A shape optimization problem on planar sets with prescribed topology

We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form $P(\Omega)T^q(\Omega)|\Omega|^{-2q-1/2}$ and the class of admissible domains consists of two-dimensional open sets $\Omega$ satisfying the topological constraints of having a prescribed number $k$ of bounded connected components of the complementary set. A relaxed procedure is needed to have a well-posed problem and we show that when $q<1/2$ an optimal relaxed domain exists. When $q>1/2$ the problem is ill-posed and for $q=1/2$ the explicit value of the infimum is provided in the cases $k=0$ and $k=1$

Regulation and functions of bacterial PNPase

Polynucleotide phosphorylase (PNPase) is an exoribonuclease that catalyzes the processive phosphorolytic degradation of RNA from the 3\u2032-end. The enzyme catalyzes also the reverse reaction of polymerization of nucleoside diphosphates that has been implicated in the generation of heteropolymeric tails at the RNA 3\u2032-end. The enzyme is widely conserved and plays a major role in RNA decay in both Gram-negative and Gram-positive bacteria. Moreover, it participates in maturation and quality control of stable RNA. PNPase autoregulates its own expression at post-transcriptional level through a complex mechanism that involves the endoribonuclease RNase III and translation control. The activity of PNPase is modulated in an intricate and still unclear manner by interactions with small molecules and recruitment in different multiprotein complexes. Not surprisingly, given the wide spectrum of PNPase substrates, PNPase-defective mutations in different bacterial species have pleiotropic effects and perturb the execution of genetic programs involving drastic changes in global gene expression such as biofilm formation, growth at suboptimal temperatures, and virulence

RNase III-independent autogenous regulation of Escherichia coli polynucleotide phosphorylase via translational repression

The complex post-transcriptional regulation mechanism of Escherichia coli pnp gene, which encodes the phosphorolytic exoribonuclease polynucleotide phosphorylase (PNPase), involves two endoribonucleases, namely RNase III and RNase E, and PNPase itself, which thus autoregulates its own expression. The models proposed for pnp autoregulation posit that the target of PNPase is a mature pnp mRNA previously processed at its 5' -end by RNase III, rather than the primary pnp transcript (RNase III-dependent models) and that PNPase activity eventually leads to pnp mRNA degradation by RNase E. However, some published data suggest that pnp expression may also be regulated through a PNPase-dependent, RNase III-independent mechanism. To address this issue, we constructed isogenic \u394pnp rnc(+) and \u394pnp \u394rnc strains with a chromosomal pnp-lacZ translational fusion and measured \u3b2-galactosidase activity in the absence and presence of PNPase expressed by a plasmid. Our results show that PNPase also regulates its own expression via a reversible RNase III-independent pathway acting upstream of the RNase III-dependent branch. This pathway requires the PNPase RNA binding domains KH and S1, but not its phosphorolytic activity. We suggest that the RNase III-independent autoregulation of PNPase occurs at the level of translational repression, possibly by competition for pnp primary transcript between PNPase and the ribosomal protein S1. In Escherichia coli, polynucleotide phosphorylase (PNPase, encoded by pnp) posttranscriptionally regulates its own expression. The two models proposed so far posit a two-step mechanism in which RNase III, by cutting the leader region of the pnp primary transcript, creates the substrate for PNPase regulatory activity, eventually leading to pnp mRNA degradation by RNase E. In this work, we provide evidence supporting an additional pathway for PNPase autogenous regulation in which PNPase acts as a translational repressor independently of RNase III cleavage. Our data make a new contribution to the understanding of the regulatory mechanism of pnp mRNA, a process long since considered a paradigmatic example of posttranscriptional regulation at the level of mRNA stability

Polynucleotide phosphorylase is implicated in homologous recombination and DNA repair in Escherichia coli

