Optimal bounds for the approximation of boolean functions and some applications

This paper presents an optimal bound on the Shannon function L(n,m,) that gives the worstcase circuit-size complexity to approximate, within an approximation degree at least , partial boolean functions having n inputs and domain size m. That is

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. Our bound applies to any partial boolean function and any approximation degree, and thus completes the study of boolean function approximation introduced by Pippenger (1977).

Our results give an upper bound for the hardness function h(ƒ), introduced by Nisan and Wigderson (1994), which denotes the minimum value l for which there exists a circuit of size at most l that approximates a boolean function ƒ with degree at least 1/l. Indeed, if H(n) denotes the maximum hardness value achieved by boolean functions with n inputs, we prove that for almost every nH(n)n/3 + n² + O(1). The exponent n/3 in the above inequality implies that no family of boolean functions exists which has ‘full’ hardness. This fact establishes connections with Allender and Strauss' (1994) work that explores the structure of BPP.

Finally, we show that for almost every n and for almost every boolean function ƒ of n inputs we have h(ƒ)2^{n/3−2 log n}. The contribution in the proof of the upper bound for L(n, m, ) can be viewed as a set of technical results that globally show how boolean linear operators are ‘well’ distributed on the class of 4-regular domains. This property is then applied to approximate partial boolean functions on general domains using a suitable composition of boolean linear operators.     

Implementation of depth‐based routing and its enhancement in AquaSim–Next Generation for underwater wireless sensor networks

In the last decade, underwater wireless sensor networks have been widely studied because of their peculiar aspects that distinguish them from common terrestrial wireless networks. Their applications range from environmental monitoring to military defense. The definition of efficient routing protocols in underwater sensor networks is a challenging topic of research because of the intrinsic characteristics of these networks, such as the need of handling the node mobility and the difficulty in balancing the energy consumed by the nodes. Depth‐based routing protocol is an opportunistic routing protocol for underwater sensor networks, which provides good performance both under high and low node mobility scenarios. The main contribution of our work is presenting a novel simulator for studying depth‐based routing protocol and its variants as well as novel routing protocols. Our simulator is based on AquaSim–Next Generation, which is a specialized tool for studying underwater networks. With our work, we improve the state of the art of underwater routing protocol simulators by implementing, among other features, a detailed cross‐layer communication and an accurate model of the operational modes of acoustic modem and their energy consumption. The simulator is open source and freely downloadable. Moreover, we propose a novel and completely distributed routing protocol, named residual energy–depth‐based routing. It takes into account the residual energy at the nodes' batteries to select the forwarder nodes and improve the network lifetime by providing a more uniform energy consumption among them. We compare its performance with that of depth‐based routing protocol and a receiver‐based routing protocol implementing a probabilistic opportunistic forwarding scheme.     

Sphk1 and Sphk2 Differentially Regulate Erythropoietin Synthesis in Mouse Renal Interstitial Fibroblast-like Cells

Erythropoietin (Epo) is a crucial hormone regulating red blood cell number and consequently the hematocrit. Epo is mainly produced in the kidney by interstitial fibroblast-like cells. Previously, we have shown that in cultures of the immortalized mouse renal fibroblast-like cell line FAIK F3-5, sphingosine 1-phosphate (S1P), by activating S1P₁ and S1P₃ receptors, can stabilize hypoxia-inducible factor (HIF)-2α and upregulate Epo mRNA and protein synthesis. In this study, we have addressed the role of intracellular iS1P derived from sphingosine kinases (Sphk) 1 and 2 on Epo synthesis in F3-5 cells and in mouse primary cultures of renal fibroblasts. We show that stable knockdown of Sphk2 in F3-5 cells increases HIF-2α protein and Epo mRNA and protein levels, while Sphk1 knockdown leads to a reduction of hypoxia-stimulated HIF-2α and Epo protein. A similar effect was obtained using primary cultures of renal fibroblasts isolated from wildtype mice, Sphk1−/−, or Sphk2−/− mice. Furthermore, selective Sphk2 inhibitors mimicked the effect of genetic Sphk2 depletion and also upregulated HIF-2α and Epo protein levels. The combined blockade of Sphk1 and Sphk2, using Sphk2−/− renal fibroblasts treated with the Sphk1 inhibitor PF543, resulted in reduced HIF-2α and Epo compared to the untreated Sphk2−/− cells. Exogenous sphingosine (Sph) enhanced HIF-2α and Epo, and this was abolished by the combined treatment with the selective S1P₁ and S1P₃ antagonists NIBR-0213 and TY52156, suggesting that Sph was taken up by cells and converted to iS1P and exported to then act in an autocrine manner through S1P₁ and S1P₃. The upregulation of HIF-2α and Epo synthesis by Sphk2 knockdown was confirmed in the human hepatoma cell line Hep3B, which is well-established to upregulate Epo production under hypoxia. In summary, these data show that sphingolipids have diverse effects on Epo synthesis. While accumulation of intracellular Sph reduces Epo synthesis, iS1P will be exported to act through S1P₁₊₃ to enhance Epo synthesis. Furthermore, these data suggest that selective inhibition of Sphk2 is an attractive new option to enhance Epo synthesis and thereby to reduce anemia development in chronic kidney disease.     

