RESUMO
BACKGROUND: Hierarchical cluster analysis (HCA) is a widely used classificatory technique in many areas of scientific knowledge. Applications usually yield a dendrogram from an HCA run over a given data set, using a grouping algorithm and a similarity measure. However, even when such parameters are fixed, ties in proximity (i.e. two equidistant clusters from a third one) may produce several different dendrograms, having different possible clustering patterns (different classifications). This situation is usually disregarded and conclusions are based on a single result, leading to questions concerning the permanence of clusters in all the resulting dendrograms; this happens, for example, when using HCA for grouping molecular descriptors to select that less similar ones in QSAR studies. RESULTS: Representing dendrograms in graph theoretical terms allowed us to introduce four measures of cluster frequency in a canonical way, and use them to calculate cluster frequencies over the set of all possible dendrograms, taking all ties in proximity into account. A toy example of well separated clusters was used, as well as a set of 1666 molecular descriptors calculated for a group of molecules having hepatotoxic activity to show how our functions may be used for studying the effect of ties in HCA analysis. Such functions were not restricted to the tie case; the possibility of using them to derive cluster stability measurements on arbitrary sets of dendrograms having the same leaves is discussed, e.g. dendrograms from variations of HCA parameters. It was found that ties occurred frequently, some yielding tens of thousands of dendrograms, even for small data sets. CONCLUSIONS: Our approach was able to detect trends in clustering patterns by offering a simple way of measuring their frequency, which is often very low. This would imply, that inferences and models based on descriptor classifications (e.g. QSAR) are likely to be biased, thereby requiring an assessment of their reliability. Moreover, any classification of molecular descriptors is likely to be far from unique. Our results highlight the need for evaluating the effect of ties on clustering patterns before classification results can be used accurately.Graphical abstractFour cluster contrast functions identifying statistically sound clusters within dendrograms considering ties in proximity.
RESUMO
Fifteen quantitative structure-activity relationship (QSAR) models developed by various authors for the prediction of mutagenicity of aromatic and heteroaromatic amines were analyzed and thirteen of them, based on 95 amines, were compared using their respective statistics and order theory (Hasse Diagram Technique, HDT) to obtain an ordering of QSAR models. The technique of Formal Concept Analysis (FCA) was applied to the set of 95 amines to extract concepts and, in general, knowledge about the relationship between structural attributes and mutagenicity. HDT may be useful as a general tool for the comparison of different classes of QSAR models. FCA turns out to be a novel mathematical technique for seeking for relationships between molecular structure and activity.
Assuntos
Aminas/química , Aminas/farmacologia , Hidrocarbonetos Aromáticos/química , Hidrocarbonetos Aromáticos/farmacologia , Mutagênicos/química , Mutagênicos/farmacologia , Relação Quantitativa Estrutura-Atividade , Aminas/toxicidade , Animais , Humanos , Hidrocarbonetos Aromáticos/toxicidade , Modelos Genéticos , Modelos Estatísticos , Testes de Mutagenicidade , Mutagênicos/toxicidadeRESUMO
There are at least two significant applications of partial order theory in chemistry: Ranking methods and substances' properties prediction. In both cases, a set of objects is endowed with a partial order relation e.g. "more polluting than", "can be obtained from", "more reactive than" etc. The couple of set and partial order relation is known in mathematics as a partially ordered set (poset). Ranking methods, such as the Hasse diagram technique, lead to a partial order where several incomparabilities (lack of order) appear between pairs of objects. This phenomenon is quite common in ranking studies, and it often is circumvented by a combination of object features leading to a total order. However, such a combination introduces subjectivities and bias in the ranking process. Here a step-by-step procedure is shown to turn incomparabilities into comparabilities taking into account all the possible bias by a linear combination of features. In such a manner, it is possible to predict how probable it is to obtain a particular total order from a given poset. Similarly, it is possible to calculate the needed bias over certain attributes to obtain a particular total order. An example application is shown where substances are ranked according to their bioconcentration factor and biodegradation potential. Another application of partial order theory to chemistry has to do with the prediction of properties for a set of substances related in a (preferably systematic) chemical fashion. A customary relation is "can be obtained from"; if such a relation is set up for a given molecular structure e.g. benzene, and all its substituted derivatives (say chlorinated ones) are considered, then the set of benzene and its chlorinated derivatives are partially ordered. Taking advantage of the poset generated, different methods can be applied to predict properties of the substances considered in the poset. Such methods include the poset-average, cluster expansion, and splinoid methods. In this paper we discuss each one of these methods, its advantages and disadvantages and we outline its applicability to estimate cooperative free energies of hemoglobins with different degree of oxygenation.
