Heterosis is defined as the superiority in performance of heterozygous genotypes compared to their corresponding genetically different homozygous parents. This phenomenon is already known since the beginning of the last century and it has been widely used in plant breeding, but the underlying genetic and molecular mechanisms are not well understood. In this work, a systems biological approach based on molecular network structures is proposed to contribute to the understanding of heterosis. Hybrids are likely to contain additional regulatory possibilities compared to their homozygous parents and, therefore, they may be able to correctly respond to a higher number of environmental challenges, which leads to a higher adaptability and, thus, the heterosis phenomenon. In the network hypothesis for heterosis, presented in this work, more regulatory interactions are expected in the molecular networks of the hybrids compared to the homozygous parents. Partial correlations were used to assess this difference in the global interaction structure of regulatory networks between the hybrids and the homozygous genotypes. This network hypothesis for heterosis was tested on metabolite profiles as well as gene expression data of the two parental Arabidopsis thaliana accessions C24 and Col-0 and their reciprocal crosses. These plants are known to show a heterosis effect in their biomass phenotype. The hypothesis was confirmed for mid-parent and best-parent heterosis for either hybrid of our experimental metabolite as well as gene expression data. It was shown that this result is influenced by the used cutoffs during the analyses. Too strict filtering resulted in sets of metabolites and genes for which the network hypothesis for heterosis does not hold true for either hybrid regarding mid-parent as well as best-parent heterosis. In an over-representation analysis, the genes that show the largest heterosis effects according to our network hypothesis were compared to genes of heterotic quantitative trait loci (QTL) regions. Separately for either hybrid regarding mid-parent as well as best-parent heterosis, a significantly larger overlap between the resulting gene lists of the two different approaches towards biomass heterosis was detected than expected by chance. This suggests that each heterotic QTL region contains many genes influencing biomass heterosis in the early development of Arabidopsis thaliana. Furthermore, this integrative analysis led to a confinement and an increased confidence in the group of candidate genes for biomass heterosis in Arabidopsis thaliana identified by both approaches. / Als Heterosis-Effekt wird die Überlegenheit in einem oder mehreren Leistungsmerkmalen (z.B. Blattgröße von Pflanzen) von heterozygoten (mischerbigen) Nachkommen über deren unterschiedlich homozygoten (reinerbigen) Eltern bezeichnet. Dieses Phänomen ist schon seit Beginn des letzten Jahrhunderts bekannt und wird weit verbreitet in der Pflanzenzucht genutzt. Trotzdem sind die genetischen und molekularen Grundlagen von Heterosis noch weitestgehend unbekannt. Es wird angenommen, dass heterozygote Individuen mehr regulatorische Möglichkeiten aufweisen als ihre homozygoten Eltern und sie somit auf eine größere Anzahl an wechselnden Umweltbedingungen richtig reagieren können. Diese erhöhte Anpassungsfähigkeit führt zum Heterosis-Effekt. In dieser Arbeit wird ein systembiologischer Ansatz, basierend auf molekularen Netzwerkstrukturen verfolgt, um zu einem besseren Verständnis von Heterosis beizutragen. Dazu wird eine Netzwerkhypothese für Heterosis vorgestellt, die vorhersagt, dass die heterozygoten Individuen, die Heterosis zeigen, mehr regulatorische Interaktionen in ihren molekularen Netzwerken aufweisen als die homozygoten Eltern. Partielle Korrelationen wurden verwendet, um diesen Unterschied in den globalen Interaktionsstrukturen zwischen den Heterozygoten und ihren homozygoten Eltern zu untersuchen. Die Netzwerkhypothese wurde anhand von Metabolit- und Genexpressionsdaten der beiden homozygoten Arabidopsis thaliana Pflanzenlinien C24 und Col-0 und deren wechselseitigen Kreuzungen getestet. Arabidopsis thaliana Pflanzen sind bekannt dafür, dass sie einen Heterosis-Effekt im Bezug auf ihre Biomasse zeigen. Die heterozygoten Pflanzen weisen bei gleichem Alter eine höhere Biomasse auf als die homozygoten Pflanzen. Die Netzwerkhypothese für Heterosis konnte sowohl im Bezug auf mid-parent Heterosis (Unterschied