Arc exchange systems and renormalization

We exhibit the construction of stable arc exchange systems from the stable laminations of hyperbolic diffeomorphisms. We prove a one-to-one correspondence between (i) Lipshitz conjugacy classes of C(1+H) stable arc exchange systems that are C(1+H) fixed points of renormalization and (ii) Lipshitz conjugacy classes of C(1+H) diffeomorphisms f with hyperbolic basic sets Lambda that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Lambda. Let HD(s)(Lambda) and HD(u)(Lambda) be, respectively, the Hausdorff dimension of the stable and unstable leaves intersected with the hyperbolic basic set L. If HD(u)(Lambda) = 1, then the Lipschitz conjugacy is, in fact, a C(1+H) conjugacy in (i) and (ii). We prove that if the stable arc exchange system is a C(1+HDs+alpha) fixed point of renormalization with bounded geometry, then the stable arc exchange system is smooth conjugate to an affine stable arc exchange system.

Role of the DHH1 Gene in the Regulation of Monocarboxylic Acids Transporters Expression in Saccharomyces cerevisiae

Previous experiments revealed that DHH1, a RNA helicase involved in the regulation of mRNA stability and translation, complemented the phenotype of a Saccharomyces cerevisiae mutant affected in the expression of genes coding for monocarboxylic-acids transporters, JEN1 and ADY2 (Paiva S, Althoff S, Casal M, Leao C. FEMS Microbiol Lett, 1999, 170∶301–306). In wild type cells, JEN1 expression had been shown to be undetectable in the presence of glucose or formic acid, and induced in the presence of lactate. In this work, we show that JEN1 mRNA accumulates in a dhh1 mutant, when formic acid was used as sole carbon source. Dhh1 interacts with the decapping activator Dcp1 and with the deadenylase complex. This led to the hypothesis that JEN1 expression is post-transcriptionally regulated by Dhh1 in formic acid. Analyses of JEN1 mRNAs decay in wild-type and dhh1 mutant strains confirmed this hypothesis. In these conditions, the stabilized JEN1 mRNA was associated to polysomes but no Jen1 protein could be detected, either by measurable lactate carrier activity, Jen1-GFP fluorescence detection or western blots. These results revealed the complexity of the expression regulation of JEN1 in S. cerevisiae and evidenced the importance of DHH1 in this process. Additionally, microarray analyses of dhh1 mutant indicated that Dhh1 plays a large role in metabolic adaptation, suggesting that carbon source changes triggers a complex interplay between transcriptional and post-transcriptional effects.