Background: Polynucleotide phosphorylase (PNPase, encoded by pnp) is generally thought of as an enzyme dedicated to RNA metabolism. The pleiotropic effects of PNPase deficiency is imputed to altered processing and turnover of mRNAs and small RNAs, which in turn leads to aberrant gene expression. However, it has long since been known that this enzyme may also catalyze template-independent polymerization of dNDPs into ssDNA and the reverse phosphorolytic reaction. Recently, PNPase has been implicated in DNA recombination, repair, mutagenesis and resistance to genotoxic agents in diverse bacterial species, raising the possibility that PNPase may directly, rather than through control of gene expression, participate in these processes. Results: In this work we present evidence that in Escherichia coli PNPase enhances both homologous recombination upon P1 transduction and error prone DNA repair of double strand breaks induced by zeocin, a radiomimetic agent. Homologous recombination does not require PNPase phosphorolytic activity and is modulated by its RNA binding domains whereas error prone DNA repair of zeocin-induced DNA damage is dependent on PNPase catalytic activity and cannot be suppressed by overexpression of RNase II, the other major enzyme (encoded by rnb) implicated in exonucleolytic RNA degradation. Moreover, E. coli pnp mutants are more sensitive than the wild type to zeocin. This phenotype depends on PNPase phosphorolytic activity and is suppressed by rnb, thus suggesting that zeocin detoxification may largely depend on RNA turnover. Conclusions: Our data suggest that PNPase may participate both directly and indirectly through regulation of gene expression to several aspects of DNA metabolism such as recombination, DNA repair and resistance to genotoxic agents

Overexpression of lpxT Gene in Escherichia coli Inhibits Cell Division and Causes Envelope Defects without Changing the Overall Phosphorylation Level of Lipid A

LpxT is an inner membrane protein that transfers a phosphate group from the essential lipid undecaprenyl pyrophosphate (C-55PP) to the lipid A moiety of lipopolysaccharide, generating a lipid A tris-phosphorylated species. The protein is encoded by the non-essential lpxT gene, which is conserved in distantly related Gram-negative bacteria. In this work, we investigated the phenotypic effect of lpxT ectopic expression from a plasmid in Escherichia coli. We found that lpxT induction inhibited cell division and led to the formation of elongated cells, mostly with absent or altered septa. Moreover, the cells became sensitive to detergents and to hypo-osmotic shock, indicating that they had cell envelope defects. These effects were not due to lipid A hyperphosphorylation or C-55PP sequestering, but most likely to defective lipopolysaccharide transport. Indeed, lpxT overexpression in mutants lacking the L,D-transpeptidase LdtD and LdtE, which protect cells with outer membrane defects from osmotic lysis, caused cell envelope defects. Moreover, we found that pyrophosphorylated lipid A was also produced in a lpxT deletion mutant, indicating that LpxT is not the only protein able to perform such lipid A modification in E. coli

The Association between serum cytokines and damage to large and small nerve fibers in diabetic peripheral neuropathy.

Diabetic peripheral neuropathy (DPN) is a frequent complication of type 2 diabetes mellitus (DM) and may involve small and large peripheral nerve fibers. Recent evidence suggests a role of cytokines in DPN. The paper is aimed at exploring whether the serum concentration of cytokines is associated with small and large nerve fiber function and with neuropathic pain (NP). We recruited a group of 32 type 2 DM patients who underwent serum cytokines (TNF-α, IL-2, IL-4, IL-6, and IL-10) dosage as well as electrodiagnostic and quantitative sensory testing (QST) assessment to explore damage to large and small nerve fibers. Raised serum levels of IL-6 and IL-10 correlated with markers of large nerve fiber sensory and motor axonal damage. Raised IL-10 serum level was associated with signs of motor nerve demyelination. No differences were found in pain characteristics and electrodiagnostic and QST markers of small nerve fiber function in relation to cytokines serum levels. IL-6 and IL-10 serum levels were associated with large nerve fiber damage but not to small fibers function or NP. IL-6 and IL-10 cytokines might play a role in the pathogenesis of nerve fiber damage or represent a compensatory or neuroprotective mechanism

