees. We find which structure will maximize the Randić index of a class of graphs known as cacti, and we find a functional relationship between the Wiener index and the degree distance for several types of graphs. We also develop an algorithm to find the structure that maximizes the number of subtrees of trees, a characterization of the second maximal tree may also follow as an immediate result of this algorithm

    Découverte par ordinateur en théorie des graphes

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    Le système AutoGraphiX -- Fonctions d'AutoGraphiX -- La recherche à voisinage variable -- Invariants disponibles dans AutoGraphiX -- Recherche automatique de conjectures -- Applications -- Étude de l'indice de Randié -- Étude de l'énergie d'un graphe -- Étude de l'index d'arbres avec contraintes de coloration -- Recherche d'arbres H-palindromiques -- Résultats et développemtns envisagés -- Conjectures de Graffiti réfutées -- Conjectures obtenues -- Recherche analytique de conjectures -- Définition automatiques des voisinages à utiliser -- Définition interactive d'invariants -- Énumération de familles de graphes -- Énumération de Benzenoides et Helicènes -- Génération ordonnée -- Énumération de polyhexes planaires simplement connectés -- Énumération de polyhexes simplement connectés -- Méthode par décomposition

    On Topological Indices And Domination Numbers Of Graphs

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    Topological indices and dominating problems are popular topics in Graph Theory. There are various topological indices such as degree-based topological indices, distance-based topological indices and counting related topological indices et al. These topological indices correlate certain physicochemical properties such as boiling point, stability of chemical compounds. The concepts of domination number and independent domination number, introduced from the mid-1860s, are very fundamental in Graph Theory. In this dissertation, we provide new theoretical results on these two topics. We study k-trees and cactus graphs with the sharp upper and lower bounds of the degree-based topological indices(Multiplicative Zagreb indices). The extremal cacti with a distance-based topological index (PI index) are explored. Furthermore, we provide the extremal graphs with these corresponding topological indices. We establish and verify a proposed conjecture for the relationship between the domination number and independent domination number. The corresponding counterexamples and the graphs achieving the extremal bounds are given as well

    Cheminformatics Modeling of Diverse and Disparate Biological Data and the Use of Models to Discover Novel Bioactive Molecules

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    Ligand-based drug design is a popular and efficient computational approach to facilitate the drug discovery process. Current approaches mainly focus on optimizing the computational algorithms to improve the efficiency or accuracy of virtual screening; however, the success of ligand-based drug design relies not only on the effectiveness and robustness of the underlying algorithms, but much more importantly, on the quality of the data for model building. Although numerous chemical probe databases have emerged recently, few evaluation of data quality and reliability have been performed. Building upon our lab's experience in Quantitative Structure-Activity Relationship (QSAR) method and methods developed in the field of cheminformatics, this dissertation focuses on: 1) Investigation and comparison of the predictive power of QSAR methods with other ligand-based drug discovery approaches, such as Similarity Ensemble Approach (SEA) and Prediction of Activity Spectra for Substances (PASS); 2) Using QSAR methods to validate the consistency and reliability of biomedical data in disparate data sources. 3) Developing a novel, rigorous and dataset-specific QSAR workflow for the application on multiple therapeutic targets in order to identify diverse hits with high potency in practical virtual screening projects. These works succeed in thoroughly investigating the current approaches for ligand-based drug discovery, exploring the consistency and quality of major annotated cheminformatics databases, and identifying many pharmaceutically important ligands. The success of our studies harshly challenges some popular multi-target profile prediction methods and contributes to the development of cheminformatics by emphasizing the importance of determining trustworthy data sources.Doctor of Philosoph

    Symmetry in Graph Theory

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    This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view

    Experimental determination and computational design of antiaggregatory effect of polyphenolics

