Aquesta memòria és un recull de diverses desigualtats d'interès principalment en regressió i anàlisi multivariant, les quals en alguns casos s'il·lustren i interpreten gràfícament.En els primers capítols es presenten resultats aparentment desconcertants, com per exemple la desigualtat de Hamilton-Roudledge-Cuadras. els quals ens poden avisar dels perills de l'ús, a la Ileugera, de la regressió lineal múltiple i altres tècniques multivariants.S'estudia també la paradoxa de Simpson i una versió multivariant com és la desigualtat en distàncies Mahalanobis més gran que Pearson.S'ha dedicat també un capítol a l'estudi d'un mètode molt general d'anàlisi multivariant presentat per Cuadras, Atkinson i Fortiana que suposa implícitament la construcció dedensitats de probabilitat a partir de distàncies.En la darrera part de la memòria es presenten desigualtats per a la variància d'una funció d'una variable aleatòria que tenen aspecte semblant a la desigualtat de Cramér-Rao, altres relacionades amb la distància de Wasserstein i altres desjgualtats que s'obtenen de la propietat d'acotació de la raó de versemblança.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / The present work describes the phytochemistry study and antimicrobial activity of the aerial parts and bark root of three species from Rhamnaceae family: Discaria americana Gilles & Hook, Colletia paradoxa Sprengel and Gouania ulmifolia Hook & Arnott. Four new cyclopeptide natural, discarene C (154), discarene D (155), discarine M (156), discarine N (157) and nine cyclopeptide alkaloids, adoutine Y (92), adoutine Y' (47), franganine (66), frangulanine (67), discarine A (59), discarine B (58), discarine C (100), discarine D (101) and myrianthine A (105), a pentacyclic triterpenoid, acid betulinic (192) and three sterols, β-Sitosterol (195), β-sitosterol-3-O-6-β-D-glucopyranoside (196) and β-sitosterol-3-O-6-stearoyl-β-D-glucopyranoside (197), were isolated of the bark root of D. americana, along with three compounds already described 192, 195, 196, two pentacyclic triterpenoids, ursolic acid (194) and ceanotic acid (193) and an ester derived from ferulic acid (198) of the aerial parts. From the aerial parts of C. paradoxa it was isolated a new compound, called seco-3,4-germanicone (205), along with the known compounds ursolic acid (194), lupeol (199), betulinic acid (192), ceanothic acid (193), taraxerol (200), taraxerone (201), seco-3,4-taraxerone (202), germanicol (203), germanicone (204), β-sitosterol (195) and β-sitosterol-3-O-6-β-D-glucopyranoside (196). From the bark root it was isolated zizyberenalic acid (206), along with compounds 192, 193, 194, 195 and 196. The extracts of the aerial parts of Gouania ulmifolia, two new pentacyclic triterpenoids were isolated, 2-hydroxy-2-nor-20(29)-lupen-27,28-dioic acid (208)and 24-hydroxy-A(1)-nor-2,20(29)-lupadien-27,28-dioic acid (209), along with the known compounds lupeol (199), betulinic acid (192), alphitolic acid (207), β-sitosterol (195) and β-sitosterol-3-O-6-β-D-glucopyranoside (196). All compounds are being described for the first time in the species. Additionally, antimicrobial activity of extracts, fractions and isolated compounds of Discaria americana, Colletia paradoxa and Gouania ulmifolia was analyzed, through the bioautography technique, measuring the inhibitory activity of the growth on different microorganisms, three Gram positive bacteria (Staphylococcus aureus, Bacillus subtilis, Staphylococcus epidermidis) and four Gram negative bacteria (Klebsiella pneumonia, Salmonella setubal, Escherichia coli and Pseudomona aeruginosa) and the fungus (Saccharomyces cerevisiae and Candida albicans). / O presente trabalho descreve o estudo fitoquímico e antimicrobiano das partes aéreas e casca da raiz de três espécies pertencentes à família Rhamnaceae: Discaria americana Gilles & Hook, Colletia paradoxa Sprengel e Gouania ulmifolia Hook & Arnott. Quatro novos ciclopeptídeos naturais, discareno C (154), discareno D (155), discarina M (156), discarina N (157) e nove alcalóides ciclopeptídicos, adoutina Y (92), adoutina Y (47), franganina (66), frangulanina (67), discarina A (59), discarina B (58), discarina C (100), discarina D (101) e miriantina A (105), um triterpeno pentacíclico, ácido betulínico (192) e três esteróides, β-sitosterol (195), β-sitosterol glicosilado (196) e β-sitosterol 6'-O-acil glicosilado (197), foram