Digital expansions with negative real bases

Similarly to Parry's characterization of $\beta$-expansions of real numbers in real bases $\beta > 1$, Ito and Sadahiro characterized digital expansions in negative bases, by the expansions of the endpoints of the fundamental interval. Parry also described the possible expansions of 1 in base $\beta > 1$. In the same vein, we characterize the sequences that occur as $(-\beta)$-expansion of $\frac{-\beta}{\beta+1}$ for some $\beta > 1$. These sequences also describe the itineraries of 1 by linear mod one transformations with negative slope

Adr1 and Cat8 Mediate Coactivator Recruitment and Chromatin Remodeling at Glucose-Regulated Genes

Adr1 and Cat8 co-regulate numerous glucose-repressed genes in S. cerevisiae, presenting a unique opportunity to explore their individual roles in coactivator recruitment, chromatin remodeling, and transcription.We determined the individual contributions of Cat8 and Adr1 on the expression of a cohort of glucose-repressed genes and found three broad categories: genes that need both activators for full derepression, genes that rely mostly on Cat8 and genes that require only Adr1. Through combined expression and recruitment data, along with analysis of chromatin remodeling at two of these genes, ADH2 and FBP1, we clarified how these activators achieve this wide range of co-regulation. We find that Adr1 and Cat8 are not intrinsically different in their abilities to recruit coactivators but rather, promoter context appears to dictate which activator is responsible for recruitment to specific genes. These promoter-specific contributions are also apparent in the chromatin remodeling that accompanies derepression: ADH2 requires both Adr1 and Cat8, whereas, at FBP1, significant remodeling occurs with Cat8 alone. Although over-expression of Adr1 can compensate for loss of Cat8 at many genes in terms of both activation and chromatin remodeling, this over-expression cannot complement all of the cat8Delta phenotypes.Thus, at many of the glucose-repressed genes, Cat8 and Adr1 appear to have interchangeable roles and promoter architecture may dictate the roles of these activators

30 years of collaboration

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more details, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gaveat the Joint Austrian-Hungarian Mathematical Conference 2015, August 25-27, 2015 in Győr (Hungary)

Transcriptional responses to glucose in Saccharomyces cerevisiae strains lacking a functional protein kinase A

Background The pattern of gene transcripts in the yeast Saccharomyces cerevisiae is strongly affected by the presence of glucose. An increased activity of protein kinase A (PKA), triggered by a rise in the intracellular concentration of cAMP, can account for many of the effects of glucose on transcription. In S. cerevisiae three genes, TPK1, TPK2, and TPK3, encode catalytic subunits of PKA. The lack of viability of tpk1 tpk2 tpk3 triple mutants may be suppressed by mutations such as yak1 or msn2/msn4. To investigate the requirement for PKA in glucose control of gene expression, we have compared the effects of glucose on global transcription in a wild-type strain and in two strains devoid of PKA activity, tpk1 tpk2 tpk3 yak1 and tpk1 tpk2 tpk3 msn2 msn4. Results We have identified different classes of genes that can be induced -or repressed- by glucose in the absence of PKA. Representative examples are genes required for glucose utilization and genes involved in the metabolism of other carbon sources, respectively. Among the genes responding to glucose in strains devoid of PKA some are also controlled by a redundant signalling pathway involving PKA activation, while others are not affected when PKA is activated through an increase in cAMP concentration. On the other hand, among genes that do not respond to glucose in the absence of PKA, some give a full response to increased cAMP levels, even in the absence of glucose, while others appear to require the cooperation of different signalling pathways. We show also that, for a number of genes controlled by glucose through a PKA-dependent pathway, the changes in mRNA levels are transient. We found that, in cells grown in gluconeogenic conditions, expression of a small number of genes, mainly connected with the response to stress, is reduced in the strains lacking PKA. Conclusions In S. cerevisiae, the transcriptional responses to glucose are triggered by a variety of pathways, alone or in combination, in which PKA is often involved. Redundant signalling pathways confer a greater robustness to the response to glucose, while cooperative pathways provide a greater flexibility.BT/BiotechnologyApplied Science