Searching for Chips of Kuiper Belt Objects in Meteorites

The Nice model [1&2] describes a scenario whereby the Jovian planets experienced a violent reshuffling event approx.3:9 Ga the giant planets moved, existing small body reservoirs were depleted or eliminated, and new reservoirs were created in particular locations. The Nice model quantitatively explains the orbits of the Jovian planets and Neptune [1], the orbits of bodies in several different small body reservoirs in the outer solar system (e.g., Trojans of Jupiter [2], the Kuiper belt and scattered disk [3], the irregular satellites of the giant planets [4], and the late heavy bombardment on the terrestrial planets approx.3:9 Ga [5]. This model is unique in plausibly explaining all of these phenomena. One issue with the Nice model is that it predicts that transported Kuiper Belt Objects (KBOs) (things looking like D class asteroids) should predominate in the outer asteroid belt, but we know only about 10% of the objects in the outer main asteroid belt appear to be D-class objects [6]. However based upon collisional modeling, Bottke et al. [6] argue that more than 90% of the objects captured in the outer main belt could have been eliminated by impacts if they had been weakly-indurated objects. These disrupted objects should have left behind pieces in the ancient regoliths of other, presumably stronger asteroids. Thus, a derived prediction of the Nice model is that ancient regolith samples (regolith-bearing meteorites) should contain fragments of collisionally-destroyed Kuiper belt objects. In fact KBO pieces might be expected to be present in most ancient regolith- bearing meteorites [7&8]

Autogenous regulation of Escherichia coli polynucleotide phosphorylase expression revisited

The Escherichia coli polynucleotide phosphorylase (PNPase, encoded by pnp), a phosphorolytic exoribonuclease, post-transcriptionally regulates its own expression at the level of mRNA stability and translation. Its primary transcript is very efficiently processed by RNase III, an endonuclease that makes a staggered double strand cleavage about in the middle of a long stem-loop in the 5'-untranslated region. The processed pnp mRNA is then rapidly degraded in a PNPase-dependent manner. Two non-mutually exclusive models have been proposed to explain PNPase autogenous regulation. The earlier one suggested that PNPase impedes translation of the RNase III processed pnp mRNA thus exposing the transcript to degradative pathways. More recently this has been replaced by the current model, which maintains that PNPase would simply degrade the promoter proximal small RNA generated by the RNase III endonucleolytic cleavage thus destroying the double stranded structure at the 5'-end that otherwise stabilizes the pnp mRNA. In our opinion, however, the first model was not completely ruled out. Moreover, the RNA decay pathway acting upon the pnp mRNA after disruption of the 5' double stranded structure remained to be determined. Here we provide additional support to the current model and show that the RNase III-processed pnp mRNA devoid of the double stranded structure at its 5'-end is not translatable and is degraded by RNase E in a PNPase-independent manner. Thus the role of PNPase in autoregulation is simply to remove, in concert with RNase III, the 5'-fragment of the cleaved structure that both allows translation and prevents the RNase E-mediated PNPase-independent degradation of the pnp transcript

Energy solutions to one-dimensional singular parabolic problems with BVBV data are viscosity solutions

We study one-dimensional very singular parabolic equations with periodic boundary conditions and initial data in $BV$, which is the energy space. We show existence of solutions in this energy space and then we prove that they are viscosity solutions in the sense of Giga-Giga.Comment: 15 page

Phage therapy against Pseudomonas aeruginosa infections in a cystic fibrosis zebrafish model

Cystic fibrosis (CF) is a hereditary disease due to mutations in the CFTR gene and causes mortality in humans mainly due to respiratory infections caused by Pseudomonas aeruginosa. In a previous work we used phage therapy, which is a treatment with a mix of phages, to actively counteract acute P. aeruginosa infections in mice and Galleria mellonella larvae. In this work we apply phage therapy to the treatment of P. aeruginosa PAO1 infections in a CF zebrafish model. The structure of the CFTR channel is evolutionary conserved between fish and mammals and cftr-loss-of-function zebrafish embryos show a phenotype that recapitulates the human disease, in particular with destruction of the pancreas. We show that phage therapy is able to decrease lethality, bacterial burden, and the pro-inflammatory response caused by PAO1 infection. In addition, phage administration relieves the constitutive inflammatory state of CF embryos. To our knowledge, this is the first time that phage therapy is used to cure P. aeruginosa infections in a CF animal model. We also find that the curative effect against PAO1 infections is improved by combining phages and antibiotic treatments, opening a useful therapeutic approach that could reduce antibiotic doses and time of administration