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    Među prirodnim spojevima prisutnim u svakodnevnoj prehrani, flavonoidi su pokazali povoljan učinak u prevenciji kardiovaskularnih bolesti koji se, barem djelomično, može pripisati antiagregacijskom učinku. S obzirom na farmakološki interes, u potrazi za antitrombocitnim lijekovima, potrebna je sustavna eksperimentalna procjena antiagregacijskog učinka flavonoida. Takvi podaci mogli bi služiti za QSAR modeliranje antiagregacijskog učinka, istraživanje signalnih putova i procjenu utjecaja na invitro testove agregacije trombocita. Skup od trideset flavonoida, odabran je za procjenu antiagregacijskog učinka, na uzorcima pune krvi pomoću Multiplate® funkcionalnog analizatora (Dynabyte, Njemačka) i ADP-a (ADPtest) kao slabog agonistaagregacije. Pet učinkovitih flavonoida iz ADPtesta je analizirano s četiri dodatna agonistaagregacije (arahidonska kiselina, kolagen, ristocetin i TRAP-6). Za računalno simuliranje antiagregacijskog učinka, generirano je 155 molekulskih deskriptora koji opisuju fizikalno-kemijska, odnosno globalna svojstva molekula i supstituenata. Od računalnih metoda za procjenu mehanizama djelovanja primijenjeno je hijerarhijsko formiranje klasteravišedimenzijskim ponovnim uzorkovanjem. Slučajna šuma, metoda statističkog učenja, korištena je za QSAR modeliranje. Laboratorijski rezultati su iskazani kao minimalna koncentracija flavonoida koja dovodi do statistički značajnog smanjenja agregacije trombocita u odnosu na netretirani uzorak (minimalna antiagregacijska koncentracija ‒ MINaAC). MINaACflavonoida, u pojedinim testovima agregacijekoja je potaknuta ADP-om, kolagenom, TRAP-6 i ristocetinom, bila je u sljedećim rasponima: 0,12‒122,07 μM; 15,26‒244,14 μM; 15,26‒122,07 μM i 0,06‒15,26 μM. U testu agregacije trombocita koja je potaknuta arahidonskom kiselinom, proagregacijski učinak je zapažen kod pinocembrin-7-metiletera, epikatehina, hesperetina i 3,6- dihidroksiflavona. Literaturni su podaci bili nedostatni za interpretaciju rezultata dobivenih tvorbom hijerarhijskih klastera uslijed raznolikih mehanizama djelovanja pojedinih flavonoida. Validacija predviđanja učinka koja se temelji na metodi slučajne šume, rezultirala je niskom točnošćupredviđanja od 40,67%. Mjerljivantiagregacijski učinak, na submikromolarnoj razini koncentracija flavonoida, sugerira da i svakodnevna konzumacija flavonoida prehranom može utjecati na in vivoagregaciju trombocita, što ukazuje i na njihovu moguću terapijsku primjenu. Temeljem antiagregacijskih testova s različitim induktorima agregacije, može se zaključiti da flavonoidi interferiraju s invitroagregacijom trombocita, ili antiagregacijski ili proagregacijski, što može utjecati na interpretaciju testova agregacije trombocita na punoj krvi. Razvoj pouzdanog QSAR modela onemogućuju raznovrsni mehanizmi djelovanja flavonoida kojima se ostvaruje antiagregacijski učinak. Stoga se daljnja istraživanja trebaju usmjeriti na pojedinačne mete i na povećanje broja analiziranih supstancija.Among natural compounds, present in every day diet, flavonoids have shown beneficial effect in prevention of cardiovascular diseases that can be attributed, at least partially, to their antiaggregatory activity. Due to the ever increasing pharmacological interest in antiplatelet agents, a systematic experimental evaluation of large flavonoid series is needed. This will serve as possible data set for QSAR modeling of antiaggregatory activity, assessment of signaling pathways and evaluation of the in vitro effects of flavonoids on platelet aggregation in whole blood. A set of thirty flavonoid aglycones was selected for the evaluation. Aggregation measurements were performed on the whole blood samples with multiple platelet functional analyzer (Dynabyte, Germany) and adenosine diphosphate (ADPtest) as a weak agonist of aggregation. Five potent flavonoids from the ADPtest were further analyzed using the four additional aggregation inducers (arachidonic acid, collagen, ristocetin and TRAP-6). Computational design of antiaggregatory effect was based on 155 molecular descriptors of physical and chemical properties; global properties of molecule and substituents. Method for the assessment of the possible mechanisms of action used was hierarchical clustering with multiscale bootstrap resampling. Random forest, a statistical learning method, was used for QSAR modeling. Laboratory results were expressed as minimal concentration of flavonoid that can significantly lower the platelet aggregation compared to the corresponding untreated sample (minimal antiaggregatory concentration ‒ MINaAC). MINaAC of flavonoids in individual tests were reported in the following ranges: 0.12‒122.07 μM; 15.26‒244.14 μM; 15.26‒122.07 μM; and 0.06‒15.26 μM for ADP, collagen, TRAP-6 and ristocetin aggregation-inducers, respectively. When arachidonic acid was used for induction of platelet aggregation, a proaggregatory effect was observed for pinocembrin-7-methylether, epicatechin, hesperetin and 3,6- dihydroxyflavone. Literature data was inconclusive for proper interpretation of hierarchical clustering due to different mechanism by which flavonoids achieve antiaggregatory effect. Validation of random forest prediction model resulted in 40.67% accuracy. Measurable antiplatelet activity established at submicromolar flavonoid concentrations suggests that even a dietary consumption of some flavonoids can make an impact on in vivo aggregation of platelets. These findings also point out a therapeutic potential of some flavonoids. Based on the test with different agonists of aggregation it can be concluded that flavonoids interfere with in vitro platelet aggregation assays exhibiting either anti- or pro-aggregatory influencing the interpretation of the results of platelet aggregation. Development of reliable QSAR model under described settings is not possible due to different mechanisms responsible for antiaggregatory effect. Further studies should focus on specific targets; number of the analyzed substances should be increased