Staphylococcus aureus Keratinocyte Invasion Is Dependent upon Multiple High-Affinity Fibronectin-Binding Repeats within FnBPA

Staphylococcus aureus is a commensal organism and a frequent cause of skin and soft tissue infections, which can progress to serious invasive disease. This bacterium uses its fibronectin binding proteins (FnBPs) to invade host cells and it has been hypothesised that this provides a protected niche from host antimicrobial defences, allows access to deeper tissues and provides a reservoir for persistent or recurring infections. FnBPs contain multiple tandem fibronectin-binding repeats (FnBRs) which bind fibronectin with varying affinity but it is unclear what selects for this configuration. Since both colonisation and skin infection are dependent upon the interaction of S. aureus with keratinocytes we hypothesised that this might select for FnBP function and thus composition of the FnBR region. Initial experiments revealed that S. aureus attachment to keratinocytes is rapid but does not require FnBRs. By contrast, invasion of keratinocytes was dependent upon the FnBR region and occurred via similar cellular processes to those described for endothelial cells. Despite this, keratinocyte invasion was relatively inefficient and appeared to include a lag phase, most likely due to very weak expression of α5β1 integrins. Molecular dissection of the role of the FnBR region revealed that efficient invasion of keratinocytes was dependent on the presence of at least three high-affinity (but not low-affinity) FnBRs. Over-expression of a single high-affinity or three low-affinity repeats promoted invasion but not to the same levels as S. aureus expressing an FnBPA variant containing three high-affinity repeats. In summary, invasion of keratinocytes by S. aureus requires multiple high-affinity FnBRs within FnBPA, and given the importance of the interaction between these cell types and S. aureus for both colonisation and infection, may have provided the selective pressure for the multiple binding repeats within FnBPA

Glucose-induced posttranslational activation of protein phosphatases PP2A and PP1 in yeast

The protein phosphatases PP2A and PP1 are major regulators of a variety of cellular processes in yeast and other eukaryotes. Here, we reveal that both enzymes are direct targets of glucose sensing. Addition of glucose to glucose-deprived yeast cells triggered rapid posttranslational activation of both PP2A and PP1. Glucose activation of PP2A is controlled by regulatory subunits Rts1, Cdc55, Rrd1 and Rrd2. It is associated with rapid carboxymethylation of the catalytic subunits, which is necessary but not sufficient for activation. Glucose activation of PP1 was fully dependent on regulatory subunits Reg1 and Shp1. Absence of Gac1, Glc8, Reg2 or Red1 partially reduced activation while Pig1 and Pig2 inhibited activation. Full activation of PP2A and PP1 was also dependent on subunits classically considered to belong to the other phosphatase. PP2A activation was dependent on PP1 subunits Reg1 and Shp1 while PP1 activation was dependent on PP2A subunit Rts1. Rts1 interacted with both Pph21 and Glc7 under different conditions and these interactions were Reg1 dependent. Reg1-Glc7 interaction is responsible for PP1 involvement in the main glucose repression pathway and we show that deletion of Shp1 also causes strong derepression of the invertase gene SUC2. Deletion of the PP2A subunits Pph21 and Pph22, Rrd1 and Rrd2, specifically enhanced the derepression level of SUC2, indicating that PP2A counteracts SUC2 derepression. Interestingly, the effect of the regulatory subunit Rts1 was consistent with its role as a subunit of both PP2A and PP1, affecting derepression and repression of SUC2, respectively. We also show that abolished phosphatase activation, except by reg1Δ, does not completely block Snf1 dephosphorylation after addition of glucose. Finally, we show that glucose activation of the cAMP-PKA (protein kinase A) pathway is required for glucose activation of both PP2A and PP1. Our results provide novel insight into the complex regulatory role of these two major protein phosphatases in glucose regulation

Stitching together Multiple Data Dimensions Reveals Interacting Metabolomic and Transcriptomic Networks That Modulate Cell Regulation

DNA variation can be used as a systematic source of perturbation in segregating populations as a way to infer regulatory networks via the integration of large-scale, high-dimensional molecular profiling data