In this dissertation, we propose methodology to analyze high dimensional genomics data, in which the observations have large number of outcome variables, in addition to exposure variables. In the Chapter 1, we investigate methods for genetic pathway analysis, where we have a small number of exposure variables. We propose two Canonical Correlation Analysis based methods, that select outcomes either sequentially or by screening, and show that the performance of the proposed methods depend on the correlation between the genes in the pathway. We also propose and investigate criterion for fixing the number of outcomes, and a powerful test for the exposure effect on the pathway. The methodology is applied to show that air pollution exposure affects gene methylation of a few genes from the asthma pathway. In Chapter 2, we study penalized multivariate regression as an efficient and flexible method to study the relationship between large number of covariates and multiple outcomes. We use penalized likelihood to shrink model parameters to zero and to select only the important effects. We use the Bayesian Information Criterion (BIC) to select tuning parameters for the employed penalty and show that it chooses the right tuning parameter with high probability. These are combined in the “two-stage procedure”, and asymptotic results show that it yields consistent, sparse and asymptotically normal estimator of the regression parameters. The method is illustrated on gene expression data in normal and diabetic patients. In Chapter 3 we propose a method for estimation of covariates-dependent principal components analysis (PCA) and covariance matrices. Covariates, such as smoking habits, can affect the variation in a set of gene methylation values. We develop a penalized regression method that incorporates covariates in the estimation of principal components. We show that the parameter estimates are consistent and sparse, and show that using the BIC to select the tuning parameter for the penalty functions yields good models. We also propose the scree plot residual variance criterion for selecting the number of principal components. The proposed procedure is implemented to show that the first three principal components of genes methylation in the asthma pathway are different in people who did not smoke, and people who did.

L’homéostasie de la taille des cellules implique l’existence de mécanismes capables de coordonner la croissance (l’augmentation du volume) avec la prolifération (l’augmentation du nombre de cellules). Il est clairement établi que la taille des cellules est affectée par la disponibilité en nutriment du milieu de culture et par la ploïdie, mais les mécanismes sous-jacents demeurent inconnus. Une étude à l’échelle du génome réalisée chez la levure par l’équipe de M. Tyers a révélée que l’inactivation d’environ 400 gènes conduisait à un volume cellulaire moyen significativement différent de celui de la souche sauvage isogénique. Le contrôle de la taille des cellules est ainsi une situation intéressante dans laquelle de nombreux loci contribuent à un caractère quantitatif complexe. La plupart de ces loci demeurant orphelin de voie de signalisation distincte, leur influence respective reste à élucider. Nous avons commencé cette étude en partant de l’observation qu’un mutant sir2 présentait un volume cellulaire augmenté. De manière cohérente, un traitement au nicotinamide (Nam), un inhibiteur de Sir2, reproduit le défaut de taille de sir2 par un mécanisme dépendant de Sir2p. Nous avons alors pu, par une approche d’épistasie chimique, identifier 22 mutants non affectés par le traitement de la Nam, parmi ~200 mutants de petite taille. De manière surprenante, 16 de ces 22 mutants de taille insensibles à la NAM, sont affectés dans la biogenèse de la grande sous unité du ribosome (60S). Une drogue capable de bloquer spécifiquement la biogenèse tardive de la 60S, la diazaborine, mime le phénotype de taille des mutants de la 60S, produisant des cellules sauvages plus petites. Un ensemble de ~200 mutants de grande taille a été traité à la diazaborine et leur volume mesuré. Cette approche chimiogénétique nous a permis d’identifier 31 mutants insensibles à la diazaborine, incluant swi4 et swi6, deux régulateurs majeurs du cycle cellulaire, critiques pour le contrôle de la taille des cellules. Ces résultats furent confirmés par la construction de double mutants. Ce travail montre qu’il est possible d’organiser des mutants de taille au sein de voies spécifiques et de définir des relations d’épistasie claires entre eux. Nos données indiquent que le contrôle de la taille par cette voie “Sir2-60S” est indépendant des effets de la ploïdie et du contrôle nutritionnel sur la taille des cellules. / Cell size homeostasis implies that specific mechanisms are devoted to coordinating growth and proliferation. It is well established that cell size is affected by nutrient availability and ploidy but the underlying mechanisms are not elucidated. A genome wide search for yeast mutants affected for cell volume homeostasis, conducted in the Tyers’lab, revealed that the inactivation of about 400 genes leads to a median cell volume diverging from the isogenic wild-type. The cell size control process is thus a very interesting situation where multiple loci contributing to a complex quantitative trait have been identified but their organisation into distinct pathways and their respective influence remain largely to be elucidated. To address this issue, we started from the observation that a sir2 mutant shows an increased cell size. Consistently, nicotinamide (NAM), a Sir2 inhibitor, mimics the sir2 size defect in a Sir2p-dependent manner. This allowed us to identify among ~200 small size mutants, 22 mutants that were clearly not affected by NAM treatment. Strikingly, 16 out of the 22 NAM unresponsive mutants affected biogenesis of the large ribosomal subunit (named 60S below). Consistently, diazaborine, a drug that blocks the large ribosomal subunit assembly and therefore mimics 60S mutants, rendered wild-type yeast cells smaller. A set of ~200 large mutants were treated with diazaborine and their cell volume was measured. This chemogenetics approach allowed us to identify 31 diazaborine-unresponsive mutants, including swi4 and swi6, two major cell cycle regulators that are critical for cell size control. These results were confirmed by constructing double mutants. This work shows that it is possible to organize cell size mutants in specific pathways and to define clear epistasis relationships between them. Our data indicate that the control of cell size by the “Sir2-60S” pathway is independent of both the ploidy and the nutritional control of cell size.