Inhibitors of Mitochondrial Human Carbonic Anhydrases VA and VB as a Therapeutic Strategy against Paclitaxel-Induced Neuropathic Pain in Mice

Neuropathy development is a major dose-limiting side effect of anticancer treatments that significantly reduces patient’s quality of life. The inadequate pharmacological approaches for neuropathic pain management warrant the identification of novel therapeutic targets. Mitochondrial dysfunctions that lead to reactive oxygen species (ROS) increase, cytosolic Ca²⁺ imbalance, and lactate acidosis are implicated in neuropathic pain pathogenesis. It has been observed that in these deregulations, a pivotal role is played by the mitochondrial carbonic anhydrases (CA) VA and VB isoforms. Hence, preclinical studies should be conducted to assess the efficacy of two novel selenides bearing benzenesulfonamide moieties, named 5b and 5d, and able to inhibit CA VA and VB against paclitaxel-induced neurotoxicity in mice. Acute treatment with 5b and 5d (30–100 mg/kg, per os – p.o.) determined a dose-dependent and long-lasting anti-hyperalgesic effect in the Cold plate test. Further, repeated daily treatment for 15 days with 100 mg/kg of both compounds (starting the first day of paclitaxel injection) significantly prevented neuropathic pain development without the onset of tolerance to the anti-hyperalgesic effect. In both experiments, acetazolamide (AAZ, 100 mg/kg, p.o.) used as the reference drug was partially active. Moreover, ex vivo analysis demonstrated the efficacy of 5b and 5d repeated treatments in reducing the maladaptive plasticity that occurs to glia cells in the lumbar portion of the spinal cord and in improving mitochondrial functions in the brain and spinal cord that were strongly impaired by paclitaxel-repeated treatment. In this regard, 5b and 5d ameliorated the metabolic activity, as observed by the increase in citrate synthase activity, and preserved an optimal mitochondrial membrane potential (ΔΨ) value, which appeared depolarized in brains from paclitaxel-treated animals. In conclusion, 5b and 5d have therapeutic and protective effects against paclitaxel-induced neuropathy without tolerance development. Moreover, 5b and 5d reduced glial cell activation and mitochondrial dysfunction in the central nervous system, being a promising candidate for the management of neuropathic pain and neurotoxicity evoked by chemotherapeutic drugs.     

Chronic Hyperkaliemia in Chronic Kidney Disease: An Old Concern with New Answers

Increasing potassium intake ameliorates blood pressure (BP) and cardiovascular (CV) prognoses in the general population; therefore the World Health Organization recommends a high-potassium diet (90–120 mEq/day). Hyperkalaemia is a rare condition in healthy individuals due to the ability of the kidneys to effectively excrete dietary potassium load in urine, while an increase in serum K⁺ is prevalent in patients with chronic kidney disease (CKD). Hyperkalaemia prevalence increases in more advanced CKD stages, and is associated with a poor prognosis. This scenario generates controversy on the correct nutritional approach to hyperkalaemia in CKD patients, considering the unproven link between potassium intake and serum K⁺ levels. Another concern is that drug-induced hyperkalaemia leads to the down-titration or withdrawal of renin-angiotensin system inhibitors (RASI) and mineralocorticoids receptors antagonists (MRA) in patients with CKD, depriving these patients of central therapeutic interventions aimed at delaying CKD progression and decreasing CV mortality. The new K⁺-binder drugs (Patiromer and Sodium-Zirconium Cyclosilicate) have proven to be adequate and safe therapeutic options to control serum K⁺ in CKD patients, enabling RASI and MRA therapy, and possibly, a more liberal intake of fruit and vegetables.     