    Experimental determination and computational design of antiaggregatory effect of polyphenolics

    Get PDF
    Među prirodnim spojevima prisutnim u svakodnevnoj prehrani, flavonoidi su pokazali povoljan učinak u prevenciji kardiovaskularnih bolesti koji se, barem djelomično, može pripisati antiagregacijskom učinku. S obzirom na farmakološki interes, u potrazi za antitrombocitnim lijekovima, potrebna je sustavna eksperimentalna procjena antiagregacijskog učinka flavonoida. Takvi podaci mogli bi služiti za QSAR modeliranje antiagregacijskog učinka, istraživanje signalnih putova i procjenu utjecaja na invitro testove agregacije trombocita. Skup od trideset flavonoida, odabran je za procjenu antiagregacijskog učinka, na uzorcima pune krvi pomoću Multiplate® funkcionalnog analizatora (Dynabyte, Njemačka) i ADP-a (ADPtest) kao slabog agonistaagregacije. Pet učinkovitih flavonoida iz ADPtesta je analizirano s četiri dodatna agonistaagregacije (arahidonska kiselina, kolagen, ristocetin i TRAP-6). Za računalno simuliranje antiagregacijskog učinka, generirano je 155 molekulskih deskriptora koji opisuju fizikalno-kemijska, odnosno globalna svojstva molekula i supstituenata. Od računalnih metoda za procjenu mehanizama djelovanja primijenjeno je hijerarhijsko formiranje klasteravišedimenzijskim ponovnim uzorkovanjem. Slučajna šuma, metoda statističkog učenja, korištena je za QSAR modeliranje. Laboratorijski rezultati su iskazani kao minimalna koncentracija flavonoida koja dovodi do statistički značajnog smanjenja agregacije trombocita u odnosu na netretirani uzorak (minimalna antiagregacijska koncentracija ‒ MINaAC). MINaACflavonoida, u pojedinim testovima agregacijekoja je potaknuta ADP-om, kolagenom, TRAP-6 i ristocetinom, bila je u sljedećim rasponima: 0,12‒122,07 μM; 15,26‒244,14 μM; 15,26‒122,07 μM i 0,06‒15,26 μM. U testu agregacije trombocita koja je potaknuta arahidonskom kiselinom, proagregacijski učinak je zapažen kod pinocembrin-7-metiletera, epikatehina, hesperetina i 3,6- dihidroksiflavona. Literaturni su podaci bili nedostatni za interpretaciju rezultata dobivenih tvorbom hijerarhijskih klastera uslijed raznolikih mehanizama djelovanja pojedinih flavonoida. Validacija predviđanja učinka koja se temelji na metodi slučajne šume, rezultirala je niskom točnošćupredviđanja od 40,67%. Mjerljivantiagregacijski učinak, na submikromolarnoj razini koncentracija flavonoida, sugerira da i svakodnevna konzumacija flavonoida prehranom može utjecati na in vivoagregaciju trombocita, što ukazuje i na njihovu moguću terapijsku primjenu. Temeljem antiagregacijskih testova s različitim induktorima agregacije, može se zaključiti da flavonoidi interferiraju s invitroagregacijom trombocita, ili antiagregacijski ili proagregacijski, što može utjecati na interpretaciju testova agregacije trombocita na punoj krvi. Razvoj pouzdanog QSAR modela onemogućuju raznovrsni mehanizmi djelovanja flavonoida kojima se ostvaruje antiagregacijski učinak. Stoga se daljnja istraživanja trebaju usmjeriti na pojedinačne mete i na povećanje broja analiziranih supstancija.Among natural compounds, present in every day diet, flavonoids have shown beneficial effect in prevention of cardiovascular diseases that can be attributed, at least partially, to their antiaggregatory activity. Due to the ever increasing pharmacological interest in antiplatelet agents, a systematic experimental evaluation of large flavonoid series is needed. This will serve as possible data set for QSAR modeling of antiaggregatory activity, assessment of signaling pathways and evaluation of the in vitro effects of flavonoids on platelet aggregation in whole blood. A set of thirty flavonoid aglycones was selected for the evaluation. Aggregation measurements were performed on the whole blood samples with multiple platelet functional analyzer (Dynabyte, Germany) and adenosine diphosphate (ADPtest) as a weak agonist of aggregation. Five potent flavonoids from the ADPtest were further analyzed using the four additional aggregation inducers (arachidonic acid, collagen, ristocetin and TRAP-6). Computational design of antiaggregatory effect was based on 155 molecular descriptors of physical and chemical properties; global properties of molecule and substituents. Method for the assessment of the possible mechanisms of action used was hierarchical clustering with multiscale bootstrap resampling. Random forest, a statistical learning method, was used for QSAR modeling. Laboratory results were expressed as minimal concentration of flavonoid that can significantly lower the platelet aggregation compared to the corresponding untreated sample (minimal antiaggregatory concentration ‒ MINaAC). MINaAC of flavonoids in individual tests were reported in the following ranges: 0.12‒122.07 μM; 15.26‒244.14 μM; 15.26‒122.07 μM; and 0.06‒15.26 μM for ADP, collagen, TRAP-6 and ristocetin aggregation-inducers, respectively. When arachidonic acid was used for induction of platelet aggregation, a proaggregatory effect was observed for pinocembrin-7-methylether, epicatechin, hesperetin and 3,6- dihydroxyflavone. Literature data was inconclusive for proper interpretation of hierarchical clustering due to different mechanism by which flavonoids achieve antiaggregatory effect. Validation of random forest prediction model resulted in 40.67% accuracy. Measurable antiplatelet activity established at submicromolar flavonoid concentrations suggests that even a dietary consumption of some flavonoids can make an impact on in vivo aggregation of platelets. These findings also point out a therapeutic potential of some flavonoids. Based on the test with different agonists of aggregation it can be concluded that flavonoids interfere with in vitro platelet aggregation assays exhibiting either anti- or pro-aggregatory influencing the interpretation of the results of platelet aggregation. Development of reliable QSAR model under described settings is not possible due to different mechanisms responsible for antiaggregatory effect. Further studies should focus on specific targets; number of the analyzed substances should be increased