isolados da casca da raiz de D. americana, juntamente com três compostos já descritos 192, 195, 196, dois triterpenos pentacíclicos, ácido ursólico (194) e ácido ceanótico (193) e um éster derivado ácido ferúlico (198) das partes aéreas. Das partes aéreas de C. paradoxa isolou-se um novo metabólito, denominado seco-3,4-germanicona (205), juntamente com os compostos conhecidos, ácido ursólico (194), lupeol (199), ácido betulínico (192), ácido ceanótico (193), taraxerol (200), taraxerona (201), seco-3,4-taraxerona (202), germanicol (203), germanicona (204), β-sitosterol (195) e β-sitosterol glicosilado (196). Da casca da raiz foi isolado ácido ziziberenálico (206), juntamente com os compostos 192, 193, 194, 195 e 196. Dos extratos das partes aéreas de Gouania ulmifolia foram isolados dois novos triterpenos pentacíclicos, ácido 2-hidroxi-2-nor-20(29)-lupen-27,28-dióico (208) e ácido 24-hidroxi-A(1)-nor-2,20(29)-lupadien-27,28-dióico (209), juntamente com os compostos conhecidos lupeol (199), ácido betulínico (192), ácido alfitólico (207), β-sitosterol (195) e β-sitosterol glicosilado (196). Todos compostos estão sendo descritos pela primeira vez na espécie. Adicionalmente, foram analisadas as atividades antimicrobianas dos extratos, frações e metabólitos isolados de Discaria americana, Colletia paradoxa e Gouania ulmifolia, através da técnica de bioautografia, medindo-se as atividades inibitórias do crescimento sobre diferentes microorganismos, três bactérias Gram positivas (Staphylococcus aureus, Bacillus subtilis, Staphylococcus epidermidis) e quatro bactérias Gram negativas (Klebsiella pneumonia, Salmonella setubal, Escherichia coli e Pseudomona aeruginosa) e os fungos (Saccharomyces cerevisiae e Candida albicans).

La méthode microgravimétrique statique a permis d’observer que la pulpe de l’aiélé est plus hygroscopique que l’amande de karité à 25°C. A l’inverse, on fait l’observation contraire entre 35 et 55°C. Le modèle d’Oswin décrit le mieux les données de sorption des deux produits sur toute la gamme d’activité de l’eau. Les isothermes de l’amande de karité et de la pulpe de l’aiélé présentent le phénomène d’hystérésis entre 25 et 55°C. La conservation de ces oléagineux doit s’effectuer dans une atmosphère d’humidité relative comprise entre 40 et 60% afin d’obtenir des teneurs en eau recommandées. Un modèle adapté de prédiction des isothermes de sorption de ces oléagineux en deçà de 25°C et au delà de 55°C a été obtenu. L’extraction de la matière grasse au CO2 supercritique donne des rendements inférieurs à ceux obtenus de l’extraction à l’hexane. L’indice d’acide des matières grasses extraites au CO2 est supérieur à celui des lipides extraits à l’hexane. Ces indices, pour les lipides extraits des produits stockés à 18°C, sont les plus élevés. Quelque soient le mode de stockage et le solvant d’extraction, l’indice d’iode baisse avec le stockage. Le CO2 présente une sélectivité vis-à-vis de l’acide linolénique. Les lipides extraits au CO2 présentent les taux d’acides gras libres les plus élevés. Il ressort des résultats que le stockage -33°C est le meilleur. Toutefois, il ne doit pas dépasser 5 mois. L’extraction des lipides au CO2 supercritique doit utiliser les fruits frais ou stockés à -33°C. Les produits stockés à 18°C sont les plus durs et la dureté est corrélée négativement à la teneur en eau, mais positivement à l’indice d’acide des matières grasses extraites / The static microgravimetric method permitted to observe that the Canarium pulp was more hygroscopic at 25°C than the sheanut kernels. On the other hand, sheanut kernel was more hygrocopic in the temperature range 35°C-55°C. The Oswin model best described the sorption data of the two products in the whole water activity range. Hysteresis was observed in the entire temperature range 25-55°C for sheanut kernel and Canarium pulp. It is suggested that these products should be stored in an environment with a relative humidity of 40-60%, in order to attain the recommended moisture content for storage. A model was adapted to predict the sorption isotherms of shea and Canarium below 25°C and above 55°C. The oil yields obtained with supercritical CO2 were lower than those obtained with hexane. The acid values of butter and oil extracted with carbon dioxide were greater than those of lipids extracted using hexane. The acid values of samples stored at 18°C were