in der Leistung des Heterozygoten im Vergleich zum Mittelwert der Eltern) als auch auf best-parent Heterosis (Unterschied in der Leistung des Heterozygoten im Vergleich zum Besseren der Eltern) für beide Kreuzungen für die Metabolit- und Genexpressionsdaten bestätigt werden. In einer Überrepräsentations-Analyse wurden die Gene, für die die größte Veränderung in der Anzahl der regulatorischen Interaktionen, an denen sie vermutlich beteiligt sind, festgestellt wurde, mit den Genen aus einer quantitativ genetischen (QTL) Analyse von Biomasse-Heterosis in Arabidopsis thaliana verglichen. Die ermittelten Gene aus beiden Studien zeigen eine größere Überschneidung als durch Zufall erwartet. Das deutet darauf hin, dass jede identifizierte QTL-Region viele Gene, die den Biomasse-Heterosis-Effekt in Arabidopsis thaliana beeinflussen, enthält. Die Gene, die in den Ergebnislisten beider Analyseverfahren überlappen, können mit größerer Zuversicht als Kandidatengene für Biomasse-Heterosis in Arabidopsis thaliana betrachtet werden als die Ergebnisse von nur einer Studie.

Glioblastoma multiforme (GMB) is an extremely aggressive and invasive brain cancer with a median survival of less than one year. In addition, due to its anaplastic nature the histological classification of this cancer is not simple. These characteristics make this disease an interesting and important target for new methodologies of analysis and classification. In recent years, molecular information has been used to segregate and analyze GBM patients, but generally this methodology utilizes single-`omic' data to perform the classification or multi-’omic’ data in a sequential manner. In this project, a novel approach for the classification and analysis of patients with GBM is presented. The main objective of this work is to find clusters of patients with distinctive profiles using multi-’omic’ data with a real integrative methodology. During the last years, the TCGA consortium has made publicly available thousands of multi-’omic’ samples for multiple cancer types. Thanks to this, it was possible to obtain numerous GBM samples (> 300) with data for gene and microRNA expression, CpG sites methylation and copy-number variation (CNV). To achieve our objective, a mixture of linear models were built for each gene using its expression as output and a mixture of multi-`omic' data as covariates. Each model was coupled with a lasso penalization scheme, and thanks to the mixture nature of the model, it was possible to fit multiple submodels to discover different linear relationships in the same model. This complex but interpretable method was used to train over \numprint{10000} models. For \texttildelow \numprint{2400} cases, two or more submodels were obtained. Using the models and their submodels, 6 different clusters of patients were discovered. The clusters were profiled based on clinical information and gene mutations. Through this analysis, a clear separation between the younger patients and with higher survival rate (Clusters 1, 2 and 3) and those from older patients and lower survival rate (Clusters 4, 5 and 6) was found. Mutations in the gene IDH1 were found almost exclusively in Cluster 2, additionally, Cluster 5 presented a hypermutated profile. Finally, several genes not previously related to GBM showed a significant presence in the clusters, such as C15orf2 and CHEK2. The most significant models for each clusters were studied, with a special focus on their covariants. It was discovered that the number of shared significant models were very small and that the well known GBM related genes appeared as significant covariates for plenty of models, such as EGFR1 and TP53. Along with them, ubiquitin-related genes (UBC and UBD) and NRF1, which have not been linked to GBM previously, had a very significant role. This work showed the potential of using a mixture of linear models to integrate multi-’omic’ data and to group patients in order to profile them and find novel markers. The resulting clusters showed unique profiles and their significant models and covariates were comprised by well known GBM related genes and novel markers, which present the possibility for new approaches to study and attack this disease. The next step of the project is to improve several elements of the methodology to achieve a more detail analysis of the models and covariates, in particular taking into account the regression coefficients of the submodels.