    Application of the Google matrix methods for characterization of directed networks

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    La théorie des réseaux complexes est un domaine récent et important de la recherche qui consiste étudier divers systèmes naturels ou artificiels d'un point de vue des graphes en considérant une collection d'objets interdépendants. Parmi les différents aspects de la théorie des réseaux complexes, cette thèse se concentre sur l'analyse des propriétés structurelles des réseaux dirigés. L'outil principal utilisé dans ce travail est la méthode de la matrice Google qui est une méthode dérivée de la théorie des chaînes de Markov. La construction de cette matrice et son lien avec les chaînes de Markov sont expliqués dans le second chapitre et les propriétés spectrales des valeurs propres y sont également discutées. L'accent est mis sur le vecteur propre principal dela matrice (le PageRank). La base du système de ranking donné par le Page Rank y est expliquée en détail et illustrée à travers plusieurs exemples dans les chapitres suivants. Les systèmes considérés ici sont: les séquences d'ADN de quelques espèces animales,le système nerveux du vers C.elegans ainsi que l'antique jeu de stratégie sur plateau, le jeu de go. Dans le premier cas nous analysons les propriétés statistiques des chaînes symboliques sous le point de vue des réseaux dirigés et nous proposons une mesure simple de similarité entre les espèces basée sur le PageRank. Dans le second cas nous introduisons le concept du ranking complémentaire (le CheiRank) permettant de caractériser en deux dimensions les réseaux dirigés. Dans le troisième cas nous utilisons les vecteurs propres principaux pour mettre en évidence les coups importants joués lors d'une partie de Go et nous montrons que les vecteurs propres suivants peuvent contenir des informations de communautés de coups. Ces diverses applications montrent que l'information apportée par le PageRank peut s'avérer utile dans de nombreuses situations différentes affin d'obtenir un aperçu du problème sous un angle différent, qui est l'approche des réseaux dirigés, enrichissant ainsi notre compréhension des systèmes étudiés.The complex network theory is a recent field of great importance to study various systems under a graph perspective by considering a collection of interdependent objects. Among the different aspects of the complex networks, this thesis is focused on the analysis of structural properties of directed networks. The primary tool used in this work is the Google matrix method which is derived from the Markov chain theory. The construction of this matrix and its link with Markov chains are explored and the spectral properties of the eigenvalues are discussed with an emphasis on the dominant eigenvalue with its associated eigenvector(PageRank vector). The ranking system given by the PageRank is explained in detail and illustrated through several examples. The systems considered here are the DNA sequences of some animal species, the neural system of the C.elegans worm and the ancient strategy board game : the game of Go. In the first case, the statistical properties of symbolic chains are analyzed through a directed network viewpoint and a similarity measure of species based on PageRank is proposed. In the second case, the complementary ranking system (CheiRank vector) is introduced to provide a two dimensional characterization of the directed networks. In the third case, the dominant eigenvectors are used to highlight the most important moves during a game of Go and it is shown that those eigenvectors contain more information than mere frequency counts of the moves. It is also discussed that eigenvectors other than the dominant ones might contain information about some community structures of moves. These applications show how the information brought by the PageRank can be useful in various situations to gain some interesting or original insight about the studied system and how it is helping to understand the organization of the underlying directed network
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