the largest. The iodine value of the oils decreased with an increase of the storage period, irrespective of the storage temperature and the solvent used for extraction. The extraction with CO2 did not extract linolenic acid. The proportion of free fatty acids increased when carbon dioxide was used for extraction. From the foregoing, it is suggested that storage at -33°C for up to 5 months presents the best means of preserving these products. Only fresh or fruits stored at -33°C should be used for the extraction of lipids using carbon dioxide. The products stored at 18°C were the most hard and the hardness was correlated negatively to the water content, but positively to the acid value of fatty material extracted

Natural products are acknowledged sources of novel compounds for use in the treatment of diseases such as cancer, malaria, and human African trypanosomiasis. However, health burdens of such diseases still remain high, with drug resistance leading to failure of current medication. Therefore, there is a need for new treatments, and this project considers the potential of Nigerian ethno-medicinal plants and their products. Firstly, the aims were to isolate cytotoxic compounds through bio-guided evaluation and fractionation from 3 medicinal plants; Vitellaria paradoxa, Cyperus articulatus and Securidaca longepedunculata used traditionally in the treatment of cancer in North-East Nigeria. Extracts from S. longepedunculata were the most active when assessed in a panel of cancer cell lines, with IC50 values below 10 µg/ml, whilst fractions isolated from V. paradoxa and C. articulatus were moderately cytotoxic and able to overcome drug resistance mechanisms in drug resistant cell lines. In the second part of the thesis, novel cryptolepine analogues were semi-synthesized using environmentally friendly methods and evaluated for cytotoxic, anti-plasmodial and anti-trypanosomal activity. The compounds were found to be highly cytotoxic in cancer cell lines with the ability to overcome drug resistant mechanisms, with sub-µM IC50 values, and were also active against drug resistant strains of Plasmodium parasites in addition to Trypanosoma brucei, with IC50 values below 500 nM, and 300 pM respectively. / Schlumberger Faculty for the Future Foundation

Conselho Nacional de Desenvolvimento Científico e Tecnológico / Soil is a structurally complex environment and an important reservoir of microbial diversity. Only a small portion of this diversity has been recovered and cultured by conventional techniques, which limits the access to genetic and metabolic information in such microorganisms. Soil bacteria synthesize a wide variety of secondary metabolites, particularly of antibiotics. Polyketide synthase (PKS) and non-ribosomal peptide synthetase have been highlighted as important enzymatic systems for the biosynthesis of these compounds. The detection of genes associated with these two biosynthetic systems in bacterial isolates has become a strategy to screening for antagonists with high biological control activity. Therefore, the objective of this study was to evaluate bacterial isolates for their in vitro antagonistic activity against plant pathogens of agricultural interest and to analyze their genomes for the presence of genes associated with the synthesis of bioactive compounds activity. Methods of soil sample pre-treatment with chloramine-T and phenol were used for selective isolation and followed by preliminary qualitative antibiosis tests of isolates against the fungal pathogens Thielaviopsis paradoxa and Plenodomus destruens. Extracellular extracts from isolates selected in this previous step were further evaluated for the in vitro antagonist potential against Thielaviopsis paradoxa, Plenodomus destruens and Xanthomonas campestris and compared with the active ingredient of a commercial biofungicide. The taxonomic affiliation of the antagonistic isolates was assessed by sequencing of 16S rDNA gene. For the detection of PKS and NRPS genes, degenerate primers described in the literature were used. Two hundred and fifty-seven bacterial isolates, in their majority belonging to the genus Bacillus or similar, were obtained. Out of those, 84 (33%) were simultaneously bioactive for both fungi in qualitative tests. Fourty-eight bacterial isolates had extracellular extracts with inhibitory effects against Thielaviopsis paradoxa, with