Assuntos
Modelos Químicos , Relação Quantitativa Estrutura-Atividade , Animais , Hemoglobinas/química , Humanos , Modelos Biológicos , Modelos Moleculares , Compostos Orgânicos/química , Compostos Orgânicos/toxicidadeRESUMO
We have shown in several papers the importance of using topology, particularly set-point topology, to deal with chemical questions related to the concept of similarity. The procedure developed has been called "chemotopology" and it has been applied to different chemical sets e.g. chemical elements, benzimidazoles, sterorids, amino acids and hydrides. The idea behind chemotopology is to run a hierarchical cluster analysis study on a set of objects characterised by different attributes. From this study a dendrogram is obtained, which gathers similarity neighbourhoods for the set of objects. By using a mathematical characterisation of a dendrogram it is possible to select a collection of objects' neighbourhoods which in turn become a basis for a topology. With this basis at hand different properties of subsets of objects can be calculated, all of them related to the concept of similarity e.g. closures, derived sets, boundaries, interiors and exteriors. We have also shown the chemical meaning of each one of these properties. In this manuscript, we review the foundations of the chemotopological method as well as its different applications to chemical sets. By means of examples we illustrate how the method can be used as a versatile tool for drug discovery. We also study the relationship between the topologies generated from dendrograms of a given set of objects and the dendrograms that can be obtained for particular topologies on the set of objects.
Assuntos
Desenho de Fármacos , Aminoácidos/química , Benzimidazóis/química , Análise por Conglomerados , Esteroides/químicaRESUMO
We discussed three dissimilarity measures between dendrograms defined over the same set, they are triples, partition, and cluster indices. All of them decompose the dendrograms into subsets. In the case of triples and partition indices, these subsets correspond to binary partitions containing some clusters, while in the cluster index, a novel dissimilarity method introduced in this paper, the subsets are exclusively clusters. In chemical applications, the dendrograms gather clusters that contain similarity information of the data set under study. Thereby, the cluster index is the most suitable dissimilarity measure between dendrograms resulting from chemical investigation. An application example of the three measures is shown to remark upon the advantages of the cluster index over the other two methods in similarity studies. Finally, the cluster index is used to measure the differences between five dendrograms obtained when applying five common hierarchical clustering algorithms on a database of 1000 molecules.
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El presente estudio evaluó el efecto de la masa antigénica y de diferentes métodos de purificación y concentración del virus de Fiebre Aftosa en la inducción de respuesta de anticuerpos específicos contra proteínas asociadas a la cápside (PC) y no asociadas a la cápside (PNC) en bovinos inmunizados con vacuna oleosa bivalente (A24 Cruzeiro y O1 Campos). Se formularon cuatro vacunas con diferente carga viral por dosis (Vacuna 1, 16.9; Vacuna 2, 8.8; Vacuna 3, 17.9; y Vacuna 4, 7.7 ug/dosis). Se inmunizaron 32 bovinos de 12 a 24 meses de edad (ocho por cada vacuna) a los días 0 y 30. La respuesta serológica contra PC fue evaluada con la prueba de ELISA CFL en términos de Expectativa de Protección Porcentual (EPP) al día 30 y la reactividad a PNC se determinó con el sistema ELISA-I 3ABC/EITB al día 60. Las vacunas formuladas con antígenos virales purificados con sales indujeron mayor EPP promedio tanto para virus A24 Cruzeiro (Vacuna 3, 89.8 por ciento; Vacuna 4, 83.4 por ciento) como O1 Campos (Vacuna 3, 92.6 por ciento; Vacuna 4, 82.2 por ciento) en comparación con los antígenos tratados con Polietilen Glicol cuyos resultados de EPP para virus A24 Cruzeiro fueron: Vacuna 1, 80.2por ciento; Vacuna 2, 71.8 por ciento; y para virus O1 Campos: Vacuna 1, 78.1 por ciento; Vacuna 2, 73.7 por ciento. Adicionalmente, un bovino inoculado con la vacuna 3 fue positivo a PNC a los 60 días post vacunación (dpv). En este estudio se encontró que, dependiendo del proceso de concentración y purificación de antígenos, se pueden obtener resultados diferentes así: para los virus tratados con sales, con una baja (vacuna 4) y alta (vacuna 3) carga antigénica, es posible lograr muy buena inmunogenicidad, mientras que con alta carga antigénica se tiene mayor riesgo de inducir reactividad a PNC; y en el caso de los virus tratados con PEG se obtuvo buena protección, sin evidencia de interferencia en la determinación de los animales infectados cuando fueron evaluados por el sistema....