Genomic Analysis Made It Possible to Identify Gene-Driver Alterations Covering the Time Window between Diagnosis of Neuroblastoma 4S and the Progression to Stage 4

Neuroblastoma (NB) is a tumor of the developing sympathetic nervous system. Despite recent advances in understanding the complexity of NB, the mechanisms that determine its regression or progression are still largely unknown. Stage 4S NB is characterized by a favorable course of disease and often by spontaneous regression, while progression to true stage 4 is a very rare event. Here, we focused on genomic analysis of an NB case that progressed from stage 4S to stage 4 with a very poor outcome. Array-comparative genomic hybridization (a-CGH) on tumor-tissue DNA, and whole-exome sequencing (WES) on exosomes DNA derived from plasma collected at the onset and at the tumor progression, pointed out relevant genetic changes that can explain this clinical worsening. The combination of a-CGH and WES data allowed for the identification iof somatic copy number aberrations and single-nucleotide variants in genes known to be responsible for aggressive NB. KLRB1, MAPK3 and FANCA genes, which were lost at the time of progression, were studied for their possible role in this event by analyzing in silico the impact of their expression on the outcome of 786 NB patients.     

A Review on Current Strategies for Extraction and Purification of Hyaluronic Acid

Since it is known that hyaluronic acid contributes to soft tissue growth, elasticity, and scar reduction, different strategies of producing HA have been explored in order to satisfy the current demand of HA in pharmaceutical products and formulations. The current interest deals with production via bacterial and yeast fermentation and extraction from animal sources; however, the main challenge is the right extraction technique and strategy since the original sources (e.g., fermentation broth) represent a complex system containing a number of components and solutes, which complicates the achievement of high extraction rates and purity. This review sheds light on the main pathways for the production of HA, advantages, and disadvantages, along with the current efforts in extracting and purifying this high-added-value molecule from different sources. Particular emphasis has been placed on specific case studies attempting production and successful recovery. For such works, full details are given together with their relevant outcomes.     

The β2-Subunit (AMOG) of Human Na+, K+-ATPase Is a Homophilic Adhesion Molecule

The β₂ subunit of Na⁺, K⁺-ATPase was originally identified as the adhesion molecule on glia (AMOG) that mediates the adhesion of astrocytes to neurons in the central nervous system and that is implicated in the regulation of neurite outgrowth and neuronal migration. While β₁ isoform have been shown to trans-interact in a species-specific mode with the β₁ subunit on the epithelial neighboring cell, the β₂ subunit has been shown to act as a recognition molecule on the glia. Nevertheless, none of the works have identified the binding partner of β₂ or described its adhesion mechanism. Until now, the interactions pronounced for β₂/AMOG are heterophilic cis-interactions. In the present report we designed experiments that would clarify whether β₂ is a cell–cell homophilic adhesion molecule. For this purpose, we performed protein docking analysis, cell–cell aggregation, and protein–protein interaction assays. We observed that the glycosylated extracellular domain of β₂/AMOG can make an energetically stable trans-interacting dimer. We show that CHO (Chinese Hamster Ovary) fibroblasts transfected with the human β₂ subunit become more adhesive and make large aggregates. The treatment with Tunicamycin in vivo reduced cell aggregation, suggesting the participation of N-glycans in that process. Protein–protein interaction assay in vivo with MDCK (Madin-Darby canine kidney) or CHO cells expressing a recombinant β₂ subunit show that the β₂ subunits on the cell surface of the transfected cell lines interact with each other. Overall, our results suggest that the human β₂ subunit can form trans-dimers between neighboring cells when expressed in non-astrocytic cells, such as fibroblasts (CHO) and epithelial cells (MDCK).