Calculation of Galois groups

In the 19th Century Galois developed a method for determining whether an equation is solvable. It relied on the close relationship between fields and their automorphism group. This paper is a survey of the techniques of Galois theory. After presenting the main results of elementary Galois theory and some useful facts about factorization, I develop the important methods of calculating the Galois group and give a proof of the Chebotarev density theorem

The challenges for molecular nutrition research 3: comparative nutrigenomics research as a basis for entering the systems level

Human nutrition and metabolism may serve as the paradigm for the complex interplay of the genome with its environment. The concept of nutrigenomics now enables science with new tools and comprehensive analytical techniques to investigate this interaction at all levels of the complexity of the organism. Moreover, nutrigenomics seeks to better define the homeostatic control mechanisms, identify the de-regulation in the early phases of diet-related diseases, and attempts to assess to what extent an individual‘s sensitizing genotype contributes to the overall health or disease state. In a comparative approach nutrigenomics uses biological systems of increasing complexity from yeast to mammalian models to define the general rules of metabolic and genetic mechanisms in adaptations to the nutritional environment. Powerful information technology, bioinformatics and knowledge management tools as well as new mathematical and computational approaches now make it possible to study these molecular mechanisms at the cellular, organ and whole organism level and take it on to modeling the processes in a “systems biology” approach. This review summarizes some of the concepts of a comparative approach to nutrigenomics research, identifies current lacks and proposes a concerted scientific effort to create the basis for nutritional systems biology

Impact of Oxidative Stress on the Endothelial Dysfunction of Children and Adolescents With Type 1 Diabetes Mellitus: Protection by Superoxide Dismutase?

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Cdk1 and Cdk2 activity levels determine the efficiency of replication origin firing in Xenopus

In this paper, we describe how, in a model embryonic system, cyclin-dependent kinase (Cdk) activity controls the efficiency of DNA replication by determining the frequency of origin activation. Using independent approaches of protein depletion and selective chemical inhibition of a single Cdk, we find that both Cdk1 and Cdk2 are necessary for efficient DNA replication in Xenopus egg extracts. Eliminating Cdk1, Cdk2 or their associated cyclins changes replication origin spacing, mainly by decreasing frequency of activation of origin clusters. Although there is no absolute requirement for a specific Cdk or cyclin, Cdk2 and cyclin E contribute more to origin cluster efficiency than Cdk1 and cyclin A. Relative Cdk activity required for DNA replication is very low, and even when both Cdk1 and Cdk2 are strongly inhibited, some origins are activated. However, at low levels, Cdk activity is limiting for the pre-replication complex to pre-initiation complex transition, origin activation and replication efficiency. As such, unlike mitosis, initiation of DNA replication responds progressively to changes in Cdk activity at low activity levels

Regulation of Microtubule Assembly and Organization in Mitosis by the AAA+ ATPase Pontin

To identify novel proteins important for microtubule assembly in mitosis, we have used a centrosome-based complementation assay to enrich for proteins with mitotic functions. An RNA interference (RNAi)-based screen of these proteins allowed us to uncover 13 novel mitotic regulators. We carried out in-depth analyses of one of these proteins, Pontin, which is known to have several functions in interphase, including chromatin remodeling, DNA repair, and transcription. We show that reduction of Pontin by RNAi resulted in defects in spindle assembly in Drosophila S2 cells and in several mammalian tissue culture cell lines. Further characterization of Pontin in Xenopus egg extracts demonstrates that Pontin interacts with the gamma tubulin ring complex (γ-TuRC). Because depletion of Pontin leads to defects in the assembly and organization of microtubule arrays in egg extracts, our studies suggest that Pontin has a mitosis-specific function in regulating microtubule assembly