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Bovinos/imunologia , Febre Aftosa , Febre Aftosa/prevenção & controle , Febre Aftosa/virologia , Vacinação/veterináriaRESUMO
We carried out a topological study of the Space of Chemical Elements, SCE, based on a clustering analysis of 72 elements, each one defined by a vector of 31 properties. We looked for neighborhoods, boundaries, and other topological properties of the SCE. Among the results one sees the well-known patterns of the Periodic Table and relationships such as the Singularity Principle and the Diagonal Relationship, but there appears also a robustness property of some of the better-known families of elements. Alkaline metals and Noble Gases are sets whose neighborhoods have no other elements besides themselves, whereas the topological boundary of the set of metals is formed by semimetallic elements.
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Este informe da cuenta de los resultados de un proyecto encaminado a determinar la posible diversidad fenotípica de la resistencia/susceptibilidad, in vitro, de la raza de ganado criollo colombiano, Blanco Orejinegro (BON), a la infección por virus de estomatitis vesicular (EV) y de Rinotraqueitis Infecciosa Bovina (RIB). Se probaron 47 muestras de fibroblastos primarios de igual número de animales, mediante titulación viral, y se determinó la Dosis Infecciosa Mínima 50 por ciento por ml (DIM50 por ciento/ml) por el método de Spearman karber. Luego se obtuvieron los Índices de Resistencia/ Susceptibilidad (IRS) y se agruparon los cultivos primarios de fibroblastos en resistentes y susceptibles con los siguientes resultados: Para RIB los 47 cultivos primarios de fibroblastos de ganado BON resultaron susceptibles; para EV serotipo Indiana, 37 fueron susceptibles y 10 resistentes, y para EV serotipo New Jersey, se encontraron 41 susceptibles y 5 resistentes. Un polimorfismo fenotípico en resistencia/susceptibilidad, in vitro, del ganado BON, se había demostrado previamente para el virus de la fiebre aftosa.
Assuntos
Bovinos , Bovinos , Doenças dos Bovinos , Imunidade Inata , Rinotraqueíte Infecciosa Bovina , Infecções/veterinária , Patologia Veterinária , Técnicas Genéticas/veterinária , Vírus da Estomatite Vesicular IndianaRESUMO
Se realizó un seguimiento bimensual durante un año, en dos fincas lecheras del Municipio de Fredonia, Antioquia, en mamíferos silvestres, vectores incriminados y en hatos centinelas, con el objetivo de determinar por seroneutralización los porcentajes de animales infectados con el virus de la Estomatitis Vesicular, realizar intentos de aislamiento viral en cada una de estas poblaciones, y detectar fragmentos del genoma viral por RT-PCR y PCR anidado. Se encontró que el porcentaje de infección fue del 57.14 por ciento para el serotipo Indiana (IN) y del 73.01 por ciento para el New Jersey (NJ), igualmente se determinó que el 37.5 por ciento de los animales silvestres capturados mostraron bajos títulos de anticuerpos, 1:8 principalmente y solamente contra el serotipo IN, lo cual parece sugerir que el ciclo de infección en la fauna silvestre no está relacionada con el ciclo en los animales domésticos. De otro lado todas las muestras de sangre de reservorios y macerados de insectos procesadas por las técnicas moleculares mencionadas mostraron resultados negativos. Se discuten los resultados y se proponen nuevos estudios.