eight of these with inhibition ≥80%, when compared to the control. Plenodomus destruens was inhibited by the extracellular extracts of 63 isolates, of which 10 inhibited ≥80% of this pathogen growth. The extract of a Bacillus isolate from a commercial biofungicide strongly inhibited P. destruens (95%), but had no effect on T. paradoxa. Thirty antagonistic isolates from this study did not differed from this commercial isolate regarding in vitro growth inhibition of P. destruens by their extracts of 27 isolates inhibited X. campestris (inhibition rates varying from 45 to 100%), of which six completely suppressed the growth of this bacteria. There was no relationship between either the presence of PKS genes or the joined occurrence of NRPS and PKS and the inhibitory action of the strains on the relative growth of the pathogens. Only the presence of NRPS genes was associated with the effect on the relative growth of Thielaviopsis paradoxa. The isolation of bacteria with promising bioactive potential associated with experiments at greenhouse and field attesting to the feasibility of its use, will enable the achievement of new biocontrol agents. / O solo é um ambiente estruturalmente complexo e um importante reservatório da diversidade microbiana. Somente uma pequena proporção desta diversidade tem sido recuperada e cultivada por técnicas convencionais, o que limita o acesso às informações genéticas e metabólicas desses micro-organismos. Bactérias do solo sintetizam uma ampla variedade de metabólitos secundários, em particular de antimicrobianos. Sintases de policetídeo (PKS) e da sintetases de peptídeo não-ribossomal (NRPS) têm se destacado como importantes sistemas enzimáticos para a biossíntese destes compostos. A detecção de genes associados com estes dois sistemas biossintéticos em isolados de bactérias é uma estratégia para a seleção de antagonistas com alta atividade de controle biológico. Diante disso, o objetivo deste estudo foi isolar e avaliar o potencial dos isolados quanto à atividade antagônica in vitro frente a fitopatógenos de interesse agrícola, e analisar em seus respectivos genomas a presença de genes associados à síntese de compostos bioativos. Métodos de pré-tratamentos das amostras de solo com cloramina T e fenol foram utilizados para o isolamento e seguidos por testes de antibiose qualitativos frente aos fitopatógenos fúngicos Thielaviopsis paradoxa e Plenodomus destruens. Filtrados extracelulares dos isolados selecionados nesta etapa foram quantitativamente avaliados a seguir quanto à capacidade de inibição de T. paradoxa, P. destruens e Xanthomonas campestris, e comparados com o ingrediente ativo de um biofungicida comercial. A afiliação taxonômica dos isolados antagonistas foi realizada com base nas sequências parciais do gene DNAr 16S. Para a detecção dos genes PKS e NRPS foram utilizados primers degenerados descritos na literatura. Dos 257 isoladas bacterianos obtidos, a grande maioria foi pertencente ao gênero Bacillus ou outros proximamente afiliados. Destes, 84 (33%) foram inibitórios de ambos os fungos nos testes qualitativos. Quarenta e oito isolados bacterianos apresentaram filtrados extracelulares com efeitos inibitórios contra T. paradoxa, com oito destes com inibições de mais de 80% comparativamente ao controle sem filtrado. P destruens foi inibido pelo filtrado extracelular de 63 isolados, dos quais 10 inibiram mais de 80% do crescimento deste patógeno. O extrato do isolado de Bacillus do biofungicida comercial apresentou forte inibição sobre P. destruens (95%), mas não afetou T. paradoxa. Trinta isolados antagonistas deste estudo não diferiram deste isolado comercial com relação à inibição do crescimento in vitro de P. destruens pelos extratos. Extratos de 27 isolados inibiram X. campestris (inibições entre 45 e 100% do crescimento), dos quais seis suprimiram totalmente o crescimento desta bactéria. A presença dos genes PKS ou a presença conjunta de genes de NRPS e PKS não foram associadas à ação inibitória dos isolados em relação ao crescimento relativo dos três fitopatógenos. Somente a presença do NRPS associou-se ao efeito sobre o crescimento relativo do Thielaviopsis paradoxa. O isolamento de bactérias com potencial bioativo promissor associado a experimentos em casa-de-vegetação e em campo que atestem a viabilidade do seu uso possibilitará a obtenção de novos agentes de biocontrole.